Datasets:

sswt

/

arxiv_sample_50K

like 0

TEMPO2, a new pulsar timing package. I Overview ; Contemporary pulsar timing experiments have reached a sensitivity level where systematic errors introduced by existing analysis procedures are limiting the achievable science. We have developed tempo2, a new pulsar timing package that contains propagation and other relevant effects implemented at the 1ns level of precision a factor of 100 more precise than previously obtainable. In contrast with earlier timing packages, tempo2 is compliant with the general relativistic framework of the IAU 1991 and 2000 resolutions and hence uses the International Celestial Reference System, Barycentric Coordinate Time and uptodate precession, nutation and polar motion models. Tempo2 provides a generic and extensible set of tools to aid in the analysis and visualisation of pulsar timing data. We provide an overview of the timing model, its accuracy and differences relative to earlier work. We also present a new scheme for predictive use of the timing model that removes existing processing artifacts by properly modelling the frequency dependence of pulse phase.

Coincidence Problem in YM Field Dark Energy Model ; The coincidence problem is studied in the effective YangMills condensate dark energy model. As the effective YM Lagrangian is completely determined by quantum field theory, there is no adjustable parameter in this model except the energy scale, and the cosmic evolution only depends on the initial conditions. For generic initial conditions with the YM condensate subdominant to the radiation and matter, the model always has a tracking solution, the Universe transits from matterdominated into the dark energy dominated stage only recently zsim 0. 3, and evolve to the present state with Omegaysim 0.73 and Omegamsim 0.27.

Can MOND take a bullet Analytical comparisons of three versions of MOND beyond spherical symmetry ; A proper test of Modified Newtonian Dynamics MOND in systems of nontrivial geometries depends on modelling subtle differences in several versions of its postulated theories. This is especially important for lensing and dynamics of barely virialised galaxy clusters with typical gravity of scale sim a0 sim 1AArm s2. The original MOND formula, the classical single field modification of the Poisson equation, and the multifield general relativistic theory of Bekenstein TeVeS all lead to different predictions as we stray from spherical symmetry. In this paper, we study a class of analytical MONDian models for a system with a semiHernquist baryonic profile. After presenting the analytical distribution function of the baryons in spherical limits, we develop orbits and gravitational lensing of the models in nonspherical geometries. In particular, we can generate a multicentred baryonic system with a weak lensing signal resembling that of the merging galaxy cluster 1E 065756 with a bulletlike light distribution. We finally present analytical scalefree highly nonspherical models to show the subtle differences between the single field classical MOND theory and the multifield TeVeS theory.

A three stage model for the inner engine of Gamma Ray Burst Prompt emission and early afterglow ; We propose a new model within the Quarknova'' scenario to interpret the recent observations of early afterglows of long GammaRay Bursts GRB with the Swift satellite. This is a threestage model within the context of a corecollapse supernova. Stage 1 is an accreting proto neutron star leading to a possible delay between the core collapse and the GRB. Stage 2 is an accreting quarkstar, generating the prompt GRB. Stage 3, which occurs only if the quarkstar collapses to form a blackhole, consists of an accreting blackhole. The jet launched in this accretion process interacts with the ejecta from stage 2, and could generate the flaring activity frequently seen in Xray afterglows. This model may be able to account for both the energies and the timescales of GRBs, in addition to the newly discovered early Xray afterglow features.

The Large Scale Structure of fR Gravity ; We study the evolution of linear cosmological perturbations in fR models of accelerated expansion in the physical frame where the gravitational dynamics are fourth order and the matter is minimally coupled. These models predict a rich and testable set of linear phenomena. For each expansion history, fixed empirically by cosmological distance measures, there exists two branches of fR solutions that are parameterized by B propto d2 fdR2. For B0, which include most of the models previously considered, there is a shorttimescale instability at high curvature that spoils agreement with high redshift cosmological observables. For the stable B0 branch, fR models can reduce the largeangle CMB anisotropy, alter the shape of the linear matter power spectrum, and qualitatively change the correlations between the CMB and galaxy surveys. All of these phenomena are accessible with current and future data and provide stringent tests of general relativity on cosmological scales.

LTB universes as alternatives to dark energy does positive averaged acceleration imply positive cosmic acceleration ; We show that positive averaged acceleration obtained in LTB models through spatial averaging can require integration over a region beyond the event horizon of the central observer. We provide an example of a LTB model with positive averaged acceleration in which the luminosity distance does not contain information about the entire spatially averaged region, making the averaged acceleration unobservable. Since the cosmic acceleration is obtained from fitting the observed luminosity distance to a FRW model we conclude that in general a positive averaged acceleration in LTB models does not imply a positive FRW cosmic acceleration.

Constraints on the unified dark energydark matter model from latest observational data ; The generalized Chaplygin gas GCG, is studied in this paper by using the latest observational data including 182 gold sample type Ia supernovae Sne Ia data, the ESSENCE Sne Ia data, the distance ratio from z0.35 to z1089 the redshift of decoupling, the CMB shift parameter and the Hubble parameter data. Our results rule out the standard Chaplygin gas model alpha1 at the 99.7 confidence level, but allow for the lambda CDM model alpha0 at the 68.3 confidence level. At a 95.4 confidence level, we obtain w0.740.090.10 and alpha0.140.190.30. In addition, we find that the phase transition from deceleration to acceleration occurs at redshift zq0sim 0.780.89 at a 1sigma confidence level for the GCG model.

Supernovae Constraints on DGP Model and Cosmic Topology ; We study the constraints that the detection of a nontrivial spatial topology may place on the parameters of braneworld models by considering the DvaliGabadadzePorrati DGP and the globally homogeneous Poincar'e dodecahedral spatial PDS topology as a circlesinthesky observable topology. To this end we reanalyze the type Ia supernovae constraints on the parameters of the DGP model and show that PDS topology gives rise to strong and complementary constraints on the parameters of the DGP model.

Helical shell models for three dimensional turbulence ; In this paper we study a new class of shell models, defined in terms of two complex dynamical variables per shell, transporting positive and negative helicity respectively. The dynamical equations are derived from a decomposition into helical modes of the velocity Fourier components of NavierStokes equations F. Waleffe, Phys. Fluids A bf 4, 350 1992. This decomposition leads to four different types of shell models, according to the possible nonequivalent combinations of helicities of the three interacting modes in each triad. Free parameters are fixed by imposing the conservation of energy and of a generalized helicity'' Halpha in the inviscid and unforced limit. For alpha1 this nonpositive invariant looks exactly like helicity in the Fourierhelical decomposition of the NavierStokes equations. Long numerical integrations are performed, allowing the computation of the scaling exponents of the velocity increments and energy flux moments. The dependence of the models on the generalized helicity parameter alpha and on the scale parameter lambda is also studied. PDEs are finally derived in the limit when the ratio between shells goes to one.

Towards Historybased Grammars Using Richer Models for Probabilistic Parsing ; We describe a generative probabilistic model of natural language, which we call HBG, that takes advantage of detailed linguistic information to resolve ambiguity. HBG incorporates lexical, syntactic, semantic, and structural information from the parse tree into the disambiguation process in a novel way. We use a corpus of bracketed sentences, called a Treebank, in combination with decision tree building to tease out the relevant aspects of a parse tree that will determine the correct parse of a sentence. This stands in contrast to the usual approach of further grammar tailoring via the usual linguistic introspection in the hope of generating the correct parse. In headtohead tests against one of the best existing robust probabilistic parsing models, which we call PCFG, the HBG model significantly outperforms PCFG, increasing the parsing accuracy rate from 60 to 75, a 37 reduction in error.

Inducing Probabilistic Grammars by Bayesian Model Merging ; We describe a framework for inducing probabilistic grammars from corpora of positive samples. First, samples are em incorporated by adding adhoc rules to a working grammar; subsequently, elements of the model such as states or nonterminals are em merged to achieve generalization and a more compact representation. The choice of what to merge and when to stop is governed by the Bayesian posterior probability of the grammar given the data, which formalizes a tradeoff between a close fit to the data and a default preference for simpler models Occam's Razor'. The general scheme is illustrated using three types of probabilistic grammars Hidden Markov models, classbased ngrams, and stochastic contextfree grammars.

GraphemetoPhoneme Conversion using Multiple Unbounded Overlapping Chunks ; We present in this paper an original extension of two datadriven algorithms for the transcription of a sequence of graphemes into the corresponding sequence of phonemes. In particular, our approach generalizes the algorithm originally proposed by Dedina and Nusbaum DN 1991, which had originally been promoted as a model of the human ability to pronounce unknown words by analogy to familiar lexical items. We will show that DN's algorithm performs comparatively poorly when evaluated on a realistic test set, and that our extension allows us to improve substantially the performance of the analogybased model. We will also suggest that both algorithms can be reformulated in a much more general framework, which allows us to anticipate other useful extensions. However, considering the inability to define in these models important notions like lexical neighborhood, we conclude that both approaches fail to offer a proper model of the analogical processes involved in reading aloud.

OneDimensional Statistical Mechanics for Identical Particles The Calogero and Anyon Cases ; The thermodynamic of particles with intermediate statistics interpolating between Bose and Fermi statistics is adressed in the simple case where there is one quantum number per particle. Such systems are essentially onedimensional. As an illustration, one considers the anyon model restricted to the lowest Landau level of a strong magnetic field at low temperature, the generalization of this model to several particles species, and the one dimensional Calogero model. One reviews a unified algorithm to compute the statistical mechanics of these systems. It is pointed out that Haldane's generalization of the Pauli principle can be deduced from the anyon model in a strong magnetic field at low temperature.

The Computational Complexity of Generating Random Fractals ; In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion limited aggregation and several widely used algorithms for equilibrating the Ising model are shown to be highly sequential; it is unlikely they can be simulated efficiently in parallel. This is in contrast to Mandelbrot percolation that can be simulated in constant parallel time. Our research helps shed light on the intrinsic complexity of these models relative to each other and to different growth processes that have been recently studied using complexity theory. In addition, the results may serve as a guide to simulation physics.

Extended Universality of the Surface Curvature in Equilibrium Crystal Shapes ; We investigate the universal property of curvatures in surface models which display a flat phase and a rough phase whose criticality is described by the Gaussian model. Earlier we derived a relation between the Hessian of the free energy and the Gaussian coupling constant in the sixvertex model. Here we show its validity in a general setting using renormalization group arguments. The general validity of the relation is confirmed numerically in the RSOS model by comparing the Hessian of the free energy and the Gaussian coupling constant in a transfer matrix finitesizescaling study. The Hessian relation gives clear understanding of the universal curvature jump at roughening transitions and facet edges and also provides an efficient way of locating the phase boundaries.

Superconductivity with s and psymmetries in an extended Hubbard model with correlated hopping ; We consider a generalized Hubbard model with onsite and nearestneighbour repulsions U and V respectively, and nearestneighbour hopping for spin up down which depends on the total occupation nb of spin down up electrons on both sites involved. The hopping parameters are tAA, tAB and tBB for nb0,1,2 respectively. We briefly summarize results which support that the model exhibits swave superconductivity for certain parameters and extend them by studying the Berry phases. Using a generalized HartreeFockHF BCS decoupling of the two and threebody terms, we obtain that at half filling, for tABtAAtBB and sufficiently small U and V the model leads to triplet pwave superconductivity for a simple cubic lattice in any dimension. In one dimension, the resulting phase diagram is compared with that obtained numerically using two quantized Berry phases topological numbers as order parameters. While this novel method supports the previous results, there are quantitative differences.

The Influence of Percolation in the generalized ChalkerCoddington Model ; We numerically investigate the influence of classical percolation on the quantum Hall localizationdelocalization transition. This is accomplished within the framework of the generalized ChalkerCoddington network model which allows us to control the number of em classical saddle points by setting the width W of the saddle point distribution. It is found that increasing this width causes a new microscopic length scale to appear which depends on W and scales with the exponent Xapprox 1.36 which indicates a close connection to the classical percolation length xi and its exponent nup43. Furthermore, the influence of an increase in W on the spectral statistics of the quasienergies of the network model is investigated. An effect similar to the increase of the potential correlation length in the Landau model is seen.

Magnetic susceptibility of the double exchange model ; Previously a manybody coherent potential approximation CPA was used to study the double exchange DE model with quantum local spins S, both for S12 and for general S in the paramagnetic state. This approximation, exact in the atomic limit, was considered to be a manybody extension of Kubo's oneelectron dynamical CPA for the DE model. We now extend our CPA treatment to the case of general S and spin polarization. We show that Kubo's oneelectron CPA is always recovered in the emptyband limit and that our CPA is equivalent to dynamical mean field theory in the classical spin limit. We then solve our CPA equations selfconsistently to obtain the static magnetic susceptibility chi in the strongcoupling limit. As in the case of the CPA for the Hubbard model we find unphysical behaviour in chi at halffilling and no magnetic transition for any finite S. We identify the reason for this failure of our approximation and propose a modification which gives the correct Curielaw behaviour of chi at halffilling and a transition to ferromagnetism for all S.

Hysteresis in vibrated granular media ; Some general dynamical properties of models for compaction of granular media based on master equations are analyzed. In particular, a onedimensional lattice model with shortranged dynamical constraints is considered. The stationary state is consistent with Edward's theory of powders. The system is submitted to processes in which the tapping strength is monotonically increased and decreased. In such processes the behavior of the model resembles the reversibleirreversible branches which have been recently obaserved in experiments. This behavior is understood in terms of the general dynamical properties of the model, and related to the hysteresis cycles exhibited by structural glasses in thermal cycles. The existence of a normal solution, i.e., a solution of the master equation which is monotonically approached by all the other solutions, plays a fundamental role in the understanding of the hysteresis effects.

Twochannel Kondo model as a generalized onedimensional inverse square longrange HaldaneShastry spin model ; Majorana fermion representations of the algebra associated with spin, charge, and flavor currents have been used to transform the twochannel Kondo Hamiltonian. Using a path integral formulation, we derive a reduced effective action with longrange impurity spinspin interactions at different imaginary times. In the semiclassical limit, it is equivalent to a onedimensional Heisenberg spin chain with twospin, threespin, etc. longrange interactions, as a generalization of the inversesquare longrange HaldaneShastry spin model. In this representation the elementary excitations are semions, and the nonFermiliquid lowenergy properties of the twochannel Kondo model are recovered.

Directed Percolation has Colors and Flavors ; A model of directed percolation processes with colors and flavors that is equivalent to a population model with many species near their extinction thresholds is presented. We use renormalized field theory and demonstrate that all renormalizations needed for the calculation of the universal scaling behavior near the multicritical point can be gained from the onespecies Gribov process Reggeon field theory. In addition this universal model shows an instability that generically leads to a total asymmetry between each pair of species of a cooperative society, and finally to unidirectionality of the interspecies couplings. It is shown that in general the universal multicritical properties of unidirectionally coupled directed percolation processes with linear coupling can also be described by the model. Consequently the crossover exponent describing the scaling of the linear coupling parameters is given by Phi 1 to all orders of the perturbation expansion. As an example of unidirectionally coupled directed percolation, we discuss the population dynamics of the tournaments of three colors.

Integrated random processes exhibiting long tails, finite moments and 1f spectra ; A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and nonGaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the results derived in the rest of the paper. One of these is an expansion for the cumulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Levy distribution which can be obtained from our model in certain limits which has no finite moments. The evaluation of the power spectrum and the form of the probability density function in the tails of the distribution shows that the model exhibits a 1f spectrum and long tails in a natural way. A careful analysis of the characteristic function shows that it may be separated into a part representing a Levy processes together with another part representing the deviation of our model from the Levy process. This allows our process to be viewed as a generalization of the Levy process which has finite moments.

Bose condensation of cavity polaritons beyond the linear regime the thermal equilibrium of a model microcavity ; We consider a generalization of the Dicke model. It describes localized, physically separated, saturable excitations, such as excitons bound on impurities, coupled to a single longlived mode of an optical cavity. We consider the thermal equilibrium of the model at a fixed total number of excitons and photons. We find a phase in which both the cavity field and the excitonic polarization are coherent. This phase corresponds to a Bose condensate of cavity polaritons, generalized to allow for the fermionic internal structure of the excitons. It is separated from the normal state by an unusual reentrant phase boundary. We calculate the excitation energies of the model, and hence the optical absorption spectra of the cavity. In the condensed phase the absorption spectrum is gapped. The presence of a gap distinguishes the polariton condensate from the normal state and from a conventional laser, even when the inhomogeneous linewidth is so large that there is no observable polariton splitting in the normal state.

Thermodynamic properties of a simple model of likecharged attracting rods ; We study the thermodynamic properties of a simple model for the possible mechanism of attraction between like charged rodlike polyions inside a polyelectrolyte solution. We consider two polyions in parallel planes, with Z charges each, in a solution containing multivalent counterions of valence alpha. The model is solved exactly for Z le 13 for a general angle theta between the rods and supposing that n counterions are condensed on each polyion. The free energy has two minima, one at theta0 parallel rods and another at thetapi2 perpendicular rods. In general, in situations where an attractive force develops at small distances between the centers of the polyions, the perpendicular configuration has the lowest free energy at large distances, while at small distances the parallel configuration minimizes the free energy of the model. However, at low temperatures, a reentrant behavior is observed, such that the perpendicular configuration is the global minimum for both large and small distances, while the parallel configuration minimizes the free energy at intermediate distances.

Out of equilibrium dynamics of a Quantum Heisenberg Spin Glass ; We study the out of equilibrium dynamics of the infinite range quantum Heisenberg spin glass model coupled to a thermal relaxation bath. The SU2 spin algebra is generalized to SUN and we analyse the largeN limit. The model displays a dynamical phase transition between a paramagnetic and a glassy phase. In the latter, the system remains out of equilibrium and displays an aging phenomenon, which we characterize using both analytical and numerical methods. In the aging regime, the quantum fluctuationdissipation relation is violated and replaced at very long time by its classical generalization, as in models involving simple spin algebras studied previously. We also discuss the effect of a finite coupling to the relaxation baths and their possible forms. This work completes and justifies previous studies on this model using a static approach.

Generalized Valence Bond State and Solvable Models for Spin12 Systems with Orbital degeneracy ; A spin12 system with double orbital degeneracy may possess SU4 symmetry. According to the group theory a global SU4 singelt state can be expressed as a linear combination of all possible configurations consisting of foursite SU4 singlets. Following P. W. Andersion's idea for spin 12 system, we propose that the ground state for the antiferromagnetic SU4 model is SU4 resonating valence bond RVB state. A shortrange SU4 RVB state is a spin and orbital liquid, and its elementary excitations has an energy gap. We construct a series of solvale models which ground states are shortrange SU4 RVB states. The results can be generalized to the antiferromagnetic SUN models.

The bosonfermion model with onsite Coulomb repulsion between fermions ; The bosonfermion model, describing a mixture of itinerant electrons hybridizing with tightly bound electron pairs represented as hardcore bosons, is here generalized with the inclusion of a term describing onsite Coulomb repulsion between fermions with opposite spins. Within the general framework of the Dynamical MeanField Theory, it is shown that around the symmetric limit of the model this interaction strongly competes with the local bosonfermion exchange mechanism, smoothly driving the system from a pseudogap phase with poor conducting properties to a metallic regime characterized by a substantial reduction of the fermionic density. On the other hand, if one starts from correlated fermions described in terms of the oneband Hubbard model, the introduction in the halffilled insulating phase of a coupling with hardcore bosons leads to the disappearance of the correlation gap, with a consequent smooth crossover to a metallic state.

Steady state properties of a mean field model of driven inelastic mixtures ; We investigate a Maxwell model of inelastic granular mixture under the influence of a stochastic driving and obtain its steady state properties in the context of classical kinetic theory. The model is studied analytically by computing the moments up to the eighth order and approximating the distributions by means of a Sonine polynomial expansion method. The main findings concern the existence of two different granular temperatures, one for each species, and the characterization of the distribution functions, whose tails are in general more populated than those of an elastic system. These analytical results are tested against Monte Carlo numerical simulations of the model and are in general in good agreement. The simulations, however, reveal the presence of pronounced nongaussian tails in the case of an infinite temperature bath, which are not well reproduced by the Sonine method.

Anomalous tag diffusion in the asymmetric exclusion model with particles of arbitrary sizes ; Anomalous behavior of correlation functions of tagged particles are studied in generalizations of the one dimensional asymmetric exclusion problem. In these generalized models the range of the hardcore interactions are changed and the restriction of relative ordering of the particles is partially brocken. The models probing these effects are those of biased diffusion of particles having size S0,1,2,..., or an effective negative size S1,2,..., in units of lattice space. Our numerical simulations show that irrespective of the range of the hardcore potential, as long some relative ordering of particles are kept, we find suitable slidingtag correlation functions whose fluctuations growth with time anomalously slow t13, when compared with the normal diffusive behavior t12. These results indicate that the critical behavior of these stochastic models are in the KardarParisiZhang KPZ universality class. Moreover a previous Betheansatz calculation of the dynamical critical exponent z, for size S geq 0 particles is extended to the case S0 and the KPZ result z32 is predicted for all values of S in Z.

Statistical Mechanics of the Bayesian Image Restoration under Spatially Correlated Noise ; We investigated the use of the Bayesian inference to restore noisedegraded images under conditions of spatially correlated noise. The generative statistical models used for the original image and the noise were assumed to obey multidimensional Gaussian distributions whose covariance matrices are translational invariant. We derived an exact description to be used as the expectation for the restored image by the Fourier transformation and restored an image distorted by spatially correlated noise by using a spatially uncorrelated noise model. We found that the resulting hyperparameter estimations for the minimum error and maximal posterior marginal criteria did not coincide when the generative probabilistic model and the model used for restoration were in different classes, while they did coincide when they were in the same class.

Modelfree derivations of the Tsallis factor constant heat capacity derivation ; The constant temperature derivation, which is a modelfree derivation of the Boltzmann factor, is generalized in order to develop a new simple modelfree derivation of a powerlaw Tsallis factor based on an environment with constant heat capacity. It is shown that the integral constant T0 appeared in the new derivation is identified with the generalized temperature Tq in Tsallis thermostatistics. A constant heat capacity environment is proposed as a onerealparameter extension of the Boltzmann reservoir, which is a model constant temperature environment developed by J.J. Prentis et al. Am. J. Phys. 67 1999 508 in order to naturally obtain the Boltzmann factor. It is also shown that the Boltzmann entropy of such a constant heat capacity environment is consistent with Clausius' entropy.

The infinite volume limit in generalized mean field disordered models ; We generalize the strategy, we recently introduced to prove the existence of the thermodynamic limit for the SherringtonKirkpatrick and pspin models, to a wider class of mean field spin glass systems, including models with multicomponent and nonIsing type spins, mean field spin glasses with an additional CurieWeiss interaction, and systems consisting of several replicas of the spin glass model, where replicas are coupled with terms depending on the mutual overlaps.

Quantum Phase Transitions in Models of Magnetic Impurities ; Zero temperature phase transitions not only occur in the bulk of quantum systems, but also at boundaries or impurities. We review recent work on quantum phase transitions in impurity models that are generalizations of the standard Kondo model describing the interaction of a localized magnetic moment with a metallic fermionic host. Whereas in the standard case the moment is screened for any antiferromagnetic Kondo coupling as T to 0, the common feature of all systems considered here is that Kondo screening is suppressed due to the competition with other processes. This competition can generate unstable fixed points associated with phase transitions, where the impurity properties undergo qualitative changes. In particular, we discuss the coupling to both nontrivial fermionic and bosonic baths as well as twoimpurity models, and make connections to recent experiments.

Gasdynamic model of street canyon ; A general proecological urban road traffic control idea for the street canyon is proposed with emphasis placed on development of advanced continuum field gasdynamical hydrodynamical control model of the street canyon. The continuum field model of optimal control of street canyon is studied. The mathematical physics approach Eulerian approach to vehicular movement, to pollutants' emission and to pollutants' dynamics is used. The rigorous mathematical model is presented, using gasdynamical hydrodynamical theory for both air constituents and vehicles, including many types of vehicles and many types of pollutant exhaust gases emitted from vehicles. The six optimal control problems are formulated and numerical simulations are performed. Comparison with measurements are provided. General traffic engineering conclusions are inferred.

Saddles and dynamics in a solvable meanfield model ; We use the saddleapproach, recently introduced in the numerical investigation of simple model liquids, in the analysis of a meanfield solvable system. The investigated system is the ktrigonometric model, a kbody interaction mean field system, that generalizes the trigonometric model introduced by Madan and Keyes J. Chem. Phys. 98, 3342 1993 and that has been recently introduced to investigate the relationship between thermodynamics and topology of the configuration space. We find a close relationship between the properties of saddles stationary points of the potential energy surface visited by the system and the dynamics. In particular the temperature dependence of saddle order follows that of the diffusivity, both having an Arrhenius behavior at low temperature and a similar shape in the whole temperature range. Our results confirm the general usefulness of the saddleapproach in the interpretation of dynamical processes taking place in interacting systems.

Transport phenomena in the urban street canyon ; A generic proecological traffic control model for the urban street canyon is proposed by development of advanced continuum field hydrodynamical control model of the street canyon. The model of optimal control of street canyon dynamics is also investigated. The mathematical physics' approach Eulerian approach to vehicular movement, to pollutants' emission, and to pollutants' dynamics is used. The rigorous mathematical model is presented, using hydrodynamical theory for both air constituents and vehicles, including many types of vehicles and many types of pollutants emitted from vehicles. The six proposed optimal monocriterial control problems consist of minimization of functionals of the total travel time, of global emissions of pollutants, and of global concentrations of pollutants, both in the studied street canyon, and in its two nearest neighbour substitute canyons, respectively. The six optimization problems are solved numerically. Generic traffic control issues are inferred. The discretization method, comparison with experiment, mathematical issues, and programming issues are discussed.

Debt Subordination and The Pricing of Credit Default Swaps ; First passage models, where corporate assets undergo a random walk and default occurs if the assets fall below a threshold, provide an attractive framework for modeling the default process. Recently such models have been generalized to allow a fluctuating default threshold or equivalently a fluctuating total recovery fraction R. For a given company a particular type of debt has a recovery fraction Ri that is greater or less than R depending on its level of subordination. In general the Ri are functions of R and since, in models with a fluctuating default threshold, the probability of default depends on R there are correlations between the recovery fractions Ri and the probability of default. We find, using a simple scenario where debt of type i is subordinate to debt of type i1, the functional dependence RiR and explore how correlations between the default probability and the recovery fractions RiR influence the par spreads for credit default swaps. This scenario captures the effect of debt cushion on recovery fractions.

Lagrangian acceleration statistics in turbulent flows ; We show that the probability densities af accelerations of Lagrangian test particles in turbulent flows as measured by Bodenschatz et al. Nature 409, 1017 2001 are in excellent agreement with the predictions of a stochastic model introduced in C. Beck, PRL 87, 180601 2001 if the fluctuating friction parameter is assumed to be lognormally distributed. In a generalized statistical mechanics setting, this corresponds to a superstatistics of lognormal type. We analytically evaluate all hyperflatnes factors for this model and obtain a flatness prediction in good agreement with the experimental data. There is also good agreement with DNS data of Gotoh et al. We relate the model to a generalized Sawford model with fluctuating parameters, and discuss a possible universality of the smallscale statistics.

A Unified Algebraic Approach to Few and ManyBody Correlated Systems ; The present article is an extended version of the paper it Phys. Rev. bf B 59, R2490 1999, where, we have established the equivalence of the CalogeroSutherland model to decoupled oscillators. Here, we first employ the same approach for finding the eigenstates of a large class of Hamiltonians, dealing with correlated systems. A number of few and manybody interacting models are studied and the relationship between their respective Hilbert spaces, with that of oscillators, is found. This connection is then used to obtain the spectrum generating algebras for these systems and make an algebraic statement about correlated systems. The procedure to generate new solvable interacting models is outlined. We then point out the inadequacies of the present technique and make use of a novel method for solving linear differential equations to diagonalize the Sutherland model and establish a precise connection between this correlated system's wave functions, with those of the free particles on a circle. In the process, we obtain a new expression for the Jack polynomials. In two dimensions, we analyze the Hamiltonian having Laughlin wave function as the groundstate and point out the natural emergence of the underlying linear W1infty symmetry in this approach.

Gasdynamic model of street canyon PCCMM'99 poster session ; A general proecological urban road traffic control idea for the street canyon is proposed with emphasis placed on development of advanced continuum field gasdynamical hydrodynamical control model of the street canyon. The continuum field model of optimal control of street canyon is studied. The mathematical physics approach Eulerian approach to vehicular movement, to pollutants' emission and to pollutants' dynamics is used. The rigorous mathematical model is presented, using gasdynamical hydrodynamical theory for both air constituents and vehicles, including many types of vehicles and many types of pollutant exhaust gases emitted from vehicles. The six optimal control problems are formulated and numerical simulations are performed. Comparison with measurements are provided. General traffic engineering conclusions are inferred. PCCMM'99 poster session.

Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic SpinBoson Model ; We describe the generalization of Wilson's Numerical Renormalization Group method to quantum impurity models with a bosonic bath, providing a general nonperturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spinboson model, describing a twolevel system coupled to a bosonic bath with powerlaw spectral density, Jomega omegas. We find clear evidence for a line of continuous quantum phase transitions for subohmic bath exponents 0s1; the line terminates in the wellknown KosterlitzThouless transition at s1. Contact is made with results from perturbative renormalization group, and various other applications are outlined.

Generalized Network Growth from Microscopic Strategies to the Real Internet Properties ; In this paper we present a generalized model for network growth that links the microscopical agent strategies with the large scale behavior. This model is intended to reproduce the largest number of features of the Internet network at the Autonomous System AS level. Our model of network grows by adding both new vertices and new edges between old vertices. In the latter case a rewarding attachment'' takes place mimicking the disassortative mixing between small routers to larger ones. We find a good agreement between experimental data and the model for the degree distribution, the betweenness distribution, the clustering coefficient and the correlation functions for the degrees.

Universal finitesize scaling analysis of Ising models with longrange interactions at the upper critical dimensionality Isotropic case ; We investigate a twodimensional Ising model with longrange interactions that emerge from a generalization of the magnetic dipolar interaction in spin systems with inplane spin orientation. This interaction is, in general, anisotropic whereby in the present work we focus on the isotropic case for which the model is found to be at its upper critical dimensionality. To investigate the critical behavior the temperature and field dependence of several quantities are studied by means of Monte Carlo simulations. On the basis of the PrivmanFisher hypothesis and results of the renormalization group the numerical data are analyzed in the framework of a finitesize scaling analysis and compared to finitesize scaling functions derived from a GinzburgLandauWilson model in zero mode meanfield approximation. The obtained excellent agreement suggests that at least in the present case the concept of universal finitesize scaling functions can be extended to the upper critical dimensionality.

Static and dynamicalphase transition in multidimensional voting models on continua ; A voting model or a generalization of the Glauber model at zero temperature on a multidimensional lattice is defined as a system composed of a lattice each site of which is either empty or occupied by a single particle. The reactions of the system are such that two adjacent sites, one empty the other occupied, may evolve to a state where both of these sites are either empty or occupied. The continuum version of this model in a Ddimensional region with boundary is studied, and two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the relaxation of the system toward its stationary state. Based on the first behavior, the static phase transition discontinuous changes in the stationary profiles of the system is studied. Based on the second behavior, the dynamical phase transition discontinuous changes in the relaxationtimes of the system is studied. It is shown that the static phase transition is induced by the bulk reactions only, while the dynamical phase transition is a result of both bulk reactions and boundary conditions.

A familynetwork model for wealth distribution in societies ; A model based on firstdegree family relations network is used to describe the wealth distribution in societies. The network structure is not apriori introduced in the model, it is generated in parallel with the wealth values through simple and realistic dynamical rules. The model has two main parameters, governing the wealth exchange in the network. Choosing their values realistically, leads to wealth distributions in good agreement with measured data. The cumulative wealth distribution function has an exponential behavior in the low and medium wealth limit, and shows the Paretolike powerlaw tail for the upper 5 of the society. The obtained Pareto indexes are in good agreement with the measured ones. The generated family networks also converges to a statistically stable topology with a simple Poissonian degree distribution. On this familynetwork many interesting correlations are studied, and the main factors leading to wealthdiversification and the formation of the Pareto law are identified.

Efficient tunable generic model for fluid bilayer membranes ; We present a model for the efficient simulation of generic bilayer membranes. Individual lipids are represented by one head and two tailbeads. By means of simple pair potentials these robustly selfassemble to a fluid bilayer state over a wide range of parameters, without the need for an explicit solvent. The model shows the expected elastic behavior on large length scales, and its physical properties eg fluidity or bending stiffness can be widely tuned via a single parameter. In particular, bending rigidities in the experimentally relevant range are obtained, at least within 330 ktextBT. The model is naturally suited to study many physical topics, including selfassembly, fusion, bilayer melting, lipid mixtures, rafts, and proteinbilayer interactions.

Nonlinear rheology of dense colloidal dispersions a phenomenological model and its connection to mode coupling theory ; Rheological properties, especially 'shearthinning', of dense colloidal dispersions are discussed on three different levels. A generalized phenomonological Maxwell model gives a broad framework connecting glassy dynamics to the linear and nonlinear rheology of dense amorphous particle solutions. First principles mode coupling theory calculations for the time or frequency dependent shear modulus give quantitative results for dispersions of hard colloidal spheres in the linear regime. Schematic models extending mode coupling theory to the nonlinear regime recover the phenomenology of the generalized Maxwell model, and predict universal features of flow curves, stress versus shearrate.

On the fundamental diagram of traffic flow ; We present a new fluiddynamical model of traffic flow. This model generalizes the model of Aw and Rascle SIAM J. Appl. Math. 60 916938 and Greenberg SIAM J. Appl. Math 62 729745 by prescribing a more general source term to the velocity equation. This source term can be physically motivated by experimental data, when taking into account relaxation and reaction time. In particular, the new model has a linearly unstable regime as observed in traffic dynamics. We develop a numerical code, which solves the corresponding system of balance laws. Applying our code to a wide variety of initial data, we find the observed inverselambda shape of the fundamental diagram of traffic flow.

Pseudofermionization of 1D bosons in optical lattices ; We present a model that generalizes the BoseFermi mapping for strongly correlated 1D bosons in an optical lattice, to cases in which the average number of atoms per site is larger than one. This model gives an accurate account of equilibrium properties of such systems, in parameter regimes relevant to current experiments. The application of this model to nonequilibrium phenomena is explored by a study of the dynamics of an atom cloud subject to a sudden displacement of the confining potential. Good agreement is found with results of recent experiments. The simplicity and intuitive appeal of this model make it attractive as a general tool for understanding bosonic systems in the strongly correlated regime.

A generative model for feedback networks ; We investigate a simple generative model for network formation. The model is designed to describe the growth of networks of kinship, trading, corporate alliances, or autocatalytic chemical reactions, where feedback is an essential element of network growth. The underlying graphs in these situations grow via a competition between cycle formation and node addition. After choosing a given node, a search is made for another node at a suitable distance. If such a node is found, a link is added connecting this to the original node, and increasing the number of cycles in the graph; if such a node cannot be found, a new node is added, which is linked to the original node. We simulate this algorithm and find that we cannot reject the hypothesis that the empirical degree distribution is a qexponential function, which has been used to model longrange processes in nonequilibrium statistical mechanics.

Stationary states of a spherical Minority Game with ergodicity breaking ; Using generating functional and replica techniques, respectively, we study the dynamics and statics of a spherical Minority Game MG, which in contrast with a spherical MG previously presented in J.Phys A Math. Gen. 36 11159 2003 displays a phase with broken ergodicity and dependence of the macroscopic stationary state on initial conditions. The model thus bears more similarity with the original MG. Still, all order parameters including the volatility can computed in the ergodic phases without making any approximations. We also study the effects of market impact correction on the phase diagram. Finally we discuss a continuoustime version of the model as well as the differences between online and batch update rules. Our analytical results are confirmed convincingly by comparison with numerical simulations. In an appendix we extend the analysis of the earlier spherical MG to a model with general timestep, and compare the dynamics and statics of the two spherical models.

Stochastic Deformations of Sample Paths of Random Walks and Exclusion Models ; This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in mathbbZ2 or in mathbbZ3. These models are immersed in multitype particle systems with exclusion. Starting from examples, we give necessary and sufficient conditions for the underlying Markov processes to be reversible, in which case their invariant measure has a Gibbs form. Letting the size of the sample path increase, we find the convenient scalings bringing to light phase transition phenomena. Stable and metastable configurations are bound to timeperiods of limiting deterministic trajectories which are solution of nonlinear differential systems in the example of the ABC model, a system of LotkaVolterra class is obtained, and the periods involve elliptic, hyperelliptic or more general functions. Lastly, we discuss briefly the contour of a general approach allowing to tackle the transient regime via differential equations of Burgers' type.

A generic method for modelling the behavior of anisotropic metallic materials application to recrystallized zirconium alloys ; A simplified polycrystalline model the socalled RL model is proposed to simulate the anisotropic viscoplastic behavior of metallic materials. A generic method is presented that makes it possible to build a simplified anisotropic material texture, based on the principal features of the pole figures. The method is applied to a recrystallized zirconium alloy, used as clad material in the fuel rods of nuclear power plants. An important database consisting in mechanical tests performed on Zircaloy tubes is collected. Only a small number of tests pure tension, pure shear are used to identify the material parameters, and the texture parameters. It is shown that six crystallographic orientations 6 grains are sufficient to describe the large anisotropy of such hcp alloy. The identified crystallographic orientations match the experimental pole figures of the material, not used in the identification procedure. Special attention is paid to the predictive ability of the model, i.e., its ability to simulate correctly experimental tests not belonging to the identification database. These predictive results are good, thanks to an identification procedure that enables to consider the contribution of each slip system in each crystallographic orientation.

Weaves A Novel Direct Code Execution Interface for Parallel High Performance Scientific Codes ; Scientific codes are increasingly being used in compositional settings, especially problem solving environments PSEs. Typical compositional modeling frameworks require significant buyin, in the form of commitment to a particular style of programming e.g., distributed object components. While this solution is feasible for newer generations of componentbased scientific codes, large legacy code bases present a veritable software engineering nightmare. We introduce Weaves a novel framework that enables modeling, composition, direct code execution, performance characterization, adaptation, and control of unmodified high performance scientific codes. Weaves is an efficient generalized framework for parallel compositional modeling that is a proper superset of the threads and processes models of programming. In this paper, our focus is on the transparent code execution interface enabled by Weaves. We identify design constraints, their impact on implementation alternatives, configuration scenarios, and present results from a prototype implementation on Intel x86 architectures.

A General Framework For Lazy Functional Logic Programming With Algebraic Polymorphic Types ; We propose a general framework for firstorder functional logic programming, supporting lazy functions, nondeterminism and polymorphic datatypes whose data constructors obey a set C of equational axioms. On top of a given C, we specify a program as a set R of Cbased conditional rewriting rules for defined functions. We argue that equational logic does not supply the proper semantics for such programs. Therefore, we present an alternative logic which includes Cbased rewriting calculi and a notion of model. We get soundness and completeness for Cbased rewriting w.r.t. models, existence of free models for all programs, and type preservation results. As operational semantics, we develop a sound and complete procedure for goal solving, which is based on the combination of lazy narrowing with unification modulo C. Our framework is quite expressive for many purposes, such as solving action and change problems, or realizing the GAMMA computation model.

A Framework for HighAccuracy PrivacyPreserving Mining ; To preserve client privacy in the data mining process, a variety of techniques based on random perturbation of data records have been proposed recently. In this paper, we present a generalized matrixtheoretic model of random perturbation, which facilitates a systematic approach to the design of perturbation mechanisms for privacypreserving mining. Specifically, we demonstrate that a the prior techniques differ only in their settings for the model parameters, and b through appropriate choice of parameter settings, we can derive new perturbation techniques that provide highly accurate mining results even under strict privacy guarantees. We also propose a novel perturbation mechanism wherein the model parameters are themselves characterized as random variables, and demonstrate that this feature provides significant improvements in privacy at a very marginal cost in accuracy. While our model is valid for randomperturbationbased privacypreserving mining in general, we specifically evaluate its utility here with regard to frequentitemset mining on a variety of real datasets. The experimental results indicate that our mechanisms incur substantially lower identity and support errors as compared to the prior techniques.

On the Convergence Speed of MDL Predictions for Bernoulli Sequences ; We consider the Minimum Description Length principle for online sequence prediction. If the underlying model class is discrete, then the total expected square loss is a particularly interesting performance measure a this quantity is bounded, implying convergence with probability one, and b it additionally specifies a rate of convergence'. Generally, for MDL only exponential loss bounds hold, as opposed to the linear bounds for a Bayes mixture. We show that this is even the case if the model class contains only Bernoulli distributions. We derive a new upper bound on the prediction error for countable Bernoulli classes. This implies a small bound comparable to the one for Bayes mixtures for certain important model classes. The results apply to many Machine Learning tasks including classification and hypothesis testing. We provide arguments that our theorems generalize to countable classes of i.i.d. models.

Dynamic Simulation of Construction Machinery Towards an Operator Model ; In dynamic simulation of complete wheel loaders, one interesting aspect, specific for the working task, is the momentary power distribution between drive train and hydraulics, which is balanced by the operator. This paper presents the initial results to a simulation model of a human operator. Rather than letting the operator model follow a predefined path with control inputs at given points, it follows a collection of general rules that together describe the machine's working cycle in a generic way. The advantage of this is that the working task description and the operator model itself are independent of the machine's technical parameters. Complete subsystem characteristics can thus be changed without compromising the relevance and validity of the simulation. Ultimately, this can be used to assess a machine's total performance, fuel efficiency and operability already in the concept phase of the product development process.

Truecluster robust scalable clustering with model selection ; Databased classification is fundamental to most branches of science. While recent years have brought enormous progress in various areas of statistical computing and clustering, some general challenges in clustering remain model selection, robustness, and scalability to large datasets. We consider the important problem of deciding on the optimal number of clusters, given an arbitrary definition of space and clusteriness. We show how to construct a cluster information criterion that allows objective model selection. Differing from other approaches, our truecluster method does not require specific assumptions about underlying distributions, dissimilarity definitions or cluster models. Truecluster puts arbitrary clustering algorithms into a generic unified samplingbased statistical framework. It is scalable to big datasets and provides robust cluster assignments and casewise diagnostics. Truecluster will make clustering more objective, allows for automation, and will save time and costs. Free R software is available.

Path Loss Models Based on Stochastic Rays ; In this paper, twodimensional percolation lattices are applied to describe wireless propagation environment, and stochastic rays are employed to model the trajectories of radio waves. We first derive the probability that a stochastic ray undergoes certain number of collisions at a specific spatial location. Three classes of stochastic rays with different constraint conditions are considered stochastic rays of random walks, and generic stochastic rays with two different anomalous levels. Subsequently, we obtain the closedform formulation of mean received power of radio waves under non lineofsight conditions for each class of stochastic ray. Specifically, the determination of model parameters and the effects of lattice structures on the path loss are investigated. The theoretical results are validated by comparison with experimental data.

A Model of Topological Affine Gravity in Two Dimensions ; A model of twodimensional gravity with an action depending only on a linear connection is considered. This model is a topological one, in the sense that the classical action does not contain a metric or zweibein at all. A metric and an additional vector field are instead introduced in the process of solving equations of motion for the connection. They satisfy the constant curvature equation. It is shown that the general solution of these equations of motion can be described by using the space of orbits under the action of the Weyl group in the functional space containing all pairs formed by a metric and a vectorfield. It is shown also that this model admits an equivalent description by using a family of actions depending on the metric and the connection as independent variables.

Conformally Invariant Cosmology Based on RiemannCartan Spacetime ; Conformally invariant GUTlike model including gravity based on Riemann Cartan spacetime U4 is considered. Cosmological scenario that follows from the model is discussed and standard quantum gravitational formalism in the ArnowittDeserMisner form is developed. General formalism is then illustrated on BianchiIX minisuperspace cosmological model. Wave functions of the universe in the de Sitter minisuperspace model with Vilenkin and HartleHawking boundary conditions are considered and corresponding probability distributions for the scalar field values are calculated.

RadiationDominated Quantum Friedmann Models ; Radiationfilled FriedmannRobertsonWalker universes are quantized according to the ArnowittDeserMisner formalism in the conformaltime gauge. Unlike previous treatments of this problem, here both closed and open models are studied, only squareintegrable wave functions are allowed, and the boundary conditions to ensure selfadjointness of the Hamiltonian operator are consistent with the space of admissible wave functions. It turns out that the tunneling boundary condition on the universal wave function is in conflict with selfadjointness of the Hamiltonian. The evolution of wave packets obeying different boundary conditions is studied and it is generally proven that all models are nonsingular. Given an initial condition on the probability density under which the classical regime prevails, it is found that a closed universe is certain to have an infinite radius, a density parameter Omega 1 becoming a prediction of the theory. Quantum stationary geometries are shown to exist for the closed universe model, but oscillating coherent states are forbidden by the boundary conditions that enforce selfadjointness of the Hamiltonian operator.

Integrability of irrotational silent cosmological models ; We revisit the issue of integrability conditions for the irrotational silent cosmological models. We formulate the problem both in 13 covariant and 13 orthonormal frame notation, and show there exists a series of constraint equations that need to be satisfied. These conditions hold identically for FLRWlinearised silent models, but not in the general exact nonlinear case. Thus there is a linearisation instability, and it is highly unlikely that there is a large class of silent models. We conjecture that there are no spatially inhomogeneous solutions with Weyl curvature of Petrov type I, and indicate further issues that await clarification.

Effects of anisotropy and spatial curvature on the prebig bang scenario ; A class of exact, anisotropic cosmological solutions to the vacuum BransDicke theory of gravity is considered within the context of the prebig bang scenario. Included in this class are the Bianchi type III, V and VIh models and the spatially isotropic, negatively curved FriedmannRobertsonWalker universe. The effects of large anisotropy and spatial curvature are determined. In contrast to negatively curved FriedmannRobertsonWalker model, there exist regions of the parameter space in which the combined effects of curvature and anisotropy prevent the occurrence of inflation. When inflation is possible, the necessary and sufficient conditions for successful prebig bang inflation are more stringent than in the isotropic models. The initial state for these models is established and corresponds in general to a gravitational plane wave.

Phaseplane analysis of FriedmannRobertsonWalker cosmologies in BransDicke gravity ; We present an autonomous phaseplane describing the evolution of FriedmannRobertsonWalker models containing a perfect fluid with barotropic index gamma in BransDicke gravity with BransDicke parameter omega. We find selfsimilar fixed points corresponding to Nariai's powerlaw solutions for spatially flat models and curvaturescaling solutions for curved models. At infinite values of the phaseplane variables we recover O'Hanlon and Tupper's vacuum solutions for spatially flat models and the Milne universe for negative spatial curvature. We find conditions for the existence and stability of these critical points and describe the qualitative evolution in all regions of the omega,gamma parameter space for 0gamma2 and omega32. We show that the condition for inflation in BransDicke gravity is always stronger than the general relativistic condition, gamma23.

Toda Chains with Type Am Lie Algebra for Multidimensional Classical Cosmology with Intersecting pBranes ; We consider a Ddimensional cosmological model describing an evolution of n1 Einstein factor spaces in the theory with several dilatonic scalar fields and generalized electromagnetic forms, admitting an interpretation in terms of intersecting pbranes. The equations of motion of the model are reduced to the EulerLagrange equations for the so called pseudoEuclidean Todalike system. We consider the case, when characteristic vectors of the model, related to pbranes configuration and their couplings to the dilatonic fields, may be interpreted as the root vectors of a Lie algebra of the type Am. The model is reduced to the open Toda chain and integrated. The exact solution is presented in the Kasnerlike form.

SL2,R model with two Hamiltonian constraints ; We describe a simple dynamical model characterized by the presence of two noncommuting Hamiltonian constraints. This feature mimics the constraint structure of general relativity, where there is one Hamiltonian constraint associated with each space point. We solve the classical and quantum dynamics of the model, which turns out to be governed by an SL2,R gauge symmetry, local in time. In classical theory, we solve the equations of motion, find a SO2,2 algebra of Dirac observables, find the gauge transformations for the Lagrangian and canonical variables and for the Lagrange multipliers. In quantum theory, we find the physical states, the quantum observables, and the physical inner product, which is determined by the reality conditions. In addition, we construct the classical and quantum evolving constants of the system. The model illustrates how to describe physical gaugeinvariant relative evolution when coordinate time evolution is a gauge.

Simplicial minisuperspace models in the presence of a scalar field ; We generalize simplicial minisuperspace models associated with restricting the topology of the universe to be that of a cone over a closed connected combinatorial 3manifold by considering the presence of a massive scalar field. By restricting all the interior edge lengths and all the boundary edge lengths to be equivalent and the scalar field to be homogenous on the 3space, we obtain a family of two dimensional models that include some of the most relevant triangulations of the spatial universe. After studying the analytic properties of the action in the space of complex edge lengths we determine its classical extrema. We then obtain steepest descents contours of constant imaginary action passing through Lorentzian classical geometries yielding a convergent wavefunction of the universe, dominated by the contributions coming from these extrema. By considering these contours we justify semiclassical approximations based on those classical solutions, clearly predicting classical spacetime in the late universe. These wavefunctions are then evaluated numerically. For all of the models examined we find wavefunctions predicting Lorentzian oscillatory behaviour in the late universe.

Invariants of spin networks with boundary in Quantum Gravity and TQFT's ; The search for classical or quantum combinatorial invariants of compact ndimensional manifolds n3,4 plays a key role both in topological field theories and in lattice quantum gravity. We present here a generalization of the partition function proposed by Ponzano and Regge to the case of a compact 3dimensional simplicial pair M3, partial M3. The resulting state sum ZM3, partial M3 contains both RacahWigner 6j symbols associated with tetrahedra and Wigner 3jm symbols associated with triangular faces lying in partial M3. The analysis of the algebraic identities associated with the combinatorial transformations involved in the proof of the topological invariance makes it manifest a common structure underlying the 3dimensional models with empty and non empty boundaries respectively. The techniques developed in the 3dimensional case can be further extended in order to deal with combinatorial models in n2,4 and possibly to establish a hierarchy among such models. As an example we derive here a 2dimensional closed state sum model including suitable sums of products of double 3jm symbols, each one of them being associated with a triangle in the surface.

Scalar Field Cosmologies with Barotropic Matter Models of Bianchi class B ; We investigate in detail the qualitative behaviour of the class of Bianchi type B spatially homogeneous cosmological models in which the matter content is composed of two noninteracting components; the first component is described by a barotropic fluid having a gammalaw equation of state, whilst the second is a noninteracting scalar field phi with an exponential potential VLambda expk phi. In particular, we study the asymptotic properties of the models both at early and late times, paying particular attention on whether the models isotropize and inflate to the future, and we discuss the genericity of the cosmological scaling solutions.

Variable LightCone Theory of Gravity ; We show how to reformulate Variable Speed of Light Theories VSLT in a covariant fashion as Variable LightCone Theories VLCT by introducing two vierbein bundles each associated with a distinct metric. The basic gravitational action relates to one bundle while matter propagates relative to the other in a conventional way. The variability of the speed of light is represented by the variability of the matter lightcone relative to the gravitational lightcone. The two bundles are related locally by an element M, of SL4,R. The dynamics of the field M is that of a SL4,Rsigma model gauged with respect to local orthochronous Lorentz transformations on each of the bundles. Only the massless'' version of the model with a single new coupling, F, that has the same dimensions as Newton's constant GN, is considered in this paper. When F vanishes the theory reduces to standard General Relativity. We verify that the modified Bianchi identities of the model are consistent with the standard conservation law for the matter energymomentum tensor in its own background metric. The implications of the model for some simple applications are examined, the Newtonian limit, the flat FRW universe and the spherically symmetric static solution.

Aspects of black hole entropy ; There have been many attempts to understand the statistical origin of blackhole entropy. Among them, entanglement entropy and the brick wall model are strong candidates. In this paper, first, we show that the entanglement approach reduces to the brick wall model when we seek the maximal entanglement entropy. After that, the stability of the brick wall model is analyzed in a rotating background. It is shown that in the Kerr background without horizon but with an inner boundary a scalar field has complexfrequency modes and that, however, the imaginary part of the complex frequency can be small enough compared with the Hawking temperature if the inner boundary is sufficiently close to the horizon, say at a proper altitude of Planck scale. Hence, the brick wall model is well defined even in a rotating background if the inner boundary is sufficiently close to the horizon. These results strongly suggest that the entanglement approach is also well defined in a rotating background.

Shell sources as a probe of relativistic effects in neutron star models ; A perturbing shell is introduced as a device for studying the excitation of fluid motions in relativistic stellar models. We show that this approach allows a reasonably clean separation of radiation from the shell and from fluid motions in the star, and provides broad flexibility in the location and timescale of perturbations driving the fluid motions. With this model we compare the relativistic and Newtonian results for the generation of even parity gravitational waves from constant density models. Our results suggest that relativistic effects will not be important in computations of the gravitational emission except possibly in the case of excitation of the neutron star on very short time scales.

Brane versus shell cosmologies in Einstein and EinsteinGaussBonnet theories ; We first illustrate on a simple example how, in existing brane cosmological models, the connection of a 'bulk' region to its mirror image creates matter on the 'brane'. Next, we present a cosmological model with no Z2 symmetry which is a spherical symmetric 'shell' separating two metrically different 5dimensional antide Sitter regions. We find that our model becomes Friedmannian at late times, like present brane models, but that its early time behaviour is very different the scale factor grows from a nonzero value at the big bang singularity. We then show how the Israel matching conditions across the membrane that is either a brane or a shell have to be modified if more general equations than Einstein's, including a GaussBonnet correction, hold in the bulk, as is likely to be the case in a low energy limit of string theory. We find that the membrane can then no longer be treated in the thin wall approximation. However its microphysics may, in some instances, be simply hidden in a renormalization of Einstein's constant, in which cases Einstein and GaussBonnet membranes are identical.

Hierarchies of invariant spin models ; In this paper we present classes of state sum models based on the recoupling theory of angular momenta of SU2 and of its qcounterpart Uqsl2, q a root of unity. Such classes are arranged in hierarchies depending on the dimension d, and include all known closed models, i.e. the PonzanoRegge state sum and the TuraevViro invariant in dimension d3, the CraneYetter invariant in d4. In general, the recoupling coefficient associated with a dsimplex turns out to be a 3d2d12j symbol, or its qanalog. Each of the state sums can be further extended to compact triangulations Td,partial Td of a PLpair Md,partial Md, where the triangulation of the boundary manifold is not keeped fixed. In both cases we find out the algebraic identities which translate complete sets of topological moves, thus showing that all state sums are actually independent of the particular triangulation chosen. Then, owing to Pachner's theorems, it turns out that classes of PLinvariant models can be defined in any dimension d.

Gravitational Statistical Mechanics A model ; Using the quantum Hamiltonian for a gravitational system with boundary, we find the partition function and derive the resulting thermodynamics. The Hamiltonian is the boundary term required by functional differentiability of the action for Lorentzian general relativity. In this model, states of quantum geometry are represented by spin networks. We show that the statistical mechanics of the model reduces to that of a simple noninteracting gas of particles with spin. Using both canonical and grand canonical descriptions, we investigate two temperature regimes determined by the fundamental constant in the theory, m. In the high temperature limit kT m, the model is thermodynamically stable. For low temperatures kT m and for macroscopic areas of the bounding surface, the entropy is proportional to area with logarithmic correction, providing a simple derivation of the BekensteinHawking result. By comparing our results to known semiclassical relations we are able to fix the fundamental scale. Also in the low temperature, macroscopic limit, the quantum geometry on the boundary forms a condensate' in the lowest energy level j12.

Structure formation in the LemaitreTolman model ; Structure formation within the LemaitreTolman model is investigated in a general manner. We seek models such that the initial density perturbation within a homogeneous background has a smaller mass than the structure into which it will develop, and the perturbation then accretes more mass during evolution. This is a generalisation of the approach taken by Bonnor in 1956. It is proved that any two spherically symmetric density profiles specified on any two constant time slices can be joined by a LemaitreTolman evolution, and exact implicit formulae for the arbitrary functions that determine the resulting LT model are obtained. Examples of the process are investigated numerically.

Model of gravitondusty universe ; Primary features of a new cosmological model, which is based on conjectures about an existence of the graviton background and superstrong gravitational quantum interaction, are considered. An expansion of the universe is impossible in such the model because of deceleration of massive objects by the graviton background, which is similar to the one for the NASA deep space probes Pioneer 10, 11. Redshifts of remote objects are caused in the model by interaction of photons with the graviton background, and the Hubble constant depends on an intensity of interaction and an equivalent temperature of the graviton background. Virtual massive gravitons would be dark matter particles. They transfer energy, lost by luminous matter radiation, which in a final stage may be collected with black holes and other massive objects.

Spin Foam Models of Riemannian Quantum Gravity ; Using numerical calculations, we compare three versions of the BarrettCrane model of 4dimensional Riemannian quantum gravity. In the version with face and edge amplitudes as described by De Pietri, Freidel, Krasnov, and Rovelli, we show the partition function diverges very rapidly for many triangulated 4manifolds. In the version with modified face and edge amplitudes due to Perez and Rovelli, we show the partition function converges so rapidly that the sum is dominated by spin foams where all the spins labelling faces are zero except for small, widely separated islands of higher spin. We also describe a new version which appears to have a convergent partition function without drastic spinzero dominance. Finally, after a general discussion of how to extract physics from spin foam models, we discuss the implications of convergence or divergence of the partition function for other aspects of a spin foam model.

The EinsteinVlasov sytemKinetic theory ; The main purpose of this article is to guide the reader to theorems on global properties of solutions to the EinsteinVlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades where the main focus has been on nonrelativistic and special relativistic physics, e.g. to model the dynamics of neutral gases, plasmas and Newtonian selfgravitating systems. In 1990 Rendall and Rein initiated a mathematical study of the EinsteinVlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models e.g. fluid models. The first part of this paper gives an introduction to kinetic theory in noncurved spacetimes and then the EinsteinVlasov system is introduced. We believe that a good understanding of kinetic theory in noncurved spacetimes is fundamental in order to get a good comprehension of kinetic theory in general relativity.

Bouncing Braneworlds ; We study cosmological braneworld models with a single timelike extra dimension. Such models admit the intriguing possibility that a contracting braneworld experiences a natural bounce without ever reaching a singular state. This feature persists in the case of anisotropic braneworlds under some additional and not very restrictive assumptions. Generalizing our study to braneworld models containing an induced brane curvature term, we find that a FRWtype singularity is once again absent if the bulk extra dimension is timelike. In this case, the universe either has a nonsingular origin or commences its expansion from a quasisingular state during which both the Hubble parameter and the energy density and pressure remain finite while the curvature tensor diverges. The nonsingular and quasisingular behaviour which we have discovered differs both qualitatively and quantitatively from what is usually observed in braneworld models with spacelike extra dimensions and could have interesting cosmological implications.

Is a classical Euclidean TOE reasonable ; We analyze both the feasibility and reasonableness of a classical Euclidean Theory of Everything TOE, which we understand as a TOE based on an Euclidean space and an absolute time over which deterministic models of particles and forces are built. The possible axiomatic complexity of a TOE in such a framework is considered and compared to the complexity of the assumptions underlying the Standard Model. Current approaches to relevant for our purposes reformulations of Special Relativity, General Relativity, inertia models and Quantum Theory are summarized, and links between some of these reformulations are exposed. A qualitative framework is suggested for a research program on a classical Euclidean TOE. Within this framework an underlying basis is suggested, in particular, for the Principle of Relativity and Principle of Equivalence. A model for gravity as an inertial phenomenon is proposed. Also, a basis for quantum indeterminacy and wave function collapse is suggested in the framework.

Magnetodilatonic BianchiI cosmology isotropization and singularity problems ; We study the evolution of BianchiI spacetimes filled with a global unidirectional electromagnetic field Fmn interacting with a massless scalar dilatonic field according to the law Psiphi Fmn Fmn where Psiphi 0 is an arbitrary function. A qualitative study, among other results, shows that i the volume factor always evolves monotonically, ii there exist models becoming isotropic at late times and iii the expansion generically starts from a singularity but there can be special models starting from a Killing horizon preceded by a static stage. All these features are confirmed for exact solutions found for the usually considered case Psi e2lambdaphi, lambda const. In particular, isotropizing models are found for lambda 1sqrt3. In the special case lambda 1, which corresponds to models of string origin, the string metric behaviour is studied and shown to be qualitatively similar to that of the Einstein frame metric.

Transition from accelerated to decelerated regimes in JT and CGHS cosmologies ; In this work we discuss the possibility of positiveacceleration regimes, and their transition to decelerated regimes, in twodimensional 2D cosmological models. We use general relativity and the thermodynamics in a 2D spacetime, where the gas is seen as the sources of the gravitational field. An earlyUniverse model is analyzed where the state equation of van der Waals is used, replacing the usual barotropic equation. We show that this substitution permits the simulation of a period of inflation, followed by a negativeacceleration era. The dynamical behavior of the system follows from the solution of the JackiwTeitelboim equations JT equations and the energymomentum conservation laws. In a second stage we focus the CallanGiddingsHarveyStrominger model CGHS model; here the transition from the inflationary period to the decelerated period is also present between the solutions, although this result depend strongly on the initial conditions used for the dilaton field. The temporal evolution of the cosmic scale function, its acceleration, the energy density and the hydrostatic pressure are the physical quantities obtained in through the analysis.

The Feynman propagator for quantum gravity spin foams, proper time, orientation, causality and timelessordering ; We discuss the notion of causality in Quantum Gravity in the context of sumoverhistories approaches, in the absence therefore of any background time parameter. In the spin foam formulation of Quantum Gravity, we identify the appropriate causal structure in the orientation of the spin foam 2complex and the data that characterize it; we construct a generalised version of spin foam models introducing an extra variable with the interpretation of proper time and show that different ranges of integration for this proper time give two separate classes of spin foam models one corresponds to the spin foam models currently studied, that are independent of the underlying orientationcausal structure and are therefore interpreted as acausal transition amplitudes; the second corresponds to a general definition of causal or orientation dependent spin foam models, interpreted as causal transition amplitudes or as the Quantum Gravity analogue of the Feynman propagator of field theory, implying a notion of ''timeless ordering''.

The EinsteinVlasov systemKinetic theory ; The main purpose of this article is to provide a guide to theorems on global properties of solutions to the EinsteinVlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on nonrelativistic and special relativistic physics, it i.e. to model the dynamics of neutral gases, plasmas, and Newtonian selfgravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the EinsteinVlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models it i.e. fluid models. This paper gives introductions to kinetic theory in noncurved spacetimes and then the EinsteinVlasov system is introduced. We believe that a good understanding of kinetic theory in noncurved spacetimes is fundamental to good comprehension of kinetic theory in general relativity.

Exact solutions of SO3 nonlinear sigma model in a conic space background ; We consider a nonlinear sigma model coupled to the metric of a conic space. We obtain restrictions for a nonlinear sigma model to be a source of the conic space. We then study nonlinear sigma model in the conic space background. We find coordinate transformations which reduce the chiral fields equations in the conic space background to field equations in Minkowski spacetime. This enables us to apply the same methods for obtaining exact solutions in Minkowski spacetime to the case of a conic spacetime. In the case the solutions depend on two spatial coordinates we employ Ivanov's geometrical ansatz. We give a general analysis and also present classes of solutions in which there is dependence on three and four coordinates. We discuss with special attention the intermediate instanton and meron solutions and their analogous in the conic space. We find differences in the total actions and topological charges of these solutions and discuss the role of the deficit angle.

Finiteness and Dual Variables for Lorentzian Spin Foam Models ; We describe here some new results concerning the Lorentzian BarrettCrane model, a wellknown spin foam formulation of quantum gravity. Generalizing an existing finiteness result, we provide a concise proof of finiteness of the partition function associated to all nondegenerate triangulations of 4manifolds and for a class of degenerate triangulations not previously shown. This is accomplished by a suitable refactoring and reordering of integration, through which a large set of variables can be eliminated. The resulting formulation can be interpreted as a dual variables'' model that uses hyperboloid variables associated to spin foam edges in place of representation variables associated to faces. We outline how this method may also be useful for numerical computations, which have so far proven to be very challenging for Lorentzian spin foam models.

On Some Accelerating Cosmological KaluzaKlein Models ; We consider 4Ddimensional KaluzaKlein cosmological model with two scaling factors, as real, padic and adelic quantum mechanical one. One of the scaling factors corresponds to the Ddimensional internal space, and second one to the 4dimensional universe. In standard quantum cosmology, i.e. over the field of real numbers R, it leads to dynamical compactification of additional dimensions and to the accelerating evolution of 4dimensional universe. We construct corresponding padic quantum model and explore existence of its padic ground state. In addition, we explore evolution of this model and a possibility for its adelic generalization. It is necessary for the further investigation of spacetime discreteness at very short distances, i.e. in a very early universe

The Futures of Bianchi type VII0 cosmologies with vorticity ; We use expansionnormalised variables to investigate the Bianchi type VII0 model with a tilted gammalaw perfect fluid. We emphasize the latetime asymptotic dynamical behaviour of the models and determine their asymptotic states. Unlike the other Bianchi models of solvable type, the type VII0 state space is unbounded. Consequently we show that, for a general noninflationary perfect fluid, one of the curvature variables diverges at late times, which implies that the type VII0 model is not asymptotically selfsimilar to the future. Regarding the tilt velocity, we show that for fluids with gamma43 which includes the important case of dust, gamma1 the tilt velocity tends to zero at late times, while for a radiation fluid, gamma43, the fluid is tilted and its vorticity is dynamically significant at late times. For fluids stiffer than radiation gamma43, the future asymptotic state is an extremely tilted spacetime with vorticity.

Matching Scherrer's k essence argument with alterations of Di Quark scalar fields permitting an eventual comological constant dominated inflationary expansion ; We previously showed that we can use di quark pairs as a model of how nucleation of a new universe occurs. We now can construct a model showing evolution from a dark matter dark energy mix to a pure cosmological constant cosmology due to changes in the slope of the resulting scalar field,using much of Scherrer's kessence model.This same construction permits a use of the speed of sound,in kessence models evolving from zero to one. Having the sound speed eventually reach unity permits matching conventional cosmological observations in the aftermath of change of slope of a di quark pair generated scalar field during the nucleation process of a new universe. These results are consistent with applying Bunyi and Hu's semi classical criteria for cosmological potentials to indicate a phase transition alluded to by Dr. Edward Kolbs model of how the initial degrees of freedom declined from over 100 to something approaching what we see today in flat space cosmology.

Geometric Constraint in BraneWorld ; The braneworlds model was inspired partly by KaluzaKlein's theory, where the gravitation and the gauge fields are obtained of a geometry of higher dimension bulk. Such a model has been showing positive in the sense of we find perspectives and probably deep modifications in the physics, such as Unification in a scale TeV, quantum gravity in this scale and deviation of Newton's law for small distances. One of the principles of this model is to suppose a spacetime embedded in a bulk of high dimension. In this note it is shown, basing on the theorem of CollinsonSzekeres, that the spacetime of Schwarzschild cannot be embedded locally and isometrically in a bulk of five dimensions with constant curvature,for example ADS5. From the point of view of the semiRiemannian geometry this last result consists constraints to the model braneworld.

Analysis of spherically symmetric black holes in Braneworld models ; Research on black holes and their physical proprieties has been active on last 90 years. With the appearance of the String Theory and the Braneworld models as alternative descriptions of our Universe, the interest on black holes, in these context, increased. In this work we studied black holes in Braneworld models. A class of spherically symmetric black holes is investigaded as well its stability under general perturbations. Thermodynamic proprieties and quasinormal modes are discussed. The black holes studied are the SM zero mass and CFM solutions, obtained by Casadio it et al. and Bronnikov it et al.. The geometry of bulk is unknown. However the CampbellMagaard Theorem guarantees the existence of a 5dimensional solution in the bulk whose projection on the brane is the class of black holes considered. They are stable under scalar perturbations. Quasinormal modes were observed in both models. The tail behavior of the perturbations is the same. The entropy upper bound of a body absorved by the black holes studied was calculated. This limit turned out to be independent of the black hole parameters.

NonSingular Bouncing Universes in Loop Quantum Cosmology ; Nonperturbative quantum geometric effects in Loop Quantum Cosmology predict a rho2 modification to the Friedmann equation at high energies. The quadratic term is negative definite and can lead to generic bounces when the matter energy density becomes equal to a critical value of the order of the Planck density. The nonsingular bounce is achieved for arbitrary matter without violation of positive energy conditions. By performing a qualitative analysis we explore the nature of the bounce for inflationary and Cyclic model potentials. For the former we show that inflationary trajectories are attractors of the dynamics after the bounce implying that inflation can be harmoniously embedded in LQC. For the latter difficulties associated with singularities in cyclic models can be overcome. We show that nonsingular cyclic models can be constructed with a small variation in the original Cyclic model potential by making it slightly positive in the regime where scalar field is negative.

A new proposal for group field theory I the 3d case ; In this series of papers, we propose a new rendition of 3d and 4d state sum models based upon the group field theory GFT approach to nonperturbative quantum gravity. We will see that the group field theories investigated in the literature to date are, when judged from the position of quantum field theory, an unusual manifestation of quantum dynamics. They are one in which the Hadamard function for the field theory propagates acausally the physical degrees of freedom of quantum gravity. This is fine if we wish to define a scalar product on the physical state space, but it is not what we generally think of as originating directly from a field theory. We propose a model in 3d more in line with standard quantum field theory, and therefore the field theory precipitates causal dynamics. Thereafter, we couple the model to point matter, and extract from the GFT the effective noncommutative field theory describing the matter dynamics on a quantum gravity background. We identify the symmetries of our new model and clarify their meaning in the GFT setting. We are aided in this process by identifying the category theory foundations of this GFT which, moreover, propel us towards a categorified version for the 4d case.

Selforganized critical behavior the evolution of frozen spin networks model in quantum gravity ; In quantum gravity, we study the evolution of a twodimensional planar open frozen spin network, in which the color i.e. the twice spin of an edge labeling edge changes but the underlying graph remains fixed. The mainly considered evolution rule, the random edge model, is depending on choosing an edge randomly and changing the color of it by an even integer. Since the change of color generally violate the gauge invariance conditions imposed on the system, detailed propagation rule is needed and it can be defined in many ways. Here, we provided one new propagation rule, in which the involved even integer is not a constant one as in previous works, but changeable with certain probability. In random edge model, we do find the evolution of the system under the propagation rule exhibits powerlaw behavior, which is suggestive of the selforganized criticality SOC, and it is the first time to verify the SOC behavior in such evolution model for the frozen spin network. Furthermore, the increase of the average color of the spin network in time can show the nature of inflation for the universe.

Nonlinear vector perturbations in a contracting universe ; A number of scalar field models proposed as alternatives to the standard inflationary scenario involve contracting phases which precede the universe's present phase of expansion. An important question concerning such models is whether there are effects which could potentially distinguish them from purely expanding cosmologies. Vector perturbations have recently been considered in this context. At first order such perturbations are not supported by a scalar field. In this paper, therefore, we consider second order vector perturbations. We show that such perturbations are generated by first order scalar modemode couplings, and give an explicit expression for them. We compare the magnitude of vector perturbations produced in collapsing models with the corresponding amplitudes produced during inflation, using a number of suitable powerlaw solutions to model the inflationary and collapsing scenarios. We conclude that the ratios of the magnitudes of these perturbations depend on the details of the collapsing scenario as well as on how the hot big bang is recovered, but for certain cases could be large, growing with the duration of the collapse.

A note on cosmology in a brane model ; We study some aspects of cosmology in a fivedimensional model with matter, radiation and cosmological constant on the fourdimensional branes and without matter in the bulk. The action of the model does not contain explicit curvature terms on the the branes. We obtain solution of the generalized Friedman equation as a function of dimensionless ratio of the scales b2 fracmu M2plM3 mu is the scale in the warp factor in the 5D metric which is taken of order 103div 4GeV, Mgeqmu is the 5D fundamental scale. We assume that there is a hierarchy between 4D and 5D scales. For b2 O1 the age of the Universe is found comparable, but below the current experimental value, for b2gg 1 it is obtained much smaller than the experimental bound. Because time dependence of temperature of the Universe in the 5D model is different from that in the standard cosmology, the abundance of 4He produced in the primordial nucleosynthesis is obtained about three times more than in the standard cosmology.

SO3 vortices as a mechanism for generating a mass gap in the 2d SU2 principal chiral model ; We propose a mechanism that can create a mass gap in the SU2 chiral spin model at arbitrarily small temperatures. We give a sufficient condition for the mass gap to be nonzero in terms of the behaviour of an external Z2 flux introduced by twisted boundary conditions. This condition in turn is transformed into an effective dual Ising model with an external magnetic field generated by SO3 vortices. We show that having a nonzero magnetic field in the effective Ising model is sufficient for the SU2 system to have a mass gap. We also show that certain vortex correlation inequalities, if satisfied, would imply a nonzero effective magnetic field. Finally we give some plausibility arguments and Monte Carlo evidence for the required correlation inequalities.