stability analysis of particle methods with corrected derivatives abstract the stability of discretizations by particle methods with corrected derivatives is analyzed it is shown that the standard particle method which is equivalent to the element free galerkin method with an eulerian kernel and nodal quadrature has two sources of instability 1 rank deficiency of the discrete equations and 2 distortion of the material instability the latter leads to the so called tensile instability it is shown that a lagrangian kernel with the addition of stress points eliminates both instabilities examples that verify the stability of the new formulation are given

moving least squares particle hydrodynamics i consistency and stability the smooth particle hydrodynamics sph method is derived in a novel manner by means of a galerkin approximation applied to the lagrangian equations of continuum mechanics as in the finite element method this derivation is modified to replace the sph interpolant with the moving least squares mls interpolant of lancaster and saulkaskas and define a new particle volume which ensures thermodynamic compatibility a variable rank modification of the mls interpolants which retains their desirable summation properties is introduced to remove the singularities that occur when divergent flow reduces the number of neighbours of a particle to less than the minimum required a surprise benefit of the galerkin sph derivation is a theoretical justification of a common ad hoc technique for variable h sph the new mlsph method is conservative if an anti symmetric quadrature rule for the stiffness matrix elements can be supplied in this paper a simple one point collocation rule is used to retain similarity with sph leading to a non conservative method several examples document how mlsph renders dramatic improvements due to the linear consistency of its gradients on three canonical difficulties of the sph method spurious boundary effects erroneous rates of strain and rotation and tension instability two of these examples are non linear lagrangian patch tests with analytic solutions with which mlsph agrees almost exactly the examples also show that mlsph is not absolutely stable if the problems are run to very long times a linear stability analysis explains both why it is more stable than sph and not yet absolutely stable and an argument is made that for realistic dynamic problems mlsph is stable enough the notion of coherent particles for which the numerical stability is identical to the physical stability is introduced the new method is easily retrofitted into a generic sph code and some observations on performance are made copyright 1999 john wiley sons ltd

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

constructing smoothing functions in smoothed particle hydrodynamics with applications this paper presents a general approach to construct analytical smoothing functions for the meshfree lagrangian and particle method of smoothed particle hydrodynamics the approach uses integral form of function representation and applies taylor series expansion to the sph function and derivative approximations the constructing conditions are derived systematically which not only interpret the consistency condition of the method but also describe the compact supportness requirement of the smoothing function examples of sph smoothing function are constructed including some existing ones with this approach a new quartic smoothing function with some advantages is constructed and is applied to the one dimensional shock problem and a one dimensional tnt detonation problem the good agreement between the sph results and those from other sources shows the effectiveness of the approach and the newly constructed smoothing function in numerical simulations

transient fokker planck kolmogorov equation solved with smoothed particle hydrodynamics method summary probabilistic theories aim at describing the properties of systems subjected to random excitations by means of statistical characteristics such as the probability density function pdf the time evolution of the pdf of the response of a randomly excited deterministic system is commonly described with the transient fokker planck kolmogorov fpk equation the fpk equation is a conservation equation of a hypothetical or abstract fluid which models the transport of probability this paper presents a generalized formalism for the resolution of the transient fpk equation by using the well known mesh free lagrangian method smoothed particle hydrodynamics numerical implementation shows notable advantages of this method in an unbounded state space 1 the conservation of total probability in the state space is explicitly written 2 no artifact is required to manage far field boundary conditions 3 the positivity of the pdf is ensured and 4 the extension to higher dimensions is straightforward furthermore thanks to the moving particles this method is adapted for a large kind of initial conditions even slightly dispersed distributions the fpk equation is solved without any a priori knowledge of the stationary distribution just a precise representation of the initial distribution is required copyright 2013 john wiley sons ltd

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

adaptive kernel estimation and sph tensile instability we propose an alternative method to remove the tensile instability in standard sph simulations of a fluid the method relies on an adaptive density kernel estimation adke algorithm which allows the width of the kernel interpolant to vary locally in such a way that only the minimum necessary smoothing is applied to the data by means of a linear perturbation analysis of the sph equations for a heat conducting viscous van der waals fluid we derive the corresponding dispersion relation solution of the dispersion relation in the short wavelength limit shows that the tensile instability is effectively removed for a wide range of the adke parameters application of the method to the formation of equilibrium liquid drops confirms the analytical results of the linear stability analysis examples of the resolving power of the method are also given for the nonlinear oscillations of an excited drop and the sedov blast wave problem

enhanced local maximum entropy approximation for stable meshfree simulations abstract we introduce an improved meshfree approximation scheme which is based on the local maximum entropy strategy as a compromise between shape function locality and entropy in an information theoretical sense the improved version is specifically designed for severe finite deformation and offers significantly enhanced stability as opposed to the original formulation this is achieved by i formulating the quasistatic mechanical boundary value problem in a suitable updated lagrangian setting ii introducing anisotropy in the shape function support to accommodate directional variations in nodal spacing with increasing deformation and eliminate tensile instability iii spatially bounding and evolving shape function support to restrict the domain of influence and increase efficiency iv truncating shape functions at interfaces in order to stably represent multi component systems like composites or polycrystals the new scheme is applied to benchmark problems of severe elastic and elastoplastic deformation that demonstrate its performance both in terms of accuracy as compared to exact solutions and where applicable finite element simulations and efficiency importantly the presented formulation overcomes the classical tensile instability found in most meshfree interpolation schemes as shown for stable simulations of e g the inhomogeneous extension of a hyperelastic block up to 100 or the torsion of a hyperelastic cube by 200 both in an updated lagrangian setting and without the need for remeshing

braid relations in the yokonuma hecke algebra abstract in this note we prove a theorem on a new presentation for the algebra of the endomorphisms of the permutation representation yokonuma hecke algebra of a simple chevalley group with respect to a maximal unipotent subgroup this presentation is given using certain nonstandard generators

lanczos generalized derivative insights and applications generalizations of the lanczos derivative provide a basis for certain grid free finite interpolation methods fims which appear to have advantages over alternatives such as the standard finite difference methods fdms or finite element methods fems for certain problems e g hypervelocity impact problems in computational material dynamics

an sph projection method for simulating fluid hypoelastic structure interaction abstract in this paper an incompressible smoothed particle hydrodynamics sph method is proposed for simulation of fluid structure interaction problems deploying the pressure poisson equation to satisfy incompressibility constraints viscous fluid flow past rigid and hypoelastic solid surfaces is studied the fluid is fully coupled with the solid structure that can undergo large structural deformations a key feature of the proposed scheme is that the no slip and coupling conditions on the contact surface are satisfied automatically to alleviate the numerical difficulties encountered when a hypoelastic solid structure is highly stretched an artificial stress term is incorporated into the momentum equation which reduces the risk of unrealistic fractures in the material to demonstrate the ability of the proposed method in dealing with large deformation of free surface the well known pure dam breaking problem is solved and then the oscillations of an cantilever beam is simulated to show the capability of the method in capturing the large deformations of an elastic solid eventually three challenging test cases deformation of an elastic plate subjected to time dependent water pressure collapse of a water column with an obstacle and breaking dam on a hypoelastic wall are solved to demonstrate the capability of the proposed scheme the simulated results are in very good agreement with available experimental and numerical results

a level set enhanced natural kernel contact algorithm for impact and penetration modeling summary a natural kernel contact nkc algorithm under the framework of the semi lagrangian reproducing kernel particle method semi lagrangian rkpm is proposed to model multi body contact with specific consideration for impact and penetration modeling the nkc algorithm utilizes the interaction of the semi lagrangian kernel functions associated with contacting bodies to serve as the non penetration condition the effects of friction are represented by introducing a layer of the friction like elasto plasticity material between contacting bodies this approach allows the frictional contact conditions and the associated kinematics to be naturally embedded in the semi lagrangian rkpm inter particle force calculation the equivalence in the karush kuhn tucker conditions between the proposed nkc algorithm and the conventional contact kinematic constraints as well as the associated state variable relationships are identified a level set method is further introduced in the nkc algorithm to represent the contact surfaces without pre defined potential contact surfaces the stability analysis performed in this work shows that temporal stability in the semi lagrangian rkpm with nkc algorithms is related to the velocity gradient between contacting bodies the proposed methods have been verified by several benchmark problems and applied to the simulation of impact and penetration processes copyright 2014 john wiley sons ltd

normalized sph with stress points smoothed particle hydrodynamics is extended to a normalized staggered particle formulation with boundary conditions a companion set of interpolation points is introduced that carry the stress velocity gradient and other derived field variables the method is stable linearly consistent and has an explicit treatment of boundary conditions also a new method for finding neighbours is introduced which selects a minimal and robust set and is insensitive to anisotropy in the particle arrangement test problems show that these improvements lead to increased accuracy and stability published in 2000 by john wiley sons ltd

a peridynamic model for plasticity micro inertia based flow rule entropy equivalence and localization residuals this article presents a non ordinary state based peridynamic pd model for thermo visco plasticity that incorporates a microinertia driven dynamic flow rule in addition to the three displacement degrees of freedom the model assigns to each particle an internal degree of freedom namely the equivalent plastic strain the flow rule itself is in the form of an integro differential micro force balance written in terms of appropriate pd states associated with micro stresses corresponding to the internal degree of freedom an equation for entropy balance adapted to the pd setup is also proposed along with the internal energy equivalence we exploit a notion of equivalence of the local entropy production for the constitutive modelling of the force states as we also demonstrate the pd model naturally accounts for the localization residual terms in the local balances for internal energy and entropy originally conceived of by edelen and co workers nearly half a century ago as a source of nonlocal interaction the model is numerically implemented for the problem of impact between two 4340 steel plates and the results show that the model provides information on nontrivial effects of micro inertia on the plastic flow and temperature generation by incorporating a classical damage model in the pd set up we also discuss an extension of the approach for ductile failure and report on the numerical results against tension test on an a440 steel plate with holes c 2017 elsevier b v all rights reserved

sph hydrocodes can be stabilized with shape shifting grid free methods such as sph smoothed particle hydrodynamics may eventually be more efficacious in their representations of material dynamics than the standard fixed grid methods however standard sph with stress and interpolation weight w has instabilities when w 0 and in tension 0 conservative smoothing can control the sph instabilities but it may smooth out more of the short wave length structure than desired sph can also be stabilized by shifting the shape of w to change the sign of w

unipotent hecke algebras of gln fq this paper describes a family of hecke algebras h endg indug where u is the subgroup of unipotent upper triangular matrices of g gln fq and is a linear character of u the main results combinatorially index a basis of h provide a large commutative subalgebra of h and after describing the combinatorics associated with the representation theory of h generalize the rsk correspondence that is typically found in the representation theory of the symmetric group

clustered generalized finite element methods for mesh unrefinement non matching and invalid meshes in spite of significant advancements in automatic mesh generation during the past decade the construction of quality finite element discretizations on complex three dimensional domains is still a difficult and time demanding task in this paper the partition of unity framework used in the generalized finite element method gfem is exploited to create a very robust and flexible method capable of using meshes that are unacceptable for the finite element method while retaining its accuracy and computational efficiency this is accomplished not by changing the mesh but instead by clustering groups of nodes and elements the clusters define a modified finite element partition of unity that is constant over part of the clusters this so called clustered partition of unity is then enriched to the desired order using the framework of the gfem the proposed generalized finite element method can correctly and efficiently deal with i elements with negative jacobian ii excessively fine meshes created by automatic mesh generators iii meshes consisting of several sub domains with non matching interfaces under such relaxed requirements for an acceptable mesh and for correctly defined geometries today s automated tetrahedral mesh generators can practically guarantee successful volume meshing that can be entirely hidden from the user a detailed technical discussion of the proposed generalized finite element method with clustering along with numerical experiments and some implementation details are presented copyright 2006 john wiley sons ltd

on the rigidity of small domains abstract let k be an algebraically closed field of arbitrary characteristic let a be an affine domain over k with transcendence degree 1 which is not isomorphic to k x and let b be a domain over k we show that the ak invariant distributes over the tensor product of a by b as a consequence we obtain a generalization of the cancellation theorem of s abhyankar p eakin and w heinzer

representation theory of the yokonuma hecke algebra abstract we develop an inductive approach to the representation theory of the yokonuma hecke algebra y d n q based on the study of the spectrum of its jucys murphy elements which are defined here we give explicit formulas for the irreducible representations of y d n q in terms of standard d tableaux we then use them to obtain a semisimplicity criterion finally we prove the existence of a canonical symmetrising form on y d n q and calculate the schur elements with respect to that form

arbitrarily smooth generalized finite element approximations this paper presents a procedure to build ck k arbitrarily large generalized finite element fe shape functions defined on non structured finite element meshes the functions have the same support as corresponding global fe lagrangian shape functions meshes with both convex and non convex clouds set of elements sharing a vertex node can be used the so called r functions are used to build ck fe based partition of unity functions with non convex support a technique to combine c0 lagrangian fe shape functions with the proposed ck partition of unity is presented the technique allows the use of ck generalized fe shape functions in parts of the computational domain where their high smoothness is required as in the case of problems with distributional boundary conditions and the less computationally demanding c0 generalized fe shape functions elsewhere in the domain a linear elasticity problem with a concentrated moment is solved using the proposed ck generalized fe method higher order distributional boundary conditions can also be handled by the method a detailed convergence analysis is presented for this class of problems as well as for problems in energy space the integrability of the functions using standard gauss legendre rules is also investigated

p adic framed braids ii abstract the yokonuma hecke algebras are quotients of the modular framed braid group and they support markov traces in this paper which is sequel to juyumaya and lambropoulou 2007 6 we explore further the structures of the p adic framed braids and the p adic yokonuma hecke algebras constructed by juyumaya and lambropoulou 2007 6 by means of dense sub structures approximating p adic elements we also construct a p adic markov trace on the p adic yokonuma hecke algebras and approximate the values of the p adic trace on p adic elements surprisingly the markov traces do not re scale directly to yield isotopy invariants of framed links this leads to imposing the e condition on the trace parameters for solutions of the e system we then define 2 variable isotopy invariants of modular framed links these lift to p adic isotopy invariants of classical framed links the yokonuma hecke algebras have topological interpretations in the context of framed knots of classical knots of singular knots and of transverse knots

a skein like multiplication algorithm for unipotent hecke algebras let g be a finite group of lie type e g gl n fq and u a maximal unipotent subgroup of g if is a linear character of u then the unipotent hecke algebra is h end cg ind g u unipotent hecke algebras have a natural basis coming from double cosets of u in g this paper describes relations for reducing products of basis elements and gives a detailed description of the implications in the case g gl n f q

a lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue we present a novel lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue linear solids are represented by the lagrangian formulation of the stress strain relationship that is extended to nonlinear solids by using the lagrangian evolution of the deformation gradient described in a moving framework the present method introduces a level set description along with the particles to capture the body deformations and to enforce the boundary conditions furthermore the accuracy of the method in cases of large deformations is ensured by implementing a particle remeshing procedure the method is validated in several benchmark problems in two and three dimensions and the results compare well with the results of respective finite elements simulations in simulations of large solid deformation under plane strain compression the finite element solver exhibits spurious structures that are not present in the lagrangian particle simulations the particle simulations are compared with experimental results in an aspiration test of liver tissue

a unified stability analysis of meshless particle methods a uni ed stability analysis of meshless methods with eulerian and lagrangian kernels is presented three types of instabilities were identi ed in one dimension an instability due to rank de ciency a tensile instability and a material instability which is also found in continua the stability of particle methods with eulerian and lagrangian kernels is markedly di erent lagrangian kernels do not exhibit the tensile instability in both kernels the instability due to rank de ciency can be suppressed by stress points in two dimensions the stabilizing e ect of stress points is dependent on their locations it was found that the best approach to stable particle discretizations is to use lagrangian kernels with stress points the stability of the least squares stabilization was also studied copyright 2000 john wiley sons ltd

a generalized smoothed particle hydrodynamics method for nonlinear dynamic problems abstract a generalized smoothed particle hydrodynamics sph method was developed for the numerical simulation of nonlinear dynamic problems the performance of the proposed method was demonstrated by solving burgers equations over a wide range of the viscosity parameters in one and two space dimensions it was shown that the present results agree very well with other existing solutions as compared to other meshless methods this algorithm is quite straightforward and simple and can be coded easily

three dimensional simulation of a solid liquid flow by the dem sph method abstract in this paper we describe a new lagrangian lagrangian algorithm which is referred to be the dem sph method for solid liquid flows involving free surfaces the dem solid phase and the sph liquid phase are coupled using the local averaging technique described by lagrangian approaches where both the continuity equation and the interaction force i e drag force are connected with the local mean voidage conservative forms of momentum transformation are derived for the dem sph interaction via a variational approach by introducing a correction to the sph approximation with explicit inclusion of boundary information arbitrary boundaries can be modeled without any extra wall particles where the boundary is used commonly for both dem and sph phases we deploy level set distance functions to efficiently construct and evaluate this boundary model to examine the validity of the present method we perform three dimensional simulations of a dynamic flow in a solid liquid dam break and a quasi steady flow in a rotating cylindrical tank and we conduct validation experiments to justify the simulation results in the dam break problem positions of wave fronts during the collapse are computed and compared with experimental measurements for the circulating tank some macroscopic aspects of the steady flow e g the shape dimension and velocity profile of the solid bed are obtained for validation data in both cases the simulation results are in good agreement with those of the experiment consequently the dem sph method is proved to be adequate in modeling solid liquid flows through this study

an hourglass control algorithm for lagrangian smooth particle hydrodynamics abstract this paper presents a stabilization scheme which addresses the rank deficiency problem in meshless collocation methods for solid mechanics specifically smooth particle hydrodynamics sph in the total lagrangian formalism is considered this method is rank deficient in the sense that the sph approximation of the deformation gradient is not unique with respect to the positions of the integration points the non uniqueness can result in the formation of zero energy modes if undetected these modes can grow and completely dominate the solution here an algorithm is introduced which effectively suppresses these modes in a fashion similar to hour glass control mechanisms in finite element methods simulations utilizing this control algorithm exhibit much improved stability accuracy and error convergence properties in contrast to an alternative method which eliminates zero energy modes namely the use of additional integration points the here presented algorithm is easy to implement and computationally very efficient

a one parameter family of interpolating kernels for smoothed particle hydrodynamics studies a set of interpolating functions of the type f v email protected p2v n is analyzed in the context of the smoothed particle hydrodynamics sph technique the behaviour of these kernels for several values of the parameter n has been studied either analytically as well as numerically in connection with several tests carried out in two dimensions the main advantage of this kernel relies in its flexibility because for n 3 it is similar to the standard widely used cubic spline whereas for n 3 the interpolating function becomes more centrally condensed being well suited to track discontinuities such as shock fronts and thermal waves

suppressing local particle oscillations in the hamiltonian particle method for elasticity the governing equation of elasticity is discretized into motion equations of the particles in a hamiltonian system a weighted least square method is adopted to evaluate the green lagrange strain using a symplectic scheme for the hamiltonian system we obtain the property of energy conservation in the discretized calculations however local particle oscillations occur and they excessively decrease low frequency motion in this study we propose the use of an artificial potential force to suppress the local oscillations the accuracy of the model with and without the inclusion of the artificial force is examined by analyzing a cantilever beam and wave propagation with the inclusion of the artificial force the local oscillations are reduced while energy conservation is maintained

an improved sph method towards higher order convergence this paper evaluates various formulations of the sph method for solving the euler equations convergence and stability aspects are discussed and tested taking into account subtleties induced by the presence of a free surface the coherence between continuity and momentum equations is considered using a variational study the use of renormalization to improve the accuracy of the simulations is investigated and discussed a new renormalization based formulation involving wide accuracy improvements of the scheme is introduced the classical sph and renormalized approaches are compared to the new method using simple test cases thus outlining the efficiency of this new improved sph method finally the so called tensile instability is shown to be prevented by this enhanced sph method through accuracy increases in the gradient approximations

on zariski s cancellation problem in positive characteristic abstract in this paper we show that when k is a field of positive characteristic the affine space a k n is not cancellative for any n 3

hamiltonian particle hydrodynamics abstract particle based hydrodynamics models offer distinct advantages over eulerian and lagrangian hydrocodes in particular shock physics applications particle models are designed to avoid the mesh distortion and state variable diffusion problems which can hinder the effective use of lagrangian and eulerian codes respectively however existing particle in cell and smooth particle hydrodynamics methods employ particles which are actually moving interpolation points the latter distinction has been emphasized in the more recent development of element free galerkin theory as a result general formulations of all of the aforementioned methods are based on the partial differential equation forms of the continuum balance laws which underlie conventional eulerian and lagrangian schemes an alternative modeling methodology based on the application of hamilton s equations to a system of deforming physical particles provides a fully lagrangian energy based approach to shock physics simulations neither interpolations of field variables nor continuum balance laws are used to establish the state equations for the particle system mechanical and thermal interaction of the particles is accounted for by nonholonomic constraints which determine both particle entropy evolution and particle collision loads application of the method is illustrated by simulation of a wall shock problem

a weighted least squares particle in cell method for solid mechanics a novel meshfree method is proposed that incorporates features of the material point mpm and generalized interpolation material point gimp methods and can be used within an existing mpm gimp implementation weighted least squares kernel functions are centered at stationary grid nodes and used to approximate field values and gradients integration is performed over cells of the background grid and material boundaries are approximated with an implicit surface the proposed method avoids nearest neighbor searches while significantly improving accuracy over mpm and gimp implementation is discussed in detail and several example problems are solved including one manufactured solution which allows measurement of dynamic non linear large deformation performance advantages and disadvantages of the method are discussed copyright 2010 john wiley sons ltd

on the fundamental groups of some open rational surfaces if d is an irreducible curve with ordinary nodes in a relatively minimal smooth projective rational surface m then from the solution of zanski s problem in 12 proposition 3 27 it follows that n m d is abelian on the other hand in 15 o zariski has given an example of an irreducible sextic d in ip 2 with six ordinary cusps lying on a conic such that q f 2 d is an infinite group in view of this the following conjecture seems significant

a stable sph discretization of the elliptic operator with heterogeneous coefficients smoothed particle hydrodynamics sph has been extensively used to model high and low reynolds number flows free surface flows and collapse of dams study pore scale flow and dispersion elasticity and thermal problems in different applications it is required to have a stable and accurate discretization of the elliptic operator with homogeneous and heterogeneous coefficients in this paper the stability and approximation analysis of different sph discretization schemes traditional and new of the diagonal elliptic operator for homogeneous and heterogeneous media are presented the optimum and new discretization scheme of specific shape satisfying thetwo point flux approximation nature is also proposed this scheme enhances the laplace approximation brookshaw s scheme 1985 and schwaiger s scheme 2008 used in the sph community for thermal viscous and pressure projection problems with an isotropic elliptic operator the numerical results are illustrated by numerical examples where the comparison between different versions of the meshless discretization methods are presented

conservative smoothing with b splines stabilizes sph material dynamics in both tension and compression smooth particle hydrodynamics sph is a grid free method for material dynamics which appears to have potential advantages over fixed grid methods with respect to grid tangling standard sph with stress s and interpolation weight w has instabilities of two types when sw 0 and tension s 0 in theory conservative smoothing can stabilize both types but carefully controlling smoothing to prevent excessive loss of fine detail had been found to be difficult in some numerical experiments here we present an easy natural way of using the sph b spline finite interpolation method to introduce sufficient conservative smoothing to stabilize sph material dynamics in both tension and compression we present numerical results for both tension and compression which provide evidence of the efficacy of this approach

an isomorphism theorem for yokonuma hecke algebras and applications to link invariants we develop several applications of the fact that the yokonuma hecke algebra of the general linear group gl is isomorphic to a direct sum of matrix algebras associated to iwahori hecke algebras of type a this includes a description of the semisimple and modular representation theory of the yokonuma hecke algebras of gl and a complete classification of all the markov traces for them finally from these markov traces we construct 3 variables polynomials which are invariants for framed and classical knots and links and investigate their properties with the help of the isomorphism in particular for classical knots a consequence of the construction is that the obtained set of invariants is topologically equivalent to the homflypt polynomial we thus recover results of chlouveraki et al 2015 arxiv 1505 06666 about the juyumaya lambropoulou invariants

an accurate multi regime sph scheme for barotropic flows abstract this paper focuses on the use of a mesh less numerical method to solve barotropic fluid flows smooth particle hydrodynamics sph such methods suffer from a severe lack of accuracy when evaluating state variables as the pressure field sph ale methods based on riemann solvers significantly improve this evaluation but increase the scheme complexity and low mach issues are difficult to prevent we propose an alternative scheme called s p h a l e relying on the combination of the sph ale formalism and a finite volume stabilizing low mach scheme applied to monophasic barotropic euler equations its characteristics are detailed and evaluated through a nonlinear stability analysis highlighting cfl like conditions on the scheme parameters as far as we know it is the first time such nonlinear analysis is performed on a sph ale scheme finally its implementation on several academic test cases reveals that the proposed scheme actually increases both stability and accuracy in reduced computation time with respect to sph ale riemann solvers

sph with dynamical smoothing length adjustment based on the local flow kinematics abstract due to the lagrangian nature of smoothed particle hydrodynamics sph the adaptive resolution remains a challenging task in this work we first analyse the influence of the simulation parameters and the smoothing length on solution accuracy in particular in high strain regions based on this analysis we develop a novel approach to dynamically adjust the kernel range for each sph particle separately accounting for the local flow kinematics we use the okubo weiss parameter that distinguishes the strain and vorticity dominated regions in the flow domain the proposed development is relatively simple and implies only a moderate computational overhead we validate the modified sph algorithm for a selection of two dimensional test cases the taylor green flow the vortex spin down the lid driven cavity and the dam break flow against a sharp edged obstacle the simulation results show good agreement with the reference data and improvement of the long term accuracy for unsteady flows for the lid driven cavity case the proposed dynamical adjustment remedies the problem of tensile instability particle clustering

stabilized updated lagrangian corrected sph for explicit dynamic problems this is the pre peer reviewed version of the following article vidal y bonet j huerta a stabilized updated lagrangian corrected sph for explicit dynamic problems international journal for numerical methods in engineering marc 2007 vol 69 num 13 p 2687 2710 which has been published in final form at http www3 interscience wiley com journal 112777203 abstract

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

an adaptive sph method for strong shocks we propose an alternative sph scheme to usual sph godunov type methods for simulating supersonic compressible flows with sharp discontinuities the method relies on an adaptive density kernel estimation adke algorithm which allows the width of the kernel interpolant to vary locally in space and time so that the minimum necessary smoothing is applied in regions of low density we have performed a von neumann stability analysis of the sph equations for an ideal gas and derived the corresponding dispersion relation in terms of the local width of the kernel solution of the dispersion relation in the short wavelength limit shows that stability is achieved for a wide range of the adke parameters application of the method to high mach number shocks confirms the predictions of the linear analysis examples of the resolving power of the method are given for a set of difficult problems involving the collision of two strong shocks the strong shock tube test and the interaction of two blast waves

on double danielewski surfaces and the cancellation problem abstract we study a two dimensional family of affine surfaces which are counter examples to the cancellation problem we describe the makar limanov invariant of these surfaces determine their isomorphism classes and characterize the automorphisms of these surfaces

an energy based criterion of crack branching and its application on the multidimensional space method abstract in this paper a criterion of crack branching based on the energy release rate is proposed theory of multidimensional space method for crack branching is established in the framework of the extended finite element method xfem in which the formula of the boundary shift energy is deduced the boundary cracking energy is obtained because the boundary shift model is abstracted into the boundary cracking model the energy release rates of the crack branching in four quadrants are determined based on boundary cracking energy further the energy release rate of the crack branching is introduced into multidimensional space method to determine the crack branching if the crack tip branching the criteria of crack branching are applied to determine the direction of the branching cracks otherwise the criteria of maximum circumferential stress are applied to determine the direction of the cracks moreover a classical numerical example is investigated to verify the correctness of the criterion of crack branching in the framework of the multidimensional space method

a stabilized fractional step runge kutta taylor sph algorithm for coupled problems in geomechanics abstract failure of geomaterials with pores filled with fluids is an important research area in both civil and geological engineering many finite element formulations for coupled problems present difficulties such as overestimating failure loads or mesh alignment dependence resulting on spurious failure mechanisms moreover the spaces where field variables are approximated have to fulfill additional requirements ensuring stability stress velocity pore pressure formulations in fe analysis provide accurate results for wave propagation and failure analysis however finite elements present important limitations when deformations are large the purpose of this paper is to present a stabilized fractional step sph algorithm which combines the advantages of the sph method for large deformation problems with those of the taylor galerkin algorithm used within the finite element framework

some results on open algebraic surfaces of logarithmic kodaira dimension zero abstract let s be a smooth open algebraic surface of logarithmic kodaira dimension zero and v d a pair of a smooth projective surface v and a simple normal crossing divisor d on v such that v d s we prove that v d 2 where d is the number of all irreducible components of supp d and determine the surface s with v d 2 and those with v d 1 and p g s 0 furthermore by using these results we determine the affine plane curves whose complements have logarithmic kodaira dimension zero

nurbs based parametric mesh free methods a mesh free error reproducing kernel method erkm has recently been proposed by a shaw d roy a nurbs based error reproducing kernel method with applications in solid mechanics comput mech 40 1 2007 127 148 the erkm is based on an initial approximation of the target function by non uniform rational b splines nurbs followed by reproduction of the error via a family of non nurbs basis functions however specifications of the window supports of non nurbs basis functions remain a tricky issue moreover nurbs in higher dimensions 1 is generally defined over rectangular cuboidal in 3d grid structures and thus in many problems of practical interest the geometric complexity of the domain would prevent making use of nurbs in the erkm presently we develop a parametric reformulation of the erkm purely using nurbs this reformulation allows the method to be applicable to non rectangular non cuboidal in 3d physical domains in two or still higher dimensions without a need to explicitly specify the support size of the window a key feature of this development is a geometric map that provides a local bijection between the physical domain and rectangular cuboidal parametric domain the shape functions and their derivatives are then constructed over the parametric domain so that polynomial reproduction and interpolation properties are satisfied over the physical domain with the geometric map being simultaneously preserved a couple of new schemes are also proposed to empower the shape functions with the interpolation property that in turn enables a precise imposition of dirichlet boundary conditions we illustrate the parametric mesh free method in the context of strong weak solutions of a few linear and non linear boundary and initial value problems of engineering interest

analysis of the incompressibility constraint in the smoothed particle hydrodynamics method summary smoothed particle hydrodynamics sph is a particle based fully lagrangian method for fluid flow simulations in this work fundamental concepts of the method are first briefly recalled then we present a thorough comparison of two different incompressibility treatments in sph the weakly compressible approach where a suitably chosen equation of state is used and the truly incompressible method in two basic variants where the velocity field projection onto a divergence free space is performed a noteworthy aspect of the study is that in each incompressibility treatment the same boundary conditions are used and further developed that allows a direct comparison to be made two dimensional and three dimensional validation cases are studied problems associated with the numerical setup are discussed and an optimal choice of the computational parameters is proposed and verified the efficiency issues of the incompressibility treatments are considered and the speed up features are highlighted the results show that the present state of the art truly incompressible methods based on a velocity correction suffer from density accumulation errors to address this issue an algorithm based on a correction for both particle velocities and positions is presented the usefulness of this density correction is examined and demonstrated copyright 2012 john wiley sons ltd

a quasi static dual particle method for solids based on dual particle dynamics summary a dual particle method for problems in solid mechanics on the basis of dual particle dynamics is extended to applications of quasi static deformations of solids the general approach incorporates the discrete strong form of the governing equation a lagrangian representation of a moving least squares approximation of field variables and a spatial discretization comprised of two particle sets motion points and stress points the quasi static dual particle method introduced in this work incorporates geometric and material nonlinearities as well as a modified method for applying traction boundary conditions some computational exercises are performed to verify the correct implementation of the method show convergence behavior and demonstrate the improved performance of the modified traction boundary condition application method copyright 2012 john wiley sons ltd

on generalized cancellation problem abstract a well known cancellation problem of zariski asks whether for two given domains fields k 1 and k 2 an isomorphism of k 1 t k t and k 2 t k 2 t implies an isomorphism of k 1 and k 2 in this paper we address a related problem whether the ring field embedding of k 1 t k 1 t into k 2 t k 2 t implies the ring field embedding of k 1 into k 2 our main result is affirmative if k 1 and k 2 are arbitrary domains fields of the finite transcendence degree and k 1 t k 1 t can be embedded into k 2 t k 2 t then k 1 can be embedded into k 2 as a consequence we answer a question of abhyankar eakin and heinzer j algebra 23 1972 310 342

stabilization algorithm for the optimal transportation meshfree approximation scheme abstract meshfree approximation schemes possess a high potential in computer aided engineering due to their large flexibility especially the tremendous progress in processor technology within recent years relativizes the increase in computation time due to the inherent search algorithm nevertheless meshfree approximation schemes are still faced with some challenges like imposition of dirichlet boundary conditions robustness of the algorithm and accuracy the recent developed optimal transportation meshfree otm method seemed to overcome most of these problems in this paper the otm solution scheme is combined with a standard search algorithm in order to allow a simple and flexible computation however this scheme is not stable for some examples of application hence an investigation is conducted which shows that the reason for this instability is due to underintegration based on this investigation a remedy to stabilize the algorithm is suggested which is based on well known concepts to control the hourglass effects in the finite element method in contrast to the original publication the otm algorithm is derived here from the principle of virtual work local maximum entropy shape functions are used which possess a weak kronecker property this enables a direct imposition of dirichlet boundary conditions if the boundary is convex the limitations of this basis function are also addressed in this paper additionally the search algorithm presented fulfills basic topological requirements several examples are investigated demonstrating the improved behavior of the stabilized otm algorithm

zariski cancellation problem for non domain noncommutative algebras we study zariski cancellation problem for noncommutative algebras that are not necessarily domains

a variationally consistent streamline upwind petrov galerkin smooth particle hydrodynamics algorithm for large strain solid dynamics this paper presents a new smooth particle hydrodynamics sph computational framework for explicit fast solid dynamics the proposed methodology explores the use of the streamline upwind petrov galerkin supg stabilisation methodology as an alternative to the jameson schmidt turkel jst stabilisation recently presented by the authors in lee et al 2016 in the context of a conservation law formulation of fast solid dynamics the work introduced in this paper puts forward three advantageous features over the recent jst sph framework first the variationally consistent nature of the supg stabilisation allows for the introduction of a locally preserving angular momentum procedure which can be solved in a monolithic manner in conjunction with the rest of the system equations this differs from the jst sph framework where an a posteriori projection procedure was required to ensure global angular momentum preservation second evaluation of expensive harmonic and bi harmonic operators necessary for the jst stabilisation is circumvented in the new supg sph framework third the supg sph framework is more accurate for the same number of degrees of freedom than its jst sph counterpart and its accuracy is comparable to that of the robust but computationally more demanding petrov galerkin finite element method pg fem technique explored by the authors in lee et al 2014 gil et al 2014 2016 bonet et al 2015 as shown in the numerical examples included a series of numerical examples are analysed in order to benchmark and assess the robustness and effectiveness of the proposed algorithm the resulting supg sph framework is therefore accurate robust and computationally efficient three key desired features that will allow the authors in forthcoming publications to explore its applicability in large scale simulations

a new jameson schmidt turkel smooth particle hydrodynamics algorithm for large strain explicit fast dynamics this paper presents a new smooth particle hydrodynamics sph computational framework for large strain explicit solid dynamics a mixed based set of total lagrangian conservation laws bonet et al 2015 gil et al 2016 is presented in terms of the linear momentum and an extended set of geometric strain measures comprised of the deformation gradient its co factor and the jacobian taking advantage of this representation the main aim of this paper is the adaptation of the very efficient jameson schmidt turkel jst algorithm jameson et al 1981 extensively used in computational fluid dynamics to a sph based discretisation of the mixed based set of conservation laws with three key distinct novelties first a conservative jst based sph computational framework is presented with emphasis in nearly incompressible materials second the suppression of numerical instabilities associated with the non physical zero energy modes is addressed through a well established stabilisation procedure third the use of a discrete angular momentum projection algorithm is presented in conjunction with a monolithic total variation diminishing runge kutta time integrator in order to guarantee the global conservation of angular momentum for completeness exact enforcement of essential boundary conditions is incorporated through the use of a lagrange multiplier projection technique a series of challenging numerical examples e g in the near incompressibility regime are examined in order to assess the robustness and accuracy of the proposed algorithm the obtained results are benchmarked against a wide spectrum of alternative numerical strategies

an algebraic proof of a cancellation theorem for surfaces let k be an algebraically closed field of arbitrary characteristic we give a self contained algebraic proof of the following statement if v is an affine surface over k such that v k k3 then v k2 this fact which is due to fujita miyanishi sugie and russell solves the zariski cancellation problem for surfaces to achieve our proof we first show that if a is a finitely generated domain with ak a a then ak a x a

a stable sph with adaptive b spline kernel abstract tensile instability often observed in smoothed particle hydrodynamics sph is a numerical artifact that manifests itself by unphysical clustering or separation of particles the instability originates in estimating the derivatives of the smoothing functions which when interact with material constitution may result in negative stiffness in the discretized system in the present study a stable formulation of sph is developed where the kernel function is continuously adapted at every material point b spline basis function with a variable intermediate knot is used as the kernel function the shape of the kernel function is then modified by changing the intermediate knot position such that the condition associated with instability does not arise while implementing the algorithm the simplicity and computational efficiency of sph are not compromised one dimensional dispersion analysis is performed to understand the effect of adaptive kernel on the stability finally the efficacy of the algorithm is demonstrated through some benchmark elastic dynamics problems

a note on retracts of polynomial rings in three variables abstract for retracts of the polynomial ring in 1 costa asks us whether every retract of k n is also the polynomial ring or not where k is a field in this paper we give an affirmative answer in the case where k is a field of characteristic zero and n 3

stable particle methods based on lagrangian kernels abstract a large deformation particle method based on the krongauz belytschko corrected gradient meshfree method with lagrangian kernels is developed in this form the gradient is corrected by a linear transformation so that linear completeness is satisfied for the test functions shepard functions are used this guarantees that the patch test is met lagrangian kernels are introduced to eliminate spurious distortions of the domain of material stability a mass allocation scheme is developed that captures correct reflection of waves without any explicit application of traction boundary conditions in addition the lagrangian kernel versions of various forms of smooth particle methods sph including the standard forms and the randles libersky modification are presented and studied results are obtained for a variety of problems that compare this method to standard forms of sph the randles libersky correction and large deformation versions of the element free galerkin method

a consistent multi resolution smoothed particle hydrodynamics method abstract we seek to accelerate and increase the size of simulations for fluid structure interactions fsi by using multiple resolutions in the spatial discretization of the equations governing the time evolution of systems displaying two way fluid solid coupling to this end we propose a multi resolution smoothed particle hydrodynamics sph approach in which subdomains of different resolutions are directly coupled without any overlap region the second order consistent discretization of spatial differential operators is employed to ensure the accuracy of the proposed method as sph particles advect with the flow a dynamic sph particle refinement coarsening is employed via splitting merging to maintain a predefined multi resolution configuration particle regularity is enforced via a particle shifting technique to ensure accuracy and stability of the lagrangian particle based method embraced the convergence accuracy and efficiency attributes of the new method are assessed by simulating four different flows in this process the numerical results are compared to the analytical finite element and consistent sph single resolution solutions we anticipate that the proposed multi resolution method will enlarge the class of sph tractable fsi applications

on the cancellation problem for the affine space mathbb a 3 in characteristic p we show that the cancellation conjecture does not hold for the affine space mathbb a 3 k over any field k of positive characteristic we prove that an example of t asanuma provides a three dimensional k algebra a for which a is not isomorphic to k x1 x2 x3 although a t is isomorphic to k x1 x2 x3 x4

representation theory and an isomorphism theorem for the framisation of the temperley lieb algebra in this paper we describe the irreducible representations and give a dimension formula for the framisation of the temperley lieb algebra we then prove that the framisation of the temperley lieb algebra is isomorphic to a direct sum of matrix algebras over tensor products of classical temperley lieb algebras this allows us to construct a basis for it we also study in a similar way the complex reflection temperley lieb algebra

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

a total lagrangian upwind smooth particle hydrodynamics algorithm for large strain explicit solid dynamics in previous work 1 2 lee et al introduced a new smooth particle hydrodynamics sph computational framework for large strain explicit solid dynamics with special emphasis on the treatment of near incompressibility a first order system of hyperbolic equations was presented expressed in terms of the linear momentum and the minors of the deformation namely the deformation gradient its co factor and its jacobian taking advantage of this representation the suppression of numerical deficiencies e g spurious pressure long term instability and or consistency issues was addressed through well established stabilisation procedures in reference 1 the adaptation of the very efficient jameson schmidt turkel algorithm was presented reference 2 introduced an adapted variationally consistent streamline upwind petrov galerkin methodology in this paper we now introduce a third alternative stabilisation strategy extremely competitive and which does not require the selection of any user defined artificial stabilisation parameter specifically a characteristic based riemann solver in conjunction with a linear reconstruction procedure is used with the aim to guarantee both consistency and conservation of the overall algorithm we show that the proposed sph formulation is very similar in nature to that of the upwind vertex centred finite volume method presented in 3 in order to extend the application range towards the incompressibility limit an artificial compressibility algorithm is also developed finally an extensive set of challenging numerical examples is analysed the new sph algorithm shows excellent behaviour in compressible nearly incompressible and truly incompressible scenarios yielding second order of convergence for velocities deviatoric and volumetric components of the stress

on affine ruled irrational surfaces let k be an algebraically closed field of characteristic p 0 and let x be a not necessarily projective nonsingular algebraic surface over k according to russell 11 we call x qffine ruled if x contains a non empty open set isomorphic to the product of a curve with a the affine line such an open set is called a cylinderlike open set assume that the logarithmic kodaira dimension x in the sense of iitaka 4 see also kambayashi 5 and russell 11 for the definition in case chark 0 is if x is rational and connected at infinity then x is affine ruled this result was proved in fujita 2 and miyanishi sugie 9 in case c h a r k 0 and proved in 11 in case c h a r k 0 see also miyanishi 8 the proof is valid in case c h a r k 0 without any modification we note that x is not necessarily affine ruled if x is rational and not connected at infinity see sugie 12 8 and 11 in case x is irrational it is shown in 9 that x is also affine ruled provided char k 0 in this article we shall prove first the following