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Glass glass transition and new dynamical singularity points in an analytically solvable pspin glass like model ; We introduce and analytically study a generalized pspin glass like model that captures some of the main features of attractive glasses, recently found by Mode Coupling investigations, such as a glassglass transition line and dynamical singularity points characterized by a logarithmic time dependence of the relaxation. The model also displays features not predicted by the Mode Coupling scenario that could further describe the attractive glasses behavior, such as aging effects with new dynamical singularity points ruled by logarithmic laws or the presence of a glass spinodal line.

Selforganized Criticality and Absorbing States Lessons from the Ising Model ; We investigate a suggested path to selforganized criticality. Originally, this path was devised to generate criticality in systems displaying an absorbingstate phase transition, but closer examination of the mechanism reveals that it can be used for any continuous phase transition. We used the Ising model as well as the Manna model to demonstrate how the finitesize scaling exponents depend on the tuning of driving and dissipation rates with system size.Our findings limit the explanatory power of the mechanism to nonuniversal critical behavior.

Representation Theory and Baxter's TQ equation for the sixvertex model. A pedagogical overview ; A summary of the construction procedure of generalized versions of Baxter's Qoperator is given. Illustrated by several figures and diagrams the use of representation theory is explained stepbystep avoiding technical details. The relation with the infinitedimensional nonabelian symmetries of the sixvertex model at roots of unity is discussed and parallels with the eightvertex case outlined.

Are defect models consistent with the entropy and specific heat of glassformers ; We show that pointlike defect model of glasses cannot explain thermodynamic properties of glassformers, as for example the excess specific heat close to the glass transition, contrary to the claim of J.P. Garrahan, D. Chandler Proc. Natl. Acad. Sci. 100, 9710 2003. More general models and approaches in terms of extended defects are also discussed.

Corrections to a mean number of droplets in nucleation ; Corrections to a mean number of droplets appeared in the process of nucleation have been analyzed. The two stage model with a fixed boundary can not lead to a write result. The multi stage generalization of this model also can not give essential changes to the two stage model. The role of several first droplets have been investigated and it is shown that an account of only first droplet with further appearance in frame of the theory based on the averaged characteristics can lead to a suitable results. Both decay of metastable phase and smooth variations of external conditions have been investigated.

Quantum Magnets with Anisotropic Infinite Range Random Interactions ; Using exact diagonalization techniques we study the dynamical response of the anisotropic disordered Heisenberg model for systems of S12 spins with infinite range random exchange interactions at temperature T0. The model can be considered as a generalization, to the quantum case, of the well known SherringtonKirkpatrick classical spinglass model. We also compute and study the behavior of the Edwards Anderson order parameter and energy per spin as the anisotropy evolves from the Ising to the Heisenberg limits.

Numerical evaluation of the dipolescattering model for the metalinsulator transition in gated high mobility Silicon inversion layers ; The dipole trap model is able to explain the main properties of the apparent metaltoinsulator transition in gated high mobility Siinversion layers. Our numerical calculations are compared with previous analytical ones and the assumptions of the model are discussed carefully. In general we find a similar behavior but include further details in the calculation. The calculated strong density dependence of the resistivity is not yet in full agreement with the experiment.

Weighted Configuration Model ; The configuration model is one of the most successful models for generating uncorrelated random networks. We analyze its behavior when the expected degree sequence follows a power law with exponent smaller than two. In this situation, the resulting network can be viewed as a weighted network with non trivial correlations between strength and degree. Our results are tested against large scale numerical simulations, finding excellent agreement.

Rigorous proof of Luttinger liquid behavior in the 1d Hubbard model ; We give the first rigorous non perturbative proof of Luttinger liquid behavior in the one dimensional Hubbard model, for small repulsive interaction and values of the density different from half filling. The analysis is based on the combination of multiscale analysis with Ward identities bases on a hidden and approximate local chiral gauge invariance. No use is done of exact solutions or special integrability properties of the Hubbard model, and the results can be in fact easily generalized to include non local interactions, magnetic fields or interaction with external potentials

The number of link and cluster states the core of the 2D q state Potts model ; Due to Fortuin and Kastelyin the q state Potts model has a representation as a sum over random graphs, generalizing the Potts model to arbitrary q is based on this representation. A key element of the Random Cluster representation is the combinatorial factor GammaGraphGClusters,Edges, which is the number of ways to form Clusters distinct clusters, consisting of totally Edges edges. We have devised a method to calculate GammaGraphGClusters,Edges from Monte Carlo simulations.

Thermodynamic origin of order parameters in meanfield models of spin glasses ; We analyze thermodynamic behavior of general ncomponent meanfield spin glass models in order to identify origin of the hierarchical structure of the order parameters from the replicasymmetry breaking solution. We derive a configurationally dependent free energy with local magnetizations and averaged local susceptibilities as order parameters. On an example of the replicated Ising spin glass we demonstrate that the hierarchy of order parameters in meanfield models results from the structure of interreplica susceptibilities. These susceptibilities serve for lifting the degeneracy due to the existence of many metastable states and for recovering thermodynamic homogeneity of the free energy.

A tomography of the GREM beyond the REM conjecture ; Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should in most circumstances be the same as in the random energy model. This was proven in a large class of models for energies that do not grow too fast with the system size. Considering the example of the generalized random energy model, we show that the conjecture breaks down for energies proportional to the volume of the system, and describe the far more complex behavior that then sets in.

Pattern formation of microtubules and motors inelastic interaction of polar rods ; We derive a model describing spatiotemporal organization of an array of microtubules interacting via molecular motors. Starting from a stochastic model of inelastic polar rods with a generic anisotropic interaction kernel we obtain a set of equations for the local rods concentration and orientation. At large enough mean density of rods and concentration of motors, the model describes orientational instability. We demonstrate that the orientational instability leads to the formation of vortices and for large density andor kernel anisotropy asters seen in recent experiments.

Schwinger Boson approach to the fully screened Kondo model ; We apply the Schwinger boson scheme to the fully screened Kondo model and generalize the method to include antiferromagnetic interactions between ions. Our approach captures the Kondo crossover from local moment behavior to a Fermi liquid with a nontrivial Wilson ratio. When applied to the two impurity model, the meanfield theory describes the Varma Jones quantum phase transition between a valence bond state and a heavy Fermi liquid.

Random Cluster Models on the Triangular Lattice ; We study percolation and the random cluster model on the triangular lattice with 3body interactions. Starting with percolation, we generalize the startriangle transformation We introduce a new parameter the 3body term and identify configurations on the triangles solely by their connectivity. In this new setup, necessary and sufficient conditions are found for positive correlations and this is used to establish regions of percolation and nonpercolation. Next we apply this set of ideas to the q1 random cluster model We derive duality relations for the suitable random cluster measures, prove necessary and sufficient conditions for them to have positive correlations, and finally prove some rigorous theorems concerning phase transitions.

Aging in a freeenergy landscape model for glassy relaxation ; The aging properties of a simple freeenergy landscape model for the primary relaxation in supercooled liquids are investigated. The intermediate scattering function and the rotational correlation functions are calculated for the generic situation of a quench from a high temperature to below the glass transition temperature. It is found that the reequilibration of molecular orientations takes longer than for translational degrees of freedom. The time scale for reequilibration is determined by that of the primary relaxation as an intrinsic property of the model.

Correlationfunction asymptotic expansions prefactors universality ; We show that the prefactors of all terms of the onedimensional Hubbard model correlationfunction asymptotic expansions have an universal form, as the corresponding critical exponents. In addition to calculating such prefactors, our study clarifies the relation of the lowenergy TomonagaLuttinger liquid behavior to the scattering mechanisms which control the spectral properties of the model at all energy scales. Our results are of general nature for many integrable interacting models and provide a broader understanding of the unusual properties of quasi1D nanostructures, organic conductors, and optical lattices of fermionic atoms.

A Derivation of Dirac's Equation From a Model of an Elastic Medium ; Starting from a model of an elastic medium, we derive equations of motion that are identical in form to Dirac's equation for a spin 12 particle with mass, coupled to electromagnetic and gravitational interactions. The mass and electromagnetic terms are not added by hand but emerge naturally from the formalism. A two dimensional version of this equation is derived by starting with a model in three dimensions and deriving equations for the dynamics of the lowest Fourier modes assuming one dimension to be periodic. Generalizations to higher dimensions are discussed.

On two descriptions of disordered phase of 2D quantum antiferromagnets monopole plasma and KalbRamond fields ; We have studied a system of light bosonic spinons interacting with compact gauge fields. By the generalization of the works by Polyakov on compact gauge fields the system is mapped to monopole plasma model and a model of open surfaces coupled to antisymmetric KalbRamond gauge fields. The monopole correlation function in the presence of light spinon is computed based on these two models.

Constructing thermodynamically consistent models with a nonideal equation of state ; A recently introduced particlebased model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multiparticle collisions which depend on local velocities and densities and conserve momentum and kinetic energy. The equation of state is derived and criteria for the correct choice of collision probabilities are discussed. In particular, it is shown how a naive implementation can lead to inconsistent density fluctuations.

Emergence of rheological properties in lattice Boltzmann simulations of gyroid mesophases ; We use a lattice Boltzmann LB kinetic scheme for modelling amphiphilic fluids that correctly predicts rheological effects in flow. No macroscopic parameters are included in the model. Instead, threedimensional hydrodynamic and rheological effects are emergent from the underlying particulate conservation laws and interactions. We report evidence of shear thinning and viscoelastic flow for a selfassembled gyroid mesophase. This purely kinetic approach is of general importance for the modelling and simulation of complex fluid flows in situations when rheological properties cannot be predicted em a priori.

Nonlinear parametric model for Granger causality of time series ; We generalize a previously proposed approach for nonlinear Granger causality of time series, based on radial basis function. The proposed model is not constrained to be additive in variables from the two time series and can approximate any function of these variables, still being suitable to evaluate causality. Usefulness of this measure of causality is shown in a physiological example and in the study of the feedback loop in a model of excitatory and inhibitory neurons.

From Scalefree to ErdosRenyi Networks ; We analyze a model that interpolates between scalefree and ErdosRenyi networks. The model introduced generates a oneparameter family of networks and allows to analyze the role of structural heterogeneity. Analytical calculations are compared with extensive numerical simulations in order to describe the transition between these two important classes of networks. Finally, an application of the proposed model to the study of the percolation transition is presented.

Interaction driven realspace condensation ; We study realspace condensation in a broad class of stochastic mass transport models. We show that the steady state of such models has a pairfactorised form which generalizes the standard factorized steady states. The condensation in this class of models is driven by interactions which give rise to a spatially extended condensate that differs fundamentally from the previously studied examples. We present numerical results as well as a theoretical analysis of the condensation transition and show that the criterion for condensation is related to the bindingunbinding transition of solidonsolid interfaces.

Slave rotor theory of antiferromagnetic Hubbard model ; The slaverotor meanfield theory of Florens and Georges is generalized to the antiferromagnetic phase of the Hubbard model. An effective action consisting of a spin rotor and a fermion is derived and the corresponding saddlepoint action is analyzed. Zerotemperature phase diagram of the antiferromagnetic Hubbard model is presented. While the magnetic phase persists for all values of the Hubbard interaction U, the singleparticle spectral function exhibits a crossover into an incoherent phase when the magnetic moment m and the corresponding U values lies within a certain window mc m 1mc, indicating a possible deviation from the HartreeFock theory.

Domino tilings and the sixvertex model at its free fermion point ; At the freefermion point, the sixvertex model with domain wall boundary conditions DWBC can be related to the Aztec diamond, a domino tiling problem. We study the mapping on the level of complete statistics for general domains and boundary conditions. This is obtained by associating to both models a set of nonintersecting lines in the LindstroemGesselViennot LGV scheme. One of the consequence for DWBC is that the boundaries of the ordered phases are described by the Airy process in the thermodynamic limit.

The mcomponent spin glass on a Bethe lattice ; We study the mcomponent vector spin glass in the limit m to infinity on a Bethe lattice. The cavity method allows for a solution of the model in a selfconsistent field approximation and for a perturbative solution of the full problem near the phase transition. The low temperature phase of the model is analyzed numerically and a generalized BoseEinstein condensation is found, as in the fully connected model. Scaling relations between four distinct zerotemperature exponents are found.

Shear Zones in granular materials Optimization in a selforganized random potential ; We introduce a model to describe the wide shear zones observed in modified Couette cell experiments with granular material. The model is a generalization of the recently proposed approach based on a variational principle. The instantaneous shear band is identified with the surface that minimizes the dissipation in a random potential that is biased by the local velocity difference and pressure. The apparent shear zone is the ensemble average of the instantaneous shear bands. The numerical simulation of this model matches excellently with experiments and has measurable predictions.

Parallel dynamics of continuous Hopfield model revisited ; We have applied the generating functional analysis GFA to the continuous Hopfield model. We have also confirmed that the GFA predictions in some typical cases exhibit good consistency with computer simulation results. When a retarded selfinteraction term is omitted, the GFA result becomes identical to that obtained using the statistical neurodynamics as well as the case of the sequential binary Hopfield model.

Phase coexistence in the hardsphere Yukawa chain fluid with chain length polydispersity High temperature approximation ; High temperature approximation HTA is used to describe the phase behavior of polydisperse multiYukawa hardsphere chain fluid mixtures with chain length polydispersity. It is demonstrated that in the frames of the HTA the model belongs to the class of truncatable free energy models'', i.e. the models with thermodynamical properties Helmholtz free energy, chemical potential and pressure defined by the finite number of generalized moments. Using this property we were able to calculate the complete phase diagram i.e., cloud and shadow curves as well as binodals and chain length distribution functions of the coexisting phases.

Theory of the Quantum Critical Fluctuations in Cuprates ; The statistical mechanics of the timereversal and inversion symmetry breaking order parameter, possibly observed in the pseudogap region of the phase diagram of the Cuprates, can be represented by the AshkinTeller model. We add kinetic energy and dissipation to the model for a quantum generalization and show that the correlations are determined by two sets of charges, one interacting locally in time and logarithmically in space and the other locally in space and logarithmically in time. The quantum critical fluctuations are derived and shown to be of the form postulated in 1989 to give the marginal fermiliquid properties. The model solved and the methods devised are likely to be of interest also to other quantum phase transitions.

Density of states of a two dimensional XY model from WangLandau algorithm ; Using Wanglandau algorithm combined with analytic method, the density of states of two dimensional XY model on square lattices of sizes 16times16, 24times24 and 32times32 is accurately calculated. Thermodynamic quantities, such as internal energy, free energy, entropy and specific heat are obtained from the resulted density of states by numerical integration. From the entropy curve symptoms of phase transition is observed. A general method of calculation of the density of states of continuous models by simulation combined with analytical method is proposed.

A Derivation of the Classical EinsteinDiracMaxwell Equations From a Model of an Elastic Medium ; Starting from a model of an elastic medium, partial differential equations with the form of the coupled EinsteinDiracMaxwell equations are derived. The form of these equations describes particles with mass and spin coupled to electromagnetic and gravitational type of interactions. A two dimensional version of these equations is obtained by starting with a model in three dimensions and deriving equations for the dynamics of the lowest fourier modes assuming one dimension to be periodic. Generalizations to higher dimensions are discussed.

Exactly solvable reaction diffusion models on a Cayley tree ; The most general reactiondiffusion model on a Cayley tree with nearestneighbor interactions is introduced, which can be solved exactly through the emptyinterval method. The stationary solutions of such models, as well as their dynamics, are discussed. Concerning the dynamics, the spectrum of the evolution Hamiltonian is found and shown to be discrete, hence there is a finite relaxation time in the evolution of the system towards its stationary state.

Molecular model for de Vries type smectic A smectic C phase transition in liquid crystals ; We develop a theory of Smectic A Smectic C phase transition with anomalously weak smectic layer contraction. We construct a phenomenological description of this transition by generalizing the ChenLubensky model. Using a meanfield molecular model, we demonstrate that a relatively simple interaction potential suffices to describe the transition. The theoretical results are in excellent agreement with experimental data.

Field Induced Supersolid Phase in SpinOne Heisenberg Models ; We use quantum Monte Carlo methods to demonstrate that the quantum phase diagram of the S1 Heisenberg model with uniaxial anisotropy contains an extended supersolid phase. We also show that this Hamiltonian is a particular case of a more general and ubiquitous model that describes the low energy spectrum of a class of it isotropic and it frustrated spin systems. This crucial result provides the required guidance for finding experimental realizations of a spin supersolid state.

The nonlinear fragmentation equation ; We study the kinetics of nonlinear irreversible fragmentation. Here fragmentation is induced by interactionscollisions between pairs of particles, and modelled by general classes of interaction kernels, and for several types of breakage models. We construct initial value and scaling solutions of the fragmentation equations, and apply the nonvanishing mass flux criterion for the occurrence of shattering transitions. These properties enable us to determine the phase diagram for the occurrence of shattering states and of scaling states in the phase space of model parameters.

The combinatorics of resource sharing ; We discuss general models of resourcesharing computations, with emphasis on the combinatorial structures and concepts that underlie the various deadlock models that have been proposed, the design of algorithms and deadlockhandling policies, and concurrency issues. These structures are mostly graphtheoretic in nature, or partially ordered sets for the establishment of priorities among processes and acquisition orders on resources. We also discuss graphcoloring concepts as they relate to resource sharing.

The model of the tables in design documentation for operating with the electronic catalogs and for specifications making in a CAD system ; The hierarchic block model of the tables in design documentation as a part of a CAD system is described, intended for automatic specifications making of elements of the drawings, with usage of the electronic catalogs. The model is created for needs of a CAD system of reconstruction of the industrial plants, where the result of designing are the drawings, which include the specifications of different types. The adequate simulation of the specification tables is ensured with technology of storing in the drawing of the visible geometric elements and invisible parametric representation, sufficient for generation of this elements.

Using Users' Expectations to Adapt Business Intelligence Systems ; This paper takes a look at the general characteristics of business or economic intelligence system. The role of the user within this type of system is emphasized. We propose two models which we consider important in order to adapt this system to the user. The first model is based on the definition of decisional problem and the second on the four cognitive phases of human learning. We also describe the application domain we are using to test these models in this type of system.

The Interpretation of Quantum Cosmological Models ; We consider the problem of extracting physical predictions from the wave function of the universe in quantum cosmological models. We state the features of quantum cosmology an interpretational scheme should confront. We discuss the Everett interpretation, and extensions of it, and their application to quantum cosmology. We review the steps that are normally taken in the process of extracting predictions from solutions to the WheelerDeWitt equation for quantum cosmological models. Some difficulties and their possible resolution are discussed. We conclude that the usual wave functionbased approach admits at best a rather heuristic interpretation, although it may in the future be justified by appeal to the decoherent histories approach.

Poincare Gauge Theories for Lineal Garvity ; We have shown that two of the most studied models of lineal gravities Liouville gravity and a stringinspired'' model exhibiting the main characteristic features of a blackhole solution can be formulated as gauge invariant theories of the Poincar'e group. The gauge invariant couplings to matter particles, scalar and spinor fields and explicit solutions for some matter field configurations, are provided. It is shown that both the models, as well as the couplings to matter, can be obtained as suitable dimensional reductions of a 21dimensional ISO2,1 gauge invariant theory.

The Isaacson expansion in quantum cosmology ; This paper is an application of the ideas of the BornOppenheimer or slowfast approximation in molecular physics and of the Isaacson or shortwave approximation in classical gravity to the canonical quantization of a perturbed minisuperspace model of the kind examined by Halliwell and Hawking. Its aim is the clarification of the role of the semiclassical approximation and the backreaction in such a model. Approximate solutions of the quantum model are constructed which are not semiclassical, and semiclassical solutions in which the quantum perturbations are highly excited.

Classical and Quantum Behaviour of Multidimensional Integrable Cosmologies ; Multidimensional cosmological models with nn 1 Einstein spaces are discussed classically and with respect to canonical quantization. These models are integrable in the case of Ricci flat internal spaces. For negative curvature of the external space we find exact classical solutions modelling dynamical as well as spontaneous compactification of the internal spaces. Spontaneous compactification turns out to be an attractor solution. Solutions of the quantum WheelerDeWitt equation are also obtained. Some of them describe the tunneling process to be interpreted as the birth of the universe from ''nothing''.

Global Properties of Locally Spatially Homogeneous Cosmological Models with Matter ; The existence and nature of singularities in locally spatially homogeneous solutions of the Einstein equations coupled to various phenomenological matter models is investigated. It is shown that, under certain reasonable assumptions on the matter, there are no singularities in an expanding phase of the evolution and that unless the spacetime is empty a contracting phase always ends in a singularity where at least one scalar invariant of the curvature diverges uniformly. The class of matter models treated includes perfect fluids, mixtures of noninteracting perfect fluids and collisionless matter.

Multidimensional EinsteinYangMills cosmological models ; We study the process of the evolution of the space of extra dimensions in the framework of EinsteinYangMills cosmological models. It is shown that, for certain classes of models, the static compact space of extra dimensions is the attractor for a wide range of initial conditions. Also the effect of isotropization of extra dimensions in the course of evolution is demonstrated.

Quantization of a FriedmannRobertsonWalker model in N1 Supergravity with Gauged Supermatter ; The theory of N 1 supergravity with gauged supermatter is studied in the context of a k 1 Friedmann minisuperspace model. It is found by imposing the Lorentz and supersymmetry constraints that there are seveni no physical states in the particular SU2 model studied.

Divergences problem in black hole brickwall model ; In this work we review, in the framework of the socalled brick wall model, the divergence problem arising in the one loop calculations of various thermodynamical quantities, like entropy, internal energy and heat capacity. Particularly we find that, if one imposes that entanglement entropy is equal to the BekensteinHawking one, the model gives problematic results. Then a proposal of solution to the divergence problem is made following the zeroth law of black hole mechanics.

Quantum Potential Approach to Class of Cosmological Models ; In this paper we discuss the quantum potential approach of Bohm in the context of quantum cosmological model. This approach makes it possible to convert the wavefunction of the universe to a set of equations describing the time evolution of the universe. Following Ashtekar et. al., we make use of quantum canonical transformation to cast a class of quantum cosmological models to a simple form in which they can be solved explicitly, and then we use the solutions do recover the time evolution.

Pregeometric modelling of the spacetime phenomenology ; At present we have only the very successful but phenomenological Einstein geometrical modelling of the spacetime phenomenon. This geometrical model provides a container' for other theories, in particular the quantum field theories. Here we report progress in developing a em Heraclitean Quantum System. This is a particular pregeometric theory for space and time in which no classical or geometric structures are assumed, but rather the emergence of such phenomena is sought.

Spacetime model with superluminal phenomena ; recent theoretical results show the existence of arbitrary speeds 0leq v infty solutions of the wave equations of mathematical physics. Some recent experiments confirm the results for sound waves. The question arises naturally What is the appropriate spacetime model to describe superluminal phenomena In this paper we present a spacetime model that incorporates the valid results of Relativity Theory and yet describes coherently superluminal phenomena without paradoxes.

Black Hole Criticality in the BransDicke Model ; We study the collapse of a free scalar field in the BransDicke model of gravity. At the critical point of black hole formation, the model admits two distinctive solutions dependent on the value of the coupling parameter. We find one solution to be discretely selfsimilar and the other to exhibit continuous selfsimilarity.

Propagating torsion from first principles ; A propagating torsion model is derived from the requirement of compatibility between minimal action principle and minimal coupling procedure in RiemannCartan spacetimes. In the proposed model, the trace of the torsion tensor is derived from a scalar potential that determines the volume element of the spacetime. The equations of the model are written down for the vacuum and for various types of matter fields. Some of their properties are discussed. In particular, we show that gauge fields can interact minimally with the torsion without the breaking of gauge symmetry.

Multidimensional Quantum Cosmology Quantum Wormholes, Third Quantization, Inflation from Nothing, etc ; A multidimensional cosmological model with spacetime consisting of n n1 Einstein spaces Mi is investigated in the presence of a cosmological constant Lambda and m homogeneous minimally coupled scalar fields as a matter source. Classes of the models integrable at classical as well as quantum levels are found. These classes are equivalent to each other. Quantum wormhole solutions are obtained for them and the procedure of the third quantization is performed. An inflationary universe arising from classically forbidden Euclidean region is investigated for a model with a cosmological constant.

Stationary Bianchi type II perfect fluid models ; Einstein's field equations for stationary Bianchi type II models with a perfect fluid source are investigated. The field equations are rewritten as a system of autonomous first order differential equations. Dimensionless variables are subsequently introduced for which the reduced phase space is compact. The system is then studied qualitatively using the theory of dynamical systems. It is shown that the locally rotationally symmetric models are not asymptotically selfsimilar for small values of the independent , tovariable. A new exact solution is also given.

Physically valid blackhole interior models ; New, simple models of black hole interiors'', namely spherically symmetric solutions of the Einstein field equations in matter matching the Schwarzschild vacuum at spacelike hypersurfaces R2M'' are constructed. The models satisfy the weak energy condition and their matter content is specified by an equation of state of the elastic type.

Oscillating shells A model for a variable cosmic object ; A model for a possible variable cosmic object is presented. The model consists of a massive shell surrounding a compact object. The gravitational and selfgravitational forces tend to collapse the shell, but the internal tangential stresses oppose the collapse. The combined action of the two types of forces is studied and several cases are presented. In particular, we investigate the spherically symmetric case in which the shell oscillates radially around a central compact object.

Origin of Structure in a Supersymmetric Quantum Universe ; In this report we advance the current repertoire of quantum cosmological models to incorporate inhomogenous field modes in a supersymmetric manner. In particular, we introduce perturbations about a supersymmetric FRW model. A quantum state of our model has properties typical of the noboundary HartleHawking proposal. This solution may then lead to a scalefree spectrum of density perturbations.

Sigma Model on de Sitter Space ; We discuss spherically symmetric, static solutions to the SU2 sigma model on a de Sitter background. Despite of its simplicity this model reflects many of the features exhibited by systems of nonlinear matter coupled to gravity e.g. there exists a countable set of regular solutions with finite energy; all of the solutions show linear instability with the number of unstable modes increasing with energy.

Perturbative Analysis of Bianchi IX using Ashtekar Formalism ; The goal of this paper is to provide a new analysis of the classical dynamics of Bianchi type I, II and IX models by applying conventional Hamiltonian methods in the language of Ashtekhar variables. We show that Bianchi type II models can be seen as a perturbation of Bianchi I ones, and integrated. Bianchi IX models can be seen, in turn, as a perturbation of Bianchi IIs, but here the integration algorithm breaks down. This is an ''interesting failure'', bringing light onto the chaotic nature of Bianchi type IX dynamics.As a by product of our analysis we filled some gaps in the literature, such us recovering the BKL map in this context.

Chaotic exit to inflation the dynamics of preinflationary universes ; We show that anisotropic Bianchi typeIX models, with matter and cosmological constant have chaotic dynamics, connected to the presence of a saddlecenter in phase space. The topology of cylinders emanating from unstable periodic orbits about the saddlecenter provides an invariant characterization of chaos in the models. The model can be thought to describe the early stages of inflation, the way out to inflation being chaotic.

Dynamical Instability of a twodimensional Quantum Black Hole ; We investigate dynamical instability of a twodimensional quantum black hole model considered by Lowe in his study of Hawking evaporation. The model is supposed to express a black hole in equilibrium with a bath of Hawking radiation. It turns out that the model has at least one instability modes for a wide range of parameters, and thus it is unstable.

Simplest cosmological model with the scalar field II. Influence of cosmological constant ; Continuing the investigation of the simplest cosmological model with the massive real scalar noninteracting inflaton field minimally coupled to gravity we study an influence of the cosmological constant on the behaviour of trajectories in closed minisuperspace FriedmannRobertsonWalker model. The transition from chaotic to regular behaviour for large values of cosmological constant is discussed. Combining numerical calculations with qualitative analysis both in configuration and phase space we present a convenient classification of trajectories.

Caustics of Compensated Spherical Lens Models ; We consider compensated spherical lens models and the caustic surfaces they create in the past light cone. Examination of cusp and crossover angles associated with particular source and lens redshifts gives explicit lensing models that confirm previous claims that area distances can differ by substantial factors from angular diameter distances even when averaged over large angular scales. Shrinking' in apparent sizes occurs, typically by a factor of 3 for a single spherical lens, on the scale of the cusp caused by the lens; summing over many lenses will still leave a residual effect.

Gravitating Model Solitons ; We study axially symmetric static solitons of O3 nonlinear sigma model coupled to 21dimensional antide Sitter gravity. The obtained solutions are not selfdual under static metric. The usual regular topological lump solution cannot form a black hole even though the scale of symmetry breaking is increased. There exist nontopological solitons of half integral winding in a given model, and the corresponding spacetimes involve charged Batilde nadosTeitelboimZanelli black holes without nonAbelian scalar hair.

From classical chaos to decoherence in RobertsonWalker cosmology ; We analyse the relationship between classical chaos and particle creation in RobertsonWalker cosmological models with gravity coupled to a scalar field. Within our class of models chaos and particle production are seen to arise in the same cases. Particle production is viewed as the seed of decoherence, which both enables the quantum to classical transition, and ensures that the correspondence between the quantum and classically chaotic models will be valid

Multidimensional Geometrical Model of the Renormalized Electrical Charge with Splitting off the Extra Coordinates ; A geometrical model of electric charge is proposed. This model has naked'' charge screened with a fur coat'' consisting of virtual wormholes. The 5D wormhole solution in the Kaluza Klein theory is the naked'' charge. The splitting off of the 5D dimension happens on the two spheres null surfaces bounding this 5D wormhole. This allows one to sew two Reissner Nordstrom black holes onto it on both sides. The virtual wormholes entrap a part of the electrical flux lines coming into the naked'' charge. This effect essentially changes the charge visible at infinity so that it satisfies the real relation m2e2.

Distanceredshift relation in an isotropic inhomogeneous universe Spherically symmertic dustshell universe ; The relation between angular diameter distance and redshift in a spherically symmetric dustshell universe is studied. This model has large inhomogeneities of matter distribution on small scales. We have discovered that the relation agrees with that of an appropriate FriedmannLemaitreFL model if we set a homogeneous'' expansion law and a homogeneous'' averaged density field. This will support the averaging hypothesis that a universe looks like a FL model in spite of smallscale fluctuations of density field, if its averaged density field is homogeneous on large scales.

Effective chiral model of a planesymmetric gravitational field properties and exact solutions ; An effective chiral model of a planesymmetric gravitational field is considered. Isometries of the target space of the model are described and exact solutions corresponding to the isometric ansatz method are obtained. New exact solutions are found using the method of functional parameters. The solutions obtained are Backlund transforms of solutions of the d'Alembert equation to those of the Einstein equations.

The Friedmannian model of our observed Universe ; According to observations, in our Universe for gravitational phenomena in a Newtonian approximation the Newtonian nonmodified relations are valid. The Friedmann equations of universe dynamics describe infinite number of relativistic universe models in Newtonian approximation, but only in one of them the Newtonian nonmodified relations are valid. From these facts it results that the Universe is described just by this only Friedmannian universe model with Newtonian nonmodified relations.

Homogeneous cosmologies with cosmological constant ; Spatially homogeneous cosmological models with a positive cosmological constant are investigated, using dynamical systems methods. We focus on the future evolution of these models. In particular, we address the question whether there are models within this class that are de Sitterlike in the future, but are tilted.

Cosmological model in 5D, stationarity, yes or no ; We consider cosmological model in 41 dimensions with variable scale factor in extra dimension and static external space. The time scale factor is changing. Variations of light velocity, gravity constant, mass and pressure are determined with fourdimensional projection of this spacetime. Data obtained by space probes Pioneer 1011 and Ulysses are analyzed within the framework of this model.

Scalefactor duality in string Bianchi cosmologies ; We apply the scale factor duality transformations introduced in the context of the effective string theory to the anisotropic Bianchitype models. We find dual models for all the Bianchitypes except for types VIII and IX and construct for each of them its explicit form starting from the exact original solution of the field equations. It is emphasized that the dual Bianchi class B models require the loss of the initial homogeneity symmetry of the dilatonic scalar field.

Inflationary cosmology with scalar field and radiation ; We present a simple, exact and selfconsistent cosmology with a phenomenological model of quantum creation of radiation due to decay of the scalar field. The decay drives a nonisentropic inflationary epoch, which exits smoothly to the radiation era, without reheating. The initial vacuum for radiation is a regular Minkowski vacuum. The created radiation obeys standard thermodynamic laws, and the total entropy produced is consistent with the accepted value. We analyze the difference between the present model and a model with decaying cosmological constant previously considered.

Starobinsky Model in Schroedinger Description ; In the Starobinsky inflationary model inflation is driven by quantum corrections to the vacuum Einstein equation. We reduce the WheelerDeWitt equation corresponding to the Starobinsky model to a Schroedinger form containing time. The Schroedinger equation is solved with a Gaussian ansatz. Using the prescription for the normalization constant of the wavefunction given in our previous work, we show that the Gaussian ansatz demands Hawking type initial conditions for the wavefunction of the universe. The wormholes induce randomness in initial states suggesting a basis for timecontained description of the WheelerDeWitt equation.

Cosmological models with variable constants ; The behavior of the constants, G,c,h,a,e,m and Lambda, considering them as variable, in the framework of a flat cosmological model with FRW symmetries described by a bulk viscous fluid and considering mechanisms of adiabatic matter creation are investigated. Within two models; one with radiation predominance and another of matter predominance, this behavior are studied.

On The Vaidya Limit of the Tolman Model ; We show that the only Tolman models which permit a Vaidya limit are those having a dust distribution that is hollow such as the selfsimilar case. Thus the naked shellfocussing singularities found in Tolman models that are dense through the origin have no Vaidya equivalent. This also casts light on the nature of the Vaidya metric. We point out a hidden assumption in Lemos' demonstration that the Vaidya metric is a null limit of the Tolman metric, and in generalising his result, we find that a different transformation of coordinates is required.

Painleve III Equation and Bianchi VII0 Model ; We examine the reduced phase space of the Bianchi VII0 cosmological model, including the moduli sector. We show that the dynamics of the relevant sector of local degrees of freedom is given by a Painleve III equation. We then obtain a zerocurvature representation of this Painleve III equation by applying the BelinskiiZakharov method to the Bianchi VII0 model.

A NonClassical Linear Xenomorph as a Model for Quantum Causal Space ; A quantum picture of the causal structure of Minkowski space M is presented. The mathematical model employed to this end is a nonclassical version of the classical topos H of real quaternion algebras used elsewhere to organize the perceptions of spacetime events of a Boolean observer into M. Certain key properties of this new quantum topos are highlighted by contrast against the corresponding ones of its classical counterpart H modelling M and are seen to accord with some key features of the algebraically quantized causal set structure.

Loop Quantum Cosmology II Volume Operators ; Volume operators measuring the total volume of space in a loop quantum theory of cosmological models are constructed. In the case of models with rotational symmetry an investigation of the Higgs constraint imposed on the reduced connection variables is necessary, a complete solution of which is given for isotropic models; in this case the volume spectrum can be calculated explicitly. It is observed that the stronger the symmetry conditions are the smaller is the volume spectrum, which can be interpreted as level splitting due to broken symmetries. Some implications for quantum cosmology are presented.

Anisotropic universes with isotropic cosmic microwave background radiation ; We show the existence of spatially homogeneous but anisotropic cosmological models whose cosmic microwave background temperature is exactly isotropic at one instant of time but whose rate of expansion is highly anisotropic. The existence of these models shows that the observation of a highly isotropic cosmic microwave background temperature cannot alone be used to infer that the universe is close to a FriedmannLemaitre model.

Integrable models, degenerate horizons and AdS2 black holes ; The near extremal ReissnerNordstrom black holes in arbitrary dimensions ca be modeled by the JackiwTeitelboim JT theory. The asymptotic Virasoro symmetry of the corresponding JT model exactly reproduces, via Cardy's formula, the deviation of the BekensteinHawking entropy of the ReissnerNordstrom black holes from extremality. We also comment how can we extend this approach to investigate the evaporation process.

Path integral in the simplest Regge calculus model ; The simplest 31D Regge calculus model with threedimensional discrete space and continuous time is considered which describes evolution of the simplest closed twotetrahedron piecewise flat manifold in the continuous time. The measure in the path integral which describes canonical quantisation of the model in terms of area bivectors and connections as independent variables is found. It is shown that selfdualantiselfdual splitting of the variables simplifies the integral although does not admit complete separation of antiselfdual sector.

Divergence of the Quantum Stress Tensor on the Cauchy Horizon in 2d Dust Collapse ; We prove that the quantum stress tensor for a massless scalar field in two dimensional nonselfsimilar Tolman Bondi dust collapse and Vaidya radiation collapse models diverges on the Cauchy horizon, if the latter exists. The two dimensional model is obtained by suppressing angular coordinates in the corresponding four dimensional spherical model.

Localization of gravitational energy in ENU model and its consequences ; The contribution provides the starting points and background of the model of Expansive Nondecelerative Universe ENU, manifests the advantage of exploitation of Vaidya metrics for the localization and quantization of gravitational energy, and offers four examples of application of the ENU model, namely energy of cosmic background radiation, energy of Z and W bosons acting in weak interactions, hyperfine splitting observed for hydrogen 1s orbital. Moreover, time evolution of vacuum permitivity and permeability is predicted.

Isotropization of twocomponent fluids ; We consider the problem of latetime isotropization in spatially homogeneous but anisotropic cosmological models when the source of the gravitational field consists of two noninteracting perfect fluids one tilted and one nontilted. In particular, we study irrotational Bianchi type V models. By introducing appropriate dimensionless variables, a full global understanding of the state space of the gravitational field equations becomes possible. The issue of isotropization can then be addressed in a simple fashion. We also discuss implications for the cosmic nohair'' theorem for Bianchi models when part of the source is a tilted fluid.

Dynamics of spatially homogeneous locally rotationally symmetric solutions of the EinsteinVlasov equations ; The dynamics of the EinsteinVlasov equations for a class of cosmological models with four Killing vectors is discussed in the case of massive particles. It is shown that in all models analysed the solutions with massive particles are asymptotic to solutions with massless particles at early times. It is also shown that in Bianchi types I and II the solutions with massive particles are asymptotic to dust solutions at late times. That Bianchi type III models are also asymptotic to dust solutions at late times is consistent with our results but is not established by them.

Wormholes and Spacetime Foam an approach to the Cosmological Constant and Entropy ; This paper summarizes the contribution presented at the IX Marcel Grossmann Meeting Rome, July 2000. A simple model of spacetime foam, made by N Schwarzschild wormholes in a semiclassical approximation, is here proposed. The Casimirlike energy of the quantum fluctuation of such a model and its probability of being realized are computed. Implications on the BekensteinHawking entropy and the cosmological constant are considered. A proposal for an alternative foamy model formed by N SchwarzschildAntide Sitter wormholes is here considered.

Discrete structures in gravity ; Discrete approaches to gravity, both classical and quantum, are reviewed briefly, with emphasis on the method using piecewiselinear spaces. Models of 3dimensional quantum gravity involving 6jsymbols are then described, and progress in generalising these models to four dimensions is discussed, as is the relationship of these models in both three and four dimensions to topological theories. Finally, the repercussions of the generalisations are explored for the original formulation of discrete gravity using edgelength variables.

Integrability and explicit solutions in some Bianchi cosmological dynamical systems ; The Einstein field equations for several cosmological models reduce to polynomial systems of ordinary differential equations. In this paper we shall concentrate our attention to the spatially homogeneous diagonal G2 cosmologies. By using Darboux's theory in order to study ordinary differential equations in the complex projective plane CP2 we solve the Bianchi V models totally. Moreover, we carry out a study of Bianchi VI models and first integrals are given in particular cases.

Nonrelativistic field theoretic setting for gravitational selfinteractions ; It is shown that a recently proposed model for the gravitational interaction in non relativistic quantum mechanics is the instantaneous action at a distance limit of a field theoretic model containing a negative energy field. It reduces to the SchroedingerNewton theory in a suitable mean field approximation. While both the exact model and its approximation lead to estimates for localization lengths, only the former gives rise to an explicit non unitary dynamics accounting for the emergence of the classical behavior of macroscopic bodies.

On Ellis' programme within fourth order gravity ; For the nontachyonic curvature squared action we show that the expanding Bianchitype I models tend to the dustfilled Einsteinde Sitter model for t tending to infinity if the metric is averaged over the typical oscillation period. Applying a conformal equivalence between curvature squared action and a minimally coupled scalar field which holds for all dimensions 2 the problem is solved by discussing a massive scalar field in an anisotropic cosmological model.

Brane World, Mass Hierarchy and the Cosmological Constant ; The brane world based on the 6D gravitational model is examined. It is regarded as a higher dimensional version of the 5D model by Randall and Sundrum . The obtained analytic solution is checked by the numerical method. The mass hierarchy is examined. Especially the it geometrical seesaw mass relation, between the Planck mass, the cosmological constant, and the neutrino mass, is suggested. Comparison with the 5D model is made.

Boundary terms in the BarrettCrane spin foam model and consistent gluing ; We extend the lattice gauge theorytype derivation of the BarrettCrane spin foam model for quantum gravity to other choices of boundary conditions, resulting in different boundary terms, and reanalyze the gluing of 4simplices in this context. This provides a consistency check of the previous derivation. Moreover we study and discuss some possible alternatives and variations that can be made to it and the resulting models.

Multidimensional Black Hole Solutions In Model With Perfect Fluid ; A family of blackhole solutions in the model with 1component perfect fluid is obtained. The metric of any solution contains n 1 Ricciflat internal space metrics and for certain equations of state coincides with the metric of black brane or black hole solution in the model with antisymmetric form. Certain examples e.g. imitating M2 and M5 black branes are considered. The postNewtonian parameters beta and gamma corresponding to the 4dimensional section of the metric are calculated.

Nonlinear Spinor Field in Anisotropic Universes ; Evolution of an anisotropic universe described by a Bianchi type I BI model in presence of nonlinear spinor field has been studied by us recently in a series of papers. On offer the Bianchi models, those are both inhomogeneous and anisotropic. Within the scope of Bianchi type VI BVI model the selfconsistent system of nonlinear spinor and gravitational fields are considered. The role of inhomogeneity in the evolution of spinor and gravitational field is studied.

Isotropic cosmological singularities other matter models ; Isotropic cosmological singularities are singularities which can be removed by rescaling the metric. In some cases already studied grqc9903008, grqc9903009, grqc9903018 existence and uniqueness of cosmological models with data at the singularity has been established. These were cosmologies with, as source, either perfect fluids with linear equations of state or massless, collisionless particles. In this article we consider how to extend these results to a variety of other matter models. These are scalar fields, massive collisionless matter, the YangMills plasma of ChoquetBruhat, or matter satisfying the EinsteinBoltzmann equation.

Spin Foam Models of YangMills Theory Coupled to Gravity ; We construct a spin foam model of YangMills theory coupled to gravity by using a discretized path integral of the BF theory with polynomial interactions and the BarretCrane ansatz. In the Euclidian gravity case we obtain a vertex amplitude which is determined by a vertex operator acting on a simple spin network function. The Euclidian gravity results can be straightforwardly extended to the Lorentzian case, so that we propose a Lorentzian spin foam model of YangMills theory coupled to gravity.

PlaneSymmetric Inhomogeneous Bulk Viscous Cosmological Models with Variable ; A planesymmetric nonstatic cosmological model representing a bulk viscous fluid distribution has been obtained which is inhomogeneous and anisotropic and a particular case of which is gravitationally radiative. Without assuming any it adhoc law, we obtain a cosmological constant as a decreasing function of time. The physical and geometric features of the models are also discussed.

Radiating fluid spheres in the effective variables approximation ; We study the evolution of spherically symmetric radiating fluid distributions using the effective variables method, implemented it ab initio in Schwarzschild coordinates. To illustrate the procedure and to establish some comparison with the original method, we integrate numerically the set of equations at the surface for two different models. The first model is derived from the Schwarzschild interior solution. The second model is inspired in the Tolman VI solution.