comparative study on accuracy and conservation properties of two particle regularization schemes and proposal of an optimized particle shifting scheme in isph context abstract the paper provides a comparative investigation on accuracy and conservation properties of two particle regularization schemes namely the dynamic stabilization ds 1 and generalized particle shifting ps 2 schemes in simulations of both internal and free surface flows in isph incompressible sph context the paper also presents an optimized ps ops scheme for accurate and consistent implementation of particle shifting for free surface flows in contrast to ps the ops does not contain any tuning parameters for free surface consistently resulting in perfect elimination of shifting normal to an interface and resolves the unphysical discontinuity beneath the interface seen in ps results

smoothed particle hydrodynamics stability analysis abstract sph smoothed particle hydrodynamics is a gridless lagrangian technique which is appealing as a possible alternative to numerical techniques currently used to analyze large deformation events recent tests of the standard sph method using the cubic b spline kernel indicated the possibility of an instability in the tensile regime even though no such difficulties were observed in compression a von neumann stability analysis of the sph algorithm has been carried out which identifies the criterion for stability or instability in terms of the stress state and the second derivative of the kernel function the analysis explains the observation that the method is unstable in tension while apparently stable in compression but shows that it is possible to construct kernel functions which are stable in tension and unstable in compression the instability is shown to result from an effective stress with a negative modulus imaginary sound speed being produced by the interaction between the constitutive relation and the kernel function and is not caused by the numerical time integration algorithm that is changes in the effective stress act to amplify rather than reduce perturbations in the strain the analysis and the stability criterion provide insight into possible methods for removing the instability

enhancement of stability and accuracy of the moving particle semi implicit method as a lagrangian gridless particle method the mps moving particle semi implicit method has been proven useful in a wide range of engineering applications up to now most of mps applications have been limited to problems with compressive stress states this paper investigates the performance and stability of mps method in simulation of more general hydrodynamic problems including those characterized by tensile stresses or by changes in the stress states it is shown that mps based simulations are prone to become destabilized in presence of attractive interparticle forces this instability appears to be similar to the so called tensile instability in sph method two new modifications namely a modified poisson pressure equation and a corrective matrix for pressure gradient model are proposed to resolve this shortcoming these two new modifications together with two previously proposed improvements are shown to stabilize and enhance the performance of mps method

simulation of surface tension in 2d and 3d with smoothed particle hydrodynamics method the methods for simulating surface tension with smoothed particle hydrodynamics sph method in two dimensions and three dimensions are developed in 2d surface tension model the sph particle on the boundary in 2d is detected dynamically according to the algorithm developed by dilts g a dilts moving least squares particle hydrodynamics ii conservation and boundaries international journal for numerical methods in engineering 48 2000 1503 1524 the boundary curve in 2d is reconstructed locally with lagrangian interpolation polynomial in 3d surface tension model the sph particle on the boundary in 3d is detected dynamically according to the algorithm developed by haque and dilts a haque g a dilts three dimensional boundary detection for particle methods journal of computational physics 226 2007 1710 1730 the boundary surface in 3d is reconstructed locally with moving least squares mls method by transforming the coordinate system it is guaranteed that the interface function is one valued in the local coordinate system the normal vector and curvature of the boundary surface are calculated according to the reconstructed boundary surface and then surface tension force can be calculated surface tension force acts only on the boundary particle density correction is applied to the boundary particle in order to remove the boundary inconsistency the surface tension models in 2d and 3d have been applied to benchmark tests for surface tension the ability of the current method applying to the simulation of surface tension in 2d and 3d is proved

embedding of the operator space oh and the logarithmic little grothendieck inequality we use voiculescu s concept of free probability to construct a completely isomorphic embedding of the operator space oh in the predual of a von neumann algebra we analyze the properties of this embedding and determine the operator space projection constant of oh n frac 1 108 sqrt frac n 1 ln n le inf p mathcal b ell 2 to oh n p 2 p left p right cb le 288 pi sqrt frac 2n 1 ln n the lower estimate is a recent result of pisier and shlyakhtenko that improves an estimate of order 1 1 lnn of the author the additional factor 1 sqrt 1 ln n indicates that the operator space oh n behaves differently than its classical counterpart ell 2 n we give an application of this formula to positive sesquilinear forms on mathcal b ell 2 this leads to logarithmic characterization of c algebras with the weak expectation property introduced by lance

a transference method in quantum probability abstract working with a rather general notion of independence we provide a transference method which allows to compare the p norm of sums of independent copies with the p norm of sums of free copies our main technique is to construct explicit operator space l p embeddings preserving independence to reduce the problem to l 1 where some recent results by the first named author can be used we find applications on noncommutative khintchine rosenthal type inequalities and on noncommutative l p embedding theory

a new model of generalized plasticity and its numerical implementation abstract a previously proposed simple model of generalized plasticity is modified so that it allows behavior that is asymptotically perfectly plastic or strain softening initially presented in uniaxial form the model is then generalized to multiaxial stress numerical implementation is developed first through direct integration of the rate equations including special cases in which the solution may be obtained analytically and then by means of a return map algorithm which is particularly well suited to the finite element method consistent algorithmic tangent moduli are derived as well numerical examples are presented to illustrate the various approaches

the haagerup property for locally compact quantum groups the haagerup property for locally compact groups is generalised to the context of locally compact quantum groups with several equivalent characterisations in terms of the unitary representations and positive definite functions established in particular it is shown that a locally compact quantum group g has the haagerup property if and only if its mixing representations are dense in the space of all unitary representations for discrete g we characterise the haagerup property by the existence of a symmetric proper conditionally negative functional on the dual quantum group hat g by the existence of a real proper cocycle on g and further if g is also unimodular we show that the haagerup property is a von neumann property of g this extends results of akemann walter bekka cherix valette and jolissaint to the quantum setting and provides a connection to the recent work of brannan we use these characterisations to show that the haagerup property is preserved under free products of discrete quantum groups

towards consistence and convergence of conservative sph approximations typical conservative smoothed particle hydrodynamics sph approximations of the gradient of a scalar field introduce two errors one smoothing error is due to smoothing of the gradient by an integration associated with a kernel function the other integration error is due to approximating the integration by summation over all particles within the kernel support when particles are not on a uniform grid the integration error leads to violation of zero order consistency i e the inability to reproduce a constant field in this paper we confirm that partition of unity is the condition under which the conservative sph approximation achieves both consistence and convergence we show that this condition can be achieved by relaxing a particle distribution under a constant pressure field and invariant particle volume the resulting particle distribution is very similar to that is typical for liquid molecules we further show that with two different typical kernel functions the sph approximation upon satisfying the partition of unity property is able to achieve very high order of the integration error which previously could be shown only with particles on a uniform grid the background pressure used in a weakly compressible sph simulation implies a self relaxation mechanism which explains that convergence with respect to increasing particle numbers could be obtained in sph simulations although not predicted by previous numerical analysis furthermore by relating the integration error to the background pressure we explain why the previously proposed transport velocity formulation of sph s adami et al 2013 1 is able to achieve unprecedented accuracy and stability

lattice points in simple polytopes in terms of fp h q x dx where the polytope p h is obtained from p by independent parallel motions of all facets this extends to simple lattice polytopes the eulermaclaurin summation formula of khovanskii and pukhlikov 8 valid for lattice polytopes such that the primitive vectors on edges through each vertex of p form a basis of the lattice as a corollary we recover results of pommersheim 9 and kantor khovanskii 6 on the coefficients of the ehrhart polynomial of p our proof is elementary in a subsequent article we will show how to adapt it to compute the equivariant todd class of any complete toric variety with quotient singularities the euler maclaurin summation formula for simple lattice polytopes has been obtained independently by ginzburg guillemin karshon 4 they used the dictionary between convex polytopes and projective toric varieties with an ample divisor class in combination with the riemann roch kawasaki formula 1 7 for complex manifolds with quotient singularities a counting formula for lattice points in lattice simplices has been announced by cappell and shaneson 2 as a consequence of their computation of the todd class of toric varieties with quotient singularities

lacunary fourier series for compact quantum groups this paper is devoted to the study of sidon sets lambda p sets and some related notions for compact quantum groups we establish several different characterizations of sidon sets and in particular prove that any sidon set in a discrete group is a strong sidon set in the sense of picardello we give several relations between sidon sets lambda p sets and lacunarities for lp fourier multipliers generalizing a previous work by blendek and michalicek we also prove the existence of lambda p sets for orthogonal systems in noncommutative lp spaces and deduce the corresponding properties for compact quantum groups central sidon sets are also discussed and it turns out that the compact quantum groups with the same fusion rules and the same dimension functions have identical central sidon sets several examples are also included

ccap for universal discrete quantum groups we show that the discrete duals of the free orthogonal quantum groups have the haagerup property and the completely contractive approximation property analogous results hold for the free unitary quantum groups and the quantum automorphism groups of finite dimensional c algebras the proof relies on the monoidal equivalence between free orthogonal quantum groups and su q 2 quantum groups on the construction of a sufficient supply of bounded central functionals for su q 2 quantum groups and on the free product techniques of ricard and xu our results generalize previous work in the kac setting due to brannan on the haagerup property and due to the second author on the ccap

generalized plasticity and shape memory alloys the theory of the generalized plasticity model is reviewed a special form for multiaxial behavior based on the drucker prager flow potential is proposed the model is applied to a simplified representation of the behavior of shape memory alloys with numerical examples

approximation properties for group algebras and group von neumann algebras let g be a locally compact group let c g resp vn g be the c algebra resp the von neumann algebra associated with the left regular representation i of g let a g be the fourier algebra of g and let moa g be the set of completely bounded multipliers of a g with the completely bounded norm moa g is a dual space and we say that g has the approximation property ap if there is a net ua of functions in a g with compact support such that ua a 1 in the associated weak topology in particular g has the ap if g is weakly amenable a g has an approximate identity that is bounded in the completely bounded norm for a discrete group f we show that f has the ap x c f has the slice map property for subspaces of any c algebra x vn jt has the slice map property for a weakly closed subspaces of any von neumann algebra property se the semidirect product of weakly amenable groups need not be weakly amenable we show that the larger class of groups with the ap is stable with respect to semidirect products and more generally this class is stable with respect to group extensions we also obtain some results concerning crossed products for example we show that the crossed product m a g of a von neumann algebra m with property s by a group g with the ap also has property s

variable resolution for sph a dynamic particle coalescing and splitting scheme abstract in this paper a novel variable resolution method using particle splitting and coalescing for the sph numerical solution of the navier stokes equations is presented the key idea of the scheme is to modify dynamically the particle sizes by means of splitting and coalescing merging individual particles to provide good resolution only where it is needed the sph scheme adopted is derived using the variational principle guaranteeing that both mass and momentum are conserved for particles with different smoothing lengths a particle shifting procedure is used to prevent unacceptable anisotropic distributions of the particles and is further generalized for treating domains with variable mass particles the algorithm has been tested against analytical solutions for poiseuille and taylor green flows showing that the shifting algorithm is effective in increasing the accuracy and that error introduced by the splitting and coalescing is negligible the capability of the numerical scheme for increasing efficiency is shown for more general problems the simulations of a moving square in a box and flow past a cylinder have shown that the particle refinement procedure is able to increase the efficiency while maintaining the same level of accuracy as a uniform distribution with the most refined resolution

a simple model of generalized plasticity abstract the generalized plasticity model which has previously been discussed by the author primarily in a theoretical way is made specific in the form of a simple version based on a single function of the state variables after a review of the basic concepts of generalized plasticity the appropriate simplifications are introduced leading to a one dimensional model that can be used to generate in closed form stress strain diagrams under arbitrary stress controlled loading including cyclic loading this model is then extended into a multiaxial form that is used to solve the problem of the plastic expansion with elastic deformations neglected of a pressurized thick walled tube

on the structural theory of ii1 factors of negatively curved groups ii actions by product groups abstract this paper contains a series of structural results for von neumann algebras arising from measure preserving actions by product groups on probability spaces expanding upon the methods used earlier by the first two authors we obtain new examples of strongly solid factors as well as von neumann algebras with unique or no cartan subalgebra for instance we show that every ii 1 factor associated with a weakly amenable group in the class s of ozawa is strongly solid there is also the following product version of this result any maximal abelian subalgebra of any ii 1 factor associated with a finite product of weakly amenable groups in the class s of ozawa has an amenable normalizing algebra finally pairing some of these results with a cocycle superrigidity result of ioana it follows that compact actions by finite products of lattices in s p n 1 n 2 are virtually w superrigid

noncommutative khintchine inequalities in interpolation spaces of lp spaces abstract we prove noncommutative khintchine inequalities for all interpolation spaces between l p and l 2 with p 2 in particular it follows that khintchine inequalities hold in l 1 using a similar method we find a new deterministic equivalent for the rc norm in all interpolation spaces between l p spaces which unifies the cases p 2 and p 2 it produces a new proof of khintchine inequalities for p 1 for free variables to complete the picture we exhibit counter examples which show that neither of the usual closed formulas for khintchine inequalities can work in l 2 we also give an application to martingale inequalities

approximation properties and absence of cartan subalgebra for free araki woods factors abstract we show that all the free araki woods factors h r u t have the complete metric approximation property using ozawa popa s techniques we then prove that every nonamenable subfactor n h r u t which is the range of a normal conditional expectation has no cartan subalgebra we finally deduce that the type iii1 factors constructed by connes in the 70s can never be isomorphic to any free araki woods factor which answers a question of shlyakhtenko and vaes

an incompressible multi phase sph method an incompressible multi phase sph method is proposed in this method a fractional time step method is introduced to enforce both the zero density variation condition and the velocity divergence free condition at each full time step to obtain sharp density and viscosity discontinuities in an incompressible multi phase flow a new multi phase projection formulation in which the discretized gradient and divergence operators do not require a differentiable density or viscosity field is proposed numerical examples for taylor green flow capillary waves drop deformation in shear flows and for rayleigh taylor instability are presented and compared to theoretical solutions or references from literature the results suggest good accuracy and convergence properties of the proposed method

strongly solid group factors which are not interpolated free group factors we give examples of non amenable infinite conjugacy classes groups with the haagerup property weakly amenable with constant cb 1 for which we show that the associated ii1 factors l are strongly solid i e the normalizer of any diffuse amenable subalgebra p subset l gamma generates an amenable von neumann algebra nevertheless for these examples of groups l is not isomorphic to any interpolated free group factor l ft for 1 t

a generalized elastoplastic plate theory and its algorithmic implementation in continuum mechanics within specific classes of problems one or two dimensional theories are often simpler to apply than the more complete three dimensional one this is for example the case of thin bodies such as plates or shells which may be studied using appropriate two dimensionai theories within this approach the reduction of the dimension is traded for a loss of information relative to the motion in the transverse direction for example in the case of non linear material behaviour classical plasticity plate theories are usually not able to model the effects related to the spreading of plasticity through the cross section in the present paper we discuss a generalized plasticity plate model which can be used to reproduce some of the three dimensional effects in a two dimensional setting we present the continuous and the discrete time model including both isotropic and kinematic hardening mechanisms moreover the form of the tangent matrix consistent with the discrete model is addressed finally some examples cantilever beam clamped circular plate and clamped square plate under monotonic and cyclic loading are studied numerically using a three dimensional classical plasticity theory a classical plasticity plate theory and the proposed plate theory the generalized plasticity plate model matches the three dimensional response with greater accuracy than the classical plasticity plate model

a new insight into the consistency of the sph interpolation formula abstract in this paper the consistency of the smoothed particle hydrodynamics sph interpolation formula is investigated by analytical means a novel error analysis is developed in n dimensional space using the poisson summation formula which enables the simultaneous treatment of both the kernel and particle approximation errors for arbitrary particle distributions new consistency integral relations are derived for the particle approximation which correspond to the cosine fourier transform of the kernel consistency conditions the functional dependence of the error bounds on the sph interpolation parameters namely the smoothing length h and the number of particles within the kernel support n is demonstrated explicitly from which consistency conditions arise as n the particle approximation converges to the kernel approximation independently of h provided that the particle mass scales with h as m h with n where n is the spatial dimension this implies that as h 0 the joint limit m 0 n and n is necessary for complete convergence to the continuum where n is the total number of particles the analysis also reveals a dominant error term of the form ln n n n for finite n as it has long been conjectured based on the similarity between the sph and the quasi monte carlo estimates when n 1 the error of the sph interpolant decays as n 1 independently of the dimension this ensures approximate partition of unity of the kernel volume

free products of c algebras small spatial free products of c algebras are constructed under certain conditions they have properties similar to those proved by paschke and salinas for the algebras c gi g2 where g1 g2 are discrete groups the freeproduct analogs of noncommutative bernoulli shifts are discussed 0 introduction let k be a field consider the category of unital algebras over k it is well known that this category admits coproducts free products of algebras 2 heuristically the free product of algebras is the algebra generated by them with no relations except for the identification of unit elements if k c the complex numbers and we consider unital algebras we can easily define a operation on the free products let a b be unital c algebras and a b their free product which is a unital algebra the question arises in what ways may one define a pre c norm on a b that extends the norms on a and b guided by analogy with tensor products we expect to have a choice among many pre c norms giving rise to many c free products of a and b one natural norm is 1c i i sup 1it c ih st representation of a b the representations of a b are in 1 1 correspondence with pairs of representations of a and b which act on the same hilbert space let a b be the completion of a b in this norm it is easy to see that this construction defines a coproduct in the category of c algebras and that a b is the biggest free product of a and b analogous to the biggest tensor product a 0 b if g 1 g2 are discrete groups we obtain c g1 c g2 c gi g2 where g1 g2 is the free product group and this is analogous to the relation c g1 0 c g2 c g1 x g2 this paper is motivated by the question is there a smallest c product a b in analogy to the smallest tensor product a b satisfying a relation cr gi g2 cr gi cr g2 received by the editors january 28 1981 and in revised form may 19 1981 1980 mathematics subject classification primary 46l05 secondary 46l55 1 982 american mathematical society 0002 9947 82 00001022 04 25

radial multipliers on reduced free products of operator algebras let ai be a family of unital c algebras respectively of von neumann algebras and n0 c we show that if a hankel matrix related to is trace class then there exists a unique completely bounded map m on the reduced free product of the ai which acts as a radial multiplier hereby we generalize a result of wysoczanski for herz schur multipliers on reduced group c algebras for free products of groups

the euler maclaurin formula for simple integral polytopes we give a euler maclaurin formula with remainder for the sum of a smooth function on the integral points in a simple integral lattice polytope our proof uses elementary methods

a constant density approach for incompressible multi phase sph a constant density approach which corrects intermediate density errors by adjusting the half time step velocity with exact projection is proposed for the multi phase sph method developed in our previous work x y hu n a adams an incompressible multi phase sph method j comput phys 227 2007 264 278 as no prescribed reference pressure is required the present approach introduces smaller numerical viscosity and allows to simulate flows with unprecedentedly high density ratios by the projection sph method numerical examples for taylor green flow capillary waves and for rayleigh taylor instability are presented and compared to theoretical solutions or references from the literature

on uniqueness of solutions in generalized plasticity at infinitesimal deformation abstract by means of the usual methodology used in proving the uniqueness of solutions of quasi static boundary value problems in solid mechanics with infinitesimal deformations it is shown that in a material modeled by generalized plasticity theory a sufficient condition for uniqueness of the strain rate field holds if the material is not merely work hardening but if its plastic modulus exceeds a certain threshold value that increases with the degree of deviation of the plastic strain rate from the normal to the loading surface

a characterization of radial herz schur multipliers on free products of discrete groups a characterization of radial herz schur multipliers on groups which are free products g ni 1gi of subgroups of the same order finite or infinite is given the multiplier norm is computed in terms of trace norms of appropriate trace operators this applies in particular to free groups fn ni 1 z with block length this method also applies to characterizing radial multipliers of free product groups of distinct orders all greater than 2 but in this case we can compute only the multiplier norm up to some constant

axis symmetrical riemann problem solved with standard sph method development of a polar formulation with artificial viscosity abstract this paper presents the development of a cylindrical sph formulation based on previous study of the literature petschek et al with an explicit formulation for the artificial viscosity the entire development is explained to propose a formulation adapted to solve euler equations in the case of a riemann problem with axis symmetric conditions thus the artificial viscosity is constructed to find smooth solutions of well known riemann problems such as sod noh and sedov problems numerical results are compared to exact solutions and observations are made on numerical parameters influence this study contributes to validate the axis symmetrical formulation for pure hydrodynamics tests

truncation error in mesh free particle methods a truncation error analysis has been developed for the approximation of spatial derivatives in smoothed particle hydrodynamics sph and related first order consistent methods such as the first order form of the reproducing kernel particle method error is shown to depend on both the smoothing length h and the ratio of particle spacing to smoothing length x h for uniformly spaced particles in one dimension analysis shows that as h is reduced while maintaining constant x h error decays as h2 until a limiting discretization error is reached which is independent of h if x h is reduced while maintaining constant h i e if the number of neighbours per particle is increased error decreases at a rate which depends on the kernel function s smoothness when particles are distributed non uniformly error can grow as h is reduced with constant x h first order consistent methods are shown to remove this divergent behaviour numerical experiments confirm the theoretical analysis for one dimension and indicate that the main results are also true in three dimensions this investigation highlights the complexity of error behaviour in sph and shows that the roles of both h and x h must be considered when choosing particle distributions and smoothing lengths copyright 2005 john wiley sons ltd

factoriality type classification and fullness for free product von neumann algebras abstract we give a complete answer to the questions of factoriality type classification and fullness for arbitrary free product von neumann algebras

numerical investigation of newtonian and non newtonian multiphase flows using isph method we have presented a multiphase incompressible smoothed particle hydrodynamics method with an improved interface treatment procedure to demonstrate the effectiveness of the interface treatment which can handle multiphase flow problems with high density and viscosity ratios we have modeled several challenging two phase flow problems namely single vortex flow square droplet deformation droplet deformation in shear flow and finally the newtonian bubble rising in viscous and viscoelastic liquids the proposed interface treatment includes the usage of i different smoothing functions in this work cubic spline kernel function for discretizing equations associated with the calculation of the surface tension force while the quintic spline for the discretization of governing equations and the relevant boundary conditions and ii a new discretization scheme for calculating the pressure gradient it is shown that with the application of the improved interface treatment it becomes possible to model multiphase flow problems with the density and viscosity ratios up to 1000 and 100 respectively while using standard projection method the utilization of cubic spline for the continuum surface force model significantly improves the quality of the calculated interface thereby eliminating the interphase particle penetrations and in turn leading to the calculation of more accurate velocity and pressure fields

modeling low reynolds number incompressible flows using sph the method of smoothed particle hydrodynamics sph is extended to model incompressible flows of low reynolds number for such flows modification of the standard sph formalism is required to minimize errors associated with the use of a quasi incompressible equation of state treatment of viscosity state equation kernel interpolation and boundary conditions are described simulations using the method show close agreement with series solutions for couette and poiseuille flows furthermore comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields the sph results exhibit small pressure fluctuations near curved boundaries further improvements to the boundary conditions may be possible which will reduce these errors a similar method to that used here may permit the simulation of other flows at low reynolds numbers using sph further development will be needed for cases involving free surfaces or substantially different equations of state