122714395
Passive-Scalar Fluctuations in Intermittent Turbulence
We discuss how the spatial intermittency of energy dissipation in 3D fully developed turbulence affects the small-scale statistics of passive scalars. We relate the passive-scalar behaviour to the diffusion properties of particle pairs in turbulent fluids. We thus find the intermittency correction to the -5/3 Obukhov-Corrsin law for the power spectrum of a passive scalar at wavenumber k where molecular diffusion and viscosity play a negligible role (inertial convective subrange). This correction is positive at difference with the negative correction to the -5/3 Kolmogorov law for the energy spectrum. We finally show that the structure functions of passive scalars have scaling exponents linear in the moment order, even in the framework of multifractal models.
15060511
Transition from regular to complex behaviour in a discrete deterministic asymmetric neural network model
The authors study the long-time behaviour of the transient before the collapse on the periodic attractors of a discrete deterministic asymmetric neural network model. The system has a finite number of possible states so it is not possible to use the term chaos in the usual sense of sensitive dependence on the initial condition. Nevertheless, on varying the asymmetry parameter, k, one observes a transition from ordered motion (i.e. short transients and short periods on the attractors) to 'complex' temporal behaviour. This transition takes place for the same value kc at which one has a change in behaviour for the mean transient length from a power law in the size of the system (N) to an exponential law in N. The 'complex' behaviour during the transient shows strong analogies with chaotic behaviour: decay of temporal correlations, positive Shannon entropy, nonconstant Renyi entropies of different orders. Moreover the transition is very similar to the intermittent transition in chaotic systems: a scaling law for the Shannon entropy and strong fluctuations of the 'effective Shannon entropy' along the transient, for k>kc.
121504553
On the masses of the glueballs in pure SU(2) lattice gauge theory
Abstract Using a Monte Carlo method to measure the correlation functions of different quantities, the mass spectrum of the glue-ball is investigated for an SU(2) gauge model in an 8 4 lattice.
123085141
Intermittency and Multifractality in Magnetic Dynamos
We study the convection of magnetic fields in the presence of Lagrangian chaos, i.e. when nearby fluid elements diverge exponentially in time. We show that the magnetic field is of a multifractal nature as a consequence of the spatial fluctuations in the exponential growth of the field. We provide numerical and theoretical evidence that the magnetic fields can concentrate in small domains of a fluid with weak Lagrangian chaos. Moreover, these properties are relevant also for the study of the case of small but nonzero magnetic diffusivity.
120014368
A new proposal for the determination of the renormalization group trajectories by the Monte Carlo renormalization group method
Abstract We present a new method for calculating block renormalized couplings by Monte Carlo renormalization group. This method has several advantages with respect to the existing ones and can be applied for any value of the coupling constants. A preliminary numerical study of the 2-dimensional O(3) non linear σ-model is also presented.
123419934
Complex singularities in the specific heat of the SU(2) lattice gauge model
Abstract A recent Monte Carlo simulation showing a sharp peak versus β in the specific heat for an SU(2) lattice gauge theory is compared with the high temperature expansion. An interpretation based on complex β -plane singularities is proposed.
9011435
Critical slowing down of cluster algorithms for Ising models coupled to 2-d gravity
Abstract We simulate single and multiple Ising models coupled to 2-d gravity using both the Swendsen-Wang and Wolff algorithms to update the spins. We study the integrated autocorrelation time and find that there is considerable critical slowing down, particularly in the magnetization. We argue that this is primarily due to the local nature of the dynamical triangulation algorithm and to the generation of a distribution of baby universes which inhibits cluster growth.
12041139
The flat phase of fixed-connectivity membranes
Abstract The statistical mechanics of flexible two-dimensional surfaces (membranes) appears in a wide variety of physical settings. In this talk we discuss the simplest case of fixed-connectivity surfaces. We first review the current theoretical understanding of the remarkable flat phase of such membranes. We then summarize the results of a recent large scale Monte Carlo simulation of the simplest conceivable discrete realization of this system [1]. We verify the existence of long-range order, determine the associated critical exponents of the flat phase and compare the results to the predictions of various theoretical models.
119499105
Anisotropic Membranes
We describe the statistical behavior of anisotropic crystalline membranes. In particular we give the phase diagram and critical exponents for phantom membranes and discuss the generalization to self-avoiding membranes.