average consensus on general strongly connected digraphs we study the average consensus problem of multi agent systems for general network topologies with unidirectional information flow we propose two linear distributed algorithms deterministic and gossip respectively for the cases where the inter agent communication is synchronous and asynchronous in both cases the developed algorithms guarantee state averaging on arbitrary strongly connected digraphs in particular this graphical condition does not require that the network be balanced or symmetric thereby extending previous results in the literature the key novelty of our approach is to augment an additional variable for each agent called surplus whose function is to locally record individual state updates for convergence analysis we employ graph theoretic and nonnegative matrix tools plus the eigenvalue perturbation theory playing a crucial role

discontinuous generalized solutions of nonlinear nonconservative hyperbolic equations abstract nonlinear nonstationary problems arising in elastodynamics have naturally a nonconservative form for these systems it is not possible to define a weak solution according to distribution theory in order to define the concept of discontinuous solutions for these systems one is confronted with multiplications of distributions this is unavoidable from a physical viewpoint since discontinuous solutions are needed to represent shock waves the theory of generalized functions of the second author in which one may multiply arbitrary distributions gives a concept of generalized solutions that may be discontinuous functions existence of such global solutions of the cauchy problem for a system of two equations is proved by a compactness argument from a convergent numerical scheme in the case under consideration the generalized solutions are bounded variation functions the results thus obtained agree with the results expected by the engineers and lead to the development of new numerical schemes

distributed subgradient methods for convex optimization over random networks we consider the problem of cooperatively minimizing the sum of convex functions where the functions represent local objective functions of the agents we assume that each agent has information about his local function and communicate with the other agents over a time varying network topology for this problem we propose a distributed subgradient method that uses averaging algorithms for locally sharing information among the agents in contrast to previous works on multi agent optimization that make worst case assumptions about the connectivity of the agents such as bounded communication intervals between nodes we assume that links fail according to a given stochastic process under the assumption that the link failures are independent and identically distributed over time possibly correlated across links we provide almost sure convergence results for our subgradient algorithm

products and compositions with the dirac delta function the need to define pointwise products and compositions with distributions is pointed out in the context of the problems of renormalisation junction conditions and curved shock waves earlier definitions are briefly reviewed and new definitions are proposed using non standard analysis basic properties are established and some products and compositions with the delta distribution are explicitly evaluated with these definitions the domain of validity of the nonlinear differential equations of classical field theory can be extended to include rankine hugoniot equations are derived from the euler equations an immediate application to quantum field theory is pointed out

distributed multi agent optimization with state dependent communication we study distributed algorithms for solving global optimization problems in which the objective function is the sum of local objective functions of agents and the constraint set is given by the intersection of local constraint sets of agents we assume that each agent knows only his own local objective function and constraint set and exchanges information with the other agents over a randomly varying network topology to update his information state we assume a state dependent communication model over this topology communication is markovian with respect to the states of the agents and the probability with which the links are available depends on the states of the agents we study a projected multi agent subgradient algorithm under state dependent communication the state dependence of the communication introduces significant challenges and couples the study of information exchange with the analysis of subgradient steps and projection errors we first show that the multi agent subgradient algorithm when used with a constant stepsize may result in the agent estimates to diverge with probability one under some assumptions on the stepsize sequence we provide convergence rate bounds on a disagreement metric between the agent estimates our bounds are time nonhomogeneous in the sense that they depend on the initial starting time despite this we show that agent estimates reach an almost sure consensus and converge to the same optimal solution of the global optimization problem with probability one under different assumptions on the local constraint sets and the stepsize sequence

nonstandard analysis and jump conditions for converging shock waves nonstandard analysis is an area of modern mathematics that studies abstract number systems containing both infinitesimal and infinite numbers this article applies nonstandard analysis to derive jump conditions for one dimensional converging shock waves in a compressible inviscid perfect gas it is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval predistributions of the heaviside function and the dirac delta measure are introduced to model the flow parameters across a shock wave the equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the flow parameters

direct adaptive fuzzy control with a self structuring algorithm this paper presents a direct self structuring adaptive fuzzy control dsafc scheme for affine nonlinear single input single output systems we show that the only restriction on the control gain is that it be positive no upper bound on this gain nor its derivative needs to be known from an initial fuzzy system with a small number of rules the self structuring algorithm adds membership functions and rules when needed to limit the size of the fuzzy system from growing indefinitely the self structuring algorithm replaces old membership functions by new ones instead of adding more membership functions so that the number of rules never exceeds a predefined upper bound the stability of the closed loop system is guaranteed using the lyapunov synthesis approach the proposed control scheme is demonstrated by application to an inverted pendulum and a magnetic levitation system

novel neural control for a class of uncertain pure feedback systems this paper is concerned with the problem of adaptive neural tracking control for a class of uncertain pure feedback nonlinear systems using the implicit function theorem and backstepping technique a practical robust adaptive neural control scheme is proposed to guarantee that the tracking error converges to an adjusted neighborhood of the origin by choosing appropriate design parameters in contrast to conventional lyapunov based design techniques an alternative lyapunov function is constructed for the development of control law and learning algorithms differing from the existing results in the literature the control scheme does not need to compute the derivatives of virtual control signals at each step in backstepping design procedures furthermore the scheme requires the desired trajectory and its first derivative rather than its first n derivatives in addition the useful property of the basis function of the radial basis function which will be used in control design is explored simulation results illustrate the effectiveness of the proposed techniques

why many theories of shock waves are necessary kinetic relations for non conservative systems for a class of nonconservative hyperbolic systems of partial dif ferential equations endowed with a strictly convex mathematical entropy we formulate the initial value problem by supplementing the equations with a ki netic relation prescribing the rate of entropy dissipation across shock waves our condition can be regarded as a generalization to nonconservative systems of a similar concept introduced by abeyaratne knowles and truskinovsky for subsonic phase transitions and by lefloch for nonclassical undercompressive shocks to nonlinear hyperbolic systems the proposed kinetic relation for non conservative systems turns out to be equivalent for the class of systems under consideration at least to dal maso lefloch and murat s definition based on a prescribed family of lipschitz continuous paths in agreement with previous theories the kinetic relation should be derived from a phase plane analysis of traveling solutions associated with an augmented version of the nonconserva tive system we illustrate with several examples that nonconservative systems arising in the applications fit in our framework and for a typical model of turbulent fluid dynamics we provide a detailed analysis of the existence and properties of traveling waves which yields the corresponding kinetic function

multiplications of distributions in elasticity and hydrodynamics it is shown how a mathematical theory of generalized functions in which the multiplications of distributions appearing in nonlinear equations of physics make sense gives new formulas and new numerical results the new methods shown here are quite general but since each particular problem requires its own study this paper is limited to elasticity and hydrodynamics in elasticity hooke s law gives systems in a nonconservative form the study of shock waves for these systems gives nonclassical multiplications of distributions of the form y y heaviside function dirac mass at the origin using this new mathematical tool new formulas are obtained more generally new numerical schemes in a first step ambiguous results are obtained then the ambiguity is removed in hydrodynamics a formulation is obtained that has a nonconservative form and is at the basis of efficient new numerical schemes strictly speaking the reader is not assumed to know anything either on distributions or on elasticity and hydrodynamics since the basic equations are recalled all computations done in this paper are rigorous from the mathematical viewpoint

macroscopic theory of multicomponent flows irreversibility and well posed equations abstract a theory of the coupling of n systems of navier stokes equations is presented a set of coupled navier stokes systems contains the macroscopic equations of motion for flows of n different material components or phases six postulates are formulated from which three navier stokes sets are derived for arbitrary n the main postulate concerns the second law of thermodynamics which the present sets satisfy for arbitrary n appropriate averages of velocities and pressures distribute the entropy production of each irreversible interaction process among the interacting components increase of entropy is guaranteed if the interaction terms are suitably constructed from positive definite operators a strictly irreversible mass exchange law expressed in the difference of gibbs free energies of the exchanging components is proposed furthermore the characteristic velocities of each navier stokes set are investigated since their realness is required for well posedness of the equations for both navier stokes sets with multiple pressures the characteristic velocities are proven to be real for arbitrary n the canonical problem of complex characteristics of incompressible multiphase flows with a single pressure is revisited a solution to this problem is found by generalizing the standard algebraic stokes drag law to a positive definite operator acting on the velocity difference in this way effects of forces due to nonuniform velocity fields can be incorporated a generalized drag law is specified by the inclusion of m th order spatial derivatives of the velocity differences between two components m 2 the characteristic polynomial is derived for an arbitrary number of components and its roots the characteristic velocities appear to be real this is rigorously proven for two and three phase flows and conjectured to be true for flows with four or more components the linear stability of the incompressible one dimensional case is also investigated ill posedness of the standard case leads to an infinite growth rate for infinitely short waves in the case of generalized drag this growth rate becomes finite for even and neutral for odd m

nonlinear generalized functions on manifolds in this work we adopt a new approach to the construction of a global theory of algebras of generalized functions on manifolds based on the concept of smoothing operators this produces a generaliz

decentralized optimization over time varying directed graphs with row and column stochastic matrices in this article we provide a distributed optimization algorithm termed as tv mathcal ab that minimizes a sum of convex functions over time varying random directed graphs contrary to the existing work the algorithm we propose does not require eigenvector estimation to estimate the non mathbf 1 perron eigenvector of a stochastic matrix instead the proposed approach relies on a novel information mixing approach that exploits both row and column stochastic weights to achieve agreement toward the optimal solution when the underlying graph is directed we show that tv mathcal ab converges linearly to the optimal solution when the global objective is smooth and strongly convex and the underlying time varying graphs exhibit bounded connectivity i e a union of every c consecutive graphs is strongly connected we derive the convergence results based on the stability analysis of a linear system of inequalities along with a matrix perturbation argument simulations confirm the findings in this article

a nonlinear conservation law with a step function involving the flux a distributional approach the present paper concerns a riemann problem for a conservation law with a nonlinear flux involving a step function in a convenient space of distributions we will see the emergence of a delta standing wave which extends the corresponding result obtained by sun in 2013 and also by shen in 2014 for a linear flux in the nonlinear setting a new phenomenon arises starting from a vanishing initial condition the concentration of matter in a fixed point becomes possible these results are easy to get essentially because in our approach the product of distributions is a distribution that does not depend of approximation processes the present paper concerns a riemann problem for a conservation law with a nonlinear flux involving a step function in a convenient space of distributions we will see the emergence of a delta standing wave which extends the corresponding result obtained by sun in 2013 and also by shen in 2014 for a linear flux in the nonlinear setting a new phenomenon arises starting from a vanishing initial condition the concentration of matter in a fixed point becomes possible these results are easy to get essentially because in our approach the product of distributions is a distribution that does not depend of approximation processes

fuzzy adaptive learning control network with on line neural learning abstract this paper addresses the structure and the associated on line learning algorithms of a feedforward multilayered connectionist network for realizing the basic elements and functions of a traditional fuzzy logic controller the proposed fuzzy adaptive learning control network falcon can be contrasted with the traditional fuzzy logic control systems in their network structure and learning ability the connectionist structure of the proposed falcon can be constructed from training examples by neural learning techniques to find proper fuzzy partitions membership functions and fuzzy logic rules two complementary on line structure parameter learning algorithms falcon fsm and falcon art are proposed for constructing the falcon dynamically the falcon fsm combines the backpropagation learning scheme for parameter learning and a fuzzy similarity measure for structure learning the falcon fsn can find proper fuzzy logic rules membership functions and the size of output partitions simultaneously in the falcon fsm algorithm the input and output spaces are partitioned into grids the grid typed space partitioning certainly makes both the fuzzy logic controller software emulation and fuzzy chip implementation convenient however as the number of input output variables increases the number of partitioned grids will grow combinatorially to avoid the problem of combinatorial growth of partitioned grids in some complex systems the falcon art algorithm is developed which can partition the input and output spaces in a more flexible way based on the distribution of the training data the falcon art combines the backpropagation learning scheme for parameter learning and a fuzzy art algorithm for structure learning the falcon art can on line partition the input and output spaces tune membership functions and find proper fuzzy logic rules dynamically computer simulations were conducted to illustrate the performance and applicability of both falcon fsm and falcon art learning algorithms

online adaptive fuzzy neural identification and control of a class of mimo nonlinear systems this paper presents a robust adaptive fuzzy neural controller afnc suitable for identification and control of a class of uncertain multiple input multiple output mimo nonlinear systems the proposed controller has the following salient features 1 self organizing fuzzy neural structure i e fuzzy control rules can be generated or deleted automatically 2 online learning ability of uncertain mimo nonlinear systems 3 fast learning speed 4 fast convergence of tracking errors 5 adaptive control where structure and parameters of the afnc can be self adaptive in the presence of disturbances to maintain high control performance 6 robust control where global stability of the system is established using the lyapunov approach simulation studies on an inverted pendulum and a two link robot manipulator show that the performance of the proposed controller is superior

numerical simulation of a compressible two layer model a first attempt with an implicit explicit splitting scheme this work is devoted to the numerical simulation of the compressible two layer model developed in 16 the latter is an hyperbolic two fluid two pressure model dedicated to gas liquid flows in pipes especially stratified air water flows using explicit schemes one obtains a cfl condition based on the celerity of fast acoustic waves which typically brings large numerical diffusivity for the slow material waves and small time steps in order to overcome these drawbacks the proposed scheme involves an operator splitting and an implicit explicit time discretization thus the full system is split into two hyperbolic subsystems the first one deals with the transport equation on the liquid height using an explicit scheme and upwind fluxes the second one deals with the averaged mass and momentum conservation equations of both phases using an implicit scheme which handles the propagation of acoustic waves at last the positivity of heights and densities is ensured under a cfl condition which involves material velocities numerical experiments are performed using acoustic as well as material time steps adding the rusanov scheme for comparison the best accuracy is obtained with the proposed scheme used with acoustic time steps when used with material time steps efficiency on the slow waves and stability are obtained regarding analytical solutions of the convective part

newton s second law and the multiplication of distributions newton s second law is applied to study the motion of a particle subjected to a time dependent impulsive force containing a dirac delta distribution within this setting we prove that this problem can be rigorously solved neither by limit processes nor by using the theory of distributions limited to the classical schwartz products however using a distributional multiplication not defined by a limit process a rigorous solution emerges

structure identification in complete rule based fuzzy systems the identification of a model is one of the key issues in the field of fuzzy system modeling and function approximation theory there are numerous approaches to the issue of parameter optimization within a fixed fuzzy system structure but no reliable method to obtain the optimal topology of the fuzzy system from a set of input output data this paper presents a reliable method to obtain the structure of a complete rule based fuzzy system for a specific approximation accuracy of the training data i e it can decide which input variables must be taken into account in the fuzzy system and how many membership functions mfs are needed in every selected input variable in order to reach the approximation target with the minimum number of parameters

distributions as initial values in a triangular hyperbolic system of conservation laws the present paper concerns the system ut u x 0 vt u v x 0 having distributions as initial conditions under certain conditions and supposing functions we explicitly solve this cauchy problem within a convenient space of distributions u v for this purpose a consistent extension of the classical solution concept defined in the setting of a distributional product not constructed by approximation processes is used shock waves shock waves and also waves defined by distributions that are not measures are presented explicitly as examples this study is carried out without assuming classical results about conservation laws for reader s convenience a brief survey of the distributional product is also included

hybrid flux splitting schemes for a two phase flow model in this paper we deal with the construction of hybrid flux vector splitting fvs schemes and flux difference splitting fds schemes for a two phase model for one dimensional flow the model consists of two mass conservation equations one for each phase and a common momentum equation the complexity of this model as far as numerical computation is concerned is related to the fact that the flux cannot be expressed in terms of its conservative variables this is the motivation for studying numerical schemes which are not based on approximate riemann solvers and or calculations of jacobian matrix this work concerns the extension of an fvs type scheme a van leer type scheme and an advection upstream splitting method ausm type scheme to the current two phase model our schemes are obtained through natural extensions of corresponding schemes studied by y wada and m s liou 1997 siam j sci comput 18 633 657 for euler equations we explore the various schemes for flow cases which involve both fast and slow transients in particular we demonstrate that the fvs scheme is able to capture fast propagating acoustic waves in a monotone way while it introduces an excessive numerical dissipation at volume fraction contact steady and moving discontinuities on the other hand the ausm scheme gives accurate resolution of contact discontinuities but produces oscillatory approximations of acoustic waves this motivates us to propose other hybrid fvs fds schemes obtained by removing numerical dissipation at contact discontinuities in the fvs and van leer schemes

microscopic profiles of shock waves and ambiguities in multiplications of distributions a rigorous mathematical method is introduced for studying discontinuous solutions for systems in nonconservative form the evidence of the agreement between the theoretical and numerical results is shown on simplified models of physics

new solutions for the one dimensional nonconservative inviscid burgers equation abstract the propagation of travelling waves is a relevant physical phenomenon as usual the understanding of a real propagating wave depends upon a correct formulation of a idealized model discontinuous functions dirac measures and their distributional derivatives are respectively idealizations of sharp jumps localized high peaks and single sharp localised oscillations in the present paper we study the propagation of distributional travelling waves for burgers inviscid equation this will be afforded by our theory of distributional products and is based on a rigorous and consistent concept of solution we have introduced in c o r sarrico distributional products and global solutions for nonconservative inviscid burgers equation j math anal appl 281 2003 641 656 our approach exhibit dirac travelling solitons they are just the infinitesimal narrow solitons of maslov omel yanov and tsupin v p maslov o a omel yanov asymptotic soliton form solutions of equations with small dispersion russian math surveys 36 1981 73 149 v p maslov v a tsupin necessary conditions for the existence of infinitely narrow solitons in gas dynamics soviet phys dokl 24 1979 354 356 and also solutions which are not measures such as for instance u x t b x b t a wave of constant speed b moreover for signals with two jump discontinuities we have in our setting the propagation of more solitons and more values for the signal speed are allowed than those afforded within classical framework

traveling waves solution of convection diffusion systems whose convection terms are weakly nonconservative application to the modeling of two phase fluid flows the paper is concerned with the derivation of explicit approximate jump conditions for the shock waves solutions of hyperbolic systems in nonconservation form extracted from a known second order convection diffusion system the shock waves are defined as the limit as the diffusion tends to zero of the traveling waves solution of the second order system although no explicit jump conditions may be found for general hyperbolic systems in nonconservation form we derive an asymptotic expansion of the nonexplicit jump relations in the case of two phase fluid flows we indeed observe that the terms in nonconservation form arise from pressure gradient forces which act on droplets and are small in the sense that the a small number appears in front of them we obtain an asymptotic expansion of the nonexplicit jump relations whose first two terms can be computed explicitly

decentralized quasi newton methods we introduce the decentralized broyden fletcher goldfarb shanno d bfgs method as a variation of the bfgs quasi newton method for solving decentralized optimization problems decentralized quasi newton methods are of interest in problems that are not well conditioned making first order decentralized methods ineffective and in which second order information is not readily available making second order decentralized methods impossible d bfgs is a fully distributed algorithm in which nodes approximate curvature information of themselves and their neighbors through the satisfaction of a secant condition we additionally provide a formulation of the algorithm in asynchronous settings convergence of d bfgs is established formally in both the synchronous and asynchronous settings and strong performance advantages relative to existing methods are shown numerically

hyperbolic two pressure models for two phase flow abstract for some time it has been known that many of the two phase flow models lead to ill posed cauchy problems because they have complex characteristic values a necessary condition at least in the linear case for the cauchy problem to be well posed is that it be stable in the sense of von neumann for systems of partial differential equations of first order stability in the sense of von neumann is essentially equivalent to the condition that the model be hyperbolic all real characteristic values and complete set of characteristic vectors herein models are developed which have real characteristic values for all physically acceptable states state space and except for a set of measure zero have a complete set of characteristic vectors in state space therefore these models are hyperbolic a e almost everywhere in state space also they are stable in the sense of von neumann a e in state space even without inclusion of viscosity terms the models discussed herein are developed for the case of two phase separated planar flow and include transverse momentum considerations these models are referred to as two pressure models because each phase is assumed to exist at an average pressure different from the average pressure in the other phase the pressure fields are related through momentum considerations numerical results on a steady state problem show good agreement with existing steady state results numerical results on a transient problem agree with a single pressure model until the onset of numerical instability in the single pressure model compared to the single pressure hydrostatic model the two pressure model approximates additional physical features and is shown to be a viable approach for the case of separated flow

a geometrical approach to nonconservative shocks and elastoplastic shocks we study systems of conservation laws with convex inequality constraints we analyze shock solutions for the underlying nonconservative system of partial differential equations then we study a model elastoplastic system of partial differential equations in the context of hypoelasticity we show that a sonic point is necessary to construct a compression solution that begins at a constrained compressed state

a split godunov scheme for solving one dimensional hyperbolic systems in a nonconservative form in this paper we developed a theoretical study for nonconservative sytems in one dimension in order to construct numerical schemes for solving the riemann problem the nonconservative form of our model system required the use of a well adapted theory in order to give us a sense of our problem we chose a framework of generalized functions for solving a scalar hyperbolic equation with a discontinuous coefficient sigma t u sigma x approx 0 where u is the velocity solution of a burgers s equation after an explicit solution of the riemann problem we derived godunov split schemes for computing an approximate solution of the cauchy problem we applied our study to a system modeling elasticity and a system modeling gas dynamics some stability properties of a scheme and its convergence to a generalized solution are proved for the first model numerical experiments confirmed this convergence result for the second model calculations of flows containing weak to moderate shocks showed that conservation errors are reduced when the mesh is refined but were not entirely eliminated

fuzzy approximation based adaptive control of nonlinear delayed systems with unknown dead zone this paper focuses on the problem of adaptive fuzzy control for a class of nonlinear systems without a strict feedback form a new adaptive fuzzy control scheme is proposed for nonlinear delayed systems with unknown dead zone nonlinearity control design is achieved by introducing a variable separation approach and employing the unique structural property of fuzzy logic systems the proposed adaptive fuzzy controller guarantees that all the closed loop signals are semiglobally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin two simulation examples illustrate the effectiveness of the proposed approach

high order wave propagation algorithms for hyperbolic systems we present a finite volume method that is applicable to hyperbolic pdes including spatially varying and semilinear nonconservative systems the spatial discretization like that of the well known clawpack software is based on solving riemann problems and calculating fluctuations not fluxes the implementation employs weighted essentially nonoscillatory reconstruction in space and strong stability preserving runge kutta integration in time the method can be extended to arbitrarily high order of accuracy and allows a well balanced implementation for capturing solutions of balance laws near steady state this well balancing is achieved through the f wave riemann solver and a novel wave slope weno reconstruction procedure the wide applicability and advantageous properties of the method are demonstrated through numerical examples including problems in nonconservative form problems with spatially varying fluxes and problems involving near equilibrium solutions of balance laws

stable auto tuning of adaptive fuzzy neural controllers for nonlinear discrete time systems in direct adaptive control the adaptation mechanism attempts to adjust a parameterized nonlinear controller to approximate an ideal controller in the indirect case however we approximate parts of the plant dynamics that are used by a feedback controller to cancel the system nonlinearities in both cases approximators such as linear mappings polynomials fuzzy systems or neural networks can be used as either the parameterized nonlinear controller or identifier model in this paper we present algorithms to tune some of the parameters e g the adaptation gain and the direction of descent for a gradient based approximator parameter update law used for a class of nonlinear discrete time systems in both direct and indirect cases in our proposed algorithms the adaptation gain and the direction of descent are obtained by minimizing the instantaneous control energy we will show that updating the adaptation gain can be viewed as a special case of updating the direction of descent we will also compare the direct and indirect adaptive control schemes and illustrate their performance via a simple surge tank example

convergence of numerical schemes involving powers of the dirac delta function abstract developments of the hull elastoplastic numerical method lead to nonconservative versions which in the case of shock waves involve multiplications of distributions of the type of powers of the dirac delta function in the one dimensional case of the shock wave equation u t uu x 0 the numerical solutions will converge to the solution of a different equation if the convergence and the latter equation are considered within the nonlinear theory of generalized functions introduced recently by the second author the study of this phenomenon presented here in one of its relevant particular cases offers for the first time a rigorous understanding of important similar situations encountered in industrial applications when numerical solutions may show either agreement with or deviations from the expected solutions

convergence of asynchronous distributed gradient methods over stochastic networks we consider distributed optimization problems in which a number of agents are to seek the global optimum of a sum of cost functions through only local information sharing in this paper we are particularly interested in scenarios where agents are operating asynchronously over stochastic networks subject to random failures most existing algorithms require coordinated and decaying stepsizes to ensure zero gap between the estimated value of each agent and the exact optimum restricting it from asynchronous implementation and resulting in slower convergence results to deal with this issue we develop a new asynchronous distributed gradient method asyndgm based on consensus theory the proposed algorithm not only allows for asynchronous implementation in a completely distributed manner but also most importantly is able to seek the exact optimum even with constant stepsizes we will show that the assumption of boundedness of gradients which is widely used in the literature can be dropped by instead imposing the standard lipschitz continuity condition on gradients moreover we derive an upper bound of stepsize within which the proposed asyndgm can achieve a linear convergence rate for strongly convex functions with lipschitz gradients a canonical example of sensor fusion problems is provided to illustrate the effectiveness of the proposed algorithm

adaptive fuzzy output feedback control of mimo nonlinear systems with unknown dead zone inputs this paper is concerned with the problem of adaptive fuzzy tracking control for a class of multi input and multi output mimo strict feedback nonlinear systems with both unknown nonsymmetric dead zone inputs and immeasurable states in this research fuzzy logic systems are utilized to evaluate the unknown nonlinear functions and a fuzzy adaptive state observer is established to estimate the unmeasured states based on the information of the bounds of the dead zone slopes as well as treating the time varying inputs coefficients as a system uncertainty a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique it is shown that the proposed control approach can assure that all the signals of the resulting closed loop system are semiglobally uniformly ultimately bounded it is also shown that the observer and tracking errors converge to a small neighborhood of the origin by selecting appropriate design parameters simulation examples are also provided to illustrate the effectiveness of the proposed approach

self organized fuzzy system generation from training examples in the synthesis of a fuzzy system two steps are generally employed the identification of a structure and the optimization of the parameters defining it the paper presents a methodology to automatically perform these two steps in conjunction using a three phase approach to construct a fuzzy system from numerical data phase 1 outlines the membership functions and system rules for a specific structure starting from a very simple initial topology phase 2 decides a new and more suitable topology with the information received from the previous step it determines for which variable the number of fuzzy sets used to discretize the domain must be increased and where these new fuzzy sets should be located this in turn decides in a dynamic way in which part of the input space the number of fuzzy rules should be increased phase 3 selects from the different structures obtained to construct a fuzzy system the one providing the best compromise between the accuracy of the approximation and the complexity of the rule set the accuracy and complexity of the fuzzy system derived by the proposed self organized fuzzy rule generation procedure sofrg are studied for the problem of function approximation simulation results are compared with other methodologies such as artificial neural networks neuro fuzzy systems and genetic algorithms

on spiking models for synaptic activity and impulsive differential equations we illustrate the problems that can arise in writing differential equations that include dirac delta functions to model equations with state dependent impulsive forcing specifically difficulties arise in the interpretation of the products of distributions with discontinuous functions we suggest several methods to resolve these ambiguities such as using limiting sequences and asymptotic analysis with applications of the results given for discrete maps these suggestions are applied to a popular model describing synaptic connections in the brain

multiobjective optimization and comparison of nonsingleton type 1 and singleton interval type 2 fuzzy logic systems singleton interval type 2 fuzzy logic systems flss have been widely applied in several real world applications where it was shown that the singleton interval type 2 flss outperform their singleton type 1 counterparts in applications with high uncertainty levels however one of the main criticisms of singleton interval type 2 flss is the fact that they outperform singleton type 1 flss solely based on their use of extra degrees of freedom extra parameters and that type 1 flss with a sufficiently large number of parameters may provide the same performance as interval type 2 flss in addition most works on type 2 flss only compare their results with singleton type 1 flss but fail to consider nonsingleton type 1 systems in this paper we aim to directly address and investigate this criticism in order to do so we will perform a comparative study between optimized singleton type 1 nonsingleton type 1 and singleton interval type 2 flss under the presence of noise we will also present a multiobjective evolutionary algorithm moea for the optimization of singleton type 1 nonsingleton type 1 and singleton interval type 2 fuzzy systems for function approximation problems the moea will aim to satisfy two objectives to maximize the accuracy of the fls and minimize the number of rules in the fls thus improving its interpretability furthermore we will present a methodology to obtain optimal consequents for the flss hence this paper has two main contributions first it provides a common methodology to learn the three types of flss i e singleton type 1 nonsingleton type 1 and singleton interval type 2 flss from data samples the second contribution is the creation of a common framework for the comparison of type 1 and type 2 flss that allows us to address the aforementioned criticism we provide details of a series of experiments and include statistical analysis showing that the type 2 fls is able to handle higher levels of noise than its nonsingleton and singleton type 1 counterparts

a combined backstepping and stochastic small gain approach to robust adaptive fuzzy output feedback control in this paper an adaptive fuzzy output feedback control approach is investigated for a class of stochastic nonlinear strict feedback systems without the requirement of states measurement the stochastic nonlinear system addressed in this paper is assumed to possess unstructured uncertainties unknown nonlinear functions and in the presence of unmodeled dynamics dynamics disturbances fuzzy logic systems are used to approximate the unstructured uncertainties and a fuzzy state observer is designed to estimate the unmeasured states by combining the backstepping design technique with the stochastic small gain approach a new adaptive fuzzy output feedback control approach is developed it is proved that the proposed control approach can guarantee that the closed loop system is input state practically stability isps in probability and the observer errors and the output of the system converge to a small neighborhood of the origin by appropriate choice of the design parameters simulation results are included to indicate that the proposed adaptive fuzzy control approach has a satisfactory control performance in addition the simulation comparisons with the previous methods show that the proposed adaptive fuzzy control approach has robustness to the dynamical uncertainties

systems with distributions and viability theorem abstract the approach to the consideration of the ordinary differential equations with distributions in the classical space d of distributions with continuous test functions has certain insufficiencies the notations are incorrect from the point of view of distribution theory the right hand side has to satisfy the restrictive conditions of equality type in the present paper we consider an initial value problem for the ordinary differential equation with distributions in the space of distributions with dynamic test functions t where the continuous operation of multiplication of distributions by discontinuous functions is defined v derr d kinzebulatov distributions with dynamic test functions and multiplication by discontinuous functions preprint arxiv math ca 0603351 2006 and show that this approach does not have the aforementioned insufficiencies we provide the sufficient conditions for viability of solutions of the ordinary differential equations with distributions a generalization of the nagumo theorem and show that the consideration of the distributional impulse controls in the problem of avoidance of encounters with the set the maximal viability time problem allows us to provide for the existence of solution which may not exist for the ordinary controls

convergence rates of distributed nesterov like gradient methods on random networks we consider distributed optimization in random networks where n nodes cooperatively minimize the sum i 1n fi x of their individual convex costs existing literature proposes distributed gradient like methods that are computationally cheap and resilient to link failures but have slow convergence rates in this paper we propose accelerated distributed gradient methods that 1 are resilient to link failures 2 computationally cheap and 3 improve convergence rates over other gradient methods we model the network by a sequence of independent identically distributed random matrices w k drawn from the set of symmetric stochastic matrices with positive diagonals the network is connected on average and the cost functions are convex differentiable with lipschitz continuous and bounded gradients we design two distributed nesterov like gradient methods that modify the d ng and d nc methods that we proposed for static networks we prove their convergence rates in terms of the expected optimality gap at the cost function let k and k be the number of per node gradient evaluations and per node communications respectively then the modified d ng achieves rates o logk k and o logk k and the modified d nc rates o 1 k2 and o 1 k2 where 0 is arbitrarily small for comparison the standard distributed gradient method cannot do better than 1 k2 3 and 1 k2 3 on the same class of cost functions even for static networks simulation examples illustrate our analytical findings

a five equation reduced model for compressible two phase flow problems this paper studies an eulerian diffuse interface model for the simulation of compressible multifluid and two phase flow problems we first show how to derive this model from a seven equation two pressure two velocity model of baer nunziato type using an asymptotic analysis in the limit of zero relaxation time we then study the mathematical properties of the system the structure of the waves the expression of the riemann s invariants and the existence of a mathematical entropy we also describe two different numerical approximation schemes for this system the first one relies on a linearized riemann solver while the second uses more heavily the mathematical structure of the system and relies on a linearization of the characteristic relations finally we present some numerical experiments and comparisons with the results obtained by the two pressure two velocity model as well as some test cases and comparisons with another five equation model recently proposed for interface computations between compressible fluids

dynamical evolution of volume fractions in multipressure multiphase flow models compared to single pressure models multipressure multiphase flow models require additional closure relations to determine the individual pressures of the different phases these relations are often taken to be evolution equations for the volume fractions we present a rigorous theoretical framework for constructing such equations for compressible multiphase mixtures in terms of submodels for the relative volumetric expansion rates ei of the phases these quantities are essentially the rates at which the phases dynamically expand or contract in response to pressure differences and represent the general tendency of the volume fractions to relax toward values that produce local pressure equilibrium we present a simple provisional model of this type in which ei is proportional to pressure differences divided by the time required for sound waves to traverse an appropriate characteristic length it is shown that the resulting approach to pressure equilibrium is monotonic rather than oscillatory and occurs instantaneously in the incompressible limit

dextra a fast algorithm for optimization over directed graphs this paper develops a fast distributed algorithm termed dextra to solve the optimization problem when n agents reach agreement and collaboratively minimize the sum of their local objective functions over the network where the communication between the agents is described by a directed graph existing algorithms solve the problem restricted to directed graphs with convergence rates of o ln k sqrt k for general convex objective functions and o ln k k when the objective functions are strongly convex where k is the number of iterations we show that with the appropriate step size dextra converges at a linear rate o tau k for 0 given that the objective functions are restricted strongly convex the implementation of dextra requires each agent to know its local out degree simulation examples further illustrate our findings

the elastoplastic shock problem as an example of the resolution of ambiguities in the multiplication of distributions one dimensional collisions between two isotropic solids in which the equations of physics lead to multiplications of distributions are considered based on this example a general physicomathematical method to be adapted to each particular case is proposed to resolve the ambiguity inherent in such products this can be achieved with the aid of a new mathematical theory of generalized functions which permits dealing with mathematical phenomena of a microscopic nature that govern products of distributions having singularities at the same point this tool has recently been applied in various situations in continuum mechanics in which the equations of physics lead to heuristic products of distributions one obtains new algebraic formulas in the simplest cases and new numerical schemes in more general cases the key to the resolution of ambiguities lies in more precise statements of the laws of physics than are permitted within distribution theory and have no analog in classical analysis so that in general a resolution cannot be obtained from formal calculations

hllc type riemann solver with approximated two phase contact for the computation of the baer nunziato two fluid model abstract the computation of compressible two phase flows with the baer nunziato model is addressed only the convective part of the model that exhibits non conservative products is considered and the source terms of the model that represent the exchange between phases are neglected based on the solver proposed by tokareva toro 1 a new hllc type riemann solver is built the key idea of this new solver lies in an approximation of the two phase contact discontinuity of the model thus the riemann invariants of the wave are approximated in the subsonic case a major consequence of this approximation is that the resulting solver can deal with any equation of state it also allows to bypass the resolution of a non linear equation based on those riemann invariants we assess the solver and compare it with others on 1d riemann problems including grid convergence and efficiency studies the ability of the proposed solver to deal with complex equations of state is also investigated finally the different solvers have been compared on challenging 2d test cases due to the presence of both material interfaces and shock waves a shock bubble interaction and underwater explosions when compared with others the present solver appears to be accurate efficient and robust

viscous shock profiles and primitive formulations weak solutions of hyperbolic systems in primitive nonconservative form for which a consistent conservation form exists are considered it is shown that for primitive formulations shock relations are not uniquely defined by the states to either side of the shock but also depend on the viscous path connecting the two consistent viscous shock profiles are enforced by adding scheme dependent small viscous perturbations that account for leading order conservation errors the resulting primitive algorithm is conservative to the order of the approximation one dimensional euler calculations of flows containing weak to moderate shocks show that conservation errors in primitive calculations are substantially reduced by including the viscous perturbation terms while not eliminating conservation errors entirely it is found that for a wide range of problems both conservative and primitive flow calculations are of comparable quality

fractional step methods for thermohydraulic calculation abstract a method of fractional steps is used to extend a semi implicit finite difference technique for multidimensional two phase flow calculations this extension permits time step size to be chosen independent of convection velocities in one space direction and still resolves multidimensional coupled sonic and phase exchange effects implicitly by forming a simple poisson problem for pressure because pure time splitting by physical phenomena was found unsuited to thermal hydraulics problems a stabilizing corrections method was chosen an application in nuclear reactor safety analysis is demonstrated

hyperbolic two pressure models for two phase flow revisited this paper presents correction to a previous paper j comput phys 53 1984 124 on stability analyses of one pressure models for two phase flow it also presents some extensions and generalization of previous work on two pressure models the extensions allow both the slopes to the interfaces and the rates of mass transfer through the interfaces to be non negligible these enlargements of the domain of applicability of the two pressure models introduce extra derivative terms into the models these extra derivative terms do not change the basic character of the model the two pressure models remain stable in the sense of von neumann a e in state space with the more complete modeling of the interface copyright 1988 academic press inc

distributional products and global solutions for nonconservative inviscid burgers equation abstract burgers equation for inviscid fluids is a simplified case of navier stokes equation which corresponds to euler equation for ideal fluids thus from a variational viewpoint burgers equation appears naturally in its nonconservative form in this form a consistent concept of a weak solution cannot be formulated because the classical distribution theory has no products which account for the term u u x this leads several authors to substitute burgers equation by the so called conservative form where one has 1 2 u 2 x in distributional sense in this paper we will treat nonconservative inviscid burgers equation and study it with the help of our theory of products also the relationship with the conservative burgers equation is considered in particular we will be able to exhibit a dirac travelling soliton solution in the sense of global solution applying our concepts solutions which are functions with jump discontinuities can also be obtained and a jump condition is derived when we replace the concept of global solution by the concept of global strong solution this jump condition coincides with the well known rankine hugoniot jump condition for the conservative burgers equation for travelling waves functions these concepts are all equivalent

adaptive fuzzy controller application to the control of the temperature of a dynamic room in real time this paper presents a direct adaptive fuzzy controller for unknown monotonic nonlinear systems thus not requiring the system model but only a little information about it the plant monotonicity and its delay without any off line pre training the algorithm achieves very high control performance through a three stage algorithm 1 output scale factor 2 adaptation of the fuzzy rule consequents and 3 optimization of the position of the membership functions the design is simple in the sense that both the membership functions and the rule base can be initialized from arbitrary values it can be applied to a large class of monotonic dynamic or static plants due the fact that the system is able to modify its behaviour in real time i e during the control process

nonlinear generalized functions and jump conditions for a standard one pressure liquid gas model abstract the mixture of a liquid and a gas is classically represented by one pressure models these models are a system of pdes in nonconservative form and shock wave solutions do not make sense within the theory of distributions they give rise to products of distributions that are not defined within distribution theory but they make sense by applying a theory of nonlinear generalized functions to these equations in contrast to the familiar case of conservative systems the jump conditions cannot be calculated a priori jump conditions for these nonconservative systems can be obtained using the theory of nonlinear generalized functions by inserting some adequate physical information into the equations the physical information that we propose to insert for the one pressure models of a mixture of a liquid and a gas is a natural mathematical expression in the theory of nonlinear generalized functions of the fact that liquids are practically incompressible while gases are very compressible and so they do not satisfy equally well their respective state laws on the shock waves this modelization gives well defined explicit jump conditions the great numerical difficulty for solving numerically nonconservative systems is due to the fact that slightly different numerical schemes can give significantly different results the jump conditions obtained above permit to select the numerical schemes and validate those that give numerical solutions that satisfy these jump conditions which can be an important piece of information in the absence of other explicit discontinuous solutions and of precise observational results we expose with care the mathematical originality of the theory of nonlinear generalized functions an original abstract analysis issued by the leopoldo nachbin team on infinite dimensional holomorphy that permits to state mathematically physical facts that cannot be formulated within distribution theory and are the key for the removal of ambiguities that classically appear when one tries to calculate on multiplications of distributions that occur in the differential equations of physics

generalized solutions of nonlinear parabolic equations with distributions as initial conditions abstract we consider the nonlinear parabolic equation u t u u 3 0 in q 0 t t 0 open set in r d d 1 2 with the boundary condition u x t 0 on 0 t and the initial condition u x 0 x in where is the dirac mass at the origin of r it is known that this problem has no weak solution in any known classical sense within the distribution theory using a theory of generalized functions we obtain existence uniqueness and consistence results which describe mathematically the behaviour of the solutions ue obtained with smooth initial conditions u e x 0 e x e d and e when e 0

a simple model for a symmetrical theory of generalized functions v some applications abstract the theory of generalized functions is shown to eliminate ambiguities in products which are unavoidable in distribution theory the physical examples are the velocity of shock waves and the ito stratonovich dilemma

parallel algorithms for implicit material dynamics schemes procedures are presented for parallelizing implicit schemes for computational material dynamics these procedures are illustrated on an implicit version of the von neumann richtmyer vnr scheme the original vnr scheme a one dimensional scheme for continuum dynamics in the material reference frame has extensions to two and three dimensional and spatial reference frames the vnr codes and codes with similar structure are representative of large classes of codes accounting for large numbers of supercomputer cycles

on the convergence of decentralized gradient descent consider the consensus problem of minimizing f x sum i 1 n f i x where x in mathbb r p and each f i is only known to the individual agent i in a connected network of n agents to solve this problem and obtain the solution all the agents collaborate with their neighbors through information exchange this type of decentralized computation does not need a fusion center offers better network load balance and improves data privacy this paper studies the decentralized gradient descent method a nedic and a ozdaglar ieee trans automat control 54 2009 pp 48 61 in which each agent i updates its local variable x i in mathbb r n by combining the average of its neighbors with a local negative gradient step alpha nabla f i x i the method is described by the iteration x i k 1 gets sum j 1 n w ij x j k alpha nabla f i x i k text for each agent i where w ij is nonzero only if i and j are neighbors or i j and the matrix

the riemann problem for pressureless fluid dynamics with distribution solutions in colombeau s sense the riemann problem for the equations of pressureless fluid dynamics was considered solutions of this problem were constructed by employing the viscosity vanishing approach for some initial data solutions showed high singularity around the shock waves a new mathematical theory of generalized functions initiated by j f colombeau was applied to dealing with the multiplication of singular distributions as a byproduct the entropy condition was obtained for singular distribution solutions

generalized solutions to a cauchy problem for a nonconservative hyperbolic system in this paper we show the existence of generalized solutions in the sense of colombeau to a cauchy problem for a nonconservative system of hyperbolic equations which has applications in elastodynamics

a simple numerical scheme for the 3 d system of ideal gases and a study of approximation in the sense of distributions we present a 3 d numerical scheme for the approximation of the system of gas dynamics we prove that as long as the boundedness of the velocity field in the cfl condition and the positiveness of the total energy are numerically verified when the space step tends to 0 the scheme provides a numerical solution which satisfies the conservation laws in the sense of distributions modulo a small remainder of order one in the space step and a slightly weaker order for the state law in the case of irregular approximate solutions in the case of classical tests sod woodward colella toro one provides numerical verifications that these conditions are verified even for very small values of the space step and correspondingly one observes that the scheme produces the known exact solutions with great precision full proofs are given in the pressureless case the scheme produces the numerical results on the six 2 d riemann problems presented by p d lax p d lax mathematics and physics bull ams 45 1 2008 135 152 up to the smallest detail therefore this result contributes to a mathematical justification of the fact that the numerical results presented by p d lax on these 2 d riemann problems are approximations of a solution this simple order one low cost 3 d scheme is obtained from the convection pressure correction method proposed by le roux et al r baraille g bourdin f dubois a y le roux une version a pas fractionnaire du schema de godunov pour l hydrodynamique comptes rendus acad sci paris 314 1992 147 152

achieving geometric convergence for distributed optimization over time varying graphs this paper considers the problem of distributed optimization over time varying graphs for the case of undirected graphs we introduce a distributed algorithm referred to as diging based on a combination of a distributed inexact gradient method and a gradient tracking technique the diging algorithm uses doubly stochastic mixing matrices and employs fixed step sizes and yet drives all the agents iterates to a global and consensual minimizer when the graphs are directed in which case the implementation of doubly stochastic mixing matrices is unrealistic we construct an algorithm that incorporates the push sum protocol into the diging structure thus obtaining the push diging algorithm push diging uses column stochastic matrices and fixed step sizes but it still converges to a global and consensual minimizer under the strong convexity assumption we prove that the algorithms converge at r linear geometric rates as long as the step sizes do not exceed some upper bounds we establish explicit est

a new methodology for the online adaptation of fuzzy self structuring controllers in this study a novel fuzzy controller which is able to self design from scratch while working online is proposed the controller does not use the information regarding the differential equations that govern the plant s behavior or any of their bounds the algorithm presented is able to determine the most adequate topology for the fuzzy controller based on the data obtained during the system s normal operation therefore the controller can start operating with an empty set of fuzzy rules and needs no offline training the proposed methodology comprises two phases adaptation of the consequents for every selected topology and online addition of new membership functions mfs some of the main advantages of this method are its robustness under changes on the plant s dynamics good performance in noisy situations and the ability to perform variable selection among a group of candidate variables unlike other online methods the modification of the topology is based on the analysis of the whole operating region of the plant thus providing higher robustness several simulation examples are used to show these features

extra an exact first order algorithm for decentralized consensus optimization recently there has been growing interest in solving consensus optimization problems in a multiagent network in this paper we develop a decentralized algorithm for the consensus optimization problem mathrm minimize x in mathbb r p bar f x frac 1 n sum i 1 n f i x which is defined over a connected network of n agents where each function f i is held privately by agent i and encodes the agent s data and objective all the agents shall collaboratively find the minimizer while each agent can only communicate with its neighbors such a computation scheme avoids a data fusion center or long distance communication and offers better load balance to the network this paper proposes a novel decentralized exact first order algorithm abbreviated as extra to solve the consensus optimization problem exact means that it can converge to the exact solution extra uses a fixed large step size which can be determined independently of the network size or topology the local variable of every a

distributed heavy ball a generalization and acceleration of first order methods with gradient tracking we study distributed optimization to minimize a sum of smooth and strongly convex functions recent work on this problem uses gradient tracking to achieve linear convergence to the exact global minimizer however a connection among different approaches has been unclear in this paper we first show that many of the existing first order algorithms are related with a simple state transformation at the heart of which lies a recently introduced algorithm known as mathcal ab we then present distributed heavy ball denoted as mathcal ab m that combines mathcal ab with a momentum term and uses nonidentical local step sizes by simultaneously implementing both row and column stochastic weights mathcal ab m removes the conservatism in the related work due to doubly stochastic weights or eigenvector estimation mathcal ab m thus naturally leads to optimization and average consensus over both undirected and directed graphs we show that mathcal ab m has a global r linear rate when the largest step size and momentum parameter are positive and sufficiently small we numerically show that mathcal ab m achieves acceleration particularly when the objective functions are ill conditioned

direct adaptive self structuring fuzzy controller for nonaffine nonlinear system a direct adaptive state feedback controller for highly nonlinear systems is proposed this paper considers uncertain or ill defined nonaffine nonlinear systems and employ a static fuzzy logic system fls with an on line structuring algorithm the fls approximates and adaptively cancels an unknown plant nonlinearity a control law and adaptive laws for unknown fuzzy parameters and bounding constant are established so that the whole closed loop system is stable in the sense of lyapunov the tracking error is guaranteed to be uniformly asymptotically stable rather than uniformly ultimately bounded with the aid of an additional robustifying control term no a priori knowledge of an upper bound on an lumped uncertainty is required

an approximate linearized riemann solver for a two fluid model an approximate linearized riemann solver is presented for the numerical simulation of two phase flows this new solver is based on a linearization of nonconservative products and uses an extension of roe s approximate riemann solver the scheme is applied to shock tube problem and to a standard test for two fluid codes

numerical solutions of one pressure models in multifluid flows flows of a mixture of several fluids can be described by one pressure models their formulation is formally simple and their efficiency has been recognized but from the mathematical viewpoint they present severe peculiarities they are not hyperbolic appear to be ill posed and are in nonconservative form so they show ambiguous products of distributions in case of shock waves a resolution of these ambiguities is proposed it gives jump conditions similar to the classical rankine hugoniot jump conditions of conservative systems this resolution attempts to solve the riemann problem and then the cauchy problem by godunov type schemes following nonconservative techniques initiated by a y le roux and collaborators

burgers equation with a passive scalar dissipation anomaly and colombeau calculus a connection between dissipation anomaly in fluid dynamics and colombeau s theory of products of distributions is exemplified by considering burgers equation with a passive scalar besides the well known viscosity independent dissipation of energy in the steadily propagating shock wave solution the lesser known case of passive scalar subject to the shock wave is studied an exact dependence of the dissipation rate of the passive scalar on the prandtl number pr is given by a simple analysis we show in particular 1 pr for large pr the passive scalar profile is shown to have a form of a sum of tanh2n 1 x with suitably scaled x thereby implying the necessity to distinguish h from hn when pr is large where h is the heaviside function and n is a positive integer an incorrect result of 1 pr would otherwise be obtained this is a typical example where colombeau calculus for products of weak solutions is required for a correct interpretation a cole hopf type transform is also given for the case o

eigenform error estimates of computational material dynamics with shocks 1 1 hooke s law materials abstract eigenform error estimates are sharper than previous a priori error bounds for the von neumann richtmyer vnr scheme theoretical results give insight into the experimental results on the test problems which include shocks the vnr rk4 scheme a runge kutta modification of the original vnr is not only more accurate than the original vnr but also the eigenform error estimates are more accurate for vnr rk4

on the wave structure of two phase flow models we explore the relationship between two common two phase flow models usually denoted as the two fluid and drift flux models they differ in their mathematical description of momentum transfer between the phases in this paper we provide a framework in which these two model formulations are unified the drift flux model employs a mixture momentum equation and treats interphasic momentum exchange indirectly through the slip relation which gives the relative velocity between the phases as a function of the flow parameters this closure law is in general highly complex which makes it difficult to analyze the model algebraically to facilitate the analysis we express the quasi linear formulation of the drift flux model as a function of three parameters the derivatives of the slip with respect to the vector of unknown variables the wave structure of this model is investigated using a perturbation technique then we rewrite the drift flux model with a general slip relation such that it is expressed in term