Terms Of Boundary Conditions Research Articles

Helium–antihydrogen scattering at low energies

We calculate cross sections for helium–antihydrogen scattering for energies up to 0.01 atomic unit. Our calculation includes elastic scattering, direct antiproton–alpha particle annihilation and rearrangement into and ground-state positronium. Elastic scattering is calculated within the Born–Oppenheimer approximation using the potential calculated by Strasburger et al (2005 J. Phys. B: At. Mol. Opt. Phys. 38 3091). Matrix elements for rearrangement are calculated using the T-matrix in the distorted wave approximation, with the initial state represented by Hylleraas-type functions. The strong force, leading to direct annihilation, was included as a short-range boundary condition in terms of the strong-force scattering length.

Design of ZrO<sub>2</sub>/Ti Functionally Graded Thermal Barreir Coatings Based on a Nonlinear Micromechanical Approarch

This study presents a design process of ZrO2/Ti functionally graded thermal barrier coatings (FG TBCs) based on a mean-field nonlinear micromechanical approach developed by Tsukamoto [1], which takes into account the time-independent and dependent inelastic deformation, such as plasticity of metals, creep of metals and ceramics, and diffusional mass flow at the ceramic/metal interface. The effect of compositional gradations on micro-stress states in the FG TBCs has been examined. The suitable compositional gradations have been proposed for typical thermo-mechanical boundary conditions in terms of thermal-stress relaxations, thermal-shielding and light-weight characteristics.

Decontamination Pilot Projects: Building a Knowledge Base for Fukushima Environmental Remediation

ABSTRACTAfter the Fukushima Dai-ichi nuclear accident, Japan Atomic Energy Agency (JAEA)was chosen by the Government to conduct decontamination pilotprojects at selected sitesin the contaminated area of Fukushima. Despite tight boundary conditions in terms of timescale and resources, the projectsprovide a good basis for developing recommendations on how to assure clean-up efficiency and worker safety and reduce time, cost, subsequent waste management and environmental impact. The results of the project can be summarised in terms of site characterisation and data interpretation, clean-up and waste minimisation and storage.

The Cauchy--Dirichlet Problem for the Finitely Extensible Nonlinear Elastic Dumbbell Model of Polymeric Fluids

The finitely extensible nonlinear elastic (FENE) dumbbell model consists of the incompressible Navier--Stokes equation for the solvent and the Fokker--Planck equation for the polymer distribution. In such a model, the polymer elongation cannot exceed a limit $m_0$ which yields all interesting features of solutions near this limit. This work is concerned with the sharpness of boundary conditions in terms of the dimensionless parameter $b=\frac{Hm_0^2}{k_BT}$. Through a careful analysis of the Fokker--Planck operator coupled with the Navier--Stokes equation, we establish a local well-posedness for the full coupled FENE dumbbell model under a class of Dirichlet-type boundary conditions dictated by the parameter $b$. For each $b>0$ we identify a sharp boundary requirement for the underlying density distribution, while the sharpness follows from the existence result for each specification of the boundary behavior. It is shown that the probability density governed by the Fokker--Planck equation approaches zero near the boundary, necessarily faster than the distance function $d$ for $b>2$, faster than $d|ln d|$ for $b=2$, and as fast as $d^{b/2}$ for $0<b<2$. Moreover, the sharp boundary requirement for $b\geq 2$ is also sufficient for the distribution to be a probability density.

SIMPLE SKEWON MEDIUM REALIZATION OF DB BOUNDARY CONDITIONS

Considering the class of bi-isotropic media, a special case called the class of simple skewon (SS) media is deflned. The SS medium depends on a single parameter. A plane wave incident on a planar interface of an SS medium is shown to re∞ect as from a DB boundary with vanishing normal components of D and B fleld vectors. This ofiers another possibility to realize the DB boundary conditions in terms of a medium interface. The same property is shown to apply for curved boundaries as well.

Influence of solid-phase wall boundary condition on CFD simulation of spouted beds

The influence of solid-phase wall boundary condition in terms of specularity coefficient and particle–wall restitution coefficient on the flow behavior of spouted beds was investigated using two-fluid model approach in the computational fluid dynamics software FLUENT 6.3. Parametric studies of specularity coefficient and particle–wall restitution coefficient were performed to evaluate their effects on the flow hydrodynamics in terms of fountain height, spout diameter, pressure drop, local voidage and particles velocity. The numerical predictions were compared with available experimental data in the literatures to obtain the suitable values of specularity coefficient and particle–wall restitution coefficient for spouted beds. The simulated results show that the solid-phase wall boundary condition plays an important role in CFD modeling of spouted beds. The specularity coefficient has a pronounced effect on the spouting behavior and a small specularity coefficient (0.05) can give good predictions, while the particle–wall restitution coefficient is not critical for the holistic flow characteristics.

Symmetrized perturbation determinants and applications to boundary data maps and Krein-type resolvent formulas

The aim of this paper is two-fold: On one hand, we discuss an abstract approach to symmetrized Fredholm perturbation determinants and an associated trace formula for a pair of operators of positive type, extending a classical trace formula. On the other hand, we continue a recent systematic study of boundary data maps, that is, 2×2 matrix-valued Dirichlet-to-Neumann and more generally, Robin-to-Robin maps, associated with one-dimensional Schrödinger operators on a compact interval [0, R] with separated boundary conditions at 0 and R. One of the principal new results in this paper reduces an appropriately symmetrized (Fredholm) perturbation determinant to the 2×2 determinant of the underlying boundary data map. In addition, as a concrete application of the abstract approach in the first part of this paper, we establish the trace formula for resolvent differences of self-adjoint Schrödinger operators corresponding to different (separated) boundary conditions in terms of boundary data maps.

Mixed-Convection Flow of Nanofluids and Regular Fluids in Vertical Porous Media with Viscous Heating

In this article, the problem of combined forced and natural convection in a vertical porous channel for both regular fluids and nanofluids has been solved by perturbation and numerical methods, taking into account the influences of viscous heating and inertial force. In this regard, various types of viscous dissipation models, including the Darcy model, the power of drag force model, and the clear fluid compatible model, were considered to account for viscous heating. In addition, the mass flux of nanoparticles was also considered in terms of Brownian and thermophoresis mechanisms. The velocity and temperature distributions of both the regular fluid and nanofluid and the Nusselt number values were determined by considering isothermal boundary conditions in terms of Grashof, Reynolds, Forchheimer, Brinkman, and Darcy numbers. Moreover, the results of the numerical method were validated against those predicted by the perturbation method for small values of the Forchheimer drag term and the Brinkman number. In addition, the results obtained for both the nanofluid and the regular fluid were compared in terms of dimensionless parameters such as Brinkman number, Forchheimer drag term, pressure drop, Grashof-to-Reynolds-number ratio, Darcy number, and nanoparticle mass flux. The predicted results clearly indicate that the presence of nanoparticles enhances the Nusselt number values significantly.

Conformal mapping and impedance tomography

Over the last decade Akduman, Haddar and Kress [1, 3, 5] have employed a conformal mapping technique for the inverse problem to recover a perfectly conducting or a non-conducting inclusion in a homogeneous background medium from Cauchy data on the accessible exterior boundary. More recently, Haddar and Kress [4] proposed an extension of this approach to two-dimensional inverse electrical impedance tomography with piecewise constant conductivities. A main ingredient of this extension is the incorporation of the transmission condition on the unknown interior boundary via a nonlocal boundary condition in terms of an integral equation. We present an outline of the foundations of this new method.

Coupled deep-water flow and climate variability in the middle Pleistocene North Atlantic

Abrupt changes in the strength of the Atlantic Meridional Overturning Circulation (comprising northward flow of warm water and a cold southward return flow) are implicated in abrupt climate changes in the late Pleistocene. A sensitive place to assess this circulation is in the cold return flow of Deep Western Boundary Currents. Here, in records of flow speed and isotopic composition of surface and bottom waters from a Deep Western Boundary Current location near the northern source of North Atlantic Deep Water, we show both orbital and millennial-scale coupling between deep ocean flow and climate in the middle Pleistocene (0.75–0.87 Ma), when the boundary conditions in terms of the mean state and amplitude of climate change were different from more recent periods. The coupling appears as a phased series of events initiated by reduced vertical density gradients and initial ventilation of deep waters. The occurrence of these events in interglacials during the middle Pleistocene suggests that the millennial-scale climate variability in the North Atlantic was more pronounced at that time than previously thought. This demonstrates that, given the right boundary conditions, rapid climate shifts can also occur during relatively warm climate conditions.

The Casimir effect for conical pistons

In this paper we utilize $\zeta$-function regularization techniques in order to compute the Casimir force for massless scalar fields subject to Dirichlet and Neumann boundary conditions in the setting of the conical piston. The piston geometry is obtained by dividing the bounded generalized cone into two regions separated by its cross section positioned at $a$ with $a\in(0,b)$ with $b>0$. We obtain expressions for the Casimir force that are valid in any dimension for both Dirichlet and Neumann boundary conditions in terms of the spectral $\zeta$-function of the piston. As a particular case, we specify the piston to be a $d$-dimensional sphere and present explicit results for $d=2,3,4,5$.

A formal method for improving the transient behaviour of a non-linear flexible link

This article presents a procedure for improving the transient response of a boundary-controlled non-linear flexible elastic beam through a feed-forward action. It is shown that it is possible to obtain a formal analytic solution of an infinite-dimensional linear system, which approximates the non-linear dynamics, under time-varying boundary conditions in terms of the free vibration modes of the structure, whose calculation is a relatively easy task. The feed-forward action is then obtained by inverting the relationship between input and output variables. A numerical example is presented and some simulation results are discussed.

Towards a fully 3D domain-decomposition strategy for water-on-deck phenomena

A numerical approach has been used to analyze the water shipping caused by head sea waves for a FPSO ship at rest. A 3D Domain-Decomposition (DD) strategy is used, where a linear potential-flow seakeeping analysis of the vessel is coupled with a local nonlinear rotational-flow investigation for the prediction of water-on-deck phenomena. The Navier-Stokes solver is applied in the region close to the ship bow. It combines a finite-difference spatial algorithm with a predictor-corrector time scheme. The sea and ship surfaces are tracked with a Level-Set (LS) technique and a hybrid Eulerian-Lagrangian algorithm. The inner solver receives the initial and boundary conditions in terms of velocity, pressure, sea-surface location and ship motions and provides the loads due to the nonlinear wave-ship interaction (including green-water loads) to the seakeeping method. Here the inner solver and its implementation within the DD are described in detail. Preliminary results in terms of water-on-deck occurrence are discussed and compared against 3D water-on-deck experiments.

Surface Impedance Boundary Conditions in Terms of Various Formalisms

When a surface impedance boundary condition is implemented in a numerical formulation, it must be represented in terms of the state variables of that formulation. The usual practice is to derive high order surface impedance boundary conditions, which take into account the curvature of the conductor surface, and express them as relations between tangential components of the electric and magnetic fields or between tangential and normal components of the magnetic field. In the present paper, general expressions of high order surface impedance boundary conditions are obtained by solving the diffusion equation using perturbation techniques, under the hypothesis that the skin depth is much smaller than the characteristic size of the conductor's surface. The obtained formulas are applicable to various electromagnetic vector quantities and describe the behavior of the fields not only on the surface of the conductor but also in the whole skin layer. A simple numerical example is used to validate the derived expressions.

Small mass expansion of functional determinants on the generalized cone

In this paper we compute the small mass expansion for the functional determinant of a scalar Laplacian defined on the bounded, generalized cone. In the framework of zeta function regularization, we obtain an expression for the functional determinant valid in any dimension for both Dirichlet and Robin boundary conditions in terms of the spectral zeta function of the base manifold. Moreover, as a particular case, we specify the base to be a d-dimensional sphere and present explicit results for d = 2, 3, 4, 5.

Solution of high-order linear Fredholm integro-differential equations with piecewise intervals

In this study, a practical matrix method is presented to find an approximate solution for high-order linear Fredholm integro-differential equations with piecewise intervals under the initial boundary conditions in terms of Taylor polynomials. The method converts the integro differential equation to a matrix equation, which corresponds to a system of linear algebraic equations. Error analysis and illustrative examples are included to demonstrate the validity and applicability of the technique. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 27: 1327–1339, 2011

Conformal mapping and impedance tomography

Akduman and Kress (2002 Inverse Problems 18 1659–1672), Haddar and Kress (2005 Inverse Problems 21 935–953), and Kress (2004 Math. Comput. Simul. 66 255–265) have employed a conformal mapping technique for the inverse problem to recover a perfectly conducting or a non-conducting inclusion in a homogeneous background medium from the Cauchy data on the accessible exterior boundary. We propose an extension of this approach to two-dimensional inverse electrical impedance tomography with piecewise constant conductivities. A main ingredient of our method is the incorporation of the transmission condition on the unknown interior boundary via a nonlocal boundary condition in terms of an integral equation. We present the foundations of the method, a local convergence result and exhibit the feasibility of the method via numerical examples.

DIFFRACTION THEORY OF WAVES BY RESISTIVE SURFACES

Difiraction of scalar plane waves by resistive surfaces are investigated by deflning a new boundary condition in terms of the Dirichlet and Neumann conditions. The scattering problems of waves by a resistive half-plane and the interface between resistive and perfectly magnetic conducting half-planes are examined with the developed method. The resulting flelds are plotted numerically. The numerical results show that the evaluated fleld expressions are in harmony with the theory.

A study of the Navier-Stokes equations with the kinematic and Navier boundary conditions

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in ℝ 3 with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the Navier boundary condition in terms of the vorticity, which is motivated by the Hodge theory on manifolds with boundary from the viewpoint of differential geometry, and establish basic elliptic estimates for vector fields subject to the kinematic and Navier boundary conditions. Then we develop a spectral theory of the Stokes operator acting on divergence-free vector fields on a domain with the kinematic and Navier boundary conditions. Finally, we employ the spectral theory and the necessary estimates to construct the Galerkin approximate solutions and establish their convergence to global weak solutions, as well as local strong solutions, of the initial-boundary value problem. Furthermore, we show as a corollary that, when the slip length tends to zero, the weak solutions constructed converge to a solution to the incompressible Navier-Stokes equations subject to the no-slip boundary condition for almost all time. The inviscid limit of the strong solutions to the unique solution of the initial-boundary value problem with the slip boundary condition for the Euler equations is also established.

A Tropical Analogue of Fay’s Trisecant Identity and the Ultra-Discrete Periodic Toda Lattice

We introduce a tropical analogue of Fay’s trisecant identity for a special family of hyperelliptic tropical curves. We apply it to obtain the general solution of the ultra-discrete Toda lattice with periodic boundary conditions in terms of the tropical Riemann’s theta function.