alternating direction implicit algorithm for unsteady potential flow art implicit finite difference scheme is presented for the efficient computation of unsteady potential flow about airfoils the formulation uses density and the velocity potential as dependent variables and is cast in conservation form to assure the theoretically correct determination of shockwave location and speed to enable boundary conditions to be imposed directly on the airfoil surface a time varying sheared rectilinear coordinate transformation is employed calculated time history solutions on a pulsating airfoil are compared with the results of other unsteady transonic codes including a previous method of the authors the present method is demonstrated to be unconditionally stable and to give accurate solutions with sharply resolved shocks

spin 32 ising model by the cluster variation method and the path probability method the spin 32 ising model hamiltonian with arbitrary bilinear j and biquadratic k pair interactions is studied by using the lowest approximation of the cluster variation method lacvm and the path probability method ppm with the point distribution first equilibrium properties of the model are presented briefly by using the lacvm in order to understand dynamics of the model easily then the ppm with the point distribution is applied to the model and the set of nonlinear differential equations which is also called the dynamic or rate equations is obtained these equations are solved by two different methods the first one is the runge kutta method and the second one is to express the solution of the equations by means of the flow diagram the results are also discussed

improvements and extensions to a full potential formulation based on independent fields the paper presents a full potential model for nonisentropic unsteady transonic flows extending a parent formulation based on an independent approximation of the density and velocity potential fields it retains the advantage of the existence of a velocity potential while granting a unique solution by combining a correction of the stagnation pressure behind a shock with a new form of kutta condition the solution procedure relies on an unstructured node based finite volume approximation with linear shape functions and nonreflecting far field boundary conditions animproved upwind density biasing allows the solution in supersonic regions to bestabilized a new proof is given for the linearized unconditional stability of the implicit solver adopted for subsupersonic asymptotic conditions numerical results show that the method can model euler solutions more accurately than an isentropic full potential formulation for both steady and unsteady conditions applications to asymptotically supersonic flows complete the numerical validation

inference by belief propagation in composite systems we devise a message passing algorithm for probabilistic inference in composite systems consisting of a large number of variables that exhibit weak random interactions among all variables and strong interactions with a small subset of randomly chosen variables the relative strength of the two interactions is controlled by a free parameter we examine the performance of the algorithm numerically on a number of systems of this type for varying mixing parameter values

pair correlations and structure factor of the j1 j2 square lattice ising model in an external field abstract we compute the structure factor of the j 1 j 2 ising model in an external field on the square lattice within the cluster variation method we use a four point plaquette approximation which is the minimal one able to capture phases with broken orientational order in real space like the recently reported ising nematic phase in the model the analysis of different local maxima in the structure factor allows us to track the different phases and phase transitions against temperature and external field although the nematic susceptibility is not directly related to the structure factor we show that because of the close relationship between the nematic order parameter and the structure factor the latter shows unambiguous signatures of the presence of a nematic phase in agreement with results from direct minimization of a variational free energy the disorder variety of the model is identified and the possibility that the cvm four point approximation be exact on the disorder variety is discussed

a new stream function formulation for the steady euler equations a new stream function formulation is presented for the solution of euler equations in the transonic flow region in this method the stream function and the density are the dependent variables the governing equations for adiabatic flow are then the momentum equations which are solved in the strong conservation law form the method differs from the recent formulation of hafez and lovell which is based on crocco s equation in that it does not require knowledge of the vorticity to study arbitrary geometries the algorithm is combined with the automatic grid solver grape of steger and sorenson results are presented for an naca 0012 airfoil at various mach numbers angles of attack and cylinders comparisons with other solutions of the euler equations show good agreement

development of an iterative boundary layer type solver for axisymmetric separated flows on presente un schema de couplage totalement implicite comparaison de la vitesse de convergence de ce schema avec d autres methodes de couplage resultats numeriques pour des ecoulements laminaires incompressibles decolles sur differentes geometries

laplace interaction law for the computation of viscous airfoil flow in low and high speed aerodynamics a new interaction law that accelerates convergence of interactive boundary layer methods is presented the law is derived from the laplace equation and allows the automatic implementation of the kutta condition for lifting airfoil flows the accurate influence coefficients of the laplace interaction law lil facilitate efficient prediction of high lift flows about multi element airfoil by direct numerical simulation taking into account suitable turbulent closure relations for boundary layer equations a fast and reliable computer code has been developed for industrial applications at deutsche aerospace airbus

finite element solutions of euler equations for lifting airfoils application d une formulation de clebsch des equations d euler aux ecoulements transsoniques autour de profils aerodynamiques

euler correction method for two and three dimensional transonic flows an euler correction method based on the clebsch formulation of the euler equations has been developed to improve shock calculations in full potential methods in the clebsch treatment of steady rotational flows the velocity is decomposed into potential and rotational components written in terms of scalar functions the potential part is computed from the continuity equation using a modified version of an existing finite volume full potential solver the rotational parts are determined analytically from the momentum equation based on small perturbation approximations the solutions obtained for airfoils and wing bodies are compared with those using the time marching euler methods the agreement between the results obtained using these two approaches is good

nonlinear functionals on c x and choquet integrals abstract we establish a retraction from monotone functionals defined on c x where x is a compact hausdorff space with pointwise convergence topology to functionals represented by choquet integrals with respect to monotone measures we prove an analogue of the riesz representation theorem in the case of choquet integrals

a note on the cluster variation method kikuchi s cluster variation method cvm is reformulated as the truncation of a mobius inversion an attempt is made to explicate and simplify the various approaches to the cvm this formulation makes apparent the connection of the method with other types of cluster approximation an illustration of the procedure is provided

non simple purely infinite c algebras the hausdorff case abstract local and global definitions of pure infiniteness for a c algebra a are compared and equivalence between them is obtained if the primitive ideal space of a is hausdorff and of finite dimension if a has real rank zero or if a is approximately divisible sufficient criteria are given for local pure infiniteness of tensor products they yield that exact simple tensorially non prime c algebras are purely infinite if they have no semi finite lower semi continuous trace one obtains that a is isomorphic to a o if a is 1 purely infinite separable stable nuclear and prim a is a hausdorff space not necessarily of finite dimension

the uniaxial brickwork model exact results and cvm approximation a complete phase diagram of the uniaxial brickwork lattice is determined first by using exact results and then by using the cluster variation method both results are in very good agreement which demonstrates the reliability of the cvm for two dimensional systems a well defined maximum in the exact specific heat and a divergence of the cvm susceptibility provide strong indication for the occurrence of a floating phase

q functions and extreme topological measures abstract q functions provide a method for constructing topological measures we give necessary and sufficient conditions for a composition of a q function and a topological measure to be a topological measure regular and extreme step q functions are characterized by certain regions in r n then extreme q functions are used to study extreme topological measures for example we prove under some assumptions on the underlying set that given n there are different types of extreme topological measures with values 0 1 n 1 in contrast in the case of measures the only extreme points are 0 1 valued i e point masses

quasi measures with image transformations as generalized variables we introduce an image transformation as a generalization of measurable maps structure properties of the image transformation is given unique extension of image transformations from solid sets is proven the multidimensional median and sample median are presented as image transformations providing a construction suitable for probability theorists

algebraic rings of integers and some 2d lattice problems in physics this paper develops the mobius inversion formula for the gaussian integers and eisenstein s integers and gives two applications the first application is to the two dimensional arithmetic fourier transform aft which is suitable for parallel processing the second application is to two dimensional inverse lattice problems and is illustrated with the recovery of interatomic potentials from the cohesive energy for monolayer graphite the paper demonstrates the potential application in the physical science of integral domains other than the standard integers

construction and properties of quasi linear functionals quasi linear functionals are shown to be uniformly continuous and decomposable into a difference of two quasi integrals a predual space for the quasi linear functionals inducing the weak topology is given general constructions of quasi linear functionals by solid set functions and q functions are given

new topologies in the phase diagram of the semi infinite blume capel model abstract the phase diagram of the blume capel model on a semi infinite simple cubic lattice with a 100 free surface is studied in the pair approximation of the cluster variation method six main topologies are found of which two are new due to the occurrence of a first order surface transition in the phase with ordered bulk separating two phases with large and small surface order parameters the latter is a new phase and is studied in some detail giving the behaviour of the order parameter profiles in two typical cases a comparison is made with the results of a low temperature expansion where these are available showing a great increase in accuracy with respect to the mean field approximation

on the convergence of kikuchi s natural iteration method in this article we investigate on the convergence of the natural iteration method a numerical procedure widely employed in the statistical mechanics of lattice systems to minimize kikuchi s cluster variational free energies we discuss a sufficient condition for the convergence based on the coefficients of the cluster entropy expansion depending on the lattice geometry we also show that such a condition is satisfied for many lattices usually studied in applications finally we consider a recently proposed class of methods for the minimization of kikuchi functionals showing that the natural iteration method turns out as a particular instance of that class

measures on projections and physical states it is shown that a finitely additive measure on the projections of a von neumann algebra withouti2 andii1 summands is the restriction of a state a definition of a physical state is proposed and it is shown that such a physical state on a simplec algebra with unit is a state

independent two fields solution for full potential unsteady transonic flows the paper introduces a new approach for the numerical solution of full potential unsteady flows based on an independent approximation of the density and velocity potential fields the solution procedure relies on an unstructured node based finite volume approximation with linear shape functions and nonreflecting farfield boundary conditions an improved upwind density biasing allows us to stabilize the solution in supersonic regions in view of linearized aeroelastic stability and response analyses unsteady boundary conditions are accounted for by means of a density flow transpiration time marching solutions are dealt using first second order implicit schemes whose unconditional linearized stability properties are demonstrated a few applications are presented to validate the method

stable propagation algorithm for the minimization of the bethe free energy we propose a new propagation algorithm for the minimization of the bethe free energy for a generic lattice model with pair interactions the algorithm turns out to be more stable than belief propagation as it reaches a fixed point also for highly frustrated systems such as spin glasses and faster than the provably convergent double loop algorithms

surface reentrance in the semi infinite spin 1 ising models abstract the critical behavior of the semi infinite blume capel and blume emery griffiths models is investigated in the pair approximation of the cluster variation method equations for bulk and surface order parameters and n n correlation functions are given from which analytical expressions for the second order bulk and surface critical temperatures are derived the phase diagrams of the blume capel model are classified and the existence of a surface first order transition is discussed this transition is shown to be under certain conditions slightly reentrant and the behavior of the surface order parameters and correlation functions is given for such a case the extension of our results to the blume emery griffiths model is briefly discussed

folding of the triangular lattice in the face centred cubic lattice with quenched random spontaneous curvature we study the folding of the regular two dimensional triangular lattice embedded in the regular three dimensional face centered cubic lattice in the presence of quenched random spontaneous curvature we consider two types of quenched randomness 1 a physical randomness arising from a prior random folding of the lattice creating a preferred spontaneous curvature on the bonds 2 a simple randomness where the spontaneous curvature is chosen at random independently on each bond we study the folding transitions of the two models within the hexagon approximation of the cluster variation method depending on the type of randomness the system shows different behaviours we finally discuss a hopfield like model as an extension of the physical randomness problem to account for the case where several different configurations are stored in the prior prefolding process

generalized cluster description of multicomponent systems a general formalism for the description of configurational cluster functions in multicomponent systems is developed the approach is based on the description of configurational cluster functions in terms of an orthogonal basis in the multidimensional space of discrete spin variables the formalism is used to characterize the reduced density matrices or cluster probability densities and the free energy functional obtained in the cluster variation method approximation for the particular representation chosen the expectation values of the base functions are the commonly used multisite correlation functions the latter form an independent set of variational parameters for the free energy which in general facilitates the minimization procedure a new interpretation of the cluster variation method as a self consistency relation on the renormalized cluster energies is also presented

position space renormalization group study of the spin 1 random semi infinite blume capel model abstract we study the spin 1 blume capel model under a random crystal field in the tridimensional semi infinite case this has been done by using the real space renormalization group approximation and specifically the migdal kadanoff technique interesting results are obtained which tell us that the randomness destroys the first order phase transitions and only those of the second order occur we give the list of nine fixed points and their topology describing the surface critical behavior five new types of phase diagram are found with a rich variety of phase transitions in accordance with the values of the bulk and surface probabilities and the ratios linking bulk and surface interactions

quasi states and quasi measures abstract it is shown that in general non linear quasi states will exist on c x where x is a compact hausdorff space we introduce the concept of a quasi measure in x and establish the connection between quasi states and quasi measures

multiple solutions of the transonic potential flow equation the two dimensional transonic potential flow equation when solved in discrete form for steady flow over an airfoil has been found to yield more than one solution in certain bands of angle of attack and mach number the most striking ex ample of this is the appearance of nonsymmetric solutions with large positive or negative lift for symmetric airfoils at zero angle of attack the behavior of these anomalous solutions is exam ined as grid size is varied by large factors and found to be not qualitatively different from that of ormalrf solutions outside the nonuniqueness band thus it appears that the effect is not due to discretization error and that the basic tran sonic potential flow partial differential equation admits nonunique solutions for certain values of angle of attack and mach number

accurate transonic wave drag prediction using simple physical models a new method is presented to compute the transonic wave drag of airfoils coupled with an inverse boundary layer procedure the calculated results have an accuracy comparable to experiments the method is robust and easy to handle without the necessity of tuning hence it is an excellent engineering tool for supercritical airfoil design the inviscid flowfield is assumed to be governed by the full potential equation except at the shock the solution is obtained by a finite difference method at shock points a shock operator is introduced it satisfies the kinematic prandtl relation for normal and oblique shocks which is the consistent condition for the velocity potential for each streamline behind the shock an entropy correction is calculated by the rankine hugoniot equations the wave drag is given by integrating the entropy rise along the shock the computational mesh formed by incompressibl e stream and potential lines allows easy coupling of the boundary layer solution at the airfoil and wake the h type singularity at the incompressible stagnation point is handled by a finite volume procedure for better physical pressure and drag solutions the condition of the normal shock has to be altered due to the boundary layer therefore an analytic model of the inviscid interference region was developed and the essential features are embedded in the numerical procedure

the two and three dimensional spin 3 2 random blume capel model by the position space renormalization group we use the migdal kadanoff renormalization group technique to study the spin 3 2 blume capel model under a random crystal field in the two and three dimensional cases studying the fixed points and the phase diagrams established we find interesting results allowing us to understand the critical behavior of the system in the two dimensional case the randomness even in small amounts removes completely the first order transition between the two ferromagnetic phases present replacing it by a smooth continuation only the second order phase transitions occur in the three dimensional case the first order phase transition disappears only at a certain threshold of randomness below this threshold we observe the presence of an end point where finishes the first order transition line inside the ferromagnetic phases this end point reaches t 0k at a critical value of probability beyond which only the second order transitions occur

numerical solution of transonic stream function equation the stream function equation in conservation form looks similar to the full potential equation and existing methods e g artificial compressibility can be readily applied rotational flows can be calculated once the vorticity due to shocks or nonuniformity is evaluated there are however two main difficulties first the density is not uniquely determined in terms of the flux there are two solutions the subsonic and the supersonic branch with a square root singularity at the sonic point methods to overcome this difficulty are studied and results are presented with some remarks on inviscid separation and closed stream lines second the need of two stream functions for three dimensional calculations is briefly discussed

application of a finite element algorithm to the solution of steady transonic euler equations a finite element algorithm for the solution of two dimensional steady euler equations is presented which through a clebsch type transformation for the velocity vector solves the conservation of mass equation with one primary variable and two additional equations for the convection of two new variables the accuracy and efficiency of this scheme is discussed and the second order accuracy attained in the analysis of the convection of the vorticity is demonstrated together with the efficient treatment of rotational and irrotational flow subregions a sample problem is used to show the accuracy of the numerical scheme and its convergence characteristics

coloring random graphs and maximizing local diversity we study a variation of the graph coloring problem on random graphs of finite average connectivity given the number of colors we aim to maximize the number of different colors at neighboring vertices i e one edge distance of any vertex two efficient algorithms belief propagation and walksat are adapted to carry out this task we present experimental results based on two types of random graphs for different system sizes and identify the critical value of the connectivity for the algorithms to find a perfect solution the problem and the suggested algorithms have practical relevance since various applications such as distributed storage can be mapped onto this problem

the half filled hubbard model in the pair approximation of the cluster variation method the half filled hubbard model is studied in the pair approximation of the cluster variation method cvm the use of the so 4 symmetry of the model makes it possible to give a complete analytical characterization of the ground state by means of explicit expressions for the double occupancy and the nearest neighbour correlation functions the finite temperature analysis is reduced to the numerical solution of only two coupled transcendental equations the behaviour of local magnetic moment specific heat and correlation functions is given for some typical cases in one and two dimensions the authors obtain good qualitative agreement with exact and numerical results in one dimension the results for finite temperatures show a rapid evolution with increasing temperature from a strongly antiferromagnetic behavior to a disordered one in the high temperature region a maximum which has been related to a gradual metal insulator transition is found in the specific heat for very large values of the coulomb repulsion

pair correlations in the cluster variation approximation abstract the cluster variation method is used to obtain approximate free energy functions for a binary system in an inhomogeneous field in order to calculate the fourier transform of the pair correlation functions in the two dimensional square lattice using the nearest neighbors square as the basic cluster the correlation functions are correctly given up to the order 7 in the inverse temperature the effect of second neighbor pairs and many body interactions is investigated

region graph partition function expansion and approximate free energy landscapes theory and some numerical results graphical models for finite dimensional spin glasses and real world combinatorial optimization and satisfaction problems usually have an abundant number of short loops the cluster variation method and its extension the region graph method are theoretical approaches for treating the complicated short loop induced local correlations for graphical models represented by non redundant or redundant region graphs approximate free energy landscapes are constructed in this paper through the mathematical framework of region graph partition function expansion several free energy functionals are obtained each of which use a set of probability distribution functions or functionals as order parameters these probability distribution function functionals are required to satisfy the region graph belief propagation equation or the region graph survey propagation equation to ensure vanishing correction contributions of region subgraphs with dangling edges as a simple application of the general theory we perform region graph belief propagation simulations on the square lattice ferromagnetic ising model and the edwards anderson model considerable improvements over the conventional bethe peierls approximation are achieved collective domains of different sizes in the disordered and frustrated square lattice are identified by the message passing procedure such collective domains and the frustrations among them are responsible for the low temperature glass like dynamical behaviors of the system

alternative variational approach to cactus lattices in this paper i will present an alternative approach to the bethe or cactus lattice approximation widely employed in the theory of cooperative phenomena this approach relies on a variational free energy which is equivalent to the bethe free energy in that it has the same stationary points but allows one to simplify analytical calculations since it is a function of only single site probability distributions in the same way as an ordinary mean field bragg williams free energy as an application i shall discuss a derivation of closed form equations for critical points in ising like models moreover i will suggest a rule of thumb to choose the cactus lattice connectivity yielding the best approximation for the corresponding model defined on an ordinary lattice

a note on cactus trees variational vs recursive approach in this article we deal with the variational approach to cactus trees husimi trees and the more common recursive approach that are in principle equivalent for finite systems we discuss in detail the conditions under which the two methods are equivalent also in the analysis of infinite self similar cactus trees usually investigated to the purpose of approximating ordinary lattice systems such issue is hardly ever considered in the literature we show on significant test models that the phase diagram and the thermodynamic quantities computed by the variational method when they deviates from the exact bulk properties of the cactus system generally provide a better approximation to the behavior of a corresponding ordinary system generalizing a property proved by kikuchi we also show that the numerical algorithm usually employed to perform the free energy minimization in the variational approach is always convergent

cluster variation method pade approximants and critical behavior in the present paper we show how nonclassical quite accurate critical exponents can be extracted in a very simple way from the pad e analysis of the results obtained by mean field like approximation schemes and in particular by the cluster variation method we study the critical behavior of the ising model on several lattices quadratic triangular simple cubic and face centered cubic and two problems of surface critical behavior both unbiased and biased approximants are used and results are in very good agreement with the exact or numerical ones

transonic flow calculations using the euler equations an implicit finite difference method with implicit boundary conditions is employed to solve the steady euler equations for flows past arbitrary geometries the resulting code is used to investigate in a systematic way various aspects of flow past airfoils at transonic speeds such as method of solution boundary conditions grid stretching and generation shock and sonic point operators the kiitta condition and smoothing results ob tained are in good agreement with results of other codes moreover it appears that the method of solution employed is such that kutta s condition need not be invoked this statement appears to be valid for other existing schemes employed in the solution of euler equations he primitive variable form of the system of partial differential equations governing the steady motion of an inviscid fluid euler equations are first order and of mixed elliptic and hyperbolic type because of this two approaches are used in obtaining steady state solutions for subcritical and supercritical flows past bodies the first seeks temporally asymptotic solutions of the time dependent equations1 7 while the second exploits relaxation methods developed for the solution of second order equations by embedding euler equations in a second order system8 or by using a stream function formulation 9 the purpose of this investigation is to develop an efficient algorithm for the steady euler equations in primitive variable form and use it to carry out numerical experiments designed to investigate in a systematic way the various aspects of flows past airfoils at transonic speeds these include method of solution i e peaceman rachford10 pr vs douglas gunn1 1 dg boundary conditions grid generation and stretching shock and sonic point operators smoothing and the kutta condition the resulting algorithm solves the strong con servation form of the euler equations with the energy equation replaced by the statement that the total enthalpy is constant using an adi finite difference scheme and implicit boundary conditions to study arbitrary geometries the algorithm is combined with the automatic grid solver grape of steger and sorenson 12 with this capability the code provides a general and efficient method for the solution of flowfields past arbitrary geometries for all speed ranges the achieved efficiency of this code can be traced to two main reasons the resulting block tridiagonal matrix for two dimensional flows is 3 x 3 and not 4 x 4 moreover the code incorporates a procedure that selects an optimum relaxation factor for each iteration formulation of the problem

the two dimensional annni model in the cvm approximation the phase diagram of the two dimensional annni model is investigated by the cluster variation method cvm we confirm the stability of the disordered phase down tot 0 and the absence of a lifshitz point at finite temperature fork 1 2 wherek the ratio of the second to the first neighbor pair interactions two different modulation regimes for the correlation functions of the disordered phase are separated by a disorder line along which theq vector of the susceptibility maximum undergoes a lock in transition the study in reciprocal space of the stability of the disordered phase allows us to define a critical line in the phase diagram along which theq vector characterizing the instability is incommensurate finally we show the existence of another lifshitz point fork tending to infinity

nonisentropic potential formulation for transonic flows a potential equation for nonisentropic transonic flows is formulated this procedure captures shock waves with rankine hugoniot strengths but retains the simplicity of the traditional potential equation numerical computations are presented that verify the efficiency of the present procedure it is also shown that crocco s theorem is not applicable to potential flows a new crocco s theorem valid for potential flows is derived and it is shown that transonic flows with nonconstant shock strengths can never be irrotational irrespective of whether the flow is isentropic or not

constrained variational approach to second order phase transitions application to a two layer ising film within the framework of the transfer matrix formalism a variational method is elaborated with a constraint related to the fundamental role of the correlation length near a critical point the method is applied to a two layer ferromagnetic film made of two horizontal ising planes interacting through a vertical coupling the critical curve of the model as well as the correlation length above and near tc are calculated the critical exponent nu obtained agrees with the expected two dimensional exact value for the two particular values of the vertical coupling for which there are numerical estimates of tc through series analysis or the monte carlo method an essential agreement with these estimates is found analytical expressions are given in the weak and strong vertical coupling regimes

critical exponents of the three dimensional blume capel model on a cellular automaton abstract the static critical exponents of the three dimensional blume capel model which has a tricritical point at d j 2 82 value are estimated for the standard and the cooling algorithms which improved from creutz cellular automaton the analyses of the data using the finite size scaling and power law relations reproduce their well established values in the d j 3 and d j 2 8 parameter region at standard and cooling algorithms respectively for the cooling algorithm at d j 2 8 value of single ion anisotropy parameter the static critical exponents are estimated as 0 31 1 6 0 32 and 0 87 these values are different from 0 31 1 25 0 12 and 0 64 universal values this case indicated that the bc model exhibits an ununiversal critical behavior at the d j 2 8 parameter value near the tricritical point d j 2 82 the simulations were carried out on a simple cubic lattice with periodic boundary conditions

cluster variation method in statistical physics and probabilistic graphical models the cluster variation method cvm is a hierarchy of approximate variational techniques for discrete ising like models in equilibrium statistical mechanics improving on the mean field approximation and the bethe peierls approximation which can be regarded as the lowest level of the cvm in recent years it has been applied both in statistical physics and to inference and optimization problems formulated in terms of probabilistic graphical models the foundations of the cvm are briefly reviewed and the relations with similar techniques are discussed the main properties of the method are considered with emphasis on its exactness for particular models and on its asymptotic properties the problem of the minimization of the variational free energy which arises in the cvm is also addressed and recent results about both provably convergent and message passing algorithms are discussed

inviscid flows over a cylinder in this paper we simulate steady inviscid flows over a cylinder using potential and stream functions including entropy and vorticity corrections for incompressible subsonic transonic and supersonic flows the present hierarchical formulation is equivalent to euler equations satisfying conservation of mass momentum and energy standard numerical schemes and iterative algorithms are used for the mixed type potential or stream function equation and for the convection equations of entropy and vorticity augmented with the proper artificial dissipation necessary for stability of computations typical results for a cylinder in uniform and shear flows are presented and the merits of the present approach are briefly discussed

numerical study of 2d annni model in the cluster variation method abstract an approximation in the cluster variation method cvm is used to investigate the modulated phases as well as the critical temperatures of the 2d and the 3d annni models it is first found that it shows the existence and the non existence of the lifshitz points in the 3d and the 2d model respectively in the second place the free energies of periodic solutions in the modulated phases of the 2d annni model are calculated under the periodic boundary condition that the system has 88 layers in the direction of the competing interactions and it is concluded from the result that the 2d annni model is always in an incommensurate phase in the modulated phase by this method

irreducible partitions and the construction of quasi measures a quasi measure is a non subadditive measure defined on only open or closed subsets of a compact hausdorf space we investigate the nature of irreducible partitions as defined by aarnes and use the results to construct quasi measures when g x 1 the cohomology ring is an important tool for this investigation

on three new cluster variation approximations abstract we discuss in some detail three new cluster variation approximations we used in a previous paper in connection with pade approximants to investigate critical behaviour of classical spin models on various lattices the approximations are applied to the ising model on the simple cubic face centered cubic and semi infinite simple cubic lattices the natural iteration equations and estimates for the critical temperatures and for the range of validity of the approximations are given

block structured solution of euler equations for transonic flows a block structured solution scheme is developed for the solution of euler equations for steady three dimensional transonic flows the euler equations are expressed in terms of clebsch variables w v svn the resulting set of equations for conservation of mass entropy 5 and the clebsch variable j are solved using a block based relaxation scheme the flowfield is divided into a series of individual blocks representing local regions of the flowfield the employed grid generation scheme provides local refinement of each block yet ensures one to one matching of grid points on the surfaces of adjoining blocks for each of the blocks either potential or euler equations can be solved for every block the conservation of mass equation is solved to determine for blocks with rotationality two additional equations for determining s and t are solved in this paper the basic steps of the developed solution scheme are presented the computational considerations involved in utilizing the present scheme are demonstrated for several two dimensional sample problems

transonic aeroelastic instability searches using sampling and aerodynamic model hierarchy doi 10 2514 1 j050509 a hierarchy of flow models is exploited for transonic aeroelastic stability analysis using the kriging interpolation technique applied within the schur complement eigenvalue framework in the schur framework a modified structural eigenvalue problem describes the coupled aeroelastic system with a precomputed interaction term depending on the response frequency the interaction term representing the influence of the high dimensional computational fluid dynamics system is approximated by reconstruction based on samples that can be computed using a frequency or time domain solver the computationally cheap approximation model is developed and discussed in this paper for two degree of freedom aerofoil cases the approximation model is used for both the parametric blind search of aeroelastic instability and for updating predictions based on aerodynamic models of different fidelities

random k satisfiability problem from an analytic solution to an efficient algorithm we study the problem of satisfiability of randomly chosen clauses each with k boolean variables using the cavity method at zero temperature we find the phase diagram for the k 3 case we show the existence of an intermediate phase in the satisfiable region where the proliferation of metastable states is at the origin of the slowdown of search algorithms the fundamental order parameter introduced in the cavity method which consists of surveys of local magnetic fields in the various possible states of the system can be computed for one given sample these surveys can be used to invent new types of algorithms for solving hard combinatorial optimizations problems one such algorithm is shown here for the k 3 satisfiability problem with very good performances

mean field method with correlations determined by linear response we introduce a mean field approximation based on the reconciliation of maximum entropy and linear response for correlations in the cluster variation method within a general formalism that includes previous mean field methods we derive formulas improving on e g the bethe approximation and the sessak monasson result at high temperature applying the method to direct and inverse ising problems we find improvements over standard implementations

spin 1 blume capel model with random crystal field effects abstract the random crystal field spin 1 blume capel model is investigated by the lowest approximation of the cluster variation method which is identical to the mean field approximation the crystal field is either turned on randomly with probability p or turned off with q 1 p in a bimodal distribution then the phase diagrams are constructed on the crystal field temperature k t j planes for given values of p and on the k t j p planes for given by studying the thermal variations of the order parameters in the latter we only present the second order phase transition lines because of the existence of irregular wiggly phase transitions which are not good enough to construct lines in addition to these phase transitions the model also yields tricritical points for all values of p and the reentrant behavior at lower p values

on the equivalence of annni model polytypes formed by square wave modulation and branching mechanisms it is proved that long period structures formed by a square wave modulation of a lattice are identical to those of stable phases found in the annni model the proof is based on a continued fraction expansion of the modulation half period producing structural formulae shown to be equivalent to those obtained by a structure combination branching process the same structures have been observed experimentally by high resolution transmission electron microscopy in certain ordered alloys

isotopy invariant topological measures on closed orientable surfaces of higher genus given a closed orientable surface of genus at least two we establish an affine isomorphism between the convex compact set of isotopy invariant topological measures on and the convex compact set of additive functions on the set of isotopy classes of certain subsurfaces of we then construct such additive functions and thus isotopy invariant topological measures from probability measures on together with some additional data the map associating topological measures to probability measures is affine and continuous certain dirac measures map to simple topological measures while the topological measures due to py and rosenberg arise from the normalized euler characteristic

quantum measures and states on jordan algebras a problem of mackey for von neumann algebras has been settled by the conjunction of the early work of gleason and the recent advances of christensen and yeadon we show that mackey s conjecture holds in much greater generality leta be a jbw algebra and letl be the lattice of all projections ina a quantum measure onl is a countably additive map m froml into the real numbers our results imply thatm always has a unique extension to a bounded linear functional ona provided thata has no typei2 direct summand

multicritical points and reentrant phenomenon in the beg model abstract the blume emery griffiths model is investigated by use of the cluster variation method in the pair approximation we determine the regions of the phase space where the reentrant phenomenon takes place two regions are found depending on the sign of the reduced quadrupole quadrupole coupling strength for negative we find para ferro para and ferro para ferro para transition sequences for positive a para ferro para sequence order parameters correlation function and specific heat are given in some typical cases by products of this work are the equations for the critical and tricritical lines

critical indices for the two dimensional ising model with nearest neighbor and next nearest neighbor interactions ii strip cluster approximation the spin pair correlation functions are calculated for the ising model with nearest neighbor interaction j 0 and next nearest neighbor interaction j on the square lattice in terms of three approximations of the simplified cluster variation method with strip clusters as the basic clusters the critical indices and are estimated from the obtained spin pair correlation functions with the aid of the coherent anomaly method for j j 0 5 we confirm that the system belongs to the onsager universality class in the sense of the weak universality hypothesis