adsorption of pulled directed paths in a slanted boundary in this paper the generating function free energy and phase diagram of a class of models of directed paths related to the models of paths adsorbing in the boundary y nx n 2 for and pulled by a vertical force in its endpoint are determined these models are related to the special classes of models of random walks in the quarter plane and which interact with the x axis generating functions are determined by solving a functional recurrence using the kernel method and are algebraic the generating function is determined for general values of n and the solutions for n 1 and n 2 are examined explicitly together with the derivation of the phase diagram and locations of critical curves three phases including a free or bulk phase an adsorbed phase and a ballistic or stretched phase are identified and the nature of the transitions between these phases are examined order parameters are defined and asymptotic expressions are determined for the critical adsorption surface as a function of the pulling force some of these results are also briefly generalized to arbitrary values of n

event structures and trace monoids event structures are a poset based model for describing the behaviour of distributed systems they give rise to a well understood class of scott domains event structures are also related to petri nets in a fundamental way trace monoids are a string based formalism for describing the behaviour of distributed systems they have an independent theory rooted in the theory of formal languages here we obtain a representation of trace monoids in terms of a subclass of labelled event structures

a homographic best approximation problem with application to optimized schwarz waveform relaxation we present and study a homographic best approximation problem which arises in the analysis of waveform relaxation algorithms with optimized transmission conditions its solution characterizes in each class of transmission conditions the one with the best performance of the associated waveform relaxation algorithm we present the particular class of first order transmission conditions in detail and show that the new waveform relaxation algorithms are well posed and converge much faster than the classical one the number of iterations to reach a certain accuracy can be orders of magnitudes smaller we illustrate our analysis with numerical experiments

error estimation and adaptation for functional outputs in time dependent flow problems the paper presents an adjoint based approach for determining global error in the time domain that is relevant to functional outputs from unsteady flow simulations the algorithm is derived for the unsteady euler equations that are discretized for second order accuracy in both space and time and takes into account the effect of dynamic meshes in addition to error due to temporal resolution the formulation also takes into account algebraic error arising from partial convergence of the governing equations at each implicit time step the resulting error distributions are then used to drive adaptation of the temporal resolution and the convergence tolerances for the governing equations at each time step the method is demonstrated in the context of both time integrated and instantaneous functionals and the results are compared against traditional adaptation methods

a new cement to glue nonconforming grids with robin interface conditions the finite element case robin interface conditions in domain decomposition methods enable the use of non overlapping subdomains and a speed up in the convergence non conforming grids make the grid generation much easier and faster since it is then a parallel task the goal of this paper is to propose and analyze a new discretization scheme which allows to combine the use of robin interface conditions with non matching grids we consider both a symmetric definite positive operator and the convection diffusion equation discretized by finite volume schemes numerical results are shown

a linear domain decomposition method for partially saturated flow in porous media abstract the richards equation is a nonlinear parabolic equation that is commonly used for modelling saturated unsaturated flow in porous media we assume that the medium occupies a bounded lipschitz domain partitioned into two disjoint subdomains separated by a fixed interface this leads to two problems defined on the subdomains which are coupled through conditions expressing flux and pressure continuity at after an euler implicit discretisation of the resulting nonlinear subproblems a linear iterative l type domain decomposition scheme is proposed the convergence of the scheme is proved rigorously in the last part we present numerical results that are in line with the theoretical finding in particular the convergence of the scheme under mild restrictions on the time step size we further compare the scheme to other approaches not making use of a domain decomposition namely we compare to a newton and a picard scheme we show that the proposed scheme is more stable than the newton scheme while remaining comparable in computational time even if no parallelisation is being adopted after presenting a parametric study that can be used to optimise the proposed scheme we briefly discuss the effect of parallelisation and give an example of a four domain implementation

well behaved flow event structures for parallel composition and action refinement flow event structures were introduced as a model for giving semantics to process algebras however it turned out that certain restrictions have to be made to make them suitable for this purpose in this paper we investigate subclasses of flow event structures which are both suited for the process algebraic composition operators and for action refinement as a means of regarding processes on different levels of abstraction first suitable subclasses are characterised then two specific subclasses are proposed the larger class generalises the one from castellani and zhang theoret comput sci 179 1997 203 215 which is not suitable for action refinement the smaller one is still sufficiently expressive for dealing with all standard process algebras and action refinement

domain decomposition methods for large linearly elliptic three dimensional problems abstract the idea of solving large problems using domain decomposition technique appears particularly attractive on present day large scale parallel computers but the performance of such techniques used on a parallel computer depends on both the numerical efficiency of the proposed algorithm and the efficiency of its parallel implementation the approach proposed herein splits the computational domain in unstructured subdomains of arbitrary shape and solves for unknown on the interface using the associated trace operator the steklov poincare operator on the continuous level or the schur complement matrix after a finite element discretization and a preconditioned conjugate gradient method this algorithm involves the solution of dirichlet and of neumann problems defined on each subdomain and which can be solved in parallel this method has been implemented on a cray 2 computer using multitasking and on an intel hypercube it was tested on a large scale industrial ill conditioned three dimensional linear elasticity problem which gives a fair indication of its performance in a real life environment in such situations the proposed method appears operational and competitive on both machines compared to standard techniques it yields faster results with far less memory requirements

transfer matrix study of the adsorption of a flexible self avoiding polymer chain in two dimensions the authors model the polymer as a self avoiding walk on a semi infinite square lattice with an energy contribution in from each step along the lattice boundary the critical adsorption temperature ta and the ordinary and special surface exponents of the walk above and at the adsorption temperature respectively are estimated with transfer matrix finite size scaling methods for the adsorption temperature they obtain exp in kta 2 041 or 0 002 and for the crossover and susceptibility exponents of the special transition phi sp 0 501 or 0 003 and gamma 1sp 1 454 or 0 004

a partial ordering semantics for ccs a new operational semantics for pure ccs is proposed that considers the parallel operator as a first class one and permits a description of the calculus in terms of partial orderings the new semantics also for unguarded agents is given in the sos style via the partial ordering derivation relation ccs agents are decomposed into sets of sequential subagents the new derivations relate sets of subagents and describe their actions and the casual dependencies among them the computations obtained by composing partial ordering derivations are observed either as interleaving or partial orderings of events interleavings coincide with milner s many step derivations and linearizations of partial orderings are all and only interleavings abstract semantics are obtained by introducing two relations of observational equivalence and congruence that preserve concurrency these relations are finer than milner s in that they distinguish interleaving of sequential nondeterministic agents from their concurrent execution

determinism event structure isomorphism step sequence equivalence abstract a concurrent system s is called determinism if for all states s of s we have that whenever s can evolve from state s into states s and s by doing an action a it must be the case that s equals s it is well known that for deterministic concurrent systems most of the interleaved equivalences bisimulation failure trace equivalence coincide in this paper we prove in the setting of event structures that also most of the non interleaved equivalences coincide with each other on this domain in the last section of the paper we show that as a consequence of our result the causal structure of a deterministic concurrent system can be unravelled by observers who are capable of observing the beginning and termination of events

index concepts for linear mixed systems of differential algebraic and hyperbolic type equations for many technical systems the use of a refined network modeling approach leads to hyperbolic type initial boundary value problems of partial differential algebraic equations pdaes the boundary conditions of these systems are governed by time dependent differential algebraic equations daes that couple the pdae system with the network elements that are modeled by daes in time only in order to classify these systems we extend some index notions that have already been introduced to treat parabolic type problems a perturbation index is considered that reflects the sensitivity of the mixed system to slight perturbations in the right hand side of the pdaes as well as in the input signals of the dae systems and initial values in order to make an a posteriori analysis of semidiscretization in space and time we introduce additionally a space and a method of lines mol index here one is especially interested in whether the semidiscretized systems properly reflect the properties of the underlying systems we will show that these indices may detect an artificial sensitivity with respect to perturbations e g if the semidiscretization does not consider the information transport along the characteristics

balancing domain decomposition for mixed finite elements the rate of convergence of the balancing domain decomposition method applied to the mixed finite element discretization of second order elliptic equations is analyzed the balancing domain decomposition method introduced by mandel in 24 is a substructuring method that involves at each iteration the solution of a local problem with dirichlet data a local problem with neumann data and a coarse grid problem to propagate information globally and to insure the consistency of the neumann problems it is shown that the condition number grows at worst like the logarithm squared of the ratio of the subdomain size to the element size in both two and three dimensions and for elements of arbitrary order the bounds are uniform with respect to coefficient jumps of arbitrary size between subdomains the key component of our analysis is the demonstration of an equivalence between the norm induced by the bilinear form on the interface and the h 1 2 norm of an interplant of the boundary data computational results from a message passing parallel implementation on an intel delta machine demonstrate the scalability properties of the method and show almost optimal linear observed speed up for up to 64 processors

analysis of finite element approximation of evolution problems in mixed form this paper deals with the finite element approximation of evolution problems in mixed form following d boffi f brezzi and l gastaldi math comp 69 2000 pp 121 140 we handle separately two types of problems a model for the first case is the heat equation in mixed form while the time dependent stokes problem fits within the second one for either case we give sufficient conditions for a good approximation in the natural functional spaces the results are not obvious in the first situation in this case the well known conditions for the well posedness and convergence of the corresponding steady problem are not sufficient for the good approximation of the time dependent problem this issue is demonstrated with a numerical counter example and justified analytically

chain polymers near an adsorbing surface we present improved estimates of critical exponents for 3d polymers near a plane adsorbing surface the improvements were possible by simulating rather long chains up to n 2000 by means of a new algorithm apart from minor but significant adjustments in the location of the tricritical point and in the various gamma exponents our main result is that the crossover exponent for critical adsorption is compatible with phi 1 2 this is much lower than previous estimates and suggests that this exponent might be superuniversal

adjoint sensitivity analysis for differential algebraic equations the adjoint dae system and its numerical solution an adjoint sensitivity method is presented for parameter dependent differential algebraic equation systems daes the adjoint system is derived along with conditions for its consistent initialization for daes of index up to two hessenberg for stable linear daes stability of the adjoint system for semi explicit daes or of an augmented adjoint system for fully implicit daes is shown in addition it is shown for these systems that numerical stability is maintained for the adjoint system or for the augmented adjoint system

adaptive algorithms for optimal control of time dependent partial differential algebraic equation systems summary this paper describes an adaptive algorithm for optimal control of time dependent partial dierential algebraic equation pdae systems a direct method based on a modied multiple shooting type technique and sequential quadratic programming sqp is used for solving the optimal control problem while an adaptive mesh renement amr algorithm is employed to dynamically adapt the spatial integration mesh issues of coupling the amr solver to the optimization algorithm are addressed for time dependent pdaes which can benet from the use of an adaptive mesh the resulting method is shown to be highly ecient copyright 2003 john wiley sons ltd

a space time domain decomposition approach using enhanced velocity mixed finite element method abstract a space time domain decomposition approach is presented as a natural extension of the enhanced velocity mixed finite element evmfe introduced by wheeler et al in 2002 26 for spatial domain decomposition the proposed approach allows for different space time discretizations on non overlapping subdomains by enforcing a mass continuity at non matching interfaces to preserve local mass conservation inherent to the mixed finite element methods to this effect we consider three different model formulations 1 a linear single phase flow problem 2 a non linear slightly compressible flow and tracer transport and 3 a non linear slightly compressible multiphase flow and transport we also present a numerical solution algorithm for the proposed domain decomposition approach where a monolithic fully coupled in space and time system is constructed that does not require subdomain iterations this space time evmfe method accurately resolves advection diffusion transport features in a heterogeneous medium while circumventing non linear solver convergence issues associated with large time step sizes for non linear problems numerical results are presented for the aforementioned three model formulations to demonstrate the applicability of this approach to a general class of flow and transport problems in porous media

a differentiation index for partial differential algebraic equations a differentiation index for nonlinear partial differential algebraic equations is presented determination of the differentiation index with respect to a direction in the space of independent variables uncovers all equations that must be satisfied by cauchy data on the hyperplane orthogonal to that direction this index is thus a generalization of the differentiation index of differential algebraic equations the motivation for this work is consistent initialization of partial differential algebraic systems the analysis is demonstrated through several examples including some taken from fluid dynamics and chemical engineering

automatic differentiation of numerical integration algorithms automatic differentiation ad is a technique for automatically augmenting computer programs with statements for the computation of derivatives this article discusses the application of automatic differentiation to numerical integration algorithms for ordinary differential equations odes in particular the ramifications of the fact that ad is applied not only to the solution of such an algorithm but to the solution procedure itself this subtle issue can lead to surprising results when ad tools are applied to variable stepsize variable order ode integrators the computation of the final time step plays a special role in determining the computed derivatives we investigate these issues using various integrators and suggest constructive approaches for obtaining the desired derivatives

a posteriori error analysis for higher order dissipative methods for evolution problems we prove a posteriori error estimates for time discretizations by the discontinuous galerkin method dg q and the corresponding implicit runge kutta radau method irk r q of arbitrary order q 0 for both linear and nonlinear evolution problems of the form u prime mathfrak f u f with 2 angle bounded operator mathfrak f the key ingredient is a novel higher order reconstruction widehat u of the discrete solution u which restores continuity and leads to the differential equation widehat u prime pi mathfrak f u f for a suitable interpolation operator and piecewise polynomial approximation f of f we discuss applications to linear pde such as the convection diffusion equation 1 2 and the wave equation formally and nonlinear pde corresponding to subgradient operators 1 such as the p laplacian as well as lipschitz operators 1 2 we also derive conditional a posteriori error estimates for the time dependent minimal surface problem

analysis of descriptor systems using numerical algorithms in this paper we analyze numerical methods for the solution of the large scale dynamical system e dot y t ay t g t y t 0 y 0 where e and a are matrices possibly singular systems of this type have been referred to as implicit systems and more recently as descriptor systems since they arise from formulating system equations in physical variables special cases of such systems are algebraic differential systems we discuss the numerical advantages of this formulation and identify a class of numerical integration algorithms which have accuracy and stability properties appropriate to descriptor systems and which preserve structure detect nonsolvable systems resolve initial value consistency problems and are applicable to stiff descriptor systems we also present an algorithm for the control of the local truncation error on only the state variables

adsorption of self avoiding walks at an impenetrable plane in the expanded phase a monte carlo study we consider self avoiding walks on the simple cubic lattice confined to the half space z0 in addition the walks interact with the plane z 0 and have a vertex vertex interaction the walks can adsorb at the plane z 0 the location of the adsorption phase transition depends in general on the contact interaction we use monte carlo methods to investigate the form of the adsorption phase boundary in the expanded phase region

trees grids and mso decidability from graphs to matroids monadic second order mso logic has proved to be a useful tool in many areas of application reaching flom decidability and complexity to picture processing correctness of programs and parallel processes to characterize the structural borderline between decidability and undecidability is a classical research problem here this problem is related to questions in computational complexity especially to the model checking problem for which many tools developed in the area of decidability have proved to be useful for more than two decades it was conjectured in d seese the structure of the models of decidable monadic theories of graphs ann pure appl logic 53 1991 169 195 that decidability of monadic theories of countable structures implies that the theory can be reduced via interpretability to a theory of trees it is one of the main goals of this article to prove a variant of this conjecture for matroids representable over a finite field matroids can be viewed as a wide generalization of graphs and they seem to capture some second order properties in a more suitable way than graphs themselves cf the recent development in matroid structure theory j f geelen a h m gerards g p whittle branch width and well quasi ordering in matroids and graphs j combin theory ser b 84 2002 270 290 j f geelen a h m gerards n robertson g p whittle excluding a planar graph from a gf q representable matroid manuscript 2003 more exactly we prove for every finite field f that any class of f representable matroids with a decidable mso theory must have uniformly bounded branch width moreover we show that bounding the branch width of all matroids in general is not sufficient to obtain a decidable mso theory our paper gives a rather detailed introduction to these different subjects and shows that a blend of ideas and methods from logic together with structural matroid theory can lead to new tools and algorithms and can shed light on some old open problems

multiple markov chain monte carlo study of adsorbing self avoiding walks in two and in three dimensions a self avoiding walk adsorbing on a line in the square lattice and on a plane in the cubic lattice is studied numerically as a model of an adsorbing polymer in dilute solution the walk is simulated by a multiple markov chain monte carlo implementation of the pivot algorithm for self avoiding walks vertices in the walk that are visits in the adsorbing line or plane are weighted by e t he critical value of where the walk adsorbs on the adsorbing line or adsorbing plane is determined by considering energy ratios and approximations to the free energy we determine that the critical values of are c 0 565 0 010 in the square lattice 0 288 0 020 in the cubic lattice in addition the value of the crossover exponent is determined 0 501 0 015 in the square lattice 0 5005 0 0036 in the cubic lattice metric quantities including the mean square radius of gyration are also considered as well as rescaling of the specific heat and free energy as the critical point is approached

optimized schwarz waveform relaxation and discontinuous galerkin time stepping for heterogeneous problems we design and analyze a schwarz waveform relaxation algorithm for domain decomposition of advection diffusion reaction problems with strong heterogeneities the interfaces are curved and we use optimized ventcell transmission conditions we analyze the semidiscretization in time with discontinuous galerkin as well we also show two dimensional numerical results using generalized mortar finite elements in space

self avoiding walks interacting with a surface discusses two models of polymer adsorption in one model a self avoiding walk on a d dimensional lattice interacts with a d 1 dimensional hyperplane in the other model this walk must also lie in or on one side of this hyperplane both models exhibit non analytic behaviour corresponding to a phase transition but these phase transitions do not occur at the same point the authors give numerical estimates of the locations of these transitions

discrete adjoint based approach for optimization problems on three dimensional unstructured meshes a comprehensive strategy for developing and implementing discrete adjoint methods for aerodynamic shape optimization problems is presented by linearizing each procedure in the entire optimization problem transposing each linearization and reversing the sequential order of operations the adjoint of the complete optimization problem including flow equations and mesh motion equations is constructed in a modular and verifiable fashion this construction is also shown to produce minimal memory overheads and retain the same convergence characteristics of the original analysis problem in the sensitivity analysis these techniques are implemented in a three dimensional unstructured multigrid navierstokes solver and demonstrated on a transonic drag reduction problem for a wing body configuration

optimal schwarz waveform relaxation for the one dimensional wave equation we introduce a nonoverlapping variant of the schwarz waveform relaxation algorithm for wave propagation problems with variable coefficients in one spatial dimension we derive transmission conditions which lead to convergence of the algorithm in a number of iterations equal to the number of subdomains independently of the length of the time interval these optimal transmission conditions are in general nonlocal but we show that the nonlocality depends on the time interval under consideration and we introduce time windows to obtain optimal performance of the algorithm with local transmission conditions in the case of piecewise constant wave speed we show that convergence in two iterations can be achieved independently of the number of subdomains in that case the algorithm thus scales optimally with the number of subdomains provided the time windows are chosen appropriately for continuously varying coefficients we prove convergence of the algorithm with local transmission conditions using energy estimates we then introduce a finite volume discretization which permits computations on nonmatching grids and we prove convergence of the fully discrete schwarz waveform relaxation algorithm we finally illustrate our analysis with numerical experiments

regular sets over extended tree structures we investigate notions of decidability and definability for the monadic second order logic over labeled tree structures and its relations with finite automata using oracles to test input prefixes a general framework is defined allowing to transfer some mso properties from a graph structure to a labeled tree structure transferred properties are the decidability of sentences and the existence of a definable model for every satisfiable formula a class of finite automata with prefix oracles is also defined recognizing exactly languages defined by mso formulas in any labeled tree structure applying these results the well known equivalence between languages recognized by finite automata sets of vertices mso definable in a tree structure and sets of pushdown contexts generated by pushdown automata is extended to k iterated pushdown automata

a pde sensitivity equation method for optimal aerodynamic design the use of gradient based optimization algorithms in inverse design is well established as a practical approach to aerodynamic design a typical procedure uses a simulation scheme to evaluate the objective function from the approximate states and its gradient then passes this information to an optimization algorithm once the simulation scheme cfd flow solver has been selected and used to provide approximate function evaluations there are several possible approaches to the problem of computing gradients one popular method is to differentiate the simulation scheme and compute design sensitivities that are then used to obtain gradients although this black box approach has many advantages in shape optimization problems one must compute mesh sensitivities in order to compute the design sensitivity in this paper we present an alternative approach using the pde sensitivity equation to develop algorithms for computing gradients this approach has the advantage that mesh sensitivities need not be computed moreover when it is possible to use the cfd scheme for both the forward problem and the sensitivity equation then there are computational advantages an apparent disadvantage of this approach is that it does not always produce consistent derivatives however for a proper combination of discretization schemes one can showasymptotic consistencyunder mesh refinement which is often sufficient to guarantee convergence of the optimal design algorithm in particular we show that when asymptotically consistent schemes are combined with a trust region optimization algorithm the resulting optimal design method converges we denote this approach as thesensitivity equation method the sensitivity equation method is presented convergence results are given and the approach is illustrated on two optimal design problems involving shocks

superconvergent functional output for time dependent problems using finite differences on summation by parts form finite difference operators satisfying the summation by parts sbp rules can be used to obtain high order accurate energy stable schemes for time dependent partial differential equations when the boundary conditions are imposed weakly by the simultaneous approximation term sat in general an sbp sat discretization is accurate of order p 1 with an internal accuracy of 2p and a boundary accuracy of p despite this it is shown in this paper that any linear functional computed from the time dependent solution will be accurate of order 2p when the boundary terms are imposed in a stable and dual consistent way the method does not involve the solution of the dual equations and superconvergent functionals are obtained at no extra computational cost four representative model problems are analyzed in terms of convergence and errors and it is shown in a systematic way how to derive schemes which gives superconvergent functional outputs

space time domain decomposition and mixed formulation for solving reduced fracture models in this paper we are interested in the fast path fracture and we aim to use global in time nonoverlapping domain decomposition methods to model flow and transport problems in a porous medium containing such a fracture we consider a reduced model in which the fracture is treated as an interface between the two subdomains two domain decomposition methods are considered one uses the time dependent steklovpoincare operator and the other uses optimized schwarz waveform relaxation oswr based on ventcell transmission conditions for each method a mixed formulation of an interface problem on the space time interface is derived and different time grids are employed to adapt to different time scales in the subdomains and in the fracture demonstrations of the well posedness of the ventcell subdomain problems is given for the mixed formulation an analysis for the convergence factor of the oswr algorithm is given in the case with fractures to compute the optimized parameters numerical results for two dimensional problems with strong heterogeneities are presented to illustrate the performance of the two methods

collapsing and adsorbing polygons the adsorption transition in the phase diagram of a self interacting lattice polygon is examined the polygon has a nearest neighbour contact fugacity and the interaction between the polygon and an impenetrable wall is modelled by a visit fugacity which is conjugate to the number of vertices of the polygon incident with the wall the partition function of this model is z c y z d p v cp c v c y v z c where p c v c is the number of polygons with c nearest neighbour contacts v visits to the wall and n edges and counted up to translations parallel to the wall the limiting free energy of this model is f c y z d limn 1 1 logz c y z and it is known to be a non analytic function of y for each z 1 for all z2 0 1

adjoint sensitivity analysis for time dependent partial differential equations with adaptive mesh refinement a new adjoint sensitivity analysis approach is presented for time dependent partial differential equations with adaptive mesh refinement the new approach called adda combines the best features of both the adjoint of the discretization ad and discretization of the adjoint da approaches it removes the obstacles of applying ad to adaptive methods and in contrast to da requires for its use only a minimal amount of knowledge about the formulation of adjoint pdes and their boundary conditions the effectiveness and efficiency of adda are demonstrated for several numerical examples

space time adaptive solution of inverse problems with the discrete adjoint method this paper develops a framework for the construction and analysis of discrete adjoint sensitivities in the context of time dependent adaptive grid adaptive step models discrete adjoints are attractive in practice since they can be generated with low effort using automatic differentiation however this approach brings several important challenges the space time adjoint of the forward numerical scheme may be inconsistent with the continuous adjoint equations a reduction in accuracy of the discrete adjoint sensitivities may appear due to the inter grid transfer operators moreover the optimization algorithm may need to accommodate state and gradient vectors whose dimensions change between iterations this work shows that several of these potential issues can be avoided through a multi level optimization strategy using discontinuous galerkin dg hp adaptive discretizations paired with runge kutta rk time integration we extend the concept of dual adjoint consistency to space time rk dg discretizations which are then shown to be well suited for the adaptive solution of time dependent inverse problems furthermore we prove that dg mesh transfer operators on general meshes are also dual consistent this allows the simultaneous derivation of the discrete adjoint for both the numerical solver and the mesh transfer logic with an automatic code generation mechanism such as algorithmic differentiation ad potentially speeding up development of large scale simulation codes the theoretical analysis is supported by numerical results reported for a two dimensional non stationary inverse problem

index and characteristic analysis of linear pdae systems automatable analyses of the index and well posedness of two general classes of linear pdaes are presented for use in equation based dynamic simulation packages these analyses determine whether a problem possesses a unique solution trajectory the potential effect of noise in the initial and boundary conditions on the calculated solution and the index of the model equations measures of the degeneracy of the system rather than a differentiation index bound the order of derivatives of forcing functions that appear in the solution

rabin s theorem in the concurrency setting a conjecture rabin s theorem says that the monadic second order theory of the infinite binary tree is decidable this result has had a far reaching influence in the theory of branching time temporal logics a simple consequence of rabin s theorem is that for every finite state transition system the monadic second order theory of its computation tree is decidable concurrency theory strongly suggests that finite 1 safe petri nets or simply net systems are a natural generalization of the notion of a finite state transition system while labelled event structures arising as the unfoldings of net systems are the proper counterparts to the computation trees obtained by unwinding finite sequential transition systems it is easy to define the monadic second order theory of such event structures it turns out that unlike the sequential case not every net system i e its event structure unfolding has a decidable monadic second order theory this gives rise to the question which net systems admit a decidable monadic second order theory here we present a conjecture based on a property called grid freeness our conjecture is that a net system has a decidable monadic second order theory iff its event structure unfolding is grid free we show that it is decidable whether a net system has this property we also prove that the monadic second order theory of a net system is undecidable if its event structure unfolding is not grid free in addition we show that our conjecture can be effectively reduced to the sub class of free choice net systems finally we point out how the positive resolution of our conjecture will settle the decidability of a range of distributed controller synthesis problems

balancing domain decomposition for problems with large jumps in coefficients the balancing domain decomposition algorithm uses in each iteration solution of local problems on the subdomains coupled with a coarse problem that is used to propagate the error globally and to guarantee that the possibly singular local problems are consistent the abstract theory introduced recently by the first named author is used to develop condition number bounds for conforming linear elements in two and three dimensions the bounds are independent of arbitrary coefficient jumps between subdomains and of the number of subdomains and grow only as the squared logarithm of the mesh size h computational experiments for two and three dimensional problems confirm the theory

space time domain decomposition methods for diffusion problems in mixed formulations this paper is concerned with global in time nonoverlapping domain decomposition methods for the mixed formulation of the diffusion problem two approaches are considered one uses the time dependent steklov poincare operator and the other uses optimized schwarz waveform relaxation oswr based on robin transmission conditions for each method a mixed formulation of an interface problem on the space time interfaces between subdomains is derived and different time grids are employed to adapt to different time scales in the subdomains demonstrations of the well posedness of the robin subdomain problems involved in the oswr method and a convergence proof of the oswr algorithm are given for the mixed formulation numerical results for two dimensional problems with strong heterogeneities are presented to illustrate the performance of the two methods

on infinite transition graphs having a decidable monadic theory we define a family of graphs whose monadic theory is in linear space reducible to the monadic theory s2s of the complete ordered binary tree this family contains strictly the context free graphs investigated by muller and schupp and also the equational graphs defined by courcelle using words as representations of vertices we give a complete set of representatives by prefix rewriting of rational languages this subset of possible representatives is a boolean algebra preserved by transitive closure of arcs and by rational restriction on vertices

petri nets event structures and domains part i abstract the general aim of this paper is to find a theory of concurrency combining the approaches of petri and scott and others in part i we introduce our formalisms to connect the abstract ideas of events and domains of information we show how casual nets induce certain kinds of domains where the information points are certain sets of events this allows translations between the languages of net theory and domain theory following the idea that events of causal nets are occurrences we generalise causal nets to occurrence nets by adding forwards conflict just as infinite flow charts unfold finite ones so transition nets can be unfolded into occurrence nets next we extend the above connections between nets and domains to these new nets event structures which are intermediate between nets and domains play an important part in all our work finally as an example of how concepts translate from one formalism to the other we show how petri s notion of confusion ties up with kahn and plotkin s concrete domains in part ii we shall continue the job of connecting up notions within net theory and the theory of domains in particular we shall examine the idea of states of computations

on the expressiveness of higher dimensional automata in this paper i compare the expressive power of several models of concurrency based on their ability to represent causal dependence to this end i translate these models in behaviour preserving ways into the model of higher dimensional automata hda which is the most expressive model under investigation in particular i propose four different translations of petri nets corresponding to the four different computational interpretations of nets found in the literature i also extend various equivalence relations for concurrent systems to hda these include the history preserving bisimulation which is the coarsest equivalence that fully respects branching time causality and their interplay as well as the st bisimulation a branching time respecting equivalence that takes causality into account to the extent that it is expressible by actions overlapping in time through their embeddings in hda it is now well defined whether members of different models of concurrency are equivalent

an event structure semantics for general petri nets abstract in this paper we address the following question what type of event structures are suitable for representing the behaviour of general petri nets as a partial answer to this question we define a new class of event structures called local event structures and identify a subclass called ul event structures we propose that ul event structures are appropriate for capturing the behaviour of general petri nets our answer is a partial one in that in the proposed event structure semantics auto concurrency is filtered out from the behaviour of petri nets it turns out that this limited event structure semantics for petri nets is nevertheless a non trivial and conservative extension of the prime event structure semantics of 1 safe petri nets provided in nielsen et al 1981 we also show that the strong relationship between prime event structures and 1 safe petri nets established in a categorical framework in winskel 1987 can be extended to the present setting provided we restrict our attention to the subclass of petri nets whose behaviours do not exhibit any auto concurrency finally we show that winskel s general and stable event structures can be smoothly related to local event structures and that similarly prime event structures can be related to ul event structures

space time domain decomposition for two phase flow between different rock types in previous work e ahmed s ali hassan c japhet m kern and m vohralik a posteriori error estimates and stopping criteria for space time domain decomposition for two phase flow between different rock types the smai journal of computational mathematics 5 2019 pp 195 227 https doi org 10 5802 smai jcm 47 a space time domain decomposition method was proposed for two phase ow in a porous medium composed of two different rock types so that the capillary pressure field is discontinuous at the interface between the rocks for this nonlinear and degenerate parabolic problem with nonlinear and discontinuous transmission conditions on the interface the optimized schwarz waveform relaxation method oswr with robin or ventcell transmission conditions was considered a guaranteed and fully computable a posteriori error estimate was derived which in particular took into account the domain decomposition error in this paper we provide a mathematical and numerical analysis of this space time domain decomposition method in the robin case complete numerical approximation is achieved by a finite volume scheme in space and the lowest order discontinuous galerkin method in time we prove the existence of a weak solution of the two phase ow subdomain problem with robin boundary conditions by analyzing the convergence of the finite volume scheme the domain decomposition algorithm is based on the solution of space time nonlinear subdomain problems over the whole time interval allowing for different time steps in dfferent parts of the domain adapted to the physical properties of each subdomain and we show that such an algorithm is well defined numerical experiments on three dimensional problems with different rock types illustrate the performance of the domain decomposition method

verification of qualitative z constraints we introduce an ltl like logic with atomic formulae built over a constraint language interpreting variables in z the constraint language includes periodicity constraints and comparison constraints of the form x y and x

differential algebraic equations indices and integral algebraic equations in a recent report hairer lubich and roche report ch 1211 dept de mathematiques universite de geneve geneve switzerland 1988 define the index of differential algebraic equations daes by considering the effect of perturbations of the equations on the solutions this index which will be called the perturbation index p i is one more than the number of derivatives of the perturbation that must appear in any estimate of the bound of the change in the solution an earlier form of index used by a number of authors including gear and petzold siam j numer anal 21 1984 pp 716 728 is determined by the number of differentiations of the daes that are required to generate an ordinary differential equation ode satisfied by the solution this will be called the differential index d i hairer lubich and roche give an example whose differential index is one and perturbation index is two and other examples where they are identical it will be shown that d i leqq p i leqq d i 1 and th

optimal control of two and three dimensional incompressible navier stokes flows the focus of this work is on the development of large scale numerical optimization methods for optimal control of steady incompressible navier stokes flows the control is affected by the suction or injection of fluid on portions of the boundary and the objective function represents the rate at which energy is dissipated in the fluid we develop reduced hessian sequential quadratic programming methods that avoid converging the flow equations at each iteration both quasi newton and newton variants are developed and compared to the approach of eliminating the flow equations and variables which is effectively the generalized reduced gradient method optimal control problems are solved for two dimensional flow around a cylinder and three dimensional flow around a sphere the examples demonstrate at least an order of magnitude reduction in time taken allowing the optimal solution of flow control problems in as little as half an hour on a desktop workstation

a new class of discretization methods for the solution of linear differential algebraic equations with variable coefficients we discuss new discretization methods for linear differential algebraic equations daes with variable coefficients we introduce numerical methods to compute the local invariants of such daes that were introduced by the authors in a previous paper p kunkel and v mehrmann j comput appl math 56 1994 pp 225 251 using these quantities we are able to determine numerically global invariances like the strangeness index which generalizes the differentiation index for daes that in particular include undetermined solution components based on these methods we then obtain regularization schemes which allow us to employ general solution methods the new methods are tested on a number of numerical examples

admitting the inadmissible adjoint formulation for incomplete cost functionals in aerodynamic optimization we derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as inadmissible for example a cost functional which depends on the density rather than on the pressure is considered inadmissible for an optimization problem governed by the euler equations we show that for such problems additional terms should be included in the lagrangian functional when deriving the adjoint equations these terms are obtained from the restriction of the interior pde to the control surface demonstrations of the explicit derivation of the adjoint equations for inadmissible cost functionals are given for the potential euler and navier stokes equations

the theory of ends pushdown automata and second order logic abstract a class of edge labeled graphs called context free are defined according to their behavior at infinity such graphs are generalizations of cayley graphs of context free groups they are also shown to be definable in a very natural way in terms of push down automata using rabin s theorem on the monadic second order theory of the finite binary tree these graphs are also shown to have a decidable monadic second order theory questions about tiling systems and cellular automata operating on these graphs are decidable even when the analogous questions are not when the systems operate on a two dimensional grid

on complexity functions of infinite words associated with generalized dyck languages in this article we construct a family of infinite words generated by countable automata and also generated by substitutions over infinite alphabets closely related to parenthesis languages and we study their complexity functions we obtain a family of binary infinite words m b indexed on the number b 1 of parenthesis types such that the growth order of the complexity function of m b is n logn 2 if b 1 and n 1 l o g 2 b b if b 2

mixed methods using standard conforming finite elements abstract we investigate the mixed finite element method mfem for solving a second order elliptic problem with a lowest order term as might arise in the simulation of single phase flow in porous media we find that traditional mixed finite element spaces are not necessary when a positive lowest order i e reaction term is present hence we propose to use standard conforming finite elements q k q k d on rectangles or p k p k d on simplices to solve for both the pressure and velocity field in d dimensions the price we pay is that we have only sub optimal order error estimates with a delicate superconvergence analysis we find some improvement for the simplest pair q k q k d with any k 1 or for p 1 p 1 d when the mesh is uniform and the solution has one extra order of regularity we also prove similar results for both parabolic and second order hyperbolic problems numerical results using q 1 q 1 2 and p 1 p 1 2 are presented in support of our analysis these observations allow us to simplify the implementation of the mfem especially for higher order approximations as might arise in an hp adaptive procedure

self avoiding walks and polymer adsorption edge and vertex weighting self avoiding walks interacting with a surface are a useful model of polymer adsorption and one can choose to weight the walk according to the number of vertices or the number of edges in the surface we consider a combined model of self avoiding walks on the d dimensional hypercubic lattice with weights associated with the numbers of vertices and edges in the surface and investigate its phase diagram we also derive inequalities relating the critical points in the edge and vertex weighting schemes

a wavelet approach to adjoint state sensitivity computation for steady state differential equations 1 the computation of the sensitivity matrix is the most time consuming part of any parameter estimation algorithm that requires sensitivity coefficients an efficient wavelet approach to adjoint sensitivity analysis is proposed to reduce the computational cost of obtaining sensitivity coefficients the method exploits a wavelet reduction of the data space to reduce the size of the linear system encountered in steady state adjoint equations in this regard wavelet transform is used as a data compression tool numerical examples applied to spatial data are used to verify and show the effectiveness of the method

configuration structures event structures and petri nets in this paper the correspondence between safe petri nets and event structures due to nielsen plotkin and winskel is extended to arbitrary nets without self loops under the collective token interpretation to this end we propose a more general form of event structure matching the expressive power of such nets these new event structures and nets are connected by relating both notions with configuration structures which can be regarded as representations of either event structures or nets that capture their behaviour in terms of action occurrences and the causal relationships between them but abstract from any auxiliary structure a configuration structure can also be considered logically as a class of propositional models or equivalently as a propositional theory in disjunctive normal from converting this theory to conjunctive normal form is the key idea in the translation of such a structure into a net for a variety of classes of event structures we characterise the associated classes of configuration structures in terms of their closure properties as well as in terms of the axiomatisability of the associated propositional theories by formulae of simple prescribed forms and in terms of structural properties of the associated petri nets

motzkin path models of long chain polymers in slits we consider motzkin path models for polymers confined to a slit the path interacts with each of the two confining lines and we define parameters a and b to characterize the strengths of the interactions with the two lines we consider the cases where i each vertex in a confining line contributes to the energy and ii where each edge in a confining line contributes to the energy for the vertex and edge versions of motzkin paths we can find the generating functions and give rigorous explicit expressions for the free energy at some special points in the a b plane and asymptotically i e for large slit widths elsewhere we find regions where the force between the lines is long range and repulsive short range and repulsive and short range and attractive our results indicate that the general form of the phase diagram is model independent and similar to previous results for a dyck path model although the details do depend on the underlying configurational model we also contrast the method used here to find the generating function with the transfer matrix and heap methods

a parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods a parallelizable interative procedure based on domain decomposition techniques is defined and analyzed for mixed finite element methods for elliptic equations with the analysis being presented for the decomposition of the domain into the individual elements associated with the mixed method or into larger subdomains applications to time dependent problems are indicated

on the complexity of a family of k context free sequences we introduce a large family of k context free sequences for which we give a polynomial upper bound on their complexity functions

true concurrency probabilistic models branching cells and distributed probabilities for event structures this paper is devoted to probabilistic models for concurrent systems under their true concurrency semantics here we address probabilistic event structures we consider a new class of event structures called locally finite that extend confusion free event structure in locally finite event structures maximal configurations can be tiled with branching cells branching cells are minimal and finite sub structures capturing the choices performed while scanning a maximal configuration the probabilistic event structures that we introduce have the property that concurrent processes are independent in the probabilistic sense

monadic second order logic on tree like structures an operation m which constructs from a given structure m a tree like structure whose domain consists of the finite sequences of elements of m is considered a notion of automata running on such tree like structures is defined it is shown that automata of this kind characterise expressive power of monadic second order logic msol over tree like structures using this characterisation it is proved that msol theory of a tree like structure is effectively reducible to that of the original structure as another application of the characterisation it is shown that msol on trees of arbitrary degree is equivalent to first order logic extended with unary least fixpoint operator

the index of general nonlinear daes in the last few years there has been considerable research on differential algebraic equations daes f t y y 0 where f y is identically singular much of the mathematical effort has focused on computing a solution that is assumed to exist more recently there has been some discussion of solvability of daes there has historically been some imprecision in the use of the two key concepts of solvability and index for daes the index is also important in control and systems theory but with different terminology the consideration of increasingly complex nonlinear daes makes a clear and correct development necessary this paper will try to clarify several points concerning the index after establishing some new and more precise terminology that we need some inaccuracies in the literature will be corrected the two types of indices most frequently used the differentiation index and the perturbation index are defined with respect to solutions of unperturbed problems examples are given to show that these indices can be very different for the same problem we define new maximum indices which are the maxima of earlier indices in a neighborhood of the solution over a set of perturbations and show that these indices are simply related to each other these indices are also related to an index defined in terms of jacobians