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Starting from the modelling requirements of the early design phase of the product development, the paper will show a possible strategy to overcome some limitations of current CAS/CAD systems. In fact, the styling stage involves both technical knowledge and fuzzy and dynamic aspects, which have to be taken into account for a proper management. The paper focuses on high-level modelling tools developed to deform surfaces with semantic (aesthetic) constraints, i.e. the crucial design elements for the stylist. Furthermore, the communication among the other actors of the design process is consequently facilitated. [ABSTRACT FROM AUTHOR]

In finance, the strong convergence properties of discretisations of stochastic differential equations (SDEs) are very important for the hedging and valuation of exotic options. In this paper we show how the use of the Milstein scheme can improve the convergence of the multilevel Monte Carlo method, so that the computational cost to achieve an accuracy of O(e) is reduced to O(ϵ−2) for a Lipschitz payoff. The Milstein scheme gives first order strong convergence for all one-dimensional systems (one Wiener process). However, for processes with two or more Wiener processes, such as correlated portfolios and stochastic volatility models, there is no exact solution for the iterated integrals of second order (Lévy area) and the Milstein scheme neglecting the Lévy area gives the same order of convergence as the Euler-Maruyama scheme. The purpose of this paper is to show that if certain conditions are satisfied, we can avoid the calculation of the Lévy area and obtain first convergence order by applying an orthogonal transformation. We demonstrate when the conditions of the two-dimensional problem permit this and give an exact solution for the orthogonal transformation. We present examples of pricing exotic options to demonstrate that the use of both the orthogonal Milstein scheme and the multilevel Monte Carlo give a substantial reduction in the computation cost. [ABSTRACT FROM AUTHOR]

This paper is meant to be the continuation of the previous work [1] where a coupled ODE/PDE method for the simulation of semiconductor devices was introduced. From a strictly mathematical viewpoint, analytical results on coupled PDE/ODE systems (as arising in integrated circuit simulation) can be found in [2]. In particular, in the present paper, we investigate numerically new algorithms of Domain Decomposition type for the simulation of circuits containing distributed devices (Sect. 2) as well as semiconductors in which some part is modeled with lumped parameters (Sect. 3). The results presented here have been investigated in the seminal work [3], while a more extended analysis is ongoing [4]. [ABSTRACT FROM AUTHOR]

Multiple Recursive Generators (MRGs) have become the most popular random number generators recently. They compute the next value iteratively from the previous k values using a k-th order recurrence equation which, in turn, corresponds to a k-th degree primitive polynomial under a prime modulus p. In general, when k and p are large, checking if a k-th degree polynomial is primitive under a prime modulus p is known to be a hard problem. A common approach is to check the conditions given in Alanen and Knuth [1964] and Knuth [1998]. However, as mentioned in Deng [2004], this approach has two obvious problems: (a) it requires the complete factorization of pk - 1, which can be difficult; (b) it does not provide any early exit strategy for non-primitive polynomials. To avoid (a), one can consider a prime order k and prime modulus p such that (pk - 1)/(p - 1) is also a prime number as considered in L'Ecuyer [1999] and Deng [2004]. To avoid (b), one can use a more efficient iterative irreducibility test proposed in Deng [2004]. In this paper, we survey several leading probabilistic and deterministic methods for the problems of primality testing and irreducibility testing. To test primality of a large number, it is known that probabilistic methods are much faster than deterministic methods. On the other hand, a probabilistic algorithm in fact has a very tiny probability of, say, 10-200 to commit a false positive error in the test result. Moreover, even when such an unlikely event had happened, for a speci.c choice of k and p, it can be argued that such an error has a negligible e.ect on the successful search of a primitive polynomial. We perform a computer search for large-order DX generators proposed in Deng and Xu [2003] and present many such generators in the paper for ready implementation. An extensive empirical study shows that these large-order DX generators have passed the stringent Crush battery of the TestU01 package. [ABSTRACT FROM AUTHOR]

It is well known that there are "nonclassical" situations where, in contrast to Lax's and Glimm's results, the Cauchy problem for a system of conservation laws does not possess a weak L∞-solution except for some particular initial data. To solve the Cauchy problem in this "nonclassical" situation, it is necessary to introduce new singular solutions called δ-shocks and singular shocks. The components of these solutions contain delta functions [ASh05], [B94], [DSh03]- [LW02], [S02]- [Sh04], [TZZ94]. The exact structure of such type solutions is given below in (2), (7) and Definition 1. The theory of δ-shocks and singular shocks has been intensively developed in the last 10 years. In particular, in numerous papers δ-shock type solutions of "zero-pressure gas dynamics" have been studied. Moreover, in the recent papers [PSh06], [Sh06] the theory of δ′-shocks was established, and a concept of δ(n)-shocks was introduced, n = 2, 3,. … They are new type singular solutions such that their components contain delta functions and their derivatives. [ABSTRACT FROM AUTHOR]

Many equations arising in continuum fluid dynamics do not, or at least are not known to, possess smooth solutions for general data. Therefore it is necessary to identify a larger class of "weak solutions" in order to develop a rigorous mathematical theory. Following the seminal paper of Leray [10] we introduce a class of weak solutions to the Navier-Stokes-Fourier system based on the concept of generalized derivatives (distributions). The main objective of the present paper is to illustrate the strength of the abstract theory reviewing several theoretical results on the asymptotic behavior of the weak solutions that are in good agreement with practical experiments as well as their numerical analysis.The main topics to be discussed include the following: [ABSTRACT FROM AUTHOR]

This paper presents a study of tunneling in saturated poro-elastoplastic soils by means of two and three-dimensional coupled numerical analyses. To perform 2D simulations of the excavation stage, we employ an approach proposed in a previous paper as an extension to the saturated case of the so-called "convergence-confinement" method. To validate the plane procedure, the comparison with results of several 3D simulations of the excavation of shallow pervious tunnels is considered. By means of the hydro-mechanically coupled formulation employed in these comparisons, we investigate the face-advance rate influence on soil response to excavation. The proposed 2D method shows to be able to reproduce with satisfying approximation the effects of tunnel-face advancement on in-plane components of displacements and water flow. [ABSTRACT FROM AUTHOR]

This paper investigates the thermal properties of a new type of hollow sphere structures. For this new type, the sphere shell is perforated by several holes in order to open the inner sphere volume and surface. The effective thermal conductivity of perforated sphere structures in several kinds of arrangements is numerically evaluated for different hole diameters. The results are compared to classical configurations without perforation. In the scope of this study, three-dimensional finite element analysis is used in order to investigate simple cubic, body-centered cubic, face-centered cubic and hexagonal unit cell models. A linear behavior was found for the heat conductivity of different hole diameters for several kinds of arrangements when the results are plotted over the average density. [ABSTRACT FROM AUTHOR]

Restarted GMRES(k) method with iterative refinement process for approximated solutions was proposed by Imakura, et al. They referred to it as IR-GMRES(k) method. Convergence of this IRGMRES(k) method depends on accuracy of the initial approximated solutions adopted at restarting phase. Then it is crucial to examine how to give preferable initial approximated solutions. Therefore, in this paper, we consider reasonable givings for the initial approximated solutions when IR-GMRES(k) method restarts, and discuss validity and robustness of our proposed givings through several numerical experiments. [ABSTRACT FROM AUTHOR]

This paper deals with a coupled system of non-linear elliptic differential equations arising in electrodeposition modelling process. We show the existence and uniqueness of the solution. A numerical algorithm to compute an approximation of the weak solution is described. We introduce a domain decomposition method to take in account the anisotropy of the solution. We show the domain decomposition method convergence. A numerical example is presented and commented. [ABSTRACT FROM AUTHOR]

State estimation is necessary in diagnosing anomalies inWater Demand Systems (WDS). In this paper we present a neural network performing such a task. State estimation is performed by using optimization, which tries to reconcile all the available information. Quantification of the uncertainty of the input data (telemetry measures and demand predictions) can be achieved by means of robust estate estimation. Using a mathematical model of the network, fuzzy estimated states for anomalous states of the network can be obtained. They are used to train a neural network capable of assessing WDS anomalies associated with particular sets of measurements. [ABSTRACT FROM AUTHOR]

The evaporation of liquid droplets is of fundamental importance to industry, with a vast number of applications including ink-jet printing, spray cooling and DNA mapping, and has been the subject of considerable theoretical and experimental research in recent years. Significant recent papers include those by Deegan [1], Deegan et al. [2], Hu and Larson [3], Poulard et al. [4], Sultan et al. [5], and Shahidzadeh-Bonn et al. [6]. [ABSTRACT FROM AUTHOR]

Thin-film flows occur in a variety of physical contexts including, for example, industry, biology and nature, and have been the subject of considerable theoretical research. (See, for example, the review by Oron, Davis and Bankoff [4].) In particular, there are several practically important situations in which an external airflow has a significant effect on the behaviour of a film of fluid, and consequently there has been considerable theoretical and numerical work done to try to understand better the various flows that can occur. (See, for example, the studies by King and Tuck [2] and Villegas-Díaz, Power and Riley [6].) The flow of a rivulet on a planar substrate subject to a shear stress at its free surface has been investigated by several authors, notably Myers, Liang and Wetton [3], Saber and El-Genk [5], and Wilson and Duffy [9]. All of these works concern a non-perfectly wetting fluid; the flow of a rivulet of a perfectly wetting fluid in the absence of a shear stress at its free surface has been treated by Alekseenko, Geshev and Kuibin [1], and by Wilson and Duffy [7,8]. In the present short paper we use the lubrication approximation to obtain a complete description of the steady unidirectional flow of a thin rivulet of a perfectly wetting fluid on an inclined substrate subject to a prescribed uniform longitudinal shear stress at its free surface. [ABSTRACT FROM AUTHOR]

This paper introduces the principles of creating the web-tool on differential equations. It can be used to support European Master Program for Mathematics in Industry. Such a Program is working already on the leading partner universities of ECMI and now the use of e-study as an innovational step is being discussed. [ABSTRACT FROM AUTHOR]

In this paper we will show an industrial application of a new framework, called LaTEX2WeB, which translates LaTEX material into an interactive Web-based document. The more important characteristic of LaTEX2WeB is the possibility of integrating, in the Web-based document, external programs produced in every languages. We exploited LaTEX2WeB to create an interactive Web-based manual, which illustrates a new software for the multiobjective optimization applied to the parameter extraction in circuit design. Thanks to LaTEX2WeB it was possible to simulate the algorithms written in C, C++, and FORTRAN, used in the multiobjective optimization software. [ABSTRACT FROM AUTHOR]

In this paper we consider the recovery of ellipsoidal 3D shapes with piecewise constant coefficients in Diffuse Optical Tomography (DOT). We use an adjoint scheme for calculating gradients for the shape parameters defining the unknown ellipsoids, and a Newton-type optimisation process for the minimization of a least squares data misfit functional. A boundary integral formulation is used for the forward modelling. An advantage of the proposed method is the implicit regularisation effect arising from the reduced dimensionality of the inverse problem. Results of a numerical experiment in 3D are shown which demonstrate the performance of the method. [ABSTRACT FROM AUTHOR]

In this paper we demonstrate model order reduction of a nonlinear academic model of a diode chain. Two reduction methods, which are suitable for nonlinear differential algebraic equation systems are used, the trajectory piecewise linear approach and the proper orthogonal decomposition with missing point estimation. [ABSTRACT FROM AUTHOR]

The general question which will make the object of this paper is the homogenization of some nonlinear problems arising in the modelling of thermal diffusion in a two-component composite. We shall consider, at the microscale, a periodic structure formed by two materials with different thermal properties. We shall deal with two situations: in the first one, we assume that we have some nonlinear sources acting in both components and that at the interface between our two materials the temperature and the flux are continuous, while in the second problem we shall address here, we assume that the flux is still continuous, but depends in a nonlinear way on the jump of the temperature field. In both cases, since the characteristic sizes of these two components are small compared with the macroscopic length-scale of the flow domain, we can apply an homogenization procedure. [ABSTRACT FROM AUTHOR]

The correct simulation of industrial plants firing pulverized fuels (pf: coal, biomass, etc.) by means of commercial CFD codes relies on a number of submodels for the various processes, including, e.g. heat transfer (radiation, conduction through deposits, etc.) and particle combustion. The latter is of major importance in the design of the combustion chamber and the selection of the mills or, conversely, regarding the feasibility of burning a new fuel in an existing boiler. In the last decade, the introduction of new, internationally traded coals and alternative fuels into the power market has motivated renewed interest in the experimental and theoretical characterization of the combustion of these fuels. Regarding experimentation, it is generally accepted that the ‘reactivity' of a fuel can not be determined in desktop analytical instruments; instead, drop tube furnaces or entrained flow reactors (EFR) must be used in order to reproduce the high temperature, high heating rate conditions found in a real pf combustion chamber [1]. Several alternative experimental procedures have been developed in the past and are still used (see, e.g. [2, 3]). On the other hand, two general approaches are used in the literature to model pulverized coal/biomass char combustion: one intends to characterize the evolution of the pores inside the burning particle, and considers both internal and external diffusion, whereas the kinetics for the basic homogeneous and heterogeneous reactions are taken from low temperature analysis or fundamental knowledge of the chemistry involved (e.g. [4]); the other one, followed here, makes use of an apparent kinetics based on the outer particle surface, and includes external diffusion [5]. In the latter case, two parameters governing an Arrhenius-like kinetics are the main unknowns to be determined from the experiments performed in an EFR. The aim of this paper is to discuss some aspects of the mathematical procedure for the determination of those parameters. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to contribute to the mathematical modelling of the combustion of coal particles in pulverised coal furnaces, and also to propose an algorithm for its numerical solution. The mathematical model includes two coupled phases: the solid phase, for the coal particles, where a Lagrangian description is used and an Eulerian description for the gas phase, where the effects of the combustion of coal particles are homogenised. [ABSTRACT FROM AUTHOR]

This paper is concerned with a fascinating phenomenon in boundary layer transition, namely, three-dimensional disturbances undergo rapid amplification despite that they have smaller linear growth rates than two-dimensional ones. Physical mechanisms are sought by considering two types of nonlinear interactions between oblique and planar instability modes. The first is the well-known subharmonic resonance. The relevant mathematical theory and its main predictions are briefly summarised. This mechanism, however, operates only among a very restrictive set of modes, and hence is unable to explain the broadband nature of the amplifying disturbances observed in experiments. The second mechanism involves the interaction between a planar and a pair of oblique Tollmien—Schlichting (T—S) waves which are phase-locked in that they travel with (nearly) the same phase speed. It is a more general type of interaction than subharmonic resonance since no further restriction is imposed on the frequencies. Yet similar to subharmonic resonance, this interaction also leads to super-exponential growth of the oblique modes, while the planar mode remains to follow linear stability theory. The dominant planar mode therefore plays the role of a catalyst, the implications of which for the eN-method and for transition control are discussed. [ABSTRACT FROM AUTHOR]

This paper deals with mathematical modelling and numerical simulation of induction heating furnaces for axisymmetric geometries. The mathematical model presented consists in a coupled thermo-magneto-hydrodynamic problem with phase change. We propose a finite element method and an iterative algorithm to solve the equations. Some numerical results for an industrial furnace used for silicon purification are shown. [ABSTRACT FROM AUTHOR]

Rank-1 lattice rules based on a weighted star discrepancy with weights of a product form have been previously constructed under the assumption that the number of points is prime. Here, we extend these results to the non-prime case. We show that if the weights are summable, there exist lattice rules whose weighted star discrepancy is O(n−1+δ), for any δ > 0, with the implied constant independent of the dimension and the number of lattice points, but dependent on δ and the weights. Then we show that the generating vector of such a rule can be constructed using a component-by-component (CBC) technique. The cost of the CBC construction is analysed in the final part of the paper. [ABSTRACT FROM AUTHOR]

It has been found recently that an increase in phase space dimension by including simulated auxiliary random variables in the number of phase coordinates can be effective for the construction of weight modifications. In this paper the effectiveness of "value" and partial "value" modelling is considered. These types of modelling are related to the construction of simulated distribution for some auxiliary random variable by multiplying the initial density by the "value" function which is usually corresponds to the solution of adjoint integral equation of the second kind. It is proved that the weight estimator variance in case of the partial value modelling is finite. On the basis of this fact a new criterion based on the use of majorant adjoint equation was proposed for finiteness of the weight estimator variance. Using this criterion the classical "exponential transformation" method is studied for the free path simulation in one and three dimensional modifications. [ABSTRACT FROM AUTHOR]

The (weighted) dyadic diaphony is a measure for the irregularity of distribution modulo one of a sequence. Recently it has been shown that the (weighted) dyadic diaphony can be interpreted as the worst-case error for QMC integration in a certain Hilbert space of functions. In this paper we give upper bounds on the weighted dyadic diaphony of digital (t, s)-sequences over ℤ2. [ABSTRACT FROM AUTHOR]

We study approximation of functions belonging to Sobolev spaces Wrp (Q) by randomized algorithms based on function values. Here 1 ≤ p ≤ ∞, Q = [0, 1]d, and r, d ∈ N. The error is measured in Lq(Q), with 1 ≤ q < ∞, and we assume r/d > 1/p − 1/q, guaranteeing that Wrp(Q) is embedded into Lq(Q). The optimal order of convergence for the case that Wrp(Q) is embedded even into C(Q) is wellknown. It is n−r/d+max(1/p−1/q,0) (n the number of function evaluations). This rate is already reached by deterministic algorithms, and randomization gives no speedup. In this paper we are concerned with the case that Wrp(Q) is not embedded into C(Q) (but, of course, still into Lq(Q)). For this situation approximation based on function values was not studied before. We prove that for randomized algorithms the above rate also holds, while for deterministic algorithms no rate whatsoever is possible. Thus, in the case of low smoothness, Monte Carlo approximation algorithms reach a considerable speedup over deterministic ones (up to n−1+ε for any ε > 0). We also give some applications to integration of functions and to approximation of solutions of elliptic PDE. [ABSTRACT FROM AUTHOR]

We study approximation of continuous linear functionals Id defined over reproducing kernel weighted Hilbert spaces of d-variate functions. Let n(ε, Id) denote the minimal number of function values needed to solve the problem to within ε. There are many papers studying polynomial tractability for which n(ε, Id) is to be bounded by a polynomial in ε−1 and d. We study generalized tractability for which we want to guarantee that either n(ε, Id) is not exponentially dependent on ε−1 and d, which is called weak tractability, or is bounded by a power of T(ε−1, d) for (ε−1, d) ∈ Ω ⊆ [1,∞) × N, which is called (T,Ω)-tractability. Here, the tractability function T is non-increasing in both arguments and does not depend exponentially on ε−1 and d. We present necessary conditions on generalized tractability for arbitrary continuous linear functionals Id defined on weighted Hilbert spaces whose kernel has a decomposable component, and sufficient conditions on generalized tractability for multivariate integration for general reproducing kernel Hilbert spaces. For some weighted Sobolev spaces these necessary and sufficient conditions coincide. They are expressed in terms of necessary and sufficient conditions on the weights of the underlying spaces. [ABSTRACT FROM AUTHOR]

In this paper we show that the Milstein scheme can be used to improve the convergence of the multilevel Monte Carlo method for scalar stochastic differential equations. Numerical results for Asian, lookback, barrier and digital options demonstrate that the computational cost to achieve a root-mean-square error of ε is reduced to O(ε-2). This is achieved through a careful construction of the multilevel estimator which computes the difference in expected payoff when using different numbers of timesteps. [ABSTRACT FROM AUTHOR]

In analogy to a recent paper by Kuo, Sloan, and Woźniakowski, which studied lattice rule algorithms for approximation in weighted Korobov spaces, we consider the approximation problem in a weighted Hilbert space of Walsh series. Our approximation uses a truncated Walsh series with Walsh coefficients approximated by numerical integration using digital nets. We show that digital nets (or more precisely, polynomial lattices) tailored specially for the approximation problem lead to better error bounds. The error bounds can be independent of the dimension s, or depend only polynomially on s, under certain conditions on the weights defining the function space. [ABSTRACT FROM AUTHOR]

DX-k, proposed by Deng and Xu [2003], is a special class of multiple Recursive Generators (MRGs) where all nonzero coefficients of the k-th order recurrence are equal. In particular, a DX-k generator requires only up to four nonzero coefficients in its recurrence equation, hence is very efficient in computation. However, a random number generator with few nonzero coefficients has a drawback that, when the k-dimensional state vector is close to the zero vector, the subsequent numbers generated may stay within a neighborhood of zero for quite many of them before they can break away from this near-zero land, a property apparently not desirable in the sense of randomness. Consequently, two generated sequences using the same DX generator with nearly identical initial state vectors may not depart from each other quickly enough. To avoid the above potential problem, we consider MRGs with very few zero coefficients. To make such generators efficient and portable, we propose selecting the same nonzero value for all coefficients (with at most one exception) in the recurrence equation. With this feature, the proposed generators can be implemented efficiently via a higher-order recurrence of few zero coefficients. Note that the new class of generators is an opposite of the DX generators in terms of the number of nonzero coefficients. Several such generators with the maximum period have been found via computer search and presented in the paper for ready implementation. [ABSTRACT FROM AUTHOR]

Some computer graphics applications, such as architectural design, generate visually realistic images of computer models. This is accomplished by either explicitly or implicitly solving the light transport equations. Accurate solutions involve high-dimensional equations, and Monte Carlo (MC) techniques are used with an emphasis on importance sampling rather than stratification. For many applications, approximate solutions are adequate, and the dimensionality of the problem can be reduced. In these cases, the distribution of samples is important, and quasi-Monte Carlo (QMC) methods are often used. It is still unknown what sampling schemes are best for these lower dimensional graphics problems, or what "best" even means in this case. This paper reviews the work in MC and QMC computer graphics, and poses some open problems in the field. [ABSTRACT FROM AUTHOR]

In this paper I present some new approaches to the random field simulation, and show in four different examples how this simulation technique works. The first example deals with a transport in turbulent flows, where the Lagrangian trajectories are described by a stochastic differential equation whose drift term involves the Eulerian velocity as a random field with a given spectral tensor. Studies of the second example concern with the flows in porous medium governed by the Darcy equation with random hydraulic conductivity. Elasticity system of elliptic Lamé equations with random loads is considered in the third example. Finally, in the fourth example we solve a nonlinear Smoluchowski equation which is used to model the process of crystal growth. [ABSTRACT FROM AUTHOR]

In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a Hilbert -valued random variable, using a nearest neighbour projection on a finite codebook. A special emphasis is made on the computational aspects and the numerical applications, in particular the pricing of some path-dependent European options. [ABSTRACT FROM AUTHOR]

Nets and (t, s)-sequences are standard sources of quasirandom points for quasi-Monte Carlo methods. Connections between nets and error-correcting codes have been noticed for a long time, and these links have become even more pronounced with the development of the duality theory for digital nets. In this paper, we further explore these fascinating connections. We present also a recent construction of digital (t, s)-sequences using global function fields and new general constructions of nets and (t, s)-sequences. [ABSTRACT FROM AUTHOR]

Wavelet transforms or wavelet analysis is a recently developed mathematical tool for many problems. Wavelets also can be applied in numerical analysis. In this paper, we apply Haar wavelet methods to solve ordinary differential equations with initial condition known. To avoid the tedious calculations and to promote the study of wavelets to beginners, we proposed a simple way to perform the calculations for the matrix representation. Three numerical examples are shown which including first, second, higher order differential equations with constant and variable coefficients. The results show that the proposed way are quite reasonable when compare to exact solution. [ABSTRACT FROM AUTHOR]

In a recent paper, Herty and Rascle (SIAM J. Appl. Math. 38:595-616, 2006) introduced some coupling conditions to model road junctions with the Aw-Rascle traffic flow model (Aw and Rascle, SIAM J. Appl. Math. 60:916-944, 2000). In this chapter, we study an extension of the work in Herty and Rascle (SIAM J. Appl. Math. 38:595-616, 2006). Here, in contrast to Herty and Rascle (SIAM J. Appl. Math. 38:595-616, 2006), we propose a general formulation for suitable coupling conditions at an intersection, without imposing any fixed mixture principle. The solution conserves mass and "pseudomomentum" and additionally maximizes the total (mass) flux at an intersection. This problem has been completely solved in the cases of 2 → 1 (merge) and 1 → 2 (diverge) junctions. Furthermore these two simple cases of merging and diverging junctions can be combined to model more complex junctions, like roundabouts. [ABSTRACT FROM AUTHOR]

We present second-order accurate central finite volume methods adapted here to three-dimensional problems in ideal magnetohydrodynamics. These methods alternate between two staggered grids, thus leading to Riemann solver-free algorithms with relatively favorable computing times. The original grid considered in this paper is Cartesian, while the dual grid features either Cartesian or diamond-shaped oblique dual cells. The div.B = 0 constraint on the magnetic field is enforced with a suitable adaptation of the constrained transport method to our central schemes. Numerical experiments show the feasibility of these methods and our results are in good agreement with existing results in the literature. [ABSTRACT FROM AUTHOR]

This paper reviews recent contributions to the numerical approximation of solutions of nonconservative hyperbolic systems with singular viscous perturbations. Various PDE models for complex compressible materials enter the proposed framework. Due to lack of a conservative form in the limit systems, associated weak solutions are known to heavily depend on the underlying viscous regularization. This small scales sensitiveness drives the classical approximate Riemann solvers to grossly fail in the capture of shock solutions. Here, small scales sensitiveness is encoded thanks to the notion of kinetic functions so as to consider a set of generalized jump conditions. To enforce for validity these jump conditions at the discrete level, we describe a systematic and effective correction procedure. Numerical experiments assess the relevance of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is devoted to the numerical solution of the instationary Maxwell equations in singular waveguides. The geometry is called singular, in the sense that its boundary can include reentrant corners or edges. The difficulties arise from the fact that those geometrical singularities generate, in their neighborhood, strong electromagnetic fields. Using some new theoretical and practical results on singular electromagnetic fields, we have built a method which allows to compute the time-dependent electromagnetic field. It is based on a splitting of the spaces of solutions into a two-term direct (orthogonal) sum. First, the subspace of regular fields, which coincides with the whole space of solutions, in the case of convex or smooth boundary. Second, a singular subspace, defined and characterized via the singularities of the Laplace operator. Numerical results are presented to illustrate how the frequency of the ingoing electromagnetic waves influences the singular solution in a L-shaped waveguide. [ABSTRACT FROM AUTHOR]

In recent years, a high speed and accurate optimization method has been expected for large scale nonlinear programming problems. As a new solution method for nonlinear programming problems, a particle swarm optimization (PSO) method was proposed by Kennedy et al. and has attracted considerable attention. However, there exist few reports with respect to successful results for constrained nonlinear programming problems by PSO-based methods. Furthermore, PSO-based methods have a shortcoming that the search is liable to stopping at a certain local solution. In this paper, incorporating the bisection method and a homomorphous mapping to carry out the search considering constraints as well as the multiple stretching technique and modified move schemes of particles to restraining the stopping around local solutions. Furthermore, we show the efficiency of the proposed revised PSO method (rPSO) by comparing it with an existing method through the application of them into the numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the Newton's method is applied to linearize a nonlinear Fredholm integral equation of the second kind and obtain a linear Fredholm integral equation and so we found the Tau's numerical solution of the linear form. [ABSTRACT FROM AUTHOR]

This paper is concerned with the identical synchronization problem for a class of chaotic systems. Under certain conditions, a dynamic compensator is proposed to achieve the synchronization only using the accessible output variables. A numerical example is included to demonstrate the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper we summarize some recent results on the asymptotic behavior of a linearized model arising in fluid-structure interaction, where a wave and a heat equation evolve in two bounded domains, with natural transmission conditions at the interface. These conditions couple, in particular, the heat unknown with the velocity of the wave solution. First, we show the strong asymptotic stability of solutions. Next, based on the construction of ray-like solutions by means of Geometric Optics expansions and a careful analysis of the transfer of the energy at the interface, we show the lack of uniform decay of solutions in general domains. Finally, we obtain a polynomial decay result for smooth solutions under a suitable geometric assumption guaranteeing that the heat domain envelopes the wave one. The system under consideration may be viewed as an approximate model for the motion of an elastic body immersed in a fluid, which, in its most rigorous modeling should be a nonlinear free boundary problem, with the free boundary being the moving interface between the fluid and the elastic body. [ABSTRACT FROM AUTHOR]

We consider a procedure for cancer therapy which consists of injecting replication-competent viruses into the tumor. The viruses infect tumor cells, replicate inside them, and eventually cause their death. As infected cells die, the viruses inside them are released and then proceed to infect adjacent tumor cells. However, a major factor influencing the efficacy of virus agents is the immune response that may limit the replication and spread of the replication-competent virus. The immune response is cytokine-mediated. The expression of viruses in tumor cells sensitize cells to lysis by the TNF (tumor necrosis factor) cytokine. The competition between tumor cells, a replication-competent virus and an immune response is modelled as a free boundary problem for a nonlinear system of partial differential equations, where the free boundary is the surface of the tumor. In this model, the immune response equation is a non-standard parabolic equation due to the chemotaxis (spatial gradients of diffusible chemicals) of the immune response. The purpose of this paper is to give the numerical methods for solving this kind of free boundary problems. Several simulation results are also given. [ABSTRACT FROM AUTHOR]

In this paper we develop further the "height fraction" technique for computing curvature directly from volume fractions. In particular we, (1) develop a systematic approach for calculating curvature from volume fractions which is accurate to any order, and (2) we test the second-order "height fraction" technique on the following two-phase problems: (1) the break-up of a cylindrical column of liquid due to Rayleigh-capillary instability, (2) surface tension induced droplet oscillations and (3) the steady motion of gas bubbles rising in liquid. [ABSTRACT FROM AUTHOR]

The first part of this paper is an announcement of a result to appear. We apply the Aleksandrov reflection to obtain regularity and stability of the free boundaries in the two-dimensional problem $$ \Delta u = \frac{{\lambda _ + }} {2}\chi \{ u > 0\} - \frac{{\lambda _ - }} {2}\chi \{ u < 0\} ,$$ where λ+ > 0 and γ− > 0. In the second part we show that the Kelvin reflection can be used in a similar way to obtain regularity of the classical obstacle problem $$ \Delta u = \chi \{ u > 0\}$$in higher dimensions. [ABSTRACT FROM AUTHOR]

In this note we summarize some results of a forthcoming paper (see [15]), where we examine, in particular, the long time behavior of the so-called quasistationary phase field model by using a gradient flow approach. Our strategy in fact, is inspired by recent existence results which show that gradient flows of suitable non-convex functionals yield solutions to the related quasistationary phase field systems. Thus, we firstly present the long-time behavior of solutions to an abstract non-convex gradient flow equation, by carefully exploiting the notion of generalized semiflows by J.M. Ball and we provide some sufficient conditions for the existence of the global attractor for the solution semiflow. Then, the existence of the global attractor for a proper subset of all the solutions to the quasistationary phase field model is obtained as a byproduct of our abstract results. [ABSTRACT FROM AUTHOR]

In this note it is shown that the weak solutions of the Stefan problem for the singular p-Laplacian are continuous up to {t = 0}. The result is a follow-up to a recent paper of the authors concerning the interior regularity. [ABSTRACT FROM AUTHOR]

We consider a gradient flow system of total variation with constraint. Our system is often used in the color image processing to remove a noise from picture. In particular, we want to preserve the sharp edges of picture and color chromaticity. Therefore, the values of solutions to our model is constrained in some fixed compact Riemannian manifold. By this reason, it is very difficult to analyze such a problem, mathematically. The main object of this paper is to show the global solvability of a constrained singular diffusion equation associated with total variation. In fact, by using abstract convergence theory of convex functions, we shall prove the existence of solutions to our models with piecewise constant initial and boundary data. [ABSTRACT FROM AUTHOR]

We present a numerical method for tracking breaking waves over sloping beaches. We use a fully non-linear potential model for incompressible, irrotational and inviscid flow, and consider the effects of beach topography on breaking waves. The algorithm uses a Boundary Element Method (BEM) to compute the velocity at the interface, coupled to a Narrow Band Level Set Method to track the evolving air/water interface, and an associated extension equation to update the velocity potential both on and off the interface. The formulation of the algorithm is applicable to two- and three-dimensional breaking waves; in this paper, we concentrate on two-dimensional results showing wave breaking and rollup, and perform numerical convergence studies and comparison with previous techniques. [ABSTRACT FROM AUTHOR]