the construction of preconditioners for elliptic problems by substructuring i in earlier parts of this series of papers we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems the resulting algorithms are well suited for implementation on computers with parallel architecture in this paper we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners the iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns these preconditioners involve an incomplete chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods

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

short time critical dynamics of the ising model studied within the n fold algorithm abstract the short time behaviour of the critical two dimensional ising model is studied for the bortz kalos lebowitz n fold way algorithm bkl algorithm for square lattices of linear sizes l 110 128 140 170 and 200 we calculate the short time critical behaviour for the bkl algorithm and also for the heat bath algorithm comparison of these results shows that although power law scaling form emerges from the early times of the dynamics there are noticeable differences which do not produce negligible effects on the estimates of critical exponents the observed universality of short time critical behaviour supplements our fundamental knowledge of critical phenomena however short time dynamics seem to be related only approximately with equilibrium critical properties therefore any attempt to estimate equilibrium critical exponents from the short time regime would be superfluous except for the purpose of comparison because these exponents have been determined very precisely by different methods

finite size scaling properties of the damage distance and dynamical critical exponent for the ising model abstract with the damage spreading method scaling properties of the damage distance on the ising model with heat bath dynamics are studied numerically with the parallel flipping scheme the scaling curves fall on two curves which depend on the odd or even lattice sizes the both scaling curves give the consistent dynamical exponent as z 2 16 0 04 for d 2 and z 2 09 0 05 for d 3 respectively by shifting one of them two curves overlap each other perfectly meanwhile all the scaling curves obtained by single spin flipping processes with different odd or even lattice sizes fall on a single curve from which the consistent dynamical critical exponent with the parallel scheme is obtained z 2 18 0 02 for d 2 and z 2 08 0 04 for d 3

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

exact two cell correlations in random cellular structures generated from a 2d ising ferromagnet abstract random 2d cellular structures are generated from distributions of spins given by a ferromagnetic ising model with nearest neighbour couplings on a square lattice topological correlations between pairs of neighbouring cells are expressed as rational functions of even number spin correlations involving two four and six spins which are exactly known for the square ising model the latter correlations have been calculated numerically in the vicinity of the curie point they agree with computer simulation results

time dependent critical properties of ising models by damage spreading abstract we use the method of damage spreading to study the time t taken for a spin at a distance r to be damaged for the first time in ising models with heat bath dynamics we report time dependent scaling exponents d t 2 0 1d 2 52 2d 2 26 3d and 2 0 4d if we assume that t r dt we also analyze our data assuming various forms of logarithmic corrections and we find that d t 2 25 or less 2d and 2 0 3d we argue that it is extremely plausible that d t is equal to z the dynamic critical exponent and thus our estimate of z in two dimensions is higher than the consensus value of 2 14 but we find good agreement in one three and four dimensions with the exact and expected values

monte carlo renormalization of the three dimensional ising model abstract we have investigated the simple cubic ising model by means of the monte carlo renormalization technique the emphasis of our study concerns the influence of truncation i e the dimensionality of the coupling subspace in which the analysis of the correlation functions generated by the monte carlo and spin blocking algorithms is performed to this purpose we have included up to 36 even and 21 odd couplings in our analysis we find that the increase in the number of couplings has a significant influence on the largest eigenvalues of the linearized renormalization transformation matrices these eigenvalues serve to estimate the renormalization exponents yi and yh remarkably we find no significant finite size effect on these eigenvalues when the maximum number of couplings is included in the analysis except for the smallest system sizes 83 43 after a suitable extrapolation to the fixed point we find good agreement with existing results for the critical exponents we have determined the critical point of the simple cubic ising model as k 0 221652 6 also in agreement with existing results

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

multicritical dynamics for the j ising model exact dynamical properties are discussed for the j ising model around the multicritical point mcp it is found that the relation of relaxations between the non equilibrium remanent magnetization m t and the equilibrium autocorrelation function q t at the mcp is different from that at the pure critical point the dynamic critical exponent for the ferromagnetic ordering defined by and that for the spin glass ordering defined by become identical at the mcp accurate numerical calculations for them are performed in two and three dimensions using the non equilibrium relaxation analysis the mcp is located at and the exponent is estimated as for the square lattice they are estimated as and for the simple cubic lattice

suitable iterative methods for solving the linear system arising in the three fields domain decomposition method abstract there are two approaches for applying substructuring preconditioner for the linear system corresponding to the discrete steklov poincare operator arising in the three fields domain decomposition method for elliptic problems one of them is to apply the preconditioner in a common way i e using an iterative method such as preconditioned conjugate gradient method s bertoluzza substructuring preconditioners for the three fields domain decomposition method i a n c n r 2000 and the other one is to apply iterative methods like for instance bi conjugate gradient method conjugate gradient square and etc which are efficient for nonsymmetric systems the preconditioned system will be nonsymmetric in this paper second approach will be followed and extensive numerical tests will be presented which imply that the considered iterative methods are efficient

non equilibrium critical dynamics of the two dimensional xy model with hamiltonian equations of motion non equilibrium critical dynamics of the two dimensional xy model is investigated with hamiltonian equations of motion critical relaxation starting from both ordered and random states is carefully analyzed and the short time dynamic scaling behavior is revealed logarithmic corrections to scaling are detected for relaxation with a random initial state while power law corrections to scaling are observed for relaxation with an ordered initial state the static exponent and dynamic exponent z are determined around and below the kosterlitz thouless phase transition temperature our results show that the deterministic dynamics described by hamiltonian equations is in the same universality class as the stochastic dynamics described by monte carlo algorithms and langevin equations

a level set based iga formulation for topology optimization of flexoelectric materials abstract this paper presents a design methodology based on a combination of isogeometric analysis iga level set and point wise density mapping techniques for topology optimization of piezoelectric flexoelectric materials the fourth order partial differential equations pdes of flexoelectricity which require at least c 1 continuous approximations are discretized using non uniform rational b spline nurbs the point wise density mapping technique with consistent derivatives is directly used in the weak form of the governing equations the boundary of the design domain is implicitly represented by a level set function the accuracy of the iga model is confirmed through numerical examples including a cantilever beam under a point load and a truncated pyramid under compression with different electrical boundary conditions finally we provide numerical examples demonstrating the significant enhancement in electromechanical coupling coefficient that can be obtained using topology optimization

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

critical slowing down in local dynamics simulations the author reports some universal and non universal aspects of the critical dynamics of the three dimensional ising model obtained in extensive monte carlo finite size simulations the author shows that the time dependence of the magnetization of finite lattices is composed of two kinds of fluctuations at the critical point i phase fluctuations from one metastable minimum of the free energy to the other dominating the long time behaviour of the magnetization ii critical fluctuations inside each minimum decaying on a comparatively short timescale both kinds of fluctuations show up the same critical exponent z 2 10 or 0 02 which is also in excellent agreement with the exponent z of energy fluctuations

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

short time dynamics and magnetic critical behavior of the two dimensional random bond potts model the critical behavior in the short time dynamics for the random bond potts ferromagnet in two dimensions is investigated by short time dynamic monte carlo simulations the numerical calculations show that this dynamic approach can be applied efficiently to study the scaling characteristic which is used to estimate the critical exponents straight theta beta nu and z for quenched disordered systems from the power law behavior of the kth moments of magnetization

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

substructuring preconditioners for the three fields domain decomposition method we study a class of preconditioners based on substructuring for the discrete steklov poincare operator arising in the three fields formulation of domain decomposition in two dimensions under extremely general assumptions on the discretization spaces involved an upper bound is provided on the condition number of the preconditioned system which is shown to grow at most as log h h 2 h and h denoting respectively the diameter and the discretization mesh size of the subdomains extensive numerical tests performed on both a plain and a stabilized version of the method confirm the optimality of such bound

the extended finite element method with new crack tip enrichment functions for an interface crack between two dissimilar piezoelectric materials summary this paper studies the static fracture problems of an interface crack in linear piezoelectric bimaterial by means of the extended finite element method x fem with new crack tip enrichment functions in the x fem crack modeling is facilitated by adding a discontinuous function and crack tip asymptotic functions to the classical finite element approximation within the framework of the partition of unity in this work the coupled effects of an elastic field and an electric field in piezoelectricity are considered corresponding to the two classes of singularities of the aforementioned interface crack problem namely class and class two classes of crack tip enrichment functions are newly derived and the former that exhibits oscillating feature at the crack tip is numerically investigated computation of the fracture parameter i e the j integral using the domain form of the contour integral is presented excellent accuracy of the proposed formulation is demonstrated on benchmark interface crack problems through comparisons with analytical solutions and numerical results obtained by the classical fem moreover it is shown that the geometrical enrichment combining the mesh with local refinement is substantially better in terms of accuracy and efficiency copyright 2015 john wiley sons ltd

comparison of monte carlo results for the 3d ising interface tension and interface energy with extrapolated series expansions abstract we compare monte carlo results for the interface tension and interface energy of the 3 dimensional ising model with pade and inhomogeneous differential approximants of the low temperature series that was recently extended by arisue to 17th order in u exp 4 the series is expected to suffer from the roughening singularity at u 0 196 the comparison with the monte carlo data shows that the pade and inhomogeneous differential approximants fail to improve the truncated series result of the interface tension and the interface energy in the region around the roughening transition the monte carlo data show that the specific heat displays a peak in the smooth phase neither the truncated series nor the pade approximants find this peak we also compared monte carlo data for the energy of the asos model with the corresponding low temperatures series that we extended to order u12

stochastic isogeometric analysis of free vibration of functionally graded plates considering material randomness abstract the paper is to develop stochastic isogeometric analysis for the free vibration of functionally graded plates with spatially varying random material properties the isogeometric analysis method is employed in the new stochastic analysis scheme which is called stochastic isogeometric analysis siga the elastic modulus and mass density are modeled as homogeneous gaussian random fields along the plane of structure the governing equation of stochastic isogeometric analysis for free vibration of functionally graded plates is derived in conjunction with perturbation expansions to predict the first and second moments of eigenvalues in order to verify proposed method the brute force monte carlo simulation is employed the mean variance and cov coefficient of variation predicted by siga and those predicted by monte carlo simulation show good agreement the numerical examples demonstrate that the randomness of material properties affects significantly the structural responses of the functionally graded plates the correlation between elastic modulus and mass density is also observed to have significant effect on the response cov of eigenvalue

effective analysis of damage spreading in ising models using large lattices and different methods of simulation and analysis the kinetic critical exponent z for damage spreading is shown to be consistent with z 2 in two to five dimensions without the logarithmic problems seen in some earlier work

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

a level set method for structural topology optimization this paper presents a new approach to structural topology optimization we represent the structural boundary by a level set model that is embedded in a scalar function of a higher dimension such level set models are flexible in handling complex topological changes and are concise in describing the boundary shape of the structure furthermore a well founded mathematical procedure leads to a numerical algorithm that describes a structural optimization as a sequence of motions of the implicit boundaries converging to an optimum solution and satisfying specified constraints the result is a 3d topology optimization technique that demonstrates outstanding flexibility of handling topological changes fidelity of boundary representation and degree of automation we have implemented the algorithm with the use of several robust and efficient numerical techniques of level set methods the benefit and the advantages of the proposed method are illustrated with several 2d examples that are widely used in the recent literature of topology optimization especially in the homogenization based methods

multicritical points for spin glass models on hierarchical lattices the locations of multicritical points on many hierarchical lattices are numerically investigated by the renormalization group analysis the results are compared with an analytical conjecture derived by using the duality the gauge symmetry and the replica method we find that the conjecture does not give the exact answer but leads to locations slightly away from the numerically reliable data we propose an improved conjecture to give more precise predictions of the multicritical points than the conventional one this improvement is inspired by a different point of view coming from the renormalization group and succeeds in deriving very consistent answers with many numerical data doi 10 1103 physreve 77 061116

modeling holes and inclusions by level sets in the extended finite element method a methodology to model arbitrary holes and material interfaces inclusions without meshing the internal boundaries is proposed the numerical method couples the level set method s osher j a sethian j comput phys 79 1 1988 12 to the extended finite element method x fem n moes j dolbow t belytschko int j numer methods engrg 46 1 1999 131 in the x fem the finite element approximation is enriched by additional functions through the notion of partition of unity the level set method is used for representing the location of holes and material interfaces and in addition the level set function is used to develop the local enrichment for material interfaces numerical examples in two dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique

time evolution of damage in the ising model the time evolution of the damage in the ising model with the heat bath and glauber dynamics has been investigated with the damage spreading method the damage density d t and the average distance r t of damaged sites from the origin have been measured numerically from the simulational data the scaling forms have been established as d t tx r t t1z and d t r t df and the corresponding exponents x z and df have been estimated

a meshfree method for inverse wave propagation using collocation and radial basis functions abstract a stable and highly accurate meshfree scheme based on strong form collocation associated with radial basis functions and explicit time integration is proposed to solve ill posed inverse wave propagation problems tikhonov regularization technique and the l curve criterion are employed to deal with the noise measurement data before solving the governing equation to get a stable solution appropriate weights are first derived for imposing boundary conditions and known conditions from the measurement data to yield the optimal convergence for inverse problems compared to the required iterative procedures in common methods no iteration is needed in the proposed method which leads to the time saving computation and avoids the instability resulting from the iterative methods dispersion analysis describes that this method has much less dispersion error than the classical finite element method fem and popular weak form meshfree methods and stability analysis is performed to predict the critical time step for the explicit time integration another outstanding advantage of this method is that it is effortless to extend the solution scheme of one dimensional inverse problem to high dimensional inverse problems furthermore the influences of the high noise into measurement data are evaluated which demonstrate that even handling with very high noise in the input data the proposed algorithm can achieve stable and high accuracy solutions

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

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

plane problems in piezoelectric media with defects abstract a two dimensional electroelastic analysis is performed on a transversely isotropic piezoelectric material containing defects a general solution is provided in terms of complex potentials with emphasis being placed on stress concentrations that arise in the vicinity of circular and elliptical holes it is shown that for this genre of problem both mechanical and electrical variables are responsible for the peak stresses

detection of multiple flaws in piezoelectric structures using xfem and level sets abstract an iterative procedure to solve the inverse problem of detecting multiple voids in piezoelectric structure is proposed in each iteration the forward problem is solved for various void configurations and at each iteration the mechanical and electrical responses of a piezoelectric structure is minimized at known specific points along the boundary to match the measured data the extended finite element method xfem is employed for determining the responses as it allows the use of a fixed mesh for varying void geometries the numerical method based on combination of classical shape derivative and of the level set method for front propagation used in structural optimization is utilized to minimize the cost function the results obtained show that this method is effectively able to determine the number of voids in a piezoelectric structure and its corresponding locations and shapes

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

non equilibrium dynamics of the ising model for t less than equal totc the growth of order in ising models with nonconserved order parameter is considered for quenches to final temperatures tf 0 and tf tc the results of numerical simulations in spatial dimension d 2 are presented in all cases a scaling regime is entered for sufficiently long times where the characteristic length scale is the domain size l t approximately t12 for tf 0 and the nonequilibrium correlation length xi t approximately t1z for tf tc the equal time correlation function has the expected scaling forms f r l t and r d 2 eta fc r xi t for tf 0 and tc respectively the scaling function fc x has interesting short distance behaviour which is elucidated using scaling arguments and by in and 1 n expansions the t 0 scaling function f x depends on whether the spin correlations present in the initial conditions are of long or short range as does the exponent which describes the decay of the autocorrelation function a t si t si o approximately l t results for a quench from the equilibrium critical state to tf 0 are consistent with theoretical predictions

locations of multicritical points for spin glasses on regular lattices we present an analysis leading to precise locations of the multicritical points for spin glasses on regular lattices the conventional technique for determination of the location of the multicritical point was previously derived using a hypothesis emerging from duality and the replica method in the present study we propose a systematic technique by an improved technique giving more precise locations of the multicritical points on the square triangular and hexagonal lattices by carefully examining the relationship between two partition functions related with each other by the duality we can find that the multicritical points of the ifmmode pm else textpm fi j ising model are located at p c 0 890 phantom rule 0 2em 0ex 813 on the square lattice where p c means the probability of j ij j g0 at p c 0 835 phantom rule 0 2em 0ex 985 on the triangular lattice and at p c 0 932 phantom rule 0 2em 0ex 593 on the hexagonal lattice these results are in excellent agreement with recent numerical estimations

a homogenization method for shape and topology optimization abstract shape and topology optimization of a linearly elastic structure is discussed using a modification of the homogenization method introduced by bendsoe and kikuchi together with various examples which may justify validity and strength of the present approach for plane structures

multi spin flip dynamics of the ising chain abstract two kinds of multi spin flip discrete time dynamics of the ising chain are solved analytically one dynamics is the two sublattice type flip and each sublattice contains n sequential spins alternately the other has the overlapped multi spin flip sequence the state of n spins at the next time step is selected from 2 n states using the heat bath type transition probability these dynamics of the ising chain are equivalent to the statics of the square lattice ising model with a 1 2 unit cell or of the triangular lattice ising model the analytic solutions of the single spin relaxation time of these dynamics are obtained using these equivalences

improved implementation and robustness study of the x fem for stress analysis around cracks numerical crack propagation schemes were augmented in an elegant manner by the x fem method the use of special tip enrichment functions as well as a discontinuous function along the sides of the crack allows one to do a complete crack analysis virtually without modifying the underlying mesh which is of industrial interest especially when a numerical model for crack propagation is desired this paper improves the implementation of the x fem method for stress analysis around cracks in three ways first the enrichment strategy is revisited the conventional approach uses a topological enrichment only the elements touching the front are enriched we suggest a geometrical enrichment in which a given domain size is enriched the improvements obtained with this enrichment are discussed second the conditioning of the x fem both for topological and geometrical enrichments is studied a preconditioner is introduced so that off the shelf iterative solver packages can be used and perform as well on x fem matrices as on standard fem matrices the preconditioner uses a local nodal cholesky based decomposition third the numerical integration scheme to build the x fem stiffness matrix is dramatically improved for tip enrichment functions by the use of an ad hoc integration scheme a 2d benchmark problem is designed to show the improvements and the robustness

critical exponents of the dilute ising model from four loop expansions four loop expansions of the coefficients of the callan symanzik equation for 3d and 2d dilute ising models are calculated fixed point coordinates and critical exponents are estimated by two methods of summation of double series a generalisation of the pade borel approximation and the first confluent form of the e algorithm of wynn summation of the double series for the 2d dilute ising model gives exponents very close to exponents of the pure ising model in accordance with the exact solution

symmetry complexity and multicritical point of the two dimensional spin glass we analyse models of spin glasses on the two dimensional square lattice by exploiting symmetry arguments the replicated partition functions of the ising and related spin glasses are shown to have many remarkable symmetry properties as functions of the edge boltzmann factors it is shown that the applications of homogeneous and hadamard inverses to the edge boltzmann matrix indicate reduced complexities when the elements of the matrix satisfy certain conditions suggesting that the system has special simplicities under such conditions using these duality and symmetry arguments we present a conjecture on the exact location of the multicritical point in the phase diagram

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

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

dynamical rushbrooke s inequality for nonequilibrium relaxation process an inequality for dynamic critical exponents is proved for relaxation processes of arbitrary magnetic systems this is a dynamical extension of rushbrooke s inequality it can be applied to any continuous transition systems with various dynamics the relation is demonstrated on the result of nonequilibrium relaxation analysis of fluctuations applied to the three dimensional ferromagnetic ising model

series and monte carlo study of high dimensional ising models ising models in high dimensions are used to compare high temperature series expansions with monte carlo simulations simulations of the magnetization on four six and seven dimensional hypercubic lattices give consistent values of the critical temperature from both equilibrium and nonequilibrium data ford 6 and 7 we tabulate 15 terms of series expansions for the susceptibility for generald and givej kbtc 0 092295 3 and 0 077706 2 ford 6 and 7 in contrast to five dimensions where earlier series found nonanalytic scaling corrections for d 6 and 7 the leading scaling correction may be analytic int tc in most cases these expansions gave more accurate results than these simulations

dynamic exponent for 2d ising model by power spectra method we consider power spectra for fluctuating quantities at a critical point p omega varies as omega phi where phi is determined by the dynamic exponent z and static exponents specific to the quantity considered from the magnetization spectra obtained with simulations z is found to be 2 13 or 0 03 for the two dimensional glauber kinetic ising model hence in accord with recent monte carlo relaxational studies but at odds with those obtained by series expansion and damage spreading methods excellent dynamic finite size scaling for system sizes l 10 to 128 supports our estimate

self averaging distribution of pseudocritical temperatures and finite size scaling in critical disordered systems we evaluate by monte carlo simulations various singular thermodynamic quantities x for ensembles of quenched random ising and ashkin teller models the measurements are taken at t c and we study how the distributions p x and in particular their relative squared width r x over the ensemble depend on the system size l the ashkin teller model was studied in the regime where bond randomness is irrelevant and we found weak self averaging r x ensuremath sim l ensuremath alpha ensuremath nu ensuremath rightarrow 0 where ensuremath alpha l0 and ensuremath nu are the exponents of the pure model fixed point governing the transition for the site dilute ising model on a cubic lattice known to be governed by a random fixed point we find that r x tends to a constant as predicted by aharony and harris we tested whether this constant is universal however this constant is different for canonical and grand canonical disorder we identify the pseudocritical temperature of each sample i t c i l as the temperature at which the susceptibility reaches its maximal value ensuremath chi mathrm max the distribution of these sample dependent t c i l was investigated we found that its variance scales as ensuremath delta t c l 2 ensuremath sim l ensuremath 2 ensuremath nu our previously proposed finite size scaling ansatz for disordered systems was tested and found to hold we did observe deviations from a single function which imply that sample dependent scaling functions are needed these deviations are however relatively small and hence to obtain a fixed statistical error it may be more computationally efficient to measure ensuremath chi mathrm max than the commonly used ensuremath chi t c ensuremath infty

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

critical dynamics a consequence of a random stepwise growth of clusters critical dynamics of correlated particles here glauber dynamics of singly flipping ising spins is explained by a random stepwise growth and contraction of clusters as follows at equilibrium a cluster of size s is described by its length l a random walk like path connecting a sequence of neighbor spins the length scales as l s where constitutes a new static critical exponent we assume that on the average the random growth of a cluster from zero to size s and length ls requires a sequence of l2 spin flips this gives for dynamic critical exponent z 2 where and are the usual static exponents exact results at dimension d 1 and 4 and simulation results at d 2 and 3 support the theory

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

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

structural optimization using sensitivity analysis and a level set method in the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level set method for front propagation we implement this method in two and three space dimensions for a model of linear or nonlinear elasticity we consider various objective functions with weight and perimeter constraints the shape derivative is computed by an adjoint method the cost of our numerical algorithm is moderate since the shape is captured on a fixed eulerian mesh although this method is not specifically designed for topology optimization it can easily handle topology changes however the resulting optimal shape is strongly dependent on the initial guess

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

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

a polytree based adaptive polygonal finite element method for multi material topology optimization abstract this study presents a polytree based adaptive methodology for multi material topology optimization mmtop polytree data structure is introduced as a general recursive multi level mesh that is automatically refined in processing based on error analysis in order to resolve hanging nodes in element edges the wachspress coordinate is employed on a reference element before using a mapping scheme to obtain shape functions and their derivatives for any polygons a new definition of filter radius is also proposed to improve the efficiency of filters and optimized results the combination of polytree meshes and adaptive filters not only clarifies the interfaces between material phases including void phase but also decreases the computing time of the overall process in comparison to using the regular fine meshes several benchmark and practical problems are considered to show distinct features of the proposed method

duality in finite dimensional spin glasses we present an analysis leading to a conjecture on the exact location of the multicritical point in the phase diagram of spin glasses in finite dimensions the conjecture in satisfactory agreement with a number of numerical results was previously derived using an ansatz emerging from duality and the replica method in the present paper we carefully examine the ansatz and reduce it to a hypothesis on analyticity of a function appearing in the duality relation thus the problem is now clearer than before from a mathematical point of view the ansatz somewhat arbitrarily introduced previously has now been shown to be closely related to the analyticity of a well defined function

sensitivity and uncertainty analysis for flexoelectric nanostructures abstract in this paper sensitivity analysis has been applied to identify the key input parameters influencing the energy conversion factor ecf of flexoelectric materials the governing equations of flexoelectricity are modeled by a nurbs based iga formulation exploiting their higher order continuity and hence avoiding a complex mixed formulation the examined input parameters include model and material properties and the sampling has been obtained using the latin hypercube sampling lhs method in the probability space the sensitivity of the model output to each of the input parameters at different aspect ratios of the beam is quantified by three various common methods i e morris one at a time moat pce sobol and extended fourier amplitude sensitivity test efast the numerical results indicate that the flexoelectric constants are the most dominant factors influencing the uncertainties in the energy conversion factor in particular the transversal flexoelectric coefficient h 12 moreover the model parameters also show considerable interaction effects of the material properties

xfem based crack detection scheme using a genetic algorithm a new computational tool is developed for the accurate detection and identification of cracks in structures to be used in conjunction with non destructive testing of specimens it is based on the solution of an inverse problem based on some measurements typically along part of the boundary of the structure that describe the response of the structure to vibration in a chosen frequency or a combination of frequencies the goal is to estimate whether the structure contains a crack and if so to find the parameters location size orientation and shape of the crack that produces a response closest to the given measurement data in some chosen norm the inverse problem is solved using a genetic algorithm ga the ga optimization process requires the solution of a very large amount of forward problems the latter are solved via the extended finite element method xfem this enables one to employ the same regular mesh for all the forward problems performance of the method is demonstrated via a number of numerical examples involving a cracked flat membrane various computational aspects of the method are discussed including the a priori estimation of the ill posedness of the crack identification problem copyright 2007 john wiley sons ltd

implementation of regularized isogeometric boundary element methods for gradient based shape optimization in two dimensional linear elasticity the present work addresses shape sensitivity analysis and optimization in two dimensional elasticity with a regularized isogeometric boundary element method igabem non uniform rational b splines are used both for the geometry and the basis functions to discretize the regularized boundary integral equations with the advantage of tight integration of design and analysis the application of igabem in shape optimization reduces the mesh generation regeneration burden greatly the work is distinct from the previous literatures in igabem shape optimization mainly in two aspects 1 the structural and sensitivity analysis takes advantage of the regularized form of the boundary integral equations eliminating completely the need of evaluating strongly singular integrals and jump terms and their shape derivatives which were the main implementation difficulty in igabem and 2 although based on the same computer aided design cad model the mesh for structural and shape sensitivity analysis is separated from the geometrical design mesh thus achieving a balance between less design variables for efficiency and refined mesh for accuracy this technique was initially used in isogeometric finite element method and was incorporated into the present igabem implementation

analysis of three dimensional crack initiation and propagation using the extended finite element method an erratum has been published for this article in international journal for numerical methods in engineering 2005 63 8 1228 we present a new formulation and a numerical procedure for the quasi static analysis of three dimensional crack propagation in brittle and quasi brittle solids the extended finite element method xfem is combined with linear tetrahedral elements a viscosity regularized continuum damage constitutive model is used and coupled with the xfem formulation resulting in a regularized crack band version of xfem the evolving discontinuity surface is discretized through a c0 surface formed by the union of the triangles and quadrilaterals that separate each cracked element in two the element s properties allow a closed form integration and a particularly efficient implementation allowing large scale 3d problems to be studied several examples of crack propagation are shown illustrating the good results that can be achieved copyright 2005 john wiley sons ltd

multilevel preconditioning this paper is concerned with multilevel techniques for preconditioning linear systems arising from galerkin methods for elliptic boundary value problems a general estimate is derived which is based on the characterization of besov spaces in terms of weighted sequence norms related to corresponding multilevel expansions the result brings out clearly how the various ingredients of a typical multilevel setting affect the growth rate of the condition numbers in particular our analysis indicates how to realize even uniformly bounded condition numbers for example the general results are used to show that the bramble pasciak xu preconditioner for piecewise linear finite elements gives rise to uniformly bounded condition numbers even when the refinements of the underlying triangulations are highly nonuniform furthermore they are applied to a general multivariate setting of refinable shift invariant spaces in particular covering those induced by various types of wavelets

the dynamic critical exponent of the three dimensional ising model we measure the dynamic exponent of the three dimensional ising model using a damage spreading monte carlo approach as described by macisaac and jan we simulate systems froml 5 tol 60 at the critical temperature tc 4 5115 we report a dynamic exponent z 2 35 0 05 a value much larger than the consensus value of 2 02 whereas if we assume logarithmic corrections we find thatz 2 05 0 05

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

damage spreading and critical exponents for model a ising dynamics abstract recent simulations by grassberger gave very precise estimates of the dynamical critical exponent z via damage spreading techniques we confirm these results using a slightly altered method and we examine larger systems up to 18161 2 and 695 2 giving z 2 18 0 02 and 2 04 0 01 respectively

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

an isogeometrical approach to structural level set topology optimization abstract this paper aims to utilize the isogeometric analysis iga for the level set structural topology optimization the level set function is parametrized using the non uniform rational b spline nurbs basis functions in a higher dimension the same basis functions are employed for approximating the unknown deformations geometry modeling of the design domain and the level set function in this research three optimization problems including minimization of the mean compliance considering a certain amount of material minimization of weight with avoiding local stress concentration as well as minimization of weight and strain energy under local stress constraints are dealt with the sensitivity analyses for the optimization problems are carried out to obtain velocity functions on the boundaries in order to move the boundaries towards optimum the hamilton jacobi h j equation is solved using the forward euler scheme in order to illustrate the performance of the method to obtain reasonable results with smooth boundaries several numerical examples are presented and compared with well known problems in literature

a polytree based adaptive polygonal finite element method for topology optimization of fluid submerged breakwater interaction abstract the polytree based adaptive polygonal finite element method was recently proved to be very efficient for a wide class of mechanics problems in this study we further exploit its advantages for topology optimization of fluid submerged breakwater interaction due to the inherent limitations of triangular and quadrilateral elements for topology optimization an alternative formulation of using arbitrary polygons based on the wachspress coordinate is employed for structural domain in addition we use a polytree based adaptive technique to enhance the accuracy for topology problem in structural domain with a minimum number of degrees of freedom dof we apply this method to fluid structure interaction fsi problems and then finding an optimal shape of submerged breakwater sbw which is as a special kind of coastal structure located in front of the beach and underwater to protect the landside from the erosion several numerical results demonstrate the effectiveness of the present method it is observed that the obtained results are in good agreement with reference solutions

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

description of critical dynamics by static geometry of clusters abstract critical slowing down of relaxation exponent z is modelled by clusters which grow and recede at the end of connected sequences of particles consequently the relaxation time of a cluster of size s is proportional to the number of back and forth steps needed to travel its typical connected length ls this and an assumption on mutual screening of ends lead to z 2 5 0 25 where is a static geometric exponent in ls s ising exponents measured elsewhere with the help of simulation give z in addition a flory like approximation is derived here it relates to and analytically giving z in d 2 3 and 4 respectively we findz 2 14 2 05 and 2 275 1 while z 2 17 4 and 2 04 4 both sets of values are in fair agreement with the literature

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