Discontinuous Sturm-Liouville Problems with Eigenvalue Dependent Boundary Condition
Amirov, R. Kh., E-mail: emirov@cumhuriyet.edu.tr; Ozkan, A. S., E-mail: sozkan@cumhuriyet.edu.tr [Cumhuriyet University, Department of Mathematics Faculty of Art and Science (Turkey)
2014-12-15
In this study, an inverse problem for Sturm-Liouville differential operators with discontinuities is studied when an eigenparameter appears not only in the differential equation but it also appears in the boundary condition. Uniqueness theorems of inverse problems according to the Prüfer angle, the Weyl function and two different eigenvalues sets are proved.
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.
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.
Pagan Munoz, R.; Hornikx, M.C.J.
The wave-based Fourier Pseudospectral time-domain (Fourier-PSTD) method was shown to be an effective way of modeling outdoor acoustic propagation problems as described by the linearized Euler equations (LEE), but is limited to real-valued frequency independent boundary conditions and predominantly
Sabri Bensid
2010-04-01
Full Text Available We study the nonlinear elliptic problem with discontinuous nonlinearity $$displaylines{ -Delta u = f(uH(u-mu quadhbox{in } Omega, cr u =h quad hbox{on }partial Omega, }$$ where $H$ is the Heaviside unit function, $f,h$ are given functions and $mu$ is a positive real parameter. The domain $Omega$ is the unit ball in $mathbb{R}^n$ with $ngeq 3$. We show the existence of a positive solution $u$ and a hypersurface separating the region where $-Delta u=0$ from the region where $-Delta u=f(u$. Our method relies on the implicit function theorem and bifurcation analysis.
Sirenko, Kostyantyn; Liu, Meilin; Bagci, Hakan
2013-01-01
A scheme that discretizes exact absorbing boundary conditions (EACs) to incorporate them into a time-domain discontinuous Galerkin finite element method (TD-DG-FEM) is described. The proposed TD-DG-FEM with EACs is used for accurately characterizing
Sirenko, Kostyantyn
2013-01-01
A scheme that discretizes exact absorbing boundary conditions (EACs) to incorporate them into a time-domain discontinuous Galerkin finite element method (TD-DG-FEM) is described. The proposed TD-DG-FEM with EACs is used for accurately characterizing transient electromagnetic wave interactions on two-dimensional waveguides. Numerical results demonstrate the proposed method\\'s superiority over the TD-DG-FEM that employs approximate boundary conditions and perfectly matched layers. Additionally, it is shown that the proposed method can produce the solution with ten-eleven digit accuracy when high-order spatial basis functions are used to discretize the Maxwell equations as well as the EACs. © 1963-2012 IEEE.
Propagation of Boundary-Induced Discontinuity in Stationary Radiative Transfer
Kawagoe, Daisuke; Chen, I.-Kun
2018-01-01
We consider the boundary value problem of the stationary transport equation in the slab domain of general dimensions. In this paper, we discuss the relation between discontinuity of the incoming boundary data and that of the solution to the stationary transport equation. We introduce two conditions posed on the boundary data so that discontinuity of the boundary data propagates along positive characteristic lines as that of the solution to the stationary transport equation. Our analysis does not depend on the celebrated velocity averaging lemma, which is different from previous works. We also introduce an example in two dimensional case which shows that piecewise continuity of the boundary data is not a sufficient condition for the main result.
Li, Ping; Shi, Yifei; Jiang, Lijun; Bagci, Hakan
2014-01-01
A scheme hybridizing discontinuous Galerkin time-domain (DGTD) and time-domain boundary integral (TDBI) methods for accurately analyzing transient electromagnetic scattering is proposed. Radiation condition is enforced using the numerical flux on the truncation boundary. The fields required by the flux are computed using the TDBI from equivalent currents introduced on a Huygens' surface enclosing the scatterer. The hybrid DGTDBI ensures that the radiation condition is mathematically exact and the resulting computation domain is as small as possible since the truncation boundary conforms to scatterer's shape and is located very close to its surface. Locally truncated domains can also be defined around each disconnected scatterer additionally reducing the size of the overall computation domain. Numerical examples demonstrating the accuracy and versatility of the proposed method are presented. © 2014 IEEE.
F.G. CANALES
2017-10-01
Full Text Available This paper presents an analytical solution for static analysis of thick rectangular beams with different boundary conditions. Carrera’s Unified Formulation (CUF is used in order to consider shear deformation theories of arbitrary order. The novelty of the present work is that a boundary discontinuous Fourier approach is used to consider clamped boundary conditions in the analytical solution, unlike Navier-type solutions which are restricted to simply supported beams. Governing equations are obtained by employing the principle of virtual work. The numerical accuracy of results is ascertained by studying the convergence of the solution and comparing the results to those of a 3D finite element solution. Beams subjected to bending due to a uniform pressure load and subjected to torsion due to opposite linear forces are considered. Overall, accurate results close to those of 3D finite element solutions are obtained, which can be used to validate finite element results or other approximate methods.
Li, Ping
2014-05-01
A scheme hybridizing discontinuous Galerkin time-domain (DGTD) and time-domain boundary integral (TDBI) methods for accurately analyzing transient electromagnetic scattering is proposed. Radiation condition is enforced using the numerical flux on the truncation boundary. The fields required by the flux are computed using the TDBI from equivalent currents introduced on a Huygens\\' surface enclosing the scatterer. The hybrid DGTDBI ensures that the radiation condition is mathematically exact and the resulting computation domain is as small as possible since the truncation boundary conforms to scatterer\\'s shape and is located very close to its surface. Locally truncated domains can also be defined around each disconnected scatterer additionally reducing the size of the overall computation domain. Numerical examples demonstrating the accuracy and versatility of the proposed method are presented. © 2014 IEEE.
Modelling classroom conditions with different boundary conditions
Marbjerg, Gerd Høy; Jeong, Cheol-Ho; Brunskog, Jonas
2014-01-01
A model that combines image source modelling and acoustical radiosity with complex boundary condition, thus including phase shifts on reflection has been developed. The model is called PARISM (Phased Acoustical Radiosity and Image Source Model). It has been developed in order to be able to model...
Albar, Arwa; Tahini, Hassan Ali; Schwingenschlö gl, Udo
2018-01-01
the electronic states at stoichiometric SnO/SnO2 (110) interphase boundaries. In this system, one would not expect polar catastrophe to have a role according to state-of-the-art theory because the interface lacks formal charge discontinuity. However, we observe
BOUNDARY CONDITIONS IN GAP GEOMETRY
Rothenstein, W.; Helholtz, J.
1963-11-15
The procedure for calculnting the monoenergetic angular flux density in lattice cells including voids between fuel and moderator is discussed. Boundary conditions describThe thermal energy of a nuclear reactor may be conserved by using as the reactor coolant a hydrocarbon fraction boiling within the range 220 to 650 deg C (preferably 340 to 550 deg C) and containing not more than 5% of extraneous materials having neutron cross sections of > 10 barns. The hot coolant may either be cracked outside of the reactor or used to heat another petroleum hydrocarbon which is to be converted. (D.L.C.)
Albar, Arwa
2018-02-09
The electronic properties of interphase boundaries are of basic importance for most materials, particularly when those properties deviate strongly from the bulk behavior. We introduce a mechanism that can result in metallicity at stoichiometric interphase boundaries between semiconductors based on the idea of polar catastrophe, which is usually considered only in the context of heterostructures. To this end, we perform ab initio calculations within density functional theory to investigate the electronic states at stoichiometric SnO/SnO2 (110) interphase boundaries. In this system, one would not expect polar catastrophe to have a role according to state-of-the-art theory because the interface lacks formal charge discontinuity. However, we observe the formation of a hole gas between the semiconductors SnO and SnO2. To explain these findings, we provide a generalized theory based on the idea that the charge density discontinuity between SnO and SnO2, a consequence of lattice mismatch, drives a polar catastrophe scenario. As a result, SnO/SnO2 (110) interphase boundaries can develop metallicity depending on the grain size. The concept of metallicity due to polar catastrophe induced by charge density discontinuity is of general validity and applies to many interphase boundaries with lattice mismatch.
Time-dependent behavior of rough discontinuities under shearing conditions
Wang, Zhen; Shen, Mingrong; Ding, Wenqi; Jang, Boan; Zhang, Qingzhao
2018-02-01
The mechanical properties of rocks are generally controlled by their discontinuities. In this study, the time-dependent behavior of rough artificial joints under shearing conditions was investigated. Based on Barton’s standard profile lines, samples with artificial joint surfaces were prepared and used to conduct the shear and creep tests. The test results showed that the shear strength of discontinuity was linearly related to roughness, and subsequently an empirical equation was established. The long-term strength of discontinuity can be identified using the inflection point of the isocreep-rate curve, and it was linearly related to roughness. Furthermore, the ratio of long-term and instantaneous strength decreased with the increase of roughness. The shear-stiffness coefficient increased with the increase of shear rate, and the influence of shear rate on the shear stiffness coefficient decreased with the decrease of roughness. Further study of the mechanism revealed that these results could be attributed to the different time-dependent behavior of intact and joint rocks.
On filter boundary conditions in topology optimization
Clausen, Anders; Andreassen, Erik
2017-01-01
Most research papers on topology optimization involve filters for regularization. Typically, boundary effects from the filters are ignored. Despite significant drawbacks the inappropriate homogeneous Neumann boundary conditions are used, probably because they are trivial to implement. In this paper...
Integrability and boundary conditions of supersymmetric systems
Yue Ruihong; Liang Hong
1996-01-01
By studying the solutions of the reflection equations, we find out a series of integrable supersymmetric systems with different boundary conditions. The Hamiltonian contains four free parameters which describe the contribution of the boundary terms
Boundary Conditions of Methamphetamine Craving
Lopez, Richard B.; Onyemekwu, Chukwudi; Hart, Carl L.; Ochsner, Kevin N.; Kober, Hedy
2015-01-01
Methamphetamine use has increased significantly and become a global health concern. Craving is known to predict methamphetamine use and relapse following abstinence. Some have suggested that cravings are automatic, generalized, and uncontrollable, but experimental work addressing these claims is lacking. In two exploratory studies we tested the boundary conditions of methamphetamine craving by asking: (1) is craving specific to users’ preferred route of administration? and (2) can craving be regulated by cognitive strategies? Two groups of methamphetamine users were recruited. In Study 1, participants were grouped by their preferred route of administration (intranasal vs. smoking), and rated their craving in response to photographs and movies depicting methamphetamine use (via the intranasal vs. smoking route). In Study 2, methamphetamine smokers implemented cognitive regulation strategies while viewing photographs depicting methamphetamine smoking. Strategies involved either focusing on the positive aspects of smoking methamphetamine or the negative consequences of doing so – the latter strategy based on treatment protocols for addiction. In Study 1, we found a significant interaction between group and route of administration, such that participants who preferred to smoke methamphetamine reported significantly stronger craving for smoking stimuli, whereas those who preferred the intranasal route reported stronger craving for intranasal stimuli. In Study 2, participants reported significantly lower craving when focusing on the negative consequences associated with methamphetamine use. Taken together, these findings suggest that strength of craving for methamphetamine is moderated by users’ route of administration and can be reduced by cognitive strategies. This has important theoretical, methodological, and clinical implications. PMID:26302338
Integrable boundary conditions and modified Lax equations
Avan, Jean; Doikou, Anastasia
2008-01-01
We consider integrable boundary conditions for both discrete and continuum classical integrable models. Local integrals of motion generated by the corresponding 'transfer' matrices give rise to time evolution equations for the initial Lax operator. We systematically identify the modified Lax pairs for both discrete and continuum boundary integrable models, depending on the classical r-matrix and the boundary matrix
Li, Ping
2014-07-01
This paper presents an algorithm hybridizing discontinuous Galerkin time domain (DGTD) method and time domain boundary integral (BI) algorithm for 3-D open region electromagnetic scattering analysis. The computational domain of DGTD is rigorously truncated by analytically evaluating the incoming numerical flux from the outside of the truncation boundary through BI method based on the Huygens\\' principle. The advantages of the proposed method are that it allows the truncation boundary to be conformal to arbitrary (convex/ concave) scattering objects, well-separated scatters can be truncated by their local meshes without losing the physics (such as coupling/multiple scattering) of the problem, thus reducing the total mesh elements. Furthermore, low frequency waves can be efficiently absorbed, and the field outside the truncation domain can be conveniently calculated using the same BI formulation. Numerical examples are benchmarked to demonstrate the accuracy and versatility of the proposed method.
Consistent boundary conditions for open strings
Lindstroem, Ulf; Rocek, Martin; Nieuwenhuizen, Peter van
2003-01-01
We study boundary conditions for the bosonic, spinning (NSR) and Green-Schwarz open string, as well as for (1+1)-dimensional supergravity. We consider boundary conditions that arise from (1) extremizing the action, (2) BRST, rigid or local supersymmetry, or κ(Siegel)-symmetry of the action, (3) closure of the set of boundary conditions under the symmetry transformations, and (4) the boundary limits of bulk Euler-Lagrange equations that are 'conjugate' to other boundary conditions. We find corrections to Neumann boundary conditions in the presence of a bulk tachyon field. We discuss a boundary superspace formalism. We also find that path integral quantization of the open string requires an infinite tower of boundary conditions that can be interpreted as a smoothness condition on the doubled interval; we interpret this to mean that for a path-integral formulation of open strings with only Neuman boundary conditions, the description in terms of orientifolds is not just natural, but is actually fundamental
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.
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.
Boundary conditions in random sequential adsorption
Cieśla, Michał; Ziff, Robert M.
2018-04-01
The influence of different boundary conditions on the density of random packings of disks is studied. Packings are generated using the random sequential adsorption algorithm with three different types of boundary conditions: periodic, open, and wall. It is found that the finite size effects are smallest for periodic boundary conditions, as expected. On the other hand, in the case of open and wall boundaries it is possible to introduce an effective packing size and a constant correction term to significantly improve the packing densities.
Quadratic Functionals with General Boundary Conditions
Dosla, Z.; Dosly, O.
1997-01-01
The purpose of this paper is to give the Reid 'Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in terms of Riccati equation solutions
Integral Method of Boundary Characteristics: Neumann Condition
Kot, V. A.
2018-05-01
A new algorithm, based on systems of identical equalities with integral and differential boundary characteristics, is proposed for solving boundary-value problems on the heat conduction in bodies canonical in shape at a Neumann boundary condition. Results of a numerical analysis of the accuracy of solving heat-conduction problems with variable boundary conditions with the use of this algorithm are presented. The solutions obtained with it can be considered as exact because their errors comprise hundredths and ten-thousandths of a persent for a wide range of change in the parameters of a problem.
Kharatishvili, G L; Tadumadze, T A
2005-01-01
Variation formulae are proved for solutions of non-linear differential equations with variable delays and discontinuous initial conditions. The discontinuity of the initial condition means that at the initial moment of time the values of the initial function and the trajectory, generally speaking, do not coincide. The formulae obtained contain a new summand connected with the discontinuity of the initial condition and the variation of the initial moment.
Solution of moving boundary problems with implicit boundary condition
Moyano, E.A.
1990-01-01
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) [es
Reconstruction of boundary conditions from internal conditions using viability theory
Hofleitner, Aude; Claudel, Christian G.; Bayen, Alexandre M.
2012-01-01
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.
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.
Boundary conditions for the gravitational field
Winicour, Jeffrey
2012-01-01
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') (topical review)
Bumiller, Elissa
The US Navy currently uses AA5xxx aluminum alloys for structures exposed to a marine environment. These alloys demonstrate excellent corrosion resistance over other aluminum alloys (e.g., AA2xxx or AA7xxx) in this environment, filling a niche in the marine structures market when requiring a light-weight alternative to steel. However, these alloys are susceptible to localized corrosion; more specifically, intergranular corrosion (IGC) is of concern. IGC of AA5xxx alloys due to the precipitation of beta phase on the grain boundaries is a well-established phenomenon referred to as sensitization. At high degrees of sensitization, the IGC path is a continuous anodic path of beta phase particles. At lower degrees of sensitization, the beta phase coverage at the grain boundaries is not continuous. The traditional ranges of susceptibility to IGC as defined by ASTM B928 are in question due to recent studies. These studies showed that even at mid range degrees of sensitization where the beta phase is no longer continuous, IGC may still occur. Previous thoughts on IGC of these alloy systems were founded on the idea that once the grain boundary precipitate became discontinuous the susceptibility to IGC was greatly reduced. Additionally, IGC susceptibility has been defined metallurgically by compositional gradients at the grain boundaries. However, AA5xxx alloys show no compositional gradients at the grain boundaries, yet are still susceptible to IGC. The goal of this work is to establish criteria necessary for IGC to occur given no continuous beta phase path and no compositional gradient at the grain boundaries. IGC performance of the bulk alloy system AA5083 has been studied along with the primary phases present in the IGC system: alpha and beta phases using electrochemistry and modeling as the primary tools. Numerical modeling supports that at steady-state the fissure tip is likely saturated with Mg in excess of the 4% dissolved in the matrix. By combining these results
Temperature jump boundary conditions in radiation diffusion
Alonso, C.T.
1976-12-01
The radiation diffusion approximation greatly simplifies radiation transport problems. Yet the application of this method has often been unnecessarily restricted to optically thick regions, or has been extended through the use of such ad hoc devices as flux limiters. The purpose of this paper is to review and draw attention to the use of the more physically appropriate temperature jump boundary conditions for extending the range of validity of the diffusion approximation. Pioneering work has shown that temperature jump boundary conditions remove the singularity in flux that occurs in ordinary diffusion at small optical thicknesses. In this review paper Deissler's equations for frequency-dependent jump boundary conditions are presented and specific geometric examples are calculated analytically for steady state radiation transfer. When jump boundary conditions are applied to radiation diffusion, they yield exact solutions which are naturally flux- limited and geometry-corrected. We believe that the presence of temperature jumps on source boundaries is probably responsible in some cases for the past need for imposing ad hoc flux-limiting constraints on pure diffusion solutions. The solution for transfer between plane slabs, which is exact to all orders of optical thickness, also provides a useful tool for studying the accuracy of computer codes
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.
Supply risk under the condition of discontinuous demand in the field of nuclear power industry
Wei Qiyan; Tian Zhilong
2006-01-01
Demands can be divided into two kinds: continuous and discontinuous demands. Based on the analysis of the results on common supply risk studies, discontinuous demand is studied concerning its definition, characteristics, and the more obvious and severe risks and consequences induced by its characteristics. Furthermore, the discontinuous characteristics and relevant precautions of demand of nuclear power industry are analyzed. Analysis and research on supply risks under the condition of discontinuous demand would be helpful to enterprises to take this issue serious and prevent the risks. (authors)
Boundary condition histograms for modulated phases
Benakli, M.; Gabay, M.; Saslow, W.M.
1997-11-01
Boundary conditions strongly affect the results of numerical computations for finite size inhomogeneous or incommensurate structures. We present a method which allows to deal with this problem, both for ground state and for critical properties: it combines fluctuating boundary conditions and specific histogram techniques. Our approach concerns classical as well as quantum systems. In particular, current-current correlation functions, which probe large scale coherence of the states, can be accurately evaluated. We illustrate our method on a frustrated two dimensional XY model. (author)
Casimir pistons with general boundary conditions
Guglielmo Fucci
2015-02-01
Full Text Available In this work we analyze the Casimir energy and force for a scalar field endowed with general self-adjoint boundary conditions propagating in a higher dimensional piston configuration. The piston is constructed as a direct product I×N, with I=[0,L]⊂R and N a smooth, compact Riemannian manifold with or without boundary. The study of the Casimir energy and force for this configuration is performed by employing the spectral zeta function regularization technique. The obtained analytic results depend explicitly on the spectral zeta function associated with the manifold N and the parameters describing the general boundary conditions imposed. These results are then specialized to the case in which the manifold N is a d-dimensional sphere.
Spectral asymmetry for bag boundary conditions
Beneventano, C G; Santangelo, E M; Wipf, A
2002-01-01
We give an expression, in terms of boundary spectral functions, for the spectral asymmetry of the Euclidean Dirac operator in two dimensions, when its domain is determined by local boundary conditions and the manifold is of product type. As an application, we explicitly evaluate the asymmetry in the case of a finite-length cylinder and check that the outcome is consistent with our general result. Finally, we study the asymmetry in a disc, which is a non-product case, and propose an interpretation
Boundary conditions in rational conformal field theories
Behrend, Roger E.; Pearce, Paul A.; Petkova, Valentina B.; Zuber, Jean-Bernard
2000-01-01
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
Automated Boundary Conditions for Wind Tunnel Simulations
Carlson, Jan-Renee
2018-01-01
Computational fluid dynamic (CFD) simulations of models tested in wind tunnels require a high level of fidelity and accuracy particularly for the purposes of CFD validation efforts. Considerable effort is required to ensure the proper characterization of both the physical geometry of the wind tunnel and recreating the correct flow conditions inside the wind tunnel. The typical trial-and-error effort used for determining the boundary condition values for a particular tunnel configuration are time and computer resource intensive. This paper describes a method for calculating and updating the back pressure boundary condition in wind tunnel simulations by using a proportional-integral-derivative controller. The controller methodology and equations are discussed, and simulations using the controller to set a tunnel Mach number in the NASA Langley 14- by 22-Foot Subsonic Tunnel are demonstrated.
Thermal Simulations, Open Boundary Conditions and Switches
Burnier, Yannis; Florio, Adrien; Kaczmarek, Olaf; Mazur, Lukas
2018-03-01
SU(N) gauge theories on compact spaces have a non-trivial vacuum structure characterized by a countable set of topological sectors and their topological charge. In lattice simulations, every topological sector needs to be explored a number of times which reflects its weight in the path integral. Current lattice simulations are impeded by the so-called freezing of the topological charge problem. As the continuum is approached, energy barriers between topological sectors become well defined and the simulations get trapped in a given sector. A possible way out was introduced by Lüscher and Schaefer using open boundary condition in the time extent. However, this solution cannot be used for thermal simulations, where the time direction is required to be periodic. In this proceedings, we present results obtained using open boundary conditions in space, at non-zero temperature. With these conditions, the topological charge is not quantized and the topological barriers are lifted. A downside of this method are the strong finite-size effects introduced by the boundary conditions. We also present some exploratory results which show how these conditions could be used on an algorithmic level to reshuffle the system and generate periodic configurations with non-zero topological charge.
Thermal Simulations, Open Boundary Conditions and Switches
Burnier Yannis
2018-01-01
Full Text Available SU(N gauge theories on compact spaces have a non-trivial vacuum structure characterized by a countable set of topological sectors and their topological charge. In lattice simulations, every topological sector needs to be explored a number of times which reflects its weight in the path integral. Current lattice simulations are impeded by the so-called freezing of the topological charge problem. As the continuum is approached, energy barriers between topological sectors become well defined and the simulations get trapped in a given sector. A possible way out was introduced by Lüscher and Schaefer using open boundary condition in the time extent. However, this solution cannot be used for thermal simulations, where the time direction is required to be periodic. In this proceedings, we present results obtained using open boundary conditions in space, at non-zero temperature. With these conditions, the topological charge is not quantized and the topological barriers are lifted. A downside of this method are the strong finite-size effects introduced by the boundary conditions. We also present some exploratory results which show how these conditions could be used on an algorithmic level to reshuffle the system and generate periodic configurations with non-zero topological charge.
Energy principle with included boundary conditions
Lehnert, B.
1994-01-01
Earlier comments by the author on the limitations of the classical form of the extended energy principle are supported by a complementary analysis on the potential energy change arising from free-boundary displacements of a magnetically confined plasma. In the final formulation of the extended principle, restricted displacements, satisfying pressure continuity by means of plasma volume currents in a thin boundary layer, are replaced by unrestricted (arbitrary) displacements which can give rise to induced surface currents. It is found that these currents contribute to the change in potential energy, and that their contribution is not taken into account by such a formulation. A general expression is further given for surface currents induced by arbitrary displacements. The expression is used to reformulate the energy principle for the class of displacements which satisfy all necessary boundary conditions, including that of the pressure balance. This makes a minimization procedure of the potential energy possible, for the class of all physically relevant test functions which include the constraints imposed by the boundary conditions. Such a procedure is also consistent with a corresponding variational calculus. (Author)
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 - others: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 in conformal and integrable theories
Petkova, V B
2000-01-01
The study of boundary conditions in rational conformal field theories is not only physically important. It also reveals a lot on the structure of the theory ``in the bulk''. The same graphs classify both the torus and the cylinder partition functions and provide data on their hidden ``quantum symmetry''. The Ocneanu triangular cells -- the 3j-symbols of these symmetries, admit various interpretations and make a link between different problems.
Exploring exotic states with twisted boundary conditions
Agadjanov, Dimitri
2017-01-01
he goal of this thesis is to develop methods to study the nature and properties of exotic hadrons from lattice simulations. The main focus lies in the application of twisted boundary conditions. The thesis consists of a general introduction and the collection of three papers, represented respectively in three chapters. The introduction of the thesis reviews the theoretical background, which is further used in the rest of the thesis. Further implementing partially twisted boundary conditions in the scalar sector of lattice QCD is studied. Then we develop a method to study the content of the exotic hadrons by determining the wave function renormalization constant from lattice simulations, exploiting the dependence of the spectrum on the twisted boundary conditions. The final chapter deals with a novel method to study the multi-channel scattering problem in a finite volume, which is relevant for exotic states. Its key idea is to extract the complex hadron-hadron optical potential, avoiding the difficulties, associated with the solution of the multi-channel Luescher equation.
Exploring exotic states with twisted boundary conditions
Agadjanov, Dimitri
2017-09-11
he goal of this thesis is to develop methods to study the nature and properties of exotic hadrons from lattice simulations. The main focus lies in the application of twisted boundary conditions. The thesis consists of a general introduction and the collection of three papers, represented respectively in three chapters. The introduction of the thesis reviews the theoretical background, which is further used in the rest of the thesis. Further implementing partially twisted boundary conditions in the scalar sector of lattice QCD is studied. Then we develop a method to study the content of the exotic hadrons by determining the wave function renormalization constant from lattice simulations, exploiting the dependence of the spectrum on the twisted boundary conditions. The final chapter deals with a novel method to study the multi-channel scattering problem in a finite volume, which is relevant for exotic states. Its key idea is to extract the complex hadron-hadron optical potential, avoiding the difficulties, associated with the solution of the multi-channel Luescher equation.
Adaptive boundary conditions for exterior flow problems
Boenisch, V; Wittwer, S
2003-01-01
We consider the problem of solving numerically the stationary incompressible Navier-Stokes equations in an exterior domain in two dimensions. This corresponds to studying the stationary fluid flow past a body. The necessity to truncate for numerical purposes the infinite exterior domain to a finite domain leads to the problem of finding appropriate boundary conditions on the surface of the truncated domain. We solve this problem by providing a vector field describing the leading asymptotic behavior of the solution. This vector field is given in the form of an explicit expression depending on a real parameter. We show that this parameter can be determined from the total drag exerted on the body. Using this fact we set up a self-consistent numerical scheme that determines the parameter, and hence the boundary conditions and the drag, as part of the solution process. We compare the values of the drag obtained with our adaptive scheme with the results from using traditional constant boundary conditions. Computati...
Galerkin methods for Boltzmann-Poisson transport with reflection conditions on rough boundaries
Morales Escalante, José A.; Gamba, Irene M.
2018-06-01
We consider in this paper the mathematical and numerical modeling of reflective boundary conditions (BC) associated to Boltzmann-Poisson systems, including diffusive reflection in addition to specularity, in the context of electron transport in semiconductor device modeling at nano scales, and their implementation in Discontinuous Galerkin (DG) schemes. We study these BC on the physical boundaries of the device and develop a numerical approximation to model an insulating boundary condition, or equivalently, a pointwise zero flux mathematical condition for the electron transport equation. Such condition balances the incident and reflective momentum flux at the microscopic level, pointwise at the boundary, in the case of a more general mixed reflection with momentum dependant specularity probability p (k →). We compare the computational prediction of physical observables given by the numerical implementation of these different reflection conditions in our DG scheme for BP models, and observe that the diffusive condition influences the kinetic moments over the whole domain in position space.
Bosonization relations as bag boundary conditions
Nadkarni, S.; Nielsen, H.B.; Zahed, I.
1984-10-01
The more sophisticated bag models of hadrons become, the less precisely they seem to determine the bag radius. Idealizing this situation leads to the concept of exact bag models - ''Cheshire Cat'' models, CCM'S - where the physics is completely insensitive to changes in the bag radius. CCM's are constructed explitly in 1+1-dimensions, where exact bosonization relations are known. In the formalism of bag models, these relations appear as boundary conditions which ensure that the shifting of the bag wall has no physical effect. Other notable features of 1+1-dimensional CCM's are: (i) Fermion number, though classically confined, can escape the bag via a vector current anomaly at the surface. (ii) Essentially the same boundary action works for a variety of models and its symmetries determine those of the external boson fields. Remarkably enough, this 1+1-dimensional boundary action has precisely the same form as the one used in 3+1-dimensional chiral bag models, lending support to the belief that the latter are indeed approximateCCM's. These 1+1-dimensional results are expected to provide useful guidelines in the attempt to, at least approximately, besonize 3+1-dimensional QCD. (orig.)
Canonical group quantization and boundary conditions
Jung, Florian
2012-01-01
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
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.
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...
Regularization of discontinuous foliations: Blowing up and sliding conditions via Fenichel theory
Panazzolo, Daniel; da Silva, Paulo R.
2017-12-01
We study the regularization of an oriented 1-foliation F on M ∖ Σ where M is a smooth manifold and Σ ⊂ M is a closed subset, which can be interpreted as the discontinuity locus of F. In the spirit of Filippov's work, we define a sliding and sewing dynamics on the discontinuity locus Σ as some sort of limit of the dynamics of a nearby smooth 1-foliation and obtain conditions to identify whether a point belongs to the sliding or sewing regions.
Surface free energy for systems with integrable boundary conditions
Goehmann, Frank; Bortz, Michael; Frahm, Holger
2005-01-01
The surface free energy is the difference between the free energies for a system with open boundary conditions and the same system with periodic boundary conditions. We use the quantum transfer matrix formalism to express the surface free energy in the thermodynamic limit of systems with integrable boundary conditions as a matrix element of certain projection operators. Specializing to the XXZ spin-1/2 chain we introduce a novel 'finite temperature boundary operator' which characterizes the thermodynamical properties of surfaces related to integrable boundary conditions
Absorbing boundary conditions for Einstein's field equations
Sarbach, Olivier [Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Edificio C-3, Cd. Universitaria. C. P. 58040 Morelia, Michoacan (Mexico)
2007-11-15
A common approach for the numerical simulation of wave propagation on a spatially unbounded domain is to truncate the domain via an artificial boundary, thus forming a finite computational domain with an outer boundary. Absorbing boundary conditions must then be specified at the boundary such that the resulting initial-boundary value problem is well posed and such that the amount of spurious reflection is minimized. In this article, we review recent results on the construction of absorbing boundary conditions in General Relativity and their application to numerical relativity.
Santos, Thays Brenner; Kramer-Soares, Juliana Carlota; Favaro, Vanessa Manchim; Oliveira, Maria Gabriela Menezes
2017-10-01
Time plays an important role in conditioning, it is not only possible to associate stimuli with events that overlap, as in delay fear conditioning, but it is also possible to associate stimuli that are discontinuous in time, as shown in trace conditioning for a discrete stimuli. The environment itself can be a powerful conditioned stimulus (CS) and be associated to unconditioned stimulus (US). Thus, the aim of the present study was to determine the parameters in which contextual fear conditioning occurs by the maintenance of a contextual representation over short and long time intervals. The results showed that a contextual representation can be maintained and associated after 5s, even in the absence of a 15s re-exposure to the training context before US delivery. The same effect was not observed with a 24h interval of discontinuity. Furthermore, optimal conditioned response with a 5s interval is produced only when the contexts (of pre-exposure and shock) match. As the pre-limbic cortex (PL) is necessary for the maintenance of a continuous representation of a stimulus, the involvement of the PL in this temporal and contextual processing was investigated. The reversible inactivation of the PL by muscimol infusion impaired the acquisition of contextual fear conditioning with a 5s interval, but not with a 24h interval, and did not impair delay fear conditioning. The data provided evidence that short and long intervals of discontinuity have different mechanisms, thus contributing to a better understanding of PL involvement in contextual fear conditioning and providing a model that considers both temporal and contextual factors in fear conditioning. Copyright © 2017 Elsevier Inc. All rights reserved.
Discrete transparent boundary conditions for Schroedinger-type equations
Schmidt, F.; Yevick, D.
1997-01-01
We present a general technique for constructing nonlocal transparent boundary conditions for one-dimensional Schroedinger-type equations. Our method supplies boundary conditions for the θ-family of implicit one-step discretizations of Schroedinger's equation in time. The use of Mikusinski's operator approach in time avoids direct and inverse transforms between time and frequency domains and thus implements the boundary conditions in a direct manner. 14 refs., 9 figs
Grain boundary engineering to control the discontinuous precipitation in multicomponent U10Mo alloy
Devaraj, Arun; Kovarik, Libor; Kautz, Elizabeth; Arey, Bruce; Jana, Saumyadeep; Lavender, Curt; Joshi, Vineet
2018-06-01
Grain boundaries in metallic alloys often play a crucial role, not only in determining the mechanical properties or thermal stability of alloys, but also in dictating the phase transformation kinetics during thermomechanical processing. We demonstrate that locally stabilized structure and compositional segregation at grain boundaries—“grain boundary complexions”—in a complex multicomponent alloy can be modified to influence the kinetics of cellular transformation during subsequent thermomechanical processing. Using aberration-corrected scanning transmission electron microscopy and atom probe tomography analysis of a metallic nuclear fuel highly relevant to worldwide nuclear non-proliferation efforts —uranium-10 wt% molybdenum (U-10Mo) alloy, new evidence for the existence of grain boundary complexion is provided. We then modified the concentration of impurities dissolved in Υ-UMo grain interiors and/or segregated to Υ-UMo grain boundaries by changing the homogenization treatment, and these effects were used used to retard the kinetics of cellular transformation during subsequent sub-eutectoid annealing in this U-10-Mo alloy during sub-eutectoid annealing. Thus, this work provided insights on tailoring the final microstructure of the U-10Mo alloy, which can potentially improve the irradiation performance of this important class of alloy fuels.
Boundary Conditions, Data Assimilation, and Predictability in Coastal Ocean Models
Samelson, Roger M; Allen, John S; Egbert, Gary D; Kindle, John C; Snyder, Chris
2007-01-01
...: The specific objectives of this research are to determine the impact on coastal ocean circulation models of open ocean boundary conditions from Global Ocean Data Assimilation Experiment (GODAE...
Quantum “violation” of Dirichlet boundary condition
I.Y. Park
2017-02-01
Full Text Available Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the ‘violation’ of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
Quantum “violation” of Dirichlet boundary condition
Park, I.Y., E-mail: inyongpark05@gmail.com
2017-02-10
Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the ‘violation’ of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
Huimin Liu
2017-01-01
Full Text Available This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique.
Fluid-solid boundary conditions for multiparticle collision dynamics
Whitmer, Jonathan K; Luijten, Erik
2010-01-01
The simulation of colloidal particles suspended in solvent requires an accurate representation of the interactions between the colloids and the solvent molecules. Using the multiparticle collision dynamics method, we examine several proposals for stick boundary conditions, studying their properties in both plane Poiseuille flow (where fluid interacts with the boundary of a stationary macroscopic solid) and particle-based colloid simulations (where the boundaries are thermally affected and in motion). In addition, our simulations compare various collision rules designed to remove spurious slip near solid surfaces, and the effects of these rules on the thermal motion of colloidal particles. Furthermore, we demonstrate that stochastic reflection of the fluid at solid boundaries fails to faithfully represent stick boundary conditions, and conclude that bounce-back conditions should be applied at both mobile and stationary surfaces. Finally, we generalize these ideas to create partial slip boundary conditions at both stationary and mobile surfaces.
Schwenke, Michael; Georgii, Joachim; Preusser, Tobias
2017-07-01
Focused ultrasound (FUS) is rapidly gaining clinical acceptance for several target tissues in the human body. Yet, treating liver targets is not clinically applied due to a high complexity of the procedure (noninvasiveness, target motion, complex anatomy, blood cooling effects, shielding by ribs, and limited image-based monitoring). To reduce the complexity, numerical FUS simulations can be utilized for both treatment planning and execution. These use-cases demand highly accurate and computationally efficient simulations. We propose a numerical method for the simulation of abdominal FUS treatments during respiratory motion of the organs and target. Especially, a novel approach is proposed to simulate the heating during motion by solving Pennes' bioheat equation in a computational reference space, i.e., the equation is mathematically transformed to the reference. The approach allows for motion discontinuities, e.g., the sliding of the liver along the abdominal wall. Implementing the solver completely on the graphics processing unit and combining it with an atlas-based ultrasound simulation approach yields a simulation performance faster than real time (less than 50-s computing time for 100 s of treatment time) on a modern off-the-shelf laptop. The simulation method is incorporated into a treatment planning demonstration application that allows to simulate real patient cases including respiratory motion. The high performance of the presented simulation method opens the door to clinical applications. The methods bear the potential to enable the application of FUS for moving organs.
Nier, Francis
2018-01-01
This article is concerned with the maximal accretive realizations of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some global subelliptic estimates. Those estimates imply nice spectral properties as well as exponential decay properties for the associated semigroup. Admissible boundary conditions cover a wide range of applications for the usual scalar Kramer-Fokker-Planck equation or Bismut's hypoelliptic laplacian.
GenCade Lateral Boundary Conditions
2017-01-01
benefit of producing perfect agreement at this boundary during model calibration. However, it would be serendipitous if this procedure also produced...the surf zone or completely to the other side of the surf zone. Any adjustment to the groin length will also modify the position of the virtual... benefit in assessing this significance. For example, if the shoreline data provided a close enough match to the LBC specifications, it could be
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....
Classically integrable boundary conditions for affine Toda field theories
Bowcock, P.; Corrigan, E.; Dorey, P.E.; Rietdijk, R.H.
1995-01-01
Boundary conditions compatible with classical integrability are studied both directly, using an approach based on the explicit construction of conserved quantities, and indirectly by first developing a generalisation of the Lax pair idea. The latter approach is closer to the spirit of earlier work by Sklyanin and yields a complete set of conjectures for permissible boundary conditions for any affine Toda field theory. (orig.)
Scattering through a straight quantum waveguide with combined boundary conditions
Briet, Ph.; Dittrich, Jaroslav; Soccorsi, E.
2014-01-01
Roč. 55, č. 11 (2014), s. 112104 ISSN 0022-2488 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : quantum waveguide * scattering * Dirichlet boundary condition * Neumann boundary condition Subject RIV: BE - Theoretical Physics Impact factor: 1.243, year: 2014
Divergence-Free Wavelets on the Hypercube : General Boundary Conditions
Stevenson, R.
2016-01-01
On the n-dimensional hypercube, for given k∈N, wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space Hk((0,1)n)n with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and suitable dual
Periodic Boundary Conditions in the ALEGRA Finite Element Code
Aidun, John B.; Robinson, Allen C.; Weatherby, Joe R.
1999-01-01
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
A non-local computational boundary condition for duct acoustics
Zorumski, William E.; Watson, Willie R.; Hodge, Steve L.
1994-01-01
A non-local boundary condition is formulated for acoustic waves in ducts without flow. The ducts are two dimensional with constant area, but with variable impedance wall lining. Extension of the formulation to three dimensional and variable area ducts is straightforward in principle, but requires significantly more computation. The boundary condition simulates a nonreflecting wave field in an infinite duct. It is implemented by a constant matrix operator which is applied at the boundary of the computational domain. An efficient computational solution scheme is developed which allows calculations for high frequencies and long duct lengths. This computational solution utilizes the boundary condition to limit the computational space while preserving the radiation boundary condition. The boundary condition is tested for several sources. It is demonstrated that the boundary condition can be applied close to the sound sources, rendering the computational domain small. Computational solutions with the new non-local boundary condition are shown to be consistent with the known solutions for nonreflecting wavefields in an infinite uniform duct.
Entropy Stability and the No-Slip Wall Boundary Condition
Svä rd, Magnus; Carpenter, Mark H.; Parsani, Matteo
2018-01-01
We present an entropy stable numerical scheme subject to no-slip wall boundary conditions. To enforce entropy stability only the no-penetration boundary condition and a temperature condition are needed at a wall, and this leads to an L bound on the conservative variables. In this article, we take the next step and design a finite difference scheme that also bounds the velocity gradients. This necessitates the use of the full no-slip conditions.
Entropy Stability and the No-Slip Wall Boundary Condition
Svärd, Magnus
2018-01-18
We present an entropy stable numerical scheme subject to no-slip wall boundary conditions. To enforce entropy stability only the no-penetration boundary condition and a temperature condition are needed at a wall, and this leads to an L bound on the conservative variables. In this article, we take the next step and design a finite difference scheme that also bounds the velocity gradients. This necessitates the use of the full no-slip conditions.
Monopole Giant Resonances and TDHF boundary conditions
Stevenson, P.D.; Almehed, D.; Reinhard, P.-G.; Maruhn, J.A.
2007-01-01
Using time-dependent Hartree-Fock, we induce isoscalar and isovector monopole vibrations and follow the subsequent vibrations of both the same and opposite isospin nature in the N Z nucleus 132 Sn. By suitable scaling of the proton and neutron parts of the excitation operators, the coupling between the modes is studied, and the approximate normal modes found. Chaotic dynamics are then analysed in the isoscalar giant monopole resonance by using reflecting boundaries in a large space to build up a large number of 0 + states whose spacings are then analysed. A Wigner-like distribution is found
Minimization of heat slab nodes with higher order boundary conditions
Solbrig, C.W.
1992-01-01
The accuracy of a numerical solution can be limited by the numerical approximation to the boundary conditions rather than the accuracy of the equations which describe the interior. The study presented in this paper compares the results from two different numerical formulations of the convective boundary condition on the face of a heat transfer slab. The standard representation of the boundary condition in a test problem yielded an unacceptable error even when the heat transfer slab was partitioned into over 300 nodes. A higher order boundary condition representation was obtained by using a second order approximation for the first derivative at the boundary and combining it with the general equation used for inner nodes. This latter formulation produced reasonable results when as few as ten nodes were used
An Irrotational Flow Field That Approximates Flat Plate Boundary Conditions
Ruffa, Anthony A.
2004-01-01
An irrotational solution is derived for the steady-state Navier-Stokes equations that approximately satisfies the boundary conditions for flow over a finite flat plate. The nature of the flow differs substantially from boundary layer flow, with severe numerical difficulties in some regions.
M. Stewart
2015-02-01
Full Text Available The determination of the piezoelectric coefficient of thin films using interferometry is hindered by bending contributions. Using finite element analysis (FEA simulations, we show that the Lefki and Dormans approximations using either single or double-beam measurements cannot be used with finite top electrode sizes. We introduce a novel method for characterising piezoelectric thin films which uses a differential measurement over the discontinuity at the electrode edge as an internal reference, thereby eliminating bending contributions. This step height is shown to be electrode size and boundary condition independent. An analytical expression is derived which gives good agreement with FEA predictions of the step height.
Variational derivation of the simplified P2 equations with boundary and interface conditions
Tomasevic, D.I.; Larsen, E.W.
1995-01-01
The Simplified P 2 (SP 2 ) approximation to the transport equation is derived using a variational principle. The variational analysis yields the SP 2 equations, together with interface and Marshak-like boundary conditions. Numerical calculations show that for problems in which the P 1 solution is a reasonably accurate approximation to the transport solution, the corresponding SP 2 Solution is generally more accurate than the P 1 solution, for calculating integral quantities and detailed flux distributions, except in the close vicinity of material interfaces, where the SP 2 solution is discontinuous
Boundary conditions for natural supply ventilation
Jansen, D.W.L.; Loomans, M.G.L.C.; Wit, de M.H.; Zeiler, W.; Seppänen, O.; Säteri, J.
2007-01-01
The development of an air jet from a controlled natural ventilation grill for different outdoor conditions is studied. Extensive laboratory measurements are taken in different situations, while the air flow rate through the grill is kept constant. The grill setting and supply temperature are varied.
Fisher, Travis C.; Carpenter, Mark H.; Nordstroem, Jan; Yamaleev, Nail K.; Swanson, R. Charles
2011-01-01
Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.
Solution to random differential equations with boundary conditions
Fairouz Tchier
2017-04-01
Full Text Available We study a family of random differential equations with boundary conditions. Using a random fixed point theorem, we prove an existence theorem that yields a unique random solution.
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.
Facilitating conditions for boundary-spanning behavior in governance networks
Meerkerk, Ingmar; Edelenbos, Jurian
2017-01-01
textabstractThis article examines the impact of two facilitating conditions for boundary-spanning behaviour in urban governance networks. While research on boundary spanning is growing, there is little attention for antecedents. Combining governance network literature on project management and organizational literature on facilitative and servant leadership, we examine two potential conditions: a facilitative project management style and executive support. We conducted survey research among p...
Classically integrable boundary conditions for symmetric-space sigma models
MacKay, N.J.; Young, C.A.S.
2004-01-01
We investigate boundary conditions for the non-linear sigma model on the compact symmetric space G/H. The Poisson brackets and the classical local conserved charges necessary for integrability are preserved by boundary conditions which correspond to involutions which commute with the involution defining H. Applied to SO(3)/SO(2), the non-linear sigma model on S 2 , these yield the great circles as boundary submanifolds. Applied to GxG/G, they reproduce known results for the principal chiral model
Lyapunov Based Estimation of Flight Stability Boundary under Icing Conditions
Binbin Pei
2017-01-01
Full Text Available Current fight boundary of the envelope protection in icing conditions is usually defined by the critical values of state parameters; however, such method does not take the interrelationship of each parameter and the effect of the external disturbance into consideration. This paper proposes constructing the stability boundary of the aircraft in icing conditions through analyzing the region of attraction (ROA around the equilibrium point. Nonlinear icing effect model is proposed according to existing wind tunnel test results. On this basis, the iced polynomial short period model can be deduced further to obtain the stability boundary under icing conditions using ROA analysis. Simulation results for a series of icing severity demonstrate that, regardless of the icing severity, the boundary of the calculated ROA can be treated as an estimation of the stability boundary around an equilibrium point. The proposed methodology is believed to be a promising way for ROA analysis and stability boundary construction of the aircraft in icing conditions, and it will provide theoretical support for multiple boundary protection of icing tolerant flight.
On the wave equation with semilinear porous acoustic boundary conditions
Graber, Philip Jameson; Said-Houari, Belkacem
2012-01-01
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.
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.
Open boundary condition, Wilson flow and the scalar glueball mass
Chowdhury, Abhishek; Harindranath, A.; Maiti, Jyotirmoy
2014-01-01
A major problem with periodic boundary condition on the gauge fields used in current lattice gauge theory simulations is the trapping of topological charge in a particular sector as the continuum limit is approached. To overcome this problem open boundary condition in the temporal direction has been proposed recently. One may ask whether open boundary condition can reproduce the observables calculated with periodic boundary condition. In this work we find that the extracted lowest glueball mass using open and periodic boundary conditions at the same lattice volume and lattice spacing agree for the range of lattice scales explored in the range 3 GeV≤(1/a)≤5 GeV. The problem of trapping is overcome to a large extent with open boundary and we are able to extract the glueball mass at even larger lattice scale ≈ 5.7 GeV. To smoothen the gauge fields we have used recently proposed Wilson flow which, compared to HYP smearing, exhibits better systematics in the extraction of glueball mass. The extracted glueball mass shows remarkable insensitivity to the lattice spacings in the range explored in this work, 3 GeV≤(1/a)≤5.7 GeV.
Einstein boundary conditions for the 3+1 Einstein equations
Frittelli, Simonetta; Gomez, Roberto
2003-01-01
In the 3+1 framework of the Einstein equations for the case of a vanishing shift vector and arbitrary lapse, we calculate explicitly the four boundary equations arising from the vanishing of the projection of the Einstein tensor along the normal to the boundary surface of the initial-boundary value problem. Such conditions take the form of evolution equations along (as opposed to across) the boundary for certain components of the extrinsic curvature and for certain space derivatives of the three-metric. We argue that, in general, such boundary conditions do not follow necessarily from the evolution equations and the initial data, but need to be imposed on the boundary values of the fundamental variables. Using the Einstein-Christoffel formulation, which is strongly hyperbolic, we show how three of the boundary equations up to linear combinations should be used to prescribe the values of some incoming characteristic fields. Additionally, we show that the fourth one imposes conditions on some outgoing fields
Khodayari, Arezoo; Olsen, Seth C.; Wuebbles, Donald J.; Phoenix, Daniel B.
2015-07-01
Atmospheric chemistry-climate models are often used to calculate the effect of aviation NOx emissions on atmospheric ozone (O3) and methane (CH4). Due to the long (∼10 yr) atmospheric lifetime of methane, model simulations must be run for long time periods, typically for more than 40 simulation years, to reach steady-state if using CH4 emission fluxes. Because of the computational expense of such long runs, studies have traditionally used specified CH4 mixing ratio lower boundary conditions (BCs) and then applied a simple parameterization based on the change in CH4 lifetime between the control and NOx-perturbed simulations to estimate the change in CH4 concentration induced by NOx emissions. In this parameterization a feedback factor (typically a value of 1.4) is used to account for the feedback of CH4 concentrations on its lifetime. Modeling studies comparing simulations using CH4 surface fluxes and fixed mixing ratio BCs are used to examine the validity of this parameterization. The latest version of the Community Earth System Model (CESM), with the CAM5 atmospheric model, was used for this study. Aviation NOx emissions for 2006 were obtained from the AEDT (Aviation Environmental Design Tool) global commercial aircraft emissions. Results show a 31.4 ppb change in CH4 concentration when estimated using the parameterization and a 1.4 feedback factor, and a 28.9 ppb change when the concentration was directly calculated in the CH4 flux simulations. The model calculated value for CH4 feedback on its own lifetime agrees well with the 1.4 feedback factor. Systematic comparisons between the separate runs indicated that the parameterization technique overestimates the CH4 concentration by 8.6%. Therefore, it is concluded that the estimation technique is good to within ∼10% and decreases the computational requirements in our simulations by nearly a factor of 8.
Asymptotic boundary conditions for dissipative waves: General theory
Hagstrom, Thomas
1990-01-01
An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.
Asymptotic boundary conditions for dissipative waves - General theory
Hagstrom, Thomas
1991-01-01
An outstanding issue in computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.
Homogenized boundary conditions and resonance effects in Faraday cages
Hewett, DP; Hewitt, IJ
2016-01-01
We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called `Faraday cage e ect'). Taking the limit as the number of wires in the cage tends to in nity we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an e ective cage boundary. We show how the resulting models depend on key cage parameters such as the...
Qingkai Kong
2012-02-01
Full Text Available In this paper, we study the existence and multiplicity of positive solutions of a class of nonlinear fractional boundary value problems with Dirichlet boundary conditions. By applying the fixed point theory on cones we establish a series of criteria for the existence of one, two, any arbitrary finite number, and an infinite number of positive solutions. A criterion for the nonexistence of positive solutions is also derived. Several examples are given for demonstration.
Effective Stress Law in Unconventional Reservoirs under Different Boundary Conditions
Saurabh, S.; Harpalani, S.
2017-12-01
Unconventional reservoirs have attracted a great deal of research interest worldwide during the past two decades. Low permeability and specialized techniques required to exploit these resources present opportunities for improvement in both production rates and ultimate recovery. Understanding subsurface stress modifications and permeability evolution are valuable when evaluating the prospects of unconventional reservoirs. These reservoir properties are functions of effective stress. As a part of this study, effective stress law, specifically the variation of anisotropic Biot's coefficient under various boundary conditions believed to exist in gas reservoirs by different researchers, has been established. Pressure-dependent-permeability (PdK) experiments were carried out on San Juan coal under different boundary conditions, that is, uniaxial strain condition and constant volume condition. Stress and strain in the vertical and horizontal directions were monitored throughout the experiment. Data collected during the experiments was used to determine the Biot's coefficient in vertical and horizontal directions under these two boundary conditions, treating coal as transversely isotropic. The variation of Biot's coefficient was found to be well correlated with the variation in coal permeability. Based on the estimated values of Biot's coefficients, a theory of variation in its value is presented for other boundary conditions. The findings of the study shed light on the inherent behavior of Biot's coefficient under different reservoir boundary conditions. This knowledge can improve the modeling work requiring estimation of effective stress in reservoirs, such as, pressure-/stress- dependent permeability. At the same time, if the effective stresses are known with more certainty by other methods, it enables assessment of the unknown reservoir boundary conditions.
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.
Simulations of QCD and QED with C* boundary conditions
Hansen, Martin; Lucini, Biagio; Patella, Agostino; Tantalo, Nazario
2018-03-01
We present exploratory results from dynamical simulations of QCD in isolation, as well as QCD coupled to QED, with C* boundary conditions. In finite volume, the use of C* boundary conditions allows for a gauge invariant and local formulation of QED without zero modes. In particular we show that the simulations reproduce known results and that masses of charged mesons can be extracted in a completely gauge invariant way. For the simulations we use a modified version of the HiRep code. The primary features of the simulation code are presented and we discuss some details regarding the implementation of C* boundary conditions and the simulated lattice action. Preprint: CP3-Origins-2017-046 DNRF90, CERN-TH-2017-214
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.
Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions
Ciprian G. Gal
2017-01-01
Full Text Available Given a bounded domain Ω⊂RN with a Lipschitz boundary ∂Ω and p,q∈(1,+∞, we consider the quasilinear elliptic equation -Δpu+α1u=f in Ω complemented with the generalized Wentzell-Robin type boundary conditions of the form bx∇up-2∂nu-ρbxΔq,Γu+α2u=g on ∂Ω. In the first part of the article, we give necessary and sufficient conditions in terms of the given functions f, g and the nonlinearities α1, α2, for the solvability of the above nonlinear elliptic boundary value problems with the nonlinear boundary conditions. In other words, we establish a sort of “nonlinear Fredholm alternative” for our problem which extends the corresponding Landesman and Lazer result for elliptic problems with linear homogeneous boundary conditions. In the second part, we give some additional results on existence and uniqueness and we study the regularity of the weak solutions for these classes of nonlinear problems. More precisely, we show some global a priori estimates for these weak solutions in an L∞-setting.
Tongchun Li
2015-01-01
element is proposed to solve the safety factor of local discontinuous rock mass. Slope system is divided into several continuous bodies and local discontinuous interface boundaries. Each block is treated as a partition of the system and contacted by discontinuous joints. The displacements of blocks are chosen as basic variables and the rigid displacements in the centroid of blocks are chosen as motion variables. The contact forces on interface boundaries and the rigid displacements to the centroid of each body are chosen as mixed variables and solved iteratively using the interface boundary equations. Flexibility matrix is formed through PFE according to the contact states of nodal pairs and spring flexibility is used to reflect the influence of weak structural plane so that nonlinear iteration is only limited to the possible contact region. With cohesion and friction coefficient reduced gradually, the states of all nodal pairs at the open or slip state for the first time are regarded as failure criterion, which can decrease the effect of subjectivity in determining safety factor. Examples are used to verify the validity of the proposed method.
Quantum communication through a spin ring with twisted boundary conditions
Bose, S.; Jin, B.-Q.; Korepin, V.E.
2005-01-01
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
Boundary conditions for quasiclassical Green's function for superfluid Fermi systems
Nagai, K.; Hara, J.
1988-01-01
The authors show that the quasiclassical Green's Function for Fermi liquids can be constructed from the solutions of the Bogoliubov-de Gennes equation within the Andreev approximation and derive self-consistent relations to be satisfied by the quasiclassical Green's function at the surfaces. The so-called normalization condition for the quasiclassical Green's function is obtained from this self-consistent relation. They consider a specularly reflecting wall, a randomly rippled wall, and a proximity boundary as model surfaces. Their boundary condition for the randomly rippled wall is different from that derived by Buchholtz and Rainer and Buchholtz
Greene, Patrick T.; Schofield, Samuel P.; Nourgaliev, Robert
2017-01-01
A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Lastly, dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.
Greene, Patrick T. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Schofield, Samuel P. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Nourgaliev, Robert [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-06-21
A new mesh smoothing method designed to cluster mesh cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered elds, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness to arbitrary Lagrangian Eulerian (ALE) methods.
Boundary conditions for the diffusion equation in radiative transfer
Haskell, R.C.; Svaasand, L.O.; Tsay, T.; Feng, T.; McAdams, M.S.; Tromberg, B.J.
1994-01-01
Using the method of images, we examine the three boundary conditions commonly applied to the surface of a semi-infinite turbid medium. We find that the image-charge configurations of the partial-current and extrapolated-boundary conditions have the same dipole and quadrupole moments and that the two corresponding solutions to the diffusion equation are approximately equal. In the application of diffusion theory to frequency-domain photon-migration (FDPM) data, these two approaches yield values for the scattering and absorption coefficients that are equal to within 3%. Moreover, the two boundary conditions can be combined to yield a remarkably simple, accurate, and computationally fast method for extracting values for optical parameters from FDPM data. FDPM data were taken both at the surface and deep inside tissue phantoms, and the difference in data between the two geometries is striking. If one analyzes the surface data without accounting for the boundary, values deduced for the optical coefficients are in error by 50% or more. As expected, when aluminum foil was placed on the surface of a tissue phantom, phase and modulation data were closer to the results for an infinite-medium geometry. Raising the reflectivity of a tissue surface can, in principle, eliminate the effect of the boundary. However, we find that phase and modulation data are highly sensitive to the reflectivity in the range of 80--100%, and a minimum value of 98% is needed to mimic an infinite-medium geometry reliably. We conclude that noninvasive measurements of optically thick tissue require a rigorous treatment of the tissue boundary, and we suggest a unified partial-current--extrapolated boundary approach
Streletskiy, Dmitry A; Shiklomanov, Nikolay I; Nyland, Kelsey E; Tananaev, Nikita I; Opel, Thomas; Streletskaya, Irina D; Tokarev, Igor’; Shiklomanov, Alexandr I
2015-01-01
Role of changing climatic conditions on permafrost degradation and hydrology was investigated in the transition zone between the tundra and forest ecotones at the boundary of continuous and discontinuous permafrost of the lower Yenisei River. Three watersheds of various sizes were chosen to represent the characteristics of the regional landscape conditions. Samples of river flow, precipitation, snow cover, and permafrost ground ice were collected over the watersheds to determine isotopic composition of potential sources of water in a river flow over a two year period. Increases in air temperature over the last forty years have resulted in permafrost degradation and a decrease in the seasonal frost which is evident from soil temperature measurements, permafrost and active-layer monitoring, and analysis of satellite imagery. The lowering of the permafrost table has led to an increased storage capacity of permafrost affected soils and a higher contribution of ground water to river discharge during winter months. A progressive decrease in the thickness of the layer of seasonal freezing allows more water storage and pathways for water during the winter low period making winter discharge dependent on the timing and amount of late summer precipitation. There is a substantial seasonal variability of stable isotopic composition of river flow. Spring flooding corresponds to the isotopic composition of snow cover prior to the snowmelt. Isotopic composition of river flow during the summer period follows the variability of precipitation in smaller creeks, while the water flow of larger watersheds is influenced by the secondary evaporation of water temporarily stored in thermokarst lakes and bogs. Late summer precipitation determines the isotopic composition of texture ice within the active layer in tundra landscapes and the seasonal freezing layer in forested landscapes as well as the composition of the water flow during winter months. (letter)
Spectral distribution of scalar particles created by a moving boundary with Robin boundary condition
Mintz, B.; Farina, C; Maia Neto, P.A.; Rodrigues, R.B.
2006-01-01
We consider a massless scalar field in 1+1 dimensions satisfying a Robin boundary condition (BC) at a non-relativistic boundary. By deriving a Bogoliubov transformation between the input and output bosonic field operators, we calculate the spectral distribution of created particles. The particular cases of Dirichlet and Neumann BC may be obtained from our result as limiting cases, yielding equal spectra (this result is valid only in this space-time dimensionality). The creation effect for the field under Dirichlet BC turns out to be an upper bound for the spectra derived for Robin BC. Also, we show that the particle creation phenomenon with Robin conditions can be considerably reduced (with respect to the Dirichlet or Neumann cases) by selecting a particular mechanical oscillation frequency of the moving boundary. (author)
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
The neutron transport with general boundary conditions (II)
Boulanouar, Mohamed
2012-01-01
This Note deals with the one-dimensional transport operator, on an unbounded domain, endowed with general boundary conditions. We show the generation of a strongly continuous semigroup and we study its spectral properties. In particular, we prove the existence of a leading eigenvalue. (author)
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.
Boundary conditions for free surface inlet and outlet problems
Taroni, M.; Breward, C. J. W.; Howell, P. D.; Oliver, J. M.
2012-01-01
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
The Hardy inequality with boundary or intermediate conditions
Kufner, Alois
2017-01-01
Roč. 8, č. 2 (2017), s. 105-109 ISSN 2077-9879 Institutional support: RVO:67985840 Keywords : Hardy's inequality * boundary conditions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics http://www.mathnet.ru/ php /archive.phtml?wshow=paper&jrnid=emj&paperid=259&option_lang=eng
Liouville equation with boundary conditions derived from classical strings
Marnelius, R.
1983-01-01
It is shown in terms of the classical string theory that a breaking of the Weyl invariance necessarily requires the Liouville equation for the variable phi=1n rho, where rho is the variable that appears in the conformal gauge gsub(α#betta#)=rhoetasub(α#betta#). Appropriate boundary conditions on phi for open and closed strings are then derived. (orig.)
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...
Boundary conditions for open quantum systems driven far from equilibrium
Frensley, William R.
1990-07-01
This is a study of simple kinetic models of open systems, in the sense of systems that can exchange conserved particles with their environment. The system is assumed to be one dimensional and situated between two particle reservoirs. Such a system is readily driven far from equilibrium if the chemical potentials of the reservoirs differ appreciably. The openness of the system modifies the spatial boundary conditions on the single-particle Liouville-von Neumann equation, leading to a non-Hermitian Liouville operator. If the open-system boundary conditions are time reversible, exponentially growing (unphysical) solutions are introduced into the time dependence of the density matrix. This problem is avoided by applying time-irreversible boundary conditions to the Wigner distribution function. These boundary conditions model the external environment as ideal particle reservoirs with properties analogous to those of a blackbody. This time-irreversible model may be numerically evaluated in a discrete approximation and has been applied to the study of a resonant-tunneling semiconductor diode. The physical and mathematical properties of the irreversible kinetic model, in both its discrete and its continuum formulations, are examined in detail. The model demonstrates the distinction in kinetic theory between commutator superoperators, which may become non-Hermitian to describe irreversible behavior, and anticommutator superoperators, which remain Hermitian and are used to evaluate physical observables.
The Hardy inequality with boundary or intermediate conditions
Kufner, Alois
2017-01-01
Roč. 8, č. 2 (2017), s. 105-109 ISSN 2077-9879 Institutional support: RVO:67985840 Keywords : Hardy's inequality * boundary conditions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=emj&paperid=259&option_lang=eng
Modulations of the processing of line discontinuities under selective attention conditions?
Giersch, Anne; Fahle, Manfred
2002-01-01
We examined whether the processing of discontinuities involved in figure-ground segmentation, like line ends, can be modulated under selective attention conditions. Subjects decided whether a gap in collinear or parallel lines was located to the right or left. Two stimuli were displayed in immediate succession. When the gaps were on the same side, reaction times (RTs) for the second stimulus increased when collinear lines followed parallel lines, or the reverse, but only when the two stimuli shared the same orientation and location. The effect did not depend on the global form of the stimuli or on the relative orientation of the gaps. A frame drawn around collinear elements affected the results, suggesting a crucial role of the "amodal" orthogonal lines produced when line ends are aligned. Including several gaps in the first stimulus also eliminated RT variations. By contrast, RT variations remained stable across several experimental blocks and were significant for interstimulus intervals from 50 to 600 msec between the two stimuli. These results are interpreted in terms of a modulation of the processing of line ends or the production of amodal lines, arising when attention is selectively drawn to a gap.
Continuity Conditions on Schrodinger Wave Functions at Discontinuities of the Potential.
Branson, David
1979-01-01
Several standard arguments which attempt to show that the wave function and its derivative must be continuous across jump discontinuities of the potential are reviewed and their defects discussed. (Author/HM)
The boundary conditions for point transformed electromagnetic invisibility cloaks
Weder, Ricardo
2008-01-01
In this paper we study point transformed electromagnetic invisibility cloaks in transformation media that are obtained by transformation from general anisotropic media. We assume that there are several point transformed electromagnetic cloaks located in different points in space. Our results apply in particular to the first-order invisibility cloaks introduced by Pendry et al and to the high-order invisibility cloaks introduced by Hendi et al and by Cai et al. We identify the appropriate cloaking boundary conditions that the solutions of Maxwell equations have to satisfy at the outside, ∂K + , and at the inside, ∂K - , of the boundary of the cloaked object K in the case where the permittivity and the permeability are bounded below and above in K. Namely, that the tangential components of the electric and the magnetic fields have to vanish at ∂K + -which is always true-and that the normal components of the curl of the electric and the magnetic fields have to vanish at ∂K - . These results are proven requiring that energy be conserved. In the case of one spherical cloak with a spherically stratified K and a radial current at ∂K we verify by an explicit calculation that our cloaking boundary conditions are satisfied and that cloaking of active devices holds, even if the current is at the boundary of the cloaked object. As we prove our results for media that are obtained by transformation from general anisotropic media, our results apply to the cloaking of objects with passive and active devices contained in general anisotropic media, in particular to objects with passive and active devices contained inside general crystals. Our results suggest a method to enhance cloaking in the approximate transformation media that are used in practice. Namely, to coat the boundary of the cloaked object (the inner boundary of the cloak) with a material that imposes the boundary conditions above. As these boundary conditions have to be satisfied for exact transformation
Jat, R.N.; Chaudhary, Santosh
2009-01-01
The flow of an electrically conducting fluid past a porous substrate attached to the flat plate with Beavers-Joseph boundary condition under the influence of a uniform transverse magnetic field has been studied. Taking suitable similar variables, the momentum equation is transformed to ordinary differential equation and solved by standard techniques. The energy equation is solved by considering two boundary layers, one in the porous substrate and the other above the porous substrate. The velocity and temperature distributions along with Nusselt number are discussed numerically and presented through graphs. (author)
Temperature field conduction solution by incomplete boundary condition
Novakovic, M; Petrasinovic, Lj; Djuric, M [Tehnoloski fakultet, Novi Sad (Yugoslavia); Perovic, N [Institut za Nuklearne Nauke Boris Kidric, Belgrade (Yugoslavia)
1977-01-01
The problem of determination of one part boundary conditions temperatures for Fourier partial differential equation when the other part of boundary condition and derivates (heat fluxes) are known is a practical interest as it enables one to determine and accessible temperature by measuring temperatures on other side, of the wall. Method developed and applied here consist of transforming the Fourier partial differential equation by time discretisation in sets of pairs of ordinary differential equations for temperature and heat flux. Such pair of differential equations of first order was solved by Runge-Kutta method. The integration proceeds along space interval simultaneosly for all time intervals. It is interesting to note that this procedure does not require the initial condition.
Matrix albedo for discrete ordinates infinite-medium boundary condition
Mathews, K.; Dishaw, J.
2007-01-01
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)
Revisiting Johnson and Jackson boundary conditions for granular flows
Li, Tingwen; Benyahia, Sofiane
2012-07-01
In this article, we revisit Johnson and Jackson boundary conditions for granular flows. The oblique collision between a particle and a flat wall is analyzed by adopting the classic rigid-body theory and a more realistic semianalytical model. Based on the kinetic granular theory, the input parameter for the partial-slip boundary conditions, specularity coefficient, which is not measurable in experiments, is then interpreted as a function of the particle-wall restitution coefficient, the frictional coefficient, and the normalized slip velocity at the wall. An analytical expression for the specularity coefficient is suggested for a flat, frictional surface with a low frictional coefficient. The procedure for determining the specularity coefficient for a more general problem is outlined, and a working approximation is provided.
Matrix factorisations for rational boundary conditions by defect fusion
Behr, Nicolas; Fredenhagen, Stefan
2015-01-01
A large class of two-dimensional N=(2,2) superconformal field theories can be understood as IR fixed-points of Landau-Ginzburg models. In particular, there are rational conformal field theories that also have a Landau-Ginzburg description. To understand better the relation between the structures in the rational conformal field theory and in the Landau-Ginzburg theory, we investigate how rational B-type boundary conditions are realised as matrix factorisations in the SU(3)/U(2) Grassmannian Kazama-Suzuki model. As a tool to generate the matrix factorisations we make use of a particular interface between the Kazama-Suzuki model and products of minimal models, whose fusion can be realised as a simple functor on ring modules. This allows us to formulate a proposal for all matrix factorisations corresponding to rational boundary conditions in the SU(3)/U(2) model.
Matrix factorisations for rational boundary conditions by defect fusion
Behr, Nicolas [Department of Mathematics, Heriot-Watt University,Riccarton, Edinburgh, EH14 4AS (United Kingdom); Maxwell Institute for Mathematical Sciences,Edinburgh (United Kingdom); Fredenhagen, Stefan [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,D-14424 Golm (Germany)
2015-05-11
A large class of two-dimensional N=(2,2) superconformal field theories can be understood as IR fixed-points of Landau-Ginzburg models. In particular, there are rational conformal field theories that also have a Landau-Ginzburg description. To understand better the relation between the structures in the rational conformal field theory and in the Landau-Ginzburg theory, we investigate how rational B-type boundary conditions are realised as matrix factorisations in the SU(3)/U(2) Grassmannian Kazama-Suzuki model. As a tool to generate the matrix factorisations we make use of a particular interface between the Kazama-Suzuki model and products of minimal models, whose fusion can be realised as a simple functor on ring modules. This allows us to formulate a proposal for all matrix factorisations corresponding to rational boundary conditions in the SU(3)/U(2) model.
New boundary conditions for 3D RF modelling
Ko, K.; Nelson, E.; Fitze, H.
1990-01-01
The new capabilities are being implemented into the 3D particle-in-cell code, ARGUS, which will reduce substantially both problem size and computing time when modeling realistic geometries with high accuracies. In the time domain, a cylindrical radiative boundary condition will enable traveling wave propagation to be simulated in accelerator structures. An application of interest is the input coupler in the SLAC x-band high-gradient structure where local field gradients and impedance matching are important issues. In the frequency domain, a quasi-periodic boundary condition will facilitate the cold-test analysis of 3D periodic structures where many calculations are required to generate an ω β diagram. Present applications include the crossed-field amplifier cavity and the cluster klystron cavity
Flow boundary conditions for chain-end adsorbing polymer blends.
Zhou, Xin; Andrienko, Denis; Delle Site, Luigi; Kremer, Kurt
2005-09-08
Using the phenol-terminated polycarbonate blend as an example, we demonstrate that the hydrodynamic boundary conditions for a flow of an adsorbing polymer melt are extremely sensitive to the structure of the epitaxial layer. Under shear, the adsorbed parts (chain ends) of the polymer melt move along the equipotential lines of the surface potential whereas the adsorbed additives serve as the surface defects. In response to the increase of the number of the adsorbed additives the surface layer becomes thinner and solidifies. This results in a gradual transition from the slip to the no-slip boundary condition for the melt flow, with a nonmonotonic dependence of the slip length on the surface concentration of the adsorbed ends.
Kyncl Martin
2017-01-01
Full Text Available We work with the system of partial differential equations describing the non-stationary compressible turbulent fluid flow. It is a characteristic feature of the hyperbolic equations, that there is a possible raise of discontinuities in solutions, even in the case when the initial conditions are smooth. The fundamental problem in this area is the solution of the so-called Riemann problem for the split Euler equations. It is the elementary problem of the one-dimensional conservation laws with the given initial conditions (LIC - left-hand side, and RIC - right-hand side. The solution of this problem is required in many numerical methods dealing with the 2D/3D fluid flow. The exact (entropy weak solution of this hyperbolical problem cannot be expressed in a closed form, and has to be computed by an iterative process (to given accuracy, therefore various approximations of this solution are being used. The complicated Riemann problem has to be further modified at the close vicinity of boundary, where the LIC is given, while the RIC is not known. Usually, this boundary problem is being linearized, or roughly approximated. The inaccuracies implied by these simplifications may be small, but these have a huge impact on the solution in the whole studied area, especially for the non-stationary flow. Using the thorough analysis of the Riemann problem we show, that the RIC for the local problem can be partially replaced by the suitable complementary conditions. We suggest such complementary conditions accordingly to the desired preference. This way it is possible to construct the boundary conditions by the preference of total values, by preference of pressure, velocity, mass flow, temperature. Further, using the suitable complementary conditions, it is possible to simulate the flow in the vicinity of the diffusible barrier. On the contrary to the initial-value Riemann problem, the solution of such modified problems can be written in the closed form for some
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.
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: 0.933, year: 2016
Scattering of wedges and cones with impedance boundary conditions
Lyalinov, Mikhail
2012-01-01
This book is a systematic and detailed exposition of different analytical techniques used in studying two of the canonical problems, the wave scattering by wedges or cones with impedance boundary conditions. It is the first reference on novel, highly efficient analytical-numerical approaches for wave diffraction by impedance wedges or cones. The applicability of the reported solution procedures and formulae to existing software packages designed for real-world high-frequency problems encountered in antenna, wave propagation, and radar cross section.
Deficiency indices and singular boundary conditions in quantum mechanics
Bulla, W.
1984-01-01
We consider Schroedinger operators H in L 2 (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
On the extraction of spectral quantities with open boundary conditions
Bruno, Mattia; Korcyl, Piotr; Lottini, Stefano; Schaefer, Stefan; Korzec, Tomasz
2014-11-01
We discuss methods to extract decay constants, meson masses and gluonic observables in the presence of open boundary conditions. The ensembles have been generated by the CLS effort and have 2+1 flavors of O(a)-improved Wilson fermions with a small twisted-mass term as proposed by Luescher and Palombi. We analyse the effect of the associated reweighting factors on the computation of different observables.
Nonsteady heat conduction code with radiation boundary conditions
Fillo, J.A.; Benenati, R.; Powell, J.
1975-01-01
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)
Time reversal method with stabilizing boundary conditions for Photoacoustic tomography
Chervova, Olga; Oksanen, Lauri
2016-01-01
We study an inverse initial source problem that models photoacoustic tomography measurements with array detectors, and introduce a method that can be viewed as a modification of the so called back and forth nudging method. We show that the method converges at an exponential rate under a natural visibility condition, with data given only on a part of the boundary of the domain of wave propagation. In this paper we consider the case of noiseless measurements. (paper)
Eigenvalue inequalities for the Laplacian with mixed boundary conditions
Lotoreichik, Vladimir; Rohleder, J.
2017-01-01
Roč. 263, č. 1 (2017), s. 491-508 ISSN 0022-0396 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : Laplace operator * mixed boundary conditions * eigenvalue inequality * polyhedral domain * Lipschitz domain Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.988, year: 2016
A Resistive Boundary Condition Enhanced DGTD Scheme for the Transient Analysis of Graphene
Li, Ping
2015-04-24
In this paper, the electromagnetic (EM) features of graphene are characterized by a discontinuous Galerkin timedomain (DGTD) algorithm with a resistive boundary condition (RBC). The atomically thick graphene is equivalently modeled using a RBC by regarding the graphene as an infinitesimally thin conductive sheet. To incorporate RBC into the DGTD analysis, the surface conductivity of the graphene composed of contributions from both intraband and interband terms is firstly approximated by rational basis functions using the fastrelaxation vector-fitting (FRVF) method in the Laplace-domain. Next, through the inverse Laplace transform, the corresponding time-domain matrix equations in integral can be obtained. Finally, these matrix equations are solved by time-domain finite integral technique (FIT). For elements not touching the graphene sheet, however, the well-known Runge-Kutta (RK) method is employed to solve the two first-order time-derivative Maxwell’s equations. The application of the surface boundary condition significantly alleviates the memory consuming and the limitation of time step size required by Courant-Friedrichs-Lewy (CFL) condition. To validate the proposed algorithm, various numerical examples are presented and compared with available references.
A Resistive Boundary Condition Enhanced DGTD Scheme for the Transient Analysis of Graphene
Li, Ping; Jiang, Li; Bagci, Hakan
2015-01-01
In this paper, the electromagnetic (EM) features of graphene are characterized by a discontinuous Galerkin timedomain (DGTD) algorithm with a resistive boundary condition (RBC). The atomically thick graphene is equivalently modeled using a RBC by regarding the graphene as an infinitesimally thin conductive sheet. To incorporate RBC into the DGTD analysis, the surface conductivity of the graphene composed of contributions from both intraband and interband terms is firstly approximated by rational basis functions using the fastrelaxation vector-fitting (FRVF) method in the Laplace-domain. Next, through the inverse Laplace transform, the corresponding time-domain matrix equations in integral can be obtained. Finally, these matrix equations are solved by time-domain finite integral technique (FIT). For elements not touching the graphene sheet, however, the well-known Runge-Kutta (RK) method is employed to solve the two first-order time-derivative Maxwell’s equations. The application of the surface boundary condition significantly alleviates the memory consuming and the limitation of time step size required by Courant-Friedrichs-Lewy (CFL) condition. To validate the proposed algorithm, various numerical examples are presented and compared with available references.
Influence of different boundary conditions on analysis of SSI
Wang Jiachun
2005-01-01
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)
Repulsive Casimir force from fractional Neumann boundary conditions
Lim, S.C.; Teo, L.P.
2009-01-01
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.
Dongyan Shi
2016-01-01
Full Text Available This paper presents free vibration analysis of open and closed shells with arbitrary boundary conditions using a spectro-geometric-Ritz method. In this method, regardless of the boundary conditions, each of the displacement components of open and closed shells is represented simultaneously as a standard Fourier cosine series and several auxiliary functions. The auxiliary functions are introduced to accelerate the convergence of the series expansion and eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries. The boundary conditions are modeled using the spring stiffness technique. All the expansion coefficients are treated equally and independently as the generalized coordinates and determined using Rayleigh-Ritz method. By using this method, a unified vibration analysis model for the open and closed shells with arbitrary boundary conditions can be established without the need of changing either the equations of motion or the expression of the displacement components. The reliability and accuracy of the proposed method are validated with the FEM results and those from the literature.
Livshits, Gideon I.
2014-01-01
Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for the mass, angular momentum, and energy loss due to radiation. The approach of Regge and Teitelboim, aimed at a clear Hamiltonian formulation with a boundary, and its extension to the Lagrangian formulation by Julia and Silva have resolved these issues, and have resulted in a consistent, well-defined and unique variational equation for the superpotential, thereby placing it on a firm footing. A hallmark solution of this equation is the KBL superpotential obtained from the first-order Lovelock Lagrangian. Nevertheless, here we show that these formulations are still insufficient for Lovelock Lagrangians of higher orders. We present a paradox, whereby the choice of fields affects the superpotential for equivalent on-shell dynamics. We offer two solutions to this paradox: either the original Lagrangian must be effectively renormalized, or that boundary conditions must be imposed, so that space-time be asymptotically maximally symmetric. Non-metricity is central to this paradox, and we show how quadratic non-metricity in the bulk of space-time contributes to the conserved charges on the boundary, where it vanishes identically. This is a realization of the gravitational Higgs mechanism, proposed by Percacci, where the non-metricity is the analogue of the Goldstone boson
Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions
Ruggeri, Fabrizio; Sawlan, Zaid A; Scavino, Marco; Tempone, Raul
2016-01-01
In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.
Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions
Ruggeri, Fabrizio
2015-01-07
In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.
Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions
Ruggeri, Fabrizio
2016-01-06
In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.
Javier A. Dottori
2015-01-01
Full Text Available A method for modeling outflow boundary conditions in the lattice Boltzmann method (LBM based on the maximization of the local entropy is presented. The maximization procedure is constrained by macroscopic values and downstream components. The method is applied to fully developed boundary conditions of the Navier-Stokes equations in rectangular channels. Comparisons are made with other alternative methods. In addition, the new downstream-conditioned entropy is studied and it was found that there is a correlation with the velocity gradient during the flow development.
Evolution of passive movement in advective environments: General boundary condition
Zhou, Peng; Zhao, Xiao-Qiang
2018-03-01
In a previous work [16], Lou et al. studied a Lotka-Volterra competition-diffusion-advection system, where two species are supposed to differ only in their advection rates and the environment is assumed to be spatially homogeneous and closed (no-flux boundary condition), and showed that weaker advective movements are more beneficial for species to win the competition. In this paper, we aim to extend this result to a more general situation, where the environmental heterogeneity is taken into account and the boundary condition at the downstream end becomes very flexible including the standard Dirichlet, Neumann and Robin type conditions as special cases. Our main approaches are to exclude the existence of co-existence (positive) steady state and to provide a clear picture on the stability of semi-trivial steady states, where we introduced new ideas and techniques to overcome the emerging difficulties. Based on these two aspects and the theory of abstract competitive systems, we achieve a complete understanding on the global dynamics.
Thermal properties of nuclear matter under the periodic boundary condition
Otuka, Naohiko; Ohnishi, Akira
1999-01-01
We present the thermal properties of nuclear matter under the periodic boundary condition by the use of our hadronic nucleus-nucleus cascade model (HANDEL) which is developed to treat relativistic heavy-ion collisions from BNL-AGS to CERN-SPS. We first show some results of p-p scattering calculation in our new version which is improved in order to treat isospin ratio and multiplicity more accurately. We then display the results of calculation of nuclear matter with baryon density ρ b = 0.77 fm 3 at some energy densities. Time evolution of particle abundance and temperature are shown. (author)
Hawking radiation, effective actions and covariant boundary conditions
Banerjee, Rabin; Kulkarni, Shailesh
2008-01-01
From an appropriate expression for the effective action, the Hawking radiation from charged black holes is derived, using only covariant boundary conditions at the event horizon. The connection of our approach with the Unruh vacuum and the recent analysis [S.P. Robinson, F. Wilczek, Phys. Rev. Lett. 95 (2005) 011303, (gr-qc/0502074); S. Iso, H. Umetsu, F. Wilczek, Phys. Rev. Lett. 96 (2006) 151302, (hep-th/0602146); R. Banerjee, S. Kulkarni, (arXiv: 0707.2449 [hep-th])] of Hawking radiation using anomalies is established
The gradient flow running coupling with twisted boundary conditions
Ramos, Alberto
2014-09-01
We study the gradient flow for Yang-Mills theories with twisted boundary conditions. The perturbative behavior of the energy density left angle E(t) right angle is used to define a running coupling at a scale given by the linear size of the finite volume box. We compute the non-perturbative running of the pure gauge SU(2) coupling constant and conclude that the technique is well suited for further applications due to the relatively mild cutoff effects of the step scaling function and the high numerical precision that can be achieved in lattice simulations. We also comment on the inclusion of matter fields.
Bound states on the lattice with partially twisted boundary conditions
Agadjanov, D.; Guo, F.-K.; Ríos, G.; Rusetsky, A.
2015-01-01
We propose a method to study the nature of exotic hadrons by determining the wave function renormalization constant Z from lattice simulations. It is shown that, instead of studying the volume-dependence of the spectrum, one may investigate the dependence of the spectrum on the twisting angle, imposing twisted boundary conditions on the fermion fields on the lattice. In certain cases, e.g., the case of the DK bound state which is addressed in detail, it is demonstrated that the partial twisting is equivalent to the full twisting up to exponentially small corrections.
The Casimir effect for pistons with transmittal boundary conditions
Fucci, Guglielmo
2017-11-01
This work focuses on the analysis of the Casimir effect for pistons subject to transmittal boundary conditions. In particular we consider, as piston configuration, a direct product manifold of the type I × N where I is a closed interval of the real line and N is a smooth compact Riemannian manifold. By utilizing the spectral zeta function regularization technique, we compute the Casimir energy of the system and the Casimir force acting on the piston. Explicit results for the force are provided when the manifold N is a d-dimensional sphere.
Nawal H. Al – Raheimy
2016-09-01
Full Text Available In this paper the approximate method of Raleigh method can be used to study the effect of additional boundary conditions (clamped – free & clamped – clamped on the free transverse vibrations of uniform pipes which have length, L (1m , inner radius, "Ri" (1cm & thickness, "t" (1mm made from composite materials, where the resin of unsaturated polyester represented the matrix material reinforced by aligned (E-fibers glass in the first case and used aligned fiber (Kevlar-49 in the second case. The length of fibers is in the two types, the first type is long fibers (continuous and the second is short fibers (discontinuous for different length all at volume fraction of fibers, "f" (0.15 & 0.25. At any construction of the pipe in composite material the natural frequency decreased when the velocity of flow increased from zero to critical velocity also can be observed the pipe at clamped – clamped boundary conditions predicts natural frequency & critical velocity greater than that pipe at clamped – free. The natural frequency and critical velocity increase with increasing volume fraction and length of discontinuous fiber. The value of natural frequency for pipes which have continuous fibers is constant at certain velocity of flow while are variable in pipes which have discontinuous fibers according to ratio between length of short fiber to critical length of discontinuous fiber whereas the natural frequency increase with increasing this ratio. Finally the pipes with Kevlar fiber have high critical velocity and natural frequency compare with pipes for fiber glass.
Magnetospheric conditions near the equatorial footpoints of proton isotropy boundaries
V. A. Sergeev
2015-12-01
Full Text Available 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.
The effects of external conditions in turbulent boundary layers
Brzek, Brian G.
The effects of multiple external conditions on turbulent boundary layers were studied in detail. These external conditions include: surface roughness, upstream turbulence intensity, and pressure gradient. Furthermore, the combined effects of these conditions show the complicated nature of many realistic flow conditions. It was found that the effects of surface roughness are difficult to generalize, given the importance of so many parameters. These parameters include: roughness geometry, roughness regime, roughness height to boundary layer thickness, (k/delta), roughness parameter, ( k+), Reynolds number, and roughness function (Delta B+). A further complication, is the difficulty in computing the wall shear stress, tauw/rho. For the sand grain type roughness, the mean velocity and Reynolds stresses were studied in inner and outer variables, as well as, boundary layer parameters, anisotropy tensor, production term, and viscous stress and form drag contributions. To explore the effects of roughness and Reynolds number dependence in the boundary layer, a new experiment was carefully designed to properly capture the x-dependence of the single-point statistics. It was found that roughness destroys the viscous layer near the wall, thus, reducing the contribution of the viscous stress in the wall region. As a result, the contribution in the skin friction due to form drag increases, while the viscous stress decreases. This yields Reynolds number invariance in the skin friction, near-wall roughness parameters, and inner velocity profiles as k + increases into the fully rough regime. However, in the transitionally rough regime, (i.e., 5 component shows the largest influence of roughness, where the high peak near the wall was decreased and became nearly flat for the fully rough regime profiles. In addition, the Reynolds stresses in outer variables show self-similarity for fixed experimental conditions. However, as the roughness parameter, k +, increases, all Reynolds stress
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
Ibrahim, O.M.; Klein, S.A.; Mitchell, J.W.
1991-01-01
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 T L.in /φT H.in where φ is a factor relating the entropy changes during heat rejection and heat addition
Biologic phosphorus elimination - influencing parameters, boundary conditions, process optimation
Dai Xiaohu.
1992-01-01
This paper first presents a systematic study of the basic process of biologic phosphorus elimination as employed by the original 'Phoredox (Main Stream) Process'. The conditions governing the process and the factors influencing its performance were determined by trial operation. A stationary model was developed for the purpose of modelling biologic phosphorus elimination in such a main stream process and optimising the dimensioning. The validity of the model was confirmed by operational data given in the literature and by operational data from the authors' own semitechnical-scale experimental plant. The model permits simulation of the values to be expected for effluent phosphorus and phosphate concentrations for given influent data and boundary conditions. It is thus possible to dimension a plant for accomodation of the original Phoredox (Main Stream) Process or any similar phosphorus eliminating plant that is to work according to the principle of the main stream process. (orig./EF) [de
Arsić Zvezdan M.
2016-01-01
Full Text Available At school, children spend the most beautiful period of their childhood and youth, and the moment they start school is always festive and exciting. However, it is known that school brings also the first concerns and problems. Problems and difficulties, which can occur at the beginning of schooling may, have long-term effects on the adaption and success of children, even on later adult life. The causes that lead to this situation are many and varied, and one of the most important is the educational gap in the educational system, whose essence lies in the disconnection between the various degrees of education. Taking into account the above findings, we discuss in this paper the most common causes that lead to the discontinuity between preschool and primary levels of education and areas in which the discontinuity is usually expressed. Also, the operation is determined and focused attention on certain assumptions and conditions that need to be accomplished in order to eliminate the effects of discontinuity abd achieve the necessary continuity between the pre-school and primary school children and facilitate the transition from lower to higher levels of education.
Influence of Spanwise Boundary Conditions on Slat Noise Simulations
Lockard, David P.; Choudhari, Meelan M.; Buning, Pieter G.
2015-01-01
The slat noise from the 30P/30N high-lift system is being investigated through computational fluid dynamics simulations with the OVERFLOW code in conjunction with a Ffowcs Williams-Hawkings acoustics solver. In the present study, two different spanwise grids are being used to investigate the effect of the spanwise extent and periodicity on the near-field unsteady structures and radiated noise. The baseline grid with periodic boundary conditions has a short span equal to 1/9th of the stowed chord, whereas the other, longer span grid adds stretched grids on both sides of the core, baseline grid to allow inviscid surface boundary conditions at both ends. The results indicate that the near-field mean statistics obtained using the two grids are similar to each other, as are the directivity and spectral shapes of the radiated noise. However, periodicity forces all acoustic waves with less than one wavelength across the span to be two-dimensional, without any variation in the span. The spanwise coherence of the acoustic waves is what is needed to make estimates of the noise that would be radiated from realistic span lengths. Simulations with periodic conditions need spans of at least six slat chords to allow spanwise variation in the low-frequencies associated with the peak of broadband slat noise. Even then, the full influence of the periodicity is unclear, so employing grids with a fine, central region and highly stretched meshes that go to slip walls may be a more efficient means of capturing the spanwise decorrelation of low-frequency acoustic phenomena.
Discrete Green's Theorem, Green's Functions and Stable Radiative FDTD Boundary Conditions
Arnold, J.M.; Hon, de B.P.
2007-01-01
We propose a radiative boundary condition for the discrete-grid formulation of Helmholtz’ equation, based on rational approximation in the frequency domain of a Green’s function for the discretised system. This boundary condition is free from instabilities.
Toroidal current asymmetry and boundary conditions in disruptions
Strauss, Henry
2014-10-01
It was discovered on JET that disruptions were accompanied by toroidal asymmetry of the plasma current. The toroidal current asymmetry ΔIϕ is proportional to the vertical current moment ΔMIZ , with positive sign for an upward vertical displacement event (VDE) and negative sign for a downward VDE. It was claimed that this could only be explained by Hiro current. It is shown that instead it is essentially a kinematic effect produced by the VDE displacement of a 3D magnetic perturbation. This is verified by M3D simulations. The simulation results do not require penetration of plasma into the boundary, as in the Hiro current model. It is shown that the normal velocity perpendicular to the magnetic field vanishes at the wall, in the small Larmor radius limit of electromagnetic sheath boundary conditions. Plasma is absorbed into the wall only via the parallel velocity, which is small, penetrates only an infinitesimal distance into the wall, and does not affect forces exerted by the plasma on the wall. Supported by USDOE and ITER.
Homogenized boundary conditions and resonance effects in Faraday cages
Hewitt, I. J.
2016-01-01
We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called ‘Faraday cage effect’). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells. PMID:27279775
Homogenized boundary conditions and resonance effects in Faraday cages
Hewett, D. P.; Hewitt, I. J.
2016-05-01
We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called `Faraday cage effect'). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells.
Evaluation of nonequilibrium boundary conditions for hypersonic rarefied gas flows
Le, N. T. P.; Greenshields, Ch. J.; Reese, J. M.
2012-01-01
A new Computational Fluid Dynamics (CFD) solver for high-speed viscous §ows in the OpenFOAM code is validated against published experimental data and Direct Simulation Monte Carlo (DSMC) results. The laminar §at plate and circular cylinder cases are studied for Mach numbers, Ma, ranging from 6 to 12.7, and with argon and nitrogen as working gases. Simulation results for the laminar §at plate cases show that the combination of accommodation coefficient values σu = 0.7 and σT = 1.0 in the Maxwell/Smoluchowski conditions, and the coefficient values A1 = 1.5 and A2 = 1.0 in the second-order velocity slip condition, give best agreement with experimental data of surface pressure. The values σu = 0.7 and σT = 1.0 also give good agreement with DSMC data of surface pressure at the stagnation point in the circular cylinder case at Kn = 0.25. The Langmuir surface adsorption condition is also tested for the laminar §at plate case, but initial results were not as good as the Maxwell/Smoluchowski boundary conditions.
Jang, Hae-Won; Ih, Jeong-Guon
2012-04-01
The time domain boundary element method (BEM) is associated with numerical instability that typically stems from the time marching scheme. In this work, a formulation of time domain BEM is derived to deal with all types of boundary conditions adopting a multi-input, multi-output, infinite impulse response structure. The fitted frequency domain impedance data are converted into a time domain expression as a form of an infinite impulse response filter, which can also invoke a modeling error. In the calculation, the response at each time step is projected onto the wave vector space of natural radiation modes, which can be obtained from the eigensolutions of the single iterative matrix. To stabilize the computation, unstable oscillatory modes are nullified, and the same decay rate is used for two nonoscillatory modes. As a test example, a transient sound field within a partially lined, parallelepiped box is used, within which a point source is excited by an octave band impulse. In comparison with the results of the inverse Fourier transform of a frequency domain BEM, the average of relative difference norm in the stabilized time response is found to be 4.4%.
Atom-partitioned multipole expansions for electrostatic potential boundary conditions
Lee, M., E-mail: michael.s.lee131.civ@mail.mil [Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States); Leiter, K. [Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States); Eisner, C. [Secure Mission Solutions, a Parsons Company (United States); Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States); Knap, J. [Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States)
2017-01-01
Applications such as grid-based real-space density functional theory (DFT) use the Poisson equation to compute electrostatics. However, the expected long tail of the electrostatic potential requires either the use of a large and costly outer domain or Dirichlet boundary conditions estimated via multipole expansion. We find that the oft-used single-center spherical multipole expansion is only appropriate for isotropic mesh domains such as spheres and cubes. In this work, we introduce a method suitable for high aspect ratio meshes whereby the charge density is partitioned into atomic domains and multipoles are computed for each domain. While this approach is moderately more expensive than a single-center expansion, it is numerically stable and still a small fraction of the overall cost of a DFT calculation. The net result is that when high aspect ratio systems are being studied, form-fitted meshes can now be used in lieu of cubic meshes to gain computational speedup.
Microlocal approach towards construction of nonreflecting boundary conditions
Vaibhav, V.
2014-09-01
This paper addresses the problem of construction of non-reflecting boundary condition for certain second-order nonlinear dispersive equations. It is shown that using the concept of microlocality it is possible to relax the requirement of compact support of the initial data. The method is demonstrated for a class of initial data such that outside the computational domain it behaves like a continuous-wave. The generalization is detailed for two existing schemes in the framework of pseudo-differential calculus, namely, Szeftel's method (Szeftel (2006) [1]) and gauge transformation strategy (Antoine et al. (2006) [2]). Efficient numerical implementation is discussed and a comparative performance analysis is presented. The paper also briefly surveys the possibility of extension of the method to higher-dimensional PDEs.
CFD Modeling of Non-Neutral Atmospheric Boundary Layer Conditions
Koblitz, Tilman
model results. A method is developed how to simulate the time-dependant non-neutral ABL flow over complex terrain: a precursor simulation is used to specify unsteady inlet boundary conditions on complex terrain domains. The advantage of the developed RANS model framework is its general applicability...... characteristics of neutral and non-neutral ABL flow. The developed ABL model significantly improves the predicted flow fields over both flat and complex terrain, when compared against neutral models and measurements....... cost than e.g. using large-eddy simulations. The developed ABL model is successfully validated using a range of different test cases with increasing complexity. Data from several large scale field campaigns, wind tunnel experiments, and previous numerical simulations is presented and compared against...
Vibration modes of a single plate with general boundary conditions
Phamová L.
2016-06-01
Full Text Available This paper deals with free flexural vibration modes and natural frequencies of a thin plate with general boundary conditions — a simply supported plate connected to its surroundings with torsional springs. Vibration modes were derived on the basis of the Rajalingham, Bhat and Xistris approach. This approach was originally used for a clamped thin plate, so its adaptation was needed. The plate vibration function was usually expressed as a single partial differential equation. This partial differential equation was transformed into two ordinary differential equations that can be solved in the simpler way. Theoretical background of the computations is briefly described. Vibration modes of the supported plate with torsional springs are presented graphically and numerically for three different values of stiffness of torsional springs.
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.
Sarna, Neeraj; Torrilhon, Manuel
2018-01-01
We define certain criteria, using the characteristic decomposition of the boundary conditions and energy estimates, which a set of stable boundary conditions for a linear initial boundary value problem, involving a symmetric hyperbolic system, must satisfy. We first use these stability criteria to show the instability of the Maxwell boundary conditions proposed by Grad (Commun Pure Appl Math 2(4):331-407, 1949). We then recognise a special block structure of the moment equations which arises due to the recursion relations and the orthogonality of the Hermite polynomials; the block structure will help us in formulating stable boundary conditions for an arbitrary order Hermite discretization of the Boltzmann equation. The formulation of stable boundary conditions relies upon an Onsager matrix which will be constructed such that the newly proposed boundary conditions stay close to the Maxwell boundary conditions at least in the lower order moments.
Dynamical Casimir effect on a cavity with mixed boundary conditions
Alves, Danilo T.; Farina, Carlos; Maia Neto, Paulo Americo
2002-01-01
The most well-known mechanical effect related to the quantum vacuum is the Casimir force between two mirrors at rest. A new effect appears when the mirrors are set to move. In this case, the vacuum field may exert a dissipative force, damping the motion. As a consequence of energy conservation, there will be creation of real particles. If the motion is non-relativistic and has a small amplitude, the dynamical Casimir force can be found via a perturbative method proposed by Ford and Vilenkin. Using their technique, the electromagnetic dynamical Casimir problem, considered when the oscillating cavity is formed by two parallel plates of the same nature (perfectly conducting or perfectly permeable), can be divided into two separated boundary condition problems, namely: one involving Dirichlet BC, related to the transverse electric polarization and the other involving a Neumann BC, related to the transverse magnetic mode. The case of conducting plates can be found in the literature. However, another interesting case, the mixed oscillating cavity where the plates are of different nature, namely, a perfectly conducting plate and a perfectly permeable one (Boyer plates), has not been studied yet. We show that,for this case, the transverse electric models will be related to mixed boundary conditions: Dirichlet-like BC at the conducting plate and Neumann-like BC at the permeable plate. Analogously, the magnetic modes are related to a Neumann BC at the conducting plate and to a Dirichlet BC at the permeable one. As a first step before attacking the three-dimensional electromagnetic problem with mixed BC, we present here a simpler model: a one-dimensional cavity, where a massless scalar field is submitted to mixed (Dirichlet-Neumann) BC. For simplicity, we consider a non-relativistic motion for the conducting wall (Dirichlet BC) and suppose that the perfectly permeable wall (Neumann BC) is at rest. From this model we can extract insights about the dynamical Casimir
The influence of the magnetic boundary conditions on the nature of astrophysical convection
Lopez, J.M.; Murphy, J.O.
1983-01-01
The effects of employing two forms of the boundary conditions for the magnetic field disturbance, H, are demonstrated. The appropriate conditions on H for current-free boundaries can be written as DHt-aH=0. The second case uses the conditions DH=0 at the lower and upper boundaries
Johannessen, Kim
2014-01-01
The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions can be expressed in terms of the Jacobi elliptic functions. The boundary conditions determine the modulus of the Jacobi elliptic functions. The boundary conditions can not be solved analytically...
The influence of boundary conditions on domain structure stability in spin wave approximation
Wachinewski, A.
1974-01-01
Instead of the usually used Born-Karman cyclic conditions, boundary conditions which take into account the situation of the boundary lattice sites lying on the crystal's surface are assumed. It is shown that the particular choice of the boundary conditions secures the stability of domain structure in ferromagnet (positive spin wave energies), without including the Winter term in Hamiltonian. (author)
Bhan, Jaemi; Kwon, Younghun
2007-01-01
Recently Yeo showed that thermal states in Heisenberg XX model with periodic boundary condition could be used for three-party quantum teleportation. However it is hard to implement the periodic boundary condition in spin chain. So instead of imposing the periodic boundary condition, we consider open boundary condition in Heisenberg XX model and investigate the possibility of using thermal states in Heisenberg XX model with open boundary condition. Using this way, we find the best fidelity conditions to three known protocols in three-party quantum teleportation. It turns out that the best fidelity in every protocol would be 23
Yang, Chuan-Fu
Inverse spectral problems are considered for differential pencils with boundary conditions depending polynomially on the spectral parameter and with a finite number of transmission conditions. We give formulations of the associated inverse problems such as Titchmarsh-Weyl theorem, Hochstadt-Lieberman theorem and Mochizuki-Trooshin theorem, and prove corresponding uniqueness theorems. The obtained results are generalizations of the similar results for the classical Sturm-Liouville operator on a finite interval.
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
Compressible turbulent channel flow with impedance boundary conditions
Scalo, Carlo; Bodart, Julien; Lele, Sanjiva K.
2015-03-01
We have performed large-eddy simulations of isothermal-wall compressible turbulent channel flow with linear acoustic impedance boundary conditions (IBCs) for the wall-normal velocity component and no-slip conditions for the tangential velocity components. Three bulk Mach numbers, Mb = 0.05, 0.2, 0.5, with a fixed bulk Reynolds number, Reb = 6900, have been investigated. For each Mb, nine different combinations of IBC settings were tested, in addition to a reference case with impermeable walls, resulting in a total of 30 simulations. The adopted numerical coupling strategy allows for a spatially and temporally consistent imposition of physically realizable IBCs in a fully explicit compressible Navier-Stokes solver. The IBCs are formulated in the time domain according to Fung and Ju ["Time-domain impedance boundary conditions for computational acoustics and aeroacoustics," Int. J. Comput. Fluid Dyn. 18(6), 503-511 (2004)]. The impedance adopted is a three-parameter damped Helmholtz oscillator with resonant angular frequency, ωr, tuned to the characteristic time scale of the large energy-containing eddies. The tuning condition, which reads ωr = 2πMb (normalized with the speed of sound and channel half-width), reduces the IBCs' free parameters to two: the damping ratio, ζ, and the resistance, R, which have been varied independently with values, ζ = 0.5, 0.7, 0.9, and R = 0.01, 0.10, 1.00, for each Mb. The application of the tuned IBCs results in a drag increase up to 300% for Mb = 0.5 and R = 0.01. It is shown that for tuned IBCs, the resistance, R, acts as the inverse of the wall-permeability and that varying the damping ratio, ζ, has a secondary effect on the flow response. Typical buffer-layer turbulent structures are completely suppressed by the application of tuned IBCs. A new resonance buffer layer is established characterized by large spanwise-coherent Kelvin-Helmholtz rollers, with a well-defined streamwise wavelength λx, traveling downstream with
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
Solutions of the Wheeler-Feynman equations with discontinuous velocities.
de Souza, Daniel Câmara; De Luca, Jayme
2015-01-01
We generalize Wheeler-Feynman electrodynamics with a variational boundary value problem for continuous boundary segments that might include velocity discontinuity points. Critical-point orbits must satisfy the Euler-Lagrange equations of the action functional at most points, which are neutral differential delay equations (the Wheeler-Feynman equations of motion). At velocity discontinuity points, critical-point orbits must satisfy the Weierstrass-Erdmann continuity conditions for the partial momenta and the partial energies. We study a special setup having the shortest time-separation between the (infinite-dimensional) boundary segments, for which case the critical-point orbit can be found using a two-point boundary problem for an ordinary differential equation. For this simplest setup, we prove that orbits can have discontinuous velocities. We construct a numerical method to solve the Wheeler-Feynman equations together with the Weierstrass-Erdmann conditions and calculate some numerical orbits with discontinuous velocities. We also prove that the variational boundary value problem has a unique solution depending continuously on boundary data, if the continuous boundary segments have velocity discontinuities along a reduced local space.
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.
A Two-Dimensional Transverse Magnetic Propagation Model of a Sine Wave Using Mur Boundary Conditions
Korjack, T
1997-01-01
.... The nonreflecting boundary conditions due to Mur were used at the boundary surfaces. Electric field intensity distributions resulted over a progressive time expansion to illustrate the propagation effect over the entire 2-D mesh...
Bessaih, Hakima; Efendiev, Yalchin; Maris, Florin
2015-01-01
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
Frittelli, Simonetta; Gomez, Roberto
2004-01-01
We show how the use of the normal projection of the Einstein tensor as a set of boundary conditions relates to the propagation of the constraints, for two representations of the Einstein equations with vanishing shift vector: the Arnowitt-Deser-Misner formulation, which is ill posed, and the Einstein-Christoffel formulation, which is symmetric hyperbolic. Essentially, the components of the normal projection of the Einstein tensor that act as nontrivial boundary conditions are linear combinations of the evolution equations with the constraints that are not preserved at the boundary, in both cases. In the process, the relationship of the normal projection of the Einstein tensor to the recently introduced 'constraint-preserving' boundary conditions becomes apparent
Decoupling in an expanding universe boundary RG-flow affects initial conditions for inflation
Schalm, K; Van der Schaar, J P; Schalm, Koenraad; Shiu, Gary; Schaar, Jan Pieter van der
2004-01-01
We study decoupling in FRW spacetimes, emphasizing a Lagrangian description throughout. To account for the vacuum choice ambiguity in cosmological settings, we introduce an arbitrary boundary action representing the initial conditions. RG flow in these spacetimes naturally affects the boundary interactions. As a consequence the boundary conditions are sensitive to high-energy physics through irrelevant terms in the boundary action. Using scalar field theory as an example, we derive the leading dimension four irrelevant boundary operators. We discuss how the known vacuum choices, e.g. the Bunch-Davies vacuum, appear in the Lagrangian description and square with decoupling. For all choices of boundary conditions encoded by relevant boundary operators, of which the known ones are a subset, backreaction is under control. All, moreover, will generically feel the influence of high-energy physics through irrelevant (dimension four) boundary corrections. Having established a coherent effective field theory framework ...
On the Boussinesq-Burgers equations driven by dynamic boundary conditions
Zhu, Neng; Liu, Zhengrong; Zhao, Kun
2018-02-01
We study the qualitative behavior of the Boussinesq-Burgers equations on a finite interval subject to the Dirichlet type dynamic boundary conditions. Assuming H1 ×H2 initial data which are compatible with boundary conditions and utilizing energy methods, we show that under appropriate conditions on the dynamic boundary data, there exist unique global-in-time solutions to the initial-boundary value problem, and the solutions converge to the boundary data as time goes to infinity, regardless of the magnitude of the initial data.
Nested Bethe Ansatz for Spin Ladder Model with Open Boundary Conditions
Wu Junfang; Zhang Chunmin; Yue Ruihong; Li Runling
2005-01-01
The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the general boundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K ± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.
Essential Boundary Conditions with Straight C1 Finite Elements in Curved Domains
Ferraro, N.M.; Jardin, S.C.; Luo, X.
2010-01-01
The implementation of essential boundary conditions in C1 finite element analysis requires proper treatment of both the boundary conditions on second-order differentials of the solution and the curvature of the domain boundary. A method for the imposition of essential boundary conditions using straight elements (where the elements are not deformed to approximate a curved domain) is described. It is shown that pre-multiplication of the matrix equation by the local rotation matrix at each boundary node is not the optimal transformation. The uniquely optimal transformation is found, which does not take the form of a similarity transformation due to the non-orthogonality of the transformation to curved coordinates.
Hejranfar, Kazem; Parseh, Kaveh
2017-09-01
The preconditioned characteristic boundary conditions based on the artificial compressibility (AC) method are implemented at artificial boundaries for the solution of two- and three-dimensional incompressible viscous flows in the generalized curvilinear coordinates. The compatibility equations and the corresponding characteristic variables (or the Riemann invariants) are mathematically derived and then applied as suitable boundary conditions in a high-order accurate incompressible flow solver. The spatial discretization of the resulting system of equations is carried out by the fourth-order compact finite-difference (FD) scheme. In the preconditioning applied here, the value of AC parameter in the flow field and also at the far-field boundary is automatically calculated based on the local flow conditions to enhance the robustness and performance of the solution algorithm. The code is fully parallelized using the Concurrency Runtime standard and Parallel Patterns Library (PPL) and its performance on a multi-core CPU is analyzed. The incompressible viscous flows around a 2-D circular cylinder, a 2-D NACA0012 airfoil and also a 3-D wavy cylinder are simulated and the accuracy and performance of the preconditioned characteristic boundary conditions applied at the far-field boundaries are evaluated in comparison to the simplified boundary conditions and the non-preconditioned characteristic boundary conditions. It is indicated that the preconditioned characteristic boundary conditions considerably improve the convergence rate of the solution of incompressible flows compared to the other boundary conditions and the computational costs are significantly decreased.
A simple and efficient outflow boundary condition for the incompressible Navier–Stokes equations
Yibao Li
2017-01-01
Full Text Available Many researchers have proposed special treatments for outlet boundary conditions owing to lack of information at the outlet. Among them, the simplest method requires a large enough computational domain to prevent or reduce numerical errors at the boundaries. However, an efficient method generally requires special treatment to overcome the problems raised by the outlet boundary condition used. For example, mass flux is not conserved and the fluid field is not divergence-free at the outlet boundary. Overcoming these problems requires additional computational cost. In this paper, we present a simple and efficient outflow boundary condition for the incompressible Navier–Stokes equations, aiming to reduce the computational domain for simulating flow inside a long channel in the streamwise direction. The proposed outflow boundary condition is based on the transparent equation, where a weak formulation is used. The pressure boundary condition is derived by using the Navier–Stokes equations and the outlet flow boundary condition. In the numerical algorithm, a staggered marker-and-cell grid is used and temporal discretization is based on a projection method. The intermediate velocity boundary condition is consistently adopted to handle the velocity–pressure coupling. Characteristic numerical experiments are presented to demonstrate the robustness and accuracy of the proposed numerical scheme. Furthermore, the agreement of computational results from small and large domains suggests that our proposed outflow boundary condition can significantly reduce computational domain sizes.
A device adaptive inflow boundary condition for Wigner equations of quantum transport
Jiang, Haiyan; Lu, Tiao; Cai, Wei
2014-01-01
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
Boundary conditions for the numerical solution of elliptic equations in exterior regions
Bayliss, A.; Gunzburger, M.; Turkel, E.
1982-01-01
Elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the well-posedness of the problem. Examples of practical applications include the Helmholtz equation and Laplace's equation. Computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition at infinity by a boundary condition on a finite artificial surface. Direct imposition of the condition at infinity along the finite boundary results in large errors. A sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain. Estimates of the error due to the finite boundary are obtained for several cases. Computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions. The examples are based on a finite element formulation but finite difference methods can also be used
System dynamics with interaction discontinuity
Luo, Albert C J
2015-01-01
This book describes system dynamics with discontinuity caused by system interactions and presents the theory of flow singularity and switchability at the boundary in discontinuous dynamical systems. Based on such a theory, the authors address dynamics and motion mechanism of engineering discontinuous systems due to interaction. Stability and bifurcations of fixed points in nonlinear discrete dynamical systems are presented, and mapping dynamics are developed for analytical predictions of periodic motions in engineering discontinuous dynamical systems. Ultimately, the book provides an alternative way to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.
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.
Liu, Ping; Shi, Junping
2018-01-01
The bifurcation of non-trivial steady state solutions of a scalar reaction-diffusion equation with nonlinear boundary conditions is considered using several new abstract bifurcation theorems. The existence and stability of positive steady state solutions are proved using a unified approach. The general results are applied to a Laplace equation with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation with superlinear nonlinearity and sublinear boundary conditions.
Cremer, Clemens; Neuweiler, Insa; Bechtold, Michel; Vanderborght, Jan
2016-04-01
behavior depends on the magnitude of the flow rates and hydraulic conductivity curves of the materials. Based on the unsaturated hydraulic conductivity at the intersection point of conductivity curves, we are able to define an estimate of flow rates at which the dynamic of the upper boundary condition significantly alters preferential flow paths through the system. If flow rates are low, with regard to the materials hydraulic conductivity at the intersection point, the influence of dynamic boundary conditions is small. If flow rates are in the range of the unsaturated hydraulic conductivity at intersection, solute is trapped in the fine material during upwards transport, which results in a more pronounced tailing. For flow rates exceeding the intersection conductivity, a redistribution at the soil surface can occur. References: Bechtold, M., S. Haber-Pohlmeier, J. Vanderborght, A. Pohlmeier, T.P.A. Ferré and H. Veerecken. 2011a. Near-surface solute redistribution during evaporation. Geophys. Res. Lett., 38, L17404, doi:10.1029/2011GL048147. Bechtold, M., J. Vanderborght, O. Ippisch and H. Vereecken. 2011b. Efficient random walk particle tracking algorithm for advective dispersive transport in media with discontinuous dispersion coefficients and water contents. Water Resour. Res., 47, W10526, doi: 10.1029/2010WR010267. Ippisch O., H.-J. Vogel and P. Bastian. 2006. Validity limits fort he van Genuchten-Mualem model and implications for parameter estimation and numerical simulation. Adv. Water Resour., 29, 1780-1789, doi: 10.1016/j.advwateres.2005.12.011. Lehmann, P. and D. Or. 2009. Evaporation and capillary coupling across vertical textural contrasts in porous media. Phys. Rev. E, 80, 046318, doi:10.1103/PhysRevE.80.046318.
Mixed problems for linear symmetric hyperbolic systems with characteristic boundary conditions
Secchi, P.
1994-01-01
We consider the initial-boundary value problem for symmetric hyperbolic systems with characteristic boundary of constant multiplicity. In the linear case we give some results about the existence of regular solutions in suitable functions spaces which take in account the loss of regularity in the normal direction to the characteristic boundary. We also consider the equations of ideal magneto-hydrodynamics under perfectly conducting wall boundary conditions and give some results about the solvability of such mixed problem. (author). 16 refs
A suitable boundary condition for bounded plasma simulation without sheath resolution
Parker, S.E.; Procassini, R.J.; Birdsall, C.K.; Cohen, B.I.
1993-01-01
We have developed a technique that allows for a sheath boundary layer without having to resolve the inherently small space and time scales of the sheath region. We refer to this technique as the logical sheath boundary condition. This boundary condition, when incorporated into a direct-implicit particle code, permits large space- and time-scale simulations of bounded systems, which would otherwise be impractical on current supercomputers. The lack of resolution of the collector sheath potential drop obtained from conventional implicit simulations at moderate values of ω pe Δt and Δz/λ De provides the motivation for the development of the logical sheath boundary condition. The algorithm for use of the logical sheath boundary condition in a particle simulation is presented. Results from simulations which use the logical sheath boundary condition are shown to compare reasonably well with those from an analytic theory and simulations in which the sheath is resolved
The analytical solution for drug delivery system with nonhomogeneous moving boundary condition
Saudi, Muhamad Hakimi; Mahali, Shalela Mohd; Harun, Fatimah Noor
2017-08-01
This paper discusses the development and the analytical solution of a mathematical model based on drug release system from a swelling delivery device. The mathematical model is represented by a one-dimensional advection-diffusion equation with nonhomogeneous moving boundary condition. The solution procedures consist of three major steps. Firstly, the application of steady state solution method, which is used to transform the nonhomogeneous moving boundary condition to homogeneous boundary condition. Secondly, the application of the Landau transformation technique that gives a significant impact in removing the advection term in the system of equation and transforming the moving boundary condition to a fixed boundary condition. Thirdly, the used of separation of variables method to find the analytical solution for the resulted initial boundary value problem. The results show that the swelling rate of delivery device and drug release rate is influenced by value of growth factor r.
Coupling the Gaussian Free Fields with Free and with Zero Boundary Conditions via Common Level Lines
Qian, Wei; Werner, Wendelin
2018-06-01
We point out a new simple way to couple the Gaussian Free Field (GFF) with free boundary conditions in a two-dimensional domain with the GFF with zero boundary conditions in the same domain: Starting from the latter, one just has to sample at random all the signs of the height gaps on its boundary-touching zero-level lines (these signs are alternating for the zero-boundary GFF) in order to obtain a free boundary GFF. Constructions and couplings of the free boundary GFF and its level lines via soups of reflected Brownian loops and their clusters are also discussed. Such considerations show for instance that in a domain with an axis of symmetry, if one looks at the overlay of a single usual Conformal Loop Ensemble CLE3 with its own symmetric image, one obtains the CLE4-type collection of level lines of a GFF with mixed zero/free boundary conditions in the half-domain.
On two-point boundary correlations in the six-vertex model with domain wall boundary conditions
Colomo, F.; Pronko, A. G.
2005-05-01
The six-vertex model with domain wall boundary conditions on an N × N square lattice is considered. The two-point correlation function describing the probability of having two vertices in a given state at opposite (top and bottom) boundaries of the lattice is calculated. It is shown that this two-point boundary correlator is expressible in a very simple way in terms of the one-point boundary correlators of the model on N × N and (N - 1) × (N - 1) lattices. In alternating sign matrix (ASM) language this result implies that the doubly refined x-enumerations of ASMs are just appropriate combinations of the singly refined ones.
Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions
Ruggeri, Fabrizio; Sawlan, Zaid A; Scavino, Marco; Tempone, Raul
2015-01-01
have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal
Latitudinal discontinuity in thermal conditions along the nearshore of central-northern Chile.
Tapia, Fabian J; Largier, John L; Castillo, Manuel; Wieters, Evie A; Navarrete, Sergio A
2014-01-01
Over the past decade, evidence of abrupt latitudinal changes in the dynamics, structure and genetic variability of intertidal and subtidal benthic communities along central-northern Chile has been found consistently at 30-32°S. Changes in the advective and thermal environment in nearshore waters have been inferred from ecological patterns, since analyses of in situ physical data have thus far been missing. Here we analyze a unique set of shoreline temperature data, gathered over 4-10 years at 15 sites between 28-35°S, and combine it with satellite-derived winds and sea surface temperatures to investigate the latitudinal transition in nearshore oceanographic conditions suggested by recent ecological studies. Our results show a marked transition in thermal conditions at 30-31°S, superimposed on a broad latitudinal trend, and small-scale structures associated with cape-and-bay topography. The seasonal cycle dominated temperature variability throughout the region, but its relative importance decreased abruptly south of 30-31°S, as variability at synoptic and intra-seasonal scales became more important. The response of shoreline temperatures to meridional wind stress also changed abruptly at the transition, leading to a sharp drop in the occurrence of low-temperature waters at northern sites, and a concurrent decrease in corticated algal biomass. Together, these results suggest a limitation of nitrate availability in nearshore waters north of the transition. The localized alongshore change results from the interaction of latitudinal trends (e.g., wind stress, surface warming, inertial period) with a major headland-bay system (Punta Lengua de Vaca at 30.25°S), which juxtaposes a southern stretch of coast characterized by upwelling with a northern stretch of coast characterized by warm surface waters and stratification. This transition likely generates a number of latitude-dependent controls on ecological processes in the nearshore that can explain species
Experimental verification of free-space singular boundary conditions in an invisibility cloak
Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Zhang, Baile; Chen, Huanyang
2016-01-01
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. (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.
How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems
Cortazar, C.; Elgueta, M.; Rossi, J. D.; Wolanski, N.
2006-01-01
We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal diffusion operators when a rescaling parameter related to the kernel of the nonlocal operator goes to zero. We prove that the solutions of this family of problems converge to a solution of the heat equation with Neumann boundary conditions.
Generating wind fluctuations for Large Eddy Simulation inflow boundary condition
Bekele, S.A.; Hangan, H.
2004-01-01
Large Eddy Simulation (LES) studies of flows over bluff bodies immersed in a boundary layer wind environment require instantaneous wind characteristics. The influences of the wind environment on the building pressure distribution are a well-established fact in the experimental study of wind engineering. Measured wind data of full or model scale are available only at a limited number of points. A method of obtaining instantaneous wind data at all mesh points of the inlet boundary for LES computation is necessary. Herein previous and new wind inflow generation techniques are presented. The generated wind data is then applied to a LES computation of a channel flow. The characteristics of the generated wind fluctuations in comparison to the measured data and the properties of the flow field computed from these two wind data are discussed. (author)
Effect of boundary conditions on radial mode structure of whistlers
Boswell, R.W.
1983-01-01
The dispersion of the radical eigen modes of a cylindrical m=1 whistler wave with Ωsub(i) << ω << Ωsub(e) << ωsub(pe) are investigated for both conducting and insulating boundaries, where Ωsub(e) and Ωsub(i) are the electron and ion gyro frequencies, Ωsub(pe) is the electron plasma frequency. The effects of electron inertia and resistivity on the modes are discussed
Trickle-down boundary conditions in aeolian dune-field pattern formation
Ewing, R. C.; Kocurek, G.
2015-12-01
One the one hand, wind-blown dune-field patterns emerge within the overarching boundary conditions of climate, tectonics and eustasy implying the presence of these signals in the aeolian geomorphic and stratigraphic record. On the other hand, dune-field patterns are a poster-child of self-organization, in which autogenic processes give rise to patterned landscapes despite remarkable differences in the geologic setting (i.e., Earth, Mars and Titan). How important are climate, tectonics and eustasy in aeolian dune field pattern formation? Here we develop the hypothesis that, in terms of pattern development, dune fields evolve largely independent of the direct influence of 'system-scale' boundary conditions, such as climate, tectonics and eustasy. Rather, these boundary conditions set the stage for smaller-scale, faster-evolving 'event-scale' boundary conditions. This 'trickle-down' effect, in which system-scale boundary conditions indirectly influence the event scale boundary conditions provides the uniqueness and richness of dune-field patterned landscapes. The trickle-down effect means that the architecture of the stratigraphic record of dune-field pattern formation archives boundary conditions, which are spatially and temporally removed from the overarching geologic setting. In contrast, the presence of an aeolian stratigraphic record itself, reflects changes in system-scale boundary conditions that drive accumulation and preservation of aeolian strata.
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.
The effect of external boundary conditions on condensation heat transfer in rotating heat pipes
Daniels, T. C.; Williams, R. J.
1979-01-01
Experimental evidence shows the importance of external boundary conditions on the overall performance of a rotating heat pipe condenser. Data are presented for the boundary conditions of constant heat flux and constant wall temperature for rotating heat pipes containing either pure vapor or a mixture of vapor and noncondensable gas as working fluid.
Casimir energy in d-dimensional rectangular geometries, under mixed boundary conditions
Silva, J.C. da; Placido, Hebe Q.; Santana, A.E.; M Neto, Arthur
1997-01-01
The Casimir energy and its temperature corrections are presented for the electromagnetic field confined in a d-dimensional hypercavity. The expressions are derived considering Dirichlet boundary conditions for each pair of hyperplanes defining a confined direction (the homogeneous case); or yet, by choosing different boundary conditions (Dirichlet or Neumann) at each hyperplane of the pair (the mixed case). (author)
B.J. Meulenbroek (Bernard); U. M. Ebert (Ute); L. Schäfer
2005-01-01
textabstractThe dynamics of ionization fronts that generate a conducting body, are in simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We
Meulenbroek, B.; Ebert, U.; Schäfer, L.
2005-01-01
The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive
Interference by amplitude division with extended sources by paraxial boundary conditions
Liñares, J; Nistal, M C
2014-01-01
We present a wave-optics paraxial approach to the interference by amplitude division produced by plane-parallel films (or plates) and non-plane-parallel films, or by equivalent optical devices such as a Michelson interferometer, when they are illuminated with extended (spatially incoherent) quasi-monochromatic sources. To the best of our knowledge, the most common approaches to the study of interference are based, for simplicity, on the combined use of geometrical optics concepts, such as the optical path length along a ray, together with some wave-optics concepts such as optical phases. However, interference phenomena have been the means by which the wave nature of light has been established and therefore geometrical and wave concepts are so far-off that their simultaneous use can give rise to misleading concepts. Therefore, the primary aim of this work is to provide an analytical homogeneous description of interference by amplitude division using only paraxial spherical waves and boundary conditions at smooth interfaces or discontinuities in such a way that the calculation of the total optical field, interference irradiance, fringe visibility, coherence degree, localization of the interference and so on, can be made in a unified way by taking a fully wave-optics approach. The paraxial regime is enough in most cases and, moreover, interference is generally collected by an optical instrument such as a lens or the eye itself, in which a paraxial approximation is required. This work is particularly aimed at university physics teachers and undergraduate and first year postgraduate students. (papers)
Kolmogorov, Dmitry; Sørensen, Niels N.; Shen, Wen Zhong
2013-01-01
An Optimized Schwarz method using Robin boundary conditions for relaxation scheme is presented in the frame of Multigrid method on discontinuous grids. At each iteration the relaxation scheme is performed in two steps: one step with Dirichlet and another step with Robin boundary conditions at inn...
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.)
Lopez, J. Gonzalez; Jansen, K.; Renner, D.B.; Shindler, A.
2012-01-01
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.)
Inferring Lower Boundary Driving Conditions Using Vector Magnetic Field Observations
Schuck, Peter W.; Linton, Mark; Leake, James; MacNeice, Peter; Allred, Joel
2012-01-01
Low-beta coronal MHD simulations of realistic CME events require the detailed specification of the magnetic fields, velocities, densities, temperatures, etc., in the low corona. Presently, the most accurate estimates of solar vector magnetic fields are made in the high-beta photosphere. Several techniques have been developed that provide accurate estimates of the associated photospheric plasma velocities such as the Differential Affine Velocity Estimator for Vector Magnetograms and the Poloidal/Toroidal Decomposition. Nominally, these velocities are consistent with the evolution of the radial magnetic field. To evolve the tangential magnetic field radial gradients must be specified. In addition to estimating the photospheric vector magnetic and velocity fields, a further challenge involves incorporating these fields into an MHD simulation. The simulation boundary must be driven, consistent with the numerical boundary equations, with the goal of accurately reproducing the observed magnetic fields and estimated velocities at some height within the simulation. Even if this goal is achieved, many unanswered questions remain. How can the photospheric magnetic fields and velocities be propagated to the low corona through the transition region? At what cadence must we observe the photosphere to realistically simulate the corona? How do we model the magnetic fields and plasma velocities in the quiet Sun? How sensitive are the solutions to other unknowns that must be specified, such as the global solar magnetic field, and the photospheric temperature and density?
Evaluation of general non-reflecting boundary conditions for industrial CFD applications
Basara, Branislav; Frolov, Sergei; Lidskii, Boris; Posvyanskii, Vladimir
2007-11-01
The importance of having proper boundary conditions for the calculation domain is a known issue in Computational Fluid Dynamics (CFD). In many situations, it is very difficult to define a correct boundary condition. The flow may enter and leave the computational domain at the same time and at the same boundary. In such circumstances, it is important that numerical implementation of boundary conditions enforces certain physical constraints leading to correct results which then ensures a better convergence rate. The aim of this paper is to evaluate recently proposed non-reflecting boundary conditions (Frolov et al., 2001, Advances in Chemical Propulsion) on industrial CFD applications. Derivation of the local non-reflecting boundary conditions at the open boundary is based on finding the solution of linearized Euler equations vanishing at infinity for both incompressible and compressible formulations. This is implemented into the in-house CFD package AVL FIRE and some numerical details will be presented as well. The key applications in this paper are from automotive industry, e.g. an external car aerodynamics, an intake port, etc. The results will show benefits of using effective non-reflecting boundary conditions.
Sprofera, Joseph D.; Clark, Robert L.; Cabell, Randolph H.; Gibbs, Gary P.
2005-05-01
Turbulent boundary layer (TBL) noise is considered a primary contribution to the interior noise present in commercial airliners. There are numerous investigations of interior noise control devoted to aircraft panels; however, practical realization is a potential challenge since physical boundary conditions are uncertain at best. In most prior studies, pinned or clamped boundary conditions were assumed; however, realistic panels likely display a range of boundary conditions between these two limits. Uncertainty in boundary conditions is a challenge for control system designers, both in terms of the compensator implemented and the location of transducers required to achieve the desired control. The impact of model uncertainties, specifically uncertain boundaries, on the selection of transducer locations for structural acoustic control is considered herein. The final goal of this work is the design of an aircraft panel structure that can reduce TBL noise transmission through the use of a completely adaptive, single-input, single-output control system. The feasibility of this goal is demonstrated through the creation of a detailed analytical solution, followed by the implementation of a test model in a transmission loss apparatus. Successfully realizing a control system robust to variations in boundary conditions can lead to the design and implementation of practical adaptive structures that could be used to control the transmission of sound to the interior of aircraft. Results from this research effort indicate it is possible to optimize the design of actuator and sensor location and aperture, minimizing the impact of boundary conditions on the desired structural acoustic control.
Hakim, Issa; Laquai, Rene; Walter, David; Mueller, Bernd; Graja, Paul; Meyendorf, Norbert; Donaldson, Steven
2017-02-01
Carbon fiber composites have been increasingly used in aerospace, military, sports, automotive and other fields due to their excellent properties, including high specific strength, high specific modulus, corrosion resistance, fatigue resistance, and low thermal expansion coefficient. Interlaminar fracture is a serious failure mode leading to a loss in composite stiffness and strength. Discontinuities formed during manufacturing process degrade the fatigue life and interlaminar fracture resistance of the composite. In his study, three approaches were implemented and their results were correlated to quantify discontinuities effecting static and fatigue interlaminar fracture behavior of carbon fiber composites. Samples were fabricated by hand layup vacuum bagging manufacturing process under three different vacuum levels, indicated High (-686 mmHg), Moderate (-330 mmHg) and Poor (0 mmHg). Discontinuity content was quantified through-thickness by destructive and nondestructive techniques. Eight different NDE methods were conducted including imaging NDE methods: X-Ray laminography, ultrasonic, high frequency eddy current, pulse thermography, pulse phase thermography and lock-in-thermography, and averaging NDE techniques: X-Ray refraction and thermal conductivity measurements. Samples were subsequently destructively serial sectioned through-thickness into several layers. Both static and fatigue interlaminar fracture behavior under Mode I were conducted. The results of several imaging NDE methods revealed the trend in percentages of discontinuity. However, the results of averaging NDE methods showed a clear correlation since they gave specific values of discontinuity through-thickness. Serial sectioning exposed the composite's internal structure and provided a very clear idea about the type, shape, size, distribution and location of most discontinuities included. The results of mechanical testing showed that discontinuities lead to a decrease in Mode I static interlaminar
Second order bounce back boundary condition for the lattice Boltzmann fluid simulation
Kim, In Chan
2000-01-01
A new bounce back boundary method of the second order in error is proposed for the lattice Boltzmann fluid simulation. This new method can be used for the arbitrarily irregular lattice geometry of a non-slip boundary. The traditional bounce back boundary condition for the lattice Boltzmann simulation is of the first order in error. Since the lattice Boltzmann method is the second order scheme by itself, a boundary technique of the second order has been desired to replace the first order bounce back method. This study shows that, contrary to the common belief that the bounce back boundary condition is unilaterally of the first order, the second order bounce back boundary condition can be realized. This study also shows that there exists a generalized bounce back technique that can be characterized by a single interpolation parameter. The second order bounce back method can be obtained by proper selection of this parameter in accordance with the detailed lattice geometry of the boundary. For an illustrative purpose, the transient Couette and the plane Poiseuille flows are solved by the lattice Boltzmann simulation with various boundary conditions. The results show that the generalized bounce back method yields the second order behavior in the error of the solution, provided that the interpolation parameter is properly selected. Coupled with its intuitive nature and the ease of implementation, the bounce back method can be as good as any second order boundary method
Oblique radiation lateral open boundary conditions for a regional climate atmospheric model
Cabos Narvaez, William; De Frutos Redondo, Jose Antonio; Perez Sanz, Juan Ignacio; Sein, Dmitry
2013-04-01
The prescription of lateral boundary conditions in regional atmospheric models represent a very important issue for limited area models. The ill-posed nature of the open boundary conditions makes it necessary to devise schemes in order to filter spurious wave reflections at boundaries, being desirable to have one boundary condition per variable. On the other side, due to the essentially hyperbolic nature of the equations solved in state of the art atmospheric models, external data is required only for inward boundary fluxes. These circumstances make radiation lateral boundary conditions a good choice for the filtering of spurious wave reflections. Here we apply the adaptive oblique radiation modification proposed by Mikoyada and Roseti to each of the prognostic variables of the REMO regional atmospheric model and compare it to the more common normal radiation condition used in REMO. In the proposed scheme, special attention is paid to the estimation of the radiation phase speed, essential to detecting the direction of boundary fluxes. One of the differences with the classical scheme is that in case of outward propagation, the adaptive nudging imposed in the boundaries allows to minimize under and over specifications problems, adequately incorporating the external information.
On problems with displacement in boundary conditions for hyperbolic equation
Elena A. Utkina
2016-03-01
Full Text Available We consider three problems for hyperbolic equation on a plane in the characteristic domain. In these problems at least one of the conditions of the Goursat problem is replaced by nonlocal condition on the relevant characteristic. Non-local conditions are the linear combinations of the normal derivatives at points on opposite characteristics. In case of replacement of one condition we solve the problem by reduction to the Goursat problem for which it exists and is unique. To find the unknown Goursat condition author receives the integral equation, rewrite it in operational form and finds its unique solvability cases. To prove the unique solvability of the equation, the author shows the continuous linear operator and the fact, that some degree of the resulting operator is a contraction mapping. It is known that in this case the required Goursat condition can be written as Neumann series. We considered in detail only one of the tasks, but for both the unique solvability theorems are formulated. If the two conditions are changed, the uniqueness of the solution on the assumption that it exists, is proved by the method of a priori estimates. For this purpose, the inner product and the norm in $L_2$ are used. As a result, the conditions were obtained for the coefficients of a hyperbolic equation that ensure the uniqueness of the solution. An example is given, confirming that these conditions are essential. Namely, constructed an equation whose coefficients do not satisfy the conditions of the last theorem, given the conditions on the characteristics and nontrivial solution is built.
Diffusive growth of a single droplet with three different boundary conditions
Tavassoli, Z.; Rodgers, G. J.
2000-02-01
We study a single, motionless three-dimensional droplet growing by adsorption of diffusing monomers on a 2D substrate. The diffusing monomers are adsorbed at the aggregate perimeter of the droplet with different boundary conditions. Models with both an adsorption boundary condition and a radiation boundary condition, as well as a phenomenological model, are considered and solved in a quasistatic approximation. The latter two models allow particle detachment. In the short time limit, the droplet radius grows as a power of the time with exponents of 1/4, 1/2 and 3/4 for the models with adsorption, radiation and phenomenological boundary conditions, respectively. In the long time limit a universal growth rate as $[t/\\ln(t)]^{1/3}$ is observed for the radius of the droplet for all models independent of the boundary conditions. This asymptotic behaviour was obtained by Krapivsky \\cite{krapquasi} where a similarity variable approach was used to treat the growth of a droplet with an adsorption boundary condition based on a quasistatic approximation. Another boundary condition with a constant flux of monomers at the aggregate perimeter is also examined. The results exhibit a power law growth rate with an exponent of 1/3 for all times.
Hansen, Dorte Gilså; Felde, Lina; Gichangi, Anthony
2007-01-01
prevalence and rate of early discontinuation of different drugs consisting of, in this study, lipid-lowering drugs, antihypertensive drugs, antidepressants, antidiabetics and drugs against osteoporosis. Material and methods This was a register study based on prescription data covering a 4-year period...... and consisting of 470,000 citizens. For each practice and group of drug, a 1-year prevalence for 2002 and the rate of early discontinuation among new users in 2002-2003 were estimated. Early discontinuation was defined as no prescriptions during the second half-year following the first prescription....... There was a positive association between the prevalence of prescribing for the specific drugs studied (antidepressants, antidiabetics, drugs against osteoporosis and lipid-lowering drugs) and early discontinuation (r = 0.29 -0.44), but not for anti-hypertensive drugs. The analysis of the association between prevalence...
Ghil, M.; Balgovind, R.
1979-01-01
The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.
First-principle proof of the modified collision boundary conditions for the hard-sphere system
Tessarotto, Massimo; Cremaschini, Claudio
2014-01-01
A fundamental issue lying at the foundation of classical statistical mechanics is the determination of the collision boundary conditions that characterize the dynamical evolution of multi-particle probability density functions (PDF) and are applicable to systems of hard-spheres undergoing multiple elastic collisions. In this paper it is proved that, when the deterministic N-body PDF is included in the class of admissible solutions of the Liouville equation, the customary form of collision boundary conditions adopted in previous literature becomes physically inconsistent and must actually be replaced by suitably modified collision boundary conditions.
An effective absorbing layer for the boundary condition in acoustic seismic wave simulation
Yao, Gang; da Silva, Nuno V.; Wu, Di
2018-04-01
Efficient numerical simulation of seismic wavefields generally involves truncating the Earth model in order to keep computing time and memory requirements down. Absorbing boundary conditions, therefore, are applied to remove the boundary reflections caused by this truncation, thereby allowing for accurate modeling of wavefields. In this paper, we derive an effective absorbing boundary condition for both acoustic and elastic wave simulation, through the simplification of the damping term of the split perfectly matched layer (SPML) boundary condition. This new boundary condition is accurate, cost-effective, and easily implemented, especially for high-performance computing. Stability analysis shows that this boundary condition is effectively as stable as normal (non-absorbing) wave equations for explicit time-stepping finite differences. We found that for full-waveform inversion (FWI), the strengths of the effective absorbing layer—a reduction of the computational and memory cost coupled with a simplistic implementation—significantly outweighs the limitation of incomplete absorption of outgoing waves relative to the SPML. More importantly, we demonstrate that this limitation can easily be overcome through the use of two strategies in FWI, namely variable cell size and model extension thereby fully compensating for the imperfectness of the proposed absorbing boundary condition.
Nonlinear $q$-fractional differential equations with nonlocal and sub-strip type boundary conditions
Bashir Ahmad
2014-06-01
Full Text Available This paper is concerned with new boundary value problems of nonlinear $q$-fractional differential equations with nonlocal and sub-strip type boundary conditions. Our results are new in the present setting and rely on the contraction mapping principle and a fixed point theorem due to O'Regan. Some illustrative examples are also presented.
Effects of microscopic boundary conditions on plastic deformations of small-sized single crystals
Kuroda, Mitsutoshi; Tvergaard, Viggo
2009-01-01
The finite deformation version of the higher-order gradient crystal plasticity model proposed by the authors is applied to solve plane strain boundary value problems, in order to obtain an understanding of the effect of the higher-order boundary conditions. Numerical solutions are carried out...
Heat conduction in a plate-type fuel element with time-dependent boundary conditions
Faya, A.J.G.; Maiorino, J.R.
1981-01-01
A method for the solution of boundary-value problems with variable boundary conditions is applied to solve a heat conduction problem in a plate-type fuel element with time dependent film coefficient. The numerical results show the feasibility of the method in the solution of this class of problems. (Author) [pt
Frank, Florian; Liu, Chen; Scanziani, Alessio; Alpak, Faruk O; Riviere, Beatrice
2018-08-01
We consider an energy-based boundary condition to impose an equilibrium wetting angle for the Cahn-Hilliard-Navier-Stokes phase-field model on voxel-set-type computational domains. These domains typically stem from μCT (micro computed tomography) imaging of porous rock and approximate a (on μm scale) smooth domain with a certain resolution. Planar surfaces that are perpendicular to the main axes are naturally approximated by a layer of voxels. However, planar surfaces in any other directions and curved surfaces yield a jagged/topologically rough surface approximation by voxels. For the standard Cahn-Hilliard formulation, where the contact angle between the diffuse interface and the domain boundary (fluid-solid interface/wall) is 90°, jagged surfaces have no impact on the contact angle. However, a prescribed contact angle smaller or larger than 90° on jagged voxel surfaces is amplified. As a remedy, we propose the introduction of surface energy correction factors for each fluid-solid voxel face that counterbalance the difference of the voxel-set surface area with the underlying smooth one. The discretization of the model equations is performed with the discontinuous Galerkin method. However, the presented semi-analytical approach of correcting the surface energy is equally applicable to other direct numerical methods such as finite elements, finite volumes, or finite differences, since the correction factors appear in the strong formulation of the model. Copyright © 2018 Elsevier Inc. All rights reserved.
An(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 rests 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 conserved quantities that depend on free boundary parameters. It also turns out that the number of local integrals of motion for SP boundary conditions is 'double' compared to those of the SNP case.
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.
On the symmetry of the boundary conditions of the volume potential
Kal'menov, Tynysbek Sh.; Arepova, Gaukhar; Suragan, Durvudkhan
2017-09-01
It is well known that the volume potential determines the mass or the charge distributed over the domain with density f. The volume potential is extensively used in function theory and embedding theorems. It is also well known that the volume potential gives a solution to an inhomogeneous equation. And it generates a linear self-adjoint operator. It is known that self-adjoint differential operators are generated by boundary conditions. In our previous papers for an arbitrary domain a boundary condition on the volume potential is given. In the past, it was not possible to prove the self-adjointness of these obtained boundary conditions. In the present paper, we prove the symmetry of boundary condition for the volume potential.
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.
Everitt, David L.; Zhu, Tuo; Zhu, H.-M.; Zhu, X. D.
2000-01-01
We present a simple experimental method that permits an empirical determination of the effective boundary condition and the extrapolated end point for the diffuse photon density in a homogeneous turbid medium. (c) 2000 Optical Society of America
Enhancement of single mode operation in coaxial optical waveguide using DB boundary conditions
Lohia, Pooja; Prajapati, Y.; Saini, J. P.; Rai, B. S.
2014-11-01
In this study, a competent numerical strategy to compute the dispersion of optical waveguides is presented and propagation of electromagnetic waves in a coaxial optical waveguide with DB boundary conditions is instigated. For this intend, cylindrical coordinates are here being used to derive the DB boundary conditions and to obtain field components for the modes. The propagation constant for the waveguide to be studied is determined by solving the Bessel and the modified Bessel functions. The cutoff frequencies for various lower order modes have been calculated and their dispersion characteristics are plotted correspondingly. The behavior of the coaxial optical waveguide under DB boundary conditions is shown to be significantly different from that of coaxial optical waveguide and conventional optical waveguide under traditional or tangential boundary conditions. Finally, the effect of waveguide dimensions on the mode cutoff frequencies and fabrication issues are also addressed.
RECTC/RECTCF, 2. Order Elliptical Partial Differential Equation, Arbitrary Boundary Conditions
Hackbusch, W.
1983-01-01
1 - Description of problem or function: A general linear elliptical second order partial differential equation on a rectangle with arbitrary boundary conditions is solved. 2 - Method of solution: Multi-grid iteration
Artificial Boundary Conditions for the Numerical Simulation of Unsteady Acoustic Waves
Tsynkov, S. V
2003-01-01
We construct non-local artificial boundary conditions (ABCs) for the numerical simulation of genuinely time-dependent acoustic waves that propagate from a compact source in an unbounded unobstructed space...
Chu, Peter C; Chen, Yuchun; Lu, Shihua
2001-01-01
... (Russell et al,, 1995) was used to verify the validity of Haney-type surface thermal boundary condition, which linearly connects net downward surface heat flux Q to air / sea temperature difference DeltaT by a relaxation coefficient K...
δ'-function perturbations and Neumann boundary-conditions by path integration
Grosche, C.
1994-02-01
δ'-function perturbations and Neumann boundary conditions are incorporated into the path integral formalism. The starting point is the consideration of the path integral representation for the one dimensional Dirac particle together with a relativistic point interaction. The non-relativistic limit yields either a usual δ-function or a δ'-function perturbation; making their strengths infinitely repulsive one obtains Dirichlet, respectively Neumann boundary conditions in the path integral. (orig.)
Thermal boundary conditions for electrons in a weakly ionized gas near a catalytic wall
Chekmarev, I.
1981-01-01
A technique of matched asymptotic expansions is used to examine the derivation of hydrodynamic transport equations for the external region of a weakly ionized multitemperature gas near an absorbing and conducting wall. An approximate moment solution is constructed for the Knudsen boundary layer. The conditions for the matching of the external and internal expansions lead to a new form of the hydrodynamic boundary conditions, from which the singular behavior of the energy equation for electrons near the wall has been eliminated
Gerbi, Sté phane; Said-Houari, Belkacem
2011-01-01
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.
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.
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...
On boundary conditions in three-dimensional AdS gravity
Miskovic, Olivera [Instituto de Fisica, P. Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso (Chile) and Departamento de Fisica, P. Universidad Catolica de Chile, Casilla 306, Santiago 22 (Chile)]. E-mail: olivera.miskovic@ucv.cl; Olea, Rodrigo [Departamento de Fisica, P. Universidad Catolica de Chile, Casilla 306, Santiago 22 (Chile) and Centro Multidisciplinar de Astrofisica, CENTRA, Departamento de Fisica, Instituto Superior Tecnico, Universidade Tecnica de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisbon (Portugal)]. E-mail: rolea@fisica.ist.utl.pt
2006-09-07
A finite action principle for three-dimensional gravity with negative cosmological constant, based on a boundary condition for the asymptotic extrinsic curvature, is considered. The bulk action appears naturally supplemented by a boundary term that is one half the Gibbons-Hawking term, that makes the Euclidean action and the Noether charges finite without additional Dirichlet counterterms. The consistency of this boundary condition with the Dirichlet problem in AdS gravity and the Chern-Simons formulation in three dimensions, and its suitability for the higher odd-dimensional case, are also discussed.
Wang, Mengjie; Herdeiro, Carlos; Jing, Jiliang
2017-11-01
We study Dirac quasinormal modes of Schwarzschild-anti-de Sitter (Schwarzschild-AdS) black holes, following the generic principle for allowed boundary conditions proposed in [M. Wang, C. Herdeiro, and M. O. P. Sampaio, Phys. Rev. D 92, 124006 (2015)., 10.1103/PhysRevD.92.124006]. After deriving the equations of motion for Dirac fields on the aforementioned background, we impose vanishing energy flux boundary conditions to solve these equations. We find a set of two Robin boundary conditions are allowed. These two boundary conditions are used to calculate Dirac normal modes on empty AdS and quasinormal modes on Schwarzschild-AdS black holes. In the former case, we recover the known normal modes of empty AdS; in the latter case, the two sets of Robin boundary conditions lead to two different branches of quasinormal modes. The impact on these modes of the black hole size, the angular momentum quantum number and the overtone number are discussed. Our results show that vanishing energy flux boundary conditions are a robust principle, applicable not only to bosonic fields but also to fermionic fields.
Effects of Uncertainties in Electric Field Boundary Conditions for Ring Current Simulations
Chen, Margaret W.; O'Brien, T. Paul; Lemon, Colby L.; Guild, Timothy B.
2018-01-01
Physics-based simulation results can vary widely depending on the applied boundary conditions. As a first step toward assessing the effect of boundary conditions on ring current simulations, we analyze the uncertainty of cross-polar cap potentials (CPCP) on electric field boundary conditions applied to the Rice Convection Model-Equilibrium (RCM-E). The empirical Weimer model of CPCP is chosen as the reference model and Defense Meteorological Satellite Program CPCP measurements as the reference data. Using temporal correlations from a statistical analysis of the "errors" between the reference model and data, we construct a Monte Carlo CPCP discrete time series model that can be generalized to other model boundary conditions. RCM-E simulations using electric field boundary conditions from the reference model and from 20 randomly generated Monte Carlo discrete time series of CPCP are performed for two large storms. During the 10 August 2000 storm main phase, the proton density at 10 RE at midnight was observed to be low (Dst index is bounded by the simulated Dst values. In contrast, the simulated Dst values during the recovery phases of the 10 August 2000 and 31 August 2005 storms tend to underestimate systematically the observed late Dst recovery. This suggests a need to improve the accuracy of particle loss calculations in the RCM-E model. Application of this technique can aid modelers to make efficient choices on either investing more effort on improving specification of boundary conditions or on improving descriptions of physical processes.
Kærn, Martin Ryhl; Elmegaard, Brian
2012-01-01
simulating the pulsating flow, thus the dynamic behavior in the mixture two-phase flow model is insufficient to model the discontinuous liquid injection principle. Despite, the fluctuations and imperfections of the model we found that the cycle time should be kept as low as possible and that the optional...
On higher-order boundary conditions at elastic-plastic boundaries in strain-gradient plasticity
Niordson, Christian Frithiof
2008-01-01
are suppressed by using a very high artificial hardening modulus. Through numerical studies of pure bending under plane strain conditions, it is shown that this method predicts the build-up of higher order stresses in the pseudo-elastic regime. This has the effect of delaying the onset of incipient yield......, as well as extending the plastic zone further toward the neutral axis of the beam, when compared to conventional models. Arguments supporting the present method are presented that rest on both mathematical and physical grounds. The results obtained are compared with other methods for dealing with higher...
Fang, Chin-Lung
2003-01-01
.... Change in either initial or boundary condition leads to a variety of model solutions. It is necessary to specify realistic initial and boundary conditions to achieve better understanding and prediction of the ocean behavior...
Tieleman, D.P; Berendsen, H.J.C.
1996-01-01
We compared molecular dynamics simulations of a bilayer of 128 fully hydrated phospholipid (DPPC) molecules, using different parameters and macroscopic boundary conditions. The same system was studied under constant pressure, constant volume, and constant surface tension boundary conditions, with
Off-wall boundary conditions for turbulent flows obtained from buffer-layer minimal flow units
Garcia-Mayoral, Ricardo; Pierce, Brian; Wallace, James
2012-11-01
There is strong evidence that the transport processes in the buffer region of wall-bounded turbulence are common across various flow configurations, even in the embryonic turbulence in transition (Park et al., Phys. Fl. 24). We use this premise to develop off-wall boundary conditions for turbulent simulations. Boundary conditions are constructed from DNS databases using periodic minimal flow units and reduced order modeling. The DNS data was taken from a channel at Reτ = 400 and a zero-pressure gradient transitional boundary layer (Sayadi et al., submitted to J . FluidMech .) . Both types of boundary conditions were first tested on a DNS of the core of the channel flow with the aim of extending their application to LES and to spatially evolving flows. 2012 CTR Summer Program.
A new approach to implement absorbing boundary condition in biomolecular electrostatics.
Goni, Md Osman
2013-01-01
This paper discusses a novel approach to employ the absorbing boundary condition in conjunction with the finite-element method (FEM) in biomolecular electrostatics. The introduction of Bayliss-Turkel absorbing boundary operators in electromagnetic scattering problem has been incorporated by few researchers. However, in the area of biomolecular electrostatics, this boundary condition has not been investigated yet. The objective of this paper is twofold. First, to solve nonlinear Poisson-Boltzmann equation using Newton's method and second, to find an efficient and acceptable solution with minimum number of unknowns. In this work, a Galerkin finite-element formulation is used along with a Bayliss-Turkel absorbing boundary operator that explicitly accounts for the open field problem by mapping the Sommerfeld radiation condition from the far field to near field. While the Bayliss-Turkel condition works well when the artificial boundary is far from the scatterer, an acceptable tolerance of error can be achieved with the second order operator. Numerical results on test case with simple sphere show that the treatment is able to reach the same level of accuracy achieved by the analytical method while using a lower grid density. Bayliss-Turkel absorbing boundary condition (BTABC) combined with the FEM converges to the exact solution of scattering problems to within discretization error.
Follin, S.
1999-06-01
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
Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid
2018-06-01
This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.
Svec, Oldrich; Skoček, Jan
2013-01-01
The ability of the Lattice Boltzmann method, as the fluid dynamics solver, to properly simulate macroscopic Navier’s slip boundary condition is investigated. An approximate equation relating the Lattice Boltzmann variable slip boundary condition with the macroscopic Navier’s slip boundary condition...
Existence and asymptotic behavior of the wave equation with dynamic boundary conditions
Graber, Philip Jameson; Said-Houari, Belkacem
2012-01-01
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.
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.
Pan, Qing; Wang, Ruofan; Reglin, Bettina; Fang, Luping; Pries, Axel R; Ning, Gangmin
2014-01-01
Estimation of the boundary condition is a critical problem in simulating hemodynamics in microvascular networks. This paper proposed a boundary estimation strategy based on a particle swarm optimization (PSO) algorithm, which aims to minimize the number of vessels with inverted flow direction in comparison to the experimental observation. The algorithm took boundary values as the particle swarm and updated the position of the particles iteratively to approach the optimization target. The method was tested in a real rat mesenteric network. With random initial boundary values, the method achieved a minimized 9 segments with an inverted flow direction in the network with 546 vessels. Compared with reported literature, the current work has the advantage of a better fit with experimental observations and is more suitable for the boundary estimation problem in pulsatile hemodynamic models due to the experiment-based optimization target selection.
An outgoing energy flux boundary condition for finite difference ICRP antenna models
Batchelor, D.B.; Carter, M.D.
1992-11-01
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
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.
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.
Fayssal, Iyad A; Moukalled, Fadl; Alam, Samir; Isma'eel, Hussain
2018-04-01
This paper reports on a new boundary condition formulation to model the total coronary myocardial flow and resistance characteristics of the myocardial vascular bed for any specific patient when considered for noninvasive diagnosis of ischemia. The developed boundary condition model gives an implicit representation of the downstream truncated coronary bed. Further, it is based on incorporating patient-specific physiological parameters that can be noninvasively extracted to account for blood flow demand to the myocardium at rest and hyperemic conditions. The model is coupled to a steady three-dimensional (3D) collocated pressure-based finite volume flow solver and used to characterize the "functional significance" of a patient diseased coronary artery segment without the need for predicting the hemodynamics of the entire arterial system. Predictions generated with this boundary condition provide a deep understanding of the inherent challenges behind noninvasive image-based diagnostic techniques when applied to human diseased coronary arteries. The overall numerical method and formulated boundary condition model are validated via two computational-based procedures and benchmarked with available measured data. The newly developed boundary condition is used via a designed computational methodology to (a) confirm the need for incorporating patient-specific physiological parameters when modeling the downstream coronary resistance, (b) explain the discrepancies presented in the literature between measured and computed fractional flow reserve (FFRCT), and (c) discuss the current limitations and future challenges in shifting to noninvasive assessment of ischemia.
Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
Fagotti, Maurizio; Calabrese, Pasquale
2011-01-01
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
Combined conduction and radiation in a two-layer planar medium with flux boundary condition
Ho, C.H.; Ozisik, M.N.
1987-01-01
The interaction of conduction and radiation is investigated under both transient and steady-state conditions for an absorbing, emitting, and isotropically scattering two-layer slab having opaque coverings at both boundaries. The slab is subjected to an externally applied constant heat flux at one boundary surface and dissipates heat by radiation into external ambients from both boundary surfaces. An analytic approach is applied to solve the radiation part of the problem, and a finite-difference scheme is used to solve the conduction part. The effects of the conduction-to-radiation parameter, the single scattering albedo, the optical thickness, and the surface emissivity on the temperature distribution are examined
Stabilizing local boundary conditions for two-dimensional shallow water equations
Dia, Ben Mansour
2018-03-27
In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary values as a requirement for the energy decrease. Using the Riemann invariant analysis, we build stabilizing local boundary conditions that guarantee the stability of the hydrodynamical state around a given steady state. Numerical results for the controller applied to the nonlinear problem demonstrate the performance of the method.
A One-Dimensional Wave Equation with White Noise Boundary Condition
Kim, Jong Uhn
2006-01-01
We discuss the Cauchy problem for a one-dimensional wave equation with white noise boundary condition. We also establish the existence of an invariant measure when the noise is additive. Similar problems for parabolic equations were discussed by several authors. To our knowledge, there is only one work which investigated the initial-boundary value problem for a wave equation with random noise at the boundary. We handle a more general case by a different method. Our result on the existence of an invariant measure relies on the author's recent work on a certain class of stochastic evolution equations
Li Xicheng; Xu Mingyu; Wang Shaowei
2008-01-01
In this paper, we give similarity solutions of partial differential equations of fractional order with a moving boundary condition. The solutions are given in terms of a generalized Wright function. The time-fractional Caputo derivative and two types of space-fractional derivatives are considered. The scale-invariant variable and the form of the solution of the moving boundary are obtained by the Lie group analysis. A comparison between the solutions corresponding to two types of fractional derivative is also given
Effect of magnetization boundary condition on cavity magnon polariton of YIG thin film
Jiang, H. H.; Xiao, Y.; Hu, C. M.; Guo, H.; Xia, K.
2018-06-01
Motivated by recent studies of cavity magnon polariton (CMP), we extended a previous theoretical work to generalize microwave transmission calculation with various magnetization boundary condition of YIG thin film embedded in cavity. It is found that numerical implementation given in this paper can be easily applied to other magnetization boundary condition and extended to magnetic multilayers. Numerical results show that ferromagnetic resonance mode of microwave transmission spectrum, which is absent in previous calculation, can be recovered by altering the pinning condition of surface spins. The demonstrated reliability of our theory opens attractive perspectives for studying CMP of thin film with complicated surface magnetization distribution and magnetic multilayers.
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.
Boundary conditions estimation of scoop dosimeter for primary sorting during earthworks
Batij, V.G.; Pravdivyj, A.A.; Stoyanov, A.I.
2005-01-01
Simple method of radioactive waste first separation using collimated dosimeter, which is placed on boom of power shovel, is proposed, and separation process mathematic modeling for boundary conditions definition of sorting under 'Ukryttya' object high gamma background condition are carry out
Atmospheric-radiation boundary conditions for high-frequency waves in time-distance helioseismology
Fournier, D.; Leguèbe, M.; Hanson, C. S.; Gizon, L.; Barucq, H.; Chabassier, J.; Duruflé, M.
2017-12-01
The temporal covariance between seismic waves measured at two locations on the solar surface is the fundamental observable in time-distance helioseismology. Above the acoustic cut-off frequency ( 5.3 mHz), waves are not trapped in the solar interior and the covariance function can be used to probe the upper atmosphere. We wish to implement appropriate radiative boundary conditions for computing the propagation of high-frequency waves in the solar atmosphere. We consider recently developed and published radiative boundary conditions for atmospheres in which sound-speed is constant and density decreases exponentially with radius. We compute the cross-covariance function using a finite element method in spherical geometry and in the frequency domain. The ratio between first- and second-skip amplitudes in the time-distance diagram is used as a diagnostic to compare boundary conditions and to compare with observations. We find that a boundary condition applied 500 km above the photosphere and derived under the approximation of small angles of incidence accurately reproduces the "infinite atmosphere" solution for high-frequency waves. When the radiative boundary condition is applied 2 Mm above the photosphere, we find that the choice of atmospheric model affects the time-distance diagram. In particular, the time-distance diagram exhibits double-ridge structure when using a Vernazza Avrett Loeser atmospheric model.
Boundary conditions for plasma fluid models at the magnetic presheath entrance
Loizu, J.; Ricci, P.; Halpern, F. D.; Jolliet, S.
2012-01-01
The proper boundary conditions at the magnetic presheath entrance for plasma fluid turbulence models based on the drift approximation are derived, focusing on a weakly collisional plasma sheath with T i ≪T e and a magnetic field oblique to a totally absorbing wall. First, the location of the magnetic presheath entrance is rigorously derived. Then boundary conditions at the magnetic presheath entrance are analytically deduced for v ||i , v ||e , n, φ, T e , and for the vorticity ω=∇ ⊥ 2 φ. The effects of E × B and diamagnetic drifts on the boundary conditions are also investigated. Kinetic simulations are performed that confirm the analytical results. Finally, the new set of boundary conditions is implemented in a three-dimensional global fluid code for the simulation of plasma turbulence and, as an example, the results of a tokamak scrape-off layer simulation are discussed. The framework presented can be generalized to obtain boundary conditions at the magnetic presheath entrance in more complex scenarios.
Antal, T [Physics Department, Simon Fraser University, Burnaby, BC V5A 1S6 (Canada); Droz, M [Departement de Physique Theorique, Universite de Geneve, CH 1211 Geneva 4 (Switzerland); Racz, Z [Institute for Theoretical Physics, Eoetvoes University, 1117 Budapest, Pazmany setany 1/a (Hungary)
2004-02-06
Finite-size scaling functions are investigated both for the mean-square magnetization fluctuations and for the probability distribution of the magnetization in the one-dimensional Ising model. The scaling functions are evaluated in the limit of the temperature going to zero (T {yields} 0), the size of the system going to infinity (N {yields} {infinity}) while N[1 - tanh(J/k{sub B}T)] is kept finite (J being the nearest neighbour coupling). Exact calculations using various boundary conditions (periodic, antiperiodic, free, block) demonstrate explicitly how the scaling functions depend on the boundary conditions. We also show that the block (small part of a large system) magnetization distribution results are identical to those obtained for free boundary conditions.
Antishocks in the ASEP with open boundaries conditioned on low current
Belitsky, V; Schütz, G M
2013-01-01
We study the time evolution of the ASEP on a finite lattice with L sites and open boundaries, conditioned on an atypically low current up to a finite time t. By an exact computation, we show that for a one-parameter family of boundary densities and a special value of the conditioned current, an initial product measure with an antishock at site k evolves into a convex combination of such antishocks at sites k′. The weights p(k′, t|k, 0) are shown to be the transition probabilities of simple biased random walk with reflecting boundaries. We compute explicitly these transition rates. Our result implies that the antishock remains microscopically stable under the locally conditioned dynamics. (paper)
I. C. Ramos
2015-10-01
Full Text Available We present the adaptation to non-free boundary conditions of a pseudospectral method based on the (complex Fourier transform. The method is applied to the numerical integration of the Oberbeck-Boussinesq equations in a Rayleigh-Bénard cell with no-slip boundary conditions for velocity and Dirichlet boundary conditions for temperature. We show the first results of a 2D numerical simulation of dry air convection at high Rayleigh number (. These results are the basis for the later study, by the same method, of wet convection in a solar still. Received: 20 Novembre 2014, Accepted: 15 September 2015; Edited by: C. A. Condat, G. J. Sibona; DOI:http://dx.doi.org/10.4279/PIP.070015 Cite as: I C Ramos, C B Briozzo, Papers in Physics 7, 070015 (2015
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.
Mirzabeigy, Alborz; Madoliat, Reza [Iran University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of); Dabbagh, Vahid [University of Malaya, Kuala Lumpur (Malaysia)
2017-02-15
In this paper, free transverse vibration of two parallel beams connected through Winkler type elastic layer is investigated. Euler- Bernoulli beam hypothesis has been applied and it is assumed that boundary conditions of upper and lower beams are similar while arbitrary without any limitation even for non-ideal boundary conditions. Material properties and cross-section geometry of beams could be different from each other. The motion of the system is described by a homogeneous set of two partial differential equations, which is solved by using the classical Bernoulli-Fourier method. Explicit expressions are derived for the natural frequencies. In order to verify accuracy of results, the problem once again solved using modified Adomian decomposition method. Comparison between results indicates excellent accuracy of proposed formulation for any arbitrary boundary conditions. Derived explicit formulation is simplest method to determine natural frequencies of double-beam systems with high level of accuracy in comparison with other methods in literature.
'Duality twisted'boundary conditions in n-state Potts Models
Schuetz, G.
1992-11-01
We discuss a new class of toroidal boundary conditions for one-dimensional quantum Hamiltonian with S n symmetry which are related to two-dimensional n-state Potts models in the extreme anisotropic Hamiltonian limit. At their self-dual point (a point were a second-order phase transition occurs for n=2,3,4) the duality transformation is shown to be an additional symmetry giving rise to a new class of 'duality twisted' toroidal boundary conditions. This corresponding Hamiltonians are given in terms of generators of the periodic Temprely-Lieb algebra with an odd number of generators. We discuss as an example the critical Ising model. Here the complete spectrum for the new boundary conditions can be obtained from a projection mechanism in the spin-1/2 XXZ Heisenberg chain. (author)
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
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.
Douillet-Grellier, Thomas; Pramanik, Ranjan; Pan, Kai; Albaiz, Abdulaziz; Jones, Bruce D.; Williams, John R.
2017-10-01
This paper develops a method for imposing stress boundary conditions in smoothed particle hydrodynamics (SPH) with and without the need for dummy particles. SPH has been used for simulating phenomena in a number of fields, such as astrophysics and fluid mechanics. More recently, the method has gained traction as a technique for simulation of deformation and fracture in solids, where the meshless property of SPH can be leveraged to represent arbitrary crack paths. Despite this interest, application of boundary conditions within the SPH framework is typically limited to imposed velocity or displacement using fictitious dummy particles to compensate for the lack of particles beyond the boundary interface. While this is enough for a large variety of problems, especially in the case of fluid flow, for problems in solid mechanics there is a clear need to impose stresses upon boundaries. In addition to this, the use of dummy particles to impose a boundary condition is not always suitable or even feasibly, especially for those problems which include internal boundaries. In order to overcome these difficulties, this paper first presents an improved method for applying stress boundary conditions in SPH with dummy particles. This is then followed by a proposal of a formulation which does not require dummy particles. These techniques are then validated against analytical solutions to two common problems in rock mechanics, the Brazilian test and the penny-shaped crack problem both in 2D and 3D. This study highlights the fact that SPH offers a good level of accuracy to solve these problems and that results are reliable. This validation work serves as a foundation for addressing more complex problems involving plasticity and fracture propagation.
Boundary terms and junction conditions for the DGP π-Lagrangian and galileon
Dyer, Ethan; Hinterbichler, Kurt
2009-01-01
In the decoupling limit of DGP, π describes the brane-bending degree of freedom. It obeys second order equations of motion, yet it is governed by a higher derivative Lagrangian. We show that, analogously to the Einstein-Hilbert action for GR, the π-Lagrangian requires Gibbons-Hawking-York type boundary terms to render the variational principle well-posed. These terms are important if there are other boundaries present besides the DGP brane, such as in higher dimensional cascading DGP models. We derive the necessary boundary terms in two ways. First, we derive them directly from the brane-localized π-Lagrangian by demanding well-posedness of the action. Second, we calculate them directly from the bulk, taking into account the Gibbons-Hawking-York terms in the bulk Einstein-Hilbert action. As an application, we use the new boundary terms to derive Israel junction conditions for π across a sheet-like source. In addition, we calculate boundary terms and junction conditions for the galileons which generalize the DGP π-Lagrangian, showing that the boundary term for the n-th order galileon is the (n-1)-th order galileon.
Boundary condition effect on response modification factor of X-braced steel frames
Walid A. Attia
2018-04-01
Full Text Available Design of the structures to resist seismic force depends on the theory of dissipation in elastic energy that already exists in response modification factor “R-factor”. The main problem in codes gives a constant value for R-factor, since change in boundary conditions of building change in behavior of braced steel frame structures and that effects on R-factor. This study is an attempt to assess overstrength, ductility and response modification factor of X-braced steel frame under change in boundary conditions, as change in the direction of strong axis of column and connection support type of column besides variation in storey and bays numbers to be 21 frames and each frame has 8 different boundary conditions as sum of 168 cases for analysis. These frames were analyzed by using nonlinear static “pushover” analysis. As results of this study change in support type and direction of strong axis of column give large change in value of R-factor; the minimum value was 4.37 and maximum value 10.97. Minimum value is close to code value that’s mean the code is more conservative in suggesting of R-factor and gives a large factor of safety. Change in the location of bracing gives change in value of R-factor for all boundary conditions. Change in direction of strong axis of columns and support type didn’t give change in value of fundamental period, all boundary conditions. Keywords: Response modification factor, Ductility reduction factor, Overstrength factor, Boundary conditions, Brace frame, Nonlinear static analysis “Pushover”
Neutron transport assembly calculation with non-zero net current boundary condition
Jo, Chang Keun
1993-02-01
Fuel assembly calculation for the homogenized group constants is one of the most important parts in the reactor core analysis. The homogenized group constants of one a quarter assembly are usually generated for the nodal calculation of the reactor core. In the current nodal calculation, one or a quarter of the fuel assembly corresponds to a unit node. The homogenized group constant calculation for a fuel assembly proceeds through cell spectrum calculations, group condensation and cell homogenization calculations, two dimensional fuel assembly calculation, and then depletion calculations of fuel rods. To obtain the assembly wise homogenized group constants, the two dimensional transport calculation is usually performed. Most codes for the assembly wise homogenized group constants employ a zero net current boundary condition. CASMO-3 is such a code that is in wide use. The zero net current boundary condition is plausible and valid in an infinite reactor composed of the same kind of assemblies. However, the reactor is finite and the core is constructed by different kinds of assemblies. Hence, the assumption of the zero net current boundary condition is not valid in the actual reactor. The objective of this study is to develop a homogenization methodology that can treat any actual boundary condition, i.e. non-zero net current boundary condition. In order to treat the non-zero net current boundary condition, we modify CASMO-3. For the two-dimensional treatment in CASMO-3, a multigroup integral transport routine based on the method of transmission probability is used. The code performs assembly calculation with zero net current boundary condition. CASMO-3 is modified to consider the inhomogeneous source at the assembly boundary surface due to the non-zero net current. The modified version of CASMO-3 is called CASMO-3M. CASMO-3M is applied to several benchmark problems. In order to obtain the inhomogeneous source, the global calculation is performed. The local calculation
G Boroni
2017-03-01
Full Text Available Lattice Boltzmann Method (LBM has shown great potential in fluid simulations, but performance issues and difficulties to manage complex boundary conditions have hindered a wider application. The upcoming of Graphic Processing Units (GPU Computing offered a possible solution for the performance issue, and methods like the Immersed Boundary (IB algorithm proved to be a flexible solution to boundaries. Unfortunately, the implicit IB algorithm makes the LBM implementation in GPU a non-trivial task. This work presents a fully parallel GPU implementation of LBM in combination with IB. The fluid-boundary interaction is implemented via GPU kernels, using execution configurations and data structures specifically designed to accelerate each code execution. Simulations were validated against experimental and analytical data showing good agreement and improving the computational time. Substantial reductions of calculation rates were achieved, lowering down the required time to execute the same model in a CPU to about two magnitude orders.
Paul, O.P.K.
1978-01-01
An approach to simulate the flux vanishing boundary condition in solving the two group coupled neutron diffusion equations in three dimensions (x, y, z) employed to calculate the flux distribution and keff of the reactor is summarised. This is of particular interest when the flux vanishing boundary in x, y, z directions is not an integral multiple of the mesh spacings in these directions. The method assumes the flux to be negative, hypothetically at the mesh points lying outside the boundary and thus the finite difference formalism for Laplacian operator, taking into account six neighbours of a mesh point in a square mesh arrangement, is expressed in a general form so as to account for the boundary mesh points of the system. This approach has been incorporated in a three dimensional diffusion code similar to TAPPS23 and has been used for IRT-2000 reactor and the results are quite satisfactory. (author)
Particles in a magnetic field and plasma analogies: doubly periodic boundary conditions
Forrester, P J
2006-01-01
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
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 - others: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
Effects of Boundary Conditions on the Parametric Resonance of Cylindrical Shells under Axial Loading
T.Y. Ng
1998-01-01
Full Text Available In this paper, a formulation for the dynamic stability analysis of circular cylindrical shells under axial compression with various boundary conditions is presented. The present study uses Love’s first approximation theory for thin shells and the characteristic beam functions as approximate axial modal functions. Applying the Ritz procedure to the Lagrangian energy expression yields a system of Mathieu–Hill equations the stability of which is analyzed using Bolotin’s method. The present study examines the effects of different boundary conditions on the parametric response of homogeneous isotropic cylindrical shells for various transverse modes and length parameters.
Ozgener, B.; Ozgener, H.A.
2005-01-01
A multiregion, multigroup collision probability method with white boundary condition is developed for thermalization calculations of light water moderated reactors. Hydrogen scatterings are treated by Nelkin's kernel while scatterings from other nuclei are assumed to obey the free-gas scattering kernel. The isotropic return (white) boundary condition is applied directly by using the appropriate collision probabilities. Comparisons with alternate numerical methods show the validity of the present formulation. Comparisons with some experimental results indicate that the present formulation is capable of calculating disadvantage factors which are closer to the experimental results than alternative methods
Role of Boundary Conditions in Monte Carlo Simulation of MEMS Devices
Nance, Robert P.; Hash, David B.; Hassan, H. A.
1997-01-01
A study is made of the issues surrounding prediction of microchannel flows using the direct simulation Monte Carlo method. This investigation includes the introduction and use of new inflow and outflow boundary conditions suitable for subsonic flows. A series of test simulations for a moderate-size microchannel indicates that a high degree of grid under-resolution in the streamwise direction may be tolerated without loss of accuracy. In addition, the results demonstrate the importance of physically correct boundary conditions, as well as possibilities for reducing the time associated with the transient phase of a simulation. These results imply that simulations of longer ducts may be more feasible than previously envisioned.
Lu Jianming; Ouyang Guangyao; Zhang Ping; Rong Bojun
2012-01-01
Combining the advantages of the finite element software in temperature field analyzing with the multivariate function optimization arithmetic, a feasibility method based on the exterior temperature was proposed to get the thermal boundary conditions, which was required in temperature field analyzing. The thermal boundary conditions can be obtained only by some temperature measurement values. Taking the identification of the convection heat transfer coefficient of a high power density diesel engine cylinder head as an example, the calculation result shows that when the temperature measurement error was less than 0.5℃, the maximum relative error was less than 2%. It is shown that the new method was feasible (authors)
On the physical solutions to the heat equation subjected to nonlinear boundary conditions
Gama, R.M.S. da.
1990-01-01
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)
Syahira Mansur
2014-01-01
Full Text Available The magnetohydrodynamic (MHD boundary layer flow of a nanofluid past a stretching/shrinking sheet with velocity, thermal, and solutal slip boundary conditions is studied. Numerical solutions to the governing equations were obtained using a shooting method. The skin friction coefficient and the local Sherwood number increase as the stretching/shrinking parameter increases. However, the local Nusselt number decreases with increasing the stretching/shrinking parameter. The range of the stretching/shrinking parameter for which the solution exists increases as the velocity slip parameter and the magnetic parameter increase. For the shrinking sheet, the skin friction coefficient increases as the velocity slip parameter and the magnetic parameter increase. For the stretching sheet, it decreases when the velocity slip parameter and the magnetic parameter increase. The local Nusselt number diminishes as the thermal slip parameter increases while the local Sherwood number decreases with increasing the solutal slip parameter. The local Nusselt number is lower for higher values of Lewis number, Brownian motion parameter, and thermophoresis parameter.
Motion of Charged Particles near Magnetic Field Discontinuities
Dodin, I.Y.; Fisch, N.J.
2000-01-01
The motion of charged particles in slowly changing magnetic fields exhibits adiabatic invariance even in the presence of abrupt magnetic discontinuities. Particles near discontinuities in magnetic fields, what we call ''boundary particles'', are constrained to remain near an arbitrarily fractured boundary even as the particle drifts along the discontinuity. A new adiabatic invariant applies to the motion of these particles
Effects of boundary conditions on thermomechanical calculations: Spent fuel test - climax
Butkovich, T.R.
1982-10-01
The effects of varying certain boundary conditions on the results of finite-element calculations were studied in relation to the Spent Fuel Test - Climax. The study employed a thermomechanical model with the ADINA structural analysis. Nodal temperature histories were generated with the compatible ADINAT heat flow codes. The boundary conditions studied included: (1) The effect of boundary loading on three progressively larger meshes. (2) Plane strain vs plane stress conditions. (3) The effect of isothermal boundaries on a small mesh and on a significantly larger mesh. The results showed that different mesh sizes had an insignificant effect on isothermal boundaries up to 5 y, while on the smallest and largest mesh, the maximum temperature difference in the mesh was 0 C. In the corresponding ADINA calculation, these different mesh sizes produce insignificant changes in the stress field and displacements in the region of interest near the heat sources and excavations. On the other hand, plane stress produces horizontal and vertical stress differences approx. 9% higher than does plane strain
Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data.
Leendert van Maanen
Full Text Available The notion of "mixtures" has become pervasive in behavioral and cognitive sciences, due to the success of dual-process theories of cognition. However, providing support for such dual-process theories is not trivial, as it crucially requires properties in the data that are specific to mixture of cognitive processes. In theory, one such property could be the fixed-point property of binary mixture data, applied-for instance- to response times. In that case, the fixed-point property entails that response time distributions obtained in an experiment in which the mixture proportion is manipulated would have a common density point. In the current article, we discuss the application of the fixed-point property and identify three boundary conditions under which the fixed-point property will not be interpretable. In Boundary condition 1, a finding in support of the fixed-point will be mute because of a lack of difference between conditions. Boundary condition 2 refers to the case in which the extreme conditions are so different that a mixture may display bimodality. In this case, a mixture hypothesis is clearly supported, yet the fixed-point may not be found. In Boundary condition 3 the fixed-point may also not be present, yet a mixture might still exist but is occluded due to additional changes in behavior. Finding the fixed-property provides strong support for a dual-process account, yet the boundary conditions that we identify should be considered before making inferences about underlying psychological processes.
Rauf, A., E-mail: raufamar@ciitsahiwal.edu.pk [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Siddiq, M.K. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Abbasi, F.M. [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Meraj, M.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Ashraf, M. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Shehzad, S.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)
2016-10-15
The present work deals with the steady laminar three-dimensional mixed convective magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid over a bidirectional stretching surface. A uniform magnetic field is applied normal to the flow direction. Similarity variables are implemented to convert the non-linear partial differential equations into ordinary ones. Convective boundary conditions are utilized at surface of the sheet. A numerical technique of Runge–Kutta–Fehlberg (RFK45) is used to obtain the results of velocity, temperature and concentration fields. The physical dimensionless parameters are discussed through tables and graphs. - Highlights: • Mixed convective boundary layer flow of Casson nanofluid is taken into account. • Impact of magnetic field is examined. • Convective heat and mass conditions are imposed. • Numerical solutions are presented and discussed.
Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces
Mantile, Andrea; Posilicano, Andrea; Sini, Mourad
2016-07-01
The theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic differential operator on Rn with linear boundary conditions on (a relatively open part of) a compact hypersurface. Our approach allows to obtain Kreĭn-like resolvent formulae where the reference operator coincides with the ;free; operator with domain H2 (Rn); this provides an useful tool for the scattering problem from a hypersurface. Concrete examples of this construction are developed in connection with the standard boundary conditions, Dirichlet, Neumann, Robin, δ and δ‧-type, assigned either on a (n - 1) dimensional compact boundary Γ = ∂ Ω or on a relatively open part Σ ⊂ Γ. Schatten-von Neumann estimates for the difference of the powers of resolvents of the free and the perturbed operators are also proven; these give existence and completeness of the wave operators of the associated scattering systems.
Bardhan, Jaydeep P; Knepley, Matthew G
2014-10-07
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, "Charge asymmetries in hydration of polar solutes," J. Phys. Chem. B 112, 2405-2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.
Bardhan, Jaydeep P.; Knepley, Matthew G.
2014-01-01
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry
Bardhan, Jaydeep P.; Knepley, Matthew G.
2014-01-01
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry. PMID:25296776
Bardhan, Jaydeep P. [Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115 (United States); Knepley, Matthew G. [Computation Institute, The University of Chicago, Chicago, Illinois 60637 (United States)
2014-10-07
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.
''Free-space'' boundary conditions for the time-dependent wave equation
Lindman, E.L.
1975-01-01
Boundary conditions for the discrete wave equation which act like an infinite region of free space in contact with the computational region can be constructed using projection operators. Propagating and evanescent waves coming from within the computational region generate no reflected waves as they cross the boundary. At the same time arbitrary waves may be launched into the computational region. Well known projection operators for one-dimensional waves may be used for this purpose in one dimension. Extensions of these operators to higher dimensions along with numerically efficient approximations to them are described for higher-dimensional problems. The separation of waves into ingoing and outgoing waves inherent in these boundary conditions greatly facilitates diagnostics
Fernandez, P.; Garcia-Mazario, M.; Lancha, A.M.; Lapena, J.
2004-01-01
The aim of this paper is to describe the microstructural investigations, the mechanical properties (hardness, tensile and charpy) and the grain boundary microchemistry studied by Auger electron spectroscopy (AES), of the Eurofer'97 steel aged in the range of temperatures from 400 to 600 deg. C up to 10,000 h. After these thermal aging treatments the steel showed a high microstructural stability, and similar values of hardness, ultimate tensile strength and 0.2% proof stress regardless of the material condition. A slight DBTT increase was observed in the material aged at 600 deg. C for 5000 and 10,000 h. The Auger results showed chromium enrichment at grain boundaries in all material conditions. In addition, phosphorus was detected at the grain boundaries after the aging treatments at 500 deg. C
Analysis on Forced Vibration of Thin-Wall Cylindrical Shell with Nonlinear Boundary Condition
Qiansheng Tang
2016-01-01
Full Text Available Forced vibration of thin-wall cylindrical shell under nonlinear boundary condition was discussed in this paper. The nonlinear boundary was modeled as supported clearance in one end of shell and the restraint was assumed as linearly elastic in the radial direction. Based on Sanders’ shell theory, Lagrange equation was utilized to derive the nonlinear governing equations of cylindrical shell. The displacements in three directions were represented by beam functions and trigonometric functions. In the study of nonlinear dynamic responses of thin-wall cylindrical shell with supported clearance under external loads, the Newmark method is used to obtain time history, frequency spectrum plot, phase portraits, Poincare section, bifurcation diagrams, and three-dimensional spectrum plot with different parameters. The effects of external loads, supported clearance, and support stiffness on nonlinear dynamics behaviors of cylindrical shell with nonlinear boundary condition were discussed.
Yanmei Sun
2012-01-01
Full Text Available By using the Leggett-Williams fixed theorem, we establish the existence of multiple positive solutions for second-order nonhomogeneous Sturm-Liouville boundary value problems with linear functional boundary conditions. One explicit example with singularity is presented to demonstrate the application of our main results.
The fermion boundary condition and the THETA-angle in QED2
Hrasko, P.
1983-09-01
The order parameter of the Schwinger model is calculated in the Euclidean functional integral approach. It is shown that the symmetry breaking angle THETA is intimately connected to the boundary condition imposed on the fermions. The transition to the Euclidean description involves both imaginary time and imaginary THETA. (author)
Modeling of Hydrophobic Surfaces by the Stokes Problem With the Stick–Slip Boundary Conditions
Kučera, R.; Šátek, V.; Haslinger, Jaroslav; Fialová, S.; Pochylý, F.
2017-01-01
Roč. 139, č. 1 (2017), č. článku 011202. ISSN 0098-2202 Institutional support: RVO:68145535 Keywords : algebra * boundary conditions * hydrophobicity * Lagrange multipliers * Navier Stokes equations Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.437, year: 2016 http://fluidsengineering.asmedigitalcollection.asme.org/article.aspx?articleid=2536532
A stable penalty method for the compressible Navier-Stokes equations: I. Open boundary conditions
Hesthaven, Jan; Gottlieb, D.
1996-01-01
The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization...
Menges, J.; Walter, F.; Vogel, B.; Bruch, H.
2011-01-01
Transformational leadership (TFL) climate describes the degree to which leaders throughout an organization engage in TFL behaviors. In this study, we investigate performance linkages, mechanisms, and boundary conditions of TFL climate at the organizational level of analysis. In a sample of 158
Formulation and numerical implementation of micro-scale boundary conditions for particle aggregates
Liu, J.; Bosco, E.; Suiker, A.S.J.
2017-01-01
Novel numerical algorithms are presented for the implementation of micro-scale boundary conditions of particle aggregates modelled with the discrete element method. The algorithms are based on a servo-control methodology, using a feedback principle comparable to that of algorithms commonly applied
Langen, Peter Lang; Vinther, Bo Møllesøe
2009-01-01
The response in northern hemisphere atmospheric circulation and the resulting changes in moisture sources for Greenland precipitation to glacial boundary conditions are studied in NCAR's CCM3 atmospheric general circulation model fitted with a moisture tracking functionality. We employ both...... seasonality, condensation temperatures and source temperatures are assessed. Udgivelsesdato: June 2009...
AdS boundary conditions and the Topologically Massive Gravity/CFT correspondence
Skenderis, K.; Taylor, M.; van Rees, B.C.
2009-01-01
The AdS/CFT correspondence provides a new perspective on recurrent questions in General Relativity such as the allowed boundary conditions at infinity and the definition of gravitational conserved charges. Here we review the main insights obtained in this direction over the last decade and apply the
Madsen, Søren; Pinna, Rodney; Randolph, M. F.
2015-01-01
of large-diameter bucket foundations. Since shell structures are generally sensitive to initially imperfect geometries, eigenmode-affine imperfections are introduced in a nonlinear finite-element analysis. The influence of modelling the real lid structure compared to classic boundary conditions...
Inference and testing on the boundary in extended constant conditional correlation GARCH models
Pedersen, Rasmus Søndergaard
2017-01-01
We consider inference and testing in extended constant conditional correlation GARCH models in the case where the true parameter vector is a boundary point of the parameter space. This is of particular importance when testing for volatility spillovers in the model. The large-sample properties...
Wassenaar, T.A.; Mark, A.E.
The effect of the box shape on the dynamic behavior of proteins simulated under periodic boundary conditions is evaluated. In particular, the influence of simulation boxes defined by the near-densest lattice packing (NDLP) in conjunction with rotational constraints is compared to that of standard
Rigorous homogenization of a Stokes-Nernst-Planck-Poisson problem for various boundary conditions
Ray, N.; Muntean, A.; Knabner, P.
2011-01-01
We perform the periodic homogenization (i. e. e ¿ 0) of the non-stationary Stokes-Nernst-Planck-Poisson system using two-scale convergence, where e is a suitable scale parameter. The objective is to investigate the influence of different boundary conditions and variable choices of scaling in e of
Creation of particles in the gravitational field and the boundary conditions for quantized fields
Khrustalev, O.A.; Silaev, P.K.
1995-01-01
We prove, that if one impose the linear constraints on the quantized fields that satisfy different boundary conditions, it can leads to such a transformation between creation-annihilation operators, that corresponds to particle creation. We also prove, that the correspondence between field, quantized in Minkowski space and the field, quantized in Rindler space has Rindler space can't be observed. 7 refs
Nonlinear parabolic problems with Neumann-type boundary conditions and L^1-data
Abderrahmane El Hachimi
2007-11-01
$$ \\frac{\\partial u}{\\partial t}-\\triangle_{p}u+\\alpha(u=f \\quad \\text{in } ]0,\\ T[\\times\\Omega, $$ with Neumann-type boundary conditions and initial data in $L^1$. Our approach is based essentially on the time discretization technique by Euler forward scheme.
Current Percolation in Medium with Boundaries under Quantum Hall Effect Conditions
M. U. Malakeeva
2012-01-01
Full Text Available The current percolation has been considered in the medium with boundaries under quantum Hall effect conditions. It has been shown that in that case the effective Hall conductivity has a nonzero value due to percolation of the Hall current through the finite number of singular points (in our model these are corners at the phase joints.
Wijnant, Ysbrand H.; Spiering, R.M.E.J.; Blijderveen, M.; de Boer, Andries
2006-01-01
Previous research has shown that viscothermal wave propagation in narrow gaps can efficiently be described by means of the low reduced frequency model. For simple geometries and boundary conditions, analytical solutions are available. For example, Beltman [4] gives the acoustic pressure in the gap
Computer code calculations of the TMI-2 accident: initial and boundary conditions
Behling, S.R.
1985-05-01
Initial and boundary conditions during the Three Mile Island Unit 2 (TMI-2) accident are described and detailed. A brief description of the TMI-2 plant configuration is given. Important contributions to the progression of the accident in the reactor coolant system are discussed. Sufficient information is provided to allow calculation of the TMI-2 accident with computer codes
Twisted boundary conditions: a non-perturbative probe for pure non-abelian gauge theories
Baal, P. van.
1984-01-01
In this thesis the author describes a pure non-abelian gauge theory on the hypertorus with gauge group SU(N). To test the flux tube picture he has studied the large distance limit of this theory, leading to a large coupling constant. To tackle this problem, he describes two approaches, in both of which twisted boundary conditions play an important role. (Auth.)
Tengfei Shen
2015-12-01
Full Text Available This paper deals with the multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects. By using critical point theory, a new result is obtained. An example is given to illustrate the main result.
On the boundary conditions and optimization methods in integrated digital image correlation
Kleinendorst, S.M.; Verhaegh, B.J.; Hoefnagels, J.P.M.; Ruybalid, A.; van der Sluis, O.; Geers, M.G.D.; Lamberti, L.; Lin, M.-T.; Furlong, C.; Sciammarella, C.
2018-01-01
In integrated digital image correlation (IDIC) methods attention must be paid to the influence of using a correct geometric and material model, but also to make the boundary conditions in the FE simulation match the real experiment. Another issue is the robustness and convergence of the IDIC
Cornelis van der Mee
2005-01-01
Full Text Available We present the complete version including proofs of the results announced in [van der Mee C., Pivovarchik V.: A Sturm-Liouville spectral problem with boundary conditions depending on the spectral parameter. Funct. Anal. Appl. 36 (2002, 315–317 [Funkts. Anal. Prilozh. 36 (2002, 74–77 (Russian
Boundary conditions in Ginsburg Landau theory and critical temperature of high-T superconductors
Lykov, A. N.
2008-06-01
New mixed boundary conditions to the Ginsburg-Landau equations are found to limit the critical temperature ( T) of high- T superconductors. Moreover, the value of the pseudogap in these superconductors can be explained by using the method. As a result, the macroscopic approach is proposed to increase T of cuprate superconductors.
Boundary conditions in Ginsburg-Landau theory and critical temperature of high-Tc superconductors
Lykov, A.N.
2008-01-01
New mixed boundary conditions to the Ginsburg-Landau equations are found to limit the critical temperature (T c ) of high-T c superconductors. Moreover, the value of the pseudogap in these superconductors can be explained by using the method. As a result, the macroscopic approach is proposed to increase T c of cuprate superconductors
OpenCL-Based FPGA Accelerator for 3D FDTD with Periodic and Absorbing Boundary Conditions
Hasitha Muthumala Waidyasooriya
2017-01-01
Full Text Available Finite difference time domain (FDTD method is a very poplar way of numerically solving partial differential equations. FDTD has a low operational intensity so that the performances in CPUs and GPUs are often restricted by the memory bandwidth. Recently, deeply pipelined FPGA accelerators have shown a lot of success by exploiting streaming data flows in FDTD computation. In spite of this success, many FPGA accelerators are not suitable for real-world applications that contain complex boundary conditions. Boundary conditions break the regularity of the data flow, so that the performances are significantly reduced. This paper proposes an FPGA accelerator that computes commonly used absorbing and periodic boundary conditions in many 3D FDTD applications. Accelerator is designed using a “C-like” programming language called OpenCL (open computing language. As a result, the proposed accelerator can be customized easily by changing the software code. According to the experimental results, we achieved over 3.3 times and 1.5 times higher processing speed compared to the CPUs and GPUs, respectively. Moreover, the proposed accelerator is more than 14 times faster compared to the recently proposed FPGA accelerators that are capable of handling complex boundary conditions.
Construction of the Nuclear Effective Interaction from Energy Eigenstates and Boundary Conditions
McElvain, Kenneth; Haxton, Wick
2017-01-01
The original Harmonic Oscillator Based Effective Theory (HOBET) work by Haxton and Luu reduced H = T +VNN , with VNN a realistic potential, to Heff in a small basis defined by projection operator P while correctly including all scattering by H through an excluded space Q. Scattering by T is analytically included to all orders, leaving the ET expansion focused on the short range VNN. Results do not depend on the size P as the effect of scattering through Q is fully included, also distinguishing HOBET from other methods. In this talk we abandon VNN and determine the LECs of the ET expansion from energy levels and boundary conditions. In the infinite volume continuum case every energy is an eigenvalue of H with an associated scattering state. In the LQCD context boundary conditions are periodic. In either case the ET LECs can be determined from energy, boundary condition pairs. We show that the Cartesian HO ET LECs can be expressed in terms of the spherical ones, giving a spherical, infinite volume ET, bypassing the use of Luscher's method. The approach cleanly isolates operator mixing induced by the finite box, sequestering effects that vanish in the continuum limit in a Green's function constrained to match the boundary conditions. Supported by the DOE under contracts DE-SC00046548 and DE-AC02-98CH10886.
GENERAL DECAY FOR A DIFFERENTIAL INCLUSION OF KIRCHHOFF TYPE WITH A MEMORY CONDITION AT THE BOUNDARY
Jum-Ran KANG
2014-01-01
In this article, we consider a differential inclusion of Kirchhoff type with a memory condition at the boundary. We prove the asymptotic behavior of the corresponding solutions. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases.
M. Denche; A. L. Marhoune
2003-01-01
In this paper, we study a mixed problem with integral boundary conditions for a high order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on energy inequality, and on the density of the range of the operator generated by the considered problem.
Backi, Christoph Josef; Bendtsen, Jan Dimon; Leth, John
2015-01-01
In this work the stability properties of a partial differential equation (PDE) with state-dependent parameters and asymmetric boundary conditions are investigated. The PDE describes the temperature distribution inside foodstuff, but can also hold for other applications and phenomena. We show...
Evidence for Cretaceous-Paleogene boundary bolide “impact winter” conditions from New Jersey, USA
Vellekoop, J.; Esmeray-Senlet, S.; Miller, K.G.; Browning, J.V.; Sluijs, A.; van de Schootbrugge, B.; Sinninghe Damsté, J.S.; Brinkhuis, H.
2016-01-01
Abrupt and short-lived “impact winter” conditions have commonly been implicated as the main mechanism leading to the mass extinction at the Cretaceous-Paleogene (K-Pg) boundary (ca. 66 Ma), marking the end of the reign of the non-avian dinosaurs. However, so far only limited evidence has been
Evidence for Cretaceous-Paleogene boundary bolide "impact winter" conditions from New Jersey, USA
Vellekoop, J.; Esmeray-Senlet, S.; Miller, K.G.; Browning, J.V.; Sluijs, A.|info:eu-repo/dai/nl/311474748; van de Schootbrugge, B.|info:eu-repo/dai/nl/376758562; Sinninghe Damsté, J.S.|info:eu-repo/dai/nl/07401370X; Brinkhuis, H.|info:eu-repo/dai/nl/095046097
2016-01-01
Abrupt and short-lived “impact winter” conditions have commonly been implicated as the main mechanism leading to the mass extinction at the Cretaceous-Paleogene (K-Pg) boundary (ca. 66 Ma), marking the end of the reign of the non-avian dinosaurs. However, so far only limited evidence has been
Boundary conditions for the use of personal ventilation over mixing ventilation in open plan offices
Petersen, Steffen; Hviid, Christian Anker
2013-01-01
This paper investigates the boundary conditions for choosing a combined Personal Ventilation (PV) and Mixing Ventilation (MV) over conventional mixing ventilation in an office with multiple workers. A simplified procedure for annual performance assessment of PV/MV systems in terms of air quality...
Andersen, Michael; Abel, Sarah Maria Niebe; Erleben, Kenny
2017-01-01
We address the task of computing solutions for a separating fluid-solid wall boundary condition model. We present an embarrassingly parallel, easy to implement, fluid LCP solver.We are able to use greater domain sizes than previous works have shown, due to our new solver. The solver exploits matr...
6d Dirac fermion on a rectangle; scrutinizing boundary conditions, mode functions and spectrum
Yukihiro Fujimoto
2017-09-01
Full Text Available We classify possible boundary conditions of a 6d Dirac fermion Ψ on a rectangle under the requirement that the 4d Lorentz structure is maintained, and derive the profiles and spectrum of the zero modes and nonzero KK modes under the two specific boundary conditions, (i 4d-chirality positive components being zero at the boundaries and (ii internal chirality positive components being zero at the boundaries. In the case of (i, twofold degenerated chiral zero modes appear which are localized towards specific directions of the rectangle pointed by an angle parameter θ. This leads to an implication for a new direction of pursuing the origin of three generations in the matter fields of the standard model, even though triple-degenerated zero modes are not realized in the six dimensions. When such 6d fermions couple with a 6d scalar with a vacuum expectation value, θ contributes to a mass matrix of zero-mode fermions consisting of Yukawa interactions. The emergence of the angle parameter θ originates from a rotational symmetry in the degenerated chiral zero modes on the rectangle extra dimensions since they do not feel the boundaries. In the case of (ii, this rotational symmetry is promoted to the two-dimensional conformal symmetry though no chiral massless zero mode appears. We also discuss the correspondence between our model on a rectangle and orbifold models in some details.
Quasilocal conservation laws in XXZ spin-1/2 chains: Open, periodic and twisted boundary conditions
Tomaž Prosen
2014-09-01
Full Text Available A continuous family of quasilocal exact conservation laws is constructed in the anisotropic Heisenberg (XXZ spin-1/2 chain for periodic (or twisted boundary conditions and for a set of commensurate anisotropies densely covering the entire easy plane interaction regime. All local conserved operators follow from the standard (Hermitian transfer operator in fundamental representation (with auxiliary spin s=1/2, and are all even with respect to a spin flip operation. However, the quasilocal family is generated by differentiation of a non-Hermitian highest weight transfer operator with respect to a complex auxiliary spin representation parameter s and includes also operators of odd parity. For a finite chain with open boundaries the time derivatives of quasilocal operators are not strictly vanishing but result in operators localized near the boundaries of the chain. We show that a simple modification of the non-Hermitian transfer operator results in exactly conserved, but still quasilocal operators for periodic or generally twisted boundary conditions. As an application, we demonstrate that implementing the new exactly conserved operator family for estimating the high-temperature spin Drude weight results, in the thermodynamic limit, in exactly the same lower bound as for almost conserved family and open boundaries. Under the assumption that the bound is saturating (suggested by agreement with previous thermodynamic Bethe ansatz calculations we propose a simple explicit construction of infinite time averages of local operators such as the spin current.
Single particle nonlocality, geometric phases and time-dependent boundary conditions
Matzkin, A.
2018-03-01
We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We discuss earlier claims according to which the quantum state of a particle remaining localized at the center of an infinite well with moving walls would be specifically modified by the change in boundary conditions due to the wall’s motion. We first prove that the evolution of an initially localized Gaussian state is not affected nonlocally by a linearly moving wall: as long as the quantum state has negligible amplitude near the wall, the boundary motion has no effect. This result is further extended to related confined time-dependent oscillators in which the boundary’s motion is known to give rise to geometric phases: for a Gaussian state remaining localized far from the boundaries, the effect of the geometric phases is washed out and the particle dynamics shows no traces of a nonlocal influence that would be induced by the moving boundaries.
Fellner, Klemens; Kovtunenko, Victor A
2016-01-01
A nonlinear Poisson-Boltzmann equation with inhomogeneous Robin type boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic multiphase medium with dilute solid particles. The key issue stems from interfacial jumps, which necessitate discontinuous solutions to the problem. Based on variational techniques, we derive the homogenisation of the discontinuous problem and establish a rigorous residual error estimate up to the first-order correction.
Comparison of mass transport using average and transient rainfall boundary conditions
Duguid, J.O.; Reeves, M.
1976-01-01
A general two-dimensional model for simulation of saturated-unsaturated transport of radionuclides in ground water has been developed and is currently being tested. The model is being applied to study the transport of radionuclides from a waste-disposal site where field investigations are currently under way to obtain the necessary model parameters. A comparison of the amount of tritium transported is made using both average and transient rainfall boundary conditions. The simulations indicate that there is no substantial difference in the transport for the two conditions tested. However, the values of dispersivity used in the unsaturated zone caused more transport above the water table than has been observed under actual conditions. This deficiency should be corrected and further comparisons should be made before average rainfall boundary conditions are used for long-term transport simulations
Stabilities of MHD rotational discontinuities
Wang, S.
1984-11-01
In this paper, the stabilities of MHD rotational discontinuities are analyzed. The results show that the rotational discontinuities in an incompressible magnetofluid are not always stable with respect to infinitesimal perturbation. The instability condition in a special case is obtained. (author)
Discontinuity formulas for multiparticle amplitudes
Stapp, H.P.
1976-03-01
It is shown how discontinuity formulas for multiparticle scattering amplitudes are derived from unitarity and analyticity. The assumed analyticity property is the normal analytic structure, which was shown to be equivalent to the space-time macrocausality condition. The discontinuity formulas to be derived are the basis of multi-particle fixed-t dispersion relations
Scalar field dynamics in a BTZ background with generic boundary conditions
Garbarz, Alan; La Madrid, Joan [UBA y IFIBA, CONICET, Departamento de Fisica, FCEyN, Buenos Aires (Argentina); Leston, Mauricio [Pabellon IAFE-CONICET, Instituto de Astronomia y Fisica del Espacio, Buenos Aires (Argentina)
2017-11-15
We revisit the dynamics of a massive scalar field in a Banados, Teitelboim, and Zanelli background taking into account the lack of global hyperbolicity of the spacetime. We approach this issue using the strategy of Ishibashi and Wald which finds a unique smooth solution as the causal evolution of initial data, each possible evolution corresponding to a positive self-adjoint extension of certain operator in a Hilbert space on the initial surface. Moreover, solutions obtained this way are the most general ones satisfying a few physically sensible requirements. This procedure is intimately related to the choice of boundary conditions and the existence of bound states. We find that the scalar field dynamics in the (effective) mass window -3/4 ≤ m{sub e}{sup 2}l{sup 2} < 0 can be well defined within a one-parametric family of distinct boundary conditions (-3/4 being the conformally coupled case), while for m{sub e}{sup 2}l{sup 2} ≥ 0 the boundary condition is unique (only one self-adjoint extension is possible). It is argued that there is no sensible evolution possible for m{sub e}{sup 2}l{sup 2} < -1, and also it is shown that in the range m{sub e}{sup 2}l{sup 2} element of [-1, -3/4) there is a U(1) family of allowed boundary conditions, however, the positivity of the self-adjoint extensions is only motivated but not proven. We focus mainly on describing the dynamics of such evolutions given the initial data and all possible boundary conditions, and in particular we show the energy is always positive and conserved. (orig.)
Berntsen, Jarle; Alendal, Guttorm; Avlesen, Helge; Thiem, Øyvind
2018-05-01
The flow of dense water along continental slopes is considered. There is a large literature on the topic based on observations and laboratory experiments. In addition, there are many analytical and numerical studies of dense water flows. In particular, there is a sequence of numerical investigations using the dynamics of overflow mixing and entrainment (DOME) setup. In these papers, the sensitivity of the solutions to numerical parameters such as grid size and numerical viscosity coefficients and to the choices of methods and models is investigated. In earlier DOME studies, three different bottom boundary conditions and a range of vertical grid sizes are applied. In other parts of the literature on numerical studies of oceanic gravity currents, there are statements that appear to contradict choices made on bottom boundary conditions in some of the DOME papers. In the present study, we therefore address the effects of the bottom boundary condition and vertical resolution in numerical investigations of dense water cascading on a slope. The main finding of the present paper is that it is feasible to capture the bottom Ekman layer dynamics adequately and cost efficiently by using a terrain-following model system using a quadratic drag law with a drag coefficient computed to give near-bottom velocity profiles in agreement with the logarithmic law of the wall. Many studies of dense water flows are performed with a quadratic bottom drag law and a constant drag coefficient. It is shown that when using this bottom boundary condition, Ekman drainage will not be adequately represented. In other studies of gravity flow, a no-slip bottom boundary condition is applied. With no-slip and a very fine resolution near the seabed, the solutions are essentially equal to the solutions obtained with a quadratic drag law and a drag coefficient computed to produce velocity profiles matching the logarithmic law of the wall. However, with coarser resolution near the seabed, there may be a
Gerbi, Sté phane; Said-Houari, Belkacem
2013-01-01
The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.
Escolano-Carrasco, José; Jacobsen, Finn
2007-01-01
Digital waveguide mesh (DWM) is a popular method for time domain modelling of sound fields. DWM consists of a recursive digital filter structure where a D'Alembert solution of the wave equation is propagated. One of the attractive characteristics of this method is related to the simplicity...... model of the boundary does not agree with the behaviour of a locally reacting surface, and this can give rise to contradictions in the physical interpretation of the reflected sound field. This paper analyses the behaviour of frequency dependent boundary conditions in DWM in order to obtain a physical...
Gerbi, Stéphane
2013-01-15
The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.
Tian, Lin-Lin; Zhao, Ning; Song, Yi-Lei; Zhu, Chun-Ling
2018-05-01
This work is devoted to perform systematic sensitivity analysis of different turbulence models and various inflow boundary conditions in predicting the wake flow behind a horizontal axis wind turbine represented by an actuator disc (AD). The tested turbulence models are the standard k-𝜀 model and the Reynolds Stress Model (RSM). A single wind turbine immersed in both uniform flows and in modeled atmospheric boundary layer (ABL) flows is studied. Simulation results are validated against the field experimental data in terms of wake velocity and turbulence intensity.
POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
FAOUZI HADDOUCHI
2015-11-01
Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
Edge states and conformal boundary conditions in super spin chains and super sigma models
Bondesan, Roberto; Jacobsen, Jesper L.; Saleur, Hubert
2011-01-01
The sigma models on projective superspaces CP N+M-1|N with topological angle θ=πmod2π 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., JHEP 1002 (2010) 015]. In the sigma model setting, these boundary conditions are associated with complex line bundles, and are labelled by an integer, related with the exact value of θ. Our approach relies on a spin chain regularization, where the boundary conditions now correspond to the introduction of additional edge states. The exact values of the exponents then follow from a lengthy algebraic analysis, a reformulation of the spin chain in terms of crossing and non-crossing loops (represented as a certain subalgebra of the Brauer algebra), and earlier results on the so-called one- and two-boundary Temperley-Lieb algebras (also known as blob algebras). A remarkable result is that the exponents, in general, turn out to be irrational. The case M=1 has direct applications to the spin quantum Hall effect, which will be discussed in a sequel.
Edge states and conformal boundary conditions in super spin chains and super sigma models
Bondesan, Roberto, E-mail: roberto.bondesan@cea.f [LPTENS, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris (France); Institute de Physique Theorique, CEA Saclay, F-91191 Gif-sur-Yvette (France); Jacobsen, Jesper L. [LPTENS, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris (France); Universite Pierre et Marie Curie, 4 place Jussieu, 75252 Paris (France); Saleur, Hubert [Institute de Physique Theorique, CEA Saclay, F-91191 Gif-sur-Yvette (France); Physics Department, USC, Los Angeles, CA 90089-0484 (United States)
2011-08-11
The sigma models on projective superspaces CP{sup N+M-1{vert_bar}N} with topological angle {theta}={pi}mod2{pi} 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., JHEP 1002 (2010) 015]. In the sigma model setting, these boundary conditions are associated with complex line bundles, and are labelled by an integer, related with the exact value of {theta}. Our approach relies on a spin chain regularization, where the boundary conditions now correspond to the introduction of additional edge states. The exact values of the exponents then follow from a lengthy algebraic analysis, a reformulation of the spin chain in terms of crossing and non-crossing loops (represented as a certain subalgebra of the Brauer algebra), and earlier results on the so-called one- and two-boundary Temperley-Lieb algebras (also known as blob algebras). A remarkable result is that the exponents, in general, turn out to be irrational. The case M=1 has direct applications to the spin quantum Hall effect, which will be discussed in a sequel.
Rezaei, M. P.; Zamanian, M.
2017-01-01
In this paper, the influences of nonideal boundary conditions (due to flexibility) on the primary resonant behavior of a piezoelectrically actuated microbeam have been studied, for the first time. The structure has been assumed to treat as an Euler-Bernoulli beam, considering the effects of geometric nonlinearity. In this work, the general nonideal supports have been modeled as a the combination of horizontal, vertical and rotational springs, simultaneously. Allocating particular values to the stiffness of these springs provides the mathematical models for the majority of boundary conditions. This consideration leads to use a two-dimensional analysis of the multiple scales method instead of previous works' method (one-dimensional analysis). If one neglects the nonideal effects, then this paper would be an effort to solve the two-dimensional equations of motion without a need of a combination of these equations using the shortening or stretching effect. Letting the nonideal effects equal to zero and comparing their results with the results of previous approaches have been demonstrated the accuracy of the two-dimensional solutions. The results have been identified the unique effects of constraining and stiffening of boundaries in horizontal, vertical and rotational directions. This means that it is inaccurate to suppose the nonideality of supports only in one or two of these directions like as previous works. The findings are of vital importance as a better prediction of the frequency response for the nonideal supports. Furthermore, the main findings of this effort can help to choose appropriate boundary conditions for desired systems.
Seo, Jongmin; Bose, Sanjeeb; Garcia-Mayoral, Ricardo; Mani, Ali
2012-11-01
Superhydrophobic surfaces are shown to be effective for surface drag reduction under laminar regime by both experiments and simulations (see for example, Ou and Rothstein, Phys. Fluids 17:103606, 2005). However, such drag reduction for fully developed turbulent flow maintaining the Cassie-Baxter state remains an open problem due to high shear rates and flow unsteadiness of turbulent boundary layer. Our work aims to develop an understanding of mechanisms leading to interface breaking and loss of gas pockets due to interactions with turbulent boundary layers. We take advantage of direct numerical simulation of turbulence with slip and no-slip patterned boundary conditions mimicking the superhydrophobic surface. In addition, we capture the dynamics of gas-water interface, by deriving a proper linearized boundary condition taking into account the surface tension of the interface and kinematic matching of interface deformation and normal velocity conditions on the wall. We will show results from our simulations predicting the dynamical behavior of gas pocket interfaces over a wide range of dimensionless surface tensions. Supported by the Office of Naval Research and the Kwanjeong Educational Scholarship Foundation.
Verschaeve, Joris C G
2011-06-13
By means of the continuity equation of the incompressible Navier-Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.
A nonlinear free boundary problem with a self-driven Bernoulli condition
Dipierro, Serena; Karakhanyan, Aram; Valdinoci, Enrico
2017-01-01
We study a Bernoulli type free boundary problem with two phases J[u]=∫Ω|∇u(x)|2dx+Φ(M−(u),M+(u)),u−u¯∈W1,20(Ω), where u¯∈W1,2(Ω) is a given boundary datum. Here, M1 and M2 are weighted volumes of {u≤0}∩Ω and {u>0}∩Ω, respectively, and Φ is a nonnegative function of two real variables. We show that, for this problem, the Bernoulli constant, which determines the gradient jump condition across the free boundary, is of global type and it is indeed determined by the weighted volumes of the phas...
Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities
Allen, Rebecca
2016-06-29
We study a multiple relaxation time lattice Boltzmann model for natural convection with moment-based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 108. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy. Copyright © 2016 Inderscience Enterprises Ltd.
Effects of boundary conditions on temperature and density in an EXTRAP Z-pinch
Drake, J.R.; Karlsson, P.
1985-08-01
Using the fluid equations, we examine transport in an Extrap configuration by carrying out calculations incorporating model profiles for the density and temperature. The goal of this analysis is to examine the scaling of the pinch equilibrium plasma density, temperature and radius with parameters that are characteristic for Extrap Z-pinches. These parameters include the discharge current, the neutral hydrogen filling density, an oxygen impurity fractional concentration and the condition at the pinch boundary. An Extrap Z-pinch is a pinch discharge where the current channel has a characteristic non-circular cross-section achieved by bounding the discharge by a magnetic separatrix produced when a vacuum octupole magnetic field, generated by currents in external conductors, combines with the self-magnetic field produced by the discharge current. The pinch boundary is changed from a plasma-vacuum boundary to an interface between a high-beta pinch plasma and a low-beta plasma contained in the vacuum magnetic field. The energy that is lost from the pinch region sustains this boundary layer. The introduction of a separatrix boundary around the pinch with four X-point nulls deteriorates the containment of the pinch somewhat. However the presence of the warm, low-beta plasma scrape-off layer, which provides a boundary condition on the pinch, tends to counteract the negative effects of the poorer confinement. Thus the equilibrium parameters that characterize the pinch may not be severely deteriorated by the introduction of the separatrix when the entire configuration, including the scrape-off layer, is considered. (author)
Air Quality and Meteorological Boundary Conditions during the MCMA-2003 Field Campaign
Sosa, G.; Arriaga, J.; Vega, E.; Magaña, V.; Caetano, E.; de Foy, B.; Molina, L. T.; Molina, M. J.; Ramos, R.; Retama, A.; Zaragoza, J.; Martínez, A. P.; Márquez, C.; Cárdenas, B.; Lamb, B.; Velasco, E.; Allwine, E.; Pressley, S.; Westberg, H.; Reyes, R.
2004-12-01
A comprehensive field campaign to characterize photochemical smog in the Mexico City Metropolitan Area (MCMA) was conducted during April 2003. An important number of equipment was deployed all around the urban core and its surroundings to measure gas and particles composition from the various sources and receptor sites. In addition to air quality measurements, meteorology variables were also taken by regular weather meteorological stations, tethered balloons, radiosondes, sodars and lidars. One important issue with regard to the field campaign was the characterization of the boundary conditions in order to feed meteorological and air quality models. Four boundary sites were selected to measure continuously criteria pollutants, VOC and meteorological variables at surface level. Vertical meteorological profiles were measured at three other sites : radiosondes in Tacubaya site were launched every six hours daily; tethered balloons were launched at CENICA and FES-Cuautitlan sites according to the weather conditions, and one sodar was deployed at UNAM site in the south of the city. Additionally to these measurements, two fixed meteorological monitoring networks deployed along the city were available to complement these measurements. In general, we observed that transport of pollutants from the city to the boundary sites changes every day, according to the coupling between synoptic and local winds. This effect were less important at elevated sites such as Cerro de la Catedral and ININ, where synoptic wind were more dominant during the field campaign. Also, local sources nearby boundary sites hide the influence of pollution coming from the city some days, particularly at the La Reforma site.
On the boundary conditions and validity of the neutral shielding model of a refuelling pellet
Chang, C.T.
1982-02-01
By comparing the ablation time of a hydrogen pellet in a tokamak discharge with the time required for the sublimation process, the vaporization of the pellet is shown to be a dynamic phase transition - i.e. the transport of heat is due to the propagation of an evaporation front. Based on this finding, an alternative boundary condition, consistent with the energy conservation law, is formulated. Computational results utilizing the new boundary condition indicate that the ablatant near the pellet surface is hotter and less dense compared with the results which make use of the previous condition of the vanishing flux. The discrepancy between the two solutions becomes less significant once the ablatant reaches the sonic radius. The scaling law of the pellet ablation rate is unaffected by this change of boundary condition. The present analysis shows that the validity of the neutral shielding model is based mainly on the existence of a thin envelope around the pellet where strong energy absorption occurs and is insensitive to the actual vaporization process occuring at the pellet surface. (Auth.)
Influence of the Outer Boundary Condition on models of AGB stars
Wagstaff, G.; Weiss, A.
2018-04-01
Current implementations of the stellar atmosphere typically derive boundary conditions for the interior model from either grey plane-parallel atmospheres or scaled solar atmospheres, neither of which can be considered to have appropriate underlying assumptions for the Thermally Pulsing Asymptotic Giant Branch (TP-AGB). This paper discusses the treatment and influence of the outer boundary condition within stellar evolution codes, and the resulting effects on the AGB evolution. The complex interaction of processes, such as the third dredge up and mass loss, governing the TP-AGB can be affected by varying the treatment of this boundary condition. Presented here are the results from altering the geometry, opacities and the implementation of a grid of MARCS/COMARCS model atmospheres in order to improve this treatment. Although there are changes in the TP-AGB evolution, observable quantities, such as the final core mass, are not significantly altered as a result of the change of atmospheric treatment. During the course of the investigation, a previously unseen phenomena in the AGB models was observed and further investigated. This is believed to be physical, although arising from specific conditions which make its presence unlikely. If it were present in stars, this phenomenon would increase the carbon-star lifetime above 10Myr and increase the final core mass by ˜0.1M⊙ in the narrow initial-mass range where it was observed (˜2 - 2.3M⊙).
Hultgren, Lennart S.; Volino, Ralph J.
2002-01-01
Modern low-pressure turbine airfoils are subject to increasingly stronger pressure gradients as designers impose higher loading in an effort to improve efficiency and to reduce part count. The adverse pressure gradients on the suction side of these airfoils can lead to boundary-layer separation, particularly under cruise conditions. Separation bubbles, notably those which fail to reattach, can result in a significant degradation of engine efficiency. Accurate prediction of separation and reattachment is hence crucial to improved turbine design. This requires an improved understanding of the transition flow physics. Transition may begin before or after separation, depending on the Reynolds number and other flow conditions, has a strong influence on subsequent reattachment, and may even eliminate separation. Further complicating the problem are the high free-stream turbulence levels in a real engine environment, the strong pressure gradients along the airfoils, the curvature of the airfoils, and the unsteadiness associated with wake passing from upstream stages. Because of the complicated flow situation, transition in these devices can take many paths that can coexist, vary in importance, and possibly also interact, at different locations and instances in time. The present work was carried out in an attempt to systematically sort out some of these issues. Detailed velocity measurements were made along a flat plate subject to the same nominal dimensionless pressure gradient as the suction side of a modern low-pressure turbine airfoil ('Pak-B'). The Reynolds number based on wetted plate length and nominal exit velocity, Re, was varied from 50;000 to 300; 000, covering cruise to takeoff conditions. Low, 0.2%, and high, 7%, inlet free-stream turbulence intensities were set using passive grids. These turbulence levels correspond to about 0.2% and 2.5% turbulence intensity in the test section when normalized with the exit velocity. The Reynolds number and free
Bekinschtein, Tristan A.; Peeters, Moos; Shalom, Diego; Sigman, Mariano
2011-01-01
Classical (trace) conditioning is a specific variant of associative learning in which a neutral stimulus leads to the subsequent prediction of an emotionally charged or noxious stimulus after a temporal gap. When conditioning is concurrent with a distraction task, only participants who can report the relationship (the contingency) between stimuli explicitly show associative learning. This suggests that consciousness is a prerequisite for trace conditioning. We review and question three main controversies concerning this view. Firstly, virtually all animals, even invertebrate sea slugs, show this type of learning; secondly, unconsciously perceived stimuli may elicit trace conditioning; and thirdly, some vegetative state patients show trace learning. We discuss and analyze these seemingly contradictory arguments to find the theoretical boundaries of consciousness in classical conditioning. We conclude that trace conditioning remains one of the best measures to test conscious processing in the absence of explicit reports. PMID:22164148
Tristan A Bekinschtein
2011-12-01
Full Text Available Classical (trace conditioning is a specific variant of associative learning in which a neutral stimulus leads to the subsequent prediction of an emotionally charged or noxious stimulus after a temporal gap. When conditioning is concurrent with a distraction task, only participants who can report the relationship (the contingency between stimuli explicitly show associative learning. This suggests that consciousness is a prerequisite for trace conditioning. We review and question three main controversies concerning this view. Firstly, virtually all animals, even invertebrate sea slugs, show this type of learning; secondly, unconsciously perceived stimuli may elicit trace conditioning; and thirdly, some vegetative state patients show trace learning. We discuss and analyze these seemingly contradictory arguments to find the theoretical boundaries of consciousness in classical conditioning. We conclude that trace conditioning remains one of the best measures to test conscious processing in the absence of explicit reports.
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...... to this problem exist, most of them have high computational costs, and stability cannot always be ensured. In this work, a solution is proposed based on "mixing modelling strategies"; this involves separating the FDTD mesh and the boundary conditions (a digital filter representation of the impedance...
Du, Kui
2011-07-01
We consider electromagnetic scattering from two-dimensional (2D) overfilled cavities embedded in an infinite ground plane. The unbounded computational domain is truncated to a bounded one by using a transparent boundary condition (TBC) proposed on a semi-ellipse. For overfilled rectangular cavities with homogeneous media, another TBC is introduced on the cavity apertures, which produces a smaller computational domain. The existence and uniqueness of the solutions of the variational formulations for the transverse magnetic and transverse electric polarizations are established. In the exterior domain, the 2D scattering problem is solved in the elliptic coordinate system using the Mathieu functions. In the interior domain, the problem is solved by a finite element method. Numerical experiments show the efficiency and accuracy of the new boundary conditions.
On flows of viscoelastic fluids under threshold-slip boundary conditions
Baranovskii, E. S.
2018-03-01
We investigate a boundary-value problem for the steady isothermal flow of an incompressible viscoelastic fluid of Oldroyd type in a 3D bounded domain with impermeable walls. We use the Fujita threshold-slip boundary condition. This condition states that the fluid can slip along a solid surface when the shear stresses reach a certain critical value; otherwise the slipping velocity is zero. Assuming that the flow domain is not rotationally symmetric, we prove an existence theorem for the corresponding slip problem in the framework of weak solutions. The proof uses methods for solving variational inequalities with pseudo-monotone operators and convex functionals, the method of introduction of auxiliary viscosity, as well as a passage-to-limit procedure based on energy estimates of approximate solutions, Korn’s inequality, and compactness arguments. Also, some properties and estimates of weak solutions are established.
Validation of a CFD code for Unsteady Flows with cyclic boundary Conditions
Kim, Jong-Tae; Kim, Sang-Baik; Lee, Won-Jae
2006-01-01
Currently Lilac code is under development to analyze thermo-hydraulics of a high-temperature gas-cooled reactor (GCR). Interesting thermo-hydraulic phenomena in a nuclear reactor are usually unsteady and turbulent. The analysis of the unsteady flows by using a three dimension CFD code is time-consuming if the flow domain is very large. Hopefully, flow domains commonly encountered in the nuclear thermo-hydraulics is periodic. So it is better to use the geometrical characteristics in order to reduce the computational resources. To get the benefits from reducing the computation domains especially for the calculations of unsteady flows, the cyclic boundary conditions are implemented in the parallelized CFD code LILAC. In this study, the parallelized cyclic boundary conditions are validated by solving unsteady laminar and turbulent flows past a circular cylinder
Confinement dynamics and boundary condition studies in the Reversed Field Pinch
Schoenberg, K.F.; Ingraham, J.C.; Moses, R.W. Jr.
1988-01-01
The study of confinement dynamics, including investigation of the boundary conditions required for plasma sustainment, are central to the development of the Reversed Field Pinch (RFP) concept. Recently, several insights into confinement have emerged from a detailed investigation RFP electron and ion dynamics. These insights derive from the recognition that both magnetohydrodynamic (MHD) and electron kinetic effects play an important and coupled role in RFP stability, sustainment, and confinement. In this paper, we summarize the results of confinement studies on the ZT-40M experiment, and boundary condition studies on the Wisconsin non-circular RFP experiment. A brief description of the newly commissioned Madison Symmetric Torus (MST) is also presented. 28 refs., 3 figs
Performance advantages of CPML over UPML absorbing boundary conditions in FDTD algorithm
Gvozdic, Branko D.; Djurdjevic, Dusan Z.
2017-01-01
Implementation of absorbing boundary condition (ABC) has a very important role in simulation performance and accuracy in finite difference time domain (FDTD) method. The perfectly matched layer (PML) is the most efficient type of ABC. The aim of this paper is to give detailed insight in and discussion of boundary conditions and hence to simplify the choice of PML used for termination of computational domain in FDTD method. In particular, we demonstrate that using the convolutional PML (CPML) has significant advantages in terms of implementation in FDTD method and reducing computer resources than using uniaxial PML (UPML). An extensive number of numerical experiments has been performed and results have shown that CPML is more efficient in electromagnetic waves absorption. Numerical code is prepared, several problems are analyzed and relative error is calculated and presented.
Influence of Contact Angle Boundary Condition on CFD Simulation of T-Junction
Arias, S.; Montlaur, A.
2018-03-01
In this work, we study the influence of the contact angle boundary condition on 3D CFD simulations of the bubble generation process occurring in a capillary T-junction. Numerical simulations have been performed with the commercial Computational Fluid Dynamics solver ANSYS Fluent v15.0.7. Experimental results serve as a reference to validate numerical results for four independent parameters: the bubble generation frequency, volume, velocity and length. CFD simulations accurately reproduce experimental results both from qualitative and quantitative points of view. Numerical results are very sensitive to the gas-liquid-wall contact angle boundary conditions, confirming that this is a fundamental parameter to obtain accurate CFD results for simulations of this kind of problems.
Futtersack, R., E-mail: romain.futtersack@cea.fr [CEA, IRFM, F-13108 Saint-Paul-lez-Durance (France); Universite Paul Sabatier Toulouse, LAPLACE, 118 Route de Narbonne, F-31062 Toulouse Cedex 9 (France); Tamain, P. [CEA, IRFM, F-13108 Saint-Paul-lez-Durance (France); Hagelaar, G. [Universite Paul Sabatier Toulouse, LAPLACE, 118 Route de Narbonne, F-31062 Toulouse Cedex 9 (France); Ghendrih, Ph.; Simonin, A. [CEA, IRFM, F-13108 Saint-Paul-lez-Durance (France)
2013-07-15
We investigate the impact of both parallel and transverse boundary conditions on the current and charge transport in open field line systems using the TOKAM2D code, which solves a minimal model for interchange turbulence. Various limit test cases are discussed and analyzed. In the parallel direction, the sheath conductivity is found to play an essential role in the stabilization of large-scale potential structures, leading to the formation of transport channel or transport barrier respectively for an insulating end wall or a wall with an enhanced sheath conductivity. On another hand, the addition of transverse boundary conditions intrinsically changes the transport characteristics, influencing both radial profiles and probability density functions. It underlines that in some cases a detailed description of the plasma-wall interaction process is required to get a proper description of the current loop pattern that determines electrostatic turbulent transport.
Reflected forward-backward SDEs and obstacle problems with boundary conditions
Jin Ma
2001-01-01
Full Text Available In this paper we study a class of forward-backward stochastic differential equations with reflecting boundary conditions (FBSDER for short. More precisely, we consider the case in which the forward component of the FBSDER is restricted to a fixed, convex region, and the backward component will stay, at each fixed time, in a convex region that may depend on time and is possibly random. The solvability of such FBSDER is studied in a fairly general way. We also prove that if the coefficients are all deterministic and the backward equation is one-dimensional, then the adapted solution of such FBSDER will give the viscosity solution of a quasilinear variational inequality (obstacle problem with a Neumann boundary condition. As an application, we study how the solvability of FBSDERs is related to the solvability of an American game option.
Effect of reactor finiteness on the boundary condition at the surface of a booster section
Wassef, W.A.
1982-01-01
Effect of reactor finiteness on the boundary condition at the surface of an absorbing booster embedded in the reactor core is studied and formulated. The model used in these calculations depends on the Pl-Transport coupling technique. This method takes into consideration the rigorous neutron transport behavior inside the booster medium, while the Pl-approximation in the bulk of the scattering medium surrounding the booster which can be considered infinite in most practical applications. The neutron flux gradient parallel to the surface of the booster is considered. The geometrical configuration of the reactor core cross section is circular or rectangular. Finiteness of the reactor is introduced in the general formulation through its dimensions or buckling. Extensive numerical results are given to demonstrate the dependence of the boundary condition at the surface of the booster section on the reactor finiteness and the different physical parameters
On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions
Hagendorf, Christian; Liénardy, Jean
2018-03-01
The square-lattice eight-vertex model with vertex weights a, b, c, d obeying the relation (a^2+ab)(b^2+ab) = (c^2+ab)(d^2+ab) and periodic boundary conditions is considered. It is shown that the transfer matrix of the model for L = 2n + 1 vertical lines and periodic boundary conditions along the horizontal direction possesses the doubly degenerate eigenvalue \\Thetan = (a+b){\\hspace{0pt}}2n+1 . This proves a conjecture by Stroganov from 2001. The proof uses the supersymmetry of a related XYZ spin-chain Hamiltonian. The eigenstates of the transfer matrix corresponding to \\Thetan are shown to be the ground states of the spin-chain Hamiltonian. Moreover, for positive vertex weights \\Thetan is the largest eigenvalue of the transfer matrix.
Javeri, V. [Gesellschaft fuer Anlagen- und Reaktorsicherheit (GRS) mbH, Koeln (Germany)
1995-03-01
After implementation of TOUGH2 at GRS in summer 91, it was first used to analyse the gas transport in a repository for the nuclear waste with negligible heat generation and to verify the results obtained with ECLIPSE/JAV 92/. Since the original version of TOUGH2 does not directly simulate the decay of radionuclide and the time dependent boundary conditions, it is not a appropriate tool to study the nuclide transport in a porous medium/PRU 87, PRU 91/. Hence, in this paper some modifications are proposed to study the nuclide transport under combined influence of natural convection diffusion, dispersion and time dependent boundary condition. Here, a single phase fluid with two liquid components is considered as in equation of state model for water and brine/PRU 91A/.
Samira Hosseini
Full Text Available Abstract One of the main drawbacks of Element Free Galerkin (EFG method is its dependence on moving least square shape functions which don’t satisfy the Kronecker Delta property, so in this method it’s not possible to apply Dirichlet boundary conditions directly. The aim of the present paper is to discuss different aspects of three widely used methods of applying Dirichlet boundary conditions in EFG method, called Lagrange multipliers, penalty method, and coupling with finite element method. Numerical simulations are presented to compare the results of these methods form the perspective of accuracy, convergence and computational expense. These methods have been implemented in an object oriented programing environment, called INSANE, and the results are presented and compared with the analytical solutions.
Source-to-Sink: An Earth/Mars Comparison of Boundary Conditions for Eolian Dune Systems
Kocurek, Gary; Ewing, Ryan C.
2012-01-01
Eolian dune fields on Earth and Mars evolve as complex systems within a set of boundary conditions. A source-to-sink comparison indicates that although differences exist in sediment production and transport, the systems largely converge at the dune-flow and pattern-development levels, but again differ in modes of accumulation and preservation. On Earth, where winds frequently exceed threshold speeds, dune fields are sourced primarily through deflation of subaqueous deposits as these sediments...
Discrete maximum principle for Poisson equation with mixed boundary conditions solved by hp-FEM
Vejchodský, Tomáš; Šolín, P.
2009-01-01
Roč. 1, č. 2 (2009), s. 201-214 ISSN 2070-0733 R&D Projects: GA AV ČR IAA100760702; GA ČR(CZ) GA102/07/0496; GA ČR GA102/05/0629 Institutional research plan: CEZ:AV0Z10190503 Keywords : discrete maximum principle * hp-FEM * Poisson equation * mixed boundary conditions Subject RIV: BA - General Mathematics
Makhan'kov, V.G.; Slavov, S.I.
1989-01-01
Vector nonlinear Schroedinger equations (VS3) is investigated under quasi-constant boundary conditions. New two-soliton solutions are obtained with such non-trivial dynamics that they may be called the breather solutions. A version of the basic Novikov-Dubrovin-Krichever algebro-geometrical approach is applied to obtain breather like solutions existing for all types of internal symmetry is specified are formulated in terms of the soliton velocity expressed via the parameters of the problem. 4 refs
Vibrational spectra of four-coordinated random networks with periodic boundary conditions
Guttman, L.
1976-01-01
Examples of perfectly four-coordinated networks satisfying periodic boundary conditions are constructed by a pseudo-random process, starting from a crystalline region. The unphysical features (high density, large deviations from the tetrahedral bond-angle) are removed by systematic modification of the bonding scheme. The vibrational spectra are calculated, using a valence-force potential, and the neutron scattering is computed by a phonon-expansion approximation
Viswanathan, K. K.; Aziz, Z. A.; Javed, Saira; Yaacob, Y. [Universiti Teknologi Malaysia, Johor Bahru (Malaysia); Pullepu, Babuji [S R M University, Chennai (India)
2015-05-15
Free vibration of symmetric angle-ply laminated truncated conical shell is analyzed to determine the effects of frequency parameter and angular frequencies under different boundary condition, ply angles, different material properties and other parameters. The governing equations of motion for truncated conical shell are obtained in terms of displacement functions. The displacement functions are approximated by cubic and quintic splines resulting into a generalized eigenvalue problem. The parametric studies have been made and discussed.
Haslinger, Jaroslav; Kučera, R.; Šátek, V.
2017-01-01
Roč. 22, October 2017 (2017), s. 1-14 ISSN 1081-2865 R&D Projects: GA MŠk LQ1602; GA ČR(CZ) GA17-01747S Institutional support: RVO:68145535 Keywords : Stokes system * threshold slip boundary conditions * solution dependent slip function Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 2.953, year: 2016 http://journals.sagepub.com/doi/abs/10.1177/1081286517716222
Viswanathan, K. K.; Aziz, Z. A.; Javed, Saira; Yaacob, Y.; Pullepu, Babuji
2015-01-01
Free vibration of symmetric angle-ply laminated truncated conical shell is analyzed to determine the effects of frequency parameter and angular frequencies under different boundary condition, ply angles, different material properties and other parameters. The governing equations of motion for truncated conical shell are obtained in terms of displacement functions. The displacement functions are approximated by cubic and quintic splines resulting into a generalized eigenvalue problem. The parametric studies have been made and discussed.
Application of the HN method to the critical slab problem for reflecting boundary conditions
Tuereci, R.G.; Guelecyuez, M.C.; Kaskas, A.; Tezcan, C.
2004-01-01
The recently developed H N method is used to solve the critical slab problem for a slab which is surrounded by a reflector. In the special case for R=0 (the reflection coefficient) the problem reduces to the one under vacuum boundary conditions. It is shown that the method is concise and leads to fast converging numerical results. The presented numerical results are compared with the data available in literature
Frost damage of roof tiles: A study on moisture boundary conditions
Iba, Chiemi; Ueda, Ayumi; Hokoi, Shuichi
2015-01-01
Freeze-thaw cycles are the most serious cause of roof tile deterioration; thus, it is important to know the temperature and moisture distributions in tile materials for protection against frost damage. This study focused on moisture boundary conditions for air layers under the tile. Temperature and humidity were measured using model structures with different types of roof tiles. The results showed that the temperatures around the roof were strongly influenced by solar and longwave radiation, ...
Haslinger, Jaroslav; Kučera, R.; Šátek, V.
2017-01-01
Roč. 22, October 2017 (2017), s. 1-14 ISSN 1081-2865 R&D Projects: GA MŠk LQ1602; GA ČR(CZ) GA17-01747S Institutional support: RVO:68145535 Keywords : Stokes system * threshold slip boundary conditions * solution dependent slip function Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 2.953, year: 2016 http:// journals .sagepub.com/doi/abs/10.1177/1081286517716222
Critical deflagration waves leading to detonation onset under different boundary conditions
Lin Wei; Zhou Jin; Lin Zhi-Yong; Fan Xiao-Hua
2015-01-01
High-speed turbulent critical deflagration waves before detonation onset in H 2 –air mixture propagated into a square cross section channel, which was assembled of optional rigid rough, rigid smooth, or flexible walls. The corresponding propagation characteristic and the influence of the wall boundaries on the propagation were investigated via high-speed shadowgraph and a high-frequency pressure sampling system. As a comprehensive supplement to the different walls effect investigation, the effect of porous absorbing walls on the detonation propagation was also investigated via smoke foils and the high-frequency pressure sampling system. Results are as follows. In the critical deflagration stage, the leading shock and the closely following turbulent flame front travel at a speed of nearly half the CJ detonation velocity. In the preheated zone, a zonary flame arises from the overlapping part of the boundary layer and the pressure waves, and then merges into the mainstream flame. Among these wall boundary conditions, the rigid rough wall plays a most positive role in the formation of the zonary flame and thus accelerates the transition of the deflagration to detonation (DDT), which is due to the boost of the boundary layer growth and the pressure wave reflection. Even though the flexible wall is not conducive to the pressure wave reflection, it brings out a faster boundary layer growth, which plays a more significant role in the zonary flame formation. Additionally, the porous absorbing wall absorbs the transverse wave and yields detonation decay and velocity deficit. After the absorbing wall, below some low initial pressure conditions, no re-initiation occurs and the deflagration propagates in critical deflagration for a relatively long distance. (paper)
Ozone and meteorological boundary-layer conditions at Summit, Greenland, during 3-21 June 2000
Helmig, D.; Boulter, J.; David, D.; Birks, J.W.; Cullen, N.J.; Steffen, K. [University of Colorado, Boulder, CO (United States). Cooperative Institute for Research in Environmental Sciences; Johnson, B.J.; Oltmans, S.J. [National Oceanic and Atmospheric Administration, Boulder, CO (United States). Climate Monitoring and Diagnostics Laboratory
2002-06-01
The temporal and spatial distributions of boundary-layer ozone were studied during June 2000 at Summit, Greenland, using surface-level measurements and vertical profiling from a tethered balloon platform. Three weeks of continuous ozone surface data, 133 meteorological vertical profile data and 82 ozone vertical profile data sets were collected from the surface to a maximum altitude of 1400 m above ground. The lower atmosphere at Summit was characterized by the prevalence of strong stable conditions with strong surface temperature inversions. These inversions reversed to neutral to slightly unstable conditions between {approx} 9.00 and 18.00 h local time with the formation of shallow mixing heights of {approx} 70-250 m above the surface. The surface ozone mixing ratio ranged from 39 to 68 ppbv and occasionally had rapid changes of up to 20 ppb in 12 h. The diurnal mean ozone mixing ratio showed diurnal trends indicating meteorological and photochemical controls of surface ozone. Vertical profiles were within the range of 37-76 ppb and showed strong stratification in the lower troposphere. A high correlation of high ozone/low water vapor air masses indicated the transport of high tropospheric/low stratospheric air into the lower boundary layer. An {approx} 0.1-3 ppb decline of the ozone mixing ratio towards the surface was frequently observed within the neutrally stable mixed layer during midday hours. These data suggest that the boundary-layer ozone mixing ratio and ozone depletion and deposition to the snowpack are influenced by the boundary-layer ozone mixing ratio and ozone depletion and deposition to the snowpack are influenced by photochemical processes and/or transport phenomena that follow diurnal dependencies. With 37 ppb of ozone being the lowest mixing ratio measured in all data no evidence was seen for the occurrence of ozone depletion episodes similar to those that have been reported within the boundary layer at coastal Arctic sites during springtime
Abadi, Mohammad Tahaye
2015-01-01
A recursive solution method is derived for the transient response of one-dimensional structures subjected to the general form of time dependent boundary conditions. Unlike previous solution methods that assumed the separation of variables, the present method involves formulating and solving the dynamic problems using the summation of two single-argument functions satisfying the motion equation. Based on boundary and initial conditions, a recursive procedure is derived to determine the single-argument functions. Such a procedure is applied to the general form of boundary conditions, and an analytical solution is derived by solving the recursive equation. The present solution method is implemented for base excitation problems, and the results are compared with those of the previous analytical solution and the Finite element (FE) analysis. The FE results converge to the present analytical solution, although considerable error is found in predicting a solution method on the basis of the separation of variables. The present analytical solution predicts the transient response for wave propagation problems in broadband excitation frequencies.
Reyes, Jonathan; Shadwick, B. A.
2016-10-01
Modeling the evolution of a short, intense laser pulse propagating through an underdense plasma is of particular interest in the physics of laser-plasma interactions. Numerical models are typically created by first discretizing the equations of motion and then imposing boundary conditions. Using the variational principle of Chen and Sudan, we spatially discretize the Lagrangian density to obtain discrete equations of motion and a discrete energy conservation law which is exactly satisfied regardless of the spatial grid resolution. Modifying the derived equations of motion (e.g., enforcing boundary conditions) generally ruins energy conservation. However, time-dependent terms can be added to the Lagrangian which force the equations of motion to have the desired boundary conditions. Although some foresight is needed to choose these time-dependent terms, this approach provides a mechanism for energy to exit the closed system while allowing the conservation law to account for the loss. An appropriate time discretization scheme is selected based on stability analysis and resolution requirements. We present results using this variational approach in a co-moving coordinate system and compare such results to those using traditional second-order methods. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY- 1104683.
Abadi, Mohammad Tahaye [Aerospace Research Institute, Tehran (Iran, Islamic Republic of)
2015-10-15
A recursive solution method is derived for the transient response of one-dimensional structures subjected to the general form of time dependent boundary conditions. Unlike previous solution methods that assumed the separation of variables, the present method involves formulating and solving the dynamic problems using the summation of two single-argument functions satisfying the motion equation. Based on boundary and initial conditions, a recursive procedure is derived to determine the single-argument functions. Such a procedure is applied to the general form of boundary conditions, and an analytical solution is derived by solving the recursive equation. The present solution method is implemented for base excitation problems, and the results are compared with those of the previous analytical solution and the Finite element (FE) analysis. The FE results converge to the present analytical solution, although considerable error is found in predicting a solution method on the basis of the separation of variables. The present analytical solution predicts the transient response for wave propagation problems in broadband excitation frequencies.
Sahmani, S.; Ansari, R.
2011-01-01
Buckling analysis of nanobeams is investigated using nonlocal continuum beam models of the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), and Levinson beam theory (LBT). To this end, Eringen's equations of nonlocal elasticity are incorporated into the classical beam theories for buckling of nanobeams with rectangular cross-section. In contrast to the classical theories, the nonlocal elastic beam models developed here have the capability to predict critical buckling loads that allowing for the inclusion of size effects. The values of critical buckling loads corresponding to four commonly used boundary conditions are obtained using state-space method. The results are presented for different geometric parameters, boundary conditions, and values of nonlocal parameter to show the effects of each of them in detail. Then the results are fitted with those of molecular dynamics simulations through a nonlinear least square fitting procedure to find the appropriate values of nonlocal parameter for the buckling analysis of nanobeams relevant to each type of nonlocal beam model and boundary conditions analysis
Sahmani, S.; Ansari, R. [University of Guilan, Rasht (Iran, Islamic Republic of)
2011-09-15
Buckling analysis of nanobeams is investigated using nonlocal continuum beam models of the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), and Levinson beam theory (LBT). To this end, Eringen's equations of nonlocal elasticity are incorporated into the classical beam theories for buckling of nanobeams with rectangular cross-section. In contrast to the classical theories, the nonlocal elastic beam models developed here have the capability to predict critical buckling loads that allowing for the inclusion of size effects. The values of critical buckling loads corresponding to four commonly used boundary conditions are obtained using state-space method. The results are presented for different geometric parameters, boundary conditions, and values of nonlocal parameter to show the effects of each of them in detail. Then the results are fitted with those of molecular dynamics simulations through a nonlinear least square fitting procedure to find the appropriate values of nonlocal parameter for the buckling analysis of nanobeams relevant to each type of nonlocal beam model and boundary conditions analysis.
Boundary conditions and dualities: vector fields in AdS/CFT
Marolf, Donald; Ross, Simo F.
2006-01-01
In AdS, scalar fields with masses slightly above the Breitenlohner-Freedman bound admit a variety of possible boundary conditions which are reflected in the Lagrangian of the dual field theory. Generic small changes in the AdS boundary conditions correspond to deformations of the dual field theory by multi-trace operators. Here we extend this discussion to the case of vector gauge fields in the bulk spacetime using the results of Ishibashi and Wald [hep-th/0402184]. As in the context of scalar fields, general boundary conditions for vector fields involve multi-trace deformations which lead to renormalization-group flows. Such flows originate in ultra-violet CFTs which give new gauge/gravity dualities. At least for AdS 4 /CFT 3 , the dual of the bulk photon appears to be a propagating gauge field instead of the usual R-charge current. Applying similar reasoning to tensor fields suggests the existence of a duality between string theory on AdS 4 and a quantum gravity theory in three dimensions
Zhang, Shuhai; Oskay, Caglar
2015-04-01
This manuscript presents the formulation and implementation of the variational multiscale enrichment (VME) method for the analysis of elasto-viscoplastic problems. VME is a global-local approach that allows accurate fine scale representation at small subdomains, where important physical phenomena are likely to occur. The response within far-fields is idealized using a coarse scale representation. The fine scale representation not only approximates the coarse grid residual, but also accounts for the material heterogeneity. A one-parameter family of mixed boundary conditions that range from Dirichlet to Neumann is employed to study the effect of the choice of the boundary conditions at the fine scale on accuracy. The inelastic material behavior is modeled using Perzyna type viscoplasticity coupled with flow stress evolution idealized by the Johnson-Cook model. Numerical verifications are performed to assess the performance of the proposed approach against the direct finite element simulations. The results of verification studies demonstrate that VME with proper boundary conditions accurately model the inelastic response accounting for material heterogeneity.
Natural frequency analysis of fluid conveying pipeline with different boundary conditions
Huang Yimin; Liu Yongshou; Li Baohui; Li Yanjiang; Yue Zhufeng
2010-01-01
In this study, the natural frequency of fluid-structure interaction in pipeline conveying fluid is investigated by eliminated element-Galerkin method, and the natural frequency equations with different boundary conditions are obtained. Furthermore, the expressions of first natural frequency are simplified in the case of different boundary conditions. Taking into account the Coriolis force, as an example, the natural frequency of a straight pipe simply supported at both ends is studied. In a given boundary condition, the four components (mass, stiffness, length and flow velocity) which relate to the natural frequency of pipeline conveying fluid are studied in detail and the results indicate that the effect of Coriolis force on natural frequency is inappreciable. Then the relationship between natural frequency of the pipeline conveying fluid and that of Euler beam is analyzed. Finally, a dimensionless flow velocity and limit values are presented, and they can be used to estimate the effect of the flow velocity on natural frequency. All the conclusions are well suited to nuclear plant and other industry fields.
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.
Effect of boundary conditions on downstream vorticity from counter-rotating swirlers
Weiye Huo
2015-02-01
Full Text Available Particle image velocimetry (PIV is utilized to measure the non-reacting flow field in a reflow combustor with multiple and single swirlers. The velocity field, vortex structure and total vorticity levels are experimentally obtained using two different boundary conditions, representing a single confined swirler and multiple swirlers in an annular combustor. The influence of the boundary conditions on the flow field at several locations downstream of the swirlers is experimentally investigated, showing that the central vortex in the multi-swirler case is more concentrated than in the single-swirler case. The vorticity of the central vortex and average cross-sectional vorticity are relatively low at the swirler outlet in both cases. Both of these statistics gradually increase to the maximum values near 20 mm downstream of the swirler outlet, and subsequently decrease. It is also found that the central vortex in the multi-swirler case is consistently greater than the single-swirler case. These results demonstrate the critical influence of boundary conditions on flow characteristic of swirling flow, providing insight into the difference of the experiments on test-bed combustor and the full-scale annular combustors.
Petar Glišović
2015-01-01
Full Text Available Although there has been significant progress in the seismic imaging of mantle heterogeneity, the outstanding issue that remains to be resolved is the unknown distribution of mantle temperature anomalies in the distant geological past that give rise to the present-day anomalies inferred by global tomography models. To address this question, we present 3-D convection models in compressible and self-gravitating mantle initialised by different hypothetical temperature patterns. A notable feature of our forward convection modelling is the use of self-consistent coupling of the motion of surface tectonic plates to the underlying mantle flow, without imposing prescribed surface velocities (i.e., plate-like boundary condition. As an approximation for the surface mechanical conditions before plate tectonics began to operate we employ the no-slip (rigid boundary condition. A rigid boundary condition demonstrates that the initial thermally-dominated structure is preserved, and its geographical location is fixed during the evolution of mantle flow. Considering the impact of different assumed surface boundary conditions (rigid and plate-like on the evolution of thermal heterogeneity in the mantle we suggest that the intrinsic buoyancy of seven superplumes is most-likely resolved in the tomographic images of present-day mantle thermal structure. Our convection simulations with a plate-like boundary condition reveal that the evolution of an initial cold anomaly beneath the Java-Indonesian trench system yields a long-term, stable pattern of thermal heterogeneity in the lowermost mantle that resembles the present-day Large Low Shear Velocity Provinces (LLSVPs, especially below the Pacific. The evolution of subduction zones may be, however, influenced by the mantle-wide flow driven by deeply-rooted and long-lived superplumes since Archean times. These convection models also detect the intrinsic buoyancy of the Perm Anomaly that has been identified as a unique
N. Bhaskar Reddy
2014-01-01
Full Text Available An analysis is carried out to investigate the influence of variable thermal conductivity and partial velocity slip on hydromagnetic two-dimensional boundary layer flow of a nanofluid with Cu nanoparticles over a stretching sheet with convective boundary condition. Using similarity transformation, the governing boundary layer equations along with the appropriate boundary conditions are transformed to a set of ordinary differential equations. Employing Runge-kutta fourth-order method along with shooting technique, the resultant system of equations is solved. The influence of various pertinent parameters such as nanofluid volume fraction parameter, the magnetic parameter, radiation parameter, thermal conductivity parameter, velocity slip parameter, Biot number, and suction or injection parameter on the velocity of the flow field and heat transfer characteristics is computed numerically and illustrated graphically. The present results are compared with the existing results for the case of regular fluid and found an excellent agreement.
Petracca, S [Salerno Univ. (Italy)
1996-08-01
Debye potentials, the Lorentz reciprocity theorem, and (extended) Leontovich boundary conditions can be used to obtain simple and accurate analytic estimates of the longitudinal and transverse coupling impedances of (piecewise longitudinally uniform) multi-layered pipes with non simple transverse geometry and/or (spatially inhomogeneous) boundary conditions. (author)
Models for Predicting Boundary Conditions in L-Mode Tokamak Plasma
Siriwitpreecha, A.; Onjun, T.; Suwanna, S.; Poolyarat, N.; Picha, R.
2009-07-01
Full text: The models for predicting temperature and density of ions and electrons at boundary conditions in L-mode tokamak plasma are developed using an empirical approach and optimized against the experimental data obtained from the latest public version of the International Pedestal Database (version 3.2). It is assumed that the temperature and density at boundary of L-mode plasma are functions of engineering parameters such as plasma current, toroidal magnetic field, total heating power, line averaged density, hydrogenic particle mass (A H ), major radius, minor radius, and elongation at the separatrix. Multiple regression analysis is carried out for these parameters with 86 data points in L-mode from Aug (61) and JT60U (25). The RMSE of temperature and density at boundary of L-mode plasma are found to be 24.41% and 18.81%, respectively. These boundary models are implemented in BALDUR code, which will be used to simulate the L-mode plasma in the tokamak
Sheng, Yin; Zhang, Hao; Zeng, Zhigang
2017-10-01
This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.
A new technique for observationally derived boundary conditions for space weather
Pagano, Paolo; Mackay, Duncan Hendry; Yeates, Anthony Robinson
2018-04-01
Context. In recent years, space weather research has focused on developing modelling techniques to predict the arrival time and properties of coronal mass ejections (CMEs) at the Earth. The aim of this paper is to propose a new modelling technique suitable for the next generation of Space Weather predictive tools that is both efficient and accurate. The aim of the new approach is to provide interplanetary space weather forecasting models with accurate time dependent boundary conditions of erupting magnetic flux ropes in the upper solar corona. Methods: To produce boundary conditions, we couple two different modelling techniques, MHD simulations and a quasi-static non-potential evolution model. Both are applied on a spatial domain that covers the entire solar surface, although they extend over a different radial distance. The non-potential model uses a time series of observed synoptic magnetograms to drive the non-potential quasi-static evolution of the coronal magnetic field. This allows us to follow the formation and loss of equilibrium of magnetic flux ropes. Following this a MHD simulation captures the dynamic evolution of the erupting flux rope, when it is ejected into interplanetary space. Results.The present paper focuses on the MHD simulations that follow the ejection of magnetic flux ropes to 4 R⊙. We first propose a technique for specifying the pre-eruptive plasma properties in the corona. Next, time dependent MHD simulations describe the ejection of two magnetic flux ropes, that produce time dependent boundary conditions for the magnetic field and plasma at 4 R⊙ that in future may be applied to interplanetary space weather prediction models. Conclusions: In the present paper, we show that the dual use of quasi-static non-potential magnetic field simulations and full time dependent MHD simulations can produce realistic inhomogeneous boundary conditions for space weather forecasting tools. Before a fully operational model can be produced there are a
Gosses, Moritz; Nowak, Wolfgang; Wöhling, Thomas
2018-05-01
In recent years, proper orthogonal decomposition (POD) has become a popular model reduction method in the field of groundwater modeling. It is used to mitigate the problem of long run times that are often associated with physically-based modeling of natural systems, especially for parameter estimation and uncertainty analysis. POD-based techniques reproduce groundwater head fields sufficiently accurate for a variety of applications. However, no study has investigated how POD techniques affect the accuracy of different boundary conditions found in groundwater models. We show that the current treatment of boundary conditions in POD causes inaccuracies for these boundaries in the reduced models. We provide an improved method that splits the POD projection space into a subspace orthogonal to the boundary conditions and a separate subspace that enforces the boundary conditions. To test the method for Dirichlet, Neumann and Cauchy boundary conditions, four simple transient 1D-groundwater models, as well as a more complex 3D model, are set up and reduced both by standard POD and POD with the new extension. We show that, in contrast to standard POD, the new method satisfies both Dirichlet and Neumann boundary conditions. It can also be applied to Cauchy boundaries, where the flux error of standard POD is reduced by its head-independent contribution. The extension essentially shifts the focus of the projection towards the boundary conditions. Therefore, we see a slight trade-off between errors at model boundaries and overall accuracy of the reduced model. The proposed POD extension is recommended where exact treatment of boundary conditions is required.
Heat and mass transfer boundary conditions at the surface of a heated sessile droplet
Ljung, Anna-Lena; Lundström, T. Staffan
2017-12-01
This work numerically investigates how the boundary conditions of a heated sessile water droplet should be defined in order to include effects of both ambient and internal flow. Significance of water vapor, Marangoni convection, separate simulations of the external and internal flow, and influence of contact angle throughout drying is studied. The quasi-steady simulations are carried out with Computational Fluid Dynamics and conduction, natural convection and Marangoni convection are accounted for inside the droplet. For the studied conditions, a noticeable effect of buoyancy due to evaporation is observed. Hence, the inclusion of moisture increases the maximum velocities in the external flow. Marangoni convection will, in its turn, increase the velocity within the droplet with up to three orders of magnitude. Results furthermore show that the internal and ambient flow can be simulated separately for the conditions studied, and the accuracy is improved if the internal temperature gradient is low, e.g. if Marangoni convection is present. Simultaneous simulations of the domains are however preferred at high plate temperatures if both internal and external flows are dominated by buoyancy and natural convection. The importance of a spatially resolved heat and mass transfer boundary condition is, in its turn, increased if the internal velocity is small or if there is a large variation of the transfer coefficients at the surface. Finally, the results indicate that when the internal convective heat transport is small, a rather constant evaporation rate may be obtained throughout the drying at certain conditions.
Homogenization of the stochastic Navier–Stokes equation with a stochastic slip boundary condition
Bessaih, Hakima
2015-11-02
The two-dimensional Navier–Stokes equation in a perforated domain with a dynamical slip boundary condition 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 holes. We consider a scaling (ᵋ for the viscosity and 1 for the density) that will lead to a time-dependent limit problem. However, the noncritical scaling (ᵋ, β > 1) is considered in front of the nonlinear term. The homogenized system in the limit is obtained as a Darcy’s law with memory with two permeabilities and an extra term that is due to the stochastic perturbation on the boundary of the holes. The nonhomogeneity on the boundary contains a stochastic part that yields in the limit an additional term in the Darcy’s law. We use the two-scale convergence method after extending the solution with 0 inside the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. Due to the stochastic integral, the pressure that appears in the variational formulation does not have enough regularity in time. This fact made us rely only on the variational formulation for the passage to the limit on the solution. We obtain a variational formulation for the limit that is solution of a Stokes system with two pressures. This two-scale limit gives rise to three cell problems, two of them give the permeabilities while the third one gives an extra term in the Darcy’s law due to the stochastic perturbation on the boundary of the holes.
Lizal Frantisek
2016-01-01
Full Text Available Correct definition of boundary conditions is crucial for the appropriate simulation of a flow. It is a common practice that simulation of sufficiently long upstream entrance section is performed instead of experimental investigation of the actual conditions at the boundary of the examined area, in the case that the measurement is either impossible or extremely demanding. We focused on the case of a benchmark channel with ventilation outlet, which models a regular automotive ventilation system. At first, measurements of air velocity and turbulence intensity were performed at the boundary of the examined area, i.e. in the rectangular channel 272.5 mm upstream the ventilation outlet. Then, the experimentally acquired results were compared with results obtained by numerical simulation of further upstream entrance section defined according to generally approved theoretical suggestions. The comparison showed that despite the simple geometry and general agreement of average axial velocity, certain difference was found in the shape of the velocity profile. The difference was attributed to the simplifications of the numerical model and the isotropic turbulence assumption of the used turbulence model. The appropriate recommendations were stated for the future work.
Ibukun Sarah Oyelakin
2016-06-01
Full Text Available In this paper we report on combined Dufour and Soret effects on the heat and mass transfer in a Casson nanofluid flow over an unsteady stretching sheet with thermal radiation and heat generation. The effects of partial slip on the velocity at the boundary, convective thermal boundary condition, Brownian and thermophoresis diffusion coefficients on the concentration boundary condition are investigated. The model equations are solved using the spectral relaxation method. The results indicate that the fluid flow, temperature and concentration profiles are significantly influenced by the fluid unsteadiness, the Casson parameter, magnetic parameter and the velocity slip. The effect of increasing the Casson parameter is to suppress the velocity and temperature growth. An increase in the Dufour parameter reduces the flow temperature, while an increase in the value of the Soret parameter causes increase in the concentration of the fluid. Again, increasing the velocity slip parameter reduces the velocity profile whereas increasing the heat generation parameter increases the temperature profile. A validation of the work is presented by comparing the current results with existing literature.
Experimental verification of electrostatic boundary conditions in gate-patterned quantum devices
Hou, H.; Chung, Y.; Rughoobur, G.; Hsiao, T. K.; Nasir, A.; Flewitt, A. J.; Griffiths, J. P.; Farrer, I.; Ritchie, D. A.; Ford, C. J. B.
2018-06-01
In a model of a gate-patterned quantum device, it is important to choose the correct electrostatic boundary conditions (BCs) in order to match experiment. In this study, we model gated-patterned devices in doped and undoped GaAs heterostructures for a variety of BCs. The best match is obtained for an unconstrained surface between the gates, with a dielectric region above it and a frozen layer of surface charge, together with a very deep back boundary. Experimentally, we find a ∼0.2 V offset in pinch-off characteristics of 1D channels in a doped heterostructure before and after etching off a ZnO overlayer, as predicted by the model. Also, we observe a clear quantised current driven by a surface acoustic wave through a lateral induced n-i-n junction in an undoped heterostructure. In the model, the ability to pump electrons in this type of device is highly sensitive to the back BC. Using the improved boundary conditions, it is straightforward to model quantum devices quite accurately using standard software.
Effect of inlet conditions for numerical modelling of the urban boundary layer
Gnatowska, Renata
2018-01-01
The paper presents the numerical results obtained with the use of the ANSYS FLUENT commercial code for analysing the flow structure around two rectangular inline surface-mounted bluff bodies immersed in a boundary layer. The effects of the inflow boundary layer for the accuracy of the numerical modelling of the flow field around a simple system of objects are described. The analysis was performed for two concepts. In the former case, the inlet velocity profile was defined using the power law, whereas the kinetic and dissipation energy was defined from the equations according to Richards and Hoxey [1]. In the latter case, the inlet conditions were calculated for the flow over the rough area composed of the rectangular components.
Adesanya, S.O.; Oluwadare, E.O.; Falade, J.A.; Makinde, O.D.
2015-01-01
In this paper, the free convective flow of magnetohydrodynamic fluid through a channel with time periodic boundary condition is investigated by taking the effects of Joule dissipation into consideration. Based on simplifying assumptions, the coupled governing equations are reduced to a set of nonlinear boundary valued problem. Approximate solutions are obtained by using semi-analytical Adomian decomposition method. The effect of pertinent parameters on the fluid velocity, temperature distribution, Nusselt number and skin friction are presented graphically and discussed. The result of the computation shows that an increase in the magnetic field intensity has significant influence on the fluid flow. - Highlights: • The influence of magnetic field on the free convective fluid flow is considered. • The coupled equations are solved by using Adomian decomposition method. • The Adomian series solution agreed with previously obtained result. • Magnetic field decreases the velocity maximum but enhances temperature field
Strong influence of periodic boundary conditions on lateral diffusion in lipid bilayer membranes
Camley, Brian A. [Center for Theoretical Biological Physics and Department of Physics, University of California, San Diego, California 92093 (United States); Department of Physics, University of California, Santa Barbara, California 93106 (United States); Lerner, Michael G. [Department of Physics and Astronomy, Earlham College, Richmond, Indiana 47374 (United States); Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892 (United States); Pastor, Richard W. [Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892 (United States); Brown, Frank L. H. [Department of Physics, University of California, Santa Barbara, California 93106 (United States); Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106 (United States)
2015-12-28
The Saffman-Delbrück hydrodynamic model for lipid-bilayer membranes is modified to account for the periodic boundary conditions commonly imposed in molecular simulations. Predicted lateral diffusion coefficients for membrane-embedded solid bodies are sensitive to box shape and converge slowly to the limit of infinite box size, raising serious doubts for the prospects of using detailed simulations to accurately predict membrane-protein diffusivities and related transport properties. Estimates for the relative error associated with periodic boundary artifacts are 50% and higher for fully atomistic models in currently feasible simulation boxes. MARTINI simulations of LacY membrane protein diffusion and LacY dimer diffusion in DPPC membranes and lipid diffusion in pure DPPC bilayers support the underlying hydrodynamic model.
Cai, Hongzhu; Hu, Xiangyun; Xiong, Bin
2017-01-01
method which is unconditionally stable. We solve the diffusion equation for the electric field with a total field formulation. The finite element system of equation is solved using the direct method. The solutions of electric field, at different time, can be obtained using the effective time stepping...... method with trivial computation cost once the matrix is factorized. We try to keep the same time step size for a fixed number of steps using an adaptive time step doubling (ATSD) method. The finite element modeling domain is also truncated using a semi-adaptive method. We proposed a new boundary...... condition based on approximating the total field on the modeling boundary using the primary field corresponding to a layered background model. We validate our algorithm using several synthetic model studies....
Strong influence of periodic boundary conditions on lateral diffusion in lipid bilayer membranes
Camley, Brian A.; Lerner, Michael G.; Pastor, Richard W.; Brown, Frank L. H.
2015-01-01
The Saffman-Delbrück hydrodynamic model for lipid-bilayer membranes is modified to account for the periodic boundary conditions commonly imposed in molecular simulations. Predicted lateral diffusion coefficients for membrane-embedded solid bodies are sensitive to box shape and converge slowly to the limit of infinite box size, raising serious doubts for the prospects of using detailed simulations to accurately predict membrane-protein diffusivities and related transport properties. Estimates for the relative error associated with periodic boundary artifacts are 50% and higher for fully atomistic models in currently feasible simulation boxes. MARTINI simulations of LacY membrane protein diffusion and LacY dimer diffusion in DPPC membranes and lipid diffusion in pure DPPC bilayers support the underlying hydrodynamic model
Electrical resistivity discontinuity of iron along the melting curve
Wagle, Fabian; Steinle-Neumann, Gerd
2018-04-01
Discontinuous changes of electrical resistivity ρel (increase), density ϱ and isothermal compressibility βT (decrease) occur across the melting temperature of metals and can be directly related by Ziman's theory in the long-wavelength approximation. By evaluating experimental data at ambient pressure, we show that Ziman's approximation holds for iron and other simple and transition metals. Using a thermodynamic model to determine βT for γ-, ɛ- and liquid Fe and a previously published model for ρel of liquid Fe, we apply Ziman's approximation to calculate ρel of solid Fe along the melting curve. For pure Fe, we find the discontinuity in ρel to decrease with pressure and to be negligibly small at inner core boundary conditions. However, if we account for light element enrichment in the liquid outer core, the electrical resistivity decrease across the inner core boundary is predicted to be as large as 36 per cent.
Marcella, Marc Pace [Ralph M. Parsons Laboratory, Department of Civil and Environmental Engineering, Cambridge, MA (United States); Massachusetts Institute of Technology, Cambridge, Massachusetts (United States); Eltahir, Elfatih A.B. [Massachusetts Institute of Technology, Cambridge, Massachusetts (United States)
2012-01-15
The importance of specifying realistic lateral boundary conditions in the regional modeling of mineral aerosols has not been examined previously. This study examines the impact of assigning values for mineral aerosol (dust) concentrations at the lateral boundaries of Regional Climate Model version 3 (RegCM3) and its aerosol model over Southwest Asia. Currently, the dust emission module of RegCM3 operates over the interior of the domain, allowing dust to be transported to the boundaries, but neglecting any dust emitted at these points or from outside the domain. To account for possible dust occurring at, or entering from the boundaries, mixing ratios of dust concentrations from a larger domain RegCM3 simulation are specified at the boundaries of a smaller domain over Southwest Asia. The lateral boundary conditions are monthly averaged concentration values ({mu}g of dust per kg of dry air) resolved in the vertical for all four dust bin sizes within RegCM3's aerosol model. RegCM3 simulations with the aerosol/dust model including lateral boundary conditions for dust are performed for a five year period and compared to model simulations without prescribed dust concentrations at the boundaries. Results indicate that specifying boundary conditions has a significant impact on dust loading across the entire domain over Southwest Asia. More specifically, a nearly 30% increase in aerosol optical depth occurs during the summer months from specifying realistic dust boundary conditions, bringing model results closer to observations such as MISR. In addition, smaller dust particles at the boundaries have a more important impact than large particles in affecting the dust loading within the interior of this domain. Moreover, increases in aerosol optical depth and dust concentrations within the interior domain are not entirely caused by inflow from the boundaries; results indicate that an increase in the gradient of concentration at the boundaries causes an increase of
Physically-consistent wall boundary conditions for the k-ω turbulence model
Fuhrman, David R.; Dixen, Martin; Jacobsen, Niels Gjøl
2010-01-01
A model solving Reynolds-averaged Navier–Stokes equations, coupled with k-v turbulence closure, is used to simulate steady channel flow on both hydraulically smooth and rough beds. Novel experimental data are used as model validation, with k measured directly from all three components of the fluc......A model solving Reynolds-averaged Navier–Stokes equations, coupled with k-v turbulence closure, is used to simulate steady channel flow on both hydraulically smooth and rough beds. Novel experimental data are used as model validation, with k measured directly from all three components...... of the fluctuating velocity signal. Both conventional k = 0 and dk/dy = 0 wall boundary conditions are considered. Results indicate that either condition can provide accurate solutions, for the bulk of the flow, over both smooth and rough beds. It is argued that the zero-gradient condition is more consistent...... with the near wall physics, however, as it allows direct integration through a viscous sublayer near smooth walls, while avoiding a viscous sublayer near rough walls. This is in contrast to the conventional k = 0 wall boundary condition, which forces resolution of a viscous sublayer in all circumstances...
Reis, Tim
2012-01-01
We present lattice Boltzmann simulations of rarefied flows driven by pressure drops along two-dimensional microchannels. Rarefied effects lead to non-zero cross-channel velocities, nonlinear variations in the pressure along the channel. Both effects are absent in flows driven by uniform body forces. We obtain second-order accuracy for the two components of velocity the pressure relative to asymptotic solutions of the compressible Navier-Stokes equations with slip boundary conditions. Since the common lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier-Maxwell slip boundary conditions that relate the tangential velocity to the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. Our moment formalism is also valuable for analysing the existing boundary conditions. It reveals the origin of numerical slip in the bounce-back other common boundary conditions that impose conditions on the higher moments, not on the local tangential velocity itself. © 2012 American Institute of Physics.
Bardeen, J.M.; Buchman, L.T.
2002-01-01
We investigate how the accuracy and stability of numerical relativity simulations of 1D colliding plane waves depends on choices of equation formulations, gauge conditions, boundary conditions, and numerical methods, all in the context of a first-order 3+1 approach to the Einstein equations, with basic variables some combination of first derivatives of the spatial metric and components of the extrinsic curvature tensor. Hyperbolic schemes, specifically variations on schemes proposed by Bona and Masso and Anderson and York, are compared with variations of the Arnowitt-Deser-Misner formulation. Modifications of the three basic schemes include raising one index in the metric derivative and extrinsic curvature variables and adding a multiple of the energy constraint to the extrinsic curvature evolution equations. Redundant variables in the Bona-Masso formulation may be reset frequently or allowed to evolve freely. Gauge conditions which simplify the dynamical structure of the system are imposed during each time step, but the lapse and shift are reset periodically to control the evolution of the spacetime slicing and the longitudinal part of the metric. We show that physically correct boundary conditions, satisfying the energy and momentum constraint equations, generically require the presence of some ingoing eigenmodes of the characteristic matrix. Numerical methods are developed for the hyperbolic systems based on decomposing flux differences into linear combinations of eigenvectors of the characteristic matrix. These methods are shown to be second-order accurate, and in practice second-order convergent, for smooth solutions, even when the eigenvectors and eigenvalues of the characteristic matrix are spatially varying
Belmiloudi, A.; Mahé, F.
2014-01-01
International audience; The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions J. Numerical si...
Large Scale Skill in Regional Climate Modeling and the Lateral Boundary Condition Scheme
Veljović, K.; Rajković, B.; Mesinger, F.
2009-04-01
Several points are made concerning the somewhat controversial issue of regional climate modeling: should a regional climate model (RCM) be expected to maintain the large scale skill of the driver global model that is supplying its lateral boundary condition (LBC)? Given that this is normally desired, is it able to do so without help via the fairly popular large scale nudging? Specifically, without such nudging, will the RCM kinetic energy necessarily decrease with time compared to that of the driver model or analysis data as suggested by a study using the Regional Atmospheric Modeling System (RAMS)? Finally, can the lateral boundary condition scheme make a difference: is the almost universally used but somewhat costly relaxation scheme necessary for a desirable RCM performance? Experiments are made to explore these questions running the Eta model in two versions differing in the lateral boundary scheme used. One of these schemes is the traditional relaxation scheme, and the other the Eta model scheme in which information is used at the outermost boundary only, and not all variables are prescribed at the outflow boundary. Forecast lateral boundary conditions are used, and results are verified against the analyses. Thus, skill of the two RCM forecasts can be and is compared not only against each other but also against that of the driver global forecast. A novel verification method is used in the manner of customary precipitation verification in that forecast spatial wind speed distribution is verified against analyses by calculating bias adjusted equitable threat scores and bias scores for wind speeds greater than chosen wind speed thresholds. In this way, focusing on a high wind speed value in the upper troposphere, verification of large scale features we suggest can be done in a manner that may be more physically meaningful than verifications via spectral decomposition that are a standard RCM verification method. The results we have at this point are somewhat
Discontinuities and the magnetospheric phenomena
Rajaram, R.; Kalra, G.L.; Tandon, J.N.
1978-01-01
Wave coupling at contact discontinuities has an important bearing on the transmission of waves from the solar wind into the magnetosphere across the cusp region of the solar wind-magnetosphere boundary and on the propagation of geomagnetic pulsations in the polar exosphere. Keeping this in view, the problems of wave coupling across a contact discontinuity in a collisionless plasma, described by a set of double adiabatic fluid equations, is examined. The magnetic field is taken normal to the interface and it is shown that total reflection is not possible for any angle of incidence. The Alfven and the magneto-acoustic waves are not coupled. The transmission is most efficient for small density discontinuities. Inhibition of the transmission of the Alfven wave by the sharp density gradients above the F2-peak in the polar exosphere appears to account for the decrease in the pulsation amplitude, on the ground, as the poles are approached from the auroral zone. (author)
Non-adiabatic pressure loss boundary condition for modelling turbocharger turbine pulsating flow
Chiong, M.S.; Rajoo, S.; Romagnoli, A.; Costall, A.W.; Martinez-Botas, R.F.
2015-01-01
Highlights: • Bespoke non-adiabatic pressure loss boundary for pulse flow turbine modelling. • Predictions show convincing results against experimental and literature data. • Predicted pulse pressure propagation is in good agreement with literature data. • New methodology is time efficient and requires minimal geometrical inputs. - Abstract: This paper presents a simplified methodology of pulse flow turbine modelling, as an alternative over the meanline integrated methodology outlined in previous work, in order to make its application to engine cycle simulation codes much more straight forward. This is enabled through the development of a bespoke non-adiabatic pressure loss boundary to represent the turbine rotor. In this paper, turbocharger turbine pulse flow performance predictions are presented along with a comparison of computation duration against the previously established integrated meanline method. Plots of prediction deviation indicate that the mass flow rate and actual power predictions from both methods are highly comparable and are reasonably close to experimental data. However, the new boundary condition required significantly lower computational time and rotor geometrical inputs. In addition, the pressure wave propagation in this simplified unsteady turbine model at different pulse frequencies has also been found to be in agreement with data from the literature, thereby supporting the confidence in its ability to simulate the wave action encountered in turbine pulse flow operation
Ruggeri, Fabrizio
2016-05-12
In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given prescribed initial condition. We show how to derive the joint likelihood function for the forward problem, given some measurements of the solution field subject to Gaussian noise. Given Gaussian priors for the time-dependent Dirichlet boundary values, we analytically marginalize the joint likelihood using the linearity of the equation. Our hierarchical Bayesian approach is fully implemented in an example that involves the heat equation. In this example, the thermal diffusivity is the unknown parameter. We assume that the thermal diffusivity parameter can be modeled a priori through a lognormal random variable or by means of a space-dependent stationary lognormal random field. Synthetic data are used to test the inference. We exploit the behavior of the non-normalized log posterior distribution of the thermal diffusivity. Then, we use the Laplace method to obtain an approximated Gaussian posterior and therefore avoid costly Markov Chain Monte Carlo computations. Expected information gains and predictive posterior densities for observable quantities are numerically estimated using Laplace approximation for different experimental setups.
A new multistack radiation boundary condition for FDTD based on self-teleportation of fields
Diaz, Rodolfo E.; Scherbatko, Igor
2005-01-01
In [Electromagnetics 23 (2003) 187], a technique for injecting perfect plane waves into finite regions of space in FDTD was reported. The essence of the technique, called Field Teleportation, is to invoke the principle of equivalent sources using FDTDs discrete definition of the curl to copy any field propagating in one FDTD domain to a finite region of another domain. In this paper, we apply this technique of Field Teleportation to the original domain itself to create a transparent boundary across which any outward traveling FDTD field produces an exact negative copy of itself. When this copied field is teleported one cell ahead and one cell forward in time it causes significant self-cancelation of the original field. Illustrative experiments in two-dimensions show that a two-layer (10-cell thick) multi-stack Radiation Boundary Condition (RBC) with a simplest Huygens's termination readily yields reflection coefficients of the order of -80 dB up to grazing incidence for all the fields radiated by a harmonic point source (λ = 30 cells) in free space located 20 cells away from the boundary. Similarly low levels of artificial reflection are demonstrated for a case in which the RBC cuts through five different magnetodielectric materials
Effect of Boundary Condition on the Shear Behaviour of Rock Joints in the Direct Shear Test
Bahaaddini, M.
2017-05-01
The common method for determination of the mechanical properties of the rock joints is the direct shear test. This paper aims to study the effect of boundary condition on the results of direct shear tests. Experimental studies undertaken in this research showed that the peak shear strength is mostly overestimated. This problem is more pronounced for steep asperities and under high normal stresses. Investigation of the failure mode of these samples showed that tensile cracks are generated at the boundary of sample close to the specimen holders and propagated inside the intact materials. In order to discover the reason of observed failure mechanism in experiments, the direct shear test was simulated using PFC2D. Results of numerical models showed that the gap zone size between the upper and lower specimen holders has a significant effect on the shear mechanism. For the high gap size, stresses concentrate at the vicinity of the tips of specimen holders and result in generation and propagation of tensile cracks inside the intact material. However, by reducing the gap size, stresses are concentrated on asperities, and damage of specimen at its boundary is not observed. Results of this paper show that understanding the shear mechanism of rock joints is an essential step prior to interpreting the results of direct shear tests.
Attraction Basins as Gauges of Robustness against Boundary Conditions in Biological Complex Systems
Demongeot, Jacques; Goles, Eric; Morvan, Michel; Noual, Mathilde; Sené, Sylvain
2010-01-01
One fundamental concept in the context of biological systems on which researches have flourished in the past decade is that of the apparent robustness of these systems, i.e., their ability to resist to perturbations or constraints induced by external or boundary elements such as electromagnetic fields acting on neural networks, micro-RNAs acting on genetic networks and even hormone flows acting both on neural and genetic networks. Recent studies have shown the importance of addressing the question of the environmental robustness of biological networks such as neural and genetic networks. In some cases, external regulatory elements can be given a relevant formal representation by assimilating them to or modeling them by boundary conditions. This article presents a generic mathematical approach to understand the influence of boundary elements on the dynamics of regulation networks, considering their attraction basins as gauges of their robustness. The application of this method on a real genetic regulation network will point out a mathematical explanation of a biological phenomenon which has only been observed experimentally until now, namely the necessity of the presence of gibberellin for the flower of the plant Arabidopsis thaliana to develop normally. PMID:20700525
Attraction basins as gauges of robustness against boundary conditions in biological complex systems.
Jacques Demongeot
Full Text Available One fundamental concept in the context of biological systems on which researches have flourished in the past decade is that of the apparent robustness of these systems, i.e., their ability to resist to perturbations or constraints induced by external or boundary elements such as electromagnetic fields acting on neural networks, micro-RNAs acting on genetic networks and even hormone flows acting both on neural and genetic networks. Recent studies have shown the importance of addressing the question of the environmental robustness of biological networks such as neural and genetic networks. In some cases, external regulatory elements can be given a relevant formal representation by assimilating them to or modeling them by boundary conditions. This article presents a generic mathematical approach to understand the influence of boundary elements on the dynamics of regulation networks, considering their attraction basins as gauges of their robustness. The application of this method on a real genetic regulation network will point out a mathematical explanation of a biological phenomenon which has only been observed experimentally until now, namely the necessity of the presence of gibberellin for the flower of the plant Arabidopsis thaliana to develop normally.
Pratt, L.R.; Haan, S.W.
1981-01-01
An exact formal theory for the effects of periodic boundary conditions on the equilibrium properties of computer simulated classical many-body systems is developed. This is done by observing that use of the usual periodic conditions is equivalent to the study of a certain supermolecular liquid, in which a supermolecule is a polyatomic molecule of infinite extent composed of one of the physical particles in the system plus all its periodic images. For this supermolecular system in the grand ensemble, all the cluster expansion techniques used in the study of real molecular liquids are directly applicable. As expected, particle correlations are translationally uniform, but explicitly anisotropic. When the intermolecular potential energy functions are of short enough range, or cut off, so that the minimum image method is used, evaluation of the cluster integrals is dramatically simplified. In this circumstance, a large and important class of cluster expansion contributions can be summed exactly, and expressed in terms of the correlation functions which result when the system size is allowed to increase without bound. This result yields a simple and useful approximation to the corrections to the particle correlations due to the use of periodic boundary conditions with finite systems. Numerical application of these results are reported in the following paper
Development of mapped stress-field boundary conditions based on a Hill-type muscle model.
Cardiff, P; Karač, A; FitzPatrick, D; Flavin, R; Ivanković, A
2014-09-01
Forces generated in the muscles and tendons actuate the movement of the skeleton. Accurate estimation and application of these musculotendon forces in a continuum model is not a trivial matter. Frequently, musculotendon attachments are approximated as point forces; however, accurate estimation of local mechanics requires a more realistic application of musculotendon forces. This paper describes the development of mapped Hill-type muscle models as boundary conditions for a finite volume model of the hip joint, where the calculated muscle fibres map continuously between attachment sites. The applied muscle forces are calculated using active Hill-type models, where input electromyography signals are determined from gait analysis. Realistic muscle attachment sites are determined directly from tomography images. The mapped muscle boundary conditions, implemented in a finite volume structural OpenFOAM (ESI-OpenCFD, Bracknell, UK) solver, are employed to simulate the mid-stance phase of gait using a patient-specific natural hip joint, and a comparison is performed with the standard point load muscle approach. It is concluded that physiological joint loading is not accurately represented by simplistic muscle point loading conditions; however, when contact pressures are of sole interest, simplifying assumptions with regard to muscular forces may be valid. Copyright © 2014 John Wiley & Sons, Ltd.
Dressing method and quadratic bundles related to symmetric spaces. Vanishing boundary conditions
Valchev, T. I.
2016-02-01
We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m + n)/S(U(m) × U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear Schrödinger equation which serves as a motivational example for our general considerations. We extensively discuss how one can apply Zakharov-Shabat's dressing procedure to derive reflectionless potentials obeying zero boundary conditions. Those could be used for one to construct fast decaying solutions to any nonlinear equation belonging to the same hierarchy. One can distinguish between generic soliton type solutions and rational solutions.
Streamline Patterns and their Bifurcations near a wall with Navier slip Boundary Conditions
Tophøj, Laust; Møller, Søren; Brøns, Morten
2006-01-01
We consider the two-dimensional topology of streamlines near a surface where the Navier slip boundary condition applies. Using transformations to bring the streamfunction in a simple normal form, we obtain bifurcation diagrams of streamline patterns under variation of one or two external parameters....... Topologically, these are identical with the ones previously found for no-slip surfaces. We use the theory to analyze the Stokes flow inside a circle, and show how it can be used to predict new bifurcation phenomena. ©2006 American Institute of Physics...
Silva, Davi J.M.; Nunes, Carlos E.A.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: davijmsilva@yahoo.com.br, E-mail: ceanunes@yahoo.com.br, E-mail: rcbarros@pq.cnpq.br [Secretaria Municipal de Educacao de Itaborai, RJ (Brazil); Universidade Estacio de Sa (UNESA), Rio de Janeiro, RJ (Brazil); Universidade do Estado do Rio de Janeiro (UERJ), Novra Friburgo, RJ (Brazil). Instituto Politecnico. Departamento de Modelagem Computacional
2017-11-01
Discussed here is the accuracy of approximate albedo boundary conditions for energy multigroup discrete ordinates (S{sub N}) eigenvalue problems in two-dimensional rectangular geometry for criticality calculations in neutron fission reacting systems, such as nuclear reactors. The multigroup (S{sub N}) albedo matrix substitutes approximately the non-multiplying media around the core, e.g., baffle and reflector, as we neglect the transverse leakage terms within these non-multiplying regions. Numerical results to a typical model problem are given to illustrate the accuracy versus the computer running time. (author)
Influence of the boundary conditions on heat and mass transfer in spacer-filled channels
Ciofalo, M.; La Cerva, M. F.; Di Liberto, M.; Tamburini, A.
2017-11-01
The purpose of this study is to discuss some problems which arise in heat or mass transfer in complex channels, with special reference to the spacer-filled channels adopted in membrane processes. Among the issues addressed are the consistent definition of local and mean heat or mass transfer coefficients; the influence of the wall boundary conditions; the influence of one-side versus two-side heat/mass transfer. Most of the results discussed were obtained by finite volume CFD simulations concerning heat transfer in Membrane Distillation or mass transfer in Electrodialysis and Reverse Electrodialysis, but many of the conclusions apply also to different processes involving geometrically complex channels
Analytical solutions of couple stress fluid flows with slip boundary conditions
Devakar M.
2014-09-01
Full Text Available In the present article, the exact solutions for fundamental flows namely Couette, Poiseuille and generalized Couette flows of an incompressible couple stress fluid between parallel plates are obtained using slip boundary conditions. The effect of various parameters on velocity for each problem is discussed. It is found that, for each of the problems, the solution in the limiting case as couple stresses approaches to zero is similar to that of classical viscous Newtonian fluid. The results indicate that, the presence of couple stresses decreases the velocity of the fluid.
Lattice study of D and D{sub s} meson form factors with twisted boundary conditions
Li, Ning; Wu, Ya-Jie [Xi' an Technological University, School of Science, Xi' an (China)
2017-03-15
We present results on the D and D{sub s} meson electromagnetic form factors using N{sub f} = 2 twisted mass Lattice Quantum Chromodynamics (LQCD) gauge configurations. In this simulation, to access spatial components of momenta that are different from the integer multiples of 2π/L, we apply twisted boundary conditions to compute corresponding correlation functions. Electromagnetic form factors with more small four-momentum transfer are determined, and further we fit the electromagnetic charge radius for D and D{sub s} mesons, respectively. (orig.)
Aqlan Mohammed H.
2016-01-01
Full Text Available We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration but also yield some new special cases for specific choices of parameters involved in the problems.
Effects from magnetic boundary conditions in superconducting-magnetic proximity systems
Thomas E. Baker
2016-05-01
Full Text Available A superconductor-magnetic proximity system displays singlet-triplet pair correlations in the magnetization as a function of inhomogeneities of the magnetic profile. We discuss how the magnetic boundary conditions affects differently the curvature and winding number of rotating magnetizations in the three commonly used structures to generate long range triplet components: an exchange spring, a helical structure and a misaligned magnetic multilayer. We conclude that the choice of the system is dictated by the goal one wishes to achieve in designing a spintronic device but note that only the exchange spring presently offers an experimentally realizable magnetic profile that is tunable.
Sun, Xiaoyan, E-mail: sunxiaoyan1@gmail.com [College of Physics and Electronic Engineering, Guangxi Teacher Education University, Nanning 530001 (China); Xie, Yanbo [Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China); He, Zhiwei [College of Science, China Agricultural University, Beijing 100083 (China); Wang, Binghong [Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China)
2011-07-11
This Letter investigates a totally asymmetric simple exclusion process (TASEP) with junctions in a one-dimensional transport system. Parallel update rules and periodic boundary condition are adopted. Two cases corresponding to different update rules are studied. The results show that the stationary states of system mainly depend on the selection behavior of particle at the bifurcation point. -- Highlights: → For no preference case, the system exists three stationary phases. → For preference case, the system exists five stationary phases. → The road lengths have not qualitative influence on the fundamental diagram.
Nkoma, J.S.
1982-08-01
The effects of three additional boundary conditions (ABC's) on the reflection and transmission spectra for exciton polaritons propagating in a spatially dispersive media are studied for both p and s configurations. An investigation of the ratios of the electric field amplitudes associated with the normal modes in these media is carried out. There is qualitative agreement among the predictions of the different ABC's, but there are significant quantitative differences, especially in the longitudinal polariton spike excited only in the p-geometry. Contact with formulations not using the ABC approach is made. The results are illustrated by parameters modelling the 1s exciton of PbI 2 . (author)
Finite temperature LGT in a finite box with BPS monopole boundary conditions
Ilgenfritz, E.-M.; Molodtsov, S.V.; Mueller-Preussker, M.; Veselov, A.I.
1999-01-01
Finite temperature SU(2) lattice gauge theory is investigated in a 3D cubic box with fixed boundary conditions (b.c.) provided by a discretized, static BPS monopole solution with varying core scale μ. For discrete μ-values we find stable classical solutions either of electro-magnetic ('dyon') or of purely magnetic type inside the box. Near the deconfinement transition we study the influence of the b.c. on the quantized fields inside the box. In contrast to the purely magnetic background field case, for the dyon case we observe confinement for temperatures above the usual critical one
Peristaltic flow of Johnson-Segalman fluid in asymmetric channel with convective boundary conditions
H YASMIN; T HAYAT; A ALSAEDI; HH ALSULAMI
2014-01-01
This work is concerned with the peristaltic transport of the Johnson-Segalman fluid in an asymmetric channel with convective boundary conditions. The mathematical modeling is based upon the conservation laws of mass, linear momentum, and energy. The resulting equations are solved after long wavelength and low Reynolds number are used. The results for the axial pressure gradient, velocity, and temperature profiles are obtained for small Weissenberg number. The expressions of the pressure gra-dient, velocity, and temperature are analyzed for various embedded parameters. Pumping and trapping phenomena are also explored.
Rehman, Aman-ur; Pu Yikang
2005-01-01
When the finiteness of plasma geometry is taken into account, the expression for classical skin depth is different from the one obtained for an unbounded plasma (for both the planar and cylindrical geometries). This change in the expression of the classical skin depth also changes the nonlocality parameter, which is defined as the square of the ratio of the effective mean free path to the classical skin depth. It is concluded that it is the compactness of the geometry due to the metallic boundary condition (E=0) that impacts nonlocal heating (particularly in the low-frequency regime) rather than the shape of the geometry
Analysis of the susceptibility in a fluid system with Neumann – plus boundary conditions
Djondjorov Peter
2018-01-01
Full Text Available The behaviour of the local and total susceptibilities of a fluid system bounded by different surfaces is studied in the framework of the Ginsburg-Landau Ising type model. The case of a plain geometry, Neumann-infinity boundary conditions under variations of the temperature and an external ordering field is considered. Exact analytic expressions for the order parameter, local and total susceptibilities in such a system are presented. They are used to analyse the phase behaviour of fluids confined in regions close to the bulk critical point of the respective infinite system.
Janssen, Hans; Blocken, Bert; Roels, Staf
2007-01-01
While the numerical simulation of moisture transfer inside building components is currently undergoing standardisation, the modelling of the atmospheric boundary conditions has received far less attention. This article analyses the modelling of the wind-driven-rain load on building facades...... though: the full variability with the perpendicular wind speed and horizontal rain intensity should be preserved, where feasible, for improved estimations of the moisture transfer in building components. In the concluding section, it is moreover shown that the dependence of the surface moisture transfer...
Analytic theory of curvature effects for wave problems with general boundary conditions
Willatzen, Morten; Gravesen, Jens; Voon, L. C. Lew Yan
2010-01-01
A formalism based on a combination of differential geometry and perturbation theory is used to obtain analytic expressions for confined eigenmode changes due to general curvature effects. In cases of circular-shaped and helix-shaped structures, where alternative analytic solutions can be found......, the perturbative solution is shown to yield the same result. The present technique allows the generalization of earlier results to arbitrary boundary conditions. The power of the method is illustrated using examples based on Maxwell’s and Schrödinger’s equations for applications in photonics and nanoelectronics....
Yoon, Gil Ho; Park, Y.K.; Kim, Y.Y.
2007-01-01
A new topology optimization scheme, called the element stacking method, is developed to better handle design optimization involving material-dependent boundary conditions and selection of elements of different types. If these problems are solved by existing standard approaches, complicated finite...... element models or topology optimization reformulation may be necessary. The key idea of the proposed method is to stack multiple elements on the same discretization pixel and select a single or no element. In this method, stacked elements on the same pixel have the same coordinates but may have...... independent degrees of freedom. Some test problems are considered to check the effectiveness of the proposed stacking method....
Lam, Yun Fat; Cheung, Hung Ming; Fu, Joshua; Huang, Kan
2015-04-01
Applying Global Chemistry Model (GCM) for regional Boundary Conditions (BC) has become a common practice to account for long-range transport of air pollutants in the regional air quality modeling. The limited domain model such as CMAQ and CAMx requires a global BC to prescribe the real-time chemical flux at the boundary grids, in order to give a realistic estimate of boundary impacts. Several GCMs have become available recently for use in regional air quality studies. In this study, three GCM models (i.e., GEOS-chem, CHASER and IFS-CB05 MACC provided by Seoul National University, Nagoya University and ECWMF, respectively) for the year of 2010 were applied in CMAQ for the East Asia domain under the framework of Model Inter-comparison Study Asia Phase III (MISC-Asia III) and task force on Hemispheric Transport of Air Pollution (HTAP) jointed experiments. Model performance evaluations on vertical profile and spatial distribution of O3 and PM2.5 have been made on those three models to better understand the model uncertainties from the boundary conditions. Individual analyses on various mega-cities (i.e., Hong Kong, Guangzhou, Taipei, Chongqing, Shanghai, Beijing, Tianjin, Seoul and Tokyo) were also performed. Our analysis found that the monthly estimates of O3 for CHASER were a bit higher than GEOS-Chem and IFS-CB05 MACC, particularly in the northern part of China in the winter and spring, while the monthly averages of PM2.5 in GEOS-Chem were the lowest among the three models. The hourly maximum values of PM2.5 from those three models (GEOS-Chem, CHASER and IFS-CB05 MACC are 450, 321, 331 μg/m3, while the maximum O3 are 158, 212, 380 ppbv, respectively. Cross-comparison of CMAQ results from the 45 km resolution were also made to investigate the boundary impacts from the global GCMs. The results presented here provide insight on how global GCM selection influences the regional air quality simulation in East Asia.
Pheiffer, Thomas S; Ou, Jao J; Ong, Rowena E; Miga, Michael I
2011-09-01
Modality-independent elastography (MIE) is a method of elastography that reconstructs the elastic properties of tissue using images acquired under different loading conditions and a biomechanical model. Boundary conditions are a critical input to the algorithm and are often determined by time-consuming point correspondence methods requiring manual user input. This study presents a novel method of automatically generating boundary conditions by nonrigidly registering two image sets with a demons diffusion-based registration algorithm. The use of this method was successfully performed in silico using magnetic resonance and X-ray-computed tomography image data with known boundary conditions. These preliminary results produced boundary conditions with an accuracy of up to 80% compared to the known conditions. Demons-based boundary conditions were utilized within a 3-D MIE reconstruction to determine an elasticity contrast ratio between tumor and normal tissue. Two phantom experiments were then conducted to further test the accuracy of the demons boundary conditions and the MIE reconstruction arising from the use of these conditions. Preliminary results show a reasonable characterization of the material properties on this first attempt and a significant improvement in the automation level and viability of the method.
Heat Kernel Asymptotics of Zaremba Boundary Value Problem
Avramidi, Ivan G. [Department of Mathematics, New Mexico Institute of Mining and Technology (United States)], E-mail: iavramid@nmt.edu
2004-03-15
The Zaremba boundary-value problem is a boundary value problem for Laplace-type second-order partial differential operators acting on smooth sections of a vector bundle over a smooth compact Riemannian manifold with smooth boundary but with discontinuous boundary conditions, which include Dirichlet boundary conditions on one part of the boundary and Neumann boundary conditions on another part of the boundary. We study the heat kernel asymptotics of Zaremba boundary value problem. The construction of the asymptotic solution of the heat equation is described in detail and the heat kernel is computed explicitly in the leading approximation. Some of the first nontrivial coefficients of the heat kernel asymptotic expansion are computed explicitly.
Bashir Ahmad
2013-02-01
Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented.
The effect of adiabatic and conducting wall boundary conditions on LES of a thermal mixing tee
Howard, Richard J.A.; Pasutto, Thomas
2009-01-01
In this paper preliminary LES simulations are carried out of the FATHERINO mixing T junction experiment. In this experiment 80degC hot water enters a lateral steel pipe which has a diameter of D=0.054m, at a speed of 1.04m/s and meets 5degC cold water which enters a perpendicular steel pipe branch that also has a diameter D=0.054m but this time at a lower speed of 0.26m/s. The modelling of the steel pipe walls is tested by comparing adiabatic and 1D conducting wall boundary conditions. The numerical grid used contains approximately 440,000 hexahedral elements. The near wall refinement is not sufficient to resolve the near wall boundary layer (y + approx. = 32) and a standard logarithmic boundary condition is used. A method known as the synthetic eddy method is used to generate the turbulent flow at the pipe inlets. Three different LES models are used (Smagorinsky, dynamic Smagorinsky and wale) to resolve the subgrid turbulent motion beyond the wall grid. An additional test is carried out where no subgrid model is used with only the wall modelling being applied. The results show that the wale model generates much less resolved turbulence than the other cases and this model shows virtually no difference between the two methods of wall thermal modelling. The dynamic Smagorinsky model shows that, downstream of the mixing T, the lower wall remains at a lower temperature for longer when the adiabatic boundary condition is applied. The Smagorinsky model is found to produce the highest level of resolved temperature fluctuation. For this model the 1D thermal modelling approach increases the unsteadiness of both the velocity and temperature fields at the onset of the mixing and in the middle of the pipe downstream of the T junction. However near the lower wall the 1D thermal modelling approach tends to reduce the unsteadiness. The case with no subgrid modelling shows higher levels of turbulence kinetic energy but lower levels of temperature fluctuation than the cases with
Kupka, F.
1997-11-01
This thesis deals with the extension of sparse grid techniques to spectral methods for the solution of partial differential equations with periodic boundary conditions. A review on boundary and initial-boundary value problems and a discussion on numerical resolution is used to motivate this research. Spectral methods are introduced by projection techniques, and by three model problems: the stationary and the transient Helmholtz equations, and the linear advection equation. The approximation theory on the hyperbolic cross is reviewed and its close relation to sparse grids is demonstrated. This approach extends to non-periodic problems. Various Sobolev spaces with dominant mixed derivative are introduced to provide error estimates for Fourier approximation and interpolation on the hyperbolic cross and on sparse grids by means of Sobolev norms. The theorems are immediately applicable to the stability and convergence analysis of sparse grid spectral methods. This is explicitly demonstrated for the three model problems. A variant of the von Neumann condition is introduced to simplify the stability analysis of the time-dependent model problems. The discrete Fourier transformation on sparse grids is discussed together with its software implementation. Results on numerical experiments are used to illustrate the performance of the new method with respect to the smoothness properties of each example. The potential of the method in mathematical modelling is estimated and generalizations to other sparse grid methods are suggested. The appendix includes a complete Fortran90 program to solve the linear advection equation by the sparse grid Fourier collocation method and a third-order Runge-Kutta routine for integration in time. (author)
Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation
Ryaben'kii, V. S.; Tsynkov, S. V.; Turchaninov, V. I.
2001-12-01
We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special nondeteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of “nonreflecting kernels” nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The nondeteriorating algorithm, which is the core of the new ABCs, is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimensional spaces. It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the unmodified scheme. In this paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABC algorithm.
Advanced quadratures and periodic boundary conditions in parallel 3D Sn transport
Manalo, K.; Yi, C.; Huang, M.; Sjoden, G.
2013-01-01
Significant updates in numerical quadratures have warranted investigation with 3D Sn discrete ordinates transport. We show new applications of quadrature departing from level symmetric ( 2 o) and Pn-Tn (>S 2 o). investigating 3 recently developed quadratures: Even-Odd (EO), Linear-Discontinuous Finite Element - Surface Area (LDFE-SA), and the non-symmetric Icosahedral Quadrature (IC). We discuss implementation changes to 3D Sn codes (applied to Hybrid MOC-Sn TITAN and 3D parallel PENTRAN) that can be performed to accommodate Icosahedral Quadrature, as this quadrature is not 90-degree rotation invariant. In particular, as demonstrated using PENTRAN, the properties of Icosahedral Quadrature are suitable for trivial application using periodic BCs versus that of reflective BCs. In addition to implementing periodic BCs for 3D Sn PENTRAN, we implemented a technique termed 'angular re-sweep' which properly conditions periodic BCs for outer eigenvalue iterative loop convergence. As demonstrated by two simple transport problems (3-group fixed source and 3-group reflected/periodic eigenvalue pin cell), we remark that all of the quadratures we investigated are generally superior to level symmetric quadrature, with Icosahedral Quadrature performing the most efficiently for problems tested. (authors)
Zhong, Rui; Wang, Qingshan; Tang, Jinyuan; Shuai, Cijun; Liang, Qian
2018-02-01
This paper presents the first known vibration characteristics of moderately thick functionally graded carbon nanotube reinforced composite rectangular plates on Pasternak foundation with arbitrary boundary conditions and internal line supports on the basis of the firstorder shear deformation theory. Different distributions of single walled carbon nanotubes (SWCNTs) along the thickness are considered. Uniform and other three kinds of functionally graded distributions of carbon nanotubes along the thickness direction of plates are studied. The solutions carried out using an enhanced Ritz method mainly include the following three points: Firstly, create the Lagrange energy function by the energy principle; Secondly, as the main innovation point, the modified Fourier series are chosen as the basic functions of the admissible functions of the plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges; Lastly, solve the natural frequencies as well as the associated mode shapes by means of the Ritz-variational energy method. In this study, the influences of the volume fraction of CNTs, distribution type of CNTs, boundary restrain parameters, location of the internal line supports, foundation coefficients on the natural frequencies and mode shapes of the FG-CNT reinforced composite rectangular plates are presented.
Chiruta, Daniel [GEMaC, Université de Versailles Saint-Quentin-en-Yvelines, CNRS-UVSQ (UMR 8635), 78035 Versailles Cedex (France); Faculty of Electrical Engineering and Computer Science, Stefan cel Mare University, Suceava 720229 (Romania); Linares, Jorge, E-mail: jorge.linares@uvsq.fr, E-mail: miya@spin.phys.s.u-tokyo.ac.jp; Boukheddaden, Kamel [GEMaC, Université de Versailles Saint-Quentin-en-Yvelines, CNRS-UVSQ (UMR 8635), 78035 Versailles Cedex (France); Miyashita, Seiji, E-mail: jorge.linares@uvsq.fr, E-mail: miya@spin.phys.s.u-tokyo.ac.jp [Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-Ku, Tokyo (Japan); CREST, JST, 4-1-8 Honcho Kawaguchi, Saitama 332-0012 (Japan)
2014-05-21
In order to explain clearly the role of the open boundary conditions (OBCs) on phase transition in one dimensional system, we consider an Ising model with both short-range (J) and long-range (G) interactions, which has allowed us to study the cooperative nature of spin-crossover (SCO) materials at the nanometer scale. At this end, we developed a transfer-matrix method for one-dimensional (1D) SCO system with free boundary conditions, and we give numerical evidences for how the thermal spin transition curves vary as a function of the physical parameters (J, G) or an applied pressure. Moreover for OBCs case, we have derived the bulk, surface and finite-size contributions to the free energy and we have investigated the variation of these energies as function of J and system size. We have found that the surface free energy behaves like J〈σ〉{sup 2}, where 〈σ〉 is the average magnetization per site. Since the properties of the nanometric scale are dramatically influenced by the system's size (N), our analytical outcomes for the size dependence represent a step to achieve new characteristic of the future devices and also a way to find various novel properties which are absent in the bulk materials.
Hermitian boundary conditions at a Dirichlet singularity: the Marletta--Rozenblum model
Berry, M V
2009-01-01
In domains B with smoothly-varying boundary conditions, points where wavefunctions are required to vanish were recently identified as 'Dirichlet singularities' (D points) where the Hamiltonian H does not define discrete eigenvalues and a scattering phase is undetermined (Berry and Dennis 2008 J. Phys. A: Math. Theor. 41 135203). This is explained (Marletta and Rozenblum 2009 J. Phys. A: Math. Theor. 42 125204) by the observation, illustrated with an exactly-solvable separable model, that a D point requires the specification of an additional parameter defining a family of self-adjoint extensions of H. Here the underlying theory is presented in an elementary way, and a D point is identified as a leak, through which current can flow into or out of B. Hermiticity seals the leak, ensuring that no current flows though the D point (as well as across the boundary of B). The solvable model is examined in detail for bound states, where B is a semidisk, and for wave reflections, where B is a half-plane. The quantization condition for a nonseparable billiard is obtained explicitly
Boyarchenkov, A.S.; Potashnikov, S.I.; Nekrasov, K.A.; Kupryazhkin, A.Ya.
2012-01-01
Highlights: ► We perform MD simulation of UO 2 nanocrystals melting (in range of 768–49 152 ions). ► T(P) melting curves intersect zero near −20 GPa and saturate near 25 GPa. ► Reciprocal size dependences of nanocrystal melting point decrease nonlinearly. ► Linear and parabolic extrapolations to macroscopic values are considered. ► Melting point and density jump are reproduced, but heat of fusion is underestimated. - Abstract: Melting of uranium dioxide (UO 2 ) nanocrystals has been studied by molecular dynamics (MD) simulation. Ten recent and widely used sets of pair potentials were assessed in the rigid ion approximation. Both isolated (in vacuum) and periodic boundary conditions (PBC) were explored. Using barostat under PBC the pressure dependences of melting point were obtained. These curves intersected zero near −20 GPa, saturated near 25 GPa and increased nonlinearly in between. Using simulation of surface under isolated boundary conditions (IBC) recommended melting temperature and density jump were successfully reproduced. However, the heat of fusion is still underestimated. These melting characteristics were calculated for nanocrystals of cubic shape in the range of 768–49 152 particles (volume range of 10–1000 nm 3 ). The obtained reciprocal size dependences decreased nonlinearly. Linear and parabolic extrapolations to macroscopic values are considered. The parabolic one is found to be better suited for analysis of the data on temperature and heat of melting.
Greenland Regional and Ice Sheet-wide Geometry Sensitivity to Boundary and Initial conditions
Logan, L. C.; Narayanan, S. H. K.; Greve, R.; Heimbach, P.
2017-12-01
Ice sheet and glacier model outputs require inputs from uncertainly known initial and boundary conditions, and other parameters. Conservation and constitutive equations formalize the relationship between model inputs and outputs, and the sensitivity of model-derived quantities of interest (e.g., ice sheet volume above floatation) to model variables can be obtained via the adjoint model of an ice sheet. We show how one particular ice sheet model, SICOPOLIS (SImulation COde for POLythermal Ice Sheets), depends on these inputs through comprehensive adjoint-based sensitivity analyses. SICOPOLIS discretizes the shallow-ice and shallow-shelf approximations for ice flow, and is well-suited for paleo-studies of Greenland and Antarctica, among other computational domains. The adjoint model of SICOPOLIS was developed via algorithmic differentiation, facilitated by the source transformation tool OpenAD (developed at Argonne National Lab). While model sensitivity to various inputs can be computed by costly methods involving input perturbation simulations, the time-dependent adjoint model of SICOPOLIS delivers model sensitivities to initial and boundary conditions throughout time at lower cost. Here, we explore both the sensitivities of the Greenland Ice Sheet's entire and regional volumes to: initial ice thickness, precipitation, basal sliding, and geothermal flux over the Holocene epoch. Sensitivity studies such as described here are now accessible to the modeling community, based on the latest version of SICOPOLIS that has been adapted for OpenAD to generate correct and efficient adjoint code.
Buckling of Nonprismatic Column on Varying Elastic Foundation with Arbitrary Boundary Conditions
Ahmad A. Ghadban
2017-01-01
Full Text Available Buckling of nonprismatic single columns with arbitrary boundary conditions resting on a nonuniform elastic foundation may be considered as the most generalized treatment of the subject. The buckling differential equation for such columns is extremely difficult to solve analytically. Thus, the authors propose a numerical approach by discretizing the column into a finite number of segments. Each segment has constants E (modulus of elasticity, I (moment of inertia, and β (subgrade stiffness. Next, an exact analytical solution is derived for each prismatic segment resting on uniform elastic foundation. These segments are then assembled in a matrix from which the critical buckling load is obtained. The derived formulation accounts for different end boundary conditions. Validation is performed by benchmarking the present results against analytical solutions found in the literature, showing excellent agreement. After validation, more examples are solved to illustrate the power and flexibility of the proposed method. Overall, the proposed method provides reasonable results, and the examples solved demonstrate the versatility of the developed approach and some of its many possible applications.
Charged hadrons in local finite-volume QED+QCD with C* boundary conditions
Lucini, Biagio; Ramos, Alberto; Tantalo, Nazario
2016-01-01
In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C* boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C* boundary conditions. In particular we learn that a certain class of electrically-charged states can be constructed in this setup in a fully consistent fashion, without relying on gauge fixing. We argue that this class of states covers most of the interesting phenomenological applications in the framework of numerical simulations. We also calculate finite-volume corrections to the mass of stable charg...
Seismic responses of an unanchored generic fixture with different simulated boundary conditions
Wu, T.S.; Blomquist, C.A.; Herceg, J.E.
1994-01-01
In the design of equipment for seismic loadings, it is common to anchor the equipment to prevent tipping or sliding. However, there are situations where the equipment should not be anchored. An unanchored piece of equipment is held to the floor only by the gravitational effect and, in the absence of friction, it could move freely. In the analytical investigation of an unanchored item during a seismic event, there is uncertainty on the proper simulation of the boundary conditions so that the analysis model will have no rigid-body motion. Seismic responses of a simple analytical model that is representative of a group of unanchored equipment have been investigated with different sets of simulated boundary conditions. The results show that, when the main interest of investigation is to assess the potential for tipping during an earthquake, the case with one of the four supporting pads simply supported, its two neighboring pads constrained against twisting motion, and all pads without vertical displacements yields the most conservative prediction. The analysis is applied to the fuel processing cell of the Integral Fast Reactor project. In order not to breach the liner of the existing facility and to keep operational flexibility of the fixtures, all new equipment to be installed within the fuel processing cell are required to be unanchored
Nanoscale roughness effect on Maxwell-like boundary conditions for the Boltzmann equation
Brull, S., E-mail: Stephane.Brull@math.u-bordeaux.fr; Charrier, P., E-mail: Pierre.Charrier@math.u-bordeaux.fr; Mieussens, L., E-mail: Luc.Mieussens@math.u-bordeaux.fr [University of Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400 Talence (France)
2016-08-15
It is well known that the roughness of the wall has an effect on microscale gas flows. This effect can be shown for large Knudsen numbers by using a numerical solution of the Boltzmann equation. However, when the wall is rough at a nanometric scale, it is necessary to use a very small mesh size which is much too expansive. An alternative approach is to incorporate the roughness effect in the scattering kernel of the boundary condition, such as the Maxwell-like kernel introduced by the authors in a previous paper. Here, we explain how this boundary condition can be implemented in a discrete velocity approximation of the Boltzmann equation. Moreover, the influence of the roughness is shown by computing the structure scattering pattern of mono-energetic beams of the incident gas molecules. The effect of the angle of incidence of these molecules, of their mass, and of the morphology of the wall is investigated and discussed in a simplified two-dimensional configuration. The effect of the azimuthal angle of the incident beams is shown for a three-dimensional configuration. Finally, the case of non-elastic scattering is considered. All these results suggest that our approach is a promising way to incorporate enough physics of gas-surface interaction, at a reasonable computing cost, to improve kinetic simulations of micro- and nano-flows.
Discrete Boltzmann Method with Maxwell-Type Boundary Condition for Slip Flow
Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua
2018-01-01
The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been known that discrete Boltzmann model (DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation. It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential momentum accommodation coefficient is introduced to implement a gas-surface interaction model. Both the velocity slip and the Knudsen layer under various Knudsen numbers and accommodation coefficients can be well described. Two kinds of slip flows, including Couette flow and Poiseuille flow, are simulated to verify the model. To dynamically compare results from different models, the relation between the definition of Knudsen number in hard sphere model and that in BGK model is clarified. Support of National Natural Science Foundation of China under Grant Nos. 11475028, 11772064, and 11502117 Science Challenge Project under Grant Nos. JCKY2016212A501 and TZ2016002
Cellular Neural Network Method for Critical Slab with Albedo Boundary Condition
Pirouzmanda, A.; Hadada, K.; Suh, K. Y.
2010-01-01
The neutron transport problems have been studied theoretically and numerically for years. A number of researchers have studied the criticality problems of one-speed neutrons in homogeneous slabs and spheres using various methods. The Chebyshev polynomial approximation method (T N method) has lately been developed and improved for the neutron transport equation in slab geometry. The one-speed time-dependent neutron transport equation using the Cellular Neural Network (CNN) for the vacuum boundary condition has previously been solved. In this paper, we demonstrate the capacity of CNN in calculating the critical slab thickness for different boundary conditions and its variation with moments N. The architecture of the CNN has already been dealt with thoroughly. Essentially, the CNN is used to model a first-order system of the partial differential equations (PDEs). The original equations in the T N approximation are also a set of PDEs. The CNN approach lends itself to analog VLSI implementation. In this study, the CNN model is implemented using the HSpice software package
Imen Boutana
2007-12-01
Full Text Available This paper provide some applications of Pettis integration to differential inclusions in Banach spaces with three point boundary conditions of the form $$ ddot{u}(t in F(t,u(t,dot u(t+H(t,u(t,dot u(t,quad hbox{a.e. } t in [0,1], $$ where $F$ is a convex valued multifunction upper semicontinuous on $Eimes E$ and $H$ is a lower semicontinuous multifunction. The existence of solutions is obtained under the non convexity condition for the multifunction $H$, and the assumption that $F(t,x,ysubset Gamma_{1}(t$, $H(t,x,ysubset Gamma_{2}(t$, where the multifunctions $Gamma_{1},Gamma_{2}:[0,1] ightrightarrows E$ are uniformly Pettis integrable.
Effect of boundary conditions on measured water retention behavior within soils
Galindo-torres, S.; Scheuermann, A.; Pedroso, D.; Li, L.
2013-12-01
The Soil Water Characteristic Curve (SWCC) is a practical representation of the behavior of soil water by relating the suction (difference between the air and water pressures to the moisture content (water saturation). The SWCC is characterized by a hysteresis loop, which is thought to be unique in that any drainage-imbibition cycle lies within a main hysteresis loop limited by two different curves for drainage and imbibition. This 'uniqueness' is the main argument for considering the SWCC as a material-intrinsic feature that characterizes the pore structure and its interaction with fluids. Models have been developed with the SWCC as input data to describe the evolution of the water saturation and the suction within soils. One example of these models is the widely used Richard's equation [1]. In this work we present a series of numerical simulations to evaluate the 'unique' nature of the SWCC. The simulations involves the use of the Lattice Boltzmann Method (LBM) [2] within a regular soil, modelling the flow behavior of two immiscible fluids: wetting and non-wetting. The soil is packed within a cubic domain to resemble the experimental setups that are commonly used for measuring the SWCC[3]. The boundary conditions ensure that the non-wetting phase enters through one cubic face and the wetting phase enters trough the opposite phase, with no flow boundary conditions in the remaining 4 cubic faces. The SWCC known features are inspected including the presence of the common limit curves for different cycles involving varying limits for the suction. For this stage of simulations, the SWCC is indeed unique. Later, different boundary conditions are applied with the two fluids each injected from 3 opposing faces into the porous medium. The effect of this boundary condition change is a net flow direction, which is different from that in the previous case. A striking result is observed when both SWCC are compared and found to be noticeable different. Further analysis is
Reis, Tim; Dellar, Paul J.
2012-01-01
lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier
Huang, Shi-Di; Wang, Fei; Xi, Heng-Dong; Xia, Ke-Qing
2014-11-01
We report an experimental study of the influences of thermal boundary condition in turbulent thermal convection. Two configurations were examined: one was fixed heat flux at the bottom boundary and fixed temperature at the top (HC cells); the other was fixed temperature at both boundaries (CC cells). It is found that the flow strength in the CC cells is on average 9% larger than that in the HC ones, which could be understood as change in plume emission ability under different boundary conditions. It is further found, rather surprisingly, that flow reversals of the large-scale circulation occur more frequently in the CC cell, despite a stronger large-scale flow and more uniform temperature distribution over the boundaries. These findings provide new insights into turbulent thermal convection and should stimulate further studies, especially experimental ones. This work is supported by the Hong Kong Research Grants Council under Grant No. CUHK 403712.
Jawad Ahmed
Full Text Available This paper examines the boundary layer flow and heat transfer characteristic in power law fluid model over unsteady radially stretching sheet under the influence of convective boundary conditions. A uniform magnetic field is applied transversely to the direction of the flow. The governing time dependent nonlinear boundary layer equations are reduced into nonlinear ordinary differential equations with the help of similarity transformations. The transformed coupled ordinary differential equations are then solved analytically by homotopy analysis method (HAM and numerically by shooting procedure. Effects of various governing parameters like, power law index n, magnetic parameter M, unsteadiness A, suction/injection S, Biot number γ and generalized Prandtl number Pr on velocity, temperature, local skin friction and the local Nusselt number are studied and discussed. It is found from the analysis that the magnetic parameter diminishes the velocity profile and the corresponding thermal boundary layer thickness. Keywords: Axisymmetric flow, Power law fluid, Unsteady stretching, Convective boundary conditions
Ishiyama, Tatsuya; Yano, Takeru; Fujikawa, Shigeo
2004-01-01
The kinetic boundary condition for the Boltzmann equation at an interface between a polyatomic vapor and its liquid phase is investigated by the numerical method of molecular dynamics, with particular emphasis on the functional form of the evaporation part of the boundary condition, including the evaporation coefficient. The present study is an extension of a previous one for argon [Ishiyama, Yano, and Fujikawa, Phys. Fluids 16, 2899 (2004)] to water and methanol, typical examples of polyatom...
Pendlebury, Diane; Gravel, Sylvie; Moran, Michael D.; Lupu, Alexandru
2018-02-01
A regional air quality forecast model, GEM-MACH, is used to examine the conditions under which a limited-area air quality model can accurately forecast near-surface ozone concentrations during stratospheric intrusions. Periods in 2010 and 2014 with known stratospheric intrusions over North America were modelled using four different ozone lateral boundary conditions obtained from a seasonal climatology, a dynamically-interpolated monthly climatology, global air quality forecasts, and global air quality reanalyses. It is shown that the mean bias and correlation in surface ozone over the course of a season can be improved by using time-varying ozone lateral boundary conditions, particularly through the correct assignment of stratospheric vs. tropospheric ozone along the western lateral boundary (for North America). Part of the improvement in surface ozone forecasts results from improvements in the characterization of near-surface ozone along the lateral boundaries that then directly impact surface locations near the boundaries. However, there is an additional benefit from the correct characterization of the location of the tropopause along the western lateral boundary such that the model can correctly simulate stratospheric intrusions and their associated exchange of ozone from stratosphere to troposphere. Over a three-month period in spring 2010, the mean bias was seen to improve by as much as 5 ppbv and the correlation by 0.1 depending on location, and on the form of the chemical lateral boundary condition.
Investigating effects of boundary conditions on the evaluation of R-factor of un-braced steel frames
Masood M.M. Irheem
2017-08-01
Full Text Available Design of Structures to resist seismic load depends on the theory of dissipation in elastic of energy that already exists in response modification factor “R-factor”. The main problem in codes gives a constant value for R-factor, since change in boundary conditions of building change in behavior of steel frame structures and that effect on R-factor. This study is an attempt to assess overstrength, ductility and response modification factor of un-braced steel frames under change in boundary conditions as change in the direction of strong axis of column and support type beside to variation in story and bay number to be 9 frame and each frame has 8 different boundary conditions as sum of 72 case for analysis. These frames were analyzed by using nonlinear static “pushover” analysis using SAP2000 program. As a result of this study R-factor does not has a constant value, when change in boundary conditions R-factor directly changes, minimum value of 8 boundary conditions is close to the code value that is mean the code is more conservative and give a large factor of safety. Ductility reduction factor increases with increasing number of story for all boundary conditions, but overstrength has different rule. Response modification factor, overstrength factor and ductility reduction factor decrease when fundamentals period increasing for the studied frames.
Wouden, Alex; Cimbala, John; Lewis, Bryan
2014-11-01
While the periodic boundary condition is useful for handling rotational symmetry in many axisymmetric geometries, its application fails for analysis of rotor-stator interaction (RSI) in multi-stage turbomachinery flow. The inadequacy arises from the underlying geometry where the blade counts per row differ, since the blade counts are crafted to deter the destructive harmonic forces of synchronous blade passing. Therefore, to achieve the computational advantage of modeling a single blade passage per row while preserving the integrity of the RSI, a phase-lag boundary condition is adapted to OpenFOAM® software's incompressible pressure-based solver. The phase-lag construct is accomplished through restating the implicit periodic boundary condition as a constant boundary condition that is updated at each time step with phase-shifted data from the coupled cells adjacent to the boundary. Its effectiveness is demonstrated using a typical Francis hydroturbine modeled as single- and double-passages with phase-lag boundary conditions. The evaluation of the phase-lag condition is based on the correspondence of the overall computational performance and the calculated flow parameters of the phase-lag simulations with those of a baseline full-wheel simulation. Funded in part by DOE Award Number: DE-EE0002667.
Artificial boundary conditions for the numerical simulation of unsteady acoustic waves
Tsynkov, S.V.
2003-01-01
We construct non-local artificial boundary conditions (ABCs) for the numerical simulation of genuinely time-dependent acoustic waves that propagate from a compact source in an unbounded unobstructed space. The key property used for obtaining the ABCs is the presence of lacunae, i.e., sharp aft fronts of the waves, in wave-type solutions in odd-dimension spaces. This property can be considered a manifestation of the Huygens' principle. The ABCs are obtained directly for the discrete formulation of the problem. They truncate the original unbounded domain and guarantee the complete transparency of the new outer boundary for all the outgoing waves. A central feature of the proposed ABCs is that the extent of their temporal non-locality is fixed and limited, and it does not come at the expense of simplifying the original model. It is rather a natural consequence of the existence of lacunae, which is a fundamental property of the corresponding solutions. The proposed ABCs can be built for any consistent and stable finite-difference scheme. Their accuracy can always be made as high as that of the interior approximation, and it will not deteriorate even when integrating over long time intervals. Besides, the ABCs are most flexible from the standpoint of geometry and can handle irregular boundaries on regular grids with no fitting/adaptation needed and no accuracy loss induced. Finally, they allow for a wide range of model settings. In particular, not only one can analyze the simplest advective acoustics case with the uniform background flow, but also the case when the waves' source (or scatterer) is engaged in an accelerated motion
Dudchenko, A. A.; Elpat'evskii, A. N.
1995-07-01
Reinforced panels are the basic load-bearing elements of various structures. Optimization of massive structures requires consideration of deformation of the panel cross-sections. This is particularly important in determining the bearing strength at buckling. The load scheme, conditions for fixation of the panel cross-section, and bend-torsional stiffness taking account of the deformation of the rod cross-section affect the buckling load in real structures. The stress distribution prior to buckling must be known to solve the buckling problem properly. The stress in the panel is proportional to the active load. The stress distribution is assumed to be known according to our previous method [1]. The load scheme and panel dimensions are shown in Fig. 1. The stress distribution in the panel prior to buckling can be found using Eqs. (1)-(3). A view of the cross-section is given in Fig. 1. The displacements in the panel at buckling for the boundary area are found using Eqs. (4)-(6), while the stresses in the skin and stiffness are found using Eq. (7). Roots k1 and k2 are those of the characteristic equation and β is a dimensionless coordinate. The problem was solved using variational theory. The potential energy is given by Eqs. (8) and (9) by orihogonalization of Eqs. (5). The basic equations are converted to Eqs. (10) by evaluation of the components in Eqs. (8) and (9). Its calculation (11) gives the compression load. Optimization of parameter α gives the critical strength P1 = 6.93 kN (without taking account of the boundary area) and P2 = 5.31 kN (taking account of the boundary area).
Liu, Biyue; Zheng, Jie; Bach, Richard; Tang, Dalin
2015-01-01
In literature, the effect of the inflow boundary condition was investigated by examining the impact of the waveform and the shape of the spatial profile of the inlet velocity on the cardiac hemodynamics. However, not much work has been reported on comparing the effect of the different combinations of the inlet/outlet boundary conditions on the quantification of the pressure field and flow distribution patterns in stenotic right coronary arteries. Non-Newtonian models were used to simulate blood flow in a patient-specific stenotic right coronary artery and investigate the influence of different boundary conditions on the phasic variation and the spatial distribution patterns of blood flow. The 3D geometry of a diseased artery segment was reconstructed from a series of IVUS slices. Five different combinations of the inlet and the outlet boundary conditions were tested and compared. The temporal distribution patterns and the magnitudes of the velocity, the wall shear stress (WSS), the pressure, the pressure drop (PD), and the spatial gradient of wall pressure (WPG) were different when boundary conditions were imposed using different pressure/velocity combinations at inlet/outlet. The maximum velocity magnitude in a cardiac cycle at the center of the inlet from models with imposed inlet pressure conditions was about 29% lower than that from models using fully developed inlet velocity data. Due to the fact that models with imposed pressure conditions led to blunt velocity profile, the maximum wall shear stress at inlet in a cardiac cycle from models with imposed inlet pressure conditions was about 29% higher than that from models with imposed inlet velocity boundary conditions. When the inlet boundary was imposed by a velocity waveform, the models with different outlet boundary conditions resulted in different temporal distribution patterns and magnitudes of the phasic variation of pressure. On the other hand, the type of different boundary conditions imposed at the
On the energetics of a damped beam-like equation for different boundary conditions
Sandilo, S.H.; Sheikh, A.H.; Soomro, A.R.
2017-01-01
In this paper, the energy estimates for a damped linear homogeneous beam-like equation will be considered. The energy estimates will be studied for different BCs (Boundary Conditions) for the axially moving continuum. The problem has physical and engineering application. The applications are mostly occurring in models of conveyor belts and band-saw blades. The research study is focused on the Dirichlet, the Neumann and the Robin type of BCs. From physical point of view, the considered mathematical model expounds the transversal vibrations of a moving belt system or moving band-saw blade. It is assumed that a viscous damping parameter and the horizontal velocity are positive and constant. It will be shown in this paper that change in geometry or the physics of the boundaries can affect the stability properties of the system in general and stability depends on the axial direction of the motion. In all cases of the BCs, it will be shown that there is energy decay due to viscous damping parameter and it will also be shown that in some cases there is no conclusion whether the beam energy decreases or increases. The detailed physical interpretation of all terms and expressions is provided and studied in detail. (author)
The D(D3)-anyon chain: integrable boundary conditions and excitation spectra
Finch, Peter E; Frahm, Holger
2013-01-01
Chains of interacting non-Abelian anyons with local interactions invariant under the action of the Drinfeld double of the dihedral group D 3 are constructed. Formulated as a spin chain the Hamiltonians are generated from commuting transfer matrices of an integrable vertex model for periodic and braided as well as open boundaries. A different anyonic model with the same local Hamiltonian is obtained within the fusion path formulation. This model is shown to be related to an integrable fusion interaction round the face model. Bulk and surface properties of the anyon chain are computed from the Bethe equations for the spin chain. The low-energy effective theories and operator content of the models (in both the spin chain and fusion path formulation) are identified from analytical and numerical studies of the finite-size spectra. For all boundary conditions considered the continuum theory is found to be a product of two conformal field theories. Depending on the coupling constants the factors can be a Z 4 parafermion or a M (5,6) minimal model. (paper)
Yinhuan Ao
2017-01-01
Full Text Available This paper reported a comprehensive analysis on the diurnal variation of the Atmospheric Boundary Layer (ABL in summer of Badain Jaran Desert and discussed deeply the effect of surface thermal to ABL, including the Difference in Surface-Air Temperature (DSAT, net radiation, and sensible heat, based on limited GPS radiosonde and surface observation data during two intense observation periods of experiments. The results showed that (1 affected by topography of the Tibetan Plateau, the climate provided favorable external conditions for the development of Convective Boundary Layer (CBL, (2 deep CBL showed a diurnal variation of three- to five-layer structure in clear days and five-layer ABL structure often occurred about sunset or sunrise, (3 the diurnal variation of DSAT influenced thickness of ABL through changes of turbulent heat flux, (4 integral value of sensible heat which rapidly converted by surface net radiation had a significant influence on the growth of CBL throughout daytime. The cumulative effect of thick RML dominated the role after CBL got through SBL in the development stage, especially in late summer, and (5 the development of CBL was promoted and accelerated by the variation of wind field and distribution of warm advection in high and low altitude.
A hybrid absorbing boundary condition for frequency-domain finite-difference modelling
Ren, Zhiming; Liu, Yang
2013-01-01
Liu and Sen (2010 Geophysics 75 A1–6; 2012 Geophys. Prospect. 60 1114–32) proposed an efficient hybrid scheme to significantly absorb boundary reflections for acoustic and elastic wave modelling in the time domain. In this paper, we extend the hybrid absorbing boundary condition (ABC) into the frequency domain and develop specific strategies for regular-grid and staggered-grid modelling, respectively. Numerical modelling tests of acoustic, visco-acoustic, elastic and vertically transversely isotropic (VTI) equations show significant absorptions for frequency-domain modelling. The modelling results of the Marmousi model and the salt model also demonstrate the effectiveness of the hybrid ABC. For elastic modelling, the hybrid Higdon ABC and the hybrid Clayton and Engquist (CE) ABC are implemented, respectively. Numerical simulations show that the hybrid Higdon ABC gets better absorption than the hybrid CE ABC, especially for S-waves. We further compare the hybrid ABC with the classical perfectly matched layer (PML). Results show that the two ABCs cost the same computation time and memory space for the same absorption width. However, the hybrid ABC is more effective than the PML for the same small absorption width and the absorption effects of the two ABCs gradually become similar when the absorption width is increased. (paper)
A new wall function boundary condition including heat release effect for supersonic combustion flows
Gao, Zhen-Xun; Jiang, Chong-Wen; Lee, Chun-Hian
2016-01-01
Highlights: • A new wall function including heat release effect is theoretically derived. • The new wall function is a unified form holding for flows with/without combustion. • The new wall function shows good results for a supersonic combustion case. - Abstract: A new wall function boundary condition considering combustion heat release effect (denoted as CWFBC) is proposed, for efficient predictions of skin friction and heat transfer in supersonic combustion flows. Based on a standard flow model including boundary-layer combustion, the Shvab–Zeldovich coupling parameters are introduced to derive a new velocity law-of-the-wall including the influence of combustion. For the temperature law-of-the-wall, it is proposed to use the enthalpy–velocity relation, instead of the Crocco–Busemann equation, to eliminate explicit influence of chemical reactions. The obtained velocity and temperature law-of-the-walls constitute the CWFBC, which is a unified form simultaneously holding for single-species, multi-species mixing and multi-species reactive flows. The subsequent numerical simulations using this CWFBC on an experimental case indicate that the CWFBC could accurately reflect the influences on the skin friction and heat transfer by the chemical reactions and heat release, and show large improvements compared to previous WFBC. Moreover, the CWFBC can give accurate skin friction and heat flux for a coarse mesh with y"+ up to 200 for the experimental case, except for slightly larger discrepancy of the wall heat flux around ignition position.
On the Energetics of a Damped Beam-Like Equation for Different Boundary Conditions
SAJAD HUSSAIN SANDILO
2017-04-01
Full Text Available In this paper, the energy estimates for a damped linear homogeneous beam-like equation will be considered. The energy estimates will be studied for different BCs (Boundary Conditions for the axially moving continuum. The problem has physical and engineering application. The applications are mostly occurring in models of conveyor belts and band-saw blades. The research study is focused on the Dirichlet, the Neumann and the Robin type of BCs. From physical point of view, the considered mathematical model expounds the transversal vibrations of a moving belt system or moving band-saw blade. It is assumed that a viscous damping parameter and the horizontal velocity are positive and constant. It will be shown in this paper that change in geometry or the physics of the boundaries can affect the stability properties of the system in general and stability depends on the axial direction of the motion. In all cases of the BCs, it will be shown that there is energy decay due to viscous damping parameter and it will also be shown that in some cases there is no conclusion whether the beam energy decreases or increases. The detailed physical interpretation of all terms and expressions is provided and studied in detail.
Patrick Terriault
2017-01-01
Full Text Available Emergent additive manufacturing processes allow the use of metallic porous structures in various industrial applications. Because these structures comprise a large number of ordered unit cells, their design using conventional modeling approaches, such as finite elements, becomes a real challenge. A homogenization technique, in which the lattice structure is simulated as a fully dense volume having equivalent material properties, can then be employed. To determine these equivalent material properties, numerical simulations can be performed on a single unit cell of the lattice structure. However, a critical aspect to consider is the boundary conditions applied to the external faces of the unit cell. In the literature, different types of boundary conditions are used, but a comparative study is definitely lacking. In this publication, a diamond-type unit cell is studied in compression by applying different boundary conditions. If the porous structure’s boundaries are free to deform, then the periodic boundary condition is found to be the most representative, but constraint equations must be introduced in the model. If, instead, the porous structure is inserted in a rigid enclosure, it is then better to use frictionless boundary conditions. These preliminary results remain to be validated for other types of unit cells loaded beyond the yield limit of the material.