WorldWideScience

Sample records for boundary conditions

  1. Reweighting twisted boundary conditions

    CERN Document Server

    Bussone, Andrea; Hansen, Martin; Pica, Claudio

    2015-01-01

    Imposing twisted boundary conditions on the fermionic fields is a procedure extensively used when evaluating, for example, form factors on the lattice. Twisting is usually performed for one flavour and only in the valence, and this causes a breaking of unitarity. In this work we explore the possibility of restoring unitarity through the reweighting method. We first study some properties of the approach at tree level and then we stochastically evaluate ratios of fermionic determinants for different boundary conditions in order to include them in the gauge averages, avoiding in this way the expensive generation of new configurations for each choice of the twisting angle, $\\theta$. As expected the effect of reweighting is negligible in the case of large volumes but it is important when the volumes are small and the twisting angles are large. In particular we find a measurable effect for the plaquette and the pion correlation function in the case of $\\theta=\\pi/2$ in a volume $16\\times 8^3$, and we observe a syst...

  2. Boundary Conditions of Weyl Semimetals

    CERN Document Server

    Hashimoto, Koji; Wu, Xi

    2016-01-01

    We find that generic boundary conditions of Weyl semimetal is dictated by only a single real parameter, in the continuum limit. We determine how the energy dispersions (the Fermi arcs) and the wave functions of edge states depend on this parameter. Lattice models are found to be consistent with our generic observation. Furthermore, the enhanced parameter space of the boundary condition is shown to support a novel topological number.

  3. Topological expansion and boundary conditions

    CERN Document Server

    Eynard, Bertrand

    2008-01-01

    In this article, we compute the topological expansion of all possible mixed-traces in a hermitian two matrix model. In other words we give a recipe to compute the number of discrete surfaces of given genus, carrying an Ising model, and with all possible given boundary conditions. The method is recursive, and amounts to recursively cutting surfaces along interfaces. The result is best represented in a diagrammatic way, and is thus rather simple to use.

  4. Quantum violation of Dirichlet boundary condition

    CERN Document Server

    Park, I Y

    2016-01-01

    Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a clash between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum corrected solution of the 1PI action no longer obeys the Dirichlet boundary conditions imposed at the classical level. We attribute the violation of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.

  5. Construction of Maximal Hypersurfaces with Boundary Conditions

    OpenAIRE

    Lambert, Ben

    2014-01-01

    We construct maximal hypersurfaces with a Neumann boundary condition in Minkowski space via mean curvature flow. In doing this we give general conditions for long time existence of the flow with boundary conditions with assumptions on the curvature of a the Lorentz boundary manifold.

  6. Absorbing Boundary Conditions for Hyperbolic Systems

    Institute of Scientific and Technical Information of China (English)

    Matthias Ehrhardt

    2010-01-01

    This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions. We prove the strict well-posedness of the resulting initial boundary value problem in 1D. Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme. Hereby, we have to extend the classical proofs, since the (discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.

  7. Boundary Conditions in an Electric Current Contact

    OpenAIRE

    Titov, O. Yu.; Giraldo, J.; Gurevich, Yu. G.

    2002-01-01

    In most electronic devices, electric current of both types (electrons and holes) flows through a junction. Usually the boundary conditions have been formulated exclusively for open circuit. The boundary conditions proposed here bypass this limitation by the first time, as far as we are aware. Besides, these new boundary conditions correctly describe current flow in a circuit, i.e., closed circuit conditions, which are the usual operation conditions for electronic devices and for the measureme...

  8. Boundary conditions of methamphetamine craving.

    Science.gov (United States)

    Lopez, Richard B; Onyemekwu, Chukwudi; Hart, Carl L; Ochsner, Kevin N; Kober, Hedy

    2015-12-01

    Methamphetamine use has increased significantly and become a global health concern. Craving is known to predict methamphetamine use and relapse following abstinence. Some have suggested that cravings are automatic, generalized, and uncontrollable, but experimental work addressing these claims is lacking. In 2 exploratory studies, we tested the boundary conditions of methamphetamine craving by asking: (a) is craving specific to users' preferred route of administration?, and (b) can craving be regulated by cognitive strategies? Two groups of methamphetamine users were recruited. In Study 1, participants were grouped by their preferred route of administration (intranasal vs. smoking), and rated their craving in response to photographs and movies depicting methamphetamine use (via the intranasal vs. smoking route). In Study 2, methamphetamine smokers implemented cognitive regulation strategies while viewing photographs depicting methamphetamine smoking. Strategies involved either focusing on the positive aspects of smoking methamphetamine or the negative consequences of doing so-the latter strategy based on treatment protocols for addiction. In Study 1, we found a significant interaction between group and route of administration, such that participants who preferred to smoke methamphetamine reported significantly stronger craving for smoking stimuli, whereas those who preferred the intranasal route reported stronger craving for intranasal stimuli. In Study 2, participants reported significantly lower craving when focusing on the negative consequences associated with methamphetamine use. Taken together, these findings suggest that strength of craving for methamphetamine is moderated by users' route of administration and can be reduced by cognitive strategies. This has important theoretical, methodological, and clinical implications.

  9. Logarithmic minimal models with Robin boundary conditions

    Science.gov (United States)

    Bourgine, Jean-Emile; Pearce, Paul A.; Tartaglia, Elena

    2016-06-01

    We consider general logarithmic minimal models LM≤ft( p,{{p}\\prime}\\right) , with p,{{p}\\prime} coprime, on a strip of N columns with the (r, s) Robin boundary conditions introduced by Pearce, Rasmussen and Tipunin. On the lattice, these models are Yang–Baxter integrable loop models that are described algebraically by the one-boundary Temperley–Lieb algebra. The (r, s) Robin boundary conditions are a class of integrable boundary conditions satisfying the boundary Yang–Baxter equations which allow loop segments to either reflect or terminate on the boundary. The associated conformal boundary conditions are organized into infinitely extended Kac tables labelled by the Kac labels r\\in {Z} and s\\in {N} . The Robin vacuum boundary condition, labelled by ≤ft(r,s-\\frac{1}{2}\\right)=≤ft(0,\\frac{1}{2}\\right) , is given as a linear combination of Neumann and Dirichlet boundary conditions. The general (r, s) Robin boundary conditions are constructed, using fusion, by acting on the Robin vacuum boundary with an (r, s)-type seam consisting of an r-type seam of width w columns and an s-type seam of width d  =  s  ‑  1 columns. The r-type seam admits an arbitrary boundary field which we fix to the special value ξ =-\\fracλ{2} where λ =\\frac≤ft( {{p}\\prime}-p\\right)π{{{p}\\prime}} is the crossing parameter. The s-type boundary introduces d defects into the bulk. We consider the commuting double-row transfer matrices and their associated quantum Hamiltonians and calculate analytically the boundary free energies of the (r, s) Robin boundary conditions. Using finite-size corrections and sequence extrapolation out to system sizes N+w+d≤slant 26 , the conformal spectrum of boundary operators is accessible by numerical diagonalization of the Hamiltonians. Fixing the parity of N for r\

  10. The Pauli equation with complex boundary conditions

    CERN Document Server

    Kochan, D; Novak, R; Siegl, P

    2012-01-01

    We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin-magnetic interaction on the interplay between the type of boundary conditions and the spectrum. A special attention is paid to PT-symmetric boundary conditions with the physical choice of the time-reversal operator T.

  11. Periodic boundary conditions on the pseudosphere

    OpenAIRE

    Sausset, François; Tarjus, Gilles

    2007-01-01

    30 pages, minor corrections, accepted to J. Phys. A International audience We provide a framework to build periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary conditions in the Euclidean plane, we introduce all the needed mathematical notions and sketch a classification of periodic boundary conditions on the hyperbolic plane. We stress the ...

  12. Periodic boundary conditions on the pseudosphere

    Energy Technology Data Exchange (ETDEWEB)

    Sausset, F; Tarjus, G [Laboratoire de Physique Theorique de la Matiere Condensee, Universite Pierre et Marie Curie, Paris 6, UMR CNRS 7600, 4 place Jussieu, 75252 Paris Cedex 05 (France)

    2007-10-26

    We provide a framework for building periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary conditions in the Euclidean plane, we introduce all the required mathematical notions and sketch a classification of periodic boundary conditions on the hyperbolic plane. We stress the possible applications in statistical mechanics for studying the bulk behavior of physical systems, and illustrate how to implement such periodic boundary conditions in two examples, the dynamics of particles on the pseudosphere and the study of classical spins on hyperbolic lattices.

  13. Absorption boundary conditions for geomertical acoustics

    DEFF Research Database (Denmark)

    Jeong, Cheol-Ho

    2012-01-01

    Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, the absorption coefficients or surface impedances of the boundary surfaces can be used, but no guideline has been developed...... solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. It is concluded that the impedance and random incidence absorption boundary conditions produce reasonable results with some exceptions at low frequencies for acoustically soft materials....

  14. Logarithmic Minimal Models with Robin Boundary Conditions

    CERN Document Server

    Bourgine, Jean-Emile; Tartaglia, Elena

    2016-01-01

    We consider general logarithmic minimal models ${\\cal LM}(p,p')$, with $p,p'$ coprime, on a strip of $N$ columns with the $(r,s)$ Robin boundary conditions introduced by Pearce, Rasmussen and Tipunin. The associated conformal boundary conditions are labelled by the Kac labels $r\\in{\\Bbb Z}$ and $s\\in{\\Bbb N}$. The Robin vacuum boundary condition, labelled by $(r,s\\!-\\!\\frac{1}{2})=(0,\\mbox{$\\textstyle \\frac{1}{2}$})$, is given as a linear combination of Neumann and Dirichlet boundary conditions. The general $(r,s)$ Robin boundary conditions are constructed, using fusion, by acting on the Robin vacuum boundary with an $(r,s)$-type seam consisting of an $r$-type seam of width $w$ columns and an $s$-type seam of width $d=s-1$ columns. The $r$-type seam admits an arbitrary boundary field which we fix to the special value $\\xi=-\\tfrac{\\lambda}{2}$ where $\\lambda=\\frac{(p'-p)\\pi}{2p'}$ is the crossing parameter. The $s$-type boundary introduces $d$ defects into the bulk. We consider the associated quantum Hamiltoni...

  15. The Pauli equation with complex boundary conditions

    International Nuclear Information System (INIS)

    We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin–magnetic interaction on the interplay between the type of boundary conditions and the spectrum. Special attention is paid to PT-symmetric boundary conditions with the physical choice of the time-reversal operator T. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’. (paper)

  16. The Pauli equation with complex boundary conditions

    Science.gov (United States)

    Kochan, D.; Krejčiřík, D.; Novák, R.; Siegl, P.

    2012-11-01

    We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin-magnetic interaction on the interplay between the type of boundary conditions and the spectrum. Special attention is paid to {PT}-symmetric boundary conditions with the physical choice of the time-reversal operator {T}. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.

  17. Numerical implementation of isolated horizon boundary conditions

    International Nuclear Information System (INIS)

    We study the numerical implementation of a set of boundary conditions derived from the isolated horizon formalism, and which characterize a black hole whose horizon is in quasiequilibrium. More precisely, we enforce these geometrical prescriptions as inner boundary conditions on an excised sphere, in the numerical resolution of the conformal thin sandwich equations. As main results, we first establish the consistency of including in the set of boundary conditions a constant surface gravity prescription, interpretable as a lapse boundary condition, and second we assess how the prescriptions presented recently by Dain et al. for guaranteeing the well-posedness of the conformal transverse traceless equations with quasiequilibrium horizon conditions extend to the conformal thin sandwich elliptic system. As a consequence of the latter analysis, we discuss the freedom of prescribing the expansion associated with the ingoing null normal at the horizon

  18. Modelling classroom conditions with different boundary conditions

    DEFF Research Database (Denmark)

    Marbjerg, Gerd Høy; Jeong, Cheol-Ho; Brunskog, Jonas;

    2014-01-01

    both specular and diffuse reflections with complex-valued acoustical descriptions of the surfaces. In this paper the PARISM model is used to simulate a rectangular room with most of the absorption located in the ceiling. This room configuration is typical for classroom conditions. The simulations...... measures which are important for evaluation of the acoustics in classrooms....

  19. Solution of moving boundary problems with implicit boundary condition

    International Nuclear Information System (INIS)

    An algorithm that solves numerically a model for studying one dimensional moving boundary problems, with implicit boundary condition, is described. Landau's transformation is used, in order to work with a fixed number of nodes at each instant. Then, it is necessary to deal with a parabolic partial differential equation, whose diffusive and convective terms have variable coefficients. The partial differential equation is implicitly discretized, using Laasonen's scheme, always stable, instead of employing Crank-Nicholson sheme, as it has been done by Ferris and Hill. Fixed time and space steps (Δt, Δξ) are used, and the iteration is made with variable positions of the interface, i.e. varying δs until a boundary condition is satisfied. The model has the same features of the oxygen diffusion in absorbing tissue. It would be capable of estimating time variant radiation treatments of cancerous tumors. (Author)

  20. Optimal Boundary Conditions for ORCA-2 Model

    CERN Document Server

    Kazantsev, Eugene

    2012-01-01

    A 4D-Var data assimilation technique is applied to a ORCA-2 configuration of the NEMO in order to identify the optimal parametrization of the boundary conditions on the lateral boundaries as well as on the bottom and on the surface of the ocean. The influence of the boundary conditions on the solution is analyzed as in the assimilation window and beyond the window. It is shown that optimal conditions for vertical operators allows to get stronger and finer jet streams (Gulf Stream, Kuroshio) in the solution. Analyzing the reasons of the jets reinforcement, we see that the major impact of the data assimilation is made on the parametrization of the bottom boundary conditions for lateral velocities u and v. Automatic generation of the tangent and adjoint codes is also discussed. Tapenade software is shown to be able to produce the adjoint code that can be used after a memory usage optimization.

  1. Student difficulties with Boundary Conditions in electrodynamics

    CERN Document Server

    Ryan, Qing X; Wilcox, Bethany R

    2015-01-01

    Boundary conditions (BCs) are considered as an important topic that advanced physics under- graduates are expected to understand and apply. We report findings from an investigation of student difficulties using boundary conditions (BCs) in electrodynamics. Our data sources include student responses to traditional exam questions, conceptual survey questions, and think-aloud interviews. The analysis was guided by an analytical framework that characterizes how students activate, con- struct, execute, and reflect on boundary conditions. Common student difficulties include: activating boundary conditions in appropriate contexts; constructing a complex expression for the E&M waves; mathematically simplifying complex exponentials and checking if the reflection and transmission co- efficient are physical. We also present potential pedagogical implications based on our observations.

  2. Neutron transport with periodic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Angelescu, N.; Marinescu, N.; Protopopescu, V.

    1976-01-01

    The initial value problem for monoenergetic neutron transport in homogeneous nonmultiplying, nonabsorbing medium with isotropic scattering and periodic boundary conditions. One completely determines the structure of the spectrum of the transport operator both in plane and parallelepipedic geometries.

  3. Scalar Boundary Conditions in Hyperscaling Violating Geometry

    CERN Document Server

    Wu, Jian-Pin

    2015-01-01

    We study the possible boundary conditions of scalar field modes in a hyperscaling violation(HV) geometry with Lifshitz dynamical exponent $z (z\\geqslant1)$ and hyperscaling violation exponent $\\theta (\\theta\

  4. Reconstruction of boundary conditions from internal conditions using viability theory

    KAUST Repository

    Hofleitner, Aude

    2012-06-01

    This article presents a method for reconstructing downstream boundary conditions to a HamiltonJacobi partial differential equation for which initial and upstream boundary conditions are prescribed as piecewise affine functions and an internal condition is prescribed as an affine function. Based on viability theory, we reconstruct the downstream boundary condition such that the solution of the Hamilton-Jacobi equation with the prescribed initial and upstream conditions and reconstructed downstream boundary condition satisfies the internal value condition. This work has important applications for estimation in flow networks with unknown capacity reductions. It is applied to urban traffic, to reconstruct signal timings and temporary capacity reductions at intersections, using Lagrangian sensing such as GPS devices onboard vehicles.

  5. Boundary conditions for the gravitational field

    International Nuclear Information System (INIS)

    A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation of Einstein's equations and a tetrad formulation of the Einstein-Bianchi system. However, a universal approach valid for other formulations is not in hand. In particular, there is no satisfactory boundary theory for the 3+1 formulations which have been highly successful in binary black hole simulation. I discuss the underlying problems that make the initial-boundary-value problem much more complicated than the Cauchy problem. I review the progress that has been made and the important open questions that remain. Science is a differential equation. Religion is a boundary condition. (Alan Turing, quoted in J D Barrow, 'Theories of Everything') (topical review)

  6. Transmitting boundary and radiation conditions at infinity

    Institute of Scientific and Technical Information of China (English)

    廖振鹏

    2001-01-01

    Relationship between the radiation conditions at infinity and the transmitting boundary for numerical simulation of the near-field wave motion has been studied in this paper. The conclusion is that the transmitting boundary is approximately equivalent to the radiation conditions at infinity for a large class of infinite media. And the errors of the approximation are of the same order of magnitude as those of the finite elements or finite differences in numerical simulation of wave motion. This result provides a sound theoretical basis for the transmitting boundary used in the numerical simulation of the near-field wave motion and gives a complete explanation for the major experiences accumulated in applications of the transmitting boundary to the numerical simulation.

  7. Constructing parametric triangular patches with boundary conditions

    Institute of Scientific and Technical Information of China (English)

    Hui Liu; Jun Ma; Fuhua Cheng

    2008-01-01

    The problem of constructing a parametric triangular patch to smoothly connect three surface patches is studied. Usually, these surface patches are defined on different parameter spaces. Therefore, it is necessary to define interpolation conditions, with values from the given surface patches, on the boundary of the triangular patch that can ensure smooth transition between different parameter spaces. In this paper we present a new method to define boundary conditions. Boundary conditions defined by the new method have the same parameter space if the three given surface patches can be converted into the same form through affine transformation. Consequently, any of the classic methods for constructing functional triangular patches can be used directly to construct a parametric triangular patch to connect given surface patches with G continuity. The resulting parametric triangular patch preserves precision of the applied classic method.

  8. Antireflective Boundary Conditions for Deblurring Problems

    Directory of Open Access Journals (Sweden)

    Marco Donatelli

    2010-01-01

    Full Text Available This survey paper deals with the use of antireflective boundary conditions for deblurring problems where the issues that we consider are the precision of the reconstruction when the noise is not present, the linear algebra related to these boundary conditions, the iterative and noniterative regularization solvers when the noise is considered, both from the viewpoint of the computational cost and from the viewpoint of the quality of the reconstruction. In the latter case, we consider a reblurring approach that replaces the transposition operation with correlation. For many of the considered items, the anti-reflective algebra coming from the given boundary conditions is the optimal choice. Numerical experiments corroborating the previous statement and a conclusion section end the paper.

  9. ADHMN boundary conditions from removing monopoles

    OpenAIRE

    Chen, Xingang; Weinberg, Erick J.

    2002-01-01

    Boundary conditions play an important role in the ADHMN construction of BPS monopole solutions. In this paper we show how different types of boundary conditions can be related to each other by removing monopoles to spatial infinity. In particular, we use this method to show how the jumping data naturally emerge. The results can be interpreted in the D-brane picture and provide a better understanding of the derivation of the ADHMN construction from D-branes. We comment briefly on the cases wit...

  10. ADHMN boundary conditions from removing monopoles

    CERN Document Server

    Chen, X; Chen, Xingang; Weinberg, Erick J.

    2003-01-01

    Boundary conditions play an important role in the ADHMN construction of BPS monopole solutions. In this paper we show how different types of boundary conditions can be related to each other by removing monopoles to spatial infinity. In particular, we use this method to show how the jumping data naturally emerge. The results can be interpreted in the D-brane picture and provide a better understanding of the derivation of the ADHMN construction from D-branes. We comment briefly on the cases with non-Abelian unbroken symmetry and massless monopoles.

  11. Mixed boundary conditions for piezoelectric plates

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    For plate bending and stretching problems in piezoelectric materials,the reciprocal theorem and the general solution of piezoelasticity are applied in a novel way to obtain the appropriate mixed boundary conditions accurate to all order.A decay analysis technique is used to establish necessary conditions that the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the plate.For the case of axisymmetric bending and stretching of a circular plate,these decaying state conditions are obtained explicitly for the first time when the mixed conditions are imposed on the plate edge.They are then used for the correct formulation of boundary conditions for the interior solution.

  12. Boundary Conditions at Infinity for Physical Theories

    CERN Document Server

    Trautman, Andrzej

    2016-01-01

    The Sommerfeld boundary conditions, imposed on hyperbolic differential equations to obtain solutions in the form of outgoing waves, are formulated here so as to make explicit the role of an appropriate null vector field. When applied to the scalar and Maxwell equations, they lead to the asymptotic form of the energy-momentum tensor representing radiation as a null, perfect dust.

  13. Quantum Transport Calculations Using Periodic Boundary Conditions

    OpenAIRE

    Wang, Lin-Wang

    2004-01-01

    An efficient new method is presented to calculate the quantum transports using periodic boundary conditions. This method allows the use of conventional ground state ab initio programs without big changes. The computational effort is only a few times of a normal ground state calculations, thus is makes accurate quantum transport calculations for large systems possible.

  14. Radiation (absorbing) boundary conditions for electromagnetic fields

    Science.gov (United States)

    Bevensee, R. M.; Pennock, S. T.

    1987-01-01

    An important problem in finite difference or finite element computation of the electromagnetic field obeying the space-time Maxwell equations with self-consistent sources is that of truncating the outer numerical boundaries properly to avoid spurious numerical reflection. Methods for extrapolating properly the fields just beyond a numerical boundary in free space have been treated by a number of workers. This report avoids plane wave assumptions and derives boundary conditions more directly related to the source distribution within the region. The Panofsky-Phillips' relations, which enable one to extrapolate conveniently the vector field components parallel and perpendicular to a radial from the coordinate origin chosen near the center of the charge-current distribution are used to describe the space-time fields.

  15. Aspects of implementing constant traction boundary conditions in computational homogenization via semi-Dirichlet boundary conditions

    Science.gov (United States)

    Javili, A.; Saeb, S.; Steinmann, P.

    2016-10-01

    In the past decades computational homogenization has proven to be a powerful strategy to compute the overall response of continua. Central to computational homogenization is the Hill-Mandel condition. The Hill-Mandel condition is fulfilled via imposing displacement boundary conditions (DBC), periodic boundary conditions (PBC) or traction boundary conditions (TBC) collectively referred to as canonical boundary conditions. While DBC and PBC are widely implemented, TBC remains poorly understood, with a few exceptions. The main issue with TBC is the singularity of the stiffness matrix due to rigid body motions. The objective of this manuscript is to propose a generic strategy to implement TBC in the context of computational homogenization at finite strains. To eliminate rigid body motions, we introduce the concept of semi-Dirichlet boundary conditions. Semi-Dirichlet boundary conditions are non-homogeneous Dirichlet-type constraints that simultaneously satisfy the Neumann-type conditions. A key feature of the proposed methodology is its applicability for both strain-driven as well as stress-driven homogenization. The performance of the proposed scheme is demonstrated via a series of numerical examples.

  16. Symmetry boundary condition in dissipative particle dynamics

    Science.gov (United States)

    Pal, Souvik; Lan, Chuanjin; Li, Zhen; Hirleman, E. Daniel; Ma, Yanbao

    2015-07-01

    Dissipative particle dynamics (DPD) is a coarse-grained particle method for modeling mesoscopic hydrodynamics. Most of the DPD simulations are carried out in 3D requiring remarkable computation time. For symmetric systems, this time can be reduced significantly by simulating only one half or one quarter of the systems. However, such simulations are not yet possible due to a lack of schemes to treat symmetric boundaries in DPD. In this study, we propose a numerical scheme for the implementation of the symmetric boundary condition (SBC) in both dissipative particle dynamics (DPD) and multibody dissipative particle dynamics (MDPD) using a combined ghost particles and specular reflection (CGPSR) method. We validate our scheme in four different configurations. The results demonstrate that our scheme can accurately reproduce the system properties, such as velocity, density and meniscus shapes of a full system with numerical simulations of a subsystem. Using a symmetric boundary condition for one half of the system, we demonstrate about 50% computation time saving in both DPD and MDPD. This approach for symmetric boundary treatment can be also applied to other coarse-grained particle methods such as Brownian and Langevin Dynamics to significantly reduce computation time.

  17. Local electrostatic moments and periodic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Schultz, P.A. [Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States)

    1999-07-01

    Electronic structure calculations frequently invoke the supercell approximation and solve for electrostatic potentials within periodic boundary conditions. For systems that are electronically charged, or contain dipole (or higher) moments, this artifice introduces spurious potentials due to interactions between the system and multipole moments of its periodic images in aperiodic directions. I describe a method to handle properly the multipole moments of the electron density in electronic structure calculations using supercells. The density is divided into two pieces. A model local density is constructed to match multipole moments of the full density. The potential from this piece is obtained treating this density as isolated. With the density of this local-moment countercharge removed from the full density, the remainder density no longer contains moments with long-range potentials, and its electrostatic potential can be evaluated accurately using periodic boundary conditions. {copyright} {ital 1999} {ital The American Physical Society}

  18. Calculating Quantum Transports Using Periodic Boundary Conditions

    OpenAIRE

    Wang, Lin-Wang

    2004-01-01

    An efficient new method is presented to calculate the quantum transports using periodic boundary conditions. This new method is based on a method we developed previously, but with an essential change in solving the Schrodinger's equation. As a result of this change, the scattering states can be solved at any given energy. Compared to the previous method, the current method is faster and numerically more stable. The total computational time of the current method is similar to a conventional gr...

  19. Semi-implicit Image Denoising Algorithm for Different Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Yuying Shi

    2013-04-01

    Full Text Available In this paper, the Crank-Nicolson semi-implicit difference scheme in matrix form is applied to discrete the Rudin-Osher-Fatemi model. We also consider different boundary conditions: Dirichlet boundary conditions, periodic boundary conditions, Neumann boundary conditions, antireflective boundary conditions and mean boundary conditions. By comparing the experimental results of Crank-Nicolson semi-implicit scheme and explicit scheme with the proposed boundary conditions, we can get that the semi-implicit scheme can overcome the instability and the number of iterations of the shortcomings that the explicit discrete scheme has, and its recovery effects are better than the explicit discrete scheme. In addition, the antireflective boundary conditions and Neumann boundary conditions can better maintain the continuity of the boundary in image denoising.

  20. Open Boundary Conditions for Dissipative MHD

    Energy Technology Data Exchange (ETDEWEB)

    Meier, E T

    2011-11-10

    In modeling magnetic confinement, astrophysics, and plasma propulsion, representing the entire physical domain is often difficult or impossible, and artificial, or 'open' boundaries are appropriate. A novel open boundary condition (BC) for dissipative MHD, called Lacuna-based open BC (LOBC), is presented. LOBC, based on the idea of lacuna-based truncation originally presented by V.S. Ryaben'kii and S.V. Tsynkov, provide truncation with low numerical noise and minimal reflections. For hyperbolic systems, characteristic-based BC (CBC) exist for separating the solution into outgoing and incoming parts. In the hyperbolic-parabolic dissipative MHD system, such separation is not possible, and CBC are numerically unstable. LOBC are applied in dissipative MHD test problems including a translating FRC, and coaxial-electrode plasma acceleration. Solution quality is compared to solutions using CBC and zero-normal derivative BC. LOBC are a promising new open BC option for dissipative MHD.

  1. Canonical group quantization and boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Jung, Florian

    2012-07-16

    In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

  2. Canonical group quantization and boundary conditions

    International Nuclear Information System (INIS)

    In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

  3. An H-Principle With Boundary Condition

    CERN Document Server

    Dotto, Emanuele

    2010-01-01

    We prove an h-principle with boundary condition for a certain class of topological spaces valued sheaves. The techniques used in the proof come from the study of the homotopy type of the cobordism categories, and they are of simplicial and categorical nature. Applying the main result of this paper to a certain sheaf we find another proof of the homotopy equivalence between the classifying space of a cobordism category and a loop space of the Thom space of the complement of the tautological bundle over the Grassmannians.

  4. An h-principle with boundary condition

    DEFF Research Database (Denmark)

    Dotto, Emanuele

    2010-01-01

    We prove an h-principle with boundary condition for a certain class of topological spaces valued sheaves. The techniques used in the proof come from the study of the homotopy type of the cobordism categories, and they are of simplicial and categorical nature. Applying the main result of this pape...... to a certain sheaf we find another proof of the homotopy equivalence between the classifying space of a cobordism category and a loop space of the Thom space of the complement of the tautological bundle over the Grassmannians....

  5. Thermal field theories and shifted boundary conditions

    CERN Document Server

    Giusti, Leonardo

    2013-01-01

    The analytic continuation to an imaginary velocity of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary conditions. The Poincare' invariance underlying a relativistic theory implies a dependence of the free-energy on the compact length L_0 and the shift xi only through the combination beta=L_0(1+xi^2)^(1/2). This in turn implies that the energy and the momentum distributions of the thermal theory are related, a fact which is encoded in a set of Ward identities among the correlators of the energy-momentum tensor. The latter have interesting applications in lattice field theory: they offer novel ways to compute thermodynamic potentials, and a set of identities to renormalize non-perturbatively the energy-momentum tensor. At fixed bare parameters the shifted boundary conditions also provide a simple method to vary the temperature in much smaller steps than with the standard procedur...

  6. Effective Hydrodynamic Boundary Conditions for Corrugated Surfaces

    CERN Document Server

    Mongruel, Anne; Asmolov, Evgeny S; Vinogradova, Olga I

    2012-01-01

    We report measurements of the hydrodynamic drag force acting on a smooth sphere falling down under gravity to a plane decorated with microscopic periodic grooves. Both surfaces are lyophilic, so that a liquid (silicone oil) invades the surface texture being in the Wenzel state. A significant decrease in the hydrodynamic resistance force as compared with that predicted for two smooth surfaces is observed. To quantify the effect of roughness we use the effective no-slip boundary condition, which is applied at the imaginary smooth homogeneous isotropic surface located at an intermediate position between top and bottom of grooves. Such an effective condition fully characterizes the force reduction measured with the real surface, and the location of this effective plane is related to geometric parameters of the texture by a simple analytical formula.

  7. On domain wall boundary conditions for the XXZ spin Hamiltonian

    DEFF Research Database (Denmark)

    Orlando, Domenico; Reffert, Susanne; Reshetikhin, Nicolai

    In this note, we derive the spectrum of the infinite quantum XXZ spin chain with domain wall boundary conditions. The eigenstates are constructed as limits of Bethe states for the finite XXZ spin chain with quantum sl(2) invariant boundary conditions.......In this note, we derive the spectrum of the infinite quantum XXZ spin chain with domain wall boundary conditions. The eigenstates are constructed as limits of Bethe states for the finite XXZ spin chain with quantum sl(2) invariant boundary conditions....

  8. Multi-reflection boundary conditions for lattice Boltzmann models

    OpenAIRE

    d´Humiéres, D.; Ginzburg, I

    2002-01-01

    We present a unified approach of several boundary conditions for lattice Boltzmann models. Its general framework is a generalization of previously introduced schemes such as the bounce-back rule, linear or quadratic interpolations, etc. The objectives are two fold: first to give theoretical tools to study the existing boundary conditions and their corresponding accuracy; secondly to design formally third- order accurate boundary conditions for general flows. Using these boundary conditions, C...

  9. Conjugate boundary condition, hidden matters, and gauge-Higgs inflation

    CERN Document Server

    Abe, Yugo; Kawamura, Yoshiharu; Nishikawa, Yasunari

    2016-01-01

    We propose an idea that hidden matters can be separated according to gauge quantum numbers from the visible ones by the difference of boundary conditions on extra dimensions. We formulate 5-dimensional gauge theories yielding conjugate boundary conditions besides ordinary ones on $S^1/Z_2$, and examine physical implications concerning hidden matters on an extension of the standard model coexisting different types of boundary conditions. A model with conjugate boundary conditions is applied on a gauge-Higgs inflation scenario.

  10. On reweighting for twisted boundary conditions

    CERN Document Server

    Bussone, Andrea; Hansen, Martin; Pica, Claudio

    2016-01-01

    We consider the possibility of using reweighting techniques in order to correct for the breaking of unitarity when twisted boundary conditions are imposed on valence fermions in simulations of lattice gauge theories. We start by studying the properties of reweighting factors and their variances at tree-level. That leads us to the introduction of a factorization for the fermionic reweighting determinant. In the numerical, stochastic, implementation of the method, we find that the effect of reweighting is negligible in the case of large volumes but it is sizeable when the volumes are small and the twisting angles are large. More importantly, we find that for un-improved Wilson fermions, and in small volumes, the dependence of the critical quark mass on the twisting angle is quite pronounced and results in large violations of the continuum dispersion relation.

  11. Thermal momentum distribution from shifted boundary conditions

    CERN Document Server

    Giusti, Leonardo

    2011-01-01

    At finite temperature the distribution of the total momentum is an observable characterizing the thermal state of a field theory, and its cumulants are related to thermodynamic potentials. In a relativistic system at zero chemical potential, for instance, the thermal variance of the total momentum is a direct measure of the entropy. We relate the generating function of the cumulants to the ratio of a path integral with properly shifted boundary conditions in the compact direction over the ordinary partition function. In this form it is well suited for Monte-Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang--Mills theory, and obtain the entropy density at three different temperatures.

  12. Boundary conditions in first order gravity: Hamiltonian and Ensemble

    OpenAIRE

    Aros, Rodrigo

    2005-01-01

    In this work two different boundary conditions for first order gravity, corresponding to a null and a negative cosmological constant respectively, are studied. Both boundary conditions allows to obtain the standard black hole thermodynamics. Furthermore both boundary conditions define a canonical ensemble. Additionally the quasilocal energy definition is obtained for the null cosmological constant case.

  13. On Hydroelastic Body-Boundary Condition of Floating Structures

    DEFF Research Database (Denmark)

    Xia, Jinzhu

    1996-01-01

    A general linear body boundary condition of hydroelastic analysis of arbitrary shaped floating structures generalizes the classic kinematic rigid-body (Timman-Newman) boundary condition for seakeeping problems. The new boundary condition is consistent with the existing theories under certain...

  14. Effects of Boundary Conditions on Single-File Pedestrian Flow

    CERN Document Server

    Zhang, Jun; Seyfried, Armin

    2015-01-01

    In this paper we investigate effects of boundary conditions on one dimensional pedestrian flow which involves purely longitudinal interactions. Qualitatively, stop-and-go waves are observed under closed boundary condition and dissolve when the boundary is open. To get more detailed information the fundamental diagrams of the open and closed systems are compared using Voronoi-based measurement method. Higher maximal specific flow is observed from the pedestrian movement at open boundary condition.

  15. Measuring the entropy from shifted boundary conditions

    CERN Document Server

    Giusti, Leonardo

    2013-01-01

    We explore a new computational strategy for determining the equation of state of the SU(3) Yang-Mills theory. By imposing shifted boundary conditions, the entropy density is computed from the vacuum expectation value of the off-diagonal components T_{0k} of the energy-momentum tensor. A step-scaling function is introduced to span a wide range in temperature values. We present preliminary numerical results for the entropy density and its step-scaling function obtained at eight temperature values in the range T_c - 15 T_c. At each temperature, discretization effects are removed by simulating the theory at several lattice spacings and by extrapolating the results to the continuum limit. Finite-size effects are always kept below the statistical errors. The absence of ultraviolet power divergences and the remarkably small discretization effects allow for a precise determination of the step-scaling function in the explored temperature range. These findings establish this strategy as a viable solution for an accurat...

  16. STOCHASTIC ANALYSIS OF GROUNDWATER FLOW SUBJECT TO RANDOM BOUNDARY CONDITIONS

    Institute of Scientific and Technical Information of China (English)

    SHI Liang-sheng; YANG Jin-zhong; CAI Shu-ying; LIN Lin

    2008-01-01

    A stochastic model was developed to simulate the flow in heterogeneous media subject to random boundary conditions.Approximate partial differential equations were derived based on the Karhunen-Loeve (KL) expansion and perturbation expansion. The effect of random boundary conditions on the two-dimensional flow was examined. It is shown that the proposed stochastic model is efficient to include the random boundary conditions. The random boundaries lead to the increase of head variance and velocity variance. The influence of the random boundary conditions on head uncertainty is exerted over the whole simulated region, while the randomness of the boundary conditions leads to the increase of the velocity variance in the vicinity of boundaries.

  17. Optimal boundary conditions at the staircase-shaped coastlines

    CERN Document Server

    Kazantsev, Eugene

    2014-01-01

    A 4D-Var data assimilation technique is applied to the rectangular-box configuration of the NEMO in order to identify the optimal parametrization of boundary conditions at lateral boundaries. The case of the staircase-shaped coastlines is studied by rotating the model grid around the center of the box. It is shown that, in some cases, the formulation of the boundary conditions at the exact boundary leads to appearance of exponentially growing modes while optimal boundary conditions allow to correct the errors induced by the staircase-like appriximation of the coastline.

  18. A qualitative theory for parabolic problems under dynamical boundary conditions

    Directory of Open Access Journals (Sweden)

    von Bellow Joachim

    2000-01-01

    Full Text Available For nonlinear parabolic problems in a bounded domain under dynamical boundary conditions, general comparison techniques are established similar to the ones under Neumann or Dirichlet boundary conditions. In particular, maximum principles and basic a priori estimates are derived, as well as lower and upper solution techniques that lead to functional band type estimates for classical solutions. Finally, attractivity properties of equilibria are discussed that also illustrate the damping effect of the dissipative dynamical boundary condition.

  19. Viscosity in molecular dynamics with periodic boundary conditions

    OpenAIRE

    Viscardy, S.; Gaspard, P.

    2003-01-01

    We report a study of viscosity by the method of Helfand moment in systems with periodic boundary conditions. We propose a new definition of Helfand moment which takes into account the minimum image convention used in molecular dynamics with periodic boundary conditions. Our Helfand-moment method is equivalent to the method based on the Green-Kubo formula and is not affected by ambiguities due to the periodic boundary conditions. Moreover, in hard-ball systems, our method is equivalent to the ...

  20. New boundary conditions for the c=-2 ghost system

    Energy Technology Data Exchange (ETDEWEB)

    Creutzig, T. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Quella, T. [Amsterdam Univ. (Netherlands). KdV Inst. for Mathematics; Schomerus, V. [Center for Mathematical Physics, Hamburg (Germany)]|[King' s College London (United Kingdom). Dept. of Mathematics

    2006-12-15

    We investigate a novel boundary condition for the bc system with central charge c=-2. Its boundary state is constructed and tested in detail. It appears to give rise to the first example of a local logarithmic boundary sector within a bulk theory whose Virasoro zero modes are diagonalizable. (orig.)

  1. Time-dependent boundary conditions for multiphase flow

    OpenAIRE

    Olsen, Robert

    2004-01-01

    In this thesis a set of boundary conditions for multiphase flow is suggested.Characteristic-based boundary conditions are reviewed for single-phase flow. The problem of open-boundary conditions is investigated, and to avoid drifting values, the use of control functions is proposed.The use of control functions is also verified with a new test which assesses the quality of the boundary conditions. Particularly, P- and PI-control functions are examined. PI-controllers have the ability to specify...

  2. Solvability of a fourth order boundary value problem with periodic boundary conditions

    Directory of Open Access Journals (Sweden)

    Chaitan P. Gupta

    1988-01-01

    Full Text Available Fourth order boundary value problems arise in the study of the equilibrium of an elastaic beam under an external load. The author earlier investigated the existence and uniqueness of the solutions of the nonlinear analogues of fourth order boundary value problems that arise in the equilibrium of an elastic beam depending on how the ends of the beam are supported. This paper concerns the existence and uniqueness of solutions of the fourth order boundary value problems with periodic boundary conditions.

  3. A Note on Boundary Conditions for the LWR Model

    OpenAIRE

    Marušić, Sanja

    2009-01-01

    The paper studies the boundary conditions for the standard LWR model describing the traffic flow. The notion of the BLN (Bardos, Leroux and Nédélec) condition is described. In the context of traffic flow the BLN conditions have some natural interpretation. The conditions on the density and on the flow and their meaning in real-life situations are discussed. KEY WORDS: LWR model, traffic flow, hyperbolic conservation law, boundary conditions

  4. Boundary Conditions and Heterotic Construction in Topological Membrane Theory

    OpenAIRE

    Cooper, Leith; Kogan, Ian I.

    1996-01-01

    Using the topological membrane approach to string theory, we suggest a geometric origin for the heterotic string. We show how different membrane boundary conditions lead to different string theories. We discuss the construction of closed oriented strings and superstrings, and demonstrate how the heterotic construction naturally arises from a specific choice of boundary conditions on the left and right boundaries of a cylindrical topological membrane.

  5. Electrostatics of solvated systems in periodic boundary conditions

    OpenAIRE

    Andreussi, Oliviero; Marzari, Nicola

    2014-01-01

    Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary conditions, their extension to materials simulations --- typically entailing periodic-boundary conditions --- is very recent, and special care is needed to address correctly the electrostatic terms. We discuss here how periodic-boundary corrections develop...

  6. Anti-Periodic Boundary Conditions in Supersymmetric DLCQ

    OpenAIRE

    Pinsky, S.; Trittmann, U.

    2000-01-01

    It is of considerable importance to have a numerical method for solving supersymmetric theories that can support a non-zero central charge. The central charge in supersymmetric theories is in general a boundary integral and therefore vanishes when one uses periodic boundary conditions. One is therefore prevented from studying BPS states in the standard supersymmetric formulation of DLCQ (SDLCQ). We present a novel formulation of SDLCQ where the fields satisfy anti-periodic boundary conditions...

  7. Neural Boundary Conditions in Optic Guides

    OpenAIRE

    Özkan-Bakbak, Pınar

    2015-01-01

    In this study, the boundary coefficients of Transverse Electric (TE) and Transverse Magnetic (TM) modes at a planar slab optic guides are modeled by Neural Networks (NN). After modal analysis, train and test files are prepared for NN. Multi-Layer Perceptron (MLP) and Radial Basis Function (RBF) neural networks are performed and compared with each other. NNs are expected to be capable of modeling optical fiber technology in industry based on the same approaches as a result of this study.

  8. Boundary Conditions for Thermoelectric Cooling in p- n Junction

    Science.gov (United States)

    Lashkevych, Igor; Gurevich, Yury G.

    2011-05-01

    The article is devoted to analysis of the boundary conditions for the Peltier effect in semiconductors containing potential barriers ( p-n junction). The full system of boundary conditions, taking into consideration the presence of nonequilibrium charge carriers, is offered. The surface recombination of charge carriers is taken into account for both the electric current and the propagation of heat.

  9. Performance of Numerical Boundary Condition based on Active Wave Absorption

    DEFF Research Database (Denmark)

    Troch, Peter; De Rouck, Julien; Frigaard, Peter

    2001-01-01

    The performance of a new active wave generating-absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces is presented.......The performance of a new active wave generating-absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces is presented....

  10. Periodic Boundary Conditions in the ALEGRA Finite Element Code

    Energy Technology Data Exchange (ETDEWEB)

    AIDUN,JOHN B.; ROBINSON,ALLEN C.; WEATHERBY,JOE R.

    1999-11-01

    This document describes the implementation of periodic boundary conditions in the ALEGRA finite element code. ALEGRA is an arbitrary Lagrangian-Eulerian multi-physics code with both explicit and implicit numerical algorithms. The periodic boundary implementation requires a consistent set of boundary input sets which are used to describe virtual periodic regions. The implementation is noninvasive to the majority of the ALEGRA coding and is based on the distributed memory parallel framework in ALEGRA. The technique involves extending the ghost element concept for interprocessor boundary communications in ALEGRA to additionally support on- and off-processor periodic boundary communications. The user interface, algorithmic details and sample computations are given.

  11. Superconducting circuit boundary conditions and the Dynamical Casimir Effect

    CERN Document Server

    Doukas, Jason

    2014-01-01

    We study analytically the time-dependent boundary conditions of superconducting microwave circuit experiments in the high plasma frequency limit, in which the conditions are Robin-type and relate the value of the field to the spatial derivative of the field. We solve the field evolution explicitly for boundary condition modulations that are small in magnitude but may have arbitrary time dependence, both for a half-open waveguide and for a closed waveguide with two independently adjustable boundaries. The correspondence between the microwave Robin boundary conditions and the mechanically-moving Dirichlet boundary conditions of the Dynamical Casimir Effect is shown to break down at high field frequencies, approximately one order of magnitude above the frequencies probed in the 2011 experiment of Wilson et al. Our results bound the parameter regime in which a microwave circuit can be used to model relativistic effects in a mechanically-moving cavity, and they show that beyond this parameter regime moving mirrors...

  12. Gravitational instability on the brane: the role of boundary conditions

    CERN Document Server

    Shtanov, Y; Sahni, V; Shtanov, Yuri; Viznyuk, Alexander; Sahni, Varun

    2007-01-01

    An outstanding issue in braneworld theory concerns the setting up of proper boundary conditions for the brane-bulk system. Boundary conditions (BC's) employing regulatory branes or demanding that the bulk metric be nonsingular have yet to be implemented in full generality. In this paper, we take a different route and specify boundary conditions directly on the brane thereby arriving at a local and closed system of equations (on the brane). We consider a one-parameter family of boundary conditions involving the anisotropic stress of the projection of the bulk Weyl tensor on the brane and derive an exact system of equations describing scalar cosmological perturbations on a generic braneworld with induced gravity. Depending upon our choice of boundary conditions, perturbations on the brane either grow moderately (region of stability) or rapidly (instability). In the instability region, the evolution of perturbations usually depends upon the scale: small scale perturbations grow much more rapidly than those on la...

  13. Finite difference time domain implementation of surface impedance boundary conditions

    Science.gov (United States)

    Beggs, John H.; Luebbers, Raymond J.; Yee, Kane S.; Kunz, Karl S.

    1991-01-01

    Surface impedance boundary conditions are employed to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In the finite difference solution, they also can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media throughout the solution volume. The standard approach is to approximate the surface impedance over a very small bandwidth by its value at the center frequency, and then use that result in the boundary condition. Here, two implementations of the surface impedance boundary condition are presented. One implementation is a constant surface impedance boundary condition and the other is a dispersive surface impedance boundary condition that is applicable over a very large frequency bandwidth and over a large range of conductivities. Frequency domain results are presented in one dimension for two conductivity values and are compared with exact results. Scattering width results from an infinite square cylinder are presented as a two dimensional demonstration. Extensions to three dimensions should be straightforward.

  14. Poynting Flux-Conserving Boundary Conditions for Global MHD Models

    Science.gov (United States)

    Xi, S.; Lotko, W.; Zhang, B.; Brambles, O.; Lyon, J.; Merkin, V. G.; Wiltberger, M. J.

    2014-12-01

    Poynting Flux-conserving boundary conditions that conserve low-frequency, magnetic field-aligned, electromagnetic energy flux across the low-altitude (or inner) boundary in global magnetospheric magnetohydrodynamics (MHD) models is presented. This method involves the mapping of both the potential from the ionosphere and the perpendicular magnetic field from the inner magnetosphere to the ghost cells of the computational domain. The single fluid Lyon-Fedder-Mobarry (LFM) model is used to verify this method. The comparisons of simulations using the standard hardwall boundary conditions of the LFM model and the flux-conserving boundary conditions show that the method reported here improves the transparency of the boundary for the flow of low-frequency (essentially DC) electromagnetic energy flux along field lines. As a consequence, the field-aligned DC Poynting flux just above the boundary is very nearly equal to the ionospheric Joule heating, as it should be if electromagnetic energy is conserved.

  15. Condition of Prequantization to Two-Dimensional Manifolds with Boundary

    Institute of Scientific and Technical Information of China (English)

    SHAO Ming-Xue; ZHU Zhong-Yuan

    2001-01-01

    The Weil's integrality condition of prequantization is generalized to two-dimensional phase space with boundaries. It is shown that in the prequantization condition a term related to the symplectic potential on the boundary appears. The necessity of the generalized condition is proved by analyzing the isolated singularities of the Hermitian bundle while the sufficiency of the condition is proved via geometric construction on the space of equivalence class.

  16. SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SEMI-LINEAR RETARDED DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

    Institute of Scientific and Technical Information of China (English)

    任景莉; 葛渭高

    2003-01-01

    A boundary value problems f or functional differenatial equations, with nonlinear boundary condition, is studied by the theorem of differential inequality. Using new method to construct the upper solution and lower solution, sufficient conditions for the existence of the problems' solution are established. A uniformly valid asymptotic expansions of the solution is also given.

  17. Periodic boundary conditions for three dimensional dislocation dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Huang, H., Diaz de la Rubia, T. [Materials Science and Technology Division, Chemistry and Materials Science Directorate, Lawrence Livermore National Lab., CA (United States)

    1997-01-01

    The boundary conditions in three dimensional Dislocation Dynamics (DD) simulations have always been a matter of concern. Two types of boundary conditions, quasi-free-surface and reflection boundaries are currently being used by groups in Grenoble, France and Pullman, Washington. In this paper, we present a mathematical transformation that enables simulations of dislocation evolution processes in single crystals using periodic boundary conditions (PBCs). The idea is graphically demonstrated with transformation matrices given for BCC crystal systems. Extension to other crystal structures is also discussed. Comparing to the existing boundary conditions, the new approach (1) balances the dislocation flux in and out of a computational cell; and (2) does not require artificial termination of dislocations in the bulk. 3 refs., 2 figs., 1 tab.

  18. Breakup of spiral wave under different boundary conditions

    Institute of Scientific and Technical Information of China (English)

    Zhao Ying-Kui; Wang Guang-Rui; Chen Shi-Gang

    2007-01-01

    In this paper, we investigate the breakup of spiral wave under no-flux, periodic and Dirichlet boundary conditions respectively. When the parameter ε is close to a critical value for Doppler-induced wave breakup, the instability of the system caused by the boundary effect occurs in the last two cases, resulting in the breakup of spiral wave near the boundary. With our defined average order measure of spiral wave (AOMSW), we quantify the degree of order of the system when the boundary-induced breakup of spiral wave happens. By analysing the AOMSW and outer diameter R of the spiral tip orbit, it is easy to find that this boundary effect is correlated with large values of R, especially under the Dirichlet boundary condition. This correlation is nonlinear, so the AOMSW sometimes oscillates with the variation of ε.

  19. On consistent boundary conditions for c = 1 string theory

    CERN Document Server

    O'Loughlin, M H

    1995-01-01

    We introduce a new parametrisation for the Fermi sea of the c = 1 matrix model. This leads to a simple derivation of the scattering matrix, and a calculation of boundary corrections in the corresponding 1+1--dimensional string theory. The new parametrisation involves relativistic chiral fields, rather than the non-relativistic fields of the usual formulations. The calculation of the boundary corrections, following recent work of Polchinski, allows us to place restrictions on the boundary conditions in the matrix model. We provide a consistent set of boundary conditions, but believe that they need to be supplemented by some more subtle relationship between the space-time and matrix model. Inspired by these boundary conditions, some thoughts on the black hole in c=1 string theory are presented.

  20. Boundary states and finite size effects in sine-Gordon model with Neumann boundary condition

    OpenAIRE

    Bajnok, Z.; Palla, L.; Takacs, G.

    2001-01-01

    The sine-Gordon model with Neumann boundary condition is investigated. Using the bootstrap principle the spectrum of boundary bound states is established. Somewhat surprisingly it is found that Coleman-Thun diagrams and bound state creation may coexist. A framework to describe finite size effects in boundary integrable theories is developed and used together with the truncated conformal space approach to confirm the bound states and reflection factors derived by bootstrap.

  1. Half-space Kinetic Equations with General Boundary Conditions

    CERN Document Server

    Li, Qin; Sun, Weiran

    2015-01-01

    We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various type of reflections, extending our previous work [LLS14] on half-space equations with incoming boundary conditions. As in [LLS14], the main technique is a damping adding-removing procedure. We establish the well-posedness of linear (or linearized) half-space equations with general boundary conditions and quasi-optimality of the numerical scheme. The numerical method is validated by examples including a two-species transport equation, a multi-frequency transport equation, and the linearized BGK equation in 2D velocity space.

  2. Integrability of the Inozemtsev Spin Chain with Open Boundary Conditions

    Institute of Scientific and Technical Information of China (English)

    XUE Wei-Xing; WANG Yu-Peng

    2004-01-01

    @@ A long range interacting quantum spin chain with open boundary conditions is proposed. By constructing the reflection spin-Dunkl operators, the integrability of the model is proven. The model is therefore exactly solvable via the asymptotic Bethe ansatz method and falls into the universal class of the usual Heisenberg spin chain with boundary fields.

  3. Numerical Solution for the Helmholtz Equation with Mixed Boundary Condition

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    We consider the numerical solution for the Helmholtz equation in R2 with mixed boundary conditions. The solvability of this mixed boundary value problem is established by the boundary integral equation method. Based on the Green formula, we express the solution in terms of the boundary data. The key to the numerical realization of this method is the computation of weakly singular integrals. Numerical performances show the validity and feasibility of our method. The numerical schemes proposed in this paper have been applied in the realization of probe method for inverse scattering problems.

  4. Analyticity of thermoelastic plates with dynamical boundary conditions

    Institute of Scientific and Technical Information of China (English)

    ZHANG; Qiong(张琼); HUANG; Falun(黄发伦)

    2003-01-01

    We consider a thermoelastic plate with dynamical boundary conditions. Using the contradictionargument of Pazy's well-known analyticity criterion and P.D.E. estimates, we prove that the corresponding C0semigroup is analytic, hence exponentially stable.

  5. Crystal potentials under invariant periodic boundary conditions at infinity

    OpenAIRE

    Kholopov, Eugene V.

    2002-01-01

    The definiteness of bulk electrostatic potentials in solids under periodic boundary conditions defined in an invariant manner has been proved in the general case of triclinic symmetry. Some principal consequences following from the universal potential correction arising are discussed briefly.

  6. Two Baryons with Twisted Boundary Conditions

    Energy Technology Data Exchange (ETDEWEB)

    Briceno, Raul [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Davoudi, Zohreh [Univ. of Washington, Seattle, WA (United States) and Institute for Nuclear Theory, Seattle, WA (United States); Luu, Thomas [Lawrence Livermore National Laboratory, Livermore, CA (United States); Savage, Martin [Univ. of Washington, Seattle, WA (United States) and Institute for Nuclear Theory, Seattle, WA (United States)

    2014-04-01

    The quantization condition for two particle systems with arbitrary number of two-body open coupled-channels, spin and masses in a finite cubic volume is presented. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. The result is fully relativistic and holds for all momenta below inelastic thresholds and is exact up to exponential volume corrections that are governed by m{sub {pi}} L, where m{sub {pi}} is the pion mass and L is the spatial extent of my box. Its implication for the studies of coupled-channel baryon-baryon systems is discussed, and the necessary tools for implementing the formalism are review.

  7. A generalized theory on the penetrating boundary conditions

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    A generalized formula for penetrating boundary conditions is derived based on the Z-transform. The well-known absorbing boundary conditions (ABCs), such as the Mur's ABC, and Liao's ABC, can be deduced from the formula. Furthermore, some new ABCs can also be deduced from it. The stability of these ABCs are demonstrated via Von Neumann method and their validity is verified by numerical examples.

  8. On the Vilenkin boundary condition proposal in anisotropic universes

    Energy Technology Data Exchange (ETDEWEB)

    Louko, J.; Vachaspati, T.

    1989-06-01

    We show that the Vilenkin boundary condition proposal, as formulated in terms of the Klein-Gordon type current, does not specify a unique wave function in the vacuum minisuperspace models of the Kantowski-Sachs type and the locally rotationally symmetric Bianchi type III. The underlying reasons are directly in the classical dynamics of the models. We also discuss the suggestion of relating the Vilenkin proposal to a lorentzian path integral with the causal boundary condition advocated by Teitelboim.

  9. SHEAR WAVES IN PERIODIC WAVEGUIDE WITH ALTERNATING BOUNDARY CONDITIONS

    OpenAIRE

    Piliposyan D.G.; Ghazaryan R.A.; Ghazaryan K.B.

    2014-01-01

    The propagation of shear waves in elastic waveguide of periodic structure consisting of three different materials with alternating along the guide walls boundary conditions is investigated. Using the transfer matrix approach the problem is reduced to the solution of a block transfer matrix eigenvalue problem. Bloth the dispersion and the band gap structure analysis have been carried out numerically. It is shown that for alternating boundary conditions along the waveguide walls, by modulating ...

  10. Electrostatics in Periodic Boundary Conditions and Real-space Corrections

    OpenAIRE

    Dabo, Ismaila; Kozinsky, Boris; Singh-Miller, Nicholas E.; Marzari, Nicola

    2007-01-01

    We address periodic-image errors arising from the use of periodic boundary conditions to describe systems that do not exhibit full three-dimensional periodicity. The difference between the periodic potential, as straightforwardly obtained from a Fourier transform, and the potential satisfying any other boundary conditions can be characterized analytically. In light of this observation, we present an efficient real-space method to correct periodic-image errors, based on a multigrid solver for ...

  11. The Density Matrix Renormalization Group technique with periodic boundary conditions

    OpenAIRE

    Gendiar, Andrej; Surda, Anton

    2000-01-01

    The Density Matrix Renormalization Group (DMRG) method with periodic boundary conditions is introduced for two dimensional classical spin models. It is shown that this method is more suitable for derivation of the properties of infinite 2D systems than the DMRG with open boundary conditions despite the latter describes much better strips of finite width. For calculation at criticality, phenomenological renormalization at finite strips is used together with a criterion for optimum strip width ...

  12. Periodic solutions to nonlinear equations with oblique boundary conditions

    OpenAIRE

    Allergretto, Walter; Papini, Duccio

    2012-01-01

    We study the existence of positive periodic solutions to nonlinear elliptic and parabolic equations with oblique and dynamical boundary conditions and non-local terms. The results are obtained through fixed point theory, topological degree methods and properties of related linear elliptic problems with natural boundary conditions and possibly non-symmetric principal part. As immediate consequences, we also obtain estimates on the principal eigenvalue for non-symmetric elliptic ...

  13. Effect of boundary conditions on thermal plume growth

    Science.gov (United States)

    Kondrashov, A.; Sboev, I.; Rybkin, K.

    2016-07-01

    We have investigated the influence of boundary conditions on the growth rate of convective plumes. Temperature and rate fields were studied in a rectangular convective cell heated by a spot heater. The results of the full-scale test were compared with the numerical data calculated using the ANSYS CFX software package. The relationship between the heat plume growth rate and heat boundary conditions, the width and height of the cell, size of heater for different kinds of liquid was established.

  14. Domain structures of ferroelectric films under different electrical boundary conditions

    OpenAIRE

    Z. D. Zhou; Wu, D Y

    2015-01-01

    A two-dimensional phase field simulation of ferroelectric films is used that incorporates Landau-Devonshire energy, gradient energy and depolarization electrical energy. A new intermediate electrical boundary condition is firstly presented to study the effects on domain structures of ferroelectric films. Two-dimensional simulations of domain structures are carried out under the open circuit (OC), short circuit (SC) and intermediate (IM) electrical boundary conditions. The simulation results s...

  15. Coleman-Gurtin type equations with dynamic boundary conditions

    Science.gov (United States)

    Gal, Ciprian G.; Shomberg, Joseph L.

    2015-02-01

    We present a new formulation and generalization of the classical theory of heat conduction with or without fading memory. As a special case, we investigate the well-posedness of systems which consist of Coleman-Gurtin type equations subject to dynamic boundary conditions, also with memory. Nonlinear terms are defined on the interior of the domain and on the boundary and subject to either classical dissipation assumptions, or to a nonlinear balance condition in the sense of Gal (2012). Additionally, we do not assume that the interior and the boundary share the same memory kernel.

  16. On Impulsive Boundary Value Problems of Fractional Differential Equations with Irregular Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Guotao Wang

    2012-01-01

    Full Text Available We study nonlinear impulsive differential equations of fractional order with irregular boundary conditions. Some existence and uniqueness results are obtained by applying standard fixed-point theorems. For illustration of the results, some examples are discussed.

  17. On the wave equation with semilinear porous acoustic boundary conditions

    KAUST Repository

    Graber, Philip Jameson

    2012-05-01

    The goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary/interior sources and a nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. The main difficulty in proving the local existence result is that the Neumann boundary conditions experience loss of regularity due to boundary sources. Using an approximation method involving truncated sources and adapting the ideas in Lasiecka and Tataru (1993) [28], we show that the existence of solutions can still be obtained. Second, we prove that under some restrictions on the source terms, then the local solution can be extended to be global in time. In addition, it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ODE and depends on the behavior of the damping terms. In several situations, the obtained ODE can be easily solved and the decay rates can be given explicitly. Third, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution ceases to exists and blows up in finite time. Moreover, in either the absence of the interior source or the boundary source, then we prove that the solution is unbounded and grows as an exponential function. © 2012 Elsevier Inc.

  18. Transmitting boundary and radiation conditions at infinity

    Institute of Scientific and Technical Information of China (English)

    LIAO; Zhenpeng; (Z.P.Liao

    2001-01-01

    Theoretical calculation of the dissociation widths of 〈10] and 1/2〈11] superdislocations with different orientations and configurations have been carried out under the equilibrium condition that the total elastic interaction force acting on partial dislocations is balanced by the fault surface tension acting in the opposite direction. The results show that the superdislocation dissociation widths depended not only on stacking fault energies and dislocation characteristics but also on elastic anisotropy, superdislocation types and dissociation modes. Under the elastic anisotropy, the dissociation width of screw 1/2〈11] superdislocation is larger than that of screw 〈10 ]superdislocation, and the dissociation width of edged 1/2〈11] superdislocation is smaller than that of edged 〈10] superdislocation with the same stacking fault energy. The dissociation widths under the twofold, threefold and fourfold dissociations are also evaluated with anisotropy. The present results help to determine the stacking fault energies and evaluate the mobility of superdislocation in TiAl.

  19. Climate model boundary conditions for four Cretaceous time slices

    Directory of Open Access Journals (Sweden)

    J. O. Sewall

    2007-06-01

    Full Text Available General circulation models (GCMs are useful tools for investigating the characteristics and dynamics of past climates. Understanding of past climates contributes significantly to our overall understanding of Earth's climate system. One of the most time consuming, and often daunting, tasks facing the paleoclimate modeler, particularly those without a geological background, is the production of surface boundary conditions for past time periods. These boundary conditions consist of, at a minimum, continental configurations derived from plate tectonic modeling, topography, bathymetry, and a vegetation distribution. Typically, each researcher develops a unique set of boundary conditions for use in their simulations. Thus, unlike simulations of modern climate, basic assumptions in paleo surface boundary conditions can vary from researcher to researcher. This makes comparisons between results from multiple researchers difficult and, thus, hinders the integration of studies across the broader community. Unless special changes to surface conditions are warranted, researcher dependent boundary conditions are not the most efficient way to proceed in paleoclimate investigations. Here we present surface boundary conditions (land-sea distribution, paleotopography, paleobathymetry, and paleovegetation distribution for four Cretaceous time slices (120 Ma, 110 Ma, 90 Ma, and 70 Ma. These boundary conditions are modified from base datasets to be appropriate for incorporation into numerical studies of Earth's climate and are available in NetCDF format upon request from the lead author. The land-sea distribution, bathymetry, and topography are based on the 1°×1° (latitude x longitude paleo Digital Elevation Models (paleoDEMs of Christopher Scotese. Those paleoDEMs were adjusted using the paleogeographical reconstructions of Ronald Blakey (Northern Arizona University and published literature and were then modified for use in GCMs. The paleovegetation

  20. Climate model boundary conditions for four Cretaceous time slices

    Directory of Open Access Journals (Sweden)

    J. O. Sewall

    2007-11-01

    Full Text Available General circulation models (GCMs are useful tools for investigating the characteristics and dynamics of past climates. Understanding of past climates contributes significantly to our overall understanding of Earth's climate system. One of the most time consuming, and often daunting, tasks facing the paleoclimate modeler, particularly those without a geological background, is the production of surface boundary conditions for past time periods. These boundary conditions consist of, at a minimum, continental configurations derived from plate tectonic modeling, topography, bathymetry, and a vegetation distribution. Typically, each researcher develops a unique set of boundary conditions for use in their simulations. Thus, unlike simulations of modern climate, basic assumptions in paleo surface boundary conditions can vary from researcher to researcher. This makes comparisons between results from multiple researchers difficult and, thus, hinders the integration of studies across the broader community. Unless special changes to surface conditions are warranted, researcher dependent boundary conditions are not the most efficient way to proceed in paleoclimate investigations. Here we present surface boundary conditions (land-sea distribution, paleotopography, paleobathymetry, and paleovegetation distribution for four Cretaceous time slices (120 Ma, 110 Ma, 90 Ma, and 70 Ma. These boundary conditions are modified from base datasets to be appropriate for incorporation into numerical studies of Earth's climate and are available in NetCDF format upon request from the lead author. The land-sea distribution, bathymetry, and topography are based on the 1°×1° (latitude × longitude paleo Digital Elevation Models (paleoDEMs of Christopher Scotese. Those paleoDEMs were adjusted using the paleogeographical reconstructions of Ronald Blakey (Northern Arizona University and published literature and were then modified for use in GCMs. The paleovegetation

  1. Incorporation of an elliptical boundary condition into the program POISSON

    International Nuclear Information System (INIS)

    This report is the third in a series which takes into account the boundary condition in electromagnetic problems such as used by the program POISSON. Here we extend the analysis to permit the use of an elliptical boundary both for two-dimensional and axisymmetric cylindrical problems. The use of an elliptical boundary instead of a circular one can reduce the mesh size when using the program POISSON and thereby save computing time. Saving cpu time can be significant for problems such as the 2-in-1 dipole proposed for the SSC or other magnets such as solenoids. We therefore expect the use of an elliptical boundary to be more general and the previous spherical boundary solution to be a special case

  2. On Cauchy conditions for asymmetric mixed convection boundary layer flows

    Energy Technology Data Exchange (ETDEWEB)

    Amaouche, Mustapha [Laboratoire de Physique Theorique, Universite de Bejaia (Algeria); Kessal, Mohand [Departement Transport et Equipement Petrolier, Faculte des Hydrocarbures et de la Chimie, Universite de Boumerdes, 35000, Boumerdes (Algeria)

    2003-06-01

    The fundamental question of how and where does an asymmetric mixed convection boundary layer flow around a heated horizontal circular cylinder begin to develop is raised. We first transform the classical boundary layer equations by using an integral method of Karman-Pohlhausen type and obtain two coupled equations governing the evolutions of the dynamic and thermal boundary layers. Because of its global character, the implemented method allows to bypass the difficulty of downstream-upstream interactions. Cauchy conditions characterizing the starting of the boundary layers are found; they are obtained in a surprisingly simple manner for the limiting cases corresponding to Pr=1, Pr{yields}0 and Pr{yields}{infinity}. Otherwise, these conditions can be found by using a prediction correction algorithm. Some numerical experiments are finally performed in order to illustrate the theory. (authors)

  3. Boundary conditions for GL-twisted N=4 SYM

    CERN Document Server

    Henningson, Mans

    2011-01-01

    We consider topologically twisted N=4 supersymmetric Yang-Mills theory on a four-manifold of the form V = W \\times R_+ or V = W \\times I, where W is a Riemannian three-manifold. Different kinds of boundary conditions apply at infinity or at finite distance. We verify that each of these conditions defines a `middle-dimensional' subspace of the space of all bulk solutions. Taking the two boundaries of V into account should thus generically give a discrete set of solutions. We explicitly find the spherically symmetric solutions when W = S^3 endowed with the standard metric. For widely separated boundaries, these consist of a pair of solutions which coincide for a certain critical value of the boundary separation and disappear for even smaller separations.

  4. PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL

    Institute of Scientific and Technical Information of China (English)

    Hussein A.H. Salem

    2011-01-01

    In this article, we investigate the existence of Pseudo solutions for some frac- tional order boundary value problem with integral boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function. To encompass the full scope of this article, we give an example illustrating the main result.

  5. Determination of optical properties by variation of boundary conditions

    Science.gov (United States)

    Nickell, Stephan; Essenpreis, Matthias; Kraemer, U.; Kohl-Bareis, Matthias; Boecker, Dirk

    1998-01-01

    Propagation of photons in multiple scattering media depends on absorbing and scattering properties as well as the boundary conditions of the semi-infinite medium. A new method is shown that makes use of differences in boundary conditions to determine the optical properties. Induced are these different conditions by varying the reflectivity of a sensor head. We describe the influence of the change in reflectivity with the common diffusion theory. By building a ratio between the spatially-resolved diffuse reflectance under different boundary conditions it is possible to calculate the optical properties of homogeneous phantoms. Due to optical heterogeneities in living tissue, limitations of the method was observed, which restricts the application to in vivo measurements.

  6. A unified slip boundary condition for flow over a surface

    CERN Document Server

    Thalakkottor, Joseph John

    2015-01-01

    Interface between two phases of matter are ubiquitous in nature and technology. Determining the correct velocity condition at an interface is essential for understanding and designing of flows over a surface. We demonstrate that both the widely used no-slip and the Navier and Maxwell slip boundary conditions do not capture the complete physics associated with complex problems, such as spreading of liquids or corner flows. Hence, we present a unified boundary condition that is applicable to a wide-range of flow problems.

  7. STURM-LIOUVILLE PROBLEMS WITH EIGENDEPENDENT BOUNDARY AND TRANSMISSIONS CONDITIONS

    Institute of Scientific and Technical Information of China (English)

    Z. Akdo(g)an; M. Demirci; O.Sh. Mukhtarov

    2005-01-01

    The purpose of this paper is to extend some fundamental spectral properties of regular Sturm-Liouville problems to special kind discontinuous boundary value problem,which consist of a Sturm-Liouville equation with piecewise continuous potential together with eigenvalue parameter on the boundary and transmission conditions. The authors suggest their own approach for finding asymptotic approximations formulas for eigenvalues and eigenfunctions of such discontinuous problems.

  8. A quasi-potential for conservation laws with boundary conditions

    CERN Document Server

    Bahadoran, Christophe

    2010-01-01

    We compute the quasi-potential and determine minimizing paths for an action functional related to scalar conservation laws on an interval with boundary conditions in the sense of Bardos et al. (1979). Taking as input an exclusion-like flux function, a strictly convex entropy, and boundary data, we obtain a generalization of the functional derived by Derrida, Lebowtiz and Speer (2003) for the stationary large deviations of the asymmetric exclusion process.

  9. Variational Data Assimilation for Optimizing Boundary Conditions in Ocean Models

    CERN Document Server

    Kazantsev, Christine; Tolstykh, Mikhail

    2016-01-01

    The review describes the development of ideas Gury Ivanovich Marchuk in the field of variational data assimilation for ocean models applied in particular in coupled models for long-range weather forecasts. Particular attention is paid to the optimization of boundary conditions on rigid boundaries. As idealized and realistic model configurations are considered. It is shown that the optimization allows us to determine the most sensitive model operators and bring the model solution closer to the assimilated data.

  10. Structural Anisotropy in Polar Fluids Subjected to Periodic Boundary Conditions

    OpenAIRE

    Stenhammar, Joakim; Karlström, Gunnar; Linse, Per

    2011-01-01

    A heuristic model based on dielectric continuum theory for the long-range solvation free energy of a dipolar system possessing periodic boundary conditions (PBCs) is presented. The predictions of the model are compared to simulation results for Stockmayer fluids simulated using three different cell geometries. The boundary effects induced by the PBCs are shown to lead to anisotropies in the apparent dielectric constant and the long-range solvation free energy of as much as 50%. However, the s...

  11. Comment on the uncertainty relation with periodic boundary conditions

    OpenAIRE

    Fujikawa, Kazuo

    2010-01-01

    The Kennard-type uncertainty relation $\\Delta x\\Delta p >\\frac{\\hbar}{2}$ is formulated for a free particle with given momentum $ inside a box with periodic boundary conditions in the large box limit. Our construction of a free particle state is analogous to that of the Bloch wave in a periodic potential. A simple Robertson-type relation, which minimizes the effect of the box boundary and may be useful in some practical applications, is also presented.

  12. Molecular Dynamics ofa Coulomb System with Deformable Periodic Boundary Conditions

    OpenAIRE

    Totsuji, Hiroo; Shirokoshi, Hideki; Nara, Shigetoshi

    1991-01-01

    Variable shape molecular dynamics is formulated for the one-component plasma and the structural transition from the fcc lattice to the bcc lattice has been observed. It is emphasized that the condition of constant volume should be imposed when deformations of periodic boundary conditions are taken into account.

  13. Ambarzumyan's theorem for the quasi-periodic boundary conditions

    Science.gov (United States)

    Kıraç, Alp Arslan

    2015-10-01

    We obtain the classical Ambarzumyan's theorem for the Sturm-Liouville operators Lt(q) with qin L1[0,1] and quasi-periodic boundary conditions, tin [0,2π ) , when there is not any additional condition on the potential q.

  14. On reversibility of cellular automata with periodic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Nobe, Atsushi [Graduate School of Engineering Science, Osaka University, Machikaneyama-cho 1-3, Toyonaka, Osaka 560-8531 (Japan); Yura, Fumitaka [Imai Quantum Computing and Information Project, ERATO, JST, Daini Hongo White Bldg 201, 5-28-3 Hongo, Bunkyo, Tokyo 113-0033 (Japan)

    2004-06-04

    Reversibility of one-dimensional cellular automata with periodic boundary conditions is discussed. It is shown that there exist exactly 16 reversible elementary cellular automaton rules for infinitely many cell sizes by means of a correspondence between elementary cellular automaton and the de Bruijn graph. In addition, a sufficient condition for reversibility of three-valued and two-neighbour cellular automaton is given.

  15. Solving wave equation with spectral methods and nonreflecting boundary conditions

    CERN Document Server

    Novák, J; Novak, Jerome; Bonazzola, Silvano

    2002-01-01

    A multidomain spectral method for solving wave equations is presented. This method relies on the expansion of functions on basis of spherical harmonics $(Y_l^m(\\theta, \\phi))$ for the angular dependence and of Chebyshev polynomials $T_n(x)$ for the radial part. The spherical domains consist of shells surrounding a nucleus and cover the space up to a finite radius $R$ at which boundary conditions are imposed. Time derivatives are estimated using standard finite-differences second order schemes, which are chosen to be implicit to allow for (almost) any size of time-step. Emphasis is put on the implementation of absorbing boundary conditions that allow for the numerical boundary to be completely transparent to the physical wave. This is done using a multipolar expansion of an exact boundary condition for outgoing waves, which is truncated at some point. Using an auxiliary function, which is solution of a wave equation on the sphere defining the outer boundary of the numerical grid, the absorbing boundary conditi...

  16. Transport Synthetic Acceleration with Opposing Reflecting Boundary Conditions

    International Nuclear Information System (INIS)

    The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations.Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iterating on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration.The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented

  17. Transport synthetic acceleration with opposing reflecting boundary conditions

    International Nuclear Information System (INIS)

    The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations. Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iterating on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration. The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented

  18. Critical effects of downstream boundary conditions on vortex breakdown

    Science.gov (United States)

    Kandil, Osama; Kandil, Hamdy A.; Liu, C. H.

    1992-01-01

    The unsteady, compressible, full Navier-Stokes (NS) equations are used to study the critical effects of the downstream boundary conditions on the supersonic vortex breakdown. The present study is applied to two supersonic vortex breakdown cases. In the first case, quasi-axisymmetric supersonic swirling flow is considered in a configured circular duct, and in the second case, quasi-axisymmetric supersonic swirling jet, that is issued from a nozzle into a supersonic jet of lower Mach number, is considered. For the configured duct flow, four different types of downstream boundary conditions are used, and for the swirling jet flow from the nozzle, two types of downstream boundary conditions are used. The solutions are time accurate which are obtained using an implicit, upwind, flux-difference splitting, finite-volume scheme.

  19. Role of the basin boundary conditions in gravity wave turbulence

    CERN Document Server

    Deike, Luc; Gutiérrez-Matus, Pablo; Jamin, Timothée; Semin, Benoit; Aumaitre, Sébastien; Berhanu, Michael; Falcon, Eric; BONNEFOY, Félicien

    2014-01-01

    Gravity wave turbulence is studied experimentally in a large wave basin where irregular waves are generated unidirectionally. The role of the basin boundary conditions (absorbing or reflecting) and of the forcing properties are investigated. To that purpose, an absorbing sloping beach opposite to the wavemaker can be replaced by a reflecting vertical wall. We observe that the wave field properties depend strongly on these boundary conditions. Quasi-one dimensional field of nonlinear waves propagate before to be damped by the beach whereas a more multidirectional wave field is observed with the wall. In both cases, the wave spectrum scales as a frequency-power law with an exponent that increases continuously with the forcing amplitude up to a value close to -4, which is the value predicted by the weak turbulence theory. The physical mechanisms involved are probably different according to the boundary condition used, but cannot be easily discriminated with only temporal measurements. We have also studied freely...

  20. Boundary conditions on internal three-body wave functions

    Energy Technology Data Exchange (ETDEWEB)

    Mitchell, Kevin A.; Littlejohn, Robert G.

    1999-10-01

    For a three-body system, a quantum wave function {Psi}{sub m}{sup {ell}} with definite {ell} and m quantum numbers may be expressed in terms of an internal wave function {chi}{sub k}{sup {ell}} which is a function of three internal coordinates. This article provides necessary and sufficient constraints on {chi}{sub k}{sup {ell}} to ensure that the external wave function {Psi}{sub k}{sup {ell}} is analytic. These constraints effectively amount to boundary conditions on {chi}{sub k}{sup {ell}} and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form r{sup |m|} at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum.

  1. Vibration Analysis of Annular Sector Plates under Different Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Dongyan Shi

    2014-01-01

    Full Text Available An analytical framework is developed for the vibration analysis of annular sector plates with general elastic restraints along each edge of plates. Regardless of boundary conditions, the displacement solution is invariably expressed as a new form of trigonometric expansion with accelerated convergence. The expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. This work allows a capability of modeling annular sector plates under a variety of boundary conditions and changing the boundary conditions as easily as modifying the material properties or dimensions of the plates. Of equal importance, the proposed approach is universally applicable to annular sector plates of any inclusion angles up to 2π. The reliability and accuracy of the current method are adequately validated through numerical examples.

  2. Some Notes on Reaction Diffusion Systems with Nonlinear Boundary Conditions

    Institute of Scientific and Technical Information of China (English)

    Wen-jun Sun

    2003-01-01

    This paper deals with the existence and nonexistence of global positive solution to a semilinear reaction-diffusion system with nonlinear boundary conditions. For the heat diffusion case, the necessary and sufficient conditions on the global existence of all positive solutions are obtained. For the general fast diffusion case, we get some conditions on the global existence and nonexistence of positive solutions. The results of this paper fill the some gaps which were left in this field.

  3. The use of toroidal boundary conditions in the program POISSON

    International Nuclear Information System (INIS)

    In circular particle accelerators of moderate size, one cannot entirely neglect the curvature of the structure and of the guide field. In practice, one may wish to restrict the region of analysis to that near the working aperture, while excluding a very substantial area closer to (and including) the axis of rotational symmetry. In this way, a more efficient mesh can be generated for a program such as POISSON. In restricting the solution to the region of interest, there must be concern regarding a suitable termination of the problem at the boundary of the mesh. For these reasons, we have employed toroidal coordinates in constructing the boundary to a relaxation mesh, and in formulating the boundary conditions that then would be imposed at such boundaries. 11 refs., 6 figs

  4. Thermodynamically admissible boundary conditions for the regularized 13 moment equations

    Energy Technology Data Exchange (ETDEWEB)

    Rana, Anirudh Singh, E-mail: anirudh@uvic.ca [Department of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju, Gyeongnam 52828 (Korea, Republic of); Struchtrup, Henning, E-mail: struchtr@uvic.ca [Department of Mechanical Engineering, University of Victoria, Victoria, British Columbia V8W 2Y2 (Canada)

    2016-02-15

    A phenomenological approach to the boundary conditions for linearized R13 equations is derived using the second law of thermodynamics. The phenomenological coefficients appearing in the boundary conditions are calculated by comparing the slip, jump, and thermal creep coefficients with linearized Boltzmann solutions for Maxwell’s accommodation model for different values of the accommodation coefficient. For this, the linearized R13 equations are solved for viscous slip, thermal creep, and temperature jump problems and the results are compared to the solutions of the linearized Boltzmann equation. The influence of different collision models (hard-sphere, Bhatnagar–Gross–Krook, and Maxwell molecules) and accommodation coefficients on the phenomenological coefficients is studied.

  5. The 8-vertex model with quasi-periodic boundary conditions

    OpenAIRE

    Niccoli, G.; Terras, V.

    2015-01-01

    We study the inhomogeneous 8-vertex model (or equivalently the XYZ Heisenberg spin-1/2 chain) with all kinds of integrable quasi-periodic boundary conditions: periodic, $\\sigma^x$-twisted, $\\sigma^y$-twisted or $\\sigma^z$-twisted. We show that in all these cases but the periodic one with an even number of sites $\\mathsf{N}$, the transfer matrix of the model is related, by the vertex-IRF transformation, to the transfer matrix of the dynamical 6-vertex model with antiperiodic boundary condition...

  6. Area coverage of radial Levy flights with periodic boundary conditions

    OpenAIRE

    Vahabi, Mahsa; Schulz, Johannes H. P.; Shokri, Babak; Metzler, Ralf

    2012-01-01

    We consider the time evolution of two-dimensional Levy flights in a finite area with periodic boundary conditions. From simulations we show that the fractal path dimension d_f and thus the degree of area coverage grows in time until it reaches the saturation value d_f=2 at sufficiently long times. We also investigate the time evolution of the probability density function and associated moments in these boundary conditions. Finally we consider the mean first passage time as function of the sta...

  7. SHEAR WAVES IN PERIODIC WAVEGUIDE WITH ALTERNATING BOUNDARY CONDITIONS

    Directory of Open Access Journals (Sweden)

    Piliposyan D.G.

    2014-06-01

    Full Text Available The propagation of shear waves in elastic waveguide of periodic structure consisting of three different materials with alternating along the guide walls boundary conditions is investigated. Using the transfer matrix approach the problem is reduced to the solution of a block transfer matrix eigenvalue problem. Bloth the dispersion and the band gap structure analysis have been carried out numerically. It is shown that for alternating boundary conditions along the waveguide walls, by modulating the ratio of the length of the unit cell to the width of the waveguide, the minimum widths of the stop bands can be moved to the middle of the Brillouin zone

  8. Planar waveguide with "twisted" boundary conditions: small width

    CERN Document Server

    Borisov, D

    2011-01-01

    We consider a planar waveguide with "twisted" boundary conditions. By twisting we mean a special combination of Dirichlet and Neumann boundary conditions. Assuming that the width of the waveguide goes to zero, we identify the effective (limiting) operator as the width of the waveguide tends to zero, establish the uniform resolvent convergence in various possible operator norm, and give the estimates for the rates of convergence. We show that studying the resolvent convergence can be treated as a certain threshold effect and we present an elegant technique which justifies such point of view.

  9. Vacuum fluctuations in the presence of nonlinear boundary conditions

    Science.gov (United States)

    Fosco, C. D.; Oxman, L. E.

    2015-12-01

    We consider a system consisting of a quantum, massless, real scalar field, in the presence of nonlinear mirrors: infinite parallel planes, upon which the field satisfies nonlinear boundary conditions. These may appear, for example, in metamaterials having nonlinear response functions. The boundary conditions are implemented by nonquadratic interaction vertices, strictly localized on the mirrors. By using the appropriate perturbative expansions, we obtain approximate expressions for the Casimir energy corresponding to weak coupling, regarding the strength of the interaction terms. We also comment on an alternative expansion scheme that may be useful when the weak coupling expansion is not justified.

  10. Modeling magnetized star-planet interactions: boundary conditions effects

    CERN Document Server

    Strugarek, Antoine; Matt, Sean P; Reville, Victor

    2013-01-01

    We model the magnetized interaction between a star and a close-in planet (SPMIs), using global, magnetohydrodynamic numerical simulations. In this proceedings, we study the effects of the numerical boundary conditions at the stellar surface, where the stellar wind is driven, and in the planetary interior. We show that is it possible to design boundary conditions that are adequate to obtain physically realistic, steady-state solutions for cases with both magnetized and unmagnetized planets. This encourages further development of numerical studies, in order to better constrain and understand SPMIs, as well as their effects on the star-planet rotational evolution.

  11. Optimal control problems for impulsive systems with integral boundary conditions

    Directory of Open Access Journals (Sweden)

    Allaberen Ashyralyev

    2013-03-01

    Full Text Available In this article, the optimal control problem is considered when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of the solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.

  12. Boundary conditions for porous solids saturated with viscous fluid

    Institute of Scientific and Technical Information of China (English)

    M.D.Sharma

    2009-01-01

    Boundary conditions are derived to represent the continuity requirements at the boundaries of a porous solid saturated with viscous fluid.They are derived from the physically grounded principles with a mathematical check on the conservation of energy.The poroelastic solid is a dissipative one for the presence of viscosity in the interstitial fluid.The dissipative stresses due to the viscosity of pore-fluid are well represented in the boundary conditions.The unequal particle motions of two constituents of porous aggregate at a boundary between two solids are explained in terms of the drainage of pore-fluid leading to imperfect bonding.A mathematical model is derived for the partial connection of surface pores at the porous-porous interface.At this interface,the loose-contact slipping and partial pore opening/connection may dissipate a part of strain energy.A numerical example shows that,at the interface between water and oil-saturated sandstone,the modified boundary conditions do affect the energies of the waves refracting into the isotropic porous medium.

  13. Effect of Boundary Conditions on Freezing in Porous Media

    Directory of Open Access Journals (Sweden)

    Rahul Basu

    2004-07-01

    Full Text Available This paper examines a model for coupled heat and mass transfer for freezing in a porous media with Dirichlet and convective boundary conditions. Variables include porosity, heat transfer coefficients, thermal and mass diffusivity, density, latent heat, and boundary temperatures. A simulation for the slab illustrates the appearance of undercooling. A stability criterion for the phase interface is linked with well-known metallurgical parameters like undercooling and freezing rate. A possible mechanism for freckling in ingots of niobium-rich superalloys is examined. It has been shown that heat and mass transfer balance at the interface can affect stability. The effect of boundary conditions on the velocity of freezing is computed for some cases, including the self-freezing process.

  14. Gravitational wave extraction and outer boundary conditions by perturbative matching

    CERN Document Server

    Abrahams, A M; Rupright, M E; Anderson, A; Anninos, P; Baumgarte, T W; Bishop, N T; Brandt, S R; Browne, J C; Camarda, K; Choptuik, M W; Cook, G B; Evans, C R; Finn, L S; Fox, G; Gómez, R; Haupt, T; Huq, M F; Kidder, L E; Klasky, S; Laguna, P; Landry, W; Lehner, L; Lenaghan, J T; Marsa, R L L; Massó, J; Matzner, R A; Mitra, S; Papadopoulos, P P; Parashar, M; Saied, F; Saylor, P E; Scheel, M A; Seidel, E; Shapiro, S L; Shoemaker, D M; Smarr, L L; Szilágyi, B; Teukolsky, S A; Van Putten, M H P M; Walker, P; Winicour, J; York, J W

    1998-01-01

    We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three dimensional numerical relativity code.

  15. On a stochastic Burgers equation with Dirichlet boundary conditions

    Directory of Open Access Journals (Sweden)

    Ekaterina T. Kolkovska

    2003-01-01

    Full Text Available We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

  16. Spectral determinant on graphs with generalized boundary conditions

    OpenAIRE

    Desbois, Jean

    2001-01-01

    The spectral determinant of the Schr\\"odinger operator ($ - \\Delta + V(x) $) on a graph is computed for general boundary conditions. ($\\Delta$ is the Laplacian and $V(x)$ is some potential defined on the graph). Applications to restricted random walks on graphs are discussed.

  17. Radiation and Boundary Conditions in the Theory of Gravitation

    CERN Document Server

    Trautman, Andrzej

    2016-01-01

    The Sommerfeld boundary conditions, applied to an asymptotically weak gravitational field, are shown to imply that the 1/r part of the curvature tensor of a space-time, satisfying the Einstein equations, is of type null in the Petrov classification and that there is then a flux of energy carried away by the outgoing gravitational wave.

  18. Discontinuous Sturm-Liouville Problems with Eigenvalue Dependent Boundary Condition

    Energy Technology Data Exchange (ETDEWEB)

    Amirov, R. Kh., E-mail: emirov@cumhuriyet.edu.tr; Ozkan, A. S., E-mail: sozkan@cumhuriyet.edu.tr [Cumhuriyet University, Department of Mathematics Faculty of Art and Science (Turkey)

    2014-12-15

    In this study, an inverse problem for Sturm-Liouville differential operators with discontinuities is studied when an eigenparameter appears not only in the differential equation but it also appears in the boundary condition. Uniqueness theorems of inverse problems according to the Prüfer angle, the Weyl function and two different eigenvalues sets are proved.

  19. BPS monopole in the space of boundary conditions

    International Nuclear Information System (INIS)

    The space of all possible boundary conditions that respect the self-adjointness of the Hamiltonian operator is known to be given by the group manifold U(2) in one-dimensional quantum mechanics. In this paper we study non-Abelian Berry’s connections in the space of boundary conditions in a simple quantum mechanical system. We consider a system for a free spinless particle on a circle with two point-like interactions described by the U(2) × U(2) family of boundary conditions. We show that, for a certain SU(2) ⊂ U(2) × U(2) subfamily of boundary conditions, all the energy levels become doubly-degenerate thanks to the so-called higher-derivative supersymmetry, and the non-Abelian Berry’s connection in the ground-state sector is given by the Bogomolny–Prasad–Sommerfield (BPS) monopole of SU(2) Yang–Mills–Higgs theory. We also show that, in the ground-state sector of this quantum mechanical model, the matrix elements of the position operator give the adjoint Higgs field that satisfies the BPS equation. It is also discussed that Berry’s connections in the excited-state sectors are given by non-BPS ’t Hooft–Polyakov monopoles. (paper)

  20. Periodic boundary conditions in a 3D hydro code

    Energy Technology Data Exchange (ETDEWEB)

    Morgan, D L; Neely, J R; Vantine, H C

    1998-09-18

    We have modified a 3D hydrodynamics code so that it has the capability to impose periodic boundary conditions on the problem being considered. This capability allows it to treat only a basic symmetry unit of the problem when translational or rotational periodic symmetries are present. The code has been run successfully for two test problems involving rotational symmetries.

  1. DMRG and periodic boundary conditions: a quantum information perspective

    OpenAIRE

    Verstraete, F.; Porras, D.; Cirac, J. I.

    2004-01-01

    We introduce a picture to analyze the density matrix renormalization group (DMRG) numerical method from a quantum information perspective. This leads us to introduce some modifications for problems with periodic boundary conditions in which the results are dramatically improved. The picture also explains some features of the method in terms of entanglement and teleportation.

  2. Light-Cone Quantization Without Periodic Boundary Conditions

    OpenAIRE

    Maeno, Masahiro

    2002-01-01

    This paper describes a light-cone quantization of a two-dimensional massive scalar field without periodic boundary conditions in order to make the quantization manifestly consistent to causality. For this purpose, the field is decomposed by the Legendre polynomials. Creation-annihilation operators for this field are defined and the Fock space was constructed.

  3. One-dimensional inhomogeneous Ising model with periodic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Percus, J.K.; Zhang, M.Q.

    1988-12-01

    In this paper, we focus on the essential difference between the inhomogeneous one-dimensional Ising model with open and periodic boundary conditions. We show that, although the profile equation in the periodic case becomes highly nonlocal, due to a topological collective mode, there exists a local free-energy functional in an extended space and one can solve the inhomogeneous problem exactly.

  4. On the algebraic Bethe ansatz: Periodic boundary conditions

    OpenAIRE

    Lima-Santos, A.

    2006-01-01

    In this paper, the algebraic Bethe ansatz with periodic boundary conditions is used to investigate trigonometric vertex models associated with the fundamental representations of the non-exceptional Lie algebras. This formulation allow us to present explicit expressions for the eigenvectors and eigenvalues of the respective transfer matrices.

  5. Boundary conditions for surface reactions in lattice Boltzmann simulations

    NARCIS (Netherlands)

    Gillissen, J.J.J.; Looije, N.

    2014-01-01

    A surface reaction boundary condition in multicomponent lattice Boltzmann simulations is developed. The method is applied to a test case with nonlinear reaction rates and nonlinear density profiles. The results are compared to the corresponding analytical solution, which shows that the error of the

  6. Positive Solutions for Nonlinear Differential Equations with Periodic Boundary Condition

    Directory of Open Access Journals (Sweden)

    Shengjun Li

    2012-01-01

    Full Text Available We study the existence of positive solutions for second-order nonlinear differential equations with nonseparated boundary conditions. Our nonlinearity may be singular in its dependent variable. The proof of the main result relies on a nonlinear alternative principle of Leray-Schauder. Recent results in the literature are generalized and significantly improved.

  7. THE NAVIER-STOKES EQUATIONS WITH THE KINEMATIC AND VORTICITY BOUNDARY CONDITIONS ON NON-FLAT BOUNDARIES

    Institute of Scientific and Technical Information of China (English)

    Gui-Qiang Chen; Dan Osborne; Zhongmin Qian

    2009-01-01

    We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in RN with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-fiat boundary. We observe that, under the nonhomogeneons boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition (without the incompressibility condition), which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in RN(n≥3) with nonhomogeneous vorticity boundary condition converge in L2 to the corresponding Euler equations satisfying the kinematic condition.

  8. Reduction of XXZ model with generalized periodic boundary conditions

    OpenAIRE

    Belavin, A. A.; Gubanov, S. Yu.

    2002-01-01

    We examine the XXZ model with generalized periodic boundary conditions and identify conditions for the truncation of the functional fusion relations of the transfer matrix fusion. After the truncation, the fusion relations become a closed system of functional equations. The energy spectrum can be obtained by solving these equations. We obtain the explicit form of the Hamiltonian eigenvalues for the special case where the anisotropy parameter $q^4=-1.

  9. Planar waveguide with "twisted" boundary conditions: discrete spectrum

    CERN Document Server

    Borisov, Denis

    2011-01-01

    We consider a planar waveguide with combined Dirichlet and Neumann conditions imposed in a "twisted" way. We study the discrete spectrum and describe it dependence on the configuration of the boundary conditions. In particular, we show that in certain cases the model can have discrete eigenvalues emerging from the threshold of the essential spectrum. We give a criterium for their existence and construct them as convergent holomorphic series.

  10. Free, transverse vibrations of thin plates with discontinuous boundary conditions

    Science.gov (United States)

    Febbo, M.; Vera, S. A.; Laura, P. A. A.

    2005-03-01

    Vibrations of circular and rectangular plates clamped on part of the boundary and simply supported along the remainder are analyzed by means of a method of perturbation of boundary conditions. This approach appears to be simple and straightforward, giving excellent results for the first mode and its versatility permits to extend it to higher modes of vibration without difficulty. Furthermore, it is shown that the fundamental frequency coefficient can also be determined using a modified Galerkin approach and very simple polynomial coordinate functions which yield good engineering accuracy.

  11. Boundary Conditions for NHEK through Effective Action Approach

    Institute of Scientific and Technical Information of China (English)

    CHEN Bin; NING Bo; ZHANG Jia-Ju

    2012-01-01

    We study the asymptotic symmetry group (ASG) of the near horizon geometry of extreme Kerr black hole through the effective action approach developed by Porfyriadis and Wilczek (arXiv:1007.1031v1[gr qc]).By requiring a finite boundary effective action,we derive a new set of asymptotic Killing vectors and boundary conditions,which are much more relaxed than the ones proposed by Matsuo Y et al.[Nucl.Phys.B 825 (2010) 231],and still allow a copy of a conformal group as its ASG.In the covariant formalism,the asymptotic charges are finite,with the corresponding central charge vanishing.By using the quasi-local charge and introducing a plausible cut-off,we find that the higher order terms of the asymptotic Killing vectors,which could not be determined through the effective action approach,contribute to the central charge as well.We also show that the boundary conditions suggested by Guica et al.[Phys.Rev.D 80 (2009)124008] lead to a divergent first-order boundary effective action.%We study the asymptotic symmetry group (ASG) of the near horizon geometry of extreme Kerr black hole through the effective action approach developed by Porfyriadis and Wilczek (arXiv:1007.1031vl[gr qc]). By requiring a finite boundary effective action, we derive a new set of asymptotic Killing vectors and boundary conditions, which are much more relaxed than the ones proposed by Matsuo Y et al. [Nucl. Phys. B 825 (2010) 231], and still allow a copy of a conformal group as its ASG. In the covariant formalism, the asymptotic charges are finite, with the corresponding central charge vanishing. By using the quasi-local charge and introducing a plausible cut-off, we find that the higher order terms of the asymptotic Killing vectors, which could not be determined through the effective action approach, contribute to the central charge as well. We also show that the boundary conditions suggested by Guica et al. [Phys. Rev. D 80 (2009) 124008] lead to a divergent first-order boundary effective action.

  12. Stretched flow of Carreau nanofluid with convective boundary condition

    Indian Academy of Sciences (India)

    T Hayat; M Waqas; S A Shehzad; A Alsaedi

    2016-01-01

    The steady laminar boundary layer flow of Carreau nanofluid over a stretching sheet is investigated. Effects of Brownian motion and thermophoresis are present. Heat transfer is characterized using convective boundary condition at the sheet. The governing partial differential equations are reduced into a set of nonlinear ordinary differential equations through suitable transformations. Results of velocity, temperature and concentration fields are computed via homotopic procedure. Numerical values of skin-friction coefficient, local Nusselt and Sherwood numbers are computed and discussed. A comparative study with existing solutions in a limiting sense is made.

  13. Driven nonequilibrium lattice systems with shifted periodic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Valles, J.L. (New York Univ., NY (USA)); Leung, K.; Zia, R.K.P. (Virginia Polytechnic Institute and State Univ., Blacksburg (USA))

    1989-07-01

    The authors present the first study of a driven nonequilibrium lattice system in the two-phase region, with shifted periodic boundary conditions, forcing steps into the interface. When the shift corresponds to small angles with respect to the driving field, they find nonanalytic behavior in the (internal) energy of the system, supporting numerical evidence that interface roughness is suppressed by the field. For larger shifts, the competition between the driving field and the boundary induces the breakup of a single strip with tilted interfaces into many narrower strips with aligned interfaces. The size and temperature dependences of the critical angles of such breakup transitions are studied.

  14. Thermo Field Dynamics of strings with definite boundary conditions

    CERN Document Server

    Vancea, Ion V

    2015-01-01

    In this paper we review the construction of the thermal bosonic string and $D$-brane in the framework of the Thermo Field Dynamics (TFD). We briefly recall the well-known light-cone quantization of the bosonic string in the conformal gauge in flat space-time. Then we give a bird's eye view of the fundamental concepts of the TFD. Also, we present the thermalization of the bosonic string and the construction of the thermal D-brane boundary state. Finally, we show the calculation of the entropy of the thermal open string states with all boundary conditions and the entropy of the thermal D-brane state.

  15. Most general AdS_3 boundary conditions

    CERN Document Server

    Grumiller, Daniel

    2016-01-01

    We consider the most general asymptotically anti-de Sitter boundary conditions in three-dimensional Einstein gravity with negative cosmological constant. The metric contains in total twelve independent functions, six of which are interpreted as chemical potentials (or non-normalizable fluctuations) and the other half as canonical boundary charges (or normalizable fluctuations). Their presence modifies the usual Fefferman-Graham expansion. The asymptotic symmetry algebra consists of two sl(2)_k current algebras, the levels of which are given by k=l/(4G_N), where l is the AdS radius and G_N the three-dimensional Newton constant.

  16. One-dimensional phase change with periodic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Rizwan-uddin [Univ. of Illinois, Urbana, IL (United States)

    1999-03-01

    Using a recently proposed semianalytical numerical scheme, the author investigated the one-dimensional phase change problem with periodic Dirichlet boundary condition. He analyzed the moving boundary and the temperature distribution for different materials (Stefan number) and for several oscillation amplitudes and oscillation frequencies of the periodically oscillating surface temperature. The effect of the oscillating surface temperature on the evolution of the moving boundary is most pronounced when the domain is small and diminishes as the domain grows. Comparison of temperature distributions at different domain sizes suggests the increasing size of the domain to be the dominant factor that determines the temperature distribution. Numerical experiments show that, for given frequency, the surface temperature variation only impacts the temperature in a region near the surface. For example, for frequency of {pi}/2, once the domain has grown larger than approximately 5 units of length, the temperature for x{prime} > 5 essentially remains constant.

  17. Nonlinear Vibration Analysis of Moving Strip with Inertial Boundary Condition

    Directory of Open Access Journals (Sweden)

    Chong-yi Gao

    2015-01-01

    Full Text Available According to the movement mechanism of strip and rollers in tandem mill, the strip between two stands was simplified to axially moving Euler beam and the rollers were simplified to the inertial component on the fixed axis rotation, namely, inertial boundary. Nonlinear vibration mechanical model of Euler beam with inertial boundary conditions was established. The transverse and longitudinal motion equations were derived based on Hamilton’s principle. Kantorovich averaging method was employed to discretize the motion equations and the inertial boundary equations, and the solutions were obtained using the modified iteration method. Depending on numerical calculation, the amplitude-frequency responses of Euler beam were determined. The axial velocity, tension, and rotational inertia have strong influences on the vibration characteristics. The results would provide an important theoretical reference to control and analyze the vertical vibration of moving strip in continuous rolling process.

  18. Time-domain implementation of an impedance boundary condition with boundary layer correction

    Science.gov (United States)

    Brambley, E. J.; Gabard, G.

    2016-09-01

    A time-domain boundary condition is derived that accounts for the acoustic impedance of a thin boundary layer over an impedance boundary, based on the asymptotic frequency-domain boundary condition of Brambley (2011) [25]. A finite-difference reference implementation of this condition is presented and carefully validated against both an analytic solution and a discrete dispersion analysis for a simple test case. The discrete dispersion analysis enables the distinction between real physical instabilities and artificial numerical instabilities. The cause of the latter is suggested to be a combination of the real physical instabilities present and the aliasing and artificial zero group velocity of finite-difference schemes. It is suggested that these are general properties of any numerical discretization of an unstable system. Existing numerical filters are found to be inadequate to remove these artificial instabilities as they have a too wide pass band. The properties of numerical filters required to address this issue are discussed and a number of selective filters are presented that may prove useful in general. These filters are capable of removing only the artificial numerical instabilities, allowing the reference implementation to correctly reproduce the stability properties of the analytic solution.

  19. Matrix albedo for discrete ordinates infinite-medium boundary condition

    International Nuclear Information System (INIS)

    Discrete ordinates problems with an infinite exterior medium (reflector) can be more efficiently computed by eliminating grid cells in the exterior medium and applying a matrix albedo boundary condition. The albedo matrix is a discretized bidirectional reflection distribution function (BRDF) that accounts for the angular quadrature set, spatial quadrature method, and spatial grid that would have been used to model a portion of the exterior medium. The method is exact in slab geometry, and could be used as an approximation in multiple dimensions or curvilinear coordinates. We present an adequate method for computing albedo matrices and demonstrate their use in verifying a discrete ordinates code in slab geometry by comparison with Ganapol's infinite medium semi-analytic TIEL benchmark. With sufficient resolution in the spatial and angular grids and iteration tolerance to yield solutions converged to 6 digits, the conventional (scalar) albedo boundary condition yielded 2-digit accuracy at the boundary, but the matrix albedo solution reproduced the benchmark scalar flux at the boundary to all 6 digits. (authors)

  20. Boundary Conditions for NHEK through Effective Action Approach

    International Nuclear Information System (INIS)

    We study the asymptotic symmetry group (ASG) of the near horizon geometry of extreme Kerr black hole through the effective action approach developed by Porfyriadis and Wilczek (arXiv:1007.1031v1[gr-qc]). By requiring a finite boundary effective action, we derive a new set of asymptotic Killing vectors and boundary conditions, which are much more relaxed than the ones proposed by Matsuo Y et al. [Nucl. Phys. B 825 (2010) 231], and still allow a copy of a conformal group as its ASG. In the covariant formalism, the asymptotic charges are finite, with the corresponding central charge vanishing. By using the quasi-local charge and introducing a plausible cut-off, we find that the higher order terms of the asymptotic Killing vectors, which could not be determined through the effective action approach, contribute to the central charge as well. We also show that the boundary conditions suggested by Guica et al. [Phys. Rev. D 80 (2009) 124008] lead to a divergent first-order boundary effective action. (the physics of elementary particles and fields)

  1. Analytical Loss Factors in Approximation of the Leontovich Boundary Conditions

    CERN Document Server

    Baturin, S S

    2014-01-01

    Recently the new method of the Cherenkov fields and loss factors of a point-like electron bunch passing through longitudinally homogeneous structures lined with arbitrary slowdown layers was proposed. It was shown that the Cherenkov loss factor of the short bunch does not depend on the waveguide system material and is a constant for any given transverse dimensions and cross-section shapes of the waveguides. It was shown that with the proposed approach one can use a relatively simple method for the calculation of the total loss factor using an integral relation based on the cylindrical slowdown waveguide model. With this paper, we demonstrate that the same integral relation that we call relativistic Gauss theorem can be applied in case impedance boundary conditions (IBC) also known as Leontovich boundary conditions.

  2. Inhibition of the dynamical Casimir effect with Robin boundary conditions

    CERN Document Server

    Rego, Andreson L C; Farina, C; Alves, Danilo T; 10.1103/PhysRevD.87.045024

    2013-01-01

    We consider a real massless scalar field in 3+1 dimensions satisfying a Robin boundary condition at a nonrelativistic moving mirror. Considering vacuum as the initial field state, we compute explicitly the number of particles created per unit frequency and per unit solid angle, exhibiting in this way the angular dependence of the spectral distribution. The well known cases of Dirichlet and Neumann boundary conditions may be reobtained as particular cases from our results. We show that the particle creation rate can be considerably reduced (with respect to the Dirichlet and Neumann cases) for particular values of the Robin parameter. Our results extend for 3+1 dimensions previous results found in the literature for 1+1 dimensions. Further, we also show that this inhibition of the dynamical Casimir effect occurs for different angles of particle emission.

  3. Revisiting Johnson and Jackson boundary conditions for granular flows

    Energy Technology Data Exchange (ETDEWEB)

    Li, Tingwen; Benyahia, Sofiane

    2012-07-01

    In this article, we revisit Johnson and Jackson boundary conditions for granular flows. The oblique collision between a particle and a flat wall is analyzed by adopting the classic rigid-body theory and a more realistic semianalytical model. Based on the kinetic granular theory, the input parameter for the partial-slip boundary conditions, specularity coefficient, which is not measurable in experiments, is then interpreted as a function of the particle-wall restitution coefficient, the frictional coefficient, and the normalized slip velocity at the wall. An analytical expression for the specularity coefficient is suggested for a flat, frictional surface with a low frictional coefficient. The procedure for determining the specularity coefficient for a more general problem is outlined, and a working approximation is provided.

  4. Slarti: A boundary condition editor for a coupled climate model

    Science.gov (United States)

    Mickelson, S. A.; Jacob, R. L.; Pierrehumbert, R.

    2006-12-01

    One of the largest barriers to making climate models more flexible is the difficulty in creating new boundary conditions, especially for "deep time" paleoclimate cases where continents are in different positions. Climate models consist of several mutually-interacting component models and the boundary conditions must be consistent between them. We have developed a program called Slarti which uses a Graphical User Interface and a set of consistency rules to aid researchers in creating new, consistent, boundary condition files for the Fast Ocean Atmosphere Model (FOAM). Users can start from existing mask, topography, or bathymetry data or can build a "world" entirely from scratch (e.g. a single island continent). Once a case has been started, users can modify mask, vegetation, bathymetry, topography, and river flow fields by drawing new data through a "paint" interface. Users activate a synchronization button which goes through the fields to eliminate inconsistencies. When the changes are complete and save is selected, Slarti creates all the necessary files for an initial run of FOAM. The data is edited at the highest resolution (the ocean-land surface in FOAM) and then interpolated to the atmosphere resolution. Slarti was implemented in Java to maintain portability across platforms. We also relied heavily on Java Swing components to create the interface. This allowed us to create an object-oriented interface that could be used on many different systems. Since Slarti allows users to visualize their changes, they are able to see areas that may cause problems when the model is ran. Some examples would be lakes from the river flow field and narrow trenches within the bathymetry. Through different checks and options available through its interface, Slarti makes the process of creating new boundary conditions for FOAM easier and faster while reducing the chance for user errors.

  5. Nonsteady heat conduction code with radiation boundary conditions

    International Nuclear Information System (INIS)

    A heat-transfer model for studying the temperature build-up in graphite blankets for fusion reactors is presented. In essence, the computer code developed is for two-dimensional, nonsteady heat conduction in heterogeneous, anisotropic solids with nonuniform internal heating. Thermal radiation as well as bremsstrahlung radiation boundary conditions are included. Numerical calculations are performed for two design options by varying the wall loading, bremsstrahlung, surface layer thickness and thermal conductivity, blanket dimensions, time step and grid size. (auth)

  6. Nonlinear Vibrations of Multiwalled Carbon Nanotubes under Various Boundary Conditions

    OpenAIRE

    Hossein Aminikhah; Milad Hemmatnezhad

    2011-01-01

    The present work deals with applying the homotopy perturbation method to the problem of the nonlinear oscillations of multiwalled carbon nanotubes embedded in an elastic medium under various boundary conditions. A multiple-beam model is utilized in which the governing equations of each layer are coupled with those of its adjacent ones via the van der Waals interlayer forces. The amplitude-frequency curves for large-amplitude vibrations of single-walled, double-walled, and triple-walled carbon...

  7. Probabilistic flood hazard mapping: effects of uncertain boundary conditions

    Science.gov (United States)

    Domeneghetti, A.; Vorogushyn, S.; Castellarin, A.; Merz, B.; Brath, A.

    2013-08-01

    Comprehensive flood risk assessment studies should quantify the global uncertainty in flood hazard estimation, for instance by mapping inundation extents together with their confidence intervals. This appears of particular importance in the case of flood hazard assessments along dike-protected reaches, where the possibility of occurrence of dike failures may considerably enhance the uncertainty. We present a methodology to derive probabilistic flood maps in dike-protected flood prone areas, where several sources of uncertainty are taken into account. In particular, this paper focuses on a 50 km reach of River Po (Italy) and three major sources of uncertainty in hydraulic modelling and flood mapping: uncertainties in the (i) upstream and (ii) downstream boundary conditions, and (iii) uncertainties in dike failures. Uncertainties in the definition of upstream boundary conditions (i.e. design-hydrographs) are assessed through a copula-based bivariate analysis of flood peaks and volumes. Uncertainties in the definition of downstream boundary conditions are characterised by uncertainty in the rating curve with confidence intervals which reflect discharge measurement and interpolation errors. The effects of uncertainties in boundary conditions and randomness of dike failures are assessed by means of the Inundation Hazard Assessment Model (IHAM), a recently proposed hybrid probabilistic-deterministic model that considers three different dike failure mechanisms: overtopping, piping and micro-instability due to seepage. The results of the study show that the IHAM-based analysis enables probabilistic flood hazard mapping and provides decision-makers with a fundamental piece of information for devising and implementing flood risk mitigation strategies in the presence of various sources of uncertainty.

  8. Probabilistic flood hazard mapping: effects of uncertain boundary conditions

    Directory of Open Access Journals (Sweden)

    A. Domeneghetti

    2013-08-01

    Full Text Available Comprehensive flood risk assessment studies should quantify the global uncertainty in flood hazard estimation, for instance by mapping inundation extents together with their confidence intervals. This appears of particular importance in the case of flood hazard assessments along dike-protected reaches, where the possibility of occurrence of dike failures may considerably enhance the uncertainty. We present a methodology to derive probabilistic flood maps in dike-protected flood prone areas, where several sources of uncertainty are taken into account. In particular, this paper focuses on a 50 km reach of River Po (Italy and three major sources of uncertainty in hydraulic modelling and flood mapping: uncertainties in the (i upstream and (ii downstream boundary conditions, and (iii uncertainties in dike failures. Uncertainties in the definition of upstream boundary conditions (i.e. design-hydrographs are assessed through a copula-based bivariate analysis of flood peaks and volumes. Uncertainties in the definition of downstream boundary conditions are characterised by uncertainty in the rating curve with confidence intervals which reflect discharge measurement and interpolation errors. The effects of uncertainties in boundary conditions and randomness of dike failures are assessed by means of the Inundation Hazard Assessment Model (IHAM, a recently proposed hybrid probabilistic-deterministic model that considers three different dike failure mechanisms: overtopping, piping and micro-instability due to seepage. The results of the study show that the IHAM-based analysis enables probabilistic flood hazard mapping and provides decision-makers with a fundamental piece of information for devising and implementing flood risk mitigation strategies in the presence of various sources of uncertainty.

  9. The XXZ model with anti-periodic twisted boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Niekamp, Soenke; Wirth, Tobias; Frahm, Holger [Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstrasse 2, 30167 Hannover (Germany)

    2009-05-15

    We derive functional equations for the eigenvalues of the XXZ model subject to anti-diagonal twisted boundary conditions by means of fusion of transfer matrices and by Sklyanin's method of separation of variables. Our findings coincide with those obtained using Baxter's method and are compared to the recent solution of Galleas. As an application we study the finite size scaling of the ground-state energy of the model in the critical regime.

  10. A 3D radiative transfer framework: III. periodic boundary conditions

    OpenAIRE

    Hauschildt, Peter H.; Baron, E.

    2008-01-01

    We present a general method to solve radiative transfer problems including scattering in the continuum as well as in lines in 3D configurations with periodic boundary conditions. he scattering problem for line transfer is solved via means of an operator splitting (OS) technique. The formal solution is based on a full characteristics method. The approximate $\\Lambda$ operator is constructed considering nearest neighbors exactly. The code is parallelized over both wavelength and solid angle usi...

  11. Efficient Matrix Product State Method for periodic boundary conditions

    OpenAIRE

    Pippan, Peter; White, Steven R.; Evertz, Hans Gerd

    2008-01-01

    We introduce an efficient method to calculate the ground state of one-dimensional lattice models with periodic boundary conditions. The method works in the representation of Matrix Product States (MPS), related to the Density Matrix Renormalization Group (DMRG) method. It improves on a previous approach by Verstraete et al. We introduce a factorization procedure for long products of MPS matrices, which reduces the computational effort from m^5 to m^3, where m is the matrix dimension, and m ~ ...

  12. The XXZ model with anti-periodic twisted boundary conditions

    OpenAIRE

    Niekamp, Sönke; Wirth, Tobias; Frahm, Holger

    2009-01-01

    We derive functional equations for the eigenvalues of the XXZ model subject to anti-diagonal twisted boundary conditions by means of fusion of transfer matrices and by Sklyanin's method of separation of variables. Our findings coincide with those obtained using Baxter's method and are compared to the recent solution of Galleas. As an application we study the finite size scaling of the ground state energy of the model in the critical regime.

  13. Allowed wavevectors under the application of incommensurate periodic boundary conditions

    OpenAIRE

    Boykin, Timothy B.; Kharche, Neerav; Klimeck, Gerhard

    2005-01-01

    While the energy bands of solids are often thought of as continuous functions of the wavevector, k, they are in fact discrete functions, due to the periodic boundary conditions applied over a finite number of primitive cells. The traditional approach enforces periodicity over a volume containing Ni primitive unit cells along the direction of the primitive lattice vector ai . While this method yields a simple formula for the allowed k, it can be problematic computer programs for lattices such ...

  14. Efficient MPS algorithm for periodic boundary conditions and applications

    OpenAIRE

    Weyrauch, Michael; Rakov, Mykhailo V.

    2013-01-01

    We present an implementation of an efficient algorithm for the calculation of the spectrum of one-dimensional quantum systems with periodic boundary conditions. This algorithm is based on a matrix product representation for quantum states (MPS), and a similar representation for Hamiltonians and other operators (MPO). It is significantly more efficient for systems of about 100 sites and more than for small quantum systems. We apply the formalism to calculate the ground state and first excited ...

  15. Micromagnetic simulations with periodic boundary conditions: Hard-soft nanocomposites

    OpenAIRE

    Wysocki, Aleksander L.; Antropov, Vladimir P.

    2015-01-01

    We developed a micromagnetic method for modeling magnetic systems with periodic boundary conditions along an arbitrary number of dimensions. The main feature is an adaptation of the Ewald summation technique for evaluation of long-range dipolar interactions. The method was applied to investigate the hysteresis process in hard-soft magnetic nanocomposites with various geometries. The dependence of the results on different micromagnetic parameters was studied. We found that for layered structur...

  16. Periodic boundary conditions for demagnetization interactions in micromagnetic simulations

    OpenAIRE

    Lebecki, Krzysztof M.; Donahue, Michael J.; Gutowski, Marek W.

    2008-01-01

    A new method for the introduction of periodic boundary conditions to the self-magnetostatic (demagnetization) tenn in micromagnetic simulations is described, using an Ewald-like summation method in real space. The long-range character of the dipolar interactions is included without any distance cut-offs. The accumulated errors are carefully monitored to provide easy control of the quality of the results. This allows the calculations to be either accurate up to floating point limitations or le...

  17. On Matrix Product States for Periodic Boundary Conditions

    OpenAIRE

    Krebs, Klaus

    1999-01-01

    The possibility of a matrix product representation for eigenstates with energy and momentum zero of a general m-state quantum spin Hamiltonian with nearest neighbour interaction and periodic boundary condition is considered. The quadratic algebra used for this representation is generated by 2m operators which fulfil m^2 quadratic relations and is endowed with a trace. It is shown that {\\em not} every eigenstate with energy and momentum zero can be written as matrix product state. An explicit ...

  18. A PNJL Model for Adjoint Fermions with Periodic Boundary Conditions

    OpenAIRE

    Nishimura, Hiromichi; Ogilvie, Michael C.

    2009-01-01

    Recent work on QCD-like theories has shown that the addition of adjoint fermions obeying periodic boundary conditions to gauge theories on $R^{3}\\times S^{1}$ can lead to a restoration of center symmetry and confinement for sufficiently small circumference $L$ of $S^{1}$. At small $L$, perturbation theory may be used reliably to compute the effective potential for the Polyakov loop $P$ in the compact direction. Periodic adjoint fermions act in opposition to the gauge fields, which by themselv...

  19. GRAPESPH with Fully Periodic Boundary Conditions: Fragmentation of Molecular Clouds

    OpenAIRE

    Klessen, Ralf

    1997-01-01

    A method of adapting smoothed particle hydrodynamics (SPH) with periodic boundary conditions for use with the special purpose device GRAPE is presented. GRAPE (GRAvity PipE) solves the Poisson and force equations for an N-body system by direct summation on a specially designed chip and in addition returns the neighbour list for each particle. Due to its design, GRAPE cannot treat periodic particle distributions directly. This limitation of GRAPESPH can be overcome by computing a correction fo...

  20. Periodic boundary conditions for the simulation of uniaxial extensional flow

    OpenAIRE

    Hunt, Thomas A.

    2013-01-01

    It is very common with molecular dynamics and other simulation techniques to apply Lees-Edwards periodic boundary conditions (PBCs) for the simulation of shear flow. However the behavior of a complex liquid can be quite different under extensional flow. Simple deformation of a simulation cell and its periodic images only allows for simulations of these flows with short duration. For the simulation of planar extensional flow it was recognized that the PBCs of Kraynik and Reinelt [Int. J. Multi...

  1. Boundary conditions for star matter and other periodic fermionic systems

    OpenAIRE

    Gulminelli, F.; Furuta, T.; Juillet, O.; Leclercq, C

    2011-01-01

    International audience Bulk fermionic matter, as it can be notably found in supernova matter and neutrons stars, is subject to correlations of infinite range due to the antisymmetrisation of the N-body wave function, which cannot be explicitly accounted for in a practical simulation. This problem is usually addressed in condensed matter physics by means of the so-called Twist Averaged Boundary Condition method. A different ansatz based on the localized Wannier representation has been propo...

  2. Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions

    NARCIS (Netherlands)

    Grunau, H.-Ch.; Sweers, G.

    2001-01-01

    Cranston, Fabes and Zhao ([26], [5]) established the uniform bound sup x; y 2 x 6= y R G1;n (x; z)G1;n (z; y) dz G1;n (x; y) M < 1; (1) where G1;n (x; y) is the Green function for the Laplacian - with Dirichlet boundary conditions on a Lipschitz domain - Rn with n 3 (see [27] for n = 2). This

  3. Maxwell boundary conditions imply non-Lindblad master equation

    Science.gov (United States)

    Bamba, Motoaki; Imoto, Nobuyuki

    2016-09-01

    From the Hamiltonian connecting the inside and outside of a Fabry-Pérot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds matters, although we can transform it to the Lindblad form by performing the rotating-wave approximation to the connecting Hamiltonian. We calculate absorption spectra by these Lindblad and non-Lindblad master equations and also by the Maxwell boundary conditions in the framework of the classical electrodynamics, which we consider the most reliable approach. We found that, compared to the Lindblad master equation, the absorption spectra by the non-Lindblad one agree better with those by the Maxwell boundary conditions. Although the discrepancy is highlighted only in the ultrastrong light-matter interaction regime with a relatively large broadening, the master equation of the non-Lindblad form is preferable rather than of the Lindblad one for pursuing the consistency with the classical electrodynamics.

  4. Maxwell boundary conditions impose non-Lindblad master equation

    CERN Document Server

    Bamba, Motoaki

    2016-01-01

    From the Hamiltonian connecting the inside and outside of an Fabry-Perot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds matters, although we can transform it to the Lindblad form by performing the rotating-wave approximation to that Hamiltonian. We calculate absorption spectra by these Lindblad and non-Lindblad master equations and also by the Maxwell boundary conditions in framework of the classical electrodynamics, which we consider the most reliable approach. We found that, compared to the Lindblad master equation, the absorption spectra by the non-Lindblad one agree better with those by the Maxwell boundary conditions. Although the discrepancy is highlighted only in the ultra-strong light-matter interaction regime with a relatively large broadening, the master equation of the non-Lindblad form is preferable rather than of the Lindblad one for pursuing the consistency with the classical elec...

  5. Outer boundary conditions for evolving cool white dwarfs

    CERN Document Server

    Rohrmann, R D; García-Berro, E; Córsico, A H; Bertolami, M M Miller

    2012-01-01

    White dwarf evolution is essentially a gravothermal cooling process, which,for cool white dwarfs, sensitively depends on the treatment of the outer boundary conditions. We provide detailed outer boundary conditions appropriate for computing the evolution of cool white dwarfs employing detailed non-gray model atmospheres for pure H composition. We also explore the impact on the white dwarf cooling times of different assumptions for energy transfer in the atmosphere of cool white dwarfs. Detailed non-gray model atmospheres are computed taken into account non-ideal effects in the gas equation of state and chemical equilibrium, collision-induced absorption from molecules, and the Lyman alpha quasi-molecular opacity. Our results show that the use of detailed outer boundary conditions becomes relevant for effective temperatures lower than 5800 and 6100K for sequences with 0.60 and 0.90 M_sun, respectively. Detailed model atmospheres predict ages that are up to approx 10% shorter at log L/L_sun=-4 when compared with...

  6. Influence of different boundary conditions on analysis of SSI

    International Nuclear Information System (INIS)

    In the discussions of structural response to earthquakes, it has been assumed that the foundation medium is very stiff and that the seismic motions applied at the structure support points are the same as the free-field earthquake motions at those locations; in other words, the effects of soil structure interaction (SSI) have been neglected. However, its effects can be significant when the structure supported on a soft soil. Structures on the ground are affected by ground motion when there is seismic loading. The inability of the foundation to resist to deformation of soil would cause huge damages on the structures. The different codes and boundary conditions affect on analysis results of SSI. A comparison of the reactor buildings response as predicted by CLASSI and FLUSH shows substantial differences. To absorb, rather than reflect, the outwardly radiated energy, transmitting boundary conditions and soil structure interface should be taken into consideration in analysis of SSI. The paper discusses influence of several different boundary conditions on analysis of SSI. (author)

  7. Solvability of a fourth-order boundary value problem with periodic boundary conditions II

    OpenAIRE

    Chaitan P. Gupta

    1991-01-01

    Let f:[0,1]×R4→R be a function satisfying Caratheodory's conditions and e(x)∈L1[0,1]. This paper is concerned with the solvability of the fourth-order fully quasilinear boundary value problem d4udx4+f(x,u(x),u′(x),u″(x),u‴(x))=e(x),   0

  8. Solitons induced by boundary conditions from the Boussinesq equation

    Science.gov (United States)

    Chou, Ru Ling; Chu, C. K.

    1990-01-01

    The behavior of solitons induced by boundary excitation is investigated at various time-dependent conditions and different unperturbed water depths, using the Korteweg-de Vries (KdV) equation. Then, solitons induced from Boussinesq equations under similar conditions were studied, making it possible to remove the restriction in the KdV equation and to treat soliton head-on collisions (as well as overtaking collisions) and reflections. It is found that the results obtained from the KdV and the Boussinesq equations are in good agreement.

  9. On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition

    CERN Document Server

    Borisov, Denis; Cardone, Giuseppe

    2010-01-01

    We consider a waveguide modeled by the Laplacian in a straight planar strip. The Dirichlet boundary condition is taken on the upper boundary, while on the lower boundary we impose periodically alternating Dirichlet and Neumann condition assuming the period of alternation to be small. We study the case when the homogenization gives the Neumann condition instead of the alternating ones. We establish the uniform resolvent convergence and the estimates for the rate of convergence. It is shown that the rate of the convergence can be improved by employing a special boundary corrector. Other results are the uniform resolvent convergence for the operator on the cell of periodicity obtained by the Floquet-Bloch decomposition, the two-terms asymptotics for the band functions, and the complete asymptotic expansion for the bottom of the spectrum with an exponentially small error term.

  10. Repulsive Casimir force from fractional Neumann boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Lim, S.C. [Faculty of Engineering, Multimedia University, Jalan Multimedia, 63100 Cyberjaya, Selangor (Malaysia)], E-mail: sclim@mmu.edu.my; Teo, L.P. [Faculty of Information Technology, Multimedia University, Jalan Multimedia, 63100 Cyberjaya, Selangor (Malaysia); Department of Applied Mathematics, Faculty of Engineering, University of Nottingham Malaysia Campus, Jalan Broga, 43500 Semenyih, Selangor Darul Ehsan (Malaysia)], E-mail: lpteo@mmu.edu.my

    2009-08-17

    This Letter studies the finite temperature Casimir force acting on a rectangular piston associated with a massless fractional Klein-Gordon field at finite temperature. Dirichlet boundary conditions are imposed on the walls of a d-dimensional rectangular cavity, and a fractional Neumann condition is imposed on the piston that moves freely inside the cavity. The fractional Neumann condition gives an interpolation between the Dirichlet and Neumann conditions, where the Casimir force is known to be always attractive and always repulsive respectively. For the fractional Neumann boundary condition, the attractive or repulsive nature of the Casimir force is governed by the fractional order which takes values from zero (Dirichlet) to one (Neumann). When the fractional order is larger than 1/2, the Casimir force is always repulsive. For some fractional orders that are less than but close to 1/2, it is shown that the Casimir force can be either attractive or repulsive depending on the aspect ratio of the cavity and the temperature.

  11. Allowed wavevectors under the application of incommensurate periodic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Boykin, Timothy B [Department of Electrical and Computer Engineering, University of Alabama in Huntsville, Huntsville, AL 35899 (United States); Kharche, Neerav [School of Electrical and Computer Engineering and Network for Computational Nanotechnology, Purdue University, West Lafayette, IN 47907 (United States); Klimeck, Gerhard [School of Electrical and Computer Engineering and Network for Computational Nanotechnology, Purdue University, West Lafayette, IN 47907 (United States)

    2006-01-01

    While the energy bands of solids are often thought of as continuous functions of the wavevector, k, they are in fact discrete functions, due to the periodic boundary conditions applied over a finite number of primitive cells. The traditional approach enforces periodicity over a volume containing N{sub i} primitive unit cells along the direction of the primitive lattice vector a{sub i}. While this method yields a simple formula for the allowed k, it can be problematic computer programs for lattices such as face-centred cubic (FCC) where the boundary faces of the primitive cell are not orthogonal. The fact that k is discrete is of critical importance for supercell calculations since they include only a finite number of unit cells, which determines the number of wavevectors, and have a given geometry, which determines their spacing. Rectangular supercells, with the faces orthogonal to the Cartesian axes, are computationally simplest but are not commensurate with the FCC unit cell, so that the traditional approach for determining the allowed k-values is no longer useful. Here, we present a simple method for finding the allowed k-values when periodic boundary conditions are applied over a rectangular supercell, answering the question in both its practical and pedagogical aspects.

  12. Electrostatics of solvated systems in periodic boundary conditions

    Science.gov (United States)

    Andreussi, Oliviero; Marzari, Nicola

    2014-12-01

    Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary conditions, their extension to materials simulations, typically entailing periodic boundary conditions, is very recent, and special care is needed to address correctly the electrostatic terms. We discuss here how periodic boundary corrections developed for systems in vacuum should be modified to take into account solvent effects, using as a general framework the self-consistent continuum solvation model developed within plane-wave density-functional theory [O. Andreussi et al., J. Chem. Phys. 136, 064102 (2012), 10.1063/1.3676407]. A comprehensive discussion of real- and reciprocal-space corrective approaches is presented, together with an assessment of their ability to remove electrostatic interactions between periodic replicas. Numerical results for zero- and two-dimensional charged systems highlight the effectiveness of the different suggestions, and underline the importance of a proper treatment of electrostatic interactions in first-principles studies of charged systems in solution.

  13. Absolute Hydration Free Energies of Ions Under Periodic Boundary Conditions

    Energy Technology Data Exchange (ETDEWEB)

    Won, Youngdo [Hanyang Univ., Seoul (Korea, Republic of)

    2012-12-15

    The additive empirical force field of a monatomic ion is composed of the charge and the Lennard-Jones (LJ) parameters, i. e., the well-depth parameter, ε, and the distance parameter, R{sub min}, at which the potential reaches the minimum. A set of LJ parameters for monocations have been developed by utilizing molecular dynamics simulations under a solvent boundary potential (SBP). A full account of the force field development is in progress and this communication addresses consideration of the air-water phase potential in calculating the absolute free energy of hydration by calculating free energies of hydration, ΔG{sub hyd}, in the presence of periodic boundary conditions (PBC)

  14. Structural Anisotropy in Polar Fluids Subjected to Periodic Boundary Conditions

    Science.gov (United States)

    2011-01-01

    A heuristic model based on dielectric continuum theory for the long-range solvation free energy of a dipolar system possessing periodic boundary conditions (PBCs) is presented. The predictions of the model are compared to simulation results for Stockmayer fluids simulated using three different cell geometries. The boundary effects induced by the PBCs are shown to lead to anisotropies in the apparent dielectric constant and the long-range solvation free energy of as much as 50%. However, the sum of all of the anisotropic energy contributions yields a value that is very close to the isotropic one derived from dielectric continuum theory, leading to a total system energy close to the dielectric value. It is finally shown that the leading-order contribution to the energetic and structural anisotropy is significantly smaller in the noncubic simulation cell geometries compared to when using a cubic simulation cell. PMID:22303290

  15. Applying Twisted Boundary Conditions for Few-body Nuclear Systems

    CERN Document Server

    Körber, Christopher

    2015-01-01

    We describe and implement twisted boundary conditions for the deuteron and triton systems within finite-volumes using the nuclear lattice EFT formalism. We investigate the finite-volume dependence of these systems with different twists angles. We demonstrate how various finite-volume information can be used to improve calculations of binding energies in such a framework. Our results suggests that with appropriate twisting of boundaries, infinite-volume binding energies can be reliably extracted from calculations using modest volume sizes with cubic length $L\\approx8-14$ fm. Of particular importance is our derivation and numerical verification of three-body analogue of `i-periodic' twist angles that eliminate the leading order finite-volume effects to the three-body binding energy.

  16. Applying twisted boundary conditions for few-body nuclear systems

    Science.gov (United States)

    Körber, Christopher; Luu, Thomas

    2016-05-01

    We describe and implement twisted boundary conditions for the deuteron and triton systems within finite volumes using the nuclear lattice EFT formalism. We investigate the finite-volume dependence of these systems with different twist angles. We demonstrate how various finite-volume information can be used to improve calculations of binding energies in such a framework. Our results suggests that with appropriate twisting of boundaries, infinite-volume binding energies can be reliably extracted from calculations using modest volume sizes with cubic length L ≈8 -14 fm. Of particular importance is our derivation and numerical verification of three-body analogs of "i-periodic" twist angles that eliminate the leading-order finite-volume effects to the three-body binding energy.

  17. Impedance-based outflow boundary conditions for human carotid haemodynamics.

    Science.gov (United States)

    Malvè, M; Chandra, S; García, A; Mena, A; Martínez, M A; Finol, E A; Doblaré, M

    2014-01-01

    In this study, we develop structured tree outflow boundary conditions for modelling the human carotid haemodynamics. The model geometry was reconstructed through computerised tomography scan. Unsteady-state computational fluid dynamic analyses were performed under different conditions using a commercial software package ADINA R&D, Inc., (Watertown, MA, USA) in order to assess the impact of the boundary conditions on the flow variables. In particular, the results showed that the peripheral vessels massively impact the pressure while the flow is relatively unaffected. As an example of application of these outflow conditions, an unsteady fluid-structure interaction (FSI) simulation was carried out and the dependence of the wall shear stress (WSS) on the arterial wall compliance in the carotid bifurcation was studied. In particular, a comparison between FSI and rigid-wall models was conducted. Results showed that the WSS distributions were substantially affected by the diameter variation of the arterial wall. In particular, even similar WSS distributions were found for both cases, and differences in the computed WSS values were also found.

  18. Downstream-Conditioned Maximum Entropy Method for Exit Boundary Conditions in the Lattice Boltzmann Method

    Directory of Open Access Journals (Sweden)

    Javier A. Dottori

    2015-01-01

    Full Text Available A method for modeling outflow boundary conditions in the lattice Boltzmann method (LBM based on the maximization of the local entropy is presented. The maximization procedure is constrained by macroscopic values and downstream components. The method is applied to fully developed boundary conditions of the Navier-Stokes equations in rectangular channels. Comparisons are made with other alternative methods. In addition, the new downstream-conditioned entropy is studied and it was found that there is a correlation with the velocity gradient during the flow development.

  19. Towards Multiphase Periodic Boundary Conditions with Flow Rate Constraint

    Science.gov (United States)

    Sawko, Robert; Thompson, Chris P.

    2011-09-01

    This paper presents the development of a solver for a two-phase, stratified flow with periodic boundary conditions. Governing equations are supplemented with a specification of constant mass fluxes for each phase. The method allows an estimate steady state phase fraction and pressure drop in the streamwise direction. The analytical solution for two-phase laminar flow is presented and serves as a validation of the numerical technique. For turbulent conditions, Reynolds-Averaged Navier-Stokes equations are employed and closed with a two-equation model. Experimental data is taken as a reference for the purpose of validation. In both flow conditions the method delivers accurate results although in the case of turbulent flow it requires the specification of interfacial viscosity showing that a direct generalisation of two-equation model is unsatisfactory. Further research avenues are outlined.

  20. Incorporation of toroidal boundary conditions into program POISSON

    International Nuclear Information System (INIS)

    A technique is developed for introduction of a boundary condition applicable to relaxation computations for magnetic problems with axial symmetry and with no sources (currents, or magnetized material) external to the boundary. The procedure as described in this note is restricted to cases in which the (toroidal) boundary will surround completely the region of physical interest but will not encompass the axis of rotational symmetry. The technique accordingly provides the opportunity of economically excluding from the relaxation process regions of no direct concern in the immediate neighborhood of the symmetry axis and hence can have useful application to annular magnetic devices with axial symmetry. The procedure adopted makes use internally of the characteristic form of the vector-potential function, in a source-free region, when expressed in toroidal coordinates. The relevant properties of associated Legendre functions of half-integral degree are summarized in this connection and their introduction into the program POISSON is outlined. Results of some test cases are included, to illustrate the application of this technique for configurations with median-plane symmetry. 8 refs., 9 figs

  1. Reconnection properties in collisionless plasma with open boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Sun, H. E. [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Ma, Z. W., E-mail: zwma@zju.edu.cn [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 310027 (China); Huang, J. [Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 310027 (China)

    2014-07-15

    Collisionless magnetic reconnection in a Harris current sheet with different initial thicknesses is investigated using a 21/2 -D Darwin particle-in-cell simulation with the magnetosonic open boundary condition. It is found that the thicknesses of the ion dissipation region and the reconnection current sheet, when the reconnection rate E{sub r} reaches its first peak, are independent of the initial thickness of the current sheet; while the peak reconnection rate depends on it. The peak reconnection rate increases with decrease of the current sheet thickness as E{sub r}∼a{sup −1/2}, where a is the initial current sheet half-thickness.

  2. Stokes Flow with Slip and Kuwabara Boundary Conditions

    Indian Academy of Sciences (India)

    Sunil Datta; Satya Deo

    2002-08-01

    The forces experienced by randomly and homogeneously distributed parallel circular cylinder or spheres in uniform viscous flow are investigated with slip boundary condition under Stokes approximation using particle-in-cell model technique and the result compared with the no-slip case. The corresponding problem of streaming flow past spheroidal particles departing but little in shape from a sphere is also investigated. The explicit expression for the stream function is obtained to the first order in the small parameter characterizing the deformation. As a particular case of this we considered an oblate spheroid and evaluate the drag on it.

  3. Cauchy-perturbative matching and outer boundary conditions computational studies

    CERN Document Server

    Rezzolla, L; Matzner, R A; Rupright, M E; Shapiro, S L; Rezzolla, Luciano; Abrahams, Andrew M; Matzner, Richard A.; Rupright, Mark E.; Shapiro, Stuart L.

    1999-01-01

    We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the solution of a Cauchy evolution of the nonlinear Einstein field equations to a set of one-dimensional linear equations obtained through perturbation techniques over a curved background. We discuss the validity of this approach in the case of linear and mildly nonlinear gravitational waves and show how a numerical module developed for this purpose is able to provide an accurate and numerically convergent description of the gravitational wave propagation and a stable numerical evolution.

  4. Quantum Nuclear Pasta Calculations with Twisted Angular Boundary Conditions

    Science.gov (United States)

    Schuetrumpf, Bastian; Nazarewicz, Witold

    2015-10-01

    Nuclear pasta, expected to be present in the inner crust of neutron stars and core collapse supernovae, can contain a wide spectrum of different exotic shapes such as nuclear rods and slabs. There are also more complicated, network-like structures, the triply periodic minimal surfaces, already known e.g. in biological systems. These shapes are studied with the Hartree-Fock method using modern Skyrme forces. Furthermore twisted angular boundary conditions are utilized to reduce finite size effects in the rectangular simulation boxes. It is shown, that this improves the accuracy of the calculations drastically and additionally more insights into the mechanism of forming minimal surfaces can be gained.

  5. Periodic boundary conditions for dislocation dynamics simulations in three dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Bulatov, V V; Rhee, M; Cai, W

    2000-11-20

    This article presents an implementation of periodic boundary conditions (PBC) for Dislocation Dynamics (DD) simulations in three dimensions (3D). We discuss fundamental aspects of PBC development, including preservation of translational invariance and line connectivity, the choice of initial configurations compatible with PBC and a consistent treatment of image stress. On the practical side, our approach reduces to manageable proportions the computational burden of updating the long-range elastic interactions among dislocation segments. The timing data confirms feasibility and practicality of PBC for large-scale DD simulations in 3D.

  6. Periodic boundary conditions for demagnetization interactions in micromagnetic simulations

    Energy Technology Data Exchange (ETDEWEB)

    Lebecki, K M; Gutowski, M W [Institute of Physics, Polish Academy of Sciences, 02-668 Warsaw (Poland); Donahue, M J [National Institute of Standards and Technology, Gaithersburg, MD 20899-8910 (United States)

    2008-09-07

    A new method for the introduction of periodic boundary conditions to the self-magnetostatic (demagnetization) term in micromagnetic simulations is described, using an Ewald-like summation method in real space. The long-range character of the dipolar interactions is included without any distance cut-offs. The accumulated errors are carefully monitored to provide easy control of the quality of the results. This allows the calculations to be either accurate up to floating point limitations or less precise when computational speed requirements dominate. This method is incorporated into a full micromagnetic program, and comparisons are made to analytic results.

  7. Implementation of a Blowing Boundary Condition in the LAURA Code

    Science.gov (United States)

    Thompson, Richard a.; Gnoffo, Peter A.

    2008-01-01

    Preliminary steps toward modeling a coupled ablation problem using a finite-volume Navier-Stokes code (LAURA) are presented in this paper. Implementation of a surface boundary condition with mass transfer (blowing) is described followed by verification and validation through comparisons with analytic results and experimental data. Application of the code to a carbon-nosetip ablation problem is demonstrated and the results are compared with previously published data. It is concluded that the code and coupled procedure are suitable to support further ablation analyses and studies.

  8. Vacuum fluctuations in the presence of nonlinear boundary conditions

    CERN Document Server

    Fosco, C D

    2014-01-01

    We consider a system consisting of a quantum, massless, real scalar field, in the presence of nonlinear mirrors: infinite parallel planes, upon which the field satisfies nonlinear boundary conditions. The latter are implemented by non-quadratic interaction vertices, strictly localized on the mirrors. By using the appropriate perturbative expansions, we obtain approximate expressions for the Casimir energy corresponding to weak coupling, regarding the strength of the interaction terms. We also comment on an alternative expansion scheme that may be useful when the weak coupling expansion is not justified.

  9. Numerical solutions of telegraph equations with the Dirichlet boundary condition

    Science.gov (United States)

    Ashyralyev, Allaberen; Turkcan, Kadriye Tuba; Koksal, Mehmet Emir

    2016-08-01

    In this study, the Cauchy problem for telegraph equations in a Hilbert space is considered. Stability estimates for the solution of this problem are presented. The third order of accuracy difference scheme is constructed for approximate solutions of the problem. Stability estimates for the solution of this difference scheme are established. As a test problem to support theoretical results, one-dimensional telegraph equation with the Dirichlet boundary condition is considered. Numerical solutions of this equation are obtained by first, second and third order of accuracy difference schemes.

  10. On the trigonometric Felderhof model with domain wall boundary conditions

    CERN Document Server

    Caradoc, A; Wheeler, M; Zuparic, M; 10.1088/1742-5468/2007/03/P03010

    2008-01-01

    We consider the trigonometric Felderhof model, of free fermions in an external field, on a finite lattice with domain wall boundary conditions. The vertex weights are functions of rapidities and external fields. We obtain a determinant expression for the partition function in the special case where the dependence on the rapidities is eliminated, but for general external field variables. This determinant can be evaluated in product form. In the homogeneous limit, it is proportional to a 2-Toda tau function. Next, we use the algebraic Bethe ansatz factorized basis to obtain a product expression for the partition function in the general case with dependence on all variables.

  11. MHD Free Convective Boundary Layer Flow of a Nanofluid past a Flat Vertical Plate with Newtonian Heating Boundary Condition

    OpenAIRE

    Uddin, Mohammed J.; Khan, Waqar A.; Ahmed I Ismail

    2012-01-01

    Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first convert...

  12. Numerical study of one-dimensional Stefan problem with periodic boundary conditions

    OpenAIRE

    Qu Liang-Hui; Ling Feng; Xing Lin

    2013-01-01

    A finite difference approach to a one-dimensional Stefan problem with periodic boundary conditions is studied. The evolution of the moving boundary and the temperature field are simulated numerically, and the effects of the Stefan number and the periodical boundary condition on the temperature distribution and the evolution of the moving boundary are analyzed.

  13. Numerical study of one-dimensional Stefan problem with periodic boundary conditions

    Directory of Open Access Journals (Sweden)

    Qu Liang-Hui

    2013-01-01

    Full Text Available A finite difference approach to a one-dimensional Stefan problem with periodic boundary conditions is studied. The evolution of the moving boundary and the temperature field are simulated numerically, and the effects of the Stefan number and the periodical boundary condition on the temperature distribution and the evolution of the moving boundary are analyzed.

  14. The NMSSM with F-theory unified boundary conditions

    CERN Document Server

    Aparicio, L; Cerdeno, D G; Ibanez, L E; Valenzuela, I

    2012-01-01

    We study the phenomenological viability of a constrained NMSSM with parameters subject to unified boundary conditions from F-theory GUTs. We find that very simple assumptions about modulus dominance SUSY breaking in F-theory unification lead to a predictive set of boundary conditions, consistent with all phenomenological constraints. The second lightest scalar Higgs H_2 can get a mass m_{H_2} ~ 125 GeV and has properties similar to the SM Higgs. On the other hand the lightest scalar H_1, with a dominant singlet component, would have barely escaped detection at LEP and could be observable at LHC as a peak in H_1 -> gamma gamma at around 100 GeV. The LSP is mostly singlino and is consistent with WMAP constraints due to coannihilation with the lightest stau, whose mass is in the range 100-250 GeV. Such light staus may lead to very characteristic signatures at LHC and be directly searched at linear colliders. In these models tan(beta) is large, of order 50, still the branching ratio for B_s -> mu+ mu- is consiste...

  15. Development of a Discrete Mass Inflow Boundary Condition for MFIX

    Directory of Open Access Journals (Sweden)

    Jordan Musser

    2011-02-01

    Full Text Available MFIX (Multiphase Flow with Interphase eXchanges is an open source software package developed by the National Energy Technology Laboratory (NETL used for modeling the chemical reactions, heat transfer, and hydrodynamics of fluid-solid systems. Currently, the stable publically available release of MFIX does not include a discrete mass inflow boundary condition (DMIBC for its discrete element method (DEM package. Inflow boundary conditions are useful for simulating systems where particles are consumed through chemical reactions and an incoming feed is necessary to sustain the reaction. To implement the DMIBC an inlet staging area is designated outside the computational domain and particles are passed through the wall region associated with the inlet. Forces incurred on entering particles, generated from collisions with particles already in the system, are ignored whereas, particles already in the system respond to contact forces and react accordingly, moving away from the inlet. This approach prevents any unphysical overlap between new and existing particles. It also ensures that particles entering the system will enter the computational domain regardless of opposing forces. Once an incoming particle is fully within the domain, it reacts appropriately to any and all contact force. This approach for a DMIBC has been implemented and is available within the current development version of MFIX.

  16. Two-Baryon Systems with Twisted Boundary Conditions

    CERN Document Server

    Briceno, Raul A; Luu, Thomas C; Savage, Martin J

    2013-01-01

    We explore the use of twisted boundary conditions in extracting the nucleon mass and the binding energy of two-baryon systems, such as the deuteron, from Lattice QCD calculations. Averaging the results of calculations performed with periodic and anti-periodic boundary conditions imposed upon the light-quark fields, or other pair-wise averages, improves the volume dependence of the deuteron binding energy from ~exp(-kappa*L)/L to ~exp(-sqrt(2)kappa*L)/L. However, a twist angle of pi/2 in each of the spatial directions improves the volume dependence from ~exp(-kappa*L)/L to ~exp(-2kappa*L)/L. Twist averaging the binding energy with a random sampling of twist angles improves the volume dependence from ~exp^(-kappa*L)/L to ~exp(-2kappa*L)/L, but with a standard deviation of ~exp(-kappa*L)/L, introducing a signal-to-noise issue in modest lattice volumes. Using the experimentally determined phase shifts and mixing angles, we determine the expected energies of the deuteron states over a range of cubic lattice volume...

  17. Interstellar Matter and the Boundary Conditions of the Heliosphere

    CERN Document Server

    Frisch, P C

    1998-01-01

    The interstellar cloud surrounding the solar system regulates the galactic environment of the Sun, and determines the boundary conditions of the heliosphere. Both the Sun and interstellar clouds move through space, so these boundary conditions change with time. Data and theoretical models now support densities in the cloud surrounding the solar system of n(HI)=0.22+/-0.06 cm^-3, and n(e-)~0.1 cm-3, with larger values allowed for n(HI) by radiative transfer considerations. Ulysses and Extreme Ultraviolet Explorer satellite HeI data yield a cloud temperature of 6,400 K. Nearby interstellar gas appears to be structured and inhomogeneous. The interstellar gas in the Local Fluff cloud complex exhibits elemental abundance patterns in which refractory elements are enhanced over the depleted abundances found in cold disk gas. Within a few parsecs of the Sun, inconclusive evidence for factors of 2--5 variation in MgII and FeII gas phase abundances is found, providing evidence for variable grain destruction. Observatio...

  18. Spatial heterogeneity of ocean surface boundary conditions under sea ice

    Science.gov (United States)

    Barthélemy, Antoine; Fichefet, Thierry; Goosse, Hugues

    2016-06-01

    The high heterogeneity of sea ice properties implies that its effects on the ocean are spatially variable at horizontal scales as small as a few meters. Previous studies have shown that taking this variability into account in models could be required to simulate adequately mixed layer processes and the upper ocean temperature and salinity structures. Although many advanced sea ice models include a subgrid-scale ice thickness distribution, potentially providing heterogeneous surface boundary conditions, the information is lost in the coupling with a unique ocean grid cell underneath. The present paper provides a thorough examination of boundary conditions at the ocean surface in the NEMO-LIM model, which can be used as a guideline for studies implementing subgrid-scale ocean vertical mixing schemes. Freshwater, salt, solar heat and non-solar heat fluxes are examined, as well as the norm of the surface stress. All of the thermohaline fluxes vary considerably between the open water and ice fractions of grid cells. To a lesser extent, this is also the case for the surface stress. Moreover, the salt fluxes in both hemispheres and the solar heat fluxes in the Arctic show a dependence on the ice thickness category, with more intense fluxes for thinner ice, which promotes further subgrid-scale heterogeneity. Our analysis also points out biases in the simulated open water fraction and in the ice thickness distribution, which should be investigated in more details in order to ensure that the latter is used to the best advantage.

  19. Analytical solution for 1D consolidation of unsaturated soil with mixed boundary condition

    Institute of Scientific and Technical Information of China (English)

    Zhen-dong SHAN; Dao-sheng LING; Hao-jiang DING

    2013-01-01

    Based on consolidation equations proposed for unsaturated soil,an analytical solution for 1D consolidation of an unsaturated single-layer soil with nonhomogeneous mixed boundary condition is developed.The mixed boundary condition can be used for special applications,such as tests occur in laboratory.The analytical solution is obtained by assuming all material parameters remain constant during consolidation.In the derivation of the analytical solution,the nonhomogeneous boundary condition is first transformed into a homogeneous boundary condition.Then,the eigenfunction and eigenvalue are derived according to the consolidation equations and the new boundary condition.Finally,using the method of undetermined coefficients and the orthogonal relation of the eigenfunction,the analytical solution for the new boundary condition is obtained.The present method is applicable to various types of boundary conditions.Several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with mixed boundary condition.

  20. Space-dependent core/reflector boundary conditions generated by the boundary element method for pressurized water reactors

    Energy Technology Data Exchange (ETDEWEB)

    Itagaki, M. (Japan Atomic Energy Research Inst., Dept. of Nuclear Ship Engineering, Aza-Kitasekine, Oaza-Sekine, Mutsu, Aomori 035 (JP)); Brebbia, C.A. (Computational Mechanics Inst., Ashurst Lodge, Ashurst, Southampton SO4 2AA (GB))

    1991-03-01

    This paper reports on the boundary element method used to generate energy-dependent matrix-type boundary conditions along core/reflector interfaces and along baffle-plate surfaces of pressurized water reactors. This method enables one to deal with all types of boundary geometries including convex and concave corners. The method is applicable to neutron diffusion problems with more than two energy groups and also can be used to model a reflector with or without a baffle plate. Excellent eigenvalue and flux shape results can be obtained when the boundary conditions generated by this technique are coupled with core-only finite difference calculations.

  1. Homogenized boundary conditions and resonance effects in Faraday cages

    Science.gov (United States)

    Hewitt, I. J.

    2016-01-01

    We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called ‘Faraday cage effect’). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells. PMID:27279775

  2. Topological susceptibility in lattice Yang-Mills theory with open boundary condition

    Energy Technology Data Exchange (ETDEWEB)

    Chowdhury, Abhishek; Harindranath, A. [Theory Division, Saha Institute of Nuclear Physics,1/AF Bidhan Nagar, Kolkata 700064 (India); Maiti, Jyotirmoy [Department of Physics, Barasat Government College,10 KNC Road, Barasat, Kolkata 700124 (India); Majumdar, Pushan [Department of Theoretical Physics, Indian Association for the Cultivation of Science,Kolkata 700032 (India)

    2014-02-11

    We find that using open boundary condition in the temporal direction can yield the expected value of the topological susceptibility in lattice SU(3) Yang-Mills theory. As a further check, we show that the result agrees with numerical simulations employing the periodic boundary condition. Our results support the preferability of the open boundary condition over the periodic boundary condition as the former allows for computation at smaller lattice spacings needed for continuum extrapolation at a lower computational cost.

  3. Specular reflective boundary conditions for Discrete Ordinate Methods in Periodic or Symmetric Geometries

    Science.gov (United States)

    Cai, Jian; Modest, Michael F.

    2016-01-01

    In simulations of periodic or symmetric geometries, computational domains are reduced by imaginary boundaries that present the symmetry conditions. In Photon Monte Carlo methods, this is achieved by imposing specular reflective boundary conditions for the radiative intensity. In this work, a similar specular reflective boundary condition is developed for Discrete Ordinate Methods. The effectiveness of the new boundary condition is demonstrated by multiple numerical examples including plane symmetry and axisymmetry.

  4. `Gas cushion' model and hydrodynamic boundary conditions for superhydrophobic textures

    CERN Document Server

    Nizkaya, Tatiana V; Vinogradova, Olga I

    2014-01-01

    Superhydrophobic Cassie textures with trapped gas bubbles reduce drag, by generating large effective slip, which is important for a variety of applications that involve a manipulation of liquids at the small scale. Here we discuss how the dissipation in the gas phase of textures modifies their friction properties and effective slip. We propose an operator method, which allows us the mapping of the flow in the gas subphase to a local slip boundary condition at the liquid/gas interface. The determined uniquely local slip length depends on the viscosity contrast and underlying topography, and can be immediately used to evaluate an effective slip of the texture. Beside Cassie surfaces our approach is valid for Wenzel textures, where a liquid follows the surface relief, as well as for rough surfaces impregnated by a low-viscosity `lubricant'. These results provide a framework for the rational design of textured surfaces for numerous applications.

  5. Boundary conditions for free surface inlet and outlet problems

    KAUST Repository

    Taroni, M.

    2012-08-10

    We investigate and compare the boundary conditions that are to be applied to free-surface problems involving inlet and outlets of Newtonian fluid, typically found in coating processes. The flux of fluid is a priori known at an inlet, but unknown at an outlet, where it is governed by the local behaviour near the film-forming meniscus. In the limit of vanishing capillary number Ca it is well known that the flux scales with Ca 2/3, but this classical result is non-uniform as the contact angle approaches π. By examining this limit we find a solution that is uniformly valid for all contact angles. Furthermore, by considering the far-field behaviour of the free surface we show that there exists a critical capillary number above which the problem at an inlet becomes over-determined. The implications of this result for the modelling of coating flows are discussed. © 2012 Cambridge University Press.

  6. Estimating Thermal Inertia with a Maximum Entropy Boundary Condition

    Science.gov (United States)

    Nearing, G.; Moran, M. S.; Scott, R.; Ponce-Campos, G.

    2012-04-01

    Thermal inertia, P [Jm-2s-1/2K-1], is a physical property the land surface which determines resistance to temperature change under seasonal or diurnal heating. It is a function of volumetric heat capacity, c [Jm-3K-1], and thermal conductivity, k [Wm-1K-1] of the soil near the surface: P=√ck. Thermal inertia of soil varies with moisture content due the difference between thermal properties of water and air, and a number of studies have demonstrated that it is feasible to estimate soil moisture given thermal inertia (e.g. Lu et al, 2009, Murray and Verhoef, 2007). We take the common approach to estimating thermal inertia using measurements of surface temperature by modeling the Earth's surface as a 1-dimensional homogeneous diffusive half-space. In this case, surface temperature is a function of the ground heat flux (G) boundary condition and thermal inertia and a daily value of P was estimated by matching measured and modeled diurnal surface temperature fluctuations. The difficulty is in measuring G; we demonstrate that the new maximum entropy production (MEP) method for partitioning net radiation into surface energy fluxes (Wang and Bras, 2011) provides a suitable boundary condition for estimating P. Adding the diffusion representation of heat transfer in the soil reduces the number of free parameters in the MEP model from two to one, and we provided a sensitivity analysis which suggests that, for the purpose of estimating P, it is preferable to parameterize the coupled MEP-diffusion model by the ratio of thermal inertia of the soil to the effective thermal inertia of convective heat transfer to the atmosphere. We used this technique to estimate thermal inertia at two semiarid, non-vegetated locations in the Walnut Gulch Experimental Watershed in southeast AZ, USA and compared these estimates to estimates of P made using the Xue and Cracknell (1995) solution for a linearized ground heat flux boundary condition, and we found that the MEP-diffusion model produced

  7. Boundary conditions for star matter and other periodic fermionic systems

    Science.gov (United States)

    Gulminelli, F.; Furuta, T.; Juillet, O.; Leclercq, C.

    2011-12-01

    Bulk fermionic matter, as can be notably found in supernova matter and neutrons stars, is subject to correlations of infinite range due to the antisymmetrization of the N-body wave function, which cannot be explicitly accounted for in a practical simulation. This problem is usually addressed in condensed matter physics by means of the so-called twist averaged boundary condition method. A different ansatz based on the localized Wannier representation has been proposed in the context of antisymmetrized molecular dynamics. In this paper we work out the formal relation between the two approaches. We show that, while the two coincide when working with exact eigenstates of the N-body Hamiltonian, differences appear in the case of variational approaches, which are currently used for the description of stellar matter. Some model applications with fermionic molecular dynamics are shown.

  8. Charged dopants in semiconductor nanowires under partially periodic boundary conditions

    Science.gov (United States)

    Chan, Tzu-Liang; Zhang, S. B.; Chelikowsky, James R.

    2011-06-01

    We develop a one-dimensional, periodic real-space formalism for examining the electronic structure of charged nanowires from first principles. The formalism removes spurious electrostatic interactions between charged unit cells by appropriately specifying a boundary condition for the Kohn-Sham equation. The resultant total energy of the charged system remains finite, and a Madelung-type correction is unnecessary. We demonstrate our scheme by examining the ionization energy of P-doped Si nanowires. We find that there is an effective repulsion between charged P dopants along the nanowire owing to the repulsive interaction of the induced surface charge between adjacent periodic cells. This repulsive interaction decays exponentially with unit cell size instead of a power law behavior assumed in typical charged calculations.

  9. Steady-State Axisymmetric MHD Solutions with Various Boundary Conditions

    CERN Document Server

    Wang, Lile

    2014-01-01

    Axisymmetric magnetohydrodynamics (MHD) can be invoked for describing astrophysical magnetized flows and formulated to model stellar magnetospheres including main sequence stars (e.g. the Sun), compact stellar objects [e.g. magnetic white dwarfs (MWDs), radio pulsars, anomalous X-ray pulsars (AXPs), magnetars, isolated neutron stars etc.], and planets as a major step forward towards a full three-dimensional model construction. Using powerful and reliable numerical solvers based on two distinct finite-difference method (FDM) and finite-element method (FEM) schemes of algorithm, we examine axisymmetric steady-state or stationary MHD models in Throumoulopoulos & Tasso (2001), finding that their separable semi-analytic nonlinear solutions are actually not unique given their specific selection of several free functionals and chosen boundary conditions. The multiplicity of nonlinear steady MHD solutions gives rise to differences in the total energies contained in the magnetic fields and flow velocity fields as ...

  10. Unsteady Squeezing Flow of Carbon Nanotubes with Convective Boundary Conditions.

    Science.gov (United States)

    Hayat, Tasawar; Muhammad, Khursheed; Farooq, Muhammad; Alsaedi, Ahmad

    2016-01-01

    Unsteady flow of nanofluids squeezed between two parallel plates is discussed in the presence of viscous dissipation. Heat transfer phenomenon is disclosed via convective boundary conditions. Carbon nanotubes (single-wall and multi-wall) are used as nanoparticles which are homogeneously distributed in the base fluid (water). A system of non-linear differential equations for the flow is obtained by utilizing similarity transformations through the conservation laws. Influence of various emerging parameters on the velocity and temperature profiles are sketched graphically and discussed comprehensively. Analyses of skin fraction coefficient and Nusselt number are also elaborated numerically. It is found out that velocity is smaller for squeezing parameter in the case of multi-wall carbon nanotubes when compared with single-wall carbon nanotubes. PMID:27149208

  11. PERIODIC BOUNDARY CONDITION IN SIMULATION OF TURBULENT FLOW

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    In this paper, the simulations of the three-di-mensional turbulent flows through hydraulic turbine compo-nents[1] were conducted based on the standard k-ε turbulentmodel with body-fitted coordinates and staggering grid sys-tem. The SIMPLEC algorithm was adopted in the numericalprocedure. A new method to treat the periodic boundary con-dition was used. The calculated results of the new methodwere compared with those of traditional ones. These resultsindicate that the new method can give much better results,and can be used in simulating flow through rotational impel-lers. The presented method can be combined with alternativeturbulent model or employed in large eddy simulation.

  12. Solution of MHD problems with mixed-type boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Antimirov, M.IA.

    1985-06-01

    The introduction of artificial anisotropy of the dynamic viscosity in one of the subregions in which the solution is sought is utilized to derive an approximation method for MHD problems with mixed-type boundary conditions. The method is demonstrated through two problems: slow rotation of a disk and motion of a finite-width infinitely long plate in an infinite volume of a conducting fluid. The velocity and magnetic field solutions are obtained in the form of integrals of Bessel functions, and the torque is found. It is shown that when the Hartmann number approaches infinity the torque of a convex body of revolution in a longitudinal magnetic field is equal to that of a disk lying at the centerline section of the body.

  13. Thermal momentum distribution from path integrals with shifted boundary conditions

    CERN Document Server

    Giusti, Leonardo

    2011-01-01

    For a thermal field theory formulated in the grand canonical ensemble, the distribution of the total momentum is an observable characterizing the thermal state. We show that its cumulants are related to thermodynamic potentials. In a relativistic system for instance, the thermal variance of the total momentum is a direct measure of the enthalpy. We relate the generating function of the cumulants to the ratio of (a) a partition function expressed as a Matsubara path integral with shifted boundary conditions in the compact direction, and (b) the ordinary partition function. In this form the generating function is well suited for Monte-Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang-Mills theory and obtain the entropy density at three different temperatures.

  14. Solution of the Boundary Value Problems with Boundary Conditions in the Form of Gravitational Curvatures

    Science.gov (United States)

    Sprlak, M.; Novak, P.; Pitonak, M.; Hamackova, E.

    2015-12-01

    Values of scalar, vectorial and second-order tensorial parameters of the Earth's gravitational field have been collected by various sensors in geodesy and geophysics. Such observables have been widely exploited in different parametrization methods for the gravitational field modelling. Moreover, theoretical aspects of these quantities have extensively been studied and are well understood. On the other hand, new sensors for observing gravitational curvatures, i.e., components of the third-order gravitational tensor, are currently under development. This fact may be documented by the terrestrial experiments Dulkyn and Magia, as well as by the proposal of the gravity-dedicated satellite mission called OPTIMA. As the gravitational curvatures represent new types of observables, their exploitation for modelling of the Earth's gravitational field is a subject of this study. Firstly, we derive integral transforms between the gravitational potential and gravitational curvatures, i.e., we find analytical solutions of the boundary value problems with gravitational curvatures as boundary conditions. Secondly, properties of the corresponding Green kernel functions are studied in the spatial and spectral domains. Thirdly, the correctness of the new analytical solutions is tested in a simulation study. The presented mathematical apparatus reveal important properties of the gravitational curvatures. It also extends the Meissl scheme, i.e., an important theoretical paradigm that relates various parameters of the Earth's gravitational field.

  15. Behavior of the reversed field pinch with nonideal boundary conditions

    International Nuclear Information System (INIS)

    The linear and nonlinear magnetohydrodynamic stability of current-driven modes are studied for a reversed field pinch with nonideal boundary conditions. The plasma is bounded by a thin resistive shell surrounded by a vacuum region out to a radius at which a perfectly conducting wall is situated. The distant wall and the thin shell problems are studied by removing either the resistive shell or the conducting wall. Linearly, growth rates of tearing modes and kink modes are calculated by analytical solutions based on the modified Bessel function model for the equilibrium. The effects of variation of the shell resistivity and wall proximity on the growth rates are investigated. The modes that may be important in different parameter regimes and with different boundary conditions are identified. The nonlinear behaviors are studied with a three-dimensional magnetohydrodynamics code. The fluctuations generally rise with increasing distance between the conducting wall and the plasma. The enhanced fluctuation induced v x b electric field primarily oppose toroidal current; hence, loop voltage must increase to sustain the constant. Quasilinear interaction between modes typically associated with the dynamo action is identified as the most probable nonlinear destabilization mechanism. The helicity and energy balance properties of the simulation results are discussed. The interruption of current density along field lines intersecting the resistive shell is shown to lead to surface helicity leakage. This effect is intimately tied to stability, as fluctuation induced v x b electric field is necessary to transport the helicity to the surface. In this manner, all aspects of helicity balance, i.e., injection, transport, and dissipation, are considered self-consistently. The importance of the helicity and energy dissipation by the mean components of the magnetic field and current density is discussed. 88 refs., 41 figs., 3 tabs

  16. Interstellar Matter and the Boundary Conditions of the Heliosphere

    Science.gov (United States)

    Frisch, Priscilla C.

    1998-07-01

    The interstellar cloud surrounding the solar system regulates the galactic environment of the Sun, and determines the boundary conditions of the heliosphere. Both the Sun and interstellar clouds move through space, so these boundary conditions change with time. Data and theoretical models now support densities in the cloud surrounding the solar system of n(H0)=0.22±0.06 cm-3, and n(e-)˜0.1 cm-3, with larger values allowed for n(H0) by radiative transfer considerations. Ulysses and Extreme Ultraviolet Explorer satellite He0 data yield a cloud temperature of 6400 K. Nearby interstellar gas appears to be structured and inhomogeneous. The interstellar gas in the Local Fluff cloud complex exhibits elemental abundance patterns in which refractory elements are enhanced over the depleted abundances found in cold disk gas. Within a few parsecs of the Sun, inconclusive evidence for factors of 2-5 variation in Mg+ and Fe+ gas phase abundances is found, providing evidence for variable grain destruction. In principle, photoionization calculations for the surrounding cloud can be compared with elemental abundances found in the pickup ion and anomalous cosmic-ray populations to model cloud properties, including ionization, reference abundances, and radiation field. Observations of the hydrogen pile up at the nose of the heliosphere are consistent with a barely subsonic motion of the heliosphere with respect to the surrounding interstellar cloud. Uncertainties on the velocity vector of the cloud that surrounds the solar system indicate that it is uncertain as to whether the Sun and α Cen are or are not immersed in the same interstellar cloud.

  17. Compressible turbulent channel flow with impedance boundary conditions

    Science.gov (United States)

    Scalo, Carlo; Bodart, Julien; Lele, Sanjiva K.

    2015-03-01

    We have performed large-eddy simulations of isothermal-wall compressible turbulent channel flow with linear acoustic impedance boundary conditions (IBCs) for the wall-normal velocity component and no-slip conditions for the tangential velocity components. Three bulk Mach numbers, Mb = 0.05, 0.2, 0.5, with a fixed bulk Reynolds number, Reb = 6900, have been investigated. For each Mb, nine different combinations of IBC settings were tested, in addition to a reference case with impermeable walls, resulting in a total of 30 simulations. The adopted numerical coupling strategy allows for a spatially and temporally consistent imposition of physically realizable IBCs in a fully explicit compressible Navier-Stokes solver. The IBCs are formulated in the time domain according to Fung and Ju ["Time-domain impedance boundary conditions for computational acoustics and aeroacoustics," Int. J. Comput. Fluid Dyn. 18(6), 503-511 (2004)]. The impedance adopted is a three-parameter damped Helmholtz oscillator with resonant angular frequency, ωr, tuned to the characteristic time scale of the large energy-containing eddies. The tuning condition, which reads ωr = 2πMb (normalized with the speed of sound and channel half-width), reduces the IBCs' free parameters to two: the damping ratio, ζ, and the resistance, R, which have been varied independently with values, ζ = 0.5, 0.7, 0.9, and R = 0.01, 0.10, 1.00, for each Mb. The application of the tuned IBCs results in a drag increase up to 300% for Mb = 0.5 and R = 0.01. It is shown that for tuned IBCs, the resistance, R, acts as the inverse of the wall-permeability and that varying the damping ratio, ζ, has a secondary effect on the flow response. Typical buffer-layer turbulent structures are completely suppressed by the application of tuned IBCs. A new resonance buffer layer is established characterized by large spanwise-coherent Kelvin-Helmholtz rollers, with a well-defined streamwise wavelength λx, traveling downstream with

  18. Solvability of a fourth order boundary value problem with periodic boundary conditions

    OpenAIRE

    Chaitan P. Gupta

    1988-01-01

    Fourth order boundary value problems arise in the study of the equilibrium of an elastaic beam under an external load. The author earlier investigated the existence and uniqueness of the solutions of the nonlinear analogues of fourth order boundary value problems that arise in the equilibrium of an elastic beam depending on how the ends of the beam are supported. This paper concerns the existence and uniqueness of solutions of the fourth order boundary value problems with periodic boundary co...

  19. DYNAMIC SURFACE BOUNDARY-CONDITIONS - A SIMPLE BOUNDARY MODEL FOR MOLECULAR-DYNAMICS SIMULATIONS

    NARCIS (Netherlands)

    JUFFER, AH; BERENDSEN, HJC

    1993-01-01

    A simple model for the treatment of boundaries in molecular dynamics simulations is presented. The method involves the positioning of boundary atoms on a surface that surrounds a system of interest. The boundary atoms interact with the inner region and represent the effect of atoms outside the surfa

  20. The height of the atmospheric boundary layer during unstable conditions

    Energy Technology Data Exchange (ETDEWEB)

    Gryning, S.E.

    2005-11-01

    The height of the convective atmospheric boundary layer, also called the mixed-layer, is one of the fundamental parameters that characterise the structure of the atmosphere near the ground. It has many theoretical and practical applications such as the prediction of air pollution concentrations, surface temperature and the scaling of turbulence. However, as pointed out by Builtjes (2001) in a review paper on Major Twentieth Century Milestones in Air Pollution Modelling and Its Application, the weakest point in meteorology data is still the determination of the height of the mixed-layer, the so-called mixing height. A simple applied model for the height of the mixed-layer over homogeneous terrain is suggested in chapter 2. It is based on a parameterised budget for the turbulent kinetic energy. In the model basically three terms - the spin-up term and the production of mechanical and convective turbulent kinetic energy - control the growth of the mixed layer. The interplay between the three terms is related to the meteorological conditions and the height of the mixed layer. A stable layer, the so-called entrainment zone, which is confined between the mixed layer and the free air above, caps the mixed layer. A parameterisation of the depth of the entrainment zone is also suggested, and used to devise a combined model for the height of the mixed layer and the entrainment zone. Another important aspect of the mixed layer development exists in coastal areas where an internal boundary layer forms downwind from the coastline. A model for the growth of the internal boundary layer is developed in analogy with the model for mixed layer development over homogeneous terrain. The strength of this model is that it can operate on a very fine spatial resolution with minor computer resources. Chapter 3 deals with the validation of the models. It is based in parts on data from the literature, and on own measurements. For the validation of the formation of the internal boundary layer

  1. Absorbing boundary conditions for simulation of gravitational waves with spectral methods in spherical coordinates

    OpenAIRE

    Novak, Jerome; Bonazzola, Silvano

    2002-01-01

    We present a new formulation of the multipolar expansion of an exact boundary condition for the wave equation, which is truncated at the quadrupolar order. Using an auxiliary function, that is the solution of a wave equation on the sphere defining the outer boundary of the numerical grid, the absorbing boundary condition is simply written as a perturbation of the usual Sommerfeld radiation boundary condition. It is very easily implemented using spectral methods in spherical coordinates. Numer...

  2. Shroud boundary condition characterization experiments at the Radiant Heat Facility.

    Energy Technology Data Exchange (ETDEWEB)

    Suo-Anttila, Jill Marie; Nakos, James Thomas; Gill, Walter

    2004-10-01

    A series of experiments was performed to better characterize the boundary conditions from an inconel heat source ('shroud') painted with Pyromark black paint. Quantifying uncertainties in this type of experimental setup is crucial to providing information for comparisons with code predictions. The characterization of this boundary condition has applications in many scenarios related to fire simulation experiments performed at Sandia National Laboratories Radiant Heat Facility (RHF). Four phases of experiments were performed. Phase 1 results showed that a nominal 1000 C shroud temperature is repeatable to about 2 C. Repeatability of temperatures at individual points on the shroud show that temperatures do not vary more than 10 C from experiment to experiment. This variation results in a 6% difference in heat flux to a target 4 inches away. IR camera images showed the shroud was not at a uniform temperature, although the control temperature was constant to about {+-}2 C during a test. These images showed that a circular shaped, flat shroud with its edges supported by an insulated plate has a temperature distribution with higher temperatures at the edges and lower temperatures in the center. Differences between the center and edge temperatures were up to 75 C. Phase 3 results showed that thermocouple (TC) bias errors are affected by coupling with the surrounding environment. The magnitude of TC error depends on the environment facing the TC. Phase 4 results were used to estimate correction factors for specific applications (40 and 63-mil diameter, ungrounded junction, mineral insulated, metal-sheathed TCs facing a cold surface). Correction factors of about 3.0-4.5% are recommended for 40 mil diameter TCs and 5.5-7.0% for 63 mil diameter TCs. When mounted on the cold side of the shroud, TCs read lower than the 'true' shroud temperature, and the TC reads high when on the hot side. An alternate method uses the average of a cold side and hot side TC of

  3. Reconstructing geographical boundary conditions for palaeoclimate modelling during the Cenozoic

    Science.gov (United States)

    Baatsen, Michiel; van Hinsbergen, Douwe J. J.; von der Heydt, Anna S.; Dijkstra, Henk A.; Sluijs, Appy; Abels, Hemmo A.; Bijl, Peter K.

    2016-08-01

    Studies on the palaeoclimate and palaeoceanography using numerical model simulations may be considerably dependent on the implemented geographical reconstruction. Because building the palaeogeographic datasets for these models is often a time-consuming and elaborate exercise, palaeoclimate models frequently use reconstructions in which the latest state-of-the-art plate tectonic reconstructions, palaeotopography and -bathymetry, or vegetation have not yet been incorporated. In this paper, we therefore provide a new method to efficiently generate a global geographical reconstruction for the middle-late Eocene. The generalised procedure is also reusable to create reconstructions for other time slices within the Cenozoic, suitable for palaeoclimate modelling. We use a plate-tectonic model to make global masks containing the distribution of land, continental shelves, shallow basins and deep ocean. The use of depth-age relationships for oceanic crust together with adjusted present-day topography gives a first estimate of the global geography at a chosen time frame. This estimate subsequently needs manual editing of areas where existing geological data indicate that the altimetry has changed significantly over time. Certain generic changes (e.g. lowering mountain ranges) can be made relatively easily by defining a set of masks while other features may require a more specific treatment. Since the discussion regarding many of these regions is still ongoing, it is crucial to make it easy for changes to be incorporated without having to redo the entire procedure. In this manner, a complete reconstruction can be made that suffices as a boundary condition for numerical models with a limited effort. This facilitates the interaction between experts in geology and palaeoclimate modelling, keeping reconstructions up to date and improving the consistency between different studies. Moreover, it facilitates model inter-comparison studies and sensitivity tests regarding certain

  4. On Consistent Boundary Conditions for c=1 String Theory

    OpenAIRE

    O'Loughlin, Martin

    1995-01-01

    We introduce a new parametrisation for the Fermi sea of the $c = 1$ matrix model. This leads to a simple derivation of the scattering matrix, and a calculation of boundary corrections in the corresponding $1+1$--dimensional string theory. The new parametrisation involves relativistic chiral fields, rather than the non-relativistic fields of the usual formulations. The calculation of the boundary corrections, following recent work of Polchinski, allows us to place restrictions on the boundary ...

  5. Solution of a Problem Linear Plane Elasticity with Mixed Boundary Conditions by the Method of Boundary Integrals

    Directory of Open Access Journals (Sweden)

    Nahed S. Hussein

    2014-01-01

    Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of …eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.

  6. Supersymmetric extension of the reflection equation algebra and integrable boundary conditions in doped spin-1 model

    International Nuclear Information System (INIS)

    The reflection equation algebra of Sklyanin is extended to the supersymmetric case. A graded reflection equation algebra is proposed and the corresponding graded (supersymmetric) boundary quantum inverse scattering method (QISM) is formulated. As an application, integrable open-boundary conditions for the doped spin-1 chain of the supersymmetric t-J model are studied in the framework of the boundary QISM. Diagonal boundary K-matrices are found and four classes of integrable boundary terms are determined. (author)

  7. On stochastic inlet boundary condition for unsteady simulations

    Directory of Open Access Journals (Sweden)

    Niedoba P.

    2014-03-01

    Full Text Available The paper deals with the stochastic generation of synthesized turbulence, which may be used for a generating of an inlet boundary condition for unsteady simulations, e.g. Direct Numerical Simulation (DNS or Large Eddy Simulation (LES. Assumptions for the generated turbulence are isotropy and homogeneity. The described method produces a stochastic turbulent velocity field using the synthesis of a finite sum of random Fourier modes. The calculation of individual Fourier modes is based on known energy spectrum of turbulent flow, and some turbulent quantities, e.g. turbulent kinetic energy and turbulent dissipation rate. A division of wave number range of the energy spectrum determines directly the number of Fourier modes, and has a direct impact on accuracy and speed of this calculation. Therefore, this work will examine the influence of the number of Fourier modes on a conservation of the first and second statistical moments of turbulent velocity components, which are prespecified. It is important to ensure a sufficient size of a computational domain, and a sufficient number of cells for meaningful comparative results. Dimensionless parameters characterizing the resolution and size of the computational domain according to a turbulent length scale will be introduced for this purpose. Subsequently, the sufficient values of this parameters will be shown for individual numbers of Fourier modes.

  8. On stochastic inlet boundary condition for unsteady simulations

    Science.gov (United States)

    Niedoba, P.; Jícha, M.; Čermák, L.

    2014-03-01

    The paper deals with the stochastic generation of synthesized turbulence, which may be used for a generating of an inlet boundary condition for unsteady simulations, e.g. Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES). Assumptions for the generated turbulence are isotropy and homogeneity. The described method produces a stochastic turbulent velocity field using the synthesis of a finite sum of random Fourier modes. The calculation of individual Fourier modes is based on known energy spectrum of turbulent flow, and some turbulent quantities, e.g. turbulent kinetic energy and turbulent dissipation rate. A division of wave number range of the energy spectrum determines directly the number of Fourier modes, and has a direct impact on accuracy and speed of this calculation. Therefore, this work will examine the influence of the number of Fourier modes on a conservation of the first and second statistical moments of turbulent velocity components, which are prespecified. It is important to ensure a sufficient size of a computational domain, and a sufficient number of cells for meaningful comparative results. Dimensionless parameters characterizing the resolution and size of the computational domain according to a turbulent length scale will be introduced for this purpose. Subsequently, the sufficient values of this parameters will be shown for individual numbers of Fourier modes.

  9. Viscous-fingering experiments with periodic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Zhao, H.; Maher, J.V. (Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA (USA))

    1990-11-15

    Experimental realization of a Hele-Shaw cell with periodic boundary conditions (PBC's) is achieved by building an azimuthal cell with two coaxial cylinders separated by a small gap. The development of viscous-fingering patterns formed by a critical binary liquid mixture at very low viscosity contrast has been observed and recorded from the onset of instability to very late stages. Comparison with the experimental results measured in cells which have sidewalls shows that PBC's yield few differences of results. At the early stage there is no sidewall disturbance so the Fourier transforms show less noise in the low-wave-number modes. Because the annular cell is larger than the earlier cells, it was possible to follow the flow to a very late nonlinear stage where, instead of showing steadily lengthening and broadening fingers, the necks of the longer fingers, crowded by fattening bulbs of the tips of the less-long fingers, constrict until their width is no longer negligible in comparison to the cell gap, at which point the pattern breaks up into a rich variety of bubbles.

  10. Stability of a flexible structure with destabilizing boundary conditions

    Science.gov (United States)

    Shubov, M.; Shubov, V.

    2016-07-01

    The Euler-Bernoulli beam model with non-dissipative boundary conditions of feedback control type is investigated. Components of the two-dimensional input vector are shear and moment at the right end, and components of the observation vector are time derivatives of displacement and slope at the right end. The codiagonal matrix depending on two control parameters relates input and observation. The paper contains five results. First, asymptotic approximation for eigenmodes is derived. Second, `the main identity' is established. It provides a relation between mode shapes of two systems: one with non-zero control parameters and the other one with zero control parameters. Third, when one control parameter is positive and the other one is zero, `the main identity' yields stability of all eigenmodes (though the system is non-dissipative). Fourth, the stability of eigenmodes is extended to the case when one control parameter is positive, and the other one is sufficiently small. Finally, existence and properties of `deadbeat' modes are investigated.

  11. Quantum spin chains of Temperley-Lieb type: periodic boundary conditions, spectral multiplicities and finite temperature

    OpenAIRE

    Aufgebauer, Britta; Kluemper, Andreas

    2010-01-01

    We determine the spectra of a class of quantum spin chains of Temperley-Lieb type by utilizing the concept of Temperley-Lieb equivalence with the S=1/2 XXZ chain as a reference system. We consider open boundary conditions and in particular periodic boundary conditions. For both types of boundaries the identification with XXZ spectra is performed within isomorphic representations of the underlying Temperley-Lieb algebra. For open boundaries the spectra of these models differ from the spectrum ...

  12. Reactive Boundary Conditions as Limits of Interaction Potentials for Brownian and Langevin Dynamics

    CERN Document Server

    Chapman, S Jonathan; Isaacson, Samuel A

    2015-01-01

    A popular approach to modeling bimolecular reactions between diffusing molecules is through the use of reactive boundary conditions. One common model is the Smoluchowski partial absorption condition, which uses a Robin boundary condition in the separation coordinate between two possible reactants. This boundary condition can be interpreted as an idealization of a reactive interaction potential model, in which a potential barrier must be surmounted before reactions can occur. In this work we show how the reactive boundary condition arises as the limit of an interaction potential encoding a steep barrier within a shrinking region in the particle separation, where molecules react instantly upon reaching the peak of the barrier. The limiting boundary condition is derived by the method of matched asymptotic expansions, and shown to depend critically on the relative rate of increase of the barrier height as the width of the potential is decreased. Limiting boundary conditions for the same interaction potential in b...

  13. The linking number in systems with Periodic Boundary Conditions

    Science.gov (United States)

    Panagiotou, E.

    2015-11-01

    Periodic Boundary Conditions (PBC) are often used for the simulation of complex physical systems. Using the Gauss linking number, we define the periodic linking number as a measure of entanglement for two oriented curves in a system employing PBC. In the case of closed chains in PBC, the periodic linking number is an integer topological invariant that depends on a finite number of components in the periodic system. For open chains, the periodic linking number is an infinite series that accounts for all the topological interactions in the periodic system. In this paper we give a rigorous proof that the periodic linking number is defined for the infinite system, i.e., that it converges for one, two, and three PBC models. It gives a real number that varies continuously with the configuration and gives a global measure of the geometric complexity of the system of chains. Similarly, for a single oriented chain, we define the periodic self-linking number and prove that it also is defined for open chains. In addition, we define the cell periodic linking and self-linking numbers giving localizations of the periodic linking numbers. These can be used to give good estimates of the periodic linking numbers in infinite systems. We also define the local periodic linking number associated to chains in the immediate cell neighborhood of a chain in order to study local linking measures in contrast to the global linking measured by the periodic linking numbers. Finally, we study and compare these measures when applied to a PBC model of polyethylene melts.

  14. Boundary-value problems for x-analytical functions with weighted boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Kapshivyi, A.A. [Kiev Univ. (Ukraine)

    1994-11-10

    We consider boundary-value problems for x-analytical functions of a complex variable z = x + iy in a number of domains. Limit values with the weight (ln x){sup {minus}1} are given for the real part of the x-analytical function on the sections of the boundary that follow the imaginary axis, and simple limits are given for the real part of the x-analytical functions on the part of the boundary outside the imaginary axis. The apparatus of integral representations of x-analytical functions is applied to obtain a solution of the problem in quadratures.

  15. Effects of boundary conditions on magnetization switching in kinetic ising models of nanoscale ferromagnets

    DEFF Research Database (Denmark)

    Richards, H.L.; Kolesik, M.; Lindgård, P.-A.;

    1997-01-01

    Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with periodic boundary conditions. In this paper we consider the...... the existence of a peak in the switching field as a function of system size in both systems with periodic boundary conditions and in systems with boundaries. The size of the peak is strongly dependent on the boundary effects. It is generally reduced by open boundary conditions, and in some cases it...... effects of boundary conditions od the switching phenomena. A rich range of behaviors is predicted by droplet theory: the specific mechanism by which switching occurs depends on the structure of the boundary, the particle size, the temperature, and the strength of the: applied field. The theory predicts...

  16. A Convective-like Energy-Stable Open Boundary Condition for Simulations of Incompressible Flows

    CERN Document Server

    Dong, Suchuan

    2015-01-01

    We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even when strong vortices or backflows occur at the outflow boundary. Under certain situations it can be reduced to a form that can be analogized to the usual convective boundary condition. One prominent feature of this boundary condition is that it provides a control over the velocity on the outflow/open boundary. This is not available with the other energy-stable open boundary conditions from previous works. Our numerical algorithm treats the proposed open boundary condition based on a rotational velocity-correction type strategy. It gives rise to a Robin-type condition for the discrete pressure and a Robin-type condition for the discrete velocity on the outflow/open boundary, respectively at the pressure and the velocity sub-steps. We present extensive numerical experiments on...

  17. Casimir Force of Piston Systems with Arbitrary Cross Sections under Different Boundary Conditions

    Institute of Scientific and Technical Information of China (English)

    XIONG Ai-Min; CHEN Xiao-Song

    2009-01-01

    We study the Casimir force between two pistons under different boundary conditions inside an infinite cylinder with arbitrary cross section.It is found that the attractive or repulsive character of the Casimir force for a scalar field is determined only by the boundary condition along the longitudinal direction and is independent of the cross section,transverse boundary conditions and the mass of the field.Under symmetric Dirichlet-Dirichlet,Neumann-Neumann and periodic longitudinal boundary conditions the Casimir force is always attractive,but is repulsive under non-symmetric Dirichlet-Neumann and anti-periodic longitudinal boundary conditions.The Casimir force of the electromagnetic field in an ideal conductive piston is also investigated.This force is always attractive regardless of the shape of the cross section and the transverse boundary conditions.

  18. A device adaptive inflow boundary condition for Wigner equations of quantum transport

    Energy Technology Data Exchange (ETDEWEB)

    Jiang, Haiyan [Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081 (China); Lu, Tiao [HEDPS and CAPT, LMAM and School of Mathematical Sciences, Peking University, Beijing 100871 (China); Cai, Wei, E-mail: wcai@uncc.edu [Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223-0001 (United States)

    2014-02-01

    In this paper, an improved inflow boundary condition is proposed for Wigner equations in simulating a resonant tunneling diode (RTD), which takes into consideration the band structure of the device. The original Frensley inflow boundary condition prescribes the Wigner distribution function at the device boundary to be the semi-classical Fermi–Dirac distribution for free electrons in the device contacts without considering the effect of the quantum interaction inside the quantum device. The proposed device adaptive inflow boundary condition includes this effect by assigning the Wigner distribution to the value obtained from the Wigner transform of wave functions inside the device at zero external bias voltage, thus including the dominant effect on the electron distribution in the contacts due to the device internal band energy profile. Numerical results on computing the electron density inside the RTD under various incident waves and non-zero bias conditions show much improvement by the new boundary condition over the traditional Frensley inflow boundary condition.

  19. Bounds on Rayleigh-Benard convection with general thermal boundary conditions. Part 1. Fixed Biot number boundaries

    OpenAIRE

    Wittenberg, Ralf W.

    2008-01-01

    We investigate the influence of the thermal properties of the boundaries in turbulent Rayleigh-Benard convection on analytical bounds on convective heat transport. Using the Doering-Constantin background flow method, we systematically formulate a bounding principle on the Nusselt-Rayleigh number relationship for general mixed thermal boundary conditions of constant Biot number \\eta which continuously interpolates between the previously studied fixed temperature ($\\eta = 0$) and fixed flux ($\\...

  20. Supersymmetry Breaking through Boundary Conditions Associated with the $U(1)_{R}$

    CERN Document Server

    Takenaga, K

    1998-01-01

    The effects of boundary conditions imposed on the fields for the compactified space directions to the supersymmetric theories are discussed. The boundary conditions can be taken to be periodic up to the degrees of freedom of localized $U(1)_{R}$ transformations. The boundary condition breaks the supersymmetry to yield universal soft supersymmetry breaking terms. The 4-dimensional supersymmetric QED with one flavour and the pure supersymmetric QCD are studied as toy models when one of the space coordinates is compactified on $S^1$.

  1. Revisit boundary conditions for the self-adjoint angular flux formulation

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Yaqi [Idaho National Lab. (INL), Idaho Falls, ID (United States); Gleicher, Frederick N. [Idaho National Lab. (INL), Idaho Falls, ID (United States)

    2015-03-01

    We revisit the boundary conditions for SAAF. We derived the equivalent parity variational form ready for coding up. The more rigorous approach of evaluating odd parity should be solving the odd parity equation coupled with the even parity. We proposed a symmetric reflecting boundary condition although neither positive definiteness nor even-odd decoupling is achieved. A simple numerical test verifies the validity of these boundary conditions.

  2. Towards a generic non-reflective characteristic boundary condition for aeroacoustic simulations

    OpenAIRE

    Fattah, Ryu; Gill, James; Zhang, Xin

    2016-01-01

    A blended zonal characteristic boundary condition is proposed following a quantita- tive investigation of the performance of several non-reflective boundary conditions. Two test cases are considered that investigate the effects of acoustic and vortical plane waves impinging on the domain outflow region. A third test case investigates the effects of broad- band turbulent flow impinging on a non-reflective outflow boundary condition. From these studies, two non-reflective boundar...

  3. RADIATION BOUNDARY CONDITIONS FOR MAXWELL'S EQUATIONS: A REVIEW OF ACCURATE TIME-DOMAIN FORMULATIONS

    Institute of Scientific and Technical Information of China (English)

    Thomas Hagstrom; Stephen Lau

    2007-01-01

    We review time-domain formulations of radiation boundary conditions for Maxwell's equations, focusing on methods which can deliver arbitrary accuracy at acceptable computational cost. Examples include fast evaluations of nonlocal conditions on symmetric and general boundaries, methods based on identifying and evaluating equivalent sources, and local approximations such as the perfectly matched layer and sequences of local boundary conditions. Complexity estimates are derived to assess work and storage requirements as a function of wavelength and simulation time.

  4. Monotone iterative technique for fractional differential equations with periodic boundary conditions

    Directory of Open Access Journals (Sweden)

    J. D. Ramírez

    2009-01-01

    Full Text Available In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary conditions in the weighted norm.

  5. Sliding periodic boundary conditions for lattice Boltzmann and lattice kinetic equations

    OpenAIRE

    Adhikari, R.; Desplat, J. -C.; Stratford, K.

    2005-01-01

    We present a method to impose linear shear flow in discrete-velocity kinetic models of hydrodynamics through the use of sliding periodic boundary conditions. Our method is derived by an explicit coarse-graining of the Lees-Edwards boundary conditions for Couette flow in molecular dynamics, followed by a projection of the resulting equations onto the subspace spanned by the discrete velocities of the lattice Boltzmann method. The boundary conditions are obtained without resort to perturbative ...

  6. Periodic Boundary Conditions for Long-time Nonequilibrium Molecular Dynamics Simulations of Incompressible Flows

    OpenAIRE

    DOBSON, Matthew

    2014-01-01

    This work presents a generalization of the Kraynik-Reinelt (KR) boundary conditions for nonequilibrium molecular dynamics simulations. In the simulation of steady, homogeneous flows with periodic boundary conditions, the simulation box moves with the flow, and it is possible for particle replicas to become arbitrarily close, causing a breakdown in the simulation. The KR boundary conditions avoid this problem for planar elongational flow and general planar mixed flow [J. Chem. Phys 133, 14116 ...

  7. Study on the thermal boundary conditions in DNS of the free-surface turbulent flow

    International Nuclear Information System (INIS)

    This paper describes thermal boundary conditions in Direct Numerical Simulation (DNS) of an open-channel turbulent flow heated at constant heat flux from the tree-surface. Numerical calculations were carried out in three thermal boundary conditions. And about the adequate thermal condition at the free-surface, revealed and discussed. (author)

  8. Conditions at the downstream boundary for simulations of viscous incompressible flow

    Science.gov (United States)

    Hagstrom, Thomas

    1990-01-01

    The proper specification of boundary conditions at artificial boundaries for the simulation of time-dependent fluid flows has long been a matter of controversy. A general theory of asymptotic boundary conditions for dissipative waves is applied to the design of simple, accurate conditions at downstream boundary for incompressible flows. For Reynolds numbers far enough below the critical value for linear stability, a scaling is introduced which greatly simplifies the construction of the asymptotic conditions. Numerical experiments with the nonlinear dynamics of vortical disturbances to plane Poiseuille flow are presented which illustrate the accuracy of our approach. The consequences of directly applying the scalings to the equations are also considered.

  9. Periodic Time-Domain Nonlocal Nonreflecting Boundary Conditions for Duct Acoustics

    Science.gov (United States)

    Watson, Willie R.; Zorumski, William E.

    1996-01-01

    Periodic time-domain boundary conditions are formulated for direct numerical simulation of acoustic waves in ducts without flow. Well-developed frequency-domain boundary conditions are transformed into the time domain. The formulation is presented here in one space dimension and time; however, this formulation has an advantage in that its extension to variable-area, higher dimensional, and acoustically treated ducts is rigorous and straightforward. The boundary condition simulates a nonreflecting wave field in an infinite uniform duct and is implemented by impulse-response operators that are applied at the boundary of the computational domain. These operators are generated by convolution integrals of the corresponding frequency-domain operators. The acoustic solution is obtained by advancing the Euler equations to a periodic state with the MacCormack scheme. The MacCormack scheme utilizes the boundary condition to limit the computational space and preserve the radiation boundary condition. The success of the boundary condition is attributed to the fact that it is nonreflecting to periodic acoustic waves. In addition, transient waves can pass rapidly out of the solution domain. The boundary condition is tested for a pure tone and a multitone source in a linear setting. The effects of various initial conditions are assessed. Computational solutions with the boundary condition are consistent with the known solutions for nonreflecting wave fields in an infinite uniform duct.

  10. S-duality of boundary conditions and the Geometric Langlands program

    CERN Document Server

    Gaiotto, Davide

    2016-01-01

    Maximally supersymmetric gauge theory in four dimensions admits local boundary conditions which preserve half of the bulk supersymmetries. The S-duality of the bulk gauge theory can be extended in a natural fashion to act on such half-BPS boundary conditions. The purpose of this note is to explain the role these boundary conditions can play in the Geometric Langlands program. In particular, we describe how to obtain pairs of Geometric Langland dual objects from S-dual pairs of half-BPS boundary conditions.

  11. An Explicit Time-Domain Hybrid Formulation Based on the Unified Boundary Condition

    Energy Technology Data Exchange (ETDEWEB)

    Madsen, N; Fasenfest, B J; White, D; Stowell, M; Jandhyala, V; Pingenot, J; Champagne, N J; Rockway, J D

    2007-02-28

    An approach to stabilize the two-surface, time domain FEM/BI hybrid by means of a unified boundary condition is presented. The first-order symplectic finite element formulation [1] is used along with a version of the unified boundary condition of Jin [2] reformulated for Maxwell's first-order equations in time to provide both stability and accuracy over the first-order ABC. Several results are presented to validate the numerical solutions. In particular the dipole in a free-space box is analyzed and compared to the Dirchlet boundary condition of Ziolkowski and Madsen [3] and to a Neuman boundary condition approach.

  12. Critical Casimir effect in the Ising strips with standard normal and ordinary boundary conditions and the grain boundary

    Science.gov (United States)

    Borjan, Z.

    2016-09-01

    We consider critical Casimir force in the Ising strips with boundary conditions defined by standard normal and ordinary surface universality classes containing also the internal grain boundary. Using exact variational approach of Mikheev and Fisher we have elaborated on behaviors of Casimir amplitudes Δ++(g) , ΔOO(g) and Δ+O(g) , corresponding to normal-normal, ordinary-ordinary and mixed normal-ordinary boundary conditions, respectively, with g as a strength of the grain boundary. Closed analytic results describe Casimir amplitudes Δ++(g) and ΔOO(g) as continuous functions of the grain boundary's strength g, changing the character of the Casimir force from repulsive to attractive and vice versa for certain domains of g. Present results reveal a new type of symmetry between Casimir amplitudes Δ++(g) and ΔOO(g) . Unexpectedly simple constant result for the Casimir amplitude Δ+O(g) = π/12 we have comprehensively interpreted in terms of equilibrium states of the present Ising strip as a complex interacting system comprising two sub-systems. Short-distance expansions of energy density profiles in the vicinity of the grain boundary reveal new distant-wall correction amplitudes that we examined in detail. Analogy of present considerations with earlier more usual short-distance expansions near one of the (N), (O) and (SB) boundaries, as well as close to surfaces with variable boundary conditions refers to the set of scaling dimensions appearing in the present calculations but also to the discovery of the de Gennes-Fisher distant wall correction amplitudes.

  13. Absorbing boundary conditions for simulation of gravitational waves with spectral methods in spherical coordinates

    Science.gov (United States)

    Novak, Jérôme; Bonazzola, Silvano

    2004-06-01

    We present a new formulation of the multipolar expansion of an exact boundary condition for the wave equation, which is truncated at the quadrupolar order. Using an auxiliary function, that is the solution of a wave equation on the sphere defining the outer boundary of the numerical grid, the absorbing boundary condition is simply written as a perturbation of the usual Sommerfeld radiation boundary condition. It is very easily implemented using spectral methods in spherical coordinates. Numerical tests of the method show that very good accuracy can be achieved and that this boundary condition has the same efficiency for dipolar and quadrupolar waves as the usual Sommerfeld boundary condition for monopolar ones. This is of particular importance for the simulation of gravitational waves, which have dominant quadrupolar terms, in General Relativity.

  14. The impact of boundary conditions on CO2 capacity estimation in aquifers

    OpenAIRE

    Smith, D.J.; Bentham, M.; Holloway, S.; Noy, D.J.; Chadwick, R.A.

    2010-01-01

    The boundary conditions of an aquifer determine the extent to which fluids (including formation water and CO2) and pressure can be transferred into adjacent geological formations, either laterally or vertically. Aquifer boundaries can be faults, lithological boundaries, formation pinch-outs, salt walls, or outcrop. In many cases compliance with regulations preventing CO2 storage influencing areas outside artificial boundaries defined by non-geological criteria (international bound...

  15. Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

    Science.gov (United States)

    Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

    2015-01-01

    Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

  16. Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations

    Science.gov (United States)

    Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

    2014-01-01

    Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

  17. Absorption and impedance boundary conditions for phased geometrical-acoustics methods

    DEFF Research Database (Denmark)

    Jeong, Cheol-Ho

    2012-01-01

    developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated......Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been...... with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce...

  18. Green's function of a heat problem with a periodic boundary condition

    Science.gov (United States)

    Erzhanov, Nurzhan E.

    2016-08-01

    In the paper, a nonlocal initial-boundary value problem for a non-homogeneous one-dimensional heat equation is considered. The domain under consideration is a rectangle. The classical initial condition with respect to t is put. A nonlocal periodic boundary condition by a spatial variable x is put. It is well-known that a solution of problem can be constructed in the form of convergent orthonormal series according to eigenfunctions of a spectral problem for an operator of multiple differentiation with periodic boundary conditions. Therefore Green's function can be also written in the form of an infinite series with respect to trigonometric functions (Fourier series). For classical first and second initial-boundary value problems there also exists a second representation of the Green's function by Jacobi function. In this paper we find the representation of the Green's function of the nonlocal initial-boundary value problem with periodic boundary conditions in the form of series according to exponents.

  19. Boundary layer Slip Flow and Heat Transfer of Nanofluid Induced by a Permeable Stretching Sheet with Convective Boundary Condition

    Directory of Open Access Journals (Sweden)

    A. Malvandi

    2015-01-01

    Full Text Available The objective of this paper is to consider both effects of slip and convective heat boundary conditions on steady two-dimensional boundary layer flow of a nanofluid over a stretching sheet in the presence of blowing/suction simultaneously. Flow meets the Navier's slip condition at the surface and Biot number is also used to consider the effects of convective heat transfer. The employed model for nanofluid includes two-component four-equation nonhomogeneous equilibrium model that incorporates the effects of nanoparticle migration owing to Brownian motion and thermophoresis. The basic partial boundary layer equations have been transformed into a two-point boundary value problem via similarity variables. Results for impermeable isothermal surface and also no-slip boundary condition were in best agreements with those existing in literatures. Effects of governing parameters such as Biot number (Bi, slip parameter (λ, thermophoresis (Nt, Prandtl number (Pr, Lewis number (Le, Brownian motion (Nb and blowing/suction (S on reduced Nusselt and Sherwood numbers are analyzed and discussed in details. The obtained results indicate that unlike heat transfer rate, concentration rate is very sensitive to all parameters among which Le, S and Pr are the most effective ones.

  20. Effect of magnetic boundary conditions on the dynamo threshold of von Karman swirling flows

    CERN Document Server

    Gissinger, Christophe; Fauve, Stephan; Dormy, Emmanuel

    2008-01-01

    We study the effect of different boundary conditions on the kinematic dynamo threshold of von Karman type swirling flows in a cylindrical geometry. Using an analytical test flow, we model different boundary conditions: insulating walls all over the flow, effect of sodium at rest on the cylinder side boundary, effect of sodium behind the impellers, effect of impellers or side wall made of a high-magnetic-permeability material. We find that using high-magnetic-permeability boundary conditions decreases the dynamo threshold, the minimum being achieved when they are implemented all over the flow.

  1. Nested Bethe Ansatz for Spin Ladder Model with Open Boundary Conditions

    Institute of Scientific and Technical Information of China (English)

    WU Jun-Fang; ZHANG Chun-Min; YUE Rui-Hong; LI Run-Ling

    2005-01-01

    The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the generalboundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.

  2. Moist turbulent Rayleigh-Benard convection with Neumann and Dirichlet boundary conditions

    CERN Document Server

    Weidauer, Thomas

    2012-01-01

    Turbulent Rayleigh-Benard convection with phase changes in an extended layer between two parallel impermeable planes is studied by means of three-dimensional direct numerical simulations for Rayleigh numbers between 10^4 and 1.5\\times 10^7 and for Prandtl number Pr=0.7. Two different sets of boundary conditions of temperature and total water content are compared: imposed constant amplitudes which translate into Dirichlet boundary conditions for the scalar field fluctuations about the quiescent diffusive equilibrium and constant imposed flux boundary conditions that result in Neumann boundary conditions. Moist turbulent convection is in the conditionally unstable regime throughout this study for which unsaturated air parcels are stably and saturated air parcels unstably stratified. A direct comparison of both sets of boundary conditions with the same parameters requires to start the turbulence simulations out of differently saturated equilibrium states. Similar to dry Rayleigh-Benard convection the differences...

  3. Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations

    OpenAIRE

    Arnold, Douglas N.; Nicolae Tarfulea

    2007-01-01

    Specifying boundary conditions continues to be a challenge in numerical relativity in order to obtain a long time convergent numerical simulation of Einstein's equations in domains with artificial boundaries. In this paper, we address this problem for the Einstein--Christoffel (EC) symmetric hyperbolic formulation of Einstein's equations linearized around flat spacetime. First, we prescribe simple boundary conditions that make the problem well posed and preserve the constraints. Next, we indi...

  4. Monotone iterative technique for fractional differential equations with periodic boundary conditions

    OpenAIRE

    J. D. Ramírez; A. S. Vatsala

    2009-01-01

    In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary con...

  5. Exterior statistics based boundary conditions for representative volume elements of elastic composites

    Science.gov (United States)

    Ghosh, Somnath; Kubair, Dhirendra V.

    2016-10-01

    Statistically equivalent representative volume elements or SERVEs are representations of the microstructure that are used for micromechanical simulations to generate homogenized material constitutive responses and properties (Swaminathan et al., 2006a; Ghosh, 2011). Typically, a SERVE is generated from the parent microstructure as a statistically equivalent region, whose size is determined from the requirements of convergence of macroscopic properties. Standard boundary conditions, such as affine transformation-based displacement boundary conditions (ATDBCs), uniform traction boundary conditions (UTBCs) or periodic boundary conditions (PBCs) are conventionally applied on the SERVE boundary for micromechanical simulations. However, when the microstructure is characterized by arbitrary, nonuniform distributions of heterogeneities, these simple boundary conditions do not represent the effect of regions exterior to the SERVE. Improper boundary conditions can result in significantly larger than optimal SERVE domains, needed for converged properties. In an attempt to overcome the limitations of the conventional boundary conditions on the SERVE, this paper explores the effect of boundary conditions that incorporate the statistics of the exterior region on the SERVE of elastic composites. Using Green's function based interaction kernels, coupled with statistical functions of the microstructural characteristics like one-point and two-point correlation functions, a novel exterior statistics-based boundary condition or ESBC is derived for the SERVE. The advantages of the ESBC are established by comparing with results of simulations using conventional boundary conditions. Results of the SERVE simulations subjected to ESBCs are also compared with those from other popular methods like statistical volume element (SVE) and weighted statistical volume element (WSVE). The proposed ESBCs offer significant advantages over other methods in the SERVE-based analysis of heterogeneous

  6. General Considerations of the Electrostatic Boundary Conditions in Oxide Heterostructures

    Energy Technology Data Exchange (ETDEWEB)

    Higuchi, Takuya

    2011-08-19

    When the size of materials is comparable to the characteristic length scale of their physical properties, novel functionalities can emerge. For semiconductors, this is exemplified by the 'superlattice' concept of Esaki and Tsu, where the width of the repeated stacking of different semiconductors is comparable to the 'size' of the electrons, resulting in novel confined states now routinely used in opto-electronics. For metals, a good example is magnetic/non-magnetic multilayer films that are thinner than the spin-scattering length, from which giant magnetoresistance (GMR) emerged, used in the read heads of hard disk drives. For transition metal oxides, a similar research program is currently underway, broadly motivated by the vast array of physical properties that they host. This long-standing notion has been recently invigorated by the development of atomic-scale growth and probe techniques, which enables the study of complex oxide heterostructures approaching the precision idealized in Fig. 1(a). Taking the subset of oxides derived from the perovskite crystal structure, the close lattice match across many transition metal oxides presents the opportunity, in principle, to develop a 'universal' heteroepitaxial materials system. Hand-in-hand with the continual improvements in materials control, an increasingly relevant challenge is to understand the consequences of the electrostatic boundary conditions which arise in these structures. The essence of this issue can be seen in Fig. 1(b), where the charge sequence of the sublayer 'stacks' for various representative perovskites is shown in the ionic limit, in the (001) direction. To truly 'universally' incorporate different properties using different materials components, be it magnetism, ferroelectricity, superconductivity, etc., it is necessary to access and join different charge sequences, labelled here in analogy to the designations 'group IV, III-V, II

  7. A theoretical study of asymptotic boundary conditions for the numerical solutions of open-boundary static electromagnetic-field problems

    Institute of Scientific and Technical Information of China (English)

    马西奎; 韩社教

    2002-01-01

    Based on the multipole expansion theory of the potential, a satisfactory interpretation is put forward of the exact nature of the approximations of asymptotic boundary condition (called the ABC) techniques for the numerical solutions of open-boundary static electromagnetic-field problems, and a definite physical meaning is bestowed on ABC, which provide a powerful theoretical background for laying down the operating rules and the key to the derivation of asymptotic boundary conditions. This paper is also intended to reveal the shortcomings of the conventional higher-order ABC, and at the same time to give the concept of a new type of higher-order ABC, and to present a somewhat different formulation of the new nth-order ABC. In order to test its feasibility, several simple problems of electrostatic potentials are analyzed. The results are found to be much better than those of conventional higher-order ABCs.

  8. Modes and exceptional points in waveguides with impedance boundary conditions

    CERN Document Server

    Midya, Bikashkali

    2016-01-01

    A planar waveguide with impedance boundary, composed of non-perfect metallic plates, and with passive or active dielectric filling is considered. We show the possibility of selective mode guiding and amplification when homogeneous pump is added to the dielectric, and analyze differences in TE and TM mode propagation. Such a non-conservative system is also shown to feature exceptional points, for specific and experimentally tunable parameters, which are described for a particular case of transparent dielectric.

  9. Controlling near shore nonlinear surging waves through bottom boundary conditions

    CERN Document Server

    Mukherjee, Abhik; Kundu, Anjan

    2016-01-01

    Instead of taking the usual passive view for warning of near shore surging waves including extreme waves like tsunamis, we aim to study the possibility of intervening and controlling nonlinear surface waves through the feedback boundary effect at the bottom. It has been shown through analytic result that the controlled leakage at the bottom may regulate the surface solitary wave amplitude opposing the hazardous variable depth effect. The theoretical results are applied to a real coastal bathymetry in India.

  10. Feedback Shift Registers as Cellular Automata Boundary Conditions

    OpenAIRE

    Salman, K.

    2013-01-01

    We present a new design for random number generatio n. The outputs of linear feedback shift registers (LFSRs) act as continuous inputs to the t wo boundaries of a one-dimensional (1-D) Elementary Cellular Automata (ECA). The results sho w superior randomness features and the output string has passed the Diehard statistical ba ttery of tests. The design is good candidate for parallel random number generation, ...

  11. Poynting flux-conserving low-altitude boundary conditions for global magnetospheric models

    Science.gov (United States)

    Xi, S.; Lotko, W.; Zhang, B.; Brambles, O. J.; Lyon, J. G.; Merkin, V. G.; Wiltberger, M.

    2015-01-01

    A method for specifying low-altitude or inner boundary conditions that conserve low-frequency, magnetic field-aligned, electromagnetic energy flux across the boundary in global magnetospheric magnetohydrodynamics (MHD) models is presented. The single-fluid Lyon-Fedder-Mobarry (LFM) model is used to verify this method, with comparisons between simulations using LFM's standard hardwall boundary conditions and the new flux-conserving boundary conditions. Identical idealized upstream solar wind and interplanetary magnetic field conditions and the same constant ionospheric conductance are used in both runs. The results show that, compared to LFM's standard hardwall boundary conditions, the flux-conserving method improves the transparency of the boundary for the flow of low-frequency (essentially DC) electromagnetic energy flux along field lines. As a consequence, the hemispheric integrated field-aligned DC Poynting flux just above the boundary is close to the hemispheric total Joule heating of the ionosphere, as it should be if electromagnetic energy is conserved. The MHD velocity and perpendicular currents are well-behaved near the inner boundary for the flux conserving boundary conditions.

  12. On the Effective Construction of Compactly Supported Wavelets Satisfying Homogenous Boundary Conditions on the Interval

    Science.gov (United States)

    Chiavassa, G.; Liandrat, J.

    1996-01-01

    We construct compactly supported wavelet bases satisfying homogeneous boundary conditions on the interval (0,1). The maximum features of multiresolution analysis on the line are retained, including polynomial approximation and tree algorithms. The case of H(sub 0)(sup 1)(0, 1)is detailed, and numerical values, required for the implementation, are provided for the Neumann and Dirichlet boundary conditions.

  13. On the Boundary Conditions in Deformed Quantum Mechanics with Minimal Length Uncertainty

    Directory of Open Access Journals (Sweden)

    Pouria Pedram

    2013-01-01

    Full Text Available We find the coordinate space wave functions, maximal localization states, and quasiposition wave functions in a GUP framework that implies a minimal length uncertainty using a formally self-adjoint representation. We show how the boundary conditions in quasiposition space can be exactly determined from the boundary conditions in coordinate space.

  14. Existence result for the kinetic neutron transport problem with a general albedo boundary condition

    International Nuclear Information System (INIS)

    We present an existence result for the kinetic neutron transport equation with a general albedo boundary condition. The proof is constructive in the sense that we build a sequence that converges to the solution of the problem by iterating on the albedo term. Both nonhomogeneous and albedo boundary conditions are studied. (authors)

  15. Open boundary conditions for ISPH and their application to micro-flow

    Science.gov (United States)

    Hirschler, Manuel; Kunz, Philip; Huber, Manuel; Hahn, Friedemann; Nieken, Ulrich

    2016-02-01

    Open boundary conditions for incompressible Smoothed Particle Hydrodynamics (ISPH) are rare. For stable simulations with open boundary conditions, one needs to specify all boundary conditions correctly in the pressure force as well as in the linear equation system for pressure calculation. Especially for homogeneous or non-homogeneous Dirichlet boundary conditions for pressure there exist several possibilities but only a few lead to stable results. However, this isn't trivial for open boundary conditions. We introduce a new approach for open boundary conditions for ISPH to enable stable simulations. In contrast to existing models for weakly-compressible SPH, we can specify open pressure boundary conditions because in ISPH, pressure can be calculated independently of the density. The presented approach is based on the mirror particle approach already introduced for solid wall boundary conditions. Here we divide the mirror axis in several segments with time-dependent positions. We validate the presented approach for the example of Poiseuille flow and flow around a cylinder at different Reynolds numbers and show that we get good agreement with references. Then, we demonstrate that the approach can be applied to free surface flows. Finally, we apply the new approach to micro-flow through a random porous medium with a different number of in- and outlets and demonstrate its benefits.

  16. Eigenstates of a particle in an array of hexagons with periodic boundary condition

    Directory of Open Access Journals (Sweden)

    A Nemati

    2013-10-01

    Full Text Available In this paper the problem of a particle in an array of hexagons with periodic boundary condition is solved. Using the projection operators, we categorize eigenfunctions corresponding to each of the irreducible representations of the symmetry group . Based on these results, the Dirichlet and Neumann boundary conditions are discussed.

  17. Finite-volume method for the Cahn-Hilliard equation with dynamic boundary conditions

    OpenAIRE

    Nabet, Flore

    2014-01-01

    In this paper, we investigate a numerical scheme for solving a diphasic Cahn-Hilliard model with dynamic boundary conditions. We propose a finite volume method for the space discretization and we prove existence and convergence results. We also present numerical simulations to show the influence of these boundary conditions.

  18. Vibrations of stretched damped beams under non-ideal boundary conditions

    Indian Academy of Sciences (India)

    Hakan Boyaci

    2006-02-01

    A simply supported damped Euler–Bernoulli beam with immovable end conditions are considered. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the boundaries are assumed to allow small deflections and moments. Approximate analytical solution of the problem is found using the method of multiple scales, a perturbation technique.

  19. The effect of external boundary conditions on condensation heat transfer in rotating heat pipes

    Science.gov (United States)

    Daniels, T. C.; Williams, R. J.

    1979-01-01

    Experimental evidence shows the importance of external boundary conditions on the overall performance of a rotating heat pipe condenser. Data are presented for the boundary conditions of constant heat flux and constant wall temperature for rotating heat pipes containing either pure vapor or a mixture of vapor and noncondensable gas as working fluid.

  20. Question of consistent boundary conditions when simulating reversed field pinch dynamics. Revision 1

    Energy Technology Data Exchange (ETDEWEB)

    Mirin, A.A.

    1986-03-01

    The issue of proper boundary conditions when performing magnetohydrodynamic simulations of the reversed field pinch is examined. Of particular concern is the choice of constant current, which when combined with other commonly used boundary conditions, may, under careless implementation, lead to an inconsistency. It is shown that this may cause erroneous results. Cases both with and without Hall terms are presented.

  1. On solvability of some boundary value problems for a biharmonic equation with periodic conditions

    Science.gov (United States)

    Karachik, Valery V.; Massanov, Saparbay K.; Turmetov, Batirkhan Kh.

    2016-08-01

    In the paper we study questions about solvability of some boundary value problems with periodic conditions for an inhomogeneous biharmonic equation. The exact conditions for solvability of the problems are found.

  2. Periodic solutions of a non-linear wave equation with homogeneous boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Rudakov, I A [M.V. Lomonosov Moscow State University, Moscow (Russian Federation)

    2006-02-28

    We prove the existence of time-periodic solutions of a non-linear wave equation with homogeneous boundary conditions. The non-linear term either has polynomial growth or satisfies a 'non-resonance' condition.

  3. THE ARTIFICIAL BOUNDARY CONDITION FOR EXTERIOR OSEEN EQUATION IN 2-D SPACE

    Institute of Scientific and Technical Information of China (English)

    Chun-xiong Zheng; Hou-de Han

    2002-01-01

    A finite element method for the solution of Oseen equation in exterior domain is proposed. In this method, a circular artificial boundary is introduced to make the computational domain finite. Then, the exact relation between the normal stress and the prescribed velocity field on the artificial boundary can be obtained analytically. This relation can serve as an boundary condition for the boundary value problem defined on the finite domain bounded by the artificial boundary. Numerical experiment is presented to demonstrate the performance of the method.

  4. The Ritz Method for Boundary Problems with Essential Conditions as Constraints

    Directory of Open Access Journals (Sweden)

    Vojin Jovanovic

    2016-01-01

    Full Text Available We give an elementary derivation of an extension of the Ritz method to trial functions that do not satisfy essential boundary conditions. As in the Babuška-Brezzi approach boundary conditions are treated as variational constraints and Lagrange multipliers are used to remove them. However, we avoid the saddle point reformulation of the problem and therefore do not have to deal with the Babuška-Brezzi inf-sup condition. In higher dimensions boundary weights are used to approximate the boundary conditions, and the assumptions in our convergence proof are stated in terms of completeness of the trial functions and of the boundary weights. These assumptions are much more straightforward to verify than the Babuška-Brezzi condition. We also discuss limitations of the method and implementation issues that follow from our analysis and examine a number of examples, both analytic and numerical.

  5. Stability of basis property of a periodic problem with nonlocal perturbation of boundary conditions

    Science.gov (United States)

    Imanbaev, Nurlan; Sadybekov, Makhmud

    2016-08-01

    The present work is the continuation of authors' researchers on stability (instability) of basis property of root vectors of a differential operator with nonlocal perturbation of one of boundary conditions. In this paper a spectral problem for a multiple differentiation operator with an integral perturbation of boundary conditions of one type, which are regular, but not strongly regular, is devoted. For this type of the boundary conditions it is known that the unperturbed problem has an asymptotically simple spectrum, and its system of normalized eigenfunctions creates the Riesz basis. We construct the characteristic determinant of the spectral problem with an integral perturbation of the boundary conditions. It is shown that the Riesz basis property of a system of eigen and adjoint functions is stable with respect to integral perturbations of the boundary condition. In the paper requirements of smoothness to the kernel of the integral perturbation are also reduced (unlike our previous researchers).

  6. Boundary Conditions for 2D Boussinesq-type Wave-Current Interaction Equations

    Directory of Open Access Journals (Sweden)

    Mera M.

    2011-01-01

    Full Text Available This research focuses on the development of a set of two-dimensional boundary conditions for specific governing equations. The governing equations are existing Boussinesqtype equations which is capable of simulating wave-current interaction. The present boundary conditions consist of for waves only case and for currents only case. To simulate wave-current interaction, the two kinds of the present boundary conditions are then combined. A numerical model based on both the existing governing equations and the present boundary conditions is applied to simulation of currents only and of wave-current interaction propagating over a basin with a submerged shoal. The results of the numerical model show that the present boundary conditions go well with the existing Boussinesq-type wave-current interaction equations.

  7. Self-consistently simulation of RF sheath boundary condition in BOUT + + framework

    Science.gov (United States)

    Gui, Bin; Xu, Xueqiao; Xia, Tianyang

    2015-11-01

    The effect of the RF sheath boundary condition on the edge-localized modes and the turbulent transport is simulated in this work. The work includes two parts. The first part is to calculate the equilibrium radial electric field with RF sheath boundary condition. It is known the thermal sheath or the rectified RF sheath will modify the potential in the SOL region. The modified potential induces addition shear flow in SOL. In this part, the equilibrium radial electric field across the separatrix is calculated by solving the 2D current continuity equation with sheath boundary condition, drifts and viscosity. The second part is applying the sheath boundary condition on the perturbed variables of the six-field two fluid model in BOUT + + framework. The six-field two-fluid model simulates the ELMs and turbulent transport. The sheath boundary condition is applied in this model and it aims to simulate effect of sheath boundary condition on the turbulent transport. It is found the sheath boundary plays as a sink in the plasma and suppresses the local perturbation. Based on this two work, the effect of RF sheath boundary condition on the ELMs and turbulent transport could be self-consistently simulated. Prepared by LLNL under Contract DE-AC52-07NA27344.

  8. Thermo Field Dynamics of strings with definite boundary conditions

    OpenAIRE

    Vancea, Ion V.

    2015-01-01

    In this paper we review the construction of the thermal bosonic string and $D$-brane in the framework of the Thermo Field Dynamics (TFD). We briefly recall the well-known light-cone quantization of the bosonic string in the conformal gauge in flat space-time. Then we give a bird's eye view of the fundamental concepts of the TFD. Also, we present the thermalization of the bosonic string and the construction of the thermal D-brane boundary state. Finally, we show the calculation of the entropy ...

  9. Boundary conditions for spacelike and timelike warped AdS_3 spaces in topologically massive gravity

    CERN Document Server

    Compère, Geoffrey

    2009-01-01

    We propose a set of consistent boundary conditions containing the spacelike warped black holes solutions of Topologically Massive Gravity. We prove that the corresponding asymptotic charges whose algebra consists in a Virasoro algebra and a current algebra are finite, integrable and conserved. A similar analysis is performed for the timelike warped AdS_3 spaces which contain a family of regular solitons. The energy of the boundary Virasoro excitations is positive while the current algebra leads to negative (for the spacelike warped case) and positive (for the timelike warped case) energy boundary excitations. We discuss the relationship with the Brown-Henneaux boundary conditions.

  10. A quenched study of the Schroedinger functional with chirally rotated boundary conditions. Non-preturbative tuning

    Energy Technology Data Exchange (ETDEWEB)

    Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik

    2012-08-23

    The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to nonperturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit. (orig.)

  11. Local absorbing boundary conditions for nonlinear wave equation on unbounded domain.

    Science.gov (United States)

    Li, Hongwei; Wu, Xiaonan; Zhang, Jiwei

    2011-09-01

    The numerical solution of the nonlinear wave equation on unbounded spatial domain is considered. The artificial boundary method is introduced to reduce the nonlinear problem on unbounded spatial domain to an initial boundary value problem on a bounded domain. Using the unified approach, which is based on the operator splitting method, we construct the efficient nonlinear local absorbing boundary conditions for the nonlinear wave equation, and give the stability analysis of the resulting boundary conditions. Finally, several numerical examples are given to demonstrate the effectiveness of our method.

  12. Modeling boundary conditions for balanced proliferation in metastatic latency

    Science.gov (United States)

    Taylor, Donald P; Wells, Jakob Z; Savol, Andrej; Chennubhotla, Chakra; Wells, Alan

    2013-01-01

    Purpose Nearly half of cancer metastases become clinically evident five or more years after primary tumor treatment; thus metastatic cells survived without emerging for extended periods. This dormancy has been explained by at least two countervailing scenarios: cellular quiescence and balanced proliferation; these entail dichotomous mechanistic etiologies. To examine the boundary parameters for balanced proliferation, we performed in silico modeling. Experimental Design To illuminate the balanced proliferation hypothesis, we explored the specific boundary probabilities under which proliferating micrometastases would remain dormant. A two-state Markov chain Monte Carlo model simulated micrometastatic proliferation and death according to stochastic survival probabilities. We varied these probabilities across 100 simulated patients each with 1,000 metastatic deposits and documented whether the micrometastases exceeded one million cells, died out, or remained dormant (survived 1,218 generations). Results The simulations revealed a narrow survival probability window (49.7 – 50.8 percent) that allowed for dormancy across a range of starting cell numbers, and even then for only a small fraction of micrometastases. The majority of micrometastases died out quickly even at survival probabilities that led to rapid emergence of a subset of micrometastases. Within dormant metastases, cell populations depended sensitively on small survival probability increments. Conclusions Metastatic dormancy as explained solely by balanced proliferation is bounded by very tight survival probabilities. Considering the far larger survival variability thought to attend fluxing microenvironments, it is more probable that these micrometastatic nodules undergo at least periods of quiescence rather than exclusively being controlled by balanced proliferation. PMID:23329811

  13. MHD free convective boundary layer flow of a nanofluid past a flat vertical plate with Newtonian heating boundary condition.

    Science.gov (United States)

    Uddin, Mohammed J; Khan, Waqar A; Ismail, Ahmed I

    2012-01-01

    Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement. PMID:23166688

  14. MHD free convective boundary layer flow of a nanofluid past a flat vertical plate with Newtonian heating boundary condition.

    Directory of Open Access Journals (Sweden)

    Mohammed J Uddin

    Full Text Available Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.

  15. Implementation of higher-order absorbing boundary conditions for the Einstein equations

    CERN Document Server

    Rinne, Oliver; Scheel, Mark A; Pfeiffer, Harald P

    2008-01-01

    We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer boundary, which is taken to be a coordinate sphere. We reformulate the boundary conditions as conditions on the gauge-invariant Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated by rewriting the boundary conditions as a system of ODEs for a set of auxiliary variables intrinsic to the boundary. From these we construct boundary data for a set of well-posed constraint-preserving boundary conditions for the Einstein equations in a first-order generalized harmonic formulation. This construction has direct applications to outer boundary conditions in simulations of isolated systems (e.g., binary black holes) as well as to the problem of Cauchy-perturbative matching. As a test problem for our numerical implementation, we consider linearized multipolar grav...

  16. Boundary conditions for simulations of oscillating bubbles using the non-linear acoustic approximation

    Science.gov (United States)

    King, J. R. C.; Ziolkowski, A. M.; Ruffert, M.

    2015-03-01

    We have developed a new boundary condition for finite volume simulations of oscillating bubbles. Our method uses an approximation to the motion outside the domain, based on the solution at the domain boundary. We then use this approximation to apply boundary conditions by defining incoming characteristic waves at the domain boundary. Our boundary condition is applicable in regions where the motion is close to spherically symmetric. We have tested our method on a range of one- and two-dimensional test cases. Results show good agreement with previous studies. The method allows simulations of oscillating bubbles for long run times (5 ×105 time steps with a CFL number of 0.8) on highly truncated domains, in which the boundary condition may be applied within 0.1% of the maximum bubble radius. Conservation errors due to the boundary conditions are found to be of the order of 0.1% after 105 time steps. The method significantly reduces the computational cost of fixed grid finite volume simulations of oscillating bubbles. Two-dimensional results demonstrate that highly asymmetric bubble features, such as surface instabilities and the formation of jets, may be captured on a small domain using this boundary condition.

  17. SU(N) gauge theories with C-periodic boundary conditions. Pt. 1; Topological structure

    Energy Technology Data Exchange (ETDEWEB)

    Kronfeld, A.S. (Fermi National Accelerator Lab., Batavia, IL (USA). Theoretical Physics Group); Wiese, U.J. (Hoechstleistungsrechenzentrum (HLRZ), Juelich (Germany, F.R.). Gruppe Theorie der Elementarteilchen)

    1991-07-01

    C-periodic boundary conditions are introduced to SU(N) gauge theory on a torus. C-periodic fields are replaced by their charge conjugates when they are shifted over the boundary. As for periodic boundary conditions the most general C-periodic boundary condition includes twist. The topological structure with C-periodic boundary conditions is quite different from the periodic case. In the periodic case twist leads to the Z{sub N}'t Hooft flux sectors. In the C-periodic case with even N the symmetry of the flux sectors is reduced to Z{sub 2}. For odd N the flux sectors are eliminated completely. Furthermore, the topological charge is an integer when N is odd, whereas it can be a half-integer when N is even. (orig.).

  18. Inverse Lax-Wendroff procedure for numerical boundary conditions of convection-diffusion equations

    Science.gov (United States)

    Lu, Jianfang; Fang, Jinwei; Tan, Sirui; Shu, Chi-Wang; Zhang, Mengping

    2016-07-01

    We consider numerical boundary conditions for high order finite difference schemes for solving convection-diffusion equations on arbitrary geometry. The two main difficulties for numerical boundary conditions in such situations are: (1) the wide stencil of the high order finite difference operator requires special treatment for a few ghost points near the boundary; (2) the physical boundary may not coincide with grid points in a Cartesian mesh and may intersect with the mesh in an arbitrary fashion. For purely convection equations, the so-called inverse Lax-Wendroff procedure [28], in which we convert the normal derivatives into the time derivatives and tangential derivatives along the physical boundary by using the equations, has been quite successful. In this paper, we extend this methodology to convection-diffusion equations. It turns out that this extension is non-trivial, because totally different boundary treatments are needed for the diffusion-dominated and the convection-dominated regimes. We design a careful combination of the boundary treatments for the two regimes and obtain a stable and accurate boundary condition for general convection-diffusion equations. We provide extensive numerical tests for one- and two-dimensional problems involving both scalar equations and systems, including the compressible Navier-Stokes equations, to demonstrate the good performance of our numerical boundary conditions.

  19. CFD Modeling of Non-Neutral Atmospheric Boundary Layer Conditions

    DEFF Research Database (Denmark)

    Koblitz, Tilman

    For wind resource assessment, the wind industry is increasingly relying on Computational Fluid Dynamics models that focus on modeling the airflow in a neutrally stratified surface-layer. Physical processes like the Coriolis force, buoyancy forces and heat transport, that are important to the atmo......For wind resource assessment, the wind industry is increasingly relying on Computational Fluid Dynamics models that focus on modeling the airflow in a neutrally stratified surface-layer. Physical processes like the Coriolis force, buoyancy forces and heat transport, that are important...... to the atmospheric boundary-layer, are mostly ignored so far. In order to decrease the uncertainty of wind resource assessment, the present work focuses on atmospheric flows that include atmospheric stability and the Coriolis effect. Within the present work a RANS model framework is developed and implemented...

  20. Boundary Conditions for a New Type of Design Task

    DEFF Research Database (Denmark)

    McAloone, Tim C.

    2011-01-01

    Manufacturing companies have traditionally focused their efforts on developing and producing physical products for the market. Currently, however, many companies are rethinking their business strategies, from selling products to providing services. In place of the product alone, the activity...... and knowledge associated with the use of the product is increasingly perceived to be the new design object. But how to organise the design of combined products and services, over expanded time domains and new stakeholder boundaries? The design research community is paying increasing attention to this new design...... object and research paradigm, studying service‐oriented approaches to product development and seeking to understand how to spell the systematic development of these so-called Product/Service‐Systems (PSS). When considering the shift towards PSS in the domain of engineering, it is in...

  1. An approximate method for solving a melting problem with periodic boundary conditions

    OpenAIRE

    Qu Liang-Hui; Xing Lin; Yu Zhi-Yun; Ling Feng; Xu Jian-Guo

    2014-01-01

    An effective thermal diffusivity method is used to solve one-dimensional melting problem with periodic boundary conditions in a semi-infinite domain. An approximate analytic solution showing the functional relation between the location of the moving boundary and time is obtained by using Laplace transform. The evolution of the moving boundary and the temperature field in the phase change domain are simulated numerically, and the numerical results are compar...

  2. Free boundary conditions and the AdS3/CFT2 correspondence

    International Nuclear Information System (INIS)

    We show that recently proposed free boundary conditions for AdS3 are dual to two-dimensional quantum gravity in certain fixed gauges. In particular, we note that an appropriate identification of the generator of Virasoro transformations leads to a vanishing total central charge in agreement with the theory at the boundary. We argue that this identification is necessary to match the bulk and boundary generators of Virasoro transformations and for consistency with the constraint equations

  3. An approximate method for solving a melting problem with periodic boundary conditions

    Directory of Open Access Journals (Sweden)

    Qu Liang-Hui

    2014-01-01

    Full Text Available An effective thermal diffusivity method is used to solve one-dimensional melting problem with periodic boundary conditions in a semi-infinite domain. An approximate analytic solution showing the functional relation between the location of the moving boundary and time is obtained by using Laplace transform. The evolution of the moving boundary and the temperature field in the phase change domain are simulated numerically, and the numerical results are compared with previous results in open literature.

  4. Functional determinants for the Dirac equation with mixed pseudodifferential boundary conditions over finite cylinders

    International Nuclear Information System (INIS)

    In this note, we explicitly compute the functional determinant of a Dirac Laplacian with nonlocal pseudodifferential boundary conditions over a finite cylinder in terms of the ζ-function of the Dirac operator on the cross section and the pseudodifferential operators defining the boundary conditions. In particular, this result reduces to our previous formula [J. Phys. A 37, 7381 (2004)] for the special case of generalized Atiyah-Patodi-Singer conditions

  5. Reconsidering the quantization of electrodynamics with boundary conditions and some measurable consequences

    OpenAIRE

    Bordag, M.

    2004-01-01

    We show that the commonly known conductor boundary conditions $E_{||}=B_\\perp=0$ can be realized in two ways which we call 'thick' and 'thin' conductor. The 'thick' conductor is the commonly known approach and includes a Neumann condition on the normal component $E_\\perp$ of the electric field whereas for a 'thin' conductor $E_\\perp$ remains without boundary condition. Both types describe different physics already on the classical level where a 'thin' conductor allows for an interaction betwe...

  6. A uniqueness theorem of a boundary inverse problem of a differential operator on an interval with integro-differential boundary conditions

    Science.gov (United States)

    Kanguzhin, Baltabek; Tokmagambetov, Niyaz

    2016-08-01

    In this work, we research a boundary inverse problem of spectral analysis of a differential operator with integral boundary conditions in the functional space L2(0, b) where b operator by its spectrum and some additional data.

  7. Time-dependent density functional theory with twist-averaged boundary conditions

    CERN Document Server

    Schuetrumpf, B; Reinhard, P -G

    2016-01-01

    Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, 3D coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a box. For finite quantum systems (atoms, molecules, nuclei), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. These artifacts can be practically cured by introducing absorbing boundary conditions (ABC) through an absorbing potential in a certain boundary region sufficiently far from the described system. But also the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust) suffer artifacts from a finite computational box. In this regime, twist- averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we exte...

  8. Analysis and discretization of the volume penalized Laplace operator with Neumann boundary conditions

    CERN Document Server

    Kolomenskiy, Dmitry; Schneider, Kai

    2014-01-01

    We study the properties of an approximation of the Laplace operator with Neumann boundary conditions using volume penalization. For the one-dimensional Poisson equation we compute explicitly the exact solution of the penalized equation and quantify the penalization error. Numerical simulations using finite differences allow then to assess the discretisation and penalization errors. The eigenvalue problem of the penalized Laplace operator with Neumann boundary conditions is also studied. As examples in two space dimensions, we consider a Poisson equation with Neumann boundary conditions in rectangular and circular domains.

  9. Adapting a Fourier pseudospectral method to Dirichlet boundary conditions for Rayleigh--B\\'enard convection

    CERN Document Server

    Ramos, I C

    2015-01-01

    We present the adaptation to non--free boundary conditions of a pseudospectral method based on the (complex) Fourier transform. The method is applied to the numerical integration of the Oberbeck--Boussinesq equations in a Rayleigh--B\\'enard cell with no-slip boundary conditions for velocity and Dirichlet boundary conditions for temperature. We show the first results of a 2D numerical simulation of dry air convection at high Rayleigh number ($R\\sim10^9$). These results are the basis for the later study, by the same method, of wet convection in a solar still.

  10. DIFFERENT ROOF BEHAVIOUR UNDER DIFFERENT UPPER MINING BOUNDARY CONDITION IN DATONG

    Institute of Scientific and Technical Information of China (English)

    康立勋

    1997-01-01

    Understanding roof behaviour and immediate roof failure patterns of Iongwall face is a prerequisite for establishing correct roof control theory and appplying effective roof control measures. Roof behaviour and immediate roof failure pattern have a close relationship with upper mining boundary conditions of Iongwall face. According to actual situation of Datong Mining Area, upper mining boundary conditions of Iongwall face have been classified into 5 types in this paper. Roof behaviour and immediate roof failure pattern under each upper mining boundary condition are discussed in details.

  11. Effects of microscopic boundary conditions on plastic deformations of small-sized single crystals

    DEFF Research Database (Denmark)

    Kuroda, Mitsutoshi; Tvergaard, Viggo

    2009-01-01

    The finite deformation version of the higher-order gradient crystal plasticity model proposed by the authors is applied to solve plane strain boundary value problems, in order to obtain an understanding of the effect of the higher-order boundary conditions. Numerical solutions are carried out...... effect of higher-order boundary conditions on the overall deformation mode of the block is observed. The bent foil has free surfaces through which dislocations can go out of the material, and we observe a strong size-dependent mechanical response resulting from the surface condition assumed....

  12. Combined effects of surface conditions, boundary layer dynamics and chemistry on diurnal SOA evolution

    NARCIS (Netherlands)

    Janssen, R.H.H.; Vilà-Guerau de Arellano, J.; Ganzeveld, L.N.; Kabat, P.; Jimenez, J.L.; Farmer, D.K.; Heerwaarden, van C.C.; Mammarella, I.

    2012-01-01

    We study the combined effects of land surface conditions, atmospheric boundary layer dynamics and chemistry on the diurnal evolution of biogenic secondary organic aerosol in the atmospheric boundary layer, using a model that contains the essentials of all these components. First, we evaluate the mod

  13. Interaction-round-a-face models with fixed boundary conditions the ABF fusion hierarchy

    CERN Document Server

    Behrend, R E; O'Brien, D L; Behrend, Roger E; Pearce, Paul A; O'Brien, David L

    1995-01-01

    We use boundary weights and reflection equations to obtain families of commuting double-row transfer matrices for interaction-round-a-face models with fixed boundary conditions. In particular, we consider the fusion hierarchy of the Andrews-Baxter-Forrester models, for which we find that the double-row transfer matrices satisfy functional equations with an su(2) structure.

  14. GENERAL DECAY OF A TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATIONS WITH BOUNDARY MEMORY CONDITION

    Institute of Scientific and Technical Information of China (English)

    Sun Hye PARK

    2014-01-01

    In this paper, we investigate the influence of boundary dissipation on the de-cay property of solutions for a transmission problem of Kirchhoff type wave equation with boundary memory condition. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of relaxation function.

  15. REGULARITY THEORY FOR SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. This type of problem is motivated by stochastic differential games. The Neumann case corresponds to stochastic differential equations with reflection on boundary of the domain.

  16. Finite-Volume Analysis for the Cahn-Hilliard equation with Dynamic boundary conditions

    OpenAIRE

    Nabet, Flore

    2014-01-01

    This work is devoted to the convergence analysis of a finite-volume approximation of the 2D Cahn-Hilliard equation with dynamic boundary conditions. The method that we propose couples a 2d-finite-volume method in a bounded, smooth domain and a 1d-finite-volume method on its boundary. We prove convergence of the sequence of approximate solutions.

  17. Numerical Simulation of Time-Dependent Wave Propagation Using Nonreflective Boundary Conditions

    Science.gov (United States)

    Ionescu, D.; Muehlhaus, H.

    2003-12-01

    Solving numerically the wave equation for modelling wave propagation on an unbounded domain with complex geometry requires a truncation of the domain, to fit the infinite region on a finite computer. Minimizing the amount of spurious reflections requires in many cases the introduction of an artificial boundary and of associated nonreflecting boundary conditions. Here, a question arises, namely which boundary condition guarantees that the solution of the time dependent problem inside the artificial boundary coincides with the solution of the original problem in the infinite region. Recent investigations have shown that the accuracy and performance of numerical algorithms and the interpretation of the results critically depend on the proper treatment of external boundaries. Despite the computational speed of finite difference schemes and the robustness of finite elements in handling complex geometries the resulting numerical error consists of two independent contributions: the discretization error of the numerical method used and the spurious reflection generated at the artificial boundary. This spurious contribution travels back and substantially degrades the accuracy of the solution everywhere in the computational domain. Unless both error components are reduced systematically, the numerical solution does not converge to the solution of the original problem in the infinite region. In the present study we present and discuss absorbing boundary condition techniques for the time-dependent scalar wave equation in three spatial dimensions. In particular, exact conditions that annihilate wave harmonics on a spherical artificial boundary up to a given order are obtained and subsequently applied in numerical simulations by employing a finite differences implementation.

  18. Transverse periodic boundary conditions in molecular dynamics with uniaxial strain shock waves

    Energy Technology Data Exchange (ETDEWEB)

    Harris, P.; Karo, A.M.

    1984-11-20

    In this report we discuss the role of transverse, periodic, boundary conditions (TPBCs) in multidimensional molecular dynamics (MD) calculations. We conclude that observed nonsteady-state shock propagation in MD calculations could easily be an artifact resulting from inadequate separation between the periodic boundaries. 20 references.

  19. The asymptotic equivalence of fixed heat flux and fixed temperature thermal boundary conditions for rapidly rotating convection

    CERN Document Server

    Calkins, Michael A; Julien, Keith; Nieves, David; Driggs, Derek; Marti, Philippe

    2015-01-01

    The influence of fixed temperature and fixed heat flux thermal boundary conditions on rapidly rotating convection in the plane layer geometry is investigated for the case of stress-free mechanical boundary conditions. It is shown that whereas the leading order system satisfies fixed temperature boundary conditions implicitly, a double boundary layer structure is necessary to satisfy the fixed heat flux thermal boundary conditions. The boundary layers consist of a classical Ekman layer adjacent to the solid boundaries that adjust viscous stresses to zero, and a layer in thermal wind balance just outside the Ekman layers adjusts the temperature such that the fixed heat flux thermal boundary conditions are satisfied. The influence of these boundary layers on the interior geostrophically balanced convection is shown to be asymptotically weak, however. Upon defining a simple rescaling of the thermal variables, the leading order reduced system of governing equations are therefore equivalent for both boundary condit...

  20. An inconvenient "truth" about using sensible heat flux as a surface boundary condition in models under stably stratified regimes

    NARCIS (Netherlands)

    Basu, S.; Holtslag, A.A.M.; Wiel, van de B.J.H.; Moene, A.F.; Steeneveld, G.J.

    2008-01-01

    In single column and large-eddy simulation studies of the atmospheric boundary layer, surface sensible heat flux is often used as a boundary condition. In this paper, we delineate the fundamental shortcomings of such a boundary condition in the context of stable boundary layer modelling and simulati

  1. Fractional-Order Variational Calculus with Generalized Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Baleanu Dumitru

    2011-01-01

    Full Text Available This paper presents the necessary and sufficient optimality conditions for fractional variational problems involving the right and the left fractional integrals and fractional derivatives defined in the sense of Riemman-Liouville with a Lagrangian depending on the free end-points. To illustrate our approach, two examples are discussed in detail.

  2. A new package for simulating periodic boundary conditions in MODFLOW and SEAWAT

    Science.gov (United States)

    Post, V. E. A.

    2011-11-01

    Modeling of coastal groundwater systems is a challenging problem due to their highly dynamic boundary conditions and the coupling between the equations for groundwater flow and solute transport. A growing number of publications on aquifers subject to tides have demonstrated various modeling approaches, ranging from analytical solutions to comprehensive numerical models. The United States Geological Survey code SEAWAT has been a popular choice in studies of this type. Although SEAWAT allows the incorporation of time-variant boundary conditions, the implementation of tidal boundaries is not straightforward, especially when a seepage face develops during falling tide. Here, a new package is presented, called the periodic boundary condition (PBC) package, that can be incorporated into MODFLOW and SEAWAT to overcome the difficulties encountered with tidal boundaries. It dynamically updates the boundary conditions for head and concentration during the simulation depending on a user-defined tidal signal and allows for the development of a seepage face. The package has been verified by comparing it to four different published models of tidally influenced groundwater systems of varying complexity. Excellent agreement was obtained in all cases. The new package is an important extension to the existing capabilities of MODFLOW and SEAWAT with respect to simulating periodic boundary conditions.

  3. Boundary Conditions and the Aeolian Sediment State of the Olympia Undae Dune Field, Mars

    Science.gov (United States)

    Middlebrook, W.; Ewing, R. C.; Ayoub, F.; Bridges, N. T.; Smith, I.; Spiga, A.

    2015-05-01

    We evaluate the boundary conditions in Olympia Undae. We map two and three dimensional dune parameters from two locations proximal and distal to Planum Boreum and constrain sediment fluxes. We compare our results with a mesoscale atmospheric model.

  4. Regular and Irregular Boundary Conditions in the AdS/CFT Correspondence

    CERN Document Server

    Mück, W

    1999-01-01

    We expand on Klebanov and Witten's recent proposal for formulating the AdS/CFT correspondence using irregular boundary conditions. The proposal is shown to be correct to any order in perturbation theory.

  5. A Kind of Discrete Non-Reflecting Boundary Conditions for Varieties of Wave Equations

    Institute of Scientific and Technical Information of China (English)

    Xiu-min Shao; Zhi-ling Lan

    2002-01-01

    In this paper, a new kind of discrete non-reflecting boundary conditions is developed. It can be used for a variety of wave equations such as the acoustic wave equation, the isotropic and anisotropic elastic wave equations and the equations for wave propagation in multi-phase media and so on. In this kind of boundary conditions, the composition of all artificial reflected waves, but not the individual reflected ones, is considered and eliminated. Thus, it has a uniform formula for different wave equations. The velocity CA of the composed reflected wave is determined in the way to make the reflection coefficients minimal, the value of which depends on equations. In this paper, the construction of the boundary conditions is illustrated and CA is found, numerical results are presented to illustrate the effectiveness of the boundary conditions.

  6. THE DYNAMICS OF SINE-GORDON SYSTEM WITH DIRICHLET BOUNDARY CONDITION

    Institute of Scientific and Technical Information of China (English)

    Liu Yingdong; Li Zhengyuan

    2000-01-01

    We prove the existence of the global attractor of Sine-Gordon system with Dirichlet boundary condition and show the attractor is the unique steady state when the damping constant and the diffusion constant are sufficiently large.

  7. Correct contractions stationary Navier-Stokes equations and boundary conditions for the setting pressure

    Science.gov (United States)

    Otelbaev, Mukhtarbay; Koshanov, Bakytbek D.

    2016-08-01

    This paper describes the correct narrowing of the Navier-Stokes equations in a stationary three-dimensional cube and clarified the correct formulation of the boundary conditions for the pressure in the environment.

  8. The Pressure Boundary Conditions for the Incompressible Navier—Stokes Equations Computation

    Institute of Scientific and Technical Information of China (English)

    YaosongCHEN; TaoJIANG

    1996-01-01

    This article devotes to the correct formulation of the pressure boundary conditions for the incompressible Navier-Stokes equation and gives the method of integration.The example has been shown for its feasibility.

  9. Evaluation of wall boundary condition parameters for gas-solids fluidized bed simulations

    Energy Technology Data Exchange (ETDEWEB)

    Li, Tingwen [URS Corporation; Morgantown, WV (United States); National Energy Technology Lab. (NETL), Morgantown, WV (United States); Benyahia, Sofiane [National Energy Technology Lab. (NETL), Morgantown, WV (United States)

    2013-10-01

    Wall boundary conditions for the solids phase have significant effects on numerical predictions of various gas-solids fluidized beds. Several models for the granular flow wall boundary condition are available in the open literature for numerical modeling of gas-solids flow. In this study, a model for specularity coefficient used in Johnson and Jackson boundary conditions by Li and Benyahia (AIChE Journal, 2012, 58, 2058-2068) is implemented in the open-source CFD code-MFIX. The variable specularity coefficient model provides a physical way to calculate the specularity coefficient needed by the partial-slip boundary conditions for the solids phase. Through a series of 2-D numerical simulations of bubbling fluidized bed and circulating fluidized bed riser, the model predicts qualitatively consistent trends to the previous studies. Furthermore, a quantitative comparison is conducted between numerical results of variable and constant specularity coefficients to investigate the effect of spatial and temporal variations in specularity coefficient.

  10. Soft-and-Hard/D'B' Boundary Conditions and their Realization by Electromagnetic Media

    CERN Document Server

    Lindell, I V

    2012-01-01

    A layer of uniaxial medium with large axial permittivity and permeability can be used as a quarter-wave transformer with interesting properties. By increasing the transverse permittivity and permeability the transformer becomes a thin sheet. It is shown that the recently introduced SHDB boundary conditions, generalizing the soft-and-hard and DB conditions, realized by the interface of a skewon-axion medium, can be transformed to form a novel class of SHD'B' boundary conditions which generalizes the soft-and-hard and D'B' boundary conditions. Reflection of a plane wave from a planar SHD'B' boundary is considered by numerical examples revealing an interesting narrow beam with radical change of reflection for certain values of parameters and incidence angles.

  11. Asymptotic behavior of solutions to nonlinear parabolic equation with nonlinear boundary conditions

    Directory of Open Access Journals (Sweden)

    Diabate Nabongo

    2008-01-01

    Full Text Available We show that solutions of a nonlinear parabolic equation of second order with nonlinear boundary conditions approach zero as t approaches infinity. Also, under additional assumptions, the solutions behave as a function determined here.

  12. Blow-up estimates for semilinear parabolic systems coupled in an equation and a boundary condition

    Institute of Scientific and Technical Information of China (English)

    王明新

    2001-01-01

    This paper deals with the blow-up rate estimates of solutions for semilinear parabolic systems coupled in an equation and a boundary condition. The upper and lower bounds of blow-up rates have been obtained.

  13. Structure and vibrational spectra of a model of a-Si:H with periodic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Winer, K.; Wooten, F.

    1983-08-01

    A ball-and -stick model of a-Si:H with periodic boundary conditions has been constructed. A computer replica of the structure has been relaxed and the density, radial distribution function and vibrational spectra calculated.

  14. Shifted periodic boundary conditions for simulations of wall-bounded turbulent flows

    Science.gov (United States)

    Munters, Wim; Meneveau, Charles; Meyers, Johan

    2016-02-01

    In wall-bounded turbulent flow simulations, periodic boundary conditions combined with insufficiently long domains lead to persistent spanwise locking of large-scale turbulent structures. This leads to statistical inhomogeneities of 10%-15% that persist in time averages of 60 eddy turnover times and more. We propose a shifted periodic boundary condition that eliminates this effect without the need for excessive streamwise domain lengths. The method is tested based on a set of direct numerical simulations of a turbulent channel flow, and large-eddy simulations of a high Reynolds number rough-wall half-channel flow. The method is very useful for precursor simulations that generate inlet conditions for simulations that are spatially inhomogeneous, but require statistically homogeneous inlet boundary conditions in the spanwise direction. The method's advantages are illustrated for the simulation of a developing wind-farm boundary layer.

  15. Near-linear dynamics in KdV with periodic boundary conditions

    OpenAIRE

    Erdogan, M. B.; Tzirakis, N.; Zharnitsky, V.

    2009-01-01

    Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction.

  16. Mean Field in Long-Range Ferromagnets and Periodic Boundary Conditions

    OpenAIRE

    Curilef, Sergio

    2004-01-01

    Periodic boundary conditions are applied to a ferromagnetic spin lattice. A symmetrical lattice and its contributions all over space are being used. Results, for the Ising model with ferromagnetic interaction that decays as a $1/r^{D+\

  17. An Overview of the Lower and Upper Solutions Method with Nonlinear Boundary Value Conditions

    Directory of Open Access Journals (Sweden)

    Cabada Alberto

    2011-01-01

    Full Text Available The aim of this paper is to point out recent and classical results related with the existence of solutions of second-order problems coupled with nonlinear boundary value conditions.

  18. Invariance of decay rate with respect to boundary conditions in thermoelastic Timoshenko systems

    Science.gov (United States)

    Alves, M. S.; Jorge Silva, M. A.; Ma, T. F.; Muñoz Rivera, J. E.

    2016-06-01

    This paper is mainly concerned with the polynomial stability of a thermoelastic Timoshenko system recently introduced by Almeida Júnior et al. (Z Angew Math Phys 65(6):1233-1249, 2014) that proved, in the general case when equal wave speeds are not assumed, different polynomial decay rates depending on the boundary conditions, namely, optimal rate {t^{-1/2}} for mixed Dirichlet-Neumann boundary condition and rate {t^{-1/4}} for full Dirichlet boundary condition. Here, our main achievement is to prove the same polynomial decay rate {t^{-1/2}} (corresponding to the optimal one) independently of the boundary conditions, which improves the existing literature on the subject. As a complementary result, we also prove that the system is exponentially stable under equal wave speeds assumption. The technique employed here can probably be applied to other kind of thermoelastic systems.

  19. Small Scale Effect on Thermal Vibration of Single-Walled Carbon Nanotubes with Nonlocal Boundary Condition

    Directory of Open Access Journals (Sweden)

    Li Ming

    2013-03-01

    Full Text Available In this study, a single beam model has been developed to analyze the thermal vibration of Single-Walled Carbon Nanotubes (SWCNT. The nonlocal elasticity takes into account the effect of small size into the formulation and the boundary condition. With exact solution of the dynamic governing equations, the thermal-vibrational characteristics of a cantilever SWCNT are obtained. Influence of nonlocal small scale effects, temperature change and vibration modes of the CNT on the frequency are investigated. The present study shows that the additional boundary conditions from small scale do not change natural frequencies at different temperature change. Thus for simplicity, one can apply the local boundary condition to replace the small scale boundary condition.

  20. Spectral analysis of nonselfadjoint Schr(o)dinger problem with eigenparameter in the boundary condition

    Institute of Scientific and Technical Information of China (English)

    M.Yakit ONGUN

    2007-01-01

    In this paper we consider the nonselfadjoint (dissipative) Schr(o)dinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator,and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schr(o)dinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schr(o)dinger boundary value problem are given.

  1. Spectral analysis of nonselfadjoint Schrdinger problem with eigenparameter in the boundary condition

    Institute of Scientific and Technical Information of China (English)

    M.Yakit; ONGUN

    2007-01-01

    In this paper we consider the nonselfadjoint (dissipative) Schrodinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator, and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schrodinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schrodinger boundary value problem are given.

  2. Kinematics and shear heat pattern of ductile simple shear zones with `slip boundary condition'

    Science.gov (United States)

    Mulchrone, Kieran F.; Mukherjee, Soumyajit

    2016-04-01

    Extrusion by Poiseuille flow and simple shear of hot lower crust has been deciphered from large hot orogens, and partial-slip boundary condition has been encountered in analogue models. Shear heat and velocity profiles are deduced from a simplified form of Navier-Stokes equation for simple shear together with extrusive Poiseuille flow and slip boundary condition for Newtonian viscous rheology. A higher velocity at the upper boundary of the shear zone promotes higher slip velocity at the lower boundary. The other parameters that affect the slip are viscosity and thickness of the shear zone and the resultant pressure gradient that drives extrusion. In the partial-slip case, depending on flow parameters (resultant pressure gradient, density and viscosity) and thickness of the shear zone, the velocity profiles can curve and indicate opposite shear senses. The corresponding shear heat profiles can indicate temperature maximum inside shear zones near either boundaries of the shear zone, or equidistant from them.

  3. Multiple boundary condition test (MBCT) approach to update mathematical models of large flexible structures

    Science.gov (United States)

    Wada, B. K.; Kuo, C.-P.; Glaser, R. J.

    1986-01-01

    A major challenge to the structural dynamicist is to validate mathematical models of large space structures which cannot be ground tested because of its size and/or flexibility. The paper presents a Multiple Boundary Condition Test (MBCT) approach which allows a systematic validation of the mathematical model by performing a number of ground tests on a large structure with variable boundary conditions. A numerical simulation is presented which illustrates the validity of the MBCT including some of the potential limitations.

  4. Boundary Condition in Liquid Thin Films Revealed through the Thermal Fluctuations of Their Free Surfaces

    OpenAIRE

    Pottier, B; Frétigny, C; Talini, L

    2015-01-01

    We investigate the properties of nanometric liquid films with a new non invasive technique. We measure the spontaneous thermal fluctuations of the free surfaces of liquids to probe their hydrodynamic boundary condition at a solid wall. The surface fluctuations of a silicon oil film could be described with a no-slip boundary condition for film thicknesses down to 20 nm. Oppositely, a 4 nm negative slip length had to be introduced to describe the behavior of n-hexadecane, consistently with prev...

  5. On the existence of orbits satisfying periodic or conormal boundary conditions for Euler-Lagrange flows

    OpenAIRE

    Asselle, Luca

    2015-01-01

    Let $(M,g)$ be a closed Riemannian manifold and $L:TM\\rightarrow \\mathbb R$ be a Tonelli Lagrangian. In this thesis we study the existence of orbits of the Euler-Lagrange flow associated with $L$ satisfying suitable boundary conditions. We first look for orbits connecting two given closed submanifolds of $M$ satisfying the conormal boundary conditions: We introduce the Ma\\~n\\'e critical value that is relevant for the problem and prove existence results for supercritical and subcritical energi...

  6. A new approach to (quasi) periodic boundary conditions in micromagnetics: the macrogeometry

    OpenAIRE

    Fangohr, Hans; Bordignon, Giuliano; Franchin, Matteo; Knittel, Andreas; de Groot, Peter A. J.; Fischbacher, Thomas

    2009-01-01

    We present a new method to simulate repetitive ferromagnetic structures. This macro geometry approach combines treatment of short-range interactions (i.e. the exchange field) as for periodic boundary conditions with a specification of the arrangement of copies of the primary simulation cell n order to correctly include effects of the demagnetizing field. This method (i) solves a consistency problem that prevents the naive application of 3d periodic boundary conditions in micromagn...

  7. Sobolev type equations of time-fractional order with periodical boundary conditions

    Science.gov (United States)

    Plekhanova, Marina

    2016-08-01

    The existence of a unique local solution for a class of time-fractional Sobolev type partial differential equations endowed by the Cauchy initial conditions and periodical with respect to every spatial variable boundary conditions on a parallelepiped is proved. General results are applied to study of the unique solvability for the initial boundary value problem to Benjamin-Bona-Mahony-Burgers and Allair partial differential equations.

  8. Chaotic Dynamics of One-Dimensional Systems with Periodic Boundary Conditions

    OpenAIRE

    Kumar, Pankaj; Miller, Bruce N.

    2014-01-01

    We provide appropriate tools for the analysis of dynamics and chaos for one-dimensional systems with periodic boundary conditions. Our approach allows for the investigation of the dependence of the largest Lyapunov exponent on various initial conditions of the system. The method employs an effective approach for defining the phase-space distance appropriate for systems with periodic boundary and allows for an unambiguous test-orbit rescaling in the phase space required to calculate the Lyapun...

  9. Assessment of a PML Boundary Condition for Simulating an MRI Radio Frequency Coil

    OpenAIRE

    Alayar Kangarlu; Feng Liu; Peterson, Bradley S.; Tamer S Ibrahim; Yunsuo Duan

    2008-01-01

    Computational methods such as the finite difference time domain (FDTD) play an important role in simulating radiofrequency (RF) coils used in magnetic resonance imaging (MRI). The choice of absorbing boundary conditions affects the final outcome of such studies. We have used FDTD to assess the Berenger's perfectly matched layer (PML) as an absorbing boundary condition for computation of the resonance patterns and electromagnetic fields of RF coils. We first experimentally constructed a high-...

  10. Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions

    KAUST Repository

    Gerbi, Stéphane

    2011-12-01

    In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.

  11. Application of generalized separation of variables to solving mixed problems with irregular boundary conditions

    Science.gov (United States)

    Gasymov, E. A.; Guseinova, A. O.; Gasanova, U. N.

    2016-07-01

    One of the methods for solving mixed problems is the classical separation of variables (the Fourier method). If the boundary conditions of the mixed problem are irregular, this method, generally speaking, is not applicable. In the present paper, a generalized separation of variables and a way of application of this method to solving some mixed problems with irregular boundary conditions are proposed. Analytical representation of the solution to this irregular mixed problem is obtained.

  12. A truncated implicit high-order finite-difference scheme combined with boundary conditions

    Science.gov (United States)

    Chang, Suo-Liang; Liu, Yang

    2013-03-01

    In this paper, first we calculate finite-difference coefficients of implicit finitedifference methods (IFDM) for the first- and second-order derivatives on normal grids and firstorder derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition (ABC) to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.

  13. Schrödinger functional boundary conditions and improvement for N > 3

    DEFF Research Database (Denmark)

    Hietanen, A.; Karavirta, T.; Vilaseca, P.

    2014-01-01

    The standard method to calculate non-perturbatively the evolution of the running coupling of a SU(N ) gauge theory is based on the Schrodinger functional (SF). In this paper we construct a family of boundary fields for general values of N which enter the standard definition of the SF coupling. We...... provide spatial boundary conditions for fermions in several representations which reduce the condition number of the squared Dirac operator. In addition, we calculate the improvement coefficients for N > 3 needed to remove boundary cutoff effects from the gauge action. After this, residual cutoff effects...

  14. A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions

    Science.gov (United States)

    Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.

    2014-01-01

    We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.

  15. ALmost EXact boundary conditions for transient Schrödinger-Poisson system

    Science.gov (United States)

    Bian, Lei; Pang, Gang; Tang, Shaoqiang; Arnold, Anton

    2016-05-01

    For the Schrödinger-Poisson system, we propose an ALmost EXact (ALEX) boundary condition to treat accurately the numerical boundaries. Being local in both space and time, the ALEX boundary conditions are demonstrated to be effective in suppressing spurious numerical reflections. Together with the Crank-Nicolson scheme, we simulate a resonant tunneling diode. The algorithm produces numerical results in excellent agreement with those in Mennemann et al. [1], yet at a much reduced complexity. Primary peaks in wave function profile appear as a consequence of quantum resonance, and should be considered in selecting the cut-off wave number for numerical simulations.

  16. The joining of code COBRA to the PERF-type boundary conditions

    International Nuclear Information System (INIS)

    The subchannel analysis method for the thermohydraulic investigation offuel element clusters of nuclear reactor cores is based on the supposition that the boundaries of the investigated space in the radial direction is either closed or the gradients of the parameters are equal to zero. When such a subchannel analysis is applied for the investigation of WWER-1000 type fuel element clusters, it should be able to accept radial boundary conditions coming from the global calculation of the whole reactor core. The paper gives a detailed description of the improvement of COBRA and COCONT subchannel codes for the acceptance of radial boundary conditions. (author) 11 refs.; 6 figs

  17. Smoothed Particle Hydrodynamics Continuous Boundary Force method for Navier-Stokes equations subject to a Robin boundary condition

    Science.gov (United States)

    Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre

    2013-11-01

    A Continuous Boundary Force (CBF) method was developed for implementing Robin (Navier) boundary condition (BC) that can describe no-slip or slip conditions (slip length from zero to infinity) at the fluid-solid interface. In the CBF method the Robin BC is replaced by a homogeneous Neumann BC and an additional volumetric source term in the governing momentum equation. The formulation is derived based on an approximation of the sharp boundary with a diffuse interface of finite thickness, across which the BC is reformulated by means of a smoothed characteristic function. The CBF method is easy to be implemented in Lagrangian particle-based methods. We first implemented it in smoothed particle hydrodynamics (SPH) to solve numerically the Navier-Stokes equations subject to spatial-independent or dependent Robin BC in two and three dimensions. The numerical accuracy and convergence is examined through comparisons with the corresponding finite difference or finite element solutions. The CBF method is further implemented in smoothed dissipative particle dynamics (SDPD), a mesoscale scheme, for modeling slip flows commonly existent in micro/nano channels and microfluidic devices. The authors acknowledge the funding support by the ASCR Program of the Office of Science, U.S. Department of Energy.

  18. An energy absorbing far-field boundary condition for the elastic wave equation

    Energy Technology Data Exchange (ETDEWEB)

    Petersson, N A; Sjogreen, B

    2008-07-15

    The authors present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional to shear wave speed. They prove stability for a second order accurate finite-difference discretization of the elastic wave equation in three space dimensions together with a discretization of the proposed non-reflecting boundary condition. The stability proof is based on a discrete energy estimate and is valid for heterogeneous materials. The proof includes all six boundaries of the computational domain where special discretizations are needed at the edges and corners. The stability proof holds also when a free surface boundary condition is imposed on some sides of the computational domain.

  19. Structural vibration a uniform accurate solution for laminated beams, plates and shells with general boundary conditions

    CERN Document Server

    Jin, Guoyong; Su, Zhu

    2015-01-01

    This book develops a uniform accurate method which is capable of dealing with vibrations of laminated beams, plates and shells with arbitrary boundary conditions including classical boundaries, elastic supports and their combinations. It also provides numerous solutions for various configurations including various boundary conditions, laminated schemes, geometry and material parameters, which fill certain gaps in this area of reach and may serve as benchmark solutions for the readers. For each case, corresponding fundamental equations in the framework of classical and shear deformation theory are developed. Following the fundamental equations, numerous free vibration results are presented for various configurations including different boundary conditions, laminated sequences and geometry and material properties. The proposed method and corresponding formulations can be readily extended to static analysis.

  20. Effects of upper disc boundary conditions on the linear Rossby wave instability

    CERN Document Server

    Lin, Min-Kai

    2012-01-01

    The linear Rossby wave instability (RWI) in global, 3D polytropic discs is revisited with a much simpler numerical method than that previously employed by the author. The governing partial differential equation is solved with finite differences in the radial direction and spectral collocation in the vertical direction. RWI modes are calculated subject to different upper disc boundary conditions. These include free surface, solid boundaries and variable vertical domain size. Boundary conditions that oppose vertical motion increase the instability growth rate by a few per cent. The magnitude of vertical flow throughout the fluid column can be affected but the overall flow pattern is qualitatively unchanged. Numerical results support the notion that the RWI is intrinsically two dimensional. This implies that inconsistent upper disc boundary conditions, such as vanishing enthalpy perturbation, may inhibit the RWI in 3D.

  1. Performance of Numerical Boundary Condition based on Active Wave Absorption System

    DEFF Research Database (Denmark)

    Trouch, P.; Rouck, J. de; Frigaard, Peter

    2001-01-01

    that was first developed in the context of physical wave flume experiments, using a wave paddle. The method applies to regular and irregular waves. Velocities are measured at one location inside the computational domain. The reflected wave train is separated from the incident wave field in front of a structure......The implementation and performance of a new active wave generating‐absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces is presented. This numerical boundary condition AWAVOF is based on an active wave absorption system...... by means of digital filtering and subsequent superposition of the measured velocity signals. The incident wave signal is corrected, so that the reflected wave is effectively absorbed at the boundary. The effectiveness of the active wave generating‐absorbing boundary condition is proved using numerical...

  2. Overcoming order reduction in diffusion-reaction splitting. Part 2: oblique boundary conditions

    CERN Document Server

    Einkemmer, Lukas

    2016-01-01

    Splitting methods constitute a well-established class of numerical schemes for the time integration of partial differential equations. Their main advantages over more traditional schemes are computational efficiency and superior geometric properties. In the presence of non-trivial boundary conditions, however, splitting methods usually suffer from order reduction and some additional loss of accuracy. For diffusion-reaction equations with inhomogeneous oblique boundary conditions, a modification of the classic second-order Strang splitting is proposed that successfully resolves the problem of order reduction. The same correction also improves the accuracy of the classic first-order Lie splitting. The proposed modification only depends on the available boundary data and, in the case of non Dirichlet boundary conditions, on the computed numerical solution. Consequently, this modification can be implemented in an efficient way, which makes the modified splitting schemes superior to their classic versions. The fra...

  3. Bouncing Dirac particles: compatibility between MIT boundary conditions and Thomas precession

    CERN Document Server

    Nicolaevici, Nistor

    2016-01-01

    We consider the reflection of a Dirac plane wave on a perfectly reflecting plane described by chiral MIT boundary conditions and determine the rotation of the spin in the reflected component of the wave. We solve the analogous problem for a classical particle using the evolution of the spin defined by the Thomas precession and make a comparison with the quantum result. We find that the rotation axes of the spin in the two problems coincide only for a vanishing chiral angle, in which case the rotation angles coincide in the nonrelativistic limit, and also remain remarkably close in the relativistic regime. The result shows that in the nonrelativistic limit the interaction between the spin and a reflecting surface with nonchiral boundary conditions is completely contained in the Thomas precession effect, in conformity with the fact that these boundary conditions are equivalent to an infinite repulsive scalar potential outside the boundary. By contrast, in the ultrarelativistic limit the rotation angle in the qu...

  4. On the Nature of Boundary Conditions for Flows with Moving Free Surfaces

    Science.gov (United States)

    Renardy, Michael; Renardy, Yuriko

    1991-04-01

    We consider small perturbations of plane parallel flow between a wall and a moving free surface. The problem is posed on a rectangle with inflow and outflow boundaries. The usual boundary conditions are posed at the wall and the free surface, and the fluid satisfies the Navier-Stokes equations. We examine the nature of boundary conditions which can be imposed at the inflow and outflow boundaries in order to yield a well-posed problem. This question turns out to be more delicate than is generally appreciated. Depending on the precise situation and on the regularity required of the solution, boundary conditions at just one or both endpoints of the free surface need to be imposed. For example, we show that if the velocities at te inflow and outflow boundaries are prescribed, then the position of the free surface at the inflow boundary can be prescribed, but not at the outflow if an H1-solution is desired. Numerical simulations with the FIDAP package are used to illustrate our analytical results.

  5. Revisiting Surface Heat-Flux and Temperature Boundary Conditions in Models of Stably Stratified Boundary-Layer Flows

    Science.gov (United States)

    Gibbs, Jeremy A.; Fedorovich, Evgeni; Shapiro, Alan

    2015-02-01

    Two formulations of the surface thermal boundary condition commonly employed in numerical modelling of atmospheric stably stratified surface-layer flows are evaluated using analytical considerations and observational data from the Cabauw site in the Netherlands. The first condition is stated in terms of the surface heat flux and the second is stated in terms of the vertical potential temperature difference. The similarity relationships used to relate the flux and the difference are based on conventional log-linear expressions for vertical profiles of wind velocity and potential temperature. The heat-flux formulation results in two physically meaningful values for the friction velocity with no obvious criteria available to choose between solutions. Both solutions can be obtained numerically, which casts doubt on discarding one of the solutions as was previously suggested based on stability arguments. This solution ambiguity problem is identified as the key issue of the heat-flux condition formulation. In addition, the agreement between the temperature difference evaluated from similarity solutions and their measurement-derived counterparts from the Cabauw dataset appears to be very poor. Extra caution should be paid to the iterative procedures used in the model algorithms realizing the heat-flux condition as they could often provide only partial solutions for the friction velocity and associated temperature difference. Using temperature difference as the lower boundary condition bypasses the ambiguity problem and provides physically meaningful values of heat flux for a broader range of stability condition in terms of the flux Richardson number. However, the agreement between solutions and observations of the heat flux is again rather poor. In general, there is a great need for practicable similarity relationships capable of treating the vertical turbulent transport of momentum and heat under conditions of strong stratification in the surface layer.

  6. Effects of temperature boundary conditions on equiaxed dendritic growth in phase-field simulations of binary alloy

    Institute of Scientific and Technical Information of China (English)

    于艳梅; 杨根仓; 赵达文; 吕衣礼

    2002-01-01

    By the phase-field approach, the dendritic growth in binary alloy melt was simulated respectively using two types of temperature boundary conditions, i.e., the constant temperature boundary by which the boundary temperature was fixed at the initial temperature, and Zero-Neumann temperature boundary. The influences of the temperature boundary conditions on numerical results are investigated. How to choose appropriate temperature boundary conditions is proposed. The results show that: 1) when the computation region is limited to a changeless size, the Zero-Neumann and constant temperature boundary conditions lead to the different dendritic growth behaviors, and the Zero-Neumann condition is preferable to the constant temperature condition; 2) when the computation region is enlarged continually with the computational time according to the increasing thermal diffusion scale, the two types of temperature boundary conditions achieve the consistent tip velocities and tip radii, and they both are appropriate choices.

  7. On the downstream boundary conditions for the vorticity-stream function formulation of two-dimensional incompressible flows

    Science.gov (United States)

    Tezduyar, T. E.; Liou, J.

    1991-01-01

    Downstream boundary conditions equivalent to the homogeneous form of the natural boundary conditions associated with the velocity-pressure formulation of the Navier-Stokes equations are derived for the vorticity-stream function formulation of two-dimensional incompressible flows. Of particular interest are the zero normal and shear stress conditions at a downstream boundary.

  8. Hydrogeological boundary settings in SR 97. Uncertainties in regional boundary settings and transfer of boundary conditions to site-scale models

    International Nuclear Information System (INIS)

    The SR 97 project presents a performance assessment (PA) of the overall safety of a hypothetical deep repository at three sites in Sweden arbitrarily named Aberg, Beberg and Ceberg. One component of this PA assesses the uncertainties in the hydrogeological modelling. This study focuses on uncertainties in boundary settings (size of model domain and boundary conditions) in the regional and site-scale hydrogeological modelling of the three sites used to simulating the possible transport of radionuclides from the emplacement waste packages through the host rock to the accessible environment. Model uncertainties associated with, for instance, parameter heterogeneity and structural interpretations are addressed in other studies. This study concludes that the regional modelling of the SR 97 project addresses uncertainties in the choice of boundary conditions and size of model domain differently at each site, although the overall handling is acceptable and in accordance with common modelling practice. For example, the treatment of uncertainties with regard to the ongoing post-glacial flushing of the Baltic Shield is creditably addressed although not exhaustive from a modelling point of view. A significant contribution of the performed modelling is the study of nested numerical models, i.e., the numerical interplay between regional and site-scale numerical models. In the site-scale modelling great efforts are made to address problems associated with (i) the telescopic mesh refinement (TMR) technique with regard to the stochastic continuum approach, and (ii) the transfer of boundary conditions between variable-density flow systems and flow systems that are constrained to treat uniform density flow. This study concludes that the efforts made to handle these problems are acceptable with regards to the objectives of the SR 97 project

  9. On the formulation of open boundary conditions at the mouth of a bay

    Science.gov (United States)

    Greatbatch, Richard J.; Otterson, Timm

    1991-10-01

    We describe our experience in formulating open boundary conditions to apply at the mouth of a reduced-gravity model of a bay. Our objective is to find a way to calculate the response of the bay to wind forcing over the bay itself, without being concerned about the influence of regions beyond. We show that open boundaries from which Kelvin waves can propagate along the coast into the model domain ("upstream" boundaries) must be treated with care. We begin by considering an "upstream" boundary which runs perpendicular to the coast. We find that if a radiation condition is applied on such a boundary, then spurious Kelvin waves of near-inertial period can propagate in from the boundary and contaminate the solution in the interior of the model domain. Also, if there is Ekman transport at the "upstream" boundary away from (toward) the coast, then upwelling (downwelling) will occur indefinitely and completely swamp the model solution in the bay. This is similar to the solution we expect when the coastline is straight and extends to infinity in the "upstream" direction. However, it is not the same, since the rate of upwelling (downwelling) is roughly half the theoretical value for that case. For the problem of a bay we suggest that the way to deal with this is to extend the coastline out to sea on the "upstream" side of the mouth and apply a condition on the artificial stretch of the boundary which suppresses Kelvin wave propagation but is also not prohibitively reflective to outgoing Poincaré waves. For our problem a condition of zero normal gradient in interface displacement seems to be sufficient. This condition also captures reasonably well the near-inertial Kelvin waves that are generated by the northwest corner of the bay (which are a genuine part of the solution) as long as the other boundaries are sufficiently far from the bay. We have also experimented with using sponge layers rather than radiation conditions on the other boundaries. We find that sponging only

  10. Effects of Boundary Condition and Helix Angle On Meshing Performance of TI Worm Gearing

    Institute of Scientific and Technical Information of China (English)

    SUN Yue-hai; DUAN Lu-qian; WANG Shu-ren; ZHANG Ce

    2006-01-01

    To exactly describe the contact state and contact area oftooth surface oftoroidalinvolute(TI) worm gearing.the authors introduced boundary condition into contact line analysis.With helix angle chosen as parameter,the criterion for the existence of meshing boundary line on the surface of TI worm gearing is derived.Results show that there can be four situations for meshing boundary line on the tooth surface of gear.namely,inexistence of meshing boundary line.a unique line,two lines,and two coincident lines.If the helix angle is equal to or slightly smaller than the bigger angle,which makes two meshing boundary lines superpose,a preferable meshing performance is obtained.Computer simulation proves the validity Of the above conclusion.

  11. Existence and asymptotic behavior of the wave equation with dynamic boundary conditions

    KAUST Repository

    Graber, Philip Jameson

    2012-03-07

    The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time. © 2012 Springer Science+Business Media, LLC.

  12. An outgoing energy flux boundary condition for finite difference ICRP antenna models

    International Nuclear Information System (INIS)

    For antennas at the ion cyclotron range of frequencies (ICRF) modeling in vacuum can now be carried out to a high level of detail such that shaping of the current straps, isolating septa, and discrete Faraday shield structures can be included. An efficient approach would be to solve for the fields in the vacuum region near the antenna in three dimensions by finite methods and to match this solution at the plasma-vacuum interface to a solution obtained in the plasma region in one dimension by Fourier methods. This approach has been difficult to carry out because boundary conditions must be imposed at the edge of the finite difference grid on a point-by-point basis, whereas the condition for outgoing energy flux into the plasma is known only in terms of the Fourier transform of the plasma fields. A technique is presented by which a boundary condition can be imposed on the computational grid of a three-dimensional finite difference, or finite element, code by constraining the discrete Fourier transform of the fields at the boundary points to satisfy an outgoing energy flux condition appropriate for the plasma. The boundary condition at a specific grid point appears as a coupling to other grid points on the boundary, with weighting determined by a kemel calctdated from the plasma surface impedance matrix for the various plasma Fourier modes. This boundary condition has been implemented in a finite difference solution of a simple problem in two dimensions, which can also be solved directly by Fourier transformation. Results are presented, and it is shown that the proposed boundary condition does enforce outgoing energy flux and yields the same solution as is obtained by Fourier methods

  13. The unified method: II. NLS on the half-line with t-periodic boundary conditions

    Science.gov (United States)

    Lenells, J.; Fokas, A. S.

    2012-05-01

    Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general method to this particular class of problems yields the solution in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the complex k-plane (the Fourier plane), which has a jump matrix with explicit (x, t)-dependence involving four scalar functions of k, called spectral functions. Two of these functions depend on the initial data, whereas the other two depend on all boundary values. The most difficult step of the new method is the characterization of the latter two spectral functions in terms of the given initial and boundary data, i.e. the elimination of the unknown boundary values. For certain boundary conditions, called linearizable, this can be achieved by simply using algebraic manipulations. Here, we first present an effective characterization of the spectral functions in terms of the given initial and boundary data for the general case of non-linearizable boundary conditions. This characterization is based on the analysis of the so-called global relation and on the introduction of the so-called Gelfand-Levitan-Marchenko representations of the eigenfunctions defining the spectral functions. We then concentrate on the physically significant case of t-periodic Dirichlet boundary data. After presenting certain heuristic arguments which suggest that the Neumann boundary values become periodic as t → ∞, we show that for the case of the NLS with a sine-wave as Dirichlet data, the asymptotics of the Neumann boundary values can be computed explicitly at least up to third order in a perturbative expansion and indeed at least up to this order are asymptotically periodic.

  14. Nonlinear fractional differential equations and inclusions of arbitrary order and multi-strip boundary conditions

    Directory of Open Access Journals (Sweden)

    Bashir Ahmad

    2012-06-01

    Full Text Available We study boundary value problems of nonlinear fractional differential equations and inclusions of order $q in (m-1, m]$, $m ge 2$ with multi-strip boundary conditions. Multi-strip boundary conditions may be regarded as the generalization of multi-point boundary conditions. Our problem is new in the sense that we consider a nonlocal strip condition of the form: $$ x(1=sum_{i=1}^{n-2}alpha_i int^{eta_i}_{zeta_i} x(sds, $$ which can be viewed as an extension of a multi-point nonlocal boundary condition: $$ x(1=sum_{i=1}^{n-2}alpha_i x(eta_i. $$ In fact, the strip condition corresponds to a continuous distribution of the values of the unknown function on arbitrary finite segments $(zeta_i,eta_i$ of the interval $[0,1]$ and the effect of these strips is accumulated at $x=1$. Such problems occur in the applied fields such as wave propagation and geophysics. Some new existence and uniqueness results are obtained by using a variety of fixed point theorems. Some illustrative examples are also discussed.

  15. Axisymmetric compressive buckling of multi-walled carbon nanotubes under different boundary conditions

    Institute of Scientific and Technical Information of China (English)

    Cheng-Qi Sun; Kai-Xin Liu; You-Shi Hong

    2012-01-01

    The paper studies the axisymmetric compressive buckling behavior of multi-walled carbon nanotubes (MWNTs) under different boundary conditions based on continuum mechanics model.A buckling condition is derived for determining the critical buckling load and associated buckling mode of MWNTs,and numerical results are worked out for MWNTs with different aspect ratios under fixed and simply supported boundary conditions.It is shown that the critical buckling load of MWNTs is insensitive to boundary conditions,except for nanotubes with smaller radii and very small aspect ratio.The associated buckling modes for different layers of MWNTs are in-phase,and the buckling displacement ratios for different layers are independent of the boundary conditions and the length of MWNTs.Moreover,for simply supported boundary conditions,the critical buckling load is compared with the corresponding one for axial compressive buckling,which indicates that the critical buckling load for axial compressive buckling can be well approximated by the corresponding one for axisymmetric compressive buckling.In particular,for axial compressive buckling of double-walled carbon nanotubes,an analytical expression is given for approximating the critical buckling load.The present investigation may be of some help in further understanding the mechanical properties of MWNTs.

  16. Poisson-Nernst-Planck model with Chang-Jaffe, diffusion, and ohmic boundary conditions

    Science.gov (United States)

    Lelidis, I.; Macdonald, J. Ross; Barbero, G.

    2016-01-01

    Using the linear Poisson-Nernst-Planck impedance-response continuum model, we investigate the possible equivalences of three different types of boundary conditions previously proposed to model the electrode behavior of an electrolytic cell in the shape of a slab. We show analytically that the boundary conditions proposed long ago by Chang-Jaffe are fully equivalent to the ohmic boundary conditions only if the positive and negative ions have the same mobility, or when only ions of a single polarity are mobile. In the case where the ions have different and non-zero mobilities, we fit exact impedance spectra created for ohmic boundary conditions by using the Chang-Jaffe Poisson-Nernst-Planck response model, one that is dominated by diffusion effects. These fits yield conditions for essentially exact or approximate numerical correspondence for the complex impedance between the two models even in the unequal mobility case. Finally, diffusion type boundary conditions are shown to be fully equivalent to the ohmic one. Some limiting cases of the model parameters are investigated.

  17. Homogenization of the evolution Stokes equation in a perforated domain with a stochastic Fourier boundary condition

    KAUST Repository

    Bessaih, Hakima

    2015-04-01

    The evolution Stokes equation in a domain containing periodically distributed obstacles subject to Fourier boundary condition on the boundaries is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the obstacles. We represent the solid obstacles by holes in the fluid domain. The macroscopic (homogenized) equation is derived as another stochastic partial differential equation, defined in the whole non perforated domain. Here, the initial stochastic perturbation on the boundary becomes part of the homogenized equation as another stochastic force. We use the twoscale convergence method after extending the solution with 0 in the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. In order to pass to the limit on the boundary integrals, we rewrite them in terms of integrals in the whole domain. In particular, for the stochastic integral on the boundary, we combine the previous idea of rewriting it on the whole domain with the assumption that the Brownian motion is of trace class. Due to the particular boundary condition dealt with, we get that the solution of the stochastic homogenized equation is not divergence free. However, it is coupled with the cell problem that has a divergence free solution. This paper represents an extension of the results of Duan and Wang (Comm. Math. Phys. 275:1508-1527, 2007), where a reaction diffusion equation with a dynamical boundary condition with a noise source term on both the interior of the domain and on the boundary was studied, and through a tightness argument and a pointwise two scale convergence method the homogenized equation was derived. © American Institute of Mathematical Sciences.

  18. Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions

    Science.gov (United States)

    Caflisch, Russel E.; Lombardo, Maria Carmela; Sammartino, Marco

    2011-05-01

    In this paper nonlocal boundary conditions for the Navier-Stokes equations are derived, starting from the Boltzmann equation in the limit for the Knudsen number being vanishingly small. In the same spirit of (Lombardo et al. in J. Stat. Phys. 130:69-82, 2008) where a nonlocal Poisson scattering kernel was introduced, a gaussian scattering kernel which models nonlocal interactions between the gas molecules and the wall boundary is proposed. It is proved to satisfy the global mass conservation and a generalized reciprocity relation. The asymptotic expansion of the boundary-value problem for the Boltzmann equation, provides, in the continuum limit, the Navier-Stokes equations associated with a class of nonlocal boundary conditions of the type used in turbulence modeling.

  19. CFD Analysis of the Human Exhalation Flow using Different Boundary Conditions and Ventilation Strategies

    DEFF Research Database (Denmark)

    Villafruela, J.M.; Olmedo, Inés; Ruiz de Adana, M.;

    2013-01-01

    different environmental conditions and to validate whether a steady boundary condition of the exhalation flow may simulate human breathing in an effective and accurate way. The results show a very good agreement of the numerical results obtained for Test a and the experimental data. This fact confirms the...... use of numerical simulation as a powerful tool to predict the contaminant distribution exhaled by a human. The numerical tests with steady boundary conditions for the exhalation flow require a transitory resolution procedure and the predictions provided by these models display some discrepancies with...

  20. NON-STATIONARY STOKES FLOWS UNDER LEAK BOUNDARY CONDITIONS OF FRICTION TYPE

    Institute of Scientific and Technical Information of China (English)

    Hiroshi Fujita

    2001-01-01

    This paper is concerned with the initial value problem for non-stationary Stokes flows,under a certain non-linear boundary condition which can be called the leak boundarycondition of friction type. Theoretically, our main purpose is to show the strong solvability(i.e.,the unique existence of the L2-strong solution) of this initial value problem by meansof the non-linear semi-group theory originated with Y. Komura. The method of analysiscan be applied to other boundary or interface conditions of friction type. It should benoted that the result yields a sound basis of simulation methods for evolution problemsinvolving these conditions.

  1. Numerical modeling of the effect of variation of boundary conditions on vadose zone hydraulic properties

    Directory of Open Access Journals (Sweden)

    Tairone Paiva Leão

    2011-02-01

    Full Text Available An accurate estimation of hydraulic fluxes in the vadose zone is essential for the prediction of water, nutrient and contaminant transport in natural systems. The objective of this study was to simulate the effect of variation of boundary conditions on the estimation of hydraulic properties (i.e. water content, effective unsaturated hydraulic conductivity and hydraulic flux in a one-dimensional unsaturated flow model domain. Unsaturated one-dimensional vertical water flow was simulated in a pure phase clay loam profile and in clay loam interlayered with silt loam distributed according to the third iteration of the Cantor Bar fractal object Simulations were performed using the numerical model Hydrus 1D. The upper and lower pressure heads were varied around average values of -55 cm for the near-saturation range. This resulted in combinations for the upper and lower constant head boundary conditions, respectively, of -50 and -60 cm, -40 and -70 cm, -30 and -80 cm, -20 and -90 cm, and -10 and -100 cm. For the drier range the average head between the upper and lower boundary conditions was set to -550 cm, resulting in the combinations -500 and -600 cm, -400 and -700 cm, -300 and -800 cm, -200 and -900 cm, and -100 and -1,000 cm, for upper and lower boundary conditions, respectively. There was an increase in water contents, fluxes and hydraulic conductivities with the increase in head difference between boundary conditions. Variation in boundary conditions in the pure phase and interlayered one-dimensional profiles caused significant deviations in fluxes, water contents and hydraulic conductivities compared to the simplest case (a head difference between the upper and lower constant head boundaries of 10 cm in the wetter range and 100 cm in the drier range.

  2. Unified semi-analytical wall boundary conditions applied to 2-D incompressible SPH

    Science.gov (United States)

    Leroy, A.; Violeau, D.; Ferrand, M.; Kassiotis, C.

    2014-03-01

    This work aims at improving the 2-D incompressible SPH model (ISPH) by adapting it to the unified semi-analytical wall boundary conditions proposed by Ferrand et al. [10]. The ISPH algorithm considered is as proposed by Lind et al. [25], based on the projection method with a divergence-free velocity field and using a stabilising procedure based on particle shifting. However, we consider an extension of this model to Reynolds-Averaged Navier-Stokes equations based on the k-ɛ turbulent closure model, as done in [10]. The discrete SPH operators are modified by the new description of the wall boundary conditions. In particular, a boundary term appears in the Laplacian operator, which makes it possible to accurately impose a von Neumann pressure wall boundary condition that corresponds to impermeability. The shifting and free-surface detection algorithms have also been adapted to the new boundary conditions. Moreover, a new way to compute the wall renormalisation factor in the frame of the unified semi-analytical boundary conditions is proposed in order to decrease the computational time. We present several verifications to the present approach, including a lid-driven cavity, a water column collapsing on a wedge and a periodic schematic fish-pass. Our results are compared to Finite Volumes methods, using Volume of Fluids in the case of free-surface flows. We briefly investigate the convergence of the method and prove its ability to model complex free-surface and turbulent flows. The results are generally improved when compared to a weakly compressible SPH model with the same boundary conditions, especially in terms of pressure prediction.

  3. Explicit construction of solutions to the Burgers equation with discontinuous initial-boundary conditions

    OpenAIRE

    Désilles, Anya; Frankowska, Hélène

    2013-01-01

    International audience Abstract. A solution of the initial-boundary value problem on the strip (0,1) × [0, 1] for scalar conservation laws with strictly convex flux can be obtained by considering gradients of the unique solution V to an associated Hamilton-Jacobi equation (with appropriately defined initial and boundary conditions). It was shown in Frankowska (2010) that V can be expressed as the minimum of three value functions arising in calculus of variations problems that, in turn, can...

  4. On half inverse problem for differential pencils with the spectral parameter in boundary conditions

    Directory of Open Access Journals (Sweden)

    Sergey Buterin

    2011-08-01

    Full Text Available A second-order differential pencil on a finite interval with spectral parameter dependent boundary conditions is considered. The inverse problem is studied of recovering the coefficients of the boundary value problem from its spectrum, provided that on one half of the interval they are known a priori. The uniqueness theorem for this inverse problem is proved and a constructive procedure for finding its solution is obtained.

  5. Heat kernel for the elliptic system of linear elasticity with boundary conditions

    OpenAIRE

    Taylor, Justin; Kim, Seick; Brown, Russell

    2013-01-01

    We consider the elliptic system of linear elasticity with bounded measurable coefficients in a domain where the second Korn inequality holds. We construct heat kernel of the system subject to Dirichlet, Neumann, or mixed boundary condition under the assumption that weak solutions of the elliptic system are H\\"older continuous in the interior. Moreover, we show that if weak solutions of the mixed problem are H\\"older continuous up to the boundary, then the corresponding heat kernel has a Gauss...

  6. Third-order operator-differential equations with discontinuous coefficients and operators in the boundary conditions

    Directory of Open Access Journals (Sweden)

    Araz R. Aliev

    2013-10-01

    Full Text Available We study a third-order operator-differential equation on the semi-axis with a discontinuous coefficient and boundary conditions which include an abstract linear operator. Sufficient conditions for the well-posed and unique solvability are found by means of properties of the operator coefficients in a Sobolev-type space.

  7. Stress and mixed boundary conditions for two-dimensional dodecagonal quasi-crystal plates

    Indian Academy of Sciences (India)

    Yan Gao; Si-Peng Xu; Bao-Sheng Zhao

    2007-05-01

    For plate bending and stretching problems in two-dimensional (2D) dodecagonal quasi-crystal (QC) media, the reciprocal theorem and the general solution for QCs are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all order. The method developed by Gregory and Wan is used to generate necessary conditions which the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the plate; these decaying state conditions are obtained explicitly for axisymmetric bending and stretching of a circular plate when stress or mixed conditions are imposed on the plate edge. They are then used for the correct formulation of boundary conditions for the interior solution. For the stress data, our boundary conditions coincide with those obtained in conventional forms of plate theories. More importantly, appropriate boundary conditions with a set of mixed edge-data are obtained for the first time. Furthermore, the corresponding necessary conditions for transversely isotropic elastic plate are obtained directly, and their isotropic elastic counterparts are also obtained.

  8. Existence of positive solutions for fourth order singular differential equations with Sturm-Liouville boundary conditions

    Institute of Scientific and Technical Information of China (English)

    Zhao Zengqin

    2007-01-01

    By using the upper and lower solutions method and fixed point theory, we investigate a class of fourth - order singular differential equations with the Sturm - Liouville Boundary conditions. Some sufficient conditions are obtained for the existence of C2 [ 0, 1 ] positive solutions and C3 [ 0, 1 ] positive solutions.

  9. A uniqueness theorem of a boundary inverse problem of a differential operator on an interval with integro-differential boundary conditions

    Science.gov (United States)

    Kanguzhin, Baltabek; Tokmagambetov, Niyaz

    2016-08-01

    In this work, we research a boundary inverse problem of spectral analysis of a differential operator with integral boundary conditions in the functional space L2(0, b) where b conditions of the operator by its spectrum and some additional data.

  10. Vectorization of diffusion computations in the presence of periodic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Abu-Shumays, I.K.

    1985-05-01

    Solutions of very large three-dimensional elliptic diffusion problems are very expensive in terms of storage requirements and computational cost even on today's supercomputers. Effective utilization of translational or rotational periodic boundary conditions, when applicable, can substantially reduce cost. Implementation of periodic boundary conditions however is not straightforward and special care should be exercised to avoid loss of computational efficiency. Application of periodic boundary conditions perturbs the overall matrix structure of the underlying discretized diffusion equations and may adversely affect standard computational methods. For simplicity, this study is restricted to the solution of two-dimensional diffusion problems. The numerical solution methods considered are the point Chebyshev and line cyclic Chebyshev iterative methods. It is straightforward to implement periodic boundary conditions within the framework of the highly vectorizable point Chebyshev iterative method. This paper presents alternative approaches for implementing periodic boundary conditions within the framework of the line cyclic Chebyshev iteration method. In the process, the method of odd-even cyclic reduction as applied to vectorization of the solution of tridiagonal systems is generalized to apply to special sparse predominantly tridiagonal matrix equations. For two-dimensional problems, it is demonstrated numerically on a CYBER 205 for model situations that the resulting line cyclic Chebyshev iterative method is computationally superior to the highly vectorizable point Chebyshev iterative method. The superiority of the line cyclic Chebyshev method over the point Chebyshev method is expected to hold for more complex problems with general mesh triangulations.

  11. Blow-up estimates for semilinear parabolic systems coupled in an equation and a boundary condition

    Institute of Scientific and Technical Information of China (English)

    WANG; Mingxin(

    2001-01-01

    [1]Wang, S., Wang, M. X., Xie, C. H., Reaction-diffusion systems with nonlinear boundary conditions, Z. angew. Math.Phys., 1997, 48(6): 994-1001.[2]Fila, M., Quittner, P., The blow-up rate for a semilinear parabolic system, J. Math. Anal. Appl., 1999, 238: 468-476.[3]Hu, B., Remarks on the blow-up estimate for solutions of the heat equation with a nonlinear boundary condition, Differential Integral Equations, 1996, 9(5): 891-901.[4]Hu, B. , Yin, H. M., The profile near blow-up time for solution of the heat equation with a nonlinear boundary condition,Trans. of Amer. Math. Soc., 1994, 346: 117-135.[5]Amann, H., Parabolic equations and nonlinear boundary conditions, J. of Diff. Eqns., 1988, 72: 201-269.[6]Deng, K., Blow-up rates for parabolic systems, Z. angew. Math. Phys. ,1996, 47: 132-143.[7]Fila, M., Levine, H. A., On critical exponents for a semilinear parabolic system coupled in an equation and a boundary condition, J. Math. Anal. Appl., 1996, 204: 494-521.

  12. Investigation on the choice of boundary conditions and shape functions for flexible multi-body system

    Science.gov (United States)

    Pan, Ke-Qi; Liu, Jin-Yang

    2012-02-01

    The objective of this investigation is to examine the correctness and efficiency of the choice of boundary conditions when using assumed mode approach to simulate flexible multi-body systems. The displacement field due to deformation is approximated by the Rayleigh-Ritz assumed modes in floating frame of reference (FFR) formulation. The deformations obtained by the absolute nodal coordinate (ANC) formulation which are transformed by two sets of reference coordinates are introduced as a criterion to verify the accuracy of the simulation results by using the FFR formulation. The relationship between the deformations obtained from different boundary conditions is revealed. Numerical simulation examples demonstrate that the assumed modes with cantilevered-free, simply-supported and free-free boundary conditions without inclusion of rigid body modes are suitable for simulation of flexible multi-body system with large over all motion, and the same physical deformation can be obtained using those mode functions, differ only by a coordinate transformation. It is also shown that when using mode shapes with statically indeterminate boundary conditions, significant error may occur. Furthermore, the slider crank mechanism with rigid crank is accurate enough for investigating boundary condition problem of flexible multi-body system, which cost significant less simulating time. The project was supported by the National Natural Science Foundation of China (10872126) and the Research Fund of the Doctoral Program of Higher Education of China (20100073110007).

  13. Investigation on the choice of boundary conditions and shape functions for flexible multi-body system

    Institute of Scientific and Technical Information of China (English)

    Ke-Qi Pan; Jin-Yang Liu

    2012-01-01

    The objective of this investigation is to examine the correctness and efficiency of the choice of boundary conditions when using assumed mode approach to simulate flexible multi-body systems.The displacement field due to deformation is approximated by the Rayleigh-Ritz assumed modes in floating frame of reference (FFR) formulation.The deformations obtained by the absolute nodal coordinate (ANC) formulation which are transformed by two sets of reference coordinates are introduced as a criterion to verify the accuracy of the simulation results by using the FFR formulation.The relationship between the deformations obtained from different boundary conditions is revealed.Numerical simulation examples demonstrate that the assumed modes with cantilevered-free,simply-supported and freefree boundary conditions without inclusion of rigid body modes are suitable for simulation of flexible multi-body system with large over all motion,and the same physical deformation can be obtained using those mode functions,differ only by a coordinate transformation.It is also shown that when using mode shapes with statically indeterminate boundary conditions,significant error may occur.Furthermore,the slider crank mechanism with rigid crank is accurate enough for investigating boundary condition problem of flexible multi-body system,which cost significant less simulating time.

  14. Improved outer boundary conditions for Einstein's field equations

    Energy Technology Data Exchange (ETDEWEB)

    Buchman, Luisa T [Center for Relativity, University of Texas at Austin, 1 University Station C1606, Austin, TX 78712-1081 (United States); Sarbach, Olivier C A [Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Edificio C-3, Cd. Universitaria, C P 58040 Morelia, Michoacan (Mexico)

    2007-06-21

    In a recent article, we constructed a hierarchy B{sub L} of outer boundary conditions for Einstein's field equations with the property that, for a spherical outer boundary, it is perfectly absorbing for linearized gravitational radiation up to a given angular momentum number L. In this paper, we generalize B{sub L} so that it can be applied to fairly general foliations of spacetime by space-like hypersurfaces and general outer boundary shapes and further, we improve B{sub L} in two steps: (i) we give a local boundary condition C{sub L}which is perfectly absorbing including first-order contributions in 2M/R of curvature corrections for quadrupolar waves (where M is the mass of the spacetime and R is a typical radius of the outer boundary) and which significantly reduces spurious reflections due to backscatter, and (ii) we give a non-local boundary condition D{sub L} which is exact when first-order corrections in 2M/R for both curvature and backscatter are considered, for quadrupolar radiation.

  15. The Navier-Stokes Equations Under a Unilateral Boundary Condition of Signorini's Type

    Science.gov (United States)

    Zhou, Guanyu; Saito, Norikazu

    2016-09-01

    We propose a new outflow boundary condition, a unilateral condition of Signorini's type, for the incompressible Navier-Stokes equations. The condition is a generalization of the standard free-traction condition. Its variational formulation is given by a variational inequality. We also consider a penalty approximation, a kind of the Robin condition, to deduce a suitable formulation for numerical computations. Under those conditions, we can obtain energy inequalities that are key features for numerical computations. The main contribution of this paper is to establish the well-posedness of the Navier-Stokes equations under those boundary conditions. Particularly, we prove the unique existence of strong solutions of Ladyzhenskaya's class using the standard Galerkin's method. For the proof of the existence of pressures, however, we offer a new method of analysis.

  16. $A_n^{(1)}$ affine Toda field theories with integrable boundary conditions revisited

    CERN Document Server

    Doikou, Anastasia

    2008-01-01

    Generic classically integrable boundary conditions for the $A_{n}^{(1)}$ affine Toda field theories (ATFT) are investigated. The present analysis relies primarily on the underlying algebra, defined by the classical version of the reflection equation. We use as a prototype example the first non-trivial model of the hierarchy i.e. the $A_2^{(1)}$ ATFT, however our results may be generalized for any $A_{n}^{(1)}$ ($n>1$). We assume here two distinct types of boundary conditions called some times soliton preserving (SP), and soliton non-preserving (SNP) associated to two distinct algebras, i.e. the reflection algebra and the ($q$) twisted Yangian respectively. The boundary local integrals of motion are then systematically extracted from the asymptotic expansion of the associated transfer matrix. In the case of SNP boundary conditions we recover previously known results. The other type of boundary conditions (SP), associated to the reflection algebra, are novel in this context and lead to a different set of conser...

  17. Velocity boundary conditions for vorticity formulations of the incompressible Navier-Stokes equations

    Energy Technology Data Exchange (ETDEWEB)

    Kempka, S.N.; Strickland, J.H.; Glass, M.W.; Peery, J.S. [Sandia National Labs., Albuquerque, NM (United States); Ingber, M.S. [Univ. of New Mexico, Albuquerque, NM (United States)

    1995-04-01

    formulation to satisfy velocity boundary conditions for the vorticity form of the incompressible, viscous fluid momentum equations is presented. The tangential and normal components of the velocity boundary condition are satisfied simultaneously by creating vorticity adjacent to boundaries. The newly created vorticity is determined using a kinematical formulation which is a generalization of Helmholtz` decomposition of a vector field. Though it has not been generally recognized, these formulations resolve the over-specification issue associated with creating voracity to satisfy velocity boundary conditions. The generalized decomposition has not been widely used, apparently due to a lack of a useful physical interpretation. An analysis is presented which shows that the generalized decomposition has a relatively simple physical interpretation which facilitates its numerical implementation. The implementation of the generalized decomposition is discussed in detail. As an example the flow in a two-dimensional lid-driven cavity is simulated. The solution technique is based on a Lagrangian transport algorithm in the hydrocode ALEGRA. ALEGRA`s Lagrangian transport algorithm has been modified to solve the vorticity transport equation and the generalized decomposition, thus providing a new, accurate method to simulate incompressible flows. This numerical implementation and the new boundary condition formulation allow vorticity-based formulations to be used in a wider range of engineering problems.

  18. Generalized nematohydrodynamic boundary conditions with application to bistable twisted nematic liquid-crystal displays.

    Science.gov (United States)

    Fang, Angbo; Qian, Tiezheng; Sheng, Ping

    2008-12-01

    Parallel to the highly successful Ericksen-Leslie hydrodynamic theory for the bulk behavior of nematic liquid crystals (NLCs), we derive a set of coupled hydrodynamic boundary conditions to describe the NLC dynamics near NLC-solid interfaces. In our boundary conditions, translational flux (flow slippage) and rotational flux (surface director relaxation) are coupled according to the Onsager variational principle of least energy dissipation. The application of our boundary conditions to the truly bistable pi -twist NLC cell reveals a complete picture of the dynamic switching processes. It is found that the thus far overlooked translation-rotation dissipative coupling at solid surfaces can accelerate surface director relaxation and enhance the flow rate. This can be utilized to improve the performance of electro-optical nematic devices by lowering the required switching voltages and reducing the switching times. PMID:19256854

  19. On Inaudible Properties of Broken Drums - Isospectral Domains with Mixed Boundary Conditions

    CERN Document Server

    Herbrich, Peter

    2011-01-01

    Since Kac raised the question "Can one hear the shape of a drum?", various families of non-smooth counterexamples have been constructed using the transplantation method, which is based on a group-theoretic technique by Sunada. We apply the transplantation method to domains with mixed boundary conditions, which can be interpreted as broken drums. The method is translated into graph theory which allows for a computer-aided search for transplantable pairs, and a classification in terms of induced representations. Several tools are developed with which new pairs can be generated from given ones. In the end, we discuss inaudible properties and present the first example of a connected drum that sounds disconnected, and of a broken drum that sounds unbroken, that is, a planar domain with mixed boundary conditions that is isospectral to a domain with Dirichlet boundary conditions. Above all, the latter example shows that an orbifold can be Dirichlet isospectral to a manifold. The appendix contains several transplanta...

  20. A unuqueness theorem for Sturm-Lioville operators with eigenparameter dependent boundary conditions

    Directory of Open Access Journals (Sweden)

    Yu-Ping Wang

    2012-03-01

    Full Text Available In this paper, we discuss the inverse problem for Sturm- Liouville operators with boundary conditions having fractional linear function of spectral parameter on the finite interval $[0, 1].$ Using Weyl m-function techniques, we establish a uniqueness theorem. i.e., If q(x is prescribed on $[0,\\frac{1}{2}+\\alpha]$ for some $\\alpha\\in [0,1,$ then the potential $q(x$ on the interval $[0, 1]$ and fractional linear function $\\frac{a_2\\lambda+b_2}{c_2\\lambda+d_2}$  of the boundary condition are uniquely determined by a subset $S\\subset \\sigma (L$ and fractional linear function $\\frac{a_1\\lambda+b_1}{c_1\\lambda+d_1}$ of the boundary condition.

  1. Exact transparent boundary conditions for the parabolic wave equations with linear and quadratic potentials

    CERN Document Server

    Feshchenko, R M

    2016-01-01

    In this paper exact 1D transparent boundary conditions (TBC) for the 2D parabolic wave equation with a linear or a quadratic dependence of the dielectric permittivity on the transversal coordinate are reported. Unlike the previously derived TBCs they contain only elementary functions. The obtained boundary conditions can be used to numerically solve the 2D parabolic equation describing the propagation of light in weakly bent optical waveguides and fibers including waveguides with variable curvature. They also are useful when solving the equivalent 1D Schr\\"odinger equation with a potential depending linearly or quadratically on the coordinate. The prospects and problems of discretization of the derived transparent boundary conditions are discussed.

  2. Boundary condition handling approaches for the model reduction of a vehicle frame

    Science.gov (United States)

    Xie, Qingxi; Zhang, Nong; Zhang, Bangji; Ji, Jinchen

    2016-06-01

    In order to apply model reduction technique to improve the computational efficiency for the large-scale FEM model of a vehicle, this paper presents the handling approaches for three widely-used boundary conditions, namely fixed boundary condition (FBC), prescribed motion (PSM) and coupling (COUP), respectively. It is found that iterated improved reduction system (IIRS) reduction method tends to generate better reduction approximation. Guyan method is not sensitive to the sequence of reduction and constraint under FBC, and can thus provide flexibility in handling different boundary conditions for the same system. As for PSM, 'constraint first' is recommended no matter which reduction method is used, and then separate reduction models can be coupled to form a new model with relative small dofs. By selecting appropriate master dofs for model reduction, the coupled model based on reduced models could produce same results as the original full one.

  3. Twist-averaged boundary conditions for nuclear pasta Hartree-Fock calculations

    CERN Document Server

    Schuetrumpf, B

    2015-01-01

    Background: Nuclear pasta phases, present in the inner crust of neutron stars, are associated with nucleonic matter at sub-saturation densities arranged in regular shapes. Those complex phases, residing in a layer which is approximately 100 m thick, impact many features of neutron stars. Theoretical quantum-mechanical simulations of nuclear pasta are usually carried out in finite 3D boxes assuming periodic boundary conditions (PBC). The resulting solutions are affected by spurious finite-size effects. Purpose: In order to remove spurious finite-size effects, it is convenient to employ twist-averaged boundary conditions (TABC) used in condensed matter, nuclear matter, and lattice QCD applications. In this work, we study the effectiveness of TABC in the context of pasta phases simulations within nuclear density functional theory. Methods: We perform Skyrme-Hartree-Fock calculations in three dimensions by implementing Bloch boundary conditions. The TABC averages are obtained by means of Gauss-Legendre integratio...

  4. Heat Transfer Boundary Conditions in the RELAP5-3D Code

    International Nuclear Information System (INIS)

    The heat transfer boundary conditions used in the RELAP5-3D computer program have evolved over the years. Currently, RELAP5-3D has the following options for the heat transfer boundary conditions: (a) heat transfer correlation package option, (b) non-convective option (from radiation/conduction enclosure model or symmetry/insulated conditions), and (c) other options (setting the surface temperature to a volume fraction averaged fluid temperature of the boundary volume, obtaining the surface temperature from a control variable, obtaining the surface temperature from a time-dependent general table, obtaining the heat flux from a time-dependent general table, or obtaining heat transfer coefficients from either a time- or temperature-dependent general table). These options will be discussed, including the more recent ones

  5. Heat Transfer Boundary Conditions in the RELAP5-3D Code

    Energy Technology Data Exchange (ETDEWEB)

    Richard A. Riemke; Cliff B. Davis; Richard R. Schultz

    2008-05-01

    The heat transfer boundary conditions used in the RELAP5-3D computer program have evolved over the years. Currently, RELAP5-3D has the following options for the heat transfer boundary conditions: (a) heat transfer correlation package option, (b) non-convective option (from radiation/conduction enclosure model or symmetry/insulated conditions), and (c) other options (setting the surface temperature to a volume fraction averaged fluid temperature of the boundary volume, obtaining the surface temperature from a control variable, obtaining the surface temperature from a time-dependent general table, obtaining the heat flux from a time-dependent general table, or obtaining heat transfer coefficients from either a time- or temperature-dependent general table). These options will be discussed, including the more recent ones.

  6. Non-diagonal boundary conditions for gl(1|1) super spin chains

    Energy Technology Data Exchange (ETDEWEB)

    Grabinski, Andre M; Frahm, Holger, E-mail: frahm@itp.uni-hannover.d [Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstrasse 2, 30167 Hannover (Germany)

    2010-01-29

    We study a one-dimensional model of free fermions with gl(1|1) supersymmetry and demonstrate how non-diagonal boundary conditions can be incorporated into the framework of the graded quantum inverse scattering method (gQISM) by means of super matrices with entries from a superalgebra. For super Hermitian twists and open boundary conditions subject to a certain constraint, we solve the eigenvalue problem for the super transfermatrix by means of the graded algebraic Bethe ansatz technique (gABA) starting from a fermionic coherent state. For generic boundary conditions the algebraic Bethe ansatz cannot be applied. In this case the spectrum of the super transfermatrix is obtained from a functional relation.

  7. Analytical solution of non-Fourier heat conduction problem on a fin under periodic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Ahmadikia, H. [University of Isfahan, Isfahan (Iran, Islamic Republic of); Rismanian, M. [Bu-Ali Sina University, Hamadan (Iran, Islamic Republic of)

    2011-11-15

    Fourier and hyperbolic models of heat transfer on a fin that is subjected to a periodic boundary condition are solved analytically. The differential equation in Fourier and non-Fourier models is solved by the Laplace transform method. The temperature distribution on the fin is obtained using the residual theorem in a complex plan for the inverse Laplace transform method. The thermal shock is generated at the base of the fin, which moves toward the tip of the fin and is reflected from the tip. The current study of various parameters on the thermal shock location shows that relaxation time has a great influence on the temperature distribution on the fin. An unsteady boundary condition in the base fin caused the shock, which is generated continuously from the base and has interacted with the other reflected thermal shocks. Results of the current study show that the hyperbolic heat conduction equation can violate the second thermodynamic law under some unsteady boundary conditions.

  8. Bragg band gaps tunability in an homogeneous piezoelectric rod with periodic electrical boundary conditions

    Science.gov (United States)

    Degraeve, S.; Granger, C.; Dubus, B.; Vasseur, J. O.; Pham Thi, M.; Hladky-Hennion, A.-C.

    2014-05-01

    An homogeneous piezoelectric rod is shown to exhibit Bragg band gaps when an electrical boundary condition is applied periodically with the help of metallic electrodes. An analytical model is developed which formulation depends on the applied electric boundary condition and reveals that Bragg band gaps occurring in this very peculiar phononic crystal are related to the electric charge located on the electrodes. Moreover, via an accurate boundary condition (electrodes connected in short circuit, in open circuit, or through an external capacitance), full tunability of the Bragg band gaps can be achieved. Measurements of ultrasonic transmission present an overall excellent agreement with the theoretical results. This phononic crystal can be easily manufactured and presents many potential applications as frequency filters especially for radio frequency telecommunications.

  9. Adapting a Fourier pseudospectral method to Dirichlet boundary conditions for Rayleigh-Bénard convection

    Directory of Open Access Journals (Sweden)

    I. C. Ramos

    2015-10-01

    Full Text Available We present the adaptation to non-free boundary conditions of a pseudospectral method based on the (complex Fourier transform. The method is applied to the numerical integration of the Oberbeck-Boussinesq equations in a Rayleigh-Bénard cell with no-slip boundary conditions for velocity and Dirichlet boundary conditions for temperature. We show the first results of a 2D numerical simulation of dry air convection at high Rayleigh number (. These results are the basis for the later study, by the same method, of wet convection in a solar still. Received: 20 Novembre 2014, Accepted: 15 September 2015; Edited by: C. A. Condat, G. J. Sibona; DOI:http://dx.doi.org/10.4279/PIP.070015 Cite as: I C Ramos, C B Briozzo, Papers in Physics 7, 070015 (2015

  10. Generalized nematohydrodynamic boundary conditions with application to bistable twisted nematic liquid-crystal displays

    KAUST Repository

    Fang, Angbo

    2008-12-08

    Parallel to the highly successful Ericksen-Leslie hydrodynamic theory for the bulk behavior of nematic liquid crystals (NLCs), we derive a set of coupled hydrodynamic boundary conditions to describe the NLC dynamics near NLC-solid interfaces. In our boundary conditions, translational flux (flow slippage) and rotational flux (surface director relaxation) are coupled according to the Onsager variational principle of least energy dissipation. The application of our boundary conditions to the truly bistable π -twist NLC cell reveals a complete picture of the dynamic switching processes. It is found that the thus far overlooked translation-rotation dissipative coupling at solid surfaces can accelerate surface director relaxation and enhance the flow rate. This can be utilized to improve the performance of electro-optical nematic devices by lowering the required switching voltages and reducing the switching times. © 2008 The American Physical Society.

  11. Accuracy of the Frensley inflow boundary condition for Wigner equations in simulating resonant tunneling diodes

    International Nuclear Information System (INIS)

    In this paper, the accuracy of the Frensley inflow boundary condition of the Wigner equation is analyzed in computing the I-V characteristics of a resonant tunneling diode (RTD). It is found that the Frensley inflow boundary condition for incoming electrons holds only exactly infinite away from the active device region and its accuracy depends on the length of contacts included in the simulation. For this study, the non-equilibrium Green's function (NEGF) with a Dirichlet to Neumann mapping boundary condition is used for comparison. The I-V characteristics of the RTD are found to agree between self-consistent NEGF and Wigner methods at low bias potentials with sufficiently large GaAs contact lengths. Finally, the relation between the negative differential conductance (NDC) of the RTD and the sizes of contact and buffer in the RTD is investigated using both methods.

  12. Reconsidering the boundary conditions for a dynamic, transient mode I crack problem

    KAUST Repository

    Leise, Tanya

    2008-11-01

    A careful examination of a dynamic mode I crack problem leads to the conclusion that the commonly used boundary conditions do not always hold in the case of an applied crack face loading, so that a modification is required to satisfy the equations. In particular, a transient compressive stress wave travels along the crack faces, moving outward from the loading region on the crack face. This does not occur in the quasistatic or steady state problems, and is a special feature of the transient dynamic problem that is important during the time interval immediately following the application of crack face loading. We demonstrate why the usual boundary conditions lead to a prediction of crack face interpenetration, and then examine how to modify the boundary condition for a semi-infinite crack with a cohesive zone. Numerical simulations illustrate the resulting approach.

  13. Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Danxia Wang

    2015-01-01

    Full Text Available Simultaneously, considering the viscous effect of material, damping of medium, and rotational inertia, we study a kind of more general Kirchhoff-type extensible beam equation utt-uxxtt+uxxxx-σ(∫0l‍(ux2dxuxx-ϕ(∫0l‍(ux2dxuxxt=q(x, in  [0,L]×R+ with the structural damping and the rotational inertia term. Little attention is paid to the longtime behavior of the beam equation under nonlinear boundary conditions. In this paper, under nonlinear boundary conditions, we prove not only the existence and uniqueness of global solutions by prior estimates combined with some inequality skills, but also the existence of a global attractor by the existence of an absorbing set and asymptotic compactness of corresponding solution semigroup. In addition, the same results also can be proved under the other nonlinear boundary conditions.

  14. Pseudoscalar mesons in a finite cubic volume with twisted boundary conditions

    CERN Document Server

    Colangelo, Gilberto

    2016-01-01

    We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We first apply chiral perturbation theory in the p-regime and calculate the corrections for masses, decay constants, pseudoscalar coupling constants and form factors at next-to-leading order. We show that the Feynman-Hellmann theorem and the relevant Ward-Takahashi identity are satisfied. We then derive asymptotic formulae a la Luscher for twisted boundary conditions. We show that chiral Ward identities for masses and decay constants are satisfied by the asymptotic formulae in finite volume as a consequence of infinite-volume Ward identities. Applying asymptotic formulae in combination with chiral perturbation theory we estimate corrections beyond next-to-leading order for twisted boundary conditions.

  15. Pseudoscalar mesons in a finite cubic volume with twisted boundary conditions

    Science.gov (United States)

    Colangelo, Gilberto; Vaghi, Alessio

    2016-07-01

    We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We first apply chiral perturbation theory in the p-regime and calculate the corrections for masses, decay constants, pseudoscalar coupling constants and form factors at next-to-leading order. We show that the Feynman-Hellmann theorem and the relevant Ward-Takahashi identity are satisfied. We then derive asymptotic formulae à la Lüscher for twisted boundary conditions. We show that chiral Ward identities for masses and decay constants are satisfied by the asymptotic formulae in finite volume as a consequence of infinite-volume Ward identities. Applying asymptotic formulae in combination with chiral perturbation theory we estimate corrections beyond next-to-leading order for twisted boundary conditions.

  16. Simple Navier’s slip boundary condition for the non-Newtonian Lattice Boltzmann fluid dynamics solver

    DEFF Research Database (Denmark)

    Svec, Oldrich; Skoček, Jan

    2013-01-01

    The ability of the Lattice Boltzmann method, as the fluid dynamics solver, to properly simulate macroscopic Navier’s slip boundary condition is investigated. An approximate equation relating the Lattice Boltzmann variable slip boundary condition with the macroscopic Navier’s slip boundary conditi...

  17. Effects of uncertainty in boundary-conditions on flood hazard assessment

    Science.gov (United States)

    Domeneghetti, A.; Vorogushyn, S.; Castellarin, A.; Merz, B.; Brath, A.

    2012-04-01

    Comprehensive flood-risk assessment studies should quantify the global uncertainty in flood hazard estimation, for instance by mapping inundation extents together with their confidence intervals. This appears of utmost importance, especially in the case of flood hazard assessments along dike-protected reaches, where dike failures have to be considered. This paper focuses on a 50km reach of River Po (Italy) and three major sources of uncertainty in inundation mapping: uncertainties in the (i) upstream and (ii) downstream boundary conditions, and (iii) uncertainties in the dike-failure location and breach morphology. We derive confidence bounds for flood hazard maps by means of the Inundation Hazard Assessment Model (IHAM) - a hybrid probabilistic-deterministic model. IHAM couples in a dynamic way a 1D hydrodynamic model and a 2D raster-based hydraulic model through a probabilistic dike-breaching analysis that considers three different failure mechanisms: overtopping, piping and micro-instability due to seepage. To address the randomness resulting from the variability in boundary conditions and dike-failures the system is run in a Monte Carlo framework. Uncertainties in the definition of upstream boundary conditions (i.e. design-hydrographs) are assessed by applying different bivariate copula families to model the frequency of flood peaks and volumes. Uncertainties in the definition of downstream boundary conditions are characterized by associating the rating-curve used as boundary condition with confidence intervals which reflect discharge measurements errors and interpolation errors. The results of the study are presented in terms of the Monte Carlo-based flood hazard mapping for different flood-intensity indicators (e.g., inundation depth, flow velocity, inundation duration, etc.) together with the corresponding uncertainty bounds. We conclude on the influence of uncertainty in boundary conditions and provide decision makers with an important piece of information

  18. Periodic Solutions of the 1D Vlasov-Maxwell System with Boundary Conditions

    OpenAIRE

    Bostan, Mihai

    1998-01-01

    We study the 1D Vlasov-Maxwell system with time periodic boundary conditions in its classical and relativistic form. For small data we prove existence of weak periodic solutions. It is necessary to impose non vanishing conditions for the incoming velocities in order to control the life-time of particles in the domain. In order to preserve the periodicity, another condition of vanishing the time average of the incoming current is imposed.

  19. (2,2) and (0,4) Supersymmetric Boundary Conditions in 3d N = 4 Theories and Type IIB Branes

    CERN Document Server

    Chung, Hee-Joong

    2016-01-01

    The half-BPS boundary conditions preserving N = (2,2) and N = (0,4) supersymmetry in 3d N = 4 supersymmetric gauge theories are examined. The BPS equations admit decomposition of the bulk supermultiplets into specific boundary supermultiplets of preserved supersymmetry. Bogomolony-like equations and Nahm-like equations arise in the vector multiplet BPS boundary conditions and Robin-type boundary conditions appear for the hypermultiplet coupled to vector multiplet. The half-BPS boundary conditions are realized in the brane configurations of Type IIB string theory.

  20. Riemann solvers and boundary conditions for two-dimensional shallow water simulations

    Science.gov (United States)

    Guinot, Vincent

    2003-04-01

    Most existing algorithms for two-dimensional shallow water simulations treat multi-dimensional waves using wave splitting or time splitting. This often results in anisotropy of the computed flow. Both wave splitting and time splitting are based on a local decomposition of the multi-dimensional problem into one-dimensional, orthogonal problems. Therefore, these algorithms handle boundary conditions in a very similar way to classical one-dimensional algorithms. This should be expected to trigger a dependence of the number of boundary conditions on the direction of the flow at the boundaries. However, most computational codes based on alternate directions do not exhibit such sensitivity, which seems to contradict the theory of existence and uniqueness of the solution. The present paper addresses these issues. A Riemann solver is presented that aims to convert two-dimensional Riemann problems into a one-dimensional equivalent Riemann problem (ERP) at the interfaces between the computational cells. The ERP is derived by applying the theory of bicharacteristics at each end of the interface and by performing a linear averaging along the interface. The proposed approach is tested against the traditional one-dimensional approach on the classical circular dambreak problem. The results show that the proposed solver allows the isotropy of the solution to be better preserved. Use of the two-dimensional solver with a first-order scheme may give better results than use of a second-order scheme with a one-dimensional solver. The theory of bicharacteristics is also used to discuss the issue of boundary conditions. It is shown that, when the flow is subcritical, the number of boundary conditions affects the accuracy of the solution, but not its existence and uniqueness. When only one boundary condition is to be prescribed, it should not be the velocity in the direction parallel to the boundary. When two boundary conditions are to be prescribed, at least one of them should involve

  1. Edge states and conformal boundary conditions in super spin chains and super sigma models

    OpenAIRE

    Bondesan, Roberto; Jacobsen, Jesper Lykke; Saleur, Hubert

    2011-01-01

    The sigma models on projective superspaces CP^{N+M-1|N} with topological angle theta=pi mod 2pi flow to non-unitary, logarithmic conformal field theories in the low-energy limit. In this paper, we determine the exact spectrum of these theories for all open boundary conditions preserving the full global symmetry of the model, generalizing recent work on the particular case M=0 [C. Candu et al, JHEP02(2010)015]. In the sigma model setting, these boundary conditions are associated with complex l...

  2. ICBC Version 3. 1: TMI-2 (Three Mile Island) Initial and Boundary Conditions data base

    Energy Technology Data Exchange (ETDEWEB)

    Brower, R W; Fackrell, L J; Golden, D W; Harris, M L; Olaveson, C L

    1988-01-01

    The TMI-2 initial and boundary conditions data base is a micro computer data base which provides the required initial and boundary conditions to simulate the TMI-2 accident. Additionally, other time series plant measurements related to the accident are included in the data base. Major features of the data base are the ability to plot, manipulate and list data as well as to enter user supplied data (e.g. results of simulations). The user guide provides the instructions for installation and operation of the data base. 10 refs., 21 figs.

  3. Mathematical analysis of the Navier-Stokes equations with non standard boundary conditions

    Science.gov (United States)

    Tidriri, M. D.

    1995-01-01

    One of the major applications of the domain decomposition time marching algorithm is the coupling of the Navier-Stokes systems with Boltzmann equations in order to compute transitional flows. Another important application is the coupling of a global Navier-Stokes problem with a local one in order to use different modelizations and/or discretizations. Both of these applications involve a global Navier-Stokes system with nonstandard boundary conditions. The purpose of this work is to prove, using the classical Leray-Schauder theory, that these boundary conditions are admissible and lead to a well posed problem.

  4. Particles in a magnetic field and plasma analogies: doubly periodic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Forrester, P J [Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia)

    2006-10-13

    The N-particle free fermion state for quantum particles in the plane subject to a perpendicular magnetic field, and with doubly periodic boundary conditions, is written in a product form. The absolute value of this is used to formulate an exactly solvable one-component plasma model and further motivates the formulation of an exactly solvable two-species Coulomb gas. The large N expansion of the free energy of both these models exhibits the same O(1) term. On the basis of a relationship to the Gaussian free field, this term is predicted to be universal for conductive Coulomb systems in doubly periodic boundary conditions.

  5. Boundary conditions at closed edge of bilayer graphene and energy bands of collapsed nanotubes

    Science.gov (United States)

    Nakanishi, Takeshi; Ando, Tsuneya

    2016-10-01

    Band structure is systematically studied in an effective-mass scheme in collapsed armchair and zigzag nanotubes based on the model in which collapsed tubes are regarded as bilayer ribbons with closed edges. Boundary conditions at closed edges, describing the connection of the envelope wave functions between the bottom and top layers, are derived. Among electronic states in bilayers, which change sensitively depending on the relative displacement of two layers, those having wave functions matching well with the obtained boundary conditions, i.e., unaffected by the presence of closed edges, constitute important states near the Fermi level in collapsed nanotubes.

  6. Some notes on the Kodama state, maximal symmetry, and the isolated horizon boundary condition

    CERN Document Server

    Bodendorfer, Norbert

    2016-01-01

    We recall some well and some less known results about the Kodama state, the related $\\theta$ ambiguity in defining canonical variables, and the isolated horizon boundary condition $F \\propto \\Sigma$. Based on them, we make some comments highlighting that the Kodama state for real connection variables can be given a precise meaning and that it implements a vacuum peaked on a (in a suitable sense) maximally symmetric geometry. We also highlight the similarity of this construction with the isolated horizon boundary condition $F \\propto \\Sigma$ and stress that it is inadequate to define the notion of a quantum horizon.

  7. The Magnetohydrodynamic Boundary Layer Flow of a Nanofluid past a Stretching/Shrinking Sheet with Slip Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Syahira Mansur

    2014-01-01

    Full Text Available The magnetohydrodynamic (MHD boundary layer flow of a nanofluid past a stretching/shrinking sheet with velocity, thermal, and solutal slip boundary conditions is studied. Numerical solutions to the governing equations were obtained using a shooting method. The skin friction coefficient and the local Sherwood number increase as the stretching/shrinking parameter increases. However, the local Nusselt number decreases with increasing the stretching/shrinking parameter. The range of the stretching/shrinking parameter for which the solution exists increases as the velocity slip parameter and the magnetic parameter increase. For the shrinking sheet, the skin friction coefficient increases as the velocity slip parameter and the magnetic parameter increase. For the stretching sheet, it decreases when the velocity slip parameter and the magnetic parameter increase. The local Nusselt number diminishes as the thermal slip parameter increases while the local Sherwood number decreases with increasing the solutal slip parameter. The local Nusselt number is lower for higher values of Lewis number, Brownian motion parameter, and thermophoresis parameter.

  8. Shifted periodic boundary conditions for large-eddy simulation of wind farms

    Science.gov (United States)

    Munters, Wim; Meneveau, Charles; Meyers, Johan

    2015-11-01

    In wall-bounded turbulent flow simulations, periodic boundary conditions combined with insufficiently long domains lead to persistent spanwise locking of large-scale turbulent structures. In the context of wind-farm large-eddy simulations, this effect induces artificial spanwise inhomogeneities in the time-averaged local wind conditions as seen by the wind turbines, leading to spurious differences in power prediction between otherwise equivalent columns of wind turbines in a wind farm (a column is defined here as a set of turbines parallel to the mean flow direction). We propose a shifted periodic boundary condition that eliminates this effect without the need for excessive streamwise domain lengths. Instead of straightforwardly reintroducing the velocity from the outlet plane back at the inlet, as in classic periodic boundary conditions, this plane is first shifted in the spanwise direction by a predefined and constant distance. The method is tested based on a set of direct numerical simulations of a turbulent channel flow, and large-eddy simulations of a high Reynolds number rough-wall half-channel flow. Finally, we apply the method in a precursor simulation, generating inlet conditions for a spatially developing wind-farm boundary layer. WM and JM are supported by the ERC (ActiveWindFarms, grant no: 306471). CM acknowledges support by the NSF (grant IIA-1243482, the WINDINSPIRE project).

  9. Swelling behavior of GMZ01 buffer/backfill material under flexible boundary condition

    International Nuclear Information System (INIS)

    In the high-level radioactive waste geological repository, the swelling properties of buffer/backfill material play an important role for insuring the long-term stability and safety of the repository. Traditionally, soil swelling behavior has been thoroughly examined under two extreme boundary conditions that included constant volume and constant stress. However, there exist infinite possible intermediate conditions that are neither constant volume nor constant stress and are termed flexible boundary conditions. In literature, the information on soil swelling behavior under flexible boundary condition is limited. In this investigation, a special flexible load ring-type device was developed to perform swelling tests on Gaomiaozi (GMZ01) bentonite under flexible boundary conditions, where the applied stress increases with increasing volume at a specified function. The initial dry density of the soil sample is 1.7 g/cm3, the applied initial axial stress is 0.2 MPa. The results indicate that the developed load ring-type device is effective to characterize the swelling behavior of soil sample under flexible boundary conditions; both the swelling strain and swelling pressure increase with increasing flooding time and then gradually reach stabilization, and the void ratio of the sample increases linearly with increasing swelling pressure; with increasing stiffness of the load ring, the finial swelling stain decreases while the final swelling pressure increases. For the tested soil sample, as the stiffness of the load ring increases from 278.5 N/mm to 2152 N/mm, the final equilibrium swelling strain decreases from 15.88% to 6.84%, while the final equilibrium swelling pressure increases from 0.59 MPa to 1.50 MPa. The experimental results highlights that choosing an appropriate swelling testing technique to simulate the field conditions is essential for design and evaluation of soil swelling potential. (authors)

  10. Modeling large wind farms in conventionally neutral atmospheric boundary layers under varying initial conditions

    Science.gov (United States)

    Allaerts, Dries; Meyers, Johan

    2014-05-01

    Atmospheric boundary layers (ABL) are frequently capped by an inversion layer limiting the entrainment rate and boundary layer growth. Commonly used analytical models state that the entrainment rate is inversely proportional to the inversion strength. The height of the inversion turns out to be a second important parameter. Conventionally neutral atmospheric boundary layers (CNBL) are ABLs with zero surface heat flux developing against a stratified free atmosphere. In this regime the inversion-filling process is merely driven by the downward heat flux at the inversion base. As a result, CNBLs are strongly dependent on the heating history of the boundary layer and strong inversions will fail to erode during the course of the day. In case of large wind farms, the power output of the farm inside a CNBL will depend on the height and strength of the inversion above the boundary layer. On the other hand, increased turbulence levels induced by wind farms may partially undermine the rigid lid effect of the capping inversion, enhance vertical entrainment of air into the farm, and increase boundary layer growth. A suite of large eddy simulations (LES) is performed to investigate the effect of the capping inversion on the conventionally neutral atmospheric boundary layer and on the wind farm performance under varying initial conditions. For these simulations our in-house pseudo-spectral LES code SP-Wind is used. The wind turbines are modelled using a non-rotating actuator disk method. In the absence of wind farms, we find that a decrease in inversion strength corresponds to a decrease in the geostrophic angle and an increase in entrainment rate and geostrophic drag. Placing the initial inversion base at higher altitudes further reduces the effect of the capping inversion on the boundary layer. The inversion can be fully neglected once it is situated above the equilibrium height that a truly neutral boundary layer would attain under the same external conditions such as

  11. Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces

    Science.gov (United States)

    Mantile, Andrea; Posilicano, Andrea; Sini, Mourad

    2016-07-01

    The theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic differential operator on Rn with linear boundary conditions on (a relatively open part of) a compact hypersurface. Our approach allows to obtain Kreĭn-like resolvent formulae where the reference operator coincides with the "free" operator with domain H2 (Rn); this provides an useful tool for the scattering problem from a hypersurface. Concrete examples of this construction are developed in connection with the standard boundary conditions, Dirichlet, Neumann, Robin, δ and δ‧-type, assigned either on a (n - 1) dimensional compact boundary Γ = ∂ Ω or on a relatively open part Σ ⊂ Γ. Schatten-von Neumann estimates for the difference of the powers of resolvents of the free and the perturbed operators are also proven; these give existence and completeness of the wave operators of the associated scattering systems.

  12. Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions

    CERN Document Server

    Dappiaggi, Claudio

    2016-01-01

    We consider a real, massive scalar field on ${\\rm PAdS}_{d+1}$, the Poincar\\'e domain of the $(d+1)$-dimensional AdS spacetime. We first determine all admissible boundary conditions that can be applied on the conformal boundary, noting that there exist instances where "bound states" solutions are present. Then, we address the problem of constructing the two-point function for the ground state satisfying those boundary conditions, finding ultimately an explicit closed form. In addition, we investigate the singularities of the resulting two-point functions, showing that they are consistent with the requirement of being of Hadamard form in every globally hyperbolic subregion of ${\\rm PAdS}_{d+1}$ and proposing a new definition of Hadamard states which applies to ${\\rm PAdS}_{d+1}$.

  13. Solutions of Laplace's equation with simple boundary conditions, and their applications for capacitors with multiple symmetries

    CERN Document Server

    Morales, Mayckol; Herrera, William J

    2015-01-01

    We find solutions of Laplace's equation with specific boundary conditions (in which such solutions take either the value zero or unity in each surface) using a generic curvilinear system of coordinates. Such purely geometrical solutions (that we shall call Basic Harmonic Functions BHF's) are utilized to obtain a more general class of solutions for Laplace's equation, in which the functions take arbitrary constant values on the boundaries. On the other hand, the BHF's are also used to obtain the capacitance of many electrostatic configurations of conductors. This method of finding solutions of Laplace's equation and capacitances with multiple symmetries is particularly simple, owing to the fact that the method of separation of variables becomes much simpler under the boundary conditions that lead to the BHF's. Examples of application in complex symmetries are given. Then, configurations of succesive embedding of conductors are also examined. In addition, expressions for electric fields between two conductors a...

  14. Modeling Charge-Sign Asymmetric Solvation Free Energies With Nonlinear Boundary Conditions

    CERN Document Server

    Bardhan, Jaydeep P

    2014-01-01

    We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory but replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [J. Phys. Chem. B, v. 112:2408, 2008]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.

  15. Mixed boundary conditions for FFT-based homogenization at finite strains

    Science.gov (United States)

    Kabel, Matthias; Fliegener, Sascha; Schneider, Matti

    2016-02-01

    In this article we introduce a Lippmann-Schwinger formulation for the unit cell problem of periodic homogenization of elasticity at finite strains incorporating arbitrary mixed boundary conditions. Such problems occur frequently, for instance when validating computational results with tensile tests, where the deformation gradient in loading direction is fixed, as is the stress in the corresponding orthogonal plane. Previous Lippmann-Schwinger formulations involving mixed boundary can only describe tensile tests where the vector of applied force is proportional to a coordinate direction. Utilizing suitable orthogonal projectors we develop a Lippmann-Schwinger framework for arbitrary mixed boundary conditions. The resulting fixed point and Newton-Krylov algorithms preserve the positive characteristics of existing FFT-algorithms. We demonstrate the power of the proposed methods with a series of numerical examples, including continuous fiber reinforced laminates and a complex nonwoven structure of a long fiber reinforced thermoplastic, resulting in a speed-up of some computations by a factor of 1000.

  16. Fatigue crack damage detection using subharmonic component with nonlinear boundary condition

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Weiliang, E-mail: wwl@whu.edu.cn; Qu, Wenzhong, E-mail: qwz@whu.edu.cn, E-mail: xiaoli6401@126.com; Xiao, Li, E-mail: qwz@whu.edu.cn, E-mail: xiaoli6401@126.com [Department of Engineering Mechanics, Wuhan University, Wuhan, Hubei (China); Shen, Yanfeng, E-mail: shen5@email.sc.edu; Giurgiutiu, Victor, E-mail: victorg@sc.edu [Department of Mechanical Engineering, University of South Carolina, Columbia, South Carolina (United States)

    2015-03-31

    In recent years, researchers have focused on structural health monitoring (SHM) and damage detection techniques using nonlinear vibration and nonlinear ultrasonic methods. Fatigue cracks may exhibit contact acoustic nonlinearity (CAN) with distinctive features such as superharmonics and subharmonics in the power spectrum of the sensing signals. However, challenges have been noticed in the practical applications of the harmonic methods. For instance, superharmonics can also be generated by the piezoelectric transducers and the electronic equipment; super/subharmonics may also stem from the nonlinear boundary conditions such as structural fixtures and joints. It is hard to tell whether the nonlinear features come from the structural damage or the intrinsic nonlinear boundary conditions. The objective of this paper is to demonstrate the application of nonlinear ultrasonic subharmonic method for detecting fatigue cracks with nonlinear boundary conditions. The fatigue crack was qualitatively modeled as a single-degree-of-freedom (SDOF) system with non-classical hysteretic nonlinear interface forces at both sides of the crack surfaces. The threshold of subharmonic generation was studied, and the influence of crack interface parameters on the subharmonic resonance condition was investigated. The different threshold behaviors between the nonlinear boundary condition and the fatigue crack was found, which can be used to distinguish the source of nonlinear subharmonic features. To evaluate the proposed method, experiments of an aluminum plate with a fatigue crack were conducted to quantitatively verify the subharmonic resonance range. Two surface-bonded piezoelectric transducers were used to generate and receive ultrasonic wave signals. The fatigue damage was characterized in terms of a subharmonic damage index. The experimental results demonstrated that the subharmonic component of the sensing signal can be used to detect the fatigue crack and further distinguish it from

  17. The effect of box shape on the dynamic properties of proteins simulated under periodic boundary conditions

    NARCIS (Netherlands)

    Wassenaar, T.A.; Mark, A.E.

    2006-01-01

    The effect of the box shape on the dynamic behavior of proteins simulated under periodic boundary conditions is evaluated. In particular, the influence of simulation boxes defined by the near-densest lattice packing (NDLP) in conjunction with rotational constraints is compared to that of standard bo

  18. General continuum boundary conditions for miscible binary fluids from molecular dynamics simulations.

    Science.gov (United States)

    Denniston, Colin; Robbins, Mark O

    2006-12-01

    Molecular dynamics simulations are used to explore the flow behavior and diffusion of miscible fluids near solid surfaces. The solid produces deviations from bulk fluid behavior that decay over a distance of the order of the fluid correlation length. Atomistic results are mapped onto two types of continuum model: Mesoscopic models that follow this decay and conventional sharp interface boundary conditions for the stress and velocity. The atomistic results, and mesoscopic models derived from them, are consistent with the conventional Marangoni stress boundary condition. However, there are deviations from the conventional Navier boundary condition that states that the slip velocity between wall and fluid is proportional to the strain rate. A general slip boundary condition is derived from the mesoscopic model that contains additional terms associated with the Marangoni stress and diffusion, and is shown to describe the atomistic simulations. The additional terms lead to strong flows when there is a concentration gradient. The potential for using this effect to make a nanomotor or pump is evaluated. PMID:17166010

  19. Chaotic Size Dependence in the Ising Model with Random Boundary Conditions

    NARCIS (Netherlands)

    Enter, A.C.D. van; Medved’, I.; Netočný, K.

    2002-01-01

    We study the nearest-neighbour Ising model with a class of random boundary conditions, chosen from a symmetric i.i.d. distribution. We show for dimensions 4 and higher that almost surely the only limit points for a sequence of increasing cubes are the plus and the minus state. For d=2 and d=3 we pro

  20. Triple fixed-sign solutions in modelling a system with Hermite boundary conditions

    OpenAIRE

    Wong Patricia JY; Soh YC

    2005-01-01

    We consider the following system of differential equations , , together with Hermite boundary conditions , , , , where , for , and . By using different fixed point theorems, we offer criteria for the existence of three solutions of the system which are of "prescribed signs" on the interval .

  1. The Brown-Henneaux's central charge from the path-integral boundary condition

    OpenAIRE

    Terashima, Hiroaki

    2000-01-01

    We derive Brown-Henneaux's commutation relation and central charge in the framework of the path integral. If we use the leading part of the asymptotic symmetry to derive the Ward-Takahashi identity, we can see the central charge arises from the fact that the boundary condition of the path integral is not invariant under the transformation.

  2. Weak versus strong no-slip boundary conditions for the Navier-Stokes equations

    OpenAIRE

    Abbas, Qaisar; Nordström, Jan

    2010-01-01

    Original Publication:Qaisar Abbas and Jan Nordström, Weak versus strong no-slip boundary conditions for the Navier-Stokes equations, 2010, Engineering Applications of Computational Fluid Mechanics, (4), 29-38. Copyright: Engineering Applications of Computational Fluid Mechanics

  3. Technical and economic justification of conditional boundaries of rock and collectors

    Energy Technology Data Exchange (ETDEWEB)

    Azamatov, V.I.; Gudkov, Y.P.; Savich, A.I.; Vlasenko, N.A.

    1982-01-01

    Examined is the question about evaluation of the balanced and over balanced reserves of oil of nonuniform deposits on the basis of a technical and economic justification of the conditional boundaries of the rock and collectors. The proposed technique is tested in specific deposits of the Soviet Union.

  4. Boundary lubrication by brushed salivary conditioning films and their degree of glycosylation

    NARCIS (Netherlands)

    Veeregowda, Deepak H; van der Mei, Henderina; de Vries, Jacob; Rutland, Mark W; Valle-Delgado, Juan J; Sharma, Prashant K; Busscher, Hendrik

    2012-01-01

    Toothbrushing, though aimed at biofilm removal, also affects the lubricative function of adsorbed salivary conditioning films (SCFs). Different modes of brushing (manual, powered, rotary-oscillatory or sonically driven) influence the SCF in different ways. Our objectives were to compare boundary lub

  5. Thermodynamics of 1D N-Component Bariev Model Under Open Boundary Conditions

    Institute of Scientific and Technical Information of China (English)

    WANG Chun; KE San-Min; YUE Rui-Hong

    2006-01-01

    The thermodynamic Bethe ansatz equations and free energy for 1D N-component Bariev model under open boundary conditions are derived based on the string hypothesis for both, a repulsive and an attractive interaction.These equations are discussed in some limiting cases, such as the ground state, weak and strong couplings.

  6. A well-conditioned boundary integral equation for transmission problems of electromagnetism

    OpenAIRE

    Levadoux, David; Millot, Florence; Pernet, Sébastien

    2015-01-01

    We propose a new well-conditioned boundary integral equation to solve transmission problems of electromagnetism. This equation is well posed and appears as a compact perturbation of the identity leading to fast iterative solutions without the help of any preconditioner. Some numerical experiments confirm this result.

  7. Solution of the Multiparticle Scattering Problems in Configuration Space by Using Trivial Boundary Conditions

    Science.gov (United States)

    Lazauskas, Rimantas

    2015-12-01

    A formalism based on the complex-scaling method is used to solve a four-nucleon scattering problem above the breakup threshold using the realistic nuclear Hamiltonians. This method allows to solve diverse scattering problems based on very trivial boundary conditions and is compatible with the techniques used to solve bound state problems.

  8. On a Time-Fractional Integrodifferential Equation via Three-Point Boundary Value Conditions

    Directory of Open Access Journals (Sweden)

    Dumitru Baleanu

    2015-01-01

    Full Text Available The existence and the uniqueness theorems play a crucial role prior to finding the numerical solutions of the fractional differential equations describing the models corresponding to the real world applications. In this paper, we study the existence of solutions for a time-fractional integrodifferential equation via three-point boundary value conditions.

  9. A stable penalty method for the compressible Navier-Stokes equations: I. Open boundary conditions

    DEFF Research Database (Denmark)

    Hesthaven, Jan; Gottlieb, D.

    1996-01-01

    The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization...

  10. Burgers equation with no-flux boundary conditions and its application for complete fluid separation

    Science.gov (United States)

    Watanabe, Shinya; Matsumoto, Sohei; Higurashi, Tomohiro; Ono, Naoki

    2016-09-01

    Burgers equation in a one-dimensional bounded domain with no-flux boundary conditions at both ends is proven to be exactly solvable. Cole-Hopf transformation converts not only the governing equation to the heat equation with an extra damping but also the nonlinear mixed boundary conditions to Dirichlet boundary conditions. The average of the solution v bar is conserved. Consequently, from an arbitrary initial condition, solutions converge to the equilibrium solution which is unique for the given v bar. The problem arises naturally as a continuum limit of a network of certain micro-devices. Each micro-device imperfectly separates a target fluid component from a mixture of more than one component, and its input-output concentration relationships are modeled by a pair of quadratic maps. The solvability of the initial boundary value problem is used to demonstrate that such a network acts as an ideal macro-separator, separating out the target component almost completely. Another network is also proposed which leads to a modified Burgers equation with a nonlinear diffusion coefficient.

  11. Boundary conditions for the use of personal ventilation over mixing ventilation in open plan offices

    DEFF Research Database (Denmark)

    Petersen, Steffen; Hviid, Christian Anker

    2013-01-01

    This paper investigates the boundary conditions for choosing a combined Personal Ventilation (PV) and Mixing Ventilation (MV) over conventional mixing ventilation in an office with multiple workers. A simplified procedure for annual performance assessment of PV/MV systems in terms of air quality,...

  12. Semilinear Evolution Problems with Ventcel-Type Conditions on Fractal Boundaries

    Directory of Open Access Journals (Sweden)

    Maria Rosaria Lancia

    2014-01-01

    Full Text Available A semilinear parabolic transmission problem with Ventcel's boundary conditions on a fractal interface S or the corresponding prefractal interface Sh is studied. Regularity results for the solution in both cases are proved. The asymptotic behaviour of the solutions of the approximating problems to the solution of limit fractal problem is analyzed.

  13. Two simple finite element methods for Reissner--Mindlin plates with clamped boundary condition

    OpenAIRE

    Bishnu P. Lamichhane

    2013-01-01

    We present two simple finite element methods for the discretization of Reissner--Mindlin plate equations with {\\em clamped} boundary condition. These finite element methods are based on discrete Lagrange multiplier spaces from mortar finite element techniques. We prove optimal a priori error estimates for both methods.

  14. Degeneracy of Multi-Component Quantum Hall States Satisfying Periodic Boundary Conditions

    OpenAIRE

    McDonald, I. A.

    1994-01-01

    In systems subject to periodic boundary conditions, Haldane has shown that states at arbitrary filling fraction possess a degeneracy with respect to center of mass translations. An analysis is carried out for multi-component electron systems and extra degeneracies are shown to exist. Their application to numerical studies is discussed.

  15. Inertial Manifolds for the 3D Cahn-Hilliard Equations with Periodic Boundary Conditions

    OpenAIRE

    Kostianko, A; Zelik, S.

    2014-01-01

    The existence of an inertial manifold for the 3D Cahn-Hilliard equation with periodic boundary conditions is verified using the proper extension of the so-called spatial averaging principle introduced by G. Sell and J. Mallet-Paret. Moreover, the extra regularity of this manifold is also obtained.

  16. Convergence in comparable almost periodic reaction-diffusion systems with Dirichlet boundary conditions

    OpenAIRE

    Feng Cao; Yelai Fu

    2014-01-01

    In this article, we study the asymptotic dynamics in nonmonotone comparable almost periodic reaction-diffusion systems with Dirichlet boundary condition, which are comparable with uniformly stable strongly order-preserving system. By appealing to the theory of skew-product semiflows, we obtain the asymptotic almost periodicity of uniformly stable solutions to the comparable reaction-diffusion system.

  17. Quasi-linear dynamics in nonlinear Schr\\" odinger equation with periodic boundary conditions

    OpenAIRE

    Erdogan, M. Burak; Zharnitsky, Vadim

    2007-01-01

    It is shown that a large subset of initial data with finite energy ($L^2$ norm)evolves nearly linearly in nonlinear Schr\\" odinger equation with periodic boundary conditions. These new solutions are not perturbations of the known ones such as solitons, semiclassical or weakly linear solutions.

  18. On The Stabilization of the Linear Kawahara Equation with Periodic Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Patricia N. da Silva

    2015-03-01

    Full Text Available We study the stabilization of global solutions of the linear Kawahara equation (K with periodic boundary conditions under the effect of a localized damping mechanism. The Kawahara equation is a model for small amplitude long waves. Using separation of variables, the Ingham inequality, multiplier techniques and compactness arguments we prove the exponential decay of the solutions of the (K model.

  19. SU(N) gauge theories with C-periodic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Kronfeld, A.S. (Theoretical Physics Group, Fermi National Accelerator Lab., Batavia, IL (United States) Inst. for Theoretical Physics, Univ. of California, Santa Barbara, CA (United States))

    1991-05-01

    This contribution sketches the topology of twisted C-periodic boundary conditions and its consequences on the Hilbert space of physical states. It also presents preliminary results pertaining to the small-volume expansion of SU(3) gauge theory in a C-periodic box. (orig.).

  20. Convergence in comparable almost periodic reaction-diffusion systems with Dirichlet boundary conditions

    Directory of Open Access Journals (Sweden)

    Feng Cao

    2014-04-01

    Full Text Available In this article, we study the asymptotic dynamics in nonmonotone comparable almost periodic reaction-diffusion systems with Dirichlet boundary condition, which are comparable with uniformly stable strongly order-preserving system. By appealing to the theory of skew-product semiflows, we obtain the asymptotic almost periodicity of uniformly stable solutions to the comparable reaction-diffusion system.

  1. Enhancement of diffusive transfer by periodic pulsation between Dirichlet and Neumann type boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Putterman, S.J. (California Univ., Los Angeles (USA). Dept. of Physics); Guibert, R.

    1983-01-01

    A solution to the equation of heat conduction is computed for the case where the boundary condition alternates periodically between fixed temperature and fixed heat flow. This problem is equivalent to a highly non-linear parametric oscillation. Applications to energy conservation and non-destructive heating are discussed.

  2. Solitary-wave solutions in binary mixtures of Bose-Einstein condensates under periodic boundary conditions

    Science.gov (United States)

    Smyrnakis, J.; Magiropoulos, M.; Kavoulakis, G. M.; Jackson, A. D.

    2013-01-01

    We derive solitary-wave solutions within the mean-field approximation in quasi-one-dimensional binary mixtures of Bose-Einstein condensates under periodic boundary conditions, for the case of an effective repulsive interatomic interaction. The particular gray-bright solutions that give the global energy minima are determined. Their characteristics and the associated dispersion relation are derived.

  3. KdV equation under periodic boundary conditions and its perturbations

    OpenAIRE

    Huang, Guan; Kuksin, Sergei

    2013-01-01

    In this paper we discuss properties of the KdV equation under periodic boundary conditions, especially those which are important to study perturbations of the equation. Next we review what is known now about long-time behaviour of solutions for perturbed KdV equations.

  4. Shocks induced by junctions in totally asymmetric simple exclusion processes under periodic boundary condition

    Science.gov (United States)

    Sun, Xiaoyan; Xie, Yanbo; He, Zhiwei; Wang, Binghong

    2011-07-01

    This Letter investigates a totally asymmetric simple exclusion process (TASEP) with junctions in a one-dimensional transport system. Parallel update rules and periodic boundary condition are adopted. Two cases corresponding to different update rules are studied. The results show that the stationary states of system mainly depend on the selection behavior of particle at the bifurcation point.

  5. Finite dimensionality of 2-D micropolar fluid flow with periodic boundary conditions

    OpenAIRE

    Szopa, Piotr

    2007-01-01

    This paper is devoted to describe the finite-dimensionality of a two-dimensional micropolar fluid flow with periodic boundary conditions. We define the notions of determining modes and nodes and estimate the number of them, we also estimate the dimension of the global attractor. Finally we compare our results with analogous results for Navier-Stokes equation.

  6. Periodic solutions of the quasilinear equation of forced beam vibrations with homogeneous boundary conditions

    Science.gov (United States)

    Rudakov, I. A.

    2015-10-01

    We prove the existence of a countable family of time-periodic solutions of the quasilinear equation of beam vibrations with homogeneous boundary conditions and time-periodic right-hand side in the case when the non-linear term has power growth.

  7. Note on the continuum thermal Wilson loop with space-periodic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Hilf, E.; Polley, L.

    1983-11-17

    For the continuum analog of the thermal Wilson loop (usually considered in a lattice gauge theory), its vanishing expectation value, in the case of periodic spatial boundary conditions and an unbroken Z(N) symmetry, can be understood already from the fact that Gauss' law has no periodic solutions for a single unscreened (colour) charge.

  8. The KdV equation under periodic boundary conditions and its perturbations

    Science.gov (United States)

    Guan, Huang; Kuksin, Sergei

    2014-09-01

    In this paper we discuss properties of the Korteweg-de Vries (KdV) equation under periodic boundary conditions, especially those which are important for studying perturbations of the equation. We then review what is known about the long-time behaviour of solutions for perturbed KdV equations.

  9. Evaluation of Coulomb potential in a triclinic cell with periodic boundary conditions

    OpenAIRE

    Tyagi, Sandeep

    2006-01-01

    Lekner and Sperb's work on the evaluation of Coulomb energy and forces under periodic boundary conditions is generalized that makes it possible to use a triclinic unit cell in simulations in 3D rather than just an orthorhombic cell. The expressions obtained are in a similar form as previously obtained by Lekner and Sperb for the especial case of orthorhombic cell.

  10. On The Stabilization of the Linear Kawahara Equation with Periodic Boundary Conditions

    OpenAIRE

    Patricia N. da Silva; Carlos F. Vasconcellos

    2015-01-01

    We study the stabilization of global solutions of the linear Kawahara equation (K) with periodic boundary conditions under the effect of a localized damping mechanism. The Kawahara equation is a model for small amplitude long waves. Using separation of variables, the Ingham inequality, multiplier techniques and compactness arguments we prove the exponential decay of the solutions of the (K) model.

  11. Neumann boundary conditions inhibiting the SSB in the Coleman-Weinberg mechanism

    CERN Document Server

    Fagundes, F N; Dilem, B B; Nogueira, J A; 10.1088/0253-6102/54/6/21

    2012-01-01

    In this work we show that homogeneous Neumann boundary conditions inhibit the Coleman-Weinberg mechanism for spontaneous symmetry breaking in the scalar electrodynamics if the length of the finite region is small enough ($a = e^{2}M^{-1}_{\\phi}$, where $M_{\\phi}$ is the mass of the scalar field generated by the Coleman-Weinberg mechanism)

  12. Numerical study of different bottom boundary conditions on water flow in lysimeters

    Science.gov (United States)

    Groh, Jannis; Vanderborght, Jan; Pütz, Thomas; Vereecken, Harry

    2015-04-01

    The separation of the bottom of the lysimeter from its surroundings in the field introduces an artificial boundary that may impact the water balance of lysimeters. The use of tension controlled lysimeter (TCL) prevents an artificial boundary at the end of the lysimeter. Water flow across the lysimeter bottom can be controlled by the adjustment of matric potentials at the lower end of the lysimeter to measured field conditions in the close vicinity of the facility. However lysimeters are often transferred from the place where the soil monoliths were sampled to another location for practical reasons or to study the effect of climate change (e.g. SOILCan). The water flux across the bottom boundary of translocated TCL can be affected if climatic conditions, soil properties and the hydrogeological setting in the field differ from the place where the lysimeter was taken from. To assess the potential impact of different bottom boundary conditions on the water balance of translocated TCL a numerical study in virtual soils was conducted. We present a comparison of different approaches using water balance simulations. Results shows that water balance components of translocated TCL are sensitive towards the soil hydraulic parameters and hydrogeological setting in the field. The change in field conditions can impact the water flux dynamic across the lysimeter bottom, change the evaporation and the plant water uptake and release. A shift in the climate regime (translocation) will modify the depth and dynamics of the water table and impact the water balance of lysimeters.

  13. SQUEEZE-E: The optimal solution for molecular simulations with periodic boundary conditions

    NARCIS (Netherlands)

    Wassenaar, T.A.; de Vries, S.J.; Bonvin, A.M.J.J.; Bekker, H.

    2012-01-01

    In molecular simulations of macromolecules, it is desirable to limit the amount of solvent in the system to avoid spending computational resources on uninteresting solvent−solvent interactions. As a consequence, periodic boundary conditions are commonly used, with a simulation box chosen as small as

  14. SQUEEZE-E : The Optimal Solution for Molecular Simulations with Periodic Boundary Conditions

    NARCIS (Netherlands)

    Wassenaar, Tsjerk A.; de Vries, Sjoerd; Bonvin, Alexandre M. J. J.; Bekker, Henk

    2012-01-01

    In molecular simulations of macromolecules, it is desirable to limit the amount of solvent in the system to avoid spending computational resources on uninteresting solvent−solvent interactions. As a consequence, periodic boundary conditions are commonly used, with a simulation box chosen as small as

  15. Effective coastal boundary conditions for tsunami wave run-up over sloping bathymetry

    NARCIS (Netherlands)

    Kristina, W.; Bokhove, O.; Groesen, van E.W.C.

    2014-01-01

    An effective boundary condition (EBC) is introduced as a novel technique for predicting tsunami wave run-up along the coast, and offshore wave reflections. Numerical modeling of tsunami propagation in the coastal zone has been a daunting task, since high accuracy is needed to capture aspects of wave

  16. A semi-analytical solution for viscothermal wave propagation in narrow gaps with arbitrary boundary conditions.

    NARCIS (Netherlands)

    Wijnant, Ysbrand; Spiering, Ruud; Blijderveen, van Maarten; Boer, de André

    2006-01-01

    Previous research has shown that viscothermal wave propagation in narrow gaps can efficiently be described by means of the low reduced frequency model. For simple geometries and boundary conditions, analytical solutions are available. For example, Beltman [4] gives the acoustic pressure in the gap b

  17. THE ANALYTICAL SOLUTION FOR SEDIMENT REACTION AND DIFFUSION EQUATION WITH GENERALIZED INITIAL-BOUNDARY CONDITIONS

    Institute of Scientific and Technical Information of China (English)

    熊岳山; 韦永康

    2001-01-01

    The sediment reaction and diffusion equation with generalized initial and boundary condition is studied. By using Laplace transform and Jordan lemma , an analytical solution is got, which is an extension of analytical solution provided by Cheng Kwokming James ( only diffusion was considered in analytical solution of Cheng ). Some problems arisen in the computation of analytical solution formula are also analysed.

  18. Mode selection and boundary conditions using MAFIA in frequency-domain

    Energy Technology Data Exchange (ETDEWEB)

    Jin, Y.

    1988-09-01

    The field solvers of the 3D code MAFIA in the frequency domain are R3 and E3: the former generates an eigenvalue equation, and the latter solves this equation for eigenfrequencies and eigenvectors (fields). They are usually expensive to use. In order to save memory space and CPU time, one may employ a part of a structure in calculations if there are certain symmetries that are embedded in the geometry. In this case, one must run R3 and E3 several times with different boundary conditions if one wants to get a complete set of modes of the whole structure. However, sometimes only some modes are of interest to the authors (e.g., TM{sub 01}) and they may then specify the appropriate boundary conditions for a part of a structure to obtain these modes. There are two types of boundary conditions that one may choose from in R3: either a zero tangential E-field, denoted by integer 1, or a zero tangential H-field, denoted by integer 2. This note will use a circularly cylindrical cavity as an example to discuss the relation between mode selection and boundary conditions when using a part of the cavity.

  19. Evidence for Cretaceous-Paleogene boundary bolide “impact winter” conditions from New Jersey, USA

    NARCIS (Netherlands)

    Vellekoop, J.; Esmeray-Senlet, S.; Miller, K.G.; Browning, J.V.; Sluijs, A.; van de Schootbrugge, B.; Sinninghe Damsté, J.S.; Brinkhuis, H.

    2016-01-01

    Abrupt and short-lived “impact winter” conditions have commonly been implicated as the main mechanism leading to the mass extinction at the Cretaceous-Paleogene (K-Pg) boundary (ca. 66 Ma), marking the end of the reign of the non-avian dinosaurs. However, so far only limited evidence has been availa

  20. Transformational leadership climate : Performance linkages, mechanisms, and boundary conditions at the organizational level

    NARCIS (Netherlands)

    Menges, J.; Walter, F.; Vogel, B.; Bruch, H.

    2011-01-01

    Transformational leadership (TFL) climate describes the degree to which leaders throughout an organization engage in TFL behaviors. In this study, we investigate performance linkages, mechanisms, and boundary conditions of TFL climate at the organizational level of analysis. In a sample of 158 indep