two and three spin triangular ising model variational approximations the implications of the known hard hexagon lattice gas results for the triangular ising model with both pair and triplet interactions are pointed out employing an appropriate generalization of the variational method of baxter we determine using the lowest order approximation the phase boundaries for this model when the pair interactions are ferromagnetic higher approximations are presented for the case of pure triplet interactions and the resulting phase diagrams are in excellent agreement with all exactly known results

laguerre z transfer function representation of linear discrete time systems in this paper the difference equation of a linear discrete time dynamical system is transformed into a rational function which is called the laguerre z lransfer functio this function is obtained from the ratio between the z transform of the laguerre spectrum of the output and the corresponding transform of the spectrum of the input simple formulas for transforming the original system into the laguerre system and vice versa are derived interesting properties of the laguerre z transfer function representation are also given this representation is then applied to the identification of models of siso discrete time systems from input output data

homogenization of some degenerate pseudoparabolic variational inequalities abstract multiscale analysis of a degenerate pseudoparabolic variational inequality modelling the two phase flow with dynamical capillary pressure in a perforated domain is the main topic of this work regularisation and penalty operator methods are applied to show the existence of a solution of the nonlinear degenerate pseudoparabolic variational inequality defined in a domain with microscopic perforations as well as to derive a priori estimates for solutions of the microscopic problem the main challenge is the derivation of a priori estimates for solutions of the variational inequality uniformly with respect to the regularisation parameter and to the small parameter defining the scale of the microstructure the method of two scale convergence is used to derive the corresponding macroscopic obstacle problem

existence uniqueness and l q estimates for the stokes problem in an exterior domain as is well known the study of the properties of solutions to the stokes system plays an essential role in the mathematical theory of viscous fluid flows governed by the navier stokes equations it is not art overstatement to say that existence uniqueness and a priori estimates in sobolev spaces for the stokes system are fundamental in every basic question related to the navier stokes equations such as existence regularity asymptotic behavior in time etc see e g ladyzhenskaya 1969 solonni ov 1977 and te am 1977 so far however the stokes system has been fully analyzed only for bounded domains see sobolevskn 1960 ladvznenskaya 1959 solonnu ov 1960 vorovlch yot oowcr 1961 cattabrma 1961 in particular in the paper of cattabriga a complete treatment is given in the sobotev spaces w l 1 1 q c for space dimension n 3 cattabriga s results essentially state that if 2 is a bounded domain in r a of class c m m max l 2 2 l 1 then given f e wt q y2 3 gc wt l q o q e wl 2 1 q q 8o a 1 q there exists one and only one distributional solution v c w1 z q q 3 p e wt l q o to the stokes system

self averaging in the statistical mechanics of some lattice models we discuss self averaging of thermodynamic properties in some random lattice models in particular we investigate when self averaging in an almost sure sense of the free energy implies self averaging of the energy and heat capacity and we discuss the connection between self averaging in the almost sure sense and self averaging in an l p sense under quite general conditions we show that the average of the finite size heat capacity converges to the second derivative of the limiting quenched average free energy we consider the application of these ideas to the problem of adsorption of a random copolymer at a surface and to some related systems

on the application of the critical minimum energy subspace method to disordered systems abstract we discuss the recent application to strongly disordered systems of the critical minimum energy subspace crmes method used to limit the energy subspace of the wang landau sampling we compare with our results on the 3d random field ising model obtained by a multi range wang landau simulation over the whole energy range we point out some problems that may arise when applying the crmes scheme to models having a complex free energy landscape

universal features and tail analysis of the order parameter distribution of the two dimensional ising model an entropic sampling monte carlo study we present a numerical study of the order parameter probability density function pdf of the square ising model for lattices with linear sizes l 80 140 a recent efficient entropic sampling scheme combining the wang landau and broad histogram methods and based on the high levels of the wang landau process in dominant energy subspaces is employed we find that for large lattices there exists a stable window of the scaled order parameter in which the full ansatz including the pre exponential factor for the tail regime of the universal pdf is well obeyed this window is used to estimate the equation of state exponent and to observe the behavior of the universal constants implicit in the functional form of the universal pdf the probability densities are used to estimate the universal privman fisher coefficient and to investigate whether one could obtain reliable estimates of the universal constants controlling the asymptotic behavior of the tail regime

critical finite size scaling of magnetization distribution function for baxter wu model abstract the distribution function pl m of the order parameter for the baxter wu model is studied using blocks of linear dimension l of a larger triangular lattice at a given temperature we use the metropolis algorithm for the generation of a sample of configurations on the triangular lattice the similarities and differences of this distribution with the usual cases of ising lattices are investigated we conclude that the present model obeys at the critical temperature a finite scaling law with the known critical exponents as expected however our numerical data strongly indicate that the analytic form of the scaling function does not conform to the corresponding function for the usual ising model an analytic expression that gives a good fit is presented

digital pid controller design via general discrete orthogonal polynomials based on the discrete orthogonal polynomials a new computer oriented algebraic method is proposed for designing a digital pid controller the pid controller can approximately achieve an arbitrarily specified closed loop response and is determined by solving a linear equation using the least squares method an example is given to demonstrate the availability of the proposed technique

modified scaling relation for the random field ising model abstract we investigate the low temperature critical behavior of the three dimensional random field ising ferromagnet by a scaling analysis we find that in the limit of temperature t 0 the usual scaling relations have to be modified as far as the exponent of the specific heat is concerned at zero temperature the rushbrooke equation is modified to 2 1 an equation which we expect to be valid also for other systems with similar critical behavior we test the scaling theory numerically for the three dimensional random field ising system with gaussian probability distribution of the random fields by a combination of calculations of exact ground states with an integer optimization algorithm and monte carlo methods by a finite size scaling analysis we calculate the critical exponents 1 0 0 05 2 9 1 5 and 0 55

three dimensional antiferromagnetic q state potts models application of the wang landau algorithm we apply a newly proposed monte carlo method the wang landau algorithm to the study of the three dimensional antiferromagnetic q state potts models on a simple cubic lattice we systematically study the phase transition of the models with q 3 4 5 and 6 we obtain the finite temperature phase transition for q 3 and 4 whereas the transition temperature is down to zero for q 5 for q 6 there exists no order for any temperature we also study the ground state properties the size dependence of the ground state entropy is investigated we find that the ground state entropy is larger than the contribution from the typical configurations of the broken sublattice symmetry state for q 3 the same situations are found for q 4 5 and 6

the random field ising model with an asymmetric trimodal probability distribution the ising model in the presence of a random field is investigated within the mean field approximation based on landau expansion the random field is drawn from the trimodal probability distribution p hi p hi h0 q hi h0 r hi where the probabilities p q r take on values within the interval 0 1 consistent with the constraint p q r 1 asymmetric distribution hi is the random field variable and h0 the respective strength this probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites the current random field ising system displays second order phase transitions which for some values of p q and h0 are followed by first order phase transitions thus confirming the existence of a tricritical point and in some cases two tricritical points also reentrance can be seen for appropriate ranges of the aforementioned variables using the variational principle we determine the equilibrium equation for magnetization solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h0

monte carlo analysis of the critical properties of the two dimensional randomly bond diluted ising model via wang landau algorithm abstract the influence of random bond dilution on the critical properties of the two dimensional ising model on a square lattice with periodic boundary conditions is presented using the monte carlo process with wang landau sampling the lattice linear size is l 20 140 and the concentration of the diluted bonds spans a wide range from weak to strong dilution namely q 0 05 0 1 0 2 0 3 0 4 the respective percolation limit for the square lattice is q c p e r c 0 5 its pure version q 0 has a second order phase transition with vanishing specific heat critical exponent an example of inapplicability of the harris criterion the main effort is focused on the temperature dependence of the specific heat and magnetic susceptibility to estimate the respective maximum values and subsequent pseudocritical temperatures for extracting the relative critical exponents we have also looked at the probability distribution of the susceptibility pseudocritical temperature and specific heat for assessing self averaging the study is carried out in the appropriately restricted but dominant energy subspaces by applying the finite size scaling analysis the critical exponents are estimated the specific heat exponent vanishes the correlation length exponent is equal to one and the critical exponents ratio retains its pure ising model value thus supporting the strong universality hypothesis

determining the density of states for classical statistical models a random walk algorithm to produce a flat histogram we describe an efficient monte carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models the density of states is modified at each step when the energy level is visited to produce a flat histogram by carefully controlling the modification factor we allow the density of states to converge to the true value very quickly even for large systems from the density of states at the end of the random walk we can estimate thermodynamic quantities such as internal energy and specific heat capacity by calculating canonical averages at any temperature using this method we not only can avoid repeating simulations at multiple temperatures but we can also estimate the free energy and entropy quantities that are not directly accessible by conventional monte carlo simulations this algorithm is especially useful for complex systems with a rough landscape since all possible energy levels are visited with the same probability as with the multicanonical monte carlo technique our method overcomes the tunneling barrier between coexisting phases at first order phase transitions in this paper we apply our algorithm to both first and second order phase transitions to demonstrate its efficiency and accuracy we obtained direct simulational estimates for the density of states for two dimensional ten state potts models on lattices up to 200 x 200 and ising models on lattices up to 256 x 256 our simulational results are compared to both exact solutions and existing numerical data obtained using other methods applying this approach to a three dimensional j spin glass model we estimate the internal energy and entropy at zero temperature and using a two dimensional random walk in energy and order parameter space we obtain the rough canonical distribution and energy landscape in order parameter space preliminary data suggest that the glass transition temperature is about 1 2 and that better estimates can be obtained with more extensive application of the method this simulational method is not restricted to energy space and can be used to calculate the density of states for any parameter by a random walk in the corresponding space

real time dynamics in spin 1 2 chains with adaptive time dependent density matrix renormalization group we investigate the influence of different interaction strengths and dimerizations on the magnetization transport in antiferromagnetic spin 1 2 phantom rule 0 3em 0ex xxz chains we focus on the real time evolution of the inhomogeneous initial state ensuremath mid ensuremath uparrow ensuremath cdots ensuremath uparrow ensuremath downarrow ensuremath cdots ensuremath downarrow in using the adaptive time dependent density matrix renormalization group adaptive t dmrg time scales accessible to us are of the order of 100 units of time measured in ensuremath hbar j for almost negligible error in the observables we find ballistic magnetization transport for small s z s z interaction and arbitrary dimerization but almost no transport for stronger s z s z interaction with a sharp crossover at j z 1 additionally we perform a detailed analysis of the error made by the adaptive time dependent dmrg using the fact that the evolution in the xx model is known exactly we find that the error at small times is dominated by the error made by the trotter decomposition whereas for longer times the dmrg truncation error becomes the most important with a very sharp crossover at some runaway time overall errors are extremely small before the runaway time

understanding and improving the wang landau algorithm we present a mathematical analysis of the wang landau algorithm prove its convergence and identify sources of errors and strategies for optimization in particular we found the histogram increases uniformly with small fluctuations after a stage of initial accumulation and the statistical error is found to scale as sqrt mathrm ln phantom rule 0 2em 0ex f with the modification factor f this has implications for strategies for obtaining fast convergence

solutions of the divergence operator on john domains if rn is a bounded domain the existence of solutions u w01 p of divu f for f lp with vanishing mean value and 1 p is a basic result in the analysis of the stokes equations it is known that the result holds when is a lipschitz domain and that it is not valid for domains with external cusps in this paper we prove that the result holds for john domains our proof is constructive the solution u is given by an explicit integral operator acting on f to prove that u w01 p we make use of the calderon zygmund singular integral operator theory and the hardy littlewood maximal function for domains satisfying the separation property introduced in s buckley p koskela sobolev poincare implies john math res lett 2 5 1995 577 593 and 1 p n we also prove a converse result thus characterizing in this case the domains for which a continuous right inverse of the divergence exists in particular our result applies to simply connected planar domains because they satisfy the separation property

continuous phase transitions with a convex dip in the microcanonical entropy the appearance of a convex dip in the microcanonical entropy of finite systems usually signals a first order transition however a convex dip also shows up in some systems with a continuous transition as for example in the baxter wu model and in the four state potts model in two dimensions we demonstrate that the appearance of a convex dip in those cases can be traced back to a finite size effect the properties of the dip are markedly different from those associated with a first order transition and can be understood within a microcanonical finite size scaling theory for continuous phase transitions results obtained from numerical simulations corroborate the predictions of the scaling theory

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

phase behavior under the averaging over disorder realizations abstract effects of the averaging over disorder realizations samples on the phase behavior are analyzed in terms of the mean field approximation for the random field ising model with infinite range interactions it is found that the averaging is equivalent to a drastic modification in the statistics of the quenched variables in its turn this lowers the critical temperature of a second order phase transition or depending on the sampling even suppresses the ordered phase possible first order transitions are shown to be softened by the sample averaging common issues and differences in the interpretation of these effects in the context of the simulation and experimental studies are discussed

lack of self averaging of the specific heat in the three dimensional random field ising model we apply the recently developed critical minimum energy subspace scheme for the investigation of the random field ising model we point out that this method is well suited for the study of this model the density of states is obtained via the wang landau and broad histogram methods in a unified implementation by employing the n fold version of the wang landau scheme the random fields are obtained from a bimodal distribution h i ifmmode pm else textpm fi 2 and the scaling of the specific heat maxima is studied on cubic lattices with sizes ranging from l 4 to l 32 observing the finite size scaling behavior of the maxima of the specific heats we examine the question of saturation of the specific heat the lack of self averaging of this quantity is fully illustrated and it is shown that this property may be related to the question mentioned above

entropic sampling of simple polymer models within wang landau algorithm in this paper we apply a new simulation technique proposed in wang and landau wl 2001 phys rev lett 86 2050 to sampling of three dimensional lattice and continuous models of polymer chains distributions obtained by homogeneous unconditional random walks are compared with results of entropic sampling es within the wl algorithm while homogeneous sampling gives reliable results typically in the range of 4 5 orders of magnitude the wl entropic sampling yields them in the range of 20 30 orders and even larger with comparable computer effort a combination of homogeneous and wl sampling provides reliable data for events with probabilities down to 10 35 for the lattice model we consider both the athermal case self avoiding walks saws and the thermal case when an energy is attributed to each contact between nonbonded monomers in a self avoiding walk for short chains the simulation results are checked by comparison with the exact data in wl calculations for chain lengths up to n 300 scaling relations for saws are well reproduced in the thermal case distribution over the number of contacts is obtained in the n range up to n 100 and the canonical averages internal energy heat capacity excess canonical entropy mean square end to end distance are calculated as a result in a wide temperature range the continuous model is studied in the athermal case by sorting conformations of a continuous phantom freely joined n bonded chain with a unit bond length over a stochastic variable the minimum distance between nonbonded beads we determine the probability distribution for the n bonded chain with hard sphere monomer units over its diameter a in the complete diameter range 0 a 2 within a single es run this distribution provides us with excess specific entropy for a set of diameters a in this range calculations were made for chain lengths up to n 100 and results were extrapolated to n for a in the range 0 a 1 25

finite size scaling analysis of the critical behavior of the baxter wu model abstract we use the recently developed critical minimum energy subspace crmes approximation scheme to study the critical behavior of the baxter wu model this scheme uses only a properly determined part of the energy spectrum and allows us to obtain high accuracy for relatively large systems with considerably reduced computational effort the density of states is constructed by a multi range wang landau sampling and from this we obtain the critical properties of specific heat and of the reduced binder cummulant the good agreement of our results with existing exact solutions demonstrates the accuracy of our approximation technique

the random field ising model with an asymmetric and anisotropic bimodal probability distribution abstract the ising model in the presence of a random field drawn from the asymmetric and anisotropic trimodal probability distribution p h i p h i h 0 q h i h 0 r h i is investigated the partial probabilities p q r take on values within the interval 0 1 consistent with the constraint p q r 1 asymmetric distribution h i is the random field variable with basic absolute value h 0 strength is the competition parameter which is the ratio between the respective strength of the random magnetic field in the two principal directions z and z and is positive so that the random fields are competing anisotropic distribution this probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites the current random field ising system displays mainly second order phase transitions which for some values of p q and h 0 are followed by first order phase transitions joined smoothly by a tricritical point occasionally two tricritical points appear implying another second order phase transition in addition to these points re entrant phenomena can be seen for appropriate ranges of the temperature and random field for specific values of p and q using the variational principle we write down the equilibrium equation for the magnetization and solve it for both phase transitions and at the tricritical point in order to determine the magnetization profile with respect to h 0 considered as an independent variable in addition to the temperature

simultaneous analysis of several models in the three dimensional ising universality class we investigate several three dimensional lattice models believed to be in the ising universality class by means of monte carlo methods and finite size scaling these models include spin 1 models with nearestneighbor interactions on the simple cubic and on the diamond lattice for the simple cubic lattice we also include models with third neighbor interactions of varying strength and some equivalent neighbor models also included are a spin 1 model and a hard core lattice gas separate analyses of the numerical data confirm the ising like critical behavior of these systems on this basis we analyze all these data simultaneously such that the universal parameters occur only once this leads to an improved accuracy the thermal magnetic and irrelevant exponents are determined as y t51 5868 3 y h52 4816 1 and y i520 821 5 respectively the binder ratio is estimated as q5 m 2 2 m 4 50 62 341 4

convergence rates in l 2 for elliptic homogenization problems we study rates of convergence of solutions in l2 and h1 2 for a family of elliptic systems mathcal l varepsilon with rapidly oscillating coefficients in lipschitz domains with dirichlet or neumann boundary conditions as a consequence we obtain convergence rates for dirichlet neumann and steklov eigenvalues of mathcal l varepsilon most of our results which rely on the recently established uniform estimates for the l2 dirichlet and neumann problems in kenig and shen math ann 350 867 917 2011 commun pure appl math 64 1 44 2011 are new even for smooth domains

uniform w 1 p estimates for systems of linear elasticity in a periodic medium abstract let l e be a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients we obtain the uniform w 1 p estimate u e p c f p in a lipschitz domain in r n for solutions to the dirichlet problem l e u e div f in and u e 0 on where 1 p 1 2 1 2 n and c 0 are constants independent of e 0 the ranges are sharp for n 2 or 3

finite size scaling of the three dimensional conserved order parameter ising model via wang landau algorithm abstract the critical properties of the conserved order parameter cop version of the three dimensional ising model with zero magnetization were investigated by means of the monte carlo mc wang landau algorithm the study was carried out in appropriate restricted but dominant energy subspaces the main effort was focused on the specific heat and binder energy cumulant by using the density of states of the model for lattices with linear size l 4 60 by applying finite size scaling analysis the estimated values for the thermal critical exponent y t and critical temperature k c are in agreement with the considered as best values leading to the conclusion that this model belongs to the ising universality class the analysis revealed the necessity of corrections to scaling functions for interpreting correctly the mc data

the probability distribution of the spectral form factor in random matrix theory we determine the probability distribution of the spectral form factor from random matrix theory in the orthogonal and unitary case we show that it is an exponential one parametrized by the average value of this quantity

backbone exponents of the two dimensional q state potts model a monte carlo investigation we determine the backbone exponent x b of several critical and tricritical q state potts models in two dimensions the critical systems include the bond percolation the ising the q 2 sqrt 3 3 and 4 state potts and the baxter wu model and the tricritical ones include the q 1 potts model and the blume capel model for this purpose we formulate several efficient monte carlo methods and sample the probability p2 of a pair of points connected via at least two independent paths finite size scaling analysis of p2 yields x b as 0 3566 2 0 2696 3 0 2105 3 and 0 127 4 for the critical q 2 sqrt 3 1 2 3 and 4 state potts model respectively at tricriticality we obtain x b 0 0520 3 and 0 0753 6 for the q 1 and 2 potts model respectively for the critical q 0 potts model it is derived that x b 3 4 from a scaling argument we find that at tricriticality x b reduces to the magnetic exponent as confirmed by the numerical results

ising spin glass under continuous distribution random magnetic fields tricritical points and instability lines the effects of random magnetic fields are considered in an ising spin glass model defined in the limit of infinite range interactions the probability distribution for the random magnetic fields is a double gaussian which consists of two gaussian distributions centered respectively at h0 andh0 presenting the same width it is argued that such a distribution is more appropriate for a theoretical description of real systems than its simpler particular two well known limits namely the single gaussian distribution h0 and the bimodal one 0 the model is investigated by means of the replica method and phase diagrams are obtained within the replica symmetric solution critical frontiers exhibiting tricritical points occur for different values of with the possibility of two tricritical points along the same critical frontier to our knowledge it is the first time that such a behavior is verified for a spin glass model in the presence of a continuous distribution random field which represents a typical situation of a real system the stability of the replica symmetric solution is ana lyzed and the usual almeida thouless instability is verified for low temperatures it is verified that the higher temperature tricritical point always appears in the region of stability of the replica symmetric solution a condition involving the parameters h0 and for the occurrence of this tricritical point only is obtained analytically some of our results are discussed in view of experimental measurements available in the literature spin glass systems 1 5 continue to challenge many re searchers in the area of magnetism from the theoretical point of view its simplest version defined in terms of ising spin variables the so called ising spin glass isg represents one of the most fascinating problems in the physics of dis ordered magnets the isg mean field solution based on the infinite range interaction model as proposed by sherrington and kirkpatrick sk6 presents a quite nontrivial behav ior the correct low temperature solution of the sk model is defined in terms of a continuous order parameter function 7 i e an infinite number of order parameters associated with many low energy states a procedure which is usually de nominated as replica symmetry breaking rsb further more a transition in the presence of an external magnetic field known as the almeida thouless at line 8 is found in the solution of the sk model such a line separates a low temperature region characterized by rsb from a high temperature one where a simple one parameter solution de nominated as replica symmetric rs solution is stable the validity of the results of the sk model for the description of more realistic systems characterized by short range interac tions represents a very polemic question 5 recent numeri cal simulations claim the absence of an at line in the three dimensional short range isg 9 as well as along the non mean field region of a one dimensional isg characterized by long range interactions 10 however these results ob tained with rather small lattice size simulations do not rule out the possibility of a crossover to a different scenario at much larger lattice sizes or also for smaller fields and or temperatures one candidate for alternative theory to the sk model is the droplet model 11 based on domain wall renormalization group arguments for spin glasses 12 13 according to the droplet model the low temperature phase of any finite dimensional short range spin glass should be described in terms of a single thermodynamic state together of course with its corresponding time reversed counterpart i e essentially a rs type solution many important features of the isg still deserve an appropriate understanding within the droplet model scenario and in particular the validity of this model becomes questionable for increasing dimension alities where one expects the existence of a finite upper criti cal dimension above which the mean field picture should prevail

the efficient determination of the percolation threshold by a frontier generating walk in a gradient the frontier in gradient percolation is generated directly by a type of self avoiding random walk the existence of the gradient permits one to generate an infinite walk on a computer of finite memory from this walk the percolation threshold pc for a two dimensional lattice can be determined with apparently maximum efficiency for a naive monte carlo calculation or n 12 for a square lattice the value pc 0 592745 or 0 000002 is found for a simulation of n 2 6 1011 total steps occupied and blocked perimeter sites the power of the method is verified on the kagome site percolation case

model reduction of digital systems using discrete walsh series this study discusses the application of discrete walsh series expansion to reduce the order of a linear time invariant digital system described by z transfer function the approach is based on matching the discrete walsh spectra to determine both the coefficients of the denominator and numerator of the reduced model the proposed method is simple for computation can preserve the dynamic characteristic of the original model satisfactorily and guarantees to have the same zero initial response as the original system

efficient energy cumulants for the baxter wu model abstract in this paper using both analytic methods and monte carlo simulations with our triangle cluster algorithm we illustrate the scaling behavior of two possible 4th order connected energy cumulants across the well known second and first order phase transitions of the baxter wu model under zero external magnetic field it is found that 4th order connected energy cumulant introduced by janke provides a very good theoretical tool for finding and distinguishing phase transitions especially in case the order parameter of a particular model is hardly known also the physical importance of the cumulants local minima and maxima is investigated showing that they are finite size scaling effects

combined methods for model reduction via discrete laguerre polynomials abstract model reduction of linear discrete systems by matching the discrete laguerre spectra of the unit step responses of the original and reduced models is first discussed in order to preserve the stable property of the original model combined methods which use conventional stable methods to determine the parameters of denominator of the reduced models and use the discrete laguerre spectrum matching to determine the parameters of the numerator are discussed

the sherrington kirkpatrick spin glass model in the presence of a random field with a joint gaussian probability density function for the exchange interactions and random fields abstract the magnetic systems with disorder form an important class of systems which are under intensive studies since they reflect real systems such a class of systems is the spin glass one which combines randomness and frustration the sherrington kirkpatrick ising spin glass with random couplings in the presence of a random magnetic field is investigated in detail within the framework of the replica method the two random variables exchange integral interaction and random magnetic field are drawn from a joint gaussian probability density function characterized by a correlation coefficient the thermodynamic properties and phase diagrams are studied with respect to the natural parameters of both random components of the system contained in the probability density the de almeida thouless line is explored as a function of temperature and other system parameters the entropy for zero temperature as well as for non zero temperatures is partly negative or positive acquiring positive branches as h 0 increases

monte carlo and series study of corrections to scaling in the baxter wu model abstract we compare the results of extensive monte carlo simulations with the exact solution and the series expansion for the baxter wu model analysis of the series and of the monte carlo simulations show the leading corrections to the critical magnetization and energy to be nonanalytic and compatible with the exact solution an in depth discussion of the uniqueness of parameter determination for both cases is given

the l p regularity problem for the stokes system on lipschitz domains we study the lp regularity problem for the stationary stokes system on lipschitz domains for any p 2 we show that a weak reverse holder inequality with exponent p is both necessary and sufficient for the solvability of the regularity problem with data in w1 p lnp we also obtain the w1 p estimate u lp q lp f lp in a bounded lipschitz domain rd for solutions to the dirichlet problem u q div f div u 0 in and u 0 on where 1p 12 12d e

effective field theory for the ising model with a fluctuating exchange integral in an asymmetric bimodal random magnetic field a differential operator technique abstract the spin 1 2 ising model on a square lattice with fluctuating bond interactions between nearest neighbors and in the presence of a random magnetic field is investigated within the framework of the effective field theory based on the use of the differential operator relation the random field is drawn from the asymmetric and anisotropic bimodal probability distribution p h i p h i h 1 q h i c h 1 where the site probabilities p q take on values within the interval 0 1 with the constraint p q 1 h i is the random field variable with strength h 1 and c the competition parameter which is the ratio of the strength of the random magnetic field in the two principal directions z and z c is considered to be positive resulting in competing random fields the fluctuating bond is drawn from the symmetric but anisotropic bimodal probability distribution p j i j 1 2 j i j j j i j j where j and represent the average value and standard deviation of j i j respectively we estimate the transition temperatures phase diagrams for various values of the system s parameters c p h 1 susceptibility and equilibrium equation for magnetization which is solved in order to determine the magnetization profile with respect to t and h 1

avoiding boundary effects in wang landau sampling a simple modification of the wang landau sampling algorithm removes the systematic error that occurs at the boundary of the range of energy over which the random walk takes place in the original algorithm

uniform regularity estimates in homogenization theory of elliptic systems with lower order terms on the neumann boundary problem abstract in this paper we mainly employed the idea of the previous paper 34 to study the sharp uniform w 1 p estimates with 1 p for more general elliptic systems with the neumann boundary condition on a bounded c 1 domain arising in homogenization theory based on the skills developed by z shen in 27 and by t suslina in 31 32 we also established the l 2 convergence rates on a bounded c 1 1 domain and a lipschitz domain respectively here we found a rough version of the first order correctors see 1 12 which can unify the proof in 27 and 32 it allows us to skip the corresponding convergence results on r d that are the preconditions in 31 32 our results can be regarded as an extension of 23 developed by c kenig f lin z shen as well as of 32 investigated by t suslina

new monte carlo algorithm entropic sampling we present a new monte carlo sampling algorithm with which one can obtain any desired distribution of the sampling in one monte carlo simulation the free energy and the entropy of a system can thus be obtained from a simple exercise of this algorithm the main idea is to sample directly the entropy of a system at infinite temperature importance sampling is shown to be a particular case of the new algorithm the algorithm is tested against the exact partition function of the ital l 4 simple cubic ising model a comparison with the multicanonical ensemble for the ital l 12 ital q 10 potts model shows that the new algorithm is more general and more efficient

on w1 p estimates for elliptic equations in divergence form first we will apply the method to study w 1 p regularity for a nonlinear elliptic operator in divergence form we would like to point out that in the particular case of a linear elliptic equation this method gives an alternative proof to the classical one which uses the general theory of singular integrals the utility of the method that we describe below is that hypotheses a and b are obtained directly by studying the deviation of the coefficients of a from the coefficients of a0 and this is usually not a difficult task a more interesting application of this kind of approximation method is to elliptic homogenization problems for which we obtain results that give w 1 p estimates with a weak hypothesis of regularity in the coefficients for instance we are able to study the following cases

analysis parameter estimation and optimal control of time delay systems via chebyshev series the chebyshev delay operational matrix is introduced first and then applied to approximate the solutions of linear time invariant and time varying delay systems with arbitrary time delay the parameter identification problem of the delay control system is also studied furthermore an approximate solution of the optimal control problem with quadratic performance measure is then discussed four examples are given and the results are shown to be very accurate and satisfactory

lipschitz estimates in almost periodic homogenization we establish uniform lipschitz estimates for second order elliptic systems in divergence form with rapidly oscillating almost periodic coefficients we give interior estimates as well as estimates up to the boundary in bounded c1 domains with either dirichlet or neumann data the main results extend those in the periodic setting due to avellaneda and lin for interior and dirichlet boundary estimates and later kenig lin and shen for the neumann boundary conditions in contrast to these papers our arguments are constructive and thus the constants are in principle computable and the results for the neumann conditions are new even in the periodic setting since we can treat nonsymmetric coefficients we also obtain uniform w1 p estimates 2015 wiley periodicals inc

convergence rates and w1 p estimates in homogenization theory of stokes systems in lipschitz domains abstract concerned with the stokes systems with rapidly oscillating periodic coefficients we mainly extend the recent works in 19 20 to those in term of lipschitz domains the arguments employed here are quite different from theirs and the basic idea comes from 37 originally motivated by 23 27 33 we obtain an almost sharp o e ln r 0 e convergence rate in l 2 space and a sharp o e error estimate in l 2 d d 1 space by a little stronger assumption under the dimensional condition d 2 we also establish the optimal o e convergence rate on pressure terms in l 2 space then utilizing the convergence rates we can derive the w 1 p estimates uniformly down to microscopic scale e without any smoothness assumption on the coefficients where 1 p 1 2 1 2 d and is a positive constant independent of e combining the local estimates based upon vmo coefficients consequently leads to the uniform w 1 p estimates here the proofs do not rely on the well known compactness methods

convergence rates in homogenization of stokes systems abstract this paper studies the convergence rates in l 2 and h 1 of dirichlet problems for stokes systems with rapidly oscillating periodic coefficients without any regularity assumptions on the coefficients

estimation of critical behavior from the density of states in classical statistical models we present a simple and efficient approximation scheme which greatly facilitates the extension of wang landau sampling or similar techniques in large systems for the estimation of critical behavior the method presented in an algorithmic approach is based on a very simple idea familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem it is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters it is proposed that the extensions of the finite size critical part of the energy space determining the specific heat satisfy a scaling law involving the thermal critical exponent the method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic ising lattices the proposed scaling law is verified by estimating the thermal critical exponent from the finite size behavior of the critical part of the energy space the density of states of the zero field ising model on these lattices is obtained via a multirange wang landau sampling

periodic homogenization of green and neumann functions for a family of second order elliptic operators with rapidly oscillating periodic coefficients we study the asymptotic behavior of the green and neumann functions using dirichlet and neumann correctors as a result we obtain asymptotic expansions of poisson kernels and the dirichlet to neumann maps as well as optimal convergence rates in lp and w1 p for solutions with dirichlet or neumann boundary conditions 2014 wiley periodicals inc

wang landau study of the critical behavior of the bimodal 3d random field ising model we apply the wang landau method to the study of the critical behavior of the three dimensional random field ising model with a bimodal probability distribution for high values of the random field intensity we find that the energy probability distribution at the transition temperature is double peaked suggesting that the phase transition is first order on the other hand the transition looks continuous for low values of the field intensity in spite of the large sample to sample fluctuations observed the double peak in the probability distribution is always present for high fields

baxter wu model in the presence of an external magnetic field abstract in this work we study an unusual phase transition of the baxter wu model in the presence of an external magnetic field the model is pure baxter wu which means that only three spin interactions are taken into account we construct a phase diagram on the temperature field plane based mainly on the singularities of the specific heat these singularities are more clearly observed than those of the magnetic susceptibility which are used in existing works we establish a discontinuity in the critical exponents when the field is changed from zero to negative

entropic sampling via wang landau random walks in dominant energy subspaces dominant energy subspaces of statistical systems are defined with the help of restrictive conditions on various characteristics of the energy distribution such as the probability density and the fourth order binder s cumulant our analysis generalizes the ideas of the critical minimum energy subspace crmes technique applied previously to study the specific heat s finite size scaling here we illustrate alternatives that are useful for the analysis of further finite size anomalies and the behavior of the corresponding dominant subspaces is presented for the two dimensional 2d baxter wu and the 2d and 3d ising models in order to show that a crmes technique is adequate for the study of magnetic anomalies we study and test simple methods which provide the means for an accurate determination of the energy order parameter e m histograms via wang landau random walks the 2d ising model is used as a test case and it is shown that high level wang landau sampling schemes yield excellent estimates for all magnetic properties our estimates compare very well with those of the traditional metropolis method the relevant dominant energy subspaces and dominant magnetization subspaces scale as expected with exponents alpha nu and gamma nu respectively using the metropolis method we examine the time evolution of the corresponding dominant magnetization subspaces and we uncover the reasons behind the inadequacy of the metropolis method to produce a reliable estimation scheme for the tail regime of the order parameter distribution

critical endpoint behavior in an asymmetric ising model application of wang landau sampling to calculate the density of states using the wang landau sampling method with a two dimensional random walk we determine the density of states for an asymmetric ising model with two and three body interactions on a triangular lattice in the presence of an external field with an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite size analyses at and away from the critical endpoint we observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint and the exponents for both divergences agree well with previous theoretical predictions

strong violation of critical phenomena universality wang landau study of the two dimensional blume capel model under bond randomness we study the pure and random bond versions of the square lattice ferromagnetic blume capel model in both the first order and second order phase transition regimes of the pure model phase transition temperatures thermal and magnetic critical exponents are determined for lattice sizes in the range l 20 100 via a sophisticated two stage numerical strategy of entropic sampling in dominant energy subspaces using mainly the wang landau algorithm the second order phase transition emerging under random bonds from the second order regime of the pure model has the same values of critical exponents as the two dimensional ising universality class with the effect of the bond disorder on the specific heat being well described by double logarithmic corrections our findings thus supporting the marginal irrelevance of quenched bond randomness on the other hand the second order transition emerging under bond randomness from the first order regime of the pure model has a distinctive universality class with nu 1 30 6 and beta nu 0 128 5 these results amount to a strong violation of universality principle of critical phenomena since these two second order transitions with different sets of critical exponents are between the same ferromagnetic and paramagnetic phases furthermore the latter of these two sets of results supports an extensive but weak universality since it has the same magnetic critical exponent but a different thermal critical exponent as a wide variety of two dimensional systems with and without quenched disorder in the conversion by bond randomness of the first order transition of the pure system to second order we detect by introducing and evaluating connectivity spin densities a microsegregation that also explains the increase we find in the phase transition temperature under bond randomness

monte carlo study of the pure and dilute baxter wu model we studied the pure and dilute baxter wu bw models using the wang landau wl sampling method to calculate the density of states dos we first used the exact result for the dos of the ising model to test our code then we calculated the dos of the dilute ising model to obtain a phase diagram in good agreement with previous studies we calculated the energy distribution together with its first second and fourth moments to give the specific heat and the energy fourth order cumulant better known as the binder parameter for the pure bw model for small samples the energy distribution displayed a doubly peaked shape and finite size scaling analysis showed the expected reciprocal scaling of the positions of the peaks with l the energy distribution yielded the expected bw 2 3 critical exponent for the specific heat the binder parameter minimum appeared to scale with lattice size l with an exponent b equal to the specific heat exponent its location temperature showed a large correction to scaling term 1 0 248 0 025 for the dilute bw model we found a clear crossover to a single peak in the energy distribution even for small sizes and the expected 0 was recovered

lack of self averaging in random systems liability or asset abstract the study of quenched random systems is facilitated by the idea that the ensemble averages describe the thermal averages for any specific realization of the couplings provided that the system is large enough careful examination suggests that this idea might have a flaw when the correlation length becomes of the order of the size of the system we find that certain bounded quantities are not self averaging when the correlation length becomes of the order of the size of the system this suggests that the lack of self averaging expressed in terms of properly chosen signal to noise ratios may serve to identify phase boundaries this is demonstrated by using such signal to noise ratios to identify the boundary of the ferromagnetic phase of the random field ising system and compare the findings with more traditional measures

energy level statistics and time relaxation in quantum systems we study a quantum mechanical system prepared at t50 in a model state that subsequently decays into a sea of other states whose energy levels form a discrete spectrum with given statistical properties an important quantity is the survival probability p t defined as the probability at time t to find the system in the original model state our main purpose is to analyze the influence of the discreteness and statistical properties of the spectrum on the behavior of p t since p t itself is a statistical quantity we restrict our attention to its ensemble average p t which is calculated analytically using random matrix techniques within certain approximations discussed in the text we find for p t an exponential decay followed by a revival governed by the two point structure function of the statistical spectrum thus giving a nonzero asymptotic value for large t s the analytic result compares well with a number of computer simulations over a time range discussed in the text s1063 651x 97 03603 9

replica exchange algorithm and results for the three dimensional random field ising model the random field ising model with gaussian disorder is studied using a different monte carlo algorithm the algorithm combines the advantages of the replica exchange method and the two replica cluster method and is much more efficient than the metropolis algorithm for some disorder realizations three dimensional systems of size 24 3 are studied each realization of disorder is simulated at a value of temperature and uniform field that is adjusted to the phase transition region for that disorder realization energy and magnetization distributions show large variations from one realization of disorder to another for some realizations of disorder there are three well separated peaks in the magnetization distribution and two well separated peaks in the energy distribution suggesting a first order transition

critical behavior of the two dimensional spin diluted ising model via the equilibrium ensemble approach the equilibrium ensemble approach to disordered systems is used to investigate the critical behavior of the two dimensional ising model in the presence of quenched random site dilution the numerical transfer matrix technique in semi infinite strips of finite width together with phenomenological renormalization and conformal invariance is particularly suited to putting the equilibrium ensemble approach to work a method by which to extract with great precision the critical temperature of the model is proposed and applied a more systematic finite size scaling analysis than in previous numerical studies has been performed a parallel investigation along the lines of the two main scenarios currently under discussion namely the logarithmic corrections scenario with critical exponents fixed in the ising universality class versus the weak universality scenario critical exponents varying with the degree of disorder is carried out in interpreting our data maximum care is constantly taken to be open to both possibilities a critical discussion shows that an unambiguous discrimination between the two scenarios is still not possible on the basis of the available finite size data s1063 651x 99 16110 5

scaling properties of the baxter wu model abstract we use a recently developed cluster algorithm for the baxter wu model to study characteristic features of its behavior magnetic scaling properties of the model are investigated for second order phase transitions we improve significantly the accuracy of monte carlo simulation results and we provide new results for the behavior of the binder cumulants for temperatures below above and at the critical point

multicritical points and crossover mediating the strong violation of universality wang landau determinations in the random bond d 2 blume capel model the effects of bond randomness on the phase diagram and critical behavior of the square lattice ferromagnetic blume capel model are discussed the system is studied in both the pure and disordered versions by the same efficient two stage wang landau method for many values of the crystal field restricted here in the second order phase transition regime of the pure model for the random bond version several disorder strengths are considered we present phase diagram points of both pure and random versions and for a particular disorder strength we locate the emergence of the enhancement of ferromagnetic order observed in an earlier study in the ex first order regime the critical properties of the pure model are contrasted and compared to those of the random model accepting for the weak random version the assumption of the double logarithmic scenario for the specific heat we attempt to estimate the range of universality between the pure and random bond models the behavior of the strong disorder regime is also discussed and a rather complex and yet not fully understood behavior is observed it is pointed out that this complexity is related to the ground state structure of the random bond version

criticality in the randomness induced second order phase transition of the triangular ising antiferromagnet with nearest and next nearest neighbor interactions abstract using a wang landau entropic sampling scheme we investigate the effects of quenched bond randomness on a particular case of a triangular ising model with nearest j n n and next nearest neighbor j n n n antiferromagnetic interactions we consider the case r j n n n j n n 1 for which the pure model is known to have a columnar ground state where rows of nearest neighbor spins up and down alternate and undergo a weak first order phase transition from the ordered to the paramagnetic state with the introduction of quenched bond randomness we observe the effects signaling the expected conversion of the first order phase transition to a second order phase transition and using the lee kosterlitz method we quantitatively verify this conversion the emerging under random bonds continuous transition shows a strongly saturating specific heat behavior corresponding to a negative exponent and belongs to a new distinctive universality class with 1 135 11 1 744 9 and 0 124 8 thus our results for the critical exponents support an extensive but weak universality and the emerged continuous transition has the same magnetic critical exponent but a different thermal critical exponent as a wide variety of two dimensional 2d systems without and with quenched disorder

critical energy distribution function of the baxter wu model abstract in this work we examine the critical finite size scaling behavior of the energy probability distribution function and its corresponding binder cumulant at critical point based on the results of monte carlo simulations at zero external magnetic field using the recently developed triangle cluster algorithm we calculate the energy distribution function s exponents and we derive the scaling relations for the energy binder cumulant finally we predict the exact form of the scaled energy distribution function most of our conclusions seem applicable not only to the baxter wu model but also to other ising like models

first order transition features of the triangular ising model with nearest and next nearest neighbor antiferromagnetic interactions abstract we implement a new and accurate numerical entropic scheme to investigate the first order transition features of the triangular ising model with nearest neighbor j nn and next nearest neighbor j nnn antiferromagnetic interactions in ratio r j nn j nnn 1 important aspects of the existing theories of first order transitions are briefly reviewed tested on this model and compared with previous work on the potts model using lattices with linear sizes l 30 40 100 120 140 160 200 240 360 and 480 we estimate the thermal characteristics of the present weak first order transition our results improve the original estimates of rastelli et al and verify all the generally accepted predictions of the finite size scaling theory of first order transitions including transition point shifts thermal and magnetic anomalies however two of our findings are not compatible with current phenomenological expectations the behavior of transition points derived from the number of phases parameter is not in accordance with the theoretically conjectured exponentially small shift behavior and the well known double gaussian approximation does not correctly describe higher correction terms of the energy cumulants it is argued that this discrepancy has its origin in the commonly neglected contributions from domain wall corrections

simple methods for the shift transformation matrix direct product matrix and summation matrix of discrete walsh series this paper presents new easy methods for directly obtaining the shift transformation matrix direct product matrix and summation matrix of discrete walsh series the proposed methods can be conveniently implemented with a digital computer they will be very useful in the study of control systems via discrete walsh series

universality and double critical end points a double critical end point in the two dimensional spin 3 2 blume capel model is studied via extensive monte carlo simulations the resultant scaling character of the probability distribution of the mixing scaling operators allows us to locate the double critical end point precisely and also to convincingly show that it indeed belongs to the same universality class as the critical points

the random field ising model with asymmetric bimodal probability distribution abstract the ising model in the presence of a random field is investigated within the mean field approximation based on landau expansion the random field is drawn from the bimodal probability distribution p h p h h 0 1 p h h 0 where the probability p assumes any value within the interval 0 1 asymmetric distribution the prevailing transitions are of second order but for some values of p and h 0 first order phase transitions take place for smaller temperatures and higher h 0 thus confirming the existence of a tricritical point also the possible reentrant phenomena in the phase diagram t h 0 plane occur for appropriate values of p and h 0 using the variational principle we determine the equilibrium equation for magnetization and solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h 0

indicators of quantum chaos based on eigenvector statistics expansion coefficients of the coherent states in the basis of hamiltonian eigenstates contain information about the local character of motion of a quantum system the author analyses three quantities the minimal number of relevant eigenvectors the sum of moduli of coefficients and the shannon entropy of a coherent state and show that all of them might be used as indicators of quantum chaos they also allow one to distinguish between three known universality classes results obtained are confirmed by a numerical study of kicked tops

self averaging in many body quantum systems out of equilibrium time dependence of distributions in a disordered system a quantity is self averaging when the ratio between its variance for disorder realizations and the square of its mean decreases as the system size increases here we consider a chaotic disordered many body quantum system and search for a relationship between self averaging behavior and the properties of the distributions over disorder realizations of various quantities and at different timescales an exponential distribution as found for the survival probability at long times explains its lack of self averaging since the mean and the dispersion are equal gaussian distributions however are obtained for both self averaging and non self averaging quantities our studies show also that one can make conclusions about the self averaging behavior of one quantity based on the distribution of another related quantity this strategy allows for semianalytical results and thus circumvents the limitations of numerical scaling analysis which are restricted to few system sizes

finite size scaling at first and second order phase transitions of baxter wu model abstract using a finite size phenomenological theory we investigate the behavior of the baxter wu model for both first and second order transitions in order to distinguish between the two kinds of transition we study the finite size scaling behavior of the order parameter and the susceptibility of the model at the critical temperature the known critical exponents of the system govern the scaling behavior while below the critical temperature the scaling exponents are the dimensionality of the system the presented scaling theory for the baxter wu model is an appropriate generalization of the corresponding theory of binder and landau for the ising model binder and landau phys rev b 30 1984 1477 we perform numerical simulations using standard monte carlo techniques and we find that our results are in good agreement with theoretical predictions

conformal invariance studies of the baxter wu model and a related site colouring problem the partition function of the baxter wu model is exactly related to the generating function of a site colouring problem on a hexagonal lattice we extend the original bethe ansatz solution of these models in order to obtain the eigenspectra of their transfer matrices in finite geometries and general toroidal boundary conditions the operator content of these models is studied by solving numerically the bethe ansatz equations and by exploring conformal invariance since the eigenspectra are calculated for large lattices the corrections to finite size scaling are also calculated