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-...
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.
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.
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
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)
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’)
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.
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.
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.
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.
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.
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.
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.
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 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.
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.
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...
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.
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.
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 ...
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.
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.)
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.
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.
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...
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.
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.
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...
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.
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.
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.
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.
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.
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.
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
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
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.
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.
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
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
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.
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.
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.
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.
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.
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.
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.
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.
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 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.
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.
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.
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
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)
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)
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.
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
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...
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.
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
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.)
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
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
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
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.
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.
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.
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.
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.
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.
Mixed singular-regular boundary conditions in multislab radiation transport
This article reports a computational method for approximately solving radiation transport problems with anisotropic scattering defined on multislab domains irradiated from one side with a beam of monoenergetic neutral particles. We assume here that the incident beam may have a monodirectional component and a continuously distributed component in angle. We begin by defining the target problem representing the class of radiation transport problems that we are focused on. We then Chandrasekhar decompose the target problem into an uncollided transport problem with left singular boundary conditions and a diffusive transport problem with regular boundary conditions. We perform an analysis of these problems to derive the exact solution of the uncollided transport problem and a discrete ordinates solution in open form to the diffusive transport problem. These solutions are the basis for the definition of a computational method for approximately solving the target problem. We illustrate the numerical accuracy of our method with three basic problems in radiative transfer and neutron transport, and we conclude this article with a discussion and directions for future work
Development of a Discrete Mass Inflow Boundary Condition for MFIX
Jordan Musser
2011-02-01
Full Text Available MFIX (Multiphase Flow with Interphase eXchanges is an open source software package developed by the National Energy Technology Laboratory (NETL used for modeling the chemical reactions, heat transfer, and hydrodynamics of fluid-solid systems. Currently, the stable publically available release of MFIX does not include a discrete mass inflow boundary condition (DMIBC for its discrete element method (DEM package. Inflow boundary conditions are useful for simulating systems where particles are consumed through chemical reactions and an incoming feed is necessary to sustain the reaction. To implement the DMIBC an inlet staging area is designated outside the computational domain and particles are passed through the wall region associated with the inlet. Forces incurred on entering particles, generated from collisions with particles already in the system, are ignored whereas, particles already in the system respond to contact forces and react accordingly, moving away from the inlet. This approach prevents any unphysical overlap between new and existing particles. It also ensures that particles entering the system will enter the computational domain regardless of opposing forces. Once an incoming particle is fully within the domain, it reacts appropriately to any and all contact force. This approach for a DMIBC has been implemented and is available within the current development version of MFIX.
Optimum heat power cycles for specified boundary conditions
In this paper optimization of the power output of Carnot and closed Brayton cycles is considered for both finite and infinite thermal capacitance rates of the external fluid streams. The method of Lagrange multipliers is used to solve for working fluid temperatures that yield maximum power. Analytical expressions for the maximum power and the cycle efficiency at maximum power are obtained. A comparison of the maximum power from the two cycles for the same boundary conditions, i.e., the same heat source/sink inlet temperatures, thermal capacitance rates, and heat exchanger conductances, shows that the Brayton cycle can produce more power than the Carnot cycle. This comparison illustrates that cycles exist that can produce more power than the Carnot cycle. The optimum heat power cycle, which will provide the upper limit of power obtained from any thermodynamic cycle for specified boundary conditions and heat exchanger conductances is considered. The optimum heat power cycle is identified by optimizing the sum of the power output from a sequence of Carnot cycles. The shape of the optimum heat power cycle, the power output, and corresponding efficiency are presented. The efficiency at maximum power of all cycles investigated in this study is found to be equal to (or well approximated by) η = 1 - sq. root TL.in/φTH.in where φ is a factor relating the entropy changes during heat rejection and heat addition
A whisker sensor: role of geometry and boundary conditions
Hans, Hendrik; Valdivia Y Alvarado, Pablo; Thekoodan, Dilip; Jianmin, Miao; Triantafyllou, Michael
2011-11-01
Harbor seal whiskers are currently being studied for their role in sensing and tracking of the fluid structures left in wakes. Seal whiskers are exposed to incoming flows and are subject to self-induced vibrations. The whisker's unusual geometry is thought to reduce these self-induced disturbances and facilitate a stable reference for wake sensing. An experimental platform was designed to measure flow-induced displacements and vibrations at the base of whisker-like models. Four different whisker-like models (scale: 3x) were towed at different speeds down a towing tank and base displacements in the direction of motion and in the perpendicular axis were measured. Each model incorporated a particular geometrical feature found in harbor seal whiskers. Three different visco-elastic supports were used to mimic various boundary conditions at the base of the whisker models. The effects of geometrical features and boundary conditions on measured base vibrations at three relevant Reynolds numbers are discussed. The material properties of a model's base influence its sensitivity. When compared to a circular cylinder model, whisker models show almost no sign of VIV.
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...
The NMSSM with F-theory unified boundary conditions
Aparicio, L; Cerdeno, D G; Ibanez, L E; Valenzuela, I
2012-01-01
We study the phenomenological viability of a constrained NMSSM with parameters subject to unified boundary conditions from F-theory GUTs. We find that very simple assumptions about modulus dominance SUSY breaking in F-theory unification lead to a predictive set of boundary conditions, consistent with all phenomenological constraints. The second lightest scalar Higgs H_2 can get a mass m_{H_2} ~ 125 GeV and has properties similar to the SM Higgs. On the other hand the lightest scalar H_1, with a dominant singlet component, would have barely escaped detection at LEP and could be observable at LHC as a peak in H_1 -> gamma gamma at around 100 GeV. The LSP is mostly singlino and is consistent with WMAP constraints due to coannihilation with the lightest stau, whose mass is in the range 100-250 GeV. Such light staus may lead to very characteristic signatures at LHC and be directly searched at linear colliders. In these models tan(beta) is large, of order 50, still the branching ratio for B_s -> mu+ mu- is consiste...
Numerical study of one-dimensional Stefan problem with periodic boundary conditions
Qu Liang-Hui; Ling Feng; Xing Lin
2013-01-01
A finite difference approach to a one-dimensional Stefan problem with periodic boundary conditions is studied. The evolution of the moving boundary and the temperature field are simulated numerically, and the effects of the Stefan number and the periodical boundary condition on the temperature distribution and the evolution of the moving boundary are analyzed.
Numerical study of one-dimensional Stefan problem with periodic boundary conditions
Qu Liang-Hui
2013-01-01
Full Text Available A finite difference approach to a one-dimensional Stefan problem with periodic boundary conditions is studied. The evolution of the moving boundary and the temperature field are simulated numerically, and the effects of the Stefan number and the periodical boundary condition on the temperature distribution and the evolution of the moving boundary are analyzed.
Uddin, Mohammed J.; Khan, Waqar A.; Ahmed I Ismail
2012-01-01
Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first convert...
This experimental study deals with a single-basin solar still using various absorbing materials with and without black painting. Different types of absorbing materials with and without black painting were used to enhance the solar still productivity through improvement in absorptivity. These materials are steel and aluminum with and without black painting and rubber. Two identical solar stills were manufactured using locally available materials. All the results were compared together to reach the best absorbing materials with and without painting that can be used for solar still. it was found that the rubber absorber has the highest water collection during daytime, followed by the black painted steel absorber, then by black painted aluminum absorber and steel without painting absorber. The average enhancement in the daily productivity was about 50% for the rubber absorber compared with the black painted aluminum absorber and about 43% for the rubber absorber compared with the black painted steel absorber.(author)
Pierluigi Colli
2015-07-01
Full Text Available In this paper we establish second-order sufficient optimality conditions for a boundary control problem that has been introduced and studied by three of the authors in the preprint arXiv:1407.3916. This control problem regards the viscous Cahn–Hilliard equation with possibly singular potentials and dynamic boundary conditions.
Analytical solution for 1D consolidation of unsaturated soil with mixed boundary condition
Zhen-dong SHAN; Dao-sheng LING; Hao-jiang DING
2013-01-01
Based on consolidation equations proposed for unsaturated soil,an analytical solution for 1D consolidation of an unsaturated single-layer soil with nonhomogeneous mixed boundary condition is developed.The mixed boundary condition can be used for special applications,such as tests occur in laboratory.The analytical solution is obtained by assuming all material parameters remain constant during consolidation.In the derivation of the analytical solution,the nonhomogeneous boundary condition is first transformed into a homogeneous boundary condition.Then,the eigenfunction and eigenvalue are derived according to the consolidation equations and the new boundary condition.Finally,using the method of undetermined coefficients and the orthogonal relation of the eigenfunction,the analytical solution for the new boundary condition is obtained.The present method is applicable to various types of boundary conditions.Several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with mixed boundary condition.
Exact solution of a new class of Hubbard-type models with open boundary conditions
A new class of Hubbard-type models with open boundary conditions in one dimension is studied in the framework of coordinate Bethe ansatz method. The energy spectrum, integrable boundary conditions and the corresponding Bethe ansatz equations are derived. (authors)
Itagaki, M. (Japan Atomic Energy Research Inst., Dept. of Nuclear Ship Engineering, Aza-Kitasekine, Oaza-Sekine, Mutsu, Aomori 035 (JP)); Brebbia, C.A. (Computational Mechanics Inst., Ashurst Lodge, Ashurst, Southampton SO4 2AA (GB))
1991-03-01
This paper reports on the boundary element method used to generate energy-dependent matrix-type boundary conditions along core/reflector interfaces and along baffle-plate surfaces of pressurized water reactors. This method enables one to deal with all types of boundary geometries including convex and concave corners. The method is applicable to neutron diffusion problems with more than two energy groups and also can be used to model a reflector with or without a baffle plate. Excellent eigenvalue and flux shape results can be obtained when the boundary conditions generated by this technique are coupled with core-only finite difference calculations.
Cai, Jian; Modest, Michael F.
2016-01-01
In simulations of periodic or symmetric geometries, computational domains are reduced by imaginary boundaries that present the symmetry conditions. In Photon Monte Carlo methods, this is achieved by imposing specular reflective boundary conditions for the radiative intensity. In this work, a similar specular reflective boundary condition is developed for Discrete Ordinate Methods. The effectiveness of the new boundary condition is demonstrated by multiple numerical examples including plane symmetry and axisymmetry.
Topological susceptibility in lattice Yang-Mills theory with open boundary condition
Chowdhury, Abhishek; Harindranath, A. [Theory Division, Saha Institute of Nuclear Physics,1/AF Bidhan Nagar, Kolkata 700064 (India); Maiti, Jyotirmoy [Department of Physics, Barasat Government College,10 KNC Road, Barasat, Kolkata 700124 (India); Majumdar, Pushan [Department of Theoretical Physics, Indian Association for the Cultivation of Science,Kolkata 700032 (India)
2014-02-11
We find that using open boundary condition in the temporal direction can yield the expected value of the topological susceptibility in lattice SU(3) Yang-Mills theory. As a further check, we show that the result agrees with numerical simulations employing the periodic boundary condition. Our results support the preferability of the open boundary condition over the periodic boundary condition as the former allows for computation at smaller lattice spacings needed for continuum extrapolation at a lower computational cost.
Estimating Thermal Inertia with a Maximum Entropy Boundary Condition
Nearing, G.; Moran, M. S.; Scott, R.; Ponce-Campos, G.
2012-04-01
Thermal inertia, P [Jm-2s-1/2K-1], is a physical property the land surface which determines resistance to temperature change under seasonal or diurnal heating. It is a function of volumetric heat capacity, c [Jm-3K-1], and thermal conductivity, k [Wm-1K-1] of the soil near the surface: P=√ck. Thermal inertia of soil varies with moisture content due the difference between thermal properties of water and air, and a number of studies have demonstrated that it is feasible to estimate soil moisture given thermal inertia (e.g. Lu et al, 2009, Murray and Verhoef, 2007). We take the common approach to estimating thermal inertia using measurements of surface temperature by modeling the Earth's surface as a 1-dimensional homogeneous diffusive half-space. In this case, surface temperature is a function of the ground heat flux (G) boundary condition and thermal inertia and a daily value of P was estimated by matching measured and modeled diurnal surface temperature fluctuations. The difficulty is in measuring G; we demonstrate that the new maximum entropy production (MEP) method for partitioning net radiation into surface energy fluxes (Wang and Bras, 2011) provides a suitable boundary condition for estimating P. Adding the diffusion representation of heat transfer in the soil reduces the number of free parameters in the MEP model from two to one, and we provided a sensitivity analysis which suggests that, for the purpose of estimating P, it is preferable to parameterize the coupled MEP-diffusion model by the ratio of thermal inertia of the soil to the effective thermal inertia of convective heat transfer to the atmosphere. We used this technique to estimate thermal inertia at two semiarid, non-vegetated locations in the Walnut Gulch Experimental Watershed in southeast AZ, USA and compared these estimates to estimates of P made using the Xue and Cracknell (1995) solution for a linearized ground heat flux boundary condition, and we found that the MEP-diffusion model produced
Unsteady Squeezing Flow of Carbon Nanotubes with Convective Boundary Conditions.
Hayat, Tasawar; Muhammad, Khursheed; Farooq, Muhammad; Alsaedi, Ahmad
2016-01-01
Unsteady flow of nanofluids squeezed between two parallel plates is discussed in the presence of viscous dissipation. Heat transfer phenomenon is disclosed via convective boundary conditions. Carbon nanotubes (single-wall and multi-wall) are used as nanoparticles which are homogeneously distributed in the base fluid (water). A system of non-linear differential equations for the flow is obtained by utilizing similarity transformations through the conservation laws. Influence of various emerging parameters on the velocity and temperature profiles are sketched graphically and discussed comprehensively. Analyses of skin fraction coefficient and Nusselt number are also elaborated numerically. It is found out that velocity is smaller for squeezing parameter in the case of multi-wall carbon nanotubes when compared with single-wall carbon nanotubes. PMID:27149208
Boundary conditions for star matter and other periodic fermionic systems
Gulminelli, F.; Furuta, T.; Juillet, O.; Leclercq, C.
2011-12-01
Bulk fermionic matter, as can be notably found in supernova matter and neutrons stars, is subject to correlations of infinite range due to the antisymmetrization of the N-body wave function, which cannot be explicitly accounted for in a practical simulation. This problem is usually addressed in condensed matter physics by means of the so-called twist averaged boundary condition method. A different ansatz based on the localized Wannier representation has been proposed in the context of antisymmetrized molecular dynamics. In this paper we work out the formal relation between the two approaches. We show that, while the two coincide when working with exact eigenstates of the N-body Hamiltonian, differences appear in the case of variational approaches, which are currently used for the description of stellar matter. Some model applications with fermionic molecular dynamics are shown.
Charged dopants in semiconductor nanowires under partially periodic boundary conditions
Chan, Tzu-Liang; Zhang, S. B.; Chelikowsky, James R.
2011-06-01
We develop a one-dimensional, periodic real-space formalism for examining the electronic structure of charged nanowires from first principles. The formalism removes spurious electrostatic interactions between charged unit cells by appropriately specifying a boundary condition for the Kohn-Sham equation. The resultant total energy of the charged system remains finite, and a Madelung-type correction is unnecessary. We demonstrate our scheme by examining the ionization energy of P-doped Si nanowires. We find that there is an effective repulsion between charged P dopants along the nanowire owing to the repulsive interaction of the induced surface charge between adjacent periodic cells. This repulsive interaction decays exponentially with unit cell size instead of a power law behavior assumed in typical charged calculations.
PERIODIC BOUNDARY CONDITION IN SIMULATION OF TURBULENT FLOW
无
2002-01-01
In this paper, the simulations of the three-di-mensional turbulent flows through hydraulic turbine compo-nents[1] were conducted based on the standard k-ε turbulentmodel with body-fitted coordinates and staggering grid sys-tem. The SIMPLEC algorithm was adopted in the numericalprocedure. A new method to treat the periodic boundary con-dition was used. The calculated results of the new methodwere compared with those of traditional ones. These resultsindicate that the new method can give much better results,and can be used in simulating flow through rotational impel-lers. The presented method can be combined with alternativeturbulent model or employed in large eddy simulation.
Dynamic behaviour of thin composite plates for different boundary conditions
In the context of composite materials technology, which is increasingly present in industry, this article covers a topic of great interest and theoretical and practical importance. Given the complex design of fiber-reinforced materials and their heterogeneous nature, mathematical modeling of the mechanical response under different external stresses is very difficult to address in the absence of simplifying assumptions. In most structural applications, composite structures can be idealized as beams, plates, or shells. The analysis is reduced from a three-dimensional elasticity problem to a oneor two-dimensional problem, based on certain simplifying assumptions that can be made because the structure is thin. This paper aims to validate a mathematical model illustrating how thin rectangular orthotropic plates respond to the actual load. Thus, from the theory of thin plates, new analytical solutions are proposed corresponding to orthotropic rectangular plates having different boundary conditions. The proposed analytical solutions are considered both for solving equation orthotropic rectangular plates and for modal analysis
`Gas cushion' model and hydrodynamic boundary conditions for superhydrophobic textures
Nizkaya, Tatiana V; Vinogradova, Olga I
2014-01-01
Superhydrophobic Cassie textures with trapped gas bubbles reduce drag, by generating large effective slip, which is important for a variety of applications that involve a manipulation of liquids at the small scale. Here we discuss how the dissipation in the gas phase of textures modifies their friction properties and effective slip. We propose an operator method, which allows us the mapping of the flow in the gas subphase to a local slip boundary condition at the liquid/gas interface. The determined uniquely local slip length depends on the viscosity contrast and underlying topography, and can be immediately used to evaluate an effective slip of the texture. Beside Cassie surfaces our approach is valid for Wenzel textures, where a liquid follows the surface relief, as well as for rough surfaces impregnated by a low-viscosity `lubricant'. These results provide a framework for the rational design of textured surfaces for numerous applications.
Casimir-Polder forces, boundary conditions and fluctuations
We review different aspects of atom-atom and atom-wall Casimir-Polder forces. We first discuss the role of a boundary condition on the interatomic Casimir-Polder potential between two ground-state atoms, and give a physically transparent interpretation of the results in terms of vacuum fluctuations and image atomic dipoles. We then discuss the known atom-wall Casimir-Polder force for ground- and excited-state atoms, using a different method which is also suited to extension to time-dependent situations. Finally, we consider the fluctuation of the Casimir-Polder force between a ground-state atom and a conducting wall, and discuss possible observation of this force fluctuation
Casimir-Polder forces, boundary conditions and fluctuations
Messina, Riccardo; Rizzuto, Lucia; Spagnolo, Salvatore; Vasile, Ruggero; 10.1088/1751-8113/41/16/164031
2012-01-01
We review different aspects of the atom-atom and atom-wall Casimir-Polder forces. We first discuss the role of a boundary condition on the interatomic Casimir-Polder potential between two ground-state atoms, and give a physically transparent interpretation of the results in terms of vacuum fluctuations and image atomic dipoles. We then discuss the known atom-wall Casimir-Polder force for ground- and excited-state atoms, using a different method which is also suited for extension to time-dependent situations. Finally, we consider the fluctuation of the Casimir-Polder force between a ground-state atom and a conducting wall, and discuss possible observation of this force fluctuation.
Boundary conditions for free surface inlet and outlet problems
Taroni, M.
2012-08-10
We investigate and compare the boundary conditions that are to be applied to free-surface problems involving inlet and outlets of Newtonian fluid, typically found in coating processes. The flux of fluid is a priori known at an inlet, but unknown at an outlet, where it is governed by the local behaviour near the film-forming meniscus. In the limit of vanishing capillary number Ca it is well known that the flux scales with Ca 2/3, but this classical result is non-uniform as the contact angle approaches π. By examining this limit we find a solution that is uniformly valid for all contact angles. Furthermore, by considering the far-field behaviour of the free surface we show that there exists a critical capillary number above which the problem at an inlet becomes over-determined. The implications of this result for the modelling of coating flows are discussed. © 2012 Cambridge University Press.
Behavior of the reversed field pinch with nonideal boundary conditions
The linear and nonlinear magnetohydrodynamic stability of current-driven modes are studied for a reversed field pinch with nonideal boundary conditions. The plasma is bounded by a thin resistive shell surrounded by a vacuum region out to a radius at which a perfectly conducting wall is situated. The distant wall and the thin shell problems are studied by removing either the resistive shell or the conducting wall. Linearly, growth rates of tearing modes and kink modes are calculated by analytical solutions based on the modified Bessel function model for the equilibrium. The effects of variation of the shell resistivity and wall proximity on the growth rates are investigated. The modes that may be important in different parameter regimes and with different boundary conditions are identified. The nonlinear behaviors are studied with a three-dimensional magnetohydrodynamics code. The fluctuations generally rise with increasing distance between the conducting wall and the plasma. The enhanced fluctuation induced v x b electric field primarily oppose toroidal current; hence, loop voltage must increase to sustain the constant. Quasilinear interaction between modes typically associated with the dynamo action is identified as the most probable nonlinear destabilization mechanism. The helicity and energy balance properties of the simulation results are discussed. The interruption of current density along field lines intersecting the resistive shell is shown to lead to surface helicity leakage. This effect is intimately tied to stability, as fluctuation induced v x b electric field is necessary to transport the helicity to the surface. In this manner, all aspects of helicity balance, i.e., injection, transport, and dissipation, are considered self-consistently. The importance of the helicity and energy dissipation by the mean components of the magnetic field and current density is discussed. 88 refs., 41 figs., 3 tabs
A Study of the Navier-Stokes Equations with the Kinematic and Navier Boundary Conditions
Chen, Gui-Qiang; Qian, Zhongmin
2008-01-01
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in $\\R^3$ with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the Navier boundary condition in terms of the vorticity, which is motivated by the Hodge theory on manifolds with boundary from the viewpoint of differential geometry, and establish basic elliptic estimates for vector fields subject to the kinematic and Navier b...
Bhattacharyya, S. K.; Premkumar, R.
2003-12-01
In a domain method of solution of exterior scalar wave equation, the radiation condition needs to be imposed on a truncation boundary of the modeling domain. The Bayliss, Gunzberger, and Turkel (BGT) boundary dampers, which require a circular cylindrical and spherical truncation boundaries in two-(2D) and three-(3D)-dimensional problems, respectively, have been particularly successful in the analysis of scattering and radiation problems. However, for an elongated body, elliptical (2D) or spheroidal (3D) truncation boundaries have potential to reduce the size of modeling domain and hence computational effort. For harmonic problems, such extensions of the first- and second-order BGT dampers are available in the literature. In this paper, BGT dampers in both elliptical and spheroidal coordinate systems have been developed for transient problems involving acoustic radiation as well as fluid-structure interaction and implemented in the context of finite-element method based upon unsymmetric pressure-displacement formulation. Applications to elongated radiators and shells are reported using several numerical examples with excellent comparisons. It is demonstrated that significant computational economy can be achieved for elongated bodies with the use of these dampers.
MITHUN V. KULKARNI
2016-01-01
Full Text Available The friction and wear properties of polyamide 6 (PA6 and poly-Acrylonitrile Butadiene Styrene (ABS sliding against metal under dry sliding, water absorption and electroplated (EP conditions were studied by using a pin-ondisc tribometer. The effect of applied load and sliding speed on the tribological behaviours of the polymer–metal sliding combinations under dry sliding, water absorbed and EP conditions were also investigated. The worn surfaces were examined by using Scanning Electron Microscope (SEM. Experimental results showed that ABS samples under water absorbed conditions showed higher wear loss compared to normal samples and the EP samples had exhibited lower wear loss compared to the water absorbed samples. Similarly EP-PA6 samples exhibited excellent wear resistance when compared with EP-ABS samples. Further, it was observed that the frictional heat produced on account of sliding action had a significant effect on the tribological behaviours of samples under dry sliding and water absorbed conditions.
Sirenko, Kostyantyn
2011-01-01
An accurate and efficient finite-difference time-domain (FDTD) method for characterizing transient waves interactions on axially symmetric structures is presented. The method achieves its accuracy and efficiency by employing localized and/or fast Fourier transform (FFT) accelerated exact absorbing conditions (EACs). The paper details the derivation of the EACs, discusses their implementation and discretization in an FDTD method, and proposes utilization of a blocked-FFT based algorithm for accelerating the computation of temporal convolutions present in nonlocal EACs. The proposed method allows transient analyses to be carried for long time intervals without any loss of accuracy and provides reliable numerical data pertinent to physical processes under resonant conditions. This renders the method highly useful in characterization of high-Q microwave radiators and energy compressors. Numerical results that demonstrate the accuracy and efficiency of the method are presented.
Experimentally constraining the boundary conditions for volcanic ash aggregation
Kueppers, U.; Auer, B.; Cimarelli, C.; Scolamacchia, T.; Guenthel, M.; Dingwell, D. B.
2011-12-01
Volcanic ash is the primary product of various volcanic processes. Due to its size, ash can remain in the atmosphere for a prolonged period of time. Aggregation processes are a first-order influence on the residence time of ash in the atmosphere and its dispersion from the vent. Due to their internal structure, ash aggregates have been classified as ash pellets or accretionary lapilli. Although several concomitant factors may play a role during aggregation, there is a broad consensus that both 1) particle collision and 2) humidity are required for particles to aggregate. However, direct observation of settling aggregates and record of the boundary conditions favourable to their formation are rare, therefore limiting our understanding of the key processes that determine ash aggregates formation. Here, we present the first results from experiments aimed at reproducing ash aggregation by constraining the required boundary conditions. We used a ProCell Lab System of Glatt Ingenieurtechnik GmbH that is conventionally used for food and chemical applications. We varied the following parameters: 1) air flow speed [40-120 m3/h], 2) air temperature [30-60°C], 3) relative humidity [20-50 %], and 4) liquid droplets composition [water and 25% water glass, Na2SiO3]. The starting material (125-90 μm) is obtained by milling natural basaltic lapilli (Etna, Italy). We found that the experimental duration and the chosen conditions were not favourable for the production of stable aggregates when using water as spraying liquid. Using a 25% water-glass solution as binder we could successfully generate and investigate aggregates of up to 2 mm size. Many aggregates are spherical and resemble ash pellets. In nature, ash pellets and accretionary lapilli are the product of complex processes taking place at very different conditions (temperature, humidity, ash concentration, degree of turbulence). These experiments shed some first light on the ash agglomeration process for which direct
The height of the atmospheric boundary layer during unstable conditions
Gryning, S.E.
2005-11-01
The height of the convective atmospheric boundary layer, also called the mixed-layer, is one of the fundamental parameters that characterise the structure of the atmosphere near the ground. It has many theoretical and practical applications such as the prediction of air pollution concentrations, surface temperature and the scaling of turbulence. However, as pointed out by Builtjes (2001) in a review paper on Major Twentieth Century Milestones in Air Pollution Modelling and Its Application, the weakest point in meteorology data is still the determination of the height of the mixed-layer, the so-called mixing height. A simple applied model for the height of the mixed-layer over homogeneous terrain is suggested in chapter 2. It is based on a parameterised budget for the turbulent kinetic energy. In the model basically three terms - the spin-up term and the production of mechanical and convective turbulent kinetic energy - control the growth of the mixed layer. The interplay between the three terms is related to the meteorological conditions and the height of the mixed layer. A stable layer, the so-called entrainment zone, which is confined between the mixed layer and the free air above, caps the mixed layer. A parameterisation of the depth of the entrainment zone is also suggested, and used to devise a combined model for the height of the mixed layer and the entrainment zone. Another important aspect of the mixed layer development exists in coastal areas where an internal boundary layer forms downwind from the coastline. A model for the growth of the internal boundary layer is developed in analogy with the model for mixed layer development over homogeneous terrain. The strength of this model is that it can operate on a very fine spatial resolution with minor computer resources. Chapter 3 deals with the validation of the models. It is based in parts on data from the literature, and on own measurements. For the validation of the formation of the internal boundary layer
Solvability of a fourth order boundary value problem with periodic boundary conditions
Chaitan P. Gupta
1988-01-01
Fourth order boundary value problems arise in the study of the equilibrium of an elastaic beam under an external load. The author earlier investigated the existence and uniqueness of the solutions of the nonlinear analogues of fourth order boundary value problems that arise in the equilibrium of an elastic beam depending on how the ends of the beam are supported. This paper concerns the existence and uniqueness of solutions of the fourth order boundary value problems with periodic boundary co...
DYNAMIC SURFACE BOUNDARY-CONDITIONS - A SIMPLE BOUNDARY MODEL FOR MOLECULAR-DYNAMICS SIMULATIONS
JUFFER, AH; BERENDSEN, HJC
1993-01-01
A simple model for the treatment of boundaries in molecular dynamics simulations is presented. The method involves the positioning of boundary atoms on a surface that surrounds a system of interest. The boundary atoms interact with the inner region and represent the effect of atoms outside the surfa
Sensitivity of African easterly waves to boundary layer conditions
A. Lenouo
2008-06-01
Full Text Available 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 gradient of perturbation stream function and the other assumes zero wind perturbation at the surface. The first case gives more realistic results since in the absence of horizontal diffusion, growth rate, phase speed and period have values of 0.5 day^{−1}, 10.83 m s^{−1} and 3.1 day, respectively. The zero wind perturbation at the surface case leads to values of these parameters that are 50 percent lower. The analysis of the sensitivity to diffusion shows that the magnitude of the growth rate decreases with this parameter. Modelled total relative vorticity has its low level maximum around 900 hPa under no-slip, and 700 hPa under free slip condition.
Sensitivity of African easterly waves to boundary layer conditions
Lenouo, A. [Douala Univ. (Cameroon). Dept. of Physics; Mkankam Kamga, F. [Yaounde I Univ. (Cameroon). LEMAP, Dept. of Physics
2008-07-01
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 gradient of perturbation stream function and the other assumes zero wind perturbation at the surface. The first case gives more realistic results since in the absence of horizontal diffusion, growth rate, phase speed and period have values of 0.5 day{sup -1}, 10.83 m s{sup -1} and 3.1 day, respectively. The zero wind perturbation at the surface case leads to values of these parameters that are 50 percent lower. The analysis of the sensitivity to diffusion shows that the magnitude of the growth rate decreases with this parameter. Modelled total relative vorticity has its low level maximum around 900 hPa under no-slip, and 700 hPa under free slip condition. (orig.)
Reconstructing geographical boundary conditions for palaeoclimate modelling during the Cenozoic
Baatsen, Michiel; van Hinsbergen, Douwe J. J.; von der Heydt, Anna S.; Dijkstra, Henk A.; Sluijs, Appy; Abels, Hemmo A.; Bijl, Peter K.
2016-08-01
Studies on the palaeoclimate and palaeoceanography using numerical model simulations may be considerably dependent on the implemented geographical reconstruction. Because building the palaeogeographic datasets for these models is often a time-consuming and elaborate exercise, palaeoclimate models frequently use reconstructions in which the latest state-of-the-art plate tectonic reconstructions, palaeotopography and -bathymetry, or vegetation have not yet been incorporated. In this paper, we therefore provide a new method to efficiently generate a global geographical reconstruction for the middle-late Eocene. The generalised procedure is also reusable to create reconstructions for other time slices within the Cenozoic, suitable for palaeoclimate modelling. We use a plate-tectonic model to make global masks containing the distribution of land, continental shelves, shallow basins and deep ocean. The use of depth-age relationships for oceanic crust together with adjusted present-day topography gives a first estimate of the global geography at a chosen time frame. This estimate subsequently needs manual editing of areas where existing geological data indicate that the altimetry has changed significantly over time. Certain generic changes (e.g. lowering mountain ranges) can be made relatively easily by defining a set of masks while other features may require a more specific treatment. Since the discussion regarding many of these regions is still ongoing, it is crucial to make it easy for changes to be incorporated without having to redo the entire procedure. In this manner, a complete reconstruction can be made that suffices as a boundary condition for numerical models with a limited effort. This facilitates the interaction between experts in geology and palaeoclimate modelling, keeping reconstructions up to date and improving the consistency between different studies. Moreover, it facilitates model inter-comparison studies and sensitivity tests regarding certain
Shroud boundary condition characterization experiments at the Radiant Heat Facility.
Suo-Anttila, Jill Marie; Nakos, James Thomas; Gill, Walter
2004-10-01
A series of experiments was performed to better characterize the boundary conditions from an inconel heat source ('shroud') painted with Pyromark black paint. Quantifying uncertainties in this type of experimental setup is crucial to providing information for comparisons with code predictions. The characterization of this boundary condition has applications in many scenarios related to fire simulation experiments performed at Sandia National Laboratories Radiant Heat Facility (RHF). Four phases of experiments were performed. Phase 1 results showed that a nominal 1000 C shroud temperature is repeatable to about 2 C. Repeatability of temperatures at individual points on the shroud show that temperatures do not vary more than 10 C from experiment to experiment. This variation results in a 6% difference in heat flux to a target 4 inches away. IR camera images showed the shroud was not at a uniform temperature, although the control temperature was constant to about {+-}2 C during a test. These images showed that a circular shaped, flat shroud with its edges supported by an insulated plate has a temperature distribution with higher temperatures at the edges and lower temperatures in the center. Differences between the center and edge temperatures were up to 75 C. Phase 3 results showed that thermocouple (TC) bias errors are affected by coupling with the surrounding environment. The magnitude of TC error depends on the environment facing the TC. Phase 4 results were used to estimate correction factors for specific applications (40 and 63-mil diameter, ungrounded junction, mineral insulated, metal-sheathed TCs facing a cold surface). Correction factors of about 3.0-4.5% are recommended for 40 mil diameter TCs and 5.5-7.0% for 63 mil diameter TCs. When mounted on the cold side of the shroud, TCs read lower than the 'true' shroud temperature, and the TC reads high when on the hot side. An alternate method uses the average of a cold side and hot side TC of
On Consistent Boundary Conditions for c=1 String Theory
O'Loughlin, Martin
1995-01-01
We introduce a new parametrisation for the Fermi sea of the $c = 1$ matrix model. This leads to a simple derivation of the scattering matrix, and a calculation of boundary corrections in the corresponding $1+1$--dimensional string theory. The new parametrisation involves relativistic chiral fields, rather than the non-relativistic fields of the usual formulations. The calculation of the boundary corrections, following recent work of Polchinski, allows us to place restrictions on the boundary ...
Influence of absorbers on the reactivity of the reactor
Influence of absorbers on the reactivity of the reactor was calculated by two-group diffusion theory applying corrections for boundary conditions derived from the transport theory because diffusion theory in not applicable in the vicinity of boundary surfaces especially in case of strong absorbers. This report shows the calculations of central absorber efficiency in the core with and without reflector, and efficiency of the group of absorbers randomly placed in the core. Approximation method for determining the efficiency of the absorber is described as well as numerical verification of results. Effective absorber dimensions and the influence of gaps on the reactor dimensions are shown
Nahed S. Hussein
2014-01-01
Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.
The reflection equation algebra of Sklyanin is extended to the supersymmetric case. A graded reflection equation algebra is proposed and the corresponding graded (supersymmetric) boundary quantum inverse scattering method (QISM) is formulated. As an application, integrable open-boundary conditions for the doped spin-1 chain of the supersymmetric t-J model are studied in the framework of the boundary QISM. Diagonal boundary K-matrices are found and four classes of integrable boundary terms are determined. (author)
Ntouyas SotirisK
2011-01-01
Full Text Available This paper studies a boundary value problem of nonlinear fractional differential equations of order with three-point integral boundary conditions. Some new existence and uniqueness results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Our results are new in the sense that the nonlocal parameter in three-point integral boundary conditions appears in the integral part of the conditions in contrast to the available literature on three-point boundary value problems which deals with the three-point boundary conditions restrictions on the solution or gradient of the solution of the problem. Some illustrative examples are also discussed.
Viscous-fingering experiments with periodic boundary conditions
Zhao, H.; Maher, J.V. (Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA (USA))
1990-11-15
Experimental realization of a Hele-Shaw cell with periodic boundary conditions (PBC's) is achieved by building an azimuthal cell with two coaxial cylinders separated by a small gap. The development of viscous-fingering patterns formed by a critical binary liquid mixture at very low viscosity contrast has been observed and recorded from the onset of instability to very late stages. Comparison with the experimental results measured in cells which have sidewalls shows that PBC's yield few differences of results. At the early stage there is no sidewall disturbance so the Fourier transforms show less noise in the low-wave-number modes. Because the annular cell is larger than the earlier cells, it was possible to follow the flow to a very late nonlinear stage where, instead of showing steadily lengthening and broadening fingers, the necks of the longer fingers, crowded by fattening bulbs of the tips of the less-long fingers, constrict until their width is no longer negligible in comparison to the cell gap, at which point the pattern breaks up into a rich variety of bubbles.
On stochastic inlet boundary condition for unsteady simulations
Niedoba, P.; Jícha, M.; Čermák, L.
2014-03-01
The paper deals with the stochastic generation of synthesized turbulence, which may be used for a generating of an inlet boundary condition for unsteady simulations, e.g. Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES). Assumptions for the generated turbulence are isotropy and homogeneity. The described method produces a stochastic turbulent velocity field using the synthesis of a finite sum of random Fourier modes. The calculation of individual Fourier modes is based on known energy spectrum of turbulent flow, and some turbulent quantities, e.g. turbulent kinetic energy and turbulent dissipation rate. A division of wave number range of the energy spectrum determines directly the number of Fourier modes, and has a direct impact on accuracy and speed of this calculation. Therefore, this work will examine the influence of the number of Fourier modes on a conservation of the first and second statistical moments of turbulent velocity components, which are prespecified. It is important to ensure a sufficient size of a computational domain, and a sufficient number of cells for meaningful comparative results. Dimensionless parameters characterizing the resolution and size of the computational domain according to a turbulent length scale will be introduced for this purpose. Subsequently, the sufficient values of this parameters will be shown for individual numbers of Fourier modes.
Optimum conditions for preparation of flue gas desulfurization absorbent from rice husk ash
Keat Teong Lee; Atikah Matlina Mohtar; Nor Fatiha Zainudin; Subhash Bhatia; Abdul Rahman Mohamed [Universiti Sains Malaysia, Penang (Malaysia). School of Chemical Engineering
2005-02-01
Several previous studies have reported the preparation of absorbents from coal fly ash variations as a source of siliceous material for the preparation of absorbents for flue gas desulfurization. On the other hand, this study presents findings from an experimental investigation of the preparation of absorbents from rice husk ash as the source of the siliceous material. The effect of various absorbent preparation variables such as hydration period, amount of rice husk ash, amount of calcium sulfate (CaSO{sub 4}) and hydration temperature on the BET (Brunner-Emmett-Teller) specific surface area of the absorbent were investigated. Based on the Central Composite Design (CCD) of experiments, a third order mathematical model was developed to correlate the absorbent preparation variables to the surface area of the absorbent. The predicted surface area was found to agree satisfactory with the experimental values. The model indicated that lower hydration period and temperature favor the formation of absorbent with higher surface area. Sulfation activity test on the absorbent revealed that the absorbent prepared from rice husk ash does have a high capacity in sulfur dioxide (SO{sub 2}) absorption. 19 refs., 7 figs., 6 tabs.
Aufgebauer, Britta; Kluemper, Andreas
2010-01-01
We determine the spectra of a class of quantum spin chains of Temperley-Lieb type by utilizing the concept of Temperley-Lieb equivalence with the S=1/2 XXZ chain as a reference system. We consider open boundary conditions and in particular periodic boundary conditions. For both types of boundaries the identification with XXZ spectra is performed within isomorphic representations of the underlying Temperley-Lieb algebra. For open boundaries the spectra of these models differ from the spectrum ...
Preliminary work on vacuum boundary conditions for the MARC Transport Theory Code
The treatment of vacuum boundaries in neutron transport theory is considered. Using an expansion of the flux in Legendre polynominals equations are derived for the one-dimensional monoenergetic case. Flux behaviour at the vacuum boundary is modelled in two ways, (a) by the addition of black absorber at the surface to simulate no incoming flux, (b) by setting the boundary flux to zero at selected inward directions. Using a small computer code a slab test case is solved by a finite difference formulation and a semi-analytic method. The results obtained show that (a) and (b) are equivalent and also give some indication of mesh size effects. (author)
Reactive Boundary Conditions as Limits of Interaction Potentials for Brownian and Langevin Dynamics
Chapman, S Jonathan; Isaacson, Samuel A
2015-01-01
A popular approach to modeling bimolecular reactions between diffusing molecules is through the use of reactive boundary conditions. One common model is the Smoluchowski partial absorption condition, which uses a Robin boundary condition in the separation coordinate between two possible reactants. This boundary condition can be interpreted as an idealization of a reactive interaction potential model, in which a potential barrier must be surmounted before reactions can occur. In this work we show how the reactive boundary condition arises as the limit of an interaction potential encoding a steep barrier within a shrinking region in the particle separation, where molecules react instantly upon reaching the peak of the barrier. The limiting boundary condition is derived by the method of matched asymptotic expansions, and shown to depend critically on the relative rate of increase of the barrier height as the width of the potential is decreased. Limiting boundary conditions for the same interaction potential in b...
Periodic sedimentation of three particles in periodic boundary conditions
Solutions of the equations of Stokesian dynamics for point particles are found for periodic boundary conditions with three particles per unit cell of a simple cubic lattice. Two particles per cell move with equal velocity, but three particles per cell usually lead to irregular motion. Special situations are of interest, where initially the distance vector of one pair is parallel to one of the horizontal axes of the cubic lattice and the members of this pair are at equal distance to the third particle. By symmetry the configuration keeps this character during the motion, and numerically the motion is found to be periodic. In our numerical work we have studied mostly the case where the initial triangle is horizontal and equilateral. We have shown that the periodic motion is neutrally stable for sizes of the initial triangle less than the critical size. Such stable solutions of the equations of Stokesian dynamics are of relevance to the theory of sedimentation. In these solutions the particles move coherently in a complicated fashion with the same mean sedimentation velocity and a periodic internal motion of the three-particle cluster. If initially the particles are sufficiently widely separated, but the motion is still stable, the mean sedimentation velocity is less than that of a single particle. In this case the solution describes a situation of hindered settling. If the initial triangle is too large, with the side length larger than the critical size, the two base particles team up with partners in neighboring cells, and we get separate motion of a base pair and a single particle with different mean vertical velocities and with periodic motions superimposed. The columns of horizontal pairs pass the columns of apex particles. The corresponding solutions are unstable. (author)
The linking number in systems with Periodic Boundary Conditions
Panagiotou, E.
2015-11-01
Periodic Boundary Conditions (PBC) are often used for the simulation of complex physical systems. Using the Gauss linking number, we define the periodic linking number as a measure of entanglement for two oriented curves in a system employing PBC. In the case of closed chains in PBC, the periodic linking number is an integer topological invariant that depends on a finite number of components in the periodic system. For open chains, the periodic linking number is an infinite series that accounts for all the topological interactions in the periodic system. In this paper we give a rigorous proof that the periodic linking number is defined for the infinite system, i.e., that it converges for one, two, and three PBC models. It gives a real number that varies continuously with the configuration and gives a global measure of the geometric complexity of the system of chains. Similarly, for a single oriented chain, we define the periodic self-linking number and prove that it also is defined for open chains. In addition, we define the cell periodic linking and self-linking numbers giving localizations of the periodic linking numbers. These can be used to give good estimates of the periodic linking numbers in infinite systems. We also define the local periodic linking number associated to chains in the immediate cell neighborhood of a chain in order to study local linking measures in contrast to the global linking measured by the periodic linking numbers. Finally, we study and compare these measures when applied to a PBC model of polyethylene melts.
Boundary-value problems for x-analytical functions with weighted boundary conditions
Kapshivyi, A.A. [Kiev Univ. (Ukraine)
1994-11-10
We consider boundary-value problems for x-analytical functions of a complex variable z = x + iy in a number of domains. Limit values with the weight (ln x){sup {minus}1} are given for the real part of the x-analytical function on the sections of the boundary that follow the imaginary axis, and simple limits are given for the real part of the x-analytical functions on the part of the boundary outside the imaginary axis. The apparatus of integral representations of x-analytical functions is applied to obtain a solution of the problem in quadratures.
Casimir Force of Piston Systems with Arbitrary Cross Sections under Different Boundary Conditions
XIONG Ai-Min; CHEN Xiao-Song
2009-01-01
We study the Casimir force between two pistons under different boundary conditions inside an infinite cylinder with arbitrary cross section.It is found that the attractive or repulsive character of the Casimir force for a scalar field is determined only by the boundary condition along the longitudinal direction and is independent of the cross section,transverse boundary conditions and the mass of the field.Under symmetric Dirichlet-Dirichlet,Neumann-Neumann and periodic longitudinal boundary conditions the Casimir force is always attractive,but is repulsive under non-symmetric Dirichlet-Neumann and anti-periodic longitudinal boundary conditions.The Casimir force of the electromagnetic field in an ideal conductive piston is also investigated.This force is always attractive regardless of the shape of the cross section and the transverse boundary conditions.
A device adaptive inflow boundary condition for Wigner equations of quantum transport
Jiang, Haiyan [Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081 (China); Lu, Tiao [HEDPS and CAPT, LMAM and School of Mathematical Sciences, Peking University, Beijing 100871 (China); Cai, Wei, E-mail: wcai@uncc.edu [Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223-0001 (United States)
2014-02-01
In this paper, an improved inflow boundary condition is proposed for Wigner equations in simulating a resonant tunneling diode (RTD), which takes into consideration the band structure of the device. The original Frensley inflow boundary condition prescribes the Wigner distribution function at the device boundary to be the semi-classical Fermi–Dirac distribution for free electrons in the device contacts without considering the effect of the quantum interaction inside the quantum device. The proposed device adaptive inflow boundary condition includes this effect by assigning the Wigner distribution to the value obtained from the Wigner transform of wave functions inside the device at zero external bias voltage, thus including the dominant effect on the electron distribution in the contacts due to the device internal band energy profile. Numerical results on computing the electron density inside the RTD under various incident waves and non-zero bias conditions show much improvement by the new boundary condition over the traditional Frensley inflow boundary condition.
The formulation of gauge-Higgs unification with dynamical boundary conditions
Yamamoto, Kengo
2014-01-01
The boundary conditions on multiply connected extra dimensions play a major rolls 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 condition, we construct a gauge-Higgs unification formulation with dynamics of boundary conditions on M^4 times S^1/Z_2. As a result, it is found that certain sets of boundary conditions which lead to nontrivial symmetry breaking practically contribute to the partition function. In particular, we show that for SU(5) gauge group, sets of boundary conditions which lead to SU(5) to SU(3) times SU(2) times U(1) symmetry breaking are naturally selected.
Richards, H.L.; Kolesik, M.; Lindgård, P.-A.;
1997-01-01
Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with periodic boundary conditions. In this paper we consider the...... the existence of a peak in the switching field as a function of system size in both systems with periodic boundary conditions and in systems with boundaries. The size of the peak is strongly dependent on the boundary effects. It is generally reduced by open boundary conditions, and in some cases it...... effects of boundary conditions od the switching phenomena. A rich range of behaviors is predicted by droplet theory: the specific mechanism by which switching occurs depends on the structure of the boundary, the particle size, the temperature, and the strength of the: applied field. The theory predicts...
Wittenberg, Ralf W.
2008-01-01
We investigate the influence of the thermal properties of the boundaries in turbulent Rayleigh-Benard convection on analytical bounds on convective heat transport. Using the Doering-Constantin background flow method, we systematically formulate a bounding principle on the Nusselt-Rayleigh number relationship for general mixed thermal boundary conditions of constant Biot number \\eta which continuously interpolates between the previously studied fixed temperature ($\\eta = 0$) and fixed flux ($\\...
Towards a generic non-reflective characteristic boundary condition for aeroacoustic simulations
Fattah, Ryu; Gill, James; Zhang, Xin
2016-01-01
A blended zonal characteristic boundary condition is proposed following a quantita- tive investigation of the performance of several non-reflective boundary conditions. Two test cases are considered that investigate the effects of acoustic and vortical plane waves impinging on the domain outflow region. A third test case investigates the effects of broad- band turbulent flow impinging on a non-reflective outflow boundary condition. From these studies, two non-reflective boundar...
Exner, Pavel; Stovicek, Pavel; Vytras, Petr
2001-01-01
The most general admissible boundary conditions are derived for an idealised Aharonov-Bohm flux intersecting the plane at the origin on the background of a homogeneous magnetic field. A standard technique based on self-adjoint extensions yields a four-parameter family of boundary conditions; other two parameters of the model are the Aharonov-Bohm flux and the homogeneous magnetic field. The generalised boundary conditions may be regarded as a combination of the Aharonov-Bohm effect with a poi...
Monotone iterative technique for fractional differential equations with periodic boundary conditions
J. D. Ramírez
2009-01-01
Full Text Available In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary conditions in the weighted norm.
Sliding periodic boundary conditions for lattice Boltzmann and lattice kinetic equations
Adhikari, R.; Desplat, J. -C.; Stratford, K.
2005-01-01
We present a method to impose linear shear flow in discrete-velocity kinetic models of hydrodynamics through the use of sliding periodic boundary conditions. Our method is derived by an explicit coarse-graining of the Lees-Edwards boundary conditions for Couette flow in molecular dynamics, followed by a projection of the resulting equations onto the subspace spanned by the discrete velocities of the lattice Boltzmann method. The boundary conditions are obtained without resort to perturbative ...
DOBSON, Matthew
2014-01-01
This work presents a generalization of the Kraynik-Reinelt (KR) boundary conditions for nonequilibrium molecular dynamics simulations. In the simulation of steady, homogeneous flows with periodic boundary conditions, the simulation box moves with the flow, and it is possible for particle replicas to become arbitrarily close, causing a breakdown in the simulation. The KR boundary conditions avoid this problem for planar elongational flow and general planar mixed flow [J. Chem. Phys 133, 14116 ...
Revisit boundary conditions for the self-adjoint angular flux formulation
Wang, Yaqi [Idaho National Lab. (INL), Idaho Falls, ID (United States); Gleicher, Frederick N. [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-03-01
We revisit the boundary conditions for SAAF. We derived the equivalent parity variational form ready for coding up. The more rigorous approach of evaluating odd parity should be solving the odd parity equation coupled with the even parity. We proposed a symmetric reflecting boundary condition although neither positive definiteness nor even-odd decoupling is achieved. A simple numerical test verifies the validity of these boundary conditions.
RADIATION BOUNDARY CONDITIONS FOR MAXWELL'S EQUATIONS: A REVIEW OF ACCURATE TIME-DOMAIN FORMULATIONS
Thomas Hagstrom; Stephen Lau
2007-01-01
We review time-domain formulations of radiation boundary conditions for Maxwell's equations, focusing on methods which can deliver arbitrary accuracy at acceptable computational cost. Examples include fast evaluations of nonlocal conditions on symmetric and general boundaries, methods based on identifying and evaluating equivalent sources, and local approximations such as the perfectly matched layer and sequences of local boundary conditions. Complexity estimates are derived to assess work and storage requirements as a function of wavelength and simulation time.
On the impact of boundary conditions on dual consistent finite difference discretizations
Berg, Jens; Nordström, Jan
2013-01-01
In this paper we derive well-posed boundary conditions for a linear incompletely parabolic system of equations, which can be viewed as a model problem for the compressible Navier{Stokes equations. We show a general procedure for the construction of the boundary conditions such that both the primal and dual equations are wellposed. The form of the boundary conditions is chosen such that reduction to rst order form with its complications can be avoided. The primal equation is discretized using ...
Study on the thermal boundary conditions in DNS of the free-surface turbulent flow
This paper describes thermal boundary conditions in Direct Numerical Simulation (DNS) of an open-channel turbulent flow heated at constant heat flux from the tree-surface. Numerical calculations were carried out in three thermal boundary conditions. And about the adequate thermal condition at the free-surface, revealed and discussed. (author)
Conditions at the downstream boundary for simulations of viscous incompressible flow
Hagstrom, Thomas
1990-01-01
The proper specification of boundary conditions at artificial boundaries for the simulation of time-dependent fluid flows has long been a matter of controversy. A general theory of asymptotic boundary conditions for dissipative waves is applied to the design of simple, accurate conditions at downstream boundary for incompressible flows. For Reynolds numbers far enough below the critical value for linear stability, a scaling is introduced which greatly simplifies the construction of the asymptotic conditions. Numerical experiments with the nonlinear dynamics of vortical disturbances to plane Poiseuille flow are presented which illustrate the accuracy of our approach. The consequences of directly applying the scalings to the equations are also considered.
Periodic Time-Domain Nonlocal Nonreflecting Boundary Conditions for Duct Acoustics
Watson, Willie R.; Zorumski, William E.
1996-01-01
Periodic time-domain boundary conditions are formulated for direct numerical simulation of acoustic waves in ducts without flow. Well-developed frequency-domain boundary conditions are transformed into the time domain. The formulation is presented here in one space dimension and time; however, this formulation has an advantage in that its extension to variable-area, higher dimensional, and acoustically treated ducts is rigorous and straightforward. The boundary condition simulates a nonreflecting wave field in an infinite uniform duct and is implemented by impulse-response operators that are applied at the boundary of the computational domain. These operators are generated by convolution integrals of the corresponding frequency-domain operators. The acoustic solution is obtained by advancing the Euler equations to a periodic state with the MacCormack scheme. The MacCormack scheme utilizes the boundary condition to limit the computational space and preserve the radiation boundary condition. The success of the boundary condition is attributed to the fact that it is nonreflecting to periodic acoustic waves. In addition, transient waves can pass rapidly out of the solution domain. The boundary condition is tested for a pure tone and a multitone source in a linear setting. The effects of various initial conditions are assessed. Computational solutions with the boundary condition are consistent with the known solutions for nonreflecting wave fields in an infinite uniform duct.
Boundary conditions control for a Shallow-Water model
Kazantsev, Eugene
2012-01-01
A variational data assimilation technique was used to estimate optimal discretization of interpolation operators and derivatives in the nodes adjacent to the rigid boundary. Assimilation of artificially generated observational data in the shallow-water model in a square box and assimilation of real observations in the model of the Black sea are discussed. It is shown in both experiments that controlling the discretization of operators near a rigid boundary can bring the model solution closer to observations as in the assimilation window and beyond the window. This type of control allows also to improve climatic variability of the model.
The impact of boundary conditions on CO2 capacity estimation in aquifers
Smith, D.J.; Bentham, M.; Holloway, S.; Noy, D.J.; Chadwick, R.A.
2010-01-01
The boundary conditions of an aquifer determine the extent to which fluids (including formation water and CO2) and pressure can be transferred into adjacent geological formations, either laterally or vertically. Aquifer boundaries can be faults, lithological boundaries, formation pinch-outs, salt walls, or outcrop. In many cases compliance with regulations preventing CO2 storage influencing areas outside artificial boundaries defined by non-geological criteria (international bound...
Borjan, Z.
2016-09-01
We consider critical Casimir force in the Ising strips with boundary conditions defined by standard normal and ordinary surface universality classes containing also the internal grain boundary. Using exact variational approach of Mikheev and Fisher we have elaborated on behaviors of Casimir amplitudes Δ++(g) , ΔOO(g) and Δ+O(g) , corresponding to normal-normal, ordinary-ordinary and mixed normal-ordinary boundary conditions, respectively, with g as a strength of the grain boundary. Closed analytic results describe Casimir amplitudes Δ++(g) and ΔOO(g) as continuous functions of the grain boundary's strength g, changing the character of the Casimir force from repulsive to attractive and vice versa for certain domains of g. Present results reveal a new type of symmetry between Casimir amplitudes Δ++(g) and ΔOO(g) . Unexpectedly simple constant result for the Casimir amplitude Δ+O(g) = π/12 we have comprehensively interpreted in terms of equilibrium states of the present Ising strip as a complex interacting system comprising two sub-systems. Short-distance expansions of energy density profiles in the vicinity of the grain boundary reveal new distant-wall correction amplitudes that we examined in detail. Analogy of present considerations with earlier more usual short-distance expansions near one of the (N), (O) and (SB) boundaries, as well as close to surfaces with variable boundary conditions refers to the set of scaling dimensions appearing in the present calculations but also to the discovery of the de Gennes-Fisher distant wall correction amplitudes.
Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2014-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2015-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Green's function of a heat problem with a periodic boundary condition
Erzhanov, Nurzhan E.
2016-08-01
In the paper, a nonlocal initial-boundary value problem for a non-homogeneous one-dimensional heat equation is considered. The domain under consideration is a rectangle. The classical initial condition with respect to t is put. A nonlocal periodic boundary condition by a spatial variable x is put. It is well-known that a solution of problem can be constructed in the form of convergent orthonormal series according to eigenfunctions of a spectral problem for an operator of multiple differentiation with periodic boundary conditions. Therefore Green's function can be also written in the form of an infinite series with respect to trigonometric functions (Fourier series). For classical first and second initial-boundary value problems there also exists a second representation of the Green's function by Jacobi function. In this paper we find the representation of the Green's function of the nonlocal initial-boundary value problem with periodic boundary conditions in the form of series according to exponents.
We introduce a set of constraint preserving boundary conditions for the Baumgarte–Shapiro–Shibata–Nakamura formulation of the Einstein evolution equations in spherical symmetry, based on its hyperbolic structure. While the outgoing eigenfields are left to propagate freely off the numerical grid, boundary conditions are set to enforce that the incoming eigenfields don't introduce spurious reflections and, more importantly, that there are no fields introduced at the boundary that violate the constraint equations. In order to do this we adopt two different approaches to set boundary conditions for the extrinsic curvature, by expressing either the radial or the time derivative of its associated ingoing eigenfield in terms of the constraints. We find that these boundary conditions are very robust in practice, allowing us to perform long lasting evolutions that remain accurate and stable, and that converge to a solution that satisfies the constraints all the way to the boundary. (paper)
Experimental verification of free-space singular boundary conditions in an invisibility cloak
Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Chen, Huanyang; Zhang, Baile
2016-04-01
A major issue in invisibility cloaking, which caused intense mathematical discussions in the past few years but still remains physically elusive, is the plausible singular boundary conditions associated with the singular metamaterials at the inner boundary of an invisibility cloak. The perfect cloaking phenomenon, as originally proposed by Pendry et al for electromagnetic waves, cannot be treated as physical before a realistic inner boundary of a cloak is demonstrated. Although a recent demonstration has been done in a waveguide environment, the exotic singular boundary conditions should apply to a general environment as in free space. Here we fabricate a metamaterial surface that exhibits the singular boundary conditions and demonstrate its performance in free space. Particularly, the phase information of waves reflected from this metamaterial surface is explicitly measured, confirming the singular responses of boundary conditions for an invisibility cloak.
Moist turbulent Rayleigh-Benard convection with Neumann and Dirichlet boundary conditions
Weidauer, Thomas
2012-01-01
Turbulent Rayleigh-Benard convection with phase changes in an extended layer between two parallel impermeable planes is studied by means of three-dimensional direct numerical simulations for Rayleigh numbers between 10^4 and 1.5\\times 10^7 and for Prandtl number Pr=0.7. Two different sets of boundary conditions of temperature and total water content are compared: imposed constant amplitudes which translate into Dirichlet boundary conditions for the scalar field fluctuations about the quiescent diffusive equilibrium and constant imposed flux boundary conditions that result in Neumann boundary conditions. Moist turbulent convection is in the conditionally unstable regime throughout this study for which unsaturated air parcels are stably and saturated air parcels unstably stratified. A direct comparison of both sets of boundary conditions with the same parameters requires to start the turbulence simulations out of differently saturated equilibrium states. Similar to dry Rayleigh-Benard convection the differences...
Effect of magnetic boundary conditions on the dynamo threshold of von Karman swirling flows
Gissinger, Christophe; Fauve, Stephan; Dormy, Emmanuel
2008-01-01
We study the effect of different boundary conditions on the kinematic dynamo threshold of von Karman type swirling flows in a cylindrical geometry. Using an analytical test flow, we model different boundary conditions: insulating walls all over the flow, effect of sodium at rest on the cylinder side boundary, effect of sodium behind the impellers, effect of impellers or side wall made of a high-magnetic-permeability material. We find that using high-magnetic-permeability boundary conditions decreases the dynamo threshold, the minimum being achieved when they are implemented all over the flow.
High intensity focused ultrasound (HIFU) enables highly localised, non-invasive tissue ablation and its efficacy has been demonstrated in the treatment of a range of cancers, including those of the kidney, prostate and breast. HIFU offers the ability to treat deep-seated tumours locally, and potentially bears fewer side effects than more established treatment modalities such as resection, chemotherapy and ionising radiation. There remains however a number of significant challenges which currently hinder its widespread clinical application. One of these challenges is the need to transmit sufficient energy through the ribcage to ablate tissue at the required foci whilst minimising the formation of side lobes and sparing healthy tissue. Ribs both absorb and reflect ultrasound strongly. This sometimes results in overheating of bone and overlying tissue during treatment, leading to skin burns. Successful treatment of a patient with tumours in the upper abdomen therefore requires a thorough understanding of the way acoustic and thermal energy is deposited. Previously, a boundary element (BE) approach based on a Generalised Minimal Residual (GMRES) implementation of the Burton-Miller formulation was developed to predict the field of a multi-element HIFU array scattered by human ribs, the topology of which was obtained from CT scan data [1]. Dissipative mechanisms inside the propagating medium have since been implemented, together with a complex surface impedance condition at the surface of the ribs. A reformulation of the boundary element equations as a constrained optimisation problem was carried out to determine the complex surface velocities of a multi-element HIFU array which generated the acoustic pressure field that best fitted a required acoustic pressure distribution in a least-squares sense. This was done whilst ensuring that an acoustic dose rate parameter at the surface of the ribs was kept below a specified threshold. The methodology was tested at an
Gélat, P.; ter Haar, G.; Saffari, N.
2014-04-01
High intensity focused ultrasound (HIFU) enables highly localised, non-invasive tissue ablation and its efficacy has been demonstrated in the treatment of a range of cancers, including those of the kidney, prostate and breast. HIFU offers the ability to treat deep-seated tumours locally, and potentially bears fewer side effects than more established treatment modalities such as resection, chemotherapy and ionising radiation. There remains however a number of significant challenges which currently hinder its widespread clinical application. One of these challenges is the need to transmit sufficient energy through the ribcage to ablate tissue at the required foci whilst minimising the formation of side lobes and sparing healthy tissue. Ribs both absorb and reflect ultrasound strongly. This sometimes results in overheating of bone and overlying tissue during treatment, leading to skin burns. Successful treatment of a patient with tumours in the upper abdomen therefore requires a thorough understanding of the way acoustic and thermal energy is deposited. Previously, a boundary element (BE) approach based on a Generalised Minimal Residual (GMRES) implementation of the Burton-Miller formulation was developed to predict the field of a multi-element HIFU array scattered by human ribs, the topology of which was obtained from CT scan data [1]. Dissipative mechanisms inside the propagating medium have since been implemented, together with a complex surface impedance condition at the surface of the ribs. A reformulation of the boundary element equations as a constrained optimisation problem was carried out to determine the complex surface velocities of a multi-element HIFU array which generated the acoustic pressure field that best fitted a required acoustic pressure distribution in a least-squares sense. This was done whilst ensuring that an acoustic dose rate parameter at the surface of the ribs was kept below a specified threshold. The methodology was tested at an
General Considerations of the Electrostatic Boundary Conditions in Oxide Heterostructures
Higuchi, Takuya
2011-08-19
When the size of materials is comparable to the characteristic length scale of their physical properties, novel functionalities can emerge. For semiconductors, this is exemplified by the 'superlattice' concept of Esaki and Tsu, where the width of the repeated stacking of different semiconductors is comparable to the 'size' of the electrons, resulting in novel confined states now routinely used in opto-electronics. For metals, a good example is magnetic/non-magnetic multilayer films that are thinner than the spin-scattering length, from which giant magnetoresistance (GMR) emerged, used in the read heads of hard disk drives. For transition metal oxides, a similar research program is currently underway, broadly motivated by the vast array of physical properties that they host. This long-standing notion has been recently invigorated by the development of atomic-scale growth and probe techniques, which enables the study of complex oxide heterostructures approaching the precision idealized in Fig. 1(a). Taking the subset of oxides derived from the perovskite crystal structure, the close lattice match across many transition metal oxides presents the opportunity, in principle, to develop a 'universal' heteroepitaxial materials system. Hand-in-hand with the continual improvements in materials control, an increasingly relevant challenge is to understand the consequences of the electrostatic boundary conditions which arise in these structures. The essence of this issue can be seen in Fig. 1(b), where the charge sequence of the sublayer 'stacks' for various representative perovskites is shown in the ionic limit, in the (001) direction. To truly 'universally' incorporate different properties using different materials components, be it magnetism, ferroelectricity, superconductivity, etc., it is necessary to access and join different charge sequences, labelled here in analogy to the designations 'group IV, III-V, II
A. Malvandi
2015-01-01
Full Text Available The objective of this paper is to consider both effects of slip and convective heat boundary conditions on steady two-dimensional boundary layer flow of a nanofluid over a stretching sheet in the presence of blowing/suction simultaneously. Flow meets the Navier's slip condition at the surface and Biot number is also used to consider the effects of convective heat transfer. The employed model for nanofluid includes two-component four-equation nonhomogeneous equilibrium model that incorporates the effects of nanoparticle migration owing to Brownian motion and thermophoresis. The basic partial boundary layer equations have been transformed into a two-point boundary value problem via similarity variables. Results for impermeable isothermal surface and also no-slip boundary condition were in best agreements with those existing in literatures. Effects of governing parameters such as Biot number (Bi, slip parameter (λ, thermophoresis (Nt, Prandtl number (Pr, Lewis number (Le, Brownian motion (Nb and blowing/suction (S on reduced Nusselt and Sherwood numbers are analyzed and discussed in details. The obtained results indicate that unlike heat transfer rate, concentration rate is very sensitive to all parameters among which Le, S and Pr are the most effective ones.
Akhtyamov, A. M.; Utyashev, I. M.
2015-11-01
The form and parameters of boundary conditions are identified for the boundary-value problem of string vibrations. It is shown that, to identify both the form and parameters of boundary conditions, two natural frequencies are sufficient. The correctness set of the given problem is determined, and its well-posedness according to Tikhonov is proved. Based on the proven theorem, a method of finding approximate solutions is proposed.
Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations
Arnold, Douglas N.; Nicolae Tarfulea
2007-01-01
Specifying boundary conditions continues to be a challenge in numerical relativity in order to obtain a long time convergent numerical simulation of Einstein's equations in domains with artificial boundaries. In this paper, we address this problem for the Einstein--Christoffel (EC) symmetric hyperbolic formulation of Einstein's equations linearized around flat spacetime. First, we prescribe simple boundary conditions that make the problem well posed and preserve the constraints. Next, we indi...
Monotone iterative technique for fractional differential equations with periodic boundary conditions
J. D. Ramírez; A. S. Vatsala
2009-01-01
In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary con...
Controlling near shore nonlinear surging waves through bottom boundary conditions
Mukherjee, Abhik; Kundu, Anjan
2016-01-01
Instead of taking the usual passive view for warning of near shore surging waves including extreme waves like tsunamis, we aim to study the possibility of intervening and controlling nonlinear surface waves through the feedback boundary effect at the bottom. It has been shown through analytic result that the controlled leakage at the bottom may regulate the surface solitary wave amplitude opposing the hazardous variable depth effect. The theoretical results are applied to a real coastal bathymetry in India.
Feedback Shift Registers as Cellular Automata Boundary Conditions
Salman, K.
2013-01-01
We present a new design for random number generatio n. The outputs of linear feedback shift registers (LFSRs) act as continuous inputs to the t wo boundaries of a one-dimensional (1-D) Elementary Cellular Automata (ECA). The results sho w superior randomness features and the output string has passed the Diehard statistical ba ttery of tests. The design is good candidate for parallel random number generation, ...
Artificial boundary conditions for axisymmetric eddy current probe problems
Haddar, Houssem; Jiang, Zixian; Lechleiter, Armin
2015-01-01
We study different strategies for the truncation of computational domains in the simulation of eddy current probes of elongated axisymmetric tubes. For axial fictitious boundaries, an exact Dirichlet-to-Neumann map is proposed and mathematically analyzed via a non-selfadjoint spectral problem: under general assumptions we show convergence of the solution to an eddy current problem involving a truncated Dirichlet-to-Neumann map to the solution on the entire, unbounded axisymmetric domain as th...
Modes and exceptional points in waveguides with impedance boundary conditions
Midya, Bikashkali
2016-01-01
A planar waveguide with impedance boundary, composed of non-perfect metallic plates, and with passive or active dielectric filling is considered. We show the possibility of selective mode guiding and amplification when homogeneous pump is added to the dielectric, and analyze differences in TE and TM mode propagation. Such a non-conservative system is also shown to feature exceptional points, for specific and experimentally tunable parameters, which are described for a particular case of transparent dielectric.
Investigating the suitability of grid and boundary conditions on simulation of a curved open channel
This research paper presents results from a numerical modeling of an open channel flow. The channel investigated in this study had a semicircular section. The bed of the channel was rough. During this work, a three dimensional Computational Fluid Dynamics code Fluent has been used. The grid was developed with the help of Gambit. Three different grid shapes including structured, unstructured and structured with a boundary layer development were employed during the simulation work. Two different boundary conditions were considered to check their suitability in this numerical modelling. The first one was velocity inlet and pressure outlet boundary conditions whereas second one was periodic boundary conditions applied at the inlet and outlet of the channel. The results were presented in the shape of primary velocity contours. It was observed that the type of grid did not have any significant impact on the flow structure although structured grid with boundary layer in the vicinity of bed has given slightly better results. As far as boundary conditions are concerned, the periodic boundary condition has reduced the time consumption of the simulation work by reducing the domain size without compromising on the accuracy of the results. From this study it can be concluded that structured grid with boundary layer when used with periodic boundary conditions will produce accurate results with least simulation time and cost consumption. (author)
Two-particle atomic coalescences: Boundary conditions for the Fock coefficient components
Liverts, Evgeny Z
2016-01-01
The exact values of the presently determined components 26of the angular Fock coefficients at the two-particle coalescences were obtained and systematized. The Green Function approach was successfully applied to simplify the most complicated calculations. The boundary conditions for the Fock coefficient components in the hyperspherical angular coordinates, which follows from the Kato cusp conditions for the two-electron wave function in the natural interparticle coordinates, were derived. The validity of the obtained boundary conditions was verified on examples of all the presently determined components. The additional boundary conditions are not arising from the Kato cusp conditions were obtained as well. The Wolfram Mathematica was used intensively.
Chiavassa, G.; Liandrat, J.
1996-01-01
We construct compactly supported wavelet bases satisfying homogeneous boundary conditions on the interval (0,1). The maximum features of multiresolution analysis on the line are retained, including polynomial approximation and tree algorithms. The case of H(sub 0)(sup 1)(0, 1)is detailed, and numerical values, required for the implementation, are provided for the Neumann and Dirichlet boundary conditions.
Existence result for the kinetic neutron transport problem with a general albedo boundary condition
We present an existence result for the kinetic neutron transport equation with a general albedo boundary condition. The proof is constructive in the sense that we build a sequence that converges to the solution of the problem by iterating on the albedo term. Both nonhomogeneous and albedo boundary conditions are studied. (authors)
Open boundary conditions for ISPH and their application to micro-flow
Hirschler, Manuel; Kunz, Philip; Huber, Manuel; Hahn, Friedemann; Nieken, Ulrich
2016-02-01
Open boundary conditions for incompressible Smoothed Particle Hydrodynamics (ISPH) are rare. For stable simulations with open boundary conditions, one needs to specify all boundary conditions correctly in the pressure force as well as in the linear equation system for pressure calculation. Especially for homogeneous or non-homogeneous Dirichlet boundary conditions for pressure there exist several possibilities but only a few lead to stable results. However, this isn't trivial for open boundary conditions. We introduce a new approach for open boundary conditions for ISPH to enable stable simulations. In contrast to existing models for weakly-compressible SPH, we can specify open pressure boundary conditions because in ISPH, pressure can be calculated independently of the density. The presented approach is based on the mirror particle approach already introduced for solid wall boundary conditions. Here we divide the mirror axis in several segments with time-dependent positions. We validate the presented approach for the example of Poiseuille flow and flow around a cylinder at different Reynolds numbers and show that we get good agreement with references. Then, we demonstrate that the approach can be applied to free surface flows. Finally, we apply the new approach to micro-flow through a random porous medium with a different number of in- and outlets and demonstrate its benefits.
Eigenstates of a particle in an array of hexagons with periodic boundary condition
A Nemati
2013-10-01
Full Text Available In this paper the problem of a particle in an array of hexagons with periodic boundary condition is solved. Using the projection operators, we categorize eigenfunctions corresponding to each of the irreducible representations of the symmetry group . Based on these results, the Dirichlet and Neumann boundary conditions are discussed.
Vibrations of stretched damped beams under non-ideal boundary conditions
Hakan Boyaci
2006-02-01
A simply supported damped Euler–Bernoulli beam with immovable end conditions are considered. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the boundaries are assumed to allow small deﬂections and moments. Approximate analytical solution of the problem is found using the method of multiple scales, a perturbation technique.
Development and Validation of a New Boundary Condition for Intake Analysis with Distortion
Foad Mehdi Zadeh
2013-01-01
flow in the air intake in the presence of distortion. This boundary condition includes a simplified fan model and a coupling strategy applied between the fan and the inlet. The results obtained with this new boundary condition are compared to full 3D unsteady CFD simulations that include the fan.
Finite-volume method for the Cahn-Hilliard equation with dynamic boundary conditions
Nabet, Flore
2014-01-01
In this paper, we investigate a numerical scheme for solving a diphasic Cahn-Hilliard model with dynamic boundary conditions. We propose a finite volume method for the space discretization and we prove existence and convergence results. We also present numerical simulations to show the influence of these boundary conditions.
On solvability of some boundary value problems for a biharmonic equation with periodic conditions
Karachik, Valery V.; Massanov, Saparbay K.; Turmetov, Batirkhan Kh.
2016-08-01
In the paper we study questions about solvability of some boundary value problems with periodic conditions for an inhomogeneous biharmonic equation. The exact conditions for solvability of the problems are found.
Periodic solutions of a non-linear wave equation with homogeneous boundary conditions
Rudakov, I A [M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
2006-02-28
We prove the existence of time-periodic solutions of a non-linear wave equation with homogeneous boundary conditions. The non-linear term either has polynomial growth or satisfies a 'non-resonance' condition.
Stability of basis property of a periodic problem with nonlocal perturbation of boundary conditions
Imanbaev, Nurlan; Sadybekov, Makhmud
2016-08-01
The present work is the continuation of authors' researchers on stability (instability) of basis property of root vectors of a differential operator with nonlocal perturbation of one of boundary conditions. In this paper a spectral problem for a multiple differentiation operator with an integral perturbation of boundary conditions of one type, which are regular, but not strongly regular, is devoted. For this type of the boundary conditions it is known that the unperturbed problem has an asymptotically simple spectrum, and its system of normalized eigenfunctions creates the Riesz basis. We construct the characteristic determinant of the spectral problem with an integral perturbation of the boundary conditions. It is shown that the Riesz basis property of a system of eigen and adjoint functions is stable with respect to integral perturbations of the boundary condition. In the paper requirements of smoothness to the kernel of the integral perturbation are also reduced (unlike our previous researchers).
Exact finite-size corrections for the spanning-tree model under different boundary conditions
Izmailian, N. Sh.; Kenna, R.
2015-02-01
We express the partition functions of the spanning tree on finite square lattices under five different sets of boundary conditions in terms of a principal partition function with twisted-boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the logarithm of the partition function for each case. We have also established several groups of identities relating spanning-tree partition functions for the different boundary conditions. We also explain an apparent discrepancy between logarithmic correction terms in the free energy for a two-dimensional spanning-tree model with periodic and free-boundary conditions and conformal field theory predictions. We have obtained corner free energy for the spanning tree under free-boundary conditions in full agreement with conformal field theory predictions.
The Ritz Method for Boundary Problems with Essential Conditions as Constraints
Vojin Jovanovic
2016-01-01
Full Text Available We give an elementary derivation of an extension of the Ritz method to trial functions that do not satisfy essential boundary conditions. As in the Babuška-Brezzi approach boundary conditions are treated as variational constraints and Lagrange multipliers are used to remove them. However, we avoid the saddle point reformulation of the problem and therefore do not have to deal with the Babuška-Brezzi inf-sup condition. In higher dimensions boundary weights are used to approximate the boundary conditions, and the assumptions in our convergence proof are stated in terms of completeness of the trial functions and of the boundary weights. These assumptions are much more straightforward to verify than the Babuška-Brezzi condition. We also discuss limitations of the method and implementation issues that follow from our analysis and examine a number of examples, both analytic and numerical.
Self-consistently simulation of RF sheath boundary condition in BOUT + + framework
Gui, Bin; Xu, Xueqiao; Xia, Tianyang
2015-11-01
The effect of the RF sheath boundary condition on the edge-localized modes and the turbulent transport is simulated in this work. The work includes two parts. The first part is to calculate the equilibrium radial electric field with RF sheath boundary condition. It is known the thermal sheath or the rectified RF sheath will modify the potential in the SOL region. The modified potential induces addition shear flow in SOL. In this part, the equilibrium radial electric field across the separatrix is calculated by solving the 2D current continuity equation with sheath boundary condition, drifts and viscosity. The second part is applying the sheath boundary condition on the perturbed variables of the six-field two fluid model in BOUT + + framework. The six-field two-fluid model simulates the ELMs and turbulent transport. The sheath boundary condition is applied in this model and it aims to simulate effect of sheath boundary condition on the turbulent transport. It is found the sheath boundary plays as a sink in the plasma and suppresses the local perturbation. Based on this two work, the effect of RF sheath boundary condition on the ELMs and turbulent transport could be self-consistently simulated. Prepared by LLNL under Contract DE-AC52-07NA27344.
CFD Modeling of Non-Neutral Atmospheric Boundary Layer Conditions
Koblitz, Tilman
For wind resource assessment, the wind industry is increasingly relying on Computational Fluid Dynamics models that focus on modeling the airflow in a neutrally stratified surface-layer. Physical processes like the Coriolis force, buoyancy forces and heat transport, that are important to the...... atmospheric boundary-layer, are mostly ignored so far. In order to decrease the uncertainty of wind resource assessment, the present work focuses on atmospheric flows that include atmospheric stability and the Coriolis effect. Within the present work a RANS model framework is developed and implemented into...
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 ...
Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2012-08-23
The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to nonperturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit. (orig.)
Boundary conditions for spacelike and timelike warped AdS_3 spaces in topologically massive gravity
Compère, Geoffrey
2009-01-01
We propose a set of consistent boundary conditions containing the spacelike warped black holes solutions of Topologically Massive Gravity. We prove that the corresponding asymptotic charges whose algebra consists in a Virasoro algebra and a current algebra are finite, integrable and conserved. A similar analysis is performed for the timelike warped AdS_3 spaces which contain a family of regular solitons. The energy of the boundary Virasoro excitations is positive while the current algebra leads to negative (for the spacelike warped case) and positive (for the timelike warped case) energy boundary excitations. We discuss the relationship with the Brown-Henneaux boundary conditions.
Modeling boundary conditions for balanced proliferation in metastatic latency
Taylor, Donald P; Wells, Jakob Z; Savol, Andrej; Chennubhotla, Chakra; Wells, Alan
2013-01-01
Purpose Nearly half of cancer metastases become clinically evident five or more years after primary tumor treatment; thus metastatic cells survived without emerging for extended periods. This dormancy has been explained by at least two countervailing scenarios: cellular quiescence and balanced proliferation; these entail dichotomous mechanistic etiologies. To examine the boundary parameters for balanced proliferation, we performed in silico modeling. Experimental Design To illuminate the balanced proliferation hypothesis, we explored the specific boundary probabilities under which proliferating micrometastases would remain dormant. A two-state Markov chain Monte Carlo model simulated micrometastatic proliferation and death according to stochastic survival probabilities. We varied these probabilities across 100 simulated patients each with 1,000 metastatic deposits and documented whether the micrometastases exceeded one million cells, died out, or remained dormant (survived 1,218 generations). Results The simulations revealed a narrow survival probability window (49.7 – 50.8 percent) that allowed for dormancy across a range of starting cell numbers, and even then for only a small fraction of micrometastases. The majority of micrometastases died out quickly even at survival probabilities that led to rapid emergence of a subset of micrometastases. Within dormant metastases, cell populations depended sensitively on small survival probability increments. Conclusions Metastatic dormancy as explained solely by balanced proliferation is bounded by very tight survival probabilities. Considering the far larger survival variability thought to attend fluxing microenvironments, it is more probable that these micrometastatic nodules undergo at least periods of quiescence rather than exclusively being controlled by balanced proliferation. PMID:23329811
King, J. R. C.; Ziolkowski, A. M.; Ruffert, M.
2015-03-01
We have developed a new boundary condition for finite volume simulations of oscillating bubbles. Our method uses an approximation to the motion outside the domain, based on the solution at the domain boundary. We then use this approximation to apply boundary conditions by defining incoming characteristic waves at the domain boundary. Our boundary condition is applicable in regions where the motion is close to spherically symmetric. We have tested our method on a range of one- and two-dimensional test cases. Results show good agreement with previous studies. The method allows simulations of oscillating bubbles for long run times (5 ×105 time steps with a CFL number of 0.8) on highly truncated domains, in which the boundary condition may be applied within 0.1% of the maximum bubble radius. Conservation errors due to the boundary conditions are found to be of the order of 0.1% after 105 time steps. The method significantly reduces the computational cost of fixed grid finite volume simulations of oscillating bubbles. Two-dimensional results demonstrate that highly asymmetric bubble features, such as surface instabilities and the formation of jets, may be captured on a small domain using this boundary condition.
DREAM-3D and the importance of model inputs and boundary conditions
Friedel, Reiner; Tu, Weichao; Cunningham, Gregory; Jorgensen, Anders; Chen, Yue
2015-04-01
Recent work on radiation belt 3D diffusion codes such as the Los Alamos "DREAM-3D" code have demonstrated the ability of such codes to reproduce realistic magnetospheric storm events in the relativistic electron dynamics - as long as sufficient "event-oriented" boundary conditions and code inputs such as wave powers, low energy boundary conditions, background plasma densities, and last closed drift shell (outer boundary) are available. In this talk we will argue that the main limiting factor in our modeling ability is no longer our inability to represent key physical processes that govern the dynamics of the radiation belts (radial, pitch angle and energy diffusion) but rather our limitations in specifying accurate boundary conditions and code inputs. We use here DREAM-3D runs to show the sensitivity of the modeled outcomes to these boundary conditions and inputs, and also discuss alternate "proxy" approaches to obtain the required inputs from other (ground-based) sources.
SU(N) gauge theories with C-periodic boundary conditions. Pt. 1; Topological structure
Kronfeld, A.S. (Fermi National Accelerator Lab., Batavia, IL (USA). Theoretical Physics Group); Wiese, U.J. (Hoechstleistungsrechenzentrum (HLRZ), Juelich (Germany, F.R.). Gruppe Theorie der Elementarteilchen)
1991-07-01
C-periodic boundary conditions are introduced to SU(N) gauge theory on a torus. C-periodic fields are replaced by their charge conjugates when they are shifted over the boundary. As for periodic boundary conditions the most general C-periodic boundary condition includes twist. The topological structure with C-periodic boundary conditions is quite different from the periodic case. In the periodic case twist leads to the Z{sub N}'t Hooft flux sectors. In the C-periodic case with even N the symmetry of the flux sectors is reduced to Z{sub 2}. For odd N the flux sectors are eliminated completely. Furthermore, the topological charge is an integer when N is odd, whereas it can be a half-integer when N is even. (orig.).
N=2 boundary conditions for non-linear sigma models and Landau-Ginzburg models
We study N=2 nonlinear two dimensional sigma models with boundaries and their massive generalizations (the Landau-Ginzburg models). These models are defined over either Kaehler or bihermitean target space manifolds. We determine the most general local N=2 superconformal boundary conditions (D-branes) for these sigma models. In the Kaehler case we reproduce the known results in a systematic fashion including interesting results concerning the coisotropic A-type branes. We further analyse the N=2 superconformal boundary conditions for sigma models defined over a bihermitean manifold with torsion. We interpret the boundary conditions in terms of different types of submanifolds of the target space. We point out how the open sigma models correspond to new types of target space geometry. For the massive Landau-Ginzburg models (both Kaehler and bihermitean) we discuss an important class of supersymmetric boundary conditions which admits a nice geometrical interpretation. (author)
Uddin, Mohammed J; Khan, Waqar A; Ismail, Ahmed I
2012-01-01
Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement. PMID:23166688
Mohammed J Uddin
Full Text Available Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.
Unified boundary conditions and Casimir forces for fields with arbitrary spin
Bennett, Robert; Stokes, Adam
The electromagnetic Casimir effect is well-known and has been extensively studied for the last half-century. This attractive force between parallel plates arises from the imposition of boundary conditions upon the fluctuating spin-1 photon field, so a natural further question is wether fields of different spin can cause similar forces when confined in the same way. However, so far it has not been clear what the appropriate boundary conditions for physically-confined spinor fields may be. Here we present work that generalises the physically well-motivated electromagnetic boundary conditions to fields of arbitrary spin, thus arriving at physically reasonable boundary conditions and Casimir forces for a selection of interesting fields. For example, the so-called `bag model' boundary conditions from nuclear physics emerge from our generalised boundary condition as a special case, as do the linearised gravity boundary conditions suggested in a remarkable recent proposal concerning possible measurement of gravitonic Casimir forces. Supported by the UK Engineering and Physical Sciences Research Council (EPSRC).
In this note, we explicitly compute the functional determinant of a Dirac Laplacian with nonlocal pseudodifferential boundary conditions over a finite cylinder in terms of the ζ-function of the Dirac operator on the cross section and the pseudodifferential operators defining the boundary conditions. In particular, this result reduces to our previous formula [J. Phys. A 37, 7381 (2004)] for the special case of generalized Atiyah-Patodi-Singer conditions
Bordag, M.
2004-01-01
We show that the commonly known conductor boundary conditions $E_{||}=B_\\perp=0$ can be realized in two ways which we call 'thick' and 'thin' conductor. The 'thick' conductor is the commonly known approach and includes a Neumann condition on the normal component $E_\\perp$ of the electric field whereas for a 'thin' conductor $E_\\perp$ remains without boundary condition. Both types describe different physics already on the classical level where a 'thin' conductor allows for an interaction betwe...
An approximate method for solving a melting problem with periodic boundary conditions
Qu Liang-Hui; Xing Lin; Yu Zhi-Yun; Ling Feng; Xu Jian-Guo
2014-01-01
An effective thermal diffusivity method is used to solve one-dimensional melting problem with periodic boundary conditions in a semi-infinite domain. An approximate analytic solution showing the functional relation between the location of the moving boundary and time is obtained by using Laplace transform. The evolution of the moving boundary and the temperature field in the phase change domain are simulated numerically, and the numerical results are compar...
Free boundary conditions and the AdS3/CFT2 correspondence
We show that recently proposed free boundary conditions for AdS3 are dual to two-dimensional quantum gravity in certain fixed gauges. In particular, we note that an appropriate identification of the generator of Virasoro transformations leads to a vanishing total central charge in agreement with the theory at the boundary. We argue that this identification is necessary to match the bulk and boundary generators of Virasoro transformations and for consistency with the constraint equations
An approximate method for solving a melting problem with periodic boundary conditions
Qu Liang-Hui
2014-01-01
Full Text Available An effective thermal diffusivity method is used to solve one-dimensional melting problem with periodic boundary conditions in a semi-infinite domain. An approximate analytic solution showing the functional relation between the location of the moving boundary and time is obtained by using Laplace transform. The evolution of the moving boundary and the temperature field in the phase change domain are simulated numerically, and the numerical results are compared with previous results in open literature.
H. R. Tohidi-Moghadam
2009-01-01
Full Text Available Problem statement: Drought stress significantly limits Canola (Brassica napus L. growth and crop productivity. Hence, efficient management of soil moisture and study metabolic changes which occur in response to drought is important for agricultural production of this Crop. Approach: For a better understanding of drought tolerance mechanisms and improving soil water content management strategies, an experiment was laid out in a randomized complete block design with factorial spilt arrangement with tree replications. Results: Irrigation strategy and super absorbent application were allotted to main plots. Irrigation strategy had two levels: 80% of evaporation as control (I1, drought stress started from flowering stage (I2 Application of super absorbent had two levels: Non-application of super absorbent as control (S1, application of super absorbent with 7% concentration. Cultivars (Rgs003 (V1, Sarigol (V2, Option500 (V3, Hyola401 (V4, Hyola330 (V5, Hyola420 (V6 were allotted to sub plots. Plants under water deficit stress and application of super absorbent showed a significant increase and decrease, respectively, in SOD, CAT and GPX activities in leaves compared with control plants. In this context, plants with higher levels of antioxidants showed higher resistance to these stress conditions and higher yield and dry matter allocation to grain filling process i.e. harvest index. Conclusion/Recommendations: Our results suggested that drought stress leads to production of oxygen radicals, which results in increased lipid peroxidation and oxidative stress in the plant. In conclusion of present study, Application of super absorbent polymer could reserve different amounts of water in itself and so increases the soil ability of water storing and preserving and at last in water deficiency, produce plant water need and approve its growth under postanthesis water deficiency.
Kanguzhin, Baltabek; Tokmagambetov, Niyaz
2016-08-01
In this work, we research a boundary inverse problem of spectral analysis of a differential operator with integral boundary conditions in the functional space L2(0, b) where b operator by its spectrum and some additional data.
Superconformal invariance in the Ashkin-Teller quantum chain with free boundary conditions
The finite-size limit of the lower part of the spectrum of the Ashkin-Teller chain with free boundary conditions is studied numerically and interpreted from the point of view of conformal invariance. Several irreducible representations of the Virasoro algebra with the central charge c=1 are identified. For two special values of the coupling constant, higher degeneracies occur and the whole spectrum can be understood in terms of a few irreducible representations of the N=2 superconformal algebra. Remarkably enough, although the spectrum is supersymmetric for free boundary conditions, it is not for periodic or twisted boundary conditions. (orig.)
DIFFERENT ROOF BEHAVIOUR UNDER DIFFERENT UPPER MINING BOUNDARY CONDITION IN DATONG
康立勋
1997-01-01
Understanding roof behaviour and immediate roof failure patterns of Iongwall face is a prerequisite for establishing correct roof control theory and appplying effective roof control measures. Roof behaviour and immediate roof failure pattern have a close relationship with upper mining boundary conditions of Iongwall face. According to actual situation of Datong Mining Area, upper mining boundary conditions of Iongwall face have been classified into 5 types in this paper. Roof behaviour and immediate roof failure pattern under each upper mining boundary condition are discussed in details.
Ramos, I C
2015-01-01
We present the adaptation to non--free boundary conditions of a pseudospectral method based on the (complex) Fourier transform. The method is applied to the numerical integration of the Oberbeck--Boussinesq equations in a Rayleigh--B\\'enard cell with no-slip boundary conditions for velocity and Dirichlet boundary conditions for temperature. We show the first results of a 2D numerical simulation of dry air convection at high Rayleigh number ($R\\sim10^9$). These results are the basis for the later study, by the same method, of wet convection in a solar still.
Casimir force in the rotor model with twisted boundary conditions.
Bergknoff, Jonathan; Dantchev, Daniel; Rudnick, Joseph
2011-10-01
We investigate the three-dimensional lattice XY model with nearest neighbor interaction. The vector order parameter of this system lies on the vertices of a cubic lattice, which is embedded in a system with a film geometry. The orientations of the vectors are fixed at the two opposite sides of the film. The angle between the vectors at the two boundaries is α where 0≤α≤π. We make use of the mean field approximation to study the mean length and orientation of the vector order parameter throughout the film--and the Casimir force it generates--as a function of the temperature T, the angle α, and the thickness L of the system. Among the results of that calculation are a Casimir force that depends in a continuous way on both the parameter α and the temperature and that can be attractive or repulsive. In particular, by varying α and/or T one controls both the sign and the magnitude of the Casimir force in a reversible way. Furthermore, for the case α=π, we discover an additional phase transition occurring only in the finite system associated with the variation of the orientations of the vectors. PMID:22181114
Interaction-round-a-face models with fixed boundary conditions the ABF fusion hierarchy
Behrend, R E; O'Brien, D L; Behrend, Roger E; Pearce, Paul A; O'Brien, David L
1995-01-01
We use boundary weights and reflection equations to obtain families of commuting double-row transfer matrices for interaction-round-a-face models with fixed boundary conditions. In particular, we consider the fusion hierarchy of the Andrews-Baxter-Forrester models, for which we find that the double-row transfer matrices satisfy functional equations with an su(2) structure.
Transverse periodic boundary conditions in molecular dynamics with uniaxial strain shock waves
Harris, P.; Karo, A.M.
1984-11-20
In this report we discuss the role of transverse, periodic, boundary conditions (TPBCs) in multidimensional molecular dynamics (MD) calculations. We conclude that observed nonsteady-state shock propagation in MD calculations could easily be an artifact resulting from inadequate separation between the periodic boundaries. 20 references.
Absorption and impedance boundary conditions for phased geometrical-acoustics methods
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, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been...... reasonable results with some exceptions at low frequencies for acoustically soft materials....
Janssen, R.H.H.; Vilà-Guerau de Arellano, J.; Ganzeveld, L.N.; Kabat, P.; Jimenez, J.L.; Farmer, D.K.; Heerwaarden, van C.C.; Mammarella, I.
2012-01-01
We study the combined effects of land surface conditions, atmospheric boundary layer dynamics and chemistry on the diurnal evolution of biogenic secondary organic aerosol in the atmospheric boundary layer, using a model that contains the essentials of all these components. First, we evaluate the mod
Sun Hye PARK
2014-01-01
In this paper, we investigate the influence of boundary dissipation on the de-cay property of solutions for a transmission problem of Kirchhoff type wave equation with boundary memory condition. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of relaxation function.
REGULARITY THEORY FOR SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS
无
2002-01-01
The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. This type of problem is motivated by stochastic differential games. The Neumann case corresponds to stochastic differential equations with reflection on boundary of the domain.
Finite-Volume Analysis for the Cahn-Hilliard equation with Dynamic boundary conditions
Nabet, Flore
2014-01-01
This work is devoted to the convergence analysis of a finite-volume approximation of the 2D Cahn-Hilliard equation with dynamic boundary conditions. The method that we propose couples a 2d-finite-volume method in a bounded, smooth domain and a 1d-finite-volume method on its boundary. We prove convergence of the sequence of approximate solutions.
Calkins, Michael A; Julien, Keith; Nieves, David; Driggs, Derek; Marti, Philippe
2015-01-01
The influence of fixed temperature and fixed heat flux thermal boundary conditions on rapidly rotating convection in the plane layer geometry is investigated for the case of stress-free mechanical boundary conditions. It is shown that whereas the leading order system satisfies fixed temperature boundary conditions implicitly, a double boundary layer structure is necessary to satisfy the fixed heat flux thermal boundary conditions. The boundary layers consist of a classical Ekman layer adjacent to the solid boundaries that adjust viscous stresses to zero, and a layer in thermal wind balance just outside the Ekman layers adjusts the temperature such that the fixed heat flux thermal boundary conditions are satisfied. The influence of these boundary layers on the interior geostrophically balanced convection is shown to be asymptotically weak, however. Upon defining a simple rescaling of the thermal variables, the leading order reduced system of governing equations are therefore equivalent for both boundary condit...
Fractional-Order Variational Calculus with Generalized Boundary Conditions
Baleanu Dumitru
2011-01-01
Full Text Available This paper presents the necessary and sufficient optimality conditions for fractional variational problems involving the right and the left fractional integrals and fractional derivatives defined in the sense of Riemman-Liouville with a Lagrangian depending on the free end-points. To illustrate our approach, two examples are discussed in detail.
A new package for simulating periodic boundary conditions in MODFLOW and SEAWAT
Post, V. E. A.
2011-11-01
Modeling of coastal groundwater systems is a challenging problem due to their highly dynamic boundary conditions and the coupling between the equations for groundwater flow and solute transport. A growing number of publications on aquifers subject to tides have demonstrated various modeling approaches, ranging from analytical solutions to comprehensive numerical models. The United States Geological Survey code SEAWAT has been a popular choice in studies of this type. Although SEAWAT allows the incorporation of time-variant boundary conditions, the implementation of tidal boundaries is not straightforward, especially when a seepage face develops during falling tide. Here, a new package is presented, called the periodic boundary condition (PBC) package, that can be incorporated into MODFLOW and SEAWAT to overcome the difficulties encountered with tidal boundaries. It dynamically updates the boundary conditions for head and concentration during the simulation depending on a user-defined tidal signal and allows for the development of a seepage face. The package has been verified by comparing it to four different published models of tidally influenced groundwater systems of varying complexity. Excellent agreement was obtained in all cases. The new package is an important extension to the existing capabilities of MODFLOW and SEAWAT with respect to simulating periodic boundary conditions.
Generalized adjoint consistent treatment of wall boundary conditions for compressible flows
Hartmann, Ralf; Leicht, Tobias
2015-11-01
In this article, we revisit the adjoint consistency analysis of Discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations with application to the Reynolds-averaged Navier-Stokes and k- ω turbulence equations. Here, particular emphasis is laid on the discretization of wall boundary conditions. While previously only one specific combination of discretizations of wall boundary conditions and of aerodynamic force coefficients has been shown to give an adjoint consistent discretization, in this article we generalize this analysis and provide a discretization of the force coefficients for any consistent discretization of wall boundary conditions. Furthermore, we demonstrate that a related evaluation of the cp- and cf-distributions is required. The freedom gained in choosing the discretization of boundary conditions without loosing adjoint consistency is used to devise a new adjoint consistent discretization including numerical fluxes on the wall boundary which is more robust than the adjoint consistent discretization known up to now. While this work is presented in the framework of Discontinuous Galerkin discretizations, the insight gained is also applicable to (and thus valuable for) other discretization schemes. In particular, the discretization of integral quantities, like the drag, lift and moment coefficients, as well as the discretization of local quantities at the wall like surface pressure and skin friction should follow as closely as possible the discretization of the flow equations and boundary conditions at the wall boundary.
Comparative Quantum Cosmology: Causality, Singularity, and Boundary Conditions
Fellman, Philip V.; Post, Jonathan Vos; Carmichael, Christine M.; Post, Andrew Carmichael
2007-01-01
In this review article we compare the recent work of Peter Lynds, "On a finite universe with no beginning or end", with that of Stephen Hawking, primarily "Quantum Cosmology, M-Theory, and the Anthropic Principle", and two foundational works by Sean M. Carroll and Jennifer Chen, "Does Inflation Provide Natural Conditions for the Universe" and "Spontaneous Inflation and the Origin of the Arrow of Time", in order to evaluate their comparative treatments of the nature and role of causality, time...
A Kind of Discrete Non-Reflecting Boundary Conditions for Varieties of Wave Equations
Xiu-min Shao; Zhi-ling Lan
2002-01-01
In this paper, a new kind of discrete non-reflecting boundary conditions is developed. It can be used for a variety of wave equations such as the acoustic wave equation, the isotropic and anisotropic elastic wave equations and the equations for wave propagation in multi-phase media and so on. In this kind of boundary conditions, the composition of all artificial reflected waves, but not the individual reflected ones, is considered and eliminated. Thus, it has a uniform formula for different wave equations. The velocity CA of the composed reflected wave is determined in the way to make the reflection coefficients minimal, the value of which depends on equations. In this paper, the construction of the boundary conditions is illustrated and CA is found, numerical results are presented to illustrate the effectiveness of the boundary conditions.
An Overview of the Lower and Upper Solutions Method with Nonlinear Boundary Value Conditions
Cabada Alberto
2011-01-01
Full Text Available The aim of this paper is to point out recent and classical results related with the existence of solutions of second-order problems coupled with nonlinear boundary value conditions.
Mouffak Benchohra; Fatima-Zohra Mostefai
2012-01-01
The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
Asymptotic behavior of solutions to nonlinear parabolic equation with nonlinear boundary conditions
Diabate Nabongo
2008-01-01
Full Text Available We show that solutions of a nonlinear parabolic equation of second order with nonlinear boundary conditions approach zero as t approaches infinity. Also, under additional assumptions, the solutions behave as a function determined here.
Structure and vibrational spectra of a model of a-Si:H with periodic boundary conditions
Winer, K.; Wooten, F.
1983-08-01
A ball-and -stick model of a-Si:H with periodic boundary conditions has been constructed. A computer replica of the structure has been relaxed and the density, radial distribution function and vibrational spectra calculated.
Shifted periodic boundary conditions for simulations of wall-bounded turbulent flows
Munters, Wim; Meneveau, Charles; Meyers, Johan
2016-02-01
In wall-bounded turbulent flow simulations, periodic boundary conditions combined with insufficiently long domains lead to persistent spanwise locking of large-scale turbulent structures. This leads to statistical inhomogeneities of 10%-15% that persist in time averages of 60 eddy turnover times and more. We propose a shifted periodic boundary condition that eliminates this effect without the need for excessive streamwise domain lengths. The method is tested based on a set of direct numerical simulations of a turbulent channel flow, and large-eddy simulations of a high Reynolds number rough-wall half-channel flow. The method is very useful for precursor simulations that generate inlet conditions for simulations that are spatially inhomogeneous, but require statistically homogeneous inlet boundary conditions in the spanwise direction. The method's advantages are illustrated for the simulation of a developing wind-farm boundary layer.
Near-linear dynamics in KdV with periodic boundary conditions
Erdogan, M. B.; Tzirakis, N.; Zharnitsky, V.
2009-01-01
Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction.
Mean Field in Long-Range Ferromagnets and Periodic Boundary Conditions
Curilef, Sergio
2004-01-01
Periodic boundary conditions are applied to a ferromagnetic spin lattice. A symmetrical lattice and its contributions all over space are being used. Results, for the Ising model with ferromagnetic interaction that decays as a $1/r^{D+\
Non-equilibrium thermodynamics of boundary conditions for rarefied gas flows
Roldugin, V. I.
A formulation of the boundary conditions for the macroscopic (bulk) gas parameters is developed, based on the separation of the bulk and Knudsen layer distribution functions. It is shown that the boundary conditions so obtained relate exactly at the gas-solid interface (while the Knudsen layer have finite thickness) and include the jumps of the mass, momentum, and energy fluxes. These jumps are due to the fluxes associated with the Knudsen distribution function. The Knudsen layer fluxes by means of nonequilibrium thermodynamics are expressed through the gas macroparameters. The interconnection between the Chapman-Enskog approximations for the bulk distribution function and the boundary conditions structure is established. Already at the first Chapman-Enskog approximation, the suggested boundary conditions differ from Waldmann's (1967) one.
Li Ming
2013-03-01
Full Text Available In this study, a single beam model has been developed to analyze the thermal vibration of Single-Walled Carbon Nanotubes (SWCNT. The nonlocal elasticity takes into account the effect of small size into the formulation and the boundary condition. With exact solution of the dynamic governing equations, the thermal-vibrational characteristics of a cantilever SWCNT are obtained. Influence of nonlocal small scale effects, temperature change and vibration modes of the CNT on the frequency are investigated. The present study shows that the additional boundary conditions from small scale do not change natural frequencies at different temperature change. Thus for simplicity, one can apply the local boundary condition to replace the small scale boundary condition.
Boundary Conditions and the Aeolian Sediment State of the Olympia Undae Dune Field, Mars
Middlebrook, W.; Ewing, R. C.; Ayoub, F.; Bridges, N. T.; Smith, I.; Spiga, A.
2015-05-01
We evaluate the boundary conditions in Olympia Undae. We map two and three dimensional dune parameters from two locations proximal and distal to Planum Boreum and constrain sediment fluxes. We compare our results with a mesoscale atmospheric model.
Evaluation of wall boundary condition parameters for gas-solids fluidized bed simulations
Li, Tingwen [URS Corporation; Morgantown, WV (United States); National Energy Technology Lab. (NETL), Morgantown, WV (United States); Benyahia, Sofiane [National Energy Technology Lab. (NETL), Morgantown, WV (United States)
2013-10-01
Wall boundary conditions for the solids phase have significant effects on numerical predictions of various gas-solids fluidized beds. Several models for the granular flow wall boundary condition are available in the open literature for numerical modeling of gas-solids flow. In this study, a model for specularity coefficient used in Johnson and Jackson boundary conditions by Li and Benyahia (AIChE Journal, 2012, 58, 2058-2068) is implemented in the open-source CFD code-MFIX. The variable specularity coefficient model provides a physical way to calculate the specularity coefficient needed by the partial-slip boundary conditions for the solids phase. Through a series of 2-D numerical simulations of bubbling fluidized bed and circulating fluidized bed riser, the model predicts qualitatively consistent trends to the previous studies. Furthermore, a quantitative comparison is conducted between numerical results of variable and constant specularity coefficients to investigate the effect of spatial and temporal variations in specularity coefficient.
Soft-and-Hard/D'B' Boundary Conditions and their Realization by Electromagnetic Media
Lindell, I V
2012-01-01
A layer of uniaxial medium with large axial permittivity and permeability can be used as a quarter-wave transformer with interesting properties. By increasing the transverse permittivity and permeability the transformer becomes a thin sheet. It is shown that the recently introduced SHDB boundary conditions, generalizing the soft-and-hard and DB conditions, realized by the interface of a skewon-axion medium, can be transformed to form a novel class of SHD'B' boundary conditions which generalizes the soft-and-hard and D'B' boundary conditions. Reflection of a plane wave from a planar SHD'B' boundary is considered by numerical examples revealing an interesting narrow beam with radical change of reflection for certain values of parameters and incidence angles.
Invariance of decay rate with respect to boundary conditions in thermoelastic Timoshenko systems
Alves, M. S.; Jorge Silva, M. A.; Ma, T. F.; Muñoz Rivera, J. E.
2016-06-01
This paper is mainly concerned with the polynomial stability of a thermoelastic Timoshenko system recently introduced by Almeida Júnior et al. (Z Angew Math Phys 65(6):1233-1249, 2014) that proved, in the general case when equal wave speeds are not assumed, different polynomial decay rates depending on the boundary conditions, namely, optimal rate {t^{-1/2}} for mixed Dirichlet-Neumann boundary condition and rate {t^{-1/4}} for full Dirichlet boundary condition. Here, our main achievement is to prove the same polynomial decay rate {t^{-1/2}} (corresponding to the optimal one) independently of the boundary conditions, which improves the existing literature on the subject. As a complementary result, we also prove that the system is exponentially stable under equal wave speeds assumption. The technique employed here can probably be applied to other kind of thermoelastic systems.
THE DYNAMICS OF SINE-GORDON SYSTEM WITH DIRICHLET BOUNDARY CONDITION
Liu Yingdong; Li Zhengyuan
2000-01-01
We prove the existence of the global attractor of Sine-Gordon system with Dirichlet boundary condition and show the attractor is the unique steady state when the damping constant and the diffusion constant are sufficiently large.
Lee, Man
2012-02-22
A microchannel heat sink, integrated with pressure and temperature microsensors, is utilized to study single-phase liquid flow forced convection under a uniform heat flux boundary condition. Utilizing a waferbond-and-etch- back technology, the heat source, temperature and pressure sensors are encapsulated in a thin composite membrane capping the microchannels, thus allowing experimentally good control of the thermal boundary conditions. A three-dimensional physical model has been constructed to facilitate numerical simulations of the heat flux distribution. The results indicate that upstream the cold working fluid absorbs heat, while, within the current operating conditions, downstream the warmer working fluid releases heat. The Nusselt number is computed numerically and compared with experimental and analytical results. The wall Nusselt number in a microchannel can be estimated using classical analytical solutions only over a limited range of the Reynolds number, Re: both the top and bottom Nusselt numbers approach 4 for Re < 1, while the top and bottom Nusselt numbers approach 0 and 5.3, respectively, for Re > 100. The experimentally estimated Nusselt number for forced convection is highly sensitive to the location of the temperature measurements used in calculating the Nusselt number. © 2012 IOP Publishing Ltd.
M.Yakit ONGUN
2007-01-01
In this paper we consider the nonselfadjoint (dissipative) Schr(o)dinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator,and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schr(o)dinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schr(o)dinger boundary value problem are given.
Kinematics and shear heat pattern of ductile simple shear zones with `slip boundary condition'
Mulchrone, Kieran F.; Mukherjee, Soumyajit
2016-04-01
Extrusion by Poiseuille flow and simple shear of hot lower crust has been deciphered from large hot orogens, and partial-slip boundary condition has been encountered in analogue models. Shear heat and velocity profiles are deduced from a simplified form of Navier-Stokes equation for simple shear together with extrusive Poiseuille flow and slip boundary condition for Newtonian viscous rheology. A higher velocity at the upper boundary of the shear zone promotes higher slip velocity at the lower boundary. The other parameters that affect the slip are viscosity and thickness of the shear zone and the resultant pressure gradient that drives extrusion. In the partial-slip case, depending on flow parameters (resultant pressure gradient, density and viscosity) and thickness of the shear zone, the velocity profiles can curve and indicate opposite shear senses. The corresponding shear heat profiles can indicate temperature maximum inside shear zones near either boundaries of the shear zone, or equidistant from them.
M.Yakit; ONGUN
2007-01-01
In this paper we consider the nonselfadjoint (dissipative) Schrodinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator, and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schrodinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schrodinger boundary value problem are given.
Linear second-order problems with Sturm-Liouville-type multi-point boundary conditions
Bryan P. Rynne
2012-08-01
Full Text Available We consider the eigenvalue problem for the equation $-u'' = lambda u$ on $(-1,1$, together with general Sturm-Liouville-type, multi-point boundary conditions at $pm 1$. We show that the basic spectral properties of this problem are similar to those of the standard Sturm-Liouville problem with separated boundary conditions. In particular, for each integer $k ge 0$ there exists a unique, simple eigenvalue $lambda_k$ whose eigenfunctions have 'oscillation count' equal to k.
Pottier, B; Frétigny, C; Talini, L
2015-01-01
We investigate the properties of nanometric liquid films with a new non invasive technique. We measure the spontaneous thermal fluctuations of the free surfaces of liquids to probe their hydrodynamic boundary condition at a solid wall. The surface fluctuations of a silicon oil film could be described with a no-slip boundary condition for film thicknesses down to 20 nm. Oppositely, a 4 nm negative slip length had to be introduced to describe the behavior of n-hexadecane, consistently with prev...
Asselle, Luca
2015-01-01
Let $(M,g)$ be a closed Riemannian manifold and $L:TM\\rightarrow \\mathbb R$ be a Tonelli Lagrangian. In this thesis we study the existence of orbits of the Euler-Lagrange flow associated with $L$ satisfying suitable boundary conditions. We first look for orbits connecting two given closed submanifolds of $M$ satisfying the conormal boundary conditions: We introduce the Ma\\~n\\'e critical value that is relevant for the problem and prove existence results for supercritical and subcritical energi...
A new approach to (quasi) periodic boundary conditions in micromagnetics: the macrogeometry
Fangohr, Hans; Bordignon, Giuliano; Franchin, Matteo; Knittel, Andreas; de Groot, Peter A. J.; Fischbacher, Thomas
2009-01-01
We present a new method to simulate repetitive ferromagnetic structures. This macro geometry approach combines treatment of short-range interactions (i.e. the exchange field) as for periodic boundary conditions with a specification of the arrangement of copies of the primary simulation cell n order to correctly include effects of the demagnetizing field. This method (i) solves a consistency problem that prevents the naive application of 3d periodic boundary conditions in micromagn...
Sobolev type equations of time-fractional order with periodical boundary conditions
Plekhanova, Marina
2016-08-01
The existence of a unique local solution for a class of time-fractional Sobolev type partial differential equations endowed by the Cauchy initial conditions and periodical with respect to every spatial variable boundary conditions on a parallelepiped is proved. General results are applied to study of the unique solvability for the initial boundary value problem to Benjamin-Bona-Mahony-Burgers and Allair partial differential equations.
Chaotic Dynamics of One-Dimensional Systems with Periodic Boundary Conditions
Kumar, Pankaj; Miller, Bruce N.
2014-01-01
We provide appropriate tools for the analysis of dynamics and chaos for one-dimensional systems with periodic boundary conditions. Our approach allows for the investigation of the dependence of the largest Lyapunov exponent on various initial conditions of the system. The method employs an effective approach for defining the phase-space distance appropriate for systems with periodic boundary and allows for an unambiguous test-orbit rescaling in the phase space required to calculate the Lyapun...
Direct numerical simulation (DNS) have been performed for the turbulent heat transfer in a channel flow. In the present study, effect of thermal boundary condition is examined. DNS has been carried out for streamwisely thermal boundary conditions (Reτ=180) with Pγ=0.71 to obtain statistical mean temperatures, temperature variances, budget terms and time scale ratios etc. The obtained results have indicated that the time scale ratio varies along a streamwise. (author)
Latyshev, A. V.; Yushkanov, A. A.
2012-01-01
Analytical solution of second Stokes problem of behaviour of rarefied gas with Cercignani boundary accomodation conditions The second Stokes problem about behaviour of rarefied gas filling half-space is analytically solved. A plane, limiting half-space, makes harmonious fluctuations in the plane. The kinetic BGK-equation (Bhatnagar, Gross, Krook) is used. The boundary accomodation conditions of Cercignani of reflexion gaseous molecules from a wall are considered. Distribution function of the ...
Michaelis, Björn
2009-01-01
There is an impressive body of research suggesting that transformational and charismatic leadership are positively associated with performance outcomes. The role of linking mechanisms that facilitate the influence of transformational and charismatic leadership and the functioning of boundary conditions, however, is less well-understood. This dissertation is an attempt to address this research gap by providing three empirical studies analyzing linking mechanisms and boundary conditions in the ...
Dirichlet Boundary Conditions in Generalized Liouville Theory toward a QCD String
Nakamura, Shin
2000-01-01
We consider bosonic noncritical strings as QCD strings and we present a basic strategy to construct them in the context of Liouville theory. We show that Dirichlet boundary conditions play important roles in generalized Liouville theory. Specifically, they are used to stabilize the classical configuration of strings and also utilized to treat tachyon condensation in our model. We point out that Dirichlet boundary conditions for the Liouville mode maintains Weyl invariance, if an appropriate c...
Gerbi, Stéphane
2011-12-01
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.
A hybrid FEM-BEM unified boundary condition with sub-cycling for electromagnetic radiation
Fasenfest, B; White, D; Stowell, M; Rieben, R; Sharpe, R; Madsen, N; Rockway, J; Champagne, N J; Jandhyala, V; Pingenot, J
2006-01-12
Hybrid solutions to time-domain electromagnetic problems offer many advantages when solving open-region scattering or radiation problems. Hybrid formulations use a finite-element or finite-difference discretization for the features of interest, then bound this region with a layer of planar boundary elements. The use of volume discretization allows for intricate features and many changes in material within the structure, while the boundary-elements provide a highly accurate radiating boundary condition. This concept has been implemented previously, using the boundary elements to set the E-field, H-field, or both for an FDTD grid, for example in [1][2][3], or as a mixed boundary condition for the second order wave equation solved by finite elements [4]. Further study has focused on using fast methods, such as the Plane Wave Time Domain method [3][4] to accelerate the BEM calculations. This paper details a hybrid solver using the coupled first-order equations for the E and H fields in the finite-element region. This formulation is explicit, with a restriction on the time step for stability. When this time step is used in conjunction with the boundary elements forming either a inhomogeneous Dirichlet or Neuman boundary condition on the finite-element mesh, late time instabilities occur. To combat this, a Unified Boundary Condition (UBC), similar to the one in [4] for the second-order wave equation, is used. Even when this UBC is used, the late time instabilities are merely delayed if standard testing in time is used. However, the late time instabilities can be removed by replacing centroid based time interpolation with quadrature point based time interpolation for the boundary elements, or by sub-cycling the boundary element portion of the formulation. This sub-cycling, used in [3] for FDTD to reduce complexity, is shown here to improve stability and overall accuracy of the technique.
Schrödinger functional boundary conditions and improvement for N > 3
Hietanen, A.; Karavirta, T.; Vilaseca, P.
2014-01-01
The standard method to calculate non-perturbatively the evolution of the running coupling of a SU(N ) gauge theory is based on the Schrodinger functional (SF). In this paper we construct a family of boundary fields for general values of N which enter the standard definition of the SF coupling. We...... provide spatial boundary conditions for fermions in several representations which reduce the condition number of the squared Dirac operator. In addition, we calculate the improvement coefficients for N > 3 needed to remove boundary cutoff effects from the gauge action. After this, residual cutoff effects...
The 3-D Inviscid Limit Result under Slip Boundary Conditions. A Negative Answer
da Veiga, H. Beirão; Crispo, F.
2010-01-01
We show that, in general, the solutions to the initial-boundary value problem for the Navier-Stokes equations under a widely adopted Navier-type slip boundary condition do not converge, as the viscosity goes to zero (in any arbitrarily small neighborhood of the initial time), to the solution of the Euler equations under the classical zero-flux boundary condition, and same smooth initial data. Convergence does not hold with respect to any space-topology which is sufficiently strong as to imply...
ALmost EXact boundary conditions for transient Schrödinger-Poisson system
Bian, Lei; Pang, Gang; Tang, Shaoqiang; Arnold, Anton
2016-05-01
For the Schrödinger-Poisson system, we propose an ALmost EXact (ALEX) boundary condition to treat accurately the numerical boundaries. Being local in both space and time, the ALEX boundary conditions are demonstrated to be effective in suppressing spurious numerical reflections. Together with the Crank-Nicolson scheme, we simulate a resonant tunneling diode. The algorithm produces numerical results in excellent agreement with those in Mennemann et al. [1], yet at a much reduced complexity. Primary peaks in wave function profile appear as a consequence of quantum resonance, and should be considered in selecting the cut-off wave number for numerical simulations.
The problem of an electron in a quantum well is treated using the new ('mirror') boundary conditions implying that the particle has a specular reflection from the well's boundaries. Solutions of the Schroedinger equation are obtained for some particular well's geometries when the variable separation method is applicable. The resemblance between the 'mirror' and periodic boundary conditions is discussed. Comparison of the results with some experimental data shows that this approach can provide a reasonably accurate (without any adjustable parameters) description of nanosystems, including those with non-traditional geometry
Vorobiev, Yu.V. [Laboratorio de Investigacion en Materiales, CINVESTAV, 76230 Queretaro (Mexico)], E-mail: vorobiev@qro.cinvestav.mx; Horley, P.P. [Department of Electronics and Energy Engineering, Chernivtsi National University, 58012 Chernivtsi (Ukraine); Centro de Fisica das Interaccoes Fundamentais (CFIF), 1049-001 Lisboa (Portugal); Gorley, P.N. [Department of Electronics and Energy Engineering, Chernivtsi National University, 58012 Chernivtsi (Ukraine); Vieira, V.R. [Centro de Fisica das Interaccoes Fundamentais (CFIF), 1049-001 Lisboa (Portugal); Louvier-Hernandez, J.F.; Luna-Barcenas, G. [Laboratorio de Investigacion en Materiales, CINVESTAV, 76230 Queretaro (Mexico); Gonzalez-Hernandez, J. [CIMAV, Miguel de Cervantes 120, 31109 Chihuahua (Mexico)
2008-11-30
The problem of an electron in a quantum well is treated using the new ('mirror') boundary conditions implying that the particle has a specular reflection from the well's boundaries. Solutions of the Schroedinger equation are obtained for some particular well's geometries when the variable separation method is applicable. The resemblance between the 'mirror' and periodic boundary conditions is discussed. Comparison of the results with some experimental data shows that this approach can provide a reasonably accurate (without any adjustable parameters) description of nanosystems, including those with non-traditional geometry.
The joining of code COBRA to the PERF-type boundary conditions
The subchannel analysis method for the thermohydraulic investigation offuel element clusters of nuclear reactor cores is based on the supposition that the boundaries of the investigated space in the radial direction is either closed or the gradients of the parameters are equal to zero. When such a subchannel analysis is applied for the investigation of WWER-1000 type fuel element clusters, it should be able to accept radial boundary conditions coming from the global calculation of the whole reactor core. The paper gives a detailed description of the improvement of COBRA and COCONT subchannel codes for the acceptance of radial boundary conditions. (author) 11 refs.; 6 figs
Analytical solutions based on Laplace transform are developed for the problem of radionuclides transport along a discrete planar fracture in porous rock. The solutions take into account advective transport in the fracture, longitudinal hydrodynamic dispersion along the fracture axis, molecular diffusion from the fracture into the rock matrix, sorption within the rock matrix, sorption onto the surface of the fracture and radioactive decay. The initial concentration in both the fracture and the rock matrix is assumed to be zero. Four boundary conditions, constant concentration, exponentially decaying concentration, exponentially decaying flux and kinetic solubility-limited dissolution are assumed. All these analytical solutions are in a form of a single integral that is evaluated by a Gauss-Legendre quadrature for each point in space and time. A comparison between the concentration profiles with a constant concentration inlet boundary condition and those with a decaying concentration inlet boundary condition shows that the concentration profile is strongly influenced by the inlet boundary condition when the retardation factor of the matrix is high. As the dissolution rate constant approaches infinity, the inlet boundary condition of the kinetic solubility-limited dissolution model can be replaced by the boundary condition of constant concentration
BAI Yingchen; WU Fengchang; WAN Guojiang; LIU Congqiang; FU Pingqing; LI Wen
2008-01-01
Strong interaction between natural dissolved organic matter (DOM) and Hg(II) may influence the transport, conversion, toxicity and bio-validity of mercury in the environment. In this paper ultraviolet (UV) absorbance titration was employed for the first time for the determination of the conditional stability constants of Hg(II) and (DOM). With increasing Hg(II) concentrations, the UV absorbance of fulvic acid, humic acid, and DOM in river increases progressively. By linear and non-linear model fitting, the conditional stability constants (lgK) of Hg(II) and DOM were worked out to be 3.54-4.93 and 3.64-4.85, respectively. The results are consistent with those acquired by the typical fluorescence quenching titration method, with the maximum relative error of lgK being 2.6% and the average relative error being 0.2%. The UV absorbance titration method has the advantages of rapid determination, simple performance, and it will probably become a new approach to studying interactions between DOM and trace metallic ions.
Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre
2013-11-01
A Continuous Boundary Force (CBF) method was developed for implementing Robin (Navier) boundary condition (BC) that can describe no-slip or slip conditions (slip length from zero to infinity) at the fluid-solid interface. In the CBF method the Robin BC is replaced by a homogeneous Neumann BC and an additional volumetric source term in the governing momentum equation. The formulation is derived based on an approximation of the sharp boundary with a diffuse interface of finite thickness, across which the BC is reformulated by means of a smoothed characteristic function. The CBF method is easy to be implemented in Lagrangian particle-based methods. We first implemented it in smoothed particle hydrodynamics (SPH) to solve numerically the Navier-Stokes equations subject to spatial-independent or dependent Robin BC in two and three dimensions. The numerical accuracy and convergence is examined through comparisons with the corresponding finite difference or finite element solutions. The CBF method is further implemented in smoothed dissipative particle dynamics (SDPD), a mesoscale scheme, for modeling slip flows commonly existent in micro/nano channels and microfluidic devices. The authors acknowledge the funding support by the ASCR Program of the Office of Science, U.S. Department of Energy.
We have developed a mode-locked diode-pumped Yb:KY(WO4)2 laser generating nearly bandwidth limited pulses as short as 101 fs. At 1.1 W of absorbed power and for 3% transmission output coupler, the laser delivers 150 mW in pulses of 110 fs duration, which corresponds to the efficiency of 14%. This has been achieved using semiconductor saturable absorber mirror (SESAM) grown by molecular beam epitaxy. The low-temperature (LT) absorbers were crystallized under the carefully optimized growth conditions. The resonantlike type structures ensured relatively high enhancement factor and in consequence high absorption modulation. The main device parameters such as group delay dispersion (GDD) and enhancement factor were chosen to be wavelength independent. The optimization of the growth conditions resulted in a reduction in the nonsaturable absorption in as-grown LT-InGaAs absorbing layer and ensured the fast carrier trapping and recombination. We assume that the nonsaturable losses of the annealed LT layers result from the absorption connected with defects generated in the crystal during LT growth. Moreover, the annealing deteriorates the interface sharpness and the crystal quality of LT pseudomorphic, nonstoichiometric InGaAs layer. On the other hand, higher growth temperature and lower ratio of group V to group III beam equivalent pressure (V/III ratio) ensure lower defect densities and high crystal quality but suffer from the absorption related to AsGa0 conduction band transitions. The careful balancing of these contradictory tendencies allowed for optimization of the absorber properties. The InGaAs quantum well absorbing layer was grown at the temperature as high as 420 deg. C, under the V/III ratio as low as 10. No postgrowth annealing was performed. The recovery time of the SESAM structure characterized by the pump-probe measurements was equal to 9.6 ps. The nonsaturable losses of 1.94% decreased the modulation depth to 1.48% but still self-starting and stable mode
О.М. Тихенко
2012-10-01
Full Text Available The aim of work has been the investigation of UV-radiation influence on the absorbing capacity of plant objects in relation to radionuclide using the new method of biological objects state registration under the conditions of stressor impact – the residual radioactivity method, that is based on measuring absorption of potassium chemical analog – caesium-137, that is brought in chloride compound into cultural medium. As a result of conducted investigation, the prognostic potential of the residual radioactivity method has been estimated. There have been determined, first, that the method could to be used in the form of impulse sprout incubation with radiotracer, second, it has to be taken into account that inhibition of absorbing capacity by certain stressor dose occurs two days earlier than the state of plant activity inhibition is fixed.
Effects of upper disc boundary conditions on the linear Rossby wave instability
Lin, Min-Kai
2012-01-01
The linear Rossby wave instability (RWI) in global, 3D polytropic discs is revisited with a much simpler numerical method than that previously employed by the author. The governing partial differential equation is solved with finite differences in the radial direction and spectral collocation in the vertical direction. RWI modes are calculated subject to different upper disc boundary conditions. These include free surface, solid boundaries and variable vertical domain size. Boundary conditions that oppose vertical motion increase the instability growth rate by a few per cent. The magnitude of vertical flow throughout the fluid column can be affected but the overall flow pattern is qualitatively unchanged. Numerical results support the notion that the RWI is intrinsically two dimensional. This implies that inconsistent upper disc boundary conditions, such as vanishing enthalpy perturbation, may inhibit the RWI in 3D.
Jin, Guoyong; Su, Zhu
2015-01-01
This book develops a uniform accurate method which is capable of dealing with vibrations of laminated beams, plates and shells with arbitrary boundary conditions including classical boundaries, elastic supports and their combinations. It also provides numerous solutions for various configurations including various boundary conditions, laminated schemes, geometry and material parameters, which fill certain gaps in this area of reach and may serve as benchmark solutions for the readers. For each case, corresponding fundamental equations in the framework of classical and shear deformation theory are developed. Following the fundamental equations, numerous free vibration results are presented for various configurations including different boundary conditions, laminated sequences and geometry and material properties. The proposed method and corresponding formulations can be readily extended to static analysis.
Overcoming order reduction in diffusion-reaction splitting. Part 2: oblique boundary conditions
Einkemmer, Lukas
2016-01-01
Splitting methods constitute a well-established class of numerical schemes for the time integration of partial differential equations. Their main advantages over more traditional schemes are computational efficiency and superior geometric properties. In the presence of non-trivial boundary conditions, however, splitting methods usually suffer from order reduction and some additional loss of accuracy. For diffusion-reaction equations with inhomogeneous oblique boundary conditions, a modification of the classic second-order Strang splitting is proposed that successfully resolves the problem of order reduction. The same correction also improves the accuracy of the classic first-order Lie splitting. The proposed modification only depends on the available boundary data and, in the case of non Dirichlet boundary conditions, on the computed numerical solution. Consequently, this modification can be implemented in an efficient way, which makes the modified splitting schemes superior to their classic versions. The fra...
Trinkaus, H.; Singh, B.N.; Victoria, M.
1996-01-01
be absorbed by extended sinks such as dislocations and grain boundaries (GBs). The loss of SIAs by this process causes a vacancy supersaturation representing an efficient driving force for void swelling, in particular in regions adjacent to GBs. Enhanced swelling in regions adjacent to GBs has been observed...... in several metals subject to irradiation by both fast fission neutrons and 600 MeV protons. In the latter case, however, the width of the region of enhanced swelling is smaller and the amount of swelling is significantly lower than in the former case. Recently, enhanced swelling near GBs as induced...
S. Basu; A. A. M. Holtslag; Wiel, van de, C.C.M.; Moene, A.F.; G. J. Steeneveld
2008-01-01
In single column and large-eddy simulation studies of the atmospheric boundary layer, surface sensible heat flux is often used as a boundary condition. In this paper, we delineate the fundamental shortcomings of such a boundary condition in the context of stable boundary layer modelling and simulation. Using an analytical approach, we are able to show that for reliable model results of the stable boundary layer accurate surface temperature prescription or prediction is needed. As such, the us...
Basu, Sukanta; Holtslag, Albert; Wiel, Bas; Moene, Arnold; Steeneveld, Gert-Jan
2008-03-01
In single column and large-eddy simulation studies of the atmospheric boundary layer, surface sensible heat flux is often used as a boundary condition. In this paper, we delineate the fundamental shortcomings of such a boundary condition in the context of stable boundary layer modelling and simulation. Using an analytical approach, we are able to show that for reliable model results of the stable boundary layer accurate surface temperature prescription or prediction is needed. As such, the use of surface heat flux as a boundary condition should be avoided in stable conditions.
Gibbs, Jeremy A.; Fedorovich, Evgeni; Shapiro, Alan
2015-02-01
Two formulations of the surface thermal boundary condition commonly employed in numerical modelling of atmospheric stably stratified surface-layer flows are evaluated using analytical considerations and observational data from the Cabauw site in the Netherlands. The first condition is stated in terms of the surface heat flux and the second is stated in terms of the vertical potential temperature difference. The similarity relationships used to relate the flux and the difference are based on conventional log-linear expressions for vertical profiles of wind velocity and potential temperature. The heat-flux formulation results in two physically meaningful values for the friction velocity with no obvious criteria available to choose between solutions. Both solutions can be obtained numerically, which casts doubt on discarding one of the solutions as was previously suggested based on stability arguments. This solution ambiguity problem is identified as the key issue of the heat-flux condition formulation. In addition, the agreement between the temperature difference evaluated from similarity solutions and their measurement-derived counterparts from the Cabauw dataset appears to be very poor. Extra caution should be paid to the iterative procedures used in the model algorithms realizing the heat-flux condition as they could often provide only partial solutions for the friction velocity and associated temperature difference. Using temperature difference as the lower boundary condition bypasses the ambiguity problem and provides physically meaningful values of heat flux for a broader range of stability condition in terms of the flux Richardson number. However, the agreement between solutions and observations of the heat flux is again rather poor. In general, there is a great need for practicable similarity relationships capable of treating the vertical turbulent transport of momentum and heat under conditions of strong stratification in the surface layer.
于艳梅; 杨根仓; 赵达文; 吕衣礼
2002-01-01
By the phase-field approach, the dendritic growth in binary alloy melt was simulated respectively using two types of temperature boundary conditions, i.e., the constant temperature boundary by which the boundary temperature was fixed at the initial temperature, and Zero-Neumann temperature boundary. The influences of the temperature boundary conditions on numerical results are investigated. How to choose appropriate temperature boundary conditions is proposed. The results show that: 1) when the computation region is limited to a changeless size, the Zero-Neumann and constant temperature boundary conditions lead to the different dendritic growth behaviors, and the Zero-Neumann condition is preferable to the constant temperature condition; 2) when the computation region is enlarged continually with the computational time according to the increasing thermal diffusion scale, the two types of temperature boundary conditions achieve the consistent tip velocities and tip radii, and they both are appropriate choices.
Tezduyar, T. E.; Liou, J.
1991-01-01
Downstream boundary conditions equivalent to the homogeneous form of the natural boundary conditions associated with the velocity-pressure formulation of the Navier-Stokes equations are derived for the vorticity-stream function formulation of two-dimensional incompressible flows. Of particular interest are the zero normal and shear stress conditions at a downstream boundary.
Existence and asymptotic behavior of the wave equation with dynamic boundary conditions
Graber, Philip Jameson
2012-03-07
The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time. © 2012 Springer Science+Business Media, LLC.
The SR 97 project presents a performance assessment (PA) of the overall safety of a hypothetical deep repository at three sites in Sweden arbitrarily named Aberg, Beberg and Ceberg. One component of this PA assesses the uncertainties in the hydrogeological modelling. This study focuses on uncertainties in boundary settings (size of model domain and boundary conditions) in the regional and site-scale hydrogeological modelling of the three sites used to simulating the possible transport of radionuclides from the emplacement waste packages through the host rock to the accessible environment. Model uncertainties associated with, for instance, parameter heterogeneity and structural interpretations are addressed in other studies. This study concludes that the regional modelling of the SR 97 project addresses uncertainties in the choice of boundary conditions and size of model domain differently at each site, although the overall handling is acceptable and in accordance with common modelling practice. For example, the treatment of uncertainties with regard to the ongoing post-glacial flushing of the Baltic Shield is creditably addressed although not exhaustive from a modelling point of view. A significant contribution of the performed modelling is the study of nested numerical models, i.e., the numerical interplay between regional and site-scale numerical models. In the site-scale modelling great efforts are made to address problems associated with (i) the telescopic mesh refinement (TMR) technique with regard to the stochastic continuum approach, and (ii) the transfer of boundary conditions between variable-density flow systems and flow systems that are constrained to treat uniform density flow. This study concludes that the efforts made to handle these problems are acceptable with regards to the objectives of the SR 97 project
Tam, Christopher K. W.; Webb, Jay C.
1994-01-01
In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The
An outgoing energy flux boundary condition for finite difference ICRP antenna models
For antennas at the ion cyclotron range of frequencies (ICRF) modeling in vacuum can now be carried out to a high level of detail such that shaping of the current straps, isolating septa, and discrete Faraday shield structures can be included. An efficient approach would be to solve for the fields in the vacuum region near the antenna in three dimensions by finite methods and to match this solution at the plasma-vacuum interface to a solution obtained in the plasma region in one dimension by Fourier methods. This approach has been difficult to carry out because boundary conditions must be imposed at the edge of the finite difference grid on a point-by-point basis, whereas the condition for outgoing energy flux into the plasma is known only in terms of the Fourier transform of the plasma fields. A technique is presented by which a boundary condition can be imposed on the computational grid of a three-dimensional finite difference, or finite element, code by constraining the discrete Fourier transform of the fields at the boundary points to satisfy an outgoing energy flux condition appropriate for the plasma. The boundary condition at a specific grid point appears as a coupling to other grid points on the boundary, with weighting determined by a kemel calctdated from the plasma surface impedance matrix for the various plasma Fourier modes. This boundary condition has been implemented in a finite difference solution of a simple problem in two dimensions, which can also be solved directly by Fourier transformation. Results are presented, and it is shown that the proposed boundary condition does enforce outgoing energy flux and yields the same solution as is obtained by Fourier methods
Bashir Ahmad
2012-06-01
Full Text Available We study boundary value problems of nonlinear fractional differential equations and inclusions of order $q in (m-1, m]$, $m ge 2$ with multi-strip boundary conditions. Multi-strip boundary conditions may be regarded as the generalization of multi-point boundary conditions. Our problem is new in the sense that we consider a nonlocal strip condition of the form: $$ x(1=sum_{i=1}^{n-2}alpha_i int^{eta_i}_{zeta_i} x(sds, $$ which can be viewed as an extension of a multi-point nonlocal boundary condition: $$ x(1=sum_{i=1}^{n-2}alpha_i x(eta_i. $$ In fact, the strip condition corresponds to a continuous distribution of the values of the unknown function on arbitrary finite segments $(zeta_i,eta_i$ of the interval $[0,1]$ and the effect of these strips is accumulated at $x=1$. Such problems occur in the applied fields such as wave propagation and geophysics. Some new existence and uniqueness results are obtained by using a variety of fixed point theorems. Some illustrative examples are also discussed.
The unified method: II. NLS on the half-line with t-periodic boundary conditions
Lenells, J.; Fokas, A. S.
2012-05-01
Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general method to this particular class of problems yields the solution in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the complex k-plane (the Fourier plane), which has a jump matrix with explicit (x, t)-dependence involving four scalar functions of k, called spectral functions. Two of these functions depend on the initial data, whereas the other two depend on all boundary values. The most difficult step of the new method is the characterization of the latter two spectral functions in terms of the given initial and boundary data, i.e. the elimination of the unknown boundary values. For certain boundary conditions, called linearizable, this can be achieved by simply using algebraic manipulations. Here, we first present an effective characterization of the spectral functions in terms of the given initial and boundary data for the general case of non-linearizable boundary conditions. This characterization is based on the analysis of the so-called global relation and on the introduction of the so-called Gelfand-Levitan-Marchenko representations of the eigenfunctions defining the spectral functions. We then concentrate on the physically significant case of t-periodic Dirichlet boundary data. After presenting certain heuristic arguments which suggest that the Neumann boundary values become periodic as t → ∞, we show that for the case of the NLS with a sine-wave as Dirichlet data, the asymptotics of the Neumann boundary values can be computed explicitly at least up to third order in a perturbative expansion and indeed at least up to this order are asymptotically periodic.
Degenerate backward SPDEs in domains: non-local boundary conditions and applications to finance
Nikolai Dokuchaev
2012-01-01
Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied and the equation can be degenerate. Some generalized solutions based on the representation theorem are suggested. In addition to problems with a standard Cauchy condition at the terminal time, problems with special non-local boundary conditions are considered. These non-local conditions connect the terminal value of the so...
Bessaih, Hakima
2015-04-01
The evolution Stokes equation in a domain containing periodically distributed obstacles subject to Fourier boundary condition on the boundaries is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the obstacles. We represent the solid obstacles by holes in the fluid domain. The macroscopic (homogenized) equation is derived as another stochastic partial differential equation, defined in the whole non perforated domain. Here, the initial stochastic perturbation on the boundary becomes part of the homogenized equation as another stochastic force. We use the twoscale convergence method after extending the solution with 0 in the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. In order to pass to the limit on the boundary integrals, we rewrite them in terms of integrals in the whole domain. In particular, for the stochastic integral on the boundary, we combine the previous idea of rewriting it on the whole domain with the assumption that the Brownian motion is of trace class. Due to the particular boundary condition dealt with, we get that the solution of the stochastic homogenized equation is not divergence free. However, it is coupled with the cell problem that has a divergence free solution. This paper represents an extension of the results of Duan and Wang (Comm. Math. Phys. 275:1508-1527, 2007), where a reaction diffusion equation with a dynamical boundary condition with a noise source term on both the interior of the domain and on the boundary was studied, and through a tightness argument and a pointwise two scale convergence method the homogenized equation was derived. © American Institute of Mathematical Sciences.
Well posed constraint-preserving boundary conditions for the linearized Einstein equations
Calabrese, G; Reula, O; Sarbach, O; Tiglio, M H; Calabrese, Gioel; Pullin, Jorge; Reula, Oscar; Sarbach, Olivier; Tiglio, Manuel
2003-01-01
In the Cauchy problem of general relativity one considers initial data that satisfies certain constraints. The evolution equations guarantee that the evolved variables will satisfy the constraints at later instants of time. This is only true within the domain of dependence of the initial data. If one wishes to consider situations where the evolutions are studied for longer intervals than the size of the domain of dependence, as is usually the case in three dimensional numerical relativity, one needs to give boundary data. The boundary data should be specified in such a way that the constraints are satisfied everywhere, at all times. In this paper we address this problem for the case of general relativity linearized around Minkowski space using the generalized Einstein-Christoffel symmetric hyperbolic system of evolution equations. We study the evolution equations for the constraints, specify boundary conditions for them that make them well posed and further choose these boundary conditions in such a way that ...
Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions
Caflisch, Russel E.; Lombardo, Maria Carmela; Sammartino, Marco
2011-05-01
In this paper nonlocal boundary conditions for the Navier-Stokes equations are derived, starting from the Boltzmann equation in the limit for the Knudsen number being vanishingly small. In the same spirit of (Lombardo et al. in J. Stat. Phys. 130:69-82, 2008) where a nonlocal Poisson scattering kernel was introduced, a gaussian scattering kernel which models nonlocal interactions between the gas molecules and the wall boundary is proposed. It is proved to satisfy the global mass conservation and a generalized reciprocity relation. The asymptotic expansion of the boundary-value problem for the Boltzmann equation, provides, in the continuum limit, the Navier-Stokes equations associated with a class of nonlocal boundary conditions of the type used in turbulence modeling.
Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
We consider the Rényi entanglement entropies in the one-dimensional XX spin-chains with open boundary conditions in the presence of a magnetic field. In the case of a semi-infinite system and a block starting from the boundary, we derive rigorously the asymptotic behavior for large block sizes on the basis of a recent mathematical theorem for the determinant of Toeplitz plus Hankel matrices. We conjecture a generalized Fisher–Hartwig form for the corrections to the asymptotic behavior of this determinant that allows the exact characterization of the corrections to the scaling at order o(l-1) for any n. By combining these results with conformal field theory arguments, we derive exact expressions also in finite chains with open boundary conditions and in the case when the block is detached from the boundary
Beyond the Fourier heat conduction law and the thermal no-slip boundary condition
The problem of heat slip flow along solid walls is investigated within the framework of modern thermodynamics. The underlying idea is to elevate the heat flux at the boundary to the status of independent variable. General boundary conditions are obtained from the constraint imposed by the second law of thermodynamics expressing that the rate of entropy production is non-negative. In parallel, evolution equations for the heat flux inside the bulk of the system are also formulated. -- Highlights: ► A modeling of thermal slip boundary conditions is proposed. ► Theoretical support is provided by Extended Irreversible Thermodynamics. ► Original idea: the heat flux and the flux of heat flux at the boundary surface are taken as independent variables. ► Model is especially useful at subscales: i.e. micro and nano scales.
Villafruela, J.M.; Olmedo, Inés; Ruiz de Adana, M.;
2013-01-01
different environmental conditions and to validate whether a steady boundary condition of the exhalation flow may simulate human breathing in an effective and accurate way. The results show a very good agreement of the numerical results obtained for Test a and the experimental data. This fact confirms the...... use of numerical simulation as a powerful tool to predict the contaminant distribution exhaled by a human. The numerical tests with steady boundary conditions for the exhalation flow require a transitory resolution procedure and the predictions provided by these models display some discrepancies with...
Tairone Paiva Leão
2011-02-01
Full Text Available An accurate estimation of hydraulic fluxes in the vadose zone is essential for the prediction of water, nutrient and contaminant transport in natural systems. The objective of this study was to simulate the effect of variation of boundary conditions on the estimation of hydraulic properties (i.e. water content, effective unsaturated hydraulic conductivity and hydraulic flux in a one-dimensional unsaturated flow model domain. Unsaturated one-dimensional vertical water flow was simulated in a pure phase clay loam profile and in clay loam interlayered with silt loam distributed according to the third iteration of the Cantor Bar fractal object Simulations were performed using the numerical model Hydrus 1D. The upper and lower pressure heads were varied around average values of -55 cm for the near-saturation range. This resulted in combinations for the upper and lower constant head boundary conditions, respectively, of -50 and -60 cm, -40 and -70 cm, -30 and -80 cm, -20 and -90 cm, and -10 and -100 cm. For the drier range the average head between the upper and lower boundary conditions was set to -550 cm, resulting in the combinations -500 and -600 cm, -400 and -700 cm, -300 and -800 cm, -200 and -900 cm, and -100 and -1,000 cm, for upper and lower boundary conditions, respectively. There was an increase in water contents, fluxes and hydraulic conductivities with the increase in head difference between boundary conditions. Variation in boundary conditions in the pure phase and interlayered one-dimensional profiles caused significant deviations in fluxes, water contents and hydraulic conductivities compared to the simplest case (a head difference between the upper and lower constant head boundaries of 10 cm in the wetter range and 100 cm in the drier range.
Unified semi-analytical wall boundary conditions applied to 2-D incompressible SPH
Leroy, A.; Violeau, D.; Ferrand, M.; Kassiotis, C.
2014-03-01
This work aims at improving the 2-D incompressible SPH model (ISPH) by adapting it to the unified semi-analytical wall boundary conditions proposed by Ferrand et al. [10]. The ISPH algorithm considered is as proposed by Lind et al. [25], based on the projection method with a divergence-free velocity field and using a stabilising procedure based on particle shifting. However, we consider an extension of this model to Reynolds-Averaged Navier-Stokes equations based on the k-ɛ turbulent closure model, as done in [10]. The discrete SPH operators are modified by the new description of the wall boundary conditions. In particular, a boundary term appears in the Laplacian operator, which makes it possible to accurately impose a von Neumann pressure wall boundary condition that corresponds to impermeability. The shifting and free-surface detection algorithms have also been adapted to the new boundary conditions. Moreover, a new way to compute the wall renormalisation factor in the frame of the unified semi-analytical boundary conditions is proposed in order to decrease the computational time. We present several verifications to the present approach, including a lid-driven cavity, a water column collapsing on a wedge and a periodic schematic fish-pass. Our results are compared to Finite Volumes methods, using Volume of Fluids in the case of free-surface flows. We briefly investigate the convergence of the method and prove its ability to model complex free-surface and turbulent flows. The results are generally improved when compared to a weakly compressible SPH model with the same boundary conditions, especially in terms of pressure prediction.
Stress and mixed boundary conditions for two-dimensional dodecagonal quasi-crystal plates
Yan Gao; Si-Peng Xu; Bao-Sheng Zhao
2007-05-01
For plate bending and stretching problems in two-dimensional (2D) dodecagonal quasi-crystal (QC) media, the reciprocal theorem and the general solution for QCs are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all order. The method developed by Gregory and Wan is used to generate necessary conditions which the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the plate; these decaying state conditions are obtained explicitly for axisymmetric bending and stretching of a circular plate when stress or mixed conditions are imposed on the plate edge. They are then used for the correct formulation of boundary conditions for the interior solution. For the stress data, our boundary conditions coincide with those obtained in conventional forms of plate theories. More importantly, appropriate boundary conditions with a set of mixed edge-data are obtained for the ﬁrst time. Furthermore, the corresponding necessary conditions for transversely isotropic elastic plate are obtained directly, and their isotropic elastic counterparts are also obtained.
Effects of microscopic boundary conditions on plastic deformations of small-sized single crystals
Kuroda, Mitsutoshi; Tvergaard, Viggo
2009-01-01
effect of higher-order boundary conditions on the overall deformation mode of the block is observed. The bent foil has free surfaces through which dislocations can go out of the material, and we observe a strong size-dependent mechanical response resulting from the surface condition assumed....
Hyers-Ulam stability for second-order linear differential equations with boundary conditions
Pasc Gavruta
2011-06-01
Full Text Available We prove the Hyers-Ulam stability of linear differential equations of second-order with boundary conditions or with initial conditions. That is, if y is an approximate solution of the differential equation $y''+ eta (x y = 0$ with $y(a = y(b =0$, then there exists an exact solution of the differential equation, near y.
Araz R. Aliev
2013-10-01
Full Text Available We study a third-order operator-differential equation on the semi-axis with a discontinuous coefficient and boundary conditions which include an abstract linear operator. Sufficient conditions for the well-posed and unique solvability are found by means of properties of the operator coefficients in a Sobolev-type space.
Désilles, Anya; Frankowska, Hélène
2013-01-01
International audience Abstract. A solution of the initial-boundary value problem on the strip (0,1) × [0, 1] for scalar conservation laws with strictly convex flux can be obtained by considering gradients of the unique solution V to an associated Hamilton-Jacobi equation (with appropriately defined initial and boundary conditions). It was shown in Frankowska (2010) that V can be expressed as the minimum of three value functions arising in calculus of variations problems that, in turn, can...
Heat kernel for the elliptic system of linear elasticity with boundary conditions
Taylor, Justin; Kim, Seick; Brown, Russell
2013-01-01
We consider the elliptic system of linear elasticity with bounded measurable coefficients in a domain where the second Korn inequality holds. We construct heat kernel of the system subject to Dirichlet, Neumann, or mixed boundary condition under the assumption that weak solutions of the elliptic system are H\\"older continuous in the interior. Moreover, we show that if weak solutions of the mixed problem are H\\"older continuous up to the boundary, then the corresponding heat kernel has a Gauss...
Donatelli, D.; Feireisl, E.; Novotný, A.
2010-01-01
We study the low Mach number limit for the compressible Navier-Stokes system supplemented with Navier's boundary condition on an unbounded domain with compact boundary. Our main result asserts that the velocities converge pointwise to a solenoidal vector field - a weak solution of the incompressible Navier-Stokes system - while the fluid density becomes constant. The proof is based on a variant of local energy decay property for the underlying acoustic equation established by Kato.
Slavin, Jonathan D.; Frisch, Priscilla C.
2007-01-01
The boundary conditions of the heliosphere are set by the ionization, density and composition of inflowing interstellar matter. Constraining the properties of the Local Interstellar Cloud (LIC) at the heliosphere requires radiative transfer ionization models. We model the background interstellar radiation field using observed stellar FUV and EUV emission and the diffuse soft X-ray background. We also model the emission from the boundary between the LIC and the hot Local Bubble (LB) plasma, as...
Nonlinear transmission problem with a dissipative boundary condition of memory type
Doherty Andrade
2006-04-01
Full Text Available We consider a differential equation that models a material consisting of two elastic components. One component is clamped while the other is in a viscoelastic fluid producing a dissipative mechanism on the boundary. So, we have a transmission problem with boundary damping condition of memory type. We prove the existence of a global solution and its uniformly decay to zero as time approaches infinity. More specifically, the solution decays exponentially provided the relaxation function decays exponentially.
On a Non-Reflecting Boundary Condition for Hyperbolic Conservation Laws
Loh, Ching Y.
2003-01-01
A non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented. The technique is based on the first principle of non-reflecting, plane wave propagation and the hyperbolicity of the Euler equation system. The NRBC is simple and effective, provided the numerical scheme maintains locally a C(sup 1) continuous solution at the boundary. Several numerical examples in 1D, 2D, and 3D space are illustrated to demonstrate its robustness in practical computations.
Vectorization of diffusion computations in the presence of periodic boundary conditions
Abu-Shumays, I.K.
1985-05-01
Solutions of very large three-dimensional elliptic diffusion problems are very expensive in terms of storage requirements and computational cost even on today's supercomputers. Effective utilization of translational or rotational periodic boundary conditions, when applicable, can substantially reduce cost. Implementation of periodic boundary conditions however is not straightforward and special care should be exercised to avoid loss of computational efficiency. Application of periodic boundary conditions perturbs the overall matrix structure of the underlying discretized diffusion equations and may adversely affect standard computational methods. For simplicity, this study is restricted to the solution of two-dimensional diffusion problems. The numerical solution methods considered are the point Chebyshev and line cyclic Chebyshev iterative methods. It is straightforward to implement periodic boundary conditions within the framework of the highly vectorizable point Chebyshev iterative method. This paper presents alternative approaches for implementing periodic boundary conditions within the framework of the line cyclic Chebyshev iteration method. In the process, the method of odd-even cyclic reduction as applied to vectorization of the solution of tridiagonal systems is generalized to apply to special sparse predominantly tridiagonal matrix equations. For two-dimensional problems, it is demonstrated numerically on a CYBER 205 for model situations that the resulting line cyclic Chebyshev iterative method is computationally superior to the highly vectorizable point Chebyshev iterative method. The superiority of the line cyclic Chebyshev method over the point Chebyshev method is expected to hold for more complex problems with general mesh triangulations.
Ke-Qi Pan; Jin-Yang Liu
2012-01-01
The objective of this investigation is to examine the correctness and efficiency of the choice of boundary conditions when using assumed mode approach to simulate flexible multi-body systems.The displacement field due to deformation is approximated by the Rayleigh-Ritz assumed modes in floating frame of reference (FFR) formulation.The deformations obtained by the absolute nodal coordinate (ANC) formulation which are transformed by two sets of reference coordinates are introduced as a criterion to verify the accuracy of the simulation results by using the FFR formulation.The relationship between the deformations obtained from different boundary conditions is revealed.Numerical simulation examples demonstrate that the assumed modes with cantilevered-free,simply-supported and freefree boundary conditions without inclusion of rigid body modes are suitable for simulation of flexible multi-body system with large over all motion,and the same physical deformation can be obtained using those mode functions,differ only by a coordinate transformation.It is also shown that when using mode shapes with statically indeterminate boundary conditions,significant error may occur.Furthermore,the slider crank mechanism with rigid crank is accurate enough for investigating boundary condition problem of flexible multi-body system,which cost significant less simulating time.
Pan, Ke-Qi; Liu, Jin-Yang
2012-02-01
The objective of this investigation is to examine the correctness and efficiency of the choice of boundary conditions when using assumed mode approach to simulate flexible multi-body systems. The displacement field due to deformation is approximated by the Rayleigh-Ritz assumed modes in floating frame of reference (FFR) formulation. The deformations obtained by the absolute nodal coordinate (ANC) formulation which are transformed by two sets of reference coordinates are introduced as a criterion to verify the accuracy of the simulation results by using the FFR formulation. The relationship between the deformations obtained from different boundary conditions is revealed. Numerical simulation examples demonstrate that the assumed modes with cantilevered-free, simply-supported and free-free boundary conditions without inclusion of rigid body modes are suitable for simulation of flexible multi-body system with large over all motion, and the same physical deformation can be obtained using those mode functions, differ only by a coordinate transformation. It is also shown that when using mode shapes with statically indeterminate boundary conditions, significant error may occur. Furthermore, the slider crank mechanism with rigid crank is accurate enough for investigating boundary condition problem of flexible multi-body system, which cost significant less simulating time. The project was supported by the National Natural Science Foundation of China (10872126) and the Research Fund of the Doctoral Program of Higher Education of China (20100073110007).
Boundary conditions for General Relativity on AdS$_{3}$ and the KdV hierarchy
Pérez, Alfredo; Troncoso, Ricardo
2016-01-01
It is shown that General Relativity with negative cosmological constant in three spacetime dimensions admits a new family of boundary conditions being labeled by a nonnegative integer $k$. Gravitational excitations are then described by "boundary gravitons" that fulfill the equations of the $k$-th element of the KdV hierarchy. In particular, $k=0$ corresponds to the Brown-Henneaux boundary conditions so that excitations are described by chiral movers. In the case of $k=1$, the boundary gravitons fulfill the KdV equation and the asymptotic symmetry algebra turns out to be infinite-dimensional, abelian and devoid of central extensions. The latter feature also holds for the remaining cases that describe the hierarchy ($k>1$). Our boundary conditions then provide a gravitational dual of two noninteracting left and right KdV movers, and hence, boundary gravitons possess anisotropic Lifshitz scaling with dynamical exponent $z=2k+1$. Remarkably, despite spacetimes solving the field equations are locally AdS, they po...
The Physical Conditions of Intermediate Redshift MgII Absorbing Clouds from Voigt Profile Analysis
Churchill, C W; Charlton, J; Churchill, Chris; Vogt, Steven; Charlton, Jane
2003-01-01
[Slightly Abridged] We present a detailed statistical analysis of the column densities, N, and Doppler parameters, b, of MgII absorbing clouds at redshifts 0.4~5 km/s for MgII and FeII and ~7 km/s for MgI. The clouds are consistent with being thermally broadened, with temperatures in the 30-40,000K range. (4) A two-component Gaussian model to the velocity two-point correlation function yielded velocity dispersions of 54 km/s and 166 km/s. The narrow component has roughly twice the amplitude of the broader component. The width and amplitude of the broader component decreases as equivalent width increases. (5) From photoionization models we find that the column density ratios are most consistent with photoionization by the extragalactic background, as opposed to stars. Based upon N(MgI)/N(MgII), it appears that at least two-phase ionization models are required to explain the data.
Disk emission and absorption lines in LMXB. Note on the physical conditions of an absorbing material
Rozanska, Agata
2014-01-01
We show that the continuum X-ray spectrum of 4U 1630-472 with iron absorption lines can be satisfactorily modeled by the spectrum from an accretion disk atmosphere. We performed full radiative transfer calculations using our code ATM21 to model the emission from an accretion disk surface that is seen at different viewing angles. Computed models are then fitted to the high-resolution X-ray spectra of 4U 1630-472 obtained by {\\it Suzaku} satellite. Absorption lines of highly ionized iron originating in a hot accretion-disk atmospheres are important part of the observed line profile, and can be an alternative or complementary explanation to the wind model usually favored for this type of sources. Next, assuming that absorption lines originate from the wind illuminated by X-ray central source in LMXBs, we can put constrains on the wind location only if we know the volume density number of the absorbing material. There are a few derivations of the distance to the wind in X-ray binaries. We show here, that the dens...
Non-diagonal boundary conditions for gl(1|1) super spin chains
Grabinski, Andre M; Frahm, Holger, E-mail: frahm@itp.uni-hannover.d [Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstrasse 2, 30167 Hannover (Germany)
2010-01-29
We study a one-dimensional model of free fermions with gl(1|1) supersymmetry and demonstrate how non-diagonal boundary conditions can be incorporated into the framework of the graded quantum inverse scattering method (gQISM) by means of super matrices with entries from a superalgebra. For super Hermitian twists and open boundary conditions subject to a certain constraint, we solve the eigenvalue problem for the super transfermatrix by means of the graded algebraic Bethe ansatz technique (gABA) starting from a fermionic coherent state. For generic boundary conditions the algebraic Bethe ansatz cannot be applied. In this case the spectrum of the super transfermatrix is obtained from a functional relation.
Compatibility between shape equation and boundary conditions of lipid membranes with free edges.
Tu, Z C
2010-02-28
Only some special open surfaces satisfying the shape equation of lipid membranes can be compatible with the boundary conditions. As a result of this compatibility, the first integral of the shape equation should vanish for axisymmetric lipid membranes, from which two theorems of nonexistence are verified: (i) there is no axisymmetric open membrane being a part of torus satisfying the shape equation; (ii) there is no axisymmetric open membrane being a part of a biconcave discodal surface satisfying the shape equation. Additionally, the shape equation is reduced to a second-order differential equation while the boundary conditions are reduced to two equations due to this compatibility. Numerical solutions to the reduced shape equation and boundary conditions agree well with the experimental data [A. Saitoh et al., Proc. Natl. Acad. Sci. U.S.A. 95, 1026 (1998)]. PMID:20192294
Heat Transfer Boundary Conditions in the RELAP5-3D Code
The heat transfer boundary conditions used in the RELAP5-3D computer program have evolved over the years. Currently, RELAP5-3D has the following options for the heat transfer boundary conditions: (a) heat transfer correlation package option, (b) non-convective option (from radiation/conduction enclosure model or symmetry/insulated conditions), and (c) other options (setting the surface temperature to a volume fraction averaged fluid temperature of the boundary volume, obtaining the surface temperature from a control variable, obtaining the surface temperature from a time-dependent general table, obtaining the heat flux from a time-dependent general table, or obtaining heat transfer coefficients from either a time- or temperature-dependent general table). These options will be discussed, including the more recent ones
Ahmadikia, H. [University of Isfahan, Isfahan (Iran, Islamic Republic of); Rismanian, M. [Bu-Ali Sina University, Hamadan (Iran, Islamic Republic of)
2011-11-15
Fourier and hyperbolic models of heat transfer on a fin that is subjected to a periodic boundary condition are solved analytically. The differential equation in Fourier and non-Fourier models is solved by the Laplace transform method. The temperature distribution on the fin is obtained using the residual theorem in a complex plan for the inverse Laplace transform method. The thermal shock is generated at the base of the fin, which moves toward the tip of the fin and is reflected from the tip. The current study of various parameters on the thermal shock location shows that relaxation time has a great influence on the temperature distribution on the fin. An unsteady boundary condition in the base fin caused the shock, which is generated continuously from the base and has interacted with the other reflected thermal shocks. Results of the current study show that the hyperbolic heat conduction equation can violate the second thermodynamic law under some unsteady boundary conditions.
Degraeve, S.; Granger, C.; Dubus, B.; Vasseur, J. O.; Pham Thi, M.; Hladky-Hennion, A.-C.
2014-05-01
An homogeneous piezoelectric rod is shown to exhibit Bragg band gaps when an electrical boundary condition is applied periodically with the help of metallic electrodes. An analytical model is developed which formulation depends on the applied electric boundary condition and reveals that Bragg band gaps occurring in this very peculiar phononic crystal are related to the electric charge located on the electrodes. Moreover, via an accurate boundary condition (electrodes connected in short circuit, in open circuit, or through an external capacitance), full tunability of the Bragg band gaps can be achieved. Measurements of ultrasonic transmission present an overall excellent agreement with the theoretical results. This phononic crystal can be easily manufactured and presents many potential applications as frequency filters especially for radio frequency telecommunications.
Fourier and hyperbolic models of heat transfer on a fin that is subjected to a periodic boundary condition are solved analytically. The differential equation in Fourier and non-Fourier models is solved by the Laplace transform method. The temperature distribution on the fin is obtained using the residual theorem in a complex plan for the inverse Laplace transform method. The thermal shock is generated at the base of the fin, which moves toward the tip of the fin and is reflected from the tip. The current study of various parameters on the thermal shock location shows that relaxation time has a great influence on the temperature distribution on the fin. An unsteady boundary condition in the base fin caused the shock, which is generated continuously from the base and has interacted with the other reflected thermal shocks. Results of the current study show that the hyperbolic heat conduction equation can violate the second thermodynamic law under some unsteady boundary conditions
Fang, Angbo
2008-12-08
Parallel to the highly successful Ericksen-Leslie hydrodynamic theory for the bulk behavior of nematic liquid crystals (NLCs), we derive a set of coupled hydrodynamic boundary conditions to describe the NLC dynamics near NLC-solid interfaces. In our boundary conditions, translational flux (flow slippage) and rotational flux (surface director relaxation) are coupled according to the Onsager variational principle of least energy dissipation. The application of our boundary conditions to the truly bistable π -twist NLC cell reveals a complete picture of the dynamic switching processes. It is found that the thus far overlooked translation-rotation dissipative coupling at solid surfaces can accelerate surface director relaxation and enhance the flow rate. This can be utilized to improve the performance of electro-optical nematic devices by lowering the required switching voltages and reducing the switching times. © 2008 The American Physical Society.
Twist-averaged boundary conditions for nuclear pasta Hartree-Fock calculations
Schuetrumpf, B
2015-01-01
Background: Nuclear pasta phases, present in the inner crust of neutron stars, are associated with nucleonic matter at sub-saturation densities arranged in regular shapes. Those complex phases, residing in a layer which is approximately 100 m thick, impact many features of neutron stars. Theoretical quantum-mechanical simulations of nuclear pasta are usually carried out in finite 3D boxes assuming periodic boundary conditions (PBC). The resulting solutions are affected by spurious finite-size effects. Purpose: In order to remove spurious finite-size effects, it is convenient to employ twist-averaged boundary conditions (TABC) used in condensed matter, nuclear matter, and lattice QCD applications. In this work, we study the effectiveness of TABC in the context of pasta phases simulations within nuclear density functional theory. Methods: We perform Skyrme-Hartree-Fock calculations in three dimensions by implementing Bloch boundary conditions. The TABC averages are obtained by means of Gauss-Legendre integratio...
Pseudoscalar mesons in a finite cubic volume with twisted boundary conditions
Colangelo, Gilberto
2016-01-01
We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We first apply chiral perturbation theory in the p-regime and calculate the corrections for masses, decay constants, pseudoscalar coupling constants and form factors at next-to-leading order. We show that the Feynman-Hellmann theorem and the relevant Ward-Takahashi identity are satisfied. We then derive asymptotic formulae a la Luscher for twisted boundary conditions. We show that chiral Ward identities for masses and decay constants are satisfied by the asymptotic formulae in finite volume as a consequence of infinite-volume Ward identities. Applying asymptotic formulae in combination with chiral perturbation theory we estimate corrections beyond next-to-leading order for twisted boundary conditions.
Su, Zhu; Jin, Guoyong; Ye, Tiangui
2016-06-01
The paper presents a unified solution for free and transient vibration analyses of a functionally graded piezoelectric curved beam with general boundary conditions within the framework of Timoshenko beam theory. The formulation is derived by means of the variational principle in conjunction with a modified Fourier series which consists of standard Fourier cosine series and supplemented functions. The mechanical and electrical properties of functionally graded piezoelectric materials (FGPMs) are assumed to vary continuously in the thickness direction and are estimated by Voigt’s rule of mixture. The convergence, accuracy and reliability of the present formulation are demonstrated by comparing the present solutions with those from the literature and finite element analysis. Numerous results for FGPM beams with different boundary conditions, geometrical parameters as well as material distributions are given. Moreover, forced vibration of the FGPM beams subjected to dynamic loads and general boundary conditions are also investigated.
Heat Transfer Boundary Conditions in the RELAP5-3D Code
Richard A. Riemke; Cliff B. Davis; Richard R. Schultz
2008-05-01
The heat transfer boundary conditions used in the RELAP5-3D computer program have evolved over the years. Currently, RELAP5-3D has the following options for the heat transfer boundary conditions: (a) heat transfer correlation package option, (b) non-convective option (from radiation/conduction enclosure model or symmetry/insulated conditions), and (c) other options (setting the surface temperature to a volume fraction averaged fluid temperature of the boundary volume, obtaining the surface temperature from a control variable, obtaining the surface temperature from a time-dependent general table, obtaining the heat flux from a time-dependent general table, or obtaining heat transfer coefficients from either a time- or temperature-dependent general table). These options will be discussed, including the more recent ones.
Boundary condition handling approaches for the model reduction of a vehicle frame
Xie, Qingxi; Zhang, Nong; Zhang, Bangji; Ji, Jinchen
2016-06-01
In order to apply model reduction technique to improve the computational efficiency for the large-scale FEM model of a vehicle, this paper presents the handling approaches for three widely-used boundary conditions, namely fixed boundary condition (FBC), prescribed motion (PSM) and coupling (COUP), respectively. It is found that iterated improved reduction system (IIRS) reduction method tends to generate better reduction approximation. Guyan method is not sensitive to the sequence of reduction and constraint under FBC, and can thus provide flexibility in handling different boundary conditions for the same system. As for PSM, 'constraint first' is recommended no matter which reduction method is used, and then separate reduction models can be coupled to form a new model with relative small dofs. By selecting appropriate master dofs for model reduction, the coupled model based on reduced models could produce same results as the original full one.
In this paper, the accuracy of the Frensley inflow boundary condition of the Wigner equation is analyzed in computing the I-V characteristics of a resonant tunneling diode (RTD). It is found that the Frensley inflow boundary condition for incoming electrons holds only exactly infinite away from the active device region and its accuracy depends on the length of contacts included in the simulation. For this study, the non-equilibrium Green's function (NEGF) with a Dirichlet to Neumann mapping boundary condition is used for comparison. The I-V characteristics of the RTD are found to agree between self-consistent NEGF and Wigner methods at low bias potentials with sufficiently large GaAs contact lengths. Finally, the relation between the negative differential conductance (NDC) of the RTD and the sizes of contact and buffer in the RTD is investigated using both methods.
Mayrhofer, Arno; Violeau, Damien; Ferrand, Martin
2013-01-01
The semi-analytical wall boundary conditions present a mathematically rigorous framework to prescribe the influence of solid walls in SPH for fluid flows. In this paper they are investigated with respect to the skew-adjoint property which implies exact energy conservation. It will be shown that this property holds only in the limit of the continuous SPH approximation, whereas in the discrete SPH formulation it is only approximately true, leading to numerical noise. This noise, interpreted as form of "turbulence", is treated using an additional volume diffusion term in the continuity equation which we show is equivalent to an approximate Riemann solver. Subsequently two extensions to the boundary conditions are presented. The first dealing with a variable driving force when imposing a volume flux in a periodic flow and the second showing a generalization of the wall boundary condition to Robin type and arbitrary-order interpolation. Two modifications for free-surface flows are presented for the volume diffusio...
Reconsidering the boundary conditions for a dynamic, transient mode I crack problem
Leise, Tanya
2008-11-01
A careful examination of a dynamic mode I crack problem leads to the conclusion that the commonly used boundary conditions do not always hold in the case of an applied crack face loading, so that a modification is required to satisfy the equations. In particular, a transient compressive stress wave travels along the crack faces, moving outward from the loading region on the crack face. This does not occur in the quasistatic or steady state problems, and is a special feature of the transient dynamic problem that is important during the time interval immediately following the application of crack face loading. We demonstrate why the usual boundary conditions lead to a prediction of crack face interpenetration, and then examine how to modify the boundary condition for a semi-infinite crack with a cohesive zone. Numerical simulations illustrate the resulting approach.
Fang, Angbo; Qian, Tiezheng; Sheng, Ping
2008-12-01
Parallel to the highly successful Ericksen-Leslie hydrodynamic theory for the bulk behavior of nematic liquid crystals (NLCs), we derive a set of coupled hydrodynamic boundary conditions to describe the NLC dynamics near NLC-solid interfaces. In our boundary conditions, translational flux (flow slippage) and rotational flux (surface director relaxation) are coupled according to the Onsager variational principle of least energy dissipation. The application of our boundary conditions to the truly bistable pi -twist NLC cell reveals a complete picture of the dynamic switching processes. It is found that the thus far overlooked translation-rotation dissipative coupling at solid surfaces can accelerate surface director relaxation and enhance the flow rate. This can be utilized to improve the performance of electro-optical nematic devices by lowering the required switching voltages and reducing the switching times. PMID:19256854
$A_n^{(1)}$ affine Toda field theories with integrable boundary conditions revisited
Doikou, Anastasia
2008-01-01
Generic classically integrable boundary conditions for the $A_{n}^{(1)}$ affine Toda field theories (ATFT) are investigated. The present analysis relies primarily on the underlying algebra, defined by the classical version of the reflection equation. We use as a prototype example the first non-trivial model of the hierarchy i.e. the $A_2^{(1)}$ ATFT, however our results may be generalized for any $A_{n}^{(1)}$ ($n>1$). We assume here two distinct types of boundary conditions called some times soliton preserving (SP), and soliton non-preserving (SNP) associated to two distinct algebras, i.e. the reflection algebra and the ($q$) twisted Yangian respectively. The boundary local integrals of motion are then systematically extracted from the asymptotic expansion of the associated transfer matrix. In the case of SNP boundary conditions we recover previously known results. The other type of boundary conditions (SP), associated to the reflection algebra, are novel in this context and lead to a different set of conser...
Kempka, S.N.; Strickland, J.H.; Glass, M.W.; Peery, J.S. [Sandia National Labs., Albuquerque, NM (United States); Ingber, M.S. [Univ. of New Mexico, Albuquerque, NM (United States)
1995-04-01
formulation to satisfy velocity boundary conditions for the vorticity form of the incompressible, viscous fluid momentum equations is presented. The tangential and normal components of the velocity boundary condition are satisfied simultaneously by creating vorticity adjacent to boundaries. The newly created vorticity is determined using a kinematical formulation which is a generalization of Helmholtz` decomposition of a vector field. Though it has not been generally recognized, these formulations resolve the over-specification issue associated with creating voracity to satisfy velocity boundary conditions. The generalized decomposition has not been widely used, apparently due to a lack of a useful physical interpretation. An analysis is presented which shows that the generalized decomposition has a relatively simple physical interpretation which facilitates its numerical implementation. The implementation of the generalized decomposition is discussed in detail. As an example the flow in a two-dimensional lid-driven cavity is simulated. The solution technique is based on a Lagrangian transport algorithm in the hydrocode ALEGRA. ALEGRA`s Lagrangian transport algorithm has been modified to solve the vorticity transport equation and the generalized decomposition, thus providing a new, accurate method to simulate incompressible flows. This numerical implementation and the new boundary condition formulation allow vorticity-based formulations to be used in a wider range of engineering problems.
Escolano-Carrasco, José; Jacobsen, Finn; López, J.J.
2008-01-01
The finite-difference time-domain (FDTD) method provides a simple and accurate way of solving initial boundary value problems. However, most acoustic problems involve frequency dependent boundary conditions, and it is not easy to include such boundary conditions in an FDTD model. Although solutions...
Effects of uncertainty in boundary-conditions on flood hazard assessment
Domeneghetti, A.; Vorogushyn, S.; Castellarin, A.; Merz, B.; Brath, A.
2012-04-01
Comprehensive flood-risk assessment studies should quantify the global uncertainty in flood hazard estimation, for instance by mapping inundation extents together with their confidence intervals. This appears of utmost importance, especially in the case of flood hazard assessments along dike-protected reaches, where dike failures have to be considered. This paper focuses on a 50km reach of River Po (Italy) and three major sources of uncertainty in inundation mapping: uncertainties in the (i) upstream and (ii) downstream boundary conditions, and (iii) uncertainties in the dike-failure location and breach morphology. We derive confidence bounds for flood hazard maps by means of the Inundation Hazard Assessment Model (IHAM) - a hybrid probabilistic-deterministic model. IHAM couples in a dynamic way a 1D hydrodynamic model and a 2D raster-based hydraulic model through a probabilistic dike-breaching analysis that considers three different failure mechanisms: overtopping, piping and micro-instability due to seepage. To address the randomness resulting from the variability in boundary conditions and dike-failures the system is run in a Monte Carlo framework. Uncertainties in the definition of upstream boundary conditions (i.e. design-hydrographs) are assessed by applying different bivariate copula families to model the frequency of flood peaks and volumes. Uncertainties in the definition of downstream boundary conditions are characterized by associating the rating-curve used as boundary condition with confidence intervals which reflect discharge measurements errors and interpolation errors. The results of the study are presented in terms of the Monte Carlo-based flood hazard mapping for different flood-intensity indicators (e.g., inundation depth, flow velocity, inundation duration, etc.) together with the corresponding uncertainty bounds. We conclude on the influence of uncertainty in boundary conditions and provide decision makers with an important piece of information
Periodic Solutions of the 1D Vlasov-Maxwell System with Boundary Conditions
Bostan, Mihai
1998-01-01
We study the 1D Vlasov-Maxwell system with time periodic boundary conditions in its classical and relativistic form. For small data we prove existence of weak periodic solutions. It is necessary to impose non vanishing conditions for the incoming velocities in order to control the life-time of particles in the domain. In order to preserve the periodicity, another condition of vanishing the time average of the incoming current is imposed.
(2,2) and (0,4) Supersymmetric Boundary Conditions in 3d N = 4 Theories and Type IIB Branes
Chung, Hee-Joong
2016-01-01
The half-BPS boundary conditions preserving N = (2,2) and N = (0,4) supersymmetry in 3d N = 4 supersymmetric gauge theories are examined. The BPS equations admit decomposition of the bulk supermultiplets into specific boundary supermultiplets of preserved supersymmetry. Bogomolony-like equations and Nahm-like equations arise in the vector multiplet BPS boundary conditions and Robin-type boundary conditions appear for the hypermultiplet coupled to vector multiplet. The half-BPS boundary conditions are realized in the brane configurations of Type IIB string theory.
Riemann solvers and boundary conditions for two-dimensional shallow water simulations
Guinot, Vincent
2003-04-01
Most existing algorithms for two-dimensional shallow water simulations treat multi-dimensional waves using wave splitting or time splitting. This often results in anisotropy of the computed flow. Both wave splitting and time splitting are based on a local decomposition of the multi-dimensional problem into one-dimensional, orthogonal problems. Therefore, these algorithms handle boundary conditions in a very similar way to classical one-dimensional algorithms. This should be expected to trigger a dependence of the number of boundary conditions on the direction of the flow at the boundaries. However, most computational codes based on alternate directions do not exhibit such sensitivity, which seems to contradict the theory of existence and uniqueness of the solution. The present paper addresses these issues. A Riemann solver is presented that aims to convert two-dimensional Riemann problems into a one-dimensional equivalent Riemann problem (ERP) at the interfaces between the computational cells. The ERP is derived by applying the theory of bicharacteristics at each end of the interface and by performing a linear averaging along the interface. The proposed approach is tested against the traditional one-dimensional approach on the classical circular dambreak problem. The results show that the proposed solver allows the isotropy of the solution to be better preserved. Use of the two-dimensional solver with a first-order scheme may give better results than use of a second-order scheme with a one-dimensional solver. The theory of bicharacteristics is also used to discuss the issue of boundary conditions. It is shown that, when the flow is subcritical, the number of boundary conditions affects the accuracy of the solution, but not its existence and uniqueness. When only one boundary condition is to be prescribed, it should not be the velocity in the direction parallel to the boundary. When two boundary conditions are to be prescribed, at least one of them should involve
On the physical solutions to the heat equation subjected to nonlinear boundary conditions
This work consists of a discussion on the physical solutions to the steady-state heat transfer equation, when it is subjected to nonlinear boundary conditions. It will be presented a functional, whose minimum occurs for the (unique) physical solution to the condidered heat transfer problem, suitable for a large class of typical (nonlinear) boundary conditions (representing the radiative/convective loss from the body to the environment). It will be demonstrated that these problems admit-always one, and only one, physical solution (which represents the absolute temperature). (author)
Topological quantum scattering under the influence of a nontrivial boundary condition
Mota, Herondy
2016-04-01
We consider the quantum scattering problem of a relativistic particle in (2 + 1)-dimensional cosmic string spacetime under the influence of a nontrivial boundary condition imposed on the solution of the Klein-Gordon equation. The solution is then shifted as consequence of the nontrivial boundary condition and the role of the phase shift is to produce an Aharonov-Bohm-like effect. We examine the connection between this phase shift and the electromagnetic and gravitational analogous of the Aharonov-Bohm effect and compare the present results with previous ones obtained in the literature, also considering non-relativistic cases.
Particles in a magnetic field and plasma analogies: doubly periodic boundary conditions
Forrester, P J [Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia)
2006-10-13
The N-particle free fermion state for quantum particles in the plane subject to a perpendicular magnetic field, and with doubly periodic boundary conditions, is written in a product form. The absolute value of this is used to formulate an exactly solvable one-component plasma model and further motivates the formulation of an exactly solvable two-species Coulomb gas. The large N expansion of the free energy of both these models exhibits the same O(1) term. On the basis of a relationship to the Gaussian free field, this term is predicted to be universal for conductive Coulomb systems in doubly periodic boundary conditions.
Edge states and conformal boundary conditions in super spin chains and super sigma models
Bondesan, Roberto; Jacobsen, Jesper Lykke; Saleur, Hubert
2011-01-01
The sigma models on projective superspaces CP^{N+M-1|N} with topological angle theta=pi mod 2pi flow to non-unitary, logarithmic conformal field theories in the low-energy limit. In this paper, we determine the exact spectrum of these theories for all open boundary conditions preserving the full global symmetry of the model, generalizing recent work on the particular case M=0 [C. Candu et al, JHEP02(2010)015]. In the sigma model setting, these boundary conditions are associated with complex l...
Rate-Independent Processes with Linear Growth Energies and Time-Dependent Boundary Conditions
Kružík, Martin; Zimmer, J.
2012-01-01
Roč. 5, č. 3 (2012), s. 591-604. ISSN 1937-1632 R&D Projects: GA AV ČR IAA100750802 Grant ostatní: GA ČR(CZ) GAP201/10/0357 Institutional research plan: CEZ:AV0Z10750506 Keywords : concentrations * oscillations * time-dependent boundary conditions * rate-independent evolution Subject RIV: BA - General Mathematics http://library.utia.cas.cz/separaty/2011/MTR/kruzik-rate-independent processes with linear growth energies and time-dependent boundary conditions.pdf
In this dissertation we use the Laplace transform to derive expressions for nonstandard albedo boundary conditions for one and two non-multiplying regions at the ends of one dimensional domains. In practice, the fuel regions of reactor cores are surrounded by reflector regions that reduce neutron leakage. In order to exclude the reflector regions from the calculations, we introduce a reflection coefficient or albedo. We use the present albedo boundary conditions to solve numerically slab-geometry monoenergetic and multigroup diffusion equations using the conventional finite difference method. Numerical results are generated for fixed source and eigenvalue diffusion problems in slab geometry(author)