Absorbing boundary conditions for linear gravity waves
Dgaygui, Kebir; Joly, Patrick
1992-01-01
In this article, we construct, analyze and implement a family of absorbing boundary conditions for linear gravity waves in dimension 2. The main difficulty consists in taking into account the dispersive nature of these waves.
Absorbing boundary conditions for second-order hyperbolic equations
Jiang, Hong; Wong, Yau Shu
1990-01-01
A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.
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...
Implementation of higher-order absorbing boundary conditions for the Einstein equations
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 gravitational waves in TT gauge, with angular momentum numbers l = 2 (Teukolsky waves), 3 and 4. We demonstrate that the perfectly absorbing boundary condition ΒL of order L = l yields no spurious reflections to linear order in perturbation theory. This is in contrast to the lower-order absorbing boundary conditions ΒL with L 0 boundary condition that imposes the vanishing of the Newman-Penrose scalar Ψ0.
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.
An energy absorbing far-field boundary condition for the elastic wave equation
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.
Solution of the time-dependent Schr(o)dinger equation with absorbing boundary conditions
Chen Zhidong; Zhang Jinyu; Yu Zhiping
2009-01-01
The performances of absorbing boundary conditions (ABCs) in four widely used finite difference time domain (FDTD) methods, I.e. Explicit, implicit, explicit staggered-time, and Chebyshev methods, for solving the time-dependent Schr(o)dinger equation are assessed and compared. The computation efficiency for each approach is also evaluated. A typical evolution problem of a single Gaussian wave packet is chosen to demonstrate the perfor-mances of the four methods combined with ABCs. It is found that ABCs perfectly eliminate reflection in implicit and explicit staggered-time methods. However, small reflection still exists in explicit and Chebyshev methods even though ABCs are applied.
Sirenko, Kostyantyn
2013-07-01
Exact absorbing and periodic boundary conditions allow to truncate grating problems\\' infinite physical domains without introducing any errors. This work presents exact absorbing boundary conditions for 3D diffraction gratings and describes their discretization within a high-order time-domain discontinuous Galerkin finite element method (TD-DG-FEM). The error introduced by the boundary condition discretization matches that of the TD-DG-FEM; this results in an optimal solver in terms of accuracy and computation time. Numerical results demonstrate the superiority of this solver over TD-DG-FEM with perfectly matched layers (PML)-based domain truncation. © 2013 IEEE.
A mixed-grid finite element method with PML absorbing boundary conditions for seismic wave modelling
We have developed a mixed-grid finite element method (MGFEM) to simulate seismic wave propagation in 2D structurally complex media. This method divides the physical domain into two subdomains. One subdomain covering the major part of the physical domain is divided by regular quadrilateral elements, while the other subdomain uses triangular elements to correctly fit a rugged free surface topography. The local stiffness matrix of any quadrilateral element is identical and matrix-vector production is calculated using an element-by-element technique, which avoids assembling a huge global stiffness matrix. As only a few triangular elements exist in the subdomain containing the rugged free surface topography, the memory requirements for storing the assembled subdomain global stiffness matrix are significantly reduced. To eliminate artificial boundary reflections, the MGFEM is also implemented to solve the system equations of PML absorbing boundary conditions (PML ABC). The accuracy and efficiency of the MGFEM is tested in numerical experiments by comparing it with conventional methods, and numerical comparisons also indicate its tremendous ability to describe rugged surfaces. (paper)
An FDTD method with FFT-accelerated exact absorbing boundary conditions
Sirenko, Kostyantyn
2011-07-01
An accurate and efficient finite-difference time-domain (FDTD) method for analyzing axially symmetric structures is presented. The method achieves its accuracy and efficiency using exact absorbing conditions (EACs) for terminating the computation domain and a blocked-FFT based scheme for accelerating the computation of the temporal convolutions present in non-local EACs. The method is shown to be especially useful in characterization of long-duration resonant wave interactions. © 2011 IEEE.
Anomalous Diffusion with Absorbing Boundary
Kantor, Yacov; Kardar, Mehran
2007-01-01
In a very long Gaussian polymer on time scales shorter that the maximal relaxation time, the mean squared distance travelled by a tagged monomer grows as ~t^{1/2}. We analyze such sub-diffusive behavior in the presence of one or two absorbing boundaries and demonstrate the differences between this process and the sub-diffusion described by the fractional Fokker-Planck equation. In particular, we show that the mean absorption time of diffuser between two absorbing boundaries is finite. Our res...
CHEN Hao; WANG Xiuming; ZHAO Haibo
2006-01-01
A rotated staggered grid finite-difference (FD) method with a perfectly matched layer (PML) method is proposed for numerically solving elastic wave equations in inhomogeneous elastic and poroe- lastic media. Compared with a standard staggered- grid FD, the former has the advantage over the latter in that its physical variables need only to be defined at two locations. In the rotated staggered grid, stress and strain components (or particle velocity and displacement components) are defined at elementary cell centers, and the velocity or displacement components (or the stress and strain components) are defined at vertexes. In this way, no elastic moduli need to be interpolated or averaged. Numerical results from the proposed method have been compared with the standard staggered FD method. The results are in good agreement with each other. Our numerical results show that the proposed algorithm can handle much stronger impedance contrast. This is especially true when simulating fractured medium filled with fluids such as water or gas without giving special treatment. On the other hand, the implemented PML absorbing boundary condition works well in efficiently reducing reflected waves from the artificial interfaces. It generates almost no reflection at artificial interfaces with a boundary of PML thickness of half a wavelength. Our theoretical analysis and numerical tests proved that the PML absorbing algorithm in the rotated staggered grid is almost identical to those in the standard staggered grid. In this paper, we also presented all of the formulations of the PML implementation and modeling examples in elastic, poroelastic, and anisotropic media.
As fundamental parameters for polarized-radiative-transfer calculations, the single-scattering phase matrix of irregularly shaped aerosol particles must be accurately modeled. In this study, a scattered-field finite-difference time-domain (FDTD) model and a scattered-field pseudo-spectral time-domain (PSTD) model are developed for light scattering by arbitrarily shaped dielectric aerosols. The convolutional perfectly matched layer (CPML) absorbing boundary condition (ABC) is used to truncate the computational domain. It is found that the PSTD method is generally more accurate than the FDTD in calculation of the single-scattering properties given similar spatial cell sizes. Since the PSTD can use a coarser grid for large particles, it can lower the memory requirement in the calculation. However, the Fourier transformations in the PSTD need significantly more CPU time than simple subtractions in the FDTD, and the fast Fourier transform requires a power of 2 elements in calculations, thus using the PSTD could not significantly reduce the CPU time required in the numerical modeling. Furthermore, because the scattered-field FDTD/PSTD equations include incident-wave source terms, the FDTD/PSTD model allows for the inclusion of an arbitrarily incident wave source, including a plane parallel wave or a Gaussian beam like those emitted by lasers usually used in laboratory particle characterizations, etc. The scattered-field FDTD and PSTD light-scattering models can be used to calculate single-scattering properties of arbitrarily shaped aerosol particles over broad size and wavelength ranges. -- Highlights: • Scattered-field FDTD and PSTD models are developed for light scattering by aerosols. • Convolutional perfectly matched layer absorbing boundary condition is used. • PSTD is generally more accurate than FDTD in calculating single-scattering properties. • Using same spatial resolution, PSTD requires much larger CPU time than FDTD
Bolesta, Alexey V.; Zheng, Lianqing; Thompson, Donald L.; Sewell, Thomas D.
2007-12-01
We report a method that enables long-time molecular dynamics (MD) simulations of shock wave loading. The goal is to mitigate the severe interference effects that arise at interfaces or free boundaries when using standard nonequilibrium MD shock wave approaches. The essence of the method is to capture between two fixed pistons the material state at the precise instant in time when the shock front, initiated by a piston with velocity up at one end of the target sample, traverses the contiguous boundary between the target and a second, stationary piston located at the opposite end of the sample, at which point the second piston is also assigned velocity up and the simulation is continued. Thus, the target material is captured in the energy-volume Hugoniot state resulting from the initial shock wave, and can be propagated forward in time to monitor any subsequent chemistry, plastic deformation, or other time-dependent phenomena compatible with the spatial scale of the simulation. For demonstration purposes, we apply the method to shock-induced chemistry in methane based on the adaptive intermolecular reactive empirical bond order force field [S. J. Stuart , J. Chem. Phys. 112, 6472 (2000)].
Directed percolation with an absorbing boundary
Lauritsen, K. B.; K. Sneppen; Markosova, M.; Jensen, M. H.
1997-01-01
We consider directed percolation with an absorbing boundary in 1+1 and 2+1 dimensions. The distribution of cluster lifetimes and sizes depend on the boundary. The new scaling exponents can be related to the exponents characterizing standard directed percolation in 1+1 dimension. In addition, we investigate the backbone cluster and red bonds, and calculate the distribution of living sites along the absorbing boundary.
Zhang, Xi; Liu, Yang; Cai, Xiaohui; Ren, Zhiming
2015-12-01
The reverse-time migration (RTM) crosscorrelation imaging condition requires that the forward-propagated source wavefield and the backward-propagated receiver wavefield must be obtained at the same time. The easiest way to get the source wavefield is to save the entire time history of the full wavefield into computer memory. However, this strategy requires huge amount of data storage. It is impossible for large-scale 3D RTM. To reduce the computer memory cost, the back-propagated source wavefield is reconstructed by using the stored boundary wavefield. Its computer memory is proportional to the saved boundary grid points. For high order of spatial finite-difference (FD) schemes, more boundary grid points are needed to be stored, which consumes a large amount of the computer memory required for RTM. To further reduce the computer memory cost, we adopt the hybrid absorbing boundary condition (ABC) combined with the arbitrarily wide-angle wave equations (AWWEs). In our method, three boundary grid points can obtain good absorption. The source wavefield can be accurately reconstructed by using these points and the mirror-image symmetry method. Numerical experiments demonstrate the correctness and effectiveness of the proposed method. We compared our method with the conventional hybrid ABC method based on the 15°one way wave equations (OWWEs). Comparisons show that our method with three boundary grid points can achieve the same absorption as the conventional method with ten boundary grid points. For twentieth order of accuracy in space, our method uses only about 30% of memory requirement and about 59% of computation time required by the conventional method.
Modeling electron dynamics coupled to continuum states in finite volumes with absorbing boundaries
De Giovannini, Umberto; Larsen, Ask Hjorth; Rubio, Angel
2015-03-01
Absorbing boundaries are frequently employed in real-time propagation of the Schrödinger equation to remove spurious reflections and efficiently emulate outgoing boundary conditions. These conditions are a fundamental ingredient for the calculation of observables involving infinitely extended continuum states in finite volumes. In the literature, several boundary absorbers have been proposed. They mostly fall into three main families: mask function absorbers, complex absorbing potentials, and exterior complex-scaled potentials. To date none of the proposed absorbers is perfect, and all present a certain degree of reflections. Characterization of such reflections is thus a critical task with strong implications for time-dependent simulations of atoms and molecules. We introduce a method to evaluate the reflection properties of a given absorber and present a comparison of selected samples for each family of absorbers. Further, we discuss the connections between members of each family and show how the same reflection curves can be obtained with very different absorption schemes.
Supersymmetry from boundary conditions
We study breaking and restoration of supersymmetry in five-dimensional theories by determining the mass spectrum of fermions from their equations of motion. Boundary conditions can be obtained from either the action principle by extremizing an appropriate boundary action (interval approach) or by assigning parities to the fields (orbifold approach). In the former, fields extend continuously from the bulk to the boundaries, while in the latter the presence of brane mass-terms cause fields to jump when one moves across the branes. We compare the two approaches and in particular we carefully compute the non-trivial jump profiles of the wavefunctions in the orbifold picture for very general brane mass terms. We also include the effect of the Scherk-Schwarz mechanism in either approach and point out that for a suitable tuning of the boundary actions supersymmetry is present for arbitrary values of the Scherk-Schwarz parameter. As an application of the interval formalism we construct bulk and boundary actions for super-Yang-Mills theory. Finally we extend our results to the warped Randall-Sundrum background
Performance of Numerical Boundary Condition based on Active Wave Absorption
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....
Ellipsoidally-shaped local absorbing boundaries for three-dimensional scalar wave propagation
Kallivokas, L. F.; Lee, S.
2004-12-01
In this paper we discuss the performance of second-order absorbing conditions prescribed on ellipsoidally-shaped truncation boundaries for the resolution of scalar wave phenomena in three dimensions. The second-order conditions employed herein belong to a larger class of arbitrarily-shaped convex absorbing boundaries developed earlier [21] for acoustic scattering and radiation problems in unbounded domains. In [21] we discussed their performance when used on spherical truncation boundaries for applications in both the time- and frequency-domains. Here, we extend their applicability to ellipsoidal geometries and demonstrate that significant computational savings are attainable due to the reduced computational domain afforded by the ellipsoid.
Solution of moving boundary problems with implicit boundary condition
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)
Tests and Applications of An Approach to Absorbing Reflected Waves Towards Incident Boundary
张洪生; 王炎; 许春辉; 商辉; 于小伟
2013-01-01
If the upstream boundary conditions are prescribed based on the incident wave only, the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become significant. This paper describes carefully an approach to specifying the incident wave boundary conditions combined with a set sponge layer to absorb the reflected waves towards the incident boundary. Incorporated into a time-dependent numerical model, whose governing equations are the Boussinesq-type ones, the effectiveness of the approach is studied in detail. The general boundary conditions, describing the down-wave boundary conditions are also generalized to the case of random waves. The numerical model is in detail examined. The test cases include both the normal one-dimensional incident regular or random waves and the two-dimensional oblique incident regular waves. The calculated results show that the present approach is effective on damping the reflected waves towards the incident wave boundary.
Boundary Conditions of Weyl Semimetals
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.
Thermal boundary conditions as constraints
Fosco, C D; Roditi, I
2006-01-01
We introduce the boundary conditions corresponding to the imaginary-time (Matsubara) formalism for the finite-temperature partition function in $d+1$ dimensions as {\\em constraints} in the path integral for the vacuum amplitude (the zero-temperature partition function). We implement those constraints by using Lagrange multipliers, which are static fields, two of them associated to each physical degree of freedom. After integrating out the original, physical fields, we obtain an effective representation for the partition function, depending only on the Lagrange multipliers. The resulting functional integral has the appealing property of involving only $d$-dimensional, {\\em time independent} fields, looking like a non local version of the classical partition function. We analyze the main properties of this novel representation for the partition function, developing the formalism within the context of two concrete examples: the real scalar and Dirac fields.
Topcolor breaking through boundary conditions
The nontrivial boundary conditions (BC's) for the topcolor breaking are investigated in the context of the TeV-scale extra dimension scenario. In the gauge symmetry breaking mechanism via the BC's we do not need to incorporate a dynamical mechanism for the topcolor breaking into the model. Moreover, the topcolor breaking can be realized without introducing explicitly a (composite) scalar field. We present a six dimensional model where the top and bottom quarks in the bulk have the topcolor charge while the other quarks in the bulk do not. We also put the electroweak gauge interaction in the six dimensional bulk. The bottom quark condensation is naturally suppressed owing to the powerlike running of the bulk U(1)Y interaction, so that only the top condensation is expected to take place. We explore such a possibility based on the ladder Schwinger-Dyson equation and show the cutoff to make the model viable
Construction of Maximal Hypersurfaces with Boundary Conditions
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.
Role of the basin boundary conditions in gravity wave turbulence
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...
Boundary Conditions in an Electric Current Contact
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...
Logarithmic minimal models with Robin boundary conditions
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\
Periodic boundary conditions on the pseudosphere
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 ...
The Pauli equation with complex boundary conditions
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.
Solving wave equation with spectral methods and nonreflecting boundary conditions
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...
Periodic boundary conditions on the pseudosphere
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.
Absorption boundary conditions for geomertical acoustics
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....
Green's functions for Neumann boundary conditions
Franklin, Jerrold
2012-01-01
Green's functions for Neumann boundary conditions have been considered in Math Physics and Electromagnetism textbooks, but special constraints and other properties required for Neumann boundary conditions have generally not been noticed or treated correctly. In this paper, we derive an appropriate Neumann Green's function with these constraints and properties incorporated.
Probability of Boundary Conditions in Quantum Cosmology
Suenobu, Hiroshi
2016-01-01
One of the main interest in quantum cosmology is to determine which type of boundary conditions for the wave function of the universe can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation numerically and evaluate probabilities for an observable representing evolution of the classical universe, especially, the number of e-foldings of the inflation. To express boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify them introducing two real parameters which discriminate boundary conditions and estimate values of these parameters resulting in observationally preferable predictions. We obtain the probability for these parameters under the requirement of the sufficient e-foldings of the inflation.
Logarithmic Minimal Models with Robin Boundary Conditions
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...
Orthogonality and Boundary Conditions in Quantum Mechanics
One dimensional particle states are constructed according to orthogonality conditions, without requiring boundary conditions. Flee particle states are constructed using Dirac's delta function orthogonality conditions. The states (doublets) de- pend on two quantum numbers: energy and parity ('+' or '-'). With the aid of projection operators the particles are confined to a constrained region -ajxja, in a way similar to the action of an infinite well potential. From the resulting over complete basis only the mutually orthogonal states are selected. Pour solutions are Sound, corresponding to different non-commuting Hamiltonians. Their energy eigen- states are labeled with the main quantum number n and parity ('+' or '-') . The energy eigenvalues are functions of n only. The four cases correspond to different boundary conditions: (I) the wave function vanishes on the boundary (energy levels: 1+,2-,3+,4-,) , (II) the derivative of the wavefunction vanishes on the boundary (energy levels 0+, 1-, 2+, 3-,) , (III) periodic, symmetric boundary conditions (energy levels: 0+,2+,2-,4+,4-6+,6-,) , (IV) periodic, antisymmetric boundary conditions (energy levels: 1+, 1-, 3+, 3-, 5+, 5-,). Orthogonality seems to be a more basic requirement than boundary conditions. By using projection operators, confinement of the particle to a definite region can be achieved in a simple and unambiguous way, and physical operators can be written so that they act only in the confined region
Modelling classroom conditions with different boundary conditions
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 are...... measures which are important for evaluation of the acoustics in classrooms....
The Pauli equation with complex boundary conditions
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)
The Pauli equation with complex boundary conditions
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’.
Numerical implementation of isolated horizon boundary conditions
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
Assessment of a PML Boundary Condition for Simulating an MRI Radio Frequency Coil
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-...
Student difficulties with Boundary Conditions in electrodynamics
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.
Neutron transport with periodic boundary conditions
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.
Scalar Boundary Conditions in Hyperscaling Violating Geometry
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\
Reconstruction of boundary conditions from internal conditions using viability theory
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.
Memory cost of absorbing conditions for the finite-difference time-domain method.
Chobeau, Pierre; Savioja, Lauri
2016-07-01
Three absorbing layers are investigated using standard rectilinear finite-difference schemes. The perfectly matched layer (PML) is compared with basic lossy layers terminated by two types of absorbing boundary conditions, all simulated using equivalent memory consumption. Lossy layers present the advantage of being scalar schemes, whereas the PML relies on a staggered scheme where both velocity and pressure are split. Although the PML gives the lowest reflection magnitudes over all frequencies and incidence angles, the most efficient lossy layer gives reflection magnitudes of the same order as the PML from mid- to high-frequency and for restricted incidence angles. PMID:27475200
Boundary conditions for the gravitational field
Winicour, Jeffrey
2012-06-01
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’)
Boundary conditions for the gravitational field
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)
Transport boundary conditions for solar cells
Volovichev, I.N.; Velazquez-Perez, J.E. [Departamento Fisica Aplicada, Universidad de Salamanca, Plaza de la Merced, E-37008 Salamanca (Spain); Gurevich, Yu.G. [Departamento de Fisica, CINVESTAV-IPN, Av. IPN 2508, Apartado Postal 14 740, Mexico DF 07000 (Mexico)
2009-01-15
Boundary conditions (BCs) to the Poisson and transport equations for stationary transport processes of nonequilibrium carriers in semiconductor structures, including solar cells, are formulated. The applicability of the resulting BCs for solar cells consisting of several various materials (metals, bipolar semiconductors, including ones in the quasineutrality approach) and their structures are analyzed for both closed and open circuit conditions. (author)
Continuity of the free boundary in elliptic problems with Neuman boundary condition
Abderachid Saadi
2015-06-01
Full Text Available We show the continuity of the free boundary in a class of two dimensional free boundary problems with Neuman boundary condition, which includes the aluminium electrolysis problem and the heterogeneous dam problem with leaky boundary condition.
Antireflective Boundary Conditions for Deblurring Problems
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.
Constructing parametric triangular patches with boundary conditions
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.
Anchored boundary conditions for locally isostatic networks
Theran, Louis; Nixon, Anthony; Ross, Elissa; Sadjadi, Mahdi; Servatius, Brigitte; Thorpe, M. F.
2015-11-01
Finite pieces of locally isostatic networks have a large number of floppy modes because of missing constraints at the surface. Here we show that by imposing suitable boundary conditions at the surface the network can be rendered effectively isostatic. We refer to these as anchored boundary conditions. An important example is formed by a two-dimensional network of corner sharing triangles, which is the focus of this paper. Another way of rendering such networks isostatic is by adding an external wire along which all unpinned vertices can slide (sliding boundary conditions). This approach also allows for the incorporation of boundaries associated with internal holes and complex sample geometries, which are illustrated with examples. The recent synthesis of bilayers of vitreous silica has provided impetus for this work. Experimental results from the imaging of finite pieces at the atomic level need such boundary conditions, if the observed structure is to be computer refined so that the interior atoms have the perception of being in an infinite isostatic environment.
ADHMN boundary conditions from removing monopoles
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...
Quantum Transport Calculations Using Periodic Boundary Conditions
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.
Boundary Conditions at Infinity for Physical Theories
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.
Boundary conditions in rational conformal field theories
Behrend, Roger E.; Pearce, Paul A.; Petkova, Valentina B.; Zuber, Jean-Bernard
2000-03-27
We develop further the theory of Rational Conformal Field Theories (RCFTs) on a cylinder with specified boundary conditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that solving Cardy's equation, expressing consistency of a RCFT on a cylinder, is equivalent to finding integer valued matrix representations of the Verlinde algebra. These matrices allow us to naturally associate a graph G to each RCFT such that the conformal boundary conditions are labelled by the nodes of G. This approach is carried to completion for sl(2) theories leading to complete sets of conformal boundary conditions, their associated cylinder partition functions and the A-D-E classification. We also review the current status for WZW sl(3) theories. Finally, a systematic generalisation of the formalism of Cardy-Lewellen is developed to allow for multiplicities arising from more general representations of the Verlinde algebra. We obtain information on the bulk-boundary coefficients and reproduce the relevant algebraic structures from the sewing constraints.
Symmetry boundary condition in dissipative particle dynamics
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.
Time-dependent density functional theory with twist-averaged boundary conditions
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...
Local electrostatic moments and periodic boundary conditions
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}
Calculating Quantum Transports Using Periodic Boundary Conditions
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...
Molecular Dynamics with Helical Periodic Boundary Conditions
Kessler, Jiří; Bouř, Petr
2014-01-01
Roč. 35, č. 21 (2014), s. 1552-1559. ISSN 0192-8651 R&D Projects: GA ČR GAP208/11/0105; GA MŠk(CZ) LH11033 Grant ostatní: GA AV ČR(CZ) M200551205; GA MŠk(CZ) LM2010005 Institutional support: RVO:61388963 Keywords : periodic boundary conditions * helical symmetry * molecular dynamics * protein structure * amyloid fibrils Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.589, year: 2014
Boundary conditions at a fluid - solid interface
Cieplak, Marek; Koplik, Joel; Banavar, Jayanth R.
2000-01-01
We study the boundary conditions at a fluid-solid interface using molecular dynamics simulations covering a broad range of fluid-solid interactions and fluid densities, and both simple and chain-molecule fluids. The slip length is shown to be independent of the type of flow, but rather is related to the fluid organization near the solid, as governed by the fluid-solid molecular interactions.
Influence of different boundary conditions on analysis of SSI
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)
Semi-implicit Image Denoising Algorithm for Different Boundary Conditions
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.
Open Boundary Conditions for Dissipative MHD
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.
Some observations on boundary conditions for numerical conservation laws
Kamowitz, David
1988-01-01
Four choices of outflow boundary conditions are considered for numerical conservation laws. All four methods are stable for linear problems, for which examples are presented where either a boundary layer forms or the numerical scheme, together with the boundary condition, is unstable due to the formation of a reflected shock. A simple heuristic argument is presented for determining the suitability of the boundary condition.
Soliton-preserving boundary condition in affine Toda field theories
Delius, Gustav W
1998-01-01
We give a new integrable boundary condition in affine Toda theory which is soliton-preserving in the sense that a soliton hitting the boundary is reflected as a soliton. All previously known integrable boundary conditions forced a soliton to be converted into an antisoliton upon reflection. We prove integrability of our boundary condition using a generalization of Sklyanin's formalism.
Canonical group quantization and boundary conditions
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.
Canonical group quantization and boundary conditions
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.
An h-principle with boundary condition
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....
Thermal field theories and shifted boundary conditions
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...
Effective Hydrodynamic Boundary Conditions for Corrugated Surfaces
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.
On domain wall boundary conditions for the XXZ spin Hamiltonian
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....
Conjugate boundary condition, hidden matters, and gauge-Higgs inflation
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.
On reweighting for twisted boundary conditions
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.
Spin chains and combinatorics: twisted boundary conditions
The finite XXZ Heisenberg spin chain with twisted boundary conditions is considered. For the case of an even number of sites N, anisotropy parameter -1/2 and twisting angle 2π/3 the Hamiltonian of the system possesses an eigenvalue -3N /2. The explicit form of the corresponding eigenvector was found for N≤12. Conjecturing that this vector is the ground state of the system we made and verified several conjectures related to the norm of the ground state vector, its component with maximal absolute value and some correlation functions, which have combinatorial nature. In particular, we conjecture that the squared norm of the ground state vector coincides with the number of half-turn symmetric alternating sign NxN matrices. (author)
On Hydroelastic Body-Boundary Condition of Floating Structures
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 assu...
Boundary conditions in first order gravity: Hamiltonian and Ensemble
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.
Nonlinear modeling of magnetorheological energy absorbers under impact conditions
Mao, Min; Hu, Wei; Choi, Young-Tai; Wereley, Norman M.; Browne, Alan L.; Ulicny, John; Johnson, Nancy
2013-11-01
Magnetorheological energy absorbers (MREAs) provide adaptive vibration and shock mitigation capabilities to accommodate varying payloads, vibration spectra, and shock pulses, as well as other environmental factors. A key performance metric is the dynamic range, which is defined as the ratio of the force at maximum field to the force in the absence of field. The off-state force is typically assumed to increase linearly with speed, but at the higher shaft speeds occurring in impact events, the off-state damping exhibits nonlinear velocity squared damping effects. To improve understanding of MREA behavior under high-speed impact conditions, this study focuses on nonlinear MREA models that can more accurately predict MREA dynamic behavior for nominal impact speeds of up to 6 m s-1. Three models were examined in this study. First, a nonlinear Bingham-plastic (BP) model incorporating Darcy friction and fluid inertia (Unsteady-BP) was formulated where the force is proportional to the velocity. Second, a Bingham-plastic model incorporating minor loss factors and fluid inertia (Unsteady-BPM) to better account for high-speed behavior was formulated. Third, a hydromechanical (HM) analysis was developed to account for fluid compressibility and inertia as well as minor loss factors. These models were validated using drop test data obtained using the drop tower facility at GM R&D Center for nominal drop speeds of up to 6 m s-1.
Nonlinear modeling of magnetorheological energy absorbers under impact conditions
Magnetorheological energy absorbers (MREAs) provide adaptive vibration and shock mitigation capabilities to accommodate varying payloads, vibration spectra, and shock pulses, as well as other environmental factors. A key performance metric is the dynamic range, which is defined as the ratio of the force at maximum field to the force in the absence of field. The off-state force is typically assumed to increase linearly with speed, but at the higher shaft speeds occurring in impact events, the off-state damping exhibits nonlinear velocity squared damping effects. To improve understanding of MREA behavior under high-speed impact conditions, this study focuses on nonlinear MREA models that can more accurately predict MREA dynamic behavior for nominal impact speeds of up to 6 m s−1. Three models were examined in this study. First, a nonlinear Bingham-plastic (BP) model incorporating Darcy friction and fluid inertia (Unsteady-BP) was formulated where the force is proportional to the velocity. Second, a Bingham-plastic model incorporating minor loss factors and fluid inertia (Unsteady-BPM) to better account for high-speed behavior was formulated. Third, a hydromechanical (HM) analysis was developed to account for fluid compressibility and inertia as well as minor loss factors. These models were validated using drop test data obtained using the drop tower facility at GM R and D Center for nominal drop speeds of up to 6 m s−1. (paper)
Wang, Y.; Shu, C.; Yang, L. M.
2016-02-01
A boundary condition-enforced-immersed boundary-lattice Boltzmann flux solver is proposed in this work for effective simulation of thermal flows with Neumann boundary conditions. In this method, two auxiliary layers of Lagrangian points are introduced and respectively placed inside and outside of the solid body, on which the temperature corrections (related to the heat source) are set as unknowns. To effectively consider the fluid-boundary interaction, these unknowns are expressed as algebraic summations of the temperature correction on Eulerian points, which are in turn obtained from biased distributions of unknown temperature corrections on the immersed boundary. By enforcing the temperature gradient at the solid boundary being equal to that approximated by the corrected temperature field, a set of algebraic equations are formed and solved to obtain all the unknowns simultaneously. They are then distributed biasedly to the inner region of the auxiliary layer so that the diffusion from the smooth delta function can be reduced substantially. In addition, the solutions of the flow and temperature fields are obtained by the thermal lattice Boltzmann flux solver with the second order of accuracy. The proposed method is well validated through its applications to simulate several benchmarks of natural, forced and mixed convection problems. It has been demonstrated that the present solver has about 1.724 order of accuracy and the error between the present result and theoretical value for the temperature gradient on the solid surface is in the order of 10-13, which indicates that the proposed method is able to satisfy the Neumann boundary condition accurately.
Power Absorption by Closely Spaced Point Absorbers in Constrained Conditions
De Backer, G.; Vantorre, M.; Beels, C.;
2010-01-01
The performance of an array of closely spaced point absorbers is numerically assessed in a frequency domain model Each point absorber is restricted to the heave mode and is assumed to have its own linear power take-off (PTO) system Unidirectional irregular incident waves are considered, represent......The performance of an array of closely spaced point absorbers is numerically assessed in a frequency domain model Each point absorber is restricted to the heave mode and is assumed to have its own linear power take-off (PTO) system Unidirectional irregular incident waves are considered...... also on the position and behaviour of the other buoys Applying the optimal control values for a single buoy to multiple closely spaced buoys results in a suboptimal solution for the array Other ways to determine the PTO parameters are diagonal optimisation (DO) and individual optimisation These methods...
Nunes, Josane C.
1991-02-01
This work quantifies the changes effected in electron absorbed dose to a soft-tissue equivalent medium when part of this medium is replaced by a material that is not soft -tissue equivalent. That is, heterogeneous dosimetry is addressed. Radionuclides which emit beta particles are the electron sources of primary interest. They are used in brachytherapy and in nuclear medicine: for example, beta -ray applicators made with strontium-90 are employed in certain ophthalmic treatments and iodine-131 is used to test thyroid function. More recent medical procedures under development and which involve beta radionuclides include radioimmunotherapy and radiation synovectomy; the first is a cancer modality and the second deals with the treatment of rheumatoid arthritis. In addition, the possibility of skin surface contamination exists whenever there is handling of radioactive material. Determination of absorbed doses in the examples of the preceding paragraph requires considering boundaries of interfaces. Whilst the Monte Carlo method can be applied to boundary calculations, for routine work such as in clinical situations, or in other circumstances where doses need to be determined quickly, analytical dosimetry would be invaluable. Unfortunately, few analytical methods for boundary beta dosimetry exist. Furthermore, the accuracy of results from both Monte Carlo and analytical methods has to be assessed. Although restricted to one radionuclide, phosphorus -32, the experimental data obtained in this work serve several purposes, one of which is to provide standards against which calculated results can be tested. The experimental data also contribute to the relatively sparse set of published boundary dosimetry data. At the same time, they may be useful in developing analytical boundary dosimetry methodology. The first application of the experimental data is demonstrated. Results from two Monte Carlo codes and two analytical methods, which were developed elsewhere, are compared
Boundary and initial conditions in protostar calculations
On first fragmentation protostars probably form part of a larger protocluster cloud already in a state of dynamic collapse. In that case it is argued that the protostar boundary is initially collapsing at supersonic speed relative to the core. This prevents information from the boundary reaching the core and calls into question models like Larson's, which start homogeneously but become centrally condensed due to the propagation of a rarefaction wave from the boundary. (author)
Attractive and Repulsive Casimir Vacuum Energy with General Boundary Conditions
Asorey, M
2013-01-01
The infrared behavior of quantum field theories confined in bounded domains is strongly dependent on the shape and structure of space boundaries. The most significant physical effect arises in the behaviour of the vacuum energy. The Casimir energy can be attractive or repulsive depending on the nature of the boundary. We calculate the vacuum energy for a massless scalar field confined between two homogeneous parallel plates with the most general type of boundary conditions depending on four parameters. The analysis provides a powerful method to identify which boundary conditions generate attractive or repulsive Casimir forces between the plates. In the interface between both regimes we find a very interesting family of boundary conditions which do not induce any type of Casimir force. We also show that the attractive regime holds far beyond identical boundary conditions for the two plates required by the Kenneth-Klich theorem and that the strongest attractive Casimir force appears for periodic boundary condit...
STOCHASTIC ANALYSIS OF GROUNDWATER FLOW SUBJECT TO RANDOM BOUNDARY CONDITIONS
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.
Optimal boundary conditions at the staircase-shaped coastlines
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.
Viscosity in molecular dynamics with periodic boundary conditions
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 ...
A qualitative theory for parabolic problems under dynamical boundary conditions
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.
New boundary conditions for the c=-2 ghost system
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.)
New boundary conditions for the c=-2 ghost system
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.)
Boundary conditions for hyperbolic formulations of the Einstein equations
Frittelli, Simonetta; Gomez, Roberto
2003-01-01
In regards to the initial-boundary value problem of the Einstein equations, we argue that the projection of the Einstein equations along the normal to the boundary yields necessary and appropriate boundary conditions for a wide class of equivalent formulations. We explicitly show that this is so for the Einstein-Christoffel formulation of the Einstein equations in the case of spherical symmetry.
Time-dependent boundary conditions for multiphase flow
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...
Simulation of boundary conditions for testing of masonry shear walls
Salmanpour, Amir Hosein; Mojsilović, Nebojša
2015-12-01
This paper is focused on the simulation of the fixed-ends boundary conditions in shear testing of unreinforced masonry walls. Two different approaches to simulate the fixed-ends boundary conditions, i.e. the static and kinematic approaches, are introduced, and their validity is discussed with the help of our own recent experimental data. It is shown that the static approach can result in unrealistic boundary conditions, and it is not a proper way to simulate the fixed-ends boundary conditions.
Numerical Simulation of Time-Dependent Wave Propagation Using Nonreflective Boundary Conditions
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.
Performance of Numerical Boundary Condition based on Active Wave Absorption System
Trouch, P.; Rouck, J. de; Frigaard, Peter
2001-01-01
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 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...
A Note on Boundary Conditions for the LWR Model
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
Solvability of a fourth order boundary value problem with periodic boundary conditions
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.
Electrostatics of solvated systems in periodic boundary conditions
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...
Anti-Periodic Boundary Conditions in Supersymmetric DLCQ
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...
Boundary Conditions and Heterotic Construction in Topological Membrane Theory
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.
Neural Boundary Conditions in Optic Guides
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.
Superconducting circuit boundary conditions and the Dynamical Casimir Effect
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...
Finite difference time domain implementation of surface impedance boundary conditions
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.
Condition of Prequantization to Two-Dimensional Manifolds with Boundary
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.
Periodic Boundary Conditions in the ALEGRA Finite Element Code
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.
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.
Periodic boundary conditions for three dimensional dislocation dynamics
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.
Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions
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.
Assessment of a PML Boundary Condition for Simulating an MRI Radio Frequency Coil
Yunsuo Duan
2008-01-01
Full Text Available 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-pass birdcage head coil, measured its resonance pattern, and used it to acquire proton (1H phantom MRI images. We then computed the resonance pattern and B1 field of the coil using FDTD with a PML as an absorbing boundary condition. We assessed the accuracy and efficiency of PML by adjusting the parameters of the PML and comparing the calculated results with measured ones. The optimal PML parameters that produce accurate (comparable to the experimental findings FDTD calculations are then provided for the birdcage head coil operating at 127.72 MHz, the Larmor frequency of 1H at 3 Tesla (T.
Breakup of spiral wave under different boundary conditions
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.
Time-dependent density functional theory with twist-averaged boundary conditions
Schuetrumpf, B.; Nazarewicz, W.; Reinhard, P.-G.
2016-05-01
Background: Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, three-dimensional (3D) coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a spatial box. For finite quantum systems (atoms, molecules, nuclei, hadrons), 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. Purpose: The finite-volume artifacts for finite systems can be practically cured by invoking an absorbing potential in a certain boundary region sufficiently far from the described system. However, such absorption cannot be applied in the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust), which suffer from unphysical effects stemming from a finite computational box used. Here, twist-averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we extend TABC to time-dependent modes. Method: We use the 3D time-dependent density functional framework with the Skyrme energy density functional. The practical calculations are carried out for small- and large-amplitude electric dipole and quadrupole oscillations of 16O. We apply and compare three kinds of boundary conditions: periodic, absorbing, and twist-averaged. Results: Calculations employing absorbing boundary conditions (ABC) and TABC are superior to those based on periodic boundary conditions. For low-energy excitations, TABC and ABC variants yield very similar results. With only four twist phases per spatial direction in TABC, one obtains an excellent reduction of spurious fluctuations. In the nonlinear regime, one has to deal with evaporated particles. In TABC, the floating nucleon gas remains in the box; the amount of nucleons in the gas is found to be
On consistent boundary conditions for c = 1 string theory
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.
On correct boundary conditions for the Asian option pricing problem
The problem of finding the price of the Asian option has been analyzed. The main goal is to construct a well-posed mathematical problem. Modified boundary conditions obtained by projecting the original equation on the boundary of the domain under consideration have been proposed
Boundary states and finite size effects in sine-Gordon model with Neumann boundary condition
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.
Two Baryons with Twisted Boundary Conditions
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.
Crystal potentials under invariant periodic boundary conditions at infinity
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.
Analyticity of thermoelastic plates with dynamical boundary conditions
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.
SHEAR WAVES IN PERIODIC WAVEGUIDE WITH ALTERNATING BOUNDARY CONDITIONS
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 ...
Electrostatics in Periodic Boundary Conditions and Real-space Corrections
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 ...
The Density Matrix Renormalization Group technique with periodic boundary conditions
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 ...
Periodic solutions to nonlinear equations with oblique boundary conditions
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 ...
Effect of boundary conditions on thermal plume growth
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.
Well Posed Problems and Boundary Conditions in Computational Fluid Dynamics
Nordström, Jan
2015-01-01
All numerical calculations will fail to provide a reliable answer unless the continuous problem under consideration is well posed. Well-posedness depends in most cases only on the choice of boundary conditions. In this paper we will highlight this fact by discussing well-posedness of the most important equations in computational uid dynamics, namely the time-dependent compressible Navier-Stokes equations. In particular, we will discuss i) how many boundary conditions are required, ii) where...
On the Vilenkin boundary condition proposal in anisotropic universes
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.
Domain structures of ferroelectric films under different electrical boundary conditions
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...
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.
On the wave equation with semilinear porous acoustic boundary conditions
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.
Transmitting boundary and radiation conditions at infinity
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.
Incorporation of an elliptical boundary condition into the program POISSON
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
On Cauchy conditions for asymmetric mixed convection boundary layer flows
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)
Boundary conditions for GL-twisted N=4 SYM
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.
Molecular Dynamics ofa Coulomb System with Deformable Periodic Boundary Conditions
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.
Ambarzumyan's theorem for the quasi-periodic boundary conditions
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.
On reversibility of cellular automata with periodic boundary conditions
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.
Structural Anisotropy in Polar Fluids Subjected to Periodic Boundary Conditions
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...
Comment on the uncertainty relation with periodic boundary conditions
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.
Variational Data Assimilation for Optimizing Boundary Conditions in Ocean Models
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.
Critical effects of downstream boundary conditions on vortex breakdown
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.
Vibration Analysis of Annular Sector Plates under Different Boundary Conditions
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.
Transport synthetic acceleration with opposing reflecting boundary conditions
Zika, M.R.; Adams, M.L.
2000-02-01
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.
Transport Synthetic Acceleration with Opposing Reflecting Boundary Conditions
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
Transport synthetic acceleration with opposing reflecting boundary conditions
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
Some Notes on Reaction Diffusion Systems with Nonlinear Boundary Conditions
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.
Thermodynamically admissible boundary conditions for the regularized 13 moment equations
Rana, Anirudh Singh; Struchtrup, Henning
2016-02-01
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.
The 8-vertex model with quasi-periodic boundary conditions
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...
Area coverage of radial Levy flights with periodic boundary conditions
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...
SHEAR WAVES IN PERIODIC WAVEGUIDE WITH ALTERNATING BOUNDARY CONDITIONS
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
Planar waveguide with "twisted" boundary conditions: small width
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.
Thermodynamically admissible boundary conditions for the regularized 13 moment equations
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.
Quantum communication through a spin ring with twisted boundary conditions
We investigate quantum communication between the sites of a spin ring with twisted boundary conditions. Such boundary conditions can be achieved by a magnetic flux through the ring. We find that a nonzero twist can improve communication through finite odd-numbered rings and enable high-fidelity multiparty quantum communication through spin rings (working near perfectly for rings of five and seven spins). We show that in certain cases, the twist results in the complete blockage of quantum-information flow to a certain site of the ring. This effect can be exploited to interface and entangle a flux qubit and a spin qubit without embedding the latter in a magnetic field
Intermediate boundary conditions for LOD, ADI and approximate factorization methods
Leveque, R. J.
1985-01-01
A general approach to determining the correct intermediate boundary conditions for dimensional splitting methods is presented. The intermediate solution U is viewed as a second order accurate approximation to a modified equation. Deriving the modified equation and using the relationship between this equation and the original equation allows us to determine the correct boundary conditions for U*. This technique is illustrated by applying it to locally one dimensional (LOD) and alternating direction implicit (ADI) methods for the heat equation in two and three space dimensions. The approximate factorization method is considered in slightly more generality.
Optimal control problems for impulsive systems with integral boundary conditions
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.
Thermodynamically admissible boundary conditions for the regularized 13 moment equations
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
The use of toroidal boundary conditions in the program POISSON
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
Boundary conditions for porous solids saturated with viscous fluid
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.
Effect of Boundary Conditions on Freezing in Porous Media
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.
Optimal Control of a Parabolic Equation with Dynamic Boundary Condition
We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the dynamic boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an Lp function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions.
On Nonlinear Coupled System with Nonlocal Boundary Conditions
U. R. Soares
2003-11-01
Full Text Available We discuss the existence, uniqueness and stability exponential andpolynomial of global solutions for a nonlinear coupled system with nonlocal boundary conditions. We show that such dissipation is strong enough to produce uniform rate of decay. Besides, the coupled is nonlinear which brings up some additional diﬃculties, which makes the problem interesting.
Periodic boundary conditions in a 3D hydro code
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.
DMRG and periodic boundary conditions: a quantum information perspective
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.
Light-Cone Quantization Without Periodic Boundary Conditions
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.
One-dimensional inhomogeneous Ising model with periodic boundary conditions
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.
On the algebraic Bethe ansatz: Periodic boundary conditions
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.
Radiation and Boundary Conditions in the Theory of Gravitation
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.
Investigation of Boundary Conditions for Flexible Multibody Spacecraft Dynamics
MacLean, John R.; Huynh, An; Quiocho, Leslie J.
2007-01-01
In support of both the Space Shuttle and International Space Station programs, a set of generic multibody dynamics algorithms integrated within the Trick simulation environment have addressed the variety of on-orbit manipulator simulation requirements for engineering analysis, procedures development and crew familiarization/training at the NASA Johnson Space Center (JSC). Enhancements to these dynamics algorithms are now being driven by a new set of Constellation program requirements for flexible multibody spacecraft simulation. One particular issue that has been discussed within the NASA community is the assumption of cantilever-type flexible body boundary conditions. This assumption has been commonly utilized within manipulator multibody dynamics formulations as it simplifies the computation of relative motion for articulated flexible topologies. Moreover, its use for modeling of space-based manipulators such as the Shuttle Remote Manipulator System (SRMS) and Space Station Remote Manipulator System (SSRMS) has been extensively validated against flight data. For more general flexible spacecraft applications, however, the assumption of cantilever-type boundary conditions may not be sufficient. This paper describes the boundary condition assumptions that were used in the original formulation, demonstrates that this formulation can be augmented to accommodate systems in which the assumption of cantilever boundary conditions no longer applies, and verifies the approach through comparison with an independent model previously validated against experimental hardware test data from a spacecraft flexible dynamics emulator.
Waveguides with combined Dirichlet and Robin boundary conditions
Freitas, P.; Krejčiřík, David
2006-01-01
Roč. 9, č. 4 (2006), s. 335-352. ISSN 1385-0172 R&D Projects: GA MŠk LC06002 Institutional research plan: CEZ:AV0Z10480505 Keywords : Dirichlet and Robin boundary conditions * eigenvalues in strips and annuli * Hardy ineguality Subject RIV: BE - Theoretical Physics Impact factor: 0.593, year: 2006
BPS monopole in the space of boundary conditions
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)
Navier-Stokes equation with slip-like boundary condition
Ken'ichi Hashizume; Tetsuya Koyama; Mitsuharu Otani
2009-01-01
The aim of this note is to investigate a time-discretized 2-dimensional Navier-Stokes equation with a slip-like boundary condition, which arises in the melting ice problem. We prove the existence and uniqueness of a weak solution.
Boundary Conditions as Mass Generation Mechanism for Complex Scalar Fields
Nogueira, J A
2003-01-01
We consider the effects of homogeneous Dirichlet's boundary conditions in the scalar electrodynamics with self-interaction. We have found for a critical scale of the compactification length that symmetry is restored and scalar field develops mass and vector field does not.
Boundary Conditions as Mass Generation Mechanism for Real Scalar Fields
Nogueira, J A; Nogueira, Jose Alexandre; Barbieri, Pedro Leite
2001-01-01
We consider the effects of homogeneous Dirichlet's boundary conditions on two infinite parallel plane surfaces separated by a small distance {\\it a}. We find that although spontaneous symmetry breaking does not occur for the theory of a massless, quartically self-interacting real scalar field, the theory becomes a theory of a massive scalar field.
Validation of Boundary Conditions for CFD Simulations on Ventilated Rooms
Topp, Claus; Jensen, Rasmus Lund; Pedersen, D.N.;
2001-01-01
The application of Computational Fluid Dynamics (CFD) for ventilation research and design of ventilation systems has increased during the recent years. This paper provides an investigation of direct description of boundary conditions for a complex inlet diffuser and a heated surface. A series of ...
Spectral determinant on graphs with generalized boundary conditions
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.
On a stochastic Burgers equation with Dirichlet boundary conditions
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.
Positive Solutions for Nonlinear Differential Equations with Periodic Boundary Condition
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.
Reduction of XXZ model with generalized periodic boundary conditions
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.
Planar waveguide with "twisted" boundary conditions: discrete spectrum
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.
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.
Influence of shock absorber condition on pavement fatigue using relative damage concept
Pablo Kubo
2015-12-01
Full Text Available Considering the importance of the road transportation nowadays, concerns related to pavement deterioration and maintenance have become relevant subjects. Especially for commercial vehicles, the vertical dynamic load (characterized by the tire-road interaction is directly related to wear on the road surface. Given this, the main objective of this paper is to analyse effects of vertical loads applied on the flexible pavement, considering the variation of the condition of shock absorbers from a truck's front suspension. The measurements were performed on a rigid truck, with 2 steering front axles, in a durability test track located in Brazil. With a constant load of 6 tons on the front suspension (the maximum allowed load on front axles according to Brazilian legislation, 3 different shock absorber conditions were evaluated: new, used and failed. By applying the relative damage concept, it is possible to conclude that the variation of the shock absorber conditions will significantly affect the vertical load applied on the pavement. Although the results clearly point to a dependent relationship between the load and the condition of the shock absorbers, it is recommended to repeat the same methodology, in future to analyse the influence of other quarter car model variants (such as spring rate, mass and tire spring stiffness.
Javier A. Dottori; Boroni, Gustavo A.; Alejandro Clausse
2015-01-01
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 th...
Driven nonequilibrium lattice systems with shifted periodic boundary conditions
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.
Stretched flow of Carreau nanofluid with convective boundary condition
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.
Most general AdS_3 boundary conditions
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.
Boundary Conditions for a New Type of Design Task
McAloone, Tim C.
2011-01-01
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...... attempt to map out some of the boundary conditions for PSS design research, in order to ensure that the phenomenon is successfully trans-formed into a well balanced design research field, including the necessary do-mains of expertise and research content to fully understand, develop and also communicate...
Thermo Field Dynamics of strings with definite boundary conditions
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.
One-dimensional phase change with periodic boundary conditions
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.
Flux change in viscous laminar flow under oscillating boundary condition
Ueda, R.; Mikada, H.; Goto, T.; Takekawa, J.
2012-12-01
The behavior of interstitial fluid is one of major interest in earth sciences in terms of the exploitation of water resources, the initiation of earthquakes, enhanced oil recovery (EOR), etc. Seismic waves are often known to increase the flux of interstitial fluid but the relationship between the flux and propagating seismic waves have not been well investigated in the past, although seismic stimulation has been applied in the oil industry for enhanced oil recovery (EOR). Many observations indicated that seismic waves could stimulate the oil production due to lowering of apparent viscosity coefficient, to the coalescence and/or the dispersion of droplets of a phase in multiphase fluids. However, the detailed mechanism of seismic stimulation has not been fully understood, either. In this study, We attempt to understand the mechanism of the flux change in viscous laminar flow under oscillating boundary condition for the simulation of interstitial flow. Here, we analyze a monophase flow in a pore throat. We first assume a Hagen-Poiseuille flow of incompressible fluid through a pore-throat in a porous medium. We adopt the Lattice Boltzmann method (LBM) in which the motion of fluid is simulated through the variation of velocity distribution function representing the distribution of discrete particle velocities. We use an improved incompressible LBKG model (d2q9i) proposed in Zou et. al. (1995) to accurately accommodate the boundary conditions of pressure and velocity in the Hagen-Poiseuille flow. We also use an half-way bounce back boundary condition as the velocity boundary condition. Also, we assume a uniform pressure (density) difference between inlet and outlet flow, and the density difference could initiate the flow in our simulation. The oscillating boundary condition is given by the body force acting on fluid particles. In this simulation, we found that the flux change is negligible under small amplitude of oscillation in both horizontal and vertical directions
Matrix albedo for discrete ordinates infinite-medium boundary condition
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)
Boundary Conditions for NHEK through Effective Action Approach
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)
Inhibition of the dynamical Casimir effect with Robin boundary conditions
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.
Analytical Loss Factors in Approximation of the Leontovich Boundary Conditions
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.
Analysis of the Schroedinger functional with chirally rotated boundary conditions
The Schroedinger functional provides a valuable tool to perform non-perturbative renormalization on the lattice, in particular in a mass independent scheme. We study two different types of chirally rotated Schroedinger functional boundary conditions which have been recently proposed to retain the bulk automatic O(a) improvement of massless Wilson fermions in finite volume. We investigate the spectral properties and the quark propagators which derive from these two proposals in the continuum at tree-level of perturbation theory. (orig.)
Probabilistic flood hazard mapping: effects of uncertain boundary conditions
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.
Probabilistic flood hazard mapping: effects of uncertain boundary conditions
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.
The XXZ model with anti-periodic twisted boundary conditions
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.
A 3D radiative transfer framework: III. periodic boundary conditions
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...
Efficient Matrix Product State Method for periodic boundary conditions
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 ~ ...
The XXZ model with anti-periodic twisted boundary conditions
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.
Allowed wavevectors under the application of incommensurate periodic boundary conditions
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 ...
Efficient MPS algorithm for periodic boundary conditions and applications
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 ...
Micromagnetic simulations with periodic boundary conditions: Hard-soft nanocomposites
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...
Periodic boundary conditions for demagnetization interactions in micromagnetic simulations
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...
On Matrix Product States for Periodic Boundary Conditions
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 ...
A PNJL Model for Adjoint Fermions with Periodic Boundary Conditions
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...
GRAPESPH with Fully Periodic Boundary Conditions: Fragmentation of Molecular Clouds
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...
Periodic boundary conditions for the simulation of uniaxial extensional flow
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...
Boundary conditions for star matter and other periodic fermionic systems
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...
Slarti: A boundary condition editor for a coupled climate model
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.
Nonsteady heat conduction code with radiation boundary conditions
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)
Nonlinear Vibrations of Multiwalled Carbon Nanotubes under Various Boundary Conditions
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...
Deficiency indices and singular boundary conditions in quantum mechanics
We consider Schroedinger operators H in L2 (Rsup(n)), n from IN, with countably infinitely many local singularities of the potential which are separated from each other by a positive distance. It is proved that due to locality each singularity yields a separate contribution to the deficiency index of H. In the special case where the singularities are pointlike and the potential exhibits certain symmetries near these points we give an explicit construction of self-adjoint boundary conditions
Bound states in waveguides with complex Robin boundary conditions
Novák, Radek
2016-01-01
Roč. 96, 3-4 (2016), s. 251-281. ISSN 0921-7134 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : non-self-adjointness * waveguide * Robin boundary conditions * spectral analysis * essential spectrum * weak coupling * Birman-Schwinger principle * reality of the spectrum Subject RIV: BE - Theoretical Physics Impact factor: 0.528, year: 2014
Boundary conditions for OH, L, and H-mode simulations
A method for prescribing appropriate boundary conditions for predictive simulations using flux-surface-averaged plasma transport codes is described. The model makes use of the present theoretical understanding of L and H-mode transport mechanisms and is consistent with trends in existing data. It is calibrated against an ASDEX experiment and used to predict the edge behavior in CIT. 14 refs., 7 figs
Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions
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
Entropy of bosonic open string and boundary conditions
Abdalla, M. C. B.; Graça, E. L.; Vancea, I. V.
2002-05-01
The entropy of the states associated to the solutions of the equations of motion of the bosonic open string with combinations of Neumann and Dirichlet boundary conditions is given. Also, the entropy of the string in the states Ai>=αi-10> and φa>=αa- 10> that describe the massless fields on the world-volume of the /Dp-brane is computed.
Entropy of Bosonic Open String and Boundary Conditions
Abdalla, M. C. B.; Graca, E. L.; Vancea, I. V.
2002-01-01
The entropy of the states associated to the solutions of the equations of motion of the bosonic open string with combinations of Neumann and Dirichlet boundary conditions is given. Also, the entropy of the string in the states $| A^i > = \\alpha^{i}_{-1} |0>$ and $| \\phi^a > = \\alpha^{a}_{-1} |0>$ that describe the massless fields on the world-volume of the Dp-brane is computed.
Sensitivity of African easterly waves to boundary layer conditions
A. Lenouo; Mkankam Kamga, F.
2008-01-01
A linearized version of the quasi-geostrophic model (QGM) with an explicit Ekman layer and observed static stability parameter and profile of the African easterly jet (AEJ), is used to study the instability properties of the environment of the West African wave disturbances. It is found that the growth rate, the propagation velocity and the structure of the African easterly waves (AEW) can be well simulated. Two different lower boundary conditions are applied. One assumes a lack of vertical g...
Maxwell boundary conditions impose non-Lindblad master equation
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...
On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition
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.
Solitons induced by boundary conditions from the Boussinesq equation
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.
Solvability of a fourth-order boundary value problem with periodic boundary conditions II
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
The formulation of gauge-Higgs unification with dynamical boundary conditions
Yamamoto, Kengo
2014-01-01
The boundary conditions on multiply connected extra dimensions play major roles in gauge-Higgs unification theory. Different boundary conditions, having been given in ad hoc manner so far, lead to different theories. To solve this arbitrariness problem of boundary conditions, we construct a formulation of gauge-Higgs unification with dynamics of boundary conditions on M4×S1/Z2 . As a result, it is found that only highly restricted sets of boundary conditions, which lead to nontrivial symmetry...
Repulsive Casimir force from fractional Neumann boundary conditions
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.
Repulsive Casimir force from fractional Neumann boundary conditions
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.
Allowed wavevectors under the application of incommensurate periodic boundary conditions
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.
Electrostatics of solvated systems in periodic boundary conditions
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.
Boundary Conditions for Kerr-AdS Perturbations
Dias, Oscar J C
2013-01-01
The Teukolsky master equation and its associated spin-weighted spheroidal harmonic decomposition simplify considerably the study of linear gravitational perturbations of the Kerr(-AdS) black hole. However, the formulation of the problem is not complete before we assign the physically relevant boundary conditions. We find a set of two Robin boundary conditions (BCs) that must be imposed on the Teukolsky master variables to get perturbations that are asymptotically global AdS, i.e. that asymptotes to the Einstein Static Universe. In the context of the AdS/CFT correspondence, these BCs allow a non-zero expectation value for the CFT stress-energy tensor while keeping fixed the boundary metric. When the rotation vanishes, we also find the gauge invariant differential map between the Teukolsky and the Kodama-Ishisbashi (Regge-Wheeler-Zerilli) formalisms. One of our Robin BCs maps to the scalar sector and the other to the vector sector of the Kodama-Ishisbashi decomposition. The Robin BCs on the Teukolsky variables ...
Absolute Hydration Free Energies of Ions Under Periodic Boundary Conditions
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)
Structural Anisotropy in Polar Fluids Subjected to Periodic Boundary Conditions
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
Applying twisted boundary conditions for few-body nuclear systems
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.
Applying Twisted Boundary Conditions for Few-body Nuclear Systems
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.
Three dimensional dynamics of rotating structures under mixed boundary conditions
Bediz, Bekir; Romero, L. A.; Ozdoganlar, O. Burak
2015-12-01
This paper presents the spectral-Tchebychev (ST) technique for solution of three dimensional (3D) dynamics of rotating structures. In particular, structures that exhibit coupled dynamic response require a 3D modeling approach to capture their dynamic behavior. Rotational motions further complicate this behavior, inducing coriolis, centrifugal softening, and (nonlinear) stress-stiffening effects. Therefore, a 3D solution approach is needed to accurately capture the rotational dynamics. The presented 3D-ST technique provides a fast-converging and precise solution approach for rotational dynamics of structures with complex geometries and mixed boundary conditions. Specifically, unlike finite elements techniques, the presented technique uses a series expansion approach considering distributed-parameter system equations: The integral boundary value problem for rotating structures is discretized using the spectral-Tchebychev approach. To simplify the domain of the structures, cross-sectional and rotational transformations are applied to problems with curved cross-section and pretwisted geometry. The nonlinear terms included in the integral boundary value problem are linearized around an equilibrium solution using the quasi-static method. As a result, mass, damping, and stiffness matrices, as well as a forcing vector, are obtained for a given rotating structure. Several case studies are then performed to demonstrate the application and effectiveness of the 3D-ST solution. For each problem, the natural frequencies and modes shapes from the 3D-ST solution are compared to those from the literature (when available) and to those from a commercial finite elements software. The case studies include rotating/spinning parallelepipeds under free and mixed boundary conditions, and a cantilevered pretwisted beam (i.e., rotating blade) with an airfoil geometry rotating on a hub. It is seen that the natural frequencies and mode shapes from the 3D-ST technique differ from those from the
Towards Multiphase Periodic Boundary Conditions with Flow Rate Constraint
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.
Chen, Gui-Qiang; Osborne, Dan; Qian, Zhongmin
2008-01-01
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in $\\R^n$ with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous 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 so...
Safety-related boundary conditions for advanced reload design
In this paper a method is discussed to overcome the discrepancy between the demands for increased fuel management flexibility on the one hand and for permanent operating licensing on the other. By defining safety-related boundary conditions it is possible to determine the safety-related characteristics of reload cores in advance, in spite of the fact that they differ from one another within certain limits. The basis of the boundary conditions is given by the essential mechanical design features of the fuel assemblies (hardware frame) and the concept behind safety analysis and safety-related requirements (software frame) together with the verified limits of the key safety parameters defined by the total amount of explicit analyses carried out during the construction phase of the plant and -possibly - in previous operating cycles. Key safety parameters denote those input/output parameters of safety analysis which determine the safety-related aspects of core behaviour. With respect to reload safety evaluation, only those safety parameters are relevant which may vary significantly from reload to reload. Safety analysis is a two-dimensional array structured by requirement categories and areas of analysis. Primary (external) design criteria are of direct relevance to safety. They define safety margins to failure and determine the range fixed by the operating license. Within reload safety evaluation, in general, it is sufficient to demonstrate that the safety-related input parameters are within the verified limits. The application of these safety-related boundary conditions to in-core fuel managements is discussed for an exemplary equilibrium core of the PWR 1300 MW characterized by a number of features typical for advanced reload design. Safety evaluation demonstrates the feasibility of the envisaged fuel management strategy. Moreover, it helps to identify, if necessary, hardware modifications indispensable or recommendable prior to realization of challenging loading
Boundary and mixed lubrication friction modeling under forming process conditions
Meinders, V. T.; Hol, J.; van den Boogaard, A. H.
2013-12-01
A multi-scale friction model for large-scale forming simulations is presented. A framework has been developed for the boundary and mixed lubrication regime, including the effect of surface changes due to normal loading, sliding and straining the underlying bulk material. Adhesion and ploughing effects have been accounted for to characterize friction conditions on the micro scale. To account for the lubricant effects special hydrodynamic contact elements have been developed. Pressure degrees of freedom are introduced to capture the pressure values which are computed by a finite element discretization of the 2D averaged Reynolds equations. The boundary friction model and the hydrodynamic friction model have been coupled to cover the boundary and mixed lubrication regime. To prove the numerical efficiency of the multi-scale friction model, finite element simulations have been carried out on a top hat section. The computed local friction coefficients show to be dependent on the punch stroke, punch speed and location in the product, and are far from constant. The location and range of friction coefficient values are in the order of what to expect from practice. The agreement between the numerical results and the experiments for different lubrication types and amount of lubrication is good. The multi-scale friction model proves to be stable, and compared to a Coulomb-based FE simulation, with only a modest increase in computation time.
Incorporation of toroidal boundary conditions into program POISSON
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
Periodic boundary conditions for dislocation dynamics simulations in three dimensions
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.
Periodic boundary conditions for demagnetization interactions in micromagnetic simulations
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.
Stokes Flow with Slip and Kuwabara Boundary Conditions
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.
Reconnection properties in collisionless plasma with open boundary conditions
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.
Boundary conditions and critical Casimir forces in helium
If a fluid near its critical point is confined between two interfaces, the long-ranged critical fluctuations in the order parameter will mediate a force. This force, known as the critical Casimir force, is a direct analog of the Casimir force in electromagnetism. Dielectric constant measurements of helium films adsorbed on Cu electrodes provide evidence for the existence of the critical Casimir force near the superfluid transition in 4He and near the tricritical point in 3He-4He mixtures. In pure 4He, we find the force is attractive but near the tricritical point the force appears repulsive, a change due to the extraordinary boundary conditions at the tricritical point
On the trigonometric Felderhof model with domain wall boundary conditions
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.
Numerical solutions of telegraph equations with the Dirichlet boundary condition
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.
General rule for boundary conditions from the action principle
Steiner, Roee
2016-03-01
We construct models where initial and boundary conditions can be found from the fundamental rules of physics, without the need to assume them, they will be derived from the action principle. Those constraints are established from physical viewpoint, and it is not in the form of Lagrange multipliers. We show some examples from the past and some new examples that can be useful, where constraint can be obtained from the action principle. Those actions represent physical models. We show that it is possible to use our rule to get those constraints directly.
Magnetospheric conditions near the equatorial footpoints of proton isotropy boundaries
Sergeev, V. A.; Chernyaev, I. A.; Angelopoulos, V.; Ganushkina, N. Y.
2015-12-01
Data from a cluster of three THEMIS (Time History of Events and Macroscale Interactions during Substorms) spacecraft during February-March 2009 frequently provide an opportunity to construct local data-adaptive magnetospheric models, which are suitable for the accurate mapping along the magnetic field lines at distances of 6-9 Re in the nightside magnetosphere. This allows us to map the isotropy boundaries (IBs) of 30 and 80 keV protons observed by low-altitude NOAA POES (Polar Orbiting Environmental Satellites) to the equatorial magnetosphere (to find the projected isotropy boundary, PIB) and study the magnetospheric conditions, particularly to evaluate the ratio KIB (Rc/rc; the magnetic field curvature radius to the particle gyroradius) in the neutral sheet at that point. Special care is taken to control the factors which influence the accuracy of the adaptive models and mapping. Data indicate that better accuracy of an adaptive model is achieved when the PIB distance from the closest spacecraft is as small as 1-2 Re. For this group of most accurate predictions, the spread of KIB values is still large (from 4 to 32), with the median value KIB ~13 being larger than the critical value Kcr ~ 8 expected at the inner boundary of nonadiabatic angular scattering in the current sheet. It appears that two different mechanisms may contribute to form the isotropy boundary. The group with K ~ [4,12] is most likely formed by current sheet scattering, whereas the group having KIB ~ [12,32] could be formed by the resonant scattering of low-energy protons by the electromagnetic ion-cyclotron (EMIC) waves. The energy dependence of the upper K limit and close proximity of the latter event to the plasmapause locations support this conclusion. We also discuss other reasons why the K ~ 8 criterion for isotropization may fail to work, as well as a possible relationship between the two scattering mechanisms.
Two-Baryon Systems with Twisted Boundary Conditions
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...