stability analysis of lattice boltzmann methods the lattice boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered although the equation is a derivative of lattice gas automata it may be interpreted as a lagrangian finite difference method for the numerical simulation of the discrete velocity boltzmann equation that makes use of a bgk collision operator as a result it is not surprising that numerical instability of lattice boltzmann methods have been frequently encountered by researchers we present an analysis of the stability of perturbations of the particle populations linearized about equilibrium values corresponding to a constant density uniform mean flow the linear stability depends on the following parameters the distribution of the mass at a site between the different discrete speeds the bgk relaxation time the mean velocity and the wavenumber of the perturbations this parameter space is too large to compute the complete stability characteristics we report some stability results for a subset of the parameter space for a 7 velocity hexagonal lattice a 9 velocity square lattice and a 15 velocity cubic lattice results common to all three lattices are 1 the bgk relaxation time must be greater than 12 corresponding to positive shear viscosity 2 there exists a maximum stable mean velocity for fixed values of the other parameters and 3 as is increased from 12 the maximum stable velocity increases monotonically until some fixed velocity is reached which does not change for larger

simulating time harmonic flows with the lattice boltzmann method we simulate time harmonic flows by the lattice boltzmann method we propose a general scheme to choose simulation parameters under the constraints of fixed reynolds and womersley numbers and with a specified simulation error under these constraints parameters are chosen to minimize the execution time numerical stability is studied in a range of reynolds and womersley numbers as an example of time harmonic flow simulations results of blood flow in a human abdominal aorta are presented

lattice boltzmann model for the incompressible navier stokes equation in this paper a lattice boltzmann lb model to simulate incompressible flow is developed the main idea is to explicitly eliminate the terms of o m2 where m is the mach number due to the density fluctuation in the existing lb models in the proposed incompressible lb model the pressure p instead of the mass density is the independent dynamic variable the incompressible navier stokes equations are derived from the incompressible lb model via chapman enskog procedure numerical results of simulations of the plane poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2d womersley flow are presented the numerical results are found to be in excellent agreement with theory

on the focal defect group of a block characters of height zero and lower defect group multiplicities abstract we discuss the focal subgroup of the defect group d of a p block b which we refer to as the focal defect group and denote by d 0 we note that the character group of d d 0 acts in a defect or height preserving fashion on irreducible characters in b and prove that the action on irreducible characters of height zero is semi regular we also prove that all orbits under this action have length divisible by z d d 0 z d as applications we prove that all cartan invariants for b are divisible by z d d 0 z d that if out d is a p group and d 1 then the number of irreducible characters of height zero in b is divisible by p and that if z d d 0 then the block b is of lefschetz type see r knorr g r robinson some remarks on a conjecture of alperin j london math soc 2 39 1 1989 48 60

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

a multigrid solver for the discrete boltzmann equation this paper introduces a nonlinear multigrid solution approach for the discrete boltzmann equation discretized by an implicit second order finite difference scheme for simplicity we restrict the discussion to the stationary case a numerical example shows the drastically improved efficiency in comparison to the widely used lattice bathnagar gross krook lbgk approach

mesoscopic simulations of systolic flow in the human abdominal aorta the complex nature of blood flow in the human arterial system is still gaining more attention as it has become clear that cardiovascular diseases localize in regions of complex geometry and complex flow fields in this article we demonstrate that the lattice boltzmann method can serve as a mesoscopic computational hemodynamic solver we argue that it may have benefits over the traditional navier stokes techniques the accuracy of the method is tested by studying time dependent systolic flow in a 3d straight rigid tube at typical hemodynamic reynolds and womersley numbers as an unsteady flow benchmark simulation results of steady and unsteady flow in a model of the human aortic bifurcation reconstructed from magnetic resonance angiography are presented as a typical hemodynamic application

ground state solutions for some indefinite variational problems abstract we consider the nonlinear stationary schrodinger equation u v x u f x u in r n here f is a superlinear subcritical nonlinearity and we mainly study the case where both v and f are periodic in x and 0 belongs to a spectral gap of v inspired by previous work of li et al 2006 11 and pankov 2005 13 we develop an approach to find ground state solutions i e nontrivial solutions with least possible energy the approach is based on a direct and simple reduction of the indefinite variational problem to a definite one and gives rise to a new minimax characterization of the corresponding critical value our method works for merely continuous nonlinearities f which are allowed to have weaker asymptotic growth than usually assumed for odd f we obtain infinitely many geometrically distinct solutions the approach also yields new existence and multiplicity results for the dirichlet problem for the same type of equations in a bounded domain

multiple solutions of schrodinger equations with indefinite linear part and super or asymptotically linear terms abstract based on new information concerning strongly indefinite functionals without palais smale conditions we study existence and multiplicity of solutions of the schrodinger equation u v x u g x u for x r n u x 0 as x where v and g are periodic with respect to x and 0 lies in a gap of v supposing g is asymptotically linear as u and symmetric in u we obtain infinitely many geometrically distinct solutions we also consider the situation where g is super linear with mild assumptions different from those studied previously and establish the existence and multiplicity

multiple solutions for a class of nonlinear schrodinger equations abstract in this paper we find new conditions to ensure the existence of infinitely many homoclinic type solutions for the schrodinger equation u v x u g x u for x r n assuming v x and g x u depend periodically on x we deal with the situations where g x u is as u asymptotically linear or superlinear with certain hypothesis different from ones used in previous related study our approach is variational and we use the cerami condition instead of the palais smale one for deformation arguments

a characteristic subgroup for fusion systems abstract as a counterpart for the prime 2 to glauberman s zj theorem stellmacher proves that any nontrivial 2 group s has a nontrivial characteristic subgroup w s with the following property for any finite 4 free group g with s a sylow 2 subgroup of g and with o 2 g self centralizing the subgroup w s is normal in g we generalize stellmacher s result to fusion systems a similar construction of w s can be done for odd primes and gives rise to a glauberman functor

lattice boltzmann method for incompressible flows with large pressure gradients conventional lattice boltzmann bhatnagar gross krook lbgk models can simulate incompressible flows correctly only if the mach number m and the density variation are negligibly small however the equation of state p rt resulting from the conventional models limits their application to incompressible flows with a rather small pressure gradient in this paper based on the enskog equation we propose a finite difference lattice bgk model for isothermal incompressible flows with the resulting equation of state and transport properties suitable for nonideal fluids we validated this model by simulating the plane poiseuille flow the two dimensional womersley flow and the backward facing step flow and found that the numerical results obtained by the proposed model are more accurate than those by the conventional lbgk models when the pressure gradient imposed on the flows increases

solutions of superlinear elliptic equations and their morse indices we consider here solutions of semilinear second order elliptic equations with superlinear nonlinearities and we present some relationships between their morse indices and some qualitative properties in particular we show that for uo subcritical nonlinearities bounds on solutions are equivalent to bounds on their morse indices

hydraulic permeability of un bounded fibrous media using the lattice boltzmann method several articles have been written regarding the hydraulic permeability of ordered and disordered fibrous media here we explore wall effects on hydraulic permeabilities for ordered and disordered media using the lattice boltzmann lb simulation method simulation results are found to be in excellent agreement with the semi analytic result of sangani and acrivos and simulation results for disordered media are in good agreement with the results of jackson and james and higdon and ford s fcc lattice the macroscopic behavior the hydraulic permeability shows a distinct connection with the geometry of the system this connection is explored and elucidated for ordered and disordered media finally hydraulic permeabilities for bounded media at various wall separations are presented for both ordered and disordered media and results are compared with hydraulic permeabilities calculated for the unbounded media and a phenomenological correlation is presented to facilitate rapid prediction of hydraulic permeabilities for both unbounded and bounded fibrous media

implementation aspects of 3d lattice bgk in many realistic fluid dynamical simulations the specification of the boundary conditions the error sources and the number of time steps to reach a steady state are important practical considerations in this paper we study these issues in the case of the lattice bgk model the objective is to present a comprehensive overview of some pitfalls and shortcomings of the lattice bgk method and to introduce some new ideas useful in practical simulations we begin with an evaluation of the widely used bounce back boundary condition in staircase geometries by simulating flow in an inclined tube it is shown that the bounce back scheme is first order accurate in space when the location of the non slip wall is assumed to be at the boundary nodes moreover for a specific inclination angle of 45 degrees the scheme is found to be second order accurate when the location of the non slip velocity is fitted halfway between the last fluid nodes and the first solid nodes the error as a function of the relaxation parameter is in that case qualitatively similar to that of flat walls next a comparison of simulations of fluid flow by means of pressure boundaries and by means of body force is presented a good agreement between these two boundary conditions has been found in the creeping flow regime for higher reynolds numbers differences have been found that are probably caused by problems associated with the pressure boundaries furthermore two widely used 3d models namelyd3q15andd3q19 are analysed it is shown that thed3q15model may induce artificial checkerboard invariants due to the connectivity of the lattice finally a new iterative method which significantly reduces the saturation time is presented and validated on different benchmark problems

generalized quasilinear asymptotically periodic schrodinger equations with critical growth this paper is concerned with the following quasilinear schrodinger equations div g 2 u u g u g u u 2 v x u f x u g u g u 2 2 g u x r n u x 0 x r n where n 3 2 2 n n 2 g u 0 u g t d t and 0 is a parameter by using a change of variable the quasilinear equation is reduced to a semilinear one whose associated functional is well defined in h 1 r n we establish the existence of positive solutions for this problem by using the mountain pass theorem in combination with the concentration compactness principle under appropriate assumptions on v x and f x u recent results from the literature are improved and extended

ground state solutions for kirchhoff type equations with asymptotically 4 linear nonlinearity this paper is concerned with the following kirchhoff type equation a b v 2 v f x v in v 0 on assuming that the primitive of f is asymptotically 4 linear as v a homeomorphism between the nehari manifold and a subset of unit sphere is constructed based on some observations and new techniques inspired by recent work of szulkin and weth 2010 ground state solutions for the equation above are obtained as well as infinitely many pairs of nontrivial solutions for case f x v is odd with respect to v

ground states for nonlinear maxwell dirac system with magnetic field abstract in this paper we study the following maxwell dirac system with magnetic field and general nonlinearity k 1 3 k i k a k u a u u a 0 u f u x u a 0 4 u u 4 u 2 a k 4 k u u k 1 2 3 for x r 3 since this problem is strongly indefinite we use linking and concentration compactness arguments to establish the existence of ground state solutions for this system

lattice boltzmann method for simulating the viscous flow in large distensible blood vessels a lattice boltzmann method for simulating the viscous flow in large distensible blood vessels is presented by introducing a boundary condition for elastic and moving boundaries the mass conservation for the boundary condition is tested in detail the viscous flow in elastic vessels is simulated with a pressure radius relationship similar to that of the pulmonary blood vessels the numerical results for steady flow agree with the analytical prediction to very high accuracy and the simulation results for pulsatile flow are comparable with those of the aortic flows observed experimentally the model is expected to find many applications for studying blood flows in large distensible arteries especially in those suffering from atherosclerosis stenosis aneurysm etc

bifurcation for some non frechet differentiable problems abstract we study the bifurcation points of an equation of the form f u u in a real hilbert space since f is only required to be hadamard but not frechet differentiable at u 0 bifurcation points need not belong to the spectrum of f 0 the abstract results are illustrated in the case of a nonlinear schrodinger equation

ground state solutions for a diffusion system in this paper we study the following diffusion system t u x u v x u g t x v t v x v v x v f t x u where z u v r r n r 2 v x c r n r is a general periodic function under weaker conditions on nonlinearity we establish the existence of ground state solutions via variational methods

control of transfer and weak closure in fusion systems we show that k1 and k 1 control transfer in every fusion system on a finite p group when p 5 and that they control weak closure of elements in every fusion system on a finite p group when p 3 this generalizes results of g glauberman concerning finite groups

subgroup families controlling p local finite groups a p local finite group consists of a finite p group s together with a pair of categories which encode conjugacy relations among subgroups of s and which are modelled on the fusion in a sylow p subgroup of a finite group it contains enough information to define a classifying space which has many of the same properties as p completed classifying spaces of finite groups in this paper we examine which subgroups control this structure more precisely we prove that the question of whether an abstract fusion system mathcal f over a finite p group s is saturated can be determined by just looking at smaller classes of subgroups of s we also prove that the homotopy type of the classifying space of a given p local finite group is independent of the family of subgroups used to define it in the sense that it remains unchanged when that family ranges from the set of mathcal f centric mathcal f radical subgroups at a minimum to the set of mathcal f quasicentric subgroups at a maximum finally we look at constrained fusion systems analogous to p constrained finite groups and prove that they in fact all arise from groups

accuracy of the lattice boltzmann method based on analytical solutions in this paper a simple method is proposed to obtain steady analytical solutions for the lattice boltzmann method based on such analytical results it is demonstrated how the accuracy of the lattice boltzmann method can depend on the relative orientation of the lattice and the flow field it is also demonstrated that the method can be useful to obtain a general class of analytical solutions for the lattice boltzmann method finally a simple relation is given between the compressibility error and the velocity field

on a periodic schrodinger equation involving periodic and nonperiodic nonlinearities in r2 abstract we study the existence of solutions for the nonlinear schrodinger equation u v x u f x u in r 2 where the potential v is 1 periodic 0 lies in a spectral gap from the spectrum of the schrodinger operator s v and the nonlinearity f x t has exponential growth in the sense of trudinger moser the main feature here is that f x t is allowed to be both periodic and nonperiodic in the x variable our proofs rely on a linking theorem and the lions concentration compactness principle

solutions for periodic schrodinger equation with spectrum zero and general superlinear nonlinearities abstract in this paper we consider the following schrodinger equation u v x u g x u for x r n u x 0 as x where v x and g x u are periodic with respect to x and 0 is a boundary point of the spectrum v replacing the classical ambrosetti rabinowitz superlinear assumption on g x u by a general super quadratic condition we are able to obtain the existence of nontrivial solutions

investigation of stability and hydrodynamics of different lattice boltzmann models stability and hydrodynamic behaviors of different lattice boltzmann models including the lattice boltzmann equation lbe the differential lattice boltzmann equation dlbe the interpolation supplemented lattice boltzmann method islbm and the taylor series expansion and least square based lattice boltzmann method tllbm are studied in detail our work is based on the von neumann linearized stability analysis under a uniform flow condition the local stability and hydrodynamic dissipation behaviors are studied by solving the evolution operator of the linearized lattice boltzmann equations numerically our investigation shows that the lbe schemes with interpolations such as dlbe islbm and tllbm improve the numerical stability by increasing hyper viscosities at large wave numbers small scales it was found that these interpolated lbe schemes with the upwind interpolations are more stable than those with central interpolations because of much larger hyper viscosities

zj theorems for fusion systems for p an odd prime we generalise the glauberman thompson p nilpotency theorem 5 ch 8 theorem 3 1 to arbitrary fusion systems we define a notion of qd p free fusion systems and show that if f is a qd p free fusion system on some finite p group p then f is controlled by w p for any glauberman functor w generalising glauberman s zj theorem 3 to arbitrary fusion systems

bifurcation in lp rn for a semilinear elliptic equation keywords lsp p bifurcation constrained minimization sobolev spaces nonlinear eigenvalue problem semilinear spectrum linearisation variational structure reference ana article 1988 001doi 10 1112 plms s3 57 3 511 record created on 2008 12 10 modified on 2016 08 08

new conditions on nonlinearity for a periodic schrodinger equation having zero as spectrum abstract we consider the semilinear schrodinger equation u v x u f x u for x r n u x 0 as x where f is a superlinear and subcritical nonlinearity we mainly study the case when both v and f are periodic in x and 0 is a boundary point of a spectral gap of v we extend a linking theorem of kryszewski and szulkin 15 and establish a new variational setting which is more suitable to the above case we obtain two theorems on the existence of ground state solutions with mild assumptions on f

preconditioned lattice boltzmann method for steady flows in this paper we propose a preconditioned lattice boltzmann lb method for steady incompressible flows for steady flows the macroscopic equations derived from this lb model are equivalent to those from the standard lb model but with an improved eigenvalue system the proposed model can be viewed as an explicit solver for preconditioned compressible navier stokes equations linear stability analysis is performed and the results show that the stability of the model is the same as that of the standard lb model for low mach numbers the proposed model retains the structure of the standard lb model and hence possesses all the advantages numerical tests show that the convergence rate can be enhanced as much as an order of magnitude compared to the standard lattice boltzmann method the accuracy of the solutions is improved as well

multiple solutions for asymptotically quadratic and superquadratic elliptic system of hamiltonian type this paper is concerned with the following nonperiodic hamiltonian elliptic system u v x u h v x u v x r n v v x v h u x u v x r n u x 0 v x 0 as x where z u v r n r i r n 3 and the potential v x is nonperiodic and sign changing by applying a generalized linking theorem for strongly indefinite functionals we establish the existence of multiple solutions for asymptotically quadratic nonlinearity as well as the existence of infinitely many solutions for superquadratic nonlinearity

lattice boltzmann computational fluid dynamics in three dimensions the recent development of the lattice gas method and its extension to the lattice boltzmann method have provided new computational schemes for fluid dynamics both methods are fully paralleled and can easily model many different physical problems including flows with complicated boundary conditions in this paper basic principles of a lattice boltzmann computational method are described and applied to several three dimensional benchmark problems in most previous lattice gas and lattice boltzmann methods a face centered hyper cubic lattice in four dimensional space was used to obtain an isotropic stress tensor to conserve computer memory we develop a model which requires 14 moving directions instead of the usual 24 directions lattice boltzmann models describing two phase fluid flows and magnetohydrodynamics can be developed based on this simpler 14 directional lattice comparisons between three dimensional spectral code results and results using our method are given for simple periodic geometries an important property of the lattice boltzmann method is that simulations for flow in simple and complex geometries have the same speed and efficiency while all other methods including the spectral method are unable to model complicated geometries efficiently

application of the lattice boltzmann method to transition in oscillatory channel flow in this study the applicability of the lattice boltzmann method to oscillatory channel flow with a zero mean velocity has been evaluated the model has been compared to exact analytical solutions in the laminar case re 100 where re is the reynolds number based on the stokes layer for the womersley parameter 1 31 in this regime there was good agreement between numerical and exact analytical solutions the model was then applied to study the primary instability of oscillatory channel flow with a zero mean velocity for these transitionary flows the parameters were varied in the range 400 re 1000 and 4 16 disturbances superimposed on the numerical solution triggered the two dimensional primary instability this phenomenon has not been numerically evaluated over the range of or re currently investigated the results are consistent with quasi steady linear stability theories and previous numerical investigations

an asymptotically periodic and asymptotically linear schrodinger equation with indefinite linear part abstract we consider the semilinear schrodinger equation u v x u f x u x r n u h 1 r n where v x is asymptotically periodic and sign changing f x u is asymptotically periodic in x and asymptotically linear as u under some weak assumptions on v and f we prove that the above problem has a nontrivial solution

infinitely many radial and non radial solutions for a fractional schrodinger equation in this paper we study the following fractional schrodinger equation s u v x u f x u x r n where s s 0 1 denotes the fractional laplacian by variational methods we obtain the existence of a sequence of radial solutions for n 2 a sequence of non radial solutions for n 4 or n 6 and a non radial solution for n 5

the homotopy theory of fusion systems the main goal of this paper is to identify and study a certain class of spaces which in many ways behave like p completed classifying spaces of finite groups these spaces occur as the classifying spaces of certain algebraic objects which we call p local finite groups a p local finite group consists roughly speaking of a finite p group s and fusion data on subgroups of s encoded in a way explained below our starting point is our earlier paper blo on p completed classifying spaces of finite groups together with the axiomatic treatment by lluis puig pu pu2 of systems of fusion among subgroups of a given p group the p completion of a space x is a space xp which isolates the properties of x at the prime p and more precisely the properties which determine its mod p cohomology for example a map of spaces x f y induces a homotopy equivalence xp y p if and only if f induces an isomorphism in mod p cohomology and h xp fp h x fp in favorable cases if x is p good when g is a finite group the p completion bgp of its classifying space encodes many of the properties of g at p for example not only the mod p cohomology of bg but also the sylow p subgroup of g together with all fusion among its subgroups are determined up to isomorphism by the homotopy type of bgp our goal here is to give a direct link between p local structures and homotopy types which arise from them this theory tries to make explicit the essence of what it means to be the p completed classifying space of a finite group and at the same time yields new spaces which are not of this type but which still enjoy most of the properties a space of the form bgp would have we hope that the ideas presented here will have further applications and generalizations in algebraic topology but this theory also fits well with certain aspects of modular representation theory in particular it may give a way of constructing classifying spaces for blocks in the group ring of a finite group over an algebraically closed field of characteristic p a saturated fusion system f over a p group s consists of a set homf p q of monomorphisms for each pair of subgroups p q s which form a category under composition include all monomorphisms induced by conjugation in s and satisfy certain other axioms formulated by puig definitions 1 1 and 1 2 below in particular these axioms are satisfied by the conjugacy homomorphisms in a finite group we refer to pu and pu2 for more details of puig s work on saturated