on some characterisations of totally unimodular matrices a characterisation of totally unimodular matrices is derived from a result of hoffman and kruskal it is similar in spirit to a result of baum and trotter its relation with some other known characterisations is discussed and in the particular case where the matrices have 0 1 entries we derive some properties of the associated unimodular hypergraphs similar results for balanced and perfect matrices are also reviewed

affine actions on lie groups and post lie algebra structures abstract we introduce post lie algebra structures on pairs of lie algebras g n defined on a fixed vector space v special cases are lr structures and pre lie algebra structures on lie algebras we show that post lie algebra structures naturally arise in the study of nil affine actions on nilpotent lie groups we obtain several results on the existence of post lie algebra structures in terms of the algebraic structure of the two lie algebras g and n one result is for example that if there exists a post lie algebra structure on g n where g is nilpotent then n must be solvable furthermore special cases and examples are given this includes a classification of all complex two dimensional post lie algebras

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

smoothed particle hydrodynamics continuous boundary force method for navier stokes equations subject to a robin boundary condition a robin boundary condition for the navier stokes equations is used to model slip conditions at the fluid solid boundaries a novel continuous boundary force cbf method is proposed for solving the navier stokes equations subject to the robin boundary condition in the cbf method the robin boundary condition is replaced by the homogeneous neumann boundary condition and a volumetric force term added to the momentum conservation equation smoothed particle hydrodynamics sph method is used to solve the resulting navier stokes equations we present solutions for two and three dimensional flows subject to various forms of the robin boundary condition in domains bounded by flat and curved boundaries the numerical accuracy and convergence are examined through comparison of the sph cbf results with the solutions of finite difference or finite element method considering the no slip boundary condition as a special case of the slip boundary condition we demonstrate that the sph cbf method accurately describes both the no slip and slip conditions

post lie algebra structures on pairs of lie algebras abstract we study post lie algebra structures on pairs of lie algebras g n which describe simply transitive nil affine actions of lie groups we prove existence results for such structures depending on the interplay of the algebraic structures of g and n we consider the classes of simple semisimple reductive perfect solvable nilpotent abelian and unimodular lie algebras furthermore we consider commutative post lie algebra structures on perfect lie algebras using lie algebra cohomology we can classify such structures in several cases we also study commutative structures on low dimensional lie algebras and on nilpotent lie algebras

incompressible smoothed particle hydrodynamics for free surface flows a generalised diffusion based algorithm for stability and validations for impulsive flows and propagating waves the incompressible smoothed particle hydrodynamics isph method with projection based pressure correction has been shown to be highly accurate and stable for internal flows and importantly for many problems the pressure field is virtually noise free in contrast to the weakly compressible sph approach xu et al 2009 31 however for almost inviscid fluids instabilities at the free surface occur due to errors associated with the truncated kernels a new algorithm is presented which remedies this issue giving stable and accurate solutions to both internal and free surface flows generalising the particle shifting approach of xu et al 2009 31 the algorithm is based upon fick s law of diffusion and shifts particles in a manner that prevents highly anisotropic distributions and the onset of numerical instability the algorithm is validated against analytical solutions for an internal flow at higher reynolds numbers than previously the flow due to an impulsively started plate and highly accurate solutions for wet bed dam break problems at zero and small times the method is then validated for progressive regular waves with paddle motion defined by linear theory the accurate predictions demonstrate the effectiveness of the algorithm in stabilising solutions and minimising the surface instabilities generated by the inevitable errors associated with truncated kernels the test cases are thought to provide a more thorough quantitative validation than previously undertaken

accuracy and stability in incompressible sph isph based on the projection method and a new approach the stability and accuracy of three methods which enforce either a divergence free velocity field density invariance or their combination are tested here through the standard taylor green and spin down vortex problems while various approaches to incompressible sph isph have been proposed in the past decade the present paper is restricted to the projection method for the pressure and velocity coupling it is shown that the divergence free isph method cannot maintain stability in certain situations although it is accurate before instability sets in the density invariant isph method is stable but inaccurate with random noise like disturbances the combined isph combining advantages in divergence free isph and density invariant isph can maintain accuracy and stability although at a higher computational cost redistribution of particles on a fixed uniform mesh is also shown to be effective but the attraction of a mesh free method is lost a new divergence free isph approach is proposed here which maintains accuracy and stability while remaining mesh free without increasing computational cost by slightly shifting particles away from streamlines although the necessary interpolation of hydrodynamic characteristics means the formulation ceases to be strictly conservative this avoids the highly anisotropic particle spacing which eventually triggers instability importantly pressure fields are free from spurious oscillations up to the highest reynolds numbers tested

graph theoretic relaxations of set covering and set partitioning problems in this paper we review the graph theoretic relaxations of the set covering problem scp and the set partitioning problem ssp these are a network relaxation which can be solved by the greedy method a matching relaxation and a graph covering relaxation other relaxations such as assignment shortest route and minimum spanning tree are also presented

a pairwise relaxing incompressible smoothed particle hydrodynamics scheme abstract we present a formulation of incompressible smoothed particle hydrodynamics isph method that utilizes pairwise relaxing kernel to achieve approximately first order consistency previous high order formulations by using reproduced and corrected kernel function have had difficulties in ensuring momentum conservation in the new scheme relaxing constants for each kernel function are determined pair wisely throughout the entire calculation domain by enforcing the taylor series consistency condition we call this modified isph method pairwise relaxing isph or pr isph pr isph retains high order accuracy for non uniform particle distributions the spatial symmetry of the kernel function is kept in pr isph thus momentum is strictly conserved several two dimensional benchmark calculations are conducted to demonstrate the accuracy as well as the conservation property of the pr isph

planarly branched rough paths and rough differential equations on homogeneous spaces abstract this work studies rough differential equations rdes on homogeneous spaces we provide an explicit expansion of the solution at each point of the real line using decorated planar forests the notion of planarly branched rough path is developed following gubinelli s branched rough paths the main difference being the replacement of the butcher connes kreimer hopf algebra of non planar rooted trees by the munthe kaas wright hopf algebra of planar rooted forests the latter underlies the extension of butcher s b series to lie butcher series known in lie group integration theory planarly branched rough paths admit the study of rdes on homogeneous spaces the same way gubinelli s branched rough paths are used for rdes on finite dimensional vector spaces an analogue of lyons extension theorem is proven under analyticity assumptions on the coefficients and when the holder index of the driving path is one we show convergence of the planar forest expansion in a small time interval

an extension of set partitioning with application to scheduling problems abstract the well known problems of set covering set partitioning and set packing are defined and their interrelationship is considered a natural generalisation called the extended set partitioning model is presented and the three standard models are shown to be special cases of this generalisation in addition the extended model includes another type of set problem which can be of greater use in certain applications the model forms the basis of a computer assisted bus crew scheduling system developed by the authors the system is in regular use by dublin city services in the republic of ireland finally the equivalence between a special case of the set partitioning problem and the shortest route problem is considered and it is shown that this equivalence also applies to the extended model

lattice boltzmann model for free surface flow and its application to filling process in casting a generalized lattice boltzmann model to simulate free surface is constructed in both two and three dimensions the proposed model satisfies the interfacial boundary conditions accurately a distinctive feature of the model is that the collision processes is carried out only on the points occupied partially or fully by the fluid to maintain a sharp interfacial front the method includes an anti diffusion algorithm the unknown distribution functions at the interfacial region are constructed according to the first order chapman enskog analysis the interfacial boundary conditions are satisfied exactly by the coefficients in the chapman enskog expansion the distribution functions are naturally expressed in the local interfacial coordinates the macroscopic quantities al the interface are extracted from the least square solutions of a locally linearized system obtained from the known distribution functions the proposed method does not require any geometric front construction and is robust for any interfacial topology simulation results of realistic filling process are presented rectangular cavity in two dimensions and hammer box campbell box sheffield box and motorblock in three dimensions to enhance the stability at high reynolds numbers various upwind type schemes are developed free slip and no slip boundary conditions are also discussed

hamiltonian formulation of the variable h sph equations in this paper a variational formulation of smooth particle hydrodynamics for dynamic problems is presented the resulting equations treat the continuum as a hamiltonian system of particles where the constitutive equation of the material is represented via an internal energy term in the case of fluids the internal energy term is a function of density the new formulation introduces a variable smoothing length for the evaluation of density and incorporates a consistent approach for the treatment of rigid boundaries the method overcomes some problems faced by standard sph approaches that use constant smoothing lengths and provides a variational context for a variable smoothing length formulation a numerical example shows the capabilities of this novel formulation

incompressible sph method based on rankine source solution for violent water wave simulation with wide applications the smoothed particle hydrodynamics method abbreviated as sph has become an important numerical tool for solving complex flows in particular those with a rapidly moving free surface for such problems the incompressible smoothed particle hydrodynamics isph has been shown to yield better and more stable pressure time histories than the traditional sph by many papers in literature however the existing isph method directly approximates the second order derivatives of the functions to be solved by using the poisson equation the order of accuracy of the method becomes low especially when particles are distributed in a disorderly manner which generally happens for modelling violent water waves this paper introduces a new formulation using the rankine source solution in the new approach to the isph the poisson equation is first transformed into another form that does not include any derivative of the functions to be solved and as a result does not need to numerically approximate derivatives the advantage of the new approach without need of numerical approximation of derivatives is obvious potentially leading to a more robust numerical method the newly formulated method is tested by simulating various water waves and its convergent behaviours are numerically studied in this paper its results are compared with experimental data in some cases and reasonably good agreement is achieved more importantly numerical results clearly show that the newly developed method does need less number of particles and so less computational costs to achieve the similar level of accuracy or to produce more accurate results with the same number of particles compared with the traditional sph and existing isph when it is applied to modelling water waves

nonabelian generalized lax pairs the classical yang baxter equation and postlie algebras we generalize the classical study of generalized lax pairs the related mathcal o operators and the modified classical yang baxter equation by introducing the concepts of nonabelian generalized lax pairs extended mathcal o operators and the extended classical yang baxter equation we study in this context the nonabelian generalized r matrix ansatz and the related double lie algebra structures relationship between extended mathcal o operators and the extended classical yang baxter equation is established especially for self dual lie algebras this relationship allows us to obtain an explicit description of the manin triples for a new class of lie bialgebras furthermore we show that a natural structure of postlie algebra is behind mathcal o operators and fits in a setup of the triple lie algebra that produces self dual nonabelian generalized lax pairs

a self adaptive oriented particles level set method for tracking interfaces a new method for tracking evolving interfaces by lagrangian particles in conjunction with a level set approach is introduced this numerical technique is based on the use of time evolution equations for fundamental vector and tensor quantities defined on the front and represents a new and convenient way to couple the advantages of the eulerian description given by a level set function f to the use of lagrangian massless particles the term oriented points out that the information advected by the particles not only concern the spatial location but also the local outward normal vector n to the interface c and the second fundamental tensor the shape operator n the particles are exactly located upon c and provide all the requested information for tracking the interface on their own in addition a self adaptive mechanism suitably modifies at each time step the markers distribution in the numerical domain each particle behaves both as a potential seeder of new markers on c so as to guarantee an accurate reconstruction of the interface and a de seeder to avoid any useless gathering of markers and to limit the computational effort the algorithm is conceived to avoid any transport equation for f and to confine the level set function to the role of a mere post processing tool thus all the numerical diffusion problems usually affecting the level set methodology are removed the method has been tested both on 2d and 3d configurations it carries out a fast reconstruction of the interface and its accuracy is only limited by the spatial resolution of the mesh

an optimal column generation with ranking algorithm for very large scale set partitioning problems in traffic assignment abstract we show in this paper how branch and bound and column generation techniques can be conbined very efficiently to solve to optimality some very large scale set partitioning problems with special structure such as the matrix decomposition problem arising in the context of satellite communication system optimization the main contribution of our approach is the use of column generation during the tree search procedure combined with a ranking procedure which ensures that the exact optimal integer solution is obtained extensive computational experiments are reported for the matrix decomposition problem encountered in the search for optimal schedules in satellite switching systems showing the effectiveness of this approach

simulating free surface flows with sph the sph smoothed particle hydrodynamics method is extended to deal with free surface incompressible flows the method is easy to use and examples will be given of its application to a breaking dam a bore the simulation of a wave maker and the propagation of waves towards a beach arbitrary moving boundaries can be included by modelling the boundaries by particles which repel the fluid particles the method is explicit and the time steps are therefore much shorter than required by other less flexible methods but it is robust and easy to program

a network relaxation based enumeration algorithm for set partitioning abstract hidden network structure in the element set incidence constraint matrix of a set partitioning problem can be identified by using procedures for testing when a binary matrix is transformable to a network the set partitioning problem is thus represented as a network with side constraints this paper reports the development of a new efficient solution procedure for the set partitioning problem facilitated by the new formulation and makes use of lagrangean duality modified subgradients efficient reoptimization and enumeration tree reduction

stabilization and smoothing of pressure in mps method by quasi compressibility in this paper a method to stabilize simulations and suppress the pressure oscillation in moving particle semi implicit method for an incompressible fluid is presented to make the pressure smooth in terms of both of space and time a new representation of the incompressible condition is proposed the incompressible condition consists of two parts the divergence free condition and the particle number density condition the divergence free condition has the effect of making the pressure smooth in terms of both space and time the particle number density condition is necessary to keep the fluid volume constant in this work the quasi compressibility is also introduced for stabilization a dam break is simulated more stably and the space distribution and the time variation of pressure are evaluated more smoothly than the traditional method moreover surface particles are detected more accurately nevertheless the proposed method is computationally cheaper some simulations such as a fluid structure interaction are supposed to be more accurate using this method

optimal solution of set covering partitioning problems using dual heuristics we present an algorithm for a mixed set covering partitioning model that includes as special cases the well known set covering problem and set partitioning problem the novel feature of our algorithm is the use of continuous heuristics applied to the dual of the linear programming relaxation to provide lower bounds for a branch and bound algorithm the heuristics are continuous adaptations of the well known greedy and 3 opt methods that have been applied to a variety of combinatorial optimization problems our algorithm has outperformed the current best set covering algorithm of balas and ho 1980 by about a factor of 3 and appears to improve on the best existing set partitioning algorithm by more than an order of magnitude

a numerical method for suspension flow abstract peskin s j comput phys 25 220 1977 immersed boundary technique is modified to give a new numerical method for studying a fluid with suspended elastic particles as before the presence of the suspended particles is transmitted to the fluid through a force density term in the fluid equations as a result one set of equations holds in the entire computational domain eliminating the need to apply boundary conditions on the surface of suspended objects the new method computes the force density by discretizing the stress strain constitutive equations for an elastic solid on a grid using data provided by clusters of lagrangian points this approach clearly specifies the material properties of the suspended objects a simple data structure for the lagrangian points makes it easy to model suspended solids with arbitrary shape and size the method is validated by comparing numerical results for elastic vibrations and particle settling in viscous fluids with theory and analysis the capability of the method to do a wide range of problems is illustrated by qualitative results for lubrication and cavity flow problems

dynamic refinement and boundary contact forces in sph with applications in fluid flow problems this paper presents a general method for dynamic particle refinement in smoothed particle hydrodynamics sph candidate particles are split into several daughter particles according to a given refinement pattern centred about the original particle through the solution of a non linear minimization problem the optimal mass distribution of the daughter particles is obtained so as to reduce the errors introduced to the underlying density field this procedure necessarily conserves the mass of the system conservation of energy and momentum results are also discussed copyright 2007 john wiley sons ltd

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

the sph equations for fluids existing smoothed particle hydrodynamics sph formulations for simulating continuous fluids have errors that may be divergent and it has been known for some time that the sph equations do not satisfy low order polynomial completeness conditions here sph equations are derived that have convergent error terms and a correction method is presented for enforcing low order polynomial completeness irrespective of how many completeness conditions are required discretization is achieved through division of the model domain in its initial state into sub domains that have lagrangian boundaries it is shown that boundary integrals appearing in one derivation of the sph equations may be treated as a convergent error in simulations of basic fluid flows convergence and zeroth order completeness are demonstrated but significant instabilities and a failure to conserve energy are observed copyright 2009 john wiley sons ltd

some numerical aspects of modelling flow around hydraulic structures using incompressible sph here we apply incompressible smoothed particle hydrodynamics isph to simulate free surface flow around hydraulic structures using several classical case studies including dambreak flow under a submerged gate and simultaneous operation of a weir and gate due to many complexities such as unknown free surface rapidly varied flow trans critical flow complicated geometry and non hydrostatic pressures flow fields have traditionally been investigated by experimental methods while powerful computational techniques such as isph are gradually being adopted for such studies this research provides further details about the application of isph in this area two projection methods to enforce incompressibility of sph were compared from mathematical and numerical view points further two pressure formulations for approximating the left hand side of the poisson equation resulted in a similar trend

an implicit boundary approach for viscous compressible high reynolds flows using a hybrid remeshed particle hydrodynamics method abstract we present an implicit boundary particle method with background mesh adaptation we use a brinkman penalisation to represent the boundary of the domain and a remeshed particle method to simulate viscous flow with high reynolds numbers a penalty term is added to the navier stokes equations to impose the boundary conditions the boundary conditions are enforced to a specific precision with no need to modify the numerical method or change the grid achieving an implicit approach for flow around complex boundaries geometries simulation the main idea of the brinkman penalisation method is to model the solid obstacle as a porous medium the governing equations for the compressible fluid and penalised navier stokes for the porous medium are solved simultaneously without need for interface conditions the accuracy of the method is tested for a number of benchmark problems starting with simple cases such as a periodic laminar flow in a channel poiseuille flow to more complex problems such as the lid driven cavity with high reynolds numbers the reflection and propagation of a compressible shock wave and finally swirling flow in a model two stroke diesel engine the remeshed particle mesh method coupled with brinkman penalisation provides a good quality simulation and the results are in agreement with analytical or reference solutions

non smooth kernels for meshfree methods in fluid dynamics a function and its first two derivatives are estimated by convolutions with well chosen non differentiable kernels the convolutions are in turn approximated by newton cotes integration techniques with the aid of a polynomial interpolation based on an arbitrary finite set of points precise numerical results are obtained with far fewer points than that in classic sph and error bounds are derived

a weighted meshfree collocation method for incompressible flows using radial basis functions abstract a weighted strong form collocation method using radial basis functions and explicit time integration is proposed to solve the incompressible navier stokes equations the velocities and pressure are solved directly at the same time step and the continuity equation is satisfied at each time step which improve the solution accuracy and stability no artificial compressibility coefficient needs to be introduced for modeling the incompressible flows and no pressure oscillation arises in the numerical solutions optimal convergence can be achieved by imposing the derived proper weights on the boundaries and the continuity equation radial basis collocation method in a lagrangian form is quite easy to capture the moving boundary or free surface in flow problems moreover solid boundary conditions can be enforced directly and no special treatments are required further critical time step for the explicit time integration is predicted in the stability analysis and the influences on the stability are evaluated numerical studies validate the high accuracy as well as good stability of the presented method

mixing process of two phase non newtonian fluids in 2d using smoothed particle hydrodynamics abstract numerical simulation of mixing process in mixers is a complicated problem due to geometries that include moving parts and sharp corners grid based numerical methods have considerable accuracy in simulating mechanical phenomena however these methods encounter problems in dealing with deformable boundaries moving interfaces and extremely large deformations smoothed particle hydrodynamics sph which is a fully lagrangian particle based method does not suffer from the problems related to grid regenerating in this research the mixing process for newtonian and non newtonian fluids in circular and elliptical one blade and two blade blenders is simulated using the sph method after validating the computational code the mixing process is simulated in different conditions the effects of geometry of mixer the number of blades and the rotating modes of the blades on the mixing performance are investigated the results show that at the end of the mixing process the one blade circular mixer has the best performance however during a certain time interval of the mixing process this interval depends on the type of mixer the other mixers have better performance than that of the one blade circular mixer therefore if the time of the mixing process is limited achieving a certain degree of homogeneity in a limited time choosing the right kind of mixer which has the best performance at the desired time is very crucial

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

cost reduction of particle simulations by an ellipsoidal particle model abstract we developed an ellipsoidal particle model to reduce the number of particles and the computational costs of the moving particle semi implicit mps method a coordinate transformation was conducted to treat ellipsoidal particles in the same manner as sphere particles the model for the mps method s laplacian operator was extended for use with ellipsoidal particles the developed method is effective in cases where the rate of change of a physical quantity or shape in any given direction is smaller than that in other directions and the authors have applied it to dam breaking problems in both two and three dimensions as a result the developed method s ability to reduce the required number of particles and the computational costs of particle simulations has been confirmed the developed ellipsoidal particle model was also applied to smoothed particle hydrodynamics

a new approach for crew pairing problems by column generation with an application to air transportation we propose a new approach to crew pairing problems arising in the context of airline companies the problem is first formulated as a large scale set covering problem with many colums each column representing a valid crew pairing we then suggest a solution procedure for the continuous relaxation of this large scale problem based on generalized linear programming in which the column generation subproblem is shown to be equivalent to a shortest path problem in an associated graph computational results obtained on a series of real problems involving up to 329 flight segments are reported confirming both computational efficiency and practical applicability of the new approach indeed not only were the resulting solutions observed to be integral for most test problems but average savings of about 4 to 5 over the best available hand built solutions were shown to be obtained

hamiltonian moving particle semi implicit hmps method for incompressible fluid flows particle methods are meshless simulation techniques in which motion of continua is approximated by discrete dynamics of a finite number of particles and thus have a great degree of flexibility for instance in dealing with the complex motion of surfaces or boundaries in this paper a particle method is developed from a direct discretization of the lagrangian for inviscid incompressible fluid flows the discretized lagrangian is transformed into a hamiltonian with holonomic constraints that stem from the incompressibility condition the rattle algorithm that is a symplectic scheme for holonomically constrained hamiltonian systems is adopted so that the resulting particle method inherits structures possessed by the partial differential equations that govern inviscid incompressible flows the algorithm of the particle method is semi implicit so we call it the hamiltonian moving particle semi implicit hmps method some numerical tests indicate the excellence of the hmps method in conservation of mechanical energy as well as linear and angular momenta

meshless local petrov galerkin method for two dimensional nonlinear water wave problems in this paper the meshless local petrov galerkin mlpg method is extended to dealing with nonlinear water wave problems the formulation is based on general fluid governing equations and a time marching procedure at each time step the boundary value problem for the pressure is solved using the mlpg method and the velocity and position of nodes are updated by numerical integration the newly extended method is applied to simulating water waves generated by a wave maker and good agreement with analytical solutions and finite element results is presented

an algorithm for set covering problem in this paper we present an algorithm for the set covering problem that combines problem reduction tests with dual ascent subgradient optimisation and linear programming computational results are presented for problems involving up to 400 rows and 4000 columns

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

a generalized wall boundary condition for smoothed particle hydrodynamics in this paper we present a new formulation of the boundary condition at static and moving solid walls in sph simulations our general approach is both applicable to two and three dimensions and is very simple compared to previous wall boundary formulations based on a local force balance between wall and fluid particles we apply a pressure boundary condition on the solid particles to prevent wall penetration this method can handle sharp corners and complex geometries as is demonstrated with several examples a validation shows that we recover hydrostatic equilibrium conditions in a static tank and a comparison of the classical dam break simulation with state of the art results in literature shows good agreement we simulate various problems such as the flow around a cylinder and the backward facing step at re 100 to demonstrate the general applicability of this new method

post symmetric braces and integration of post lie algebras abstract the aim of this letter is twofold firstly we introduce the post lie analogue of the notion of a symmetric brace algebra termed in the sequel post symmetric brace algebra these brace algebras are defined using a suitable algebraic operad which turns out to be isomorphic to the operad of the post lie algebras secondly using these new brace algebras together with the so called post lie magnus expansion we aim both to analyze the enveloping algebra of the corresponding post lie algebra and to compare the two baker campbell hausdorff series there naturally defined

genetic clustering algorithms abstract this study employs genetic algorithms to solve clustering problems three models sicm stcm cspm are developed according to different coding decoding techniques the effectiveness and efficiency of these models under varying problem sizes are analyzed in comparison to a conventional statistics clustering method the agglomerative hierarchical clustering method the results for small scale problems 10 50 objects indicate that cspm is the most effective but least efficient method stcm is second most effective and efficient sicm is least effective because of its long chromosome the results for medium to large scale problems 50 200 objects indicate that cspm is still the most effective method furthermore we have applied cspm to solve an exemplified p median problem the good results demonstrate that cspm is usefully applicable