Random Initial State Research Articles

Hadron spectra from nuclear collisions

We describe high energy nuclear collisions by a superposition of isotropically decaying thermal sources (“fireballs”) of freeze-out temperature T = 0.15 GeV. The longitudinal fireball superposition is taken as boost-invariant, in a rapidity range determined by the average energy loss of nucleons in p - p collisions. The transverse fireball motion is assumed to be due to random walk initial state collisions; it is determined by p - A data and then extrapolated to central A - B interactions. We thus obtain parameter-free predictions for the rapidity and transverse momentum spectra of hadrons produced in high energy nucleus-nucleus collisions. The results account fully for the observed broadening of transverse momentum distributions, so that single-particle spectra require neither collective flow nor temperature increase.

Diffusion–annihilation dynamics in one spatial dimension

We discuss a reaction–diffusion model in one dimension subjected to an external driving force. Each lattice site may be occupied by at most one particle. The particles hop with rates (1±η)/2 to the right or left nearest neighbor site if it is vacant, and annihilate with rate one if it is occupied. The representation of an uncorrelated random initial state in terms of free fermions allows the calculation of multiple time-dependent higher order correlation functions of the local density. We outline the procedure using a field theoretic approach. We also compute the long time behavior of the density profile if the initial density profile is a step function. The fermion representation of the step function state also allows the calculation of multiple time-dependent correlation functions. Experimental applications of these results are pointed out.

Initial and transient response improvement for singular systems

This paper deals with a generalized LQ regulator problem for singular systems with random initial states. The idea of the generalization is to take care of instantaneous jumps, and the problem is solved using the gradient flow approach. The designed output feedback will ensure that the closed-loop system has not only a satisfactory transient response but also significantly low instantaneous jumps with respect to any random initial state with given expectation and covariance.

Nonequilibrium correlation functions in the A+A-->0 system with driven diffusion.

We solve the one-dimensional stochastic reaction-diffusion system A+A\ensuremath{\rightarrow}0/ with driven diffusional relaxation and hard-core particles. Fluctuations in the total density (i.e., the mth moments 〈${\mathit{N}}^{\mathit{m}}$〉 of the density distribution at any time t\ensuremath{\ge}0) do not depend on the driving field, irrespective of the initial condition. For random initial conditions even local density fluctuations do not depend on the driving. A local perturbation in a random initial state evolves diffusively with a superimposed algebraic decay in time. The effect of the driving can be absorbed in a Galilei transformation. \textcopyright{} 1996 The American Physical Society.

Simulation of the quasi-static mechanics and scalar transport properties of ideal granular assemblages

The current article reports on the further development of a new technique for the computer simulation of the quasi-static mechanics and scalar transport properties of sphere assemblages. In an extension of a previous 2D simulation to 3D, we have developed an improved computation based on several innovations: a shuffling algorithm to rapidly generate random loose-packed configurations of particles; a microcell-adjacency method to accelerate particle-contact search; a relaxation method to overcome singularities in the static transport equations; and a simulated mechanical compression to generate dense random initial states. The improved algorithm allows for 3D simulations on a workstation platform. As major results, the dilatancy (volume expansion) computed for random dense-packed assemblages is found to depend on interparticle friction, contrary to the classical Reynolds hypothesis. Also, the use of linear-elastic contacts is found to be valid near the rigid-particle limit of interest here. Experimental data from (''triaxial'' compression) tests agree well with the simulations of both the shear strength and the electrical conductivity of sphere assemblages, when proper account is taken of the actual electrical contact resistance between steel balls as a function of load. One major conclusion is that scalar transport can serve as a useful macroscopic probe of particle-contact topology in granular media.

"Fuzzy" tight-binding Monte Carlo method: A O(N) technique for calculating structural and electronic properties of materials.

We present a novel approach to computer simulations of the structural and electronic properties of materials that scales linearly with the number of electrons in the system. The approach is based on the following: (i) The introduction of a ``fuzzy'' Monte Carlo technique based on the approximate calculation of the total energy of the system. We show that a statistical error in the energy may be included in the thermal distribution via a new formulation of the Glauber dynamics of the Monte Carlo method. (ii) The calculation of the total energy via a recursion technique for a set of random initial states and a decomposition into individual atomic contributions. Applications to the simulation of liquid iron, silicon, and carbon are presented.

Dynamical scaling and decay of correlations for spinodal decomposition at Tc.

We have investigated the nonequilibrium critical dynamics of a two-dimensional, spin-exchange (i.e., conserved magnetization), kinetic Ising model following quenches to ${\mathit{T}}_{\mathit{c}}$ from random initial states. As in the case of subcritical quenches, we observe dynamical scaling of the equal time order parameter correlation function G(r,t,t), but here the nonequilibrium correlation length grows as L(t)\ensuremath{\sim}${\mathit{t}}^{1/\mathit{z}}$, where z=4/15 is the usual dynamic critical exponent for this system. Moreover, we find dynamical scaling for correlations with the initial condition G(r,0,t). The temporal decay of autocorrelations at ${\mathit{T}}_{\mathit{c}}$ yields a critical exponent ${\ensuremath{\lambda}}_{\mathit{c}}$=1.96\ifmmode\pm\else\textpm\fi{}0.05 for the nonequilibrium dynamics: G(r,0,t)\ensuremath{\approxeq}${\mathit{L}}_{\mathit{c}}^{\mathrm{\ensuremath{-}}\ensuremath{\lambda}}$(t)G\ifmmode \tilde{}\else \~{}\fi{}(r/L(t)).

A computer simulation of the microstructure of a particulate dispersion

A computational simulation of a dispersion of iron particles undertaken to study the influence of the magnetostatic interactions on the microstructure of a particle ensemble is reported herein. The simulation considers an equilibrium state derived from an initial random state by the force-bias Monte Carlo technique. This method favors particle moves in the direction of the magnetostatic forces. A three dimensional ensemble in zero field and a saturating field are studied. An approach which takes into account the magnetostatic interactions between clusters by allowing Monte Carlo moves of whole clusters has been developed. This approach leads to the formation of extended networks consisting of particles in strongly bound clusters which themselves interact and give rise to an extended network. This is similar to the long-range order observed in practical dispersions. The structure analysis is found to characterize the local order, being especially sensitive to anisotropy in the order produced by an aligning field.

On the initialization and optimization of multilayer perceptrons

Multilayer perceptrons are now widely used for pattern recognition, although the training remains a time consuming procedure often converging toward a local optimum. Moreover, as the optimum network size and topology are usually unknown, the search of this optimum requires a lot of networks to be trained. In this paper the authors propose a method for properly initializing the parameters (weights) of a two-layer perceptron, and for identifying (without the need for any error-backpropagation training) the most suitable network size and topology for solving the problem under investigation. The initialized network can then be optimized by means of the standard error-backpropagation (EBP) algorithm. The authors' method is applicable to any two-layer perceptron comprising concentric as well as squashing units on its hidden layer. The output units are restricted to squashing units, but direct connections from the input to the output layer are also accommodated. To illustrate the power of the method, results obtained for different classification tasks are compared to similar results obtained using a traditional error-backpropagation training starting from a random initial state.

Estimation of in situ hydraulic conductivity function from nonlinear filtering theory

A method based on an optimal nonlinear filtering technique is proposed and tested for the determination of the hydraulic conductivity function from a field drainage experiment. Simplifications to Richards's equation lead to a Langevin type differential equation to describe the redistribution of stored water as a function of drainage flux excited by a random initial condition and state forcing. The derived equation is then utilized in an optimal estimation scheme that explicitly accounts for the formulation and observation uncertainty in determining the hydraulic conductivity parameters. A field drainage experiment was carried out to study the usefulness of the proposed method for routine in situ hydraulic conductivity function estimation.

Asymptotic Behavior of Excitable Cellular Automata

We study two families of excitable cellular automata known as the Greenberg-Hastings model and the cyclic cellular automaton. Each family consists of focal deterministic oscillating lattice dynamics, with parallel discrete-time updating, parametrized by the range ρ of interaction, l p shape of its neighbor set, threshold θ for contact updating, and number K. of possible states per site. These models are mathematically tractable prototypes for the spatially distributed periodic wave activity of so-called excitable media observed in diverse disciplines of experimental science. Fisch, Gravner and Griffeath [Fisch et al. 1991] studied experimentally the ergodic behavior of these models on Z 2, started from random initial states. Among other phenomena, they noted the emergence of asymptotic phase diagrams (and dynamics on R 2) in the threshold-range scaling limit as ρ, θ → ∊ with θ/ρ2 constant. Mere we present several rigorous results and some experimental findings concerning various phase transitions in the asymptotic diagrams. Our efforts focus on evaluating bend(p), the limiting threshold cutoff for existence of the spirals that characterize many excitable media. Our main results are formulated in terms of spo(p), the cutoff for existence of stable periodic objects that arise asspiral cores. Somesubtle consequences of anisotropic neighbor sets (p ≠ 2) are also discussed; the case of box neighborhoods (p = ∊) is examined in detail.

Remarks on the rule classification of symmetric two-dimensional homogeneous cellular automata

Results generated in time by the dynamic of some homogeneous cellular automata from random initial states are presented. Geometrical connections between a rule and a final pattern are analyzed. A necessary condition for a stabilization of two macroscopic functions: Contents and Activity, is formulated also.

Associative memory in an analog iterated-map neural network.

The behavior of an analog neural network with parallel dynamics is studied analytically and numerically for two associative-memory learning algorithms, the Hebb rule and the pseudoinverse rule. Phase diagrams in the parameter space of analog gain \ensuremath{\beta} and storage ratio \ensuremath{\alpha} are presented. For both learning rules, the networks have large ``recall'' phases in which retrieval states exist and convergence to a fixed point is guaranteed by a global stability criterion. We also demonstrate numerically that using a reduced analog gain increases the probability of recall starting from a random initial state. This phenomenon is comparable to thermal annealing used to escape local minima but has the advantage of being deterministic, and therefore easily implemented in electronic hardware. Similarities and differences between analog neural networks and networks with two-state neurons at finite temperature are also discussed.

A study of network dynamics

The dynamics of a discrete-time neural network model are investigated. First, a numerical survey of network power spectra is reported for networks of varying size with random weight matrices and initial states. The steepness of the logistic function and a symmetry measure of the weight matrix are taken as control parameters. Summary statistics are presented to give gross measures of the model's temporal activity in parameter space. Second, a detailed study of the dynamics of a particular network is described. Complex dynamical behavior is observed, including Hopf bifurcations, the Ruelle-Takens-Newhouse route to chaos (showing mode-locking at rational winding numbers and the destruction of an invariant torus), and the period-doubling route to chaos.

A cellular automaton describing the formation of spatially ordered structures in chemical systems

A cellular automaton describing a certain heterogeneous catalytic reaction is introduced as a theoretical approach towards the investigation of pattern formation in chemical systems. The numerically obtained results demonstrate that the time evolution of this cellular automaton leads to a self-sustained organization of circular and spiral wave-like structures, even starting from random initial states.

An exact representation of the space-time characteristic functional of turbulent Navier-Stokes flows with prescribed random initial states and driving forces

By adopting a formal operator viewpoint, the space-time characteristic functional associated with Navier-Stokes turbulence is expressed in terms of a linear operator acting on the space of functionals. Obtained by a simple similarity transformation of the local translation operator generated by the nonlinear terms in the Navier-Stokes equation, this operator is unitary with respect to the formal scalar product of functionals. The equivalence of this operator representation to the functional integral representation of Rosen is shown and, for Gaussian initial velocity and external force fields, some consequences of this representation are presented.

Dynamic percolation transition induced by phase separation: A Monte Carlo analysis

The percolation transition of geometric clusters in the three-dimensional, simple cubic, nearest neighbor Ising lattice gas model is investigated in the temperature and concentration region inside the coexistence curve. We consider “quenching experiments,” where the system starts from an initially completely random configuration (corresponding to equilibrium at infinite temperature), letting the system evolve at the considered temperature according to the Kawasaki “spinexchange” dynamics. Analyzing the distributionnl(t) of clusters of sizel at timet, we find that after a time of the order of about 100 Monte Carlo steps per site a percolation transition occurs at a concentration distinctly lower than the percolation concentration of the initial random state. This dynamic percolation transition is analyzed with finite-size scaling methods. While at zero temperature, where the system settles down at a frozen-in cluster distribution and further phase separation stops, the critical exponents associated with this percolation transition are consistent with the universality class of random percolation, the critical behavior of the transient time-dependent percolation occurring at nonzero temperature possibly belongs to a different, new universality class.

Field quenching: A method to achieve a random initial state for aging experiments on spin glasses.

FIELD QUENCHING - A METHOD TO ACHIEVE A RANDOM INITIAL STATE FOR AGING EXPERIMENTS ON SPIN-GLASSES

A multimodel approach to stochastic team problems

This paper develops decentralized team strategies for decision makers using different models of the same large-scale system. Multiparameter singular perturbations are employed to capture the multimodel nature of the fast dynamic subsystems interconnected through slow dynamic variables. The small parameters are appropriately scaled so that the variables in both time scales are well defined. The system considered is linear and the cost criterion is quadratic. First, a multimodel solution is obtained when the decision makers make different noisy linear observations of the random initial state only. Then the solution to this static team problem is utilized to obtain a multimodel solution to the dynamic team problem with sampled observations under the one-step-delay observation sharing pattern. In both cases, the well-posedness of the multimodel solution is demonstrated.

Computer simulation of spinodal decomposition on cubic and N-dimensional hypercubic lattices at zero temperature

Abstract Phase separation in the limit T → 0 was simulated for 50:50 mixtures using Monte Carlo methods on 3D cubic, 4D hypercubic and 5D lattices. The systems eventually find a local energy minimum which can be characterized by the parameter S;S is the total number of “bonds” between like objects/ the total number of lattice sites. The value of S/Z ( Z = coordination number of lattice) reaches a constant value in the limit of large system size and large number of Monte Carlo trials (time) which are independent of dimensionality ( d ) for d ⩾ 3. S/Z has the value 0.363 ± 0.0015 for a random initial state and 0.3598 ± 0.0005 for an ordered initial state in which nearest-neighbor lattice sites are occupied by unlike objects.