asymptotic behavior of the solution to the non isothermal phase field equation we consider the penrose fife phase field model thermodynamically consistent models of phase field type for the kinetics of phase transitions physica d 43 1990 44 62 with homogeneous neumann boundary condition to the nonlinear heat flux q 1 i e q 0 on the boundary where 0 is the temperature there is a unique h1 solution globally in time with the non empty connected compact limit set composed of stationary solutions and the linearized stable stationary solution is dynamically stable

a non isothermal phase separation with constraints and dirichlet boundary condition for temperature abstract we consider non isothermal phase separation models of the penrose fife type which were proposed in o penrose p c fife thermodynamically consistent models of phase field type for the kinetics of phase transitions physica d 43 1990 44 62 in the present paper we impose a non homogeneous dirichlet boundary condition on the nonlinear heat flux moreover we consider two cases as boundary conditions for the conserved order parameter one is the homogeneous neumann boundary condition and the other is the signorini boundary condition which is nonlinear we show the existence and uniqueness of solutions to these models

asymptotic behavior of the solution to the non isothermal phase separation abstract we consider the non isothermal phase separation models of the penrose fife type which were proposed in o penrose p c fife thermodynamically consistent models of phase field type for the kinetics of phase transitions physica d 43 1990 44 62 with homogeneous neumann boundary conditions on the nonlinear heat flux q u i e q n 0 on the boundary of a region which the material occupies here u represents the absolute temperature for this model we first show that there exists a unique solution globally in time moreover the limit set associated with the trajectory of the unique global solution is non empty connected and compact in some suitable space as well as being composed of solutions to the steady state problem for the stability of stationary solutions we show that the dynamically stable solutions to the steady state problem are characterized by linearized stable solutions to the elliptic problem with a non local term which is equivalent to our steady state problem

an automata theoretic approach to constraint ltl we consider an extension of linear time temporal logic ltl with constraints interpreted over a concrete domain we use a new automata theoretic technique to show pspace decidability of the logic for the constraint systems z and n along the way we give an automata theoretic proof of a result of balbiani and condotta when the constraint system satisfies the completion property our decision procedures extend easily to handle extensions of the logic with past time operators and constants as well as an extension of the temporal language itself to monadic second order logic finally we show that the logic becomes undecidable when one considers constraint systems that allow a counting mechanism

continuous time temporal logic with counting we add to the standard temporal logic tl u s a sequence of counting modalities for each n the modality c n x which says that x will be true at least at n points in the next unit of time and its dual c n which says that x has happened n times in the last unit of time we show that this temporal logic is expressively complete for the metric predicate logic q2mlo which is expressive decidable and easy to use in particular the pnueli modalities p n x 1 x n there is an increasing sequence t 1 t n of points in the unit interval ahead such that t i satisfies x i are definable in tl u s with the counting modalities

global existence for a phase separation system deduced from the entropy balance abstract this paper is concerned with a thermomechanical model describing phase separation phenomena in terms of the entropy balance and equilibrium equations for the microforces the related system is highly nonlinear and admits singular potentials in the phase equation both the viscous and the non viscous cases are considered in the cahn hilliard relations characterizing the phase dynamics the entropy balance is written in terms of the absolute temperature and of its logarithm appearing under time derivative the initial and boundary value problem is considered for the system of partial differential equations the existence of a global solution is proved via some approximations involving yosida regularizations and a suitable time discretization

well posedness for solid liquid phase transitions with a fourth order nonlinearity abstract a phase field system which describes the evolution of both the absolute temperature and the phase variable f during first order transitions in thermal insulators is considered a thermodynamic approach is developed by regarding the order parameter as a phase field and its evolution equation as a balance law by virtue of the special form of the internal energy a third order nonlinearity g 2 f appears in the energy balance in place of the customarily constant latent heat as a consequence the bounds 0 f 1 hold whenever is positive valued in addition a nonlinear fourier law with conductivity proportional to temperature is assumed well posedness for the resulting initial and boundary value problem are then established in a suitable setting

periodic solutions of non isothermal phase separation models with constraint abstract in this paper we consider the existence of time periodic solutions to the non isothermal phase separation models with constraints for the order parameter and the dirichlet boundary condition for the temperature we firstly address some approximate problems by the leray schauder fixed point theorem then the periodic solutions of the original problem are obtained by establishing some a priori estimates and performing a limiting procedure

complexity of metric temporal logics with counting and the pnueli modalities the common metric temporal logics for continuous time were shown to be insufficient when it was proved in hirshfeld and rabinovich 1999 2007 7 12 that they cannot express a modality suggested by pnueli moreover no temporal logic with a finite set of modalities can express all the natural generalizations of this modality the temporal logic with counting modalities tlc is the extension of until since temporal logic tl u s by counting modalities c n x and email protected n email protected n for each n the modality c n x says that x will be true at least at n points in the next unit of time and its dual email protected n x says that x has happened n times in the last unit of time in hirshfeld and rabinovich 2006 11 it was proved that this temporal logic is expressively complete for a natural decidable metric predicate logic in particular the pnueli modalities pn k x 1 x k there is an increasing sequence t 1 t k of points in the unit interval ahead such that x i holds at t i are definable in tlc in this paper we investigate the complexity of the satisfiability problem for tlc and show that the problem is pspace complete when the index of c n is coded in unary and expspace complete when the index is coded in binary we also show that the satisfiability problem for the until since temporal logic extended by the pnueli modalities is pspace complete

thermodynamically consistent models of phase field type for the kinetics of phase transitions abstract a general framework is given for the phenomenological kinetics of phase transitions in which not only the order parameter but also the temperature may vary in time and space instead of a ginzburg landau free energy functional as used in formulating the cahn hilliard equation we use the analogous entropy functional model entropy functionals and the kinetic equations resulting from them are constructed for various cases phase transitions with and without a critical point and in the former case with or without a latent heat the class considered is general enough to include the entropy functionals for the ising model in mean field approximation the van der waals fluid and a simplified version of the density functional theory of freezing a case without critical point for which the energy is conserved but the order parameter is not provides a thermodynamically consistent derivation of the phase field equations studied by caginalp fix and others and also leads in a natural way to the lyapunov functional given by langer for these equations but the treatment also suggests that a modified version of the phase field equations might provide a more realistic model of freezing

the phase field transition system with non homogeneous cauchy stefan boltzmann and homogeneous neumann boundary conditions and non constant thermal conductivity abstract the paper establishes the existence estimate uniqueness and regularity for the solution of a nonlinear parabolic system a two phase caginalp type system with non homogeneous cauchy stefan boltzmann and homogeneous neumann boundary conditions and non constant thermal conductivity it extends the already studied types of boundary conditions which makes the mathematical model to be richer and more flexible to describe the real physical phenomena including phase separation

an analysis of a phase field model of a free boundary a mathematical analysis of a new approach to solidification problems is presented a free boundary arising from a phase transition is assumed to have finite thickness the physics leads to a system of nonlinear parabolic differential equations existence and regularity of solutions are proved invariant regions of the solution space lead to physical interpretations of the interface a rigorous asymptotic analysis leads to the gibbs thompson condition which relates the temperature at the interface to the surface tension and curvature

a dynamic data structure for 3 d convex hulls and 2 d nearest neighbor queries we present a fully dynamic randomized data structure that can answer queries about the convex hull of a set of n points in three dimensions where insertions take o log3n expected amortized time deletions take o log6n expected amortized time and extreme point queries take o log2n worst case time this is the first method that guarantees polylogarithmic update and query cost for arbitrary sequences of insertions and deletions and improves the previous o ne time method by agarwal and matousek a decade ago as a consequence we obtain similar results for nearest neighbor queries in two dimensions and improved results for numerous fundamental geometric problems such as levels in three dimensions and dynamic euclidean minimum spanning trees in the plane

random sampling halfspace range reporting and construction of lowercase le k levels in three dimensions given n points in three dimensions we show how to answer halfspace range reporting queries in o log n k expected time for an output size k our data structure can be preprocessed in optimal o n log n expected time we apply this result to obtain the first optimal randomized algorithm for the construction of the le k level in an arrangement of n planes in three dimensions the algorithm runs in o n log n nk2 expected time our techniques are based on random sampling applications in two dimensions include an improved data structure for k nearest neighbors queries and an algorithm that constructs the order k voronoi diagram in o n log n nk log k expected time

analysis of an iterative scheme of fractional steps type associated to the reaction diffusion equation endowed with a general nonlinearity and cauchy neumann boundary conditions abstract the paper studies the existence uniqueness regularity and the approximation of solutions to the reaction diffusion equation endowed with a general nonlinear regular potential and cauchy neumann boundary conditions the convergence and error estimate results for an iterative scheme of fractional steps type associated to the nonlinear parabolic equation are also established the advantage of such method consists in simplifying the numerical computation necessary to be done in order to approximate the solution of nonlinear parabolic equation

global smooth solutions to a thermodynamically consistent model of phase field type in higher space dimensions abstract in a recent paper penrose and fife proposed a thermodynamically consistent model of phase field type for phase transition phenomena such as liquid solid phase transitions the model is based on the observation that the second law of thermodynamics postulates that the entropy functional cannot decrease along solution paths it turns out that the resulting field equations form a system of partial differential equations which is considerably more difficult than the phase field equations studied by caginalp and others for one space dimension global existence uniqueness and asymptotic behaviour of smooth solutions of the initial boundary value problem with neumann boundary data have been obtained in a recent paper by zheng in this paper we prove global existence and uniqueness in three space dimensions for the initial boundary value problem with a third boundary condition

well posedness of initial boundary value problem of degenerate parabolic equations abstract we study a nonlinear degenerate parabolic equation associated with an arbitrary maximal monotone graph we impose initial and dirichlet boundary conditions and prove that the problem is well posed

a phase field model with temperature dependent constraint this paper is concerned with a phase field model with temperature dependent constraint for the order parameter in the kinetic equation of the order parameter we take account of diffusion as well as undercooled superheated state which is modelled by means of a hysteresis input output relation the input is the temperature field and the output is the order parameter in this paper we shall show that there exists a solution globally in time in a physically reasonable sense when the coefficient of interfacial energy is sufficiently small

on the existence uniqueness and regularity of solutions to the phase field system with a general regular potential and a general class of nonlinear and non homogeneous boundary conditions abstract this paper studies a caginalp phase field transition system endowed with a general regular potential as well as a general class in both unknown functions of nonlinear and non homogeneous depending on time and space variables boundary conditions we first prove the existence uniqueness and regularity of solutions to the allen cahn equation subject to the nonlinear and non homogeneous dynamic boundary conditions the existence uniqueness and regularity of solutions to the caginalp system in this new formulation are also proved this extends previous works concerned with regular potential and nonlinear boundary conditions allowing the present mathematical model to better approximate the real physical phenomena especially phase transitions

computing closest and farthest points for a query segment in this paper we present an improved algorithm for finding k closest farthest points for a given arbitrary query segment we show how to preprocess a planar set p of n given points in o n 2logn expected time or alternatively in o n 2log 2n deterministic time and a subquadratic space in order to report k closest points to an arbitrary given query line segment in o k log 2nloglogn time here for the first time the data structure that provides polylogarithmic query time and uses subquadratic space is presented we also show an algorithm for reporting the k farthest points from an arbitrary given query line segment

transdichotomous results in computational geometry i point location in sublogarithmic time given a planar subdivision whose coordinates are integers bounded by u leq2 w we present a linear space data structure that can answer point location queries in o min lg n lg lg n sqrt lg u lg lg u time on the unit cost random access machine ram with word size w this is the first result to beat the standard theta lg n bound for infinite precision models as a consequence we obtain the first o n lg n randomized algorithms for many fundamental problems in computational geometry for arbitrary integer input on the word ram including constructing the convex hull of a three dimensional 3d point set computing the voronoi diagram or the euclidean minimum spanning tree of a planar point set triangulating a polygon with holes and finding intersections among a set of line segments higher dimensional extensions and applications are also discussed though computational geometry with bounded precision input has been investigated for a long time improvements have been limited largely to problems of an orthogonal flavor our results surpass this long standing limitation answering for example a question of willard soda 92

instance optimal geometric algorithms we prove the existence of an algorithm a for computing 2d or 3d convex hulls that is optimal for every point set in the following sense for every sequence of n points and for every algorithm a in a certain class a the running time of a on input is at most a constant factor times the running time of a on the worst possible permutation of for a in fact we can establish a stronger property for every sequence of points and every algorithm a the running time of a on is at most a constant factor times the average running time of a over all permutations of we call algorithms satisfying these properties instance optimal in the order oblivious and random order setting such instance optimal algorithms simultaneously subsume output sensitive algorithms and distribution dependent average case algorithms and all algorithms that do not take advantage of the order of the input or that assume the input are given in a random order the class a under consideration consists of all algorithms in a decision tree model where the tests involve only multilinear functions with a constant number of arguments to establish an instance specific lower bound we deviate from traditional ben or style proofs and adopt a new adversary argument for 2d convex hulls we prove that a version of the well known algorithm by kirkpatrick and seidel 1986 or chan snoeyink and yap 1995 already attains this lower bound for 3d convex hulls we propose a new algorithm we further obtain instance optimal results for a few other standard problems in computational geometry such as maxima in 2d and 3d orthogonal line segment intersection in 2d finding bichromatic l close pairs in 2d offline orthogonal range searching in 2d offline dominance reporting in 2d and 3d offline half space range reporting in 2d and 3d and offline point location in 2d our framework also reveals a connection to distribution sensitive data structures and yields new results as a byproduct for example on online orthogonal range searching in 2d and online half space range reporting in 2d and 3d

a logical characterization of timed regular languages cltloc constraint ltl over clocks is a quantifier free extension of ltl allowing variables behaving like clocks over real numbers cltloc is in pspace 1 and its satisfiability can polynomially be reduced to a satisfiability modulo theories smt problem allowing a feasible implementation of a decision procedure we used cltloc to capture the semantics of metric temporal logics over continuous time such as metric interval temporal logic mitl resulting in the first successful implementation of a tool for checking mitl satisfiability 2 3 in this paper we assess the expressive power of cltloc by comparing it with various temporal formalisms over dense time we restrict the analysis to well initialized models of formulae where the value of all clocks in the origin is either 0 or equal to a positive real constant under this assumption when interpreted over timed words the class of timed languages defined by cltloc formulae coincides with the class defined by timed automata we also define a timed monadic first order logic of order extending the one introduced by kamp which is expressively equivalent to cltloc for the class of timed languages that are defined by well initialized models

non linear system for non isothermal diffusive phase separation abstract an evolution system which extends the cahn hilliard model to non isothermal situations subject to convex constraints for solutions is studied the problem can be considered as representing a simple model of non isothermal phase separation driven by diffusive mechanisms a variational formulation of the problem is introduced using t dependent subdifferential operator techniques in hilbert spaces existence and uniqueness of weak solutions are proved

variational inequalities for a system of elliptic parabolic equations abstract we create a general framework for mathematical study of variational inequalities for a system of elliptic parabolic equations in this paper we establish a solvability theorem concerning the existence of solutions for the vector valued elliptic parabolic variational inequality with time dependent constraint moreover we give some applications of the system for example time dependent boundary obstacle problem and time dependent interior obstacle problem

an smt based approach to satisfiability checking of mitl we present a satisfiability preserving reduction from mitl interpreted over finitely variable continuous behaviors to constraint ltl over clocks a variant of cltl that is decidable and for which an smt based bounded satisfiability checker is available the result is a new complete and effective decision procedure for mitl although decision procedures for mitl already exist the automata based techniques they employ appear to be very difficult to realize in practice and to the best of our knowledge no implementation currently exists for them a prototype tool for mitl based on the encoding presented here has instead been implemented and is publicly available

a class of nonlinear elliptic parabolic equations with time dependent constraints on etudie les equations d evolutions non lineaires de la forme f t du t dt t v t v t bu t 0 t t dans un espace de hilbert h ou t est la sous differentielle d une fonction convexe t definie sur h b est un operateur monotone maximal dans h on considere l existence et l unicite des solutions ainsi que des estimations a priori

dynamic planar convex hull operations in near logarithmic amortized time we give a data structure that allows arbitrary insertions and deletions on a planar point set p and supports basic queries on the convex hull of p such as membership and tangent finding updates take o log 1 e n amori tzed time and queries take o log n time each where n is the maximum size of p and e is any fixed positive constant for some advanced queries such as bridge finding both our bounds increase to o log 3 2 n the only previous fully dynamic solution was by overmars and van leeuwen from 1981 and required o log 2 n time per update and o log n time per query

nonlinear degenerate parabolic equations with neumann boundary condition abstract we study neumann problem for a class of nonlinear degenerate parabolic pde a typical nonlinearity we have in mind is for instance u 1 u u 0 we establish a necessary and sufficient condition on given data for existence of solution

timer formulas and decidable metric temporal logic we define a quantitative temporal logic that is based on a simple modality within the framework of monadic predicate logic its canonical model is the real line and not an w sequence of some type it can be interpreted either by behaviors with finite variability or by unrestricted behaviors for finite variability models it is as expressive as any logic suggested in the literature for unrestricted behaviors our treatment is new in both cases we prove decidability and complexity bounds using general theorems from logic and not from automata theory the technical proof uses a sublanguage of the metric monadic logic of order the language of timer normal form formulas metric formulas are reduced to timer normal form and timer normal form formulas allow elimination of the metric

the conserved penrose fife system with temperature dependent memory abstract a nonlinear parabolic system of penrose fife type with a singular evolution term arising from modelling dynamic phenomena of the nonisothermal diffusive phase separation is studied here we consider the evolution of a material in which the heat flux is a superposition of two different contributions one part is proportional to the spacial gradient of the inverse of the absolute temperature while the other agrees with the gurtin pipkin law introduced in the theory of materials with thermal memory the phase transition here is described through the evolution of the conserved order parameter which may represent the density or concentration of some substance it is shown that an initial boundary value problem for the resulting state equations has a unique solution

non isothermal phase transition models with neumann boundary conditions abstract we study the systems of nonlinear parabolic pdes for penrose fife models of non isothermal phase transitions both models with conserved and non conserved order parameters are studied with neumann boundary conditions imposed on the systems in multi dimensional spatial domain