exact energy and momentum conserving algorithms for general models in nonlinear elasticity implicit time integration schemes that inherit the conservation laws of total energy linear and angular momentum are considered for initial boundary value problems in finite deformation elastodynamics conserving schemes are constructed for general hyperelastic material models both compressible and incompressible and are formulated in a way that is independent of spatial discretization three numerical examples for ogden type material models implemented using a finite element discretization in space are given to illustrate the performance of the proposed schemes these examples show that relative to the standard implicit mid point rule the conserving schemes exhibit superior numerical stability properties without a compromise in accuracy

adjustable robust solutions of uncertain linear programs we consider linear programs with uncertain parameters lying in some prescribed uncertainty set where part of the variables must be determined before the realization of the uncertain parameters non adjustable variables while the other part are variables that can be chosen after the realization adjustable variables we extend the robust optimization methodology 1 3 6 9 13 14 to this situation by introducing the adjustable robust counterpart arc associated with an lp of the above structure often the arc is significantly less conservative than the usual robust counterpart rc however in most cases the arc is computationally intractable np hard this difficulty is addressed by restricting the adjustable variables to be affine functions of the uncertain data the ensuing affinely adjustable robust counterpart aarc problem is then shown to be in certain important cases equivalent to a tractable optimization problem typically an lp or a semidefinite problem and in other cases having a tight approximation which is tractable the aarc approach is illustrated by applying it to a multi stage inventory management problem

singularly perturbed differential algebraic equations i asymptotic expansion of outer solutions abstract singularly perturbed nonlinear differential algebraic equations dae s are considered which are decomposed into two auxiliary problems called the outer and inner problems respectively the structure of solutions of the singularly perturbed dae s is determined by the outer and inner solutions both of which are proved to exist asymptotic expansions for outer and inner solutions are obtained and proved to be uniformly convergent this generalizes known results about asymptotic expansions of singularly perturbed ordinary differential equations the presentation of this work is separated into two parts because of the limitation of space the first part concerns the derivation of outer and inner problem and the existence and asymptotic expansion of outer solutions while the second part mainly focuses on the inner problem

multi multiplier ambient space formulations of constrained dynamical systems with an application to elastodynamics various formulations of the equations of motion for both finite and infinite dimensional constrained lagrangian dynamical systems are studied the different formulations correspond to different ways of enforcing constraints through multiplier fields all the formulations considered are posed on ambient spaces whose members are unrestricted by the need to satisfy constraint equations but each formulation is shown to possess an invariant set on which the constraint equations and physical balance laws are satisfied the stability properties of the invariant set within its ambient space are shown to be different in each case we use the specific model problem of linearized incompressible elastodynamics to compare properties of three different ambient space formulations we establish the well posedness of one formulation in the particular case of a homogeneous isotropic body subject to specified tractions on its boundary

differential algebraic systems as differential equations on manifolds based on the theory of differential equations on manifolds existence and uniqueness results are proved for a class of mixed systems of differential and algebraic equations as they occur in various applications both the autonomous and nonautonomous case are considered moreover a class of algebraically incomplete systems is introduced for which existence and uniqueness results only hold on certain lower dimensional manifolds this class includes systems for which the application of ode solvers is known to lead to difficulties finally some solution approach based on continuation techniques is outlined

numerical solution of differential algebraic equations for constrained mechanical motion the two most popular formulations of the equations of constrained mechanical motion thedescriptor andstate space forms each have severe practical limitations in this paper we discuss and relate some proposed reformulations of the equations which have improved numerical properties

weyl solutions and j selfadjointness for dirac operators we consider a non selfadjoint dirac type differential expression 0 1 d q y j n dy over dx q x y with a non selfadjoint potential matrix q epsilon l 1 loc scr j bbb c n times n and a signature matrix j n j j n j n epsilon bbb c n times n here scr j denotes either the line bbb r or the half line bbb r with this differential expression one associates in l 2 scr j bbb c n the closed maximal and minimal operators d max q and d min q respectively one of our main results for the whole line case states that d max q d min q in l 2 bbb r bbb c n moreover we show that if the minimal operator d min q in l 2 bbb r bbb c n is j symmetric with respect to an appropriate involution j then it is j selfadjoint similar results are valid in the case of the semiaxis bbb r in particular we show that if n 2p and the minimal operator d min q in l 2 bbb r bbb c 2p is j symmetric then there exists a 2p times p weyl type matrix solution psi z cdot epsilon l 2 bbb r bbb c 2p times p of the equation d max q psi z cdot z psi z cdot a similar result is valid for the expression 0 1 whenever there exists a proper extension tilde a with dim dom tilde a dom d min q p and nonempty resolvent set in particular it holds if a potential matrix q has a bounded imaginary part this leads to the existence of a unique weyl function for the express 0 1 the main results are proven by means of a reduction to the self adjoint case by using the technique of dual pairs of operators the differential expression 0 1 is of significance as it appears in the lax formulation of the vector valued nonlinear schrodinger equation

a generalized forward gradient procedure for rate sensitive constitutive equations many forward gradient schemes have been proposed for the time integration of the stiff constitutive equations of rate sensitive solids it is shown here that one of these methods can be interpreted as a hybrid ordinary differential equation integrator which combines explicit and semi implicit runge kutta methods this observation permits development of higher order schemes illustrated here by one of second order an embedded first order estimate provides a reliable step size control the method is applied to an overstress model and to an internal variable model and is used in a finite element analysis of hydrostatic bulging of sheet metal

review paper efficient numerical methods for the solution of stiff initial value problems and differential algebraic equations in recent years after a prolonged period of intense activity the study of numerical methods for solving stiff initial value problems for ordinary differential equations and differential algebraic equations has reached a certain maturity there now exist some excellent codes which are both efficient and reliable for solving these particular classes of problems in this paper we sketch some of the main theory which underpins stiff integration methods and we use this to describe and put into context some of the best codes currently available by referencing only codes which have been thoroughly tested and are widely available our aim is to direct users of numerical software to those codes which they should try initially if faced with the problem of solving ordinary differential equations of this type an additional feature is that the codes which we propose serve as benchmarks against which any new codes can be evaluated

mechanical systems subject to holonomic constraints differential algebraic formulations and conservative integration abstract the numerical integration in time of the equations of motion for mechanical systems subject to holonomic constraints is considered schemes are introduced for the direct treatment of a differential algebraic form of the equations that preserve the constraints the total energy and other integrals such as linear and angular momentum arising from affine symmetries moreover the schemes can be shown to preserve the property of time reversibility in an appropriate sense an example is given to illustrate various aspects of the proposed methods

j self adjoint extensions of a class of hamiltonian differential systems abstract this paper is concerned with j self adjoint extensions for a class of hamiltonian differential systems the domains of the corresponding minimal and maximal operators are described a classification of limit types of the systems at each of endpoints is given a property of the regularity field of the corresponding minimal operator is derived and an expression of the j defect index of the minimal operator by those of the left and right minimal operators is presented based on them a characterization of all j self adjoint extensions for the hamiltonian system is obtained in terms of square integrable solutions of a certain equation which is generated by this hamiltonian system and its formal adjoint as a consequence characterizations of all j self adjoint extensions are given for the systems in some special cases in particular all j self adjoint extensions are characterized in terms of square integrable solutions of the system itself in certain special cases

norm estimates of complex symmetric operators applied to quantum systems this paper communicates recent results in the theory of complex symmetric operators and shows through two non trivial examples their potential usefulness in the study of schrodinger operators in particular we propose a formula for computing the norm of a compact complex symmetric operator this observation is applied to two concrete problems related to quantum mechanical systems first we give sharp estimates on the exponential decay of the resolvent and the single particle density matrix for schrodinger operators with spectral gaps second we provide new ways of evaluating the resolvent norm for schrodinger operators appearing in the complex scaling theory of resonances

j self adjoint operators with mathcal c symmetries an extension theory approach a well known tool in conventional von neumann quantum mechanics is the self adjoint extension technique for symmetric operators it is used e g for the construction of dirac hermitian hamiltonians with point interaction potentials here we reshape this technique to allow for the construction of pseudo hermitian j self adjoint hamiltonians with complex point interactions we demonstrate that the resulting hamiltonians are bijectively related to the so called hypermaximal neutral subspaces of the defect krein space of the symmetric operator this symmetric operator is allowed to have arbitrary but equal deficiency indices n n general properties of the operators for these hamiltonians are derived a detailed study of operator parametrizations and krein type resolvent formulae is provided for j self adjoint extensions of symmetric operators with deficiency indices 2 2 the technique is exemplified on 1d pseudo hermitian schr dinger and dirac hamiltonians with complex point interaction potentials

one step collocation methods for differential algebraic systems of index 1 abstract in this paper we propose one step collocation methods for linear differential algebraic equation dae systems of index 1 the proposed methods give a continuous approximate solution on the integration interval t0 tn we study the uniform convergence properties of the proposed collocation methods some of the methods show an order reduction phenomenon at the nodes similar to that observed for runge kutta methods petzold 1986 since dae systems may be considered as a kind of very stiff differential systems the collocation methods for dae systems have to verify strong stability properties for example collocation methods at radau points are particularly suitable for solving dae systems however the numerical results will also show that gauss legendre collocation methods may be applied successfully to dae systems also if these are only a stable methods

pareto efficiency in robust optimization this paper formalizes and adapts the well known concept of pareto efficiency in the context of the popular robust optimization ro methodology for linear optimization problems we argue that the classical ro paradigm need not produce solutions that possess the associated property of pareto optimality and we illustrate via examples how this could lead to inefficiencies and suboptimal performance in practice we provide a basic theoretical characterization of pareto robustly optimal pro solutions and extend the ro framework by proposing practical methods that verify pareto optimality and generate solutions that are pro critically important our methodology involves solving optimization problems that are of the same complexity as the underlying robust problems hence the potential improvements from our framework come at essentially limited extra computational cost we perform numerical experiments drawn from three different application areas portfolio optimization inventory management and project management which demonstrate that pro solutions have a significant potential upside compared with solutions obtained using classical ro methods this paper was accepted by gerard p cachon optimization

regular solutions of nonlinear differential algebraic equations and their numerical determination for a general class of nonlinear possibly higher index differential algebraic equations we show existence and uniqueness of solutions these solutions are regular in the sense that newton s method will converge locally and quadratically on the basis of the presented theoretical results numerical methods for the determination of consistent initial values and for the computation of regular solutions are developed several numerical examples are included

punch stretching of sheet metal and differential equations on manifolds the goal of mathematical modelling of sheet metal forming processes is to provide predictive tools for use in the design of stamping processes and the selection of sheet materials most current approaches to finite element modelling of large deformation elastic plastic sheet metal forming problems use a rate form of the virtual work equilibrium equations and a single field finite element representation of the displacement components called the incremental method this approach does not produce approximations which satisfy the discrete equilibrium equations at all times and consequently it demands small time steps to insure stability and numerical accuracy this paper describes a variant of the mixed method in which displacements stresses effective strain and pressures are all given separate finite element representations the equilibrium equations in non rate form are discretized to produce a system of algebraic equations which are coupled with the constitutive equations and then integrated using state of the art numerical software when used to model rate sensitive sheet materials in hydrostatic bulging plane strain punch stretching and hemispherical punch stretching the new approach proved to be between 6 and 26 times as fast as the old incremental method

rosenbrook methods for differential algebraic equations this paper deals with the numerical solution of differential algebraic equations dae of index one it begins with the development of a general theory on the taylor expansion for the exact solutions of these problems which extends the well known theory of butcher for first order ordinary differential equations to dae s of index one as an application we obtain butcher type results for rosenbrock methods applied to dae s of index one we characterize numerical methods as applications of certain sets of trees we derive convergent embedded methods of order 4 3 which require 4 or 5 evaluations of the functions 1 evaluation of the jacobian and 1 lu factorization per step

on the strong limit point and dirichlet properties of second order differential expressions second order differential expressions of the form w 1 pf qf are considered at a singular end point some of the known relationships between properties such as dirichlet weak dirichlet and strong limit point are extended to incorporate an arbitrary positive weight function and complexvalued coefficients

a system level model reduction technique for the efficient simulation of flexible multibody systems flexible multibody systems are governed by sets of non linear differential algebraic equations dae the number of degrees of freedom dofs required for accurate body flexibility modeling as well as the presence of the algebraic constraint equations limit the simulation speed body level model reduction and general purpose system level model reduction techniques do not result in optimal model dimension reduction and do not necessarily transform the dae set into a cheaper to solve set of ordinary differential equations as opposed to model reduction techniques such as global modal parameterization gmp which are based on describing the system motion by the contribution of its dominant configuration dependent system level modal patterns their use as a simulation tool has not been thoroughly investigated this paper investigates the influence of the modal content of the configuration dependent mode set on the simulation accuracy through numerical experiments by including the dynamically excited eigenmodes and static deformation patterns for dofs in which the system is externally loaded the system can be accurately represented by a very limited number of dofs phenomena such as mode veering and mode crossing in which the modal content of eigenmodes rapidly varies can be expected to be problematic for such a description which is confirmed with numerical experiments copyright 2010 john wiley sons ltd

on the boundary conditions characterizing j selfadjoint extensions of j symmetric operators the study of boundary value problems involving linear differentiai equations with real valued coefficients is by now a well established area of analysis on the other hand much less is known about the solvability of such problems when the coefficients or boundary conditions are known to be complex examples of this latter type arise naturally for example in nuclear physics e g the so called optical mode1 for low energy scattering 1 p ijo electromagnetic field theory dielectric waveguides with heat loss c f 19 i or the propagation of radio waves through inhomogeneous media s and elsewhere in cases like these the relevant differential expressions are no longer formally symmetric and hence the powerful methods associated with the spectral theory of selfadjoint operators are not available to facilitate the study of such problems glazman introduced in 4 the concept of a j symmetric operator in a complex hilbert space r let j be a given conjugation operator on 2 i e j is a conjugate linear involution with jx 3 u x for all x and y in 2 a closed densely defined linear operator t in 3 is said to be j symmetric if

one step and extrapolation methods for differential algebraic systems the paper analyzes one step methods for differential algebraic equations dae in terms of convergence order in view of extrapolation methods certain perturbed asymptotic expansions are shown to hold for the special dae extrapolation solver based on the semi implicit euler discretization the perturbed order pattern of the extrapolation tableau is derived in detail the theoretical results lead to modifications of the known code the efficiency of the modifications is illustrated by numerical comparisons over critical examples mainly from chemical combustion

manpak a set of algorithms for computations on implicitly defined manifolds abstract mathematical models often involve differentiable manifolds that are implicitly defined as the solution sets of systems of nonlinear equations the resulting computational tasks differ considerably from those arising for manifolds defined in parametric form here a collection of algorithms is presented for performing a range of essential tasks on general implicitly specified submanifolds of a finite dimensional space this includes algorithms for determining local parametrizations and their derivatives and for evaluating quantities related to the curvature with sensitivity measures the methods have been implemented as a fortran 77 package called manpak

dem a new computational approach to sheet metal forming problems many current approaches to finite element modelling of large deformation elastic plastic forming problems use a rate form of the virtual work equilibrium equations and a finite element representation of the displacement components called the incremental method this approach produces a three field formulation in which displacements stresses and effective strain are dependent variables next the formulation is converted to a one field displacement formulation by an algebraic time discretization which uses a low order explicit time stepping procedure to integrate the equations this approach does not produce approximations which satisfy the discrete equilibrium equations at all times and moreover the advantage of the single field algebraic formulation is realized at the expense of very small time steps needed to produce stability and accuracy in the numerical calculations this paper describes a variant of the mixed method in which all three field variables displacements stresses and effective strain are given finite element representations the discrete equilibrium equations then generate a nonlinear system of algebraic equations whose solutions represent a manifold while the constitutive equations form a system of ordinary differential equations a commercially available variable time step variable order code is then used to integrate this differential algebraic system when applied to the problem of hydrostatic bulging of a membrane the new approach requires far less computer time than the incremental method

canonical projectors for linear differential algebraic equations abstract this paper aims at improving the decoupling projector chain approach for daes to provide complete decouplings these special canonical projectors are shown to form exactly the spectral projection related to the matrix coefficient pair given by the dae further they prove their value when describing the constraint manifolds of the dae

on the discretization error of parametrized nonlinear equations many applications lead to nonlinear parameter dependent equations h y t y 0 where h y times t to y y 0 in operatorname rge h and the state space y is infinite dimensional while the parameter space t has finite dimension the case dim t 1 is of special interest in connection with continuation methods for this case a general theory is developed which provides for the existence of solution paths of a rather general class of such equations and of their finite dimensional approximations and which allows for an assessment of the error between these paths a principal tool in this analysis is the theory of nonlinear fredholm operators the results cover a more general class of operators than the mildly nonlinear mappings to which other approaches appear to be restricted

optimality of affine policies in multistage robust optimization in this paper we prove the optimality of disturbance affine control policies in the context of one dimensional constrained multistage robust optimization our results cover the finite horizon case with minimax worst case objective and convex state costs plus linear control costs we develop a new proof methodology which explores the relationship between the geometrical properties of the feasible set of solutions and the structure of the objective function apart from providing an elegant and conceptually simple proof technique the approach also entails very fast algorithms for the case of piecewise affine state costs which we explore in connection with a classical inventory management application

feedback stabilization of control systems described by a class of nonlinear differential algebraic equations a theoretical framework for the stabilization of con trol systems defined by a class of nonlinear differential alge braic equations is established assumptions are stated which guarantee that the nonlinear differential algebraic equations can be described by a nonlinear control system defined on a smooth manifold a procedure for obtaining a local state realization is developed conditions for local stabilization of a single equilibrium solution including one set of conditions which can easily be checked using standard computations are indicated

on nonlinear singularly perturbed initial value problems the study of singularly perturbed initial value problems for nonlinear systems of ordinary differential equations parallels the analysis underlying the development of numerical algorithms for obtaining solutions to systems of stiff differential equations this paper seeks to emphasize the advantages of combining these two substantial research efforts it develops insight and intuition based on a sequence of solvable model problems and it relates a variety of literature scattered throughout asymptotic and numerical analyses stability and control theory and specific topics in applied mathematical modeling

complex symmetric differential operators on fock space abstract the space of entire functions which are integrable with respect to the gaussian weight known also as the fock space is one of the preferred functional hilbert spaces for modeling and experimenting harmonic analysis quantum mechanics or spectral analysis phenomena this space of entire functions carries a three parameter family of canonical isometric involutions we characterize the linear differential operators acting on fock space which are complex symmetric with respect to these conjugations in parallel as a basis of comparison we discuss the structure of self adjoint linear differential operators the computation of the point spectrum of some of these operators is carried out in detail

desingularization of implicit analytic differential equations the question of finding solutions to a given implicit differential equation ide is an important one in part because it appears very naturally in several problems in physics engineering and many other fields in this work we show how to reduce a given analytic ide to an analytic ide of locally constant rank this can be done by using some fundamental results on subanalytic subsets and desingularization of closed subanalytic subsets an example from nonholonomic mechanics is studied using these methods

on observing nonlinear descriptor systems we study the problem of observing the state of continuous nonlinear descriptor systems in quasilinear form and present a method to construct a state observer our approach is based on rewriting the descriptor system as an equivalent system of explicit differential equations on a restricted manifold finally the restrictions are replaced by measurement equations thus an observer for the descriptor system can be constructed by common state space techniques for explicit systems

automatic integration of euler lagrange equations with constraints abstract numerical difficulties in the integration of euler lagrange and similar equations are discussed a technique for reducing their index from three to two is introduced and it is shown that variable order variable step bdf methods converge for these index two problems the practical application of this reduction in a numerical setting is examined

complex symmetric operators and applications ii a bounded linear operator t on a complex hilbert space h is called complex symmetric if t ct c where c is a conjugation an isometric antilinear involution of h we prove that t cj t where j is an auxiliary conjugation commuting with t t t we consider numerous examples including the poincare neumann singular integral bounded operator and the jordan model operator compressed shift the decomposition t cj t also extends to the class of unbounded c selfadjoint operators originally introduced by glazman in this context it provides a method for estimating the norms of the resolvents of certain unbounded operators

j self adjointness of a class of dirac type operators in this note we prove that the maximally defined operator associated with the dirac type differential expression m q iddxim q q ddxim where q represents a symmetric m m matrix i e q x q x a e with entries in l1loc r is j self adjoint where j is the antilinear conjugation defined by j 1c 1 0imim0 and c a1 am b1 bm a1 am b1 bm the differential expression m q is of significance as it appears in the lax formulation of the non abelian matrix valued focusing nonlinear schrodinger hierarchy of evolution equations

nonstandard singular perturbation systems and higher index differential algebraic systems in order to obtain trajectory approximation results for a given singular perturbation system sps two systems are derived from it the slow and the fast one tikhonov s theorem gives sufficient conditions on them to ensure a good approximation for a standard sps i e its corresponding slow system is a differential algebraic system das of index 1 in this paper it is shown that a nonstandard sps with the parameter set to zero can be seen as a das of higher index this connection allows us to obtain a tikhonov s theorem when this das is of index 2

implicit and explicit representations of continuous time port hamiltonian systems implicit and explicit representations of smooth nite dimensional port hamiltonian systems are studied from the perspective of their use in numerical simulation and control design implicit representations arise when a system is modeled in cartesian coordinates and when the system constraints are applied in the form of additional algebraic equations explicit representations are derived when generalized coordinates are used a relationship between the phase spaces for both system representations is derived in this article justifying the equivalence of the representations in the sense of preserving their hamiltonian functions as well as their hamiltonian symplectic forms ultimately resulting in the same hamiltonian ow

associating matrix pencils to generalized linear multivariable systems we consider quadruples of matrices e a b c representing generalized linear multivariable systems ex t ax t bu t y t cx t with e a square matrices and b c rectangular matrices we characterize equivalent quadruples by associating matrix pencils to them with respect to the equivalence relation corresponding to standard transformations basis changes for the state control and output spaces state feedback derivative feedback and output injection equivalent quadruples are those whose associated matrix pencils are simultaneously equivalent

the application of rosenbrock wanner type methods with stepsize control in differential algebraic equations two rosenbrock wanner type methods for the numerical treatment of differential algebraic equations are presented both methods possess a stepsize control and an index 1 monitor the first method dae34 is of order 3 4 and uses a full semi implicit rosenbrock wanner scheme the second method rkf4da is derived from the runge kutta fehlberg 4 5 pair where a semi implicit rosenbrock wanner method is embedded in order to solve the nonlinear equations the performance of both methods is discussed in artificial test problems and in technical applications

ode methods for the solution of differential algebraic systems in this paper we study the numerical solution of the differential algebraic systems f t y y 0 many of these systems can be solved conveniently and economically using a range of ode methods others can be solved only by a small subset of ode methods and still others present insurmountable difficulty for all current ode methods we examine the first two groups of problems and indicate which methods we believe to be best for them then we explore the properties of the third group which cause the methods to fail we describe a reduction technique which allows systems to be reduced to ones that can be solved it also provides a tool for the analytical study of the structure of systems

rosenbrock type methods adapted to differential algebraic systems we consider the numerical solution of differential algebraic systems of index one given in kronecker canonical form the methods described here are derived from the rosenbrock approach hence they do not require the solution of nonlinear systems of equations but one evaluation of the jacobian and one lu decomposition per step by construction the s stage method coincides with a solver for nonlinear equations of order s 1 if the stepsize is set to zero in this sense the adaptation to differential algebraic equations is performed the special structure of the method leads to simplified order conditions and to an easy implementation some particular methods up to order 4 are given especially an embedded 4 stage method of order 4 3 is derived

convergence results for a coordinate projection method applied to mechanical systems with algebraic constraints the equations of motion of mechanical multibody systems with algebraic constraints are of index 3 and therefore not directly solvable by standard ode or dae methods reducing the index by different

approximation methods for the consistent initialization of differential algebraic equations the algebraic constraints in a system of differential algebraic equations daes impose a consistency requirement on the initial values that can be difficult to satisfy in this thesis the consistency requirement is characterized by a system of equations an approximation method is introduced for these equations and the numerical solution of the resulting system is analyzed for certain important classes of daes finally some numerical experiments are described

completions of nonlinear dae flows based on index reduction techniques and their stabilization differential algebraic equations daes define a differential equation on a manifold a number of ways have been developed to numerically solve some classes of daes motivated by problems in control theory numerical simulation and the use of general purpose modeling environments recent research has considered the embedding of the dae solutions of a general dae into the solutions of an ode where the added dynamics have special properties this paper both provides new results on the linear time varying case and considers the important nonlinear case

least squares completions for nonlinear differential algebraic equations a method has been proposed for numerically solving lower dimensional nonlinear higher index differential algebraic equations for which more classical methods such as backward differentiation or implicit runge kutta may not be appropriate this method is based on solving nonlinear dae derivative arrays using nonlinear singular least squares methods the theoretical foundations generality and limitations of this approach remain to be determined this paper carefully examines several key aspects of this approach the emphasis is on general results rather than specific results based on the structure of various applications

dependence of solutions of nonsmooth differential algebraic equations on parameters abstract the well posedness of nonsmooth differential algebraic equations daes is investigated more specifically semi explicit daes with caratheodory style assumptions on the differential right hand side functions and local lipschitz continuity assumptions on the algebraic equations the daes are classified as having differential index one in a generalized sense solution regularity is formulated in terms of projections of generalized clarke jacobians existence of solutions is derived under consistency and regularity of the initial data uniqueness of a solution is guaranteed under analogous caratheodory ordinary differential equation uniqueness assumptions the continuation of solutions is established and sufficient conditions for continuous and lipschitzian parametric dependence of solutions are also provided to accomplish these results a theoretical tool for analyzing nonsmooth daes is provided in the form of an extended nonsmooth implicit function theorem the findings here are a natural extension of classical results and lay the foundation for further theoretical and computational analyses of nonsmooth daes

linearly implicit extrapolation methods for differential algebraic systems we consider the numerical solution of implicit differential equations in which the solution derivative appears multiplied by a solution dependent singular matrix we study extrapolation methods based on two linearly implicit euler discretizations their error behaviour is explained by perturbed asymptotic expansions

global observability analysis of sensorless induction motors the current problems to successfully apply sensorless controllers for induction motors are the existence of operation regimes for which the performance is remarkably deteriorated due to the difficulties in estimating correctly motor speed and flux and the lack of a theoretical explanation for this kind of behavior in this paper a global observability analysis for these machines is carried out it is first shown that all indistinguishable trajectories of the system i e pairs of state trajectories with the same input output behavior can be described by a differential equation on a manifold named here the indistinguishable dynamics studying the stability properties of this latter system it can be shown that the induction motor is not completely observable nor detectable in a local or in a global sense and for every set of parameters this implies that it is impossible to construct a state observer for the motor that converges for every trajectory of the system moreover the indistinguishable dynamics provides a systematic method to study understand and explain particular operation regimes and this is illustrated by some case studies of practical relevant operating conditions

a new look at pencils of matrix valued functions abstract matrix pencils depending on a parameter and their canonical forms under equivalence are discussed the study of matrix pencils or generalized eigenvalue problems is often motivated by applications from linear differential algebraic equations daes based on the weierstrass kronecker canonical form of the underlying matrix pencil one gets existence and uniqueness results for linear constant coefficients daes in order to study the solution behavior of linear daes with variable coefficients one has to look at new types of equivalence transformations this then leads to new canonical forms and new invariances for pencils of matrix valued functions we give a survey of recent results for square pencils and extend these results to nonsquare pencils furthermore we partially extend the results for canonical forms of hermitian pencils and give new canonicalforms there too based on these results we obtain new existence and uniqueness theorems for differential algebraic systems which generalize the classical results of weierstrass and kronecker

the impact of the existence of multiple adjustable robust solutions in this note we show that multiple solutions exist for the production inventory example in the seminal paper on adjustable robust optimization in ben tal et al math program 99 2 351 376 2004 all these optimal robust solutions have the same worst case objective value but the mean objective values differ up to 21 9 and for individual realizations this difference can be up to 59 4 we show via additional experiments that these differences in performance become negligible when using a folding horizon approach the aim of this paper is to convince users of adjustable robust optimization to check for existence of multiple solutions using the production inventory example and an illustrative toy example we deduce three important implications of the existence of multiple optimal robust solutions first if one neglects this existence of multiple solutions then one can wrongly conclude that the adjustable robust solution does not outperform the nonadjustable robust solution second even when it is a priori known that the adjustable and nonadjustable robust solutions are equivalent on worst case objective value they might still differ on the mean objective value third even if it is known that affine decision rules yield near optimal performance in the adjustable robust optimization setting then still nonlinear decision rules can yield much better mean objective values

elastic viscoplastic differential equations on a manifold modelling of in plane stretching of sheet metal the computational method for large deformation plasticity called differential equations on a manifold dem has previously been shown to be effective for axisymmetric and plane strain sheet metal forming problems the method has now been formulated for in plane stretching problems incorporated into a computer code and applied to several problems the code s performance is robust and accurate as evidenced by a comparison with other published results incorporation of an automatic mesh generator significantly reduces data preparation time

classification of sturm liouville differential equations with complex coefficients and operator realizations in this paper a new classification of sturm liouville differential equations with complex coefficients is given compared with the corresponding result of brown et al this classification reveals the great effects of rotation angle and it is independent of the rotation angles moreover the asymptotic behaviours of functions in the maximal domain are presented and j self adjoint extensions associated with the differential equations are characterized

backward differentiation approximations of nonlinear differential algebraic systems finite difference approximations of dynamical systems modeled by nonlinear semiexplicit differential algebraic equations are analyzed convergence for the backward differentiation method is proved for index two and index three problems when the numerical initial values obey certain constraints the appropriate asymptotic convergence rates and the leading error terms are determined

stability analysis of the equilibrium of a constrained mechanical system this paper studies the local stability properties of the motion of mechanical systems with holonomic constraints a set of linear differential algebraic equations is used to characterize local constrained motion and to determine local stability properties of an equilibrium of the nonlinear differential algebraic equations stability conditions are developed for linear differential algebraic equations examples are shown to demonstrate that the constraint functions play an important role in stability properties of an equilibrium conditions are given that guarantee that constraints will not affect local stability properties

a note on bifurcation points for index 1 differential algebraic problems the arclength continuation method is proposed for index 1 daes with singular points in particular the cusp points the tangency points and equilibrium points are investigated the numerical iterative matrix is studied at a singular point the numerical examples are given to illustrate the robustness of the continuation method

an efficient approach for the numerical simulation of multibody systems the field of kinematics and dynamics of mechanical systems has progressed from a manual graphics art to a highly developed discipline in analytical geometry and dynamics various general purpose formulations for the dynamic analysis of constrained mechanical systems cms lead to mixed differential algebraic equations daes called the euler lagrange equations during the past fifteen years many contributions have been made to the theory of computational kinematics and dynamics of cms also called mutibody dynamics the recent advances in computer hardware and software have tremendously revolutionized the analysis of cms there are various numerical approaches for solving general vector fields in the previous paper appl math comput 92 1998 153 193 a complete and detailed analysis of various approaches for the numerical solution of vector fields is given in this paper we extend the algorithms presented in the above mentioned reference to solve the euler lagrange equations of motion for cms the numerical experiments suggest that perturbation approach performs better than the other approaches

symmetries and infinitesimal symmetries of singular differential equations the aim of this paper is to study symmetries of linearly singular differential equations namely equations that cannot be written in normal form because the derivatives are multiplied by a singular linear operator the concept of geometric symmetry of a linearly singular differential equation is introduced as a transformation that preserves the geometric data that define the problem it is proved that such symmetries are essentially equivalent to dynamic symmetries that is transformations mapping solutions into solutions similar results are given for infinitesimal symmetries to study the invariance of several objects under the flows of vector fields a careful study of infinitesimal variations is performed with a special emphasis on infinitesimal vector bundle automorphisms

implementation of linear multistep methods for solving constrained equations of motion a class of multistep methods for numerical integration of the equations of motion of constrained mechanical systems is considered they are based on different local parametrizations of the differentiable manifold defined by the kinematic constraints during integration the kinematic constraints are preserved at all levels position velocity and acceleration the numerical implementations described in the paper require only one symmetric matrix factorization at each integration step

on j selfadjoint extensions of j symmetric ordinary differential operators on donne une caracterisation des conditions aux limites qui determinent le domaine d une extension j autoadjointe d un operateur differentiel j symetrique t 0 qui a une extremite singuliere

forcing function diagnostics for nonlinear dynamics this article investigates the problem of model diagnostics for systems described by nonlinear ordinary differential equations odes i propose modeling lack of fit as a time varying correction to the right hand side of a proposed differential equation this correction can be described as being a set of additive forcing functions estimated from data representing lack of fit in this manner allows us to graphically investigate model inadequacies and to suggest model improvements i derive lack of fit tests based on estimated forcing functions model building in partially observed systems of odes is particularly difficult and i consider the problem of identification of forcing functions in these systems the methods are illustrated with examples from computational neuroscience

tracking in nonlinear differential algebraic control systems with applications to constrained robot systems we consider the design of a feedback control law for control systems described by a class of nonlinear differential algebraic equations so that certain desired outputs track given reference inputs the nonlinear differential algebraic control system being considered is not in state variable form assumptions are introduced and a procedure is developed such that an equivalent state realization of the control system described by nonlinear differential algebraic equations is expressed in a familiar normal form a nonlinear feedback control law is then proposed which ensures under appropriate assumptions that the tracking error in the closed loop differential algebraic system approaches zero exponentially applications to simultaneous contact force and position tracking in constrained robot systems with rigid joints constrained robot systems with joint flexibility and constrained robot systems with significant actuator dynamics are discussed

primal and dual linear decision rules in stochastic and robust optimization linear stochastic programming provides a flexible toolbox for analyzing real life decision situations but it can become computationally cumbersome when recourse decisions are involved the latter are usually modeled as decision rules i e functions of the uncertain problem data it has recently been argued that stochastic programs can quite generally be made tractable by restricting the space of decision rules to those that exhibit a linear data dependence in this paper we propose an efficient method to estimate the approximation error introduced by this rather drastic means of complexity reduction we apply the linear decision rule restriction not only to the primal but also to a dual version of the stochastic program by employing techniques that are commonly used in modern robust optimization we show that both arising approximate problems are equivalent to tractable linear or semidefinite programs of moderate sizes the gap between their optimal values estimates the loss of optimality incurred by the linear decision rule approximation our method remains applicable if the stochastic program has random recourse and multiple decision stages it also extends to cases involving ambiguous probability distributions

brief paper an observer for non linear differential algebraic systems in this paper we consider design of observers for non linear models containing both dynamic and algebraic equations so called differential algebraic equations dae of index 1 the observer is formulated as a dae that by construction has index 1 the main results of the paper include conditions that ensure local stability of the observer error dynamics design methodology is presented and illustrated using a small simulation study

implicit differential equations near a singular point abstract this paper presents general and precise results on existence and number of solutions to implicitly defined ordinary differential equations in the vicinity of a singular point where the equation is not equivalent to an explicit one unlike in most if not in all other studies devoted to this problem in the literature it is not assumed that either rank drop occurs on an entire neighborhood of the singular point or that the equation is a scalar one attention is confined to the simplest but most frequently encountered kind of singular points it is shown that such standard singular points split into two complementary classes those from which exactly two distinct solutions emanate and those at which exactly two distinct solutions terminate whether a point of the latter class is eventually encountered is unaffected by slight modifications of the nonsingular initial condition and further evolution of the system governed by the singular ode then requires using a suitable jump condition according to appropriate physical criteria points of the former class are also shown to play a more subtle but equally important role in the dynamics the phenomena described here are relevant in various problems from the sciences such as phase transitions or plasticity they should also be relevant in some aspects of the classical domain of application of differential algebraic equations singular perturbations of ode s