random sampling and greedy sparsification for matroid optimization problems random sampling is a powerful tool for gathering information about a group by considering only a small part of it we discuss some broadly applicable paradigms for using random sampling in combinatorial optimization and demonstrate the effectiveness of these paradigms for two optimization problems on matroids finding an optimum matroid basis and packing disjoint matroid bases application of these ideas to the graphic matroid led to fast algorithms for minimum spanning trees and minimum cuts an optimum matroid basis is typically found by agreedy algorithm that grows an independent set into an optimum basis one element at a time this continuous change in the independent set can make it hard to perform the independence tests needed by the greedy algorithm we simplify matters by using sampling to reduce the problem of finding an optimum matroid basis to the problem of verifying that a givenfixed basis is optimum showing that the two problems can be solved in roughly the same time another application of sampling is to packing matroid bases also known as matroid partitioning sampling reduces the number of bases that must be packed we combine sampling with a greedy packing strategy that reduces the size of the matroid together these techniques give accelerated packing algorithms we give particular attention to the problem of packing spanning trees in graphs which has applications in network reliability analysis our results can be seen as generalizing certain results from random graph theory the techniques have also been effective for other packing problems 1998 the mathematical programming society inc published by elsevier science b v

las vegas algorithms for linear and integer programming when the dimension is small this paper gives an algorithm for solving linear programming problems for a problem with n constraints and d variables the algorithm requires an expected o d2n logn o d d 2 o 1 o d4 n logn arithmetic operations as n the constant factors do not depend on d also an algorithm is given for integer linear programming let 4 bound the number of bits required to specify the rational numbers defining an input constraint or the objective function vector let n and d be as before then the algorithm requires expected o 2ddn 8dd n l n n ln n do d 4 ln n operations on numbers with do 1 4 bits as n where the constant factors do not depend on d or 4 to other convex programming problems for example an algorithm for finding the smallest sphere enclosing a set of n points in ed has the same time bound

existence results for the flow of viscoelastic fluids with a differential constitutive law where 2 is the symmetric extra stress tensor the total stress is given by g pl i where p is the hydrodynamic pressure 4 is the rate of deformation tensor g u vu vu u being the velocity field a is the relaxation time a2 the retardation time 0 i a a1 and q is the fluid viscosity the symbol a d t denotes an objective frame indifferent derivative i 181 more precisely

center manifolds and contractions on a scale of banach spaces we give a new proof for the existence of a ck center manifold at a nonhyperbolic equilibrium point of a finite dimensional vector field of class ck the problem is reduced to a fixed point problem on a scale of banach spaces these banach spaces consist of mappings with a certain maximal exponential growth at infinity we give conditions under which there is a unique fixed point depending differentiably on the parameters the main difficulty is that the mappings under consideration become only differentiable after composition with appropriate embeddings on the scale of banach spaces

on the thermally induced bistability of composite cylindrical shells for morphing structures abstract the multistability of composite thin structures has shown potential for morphing applications the present work combines a ritz model with path following algorithms to study bistable cylindrical panels polynomial discretisations of the displacements field are used to predict stable shapes geometry and other aspects of the nonlinear structural behaviour in order to improve the inherently poor conditioning properties of ritz approximations of slender structures a non dimensional shell lamination theory with sanders nonlinear strains is developed and presented an investigation on the relative importance of different nonlinear strain terms is shown to provide useful insight into the applicability of common assumptions about shell kinematics in the current approach we continue numerical solutions in parameter space that is we path follow equilibrium configurations as the control parameter varies find stable and unstable configurations and identify bifurcations the numerics is carried out using a set of in house m atlab routines for numerical continuation results are compared with detailed finite elements analysis throughout the course of the paper

linear programming in linear time when the dimension is fixed it is demonstrated that the linear programming problem in d variables and n constraints can be solved in o n time when d is fixed this bound follows from a multidimensional search technique which is applicable for quadratic programming as well there is also developed an algorithm that is polynomial in both n and d provided d is bounded by a certain slowly growing function of n

bifurcation and distribution of limit cycles for quadratic differential systems of type ii abstract in this paper we first solve an open problem of quadratic differential systems of type ii l 0 in the chinese classification then by making use of the theory of rotated vector fields we investigate the bifurcation phenomena and all the possible distributions of the limit cycles for quadratic systems of type ii moreover under a conjecture of ye yanqian we prove that the 2 2 limit cycle distribution is impossible

randomized approximation schemes for cuts and flows in capacitated graphs we describe random sampling techniques for approximately solving problems that involve cuts and flows in graphs we give a near linear time randomized combinatorial construction that transforms any graph on n vertices into an o n log n edge graph on the same vertices whose cuts have approximately the same value as the original graph s in this new graph for example we can run the tilde o m 3 2 time maximum flow algorithm of goldberg and rao to find an s t minimum cut in tilde o n 3 2 time this corresponds to a 1 epsilon times minimum s t cut in the original graph a related approach leads to a randomized divide and conquer algorithm producing an approximately maximum flow in tilde o m sqrt n time our algorithm can also be used to improve the running time of sparsest cut approximation algorithms from tilde o mn to tilde o n 2 and to accelerate several other recent cut and flow algorithms our algorithms are based on a general theorem analyzing the concent

shockless acceleration of thin plates modeled by a tracked random choice method a method for accelerating thin metallic plates to hypervelociti es has been proposed by g mccall in this method a shock in a propellant generates a strong expansion wave that smoothly accelerates the plate we have studied the hydrodynamics of this process in one dimension both analytically and computationally the metal was modeled as a stiffened gas and the corresponding riemann problem was solved the asymptotic behavior of the solution was determined analytically the one dimensional random choice method modified so that material boundaries are tracked and the spatial mesh is refined locally was used to compute the flow comparison with the asymptotic solution demonstrated its accuracy with this method shocks that form within the accelerating plate were accurately resolved so that possible structural damage to the plate could be evaluated

the singular limit dynamics of semilinear damped wave equations on considere la dynamique qualitative d une equation d onde amortie semi lineaire a une dimension dans la limite singuliere correspondant a l annulation du coefficient de la derivee d ordre 2 en temps

a randomized algorithm for fixed dimensional linear programming we give a las vegas randomized algorithm for linear programming in a fixed dimensiond for which the expected computation time is o d 3 varepsilon d d n where limd e d 0 this improves the corresponding worst case complexity o 3 d 2 n the method is based on a recent idea of clarkson two variations on the algorithm are examined briefly

sparse reliable graph backbones given a connected graph g and a failure probability p e for each edge e in g the reliability of g is the probability that g remains connected when each edge e is removed independently with probability p e in this paper it is shown that every n vertex graph contains a sparse backbone i e a spanning subgraph with o nlogn edges whose reliability is at least 1 n w 1 times that of g moreover for any pair of vertices s t in g the s t reliability of the backbone namely the probability that s and t remain connected is also at least 1 n w 1 times that of g our proof is based on a polynomial time randomized algorithm for constructing the backbone in addition it is shown that the constructed backbone has nearly the same tutte polynomial as the original graph in the quarter plane x 1 y 1 and hence the graph and its backbone share many additional features encoded by the tutte polynomial

a randomized linear time algorithm to find minimum spanning trees we present a randomized linear time algorithm to find a minimum spanning tree in a connected graph with edge weights the algorithm uses random sampling in combination with a recently discovered linear time algorithm for verifying a minimum spanning tree our computational model is a unit cost random access machine with the restriction that the only operations allowed on edge weights are binary comparisons

multiparameter actuation for shape control of bistable composite plates this paper studies the stable equilibrium shapes of free multilayered orthotropic plates loaded by inelastic deformations induced by thermal and piezoelectric effects starting with a von karman plate kinematics and an energetic formulation a discrete intrinsic nonlinear model in terms of curvatures only is deduced the model has 3 degrees of freedom namely the components of the symmetric curvature tensor which is supposed to be uniform in space despite of this rough assumption the analytical results about the equilibrium shapes and their stability show a good agreement with the finite element simulations performed with a commercial code literature results about the bistable behavior of isotropic plates under a single parameter loading are extended to the orthotropic case with two loading parameters in light of a global stability analysis and a phase portrait as a function of the inelastic curvatures we study possible actuation techniques for controlling the transition of the plate between its two stable configurations we show that with a suitable two parameter actuation it is possible to get a controlled quasi static transition avoiding any instability phenomenon numerical simulations on a realistic case study support the technological feasibility of the proposed actuation technique when using active piezoelectric layers to control the inelastic curvature

inertial manifolds for nonlinear evolutionary equations abstract in this paper we introduce the concept of an inertial manifold for nonlinear evolutionary equations in particular for ordinary and partial differential equations these manifolds which are finite dimensional invariant lipschitz manifolds seem to be an appropriate tool for the study of questions related to the long time behavior of solutions of the evolutionary equations the inertial manifolds contain the global attractor they attract exponentially all solutions and they are stable with respect to perturbations furthermore in the infinite dimensional case they allow for the reduction of the dynamics to a finite dimensional ordinary differential equation

faster approximation algorithms for the unit capacity concurrent flow problem with applications to routing and finding sparse cuts this paper describes new algorithms for approximately solving the concurrent multicommodity flow problem with uniform capacities these algorithms are much faster than algorithms discovered previously besides being an important problem in its own right the uniform capacity concurrent flow problem has many interesting applications leighton and rao used uniform capacity concurrent flow to find an approximately sparsest cut in a graph and thereby approximately solve a wide variety of graph problems including minimum feedback arc set minimum cut linear arrangement and minimum area layout however their method appeared to be impractical as it required solving a large linear program this paper shows that their method might be practical by giving an o m 2 log m expected time randomized algorithm for their concurrent flow problem on an m edge graph raghavan and thompson used uniform capacity concurrent flow to solve approximately a channel width minimization problem in very large scale integration an o k 3 2 m n log n expected time randomized algorithm and an o k min n k m n log n log k deterministic algorithm is given for this problem when the channel width is omega log n where k denotes the number of wires to be routed in an n node m edge network

finding structure with randomness probabilistic algorithms for constructing approximate matrix decompositions low rank matrix approximations such as the truncated singular value decomposition and the rank revealing qr decomposition play a central role in data analysis and scientific computing this work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing low rank matrix approximation these techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets this paper presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions these methods use random sampling to identify a subspace that captures most of the action of a matrix the input matrix is then compressed either explicitly or implicitly to this subspace and the reduced matrix is manipulated deterministically to obtain the desired low rank factorization in many cases this approach beats its classical competitors in terms of accuracy robustness and or speed these claims are supported by extensive numerical experiments and a detailed error analysis the specific benefits of randomized techniques depend on the computational environment consider the model problem of finding the k dominant components of the singular value decomposition of an m times n matrix i for a dense input matrix randomized algorithms require bigo mn log k floating point operations flops in contrast to bigo mnk for classical algorithms ii for a sparse input matrix the flop count matches classical krylov subspace methods but the randomized approach is more robust and can easily be reorganized to exploit multiprocessor architectures iii for a matrix that is too large to fit in fast memory the randomized techniques require only a constant number of passes over the data as opposed to bigo k passes for classical algorithms in fact it is sometimes possible to perform matrix approximation with a single pass over the data

a new class of quadratic systems abstract we study quadratic systems whose second degree terms have the form p 2 x y ax by dx ey q 2 x y cx ay dx ey it is shown that if such a system has at most two critical points at infinity then it has at most one limit cycle an application is made to the shear flow of a non newtonian fluid

an o log k approximate min cut max flow theorem and approximation algorithm it is shown that the minimum cut ratio is within a factor of o log k of the maximum concurrent flow for k commodity flow instances with arbitrary capacities and demands this improves upon the previously best known bound of o log2 k and is existentially tight up to a constant factor an algorithm for finding a cut with ratio within a factor of o log k of the maximum concurrent flow and thus of the optimal min cut ratio is presented

a stable and convergent scheme for viscoelastic flow in contraction channels we present a new algorithm to simulate unsteady viscoelastic flows in abrupt contraction channels in our approach we split the viscoelastic terms of the oldroyd b constitutive equation using duhamel s formula and discretize the resulting pdes using a semi implicit finite difference method based on a lax wendroff method for hyperbolic terms in particular we leave a small residual elastic term in the viscous limit by design to make the hyperbolic piece well posed a projection method is used to impose the incompressibility constraint we are able to compute the full range of unsteady elastic flows in an abrupt contraction channel from the viscous limit to the elastic limit in a stable and convergent manner we demonstrate the range of our method for unsteady flow of a maxwell fluid with and without viscosity in planar contraction channels we also demonstrate stable and convergent results for benchmark high weissenberg number problems at we 1 and we 10

a new approach to the minimum cut problem this paper present a new approach to finding minimum cuts in undirected graphs the fundamental principle is simple the edges in a graph s minimum cut form an extremely small fraction of the graph s edges using this idea we give a randomized strongly polynomial algorithm that finds the minimum cut in an arbitrarily weighted undirected graph with high probability the algorithm runs in o n 2 log 3 n time a significant improvement over the previous o mn time bounds based on maximum flows it is simple and intuitive and uses no complex data structures our algorithm can be parallelized to run in rnc with n 2 processors this gives the first proof that the minimum cut problem can be solved in rnc the algorithm does more than find a single minimum cut it finds all of them with minor modifications our algorithm solves two other problems of interest our algorithm finds all cuts with value within a multiplicative factor of of the minimum cut s in expected o n 2 time or in rnc with n 2 processors the problem of finding a minimum multiway cut of graph into r pieces is solved in expected o n 2 r 1 time or in rnc with n 2 r 1 processors the trace of the algorithm s execution on these two problems forms a new compact data structure for representing all small cuts and all multiway cuts in a graph this data structure can be efficiently transformed into the more standard cactus representing for minimum cuts

a wave propagation method for hyperbolic systems on the sphere presented in this work is an explicit finite volume method for solving general hyperbolic systems on the surface of a sphere applications where such systems arise include passive tracer advection in the atmosphere shallow water models of the ocean and atmosphere and shallow water magnetohydrodynamic models of the solar tachocline the method is based on the curved manifold wave propagation algorithm of rossmanith bale and leveque a wave propagation algorithm for hyperbolic systems on curved manifolds j comput phys 199 2004 631 662 which makes use of parallel transport to approximate geometric source terms and orthonormal riemann solvers to carry out characteristic decompositions this approach employs tvd wave limiters which allows the method to be accurate for both smooth solutions and solutions in which large gradients or discontinuities can occur in the form of material interfaces or shock waves the numerical grid used in this work is the cubed sphere grid of ronchi iacono and paolucci the cubed sphere a new method for the solution of partial differential equations in spherical geometry j comput phys 124 1996 93 114 which covers the sphere with nearly uniform resolution using six identical grid patches with grid lines lying on great circles boundary conditions across grid patches are applied either through direct copying from neighboring grid cells in the case of scalar equations or 1d interpolation along great circles in the case of more complicated systems the resulting numerical method is applied to several test problems for the advection equation the shallow water equations and the shallow water magnetohydrodynamic smhd equations for the smhd equations we make use of an unstaggered constrained transport method to maintain a discrete divergence free magnetic field

dynamics of shear flow of a non newtonian fluid abstract viscoelastic materials with fading memory e g polymers suspensions and emulsions exhibit behavior that is intermediate between the nonlinear hyperbolic response of purely elastic materials and the strongly diffusive parabolic response of viscous fluids many popular numerical methods used in the computation of steady viscoelastic flows fail in important flow regimes and thus do not capture significant non newtonian phenomena a key to satisfactory explanation of these phenomena is the study of the full dynamics of the flow this paper studies the dynamics of shear flow presenting a description of non newtonian phenomena caused by a non monotone relation between the steady shear stress and shear strain rate analytical results for such phenomena are surveyed and three distinct numerical methods are developed to accurately compute the dynamics the computations reproduce experimental measurements of non newtonian spurt in shearing flow through a slit die they also predict related phenomena such as hysteresis and shape memory experiments are suggested to verify these predictions

stable patterns in a viscous diffusion equation we consider a pseudoparabolic regularization of a forward backward nonlinear diffusion equation ut a f u vut motivated by the problem of phase separation in a viscous binary mixture the function f is nonmonotone so there are discontinuous steady state solutions corresponding to arbitrary arrangements of phases we find that any bounded measurable steady state solution u x satisfying f u constant f u x 0 a e is dynamically stable to perturbations in the sense of convergence in measure in particular smooth solutions may achieve discontinuous asymptotic states furthermore stable states need not correspond to absolute minimizers of free energy thus violating gibbs principle of stability for phase mixtures

edge disjoint paths in moderately connected graphs we study the edge disjoint paths edp problem in undirected graphs given a graph g with n nodes and a set mathcal t of pairs of terminals connect as many terminal pairs as possible using paths that are mutually edge disjoint this leads to a variety of classic np complete problems for which approximability is not well understood we show a polylogarithmic approximation algorithm for the undirected edp problem in general graphs with a moderate restriction on graph connectivity we require the global minimum cut of g to be omega log 5n previously constant or polylogarithmic approximation algorithms were known for trees with parallel edges expanders grids grid like graphs and most recently even degree planar graphs these graphs either have special structure e g they exclude minors or have large numbers of short disjoint paths our algorithm extends previous techniques in that it applies to graphs with high diameters and asymptotically large minors

efficient parallel algorithms for testing k connectivity and finding disjoint s t paths in graphs an efficient parallel algorithm for testing whether a graph g is k vertex connected is presented the algorithm runs in o k 2 log n time and uses n k 2 kc n m processors on a crow pram where n and m are the number of vertices and edges of g and c n m is the number of processors required to compute the connected components of g in logarithmic time for fixed k the algorithm runs in logarithmic time and uses nc n m processors to develop our algorithm an efficient parallel algorithm is designed for the following disjoint s t paths problem given a graph g and two specified vertices s and t find k vertex disjoint paths between s and t if they exist if no such paths exist find a set of at most k 1 vertices whose removal disconnects s and t the parallel algorithm for this problem runs in o k 2 log n time and uses kc n m processors the way to modify the algorithm to find k edge disjoint paths if they exist is shown this yields an efficient parallel algorithm for testing w

stokes second problem for a johnson segalman fluid the laminar flow of a johnson segalman fluid on oscillating plate in its own plane is considered the governing partial differential equations for unsteady motion are constructed analytical solution exists for the problem the differences between these solutions and the corresponding cases in the navier stokes theory are delineated

tristability of thin orthotropic shells with uniform initial curvature composite shells show a rich multistable behaviour of interest for the design of shape changing morphing structures previous studies have investigated how the initial shape determines the shell

multiscale simulations for suspensions of rod like molecules we study the doi model for suspensions of rod like molecules the doi model couples a microscopic fokker planck type equation smoluchowski equation to the macroscopic stokes equation the smoluchowski equation describes the evolution of the distribution of the rod orientations it comes as a drift diffusion equation on the sphere at every point in physical space for sufficiently high macroscopic shear rates high deborah numbers the solution of the coupled system develops internal layers in the macroscopic strain rate the spurt phenomenon in the high deborah numbers regime the drift term in the smoluchowski equation is dominant we thus introduce a finite volume type discretization of the microscopic smoluchowski equation which is motivated by transport dominated pdes we carry out direct numerical simulations of the spurt phenomenon both in the dilute and concentrated regimes below the isotropic nematic transition the solution structure is identical to the one described by purely macroscopic models jso model for higher concentrations we observe the formation of microstructure coming from a position dependent tumbling rate we also investigate the 2 d stability of the spurted solution

the periodic solution of a class of epidemic models abstract this paper has completely studied the dynamical properties of a class of epidemiological models obtained the necessary and sufficient condition for a unique periodic solution which is asymptotically orbitally stable and the necessary and sufficient conditions for the global asymptotic stability of the positive equilibrium

thin film flow of magnetohydrodynamic mhd johnson segalman fluid on vertical surfaces using the adomian decomposition method abstract in this paper the magnetohydrodynamic mhd thin film flow of johnson segalman fluid for lifting and drainage problems on a vertical surfaces are investigated the nonlinear differential equations arising from the mathematical modeling of the johnson segalman fluid the laws of momentum mass and suitable boundary conditions are solved analytically using the adomian decomposition method adm a constant magnetic field is applied transversely to the direction of flow and particular attention is given to the effects of magnetic parameters on the velocity the influence on the velocity field of various non newtonian parameters such as the weissenberg number stokes number and applied magnetic field are investigated several graphs illustrate the influence of various pertinent parameters on the velocity it is observed that increasing the applied magnetic field will generally reduce the flow velocity in the lifting case while in the drainage case the magnetic field and the velocity field are shown to have a direct relation

uniqueness of limit cycles for a class of cubic system with an invariant straight line abstract a class of cubic system with an invariant straight line as given in an equation is studied it is proved that this system has at most one limit cycle surrounding a weak focal o 0 0 and has at most one limit cycle surrounding weak focal n 1 n 0

bistable plates for morphing structures a refined analytical approach with high order polynomials abstract the multistability of composite thin structures has shown potential for morphing applications the present work combines a ritz model with path following algorithms to study bistable plates behaviour classic low order ritz models predict stable shapes geometry with reasonable accuracy however they may fail when modelling other aspects of the elastic structural behaviour a refined higher order model is here presented in order to improve the inherently poor conditioning properties of ritz approximations of slender structures a non dimensional version of classical plate lamination theory with von karman nonlinear strains is developed and presented in the current approach we continue numerical solutions in parameter space that is we path follow equilibrium configurations as the control parameter varies find stable and unstable configurations and identify bifurcations the numerics are carried out using a set of in house matlab routines for numerical continuation the increased degrees of freedom within the model are shown to accurately reflect buckling loads and provide useful insight into the relative importance of different aspects of nonlinear behaviour finally the complex experimentally observed snap through geometry is captured analytically for the first time results are validated against finite elements analysis throughout the course of the paper

integer programming with a fixed number of variables it is shown that the integer linear programming problem with a fixed number of variables is polynomially solvable the proof depends on methods from geometry of numbers

a fast algorithm for the two variable integer programming problem an algorithm that solves any two variable integer programming problem is presented a constant word length model for the data is assumed the complexity for a problem with m constraints and word length of l digits is bounded by the maximum of two values the first which is o mlogm steps is a bound on the complexity of finding the convex region bounded by the constraints each step being an arithmetic orperation or a compare the second which is o ml steps is the complexity of solving m greatest common divisor problems the algorithm finds a minimal binding set of constraints for any given problem in addition to finding the soluuon set a new method of solving three constraint problems is introduced

qualitative analysis of a ratio dependent holling tanner model abstract in this paper we consider a holling tanner system with ratio dependence first we establish the sufficient conditions for the global stability of positive equilibrium by constructing lyapunov function second through a simple change of variables we transform the ratio dependent holling tanner model into a better studied lienard equation as a result the uniqueness of limit cycle can be solved

solution of steady thin film flow of johnson segalman fluid on a vertical moving belt for lifting and drainage problems using adomian decomposition method abstract the steady thin film flow on a vertical belt of a non newtonian johnson segalman fluid for lifting and drainage problems are investigated in this paper the analytical solutions of the non linear problems are obtained by adomian decomposition method adm and homotopy perturbation method hpm expressions for the velocity profile average velocity volume flux the belt speed of the lifting and the shear stress at the belt have been derived for weissenberg number w e 0 we retrieve newtonian cases for both the problems we also obtain the results for maxwell fluid by taking slip parameter a 1 the manner in which the stokes number s t weissenberg number w e the ratio of viscosities and the slip parameter a affect the structure of the velocity profile for lifting and drainage problems are delineated comparison between the adm solutions and homotopy perturbation method hpm solutions are made

non axisymmetric bending of thin annular plates due to circumferentially distributed moments abstract the non linear deformation of a thin annular plate subjected to circumferentially distributed bending moments is studied a von karman plate model is adopted to formulate the equations of motion free free boundary conditions have been applied at both inner and outer edges the matrix formulation of the differential quadrature method is used to discretise and solve the governing equations linear analysis predicts that the annular disk deforms axisymmetrically into a spherical dome however the proposed non linear analysis shows that a symmetry breaking bifurcation may occur after which the linear solution becomes unstable and the plate transitions into a non axisymmetric cylindrical deformation this is the case when at least one of two parameters reaches a critical value these parameters are the non dimensionalised ratio between applied moment and bending stiffness and the ratio between inner and outer radius furthermore it is noted that free free boundary conditions and circumferentially distributed bending moments do not break the circular symmetry of the annular disk hence the principal axes of curvature in the deformed configuration do not have a preferred orientation therefore the present work describes a shell possessing infinite identical equilibria having different yet no favoured direction and hence links to previous researches on neutrally stable structures

a mathematical description of peristaltic hydromagnetic flow in a tube abstract peristaltic motion of an incompressible non newtonian fluid in a deformable tube is studied under long wavelength and low reynolds number the effect of magnetic field on the motion of a johnson segalman fluid has been modelled analytical solutions are obtained for the stream function axial velocity and axial pressure gradient under the small weissenberg number the pressure rise and frictional force per wavelength have been computed through numerical integration the study shows that in addition to weissenberg number and the effect of magnetic field the occlusion and volume flux also affect the peristaltic flow these effects are noticeable in the stream function axial velocity axial pressure gradient the pressure rise and the frictional force graphs are plotted for axial pressure gradient pressure rise and frictional force and discussed in detail

analytical investigation of structurally stable configurations in shape memory alloy actuated plates strains produced by active materials embedded in plates have been extensively used to manipulate the shape of surface like engineering structures shape memory alloys smas are active materials that provide a significant amount of strain under large stresses a characteristic of great utility in such morphing structures in this work an analytical approach to approximate the deformation of plates with sma constituents is developed via the rayleigh ritz method an additive set of kinematically admissible displacement fields with unknown coefficients is used to describe the plate displacement field the total potential energy is then calculated using the displacement field loading conditions and constitutive relations for the plate layer s composed of sma wire meshes dense sma films and or elastic material the unknown coefficients are then found via minimization of the total potential energy this approach provides closed form expressions for the approximate deformation of the plates including multistable configurations the response of circular sma based plates is studied herein the results show that temperature fields with a linear variation in the radial direction induce multistable configurations in which the plate gaussian curvature is determined by the direction of the temperature gradient an alternative inversion of the proposed approach is used to directly compute the temperature field required to morph a plate towards a prescribed goal shape the obtained closed form expressions show good agreement with detailed non linear finite element analysis simulations the proposed approach provides analysts with a low computational cost and relatively simple implementation to assess the potentially stable configurations of sma based plates under given loading conditions knowledge of such stable configurations is very valuable in the design of sma based morphing structures c 2015 elsevier ltd all rights reserved

on the generation of discontinuous shearing motions of a non newtonian fluid the system under study models unsteady one dimensional shear flow of a highly elastic and viscous incompressible non newtonian fluid with fading memory under isothermal conditions the flow in a channel is driven by a constant pressure gradient is symmetric about the center line and satisfies a no slip boundary condition at the wall the non newtonian contribution to the stress is assumed to obey a differential constitutive law due to oldroyd johnson segalman the key feature of which is a non monotone relation between the total steady shear stress and strain rate in a regime in which the reynolds number is much smaller than the deborah or weissenberg number one obtains a degenerate singularly perturbed system of nonlinear reaction diffusion equations it is shown that if the driving pressure gradient exceeds a critical value the local shear stress maximum of the steady stress vs strain rate relation then the solution to the governing system starting from rest at tends as to a particular discontinuous steady state solution the top jumping steady state except in a small neighborhood of the discontinuity this discontinuous steady state is shown to be nonlinearly stable in a precise sense with respect to perturbations yielding smooth initial data such discontinuous steady states have been proposed to explain spurting flows which exhibit a large increase in mean flow rate when the driving pressure is raised above a critical value

discrete approximations of the foppl von karman shell model from coarse to more refined models abstract the problem of deducing from the foppl von karman energy functional a sequence of reduced discrete models having few degrees of freedom is analyzed similar discrete models have been recently intensively studied to analyze the multistable behavior of shallow shells the bifurcations of composite laminates under temperature loads or the wrinkling in soft tissues in particular three relevant examples are discussed and compared among them where the curvature is assumed uniform linearly and quadratically varying through the shell while the uniform curvature assumption dates back to mansfield 1962 linear variations of the shell curvatures can describe smooth transitions between everted configurations while quadratic variations can account for the usually disregarded bending boundary conditions for their deduction we revisit the maxwell mohr method accordingly a sequence of auxiliary elliptic problems of plane elasticity is solved to determine the statically unknown membranal stresses this is a key ingredient for the presented models to compare extremely well with finite element approximations or with literature models with far more degrees of freedom

minimum cuts in near linear time we significantly improve known time bounds for solving the minimum cut problem on undirected graphs we use a semiduality between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling techniques we give a randomized monte carlo algorithm that finds a minimum cut in an m edge n vertex graph with high probability in o m log 3 n time we also give a simpler randomized algorithm that finds all minimum cuts with high probability in o m log 3 n time this variant has an optimal rnc parallelization both variants improve on the previous best time bound of o n 2 log 3 n other applications of the tree packing approach are new nearly tight bounds on the number of near minimum cuts a graph may have and a new data structure for representing them in a space efficient manner

continuity of velocity gradients in suspensions of rod like molecules we investigate the doi model for suspensions of rod like molecules in the dilute regime for certain parameter values the velocity gradient vs stress relation defined by the stationary and homogeneous flow is not rank one monotone we then consider the evolution of possibly large perturbations of stationary flows we prove that even in the absence of a microscopic cut off discontinuities in the velocity gradient cannot occur in finite time the proof relies on a novel type of estimate for the smoluchowski equation

random sampling in cut flow and network design problems we use random sampling as a tool for solving undirected graph problems we show that the sparse graph or skeleton that arises when we randomly sample a graph s edges will accurately approximate the value of all cuts in the original graph with high probability this makes sampling effective for problems involving cuts in graphs we present fast randomized monte carlo and las vegas algorithms for approximating and exactly finding minimum cuts and maximum flows in unweighted undirected graphs our cut approximation algorithms extend unchanged to weighted graphs while our weighted graph flow algorithms are somewhat slower our approach gives a general paradigm with potential applications to any packing problem it has since been used in a near linear time algorithm for finding minimum cuts as well as faster cut and flow algorithms our sampling theorems also yield faster algorithms for several other cut based problems including approximating the best balanced cut of a graph finding a k connected orientation of a 2k connected graph and finding integral multicommodity flows in graphs with a great deal of excess capacity our methods also improve the efficiency of some parallel cut and flow algorithms our methods also apply to the network design problem where we wish to build a network satisfying certain connectivity requirements between vertices we can purchase edges of various costs and wish to satisfy the requirements at minimum total cost since our sampling theorems apply even when the sampling probabilities are different for different edges we can apply randomized rounding to solve network design problems this gives approximation algorithms that guarantee much better approximations than previous algorithms whenever the minimum connectivity requirement is large as a particular example we improve the best approximation bound for the minimum k connected subgraph problem from 1 85 to math not displayed

on the capacity of network coding for random networks we study the maximum flow possible between a single source and multiple terminals in a weighted random graph modeling a wired network and a weighted random geometric graph modeling an ad hoc wireless network using network coding for the weighted random graph model we show that the network coding capacity concentrates around the expected number of nearest neighbors of the source and the terminals specifically for a network with a single source l terminals and n relay nodes such that the link capacities between any two nodes is independent and identically distributed i i d spl sim x the maximum flow between the source and the terminals is approximately ne x with high probability for the weighted random geometric graph model where two nodes are connected if they are within a certain distance of each other we show that with high probability the network coding capacity is greater than or equal to the expected number of nearest neighbors of the node with the least coverage area

survivable networks linear programming relaxations and the parsimonious property we consider the survivable network design problem the problem of designing at minimum cost a network with edge connectivity requirements as special cases this problem encompasses the steiner tree problem the traveling salesman problem and thek edge connected network design problem we establish a property referred to as the parsimonious property of the linear programming lp relaxation of a classical formulation for the problem the parsimonious property has numerous consequences for example we derive various structural properties of these lp relaxations we present some algorithmic improvements and we perform tight worst case analyses of two heuristics for the survivable network design problem

a certified reduced basis method for the fokker planck equation of dilute polymeric fluids fene dumbbells in extensional flow in this paper we present a reduced basis method for the parametrized fokker planck equation associated with evolution of finitely extensible nonlinear elastic fene dumbbells in a newtonian solvent for a prescribed extensional macroscale flow we apply a proper orthogonal decomposition pod greedy sampling procedure for the stable identification of optimal reduced basis spaces and we develop a rigorous finite time a posteriori bound for the error in the reduced basis prediction of the two outputs of interest the optical anisotropy and the first normal stress difference we present numerical results for stress conformation hysteresis as a function of weissenberg number and final time that demonstrate the rapid convergence of the reduced basis approximation and the effectiveness of the a posteriori error bounds

analysis of new phenomena in shear flow of non newtonian fluids phase plane and small parameter asymptotic techniques are used to analyze systems of ordinary differential equations that describe the transient behavior of non newtonian fluids in shear flow these systems approximate the partial differential equations that derive from three dimensional balance laws and from differential constitutive models for highly elastic liquids two models are considered one with a single relaxation time and small newtonian viscosity the other with two relaxation times and no newtonian viscosity both possess the key feature that the variation of steady shear stress with strain rate is not monotone the analysis shows that both models exhibit several distinctive phenomena spurt shape memory hysteresis latency and normal stress oscillations the predictions for the spurt phenomenon agree quantitatively with experimental results for polymer melts the other new phenomena which were discovered recently in numerical simulation should also be observable in rheological experiments

on a multidimensional search technique and its application to the euclidean one centre problem the paper is divided into two main sections the first deals with a multidimensional search technique of megiddo j assoc comput mach 31 1984 pp 114 127 and suggests an improvement the second gives an application of the technique to the euclidean one centre problem in mathbb r d an algorithm of time complexity o 3 d 2 2 n is derived for this problem this improves the best previous bound even in the case d 2

deterministic edge connectivity in near linear time we present a deterministic algorithm that computes the edge connectivity of a graph in near linear time this is for a simple undirected unweighted graph g with n vertices and m edges this is the first o mn time deterministic algorithm for the problem our algorithm is easily extended to find a concrete minimum edge cut in fact we can construct the classic cactus representation of all minimum cuts in near linear time the previous fastest deterministic algorithm by gabow from stoc 91 took o m 2 n where is the edge connectivity but can be as big as n 1 karger presented a randomized near linear time monte carlo algorithm for the minimum cut problem at stoc 96 but the returned cut is only minimum with high probability our main technical contribution is a near linear time algorithm that contracts vertex sets of a simple input graph g with minimum degree producing a multigraph with o m edges which preserves all minimum cuts of g with at least two vertices on each side in our deterministic near linear time algorithm we will decompose the problem via low conductance cuts found using pagerank a la brin and page 1998 as analyzed by andersson chung and lang at focs 06 normally such algorithms for low conductance cuts are randomized monte carlo algorithms because they rely on guessing a good start vertex however in our case we have so much structure that no guessing is needed

hyperbolicity and change of type in the flow of viscoelastic fluids the equations governing the flow of viscoelastic liquids are classified according to the symbol of their differential operators propagation of singularities is discussed and conditions for a change of type are investigated the vorticity equation for steady flow can change type when a critical condition involving speed and stresses is satisfied this leads to a partitioning of the field of flow into subcritical and supercritical regions as in the problem of transonic flow

minkowski s convex body theorem and integer programming the paper presents an algorithm for solving integer programming problems whose running time depends on the number n of variables as non this is done by reducing an n variable problem to 2n5i 2 problems in n i variables for some i greater than zero chosen by the algorithm the factor of on5 2 per variable improves the best previously known factor which is exponential in n minkowski s convex body theorem and other results from geometry of numbers play a crucial role in the algorithm several related algorithms for lattice problems are presented the complexity of these problems with respect to polynomial time reducibilities is studied

when trees collide an approximation algorithm for thegeneralized steiner problem on networks we give the first approximation algorithm for the generalized network steiner problem a problem in network design an instance consists of a network with link costs and for each pair i j of nodes an edge connectivity requirement r ij the goal is to find a minimum cost network using the available links and satisfying the requirements our algorithm outputs a solution whose cost is within 2 lceil log 2 r 1 rceil of optimal where r is the highest requirement value in the course of proving the performance guarantee we prove a combinatorial min max approximate equality relating minimum cost networks to maximum packings of certain kinds of cuts as a consequence of the proof of this theorem we obtain an approximation algorithm for optimally packing these cuts we show that this algorithm has application to estimating the reliability of a probabilistic network

versal unfoldings of predator prey systems with ratio dependent functional response abstract in this paper we study the versal unfolding of a predator prey system with ratio dependent functional response near a degenerate equilibrium in order to obtain all possible phase portraits for its perturbations we first construct the unfolding and prove its versality and degeneracy of codimension 2 then we discuss all its possible bifurcations including transcritical bifurcation hopf bifurcation and heteroclinic bifurcation give conditions of parameters for the appearance of closed orbits and heteroclinic loops and describe the bifurcation curves phase portraits for all possible cases are presented

biconnectivity approximations and graph carvings a spanning tree in a graph is the smallest connected spanning subgraph given a graph how does one find the smallest i e least number of edges 2 connected spanning subgraph connectivity refers to both edge and vertex connectivity if not specified unfortunately the problem is known to be np hard we consider the problem of finding a better approximation to the smallest 2 connected subgraph by an efficient algorithm for 2 edge connectivity our algorithm guarantees a solution that is no more than 3 2 times the optimal for 2 vertex connectivity our algorithm guarantees a solution that is no more than 5 3 times the optimal the previous best approximation factor is 2 for each of these problems the new algorithms and their analyses depend upon a structure called a carving of a graph which is of independent interest we show that approximating the optimal solution to within an additive constant is np hard as well we also consider the case where the graph has edge weights for this case we show that an approximation factor of 2 is possible in polynomial time for finding a k edge connected spanning subgraph this improves an approximation factor of 3 for k 2 due to frederickson and ja ja 1981 and extends it for any k with an increased running time though

asymptotic behaviour and changes of phase in one dimensional nonlinear viscoelasticity in this paper we study the asymptotic behaviour as t co of solutions u x t to the nonlinear partial differential equation ut m4 a o o 1 1 with initial conditions u 0 q x u x u x o 0 1 3a

invariant manifolds for flows in banach spaces on presente une theorie des varietes invariantes lisses basee sur la methode classique de lyapunov penon pour des semi flots continus dans des espaces de banach

inertial manifolds associated to partly dissipative reaction diffusion systems abstract in a previous work we established the existence of finite dimensional attractors for partly dissipative reaction diffusion systems of two types systems with a polynomial growth nonlinearity and systems admitting an invariant region the aim of this article is to show that these problems possess inertial manifolds in space dimension n 2 these inertial manifolds contain the universal attractor attract exponentially all the solutions as time goes to infinity and due to the weak dissipation are here infinite dimensional our results are applied to several classical systems borrowed from mathematical biology physics and chemistry