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

convergence of the fractional step lax friedrichs scheme and godunov scheme for the isentropic system of gas dynamics a convergence theorem of the fractional step lax friedrichs scheme and godunov scheme for an inhomogeneous system of isentropic gas dynamics 1 5 3 is established by using the framework of compensated compactness meanwhile a corresponding existence theorem of global solutions with large data containing the vacuum is obtained

the relaxation of the hydrodynamic model for semiconductors to the drift diffusion equations abstract we establish the convergence and consistency of approximate solutions derived by the modified godunov scheme for the initial boundary value problem to a simplified one dimensional hydrodynamic model for semiconductors using the compensated compactness method the traces of weak solutions are introduced and then the weak solutions are proved to satisfy the natural boundary conditions the zero relaxation limit of the hydrodynamic model to the drift diffusion model is proved when the momentum relaxation time tends to zero

pointwise error estimates of linear finite element method for neumann boundary value problems in a smooth domain pointwise error analysis of the linear finite element approximation for delta u u f in omega partial n u tau on partial omega where omega is a bounded smooth domain in mathbb r n is presented we establish o h 2 log h and o h error bounds in the l infty and w 1 infty norms respectively by adopting the technique of regularized green s functions combined with local h 1 and l 2 estimates in dyadic annuli since the computational domain omega h is only polyhedral one has to take into account non conformity of the approximation caused by the discrepancy omega h ne omega in particular the so called galerkin orthogonality relation utilized three times in the proof does not exactly hold and involves domain perturbation terms or boundary skin terms which need to be addressed carefully a numerical example is provided to confirm the theoretical result

the second generation shifted boundary method and its numerical analysis abstract recently the shifted boundary method sbm was proposed within the class of unfitted or immersed or embedded finite element methods by reformulating the original boundary value problem over a surrogate approximate computational domain the sbm avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning accuracy is maintained by modifying the original boundary conditions using taylor expansions hence the name of the method that shifts the location and values of the boundary conditions in this article we present enhanced variational sbm formulations for the poisson and stokes problems with improved flexibility and robustness these simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations first we show that these new sbm implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive second we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at dirichlet boundaries therefore avoiding the calibration of an additional stabilization parameter finally we prove enhanced l 2 estimates without the cumbersome assumption of earlier proofs that the surrogate domain is convex instead we rely on a conventional assumption that the boundary of the true domain is smooth which can also be replaced by requiring convexity of the true domain the aforementioned improvements open the way to a more general and efficient implementation of the shifted boundary method particularly in complex three dimensional geometries we complement these theoretical developments with numerical experiments in two and three dimensions

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

a priori and a posteriori error analyses of a high order unfitted mixed fem for stokes flow abstract we propose and analyze a high order unfitted mixed finite element method for the pseudostress velocity formulation of the stokes problem with dirichlet boundary condition on a fluid domain with curved boundary the method consists of approximating by a polyhedral subdomain d h with boundary h where a galerkin method is applied to approximate the solution and on a transferring technique based on integrating the extrapolated discrete gradient of the velocity to approximate the dirichlet boundary data on the computational boundary h the associated galerkin scheme is defined by raviart thomas elements of order k 0 for the pseudostress and discontinuous polynomials of degree k for the velocity provided suitable hypotheses on the mesh near the boundary we prove well posedness of the galerkin scheme by means of the babuska brezzi theory and establish the corresponding optimal convergence of o h k 1 moreover for the case when h is constructed through a piecewise linear interpolation of we propose a reliable and quasi efficient residual based a posteriori error estimator its definition makes use of a postprocessed velocity with enhanced accuracy to achieve the same rate of convergence of the method when the solution is smooth enough numerical experiments illustrate the performance of the scheme show the behavior of the associated adaptive algorithm and validate the theory

convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

universal meshes a method for triangulating planar curved domains immersed in nonconforming meshes summary we introduce a new method to triangulate planar curved domains that transforms a specific collection of triangles in a background mesh to conform to the boundary in the process no new vertices are introduced and connectivities of triangles are left unaltered the method relies on a novel way of parameterizing an immersed boundary over a collection of nearby edges with its closest point projection to guarantee its robustness we require that the domain be c2 regular the background mesh be sufficiently refined near the boundary and that specific angles in triangles near the boundary be strictly acute the method can render both straight edged and curvilinear triangulations for the immersed domain the latter includes curved triangles that conform exactly to the immersed boundary and ones constructed with isoparametric mappings to interpolate the boundary at select points high order finite elements constructed over these curved triangles achieve optimal accuracy which has customarily proven difficult in numerical schemes that adopt nonconforming meshes aside from serving as a quick and simple tool for meshing planar curved domains with complex shapes the method provides significant advantages for simulating problems with moving boundaries and in numerical schemes that require iterating over the geometry of domains with no conformity requirements the same background mesh can be adopted to triangulate a large family of domains immersed in it including ones realized over several updates during the coarse of simulating problems with moving boundaries we term such a background mesh as a universal mesh for the family of domains it can be used to triangulate universal meshes hence facilitate a framework for finite element calculations over evolving domains while using only fixed background meshes furthermore because the evolving geometry can be approximated with any desired order numerical solutions can be computed with high order accuracy we present demonstrative examples using universal meshes to simulate the interaction of rigid bodies with stokesian fluids copyright 2014 john wiley sons ltd

a low storage curvilinear discontinuous galerkin method for wave problems the low storage curvilinear discontinuous galerkin lsc dg method reduces the storage requirements for solving symmetric and linear linear symmetric conservation laws in curvilinear domains when compared to the standard discontinuous galerkin method we perform a semidiscrete a priori convergence analysis of lsc dg and determine sufficient conditions on sequences of meshes to guarantee the same rate of convergence as the original upwind dg method on curvilinear domains computational results confirm the optimal order convergence on sample mesh sequences that satisfy the sufficiency conditions additional results show that the sufficient conditions for optimal order convergence of lsc dg may also be necessary conditions

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

strong disorder paramagnetic ferromagnetic fixed point in the square lattice j ising model we consider the random bond j ising model on a square lattice as a function of the temperature t and of the disorder parameter p p 1 corresponds to the pure ising model we investigate the critical behavior along the paramagnetic ferromagnetic transition line at low temperatures below the temperature of the multicritical nishimori point at t 0 9527 1 p 0 89083 3 we present finite size scaling analyses of monte carlo results at two temperature values t 0 645 and t 0 5 the results show that the paramagnetic ferromagnetic transition line is reentrant for t t that the transitions are continuous and controlled by a strong disorder fixed point with critical exponents 1 50 4 0 128 8 and 0 095 5 this fixed point is definitely different from the ising fixed point controlling the paramagnetic ferromagnetic transitions for t t our results for the critical exponents are consistent with the hyperscaling relation 2 d 2 0

large time behavior of the solutions to a hydrodynamic model for semiconductors we establish the global existence of smooth solutions to the cauchy problem for the one dimensional isentropic euler poisson or hydrodynamic model for semiconductors for small initial data in particular we show that as t to infty these solutions converge to the stationary solutions of the drift diffusion equations the existence and uniqueness of stationary solutions to the drift diffusion equations are proved without the smallness assumption

a priori error analysis for hdg methods using extensions from subdomains to achieve boundary conformity we present the first a priori error analysis of a technique that allows us to numerically solve steady state diffusion problems defined on curved domains by using finite element methods defined in polyhedral subdomains dh for a wide variety of hybridizable discontinuous galerkin and mixed methods we prove that the order of convergence in the l2 norm of the approximate flux and scalar unknowns is optimal as long as the distance between the boundary of the original domain and that of the computational domain h is of order h we also prove that the l 2 norm of a projection of the error of the scalar variable superconverges with a full additional order when the distance between and h is of order h 5 4 but with only half an additional order when such a distance is of order h finally we present numerical experiments confirming the theoretical results and showing that even when the distance between and h is of order h the above mentioned projection of the error of the scalar variable can still superconverge with a full additional order

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

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

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

convergence of the godunov scheme for a simplified one dimensional hydrodynamic model for semiconductor devices convergence of approximate solutions derived by the godunov scheme for a simplified one dimensional hydrodynamic model for semiconductor devices is established by using the compensated compactness method a global existence theorem is shown and a numerical method for the computation of the physical global solution of this model is provided by this approach

duality analysis on random planar lattices the conventional duality analysis is employed to identify a location of a critical point on a uniform lattice without any disorder in its structure in the present study we deal with the random planar lattice which consists of the randomized structure based on the square lattice we introduce the uniformly random modification by the bond dilution and contraction on a part of the unit square the random planar lattice includes the triangular and hexagonal lattices in extreme cases of a parameter to control the structure a modern duality analysis fashion with real space renormalization is found to be available for estimating the location of the critical points with a wide range of the randomness parameter as a simple test bed we demonstrate that our method indeed gives several critical points for the cases of the ising and potts models and the bond percolation thresholds on the random planar lattice our method leads to not only such an extension of the duality analyses on the classical statistical mechanics but also a fascinating result associated with optimal error thresholds for a class of quantum error correction code the surface code on the random planar lattice which is known as a skillful technique to protect the quantum state

existence of the ferromagnetic phase in a random bond ising model on the square lattice extend griffiths 1972 arguments to show that there exists the thermodynamic limit in a quenched random bond ising model with competing interactions on the square lattice peierls 1936 arguments are extended to give 0 97394 for an upper bound of the critical concentration of the ferromagnetic phase for the system in which the exchange integrals take on j o and j with respective probabilities p and 1 p

analysis of the shifted boundary method for the stokes problem abstract the analysis of stability and accuracy of the shifted boundary method is developed for the stokes flow equations the key feature of the shifted boundary method an embedded finite element method is the shifting of the location where boundary conditions are applied from the true to a surrogate boundary and an appropriate modification shifting of the value of the boundary conditions an inf sup condition is proved for the variational formulation associated to the shifted boundary method and we derive by way of strang s second lemma an optimal error estimate in the natural sbm norm we also derive an l 2 error estimate for the velocity field by means of an extension of the aubin nitsche approach to embedded non consistent mixed finite element methods

upper bounds to the correlation functions of the random bond ising model and n vector model with competing interactions studies a correlation function which is given by the canonical average of a product of one or more spin variables for the random bond ising model in which the exchange integrals are j j o and j with probabilities p and 1 p respectively the authors show that an upper bound to the configurational average of the correlation functions calculated in the thermodynamic limit in the zero external field limit is the product of the same correlation function for the corresponding ferromagnetic ising model at the temperature under consideration and the same quantity at the temperature t1 which is determined by the condition t1 2j mod kb1n p 1 p mod where kb is the boltzmann constant the results are given for the random bond ising model of an arbitrary spin s and also for the diluted random bond ising models of an arbitrary spin s with the pair interaction and with general interaction and for the diluted and undiluted random bond n vector model

solving dirichlet boundary value problems on curved domains by extensions from subdomains we present a technique for numerically solving dirichlet boundary value problems for second order elliptic equations on domains omega with curved boundaries this is achieved by using suitably defined extensions from polyhedral subdomains textsf d h the problem of dealing with curved boundaries is thus reduced to the evaluations of simple line integrals the technique is independent of the representation of the boundary of the space dimension and allows for the use of only polyhedral elements we apply this technique to the hybridizable discontinuous galerkin method and provide extensive numerical experiments showing that the convergence properties of the resulting method are the same as those for the case in which omega textsf d h whenever the distance of textsf d h to partial omega is of order h in particular we find that when using polynomial approximations of degree k on the polyhedral subdomains textsf d h both the scalar and vector unknowns converge with the optimal order of k 1 in the whole domain omega for k ge0 moreover we also find that for k ge1 both a postprocessing of the scalar unknown in the polyhedral subdomain textsf d h as well as its extension from it converge with order k 2 the extension also converges with order 2 for k 0

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

the bipolar hydrodynamic model for semiconductors and the drift diffusion equations we establish the existence of entropy solutions for a bipolar hydrodynamic model for semiconductors we show also that the limit as the relaxation time goes to zero of an appropriate scaled sequence of entropy solutions is a solution of the classical drift diffusion equations

global solutions to the isothermal euler poisson system with arbitrarily large data abstract we prove the global existence of a solution to the euler poisson system with arbitrarily large data in a one dimensional geometry the pressure law we consider is deduced from an isothermal assumption for the electrons gas in this case nishida has already pointed out that the linear part of the glimm functional is decreasing with respect to time using a glimm scheme he used this property to construct globally defined weak solutions for the euler system with arbitrary large data we follow his outline of proof here a new difficulty arises with the source term due to the electric field a key point is that the glimm scheme is almost conservative this quasi conservation of charge leads to a uniform estimate of the total variation of the electric field this estimate allows to prove the convergence of the scheme