Boundary Element Methods

The interaction of electromagnetic waves with pairs of nanotubes having arbitrary-shaped cross sections is investigated. The study starts by thoroughly examining nanotube couples with circular boundaries to identify the structural, textural and excitation parameters that enhance the electric field concentration. Such an initial step generates a design space across which the regions of interest are determined to formulate a shape optimization problem targeting at the maximization of the signal internally to the nanotubes by modifying their boundary surface while maintaining the values for the remaining operational parameters. An IsoGeometric-Analysis-based Boundary Element Method (IGABEM) is employed for estimating the electric field around nanotube boundaries, which is subsequently used towards the overall solution of the boundary value problem. A hybrid optimization approach, employing global and local optimizers, along with two geometric parametric models that generate valid nanotube cross sections complement the IGABEM method in the quest of optimal designs. The achieved optimal shapes attain substantial boost in the concentration of the electric field which can easily exceed, by 30 times or more, the corresponding value obtained by circular nanotube pairs. This superior performance is maintained for a large range of wave angles and nanotube areas and, accordingly, the robustness of the obtained results and their potential applicability in a wide range of applications, is demonstrated. Finally, the computational method developed in this work can be easily extended for analyzing a finite array of nanotubes, while insights gained by the reported optimal shapes pave the way for their optimization and fine tuning in collective setups like electromagnetic gratings and photonic metasurfaces.

Abstract. This paper discusses a method based on Laguerre polynomials co mbined with a Filtered Conjugate Residual (FCR) framework to compute the product of the exponen tial of a matrix by a vector. The method implicitly uses an expansion of the exponential function in a series of o rthogonal Laguerre polynomials, much like existing methods based on Chebyshev polynomials do. Owing to the fact th t orthogonal polynomials satisfy a three-term recurrence, what these series expansion methods offer over o ther approaches such as Krylov subspace methods lies in the elimination of inner products and the economy in storage since there is no need to compute and keep a set of basis vectors. Compared with Chebyshev polynomials that ar e orthogonal within a restricted interval and need estimates of the outermost eigenvalues, Laguerre polynomials offer the added feature that they are orthogonal on the half real line, alleviating therefore the need to estimate ei g nvalues.

This paper proposes induction hardening method of gear used in a conveyor. The heating analysisin case of treat piece needs solution with thermal diffusion problems coupled with eddy currents problem. Therefore the experiments number in designing process can be decreased for a better knowledge of the process can be obtained.

The study of defected axisymmetric structures is among important industrial applications. Detection of such defects, and or the evaluation of intrinsic parameter leads to a better design of those mechanical parts. The first part of the conducting research concerns the evaluation of the stress intensity factors (SIF) in axisymmetric elastic structures with internal or circumferential edge crack using the dual boundary element method (DBEM). Its application to axisymmetric problems requires a stress (hypersingular) boundary integral equation together with the displacement (standard) boundary integral equation, one applied to each side of the crack. This process requires a great algebraic handling due to the complexity of the axisymmetric kernels. Crack surfaces are discretized with discontinuous quadratic boundary elements to satisfy the existence of the finite-part integrals and the continuity of the unit outward normal at corners. SIF evaluation is done using displacements extrapolation at the crack tip. Examples of axisymmetric geometries are analyzed and obtained results are compared to others researchers.

This paper presents the several possibilities of using the Coons' interpolation in both CAD and CAE applications. It is shown that not only curvilinear surfaces may be interpolated (as it is well known from the literature), but also finite element meshes may be developed in any arbitrarily-shaped domain. Moreover, it is shown how it is possible to built-up isoparametric macro-finite-elements with degrees of freedom appearing at the boundaries only, using global shape functions that are based on the same interpolation. The theory is sustained by one typical two-dimensional application of a U-notched elastic structural member.

We consider a collocation method for Cauchy singular integral equations on an interval based on weighted polynomials. Using Banach algebra methods, necessary and sufficient stability conditions are given in the case of continuous coefficients.

We consider a collocation method for Cauchy singular integral equations on an interval based on weighted polynomials. Using Banach algebra methods, necessary and sufficient stability conditions are given in the case of continuous coefficients.

This paper is concerned with the stability of collocation methods for Cauchy singular integral equations with fixed singularities on the interval [-1, 1]. The operator in these equations is supposed to be of the form aL+bS+B-+/- with piecewise continuous functions a and b. The operator S is the Cauchy singular integral operator and B-+/- is a finite sum of integral operators with fixed singularities at the points +/- 1 of special kind. The collocation methods search for approximate solutions of the form nu(x)p(n)(x) or mu(x)p(n)(x) with Chebyshev weights nu(x) = root 1+ x/1-x or mu(x) = root 1-x/1+x, respectively, and collocation with respect to Chebyshev nodes of first and third or fourth kind is considered. For the stability of collocation methods in a weighted L-2-space, we derive necessary and sufficient conditions.

The main concrete result of this paper is the first explicit construction of constant degree lossless expanders. In these graphs, the expansion factor is almost as large as possible: , where is the degree and is an arbitrarily small constant. Such graphs are essential components in networks that can implement fast distributed, routing algorithms e.g. (PU89, ALM96, BFU99). They are

Detailed modeling of the free solution electrophoresis of five proteins (bovine R-lactalbumin, hen egg white lysozyme, bovine superoxide dismutase, human carbonic anhydrase II, and hen ovalbumin) is carried out within the framework of the continuum primitive model. Protein crystal structures and translational diffusion constants are used to design and parametrize the models. The modeling results are compared with experimental mobilities of protein charge ladders, collections of protein derivatives where the number of charge groups is varied by partial acylation of lysine residues or by amidation of glutamic and aspartic acid residues. The simplest model considered is the Yoon and Kim model of a prolate/oblate ellipsoid with uniform surface potential, electrostatics treated at the level of the linear Poisson-Boltzmann equation, and distortion of the ion atmosphere from equilibrium (ion relaxation) ignored (Yoon, B. J.; Kim, S. J. Colloid Interface Sci. 1989, 128, 275). This model provides good agreement with experiment but only if the net absolute protein charge is low or the average absolute surface, or ζ, potential is less than ∼25 mV. Boundary element (BE) modeling is also carried out in which detailed surface models are employed and the electrostatics are solved at the level of the nonlinear Poisson-Boltzmann equation. Ion relaxation is also included in some of the BE studies. All of the experimental mobilities are in good (human carbonic anhydrase II and hen ovalbumin) to excellent (bovine R-lactalbumin, hen egg white lysozyme, and bovine superoxide dismutase) agreement with BE modeling that includes ion relaxation. We believe that these results taken as a whole serve to confirm the ability of the continuum primitive model to predict, with quantitative accuracy, the free solution electrophoretic mobilities of proteins, provided the underlying models are sufficiently realistic. When a discrepancy occurs, it may be due to error in modeling either the protein charge or the solution conformation. The models described in this work also provide a useful approach for determining values of ∆Z, the change in net charge of proteins due to the chemical modification of charged groups. Knowledge of ∆Z is essential for the use of protein charge ladders in the quantitative description of the electrostatic properties and interactions of proteins. This paper supports the view that the continuum primitive model may be more appropriate for the modeling of electrokinetics than for electrostatics. The main challenge to the accurate predictions of electrophoretic mobilities may lie primarily in the modeling of electrostatics, not electrokinetics.

In this work, boundary element modeling is used to study the transport of highly charged rod-like model polyions of various length under a variety of different aqueous salt conditions. Transport properties considered include free solution electrophoretic mobility, translational diffusion, and the components of the "tether force" tensor. The model parameters are chosen to coincide with transport measurements of duplex DNA carried out under six different salt/ temperature conditions. The focus of the analysis is on the length dependence of the free solution electrophoretic mobility. In a solution containing 0.04 M Tris-acetate buffer at 25°C, calculated mobilities using straight rod models show a stronger dependence on fragment length than that observed experimentally. By carrying out model studies on curved rod models, it is concluded that the "leveling off" of mobility with fragment length is due, in part at least, to the finite curvature of DNA. Experimental mobilities of long duplex DNA in monovalent alkali salts are reasonably well explained once account is taken of long-range bending and the simplifying assumptions of the model studies.

Le problème de l'évaluation de l'intensité et de la cohérence du signal sonore reçu par les systèmes de détection sous-marine est résolu en milieu déterministe. Dans cette étude on introduit une composante aléatoire dans la célérité du milieu modélisant les fluctuations aléatoires du milieu marin. Pour caractériser ces effets du milieu sur la propagation sonore, l'estimation des moments du champ sonore est nécessaire. On rappelle les équations de propagation des moments du champ sonore en milieu aléatoire en présence d'un bruit blanc gaussien (perturbations du milieu marin dues aux ondes internes): équations de propagation paraboliques des moments du champ sonore obtenues par Tatarskii. L'obtention de ces équations peut être généralisée dans le formalisme de Ito . De plus alors, l'application du théorème limite de Papanicolaou-Kohler permet d'affaiblir les hypothèses sur l'indice de réfraction et d'estimer le domaine de validité des équations paraboliques des moments.

This present work refers to the construction of a scratch test machine build in the Federal University of Rio de Janeiro. The Scratch test is used to quantify the quality of a coating material. It is used to study material, failure, and development of theories of coating. This test consists on a tip used to scratch the coating and measure the normal and friction force necessary to break the coating. The scratch test was conceived taking advantage of an ABBE-Komparator. Tree systems were developed to convert this machine. One to move the specimen, other to apply a normal force, and another to measure de friction force. Those systems were designed to allow the machine to be used in the former use with little trouble. The system used to apply normal force was conceived using pneumatics, and was conceived to apply forces up to 200 N. The drive system was designed using a rolled ball precision screw. The velocity of the specimen is specified up to 10 mm/min. Both the normal and friction ...

The DECOVALEX project is an international cooperative project initiated by SKI, the Swedish Nuclear Power Inspectorate, with participation of about 10 international organizations. The general goal of this project is to encourage multidisciplinary interactive and cooperative research on modelling coupled thermo-hydro-mechanical-chemical (THMC) processes in geologic formations in support of the performance assessment for underground storage of radioactive waste. One of the research tasks, initiated in 2004 by the U.S. Department of Energy (DOE), addresses the long-term impact of geomechanical and geochemical processes on the flow conditions near waste emplacement tunnels. Within this task, four international research teams conduct predictive analysis of the coupled processes in two generic repositories, using multiple approaches and different computer codes. Below, we give an overview of the research task and report its current status.

The Indirect Boundary Element Method (IBEM) is used to compute the seismic response of a three-dimensional rockfill dam model. The IBEM is based on a single layer integral representation of elastic fields in terms of the full-space Green function, or fundamental solution of the equations of dynamic elasticity, and the associated force densities along the boundaries. The method has been applied to simulate the ground motion in several configurations of surface geology. Moreover, the IBEM has been used as benchmark to test other procedures. We compute the seismic response of a threedimensional rockfill dam model placed within a canyon that constitutes an irregularity on the surface of an elastic half-space. The rockfill is also assumed elastic with hysteretic damping to account for energy dissipation. Various types of incident waves are considered to analyze the physical characteristics of the response: symmetries, amplifications, impulse response and the like. Computations are performed in the frequency domain and lead to time response using Fourier analysis. In the present implementation a symmetrical model is used to test symmetries. The boundaries of each region are discretized into boundary elements whose size depends on the shortest wavelength, typically, six boundary segments per wavelength. Usually, the seismic response of rockfill dams is simulated using either finite elements (FEM) or finite differences (FDM). In most applications, commercial tools that combine features of these methods are used to assess the seismic response of the system for a given motion at the base of model. However, in order to consider realistic excitation of seismic waves with different incidence angles and azimuth we explore the IBEM.

Monthly cross shore beach profiles measured at the Ogata Wave Observation pier located in Joetsu-Ogata Coast, Niigata Prefecture, Japan, was analyzed to investigate multi-scale morphodynamic beach behavior. The Ogata beach, facing the Sea of Japan, is subjected to high energy wave conditions that has a strong winter/summer seasonal signature. The measured beach profiles at the beach show very significant variability where cross-shore movement of shoreline position and lowering of the beach at the location of measurements exceed 20 and 4 m respectively. The shoreline position seems to follow the seasonal variability of incident wave climate where a correlation coefficient of 0.77 was found between monthly averaged incident significant wave height and the measured monthly shoreline position. During the summer months, the beach variability mostly concentrated in the sub-tidal part of the profile, while a significant amount of upper beach change was observed during the winter months. The beach profile shape was found to rotate between three different beach states in time; (i) concave reflective profile; (ii) profile with sub-tidal berm; and (iii) gentle, dissipative profile. Empirical Orthogonal Function (EOF) analysis of the profiles show that the variability of beach profile shape is dominated by (a) upper shoreface steepening; (b) sub tidal berm development and dissipation; and (c) variability of the overall profile slope, which have some longer than seasonal cyclic signatures. Comparison of temporal EOFs with climate indices such as Southern Oscillation Index and Pacific Decadal Oscillation index shows some correlations between profile change and climatic variability in the region. The analysis also shows that the morphological variability of Joetsu-Ogata Coast has similarities and some distinct spatial and temporal differences to beaches of similar kind found elsewhere.

The majority of hydrocarbon reservoirs worldwide are fractured reservoirs, mostly hosted by sedimentary rocks. Fracture development in reservoirs is still poorly understood, and so is the associated permeability. Here we present new results on fracture networks in limestone and shale layers, part of the Lias Group of Early Jurassic (about 200 Ma), from Kilve, Southwest England. The fractures are mostly joints (extension or mode I fractures). The apertures of 300 measured fractures range from 0.1 to 16 mm, the great majority being in the range 0.1-2 mm, and follow a crude power-law size distribution. The fracture frequency is significantly higher in the limestone layers than in the shale layers, many of the limestone fractures becoming arrested (stopping their propagation) at the contacts with shale layers. More specifically, of the fractures that meet contacts there is similar number of arrested and penetrating fractures, whereas many fractures that penetrate change their attitude o...

The boundary element method is specially well suited for the analysis of the seismic response of valleys of complicated topography and stratigraphy. In this paper the method's capabilities are illustrated using as an example an irregularity stratified (test site) sedimentary basin that has been modelled using 2D discretization and the Direct Boundary Element Method (DBEM). Site models displaying different levels of complexity are used in practice. The multi-layered model's seismic response shows generally good agreement with observed data amplification levels, fundamental frequencies and the high spatial variability. Still important features such as the location of high frequencies peaks are missing. Even 2D simplified models reveal important characteristics of the wave field that ID modelling does not show up.

Knowledge on juvenile tree growth is crucial to understand how trees reach the canopy in tropical forests. However, long-term data on juvenile tree growth are usually unavailable. Annual tree rings provide growth information for the entire life of trees and their analysis has become more popular in tropical forest regions over the past decades. Nonetheless, tree ring studies mainly deal with adult rings as the annual character of juvenile rings has been questioned. We evaluated whether juvenile tree rings can be used for three Bolivian rainforest species. First, we characterized the rings of juvenile and adult trees anatomically. We then evaluated the annual nature of tree rings by a combination of three indirect methods: evaluation of synchronous growth patterns in the tree-ring series, 14 C bomb peak dating and correlations with rainfall. Our results indicate that rings of juvenile and adult trees are defined by similar ring-boundary elements. We built juvenile tree-ring chronologies and verified the ring age of several samples using 14 C bomb peak dating. We found that ring width was correlated with rainfall in all species, but in different ways. In all, the chronology, rainfall correlations and 14 C dating suggest that rings in our study species are formed annually.

The monotone iteration scheme is a constructive method for solving a wide class of semilinear elliptic boundary value problems. With the availability of a supersolution and a subsolution, the iterates converge monotonically to one or two solutions of the nonlinear PDE. However, the rates of such monotone convergence cannot be determined in general. In addition, when the monotone iteration scheme is implemented numerically through the boundary element method, error estimates have not been analyzed in earlier studies. In this paper, we formulate a working assumption to obtain an exponentially fast rate of convergence. This allows a margin δ \delta for the numerical implementation of boundary elements within the range of monotone convergence. We then interrelate several approximate solutions, and use the Aubin-Nitsche lemma and the triangle inequalities to derive error estimates for the Galerkin boundary-element iterates with respect to the H r ( Ω ) H^{r}(\Omega ) , 0 ≤ r ≤ 2 0\le r \...

First, I would like to express my profound gratitude to my PhD supervisors, Prof. Slim Chaabane and Prof. Houssem Haddar. I sincerely thank you both for your trust, granting me research freedom, your invaluable guidance and mentorship, and most importantly, for standing by my side during all the difficult moments. I would also like to extend my thanks to Professors Amel Ben Abda and Maher Moakher for agreeing to review this work and for the time they dedicated to reading and assessing this thesis, as well as for preparing their reports. I am deeply grateful to Professors Afif Masmoudi, Mondher Benjemaa, and Mohamed Hbaib for agreeing to be part of the jury. My appreciation extends to all the members of the Mathematics Department at the Faculty of Sciences of Sfax and the LAMHA laboratory for providing me with such a friendly and supportive environment. Special thanks to Bilel Charfi and Zouhour Jlali for our enjoyable discussions, and to Assistant Fatma Abid for her valuable administrative assistance. I also want to acknowledge my doctoral friends, Mariem Ammar, Yosra Barkaoui, Khouloud Dammak, and Chaima Hmani, with whom I shared many cherished moments during my thesis. Additionally, I want to express my gratitude to all the members of the IDEFIX team for their warmth and friendliness. A special thanks goes to Marcella, who provided invaluable assistance during my internship when we shared the same office, and to my doctoral and post-doctoral friends, Amal, Nouha, and Mohamed Aziz, for the fantastic moments we shared during my internships. A huge thank you to my friends Yassmine, Vanessa and Walid, who provided invaluable assistance during my stays in France and with whom I shared wonderful moments. Before I wrap up, I want to thank my friends whom I met in Albania during my participation in the CIMPA summer school and who have remained in contact with me, especially Ina Hila, Gazi Ozdemir and Destiny S. Lutero. Finally, I want to express my deepest gratitude to my family, with a special mention of my sister Hanen, for their unwavering support during these years of my thesis.

The modified mild slope equation of is solved using a combination of the boundary element method (BEM) and the finite difference method (FDM). The exterior domain of constant depth and infinite horizontal extent is solved by a BEM using linear or quadratic elements. The interior domain with variable depth is solved by a flexible order of accuracy FDM in boundary-fitted curvilinear coordinates. The two solutions are matched along the common boundary of two methods (the BEM boundary) to ensure continuity of value and normal flux. Convergence of the individual methods is shown and the combined solution is tested against several test cases. Results for refraction and diffraction of waves from submerged bottom mounted obstacles compare well with experimental measurements and other computed results from the literature.

Water entry (including slamming) and exit phenomena as well as green water on deck were observed during survivability model tests of a combined wind and wave energy converter concept. Here, a nonlinear numerical model based on a blended station-keeping potential-flow solver with a local impact solution for bottom slamming events and an approximated model for the water shipped on the deck is proposed to simulate these nonlinear phenomena. Viscous damping loads are modelled through empirical formulas. The comparisons between the numerical model and model tests are globally satisfactory in terms of platform motions, mooring-line tensions, and occurrence and features of water-entry, water-exit and water on deck events. The results show that, in almost all examined cases, the slamming starts from the center of the torus bottom, the water shipping occurs almost contemporary from the wave and lee side of the deck. In the shortest examined waves both phenomena start from the wave side. From the investigation, the water on deck is very effective in reducing the double wave frequency (2) component of the surge, heave and pitch motions for sufficiently large incident-wave periods and in reducing the mean surge and pitch motions close to the heave resonance. The slamming events have a limited effect on the body motions.

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In contrast with the well-known methods of matching asymptotics and multiscale (or compound) asymptotics, the "functional analytic approach" of Lanza de Cristoforis (Analysis 28, 2008) allows to prove convergence of expansions around interior small holes of size ε for solutions of elliptic boundary value problems. Using the method of layer potentials, the asymptotic behavior of the solution as ε tends to zero is described not only by asymptotic series in powers of ε, but by convergent power series. Here we use this method to investigate the Dirichlet problem for the Laplace operator where holes are collapsing at a polygonal corner of opening ω. Then in addition to the scale ε there appears the scale η = ε π/ω . We prove that when π/ω is irrational, the solution of the Dirichlet problem is given by convergent series in powers of these two small parameters. Due to interference of the two scales, this convergence is obtained, in full generality, by grouping together integer powers of the two scales that are very close to each other. Nevertheless, there exists a dense subset of openings ω (characterized by Diophantine approximation properties), for which real analyticity in the two variables ε and η holds and the power series converge unconditionally. When π/ω is rational, the series are unconditionally convergent, but contain terms in log ε.

This study presents a new method, called the Radial Interpolation Method, to interpolate data characterized by an approximately radial pattern around a relatively constrained central zone, such as the ground deformation patterns shown in many active volcanic areas. The method enables the fast production of short-term deformation maps on the base of spatially sparse ground deformation measurements and can provide uncertainty quantification on the interpolated values, fundamental for hazard assessment purposes and deformation source reconstruction. The presented approach is not dependent on a priori assumptions about the geometry, location and physical properties of the source, except for the requirement of a locally radial pattern, i.e., allowing multiple centers of symmetry. We test the new method on a synthetic point source example, and then, we apply the method to selected time intervals of real geodetic data collected at the Campi Flegrei caldera during the last 39 years, including examples of leveling, Geodetic Precise Traversing measurements and Global Positioning System. The maps of horizontal displacement, calculated inland, show maximum values lying along a semicircular annular region with a radius of about 2-3 km in size. This semi-annular area is marked by mesoscale structures such as faults, sand dikes and fractures. The maps of vertical displacement describe a linear relation between the maximum vertical uplift measured and the volume variation. The multiplicative factor in the linear relation is about 0.3 × 10 6 m 3 /cm if we estimate the proportion of the ΔV that is captured by the GPS network onland and we use this to estimate the full ΔV. In this case, the 95% confidence interval on K because of linear regression is ± 5%. Finally, we briefly discuss how the new method could be used for the production of short-term vent opening maps on the base of real-time geodetic measurements of the horizontal and vertical displacements.

From May 1985 to April 1986 five discrete eruptions have occurred at Piton de la Fournaise volcano. On March the 17th, a sixth episode began with four distinct stages. They took place along the southeast rift zone of the volcano, from the summit to the sea coast. It was the first rift zone eruption in the south since 1800 A.D. and the first ever monitored at Piton de la Fournaise volcano. Three fissural vents opened at decreasing altitude emitting about 12 to 15 X 106 m :~ of olivine basalts between 19th March and 1st April. Strong seismic activity was accompanied by deformation of the summit area, and large-scale variations of the magnetic field. A summital event characterized the end of the flank activity with collapse of a new pit-crater and outflow of small amounts of degassed aphyric basalt.

In this paper we are interested in polynomial interpolation of irregular functions namely those elements of L 2 (R, µ) for µ a given probability measure. This is of course doesn't make any sense unless for L 2 functions that, at least, admit a continuous version. To characterize those functions we have, first, constructed, in an abstract fashion, a chain of Sobolev like subspaces of a given Hilbert space H 0 . Then we have proved that the chain of Sobolev like subspaces controls the existence of a continuous version for L 2 functions and gives a pointwise polynomial approximation with a quite accurate error estimation.

The axisymmetric, thermocapillary-driven motion of a pair of non-conducting, spherical drops in near contact is analysed for conditions of small Reynolds and Marangoni numbers. The pairwise motion and an associated contact force are computed by considering touching drops in point contact. Relative motion for nearly touching drops results from the contact force balanced by a lubrication resistance. A new, analytical solution is obtained for the axisymmetric temperature field around an unequal pair of non-conducting, tangent spheres embedded in an ambient temperature gradient. Numerical results for the painvise migration velocity, contact force, and the relative and individual drop velocities are presented for all size ratios and a wide range of viscosity ratios, and asymptotic formulae are derived for small size ratios. For nearly equisized drops, the ratio of the relative velocity for two drops in near contact to that for widely separated drops is similar for thermocapillary-driven and gravity-driven motion. For small and moderate size ratios, however, this ratio is much larger for thermocapillary-driven relative motion than for gravity-driven relative motion, indicating that the former represents a more efficient coalescence mechanism. An explanation for this finding is provided in terms of the thermocapillary motion of the interface of the larger drop aiding the withdrawal of continuous phase from between the two drops.

The unsteady (oscillatory) Stokes resistance is numerically computed for finite-length, circular cylinders using a first-kind, boundary integral formulation for low and moderate dimensionless frequencies. Translational oscillations parallel and perpendicular to the cylinder axis (axial and transverse oscillations) are considered. For arbitrarily oriented cylinders with length-to-width ratios in the range: l/lO<a/b<lO, a simple, previously proposed, expression accurately ( f 5%) describes the oscillatory Stokes resistance at all frequencies in terms of steady Stokes and inviscid flow resistance parameters. Numerical calculations for spheroids agree with previous results; the results for cylinders and transverse oscillations of oblate spheroids are new.

This study deals with a boundary-value problem for a linear Fred-holm integro-differential equation subject to impulse effects at fixed time points. Solvability criteria are provided in terms of input data, without the use of a fundamental matrix and a resolvent. We also propose an algorithm to solve the problem under consideration, establish its convergence conditions, and provide a numerical version of the algorithm. MSC Classification: 34A37; 34B37; 45J05; 45J99; 34K28

Nous proposons une modélisation mathématique de structures naturelles irrégulières et compactes, inspirées de l'agencement des grains de maïs sur un épi et des pierres cyclopéennes dans les architectures incas et égyptiennes. Chaque élément possède une forme unique tout en s'imbriquant parfaitement avec ses voisins. Ce modèle vise à formaliser la notion de structure autoportée, auto-emboîtée et parasismique dans une perspective géométrique et topologique.

Chemotaxis is a biological phenomenon widely studied these last years, at the biological level but also at the mathematical level. Various models have been proposed, from microscopic to macroscopic scales. In this article, we consider in particular two hyperbolic models for the density of organisms, a semi-linear system based on the hyperbolic heat equation (or dissipative waves equation) and a quasi-linear system based on incompressible Euler equation. These models possess relatively stiff solutions and well-balanced and asymptotic-preserving schemes are necessary to approximate them accurately. The aim of this article is to present various techniques of well-balanced and asymptotic-preserving schemes for the two hyperbolic models for chemotaxis.

We consider two models which were both designed to describe the movement of eukaryotic cells responding to chemical signals. Besides a common standard parabolic equation for the diffusion of a chemoattractant, like chemokines or growth factors, the two models differ for the equations describing the movement of cells. The first model is based on a quasilinear hyperbolic system with damping, the other one on a degenerate parabolic equation. The two models have the same stationary solutions, which may contain some regions with vacuum. We first explain in details how to discretize the quasilinear hyperbolic system through an upwinding technique, which uses an adapted reconstruction, which is able to deal with the transitions to vacuum. Then we concentrate on the analysis of asymptotic preserving properties of the scheme towards a discretization of the parabolic equation, obtained in the large time and large damping limit, in order to present a numerical comparison between the asymptotic behavior of these two models. Finally we perform an accurate numerical comparison of the two models in the time asymptotic regime, which shows that the respective solutions have a quite different behavior for large times.

In this article, we consider a simple hyperbolic relaxation system on networks which models the movement of fibroblasts on an artificial scaffold. After proving the uniqueness of stationary solutions with a given total mass, we present an adapted numerical scheme which takes care of boundary conditions and display some numerical tests.

We introduce a new class of finite difference schemes for approximating the solutions to an initial-boundary value problem on a bounded interval for a one dimensional dissipative hyperbolic system with an external source term, which arises as a simple model of chemotaxis. Since the solutions to this problem may converge to non constant asymptotic states for large times, standard schemes usually fail to yield a good approximation. Therefore, we propose a new class of schemes, which use an asymptotic higher order correction, second and third order in our examples, to balance the effects of the source term and the influence of the asymptotic solutions. A special care is needed to deal with boundary conditions, to avoid harmful loss of mass. Convergence results are proven for these new schemes, and several numerical tests are presented and discussed to verify the effectiveness of their behavior.

In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the behavior of solutions and to discuss the stability and the accuracy of our approximation.

The transmission of elastic waves in infinite/finite unidirectional phononic crystals is investigated by using the boundary element method (BEM). For the infinite periodic structure, we use BEM to formulate a Bloch's eigenvalue problem which has a nonlinear property caused by the Hankel functions in the fundamental solution. This nonlinear eigenvalue problem is solved by employing a contour integral method and band gaps are found in the dispersion curves. For the finite structure, a certain number of layers for cells are given to connect the input and output domains. The numerical simulation shows that the finite structure also presents a frequency banded nature which coincides with the band gaps of the infinite structure.

The ¯ow through a two-dimensional centrifugal impeller ®tted with equiangular blades of arbitrary geometry is investigated using a combination of conformal mapping with a boundary element technique. The blades can be thin or thick of arbitrary cross-section. A theoretical analysis and a numerical procedure are developed to determine the pressure distributions along the blade.