growth rates and explosions in sandpiles we study the abelian sandpile growth model where n particles are added at the origin on a stable background configuration in zd any site with at least 2d particles then topples by sending one particle to each neighbor we find that with constant background height h 2d 2 the diameter of the set of sites that topple has order n1 d this was previously known only for h d our proof uses a strong form of the least action principle for sandpiles and a novel method of background modification we can extend this diameter bound to certain backgrounds in which an arbitrarily high fraction of sites have height 2d 1 on the other hand we show that if the background height 2d 2 is augmented by 1 at an arbitrarily small fraction of sites chosen independently at random then adding finitely many particles creates an explosion a sandpile that never stabilizes

a fast and robust solver for the scattering from a layered periodic structure containing multi particle inclusions we present a solver for plane wave scattering from a periodic dielectric grating with a large number m of inclusions lying in each period of its middle layer such composite material geometries have a growing role in modern photonic devices and solar cells the high order scheme is based on boundary integral equations and achieves many digits of accuracy with ease the usual way to periodize the integral equation via the quasi periodic green s function fails at wood s anomalies we instead use the free space green s kernel for the near field add auxiliary basis functions for the far field and enforce periodicity in an expanded linear system this is robust for all parameters inverting the periodic and layer unknowns we are left with a square linear system involving only the inclusion scattering coefficients preconditioning by the single inclusion scattering matrix this is solved iteratively in o m time using a fast matrix vector product numerical experiments show that a diffraction grating containing m 1000 inclusions per period can be solved to 9 digit accuracy in under 5 minutes on a laptop

adaptive control for regulation of a quadratic function of the state we propose an adaptive controller for a dynamical system where we need a quadratic function of the state to track a given reference signal this problem appears in the control of generators in weak grid conditions for example while the controller can measure the tracking error the main difficulty arises from the fact that the parameters of the quadratic function itself are not known to the controller our approach consists of simultaneously estimating the quadratic function while tracking the reference signal similar to the approach employed in adaptive control the quadratic structure of the tracking function necessitates however a new adaptive law for estimating the parameters even though estimation and control are in general two contradicting requirements using this new adaptive law and a multilevel controller we prove that the tracking error converges to zero in the absence of measurement noise in the presence of bounded noise we show that the tracking error can be driven to a neighborhood around the origin

direct adaptive controller for nonaffine nonlinear systems using self structuring neural networks a direct adaptive state feedback controller is proposed for highly nonlinear systems we consider uncertain or ill defined nonaffine nonlinear systems and employ a neural network nn with flexible structure i e an online variation of the number of neurons the nn approximates and adaptively cancels an unknown plant nonlinearity a control law and adaptive laws for the weights in the hidden layer and output layer of the nn are established so that the whole closed loop system is stable in the sense of lyapunov moreover the tracking error is guaranteed to be uniformly asymptotically stable uas rather than uniformly ultimately bounded uub with the aid of an additional robustifying control term the proposed control algorithm is relatively simple and requires no restrictive conditions on the design constants for the stability the efficiency of the proposed scheme is shown through the simulation of a simple nonaffine nonlinear system

spectral method determination of dynamic exponents for ising models abstract we have carried out extensive monte carlo simulations of the ferromagnetic ising model on square and cubic lattices by analysing the power spectrum of the magnetization autocorrelation function we have values of the dynamic exponents for the two models our results are z 2 13 0 02 in two dimensions and z 2 04 0 03 in three dimensions

exact location of the multicritical point for finite dimensional spin glasses a conjecture we present a conjecture on the exact location of the multicritical point in the phase diagram of spin glass models in finite dimensions by generalizing our previous work we combine duality and gauge symmetry for replicated random systems to derive formulae which make it possible to understand all the relevant available numerical results in a unified way the method applies to non self dual lattices as well as to self dual cases in the former case of which we derive a relation for a pair of values of multicritical points for mutually dual lattices the examples include the j and gaussian ising spin glasses on the square hexagonal and triangular lattices the potts and zq models with chiral randomness on these lattices and the three dimensional j ising spin glass and the random plaquette gauge model

adaptive estimation for a class of nonlinearly parameterized dynamical systems the technical note presents a new technique for the adaptive parameter estimation in nonlinear parameterized dynamical systems the technique proposes an uncertainty set update approach that guarantees forward invariance of the true value of the parameters in addition it is shown that in the presence of sufficiently exciting state trajectories the parameter estimates converge to the true values and the uncertainty set vanishes around the true value of the parameters the set based approach is also shown to identify when the parameter estimates are biased two simulation examples are presented that demonstrate the effectiveness of the technique

attempt to distinguish electric signals of a dichotomous nature three types of electric signals were analyzed ion current fluctuations in membrane channels icfmc seismic electric signals activities ses and artificial noises an the wavelet transform when applied to the conventional time domain does not allow a classification of these signals but does so in the natural time domain a classification also becomes possible if we study q versus q where chi stands for the natural time for q values approximately between 1 and 2 the signals are classified and icfmc lies between the other two types for q 1 the entropy s identical with ln of icfmc almost equals that of a uniform distribution while the an and ses have larger and smaller s values respectively the recent p varotsos n sarlis and e skordas phys rev e 67 021109 2003 finding that in short time scales both ses and an which are shown to be non markovian result in comparable detrended fluctuation analysis exponents alpha in 1 0 1 5 is revisited even a markovian dichotomous time series in short time scales leads to similar alpha exponents

surface tension and universality in the ising model abstract we report on a new numerical computation of the surface tension between domains of opposite magnetisation in the ising model in two and three dimensions the method is quite general and can be applied to any statistical mechanics model it is based on a partition of the lattice into two halves which are slowly driven from one magnetization state to the other the free energy of the interface is the result of the difference between the total free energies of the homogeneous and of the mixed phases we first test the method in the two dimensional ferromagnetic ising model by comparing with the onsager solution we then compare the results in three dimensions with previous monte carlo simulations of thermal equilibrium and of decays via nucleation the three dimensional results are also used in the computation of the universal amplitude combination that involves the correlation length and the surface tension near the critical temperature the numerical results agree well with measurements performed in the laboratory

adaptive output feedback control of nonlinear systems using neural networks a direct adaptive output feedback control design procedure is developed for highly uncertain nonlinear systems that does not rely on state estimation the approach is also applicable to systems of unknown but bounded dimension in particular we consider single input single output nonlinear systems whose output has known but otherwise arbitrary relative degree this includes systems with both parameter uncertainty and unmodeled dynamics the result is achieved by extending the universal function approximation property of linearly parameterized neural networks to model unknown system dynamics from input output data the network weight adaptation rule is derived from lyapunov stability analysis and guarantees that the adapted weight errors and the tracking error are bounded numerical simulations of an output feedback controlled van der pol oscillator coupled with a linear oscillator is used to illustrate the practical potential of the theoretical results

tracking control for nonaffine systems a self organizing approximation approach this paper considers tracking control for single input single output nonaffine dynamic systems a performance dependent self organizing approximation based approach is proposed the designer specifies a positive tracking error criterion the self organizing approximation based controller then monitors the tracking performance and adds basis elements only as needed to achieve the tracking specification even though the system is not affine the approach is defined such that the approximated function is independent of the control variable u stability is proved and the self organization is derived in a lyapunov based methodology to illustrate certain novel aspects of the proposed controller a numerical example is included

a non overlapping domain decomposition method with non matching grids for modeling large finite antenna arrays a non overlapping domain decomposition method ddm is proposed herein to solve maxwell equations in r 3 in this work the maxwell equations are discretized using a vector finite element method with hierarchical h curl vector basis functions there are two major ingredients in the proposed non overlapping ddm a a proper 1st order transmission condition to enforce field continuity across domain boundaries and b a cement technique to allow non matching grids for neighboring domains moreover a detail fourier analysis of the transmission condition for a canonical half space example is presented the analysis provides significant insights into the convergence behavior of the proposed non overlapping ddm for solving electromagnetic radiation problems such as the large finite antenna arrays particularly for the antenna arrays the proposed non overlapping ddm is extremely efficient since the formulation can easily incorporate geometrical repetitions exponentially tapered notch vivaldi antenna arrays with size up to 100x100 elements are solved on a common pc to validate the proposed non overlapping ddm

universal approximation using radial basis function networks there have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables some of these studies deal with cases in which the hidden layer nonlinearity is not a sigmoid this was motivated by successful applications of feedforward networks with nonsigmoidal hidden layer units this paper reports on a related study of radial basis function rbf networks and it is proved that rbf networks having one hidden layer are capable of universal approximation here the emphasis is on the case of typical rbf networks and the results show that a certain class of rbf networks with the same smoothing factor in each kernel node is broad enough for universal approximation

peaking free output feedback adaptive neural control under a nonseparation principle high gain observers have been extensively applied to construct output feedback adaptive neural control anc for a class of feedback linearizable uncertain nonlinear systems under a nonlinear separation principle yet due to static gain and linear properties high gain observers are usually subject to peaking responses and noise sensitivity existing adaptive neural network nn observers cannot effectively relax the limitations of high gain observers this paper presents an output feedback indirect anc strategy under a nonseparation principle where a hybrid estimation scheme that integrates an adaptive nn observer with state variable filters is proposed to estimate plant states by applying a single lyapunov function candidate to the entire system it is proved that the closed loop system achieves practical asymptotic stability under a relatively low observer gain dominated by controller parameters our approach can completely avoid peaking responses without control saturation while keeping favourable noise rejection ability simulation results have shown effectiveness and superiority of this approach

fdtd local grid with material traverse often a finite difference time domain fdtd calculation requires a relatively higher mesh resolution in only small subvolumes of the total mesh space by locally applying finer grids local grids to these volumes the necessary resolution can be obtained computation time and memory requirements may be far less than for an fdtd space with the smaller mesh resolution throughout in many situations it is important that these local grids function when materials traverse the main grid local grid mg lg boundary surfaces since the volumes that require local grids may not be isolated in a homogeneous medium a local grid method which allows dielectric and or conducting materials to traverse the boundaries is developed three different fdtd problems that utilize the local grid method are used as validation tests results are compared with uniform mesh fdtd solutions

long range correlations in the electric signals that precede rupture further investigations the correlations within the time series of the seismic electric signal ses activities have been studied in a previous paper p varotsos n sarlis and e skordas phys rev e 66 011902 2002 here we analyze the time series of successive high and low level states durations the existence of correlation between the states is investigated by means of hurst and detrended fluctuation analysis dfa the multifractal dfa mf dfa is also employed the results point to a stronger correlation and hence longer memory in the series of the high level states furthermore an analysis in the natural time domain reveals that certain power spectrum characteristics seem to distinguish ses activities from artificial man made electric noises more precisely for natural frequencies 0 f 0 5 the curves of the ses activities and artificial noises lie above and below respectively that of the uniform distribution ud a classification of these two types of electric signals ses activities artificial noises cannot be achieved on the basis of the values of the power law exponents alone if the hurst analysis dfa and mf dfa are applied to the original time series the latter two methods however seem to allow a distinction between the ses activities and artificial noises when treating them not in conventional the time frame but in the natural time domain to further test the techniques a time series produced by another system was examined we chose a signal of ion current fluctuations in membrane channels icfmcs the following conclusions among others have been obtained first the power spectrum analysis in the natural time domain shows that the icfmc curve almost coincides in the range 0 f 0 5 with that of the ud and hence icfmc lies just in the boundary between the ses activities and artificial noises second mf dfa indicates monofractality for the icfmcs with a generalized hurst exponent h 50 8460 03 in the range 7 70 ms

critical slowing down in ising model for creutz algorithm abstract dynamical critical exponents for the two dimensional ising model are computed on a cellular automaton from the relaxations of the time displaced correlation and auto correlation functions for the order parameter and the internal energy at the critical temperatures and from the nonlinear relaxation time for the order parameter near the critical temperature the analysis of the data within the frame of the dynamical finite size scaling hypothesis gives z m z e 2 20 and z a m 1 91 and z a e 0 19 for the linear dynamical exponents corresponding respectively to the relaxations of the correlation and the autocorrelation functions for the order parameter and the internal energy and nl m 2 07 for the nonlinear dynamical exponent for the order parameter these values verify the scaling relations between the dynamical exponents

long range correlations in the electric signals that precede rupture the smoluchowski chapman kolmogorov functional equation is applied to the electric signals that precede rupture the results suggest a non markovian character of the analyzed data the rescaled range hurst and detrended fluctuation analyses as well as that related with the mean distance a walker spanned lead to power law exponents which are consistent with the existence of long range correlations a universality in the power spectrum characteristics of these signals emerges if an analysis is made not in the conventional time frame but in the natural time domain within this frame it seems that certain power spectrum characteristics of ion current fluctuations in membrane channels distinguish them from the electric signals preceding rupture the latter exhibit a behavior compatible with that expected from a model based on the random field ising hamiltonian at the critical point

saturated finite interval iterative learning for tracking of dynamic systems with hnn structural output this brief investigates the interval iterative learning problem for dynamic systems with hierarchical neural network hnn structural output the first objective is to design the output of a dynamic system with hnn structure a sufficient condition is obtained to achieve the interval tracking in a finite interval by applying iterative learning control ilc then the saturated ilc is considered into the discussed system and a less conservative criterion is obtained to achieve the tracking in a finite interval using a network structure decomposition technique finally simulation results are given to illustrate the usefulness of the developed criteria

the dynamical critical exponent of the two three and five dimensional kinetic ising model abstract we present monte carlo simulation results for the dynamical critical exponent z of the two three and five dimensional kinetic ising model we used glauber as well as metropolis dynamics both type of dynamics lead to the same z values in two and three dimensions the z values were calculated from the magnetization relaxation from an ordered state into the equilibrium state at tc for very large systems up to 169984 2 3072 3 and 48 5 for the two dimensional case we obtain z 2 21 0 03 and for the three dimensional case z 2 08 0 03 for the five dimensional glauber case the requirement z 2 gives a critical point j kbtc 0 11391 from monte carlo simulations whereas new series expansions with four more terms give 0 113935 0 000015 for this ratio

bayesian nonparametric adaptive control using gaussian processes most current model reference adaptive control mrac methods rely on parametric adaptive elements in which the number of parameters of the adaptive element are fixed a priori often through expert judgment an example of such an adaptive element is radial basis function networks rbfns with rbf centers preallocated based on the expected operating domain if the system operates outside of the expected operating domain this adaptive element can become noneffective in capturing and canceling the uncertainty thus rendering the adaptive controller only semiglobal in nature this paper investigates a gaussian process based bayesian mrac architecture gp mrac which leverages the power and flexibility of gp bayesian nonparametric models of uncertainty the gp mrac does not require the centers to be preallocated can inherently handle measurement noise and enables mrac to handle a broader set of uncertainties including those that are defined as distributions over functions we use stochastic stability arguments to show that gp mrac guarantees good closed loop performance with no prior domain knowledge of the uncertainty online implementable gp inference methods are compared in numerical simulations against rbfn mrac with preallocated centers and are shown to provide better tracking and improved long term learning

domain growth properties of a two dimensional kinetic ising model the domain growth properties of the two dimensional single spin flip kinetic ising model with a metropolis type transition function and checkerboard updating are investigated numerically with quenches from the high temperature phase to temperatures in the ordered phase and to tc measuring the structure factor s 0 t varies as t2x and the autocorrelation function a t varies as t lambda x as a function of time the effect of deterministic dynamics at t 0 with x 1 0 is followed throughout the ordered phase at t tc tnot approximately tc crossover from x 1 0 to x 0 5 is shown to occur with increasing time and even at t tc the scaling exponents are still discernibly dependent on time lambda however is found to be unaffected in the whole temperature range

output feedback adaptive stabilization and command following for minimum phase dynamical systems with unmatched uncertainties and disturbances in this article we develop an output feedback adaptive control framework for continuous time minimum phase multivariable dynamical systems for output stabilisation and command following the approach is based on a nonminimal state space realisation that generates an expanded set of states using the filtered inputs and filtered outputs and their derivatives of the original system specifically a direct adaptive controller for the nonminimal state space model is constructed using the expanded states of the nonminimal realisation and is shown to be effective for multi input multi output linear dynamical systems with unmatched disturbances unmatched uncertainties and unstable dynamics the proposed adaptive control architecture requires only knowledge of the open loop system s relative degree as well as a bound on the system s order several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach

domain growth morphology in curvature driven two dimensional coarsening we study the distribution of domain areas areas enclosed by domain boundaries hulls and perimeters for curvature driven two dimensional coarsening employing a combination of exact analysis and numerical studies for various initial conditions we show that the number of hulls per unit area n h a t da with enclosed area in the interval a a da is described for a disordered initial condition by the scaling function n h a t 2 c h a ensuremath lambda h t 2 where c h 1 8 ensuremath pi sqrt 3 ensuremath approx 0 023 is a universal constant and ensuremath lambda h is a material parameter for a critical initial condition the same form is obtained with the same ensuremath lambda h but with c h replaced by c h 2 for the distribution of domain areas we argue that the corresponding scaling function has for random initial conditions the form n d a t 2 c d ensuremath lambda d t ensuremath tau ensuremath ensuremath 2 a ensuremath lambda d t ensuremath tau ensuremath where c d and ensuremath lambda d are numerically very close to c h and ensuremath lambda h respectively and ensuremath tau ensuremath 187 91 ensuremath approx 2 055 for critical initial conditions one replaces c d by c d 2 and the exponent is ensuremath tau 379 187 ensuremath approx 2 027 these results are extended to describe the number density of the length of hulls and domain walls surrounding connected clusters of aligned spins these predictions are supported by extensive numerical simulations we also study numerically the geometric properties of the boundaries and areas

static and dynamic critical phenomena of the two dimensional q state potts model theq state potts model on the square lattice is studied by monte carlo simulation forq 3 4 5 6 very good agreement is obtained with exact results of kiharaet al and baxter for energy and free energy at the critical point critical exponent estimates forq 3 are 0 4 0 1 1 45 in rough agreement with high temperature series extrapolation and real space renormalization group methods the transition forq 5 6 is found to be a very weakly first order transition i e pronounced pseudocritical phenomena occur specific heat susceptibility etc nearly diverge at the first order transition temperature dynamics is associated to the model in the same way as for the kinetic ising model and the nonlinear slowing down of the order parameter and of the energy is studied the dynamic exponent is estimated to be zv 1 9 within our accuracy noq dependence is detected the relaxation is found to be consistent with dynamic scaling predictions and dynamic scaling functions associated with the nonlinear relaxation are estimated

some experiences from fdtd analysis of infinite and finite multi octave phased arrays some experiences from finite differences time domain fdtd analysis of infinite and finite multi octave phased arrays are presented first a more unified derivation of equations suitable for unit cell analysis of phased arrays or other types of periodic structures using fdtd is presented second results from fdtd calculations of small to very large multi octave finite arrays are summarized in order to answer the question of how large an array model must be in order to capture the characteristics of both the interior and the edge elements of a large multi octave phased array it is found that a considerably larger number of elements is required in the broad band case than in the normal narrow band case and it is also found that fdtd is well suited for such calculations third simple methods to save computer memory using locally fine grids in an otherwise coarse fdtd grid to model finite phased arrays are explored the two local grid methods tested were found in our application to suffer from numerical instabilities

tracking control for a class of unknown nonsquare mimo nonaffine systems a deep rooted information based robust adaptive approach the tracking control problem of multi input multi output mimo nonaffine dynamic systems is studied in this note a globally uniformly ultimately bounded guub stable tracking control solution for non square mimo nonaffine systems with unknown dynamics and disturbances is established different from most existing methods the proposed control design is based on the readily computable deep rooted information on the system and does not involve linearization or approximation and the resultant control algorithms are simple in structure inexpensive in computation user friendly in design and undemanding in implementation both theoretical analysis and numerical simulation verify the effectiveness and benefits of the proposed method

adaptive dynamic inversion via time scale separation this paper presents a full state feedback adaptive dynamic inversion method for uncertain systems that depend nonlinearly upon the control input using a specialized set of basis functions that respect the monotonic property of the system nonlinearities with respect to control input a state predictor is defined for derivation of the adaptive laws the adaptive dynamic inversion controller is defined as a solution of a fast dynamical equation which achieves time scale separation between the state predictor and the controller dynamics lyapunov based adaptive laws ensure that the predictor tracks the state of the nonlinear system with bounded errors as a result the system state tracks the desired reference model with bounded errors benefits of the proposed design method are demonstrated using van der pol dynamics with nonlinear control input

brief paper robust adaptive control of nonlinear non minimum phase systems with uncertainties this paper presents a robust adaptive control method for a class of nonlinear non minimum phase systems with uncertainties the development of the control method comprises two steps first stabilization of the system is considered based on the availability of the output and internal dynamics of the system the reference signal is designed to stabilize the internal dynamics with respect to the output tracking error moreover a combined neuro adaptive controller is proposed to guarantee asymptotic stability of the tracking error then the overall stability is achieved using the small gain theorem next the availability of internal dynamics is relaxed by using a linear error observer the unmatched uncertainty is compensated using a suitable reference signal the ultimate boundedness of the reconstruction error signals is analytically shown using an extension of the lyapunov theory the theoretical results are applied to a translational oscillator rotational actuator model to illustrate the effectiveness of the proposed scheme

fuzzy approximation based global adaptive control for uncertain strict feedback systems with a priori known tracking accuracy abstract in this study we propose a novel adaptive backstepping fuzzy control scheme for a class of uncertain strict feedback systems where the tracking accuracy is known a priori and we also introduce a multiswitching based adaptive fuzzy controller compared with the existing method for adaptive fuzzy control the advantages of the proposed scheme are as follows first the controller guarantees that all the closed loop signals are globally uniformly ultimately bounded which differs from most existing adaptive fuzzy control approaches where the semi global boundedness of the closed loop signals is ensured under a harsh assumption on the approximation domain of the fuzzy logic system second our controller ensures that the tracking error converges to an accuracy that is given a priori for the uncertain strict feedback system which cannot be achieved using existing adaptive fuzzy control methods third based on some nonnegative functions we analyze the convergence of the tracking error using barbalat s lemma fourth the main technical novelty is the construction of three new n th order continuously differentiable switching functions which are used to design the desired controller finally three simulation examples are provided that illustrate the effectiveness of the proposed control strategy

scaling of waves in the bak tang wiesenfeld sandpile model n with aen ae0 n a similar ansatzes should according to this view hold for the number of topplings s which difiers from a because sites can topple more than once in an avalanche and for the radius and duration of avalanches but recent inves tigations 10 12 show that the two dimensional btw model may be characterized by a multifractal behavior where difierent moments of a are governed by exponents aen which are not linear in n and are indeed not related to each other for difierent n difierent reasons for this have been proposed in 10 11 and in 12 notice that multi fractality of avalanches can be proven for certain variants of the 1 d sandpile model 14 deviations from pure power laws had been seen already in early simulations but were usually interpreted as fl nite size efiects due to avalanches which touch the bound ary of the lattice to illustrate that this is most likely not true and that there is a real problem with simple scaling we show in fig 1 the ratio ps x l pa x l of the integrated distributions ps x l r 1 x dx 0 ps x 0 l for d 2 and for difierent values of l in these simula tions cylindrical boundary conditions were used open at y l 2 and periodic at x 0 l and data were col lected only for avalanches starting at y 0 in this way we hope to have minimized boundary efiects also since we do not make separate flts to ps x l and pa x l we have none of the uncertainties inherent in such flts due

robust decentralized direct adaptive output feedback fuzzy control for a class of large sale nonaffine nonlinear systems in the previous work of huang et al a decentralized direct adaptive fuzzy h tracking controller of large scale nonaffine nonlinear systems is obtained predicated upon the assumption that the mismatching error dynamics stay squared integrable in this note we focus in the absence of the conservative assumption upon developing a robust decentralized direct adaptive output feedback fuzzy controller by combination of a state observer a fuzzy inference system and robust control technique the previous controller design is modified and no a priori knowledge of bounds on lumped uncertainties is required all the signals of the closed loop large scale system are proved to be uniformly ultimately bounded the effectiveness of the developed scheme is demonstrated through the simulation results of interconnected inverted pendulums

infinite phased array analysis using fdtd periodic boundary conditions pulse scanning in oblique directions unit cell analysis of infinite phased arrays in the finite difference time domain fdtd is performed by implementation of periodic boundary conditions the technique allows for pulse excitation and oblique scan directions in both the cardinal and intercardinal planes to our knowledge this is the first paper presenting fdtd computations for intercardinal pulse scanning in oblique directions the ordinary yee lattice is used which makes the algorithm easy to incorporate in an already existing fdtd code nonperiodic boundaries are truncated by berenger s see j comput phys vol 127 p 363 79 1996 perfectly matched layer pml active impedance of an infinite dipole array is calculated with the new method and validation is performed via the element by element approach i e by a conventional fdtd simulation of a corresponding large finite array excellent agreement is found and the technique has been numerically stable in all cases analyzed

non equilibrium critical relaxation of the three dimensional ising model abstract the non equilibrium relaxation process at the critical point is studied using monte carlo simulation for the ferromagnetic ising model on a cubic lattice it was observed that the time dependent magnetization decayed following a power law t from the all up initial condition three kinds of single spin flip dynamics were studied for several lattices up to 1536 3 the system size dependences are also studied the value of was estimated to be 0 250 2 this value of leads to the estimation of the dynamical exponent z to be 2 06 2 if we assume z where and denote the critical exponents for spontaneous magnetization and correlation length in equilibrium state respectively and 0 515 the result of the non equilibrium relaxation in the ordered phase is also given

critical dynamics of finite ising model the glauber kinetics of ising spins is considered as a queueing process and simulated event by event as first proposed by bortz kalos and lebowitz the advantage of this algorithm compared to the standard single flip monte carlo method is discussed for the situation of slowing down of dynamics this process is used to generate fluctuations of magnetization and energy in the critical regimet tc of two dimensional ising models the analysis of these fluctuations leads to numerical determination of the critical exponents for dynamics for the size dependence of correlation time attc and for frequency dependence of the power spectrums from the finite size scaling hypothesis scaling relations are settled which are confirmed by this numerical experiment

energy relaxation in ising models starting with all spins parallel simulations show the energy to relax at the critical point as t 1 z with z near 2 2 for 1699802 no logarithm and 2 1 for 28003

non equilibrium relaxation and interface energy of the ising model abstract from the non equilibrium critical relaxation study of the two dimensional ising model the dynamical critical exponent z is estimated to be 2 165 0 010 for this model the relaxation in the ordered phase of this model is consistent with exp t behavior the interface energy of the three dimensional ising model is studied and the critical exponent of the correlation length and the critical amplitude of the surface tension 0 are estimated to be 0 6250 0 0025 and 1 42 0 04 respectively a dynamic monte carlo renormalization group method is successfully applied to the equilibrium properties of the three dimensional ising model

a novel error observer based adaptive output feedback approach for control of uncertain systems we develop an adaptive output feedback control methodology for nonaffine in control of uncertain systems having full relative degree given a smooth reference trajectory the objective is to design a controller that forces the system measurement to track it with bounded errors a neural network with linear parameters is introduced as an adaptive signal a simple linear observer is proposed to generate an error signal for the adaptive laws ultimate boundedness is shown through lyapunov s direct method simulations of a nonlinear second order system illustrate the theoretical results

microcanonical simulations with a large number of demons we generalize the microcanonical algorithm developed by creutz et al 1986 and make a detailed comparison with the exact solution in the case of a two dimensional ising model at finite volume we present a new numerical method to compute the temperature in the microcanonical ensemble this allows us to define a thermalization criterion to estimate the point where the differences between canonical and microcanonical results are the smallest this criterion is shown to work well in the case of the two dimensional ising system

locally weighted online approximation based control for nonaffine systems this paper is concerned with tracking control problems for nonlinear systems that are not affine in the control signal and that contain unknown nonlinearities in the system dynamic equations this paper develops a piecewise linear approximation to the unknown functions during the system operation new control and parameter adaptation algorithms are designed and analyzed using lyapunov like methods the objectives are to achieve semiglobal stability of the state accurate tracking of bounded reference signals contained within a known domain and at least boundedness of the function approximator parameter estimates numerical simulations are included to illustrate the effectiveness of the learning algorithm

three dimensional perfectly matched layer for the absorption of electromagnetic waves the perfectly matched layer is a technique of free space simulation developed for solving unbounded electromagnetic problems with the finite difference time domain method referred to as pml this technique has been described in a previous paper for two dimensional problems the present paper is devoted to the three dimensional case the theory of the perfectly matched layer is generalized to three dimensions and some numerical experiments are shown to illustrate the efficiency of this new method of free space simulation

natural time analysis of critical phenomena a quantity exists by which one can identify the approach of a dynamical system to the state of criticality which is hard to identify otherwise this quantity is the variance of natural time where and pk is the normalized energy released during the kth event of which the natural time is defined as k k n and n stands for the total number of events then we show that 1 becomes equal to 0 070 at the critical state for a variety of dynamical systems this holds for criticality models such as 2d ising and the bak tang wiesenfeld sandpile which is the standard example of self organized criticality this condition of 1 0 070 holds for experimental results of critical phenomena such as growth of rice piles seismic electric signals and the subsequent seismicity before the associated main shock

adaptive control of uncertain nonaffine nonlinear systems with input saturation using neural networks this paper presents a tracking control methodology for a class of uncertain nonlinear systems subject to input saturation constraint and external disturbances unlike most previous approaches on saturated systems which assumed affine nonlinear systems in this paper tracking control problem is solved for uncertain nonaffine nonlinear systems with input saturation to deal with the saturation constraint an auxiliary system is constructed and a modified tracking error is defined then by employing implicit function theorem mean value theorem and modified tracking error updating rules are derived based on the well known back propagation bp algorithm which has been proven to be the most relevant updating rule to control problems however most of the previous approaches on bp algorithm suffer from lack of stability analysis by injecting a damping term to the standard bp algorithm uniformly ultimately boundedness of all the signals of the closed loop system is ensured via lyapunov s direct method furthermore the presented approach employs nonlinear in parameter neural networks hence the proposed scheme is applicable to systems with higher degrees of nonlinearity using a high gain observer to reconstruct the states of the system an output feedback controller is also presented finally the simulation results performed on a duffing holmes chaotic system a generalized pendulum type system and a numerical system are presented to demonstrate the effectiveness of the suggested state and output feedback control schemes

predictability of the coherent noise model and its applications we study the threshold distribution function of the coherent noise model for the case of infinite number of agents this function is piecewise constant with a finite number of steps n the latter exhibits a 1 f behavior as a function of the order of occurrence of an avalanche and hence versus natural time an analytic expression of the expectation value mathcal e s for the size s of the next avalanche is obtained and used for the prediction of the next avalanche apart from mathcal e s the number of steps n can also serve for this purpose this enables the construction of a similar prediction scheme which can be applied to real earthquake aftershock data

simulation of time exponent in 2d glauber kinetic ising model abstract simulations of the magnetization relaxation of large square lattices at the curie point give a dynamical exponent near 2 2 somewhat higher than expected

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

attempt to distinguish long range temporal correlations from the statistics of the increments by natural time analysis most probable value of 1 of the shuffled data is found to be approximately equal to that of the original data the difference most likely arising from temporal correlation finally it is found that the differential entropy associated with the probability p1 maximizes for around 1 6 1 7 which is comparable to the value determined experimentally in diverse phenomena e g solar flares icequakes dislocation glide in stressed single crystals of ice etc it also agrees with the b value in the gutenberg richter law of earthquakes in addition the case of multiplicative cascades is studied in the natural time domain

critical ising on the square lattice mixes in polynomial time the ising model is widely regarded as the most studied model of spin systems in statistical physics the focus of this paper is its dynamic stochastic version the glauber dynamics introduced in 1963 and by now the most popular means of sampling the ising measure intensive study throughout the last three decades has yielded a rigorous understanding of the spectral gap of the dynamics on mathbb z 2 everywhere except at criticality while the critical behavior of the ising model has long been the focus for physicists mathematicians have only recently developed an understanding of its critical geometry with the advent of sle cle and new tools to study conformally invariant systems

adaptive control of a class of nonaffine systems using neural networks a neural control synthesis method is considered for a class of nonaffine uncertain single input single output siso systems the method eliminates a fixed point assumption and does not assume boundedness on the time derivative of a control effectiveness term one or the other of these assumptions exist in earlier papers on this subject using lyapunov s direct method it is shown that all the signals of the closed loop system are uniformly ultimately bounded and that the tracking error converges to an adjustable neighborhood of the origin simulation with a van der pol equation with nonaffine control terms illustrates the approach

damage spreading and critical exponents for model a ising dynamics using damage spreading and heat bath dynamics we study the ising model in 2 and 3 dimensions with non conservative dynamics our algorithm differs in some important points from previous ones which makes it rather efficient we give estimates for the exponent z which seem to be the most precise published so far 2 172 0 006 for d 2 2 032 0 004 for d 3 we also give precise estimates of the exponent introduced by janssen et al z phys b 73 1989 539 and of analogous but in principle independent exponents we find surprisingly that some of the latter agree with and give an explanation for this

relaxation to equilibrium of single cluster dynamics of the ising model abstract the approach to equilibrium at the critical temperature of the two dimensional ising model from an initial ordered spin configuration is investigated using the single cluster monte carlo dynamics introduced by wolff an initial configuration of all up spins and its dual a checkerboard state are considered we give simple mean field and scaling arguments for the existence of power law decay because the usual arguments for time rescaling might not be applicable when the system is approaching equilibrium we directly determine the relation of the number of cluster flips to the number of monte carlo steps per spin for both initial configurations we find that the effective dynamical critical exponent determined from the power law behavior and the proper time rescaling differs from the estimates of the equilibrium dynamical exponent and depends on the initial conditions for the system sizes and times we have investigated

direct adaptive self structuring fuzzy controller for nonaffine nonlinear system a direct adaptive state feedback controller for highly nonlinear systems is proposed this paper considers uncertain or ill defined nonaffine nonlinear systems and employ a static fuzzy logic system fls with an on line structuring algorithm the fls approximates and adaptively cancels an unknown plant nonlinearity a control law and adaptive laws for unknown fuzzy parameters and bounding constant are established so that the whole closed loop system is stable in the sense of lyapunov the tracking error is guaranteed to be uniformly asymptotically stable rather than uniformly ultimately bounded with the aid of an additional robustifying control term no a priori knowledge of an upper bound on an lumped uncertainty is required

a domain decomposition method with nonconformal meshes for finite periodic and semi periodic structures we present a domain decomposition method as a preconditioner for krylov type solvers to model complex electromagnetic problems containing periodicities the method reduces memory requirements by decomposing the original problem into several nonoverlapping sub domains the 1st order transmission condition is employed on interfaces between adjacent sub domains to enforce continuity of electromagnetic fields and to ensure the sub domain problems are well posed by following the spirit of duality paring a symmetric system is obtained to reduce the computational burdens of the present method the finite element tearing and interconnecting like algorithm is adopted this algorithm results in the computation of the so called numerical green s function which can be compressed efficiently via a rank revealing matrix factorization algorithm the final system matrix is solved by krylov solvers instead of classical stationary solvers to improve the convergence of iterative solvers several robust implementation details are discussed and the choice of some popular krylov subspace solvers is studied through numerical examples

nonequilibrium relaxation study on spin glass model ferromagnetic fm transition point and universality class of the j ising model on cubic lattice are studied by computer simulation using the nonequilibrium relaxation ner method at fm bond density p between multicritical one pmc and 1 static exponents take universal values which are different from those of p 1 or p pmc and they are consistent with the values of the random fixed point and of the simulations and experiments for diluted ising systems the dynamical exponent however seems to depend on p and not to be universal although it may be due to finite time correction the estimation of pmc on square lattice is also refined to be 0 8894 9 which is consistent with the nishimori and nemoto s conjecture 0 889972

theoretical studies of self organized criticality these notes are intended to provide a pedagogical introduction to the abelian sandpile model of self organized criticality and its related models the abelian group the algebra of particle addition operators the burning test for recurrent states equivalence to the spanning trees problem are described the exact solution of the directed version of the model in any dimension is explained the model s equivalence to scheidegger s model of river basins takayasu s aggregation model and the voter model is discussed for the undirected case the solution for one dimensional lattices and the bethe lattice is briefly described known results about the two dimensional case are summarized generalization to the abelian distributed processors model is discussed time dependent properties and the universality of critical behavior in sandpiles are briefly discussed i conclude by listing some still unsolved problems

ageing properties of critical systems in the past few years systems with slow dynamics have attracted considerable theoretical and experimental interest ageing phenomena are observed during this everlasting non equilibrium evolution a simple instance of such a behaviour is provided by the dynamics that takes place when a system is quenched from its high temperature phase to the critical point the aim of this review is to summarize the various numerical and analytical results that have been recently obtained for this case particular emphasis is put on the field theoretical methods that can be used to provide analytical predictions for the relevant dynamical quantities fluctuation dissipation relations are discussed and in particular the concept of fluctuation dissipation ratio fdr is reviewed emphasizing its connection with the definition of a possible effective temperature the renormalization group approach to critical dynamics is summarized and the scaling forms of the time dependent non equilibrium correlation and response functions of a generic observable are discussed from them the universality of the associated fdr follows as an amplitude ratio it is then possible to provide predictions for ageing quantities in a variety of different models in particular the results for models a b and c dynamics of the o n ginzburg landau hamiltonian and model a dynamics of the weakly dilute ising magnet and of the 3 theory are reviewed and compared with the available numerical results and exact solutions the effect of a planar surface on the ageing behaviour of model a dynamics is also addressed within the mean field approximation

non equilibrium critical relaxation of the wolff dynamics of the ising model abstract the non equilibrium critical relaxation of the single cluster dynamics is studied for the ferromagnetic ising model on the square and cubic lattices power law behavior is observed in the energy relaxation process starting from an all up spin configuration from this power decay the dynamical exponent z is estimated to be 0 50 0 05 and 1 3 0 1 for the square and cubic lattices respectively where the time is defined by the number of cluster flip trials if the time scale is normalized by cluster mass they are 0 25 0 05 and 0 3 0 1 respectively