Open Boundary Conditions for Dissipative MHD
Energy Technology Data Exchange (ETDEWEB)
Meier, E T
2011-11-10
In modeling magnetic confinement, astrophysics, and plasma propulsion, representing the entire physical domain is often difficult or impossible, and artificial, or 'open' boundaries are appropriate. A novel open boundary condition (BC) for dissipative MHD, called Lacuna-based open BC (LOBC), is presented. LOBC, based on the idea of lacuna-based truncation originally presented by V.S. Ryaben'kii and S.V. Tsynkov, provide truncation with low numerical noise and minimal reflections. For hyperbolic systems, characteristic-based BC (CBC) exist for separating the solution into outgoing and incoming parts. In the hyperbolic-parabolic dissipative MHD system, such separation is not possible, and CBC are numerically unstable. LOBC are applied in dissipative MHD test problems including a translating FRC, and coaxial-electrode plasma acceleration. Solution quality is compared to solutions using CBC and zero-normal derivative BC. LOBC are a promising new open BC option for dissipative MHD.
Normal ordering and boundary conditions in open bosonic strings
Braga, N R F; Carrion, H L; Braga, Nelson R. F.; Godinho, Cresus F. L.; Carrion, Hector L.
2004-01-01
Boundary conditions play a non trivial role in string theory. For instance the rich structure of D-branes is generated by choosing appropriate combinations of Dirichlet and Neumann boundary conditions. Furthermore, when an antisymmetric background is present at the string end-points (corresponding to mixed boundary conditions) space time becomes non-commutative there. We show here how to build up normal ordered products for bosonic string position operators that satisfy both equations of motion and open string boundary conditions at quantum level. We also calculate the equal time commutator of these normal ordered products in the presence of antisymmetric tensor background.
Reconnection Rate in Collisionless Magnetic Reconnection under Open Boundary Conditions
Institute of Scientific and Technical Information of China (English)
HUANG Jun; MA Zhi-Wei
2008-01-01
Collisionless magnetic reconnection is studied by using two-dimensional Darwin particle-in-cell simulations with different types of open boundary conditions.The simulation results indicate that reconnection rates are strongly dependent on the imposed boundary conditions of the magnetic field Bx in the inward side. Under the zerogradient Bx boundary condition,the reconnection rate quickly decreases after reaching its maximum and no steady-state is found.Under both electromagnetic and magnetosonic boundary conditions,the system can reach a quasi-steady state.However,the reconnection rate Er≈ 0.08 under the electromagnetic boundary condition is weaker than Er≈ 0.13 under the magnetosonic boundary condition.
Approximate open boundary conditions for a class of hyperbolic equations
Maikov, A. R.
2006-06-01
Initial-boundary value problems formulated in spatially unbounded domains can be sometimes reduced to problems in their bounded subdomains by using the so-called open boundary conditions. These conditions are set on the surface separating the subdomain from the rest of the domain. One of the approaches to obtaining such a kind of conditions is based on an approximation of the kernels of the time convolution operators in the relations connecting the exact solution of the original problem and its derivatives on the open boundary. In this case, it is possible to considerably reduce the requirements for system resources required to solve numerically for a wide range of physical and engineering problems. Estimates of the perturbations of the exact solution due to the approximate conditions are obtained for a model problem with one space variable.
On the extraction of spectral quantities with open boundary conditions
Bruno, Mattia; Korzec, Tomasz; Lottini, Stefano; Schaefer, Stefan
2014-01-01
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 L\\"uscher and Palombi. We analyse the effect of the associated reweighting factors on the computation of different observables.
Topological susceptibility in lattice Yang-Mills theory with open boundary condition
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, Abhishek; Harindranath, A. [Theory Division, Saha Institute of Nuclear Physics,1/AF Bidhan Nagar, Kolkata 700064 (India); Maiti, Jyotirmoy [Department of Physics, Barasat Government College,10 KNC Road, Barasat, Kolkata 700124 (India); Majumdar, Pushan [Department of Theoretical Physics, Indian Association for the Cultivation of Science,Kolkata 700032 (India)
2014-02-11
We find that using open boundary condition in the temporal direction can yield the expected value of the topological susceptibility in lattice SU(3) Yang-Mills theory. As a further check, we show that the result agrees with numerical simulations employing the periodic boundary condition. Our results support the preferability of the open boundary condition over the periodic boundary condition as the former allows for computation at smaller lattice spacings needed for continuum extrapolation at a lower computational cost.
A Convective-like Energy-Stable Open Boundary Condition for Simulations of Incompressible Flows
Dong, Suchuan
2015-01-01
We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even when strong vortices or backflows occur at the outflow boundary. Under certain situations it can be reduced to a form that can be analogized to the usual convective boundary condition. One prominent feature of this boundary condition is that it provides a control over the velocity on the outflow/open boundary. This is not available with the other energy-stable open boundary conditions from previous works. Our numerical algorithm treats the proposed open boundary condition based on a rotational velocity-correction type strategy. It gives rise to a Robin-type condition for the discrete pressure and a Robin-type condition for the discrete velocity on the outflow/open boundary, respectively at the pressure and the velocity sub-steps. We present extensive numerical experiments on...
Nested Bethe Ansatz for Spin Ladder Model with Open Boundary Conditions
Institute of Scientific and Technical Information of China (English)
WU Jun-Fang; ZHANG Chun-Min; YUE Rui-Hong; LI Run-Ling
2005-01-01
The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the generalboundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.
Dong, Suchuan
2014-01-01
We present a generalized form of open boundary conditions, and an associated numerical algorithm, for simulating incompressible flows involving open or outflow boundaries. The generalized form represents a family of open boundary conditions, which all ensure the energy stability of the system, even in situations where strong vortices or backflows occur at the open/outflow boundaries. Our numerical algorithm for treating these open boundary conditions is based on a rotational pressure correction-type strategy, with a formulation suitable for $C^0$ spectral-element spatial discretizations. We have introduced a discrete equation and associated boundary conditions for an auxiliary variable. The algorithm contains constructions that prevent a numerical locking at the open/outflow boundary. In addition, we have also developed a scheme with a provable unconditional stability for a sub-class of the open boundary conditions. Extensive numerical experiments have been presented to demonstrate the performance of our meth...
Open boundary conditions for the Diffuse Interface Model in 1-D
Desmarais, J. L.; Kuerten, J. G. M.
2014-04-01
New techniques are developed for solving multi-phase flows in unbounded domains using the Diffuse Interface Model in 1-D. They extend two open boundary conditions originally designed for the Navier-Stokes equations. The non-dimensional formulation of the DIM generalizes the approach to any fluid. The equations support a steady state whose analytical approximation close to the critical point depends only on temperature. This feature enables the use of detectors at the boundaries switching between conventional boundary conditions in bulk phases and a multi-phase strategy in interfacial regions. Moreover, the latter takes advantage of the steady state approximation to minimize the interface-boundary interactions. The techniques are applied to fluids experiencing a phase transition and where the interface between the phases travels through one of the boundaries. When the interface crossing the boundary is fully developed, the technique greatly improves results relative to cases where conventional boundary conditions can be used. Limitations appear when the interface crossing the boundary is not a stable equilibrium between the two phases: the terms responsible for creating the true balance between the phases perturb the interior solution. Both boundary conditions present good numerical stability properties: the error remains bounded when the initial conditions or the far field values are perturbed. For the PML, the influence of its main parameters on the global error is investigated to make a compromise between computational costs and maximum error. The approach can be extended to multiple spatial dimensions.
Algebraic Bethe Ansatz Solution to CN Vertex Model with Open Boundary Conditions
Institute of Scientific and Technical Information of China (English)
LI Guang-Liang; SHI Kang-Jie; YUE Rui-Hong
2005-01-01
We present three diagonal reflecting matrices for the CN vertex model with open boundary conditions and exactly solve the model by using the algebraic Bethe ansatz. The eigenvector is constructed and the eigenvalue and the associated Bethe equations are achieved. All the unwanted terms are cancelled out by three kinds of identities.
On the formulation of open boundary conditions at the mouth of a bay
Greatbatch, Richard J.; Otterson, Timm
1991-10-01
We describe our experience in formulating open boundary conditions to apply at the mouth of a reduced-gravity model of a bay. Our objective is to find a way to calculate the response of the bay to wind forcing over the bay itself, without being concerned about the influence of regions beyond. We show that open boundaries from which Kelvin waves can propagate along the coast into the model domain ("upstream" boundaries) must be treated with care. We begin by considering an "upstream" boundary which runs perpendicular to the coast. We find that if a radiation condition is applied on such a boundary, then spurious Kelvin waves of near-inertial period can propagate in from the boundary and contaminate the solution in the interior of the model domain. Also, if there is Ekman transport at the "upstream" boundary away from (toward) the coast, then upwelling (downwelling) will occur indefinitely and completely swamp the model solution in the bay. This is similar to the solution we expect when the coastline is straight and extends to infinity in the "upstream" direction. However, it is not the same, since the rate of upwelling (downwelling) is roughly half the theoretical value for that case. For the problem of a bay we suggest that the way to deal with this is to extend the coastline out to sea on the "upstream" side of the mouth and apply a condition on the artificial stretch of the boundary which suppresses Kelvin wave propagation but is also not prohibitively reflective to outgoing Poincaré waves. For our problem a condition of zero normal gradient in interface displacement seems to be sufficient. This condition also captures reasonably well the near-inertial Kelvin waves that are generated by the northwest corner of the bay (which are a genuine part of the solution) as long as the other boundaries are sufficiently far from the bay. We have also experimented with using sponge layers rather than radiation conditions on the other boundaries. We find that sponging only
Institute of Scientific and Technical Information of China (English)
马西奎; 韩社教
2002-01-01
Based on the multipole expansion theory of the potential, a satisfactory interpretation is put forward of the exact nature of the approximations of asymptotic boundary condition (called the ABC) techniques for the numerical solutions of open-boundary static electromagnetic-field problems, and a definite physical meaning is bestowed on ABC, which provide a powerful theoretical background for laying down the operating rules and the key to the derivation of asymptotic boundary conditions. This paper is also intended to reveal the shortcomings of the conventional higher-order ABC, and at the same time to give the concept of a new type of higher-order ABC, and to present a somewhat different formulation of the new nth-order ABC. In order to test its feasibility, several simple problems of electrostatic potentials are analyzed. The results are found to be much better than those of conventional higher-order ABCs.
Biswas, Debabrata; Kumar, Raghwendra
2015-01-01
Numerical solution of the Poisson equation in metallic enclosures, open at one or more ends, is important in many practical situations such as High Power Microwave (HPM) or photo-cathode devices. It requires imposition of a suitable boundary condition at the open end. In this paper, methods for solving the Poisson equation are investigated for various charge densities and aspect ratios of the open ends. It is found that a mixture of second order and third order local asymptotic boundary condition (ABC) is best suited for large aspect ratios while a proposed non-local matching method, based on the solution of the Laplace equation, scores well when the aspect ratio is near unity for all charge density variations, including ones where the centre of charge is close to an open end or the charge density is non-localized. The two methods complement each other and can be used in electrostatic calculations where the computational domain needs to be terminated at the open boundaries of the metallic enclosure.
OpenCL-Based FPGA Accelerator for 3D FDTD with Periodic and Absorbing Boundary Conditions
Directory of Open Access Journals (Sweden)
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.
Quasilocal conservation laws in XXZ spin-1/2 chains: Open, periodic and twisted boundary conditions
Directory of Open Access Journals (Sweden)
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.
Topology and glueballs in SU(7) Yang-Mills with open boundary conditions
Amato, Alessandro; Lucini, Biagio
2015-01-01
It is well known that the topology of gauge configurations generated in a Markov Monte-Carlo chain freezes as the continuum limit is approached. The corresponding autocorrelation time increases exponentially with the inverse lattice spacing, affecting the ergodicity of the simulation. In SU(N) gauge theories for large N this problem sets in at much coarser lattice spacings than for N=3. This means that its systematics can be studied on lattices that are smaller in terms of the number of lattice sites. It has been shown that using open boundary conditions in time allows instantons to be created and destroyed, restoring topological mobility and ergodicity. However, with open boundary conditions translational invariance is lost and the influence of spurious states propagating from the boundary into the bulk on physical correlators needs to be carefully evaluated. Moreover, while the total topological charge can be changed, the mobility of instantons across the lattice is still reduced. We consider SU(7) Yang-Mil...
Directory of Open Access Journals (Sweden)
D. Diederen
2015-06-01
Full Text Available We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave in a frictionless, prismatic, tidal channel with a horizontal bed. Assessment of a large number of numerical simulations, where an open boundary condition is posed at a certain distance landward, suggests that it can also be considered accurate in the more natural case of converging estuaries with nonlinear friction and a bed slope. The equation follows from the open boundary condition and is therefore a part of the problem formulation for an infinite tidal channel. This finding provides a practical tool for evaluating tidal wave dynamics, by reconstructing the temporal variation of the velocity based on local observations of the water level, providing a fully local open boundary condition and allowing for local friction calibration.
Solution Transformations and Their Effects on the Systems with Open Boundary Conditions
Institute of Scientific and Technical Information of China (English)
JU Guo-Xing; ZHAO Xian-Lin
2002-01-01
The solution transformations and properties of the R-matrices for two-component systems uner these transformations are analyzed in details.Not all transformed R-matrices can be put into the Skalyanin's formalism.For those R-matrices with all required properties,the effects of solution transformations to the six- and eight-vertex systems with open boundary conditions are discussed.These effects can be one of the following types: The Hamiltonian is invariant or transposition-invariant or made in a similarity transformation,or its coupling coefficients are multiplied by an overall factor,or the spin of the system is rotated around the z axis or/and reflected with respect to some plane.In these cases,the transformed systems remain to be integrable.
Solutions from boundary condition changing operators in open string field theory
Kiermaier, Michael; Soler, Pablo
2010-01-01
We construct analytic solutions of open string field theory using boundary condition changing (bcc) operators. We focus on bcc operators with vanishing conformal weight such as those for regular marginal deformations of the background. For any Fock space state phi, the component string field of the solution Psi exhibits a remarkable factorization property: it is given by the matter three-point function of phi with a pair of bcc operators, multiplied by a universal function that only depends on the conformal weight of phi. This universal function is given by a simple integral expression that can be computed once and for all. The three-point functions with bcc operators are thus the only needed physical input of the particular open string background described by the solution. We illustrate our solution with the example of the rolling tachyon profile, for which we prove convergence analytically. The form of our solution, which involves bcc operators instead of explicit insertions of the marginal operator, can b...
Zakharenko, A. A.
2013-11-01
This report studies the dispersive wave propagation in the transversely isotropic (6 mm) piezoelectromagnetic (PEM) plate when the mechanical, electrical, and magnetic boundary conditions for both the upper and lower free surfaces of the plate are as follows: the mechanically free, electrically open, and magnetically open surfaces. This study follows some original results obtained in book. The fundamental modes' dispersion relations are graphically shown for the following well-known PEM composite materials: BaTiO3-CoFe2O4 and PZT-5H-Terfenol-D. It is natural that for large values of the nondimensional parameter kd (k is the wave number and d is the plate half-thickness), the velocities of both the fundamental modes approach the surface shear-horizontal wave called the piezomagnetic exchange surface Melkumyan wave. It is well known that plate waves are usually utilized in the nondestructive testing and evaluation, for instance, in the airspace industry. Also, PEM materials are used as smart ones in various technical devices such as dispersive wave delay lines, (biochemi)sensors, lab-on-a-chip, etc.
González-Ruiz, A
1994-01-01
We consider integrable open-boundary conditions for the supersymmetric t-J model commuting with the number operator $n$ and $S^{z}$. We find four families, each one depending on two arbitrary parameters. The associated eigenvalue problem is solved by generalizing the Nested Algebraic Bethe Ansatz of the quantum group invariant case (which is obtained as a special limit). For the quantum group invariant case the Bethe ansatz states are shown to be highest weights of $spl_{q}(2,1)$. We also discuss the relation between Sklyanin's method of constructing open boundary conditions and the one for the quantum group invariant case based on Markov traces.
Boundary conditions for the use of personal ventilation over mixing ventilation in open plan offices
DEFF Research Database (Denmark)
Petersen, Steffen; Hviid, Christian Anker
2013-01-01
This paper investigates the boundary conditions for choosing a combined Personal Ventilation (PV) and Mixing Ventilation (MV) over conventional mixing ventilation in an office with multiple workers. A simplified procedure for annual performance assessment of PV/MV systems in terms of air quality...... of the investigated PV/MV systems has similar performance to pure MV systems. This means that optimised PV/MV systems have the potential to generate energy savings....
Fluctuations in the Weakly Asymmetric Exclusion Process with Open Boundary Conditions
Derrida, B.; Enaud, C.; Landim, C.; Olla, S.
2005-03-01
We investigate the fluctuations around the average density profile in the weakly asymmetric exclusion process with open boundaries in the steady state. We show that these fluctuations are given, in the macroscopic limit, by a centered Gaussian field and we compute explicitly its covariance function. We use two approaches. The first method is dynamical and based on fluctuations around the hydrodynamic limit. We prove that the density fluctuations evolve macroscopically according to an autonomous stochastic equation, and we search for the stationary distribution of this evolution. The second approach, which is based on a representation of the steady state as a sum over paths, allows one to write the density fluctuations in the steady state as a sum over two independent processes, one of which is the derivative of a Brownian motion, the other one being related to a random path in a potential.
Directory of Open Access Journals (Sweden)
Anzhou Cao
2013-01-01
Full Text Available Based on the theory of inverse problem, the optimization of open boundary conditions (OBCs in a 3D internal tidal model is investigated with the adjoint method. Fourier coefficients of M2 internal tide on four open boundaries, which are regarded as OBCs, are inverted simultaneously. During the optimization, the steepest descent method is used to minimize cost function. The reasonability and feasibility of the model are tested by twin experiments (TEs. In TE1, OBCs on four open boundaries are successfully inverted by using independent point (IP strategy, suggesting that IP strategy is useful in parameter estimation. Results of TE2 indicate that the model is effective even by assimilating inaccurate “observations.” Based on conclusions of TEs, the M2 internal tide around Hawaii is simulated by assimilating T/P data in practical experiment. The simulated cochart shows good agreement with that obtained from the Oregon State University tidal model and T/P observations. Careful inspection shows that the major difference between simulated results and OSU model results is short-scale fluctuations superposed on coamplitude lines, which can be treated as the surface manifestation modulated by the internal tide. The computed surface manifestation along T/P tracks is comparable to the estimation in previous work.
Institute of Scientific and Technical Information of China (English)
CAO Anzhou; GUO Zheng; L(U) Xianqing
2012-01-01
Two-dimensional tidal open boundary conditions of the M2 constituent in the Bohai and Yellow Seas(BYS)have been estimated by assimilating T/P altimeter data.During inversion,independent point (IP)strategy was used,in which several IPs on the open boundary is assumed,values at these IPs can be optimized with an adjoint method,and those at other grid points are determined by linearly interpolating the values at IPs.The reasonability and feasibility of the model are tested by ideal twin experiments.In the practical experiment(PE)after assimilation,the cost function may reach 1％ or less of its initial value.Mean absolute errors in amplitude and phase can be less than 5 cm and 5°,respectively,and the obtained co-chart can show the character of the M2 constituent in the BYS.The results of the PE indicate that using only two IPs on the open boundary can yield better simulated results.
Qiang, Ji
2016-01-01
A three-dimensional (3D) Poisson solver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. In this paper, we present a fast efficient method to solve the Poisson equation using a spectral finite-difference method. This method uses a computational domain that contains the charged particle beam only and has a computational complexity of $O(N_u(logN_{mode}))$, where $N_u$ is the total number of unknowns and $N_{mode}$ is the maximum number of longitudinal or azimuthal modes. This saves both the computational time and the memory usage by using an artificial boundary condition in a large extended computational domain.
Directory of Open Access Journals (Sweden)
Xiaotian Xu
2015-09-01
Full Text Available The small polaron, a one-dimensional lattice model of interacting spinless fermions, with generic non-diagonal boundary terms is studied by the off-diagonal Bethe ansatz method. The presence of the Grassmann valued non-diagonal boundary fields gives rise to a typical U(1-symmetry-broken fermionic model. The exact spectra of the Hamiltonian and the associated Bethe ansatz equations are derived by constructing an inhomogeneous T–Q relation.
Directory of Open Access Journals (Sweden)
Haibo Chen
2013-01-01
Full Text Available Based on an internal tidal model, the practical performances of the limited-memory BFGS (L-BFGS method and two gradient descent (GD methods (the normal one with Wolfe’s line search and the simplified one are investigated computationally through a series of ideal experiments in which the open boundary conditions (OBCs are inverted by assimilating the interior observations with the adjoint method. In the case that the observations closer to the unknown boundary are included for assimilation, the L-BFGS method performs the best. As compared with the simplified GD method, the normal one really uses less iteration to reach a satisfactory solution, but its advantage over the simplified one is much smaller than expected. In the case that only the observations that are further from the unknown boundary are assimilated, the simplified GD method performs the best instead, whereas the performances of the other two methods are not satisfactory. The advanced L-BFGS algorithm and Wolfe’s line search still need to be improved when applied to the practical cases. The simplified GD method, which is controllable and easy to implement, should be regarded seriously as a choice, especially when the classical advanced optimization techniques fail or perform poorly.
Boundary condition may change chaos
Energy Technology Data Exchange (ETDEWEB)
Itoh, Sanae-I.; Yagi, Masatoshi [Kyushu Univ., RIAM, Kasuga, Fukuoka (Japan); Kawai, Yoshinobu [Kyushu Univ., Interdisciplinary Graduate School of Engineering Sciences, Kasuga, Fukuoka (Japan)
2001-07-01
Role of boundary condition for the appearance of chaos is examined. Imposition of the boundary condition is interpreted as the reduction of the system size L. For a demonstration, Rayleigh-Benard instability is considered and the shell model analysis is applied. It is shown that the reduction of L reduces the number of positive Lyapunov exponent of the system, hence opens the route from the turbulence, to the chaos and to the limit cycle/fixed point. (author)
Normal transmitting boundary conditions
Institute of Scientific and Technical Information of China (English)
廖振鹏
1996-01-01
The multi-transmitting formula (MTF) governed by a single artificial speed is analytically developed into a generalized MTF governed by a few artificial speeds to improve its capacity in simultaneous simulation of several one-way waves propagating at different speeds.The generalized MTF is then discretized and further generalized using the space extrapolation to improve its accuracies in numerical simulation of transient waves at large angles of incidence.The above two successive generalizitions of MTF based on the notion of normal transmission lead to a compact formula of local non-reflecting boundary condition.The formula not only provides a general representation of the major schemes of existing local boundary conditions but can be used to generate new schemes,which combine advantages of different schemes.
Directory of Open Access Journals (Sweden)
K. Schäfer
2012-07-01
Full Text Available Measurements of land-surface emission rates of greenhouse and other gases at large spatial scales (10 000 m^{2} are needed to assess the spatial distribution of emissions. This can be readily done using spatial-integrating micro-meteorological methods like flux-gradient methods which were evaluated for determining land-surface emission rates of trace gases under stable boundary layers. Non-intrusive path-integrating measurements are utilized. Successful application of a flux-gradient method requires confidence in the gradients of trace gas concentration and wind, and in the applicability of boundary-layer turbulence theory; consequently the procedures to qualify measurements that can be used to determine the flux is critical. While there is relatively high confidence in flux measurements made under unstable atmospheres with mean winds greater than 1 m s^{−1}, there is greater uncertainty in flux measurements made under free convective or stable conditions. The study of N_{2}O emissions of flat grassland and NH_{3} emissions from a cattle lagoon involves quality-assured determinations of fluxes under low wind, stable or night-time atmospheric conditions when the continuous "steady-state" turbulence of the surface boundary layer breaks down and the layer has intermittent turbulence. Results indicate that following the Monin-Obukhov similarity theory (MOST flux-gradient methods that assume a log-linear profile of the wind speed and concentration gradient incorrectly determine vertical profiles and thus flux in the stable boundary layer. An alternative approach is considered on the basis of turbulent diffusivity, i.e. the measured friction velocity as well as height gradients of horizontal wind speeds and concentrations without MOST correction for stability. It is shown that this is the most accurate of the flux-gradient methods under stable conditions.
Reweighting twisted boundary conditions
Bussone, Andrea; Hansen, Martin; Pica, Claudio
2015-01-01
Imposing twisted boundary conditions on the fermionic fields is a procedure extensively used when evaluating, for example, form factors on the lattice. Twisting is usually performed for one flavour and only in the valence, and this causes a breaking of unitarity. In this work we explore the possibility of restoring unitarity through the reweighting method. We first study some properties of the approach at tree level and then we stochastically evaluate ratios of fermionic determinants for different boundary conditions in order to include them in the gauge averages, avoiding in this way the expensive generation of new configurations for each choice of the twisting angle, $\\theta$. As expected the effect of reweighting is negligible in the case of large volumes but it is important when the volumes are small and the twisting angles are large. In particular we find a measurable effect for the plaquette and the pion correlation function in the case of $\\theta=\\pi/2$ in a volume $16\\times 8^3$, and we observe a syst...
Effects of Boundary Conditions on Single-File Pedestrian Flow
Zhang, Jun; Seyfried, Armin
2015-01-01
In this paper we investigate effects of boundary conditions on one dimensional pedestrian flow which involves purely longitudinal interactions. Qualitatively, stop-and-go waves are observed under closed boundary condition and dissolve when the boundary is open. To get more detailed information the fundamental diagrams of the open and closed systems are compared using Voronoi-based measurement method. Higher maximal specific flow is observed from the pedestrian movement at open boundary condition.
Liu, Zhiqiang; Gan, Jianping
2016-08-01
In limited-area ocean models, open boundary conditions (OBCs) often create dynamic inconsistencies and perform poorly in resolving tidal or subtidal flow when both forces exist. Orlanski-type radiation OBCs are reasonably efficient at treating the subtidally forced flow, and Flather-type OBCs are commonly adapted for the tidally forced flow. However, neither of them performs well when tidal and subtidal forces simultaneously drive the flows. We have developed a novel OBC that integrates the active OBC in Gan and Allen (2005) and a Flather-type OBC. This new OBC accommodates the concurrent Tidal and Subtidal (TST) forcing, and the respective tidal or subtidal forcing, at the open boundary of a limited-area model. This new TST-OBC treats the tidal component with a Flather-type OBC, and it separates subtidal barotropic and baroclinic components into local (forced) and global (unforced) components. Then an unforced Orlanski-type OBC can be applied to the global part. We applied the TST-OBC to all model variables to reduce dynamic inconsistence. Using the Regional Ocean Modeling System, we applied the TST-OBC to the shallow East China Sea shelf where strong tidal and subtidal forces over complex topography govern the circulation. Our numerical experiments and analyses suggest that the TST-OBC was robust for both concurrent tidal-subtidal forcing and solely tidal or subtidal forcing at the open boundary. It reduced spurious energy reflection, and, overall, it performed better than an Orlanski-type or Flather-type OBC in reproducing realistic tidal and subtidal shelf circulation.
Boundary Conditions of Weyl Semimetals
Hashimoto, Koji; Wu, Xi
2016-01-01
We find that generic boundary conditions of Weyl semimetal is dictated by only a single real parameter, in the continuum limit. We determine how the energy dispersions (the Fermi arcs) and the wave functions of edge states depend on this parameter. Lattice models are found to be consistent with our generic observation. Furthermore, the enhanced parameter space of the boundary condition is shown to support a novel topological number.
Spectrum of boundary states in the open Hubbard chain
Energy Technology Data Exchange (ETDEWEB)
Beduerftig, Gerald; Frahm, Holger [Institut fuer Theoretische Physik, Universitaet Hannover, Hannover (Germany)
1997-06-21
We use the Bethe ansatz solution for the one-dimensional Hubbard model with open boundary conditions and applied boundary fields to study the spectrum of bound states at the boundary. Depending on the strength of the boundary potentials, one finds that the true ground state contains a single charge or, for boundary potentials comparable with the Hubbard interaction, a pair of electrons in a bound state. If these are left unoccupied one finds holon and spinon bound states. We compute the finite size corrections to the low-lying energies in this system and use the predictions of boundary conformal field theory to study the exponents related to the orthogonality catastrophe. (author)
Boundary conditions for the gravitational field
Winicour, Jeffrey
2012-06-01
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation of Einstein's equations and a tetrad formulation of the Einstein-Bianchi system. However, a universal approach valid for other formulations is not in hand. In particular, there is no satisfactory boundary theory for the 3+1 formulations which have been highly successful in binary black hole simulation. I discuss the underlying problems that make the initial-boundary-value problem much more complicated than the Cauchy problem. I review the progress that has been made and the important open questions that remain. Science is a differential equation. Religion is a boundary condition. (Alan Turing, quoted in J D Barrow, ‘Theories of Everything’)
Higgsless Deconstruction Without Boundary Condition
He, H J
2004-01-01
Deconstruction is a powerful means to explore the rich dynamics of gauge theories in four and higher dimensions. We demonstrate that gauge symmetry breaking in a compactified higher dimensional theory can be formulated via deconstructed 4D moose theory with {\\it spontaneous symmetry breaking} and {\\it without boundary condition.} The proper higher-D boundary conditions are automatically induced in the continuum limit rather than being imposed. We identify and analyze the moose theories which exhibit {\\it delayed unitarity violation} (effective unitarity) as a {\\it collective effect} of many gauge groups, without resorting to any known 5D geometry. Relevant phenomenological constraints are also addressed.
Incoherent boundary conditions and metastates
Enter, Aernout C.D. van; Netočný, Karel; Schaap, Hendrikjan G.
2006-01-01
In this contribution we discuss the role which incoherent boundary conditions can play in the study of phase transitions. This is a question of particular relevance for the analysis of disordered systems, and in particular of spin glasses. For the moment our mathematical results only apply to ferrom
Topological expansion and boundary conditions
Eynard, Bertrand
2008-01-01
In this article, we compute the topological expansion of all possible mixed-traces in a hermitian two matrix model. In other words we give a recipe to compute the number of discrete surfaces of given genus, carrying an Ising model, and with all possible given boundary conditions. The method is recursive, and amounts to recursively cutting surfaces along interfaces. The result is best represented in a diagrammatic way, and is thus rather simple to use.
Surface free energy for systems with integrable boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Goehmann, Frank [Fachbereich C-Physik, Bergische Universitaet Wuppertal, 42097 Wuppertal (Germany); Bortz, Michael [Department of Theoretical Physics, Australian National University, Canberra ACT 0200 (Australia); Frahm, Holger [Institut fuer Theoretische Physik, Universitaet Hannover, 30167 Hannover (Germany)
2005-12-16
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.
Quantum "violation" of Dirichlet boundary condition
Park, I. Y.
2017-02-01
Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a 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
2016-01-01
Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a clash between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum corrected solution of the 1PI action no longer obeys the Dirichlet boundary conditions imposed at the classical level. We attribute the violation of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
Probability of boundary conditions in quantum cosmology
Suenobu, Hiroshi; Nambu, Yasusada
2017-02-01
One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with a constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.
Absorbing Boundary Conditions for Hyperbolic Systems
Institute of Scientific and Technical Information of China (English)
Matthias Ehrhardt
2010-01-01
This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions. We prove the strict well-posedness of the resulting initial boundary value problem in 1D. Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme. Hereby, we have to extend the classical proofs, since the (discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.
Compact difference approximation with consistent boundary condition
Institute of Scientific and Technical Information of China (English)
FU Dexun; MA Yanwen; LI Xinliang; LIU Mingyu
2003-01-01
For simulating multi-scale complex flow fields it should be noted that all the physical quantities we are interested in must be simulated well. With limitation of the computer resources it is preferred to use high order accurate difference schemes. Because of their high accuracy and small stencil of grid points computational fluid dynamics (CFD) workers pay more attention to compact schemes recently. For simulating the complex flow fields the treatment of boundary conditions at the far field boundary points and near far field boundary points is very important. According to authors' experience and published results some aspects of boundary condition treatment for far field boundary are presented, and the emphasis is on treatment of boundary conditions for the upwind compact schemes. The consistent treatment of boundary conditions at the near boundary points is also discussed. At the end of the paper are given some numerical examples. The computed results with presented method are satisfactory.
Probability of boundary conditions in quantum cosmology
Nambu, Yasusada; Suenobu, Hiroshi
2017-08-01
One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with a constant scalar field potential. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.
Boundary conditions of methamphetamine craving.
Lopez, Richard B; Onyemekwu, Chukwudi; Hart, Carl L; Ochsner, Kevin N; Kober, Hedy
2015-12-01
Methamphetamine use has increased significantly and become a global health concern. Craving is known to predict methamphetamine use and relapse following abstinence. Some have suggested that cravings are automatic, generalized, and uncontrollable, but experimental work addressing these claims is lacking. In 2 exploratory studies, we tested the boundary conditions of methamphetamine craving by asking: (a) is craving specific to users' preferred route of administration?, and (b) can craving be regulated by cognitive strategies? Two groups of methamphetamine users were recruited. In Study 1, participants were grouped by their preferred route of administration (intranasal vs. smoking), and rated their craving in response to photographs and movies depicting methamphetamine use (via the intranasal vs. smoking route). In Study 2, methamphetamine smokers implemented cognitive regulation strategies while viewing photographs depicting methamphetamine smoking. Strategies involved either focusing on the positive aspects of smoking methamphetamine or the negative consequences of doing so-the latter strategy based on treatment protocols for addiction. In Study 1, we found a significant interaction between group and route of administration, such that participants who preferred to smoke methamphetamine reported significantly stronger craving for smoking stimuli, whereas those who preferred the intranasal route reported stronger craving for intranasal stimuli. In Study 2, participants reported significantly lower craving when focusing on the negative consequences associated with methamphetamine use. Taken together, these findings suggest that strength of craving for methamphetamine is moderated by users' route of administration and can be reduced by cognitive strategies. This has important theoretical, methodological, and clinical implications. (PsycINFO Database Record (c) 2015 APA, all rights reserved).
Conformal Boundary Conditions and what they teach us
Petkova, V B
2001-01-01
The question of boundary conditions in conformal field theories is discussed, in the light of recent progress. Two kinds of boundary conditions are examined, along open boundaries of the system, or along closed curves or ``seams''. Solving consistency conditions known as Cardy equation is shown to amount to the algebraic problem of finding integer valued representations of (one or two copies of) the fusion algebra. Graphs encode these boundary conditions in a natural way, but are also relevant in several aspects of physics ``in the bulk''. Quantum algebras attached to these graphs contain information on structure constants of the operator algebra, on the Boltzmann weights of the corresponding integrable lattice models etc. Thus the study of boundary conditions in Conformal Field Theory offers a new perspective on several old physical problems and offers an explicit realisation of recent mathematical concepts.
Boundary conditions for viscous vortex methods
Energy Technology Data Exchange (ETDEWEB)
Koumoutsakos, P.; Leonard, A.; Pepin, F. (California Institute of Technology, Pasadena, CA (United States))
1994-07-01
This paper presents a Neumann-type vorticity boundary condition for the vorticity formulation of the Navier-Stokes equations. The vorticity creation process at the boundary, due to the no-slip condition, is expressed in terms of a vorticity flux. The scheme is incorporated then into a Lagrangian vortex blob method that uses a particle strength exchange algorithm for viscous diffusion. The no-slip condition is not enforced by the generation of new vortices at the boundary but instead by modifying the strength of the vortices in the vicinity of the boundary. 19 refs., 5 figs.
Born series for the Robin boundary condition
Machida, Manabu; Nakamura, Gen
2017-01-01
We solve the diffusion equation by constructing the Born series for the Robin boundary condition. We develop a general theory for arbitrary domains with smooth enough boundaries and explore the convergence. The proposed Born series is validated by numerical calculation in the three-dimensional half space. We show that in this case the Born series converges regardless the value of the impedance term in the Robin boundary condition. We point out that the solution from the so-called extrapolated...
Absorption boundary conditions for geomertical acoustics
DEFF Research Database (Denmark)
Jeong, Cheol-Ho
2012-01-01
Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, the absorption coefficients or surface impedances of the boundary surfaces can be used, but no guideline has been developed...... solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. It is concluded that the impedance and random incidence absorption boundary conditions produce reasonable results with some exceptions at low frequencies for acoustically soft materials....
Percolation of open grain boundaries and change in electrical conductivity
Watanabe, T.
2016-12-01
Numerical experiments were conducted on the percolation of open grain boundaries to study the percolation threshold and evolution of connectivity. Open grain boundaries are a major component of pores in crustal materials. Electrical conductivity and permeability are highly sensitive to the connectivity of open brain boundaries. The length and size of the largest cluster was surveyed in a 3D array of cubic grains for various fractions of open grain boundary. For sufficiently large size of array, the percolation threshold was found to be 0.25. If more than 25% of grain boundaries are open, an interconnected network of open grain boundaries is formed. If the aggregate is saturated with brine, the electrical conduction can occur through open grain boundaries. The connectivity of open grain boundaries steeply increases to 1 around the threshold. The electrical conductivity is also expected to increase steeply. The crack density parameter for the percolation threshold is estimated to be 0.1. The large change in electrical conductivity for a small change in crack density parameter is thus expected around crack density parameter of 0.1. Simultaneous measurements on elastic wave velocity and electrical conductivity in a brine saturated granitic rock (Watanabe and Higuchi, 2015) showed a steep change in electrical conductivity around the crack density parameter of 0.1. XCT images show that open grain boundaries are the dominant pores in the sample. The steep change in conductivity must thus be related to the percolation of open grain boundaries.
Boundary conditions: The path integral approach
Energy Technology Data Exchange (ETDEWEB)
Asorey, M [Departamento de Fisica Teorica, Universidad de Zaragoza 50009 Zaragoza (Spain); Clemente-Gallardo, J [BIFI, Universidad de Zaragoza, 50009 Zaragoza (Spain); Munoz-Castaneda, J M [Departamento de Fisica Teorica, Universidad de Zaragoza 50009 Zaragoza (Spain)
2007-11-15
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Nonlocal boundary conditions can be introduced in Feynman's approach by means of boundary amplitude distributions and complex phases to describe the quantum dynamics in terms of the classical trajectories. The different prescriptions involve only trajectories reaching the boundary and correspond to different choices of boundary conditions of selfadjoint extensions of the Hamiltonian. One dimensional particle dynamics is analysed in detail.
On filter boundary conditions in topology optimization
DEFF Research Database (Denmark)
Clausen, Anders; Andreassen, Erik
2017-01-01
we define three requirements that boundary conditions must fulfill in order to eliminate boundary effects. Previously suggested approaches are briefly reviewed in the light of these requirements. A new approach referred to as the “domain extension approach” is suggested. It effectively eliminates......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...
Probability of Boundary Conditions in Quantum Cosmology
Suenobu, Hiroshi
2016-01-01
One of the main interest in quantum cosmology is to determine which type of boundary conditions for the wave function of the universe can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation numerically and evaluate probabilities for an observable representing evolution of the classical universe, especially, the number of e-foldings of the inflation. To express boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify them introducing two real parameters which discriminate boundary conditions and estimate values of these parameters resulting in observationally preferable predictions. We obtain the probability for these parameters under the requirement of the sufficient e-foldings of the inflation.
Logarithmic Minimal Models with Robin Boundary Conditions
Bourgine, Jean-Emile; Tartaglia, Elena
2016-01-01
We consider general logarithmic minimal models ${\\cal LM}(p,p')$, with $p,p'$ coprime, on a strip of $N$ columns with the $(r,s)$ Robin boundary conditions introduced by Pearce, Rasmussen and Tipunin. The associated conformal boundary conditions are labelled by the Kac labels $r\\in{\\Bbb Z}$ and $s\\in{\\Bbb N}$. The Robin vacuum boundary condition, labelled by $(r,s\\!-\\!\\frac{1}{2})=(0,\\mbox{$\\textstyle \\frac{1}{2}$})$, is given as a linear combination of Neumann and Dirichlet boundary conditions. The general $(r,s)$ Robin boundary conditions are constructed, using fusion, by acting on the Robin vacuum boundary with an $(r,s)$-type seam consisting of an $r$-type seam of width $w$ columns and an $s$-type seam of width $d=s-1$ columns. The $r$-type seam admits an arbitrary boundary field which we fix to the special value $\\xi=-\\tfrac{\\lambda}{2}$ where $\\lambda=\\frac{(p'-p)\\pi}{2p'}$ is the crossing parameter. The $s$-type boundary introduces $d$ defects into the bulk. We consider the associated quantum Hamiltoni...
Experimental studies of pedestrian flows under different boundary conditions
Zhang, Jun
2015-01-01
In this article the dynamics of pedestrian streams in four different scenarios are compared empirically to investigate the influence of boundary conditions on it. The Voronoi method, which allows high resolution and small fluctuations of measured density in time and space, is used to analyze the experiments. It is found that pedestrian movement in systems with different boundary conditions (open, periodic boundary conditions and outflow restrained) presents various characteristics especially when the density is larger than 2 m-2. In open corridor systems the specific flow increases continuously with increasing density till 4 m-2. The specific flow keeps constant in systems with restrained outflow, whereas it decreases from 1 (m.s)-1 to zero in system with closed periodical condition.
Numerical implementation of isolated horizon boundary conditions
Jaramillo, J L; Limousin, F
2006-01-01
We study the numerical implementation of a set of boundary conditions derived from the isolated horizon formalism, and which characterize a black hole whose horizon is in quasi-equilibrium. More precisely, we enforce these geometrical prescriptions as inner boundary conditions on an excised sphere, in the numerical resolution of the Conformal Thin Sandwich equations. As main results, we firstly establish the consistency of including in the set of boundary conditions a "constant surface gravity" prescription, interpretable as a lapse boundary condition, and secondly we assess how the prescriptions presented recently by Dain et al. for guaranteeing the well-posedness of the Conformal Transverse Traceless equations with quasi-equilibrium horizon conditions extend to the Conformal Thin Sandwich elliptic system. As a consequence of the latter analysis, we discuss the freedom of prescribing the expansion associated with the ingoing null normal at the horizon.
Normal ordering and boundary conditions for fermionic string coordinates
Braga, N R F; Godinho, C F L; Braga, Nelson R. F.; Carrion, Hector L.; Godinho, Cresus F. L.
2006-01-01
We build up normal ordered products for fermionic open string coordinates consistent with boundary conditions. The results are obtained considering the presence of antisymmetric tensor fields. We find a discontinuity of the normal ordered products at string endpoints even in the absence of the background. We discuss how the energy momentum tensor also changes at the world-sheet boundary in such a way that the central charge keeps the standard value at string end points.
Normal ordering and boundary conditions for fermionic string coordinates
Energy Technology Data Exchange (ETDEWEB)
Braga, Nelson R.F. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro, RJ (Brazil)]. E-mail: braga@if.ufrj.br; Carrion, Hector L. [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP (Brazil)]. E-mail: hlc@fma.if.usp.br; Godinho, Cresus F.L. [Centro Brasileiro de Pesquisas Fisicas, Rua Dr Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ (Brazil)]. E-mail: godinho@cbpf.br
2006-07-06
We build up normal ordered products for fermionic open string coordinates consistent with boundary conditions. The results are obtained considering the presence of antisymmetric tensor fields. We find a discontinuity of the normal ordered products at string endpoints even in the absence of the background. We discuss how the energy-momentum tensor also changes at the world-sheet boundary in such a way that central charge keeps the standard value at string end points.
Efficient simulations with electronic open boundaries
Horsfield, Andrew P.; Boleininger, Max; D'Agosta, Roberto; Iyer, Vyas; Thong, Aaron; Todorov, Tchavdar N.; White, Catherine
2016-08-01
We present a reformulation of the hairy-probe method for introducing electronic open boundaries that is appropriate for steady-state calculations involving nonorthogonal atomic basis sets. As a check on the correctness of the method we investigate a perfect atomic wire of Cu atoms and a perfect nonorthogonal chain of H atoms. For both atom chains we find that the conductance has a value of exactly one quantum unit and that this is rather insensitive to the strength of coupling of the probes to the system, provided values of the coupling are of the same order as the mean interlevel spacing of the system without probes. For the Cu atom chain we find in addition that away from the regions with probes attached, the potential in the wire is uniform, while within them it follows a predicted exponential variation with position. We then apply the method to an initial investigation of the suitability of graphene as a contact material for molecular electronics. We perform calculations on a carbon nanoribbon to determine the correct coupling strength of the probes to the graphene and obtain a conductance of about two quantum units corresponding to two bands crossing the Fermi surface. We then compute the current through a benzene molecule attached to two graphene contacts and find only a very weak current because of the disruption of the π conjugation by the covalent bond between the benzene and the graphene. In all cases we find that very strong or weak probe couplings suppress the current.
Modelling classroom conditions with different boundary conditions
DEFF Research Database (Denmark)
Marbjerg, Gerd Høy; Jeong, Cheol-Ho; Brunskog, Jonas
2014-01-01
both specular and diffuse reflections with complex-valued acoustical descriptions of the surfaces. In this paper the PARISM model is used to simulate a rectangular room with most of the absorption located in the ceiling. This room configuration is typical for classroom conditions. The simulations...... measures which are important for evaluation of the acoustics in classrooms....
Modelling classroom conditions with different boundary conditions
DEFF Research Database (Denmark)
Marbjerg, Gerd Høy; Jeong, Cheol-Ho; Brunskog, Jonas
2014-01-01
both specular and diffuse reflections with complex-valued acoustical descriptions of the surfaces. In this paper the PARISM model is used to simulate a rectangular room with most of the absorption located in the ceiling. This room configuration is typical for classroom conditions. The simulations...
Student difficulties with Boundary Conditions in electrodynamics
Ryan, Qing X; Wilcox, Bethany R
2015-01-01
Boundary conditions (BCs) are considered as an important topic that advanced physics under- graduates are expected to understand and apply. We report findings from an investigation of student difficulties using boundary conditions (BCs) in electrodynamics. Our data sources include student responses to traditional exam questions, conceptual survey questions, and think-aloud interviews. The analysis was guided by an analytical framework that characterizes how students activate, con- struct, execute, and reflect on boundary conditions. Common student difficulties include: activating boundary conditions in appropriate contexts; constructing a complex expression for the E&M waves; mathematically simplifying complex exponentials and checking if the reflection and transmission co- efficient are physical. We also present potential pedagogical implications based on our observations.
Optimal Boundary Conditions for ORCA-2 Model
Kazantsev, Eugene
2012-01-01
A 4D-Var data assimilation technique is applied to a ORCA-2 configuration of the NEMO in order to identify the optimal parametrization of the boundary conditions on the lateral boundaries as well as on the bottom and on the surface of the ocean. The influence of the boundary conditions on the solution is analyzed as in the assimilation window and beyond the window. It is shown that optimal conditions for vertical operators allows to get stronger and finer jet streams (Gulf Stream, Kuroshio) in the solution. Analyzing the reasons of the jets reinforcement, we see that the major impact of the data assimilation is made on the parametrization of the bottom boundary conditions for lateral velocities u and v. Automatic generation of the tangent and adjoint codes is also discussed. Tapenade software is shown to be able to produce the adjoint code that can be used after a memory usage optimization.
Multireflection boundary conditions for lattice Boltzmann models.
Ginzburg, Irina; d'Humières, Dominique
2003-12-01
We present a general framework for several previously introduced boundary conditions for lattice Boltzmann models, such as the bounce-back rule and the linear and quadratic interpolations. The objectives are twofold: first to give theoretical tools to study the existing link-type boundary conditions and their corresponding accuracy; second to design boundary conditions for general flows which are third-order kinetic accurate. Using these new boundary conditions, Couette and Poiseuille flows are exact solutions of the lattice Boltzmann models for a Reynolds number Re=0 (Stokes limit) for arbitrary inclination with the lattice directions. Numerical comparisons are given for Stokes flows in periodic arrays of spheres and cylinders, linear periodic array of cylinders between moving plates, and for Navier-Stokes flows in periodic arrays of cylinders for Re<200. These results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce-back reflection (up to an order of magnitude on the hydrodynamics fields). Further improvement is achieved with the new multireflection boundary conditions, reaching a level of accuracy close to the quasianalytical reference solutions, even for rather modest grid resolutions and few points in the narrowest channels. More important, the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions. Finally the good stability of these schemes is highlighted by some simulations of moving obstacles: a cylinder between flat walls and a sphere in a cylinder.
Twisted Boundary Conditions in Lattice Simulations
Sachrajda, Christopher T C
2004-01-01
By imposing twisted boundary conditions on quark fields it is possible to access components of momenta other than integer multiples of 2pi/L on a lattice with spatial volume L^3. We use Chiral Perturbation Theory to study finite-volume effects with twisted boundary conditions for quantities without final-state interactions, such as meson masses, decay constants and semileptonic form factors, and confirm that they remain exponentially small with the volume. We show that this is also the case for "partially twisted" boundary conditions, in which (some of) the valence quarks satisfy twisted boundary conditions but the sea quarks satisfy periodic boundary conditions. This observation implies that it is not necessary to generate new gluon configurations for every choice of the twist angle, making the method much more practicable. For K->pipi decays we show that the breaking of isospin symmetry by the twisted boundary conditions implies that the amplitudes cannot be determined in general (on this point we disagree ...
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.
Future Boundary Conditions in De Sitter Space
Anninos, Dionysios; Strominger, Andrew
2011-01-01
We consider asymptotically future de Sitter spacetimes endowed with an eternal observatory. In the conventional descriptions, the conformal metric at the future boundary I^+ is deformed by the flux of gravitational radiation. We however impose an unconventional future "Dirichlet" boundary condition requiring that the conformal metric is flat everywhere except at the conformal point where the observatory arrives at I^+. This boundary condition violates conventional causality, but we argue the causality violations cannot be detected by any experiment in the observatory. We show that the bulk-to-bulk two-point functions obeying this future boundary condition are not realizable as operator correlation functions in any de Sitter invariant vacuum, but they do agree with those obtained by double analytic continuation from anti-de Sitter space.
Transmitting boundary and radiation conditions at infinity
Institute of Scientific and Technical Information of China (English)
廖振鹏
2001-01-01
Relationship between the radiation conditions at infinity and the transmitting boundary for numerical simulation of the near-field wave motion has been studied in this paper. The conclusion is that the transmitting boundary is approximately equivalent to the radiation conditions at infinity for a large class of infinite media. And the errors of the approximation are of the same order of magnitude as those of the finite elements or finite differences in numerical simulation of wave motion. This result provides a sound theoretical basis for the transmitting boundary used in the numerical simulation of the near-field wave motion and gives a complete explanation for the major experiences accumulated in applications of the transmitting boundary to the numerical simulation.
Generalized additional boundary conditions for wire media
Energy Technology Data Exchange (ETDEWEB)
Maslovski, Stanislav I; Morgado, Tiago A; Silveirinha, Mario G [Departamento de Engenharia Electrotecnica, Instituto de Telecomunicacoes, Universidade de Coimbra, Polo II, 3030-290 Coimbra (Portugal); Kaipa, Chandra S R; Yakovlev, Alexander B, E-mail: stas@co.it.p [Department of Electrical Engineering, University of Mississippi, University, MS 38677-1848 (United States)
2010-11-15
We generalize additional boundary conditions (ABCs) for wire media by including arbitrary wire junctions with impedance loading. Special attention is given to the conditions at the interface of two uniaxial wire media with metallic patches at the junction. The derived ABCs are validated against full-wave numerical simulations.
Anchored boundary conditions for locally isostatic networks
Theran, Louis; Nixon, Anthony; Ross, Elissa; Sadjadi, Mahdi; Servatius, Brigitte; Thorpe, M. F.
2015-11-01
Finite pieces of locally isostatic networks have a large number of floppy modes because of missing constraints at the surface. Here we show that by imposing suitable boundary conditions at the surface the network can be rendered effectively isostatic. We refer to these as anchored boundary conditions. An important example is formed by a two-dimensional network of corner sharing triangles, which is the focus of this paper. Another way of rendering such networks isostatic is by adding an external wire along which all unpinned vertices can slide (sliding boundary conditions). This approach also allows for the incorporation of boundaries associated with internal holes and complex sample geometries, which are illustrated with examples. The recent synthesis of bilayers of vitreous silica has provided impetus for this work. Experimental results from the imaging of finite pieces at the atomic level need such boundary conditions, if the observed structure is to be computer refined so that the interior atoms have the perception of being in an infinite isostatic environment.
Constructing parametric triangular patches with boundary conditions
Institute of Scientific and Technical Information of China (English)
Hui Liu; Jun Ma; Fuhua Cheng
2008-01-01
The problem of constructing a parametric triangular patch to smoothly connect three surface patches is studied. Usually, these surface patches are defined on different parameter spaces. Therefore, it is necessary to define interpolation conditions, with values from the given surface patches, on the boundary of the triangular patch that can ensure smooth transition between different parameter spaces. In this paper we present a new method to define boundary conditions. Boundary conditions defined by the new method have the same parameter space if the three given surface patches can be converted into the same form through affine transformation. Consequently, any of the classic methods for constructing functional triangular patches can be used directly to construct a parametric triangular patch to connect given surface patches with G continuity. The resulting parametric triangular patch preserves precision of the applied classic method.
ADHMN boundary conditions from removing monopoles
Chen, X; Chen, Xingang; Weinberg, Erick J.
2003-01-01
Boundary conditions play an important role in the ADHMN construction of BPS monopole solutions. In this paper we show how different types of boundary conditions can be related to each other by removing monopoles to spatial infinity. In particular, we use this method to show how the jumping data naturally emerge. The results can be interpreted in the D-brane picture and provide a better understanding of the derivation of the ADHMN construction from D-branes. We comment briefly on the cases with non-Abelian unbroken symmetry and massless monopoles.
Mixed boundary conditions for piezoelectric plates
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
For plate bending and stretching problems in piezoelectric materials,the reciprocal theorem and the general solution of piezoelasticity are applied in a novel way to obtain the appropriate mixed boundary conditions accurate to all order.A decay analysis technique is used to establish necessary conditions that the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the plate.For the case of axisymmetric bending and stretching of a circular plate,these decaying state conditions are obtained explicitly for the first time when the mixed conditions are imposed on the plate edge.They are then used for the correct formulation of boundary conditions for the interior solution.
Casimir pistons with general boundary conditions
Directory of Open Access Journals (Sweden)
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.
Energy Technology Data Exchange (ETDEWEB)
Rian, Kjell Erik
2003-07-01
In numerical simulations of turbulent reacting compressible flows, artificial boundaries are needed to obtain a finite computational domain when an unbounded physical domain is given. Artificial boundaries which fluids are free to cross are called open boundaries. When calculating such flows, non-physical reflections at the open boundaries may occur. These reflections can pollute the solution severely, leading to inaccurate results, and the generation of spurious fluctuations may even cause the numerical simulation to diverge. Thus, a proper treatment of the open boundaries in numerical simulations of turbulent reacting compressible flows is required to obtain a reliable solution for realistic conditions. A local quasi-one-dimensional characteristic-based open-boundary treatment for the Favre-averaged governing equations for time-dependent three-dimensional multi-component turbulent reacting compressible flow is presented. A k-{epsilon} model for turbulent compressible flow and Magnussen's EDC model for turbulent combustion is included in the analysis. The notion of physical boundary conditions is incorporated in the method, and the conservation equations themselves are applied on the boundaries to complement the set of physical boundary conditions. A two-dimensional finite-difference-based computational fluid dynamics code featuring high-order accurate numerical schemes was developed for the numerical simulations. Transient numerical simulations of the well-known, one-dimensional shock-tube problem, a two-dimensional pressure-tower problem in a decaying turbulence field, and a two-dimensional turbulent reacting compressible flow problem have been performed. Flow- and combustion-generated pressure waves seem to be well treated by the non-reflecting subsonic open-boundary conditions. Limitations of the present open-boundary treatment are demonstrated and discussed. The simple and solid physical basis of the method makes it both favourable and relatively easy to
Boundary Value Problems With Integral Conditions
Karandzhulov, L. I.; Sirakova, N. D.
2011-12-01
The weakly perturbed nonlinear boundary value problems (BVP) for almost linear systems of ordinary differential equations (ODE) are considered. We assume that the nonlinear part contain an additional function, which defines the perturbation as singular. Then the Poincare method is not applicable. The problem of existence, uniqueness and construction of a solution of the posed BVP with integral condition is studied.
Boundary Conditions at Infinity for Physical Theories
Trautman, Andrzej
2016-01-01
The Sommerfeld boundary conditions, imposed on hyperbolic differential equations to obtain solutions in the form of outgoing waves, are formulated here so as to make explicit the role of an appropriate null vector field. When applied to the scalar and Maxwell equations, they lead to the asymptotic form of the energy-momentum tensor representing radiation as a null, perfect dust.
An h-principle with boundary condition
DEFF Research Database (Denmark)
Dotto, Emanuele
2010-01-01
We prove an h-principle with boundary condition for a certain class of topological spaces valued sheaves. The techniques used in the proof come from the study of the homotopy type of the cobordism categories, and they are of simplicial and categorical nature. Applying the main result of this paper...
Abstract wave equations with acoustic boundary conditions
Mugnolo, Delio
2010-01-01
We define an abstract setting to treat wave equations equipped with time-dependent acoustic boundary conditions on bounded domains of ${\\bf R}^n$. We prove a well-posedness result and develop a spectral theory which also allows to prove a conjecture proposed in (Gal-Goldstein-Goldstein, J. Evol. Equations 3 (2004), 623-636). Concrete problems are also discussed.
Radiation (absorbing) boundary conditions for electromagnetic fields
Bevensee, R. M.; Pennock, S. T.
1987-01-01
An important problem in finite difference or finite element computation of the electromagnetic field obeying the space-time Maxwell equations with self-consistent sources is that of truncating the outer numerical boundaries properly to avoid spurious numerical reflection. Methods for extrapolating properly the fields just beyond a numerical boundary in free space have been treated by a number of workers. This report avoids plane wave assumptions and derives boundary conditions more directly related to the source distribution within the region. The Panofsky-Phillips' relations, which enable one to extrapolate conveniently the vector field components parallel and perpendicular to a radial from the coordinate origin chosen near the center of the charge-current distribution are used to describe the space-time fields.
A Rotational Pressure-Correction Scheme for Incompressible Two-Phase Flows with Open Boundaries.
Dong, S; Wang, X
2016-01-01
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present several new forms of open boundary conditions for two-phase outflow simulations within the phase field framework, as well as a rotational pressure correction based algorithm for numerically treating these open boundary conditions. Our algorithm gives rise to linear algebraic systems for the velocity and the pressure that involve only constant and time-independent coefficient matrices after discretization, despite the variable density and variable viscosity of the two-phase mixture. By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results. We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries.
Javili, A.; Saeb, S.; Steinmann, P.
2016-10-01
In the past decades computational homogenization has proven to be a powerful strategy to compute the overall response of continua. Central to computational homogenization is the Hill-Mandel condition. The Hill-Mandel condition is fulfilled via imposing displacement boundary conditions (DBC), periodic boundary conditions (PBC) or traction boundary conditions (TBC) collectively referred to as canonical boundary conditions. While DBC and PBC are widely implemented, TBC remains poorly understood, with a few exceptions. The main issue with TBC is the singularity of the stiffness matrix due to rigid body motions. The objective of this manuscript is to propose a generic strategy to implement TBC in the context of computational homogenization at finite strains. To eliminate rigid body motions, we introduce the concept of semi-Dirichlet boundary conditions. Semi-Dirichlet boundary conditions are non-homogeneous Dirichlet-type constraints that simultaneously satisfy the Neumann-type conditions. A key feature of the proposed methodology is its applicability for both strain-driven as well as stress-driven homogenization. The performance of the proposed scheme is demonstrated via a series of numerical examples.
Javili, A.; Saeb, S.; Steinmann, P.
2017-01-01
In the past decades computational homogenization has proven to be a powerful strategy to compute the overall response of continua. Central to computational homogenization is the Hill-Mandel condition. The Hill-Mandel condition is fulfilled via imposing displacement boundary conditions (DBC), periodic boundary conditions (PBC) or traction boundary conditions (TBC) collectively referred to as canonical boundary conditions. While DBC and PBC are widely implemented, TBC remains poorly understood, with a few exceptions. The main issue with TBC is the singularity of the stiffness matrix due to rigid body motions. The objective of this manuscript is to propose a generic strategy to implement TBC in the context of computational homogenization at finite strains. To eliminate rigid body motions, we introduce the concept of semi-Dirichlet boundary conditions. Semi-Dirichlet boundary conditions are non-homogeneous Dirichlet-type constraints that simultaneously satisfy the Neumann-type conditions. A key feature of the proposed methodology is its applicability for both strain-driven as well as stress-driven homogenization. The performance of the proposed scheme is demonstrated via a series of numerical examples.
Discrete holomorphicity and integrability in loop models with open boundaries
de Gier, Jan; Rasmussen, Jorgen
2012-01-01
We consider boundary conditions compatible with discrete holomorphicity for the dilute O(n) and C_2^(1) loop models. In each model, for a general set of boundary plaquettes, multiple types of loops can appear. A generalisation of Smirnov's parafermionic observable is therefore required in order to maintain the discrete holomorphicity property in the bulk. We show that there exist natural boundary conditions for this observable which are consistent with integrability, that is to say that, by imposing certain boundary conditions, we obtain a set of linear equations whose solutions also satisfy the corresponding reflection equation. In both loop models, several new sets of integrable weights are found using this approach.
Restructuring surface tessellation with irregular boundary conditions
Directory of Open Access Journals (Sweden)
Tsung-Hsien Wang
2014-12-01
Full Text Available In this paper, the surface tessellation problem is explored, in particular, the task of meshing a surface with the added consideration of incorporating constructible building components. When a surface is tessellated into discrete counterparts, certain unexpected conditions usually occur at the boundary of the surface, in particular, when the surface is being trimmed. For example, irregularly shaped panels form at the trimmed edges. To reduce the number of irregular panels that may form during the tessellation process, this paper presents an algorithmic approach to restructuring the surface tessellation by investigating irregular boundary conditions. The objective of this approach is to provide an alternative way for freeform surface manifestation from a well-structured discrete model of the given surface.
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.
Semi-implicit Image Denoising Algorithm for Different Boundary Conditions
Directory of Open Access Journals (Sweden)
Yuying Shi
2013-04-01
Full Text Available In this paper, the Crank-Nicolson semi-implicit difference scheme in matrix form is applied to discrete the Rudin-Osher-Fatemi model. We also consider different boundary conditions: Dirichlet boundary conditions, periodic boundary conditions, Neumann boundary conditions, antireflective boundary conditions and mean boundary conditions. By comparing the experimental results of Crank-Nicolson semi-implicit scheme and explicit scheme with the proposed boundary conditions, we can get that the semi-implicit scheme can overcome the instability and the number of iterations of the shortcomings that the explicit discrete scheme has, and its recovery effects are better than the explicit discrete scheme. In addition, the antireflective boundary conditions and Neumann boundary conditions can better maintain the continuity of the boundary in image denoising.
Magnetic Structure of the Magnetopause Boundary Layer for Open Magnetosphere
Ma, Yonghui; Shen, Chao; Zeng, Gang
2017-04-01
Using Cluster and Magnetospheric MultiScale (MMS) spacecraft 4 point magnetic field measurements, we analyzed the magnetic structure of magnetopause boundary layer of the open magnetosphere. It is indicated that the magnetopause boundary layer is very thin under strong magnetic shear and the thickness is usually 0.1 Re. We found that the Rotational Discontinuity (RD) is very important structure at magnetopause when the Interplanetary Magnetic Field (IMF) is southward. Within the boundary layer, the magnetic field has a large rotation. Using curvature calculation method, we got that the minimum curvature radius of magnetic field of RD is 0.02 - 0.1Re, implying that the magnetosphere is open when the IMF is southward. Advanced research showed that the field-aligned currents are common in the magnetopause boundary layer.
Boundary energy of the open XXX chain with a non-diagonal boundary term
Nepomechie, Rafael I.; Wang, Chunguang
2014-01-01
We analyze the ground state of the open spin-1/2 isotropic quantum spin chain with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots split evenly into two sets: those that remain finite, and those that become infinite. We argue that the former satisfy conventional Bethe equations, while the latter satisfy a generalization of the Richardson-Gaudin equations. We derive an expression for the leading correction to the boundary energy in terms of the boundary parameters.
Boundary energy of the open XXX chain with a non-diagonal boundary term
Nepomechie, Rafael I
2013-01-01
We analyze the ground state of the open spin-1/2 isotropic quantum spin chain with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots split evenly into two sets: those that remain finite, and those that become infinite. We argue that the former satisfy conventional Bethe equations, while the latter satisfy a generalization of the Richardson-Gaudin equations. We derive an expression for the leading correction to the boundary energy in terms of the boundary parameters.
Canonical group quantization and boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Jung, Florian
2012-07-16
In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.
An H-Principle With Boundary Condition
Dotto, Emanuele
2010-01-01
We prove an h-principle with boundary condition for a certain class of topological spaces valued sheaves. The techniques used in the proof come from the study of the homotopy type of the cobordism categories, and they are of simplicial and categorical nature. Applying the main result of this paper to a certain sheaf we find another proof of the homotopy equivalence between the classifying space of a cobordism category and a loop space of the Thom space of the complement of the tautological bundle over the Grassmannians.
An h-principle with boundary condition
DEFF Research Database (Denmark)
Dotto, Emanuele
2010-01-01
We prove an h-principle with boundary condition for a certain class of topological spaces valued sheaves. The techniques used in the proof come from the study of the homotopy type of the cobordism categories, and they are of simplicial and categorical nature. Applying the main result of this paper...... to a certain sheaf we find another proof of the homotopy equivalence between the classifying space of a cobordism category and a loop space of the Thom space of the complement of the tautological bundle over the Grassmannians....
The Natural Helmholtz-Hodge Decomposition for Open-Boundary Flow Analysis.
Bhatia, Harsh; Pascucci, Valerio; Bremer, Peer-Timo
2014-11-01
The Helmholtz-Hodge decomposition (HHD), which describes a flow as the sum of an incompressible, an irrotational, and a harmonic flow, is a fundamental tool for simulation and analysis. Unfortunately, for bounded domains, the HHD is not uniquely defined, traditionally, boundary conditions are imposed to obtain a unique solution. However, in general, the boundary conditions used during the simulation may not be known known, or the simulation may use open boundary conditions. In these cases, the flow imposed by traditional boundary conditions may not be compatible with the given data, which leads to sometimes drastic artifacts and distortions in all three components, hence producing unphysical results. This paper proposes the natural HHD, which is defined by separating the flow into internal and external components. Using a completely data-driven approach, the proposed technique obtains uniqueness without assuming boundary conditions a priori. As a result, it enables a reliable and artifact-free analysis for flows with open boundaries or unknown boundary conditions. Furthermore, our approach computes the HHD on a point-wise basis in contrast to the existing global techniques, and thus supports computing inexpensive local approximations for any subset of the domain. Finally, the technique is easy to implement for a variety of spatial discretizations and interpolated fields in both two and three dimensions.
Pushing Firm Boundaries through Research and Open Innovation
DEFF Research Database (Denmark)
Borup Lynggaard, Aviaja
2011-01-01
In this paper we will exemplify open innovation through a university-industry collaboration called Mobile Home Center (MHC). We will demonstrate how the model by Chesbrough can be used as a tool for mapping out a research process and furthermore illustrate what kind of outcast such project can...... provide into the company and bring forward the effect it has inside a company when performing open innovation together with research partners. We seek to bring forward how performing university-research collaboration can also change the practices inside a company and thus push the firm boundaries in new...... directions. Rather than looking at the firm as something static we will demonstrate how Chesbrough’s model on Open Innovation can be used to illustrate the dynamics of a company’s boundaries through Open Innovation....
Thermal field theories and shifted boundary conditions
Giusti, Leonardo
2013-01-01
The analytic continuation to an imaginary velocity of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary conditions. The Poincare' invariance underlying a relativistic theory implies a dependence of the free-energy on the compact length L_0 and the shift xi only through the combination beta=L_0(1+xi^2)^(1/2). This in turn implies that the energy and the momentum distributions of the thermal theory are related, a fact which is encoded in a set of Ward identities among the correlators of the energy-momentum tensor. The latter have interesting applications in lattice field theory: they offer novel ways to compute thermodynamic potentials, and a set of identities to renormalize non-perturbatively the energy-momentum tensor. At fixed bare parameters the shifted boundary conditions also provide a simple method to vary the temperature in much smaller steps than with the standard procedur...
Effective Hydrodynamic Boundary Conditions for Corrugated Surfaces
Mongruel, Anne; Asmolov, Evgeny S; Vinogradova, Olga I
2012-01-01
We report measurements of the hydrodynamic drag force acting on a smooth sphere falling down under gravity to a plane decorated with microscopic periodic grooves. Both surfaces are lyophilic, so that a liquid (silicone oil) invades the surface texture being in the Wenzel state. A significant decrease in the hydrodynamic resistance force as compared with that predicted for two smooth surfaces is observed. To quantify the effect of roughness we use the effective no-slip boundary condition, which is applied at the imaginary smooth homogeneous isotropic surface located at an intermediate position between top and bottom of grooves. Such an effective condition fully characterizes the force reduction measured with the real surface, and the location of this effective plane is related to geometric parameters of the texture by a simple analytical formula.
Modified Pressure-Correction Projection Methods: Open Boundary and Variable Time Stepping
Bonito, Andrea
2014-10-31
© Springer International Publishing Switzerland 2015. In this paper, we design and study two modifications of the first order standard pressure increment projection scheme for the Stokes system. The first scheme improves the existing schemes in the case of open boundary condition by modifying the pressure increment boundary condition, thereby minimizing the pressure boundary layer and recovering the optimal first order decay. The second scheme allows for variable time stepping. It turns out that the straightforward modification to variable time stepping leads to unstable schemes. The proposed scheme is not only stable but also exhibits the optimal first order decay. Numerical computations illustrating the theoretical estimates are provided for both new schemes.
Trapping Horizons as inner boundary conditions for black hole spacetimes
Jaramillo, J L; Cordero-Carrion, I; Ibáñez, J M
2007-01-01
We present a set of inner boundary conditions for the numerical construction of dynamical black hole space-times, when employing a 3+1 constrained evolution scheme and an excision technique. These inner boundary conditions are heuristically motivated by the dynamical trapping horizon framework and are enforced in an elliptic subsystem of the full Einstein equation. In the stationary limit they reduce to existing isolated horizon boundary conditions. A characteristic analysis completes the discussion of inner boundary conditions for the radiative modes.
A Boundary Control Problem for the Viscous Cahn–Hilliard Equation with Dynamic Boundary Conditions
Energy Technology Data Exchange (ETDEWEB)
Colli, Pierluigi, E-mail: pierluigi.colli@unipv.it; Gilardi, Gianni, E-mail: gianni.gilardi@unipv.it [Universitá di Pavia and Research Associate at the IMATI – C.N.R. PAVIA, Dipartimento di Matematica “F. Casorati” (Italy); Sprekels, Jürgen, E-mail: juergen.sprekels@wias-berlin.de [Weierstrass Institute (Germany)
2016-04-15
A boundary control problem for the viscous Cahn–Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved.
On Hydroelastic Body-Boundary Condition of Floating Structures
DEFF Research Database (Denmark)
Xia, Jinzhu
1996-01-01
A general linear body boundary condition of hydroelastic analysis of arbitrary shaped floating structures generalizes the classic kinematic rigid-body (Timman-Newman) boundary condition for seakeeping problems. The new boundary condition is consistent with the existing theories under certain assu...
Thermal momentum distribution from shifted boundary conditions
Giusti, Leonardo
2011-01-01
At finite temperature the distribution of the total momentum is an observable characterizing the thermal state of a field theory, and its cumulants are related to thermodynamic potentials. In a relativistic system at zero chemical potential, for instance, the thermal variance of the total momentum is a direct measure of the entropy. We relate the generating function of the cumulants to the ratio of a path integral with properly shifted boundary conditions in the compact direction over the ordinary partition function. In this form it is well suited for Monte-Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang--Mills theory, and obtain the entropy density at three different temperatures.
On reweighting for twisted boundary conditions
Bussone, Andrea; Hansen, Martin; Pica, Claudio
2016-01-01
We consider the possibility of using reweighting techniques in order to correct for the breaking of unitarity when twisted boundary conditions are imposed on valence fermions in simulations of lattice gauge theories. We start by studying the properties of reweighting factors and their variances at tree-level. That leads us to the introduction of a factorization for the fermionic reweighting determinant. In the numerical, stochastic, implementation of the method, we find that the effect of reweighting is negligible in the case of large volumes but it is sizeable when the volumes are small and the twisting angles are large. More importantly, we find that for un-improved Wilson fermions, and in small volumes, the dependence of the critical quark mass on the twisting angle is quite pronounced and results in large violations of the continuum dispersion relation.
OpenBEM - An open source Boundary Element Method software in Acoustics
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2010-01-01
OpenBEM is a collection of open source programs for solving the Helmholtz Equation using the Boundary Element Method. The collection is written in Matlab by the authors and contains codes for dealing with exterior and interior problems in two or three dimensions as well as implementation of axi...
Negative bending mode curvature via Robin boundary conditions
Adams, Samuel D. M.; Craster, Richard V.; Guenneau, Sébastien
2009-06-01
We examine the band spectrum, and associated Floquet-Bloch eigensolutions, arising in straight walled acoustic waveguides that have periodic structure along the guide. Homogeneous impedance (Robin) conditions are imposed along the guide walls and we find that in certain circumstances, negative curvature of the lowest (bending) mode can be achieved. This is unexpected, and has not been observed in a variety of physical situations examined by other authors. Further unexpected properties include the existence of the bending mode only on a subset of the Brillouin zone, as well as permitting otherwise unobtainable velocities of energy transmission. We conclude with a discussion of how such boundary conditions might be physically reproduced using effective conditions and homogenization theory, although the methodology to achieve these effective conditions is an open problem. To cite this article: S.D.M. Adams et al., C. R. Physique 10 (2009).
Two Baryons with Twisted Boundary Conditions
Energy Technology Data Exchange (ETDEWEB)
Briceno, Raul [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Davoudi, Zohreh [Univ. of Washington, Seattle, WA (United States) and Institute for Nuclear Theory, Seattle, WA (United States); Luu, Thomas [Lawrence Livermore National Laboratory, Livermore, CA (United States); Savage, Martin [Univ. of Washington, Seattle, WA (United States) and Institute for Nuclear Theory, Seattle, WA (United States)
2014-04-01
The quantization condition for two particle systems with arbitrary number of two-body open coupled-channels, spin and masses in a finite cubic volume is presented. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. The result is fully relativistic and holds for all momenta below inelastic thresholds and is exact up to exponential volume corrections that are governed by m{sub {pi}} L, where m{sub {pi}} is the pion mass and L is the spatial extent of my box. Its implication for the studies of coupled-channel baryon-baryon systems is discussed, and the necessary tools for implementing the formalism are review.
Alternate model of Chladni figures for the circular homogenous thin plate case with open boundaries
Trejo-Mandujano, H. A.; Mijares-Bernal, G.; Ordoñez-Casanova, E. G.
2015-01-01
The wave equation is a direct but a complex approach to solve analytically for the Chladni figures, mainly because of the complications that non-smooth and open boundary conditions impose. In this paper, we present an alternate solution model based on the principle of Huygens-Fresnel and on the ideas of Bohr for the hydrogen atom. The proposed model has been implemented numerically and compared, with good agreement, to our own experimental results for the case of a thin homogenous circular plate with open boundaries.
Spatial heterogeneity of ocean surface boundary conditions under sea ice
Barthélemy, Antoine; Fichefet, Thierry; Goosse, Hugues
2016-06-01
The high heterogeneity of sea ice properties implies that its effects on the ocean are spatially variable at horizontal scales as small as a few meters. Previous studies have shown that taking this variability into account in models could be required to simulate adequately mixed layer processes and the upper ocean temperature and salinity structures. Although many advanced sea ice models include a subgrid-scale ice thickness distribution, potentially providing heterogeneous surface boundary conditions, the information is lost in the coupling with a unique ocean grid cell underneath. The present paper provides a thorough examination of boundary conditions at the ocean surface in the NEMO-LIM model, which can be used as a guideline for studies implementing subgrid-scale ocean vertical mixing schemes. Freshwater, salt, solar heat and non-solar heat fluxes are examined, as well as the norm of the surface stress. All of the thermohaline fluxes vary considerably between the open water and ice fractions of grid cells. To a lesser extent, this is also the case for the surface stress. Moreover, the salt fluxes in both hemispheres and the solar heat fluxes in the Arctic show a dependence on the ice thickness category, with more intense fluxes for thinner ice, which promotes further subgrid-scale heterogeneity. Our analysis also points out biases in the simulated open water fraction and in the ice thickness distribution, which should be investigated in more details in order to ensure that the latter is used to the best advantage.
Bucur, Dorin; Feireisl, Eduard; Nečasová, Šárka
2010-07-01
We consider a family of solutions to the evolutionary Navier-Stokes system supplemented with the complete slip boundary conditions on domains with rough boundaries. We give a complete description of the asymptotic limit by means of Γ-convergence arguments, and identify a general class of boundary conditions.
Measuring the entropy from shifted boundary conditions
Giusti, Leonardo
2013-01-01
We explore a new computational strategy for determining the equation of state of the SU(3) Yang-Mills theory. By imposing shifted boundary conditions, the entropy density is computed from the vacuum expectation value of the off-diagonal components T_{0k} of the energy-momentum tensor. A step-scaling function is introduced to span a wide range in temperature values. We present preliminary numerical results for the entropy density and its step-scaling function obtained at eight temperature values in the range T_c - 15 T_c. At each temperature, discretization effects are removed by simulating the theory at several lattice spacings and by extrapolating the results to the continuum limit. Finite-size effects are always kept below the statistical errors. The absence of ultraviolet power divergences and the remarkably small discretization effects allow for a precise determination of the step-scaling function in the explored temperature range. These findings establish this strategy as a viable solution for an accurat...
Positive solutions for the beam equation under certain boundary conditions
Directory of Open Access Journals (Sweden)
Bo Yang
2005-07-01
Full Text Available We consider a boundary-value problem for the beam equation, in which the boundary conditions mean that the beam is embedded at one end and fastened with a sliding clamp at the other end. Some priori estimates to the positive solutions for the boundary-value problem are obtained. Sufficient conditions for the existence and nonexistence of positive solutions for the boundary-value problem are established.
STOCHASTIC ANALYSIS OF GROUNDWATER FLOW SUBJECT TO RANDOM BOUNDARY CONDITIONS
Institute of Scientific and Technical Information of China (English)
SHI Liang-sheng; YANG Jin-zhong; CAI Shu-ying; LIN Lin
2008-01-01
A stochastic model was developed to simulate the flow in heterogeneous media subject to random boundary conditions.Approximate partial differential equations were derived based on the Karhunen-Loeve (KL) expansion and perturbation expansion. The effect of random boundary conditions on the two-dimensional flow was examined. It is shown that the proposed stochastic model is efficient to include the random boundary conditions. The random boundaries lead to the increase of head variance and velocity variance. The influence of the random boundary conditions on head uncertainty is exerted over the whole simulated region, while the randomness of the boundary conditions leads to the increase of the velocity variance in the vicinity of boundaries.
Optimal boundary conditions at the staircase-shaped coastlines
Kazantsev, Eugene
2014-01-01
A 4D-Var data assimilation technique is applied to the rectangular-box configuration of the NEMO in order to identify the optimal parametrization of boundary conditions at lateral boundaries. The case of the staircase-shaped coastlines is studied by rotating the model grid around the center of the box. It is shown that, in some cases, the formulation of the boundary conditions at the exact boundary leads to appearance of exponentially growing modes while optimal boundary conditions allow to correct the errors induced by the staircase-like appriximation of the coastline.
Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations
Ehrlacher, V.; Ortner, C.; Shapeev, A. V.
2016-12-01
Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline environment. This work develops a rigorous framework within which the accuracy of different types of boundary conditions can be precisely assessed. We formulate the equilibration of crystal defects as variational problems in a discrete energy space and establish qualitatively sharp regularity estimates for minimisers. Using this foundation we then present rigorous error estimates for (i) a truncation method (Dirichlet boundary conditions), (ii) periodic boundary conditions, (iii) boundary conditions from linear elasticity, and (iv) boundary conditions from nonlinear elasticity. Numerical results confirm the sharpness of the analysis.
Phase modulated solitary waves controlled by bottom boundary condition
Mukherjee, Abhik
2014-01-01
A forced KdV equation is derived to describe weakly nonlinear, shallow water surface wave propagation over non trivial bottom boundary condition. We show that different functional forms of bottom boundary conditions self-consistently produce different forced kdV equations as the evolution equations for the free surface. Solitary wave solutions have been analytically obtained where phase gets modulated controlled by bottom boundary condition whereas amplitude remains constant.
Quantum “violation” of Dirichlet boundary condition
Directory of Open Access Journals (Sweden)
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.
Evaluation of wall boundary condition parameters for gas-solids fluidized bed simulations
Energy Technology Data Exchange (ETDEWEB)
Li, Tingwen [URS Corporation; Morgantown, WV (United States); National Energy Technology Lab. (NETL), Morgantown, WV (United States); Benyahia, Sofiane [National Energy Technology Lab. (NETL), Morgantown, WV (United States)
2013-10-01
Wall boundary conditions for the solids phase have significant effects on numerical predictions of various gas-solids fluidized beds. Several models for the granular flow wall boundary condition are available in the open literature for numerical modeling of gas-solids flow. In this study, a model for specularity coefficient used in Johnson and Jackson boundary conditions by Li and Benyahia (AIChE Journal, 2012, 58, 2058-2068) is implemented in the open-source CFD code-MFIX. The variable specularity coefficient model provides a physical way to calculate the specularity coefficient needed by the partial-slip boundary conditions for the solids phase. Through a series of 2-D numerical simulations of bubbling fluidized bed and circulating fluidized bed riser, the model predicts qualitatively consistent trends to the previous studies. Furthermore, a quantitative comparison is conducted between numerical results of variable and constant specularity coefficients to investigate the effect of spatial and temporal variations in specularity coefficient.
Asymmetric Simple Exclusion Process with Open Boundaries and Quadratic Harnesses
Bryc, Włodek; Wesołowski, Jacek
2017-04-01
We show that the joint probability generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of Markov processes called quadratic harnesses. We use our representation to prove the large deviations principle for the total number of particles in the system. We use the generator of the Markov process to show how explicit formulas for the average occupancy of a site arise for special choices of parameters. We also give similar representations for limits of stationary measures as the number of sites tends to infinity.
Wang, Wei-Hsiang; Fu, Wu-Shung; Tsubokura, Makoto
2016-11-01
Unstable phenomena of low speed compressible natural convection are investigated numerically. Geometry contains parallel square plates or single heated plate with open boundaries is taken into consideration. Numerical methods of the Roe scheme, preconditioning and dual time stepping matching the DP-LUR method are used for low speed compressible flow. The absorbing boundary condition and modified LODI method is adopted to solve open boundary problems. High performance parallel computation is achieved by multi-GPU implementation with CUDA platform. The effects of natural convection by isothermal plates facing upwards in air is then carried out by the methods mentioned above Unstable behaviors appeared upon certain Rayleigh number with characteristic length respect to the width of plates or height between plates.
Nonlinear Vibrations of Multiwalled Carbon Nanotubes under Various Boundary Conditions
Directory of Open Access Journals (Sweden)
Hossein Aminikhah
2011-01-01
Full Text Available The present work deals with applying the homotopy perturbation method to the problem of the nonlinear oscillations of multiwalled carbon nanotubes embedded in an elastic medium under various boundary conditions. A multiple-beam model is utilized in which the governing equations of each layer are coupled with those of its adjacent ones via the van der Waals interlayer forces. The amplitude-frequency curves for large-amplitude vibrations of single-walled, double-walled, and triple-walled carbon nanotubes are obtained. The influences of some commonly used boundary conditions, changes in material constant of the surrounding elastic medium, and variations of the nanotubes geometrical parameters on the vibration characteristics of multiwalled carbon nanotubes are discussed. The comparison of the generated results with those from the open literature illustrates that the solutions obtained are of very high accuracy and clarifies the capability and the simplicity of the present method. It is worthwhile to say that the results generated are new and can be served as a benchmark for future works.
Parameter identification of stochastic diffusion systems with unknown boundary conditions
Aihara, Shin Ichi; Bagchi, Arunabha
2013-01-01
This paper treats the filtering and parameter identification for the stochastic diffusion systems with unknown boundary conditions. The physical situation of the unknown boundary conditions can be found in many industrial problems,i.g., the salt concentration model of the river Rhine is a typical ex
On domain wall boundary conditions for the XXZ spin Hamiltonian
DEFF Research Database (Denmark)
Orlando, Domenico; Reffert, Susanne; Reshetikhin, Nicolai
In this note, we derive the spectrum of the infinite quantum XXZ spin chain with domain wall boundary conditions. The eigenstates are constructed as limits of Bethe states for the finite XXZ spin chain with quantum sl(2) invariant boundary conditions....
Performance of Numerical Boundary Condition based on Active Wave Absorption
DEFF Research Database (Denmark)
Troch, Peter; De Rouck, Julien; Frigaard, Peter
2001-01-01
The performance of a new active wave generating-absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces is presented.......The performance of a new active wave generating-absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces is presented....
Periodic Boundary Conditions in the ALEGRA Finite Element Code
Energy Technology Data Exchange (ETDEWEB)
AIDUN,JOHN B.; ROBINSON,ALLEN C.; WEATHERBY,JOE R.
1999-11-01
This document describes the implementation of periodic boundary conditions in the ALEGRA finite element code. ALEGRA is an arbitrary Lagrangian-Eulerian multi-physics code with both explicit and implicit numerical algorithms. The periodic boundary implementation requires a consistent set of boundary input sets which are used to describe virtual periodic regions. The implementation is noninvasive to the majority of the ALEGRA coding and is based on the distributed memory parallel framework in ALEGRA. The technique involves extending the ghost element concept for interprocessor boundary communications in ALEGRA to additionally support on- and off-processor periodic boundary communications. The user interface, algorithmic details and sample computations are given.
Gravitational instability on the brane: the role of boundary conditions
Shtanov, Y; Sahni, V; Shtanov, Yuri; Viznyuk, Alexander; Sahni, Varun
2007-01-01
An outstanding issue in braneworld theory concerns the setting up of proper boundary conditions for the brane-bulk system. Boundary conditions (BC's) employing regulatory branes or demanding that the bulk metric be nonsingular have yet to be implemented in full generality. In this paper, we take a different route and specify boundary conditions directly on the brane thereby arriving at a local and closed system of equations (on the brane). We consider a one-parameter family of boundary conditions involving the anisotropic stress of the projection of the bulk Weyl tensor on the brane and derive an exact system of equations describing scalar cosmological perturbations on a generic braneworld with induced gravity. Depending upon our choice of boundary conditions, perturbations on the brane either grow moderately (region of stability) or rapidly (instability). In the instability region, the evolution of perturbations usually depends upon the scale: small scale perturbations grow much more rapidly than those on la...
Poynting Flux-Conserving Boundary Conditions for Global MHD Models
Xi, S.; Lotko, W.; Zhang, B.; Brambles, O.; Lyon, J.; Merkin, V. G.; Wiltberger, M. J.
2014-12-01
Poynting Flux-conserving boundary conditions that conserve low-frequency, magnetic field-aligned, electromagnetic energy flux across the low-altitude (or inner) boundary in global magnetospheric magnetohydrodynamics (MHD) models is presented. This method involves the mapping of both the potential from the ionosphere and the perpendicular magnetic field from the inner magnetosphere to the ghost cells of the computational domain. The single fluid Lyon-Fedder-Mobarry (LFM) model is used to verify this method. The comparisons of simulations using the standard hardwall boundary conditions of the LFM model and the flux-conserving boundary conditions show that the method reported here improves the transparency of the boundary for the flow of low-frequency (essentially DC) electromagnetic energy flux along field lines. As a consequence, the field-aligned DC Poynting flux just above the boundary is very nearly equal to the ionospheric Joule heating, as it should be if electromagnetic energy is conserved.
Exact diffusion constant of a one-dimensional asymmetric exclusion model with open boundaries
Derrida, B.; Evans, M. R.; Mallick, K.
1995-06-01
For the 1D fully asymmetric exclusion model with open boundary conditions, we calculate exactly the fluctuations of the current of particles. The method used is an extension of a matrix technique developed recently to describe the equatime steady-state properties for open boundary conditions and the diffusion constant for particles on a ring. We show how the fluctuations of the current are related to non-equal-time correlations. In the thermodynamic limit, our results agree with recent results of Ferrari and Fontes obtained by working directly in the infinite system. We also show that the fluctuations of the current become singular when the system undergoes a phase transition with discontinuities along the first-order transition line.
Chiral boundary conditions for singletons and W-branes
Raeymaekers, Joris; Van den Bleeken, Dieter
2017-07-01
We revisit the holographic dictionary for a free massless scalar in AdS3, focusing on the `singleton' solutions for which the boundary profile is an arbitrary chiral function. We look for consistent boundary conditions which include this class of solutions. On one hand, we give a no-go argument that they cannot be interpreted within any boundary condition which preserves full conformal invariance. On the other hand, we show that such solutions fit naturally in a generalization of the Compère-Song-Strominger boundary conditions, which preserve a chiral Virasoro and current algebra. These observations have implications for the black hole deconstruction proposal, which proposes singleton solutions as candidate black hole microstate geometries. Our results suggest that the chiral boundary condition, which also contains the extremal BTZ black hole, is the natural setting for holographically interpreting the black hole deconstruction proposal.
Breakup of spiral wave under different boundary conditions
Institute of Scientific and Technical Information of China (English)
Zhao Ying-Kui; Wang Guang-Rui; Chen Shi-Gang
2007-01-01
In this paper, we investigate the breakup of spiral wave under no-flux, periodic and Dirichlet boundary conditions respectively. When the parameter ε is close to a critical value for Doppler-induced wave breakup, the instability of the system caused by the boundary effect occurs in the last two cases, resulting in the breakup of spiral wave near the boundary. With our defined average order measure of spiral wave (AOMSW), we quantify the degree of order of the system when the boundary-induced breakup of spiral wave happens. By analysing the AOMSW and outer diameter R of the spiral tip orbit, it is easy to find that this boundary effect is correlated with large values of R, especially under the Dirichlet boundary condition. This correlation is nonlinear, so the AOMSW sometimes oscillates with the variation of ε.
Boundary condition effects on maximum groundwater withdrawal in coastal aquifers.
Lu, Chunhui; Chen, Yiming; Luo, Jian
2012-01-01
Prevention of sea water intrusion in coastal aquifers subject to groundwater withdrawal requires optimization of well pumping rates to maximize the water supply while avoiding sea water intrusion. Boundary conditions and the aquifer domain size have significant influences on simulating flow and concentration fields and estimating maximum pumping rates. In this study, an analytical solution is derived based on the potential-flow theory for evaluating maximum groundwater pumping rates in a domain with a constant hydraulic head landward boundary. An empirical correction factor, which was introduced by Pool and Carrera (2011) to account for mixing in the case with a constant recharge rate boundary condition, is found also applicable for the case with a constant hydraulic head boundary condition, and therefore greatly improves the usefulness of the sharp-interface analytical solution. Comparing with the solution for a constant recharge rate boundary, we find that a constant hydraulic head boundary often yields larger estimations of the maximum pumping rate and when the domain size is five times greater than the distance between the well and the coastline, the effect of setting different landward boundary conditions becomes insignificant with a relative difference between two solutions less than 2.5%. These findings can serve as a preliminary guidance for conducting numerical simulations and designing tank-scale laboratory experiments for studying groundwater withdrawal problems in coastal aquifers with minimized boundary condition effects.
Heat-kernel coefficients for oblique boundary conditions
Dowker, John S; Kirsten, Klaus
1997-01-01
We calculate the heat-kernel coefficients, up to $a_2$, for a U(1) bundle on the 4-Ball for boundary conditions which are such that the normal derivative of the field at the boundary is related to a first-order operator in boundary derivatives acting on the field. The results are used to place restrictions on the general forms of the coefficients. In the specific case considered, there can be a breakdown of ellipticity.
Effective boundary condition at a rough surface starting from a slip condition
Dalibard, Anne-Laure
2010-01-01
We consider the homogenization of the Navier-Stokes equation, set in a channel with a rough boundary, of small amplitude and wavelength $\\epsilon$. It was shown recently that, for any non-degenerate roughness pattern, and for any reasonable condition imposed at the rough boundary, the homogenized boundary condition in the limit $\\epsilon = 0$ is always no-slip. We give in this paper error estimates for this homogenized no-slip condition, and provide a more accurate effective boundary condition, of Navier type. Our result extends those obtained in previous works, in which the special case of a Dirichlet condition at the rough boundary was examined.
HYCOM Initial and Boundary Conditions for Coupled COAMPS/NCOM
2016-06-07
conditions (BCs and ICs) into globally- relocatable coupled COAMPS/NCOM, (2) quantitatively evaluate HYCOM sources of ICs and BCs against other...HYCOM Initial and Boundary Conditions for Coupled COAMPS/NCOM Julie Pullen Naval Research Laboratory 7 Grace Hopper Ave. Stop 2 Monterey, CA...long-term goal of this effort is to evaluate HYbrid Coordinate Ocean Model (HYCOM) initial and boundary conditions supplied to the air-ocean coupled
Soliton and kink jams in traffic flow with open boundaries.
Muramatsu, M; Nagatani, T
1999-07-01
Soliton density wave is investigated numerically and analytically in the optimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave is distinguished from the kink density wave. It is shown that the soliton density wave appears only at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) equation is derived from the optimal velocity model by the use of the nonlinear analysis. It is found that the traffic soliton appears only near the neutral stability line. The soliton solution is analytically obtained from the perturbed KdV equation. It is shown that the soliton solution obtained from the nonlinear analysis is consistent with that of the numerical simulation.
Yusop, Nur Syaza Mohd; Mohamed, Nurul Akmal
2017-05-01
Boundary Element Method (BEM) is a numerical way to approximate the solutions of a Boundary Value Problem (BVP). The potential problem which involves the Laplace's equation on the square shape domain will be considered where the boundary is divided into four sets of linear boundary elements. We study the derivation system of equation for mixed BVP with one Dirichlet Boundary Condition (BC) is prescribed on one element of the boundary and Neumann BC on the other three elements. The mixed BVP will be reduced to a Boundary Integral Equation (BIE) by using a direct method which involves Green's second identity representation formula. Then, linear interpolation is used where the boundary will be discretized into some linear elements. As the result, we then obtain the system of linear equations. In conclusion, the specific element in the mixed BVP will have the specific prescribe value depends on the type of boundary condition. For Dirichlet BC, it has only one value at each node but for the Neumann BC, there will be different values at the corner nodes due to outward normal. Therefore, the assembly process for the system of equations related to the mixed BVP may not be as straight forward as Dirichlet BVP and Neumann BVP. For the future research, we will consider the different shape domains for mixed BVP with different prescribed boundary conditions.
Boundary states and finite size effects in sine-Gordon model with Neumann boundary condition
Bajnok, Z; Takács, G
2001-01-01
The sine-Gordon model with Neumann boundary condition is investigated. Using the bootstrap principle the spectrum of boundary bound states is established. Somewhat surprisingly it is found that Coleman-Thun diagrams and bound state creation may coexist. A framework to describe finite size effects in boundary integrable theories is developed and used together with the truncated conformal space approach to confirm the bound states and reflection factors derived by bootstrap.
Exponential reduction of finite volume effects with twisted boundary conditions
Cherman, Aleksey; Wagman, Michael L; Yaffe, Laurence G
2016-01-01
Flavor-twisted boundary conditions can be used for exponential reduction of finite volume artifacts in flavor-averaged observables in lattice QCD calculations with $SU(N_f)$ light quark flavor symmetry. Finite volume artifact reduction arises from destructive interference effects in a manner closely related to the phase averaging which leads to large $N_c$ volume independence. With a particular choice of flavor-twisted boundary conditions, finite volume artifacts for flavor-singlet observables in a hypercubic spacetime volume are reduced to the size of finite volume artifacts in a spacetime volume with periodic boundary conditions that is four times larger.
Hydrodynamic Boundary Conditions and Dynamic Forces between Bubbles and Surfaces
Manor, Ofer; Vakarelski, Ivan U.; Tang, Xiaosong; O'Shea, Sean J.; Stevens, Geoffrey W.; Grieser, Franz; Dagastine, Raymond R.; Chan, Derek Y. C.
2008-07-01
Dynamic forces between a 50μm radius bubble driven towards and from a mica plate using an atomic force microscope in electrolyte and in surfactant exhibit different hydrodynamic boundary conditions at the bubble surface. In added surfactant, the forces are consistent with the no-slip boundary condition at the mica and bubble surfaces. With no surfactant, a new boundary condition that accounts for the transport of trace surface impurities explains variations of dynamic forces at different speeds and provides a direct connection between dynamic forces and surface transport effects at the air-water interface.
Extensions of diffusion processes on intervals and Feller's boundary conditions
Yano, Kouji
2012-01-01
For a minimal diffusion process on $ (a,b) $, any possible extension of it to a standard process on $ [a,b] $ is characterized by the characteristic measures of excursions away from the boundary points $ a $ and $ b $. The generator of the extension is proved to be characterized by Feller's boundary condition.
Facilitating conditions for boundary-spanning behaviour in governance networks
I.F. van Meerkerk (Ingmar); J. 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
Facilitating conditions for boundary-spanning behavior in governance networks
I.F. van Meerkerk (Ingmar); J. 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
Numerical Solution for the Helmholtz Equation with Mixed Boundary Condition
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We consider the numerical solution for the Helmholtz equation in R2 with mixed boundary conditions. The solvability of this mixed boundary value problem is established by the boundary integral equation method. Based on the Green formula, we express the solution in terms of the boundary data. The key to the numerical realization of this method is the computation of weakly singular integrals. Numerical performances show the validity and feasibility of our method. The numerical schemes proposed in this paper have been applied in the realization of probe method for inverse scattering problems.
Boundary Conditions for Free Interfaces with the Lattice Boltzmann Method
Bogner, Simon; Rüde, Ulrich
2014-01-01
In this paper we analyze the boundary treatment of the Lattice Boltzmann method for simulating 3D flows with free surfaces. The widely used free surface boundary condition of K\\"orner et al. (2005) is shown to be first order accurate. The article presents new free surface boundary schemes that are suitable for the lattice Boltzmann method and that have second order spatial accuracy. The new method takes the free boundary position and orientation with respect to the computational lattice into account. Numerical experiments confirm the theoretical findings and illustrate the the difference between the old and the new method.
Implementation of a discrete Immersed Boundary Method in OpenFOAM
Constant, E; Favier, J; Meldi, M; Meliga, P; Serre, E
2016-01-01
In this paper, the Immersed Boundary Method (IBM) proposed by Pinelli is implemented for finite volume approximations of incompressible Navier-Stokes equations solutions in the open source toolbox OpenFOAM version 2.2. Solid obstacles are described using a discrete forcing approach for boundary conditions. Unlike traditional approaches encompassing the presence of a solid body using conformal meshes and imposing no-slip boundary conditions on the boundary faces of the mesh, the solid body is here represented on the Eulerian Cartesian mesh through an ad-hoc body force evaluated on a set of Lagrangian markers. The markers can move across the Eulerian mesh, hence allowing for a straightforward analysis of motion or deformation of the body. The IBM method is described and implemented in PisoFOAM, whose Pressure-Implicit Split-Operator (PISO) solver is modified accordingly. The presence of the solid body and the divergence-free of the fluid velocity are imposed simultaneously by sub-iterating between IBM and the p...
Topological boundary conditions in abelian Chern-Simons theory
Energy Technology Data Exchange (ETDEWEB)
Kapustin, Anton [California Institute of Technology, Pasadena, CA 91125 (United States); Saulina, Natalia, E-mail: saulina@theory.caltech.ed [Perimeter Institute, Waterloo (Canada)
2011-04-21
We study topological boundary conditions in abelian Chern-Simons theory and line operators confined to such boundaries. From the mathematical point of view, their relationships are described by a certain 2-category associated to an even integer-valued symmetric bilinear form (the matrix of Chern-Simons couplings). We argue that boundary conditions correspond to Lagrangian subgroups in the finite abelian group classifying bulk line operators (the discriminant group). We describe properties of boundary line operators; in particular we compute the boundary associator. We also study codimension one defects (surface operators) in abelian Chern-Simons theories. As an application, we obtain a classification of such theories up to isomorphism, in general agreement with the work of Belov and Moore.
A non-slip boundary condition for lattice Boltzmann simulations
Inamuro, T; Ogino, F; Inamuro, Takaji; Yoshino, Masato; Ogino, Fumimaru
1995-01-01
A non-slip boundary condition at a wall for the lattice Boltzmann method is presented. In the present method unknown distribution functions at the wall are assumed to be an equilibrium distribution function with a counter slip velocity which is determined so that fluid velocity at the wall is equal to the wall velocity. Poiseuille flow and Couette flow are calculated with the nine-velocity model to demonstrate the accuracy of the present boundary condition.
A generalized theory on the penetrating boundary conditions
Institute of Scientific and Technical Information of China (English)
邵振海; 洪伟; 周健义
2000-01-01
A generalized formula for penetrating boundary conditions is derived based on the Z-transform. The well-known absorbing boundary conditions (ABCs), such as the Mur’s ABC, and Liao’s ABC, can be deduced from the formula. Furthermore, some new ABCs can also be deduced from it. The stability of these ABCs are demonstrated via Von Neumann method and their validity is verified by numerical examples.
A generalized theory on the penetrating boundary conditions
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A generalized formula for penetrating boundary conditions is derived based on the Z-transform. The well-known absorbing boundary conditions (ABCs), such as the Mur's ABC, and Liao's ABC, can be deduced from the formula. Furthermore, some new ABCs can also be deduced from it. The stability of these ABCs are demonstrated via Von Neumann method and their validity is verified by numerical examples.
A review of time domain impedance boundary conditions
Richter, Christoph
2012-01-01
International audience; Over the last 15 years, time domain impedance boundary conditions have been investigated by various authors. In a review, a general framework of time domain impedance boundary conditions is presented and then filled with a set of outstanding mathematical and numerical methods from literature. All of the authors struggled with an instability with grazing flow. Mainly this is linked to the Ingard or Myers model of the sound propagation through a sheared flow. This is rev...
Coleman-Gurtin type equations with dynamic boundary conditions
Gal, Ciprian G.; Shomberg, Joseph L.
2015-02-01
We present a new formulation and generalization of the classical theory of heat conduction with or without fading memory. As a special case, we investigate the well-posedness of systems which consist of Coleman-Gurtin type equations subject to dynamic boundary conditions, also with memory. Nonlinear terms are defined on the interior of the domain and on the boundary and subject to either classical dissipation assumptions, or to a nonlinear balance condition in the sense of Gal (2012). Additionally, we do not assume that the interior and the boundary share the same memory kernel.
Directory of Open Access Journals (Sweden)
Guotao Wang
2012-01-01
Full Text Available We study nonlinear impulsive differential equations of fractional order with irregular boundary conditions. Some existence and uniqueness results are obtained by applying standard fixed-point theorems. For illustration of the results, some examples are discussed.
Evaluation of the ETS-Lindgren Open Boundary Quad-Ridged Horn 3164-06
2015-04-01
Evaluation of the ETS -Lindgren Open Boundary Quad-Ridged Horn 3164-06 by Christopher S Kenyon ARL-TR-7272 April 2015...Evaluation of the ETS -Lindgren Open Boundary Quad-Ridged Horn 3164-06 Christopher S Kenyon Sensors and Electron Devices Directorate, ARL...2014 4. TITLE AND SUBTITLE Evaluation of the ETS -Lindgren Open Boundary Quad-Ridged Horn 3164-06 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM
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.
Smirnov's Observable for Free Boundary Conditions, Interfaces and Crossing Probabilities
Izyurov, Konstantin
2015-07-01
We prove convergence results for variants of Smirnov's fermionic observable in the critical planar Ising model in the presence of free boundary conditions. One application of our analysis is a simple proof of a theorem by Hongler and Kytölä on convergence of critical Ising interfaces with plus-minus-free boundary conditions to dipolar SLE(3), and a generalization of this result to an arbitrary number of arcs carrying plus, minus or free boundary conditions. Another application is a computation of scaling limits of crossing probabilities in the critical FK-Ising model with an arbitrary number of alternating wired/free boundary arcs. We also deduce a new crossing formula for the spin Ising model.
Climate model boundary conditions for four Cretaceous time slices
Directory of Open Access Journals (Sweden)
J. O. Sewall
2007-06-01
Full Text Available General circulation models (GCMs are useful tools for investigating the characteristics and dynamics of past climates. Understanding of past climates contributes significantly to our overall understanding of Earth's climate system. One of the most time consuming, and often daunting, tasks facing the paleoclimate modeler, particularly those without a geological background, is the production of surface boundary conditions for past time periods. These boundary conditions consist of, at a minimum, continental configurations derived from plate tectonic modeling, topography, bathymetry, and a vegetation distribution. Typically, each researcher develops a unique set of boundary conditions for use in their simulations. Thus, unlike simulations of modern climate, basic assumptions in paleo surface boundary conditions can vary from researcher to researcher. This makes comparisons between results from multiple researchers difficult and, thus, hinders the integration of studies across the broader community. Unless special changes to surface conditions are warranted, researcher dependent boundary conditions are not the most efficient way to proceed in paleoclimate investigations. Here we present surface boundary conditions (land-sea distribution, paleotopography, paleobathymetry, and paleovegetation distribution for four Cretaceous time slices (120 Ma, 110 Ma, 90 Ma, and 70 Ma. These boundary conditions are modified from base datasets to be appropriate for incorporation into numerical studies of Earth's climate and are available in NetCDF format upon request from the lead author. The land-sea distribution, bathymetry, and topography are based on the 1°×1° (latitude x longitude paleo Digital Elevation Models (paleoDEMs of Christopher Scotese. Those paleoDEMs were adjusted using the paleogeographical reconstructions of Ronald Blakey (Northern Arizona University and published literature and were then modified for use in GCMs. The paleovegetation
Climate model boundary conditions for four Cretaceous time slices
Directory of Open Access Journals (Sweden)
J. O. Sewall
2007-11-01
Full Text Available General circulation models (GCMs are useful tools for investigating the characteristics and dynamics of past climates. Understanding of past climates contributes significantly to our overall understanding of Earth's climate system. One of the most time consuming, and often daunting, tasks facing the paleoclimate modeler, particularly those without a geological background, is the production of surface boundary conditions for past time periods. These boundary conditions consist of, at a minimum, continental configurations derived from plate tectonic modeling, topography, bathymetry, and a vegetation distribution. Typically, each researcher develops a unique set of boundary conditions for use in their simulations. Thus, unlike simulations of modern climate, basic assumptions in paleo surface boundary conditions can vary from researcher to researcher. This makes comparisons between results from multiple researchers difficult and, thus, hinders the integration of studies across the broader community. Unless special changes to surface conditions are warranted, researcher dependent boundary conditions are not the most efficient way to proceed in paleoclimate investigations. Here we present surface boundary conditions (land-sea distribution, paleotopography, paleobathymetry, and paleovegetation distribution for four Cretaceous time slices (120 Ma, 110 Ma, 90 Ma, and 70 Ma. These boundary conditions are modified from base datasets to be appropriate for incorporation into numerical studies of Earth's climate and are available in NetCDF format upon request from the lead author. The land-sea distribution, bathymetry, and topography are based on the 1°×1° (latitude × longitude paleo Digital Elevation Models (paleoDEMs of Christopher Scotese. Those paleoDEMs were adjusted using the paleogeographical reconstructions of Ronald Blakey (Northern Arizona University and published literature and were then modified for use in GCMs. The paleovegetation
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.
PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL
Institute of Scientific and Technical Information of China (English)
Hussein A.H. Salem
2011-01-01
In this article, we investigate the existence of Pseudo solutions for some frac- tional order boundary value problem with integral boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function. To encompass the full scope of this article, we give an example illustrating the main result.
Determination of optical properties by variation of boundary conditions
Nickell, Stephan; Essenpreis, Matthias; Kraemer, U.; Kohl-Bareis, Matthias; Boecker, Dirk
1998-01-01
Propagation of photons in multiple scattering media depends on absorbing and scattering properties as well as the boundary conditions of the semi-infinite medium. A new method is shown that makes use of differences in boundary conditions to determine the optical properties. Induced are these different conditions by varying the reflectivity of a sensor head. We describe the influence of the change in reflectivity with the common diffusion theory. By building a ratio between the spatially-resolved diffuse reflectance under different boundary conditions it is possible to calculate the optical properties of homogeneous phantoms. Due to optical heterogeneities in living tissue, limitations of the method was observed, which restricts the application to in vivo measurements.
A unified slip boundary condition for flow over a surface
Thalakkottor, Joseph John
2015-01-01
Interface between two phases of matter are ubiquitous in nature and technology. Determining the correct velocity condition at an interface is essential for understanding and designing of flows over a surface. We demonstrate that both the widely used no-slip and the Navier and Maxwell slip boundary conditions do not capture the complete physics associated with complex problems, such as spreading of liquids or corner flows. Hence, we present a unified boundary condition that is applicable to a wide-range of flow problems.
STURM-LIOUVILLE PROBLEMS WITH EIGENDEPENDENT BOUNDARY AND TRANSMISSIONS CONDITIONS
Institute of Scientific and Technical Information of China (English)
Z. Akdo(g)an; M. Demirci; O.Sh. Mukhtarov
2005-01-01
The purpose of this paper is to extend some fundamental spectral properties of regular Sturm-Liouville problems to special kind discontinuous boundary value problem,which consist of a Sturm-Liouville equation with piecewise continuous potential together with eigenvalue parameter on the boundary and transmission conditions. The authors suggest their own approach for finding asymptotic approximations formulas for eigenvalues and eigenfunctions of such discontinuous problems.
Variational Data Assimilation for Optimizing Boundary Conditions in Ocean Models
Kazantsev, Christine; Tolstykh, Mikhail
2016-01-01
The review describes the development of ideas Gury Ivanovich Marchuk in the field of variational data assimilation for ocean models applied in particular in coupled models for long-range weather forecasts. Particular attention is paid to the optimization of boundary conditions on rigid boundaries. As idealized and realistic model configurations are considered. It is shown that the optimization allows us to determine the most sensitive model operators and bring the model solution closer to the assimilated data.
Comment on the uncertainty relation with periodic boundary conditions
Fujikawa, Kazuo
2010-01-01
The Kennard-type uncertainty relation $\\Delta x\\Delta p >\\frac{\\hbar}{2}$ is formulated for a free particle with given momentum $ inside a box with periodic boundary conditions in the large box limit. Our construction of a free particle state is analogous to that of the Bloch wave in a periodic potential. A simple Robertson-type relation, which minimizes the effect of the box boundary and may be useful in some practical applications, is also presented.
Current leakage performance of dielectric elastomers under different boundary conditions
Lu, Tongqing; Shi, Zhibao; Chen, Zhiqiang; Huang, He; Wang, T. J.
2015-10-01
In the past decade, dielectric elastomers have become promising candidates in the applications of soft electromechanical transducers due to their outstanding properties of large deformation and high energy density. Current leakage of dielectric elastomer is one of the important dissipative mechanisms affecting the energy conversion efficiency. In this work, we experimentally investigate the current leakage performance of dielectric elastomers with different boundary conditions. We find that for displacement-type boundary conditions, the transition from Ohmic conduction to non-Ohmic conduction is abrupt near the critical electric field. By comparison, for force-type boundary conditions, the current leakage density versus electric field curve is smooth and is fit well by an exponential function. The equivalent resistivity of dielectric elastomers under force-type boundary conditions is approximately an order of magnitude smaller than that under displacement-type boundary conditions. The difference is qualitatively explained by a microscopic physical model. These results will help to design and optimize dielectric elastomer transducers to improve their energy conversion efficiency.
Institute of Scientific and Technical Information of China (English)
WANG Yue; WANG Jianguo; ZHANG Dianhui
2005-01-01
In order to solve the problem of truncating the open boundaries of cylindrical waveguides used in the simulation of high power microwave (HPM) sources, this paper studies the convolutional PML (CPML) in the cylindrical coordinate system. The electromagnetic field's FDTD equations and the expressions of axis boundary conditions are presented. Numerical experiments are conducted to validate the equations and axis boundary conditions. The performance of CPML is simulated when it is used to truncate the cylindrical waveguides excited by the sources with different frequencies and modes in the 2.5-dimensional problems. Numerical results show that the maximum relative errors are all less than -90 dB. The CPML method is introduced in the 2.5-dimensional electromagnetic PIC software, and the relativistic backward wave oscillator is simulated by using this method. The results show that the property of CPML is much better than that of the Mur-type absorbing boundary condition when they are used to truncate the open boundaries of waveguides. The CPML is especially suitable for truncating the open boundaries of the dispersive waveguide devices in the simulation of HPM sources.
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.
Transport synthetic acceleration with opposing reflecting boundary conditions
Energy Technology Data Exchange (ETDEWEB)
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.
Vibration Analysis of Annular Sector Plates under Different Boundary Conditions
Directory of Open Access Journals (Sweden)
Dongyan Shi
2014-01-01
Full Text Available An analytical framework is developed for the vibration analysis of annular sector plates with general elastic restraints along each edge of plates. Regardless of boundary conditions, the displacement solution is invariably expressed as a new form of trigonometric expansion with accelerated convergence. The expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. This work allows a capability of modeling annular sector plates under a variety of boundary conditions and changing the boundary conditions as easily as modifying the material properties or dimensions of the plates. Of equal importance, the proposed approach is universally applicable to annular sector plates of any inclusion angles up to 2π. The reliability and accuracy of the current method are adequately validated through numerical examples.
Nonlinear Vibrations of Timoshenko Beams with Various Boundary Conditions
Institute of Scientific and Technical Information of China (English)
郭强; 刘曦; 钟宏志
2004-01-01
This paper is concerned with the effects of boundary conditions on the large-amplitude free vibrations of Timoshenko beams. The effects of nonlinear terms on the frequency of Timoshenko beams with simply supported ends (supported-supported, SS), clamped ends (clamped-clamped, CC) and one end simply supported and the other end clamped (clamped-supported, CS) are discussed in detail. Given a specific vibration amplitude, the change of nonlinear frequency according to the effects of boundary conditions is always in the following descending order: SS, CS, and CC. It is found that the slenderness ratio has a significant influence on the nonlinear frequency. For slender beams, the nonlinear effects of bending curvature and shear strain are negligible regardless of the boundary conditions. For short beams and especially for those of large amplitude vibrations, however, the nonlinear effects of bending curvature and shear strain become noticeable in the following ascending order: SS, CS, and CC.
Boundary conditions on internal three-body wave functions
Energy Technology Data Exchange (ETDEWEB)
Mitchell, Kevin A.; Littlejohn, Robert G.
1999-10-01
For a three-body system, a quantum wave function {Psi}{sub m}{sup {ell}} with definite {ell} and m quantum numbers may be expressed in terms of an internal wave function {chi}{sub k}{sup {ell}} which is a function of three internal coordinates. This article provides necessary and sufficient constraints on {chi}{sub k}{sup {ell}} to ensure that the external wave function {Psi}{sub k}{sup {ell}} is analytic. These constraints effectively amount to boundary conditions on {chi}{sub k}{sup {ell}} and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form r{sup |m|} at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum.
Quarks with Twisted Boundary Conditions in the Epsilon Regime
Energy Technology Data Exchange (ETDEWEB)
Thomas Mehen; Brian C. Tiburzi
2005-05-01
We study the effects of twisted boundary conditions on the quark fields in the epsilon regime of chiral perturbation theory. We consider the SU(2){sub L} x SU(2){sub R} chiral theory with non-degenerate quarks and the SU(3){sub L} x SU(3){sub R} chiral theory with massless up and down quarks and massive strange quarks. The partition function and condensate are derived for each theory. Because flavor-neutral Goldstone bosons are unaffected by twisted boundary conditions chiral symmetry is still restored in finite volumes. The dependence of the condensate on the twisting parameters can be used to extract the pion decay constant from simulations in the epsilon regime. The relative contribution to the partition function from sectors of different topological charge is numerically insensitive to twisted boundary conditions.
Role of the basin boundary conditions in gravity wave turbulence
Deike, Luc; Gutiérrez-Matus, Pablo; Jamin, Timothée; Semin, Benoit; Aumaitre, Sébastien; Berhanu, Michael; Falcon, Eric; BONNEFOY, Félicien
2014-01-01
Gravity wave turbulence is studied experimentally in a large wave basin where irregular waves are generated unidirectionally. The role of the basin boundary conditions (absorbing or reflecting) and of the forcing properties are investigated. To that purpose, an absorbing sloping beach opposite to the wavemaker can be replaced by a reflecting vertical wall. We observe that the wave field properties depend strongly on these boundary conditions. Quasi-one dimensional field of nonlinear waves propagate before to be damped by the beach whereas a more multidirectional wave field is observed with the wall. In both cases, the wave spectrum scales as a frequency-power law with an exponent that increases continuously with the forcing amplitude up to a value close to -4, which is the value predicted by the weak turbulence theory. The physical mechanisms involved are probably different according to the boundary condition used, but cannot be easily discriminated with only temporal measurements. We have also studied freely...
The Open Boundary Dynamical Elliptic Quantum Gaudin Model and Its Solution
Institute of Scientific and Technical Information of China (English)
ZHAO Shao-You; YUE Rui-Hong
2001-01-01
We construct the Hamiltonians of open elliptic quantum Gaudin model and show its relation with the open boundary elliptic quantum group. We define eigenstates of the model to be Bethe vectors with η = 0 of the boundary elliptic quantum group. Then, the Hamiltonian is exactly diagonalized by using the algebraic Bethe ansatz method.``
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper investigates the existence and multiplicity of nonnegative solutions to a singular nonlinear boundary value problem of second order differential equations with integral boundary conditions in a Banach space. The arguments are based on the construction of a nonempty bounded open convex set and fixed point index theory. Our nonlinearity possesses singularity and first derivative which makes it different with that in [10].
Technique for observation derived boundary conditions for Space Weather
Pagano, Paolo; Mackay, Duncan; Yeates, Anthony
2017-04-01
We propose a new efficient and accurate modelling technique suitable for the next generation of Space Weather predictive tools. Specifically, we put forward an approach that can provide interplanetary Space Weather forecasting models with an accurate time dependent boundary condition of erupting flux ropes in the upper Solar Corona. The unique strength of this technique is that it follows the time evolution of coronal magnetic fields directly driven from observations and captures the full life span of magnetic flux ropes from formation to ejection. To produce accurate and effective boundary conditions we couple two different modelling techniques, MHD simulations with quasi-static non-potential modelling. Our modelling approach uses a time series of observed synoptic magnetograms to drive the non-potential evolution model of the coronal magnetic field to follow the formation and loss of equilibrium of magnetic flux ropes. Following this a MHD simulation captures the dynamic evolution of the ejection phase of the flux rope into interplanetary space. We focus here on the MHD simulation that describes the ejection of two magnetic flux ropes through the solar corona to the outer boundary. At this boundary we then produce time dependent boundary conditions for the magnetic field and plasma that in the future may be applied to interplanetary space weather prediction models. We illustrate that the coupling of observationally derived quasi-static non-potential magnetic field modelling and MHD simulations can significantly reduce the computational time for producing realistic observationally derived boundary conditions at the boundary between the corona and interplanetary space.
Dirichlet-to-Neumann boundary conditions for multiple scattering problems
Grote, Marcus J.; Kirsch, Christoph
2004-12-01
A Dirichlet-to-Neumann (DtN) condition is derived for the numerical solution of time-harmonic multiple scattering problems, where the scatterer consists of several disjoint components. It is obtained by combining contributions from multiple purely outgoing wave fields. The DtN condition yields an exact non-reflecting boundary condition for the situation, where the computational domain and its exterior artificial boundary consist of several disjoint components. Because each sub-scatterer can be enclosed by a separate artificial boundary, the computational effort is greatly reduced and becomes independent of the relative distances between the different sub-domains. The DtN condition naturally fits into a variational formulation of the boundary-value problem for use with the finite element method. Moreover, it immediately yields as a by-product an exact formula for the far-field pattern of the scattered field. Numerical examples show that the DtN condition for multiple scattering is as accurate as the well-known DtN condition for single scattering problems [J. Comput. Phys. 82 (1989) 172; Numerical Methods for Problems in Infinite Domains, Elsevier, Amsterdam, 1992], while being more efficient due to the reduced size of the computational domain.
Function Substitution in Partial Differential Equations: Nonhomogeneous Boundary Conditions
Directory of Open Access Journals (Sweden)
T. V. Oblakova
2017-01-01
Full Text Available In this paper we consider a mixed initial-boundary value problem for a parabolic equation with nonhomogeneous boundary conditions. The classical methods of searching for an analytical solution of such problems in the first stage involve variable substitution , leading to a problem with homogeneous boundary conditions. In the reference literature ([1], as a rule, the simplest types of variable substitutions are given, under which the new and old unknown functions differ by a term linear in the spatial variable. The form of this additional term depends on the type of the boundary conditions, but is in no way connected with the equation under consideration. Moreover, in the case of the second boundary-value problem, it is necessary to use quadratic additives, since a linear replacement for this type of conditions may not exist. In the educational literature ([2] - [4], it is usually limited to considering only the first boundary-value problem in the general formulation.In this paper, we consider a substitution that takes into account in principle the form of a linear differential operator. Namely, as an additive term, it is proposed to use the parametrically time-dependent solution of the boundary value problem for an ordinary differential equation obtained from the original partial differential equation by the method of separation of the Fourier variables.The existence of the proposed replacement for boundary conditions of any type is proved on the example of a nonstationary heat equation in the presence of heat exchange with the surrounding medium. In this case, the additional term is a linear combination of hyperbolic functions. It is shown that in addition to the "insensitivity" to the type of boundary conditions, the advantages of a new replacement in comparison with the traditional linear (or quadratic substitution include a much simpler structure of the resulting solution. Namely, the described approach allows one to obtain a solution
Optimal control problems for impulsive systems with integral boundary conditions
Directory of Open Access Journals (Sweden)
Allaberen Ashyralyev
2013-03-01
Full Text Available In this article, the optimal control problem is considered when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of the solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.
Thermodynamically admissible boundary conditions for the regularized 13 moment equations
Energy Technology Data Exchange (ETDEWEB)
Rana, Anirudh Singh, E-mail: anirudh@uvic.ca [Department of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju, Gyeongnam 52828 (Korea, Republic of); Struchtrup, Henning, E-mail: struchtr@uvic.ca [Department of Mechanical Engineering, University of Victoria, Victoria, British Columbia V8W 2Y2 (Canada)
2016-02-15
A phenomenological approach to the boundary conditions for linearized R13 equations is derived using the second law of thermodynamics. The phenomenological coefficients appearing in the boundary conditions are calculated by comparing the slip, jump, and thermal creep coefficients with linearized Boltzmann solutions for Maxwell’s accommodation model for different values of the accommodation coefficient. For this, the linearized R13 equations are solved for viscous slip, thermal creep, and temperature jump problems and the results are compared to the solutions of the linearized Boltzmann equation. The influence of different collision models (hard-sphere, Bhatnagar–Gross–Krook, and Maxwell molecules) and accommodation coefficients on the phenomenological coefficients is studied.
Modeling magnetized star-planet interactions: boundary conditions effects
Strugarek, Antoine; Matt, Sean P; Reville, Victor
2013-01-01
We model the magnetized interaction between a star and a close-in planet (SPMIs), using global, magnetohydrodynamic numerical simulations. In this proceedings, we study the effects of the numerical boundary conditions at the stellar surface, where the stellar wind is driven, and in the planetary interior. We show that is it possible to design boundary conditions that are adequate to obtain physically realistic, steady-state solutions for cases with both magnetized and unmagnetized planets. This encourages further development of numerical studies, in order to better constrain and understand SPMIs, as well as their effects on the star-planet rotational evolution.
Off-shell scalar products for the XXZ spin chain with open boundaries
Directory of Open Access Journals (Sweden)
W. Galleas
2015-04-01
Full Text Available In this work we study scalar products of Bethe vectors associated with the XXZ spin chain with open boundary conditions. The scalar products are obtained as solutions of a system of functional equations. The description of scalar products through functional relations follows from a particular map having the reflection algebra as its domain and a function space as the codomain. Within this approach we find a multiple contour integral representation for the scalar products in which the homogeneous limit can be obtained trivially.
Kitanine, N; Niccoli, G
2014-01-01
We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains. The corresponding homogeneous limit reproduces the spectrum of the Hamiltonian of the spin-1/2 open XXZ and XXX quantum chains with the most general integrable boundaries. The spectrum is characterized by a second order finite difference functional equation of Baxter type with an inhomogeneous term which vanishes only for some special but yet interesting non-diagonal boundary conditions. This functional equation is shown to be equivalent to the known separation of variable (SOV) representation hence proving that it defines a complete characterization of the transfer matrix spectrum. The polynomial character of the Q-function allows us then to show that a finite system of equations of generalized Bethe type can be similarly used to describe the complete transfer matrix spectru...
Sub-Alfvenic inlet boundary conditions for axisymmetric MHD nozzles
Energy Technology Data Exchange (ETDEWEB)
Cassibry, J T [Propulsion Research Center, University of Alabama in Huntsville, Huntsville, AL 35899 (United States); Wu, S T [Center for Space Plasma and Aeronomy Research, University of Alabama in Huntsville, Huntsville, AL 35899 (United States)
2007-09-07
There are numerous electromagnetic accelerator concepts which require plasma expansion through a magnetic nozzle. If the inlet flow is slower than one or all of the outgoing characteristics, namely, the Alfven, slow and fast magnetosonic speeds, then the number of inlet conditions which could be arbitrarily specified are reduced by the number of outgoing characteristics (up to three). We derive the axisymmetric compatibility equations using the method of projected characteristics for the inlet conditions in the z-plane to assure the boundary conditions being consistent with flow properties. We make simplifications to the equations assuming that the inlet Alfven speed is much faster than the sonic and slow magnetosonic speeds. We compare results for various inlet boundary conditions, including a modified Lax-Wendroff implementation of the compatibility equations, first order extrapolation and arbitrarily specifying the inlet conditions, in order to assess the stability and accuracy of various approaches.
Optimal Control of a Parabolic Equation with Dynamic Boundary Condition
Energy Technology Data Exchange (ETDEWEB)
Hoemberg, D., E-mail: hoemberg@wias-berlin.de; Krumbiegel, K., E-mail: krumbieg@wias-berlin.de [Weierstrass Institute for Applied Mathematics and Stochastics, Nonlinear Optimization and Inverse Problems (Germany); Rehberg, J., E-mail: rehberg@wias-berlin.de [Weierstrass Institute for Applied Mathematics and Stochastics, Partial Differential Equations (Germany)
2013-02-15
We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the dynamic boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an L{sup p} function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions.
Interpolated lattice Boltzmann boundary conditions for surface reaction kinetics.
Walsh, S D C; Saar, M O
2010-12-01
This paper describes a method for implementing surface reaction kinetics in lattice Boltzmann simulations. The interpolated boundary conditions are capable of simulating surface reactions and dissolution at both stationary and moving solid-fluid and fluid-fluid interfaces. Results obtained with the boundary conditions are compared to analytical solutions for first-order and constant-flux kinetic surface reactions in a one-dimensional half space, as well as to the analytical solution for evaporation from the surface of a cylinder. Excellent agreement between analytical and simulated results is obtained for a wide range of diffusivities, lattice velocities, and surface reaction rates. The boundary model's ability to represent dissolution in binary fluid mixtures is demonstrated by modeling diffusion from a rising bubble and dissolution of a droplet near a flat plate.
Non-diagonal boundary conditions for gl(1|1) super spin chains
Energy Technology Data Exchange (ETDEWEB)
Grabinski, Andre M; Frahm, Holger, E-mail: frahm@itp.uni-hannover.d [Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstrasse 2, 30167 Hannover (Germany)
2010-01-29
We study a one-dimensional model of free fermions with gl(1|1) supersymmetry and demonstrate how non-diagonal boundary conditions can be incorporated into the framework of the graded quantum inverse scattering method (gQISM) by means of super matrices with entries from a superalgebra. For super Hermitian twists and open boundary conditions subject to a certain constraint, we solve the eigenvalue problem for the super transfermatrix by means of the graded algebraic Bethe ansatz technique (gABA) starting from a fermionic coherent state. For generic boundary conditions the algebraic Bethe ansatz cannot be applied. In this case the spectrum of the super transfermatrix is obtained from a functional relation.
Hobrecht, Hendrik
2016-01-01
We present a systematic method to calculate the scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer representation of the corresponding partition function $Z$ on an $L\\times M$ square lattice, wrapped around a torus with aspect ratio $\\rho=L/M$. By assuming periodic boundary conditions and translational invariance in at least one direction, we systematically reduce the problem to a $2\\times2$ transfer matrix representation. For the torus we first reproduce the results by Kaufman and then give a detailed calculation of the scaling functions. Afterwards we present the calculation for the cylinder with open boundary conditions. All scaling functions are given in form of combinations of infinite products and integrals. Our results reproduce the known scaling functions in the limit of thin films $\\rho\\to 0$. Additionally, for the cylinder at criticality our result confirms the predictions...
Institute of Scientific and Technical Information of China (English)
Gui-Qiang Chen; Dan Osborne; Zhongmin Qian
2009-01-01
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in RN with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-fiat boundary. We observe that, under the nonhomogeneons boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition (without the incompressibility condition), which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in RN(n≥3) with nonhomogeneous vorticity boundary condition converge in L2 to the corresponding Euler equations satisfying the kinematic condition.
On a stochastic Burgers equation with Dirichlet boundary conditions
Directory of Open Access Journals (Sweden)
Ekaterina T. Kolkovska
2003-01-01
Full Text Available We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.
Seawall Boundary Condition in Numerical Models of Shoreline Evolution.
1986-04-01
o _ 11111 41 11u MICROCOPY RESOLUTION TESI CHART A NATIONAL BUREAU OF STANDARDS 196, A i TECHNICAL REPORT CERC-86-3 SEAWALL BOUNDARY CONDITION IN...numerical accu- racy. Engineering judgment must be exercised on a case-by-case basis to de- cide if a 24-hr time step will give acceptable physical
New approach to streaming semigroups with multiplying boundary conditions
Directory of Open Access Journals (Sweden)
Mohamed Boulanouar
2008-11-01
Full Text Available This paper concerns the generation of a C_0-semigroup by the streaming operator with general multiplying boundary conditions. A first approach, presented in [2], is based on the Hille-Yosida's Theorem. Here, we present a second approach based on the construction of the generated semigroup, without using the Hille-Yosida's Theorem.
Gravitational wave extraction and outer boundary conditions by perturbative matching
Abrahams, A M; Rupright, M E; Anderson, A; Anninos, P; Baumgarte, T W; Bishop, N T; Brandt, S R; Browne, J C; Camarda, K; Choptuik, M W; Cook, G B; Evans, C R; Finn, L S; Fox, G; Gómez, R; Haupt, T; Huq, M F; Kidder, L E; Klasky, S; Laguna, P; Landry, W; Lehner, L; Lenaghan, J T; Marsa, R L L; Massó, J; Matzner, R A; Mitra, S; Papadopoulos, P P; Parashar, M; Saied, F; Saylor, P E; Scheel, M A; Seidel, E; Shapiro, S L; Shoemaker, D M; Smarr, L L; Szilágyi, B; Teukolsky, S A; Van Putten, M H P M; Walker, P; Winicour, J; York, J W
1998-01-01
We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three dimensional numerical relativity code.
Carleman Estimates for Parabolic Equations with Nonhomogeneous Boundary Conditions
Institute of Scientific and Technical Information of China (English)
Oleg Yu IMANUVILOV; Jean Pierre PUEL; Masahiro YAMAMOTO
2009-01-01
The authors prove a new Carleman estimate for general linear second order parabolic equation with nonhomogeneous boundary conditions.On the basis of this estimate,improved Carleman estimates for the Stokes system and for a system of parabolic equations with a penalty term are obtained.This system can be viewed as an approximation of the Stokes system.
Heat Flow for the Minimal Surface with Plateau Boundary Condition
Institute of Scientific and Technical Information of China (English)
Kung Ching CHANG; Jia Quan LIU
2003-01-01
The heat flow for the minimal surface under Plateau boundary condition is defined to be aparabolic variational inequality, and then the existence, uniqueness, regularity, continuous dependenceon the initial data and the asymptotics are studied. It is applied as a deformation of the level sets inthe critical point theory.
BPS Monopole in the Space of Boundary Conditions
Ohya, Satoshi
2015-01-01
The space of all possible boundary conditions that respect self-adjointness of Hamiltonian operator is known to be given by the group manifold $U(2)$ in one-dimensional quantum mechanics. In this paper we study non-Abelian Berry's connections in the space of boundary conditions in a simple quantum mechanical system. We consider a system for a free spinless particle on a circle with two point-like interactions described by the $U(2) \\times U(2)$ family of boundary conditions. We show that, for a certain $SU(2) \\subset U(2) \\times U(2)$ subfamily of boundary conditions, all the energy levels become doubly-degenerate thanks to the so-called higher-derivative supersymmetry, and non-Abelian Berry's connection in the ground-state sector is given by the Bogomolny-Prasad-Sommerfield (BPS) monopole of $SU(2)$ Yang-Mills-Higgs theory. We also show that, in the ground-state sector of this quantum mechanical model, matrix elements of position operator give the adjoint Higgs field that satisfies the BPS equation. It is al...
Poroelastic modeling of seismic boundary conditions across a fracture.
Nakagawa, Seiji; Schoenberg, Michael A
2007-08-01
Permeability of a fracture can affect how the fracture interacts with seismic waves. To examine this effect, a simple mathematical model that describes the poroelastic nature of wave-fracture interaction is useful. In this paper, a set of boundary conditions is presented which relate wave-induced particle velocity (or displacement) and stress including fluid pressure across a compliant, fluid-bearing fracture. These conditions are derived by modeling a fracture as a thin porous layer with increased compliance and finite permeability. Assuming a small layer thickness, the boundary conditions can be derived by integrating the governing equations of poroelastic wave propagation. A finite jump in the stress and velocity across a fracture is expressed as a function of the stress and velocity at the boundaries. Further simplification for a thin fracture yields a set of characteristic parameters that control the seismic response of single fractures with a wide range of mechanical and hydraulic properties. These boundary conditions have potential applications in simplifying numerical models such as finite-difference and finite-element methods to compute seismic wave scattering off nonplanar (e.g., curved and intersecting) fractures.
Validation of Boundary Conditions for CFD Simulations on Ventilated Rooms
DEFF Research Database (Denmark)
Topp, Claus; Jensen, Rasmus Lund; Pedersen, D.N.
2001-01-01
The application of Computational Fluid Dynamics (CFD) for ventilation research and design of ventilation systems has increased during the recent years. This paper provides an investigation of direct description of boundary conditions for a complex inlet diffuser and a heated surface. A series of ...
Directory of Open Access Journals (Sweden)
Jeffrey W. Lyons
2017-01-01
Full Text Available For \\(\\alpha\\in(1,2]\\, the singular fractional boundary value problem \\[D^{\\alpha}_{0^+}x+f\\left(t,x,D^{\\mu}_{0^+}x\\right=0,\\quad 0\\lt t\\lt 1,\\] satisfying the boundary conditions \\(x(0=D^{\\beta}_{0^+}x(1=0\\, where \\(\\beta\\in(0,\\alpha-1]\\, \\(\\mu\\in(0,\\alpha-1]\\, and \\(D^{\\alpha}_{0^+}\\, \\(D^{\\beta}_{0^+}\\ and \\(D^{\\mu}_{0^+}\\ are Riemann-Liouville derivatives of order \\(\\alpha\\, \\(\\beta\\ and \\(\\mu\\ respectively, is considered. Here \\(f\\ satisfies a local Carathéodory condition, and \\(f(t,x,y\\ may be singular at the value 0 in its space variable \\(x\\. Using regularization and sequential techniques and Krasnosel'skii's fixed point theorem, it is shown this boundary value problem has a positive solution. An example is given.
On accurate boundary conditions for a shape sensitivity equation method
Duvigneau, R.; Pelletier, D.
2006-01-01
This paper studies the application of the continuous sensitivity equation method (CSEM) for the Navier-Stokes equations in the particular case of shape parameters. Boundary conditions for shape parameters involve flow derivatives at the boundary. Thus, accurate flow gradients are critical to the success of the CSEM. A new approach is presented to extract accurate flow derivatives at the boundary. High order Taylor series expansions are used on layered patches in conjunction with a constrained least-squares procedure to evaluate accurate first and second derivatives of the flow variables at the boundary, required for Dirichlet and Neumann sensitivity boundary conditions. The flow and sensitivity fields are solved using an adaptive finite-element method. The proposed methodology is first verified on a problem with a closed form solution obtained by the Method of Manufactured Solutions. The ability of the proposed method to provide accurate sensitivity fields for realistic problems is then demonstrated. The flow and sensitivity fields for a NACA 0012 airfoil are used for fast evaluation of the nearby flow over an airfoil of different thickness (NACA 0015).
Directory of Open Access Journals (Sweden)
Yichao Gao
2011-01-01
Full Text Available The dam-reservoir system is divided into the near field modeled by the finite element method, and the far field modeled by the excellent high-order doubly asymptotic open boundary (DAOB. Direct and partitioned coupled methods are developed for the analysis of dam-reservoir system. In the direct coupled method, a symmetric monolithic governing equation is formulated by incorporating the DAOB with the finite element equation and solved using the standard time-integration methods. In contrast, the near-field finite element equation and the far-field DAOB condition are separately solved in the partitioned coupled methodm, and coupling is achieved by applying the interaction force on the truncated boundary. To improve its numerical stability and accuracy, an iteration strategy is employed to obtain the solution of each step. Both coupled methods are implemented on the open-source finite element code OpenSees. Numerical examples are employed to demonstrate the performance of these two proposed methods.
Tam, Christopher K. W.; Webb, Jay C.
1994-01-01
In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The
The spectrum of boundary states in sine-Gordon model with integrable boundary conditions
Bajnok, Z; Takács, G; Tóth, G
2002-01-01
The bound state spectrum and the associated reflection factors are determined for the sine-Gordon model with arbitrary integrable boundary condition by closing the bootstrap. Comparing the symmetries of the bound state spectrum with that of the Lagrangian it is shown how one can "derive" the relationship between the UV and IR parameters conjectured earlier.
The boundary conditions for point transformed electromagnetic invisibility cloaks
Energy Technology Data Exchange (ETDEWEB)
Weder, Ricardo [Departamento de Metodos Matematicos y Numericos, Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Universidad Nacional Autonoma de Mexico, Apartado Postal 20-726, Mexico DF 01000 (Mexico)], E-mail: weder@servidor.unam.mx
2008-10-17
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, {partial_derivative}K{sub +}, and at the inside, {partial_derivative}K{sub -}, 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 {partial_derivative}K{sub +}-which is always true-and that the normal components of the curl of the electric and the magnetic fields have to vanish at {partial_derivative}K{sub -}. 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 {partial_derivative}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
Free, transverse vibrations of thin plates with discontinuous boundary conditions
Febbo, M.; Vera, S. A.; Laura, P. A. A.
2005-03-01
Vibrations of circular and rectangular plates clamped on part of the boundary and simply supported along the remainder are analyzed by means of a method of perturbation of boundary conditions. This approach appears to be simple and straightforward, giving excellent results for the first mode and its versatility permits to extend it to higher modes of vibration without difficulty. Furthermore, it is shown that the fundamental frequency coefficient can also be determined using a modified Galerkin approach and very simple polynomial coordinate functions which yield good engineering accuracy.
Boundary Conditions for NHEK through Effective Action Approach
Institute of Scientific and Technical Information of China (English)
CHEN Bin; NING Bo; ZHANG Jia-Ju
2012-01-01
We study the asymptotic symmetry group (ASG) of the near horizon geometry of extreme Kerr black hole through the effective action approach developed by Porfyriadis and Wilczek (arXiv:1007.1031v1[gr qc]).By requiring a finite boundary effective action,we derive a new set of asymptotic Killing vectors and boundary conditions,which are much more relaxed than the ones proposed by Matsuo Y et al.[Nucl.Phys.B 825 (2010) 231],and still allow a copy of a conformal group as its ASG.In the covariant formalism,the asymptotic charges are finite,with the corresponding central charge vanishing.By using the quasi-local charge and introducing a plausible cut-off,we find that the higher order terms of the asymptotic Killing vectors,which could not be determined through the effective action approach,contribute to the central charge as well.We also show that the boundary conditions suggested by Guica et al.[Phys.Rev.D 80 (2009)124008] lead to a divergent first-order boundary effective action.%We study the asymptotic symmetry group (ASG) of the near horizon geometry of extreme Kerr black hole through the effective action approach developed by Porfyriadis and Wilczek (arXiv:1007.1031vl[gr qc]). By requiring a finite boundary effective action, we derive a new set of asymptotic Killing vectors and boundary conditions, which are much more relaxed than the ones proposed by Matsuo Y et al. [Nucl. Phys. B 825 (2010) 231], and still allow a copy of a conformal group as its ASG. In the covariant formalism, the asymptotic charges are finite, with the corresponding central charge vanishing. By using the quasi-local charge and introducing a plausible cut-off, we find that the higher order terms of the asymptotic Killing vectors, which could not be determined through the effective action approach, contribute to the central charge as well. We also show that the boundary conditions suggested by Guica et al. [Phys. Rev. D 80 (2009) 124008] lead to a divergent first-order boundary effective action.
Most general AdS_3 boundary conditions
Grumiller, Daniel
2016-01-01
We consider the most general asymptotically anti-de Sitter boundary conditions in three-dimensional Einstein gravity with negative cosmological constant. The metric contains in total twelve independent functions, six of which are interpreted as chemical potentials (or non-normalizable fluctuations) and the other half as canonical boundary charges (or normalizable fluctuations). Their presence modifies the usual Fefferman-Graham expansion. The asymptotic symmetry algebra consists of two sl(2)_k current algebras, the levels of which are given by k=l/(4G_N), where l is the AdS radius and G_N the three-dimensional Newton constant.
Most general AdS{sub 3} boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Grumiller, Daniel; Riegler, Max [Institute for Theoretical Physics, TU Wien,Wiedner Hauptstr. 8-10/136, A-1040 Vienna (Austria)
2016-10-06
We consider the most general asymptotically anti-de Sitter boundary conditions in three-dimensional Einstein gravity with negative cosmological constant. The metric contains in total twelve independent functions, six of which are interpreted as chemical potentials (or non-normalizable fluctuations) and the other half as canonical boundary charges (or normalizable fluctuations). Their presence modifies the usual Fefferman-Graham expansion. The asymptotic symmetry algebra consists of two sl(2){sub k} current algebras, the levels of which are given by k=ℓ/(4G{sub N}), where ℓ is the AdS radius and G{sub N} the three-dimensional Newton constant.
Stretched flow of Carreau nanofluid with convective boundary condition
Indian Academy of Sciences (India)
T Hayat; M Waqas; S A Shehzad; A Alsaedi
2016-01-01
The steady laminar boundary layer flow of Carreau nanofluid over a stretching sheet is investigated. Effects of Brownian motion and thermophoresis are present. Heat transfer is characterized using convective boundary condition at the sheet. The governing partial differential equations are reduced into a set of nonlinear ordinary differential equations through suitable transformations. Results of velocity, temperature and concentration fields are computed via homotopic procedure. Numerical values of skin-friction coefficient, local Nusselt and Sherwood numbers are computed and discussed. A comparative study with existing solutions in a limiting sense is made.
Nonlinear Vibration Analysis of Moving Strip with Inertial Boundary Condition
Directory of Open Access Journals (Sweden)
Chong-yi Gao
2015-01-01
Full Text Available According to the movement mechanism of strip and rollers in tandem mill, the strip between two stands was simplified to axially moving Euler beam and the rollers were simplified to the inertial component on the fixed axis rotation, namely, inertial boundary. Nonlinear vibration mechanical model of Euler beam with inertial boundary conditions was established. The transverse and longitudinal motion equations were derived based on Hamilton’s principle. Kantorovich averaging method was employed to discretize the motion equations and the inertial boundary equations, and the solutions were obtained using the modified iteration method. Depending on numerical calculation, the amplitude-frequency responses of Euler beam were determined. The axial velocity, tension, and rotational inertia have strong influences on the vibration characteristics. The results would provide an important theoretical reference to control and analyze the vertical vibration of moving strip in continuous rolling process.
Diffusion processes, Feller semigroups and Wentzell boundary conditions.
Romanelli, S
2001-01-01
Different approaches to the study of many diffusion processes in Genetics involve Probability, Functional Analysis and Partial Differential Equations, as in the case of changes in gene frequency due only to random sampling or under random fluctuation of selective advantages. In the one-dimensional case, a unified treatment of them was given by Feller. For particular classes of Markov processes, Taira showed that these different approaches are equivalent even in the N-dimensional case. It follows that the generator of a Feller semigroup on the space of real-valued continuous functions C(D), where D is a bounded domain of RN with smooth boundary, can be identified with a particular Markov transition function. Under suitable assumptions, Taira, Favini and the author proved that some classes of degenerate elliptic operators with Wentzell boundary condition generate Feller semigroups on C(D), in such a way that the diffusion phenomenon of viscosity occurs at each point of the boundary.
DYNA3D Non-reflecting Boundary Conditions - Test Problems
Energy Technology Data Exchange (ETDEWEB)
Zywicz, E
2006-09-28
Two verification problems were developed to test non-reflecting boundary segments in DYNA3D (Whirley and Engelmann, 1993). The problems simulate 1-D wave propagation in a semi-infinite rod using a finite length rod and non-reflecting boundary conditions. One problem examines pure pressure wave propagation, and the other problem explores pure shear wave propagation. In both problems the non-reflecting boundary segments yield results that differ only slightly (less than 6%) during a short duration from their corresponding theoretical solutions. The errors appear to be due to the inability to generate a true step-function compressive wave in the pressure wave propagation problem and due to segment integration inaccuracies in the shear wave propagation problem. These problems serve as verification problems and as regression test problems for DYNA3D.
Exact phi (cursive,open) Greek{sub 1,3} boundary flows in the tricritical Ising model
Energy Technology Data Exchange (ETDEWEB)
Feverati, Giovanni E-mail: feverati@ms.unimelb.edu.au; Pearce, Paul A. E-mail: p.pearce@ms.unimelb.edu.au; Ravanini, Francesco E-mail: ravanini@bologna.infn.it
2003-12-29
We consider the tricritical Ising model on a strip or cylinder under the integrable perturbation by the thermal phi (cursive,open) Greek{sub 1,3} boundary field. This perturbation induces five distinct renormalization group (RG) flows between Cardy type boundary conditions labelled by the Kac labels (r,s). We study these boundary RG flows in detail for all excitations. Exact thermodynamic Bethe ansatz (TBA) equations are derived using the lattice approach by considering the continuum scaling limit of the A{sub 4} lattice model with integrable boundary conditions. Fixing the bulk weights to their critical values, the integrable boundary weights admit a thermodynamic boundary field {xi} which induces the flow and, in the continuum scaling limit, plays the role of the perturbing boundary field phi Greek{sub 1,3}. The excitations are completely classified, in terms of string content, by (m,n) systems and quantum numbers but the string content changes by either two or three well-defined mechanisms along the flow. We identify these mechanisms and obtain the induced maps between the relevant finitized Virasoro characters. We also solve the TBA equations numerically to determine the boundary flows for the leading excitations.
Flux change in viscous laminar flow under oscillating boundary condition
Ueda, R.; Mikada, H.; Goto, T.; Takekawa, J.
2012-12-01
The behavior of interstitial fluid is one of major interest in earth sciences in terms of the exploitation of water resources, the initiation of earthquakes, enhanced oil recovery (EOR), etc. Seismic waves are often known to increase the flux of interstitial fluid but the relationship between the flux and propagating seismic waves have not been well investigated in the past, although seismic stimulation has been applied in the oil industry for enhanced oil recovery (EOR). Many observations indicated that seismic waves could stimulate the oil production due to lowering of apparent viscosity coefficient, to the coalescence and/or the dispersion of droplets of a phase in multiphase fluids. However, the detailed mechanism of seismic stimulation has not been fully understood, either. In this study, We attempt to understand the mechanism of the flux change in viscous laminar flow under oscillating boundary condition for the simulation of interstitial flow. Here, we analyze a monophase flow in a pore throat. We first assume a Hagen-Poiseuille flow of incompressible fluid through a pore-throat in a porous medium. We adopt the Lattice Boltzmann method (LBM) in which the motion of fluid is simulated through the variation of velocity distribution function representing the distribution of discrete particle velocities. We use an improved incompressible LBKG model (d2q9i) proposed in Zou et. al. (1995) to accurately accommodate the boundary conditions of pressure and velocity in the Hagen-Poiseuille flow. We also use an half-way bounce back boundary condition as the velocity boundary condition. Also, we assume a uniform pressure (density) difference between inlet and outlet flow, and the density difference could initiate the flow in our simulation. The oscillating boundary condition is given by the body force acting on fluid particles. In this simulation, we found that the flux change is negligible under small amplitude of oscillation in both horizontal and vertical directions
Zhao, Shan; Wei, G W
2009-03-19
High-order central finite difference schemes encounter great difficulties in implementing complex boundary conditions. This paper introduces the matched interface and boundary (MIB) method as a novel boundary scheme to treat various general boundary conditions in arbitrarily high-order central finite difference schemes. To attain arbitrarily high order, the MIB method accurately extends the solution beyond the boundary by repeatedly enforcing only the original set of boundary conditions. The proposed approach is extensively validated via boundary value problems, initial-boundary value problems, eigenvalue problems, and high-order differential equations. Successful implementations are given to not only Dirichlet, Neumann, and Robin boundary conditions, but also more general ones, such as multiple boundary conditions in high-order differential equations and time-dependent boundary conditions in evolution equations. Detailed stability analysis of the MIB method is carried out. The MIB method is shown to be able to deliver high-order accuracy, while maintaining the same or similar stability conditions of the standard high-order central difference approximations. The application of the proposed MIB method to the boundary treatment of other non-standard high-order methods is also considered.
Institute of Scientific and Technical Information of China (English)
张兴武; 刘凯欣
2003-01-01
The solutions for a mode Ⅲ crack growing along an arbitrary propagation path in a piezoelectric plane are studied under the impermeable surface condition and the electrical contact surface condition respectively.According to the two kinds of electric boundary conditions,the Hilbert and Riemann boundary value problems in a half-plane including opening smooth arc are obtained from the theoretical analysis.Moreover,the equipollence of the solution formed under these two electric boundaries is proved,and unified solutions for the stress and electric displacement distribution in the crack-tipfield of the piezoelectric plane are achieved.
Second-order schemes for a boundary value problem with Neumann's boundary conditions
Dehghan, Mehdi
2002-01-01
A new second-order finite difference scheme based on the (3, 3) alternating direction implicit method and a new second-order finite difference technique based on the (5, 5) implicit formula are discussed for solving a nonlocal boundary value problem for the two-dimensional diffusion equation with Neumann's boundary conditions. While sharing some common features with the one-dimensional models, the solution of two-dimensional equations are substantially more difficult, thus some considerations are taken to be able to extend some ideas of the one-dimensional case. Using a suitable transformation the solution of this problem is equivalent to the solution of two other problems. The former, which is a one-dimensional nonlocal boundary value problem giving the value of [mu] through using the unconditionally stable standard implicit (3, 1) backward time-centred space (denoted BTCS) scheme. Using this result the second problem will be changed to a classical two-dimensional diffusion equation with Neumann's boundary conditions which will be solved numerically by using the unconditionally stable alternating direction implicit (3, 3) technique or the fully implicit finite difference scheme. The results of a numerical example are given and computation times are presented. Error estimates derived in the maximum norm are also tabulated.
Vibration suppression for laminated composite plates with arbitrary boundary conditions
Li, J.; Narita, Y.
2013-11-01
An analysis of vibration suppression for laminated composite plates subject to active constrained layer damping under various boundary conditions is presented. Piezoelectric-fiber-reinforced composites (PFRCs) are used as active actuators, and the effect of PFRC patches on vibration control is reported here. An analytical approach is expanded to analyze the vibration of laminated composites with arbitrary boundary conditions. By using Hamilton's principle and the Rayleigh-Ritz method, the equation of motion for the resulting electromechanical coupling system is derived. A velocity feedback control rule is employed to obtain an effective active damping in the vibration control. The orientation effect of piezoelectric fibers in the PFRC patches on the suppression of forced vibrations is also investigated.
Revisiting Johnson and Jackson boundary conditions for granular flows
Energy Technology Data Exchange (ETDEWEB)
Li, Tingwen; Benyahia, Sofiane
2012-07-01
In this article, we revisit Johnson and Jackson boundary conditions for granular flows. The oblique collision between a particle and a flat wall is analyzed by adopting the classic rigid-body theory and a more realistic semianalytical model. Based on the kinetic granular theory, the input parameter for the partial-slip boundary conditions, specularity coefficient, which is not measurable in experiments, is then interpreted as a function of the particle-wall restitution coefficient, the frictional coefficient, and the normalized slip velocity at the wall. An analytical expression for the specularity coefficient is suggested for a flat, frictional surface with a low frictional coefficient. The procedure for determining the specularity coefficient for a more general problem is outlined, and a working approximation is provided.
A Boundary Condition for Simulation of Flow Over Porous Surfaces
Frink, Neal T.; Bonhaus, Daryl L.; Vatsa, Veer N.; Bauer, Steven X. S.; Tinetti, Ana F.
2001-01-01
A new boundary condition is presented.for simulating the flow over passively porous surfaces. The model builds on the prior work of R.H. Bush to eliminate the need for constructing grid within an underlying plenum, thereby simplifying the numerical modeling of passively porous flow control systems and reducing computation cost. Code experts.for two structured-grid.flow solvers, TLNS3D and CFL3D. and one unstructured solver, USM3Dns, collaborated with an experimental porosity expert to develop the model and implement it into their respective codes. Results presented,for the three codes on a slender forebody with circumferential porosity and a wing with leading-edge porosity demonstrate a good agreement with experimental data and a remarkable ability to predict the aggregate aerodynamic effects of surface porosity with a simple boundary condition.
Modeling Plasmas with Strong Anisotropy, Neutral Fluid Effects, and Open Boundaries
Meier, Eric T.
Three computational plasma science topics are addressed in this research: the challenge of modeling strongly anisotropic thermal conduction, capturing neutral fluid effects in collisional plasmas, and modeling open boundaries in dissipative plasmas. The research efforts on these three topics contribute to a common objective: the improvement and extension of existing magnetohydrodynamic modeling capability. Modeling magnetically confined fusion-related plasmas is the focus of the research, but broader relevance is recognized and discussed. Code development is central to this work, and has been carried out within the flexible physics framework of the highly parallel HiFi implicit spectral element code. In magnetic plasma confinement, heat conduction perpendicular to the magnetic field is extremely slow compared to conduction parallel to the field. The anisotropy in heat conduction can be many orders of magnitude, and the inaccuracy of low-order representations can allow parallel heat transport to "leak" into the perpendicular direction, resulting in numerical perpendicular transport. If the computational grid is aligned to the magnetic field, this numerical error can be eliminated, even for low-order representations. However, grid alignment is possible only in idealized problems. In realistic applications, magnetic topology is chaotic. A general approach for accurately modeling the extreme anisotropy of fusion plasmas is to use high-order representations which do not require grid alignment for sufficient resolution. This research provides a comprehensive assessment of spectral element representation of anisotropy, in terms of dependence of accuracy on grid alignment, polynomial degree, and grid cell size, and gives results for two- and three-dimensional cases. Truncating large physical domains to concentrate computational resources is often necessary or desirable in simulating natural and man-made plasmas. A novel open boundary condition (BC) treatment for such
On Nonlinear Approximations to Cosmic Problems with Mixed Boundary Conditions
Mancinelli, Paul J.; Yahil, Amos; Ganon, Galit; Dekel, Avishai
1993-01-01
Nonlinear approximations to problems with mixed boundary conditions are useful for predicting large-scale streaming velocities from the density field, or vice-versa. We evaluate the schemes of Bernardeau \\cite{bernardeau92}, Gramann \\cite{gramann93}, and Nusser \\etal \\cite{nusser91}, using smoothed density and velocity fields obtained from $N$-body simulations of a CDM universe. The approximation of Nusser \\etal is overall the most accurate and robust. For Gaussian smoothing of 1000\\kms\\ the ...
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.
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.
The XXZ model with anti-periodic twisted boundary conditions
Niekamp, Sönke; Frahm, Holger
2009-01-01
We derive functional equations for the eigenvalues of the XXZ model subject to anti-diagonal twisted boundary conditions by means of fusion of transfer matrices and by Sklyanin's method of separation of variables. Our findings coincide with those obtained using Baxter's method and are compared to the recent solution of Galleas. As an application we study the finite size scaling of the ground state energy of the model in the critical regime.
The XXZ model with anti-periodic twisted boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Niekamp, Soenke; Wirth, Tobias; Frahm, Holger [Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstrasse 2, 30167 Hannover (Germany)
2009-05-15
We derive functional equations for the eigenvalues of the XXZ model subject to anti-diagonal twisted boundary conditions by means of fusion of transfer matrices and by Sklyanin's method of separation of variables. Our findings coincide with those obtained using Baxter's method and are compared to the recent solution of Galleas. As an application we study the finite size scaling of the ground-state energy of the model in the critical regime.
Asymptotic stability of the Boltzmann equation with Maxwell boundary conditions
Briant, Marc; Guo, Yan
2016-12-01
In a general C1 domain, we study the perturbative Cauchy theory for the Boltzmann equation with Maxwell boundary conditions with an accommodation coefficient α in (√{ 2 / 3 } , 1 ], and discuss this threshold. We consider polynomial or stretched exponential weights m (v) and prove existence, uniqueness and exponential trend to equilibrium around a global Maxwellian in Lx,v∞ (m). Of important note is the fact that the methods do not involve contradiction arguments.
On Vector Helmholtz Equation with a Coupling Boundary Condition
Institute of Scientific and Technical Information of China (English)
Gang Li; Jiangsong Zhang; Jiang Zhu; Danping Yang
2007-01-01
The Helmholtz equation is sometimes supplemented by conditions that include the specification of the boundary value of the divergence of the unknown. In this paper,we study the vector Helmholtz problem in domains of both C1,1 and Lipschitz. We establish a rigorous variational analysis such as equivalence, existence and uniqueness.And we propose finite element approximations based on the uncoupled solutions. Finally we present a convergence analysis and error estimates.
Hydrodynamic boundary condition of water on hydrophobic surfaces.
Schaeffel, David; Yordanov, Stoyan; Schmelzeisen, Marcus; Yamamoto, Tetsuya; Kappl, Michael; Schmitz, Roman; Dünweg, Burkhard; Butt, Hans-Jürgen; Koynov, Kaloian
2013-05-01
By combining total internal reflection fluorescence cross-correlation spectroscopy with Brownian dynamics simulations, we were able to measure the hydrodynamic boundary condition of water flowing over a smooth solid surface with exceptional accuracy. We analyzed the flow of aqueous electrolytes over glass coated with a layer of poly(dimethylsiloxane) (advancing contact angle Θ = 108°) or perfluorosilane (Θ = 113°). Within an error of better than 10 nm the slip length was indistinguishable from zero on all surfaces.
Maxwell boundary conditions impose non-Lindblad master equation
Bamba, Motoaki
2016-01-01
From the Hamiltonian connecting the inside and outside of an Fabry-Perot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds matters, although we can transform it to the Lindblad form by performing the rotating-wave approximation to that Hamiltonian. We calculate absorption spectra by these Lindblad and non-Lindblad master equations and also by the Maxwell boundary conditions in framework of the classical electrodynamics, which we consider the most reliable approach. We found that, compared to the Lindblad master equation, the absorption spectra by the non-Lindblad one agree better with those by the Maxwell boundary conditions. Although the discrepancy is highlighted only in the ultra-strong light-matter interaction regime with a relatively large broadening, the master equation of the non-Lindblad form is preferable rather than of the Lindblad one for pursuing the consistency with the classical elec...
Maxwell boundary conditions imply non-Lindblad master equation
Bamba, Motoaki; Imoto, Nobuyuki
2016-09-01
From the Hamiltonian connecting the inside and outside of a Fabry-Pérot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds matters, although we can transform it to the Lindblad form by performing the rotating-wave approximation to the connecting Hamiltonian. We calculate absorption spectra by these Lindblad and non-Lindblad master equations and also by the Maxwell boundary conditions in the framework of the classical electrodynamics, which we consider the most reliable approach. We found that, compared to the Lindblad master equation, the absorption spectra by the non-Lindblad one agree better with those by the Maxwell boundary conditions. Although the discrepancy is highlighted only in the ultrastrong light-matter interaction regime with a relatively large broadening, the master equation of the non-Lindblad form is preferable rather than of the Lindblad one for pursuing the consistency with the classical electrodynamics.
Outer boundary conditions for evolving cool white dwarfs
Rohrmann, R D; García-Berro, E; Córsico, A H; Bertolami, M M Miller
2012-01-01
White dwarf evolution is essentially a gravothermal cooling process, which,for cool white dwarfs, sensitively depends on the treatment of the outer boundary conditions. We provide detailed outer boundary conditions appropriate for computing the evolution of cool white dwarfs employing detailed non-gray model atmospheres for pure H composition. We also explore the impact on the white dwarf cooling times of different assumptions for energy transfer in the atmosphere of cool white dwarfs. Detailed non-gray model atmospheres are computed taken into account non-ideal effects in the gas equation of state and chemical equilibrium, collision-induced absorption from molecules, and the Lyman alpha quasi-molecular opacity. Our results show that the use of detailed outer boundary conditions becomes relevant for effective temperatures lower than 5800 and 6100K for sequences with 0.60 and 0.90 M_sun, respectively. Detailed model atmospheres predict ages that are up to approx 10% shorter at log L/L_sun=-4 when compared with...
New boundary conditions for oil reservoirs with fracture
Andriyanova, Elena; Astafev, Vladimir
2017-06-01
Based on the fact that most of oil fields are on the late stage of field development, it becomes necessary to produce hard-to-extract oil, which can be obtained only by use of enhance oil recovery methods. For example many low permeable or shale formations can be developed only with application of massive hydraulic fracturing technique. In addition, modern geophysical researches show that mostly oil bearing formations are complicated with tectonic faults of different shape and permeability. These discontinuities exert essential influence on the field development process and on the well performance. For the modeling of fluid flow in the reservoir with some area of different permeability, we should determine the boundary conditions. In this article for the first time the boundary conditions for the problem of fluid filtration in the reservoir with some discontinuity are considered. This discontinuity represents thin but long area, which can be hydraulic fracturing of tectonic fault. The obtained boundary condition equations allow us to take into account pressure difference above and below the section and different values of permeability.
Bethe ansatz for an AdS/CFT open spin chain with non-diagonal boundaries
Energy Technology Data Exchange (ETDEWEB)
Zhang, Xin [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics,Chinese Academy of Sciences,Beijing, 100190 (China); Cao, Junpeng [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics,Chinese Academy of Sciences,Beijing, 100190 (China); Collaborative Innovation Center of Quantum Matter,Beijing (China); Cui, Shuai [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics,Chinese Academy of Sciences,Beijing, 100190 (China); Nepomechie, Rafael I. [Physics Department, University of Miami,P.O. Box 248046, Coral Gables, FL 33124 (United States); Yang, Wen-Li [Institute of Modern Physics, Northwest University,Xian, 710069 (China); Beijing Center for Mathematics and Information Interdisciplinary Sciences,Beijing, 100048 (China); Shi, Kangjie [Institute of Modern Physics, Northwest University,Xian, 710069 (China); Wang, Yupeng [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics,Chinese Academy of Sciences,Beijing, 100190 (China); Collaborative Innovation Center of Quantum Matter,Beijing (China)
2015-10-21
We consider the integrable open-chain transfer matrix corresponding to a Y=0 brane at one boundary, and a Y{sub θ}=0 brane (rotated with the respect to the former by an angle θ) at the other boundary. We determine the exact eigenvalues of this transfer matrix in terms of solutions of a corresponding set of Bethe equations.
Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre M.
2014-02-01
A Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel continuous boundary force (CBF) method is proposed for solving the Navier-Stokes equations subject to the Robin boundary condition. In the CBF method, the Robin boundary condition is replaced by the homogeneous Neumann boundary condition and a volumetric force term added to the momentum conservation equation. Smoothed particle hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two- and three-dimensional flows subject to various forms of the Robin boundary condition in domains bounded by flat and curved boundaries. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite-element method. Considering the no-slip boundary condition as a special case of the slip boundary condition, we demonstrate that the SPH-CBF method accurately describes both the no-slip and slip conditions.
High Energy Boundary Conditions for a Cartesian Mesh Euler Solver
Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.
2004-01-01
Inlets and exhaust nozzles are often omitted or fared over in aerodynamic simulations of aircraft due to the complexities involving in the modeling of engine details such as complex geometry and flow physics. However, the assumption is often improper as inlet or plume flows have a substantial effect on vehicle aerodynamics. A tool for specifying inlet and exhaust plume conditions through the use of high-energy boundary conditions in an established inviscid flow solver is presented. The effects of the plume on the flow fields near the inlet and plume are discussed.
Solitons induced by boundary conditions from the Boussinesq equation
Chou, Ru Ling; Chu, C. K.
1990-01-01
The behavior of solitons induced by boundary excitation is investigated at various time-dependent conditions and different unperturbed water depths, using the Korteweg-de Vries (KdV) equation. Then, solitons induced from Boussinesq equations under similar conditions were studied, making it possible to remove the restriction in the KdV equation and to treat soliton head-on collisions (as well as overtaking collisions) and reflections. It is found that the results obtained from the KdV and the Boussinesq equations are in good agreement.
Repulsive Casimir force from fractional Neumann boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Lim, S.C. [Faculty of Engineering, Multimedia University, Jalan Multimedia, 63100 Cyberjaya, Selangor (Malaysia)], E-mail: sclim@mmu.edu.my; Teo, L.P. [Faculty of Information Technology, Multimedia University, Jalan Multimedia, 63100 Cyberjaya, Selangor (Malaysia); Department of Applied Mathematics, Faculty of Engineering, University of Nottingham Malaysia Campus, Jalan Broga, 43500 Semenyih, Selangor Darul Ehsan (Malaysia)], E-mail: lpteo@mmu.edu.my
2009-08-17
This Letter studies the finite temperature Casimir force acting on a rectangular piston associated with a massless fractional Klein-Gordon field at finite temperature. Dirichlet boundary conditions are imposed on the walls of a d-dimensional rectangular cavity, and a fractional Neumann condition is imposed on the piston that moves freely inside the cavity. The fractional Neumann condition gives an interpolation between the Dirichlet and Neumann conditions, where the Casimir force is known to be always attractive and always repulsive respectively. For the fractional Neumann boundary condition, the attractive or repulsive nature of the Casimir force is governed by the fractional order which takes values from zero (Dirichlet) to one (Neumann). When the fractional order is larger than 1/2, the Casimir force is always repulsive. For some fractional orders that are less than but close to 1/2, it is shown that the Casimir force can be either attractive or repulsive depending on the aspect ratio of the cavity and the temperature.
Nonstationary Stokes System in Cylindrical Domains Under Boundary Slip Conditions
Zaja¸czkowski, Wojciech M.
2017-03-01
Existence and uniqueness of solutions to the nonstationary Stokes system in a cylindrical domain {Ωsubset{R}^3} and under boundary slip conditions are proved in anisotropic Sobolev spaces. Assuming that the external force belong to {L_r(Ω×(0,T))} and initial velocity to {W_r^{2-2/r}(Ω)} there exists a solution such that velocity belongs to {W_r^{2,1}(Ω×(0,T))} and gradient of pressure to {L_r(Ω×(0,T))}, {rin(1,∞)}, {T > 0}. Thanks to the slip boundary conditions and a partition of unity the Stokes system is transformed to the Poisson equation for pressure and the heat equation for velocity. The existence of solutions to these equations is proved by applying local considerations. In this case we have to consider neighborhoods near the edges which by local mapping can be transformed to dihedral angle {π/2}. Hence solvability of the problem bases on construction local Green functions (near an interior point, near a point of a smooth part of the boundary, near a point of the edge) and their appropriate estimates. The technique presented in this paper can also work in other functional spaces: Sobolev-Slobodetskii, Besov, Nikolskii, Hölder and so on.
Current Large Deviations for Asymmetric Exclusion Processes with Open Boundaries
Bodineau, T.; Derrida, B.
2006-04-01
We study the large deviation functional of the current for the Weakly Asymmetric Simple Exclusion Process in contact with two reservoirs. We compare this functional in the large drift limit to the one of the Totally Asymmetric Simple Exclusion Process, in particular to the Jensen-Varadhan functional. Conjectures for generalizing the Jensen-Varadhan functional to open systems are also stated.
Boundary conditions towards realistic simulation of jet engine noise
Dhamankar, Nitin S.
Strict noise regulations at major airports and increasing environmental concerns have made prediction and attenuation of jet noise an active research topic. Large eddy simulation coupled with computational aeroacoustics has the potential to be a significant research tool for this problem. With the emergence of petascale computer clusters, it is now computationally feasible to include the nozzle geometry in jet noise simulations. In high Reynolds number experiments on jet noise, the turbulent boundary layer on the inner surface of the nozzle separates into a turbulent free shear layer. Inclusion of a nozzle with turbulent inlet conditions is necessary to simulate this phenomenon realistically. This will allow a reasonable comparison of numerically computed noise levels with the experimental results. Two viscous wall boundary conditions are implemented for modeling the nozzle walls. A characteristic-based approach is compared with a computationally cheaper, extrapolation-based formulation. In viscous flow over a circular cylinder under two different regimes, excellent agreement is observed between the results of the two approaches. The results agree reasonably well with reference experimental and numerical results. Both the boundary conditions are thus found to be appropriate, the extrapolation-based formulation having an edge with its low cost. This is followed with the crucial step of generation of a turbulent boundary layer inside the nozzle. A digital filter-based turbulent inflow condition, extended in a new way to non-uniform curvilinear grids is implemented to achieve this. A zero pressure gradient flat plate turbulent boundary layer is simulated at a high Reynolds number to show that the method is capable of producing sustained turbulence. The length of the adjustment region necessary for synthetic inlet turbulence to recover from modeling errors is estimated. A low Reynolds number jet simulation including a round nozzle geometry is performed and the method
Applying Twisted Boundary Conditions for Few-body Nuclear Systems
Körber, Christopher
2015-01-01
We describe and implement twisted boundary conditions for the deuteron and triton systems within finite-volumes using the nuclear lattice EFT formalism. We investigate the finite-volume dependence of these systems with different twists angles. We demonstrate how various finite-volume information can be used to improve calculations of binding energies in such a framework. Our results suggests that with appropriate twisting of boundaries, infinite-volume binding energies can be reliably extracted from calculations using modest volume sizes with cubic length $L\\approx8-14$ fm. Of particular importance is our derivation and numerical verification of three-body analogue of `i-periodic' twist angles that eliminate the leading order finite-volume effects to the three-body binding energy.
Boundary Condition Effects on Taylor States in SSX
Han, Jeremy; Shrock, Jaron; Kaur, Manjit; Brown, Michael; Schaffner, David
2016-10-01
Three different boundary conditions are applied to the SSX 0.15 m diameter plasma wind tunnel and the resultant Taylor states are characterized. The glass walls of the wind tunnel act as an insulating boundary condition. For the second condition, a flux conserver is wrapped around the tunnel to trap magnetic field lines inside the SSX. For the last condition, the flux conserver is segmented to add theta pinch coils, which will accelerate the plasma. We used resistive stainless steel and copper mesh for the flux conservers, which have soak times of 3 μs and 250 μs , respectively. The goal is to increase the speed, temperature, and density of the plasma plume by adding magnetic energy into the system using the coils and compressing the plasma into small volumes by stagnation. The time of flight is measured by using a linear array of magnetic pick-up loops, which track the plasma plume's location as a function of time. The density is measured by precision quadrature He-Ne laser interferometry, and the temperature is measured by ion Doppler spectroscopy. Speed and density without the coils are 30km /s and 1015cm-3 . We will reach a speed of 100km /s and density of 1016cm-3 by adding the coil. Work supported by DOE OFES and ARPA-E ALPHA program.
Acoustic boundary conditions at an impedance lining in inviscid shear flow
Khamis, Doran; Brambley, Edward James
2016-01-01
This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Cambridge University Press. The accuracy of existing impedance boundary conditions is investigated, and new impedance boundary conditions are derived, for lined ducts with inviscid shear flow. The accuracy of the Ingard–Myers boundary condition is found to be poor. Matched asymptotic expansions are used to derive a boundary condition accurate to second order in the boundary layer thic...
Current Fluctuations in the One-Dimensional Symmetric Exclusion Process with Open Boundaries
Derrida, B.; Douçot, B.; Roche, P.-E.
2004-05-01
We calculate the first four cumulants of the integrated current of the one dimensional symmetric simple exclusion process of $N$ sites with open boundary conditions. For large system size $N$, the generating function of the integrated current depends on the densities $\\rho_a$ and $\\rho_b$ of the two reservoirs and on the fugacity $z$, the parameter conjugated to the integrated current, through a single parameter. Based on our expressions for these first four cumulants, we make a conjecture which leads to a prediction for all the higher cumulants. In the case $\\rho_a=1$ and $\\rho_b=0$, our conjecture gives the same universal distribution as the one obtained by Lee, Levitov and Yakovets for one dimensional quantum conductors in the metallic regime.
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.
Boundary conditions for soft glassy flows: slippage and surface fluidization.
Mansard, Vincent; Bocquet, Lydéric; Colin, Annie
2014-09-28
We explore the question of surface boundary conditions for the flow of a dense emulsion. We make use of microlithographic tools to create surfaces with well controlled roughness patterns and measure using dynamic confocal microscopy both the slip velocity and the shear rate close to the wall, which we relate to the notion of surface fluidization. Both slippage and wall fluidization depend non-monotonously on the roughness. We interpret this behavior within a simple model in terms of the building of a stratified layer and the activation of plastic events by the surface roughness.
Stokes Flow with Slip and Kuwabara Boundary Conditions
Indian Academy of Sciences (India)
Sunil Datta; Satya Deo
2002-08-01
The forces experienced by randomly and homogeneously distributed parallel circular cylinder or spheres in uniform viscous flow are investigated with slip boundary condition under Stokes approximation using particle-in-cell model technique and the result compared with the no-slip case. The corresponding problem of streaming flow past spheroidal particles departing but little in shape from a sphere is also investigated. The explicit expression for the stream function is obtained to the first order in the small parameter characterizing the deformation. As a particular case of this we considered an oblate spheroid and evaluate the drag on it.
Cauchy-perturbative matching and outer boundary conditions computational studies
Rezzolla, L; Matzner, R A; Rupright, M E; Shapiro, S L; Rezzolla, Luciano; Abrahams, Andrew M; Matzner, Richard A.; Rupright, Mark E.; Shapiro, Stuart L.
1999-01-01
We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the solution of a Cauchy evolution of the nonlinear Einstein field equations to a set of one-dimensional linear equations obtained through perturbation techniques over a curved background. We discuss the validity of this approach in the case of linear and mildly nonlinear gravitational waves and show how a numerical module developed for this purpose is able to provide an accurate and numerically convergent description of the gravitational wave propagation and a stable numerical evolution.
Quantum Nuclear Pasta Calculations with Twisted Angular Boundary Conditions
Schuetrumpf, Bastian; Nazarewicz, Witold
2015-10-01
Nuclear pasta, expected to be present in the inner crust of neutron stars and core collapse supernovae, can contain a wide spectrum of different exotic shapes such as nuclear rods and slabs. There are also more complicated, network-like structures, the triply periodic minimal surfaces, already known e.g. in biological systems. These shapes are studied with the Hartree-Fock method using modern Skyrme forces. Furthermore twisted angular boundary conditions are utilized to reduce finite size effects in the rectangular simulation boxes. It is shown, that this improves the accuracy of the calculations drastically and additionally more insights into the mechanism of forming minimal surfaces can be gained.
On the trigonometric Felderhof model with domain wall boundary conditions
Caradoc, A; Wheeler, M; Zuparic, M; 10.1088/1742-5468/2007/03/P03010
2008-01-01
We consider the trigonometric Felderhof model, of free fermions in an external field, on a finite lattice with domain wall boundary conditions. The vertex weights are functions of rapidities and external fields. We obtain a determinant expression for the partition function in the special case where the dependence on the rapidities is eliminated, but for general external field variables. This determinant can be evaluated in product form. In the homogeneous limit, it is proportional to a 2-Toda tau function. Next, we use the algebraic Bethe ansatz factorized basis to obtain a product expression for the partition function in the general case with dependence on all variables.
Boundary conditions and generalized functions in a transition radiation problem
Villavicencio, M.; Jiménez, J. L.
2017-03-01
The aim of this work is to show how all the components of the electromagnetic field involved in the transition radiation problem can be obtained using distribution functions. The handling of the products and derivatives of distributions appearing in the differential equations governing transition radiation, allows to obtain the necessary boundary conditions, additional to those implied by Maxwell's equations, in order to exactly determine the longitudinal components of the electromagnetic field. It is shown that this method is not only useful but it is really convenient to achieve a full analysis of the problem.
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
Directory of Open Access Journals (Sweden)
Darae Jeong
2015-01-01
Full Text Available We briefly review and investigate the performance of various boundary conditions such as Dirichlet, Neumann, linear, and partial differential equation boundary conditions for the numerical solutions of the Black-Scholes partial differential equation. We use a finite difference method to numerically solve the equation. To show the efficiency of the given boundary condition, several numerical examples are presented. In numerical test, we investigate the effect of the domain sizes and compare the effect of various boundary conditions with pointwise error and root mean square error. Numerical results show that linear boundary condition is accurate and efficient among the other boundary conditions.
FINITE VOLUME NUMERICAL ANALYSIS FOR PARABOLIC EQUATION WITH ROBIN BOUNDARY CONDITION
Institute of Scientific and Technical Information of China (English)
Xia Cui
2005-01-01
In this paper, finite volume method on unstructured meshes is studied for a parabolic convection-diffusion problem on an open bounded set of Rd (d = 2 or 3) with Robin boundary condition. Upwinding approximations are adapted to treat both the convection term and Robin boundary condition. By directly getting start from the formulation of the finite volume scheme, numerical analysis is done. By using several discrete functional analysis techniques such as summation by parts, discrete norm inequality, et al, the stability and error estimates on the approximate solution are established, existence and uniqueness of the approximate solution and the 1st order temporal norm and L2 and H1 spacial norm convergence properties are obtained.
Institute of Scientific and Technical Information of China (English)
Hou-de Han; Xin Wen
2004-01-01
We consider the numerical approximations of the complex amplitude in a coupled bay-river system in this work. One half-circumference is introduced as the artificial boundary in the open sea, and one segment is introduced as the artificial boundary in the river if the river is semi-infinite. On the artificial boundary a sequence of high-order artificial boundary conditions are proposed. Then the original problem is solved in a finite computational domain, which is equivalent to a variational problem. The numerical approximations for the original problem are obtained by solving the variational problem with the finite element method. The numerical examples show that the artificial boundary conditions given in this work are very effective.
Boundary conditions and phase transitions in neural networks. Simulation results.
Demongeot, Jacques; Sené, Sylvain
2008-09-01
This paper gives new simulation results on the asymptotic behaviour of theoretical neural networks on Z and Z(2) following an extended Hopfield law. It specifically focuses on the influence of fixed boundary conditions on such networks. First, we will generalise the theoretical results already obtained for attractive networks in one dimension to more complicated neural networks. Then, we will focus on two-dimensional neural networks. Theoretical results have already been found for the nearest neighbours Ising model in 2D with translation-invariant local isotropic interactions. We will detail what happens for this kind of interaction in neural networks and we will also focus on more complicated interactions, i.e., interactions that are not local, neither isotropic, nor translation-invariant. For all these kinds of interactions, we will show that fixed boundary conditions have significant impacts on the asymptotic behaviour of such networks. These impacts result in the emergence of phase transitions whose geometric shape will be numerically characterised.
Boundary conditions for NLTE polarized radiative transfer with incident radiation
Faurobert, Marianne; Atanackovic, Olga
2013-01-01
Polarized NLTE radiative transfer in the presence of scattering in spectral lines and/or in continua may be cast in a so-called reduced form for six reduced components of the radiation field. In this formalism the six components of the reduced source function are angle-independent quantities. It thus reduces drastically the storage requirement of numerical codes. This approach encounters a fundamental problem when the medium is illuminated by a polarized incident radiation, because there is a priori no way of relating the known (and measurable) Stokes parameters of the incident radiation to boundary conditions for the reduced equations. The origin of this problem is that there is no unique way of deriving the radiation reduced components from its Stokes parameters (only the inverse operation is clearly defined). The method proposed here aims at enabling to work with arbitrary incident radiation field (polarized or unpolarized). In previous works an ad-hoc treatment of the boundary conditions, applying to case...
Complex Wall Boundary Conditions for Modeling Combustion in Catalytic Channels
Zhu, Huayang; Jackson, Gregory
2000-11-01
Monolith catalytic reactors for exothermic oxidation are being used in automobile exhaust clean-up and ultra-low emissions combustion systems. The reactors present a unique coupling between mass, heat, and momentum transport in a channel flow configuration. The use of porous catalytic coatings along the channel wall presents a complex boundary condition when modeled with the two-dimensional channel flow. This current work presents a 2-D transient model for predicting the performance of catalytic combustion systems for methane oxidation on Pd catalysts. The model solves the 2-D compressible transport equations for momentum, species, and energy, which are solved with a porous washcoat model for the wall boundary conditions. A time-splitting algorithm is used to separate the stiff chemical reactions from the convective/diffusive equations for the channel flow. A detailed surface chemistry mechanism is incorporated for the catalytic wall model and is used to predict transient ignition and steady-state conversion of CH4-air flows in the catalytic reactor.
Comparative Quantum Cosmology: Causality, Singularity, and Boundary Conditions
Fellman, Philip V; Carmichael, Christine M; Post, Andrew Carmichael
2007-01-01
In this review article we compare the recent work of Peter Lynds, "On a finite universe with no beginning or end", with that of Stephen Hawking, primarily "Quantum Cosmology, M-Theory, and the Anthropic Principle", and two foundational works by Sean M. Carroll and Jennifer Chen, "Does Inflation Provide Natural Conditions for the Universe" and "Spontaneous Inflation and the Origin of the Arrow of Time", in order to evaluate their comparative treatments of the nature and role of causality, time ordering, thermodynamic reversibility, singularities and boundary conditions in the formation of the early universe. We briefly reference Smolin and Kauffman's recent arguments with respect to possible processes of "evolutionary selection" in early universe formation as an alternative explanation to key elements of Hawking's earlier "M-Theory", and its attendant anthropic principle. We also briefly excerpt a short section of Smolin's recent work on topology in quantum loop gravity, simply as an illustrative example of th...
Survey of Condition Indicators for Condition Monitoring Systems (Open Access)
2014-09-29
Renewable Energy Laboratory (NREL) published a document named ‘Wind Turbine Gearbox Condition Monitoring Round Robin Study – Vibration Analysis’ in 2012... Mean Square (RMS) RMS describes the energy content of the signal. RMS is used to evaluate the overall condition of the components. Therefore, it...13) ̅ is the mean value of signal N is the number of data point in the dataset x Energy
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.
Theory of a curved planar waveguide with Robin boundary conditions
Olendski, O.; Mikhailovska, L.
2010-03-01
A model of a thin straight strip with a uniformly curved section and with boundary requirements zeroing at the edges a linear superposition of the wave function and its normal derivative (Robin boundary condition) is analyzed theoretically within the framework of the linear Schrödinger equation and is applied to the study of the processes in the bent magnetic multilayers, superconducting films and metallic ferrite-filled waveguides. In particular, subband thresholds of the straight and curved parts of the film are calculated and analyzed as a function of the Robin parameter 1/Λ , with Λ being an extrapolation length entering Robin boundary condition. For the arbitrary Robin coefficients which are equal on the opposite interfaces of the strip and for all bend parameters the lowest-mode energy of the continuously curved duct is always smaller than its straight counterpart. Accordingly, the bound state below the fundamental propagation threshold of the straight arms always exists as a result of the bend. In terms of the superconductivity language it means an increased critical temperature of the curved film compared to its straight counterpart. Localized-level dependence on the parameters of the curve is investigated with its energy decreasing with increasing bend angle and decreasing bend radius. Conditions of the bound-state existence for the different Robin parameters on the opposite edges are analyzed too; in particular, it is shown that the bound state below the first transverse threshold of the straight arm always exists if the inner extrapolation length is not larger than the outer one. In the opposite case there is a range of the bend parameters where the curved film cannot trap the wave and form the localized mode; for example, for the fixed bend radius the bound state emerges from the continuum at some nonzero bend angle that depends on the difference of the two lengths Λ at the opposite interfaces. Various transport properties of the film such as
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.
Theoretical Foundations of Incorporating Local Boundary Conditions into Nonlocal Problems
Aksoylu, Burak; Beyer, Horst Reinhard; Celiker, Fatih
2017-08-01
We study nonlocal equations from the area of peridynamics on bounded domains. We present four main results. In our recent paper, we have discovered that, on R, the governing operator in peridynamics, which involves a convolution, is a bounded function of the classical (local) governing operator. Building on this, as main result 1, we construct an abstract convolution operator on bounded domains which is a generalization of the standard convolution based on integrals. The abstract convolution operator is a function of the classical operator, defined by a Hilbert basis available due to the purely discrete spectrum of the latter. As governing operator of the nonlocal equation we use a function of the classical operator, this allows us to incorporate local boundary conditions into nonlocal theories. As main result 2, we prove that the solution operator can be uniquely decomposed into a Hilbert-Schmidt operator and a multiple of the identity operator. As main result 3, we prove that Hilbert-Schmidt operators provide a smoothing of the input data in the sense a square integrable function is mapped into a function that is smooth up to boundary of the domain. As main result 4, for the homogeneous nonlocal wave equation, we prove that continuity is preserved by time evolution. Namely, the solution is discontinuous if and only if the initial data is discontinuous. As a consequence, discontinuities remain stationary.
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.
OpenMP for 3D potential boundary value problems solved by PIES
KuŻelewski, Andrzej; Zieniuk, Eugeniusz
2016-06-01
The main purpose of this paper is examination of an application of modern parallel computing technique OpenMP to speed up the calculation in the numerical solution of parametric integral equations systems (PIES). The authors noticed, that solving more complex boundary problems by PIES sometimes requires large computing time. This paper presents the use of OpenMP and fast C++ linear algebra library Armadillo for boundary value problems modelled by 3D Laplace's equation and solved using PIES. The testing example shows that the use of mentioned technologies significantly increases speed of calculations in PIES.
A radial distribution function-based open boundary force model for multi-centered molecules
Neumann, Philipp
2014-06-01
We derive an expression for radial distribution function (RDF)-based open boundary forcing for molecules with multiple interaction sites. Due to the high-dimensionality of the molecule configuration space and missing rotational invariance, a computationally cheap, 1D approximation of the arising integral expressions as in the single-centered case is not possible anymore. We propose a simple, yet accurate model invoking standard molecule- and site-based RDFs to approximate the respective integral equation. The new open boundary force model is validated for ethane in different scenarios and shows very good agreement with data from periodic simulations. © World Scientific Publishing Company.
DEFF Research Database (Denmark)
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...
`Gas cushion' model and hydrodynamic boundary conditions for superhydrophobic textures
Nizkaya, Tatiana V; Vinogradova, Olga I
2014-01-01
Superhydrophobic Cassie textures with trapped gas bubbles reduce drag, by generating large effective slip, which is important for a variety of applications that involve a manipulation of liquids at the small scale. Here we discuss how the dissipation in the gas phase of textures modifies their friction properties and effective slip. We propose an operator method, which allows us the mapping of the flow in the gas subphase to a local slip boundary condition at the liquid/gas interface. The determined uniquely local slip length depends on the viscosity contrast and underlying topography, and can be immediately used to evaluate an effective slip of the texture. Beside Cassie surfaces our approach is valid for Wenzel textures, where a liquid follows the surface relief, as well as for rough surfaces impregnated by a low-viscosity `lubricant'. These results provide a framework for the rational design of textured surfaces for numerous applications.
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.
Thermal momentum distribution from path integrals with shifted boundary conditions
Giusti, Leonardo
2011-01-01
For a thermal field theory formulated in the grand canonical ensemble, the distribution of the total momentum is an observable characterizing the thermal state. We show that its cumulants are related to thermodynamic potentials. In a relativistic system for instance, the thermal variance of the total momentum is a direct measure of the enthalpy. We relate the generating function of the cumulants to the ratio of (a) a partition function expressed as a Matsubara path integral with shifted boundary conditions in the compact direction, and (b) the ordinary partition function. In this form the generating function is well suited for Monte-Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang-Mills theory and obtain the entropy density at three different temperatures.
Physiologically structured populations with diffusion and dynamic boundary conditions.
Farkas, József Z; Hinow, Peter
2011-04-01
We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. We equip the model with generalized Wentzell-Robin (or dynamic) boundary conditions. This approach allows the modelling of populations in which individuals may have distinguished physiological states. We establish existence and positivity of solutions by showing that solutions are governed by a positive quasicontractive semigroup of linear operators on the biologically relevant state space. These results are obtained by establishing dissipativity of a suitably perturbed semigroup generator. We also show that solutions of the model exhibit balanced exponential growth, that is, our model admits a finite-dimensional global attractor. In case of strictly positive fertility we are able to establish that solutions in fact exhibit asynchronous exponential growth.
Boundary Conditions for a New Type of Design Task
DEFF Research Database (Denmark)
McAloone, Tim C.
2011-01-01
object and research paradigm, studying service‐oriented approaches to product development and seeking to understand how to spell the systematic development of these so-called Product/Service‐Systems (PSS). When considering the shift towards PSS in the domain of engineering, it is in......-teresting to understand the shifting focus and identification of boundary conditions that manufacturing organisations must undergo, in order to develop just as systematic an approach to the service-related aspects of their business development, as they have in place for their product development. This chapter......Manufacturing companies have traditionally focused their efforts on developing and producing physical products for the market. Currently, however, many companies are rethinking their business strategies, from selling products to providing services. In place of the product alone, the activity...
Steady-State Axisymmetric MHD Solutions with Various Boundary Conditions
Wang, Lile
2014-01-01
Axisymmetric magnetohydrodynamics (MHD) can be invoked for describing astrophysical magnetized flows and formulated to model stellar magnetospheres including main sequence stars (e.g. the Sun), compact stellar objects [e.g. magnetic white dwarfs (MWDs), radio pulsars, anomalous X-ray pulsars (AXPs), magnetars, isolated neutron stars etc.], and planets as a major step forward towards a full three-dimensional model construction. Using powerful and reliable numerical solvers based on two distinct finite-difference method (FDM) and finite-element method (FEM) schemes of algorithm, we examine axisymmetric steady-state or stationary MHD models in Throumoulopoulos & Tasso (2001), finding that their separable semi-analytic nonlinear solutions are actually not unique given their specific selection of several free functionals and chosen boundary conditions. The multiplicity of nonlinear steady MHD solutions gives rise to differences in the total energies contained in the magnetic fields and flow velocity fields as ...
Solution of MHD problems with mixed-type boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Antimirov, M.IA.
1985-06-01
The introduction of artificial anisotropy of the dynamic viscosity in one of the subregions in which the solution is sought is utilized to derive an approximation method for MHD problems with mixed-type boundary conditions. The method is demonstrated through two problems: slow rotation of a disk and motion of a finite-width infinitely long plate in an infinite volume of a conducting fluid. The velocity and magnetic field solutions are obtained in the form of integrals of Bessel functions, and the torque is found. It is shown that when the Hartmann number approaches infinity the torque of a convex body of revolution in a longitudinal magnetic field is equal to that of a disk lying at the centerline section of the body.
Sprlak, M.; Novak, P.; Pitonak, M.; Hamackova, E.
2015-12-01
Values of scalar, vectorial and second-order tensorial parameters of the Earth's gravitational field have been collected by various sensors in geodesy and geophysics. Such observables have been widely exploited in different parametrization methods for the gravitational field modelling. Moreover, theoretical aspects of these quantities have extensively been studied and are well understood. On the other hand, new sensors for observing gravitational curvatures, i.e., components of the third-order gravitational tensor, are currently under development. This fact may be documented by the terrestrial experiments Dulkyn and Magia, as well as by the proposal of the gravity-dedicated satellite mission called OPTIMA. As the gravitational curvatures represent new types of observables, their exploitation for modelling of the Earth's gravitational field is a subject of this study. Firstly, we derive integral transforms between the gravitational potential and gravitational curvatures, i.e., we find analytical solutions of the boundary value problems with gravitational curvatures as boundary conditions. Secondly, properties of the corresponding Green kernel functions are studied in the spatial and spectral domains. Thirdly, the correctness of the new analytical solutions is tested in a simulation study. The presented mathematical apparatus reveal important properties of the gravitational curvatures. It also extends the Meissl scheme, i.e., an important theoretical paradigm that relates various parameters of the Earth's gravitational field.
Behavior of the reversed field pinch with nonideal boundary conditions
Ho, Yung-Lung
1988-11-01
The linear and nonlinear magnetohydrodynamic stability of current-driven modes are studied for a reversed field pinch with nonideal boundary conditions. The plasma is bounded by a thin resistive shell surrounded by a vacuum region out to a radius at which a perfectly conducting wall is situated. The distant wall and the thin shell problems are studied by removing either the resistive shell or the conducting wall. Linearly, growth rates of tearing modes and kink modes are calculated by analytical solutions based on the modified Bessel function model for the equilibrium. The effects of variation of the shell resistivity and wall proximity on the growth rates are investigated. The modes that may be important in different parameter regimes and with different boundary conditions are identified. The nonlinear behaviors are studied with a three-dimensional magnetohydrodynamics code. The fluctuations generally rise with increasing distance between the conducting wall and the plasma. The enhanced fluctuation induced v x b electric field primarily oppose toroidal current; hence, loop voltage must increase to sustain the constant. Quasilinear interaction between modes typically associated with the dynamo action is identified as the most probable nonlinear destabilization mechanism. The helicity and energy balance properties of the simulation results are discussed. The interruption of current density along field lines intersecting the resistive shell is shown to lead to surface helicity leakage. This effect is intimately tied to stability, as fluctuation induced v x b electric field is necessary to transport the helicity to the surface. In this manner, all aspects of helicity balance, i.e., injection, transport, and dissipation, are considered self-consistently. The importance of the helicity and energy dissipation by the mean components of the magnetic field and current density is discussed.
The height of the atmospheric boundary layer during unstable conditions
Energy Technology Data Exchange (ETDEWEB)
Gryning, S.E.
2005-11-01
The height of the convective atmospheric boundary layer, also called the mixed-layer, is one of the fundamental parameters that characterise the structure of the atmosphere near the ground. It has many theoretical and practical applications such as the prediction of air pollution concentrations, surface temperature and the scaling of turbulence. However, as pointed out by Builtjes (2001) in a review paper on Major Twentieth Century Milestones in Air Pollution Modelling and Its Application, the weakest point in meteorology data is still the determination of the height of the mixed-layer, the so-called mixing height. A simple applied model for the height of the mixed-layer over homogeneous terrain is suggested in chapter 2. It is based on a parameterised budget for the turbulent kinetic energy. In the model basically three terms - the spin-up term and the production of mechanical and convective turbulent kinetic energy - control the growth of the mixed layer. The interplay between the three terms is related to the meteorological conditions and the height of the mixed layer. A stable layer, the so-called entrainment zone, which is confined between the mixed layer and the free air above, caps the mixed layer. A parameterisation of the depth of the entrainment zone is also suggested, and used to devise a combined model for the height of the mixed layer and the entrainment zone. Another important aspect of the mixed layer development exists in coastal areas where an internal boundary layer forms downwind from the coastline. A model for the growth of the internal boundary layer is developed in analogy with the model for mixed layer development over homogeneous terrain. The strength of this model is that it can operate on a very fine spatial resolution with minor computer resources. Chapter 3 deals with the validation of the models. It is based in parts on data from the literature, and on own measurements. For the validation of the formation of the internal boundary layer
DYNAMIC SURFACE BOUNDARY-CONDITIONS - A SIMPLE BOUNDARY MODEL FOR MOLECULAR-DYNAMICS SIMULATIONS
JUFFER, AH; BERENDSEN, HJC
1993-01-01
A simple model for the treatment of boundaries in molecular dynamics simulations is presented. The method involves the positioning of boundary atoms on a surface that surrounds a system of interest. The boundary atoms interact with the inner region and represent the effect of atoms outside the surfa
Active open boundary forcing using dual relaxation time-scales in downscaled ocean models
Herzfeld, M.; Gillibrand, P. A.
2015-05-01
Regional models actively forced with data from larger scale models at their open boundaries often contain motion at different time-scales (e.g. tidal and low frequency). These motions are not always individually well specified in the forcing data, and one may require a more active boundary forcing while the other exert less influence on the model interior. If a single relaxation time-scale is used to relax toward these data in the boundary equation, then this may be difficult. The method of fractional steps is used to introduce dual relaxation time-scales in an open boundary local flux adjustment scheme. This allows tidal and low frequency oscillations to be relaxed independently, resulting in a better overall solution than if a single relaxation parameter is optimized for tidal (short relaxation) or low frequency (long relaxation) boundary forcing. The dual method is compared to the single relaxation method for an idealized test case where a tidal signal is superimposed on a steady state low frequency solution, and a real application where the low frequency boundary forcing component is derived from a global circulation model for a region extending over the whole Great Barrier Reef, and a tidal signal subsequently superimposed.
Exact solution of the XXX Gaudin model with generic open boundaries
Hao, Kun; Cao, Junpeng; Yang, Tao; Yang, Wen-Li
2015-03-01
The XXX Gaudin model with generic integrable open boundaries specified by the most general non-diagonal reflecting matrices is studied. Besides the inhomogeneous parameters, the associated Gaudin operators have six free parameters which break the U(1) -symmetry. With the help of the off-diagonal Bethe ansatz, we successfully obtained the eigenvalues of these Gaudin operators and the corresponding Bethe ansatz equations.
Two-dimensional cellular automaton model of traffic flow with open boundaries
Tadaki, S I
1996-01-01
A two-dimensional cellular automaton model of traffic flow with open boundaries are investigated by computer simulations. The outflow of cars from the system and the average velocity are investigated. The time sequences of the outflow and average velocity have flicker noises in a jamming phase. The low density behavior are discussed with simple jam-free approximation.
Algebraic Bethe Ansatz for Open XXX Model with Triangular Boundary Matrices
Belliard, Samuel; Crampé, Nicolas; Ragoucy, Eric
2013-05-01
We consider an open XXX spin chain with two general boundary matrices whose entries obey a relation, which is equivalent to the possibility to put simultaneously the two matrices in a upper-triangular form. We construct Bethe vectors by means of a generalized algebraic Bethe ansatz. As usual, the method uses Bethe equations and provides transfer matrix eigenvalues.
Managing Knowledge Boundaries for Open Innovation : Lessons from the Automotive Industry
Wilhelm, Miriam; Dolfsma, Willem
2017-01-01
The rising need to innovate and obtain knowledge from more distant knowledge sources calls for new innovation strategies and a better integration of other external actors who lie outside the traditional automotive supply chain. Such an open innovation strategy challenges organizational boundaries
Sensitivity of African easterly waves to boundary layer conditions
Directory of Open Access Journals (Sweden)
A. Lenouo
2008-06-01
Full Text Available A linearized version of the quasi-geostrophic model (QGM with an explicit Ekman layer and observed static stability parameter and profile of the African easterly jet (AEJ, is used to study the instability properties of the environment of the West African wave disturbances. It is found that the growth rate, the propagation velocity and the structure of the African easterly waves (AEW can be well simulated. Two different lower boundary conditions are applied. One assumes a lack of vertical gradient of perturbation stream function and the other assumes zero wind perturbation at the surface. The first case gives more realistic results since in the absence of horizontal diffusion, growth rate, phase speed and period have values of 0.5 day^{−1}, 10.83 m s^{−1} and 3.1 day, respectively. The zero wind perturbation at the surface case leads to values of these parameters that are 50 percent lower. The analysis of the sensitivity to diffusion shows that the magnitude of the growth rate decreases with this parameter. Modelled total relative vorticity has its low level maximum around 900 hPa under no-slip, and 700 hPa under free slip condition.
Effects of Boundary Conditions on Near Field Plasma Plume Simulations
Boyd, Iain
2004-11-01
The successful development of various types of electric propulsion devices is providing the need for accurate assessment of integration effects generated by the interaction of the plasma plumes of these thrusters with the host spacecraft. Assessment of spacecraft interaction effects in ground based laboratory facilities is inadequate due to the technical difficulties involved in accurately recreating the near vacuum ambient conditions experienced in space. This situation therefore places a heavy demand on computational modeling of plasma plume phenomena. Recently (Boyd and Yim, Journal of Applied Physics, Vol. 95, 2004, pp. 4575-5484) a hybrid model of the near field of the plume of a Hall thruster was reported in which the heavy species are modeled using particles and the electrons are modeled using a detailed fluid description. The present study continues the model development and assessment by considering the sensitivity of computed results to different types of boundary conditions that must be formulated for the thruster exit, for the cathode exit, for the thruster walls, and for the plume far field. The model is assessed through comparison of its predictions with several sets of experimental data measured in the plume of the BHT-200 Hall thruster.
Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions
Directory of Open Access Journals (Sweden)
Nemat Nyamoradi
2013-01-01
Full Text Available We consider a system of boundary value problems for fractional differential equation given by D0+βϕp(D0+αu(t=λ1a1(tf1(u(t,v(t, t∈(0,1, D0+βϕp(D0+αv(t=λ2a2(tf2(u(t,v(t, t∈(0,1, where 1<α, β≤2, 2<α+β≤4, λ1, λ2 are eigenvalues, subject either to the boundary conditions D0+αu(0=D0+αu(1=0, u(0=0, D0+β1u(1-Σi=1m-2a1i D0+β1u(ξ1i=0, D0+αv(0=D0+αv(1=0, v(0=0, D0+β1v(1-Σi=1m-2a2i D0+β1v(ξ2i=0 or D0+αu(0=D0+αu(1=0, u(0=0, D0+β1u(1-Σi=1m-2a1i D0+β1u(ξ1i=ψ1(u, D0+αv(0=D0+αv(1=0, v(0=0, D0+β1v(1-Σi=1m-2a2i D0+β1v(ξ2i=ψ2(v, where 0<β1<1, α-β1-1≥0 and ψ1, ψ2:C([0,1]→[0, ∞ are continuous functions. The Krasnoselskiis fixed point theorem is applied to prove the existence of at least one positive solution for both fractional boundary value problems. As an application, an example is given to demonstrate some of main results.
Lācis, Uǧis
2016-01-01
Interfacial boundary conditions determined from empirical or ad-hoc models remain the standard approach to model fluid flows over porous media, even in situations where the topology of the porous medium is known. We propose a non-empirical and accurate method to compute the effective boundary conditions at the interface between a porous surface and an overlying flow. Using multiscale expansion (homogenization) approach, we derive a tensorial generalized version of the empirical condition suggested by Beavers & Joseph (1967). The components of the tensors determining the effective slip velocity at the interface are obtained by solving a set of Stokes equations in a small computational domain near the interface containing both free flow and porous medium. Using the lid-driven cavity flow with a porous bed, we demonstrate that the derived boundary condition is accurate and robust by comparing an effective model to direct numerical simulations. Finally, we provide an open source code that solves the microscal...
A Note on Fractional Differential Equations with Fractional Separated Boundary Conditions
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2012-01-01
Full Text Available We consider a new class of boundary value problems of nonlinear fractional differential equations with fractional separated boundary conditions. A connection between classical separated and fractional separated boundary conditions is developed. Some new existence and uniqueness results are obtained for this class of problems by using standard fixed point theorems. Some illustrative examples are also discussed.
An Artificial Boundary Condition for the Vortex Movements in Two Dimensions
Institute of Scientific and Technical Information of China (English)
Qiyuan Cheng
2006-01-01
An approximate artificial boundary condition based on a boundary integral equation is designed for the vortex movements. Point vortex and cloud in cell methods are used in numerical simulation of vortex motions. The numerical experiments show that the approximate artificial boundary condition is useful and sufficiently accurate in hydrodynamics.
Directory of Open Access Journals (Sweden)
Nahed S. Hussein
2014-01-01
Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.
Mirror-type Boundary Condition in Smoothed Particle Hydrodynamics
Marjani, A.; Edge, B. L.
2013-12-01
The main purpose of this study is to enhance the Smoothed Particle Hydrodynamics (SPH) method that can accurately simulate the hydrodynamic forces on a structure and can be used for determining efficient designs for wave energy devices. Smoothed particle hydrodynamics is a method used in various fields of study. Unlike the finite difference method (FDM), SPH is a Lagrangian mesh-free method in which each particle moves according to the property of the surrounding flow and governing conservation equations, and carries the properties of water such as density, pressure and mass. Smoothed Particle Hydrodynamics is recently applied to a wide range of fluid mechanics problems. Although it is known as a highly accurate model, slow performance in 3D interface is one of its drawbacks. Not only the computational time becomes very long but also the number of processors and required memory are not easily available. Practical applications deal with high Reynolds numbers that requires high resolution to achieve adequate accuracy. A large number of coastal engineering problems are geometrically symmetric; hence, as a solution, mirror boundary condition is introduced and applied to two different tests in this paper, one is the impact of solitary wave on a large circular cylinder and the other is the interaction of dam break wave and structure. Mirror boundary condition can either produce a remarkable speedup with the same number of processors or the same running time with less number of processors. Regarding the fact that SPH algorithm yields Np log(Np) particle interactions at each time step, reducing the number of particles by a factor of 2 decreases the total number of interactions by a factor greater than 2. In other words, the relation between computational time and the number of particles does not behave like a linear function. Results show that smaller number of particles results in fewer particle interactions and less communications between processors. We believe that this
Reconstructing geographical boundary conditions for palaeoclimate modelling during the Cenozoic
Baatsen, Michiel; van Hinsbergen, Douwe J. J.; von der Heydt, Anna S.; Dijkstra, Henk A.; Sluijs, Appy; Abels, Hemmo A.; Bijl, Peter K.
2016-08-01
Studies on the palaeoclimate and palaeoceanography using numerical model simulations may be considerably dependent on the implemented geographical reconstruction. Because building the palaeogeographic datasets for these models is often a time-consuming and elaborate exercise, palaeoclimate models frequently use reconstructions in which the latest state-of-the-art plate tectonic reconstructions, palaeotopography and -bathymetry, or vegetation have not yet been incorporated. In this paper, we therefore provide a new method to efficiently generate a global geographical reconstruction for the middle-late Eocene. The generalised procedure is also reusable to create reconstructions for other time slices within the Cenozoic, suitable for palaeoclimate modelling. We use a plate-tectonic model to make global masks containing the distribution of land, continental shelves, shallow basins and deep ocean. The use of depth-age relationships for oceanic crust together with adjusted present-day topography gives a first estimate of the global geography at a chosen time frame. This estimate subsequently needs manual editing of areas where existing geological data indicate that the altimetry has changed significantly over time. Certain generic changes (e.g. lowering mountain ranges) can be made relatively easily by defining a set of masks while other features may require a more specific treatment. Since the discussion regarding many of these regions is still ongoing, it is crucial to make it easy for changes to be incorporated without having to redo the entire procedure. In this manner, a complete reconstruction can be made that suffices as a boundary condition for numerical models with a limited effort. This facilitates the interaction between experts in geology and palaeoclimate modelling, keeping reconstructions up to date and improving the consistency between different studies. Moreover, it facilitates model inter-comparison studies and sensitivity tests regarding certain
Energy Technology Data Exchange (ETDEWEB)
Jang, Jin Seok; Yoo, Wan Suk [Pusan National University, Busan (Korea, Republic of); Kim, Kun Woo; Lee, Jae Wook [Korea Institute of Industrial Technology, Daegu (Korea, Republic of)
2015-07-15
The unwinding behavior of thin cable has been studied in textile engineering. Recently, J.W. Lee derived transient equations of motion for an unwinding cable. Thus, this paper discusses numerical simulations of unwinding behavior as compared to experiments. The cable unwinding system is modeled using cylindrical coordinates, and Hamilton's principle in an open system is used to represent the mass change of the cable in the control volume. In a transient equation of unwinding motion, the transient-state response is affected by two point boundary conditions, such as the guide-eyelet point and the lift-off point. In previous research, only the unwinding velocity at the guide-eyelet point defined the boundary. Here, a boundary condition at the lift-off point is also considered in the unwinding velocity along with the unwinding length of cable in the control volume. The results of this study show that transient equations of motion should be derived by considering angular acceleration because of time-varying angular velocity.
Eigenmode Analysis of Boundary Conditions for One-Dimensional Preconditioned Euler Equations
Darmofal, David L.
1998-01-01
An analysis of the effect of local preconditioning on boundary conditions for the subsonic, one-dimensional Euler equations is presented. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective with preconditioning, and, at low Mach numbers, disturbances do not decay. Other boundary conditions are investigated which are non-reflective with preconditioning and numerical results are presented confirming the analysis.
Positive solutions of quasilinear parabolic systems with nonlinear boundary conditions
Pao, C. V.; Ruan, W. H.
2007-09-01
The aim of this paper is to investigate the existence, uniqueness, and asymptotic behavior of solutions for a coupled system of quasilinear parabolic equations under nonlinear boundary conditions, including a system of quasilinear parabolic and ordinary differential equations. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system as well as the uniqueness of a positive steady-state solution. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients Di(ui) may have the property Di(0)=0 for some or all i. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. It is shown that the time-dependent solution converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a porous medium type of problem, a heat-transfer problem, and a two-component competition model in ecology. These applications illustrate some very interesting distinctive behavior of the time-dependent solutions between density-independent and density-dependent diffusions.
Positive solutions of quasilinear parabolic systems with Dirichlet boundary condition
Pao, C. V.; Ruan, W. H.
Coupled systems for a class of quasilinear parabolic equations and the corresponding elliptic systems, including systems of parabolic and ordinary differential equations are investigated. The aim of this paper is to show the existence, uniqueness, and asymptotic behavior of time-dependent solutions. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients D(u) may have the property D(0)=0 for some or all i=1,…,N, and the boundary condition is u=0. Using the method of upper and lower solutions, we show that a unique global classical time-dependent solution exists and converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a scalar polynomial growth problem, a coupled system of polynomial growth problem, and a two component competition model in ecology.
Stability of a flexible structure with destabilizing boundary conditions
Shubov, M.; Shubov, V.
2016-07-01
The Euler-Bernoulli beam model with non-dissipative boundary conditions of feedback control type is investigated. Components of the two-dimensional input vector are shear and moment at the right end, and components of the observation vector are time derivatives of displacement and slope at the right end. The codiagonal matrix depending on two control parameters relates input and observation. The paper contains five results. First, asymptotic approximation for eigenmodes is derived. Second, `the main identity' is established. It provides a relation between mode shapes of two systems: one with non-zero control parameters and the other one with zero control parameters. Third, when one control parameter is positive and the other one is zero, `the main identity' yields stability of all eigenmodes (though the system is non-dissipative). Fourth, the stability of eigenmodes is extended to the case when one control parameter is positive, and the other one is sufficiently small. Finally, existence and properties of `deadbeat' modes are investigated.
On Nonlinear Approximations to Cosmic Problems with Mixed Boundary Conditions
Mancinelli, P J; Ganon, G; Dekel, A; Mancinelli, Paul J.; Yahil, Amos; Ganon, Galit; Dekel, Avishai
1993-01-01
Nonlinear approximations to problems with mixed boundary conditions are useful for predicting large-scale streaming velocities from the density field, or vice-versa. We evaluate the schemes of Bernardeau \\cite{bernardeau92}, Gramann \\cite{gramann93}, and Nusser \\etal \\cite{nusser91}, using smoothed density and velocity fields obtained from $N$-body simulations of a CDM universe. The approximation of Nusser \\etal is overall the most accurate and robust. For Gaussian smoothing of 1000\\kms\\ the mean error in the approximated relative density perturbation, $\\delta$, is smaller than 0.06, and the dispersion is 0.1. The \\rms\\ error in the estimated velocity is smaller than 60\\kms, and the dispersion is 40\\kms. For smoothing of 500\\kms\\ these numbers increase by about a factor $\\sim 2$ for $\\delta < 4-5$, but deteriorate at higher densities. The other approximations are comparable to those of Nusser \\etal for smoothing of 1000\\kms, but are much less successful for the smaller smoothing of 500\\kms.
Advanced boundary condition method in quantum transport and its application in nanodevices
He, Yu
Modern semiconductor devices have reached critical dimensions in the sub-20nm range. During the last decade, quantum transport methods have become the standard approaches to model nanoscale devices. In quantum transport methods, Schrodinger equations are solved in the critical device channel with the contacts served as the open boundary conditions. Proper and efficient treatments of these boundary conditions are essential to provide accurate prediction of device performance. The open boundary conditions, which represent charge injection and extraction effects, are described by contact self-energies. All existing contact self-energy methods assume periodic and semiinfinite contacts, which are in stark contrast to realistic devices where the contacts often have complicated geometries or imperfections. On the other hand, confined structures such as quantum dots, nanowires, and ultra-thin bodies play an important role in nanodevice designs. In the tight binding models of these confined structures, the surfaces require appropriate boundary treatments to remove the dangling bonds. The existing boundary treatments fall into two categories. One is to explicitly include the passivation atoms in the device. This is limited to passivation with atoms and small molecules due to the increasing rank of the Hamiltonian. The other is to implicitly incorporate passivation by altering the orbital energies of the dangling bonds with a passivation potential. This method only works for certain crystal structures and symmetries, and fails to distinguish different passivation scenarios, such as hydrogen and oxygen passivation. In this work, an efficient self-energy method applicable for arbitrary contact structures is developed. This method is based on an iterative algorithm which considers the explicit contact segments. The method is demonstrated on a graphene nanoribbon structure with trumpet shape contacts and a Si0.5Ge0.5 nanowire transistor with alloy disorder contacts. Furthermore
CT image segmentation using FEM with optimized boundary condition.
Directory of Open Access Journals (Sweden)
Hiroyuki Hishida
Full Text Available The authors propose a CT image segmentation method using structural analysis that is useful for objects with structural dynamic characteristics. Motivation of our research is from the area of genetic activity. In order to reveal the roles of genes, it is necessary to create mutant mice and measure differences among them by scanning their skeletons with an X-ray CT scanner. The CT image needs to be manually segmented into pieces of the bones. It is a very time consuming to manually segment many mutant mouse models in order to reveal the roles of genes. It is desirable to make this segmentation procedure automatic. Although numerous papers in the past have proposed segmentation techniques, no general segmentation method for skeletons of living creatures has been established. Against this background, the authors propose a segmentation method based on the concept of destruction analogy. To realize this concept, structural analysis is performed using the finite element method (FEM, as structurally weak areas can be expected to break under conditions of stress. The contribution of the method is its novelty, as no studies have so far used structural analysis for image segmentation. The method's implementation involves three steps. First, finite elements are created directly from the pixels of a CT image, and then candidates are also selected in areas where segmentation is thought to be appropriate. The second step involves destruction analogy to find a single candidate with high strain chosen as the segmentation target. The boundary conditions for FEM are also set automatically. Then, destruction analogy is implemented by replacing pixels with high strain as background ones, and this process is iterated until object is decomposed into two parts. Here, CT image segmentation is demonstrated using various types of CT imagery.
Hine, N D M; Haynes, P D; Skylaris, C K
2011-01-01
We present a comparison of methods for treating the electrostatic interactions of finite, isolated systems within periodic boundary conditions (PBCs), within Density Functional Theory (DFT), with particular emphasis on linear-scaling (LS) DFT. Often, PBCs are not physically realistic but are an unavoidable consequence of the choice of basis set and the efficacy of using Fourier transforms to compute the Hartree potential. In such cases the effects of PBCs on the calculations need to be avoided, so that the results obtained represent the open rather than the periodic boundary. The very large systems encountered in LS-DFT make the demands of the supercell approximation for isolated systems more difficult to manage, and we show cases where the open boundary (infinite cell) result cannot be obtained from extrapolation of calculations from periodic cells of increasing size. We discuss, implement and test three very different approaches for overcoming or circumventing the effects of PBCs: truncation of the Coulomb ...
Reactive Boundary Conditions as Limits of Interaction Potentials for Brownian and Langevin Dynamics
Chapman, S Jonathan; Isaacson, Samuel A
2015-01-01
A popular approach to modeling bimolecular reactions between diffusing molecules is through the use of reactive boundary conditions. One common model is the Smoluchowski partial absorption condition, which uses a Robin boundary condition in the separation coordinate between two possible reactants. This boundary condition can be interpreted as an idealization of a reactive interaction potential model, in which a potential barrier must be surmounted before reactions can occur. In this work we show how the reactive boundary condition arises as the limit of an interaction potential encoding a steep barrier within a shrinking region in the particle separation, where molecules react instantly upon reaching the peak of the barrier. The limiting boundary condition is derived by the method of matched asymptotic expansions, and shown to depend critically on the relative rate of increase of the barrier height as the width of the potential is decreased. Limiting boundary conditions for the same interaction potential in b...
Coupling the Gaussian free fields with free and with zero boundary conditions via common level lines
Qian, Wei; Werner, Wendelin
2017-01-01
We describe level-line decompositions of the two-dimensional Gaussian Free Field (GFF) with free boundary conditions. In particular, we point out a simple way to couple the GFF with free boundary conditions in a 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 0-level lines (these signs are alternating for the zero-boundary GFF) in order to obtain a free bo...
Open Innovation and the Erosion of the Traditional Information Systems Project's Boundaries
Elbanna, Amany
This paper examines the notion of open innovation and its implication on information systems management. It investigates a project of an enterprise resource planning system implementation in an international organization to unravel the resemblance with the open innovation model. The study shows that the conceptualization of ERP project as an open innovation could reveal the complex architecture of today's organization from which the ERP project cannot be isolated. It argues that the traditional boundaries around IS projects are dissolving and the relationship between what used to be outside and what used to be inside the project is increasingly blurred. The study calls for a different perspective of project management that goes beyond single and multiple project management to scan the open space of innovation and actively look for partners, competitors, and collaborators.
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.
Error transport equation boundary conditions for the Euler and Navier-Stokes equations
Phillips, Tyrone S.; Derlaga, Joseph M.; Roy, Christopher J.; Borggaard, Jeff
2017-02-01
Discretization error is usually the largest and most difficult numerical error source to estimate for computational fluid dynamics, and boundary conditions often contribute a significant source of error. Boundary conditions are described with a governing equation to prescribe particular behavior at the boundary of a computational domain. Boundary condition implementations are considered sufficient when discretized with the same order of accuracy as the primary governing equations; however, careless implementations of boundary conditions can result in significantly larger numerical error. Investigations into different numerical implementations of Dirichlet and Neumann boundary conditions for Burgers' equation show a significant impact on the accuracy of Richardson extrapolation and error transport equation discretization error estimates. The development of boundary conditions for Burgers' equation shows significant improvements in discretization error estimates in general and a significant improvement in truncation error estimation. The latter of which is key to accurate residual-based discretization error estimation. This research investigates scheme consistent and scheme inconsistent implementations of inflow and outflow boundary conditions up to fourth order accurate and a formulation for a slip wall boundary condition for truncation error estimation are developed for the Navier-Stokes and Euler equations. The scheme consistent implementation resulted in much smoother truncation error near the boundaries and more accurate discretization error estimates.
Impact of the kinetic boundary condition on porous media flow in the lattice Boltzmann formulation
Singh, Shiwani; Jiang, Fei; Tsuji, Takeshi
2017-07-01
To emphasize the importance of the kinetic boundary condition for micro- to nanoscale flow, we present an ad hoc kinetic boundary condition suitable for torturous geological porous media. We found that the kinetic boundary condition is one of the essential features which should be supplemented to the standard lattice Boltzmann scheme in order to obtain accurate continuum observables. The claim is validated using a channel flow setup by showing the agreement of mass flux with analytical value. Further, using a homogeneous porous structure, the importance of the kinetic boundary condition is shown by comparing the permeability correction factor with the analytical value. Finally, the proposed alternate to the kinetic boundary condition is validated by showing its capability to capture the basic feature of the kinetic boundary condition.
Design of an internal waste dump within the boundaries of the open pit
Panov, Zoran; Minov, Kirco; Karanakova Stefanovska, Radmila; Stojanov, Slobodan; Doneva, Blagica
2011-01-01
With the deepening of the open pit, the transport distances for the sterile mass and the ore increased. This paper deals with the formation of an internal waste dump within the boundaries of the open pit. The development of such waste dump should be in function of the space for disposing the waste according to existing situation on the field and the space for dumping. The internal waste dump will be used for permanent dumping and waste storage. Modern methods will be used to asses...
Generalized Coordinate Bethe Ansatz for open spin chains with non-diagonal boundaries
Ragoucy, E
2011-01-01
We introduce a generalization of the original Coordinate Bethe Ansatz that allows to treat the case of open spin chains with non-diagonal boundary matrices. We illustrate it on two cases: the XXX and XXZ chains. Short review on a joint work with N. Crampe (L2C) and D. Simon (LPMA), see arXiv:1009.4119, arXiv:1105.4119 and arXiv:1106.3264.
RADIATION BOUNDARY CONDITIONS FOR MAXWELL'S EQUATIONS: A REVIEW OF ACCURATE TIME-DOMAIN FORMULATIONS
Institute of Scientific and Technical Information of China (English)
Thomas Hagstrom; Stephen Lau
2007-01-01
We review time-domain formulations of radiation boundary conditions for Maxwell's equations, focusing on methods which can deliver arbitrary accuracy at acceptable computational cost. Examples include fast evaluations of nonlocal conditions on symmetric and general boundaries, methods based on identifying and evaluating equivalent sources, and local approximations such as the perfectly matched layer and sequences of local boundary conditions. Complexity estimates are derived to assess work and storage requirements as a function of wavelength and simulation time.
Supersymmetry Breaking through Boundary Conditions Associated with the $U(1)_{R}$
Takenaga, K
1998-01-01
The effects of boundary conditions imposed on the fields for the compactified space directions to the supersymmetric theories are discussed. The boundary conditions can be taken to be periodic up to the degrees of freedom of localized $U(1)_{R}$ transformations. The boundary condition breaks the supersymmetry to yield universal soft supersymmetry breaking terms. The 4-dimensional supersymmetric QED with one flavour and the pure supersymmetric QCD are studied as toy models when one of the space coordinates is compactified on $S^1$.
Revisit boundary conditions for the self-adjoint angular flux formulation
Energy Technology Data Exchange (ETDEWEB)
Wang, Yaqi [Idaho National Lab. (INL), Idaho Falls, ID (United States); Gleicher, Frederick N. [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-03-01
We revisit the boundary conditions for SAAF. We derived the equivalent parity variational form ready for coding up. The more rigorous approach of evaluating odd parity should be solving the odd parity equation coupled with the even parity. We proposed a symmetric reflecting boundary condition although neither positive definiteness nor even-odd decoupling is achieved. A simple numerical test verifies the validity of these boundary conditions.
Analysis of boundary conditions for SSME subsonic internal viscous flow analysis
Baker, A. J.
1986-01-01
A study was completed of mathematically proper boundary conditions for unique numerical solution of internal, viscous, subsonic flows in the space shuttle main engine. The study has concentrated on well posed considerations, with emphasis on computational efficiency and numerically stable boundary condition statements. The method of implementing the established boundary conditions is applicable to a wide variety of finite difference and finite element codes, as demonstrated.
Hine, Nicholas D M; Dziedzic, Jacek; Haynes, Peter D; Skylaris, Chris-Kriton
2011-11-28
We present a comparison of methods for treating the electrostatic interactions of finite, isolated systems within periodic boundary conditions (PBCs), within density functional theory (DFT), with particular emphasis on linear-scaling (LS) DFT. Often, PBCs are not physically realistic but are an unavoidable consequence of the choice of basis set and the efficacy of using Fourier transforms to compute the Hartree potential. In such cases the effects of PBCs on the calculations need to be avoided, so that the results obtained represent the open rather than the periodic boundary. The very large systems encountered in LS-DFT make the demands of the supercell approximation for isolated systems more difficult to manage, and we show cases where the open boundary (infinite cell) result cannot be obtained from extrapolation of calculations from periodic cells of increasing size. We discuss, implement, and test three very different approaches for overcoming or circumventing the effects of PBCs: truncation of the Coulomb interaction combined with padding of the simulation cell, approaches based on the minimum image convention, and the explicit use of open boundary conditions (OBCs). We have implemented these approaches in the ONETEP LS-DFT program and applied them to a range of systems, including a polar nanorod and a protein. We compare their accuracy, complexity, and rate of convergence with simulation cell size. We demonstrate that corrective approaches within PBCs can achieve the OBC result more efficiently and accurately than pure OBC approaches.
The DtN nonreflecting boundary condition for multiple scattering problems in the half-plane
Acosta, Sebastian; Malone, Bruce
2013-01-01
The multiple-Dirichlet-to-Neumann (multiple-DtN) non-reflecting boundary condition is adapted to acoustic scattering from obstacles embedded in the half-plane. The multiple-DtN map is coupled with the method of images as an alternative model for multiple acoustic scattering in the presence of acoustically soft and hard plane boundaries. As opposed to the current practice of enclosing all obstacles with a large semicircular artificial boundary that contains portion of the plane boundary, the proposed technique uses small artificial circular boundaries that only enclose the immediate vicinity of each obstacle in the half-plane. The adapted multiple-DtN condition is simultaneously imposed in each of the artificial circular boundaries. As a result the computational effort is significantly reduced. A computationally advantageous boundary value problem is numerically solved with a finite difference method supported on boundary-fitted grids. Approximate solutions to problems involving two scatterers of arbitrary geo...
An Explicit Time-Domain Hybrid Formulation Based on the Unified Boundary Condition
Energy Technology Data Exchange (ETDEWEB)
Madsen, N; Fasenfest, B J; White, D; Stowell, M; Jandhyala, V; Pingenot, J; Champagne, N J; Rockway, J D
2007-02-28
An approach to stabilize the two-surface, time domain FEM/BI hybrid by means of a unified boundary condition is presented. The first-order symplectic finite element formulation [1] is used along with a version of the unified boundary condition of Jin [2] reformulated for Maxwell's first-order equations in time to provide both stability and accuracy over the first-order ABC. Several results are presented to validate the numerical solutions. In particular the dipole in a free-space box is analyzed and compared to the Dirchlet boundary condition of Ziolkowski and Madsen [3] and to a Neuman boundary condition approach.
S-duality of boundary conditions and the Geometric Langlands program
Gaiotto, Davide
2016-01-01
Maximally supersymmetric gauge theory in four dimensions admits local boundary conditions which preserve half of the bulk supersymmetries. The S-duality of the bulk gauge theory can be extended in a natural fashion to act on such half-BPS boundary conditions. The purpose of this note is to explain the role these boundary conditions can play in the Geometric Langlands program. In particular, we describe how to obtain pairs of Geometric Langland dual objects from S-dual pairs of half-BPS boundary conditions.
Pekker, Leonid
2015-01-01
In this paper we propose new boundary conditions at the hot walls with thermionic electron emission for two-temperature thermal arc models. In the derived boundary conditions the walls are assumed to be made from refractory metals and that the erosion of the wall is small and, therefore, is not taken into account in the model. In these boundary conditions the plasma sheath formed at the electrode is considered as the interface between the plasma and the wall. The derived boundary conditions allow the calculation of the heat flux to the walls from the plasma and consequently the thermionic electron current that makes the two temperature thermal model self consistent.
Solitonic sectors, conformal boundary conditions and three-dimensional topological field theory
Schweigert, C
2000-01-01
The correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary world sheets can be expressed in terms of Wilson graphs in appropriate three-manifolds. We present a systematic approach to boundary conditions that break bulk symmetries. It is based on the construction, by `alpha-induction', of a fusion ring for the boundary fields. Its structure constants are the annulus coefficients and its 6j-symbols give the OPE of boundary fields. Symmetry breaking boundary conditions correspond to solitonic sectors.
Borjan, Z.
2016-09-01
We consider critical Casimir force in the Ising strips with boundary conditions defined by standard normal and ordinary surface universality classes containing also the internal grain boundary. Using exact variational approach of Mikheev and Fisher we have elaborated on behaviors of Casimir amplitudes Δ++(g) , ΔOO(g) and Δ+O(g) , corresponding to normal-normal, ordinary-ordinary and mixed normal-ordinary boundary conditions, respectively, with g as a strength of the grain boundary. Closed analytic results describe Casimir amplitudes Δ++(g) and ΔOO(g) as continuous functions of the grain boundary's strength g, changing the character of the Casimir force from repulsive to attractive and vice versa for certain domains of g. Present results reveal a new type of symmetry between Casimir amplitudes Δ++(g) and ΔOO(g) . Unexpectedly simple constant result for the Casimir amplitude Δ+O(g) = π/12 we have comprehensively interpreted in terms of equilibrium states of the present Ising strip as a complex interacting system comprising two sub-systems. Short-distance expansions of energy density profiles in the vicinity of the grain boundary reveal new distant-wall correction amplitudes that we examined in detail. Analogy of present considerations with earlier more usual short-distance expansions near one of the (N), (O) and (SB) boundaries, as well as close to surfaces with variable boundary conditions refers to the set of scaling dimensions appearing in the present calculations but also to the discovery of the de Gennes-Fisher distant wall correction amplitudes.
Boundary conditions control for a Shallow-Water model
Kazantsev, Eugene
2012-01-01
A variational data assimilation technique was used to estimate optimal discretization of interpolation operators and derivatives in the nodes adjacent to the rigid boundary. Assimilation of artificially generated observational data in the shallow-water model in a square box and assimilation of real observations in the model of the Black sea are discussed. It is shown in both experiments that controlling the discretization of operators near a rigid boundary can bring the model solution closer to observations as in the assimilation window and beyond the window. This type of control allows also to improve climatic variability of the model.
Nonlinear solution for radiation boundary condition of heat transfer process in human eye.
Dehghani, A; Moradi, A; Dehghani, M; Ahani, A
2011-01-01
In this paper we propose a new method based on finite element method for solving radiation boundary condition of heat equation inside the human eye and other applications. Using this method, we can solve heat equation inside human eye without need to model radiation boundary condition to a robin boundary condition. Using finite element method we can obtain a nonlinear equation, and finally we use nonlinear algorithm to solve it. The human eye is modeled as a composition of several homogeneous regions. The Ritz method in the finite element method is used for solving heat differential equation. Applying the boundary conditions, the heat radiation condition and the robin condition on the cornea surface of the eye and on the outer part of sclera are used, respectively. Simulation results of solving nonlinear boundary condition show the accuracy of the proposed method.
Investigating the non-classical boundary conditions relevant to strain gradient theories
Jafari, Akbar; Ezzati, Meysam
2017-02-01
In the present study, two classes of non-classical constitutive equations consisting of the first and the second order strain gradients theories (FSG and SSG) were applied in order to develop the governing equations of static and free vibrational behavior of beam structures. The governing equations in orders of six and eight were constructed for FSG and SSG theories, respectively. Therefore, higher order or in other words non-classical boundary conditions (HOBCs or NCBCs) came into play in addition to the classical ones (CBCs). Some explanations were presented about the concept of the non-classical boundary conditions. Analytical and finite element (FE) approaches were employed to solve the governing equations. The analytical solutions were utilized in validation and convergence study of FE results. Comparisons were made with the relevant data reported in the open literature; however, to the best of the authors' knowledge, few references have been published on SSG theory and HOBCs. In the numerical studies, the effects of applying different combinations of CBCs and HOBCs to the static and free vibration behaviors of the beam were investigated. Moreover, the impacts of non-classical elastic constants and the beam size on its behavior were also studied.
Habermann, M.; Maxwell, D. A.; Truffer, M.
2012-04-01
A crucial assumption in all ice sheet models concerns the nature and parametrization of the basal boundary condition. Direct observations on large spatial scales are not possible, but inverse methods can be used to determine the distribution of basal properties from surface measurements. We developed open-source iterative inverse algorithms and applied them to PISM, a hybrid ice sheet model that solves a combination of the Shallow Ice and Shallow Shelf Approximations. In a regional-scale model of Jakobshavn Isbræ, the fastest flowing ice stream of Greenland, we invert for basal stickiness over the entire drainage basin. The sensitivity of the reconstructed basal stickiness to the following modeling choices is evaluated: temperature distribution within the ice, definition of the misfit functional, tolerance for the stopping criterion and initial estimates of basal stickiness. The effects and the management of missing data are analyzed. In 2002 the floating tongue of Jakobshavn Isbræ disintegrated catastrophically, leading to increased speeds and rapid thinning of the inland ice. Detailed velocity maps from before and after this breakup allow us to compare retrieved basal parameters and to track the continuing evolution of the basal boundary condition.
Conformal field theory, boundary conditions and applications to string theory
Schweigert, C.; Fuchs, J.; Walcher, J.
2000-01-01
This is an introduction to two-dimensional conformal field theory and its applications in string theory. Modern concepts of conformal field theory are explained, and it is outlined how they are used in recent studies of D-branes in the strong curvature regime by means of CFT on surfaces with boundary.
Green's function of a heat problem with a periodic boundary condition
Erzhanov, Nurzhan E.
2016-08-01
In the paper, a nonlocal initial-boundary value problem for a non-homogeneous one-dimensional heat equation is considered. The domain under consideration is a rectangle. The classical initial condition with respect to t is put. A nonlocal periodic boundary condition by a spatial variable x is put. It is well-known that a solution of problem can be constructed in the form of convergent orthonormal series according to eigenfunctions of a spectral problem for an operator of multiple differentiation with periodic boundary conditions. Therefore Green's function can be also written in the form of an infinite series with respect to trigonometric functions (Fourier series). For classical first and second initial-boundary value problems there also exists a second representation of the Green's function by Jacobi function. In this paper we find the representation of the Green's function of the nonlocal initial-boundary value problem with periodic boundary conditions in the form of series according to exponents.
Absorption and impedance boundary conditions for phased geometrical-acoustics methods
DEFF Research Database (Denmark)
Jeong, Cheol-Ho
2012-01-01
developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated...... with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce......Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been...
Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2014-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2015-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Absorption and impedance boundary conditions for phased geometrical-acoustics methods.
Jeong, Cheol-Ho
2012-10-01
Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce reasonable results with some exceptions at low frequencies for acoustically soft materials.
An Implicit Method for Solving Fuzzy Partial Differential Equation with Nonlocal Boundary Conditions
Directory of Open Access Journals (Sweden)
B. Orouji
2015-06-01
Full Text Available In this paper we introduce a numerical solution for the fuzzy heat equation with nonlocal boundary conditions. The main purpose is finding a difference scheme for the one dimensional heat equation with nonlocal boundary conditions. In these types of problems, an integral equation is appeared in the boundary conditions. We first express the necessary materials and definitions, and then consider our difference scheme and next the integrals in the boundary equations are approximated by the composite trapezoid rule. In the final part, we present an example for checking the numerical results. In this example we obtain the Hausdorff distance between exact solution and approximate solution.
Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations
Directory of Open Access Journals (Sweden)
Douglas N. Arnold
2007-02-01
Full Text Available Specifying boundary conditions continues to be a challenge in numerical relativity in order to obtain a long time convergent numerical simulation of Einstein's equations in domains with artificial boundaries. In this paper, we address this problem for the Einstein-Christoffel (EC symmetric hyperbolic formulation of Einstein's equations linearized around flat spacetime. First, we prescribe simple boundary conditions that make the problem well posed and preserve the constraints. Next, we indicate boundary conditions for a system that extends the linearized EC system by including the momentum constraints and whose solution solves Einstein's equations in a bounded domain.
Moist turbulent Rayleigh-Benard convection with Neumann and Dirichlet boundary conditions
Weidauer, Thomas
2012-01-01
Turbulent Rayleigh-Benard convection with phase changes in an extended layer between two parallel impermeable planes is studied by means of three-dimensional direct numerical simulations for Rayleigh numbers between 10^4 and 1.5\\times 10^7 and for Prandtl number Pr=0.7. Two different sets of boundary conditions of temperature and total water content are compared: imposed constant amplitudes which translate into Dirichlet boundary conditions for the scalar field fluctuations about the quiescent diffusive equilibrium and constant imposed flux boundary conditions that result in Neumann boundary conditions. Moist turbulent convection is in the conditionally unstable regime throughout this study for which unsaturated air parcels are stably and saturated air parcels unstably stratified. A direct comparison of both sets of boundary conditions with the same parameters requires to start the turbulence simulations out of differently saturated equilibrium states. Similar to dry Rayleigh-Benard convection the differences...
Directory of Open Access Journals (Sweden)
A. Malvandi
2015-01-01
Full Text Available The objective of this paper is to consider both effects of slip and convective heat boundary conditions on steady two-dimensional boundary layer flow of a nanofluid over a stretching sheet in the presence of blowing/suction simultaneously. Flow meets the Navier's slip condition at the surface and Biot number is also used to consider the effects of convective heat transfer. The employed model for nanofluid includes two-component four-equation nonhomogeneous equilibrium model that incorporates the effects of nanoparticle migration owing to Brownian motion and thermophoresis. The basic partial boundary layer equations have been transformed into a two-point boundary value problem via similarity variables. Results for impermeable isothermal surface and also no-slip boundary condition were in best agreements with those existing in literatures. Effects of governing parameters such as Biot number (Bi, slip parameter (λ, thermophoresis (Nt, Prandtl number (Pr, Lewis number (Le, Brownian motion (Nb and blowing/suction (S on reduced Nusselt and Sherwood numbers are analyzed and discussed in details. The obtained results indicate that unlike heat transfer rate, concentration rate is very sensitive to all parameters among which Le, S and Pr are the most effective ones.
Poynting flux-conserving low-altitude boundary conditions for global magnetospheric models
Xi, S.; Lotko, W.; Zhang, B.; Brambles, O. J.; Lyon, J. G.; Merkin, V. G.; Wiltberger, M.
2015-01-01
A method for specifying low-altitude or inner boundary conditions that conserve low-frequency, magnetic field-aligned, electromagnetic energy flux across the boundary in global magnetospheric magnetohydrodynamics (MHD) models is presented. The single-fluid Lyon-Fedder-Mobarry (LFM) model is used to verify this method, with comparisons between simulations using LFM's standard hardwall boundary conditions and the new flux-conserving boundary conditions. Identical idealized upstream solar wind and interplanetary magnetic field conditions and the same constant ionospheric conductance are used in both runs. The results show that, compared to LFM's standard hardwall boundary conditions, the flux-conserving method improves the transparency of the boundary for the flow of low-frequency (essentially DC) electromagnetic energy flux along field lines. As a consequence, the hemispheric integrated field-aligned DC Poynting flux just above the boundary is close to the hemispheric total Joule heating of the ionosphere, as it should be if electromagnetic energy is conserved. The MHD velocity and perpendicular currents are well-behaved near the inner boundary for the flux conserving boundary conditions.
General Considerations of the Electrostatic Boundary Conditions in Oxide Heterostructures
Energy Technology Data Exchange (ETDEWEB)
Higuchi, Takuya
2011-08-19
When the size of materials is comparable to the characteristic length scale of their physical properties, novel functionalities can emerge. For semiconductors, this is exemplified by the 'superlattice' concept of Esaki and Tsu, where the width of the repeated stacking of different semiconductors is comparable to the 'size' of the electrons, resulting in novel confined states now routinely used in opto-electronics. For metals, a good example is magnetic/non-magnetic multilayer films that are thinner than the spin-scattering length, from which giant magnetoresistance (GMR) emerged, used in the read heads of hard disk drives. For transition metal oxides, a similar research program is currently underway, broadly motivated by the vast array of physical properties that they host. This long-standing notion has been recently invigorated by the development of atomic-scale growth and probe techniques, which enables the study of complex oxide heterostructures approaching the precision idealized in Fig. 1(a). Taking the subset of oxides derived from the perovskite crystal structure, the close lattice match across many transition metal oxides presents the opportunity, in principle, to develop a 'universal' heteroepitaxial materials system. Hand-in-hand with the continual improvements in materials control, an increasingly relevant challenge is to understand the consequences of the electrostatic boundary conditions which arise in these structures. The essence of this issue can be seen in Fig. 1(b), where the charge sequence of the sublayer 'stacks' for various representative perovskites is shown in the ionic limit, in the (001) direction. To truly 'universally' incorporate different properties using different materials components, be it magnetism, ferroelectricity, superconductivity, etc., it is necessary to access and join different charge sequences, labelled here in analogy to the designations 'group IV, III-V, II
Vibrations of stretched damped beams under non-ideal boundary conditions
Indian Academy of Sciences (India)
Hakan Boyaci
2006-02-01
A simply supported damped Euler–Bernoulli beam with immovable end conditions are considered. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the boundaries are assumed to allow small deﬂections and moments. Approximate analytical solution of the problem is found using the method of multiple scales, a perturbation technique.
Eigenstates of a particle in an array of hexagons with periodic boundary condition
Directory of Open Access Journals (Sweden)
A Nemati
2013-10-01
Full Text Available In this paper the problem of a particle in an array of hexagons with periodic boundary condition is solved. Using the projection operators, we categorize eigenfunctions corresponding to each of the irreducible representations of the symmetry group . Based on these results, the Dirichlet and Neumann boundary conditions are discussed.
Daalen, van Edwin F.G.; Broeze, Jan; Groesen, van Embrecht
1992-01-01
Radiation boundary conditions are derived for partial differential equations which describe wave phenomena. Assuming the evolution of the system to be governed by a Lagrangian variational principle, boundary conditions are obtained with Noether's theorem from the requirement that they transmit some
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper is concerned with the existence of extreme solutions to three-point boundary value problems with nonlinear boundary conditions for a class of first order impulsive differential equations. We obtain suficient conditions for the existence of extreme solutions by the upper and lower solutions method coupled with a monotone iterative technique.
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.
Question of consistent boundary conditions when simulating reversed field pinch dynamics. Revision 1
Energy Technology Data Exchange (ETDEWEB)
Mirin, A.A.
1986-03-01
The issue of proper boundary conditions when performing magnetohydrodynamic simulations of the reversed field pinch is examined. Of particular concern is the choice of constant current, which when combined with other commonly used boundary conditions, may, under careless implementation, lead to an inconsistency. It is shown that this may cause erroneous results. Cases both with and without Hall terms are presented.
Controlling near shore nonlinear surging waves through bottom boundary conditions
Mukherjee, Abhik; Kundu, Anjan
2016-01-01
Instead of taking the usual passive view for warning of near shore surging waves including extreme waves like tsunamis, we aim to study the possibility of intervening and controlling nonlinear surface waves through the feedback boundary effect at the bottom. It has been shown through analytic result that the controlled leakage at the bottom may regulate the surface solitary wave amplitude opposing the hazardous variable depth effect. The theoretical results are applied to a real coastal bathymetry in India.
On the Boundary Condition Between Two Multiplying Media
Friedman, F. L.; Wigner, E. P.
1944-04-19
The transition region between two parts of a pile which have different compositions is investigated. In the case where the moderator is the same in both parts of the pile, it is found that the diffusion constant times thermal neutron density plus diffusion constant times fast neutron density satisfies the usual pile equations everywhere, right to the boundary. More complicated formulae apply in a more general case.
Conformal Boundary Conditions and Three-Dimensional Topological Field Theory
Felder, Giovanni; Fröhlich, Jürg; Fuchs, Jürgen; Schweigert, Christoph
2000-02-01
We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of Wilson graphs in a certain three-manifold, the connecting manifold. The amplitudes constructed this way can be shown to be modular invariant and to obey the correct factorization rules.
Conformal boundary conditions and three-dimensional topological field theory
Felder, G; Fuchs, J; Schweigert, C
2000-01-01
We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of Wilson graphs in a certain three-manifold, the connecting manifold. The amplitudes constructed this way can be shown to be modular invariant and to obey the correct factorization rules.
Modes and exceptional points in waveguides with impedance boundary conditions
Midya, Bikashkali
2016-01-01
A planar waveguide with impedance boundary, composed of non-perfect metallic plates, and with passive or active dielectric filling is considered. We show the possibility of selective mode guiding and amplification when homogeneous pump is added to the dielectric, and analyze differences in TE and TM mode propagation. Such a non-conservative system is also shown to feature exceptional points, for specific and experimentally tunable parameters, which are described for a particular case of transparent dielectric.
THE ARTIFICIAL BOUNDARY CONDITION FOR EXTERIOR OSEEN EQUATION IN 2-D SPACE
Institute of Scientific and Technical Information of China (English)
Chun-xiong Zheng; Hou-de Han
2002-01-01
A finite element method for the solution of Oseen equation in exterior domain is proposed. In this method, a circular artificial boundary is introduced to make the computational domain finite. Then, the exact relation between the normal stress and the prescribed velocity field on the artificial boundary can be obtained analytically. This relation can serve as an boundary condition for the boundary value problem defined on the finite domain bounded by the artificial boundary. Numerical experiment is presented to demonstrate the performance of the method.
Mogilevskii, Vadim
2011-01-01
We investigate in the paper general (not necessarily definite) canonical systems of differential equation in the framework of extension theory of symmetric linear relations. For this aim we first introduce the new notion of a boundary relation $\\G:\\gH^2\\to\\HH$ for $A^*$, where $\\gH$ is a Hilbert space, $A$ is a symmetric linear relation in $\\gH, \\cH_0$ is a boundary Hilbert space and $\\cH_1$ is a subspace in $\\cH_0$. Unlike known concept of a boundary relation (boundary triplet) for $A^*$ our definition of $\\G$ is applicable to relations $A$ with possibly unequal deficiency indices $n_\\pm(A)$. Next we develop the known results on minimal and maximal relations induced by the general canonical system $ J y'(t)-B(t)y(t)=\\D (t)f(t)$ on an interval $\\cI=(a,b),\\; -\\infty\\leq aboundary relation for $\\Tma$ we describe in terms of boundary conditions proper extensions of $\\Tmi$ in the case of the regular endpoint $a$ and arbitrary (possibly unequal)...
Boundary Conditions for 2D Boussinesq-type Wave-Current Interaction Equations
Directory of Open Access Journals (Sweden)
Mera M.
2011-01-01
Full Text Available This research focuses on the development of a set of two-dimensional boundary conditions for specific governing equations. The governing equations are existing Boussinesqtype equations which is capable of simulating wave-current interaction. The present boundary conditions consist of for waves only case and for currents only case. To simulate wave-current interaction, the two kinds of the present boundary conditions are then combined. A numerical model based on both the existing governing equations and the present boundary conditions is applied to simulation of currents only and of wave-current interaction propagating over a basin with a submerged shoal. The results of the numerical model show that the present boundary conditions go well with the existing Boussinesq-type wave-current interaction equations.
Exact finite-size corrections for the spanning-tree model under different boundary conditions
Izmailian, N. Sh.; Kenna, R.
2015-02-01
We express the partition functions of the spanning tree on finite square lattices under five different sets of boundary conditions in terms of a principal partition function with twisted-boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the logarithm of the partition function for each case. We have also established several groups of identities relating spanning-tree partition functions for the different boundary conditions. We also explain an apparent discrepancy between logarithmic correction terms in the free energy for a two-dimensional spanning-tree model with periodic and free-boundary conditions and conformal field theory predictions. We have obtained corner free energy for the spanning tree under free-boundary conditions in full agreement with conformal field theory predictions.
The Ritz Method for Boundary Problems with Essential Conditions as Constraints
Directory of Open Access Journals (Sweden)
Vojin Jovanovic
2016-01-01
Full Text Available We give an elementary derivation of an extension of the Ritz method to trial functions that do not satisfy essential boundary conditions. As in the Babuška-Brezzi approach boundary conditions are treated as variational constraints and Lagrange multipliers are used to remove them. However, we avoid the saddle point reformulation of the problem and therefore do not have to deal with the Babuška-Brezzi inf-sup condition. In higher dimensions boundary weights are used to approximate the boundary conditions, and the assumptions in our convergence proof are stated in terms of completeness of the trial functions and of the boundary weights. These assumptions are much more straightforward to verify than the Babuška-Brezzi condition. We also discuss limitations of the method and implementation issues that follow from our analysis and examine a number of examples, both analytic and numerical.
Entropy stable wall boundary conditions for the compressible Navier-Stokes equations
Parsani, Matteo; 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...
Meulenbroek, B.J.; Ebert, U.; Schäfer, L.
2005-01-01
The 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 derive exact
Johnson, Anthony N; Hromadka, T V
2015-01-01
The Laplace equation that results from specifying either the normal or tangential force equilibrium equation in terms of the warping functions or its conjugate can be modeled as a complex variable boundary element method or CVBEM mixed boundary problem. The CVBEM is a well-known numerical technique that can provide solutions to potential value problems in two or more dimensions by the use of an approximation function that is derived from the Cauchy Integral in complex analysis. This paper highlights three customizations to the technique.•A least squares approach to modeling the complex-valued approximation function will be compared and analyzed to determine if modeling error on the boundary can be reduced without the need to find and evaluated additional linearly independent complex functions.•The nodal point locations will be moved outside the problem domain.•Contour and streamline plots representing the warping function and its complementary conjugate are generated simultaneously from the complex-valued approximating function.
Hou, J S; Holmes, M H; Lai, W M; Mow, V C
1989-02-01
The objective of this study is to establish and verify the set of boundary conditions at the interface between a biphasic mixture (articular cartilage) and a Newtonian or non-Newtonian fluid (synovial fluid) such that a set of well-posed mathematical problems may be formulated to investigate joint lubrication problems. A "pseudo-no-slip" kinematic boundary condition is proposed based upon the principle that the conditions at the interface between mixtures or mixtures and fluids must reduce to those boundary conditions in single phase continuum mechanics. From this proposed kinematic boundary condition, and balances of mass, momentum and energy, the boundary conditions at the interface between a biphasic mixture and a Newtonian or non-Newtonian fluid are mathematically derived. Based upon these general results, the appropriate boundary conditions needed in modeling the cartilage-synovial fluid-cartilage lubrication problem are deduced. For two simple cases where a Newtonian viscous fluid is forced to flow (with imposed Couette or Poiseuille flow conditions) over a porous-permeable biphasic material of relatively low permeability, the well known empirical Taylor slip condition may be derived using matched asymptotic analysis of the boundary layer at the interface.
Local absorbing boundary conditions for nonlinear wave equation on unbounded domain.
Li, Hongwei; Wu, Xiaonan; Zhang, Jiwei
2011-09-01
The numerical solution of the nonlinear wave equation on unbounded spatial domain is considered. The artificial boundary method is introduced to reduce the nonlinear problem on unbounded spatial domain to an initial boundary value problem on a bounded domain. Using the unified approach, which is based on the operator splitting method, we construct the efficient nonlinear local absorbing boundary conditions for the nonlinear wave equation, and give the stability analysis of the resulting boundary conditions. Finally, several numerical examples are given to demonstrate the effectiveness of our method.
Energy Technology Data Exchange (ETDEWEB)
Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2012-08-23
The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to nonperturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2012-08-23
The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to nonperturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit. (orig.)
Towards Perfectly Absorbing Boundary Conditions for Euler Equations
Hayder, M. Ehtesham; Hu, Fang Q.; Hussaini, M. Yousuff
1997-01-01
In this paper, we examine the effectiveness of absorbing layers as non-reflecting computational boundaries for the Euler equations. The absorbing-layer equations are simply obtained by splitting the governing equations in the coordinate directions and introducing absorption coefficients in each split equation. This methodology is similar to that used by Berenger for the numerical solutions of Maxwell's equations. Specifically, we apply this methodology to three physical problems shock-vortex interactions, a plane free shear flow and an axisymmetric jet- with emphasis on acoustic wave propagation. Our numerical results indicate that the use of absorbing layers effectively minimizes numerical reflection in all three problems considered.
CFD Modeling of Non-Neutral Atmospheric Boundary Layer Conditions
DEFF Research Database (Denmark)
Koblitz, Tilman
to the atmospheric boundary-layer, are mostly ignored so far. In order to decrease the uncertainty of wind resource assessment, the present work focuses on atmospheric flows that include atmospheric stability and the Coriolis effect. Within the present work a RANS model framework is developed and implemented......For wind resource assessment, the wind industry is increasingly relying on Computational Fluid Dynamics models that focus on modeling the airflow in a neutrally stratified surface-layer. Physical processes like the Coriolis force, buoyancy forces and heat transport, that are important...
The D(D3)-anyon chain: integrable boundary conditions and excitation spectra
Finch, Peter E.; Frahm, Holger
2013-05-01
Chains of interacting non-Abelian anyons with local interactions invariant under the action of the Drinfeld double of the dihedral group D3 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 Z4 parafermion or a {M}_{(5,6)} minimal model.
Implementation of higher-order absorbing boundary conditions for the Einstein equations
Rinne, Oliver; Scheel, Mark A; Pfeiffer, Harald P
2008-01-01
We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer boundary, which is taken to be a coordinate sphere. We reformulate the boundary conditions as conditions on the gauge-invariant Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated by rewriting the boundary conditions as a system of ODEs for a set of auxiliary variables intrinsic to the boundary. From these we construct boundary data for a set of well-posed constraint-preserving boundary conditions for the Einstein equations in a first-order generalized harmonic formulation. This construction has direct applications to outer boundary conditions in simulations of isolated systems (e.g., binary black holes) as well as to the problem of Cauchy-perturbative matching. As a test problem for our numerical implementation, we consider linearized multipolar grav...
Boundary conditions for Maxwell fields in Kerr-AdS spacetimes
Wang, Mengjie
2016-05-01
Perturbative methods are useful to study the interaction between black holes and test fields. The equation for a perturbation itself, however, is not complete to study such a composed system if we do not assign physically relevant boundary conditions. Recently we have proposed a new type of boundary conditions for Maxwell fields in Kerr-anti-de Sitter (Kerr-AdS) spacetimes, from the viewpoint that the AdS boundary may be regarded as a perfectly reflecting mirror, in the sense that energy flux vanishes asymptotically. In this paper, we prove explicitly that a vanishing energy flux leads to a vanishing angular momentum flux. Thus, these boundary conditions may be dubbed as vanishing flux boundary conditions.
Second order bounce back boundary condition for the lattice Boltzmann fluid simulation
Energy Technology Data Exchange (ETDEWEB)
Kim, In Chan [Kunsan National Univ., Kunsan (Korea, Republic of)
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.
Directory of Open Access Journals (Sweden)
Mohammed J Uddin
Full Text Available Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.
Uddin, Mohammed J; Khan, Waqar A; Ismail, Ahmed I
2012-01-01
Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.
The effect of traffic light on accident probability in open and periodic boundaries system
Mhirech, Abdelaziz; Alaoui-Ismaili, Assia
2015-09-01
In this paper we numerically study the dependence of car accident probability Pac, per site and per time step on cycle time T of traffic light, both in open and periodic boundaries system. In this study one traffic light is placed in the middle of the system. This work is based on Nagel and Schreckenberg (NaSch) model (Nagel and Schreckenberg (1992)) in parallel dynamics. The Pac dependence on T and the (α, β) phase diagrams are established. α and β are the injecting and extracting rates of cars in the traffic lane respectively. The increase of the cycle time light T causes an important decrease of the accident probability Pac both in the open and periodic cases.
Marenda, Mattia; Zanardo, Marina; Trovato, Antonio; Seno, Flavio; Squartini, Andrea
2016-12-01
Bacterial communities undergo collective behavioural switches upon producing and sensing diffusible signal molecules; a mechanism referred to as Quorum Sensing (QS). Exemplarily, biofilm organic matrices are built concertedly by bacteria in several environments. QS scope in bacterial ecology has been debated for over 20 years. Different perspectives counterpose the role of density reporter for populations to that of local environment diffusivity probe for individual cells. Here we devise a model system where tubes of different heights contain matrix-embedded producers and sensors. These tubes allow non-limiting signal diffusion from one open end, thereby showing that population spatial extension away from an open boundary can be a main critical factor in QS. Experimental data, successfully recapitulated by a comprehensive mathematical model, demonstrate how tube height can overtake the role of producer density in triggering sensor activation. The biotic degradation of the signal is found to play a major role and to be species-specific and entirely feedback-independent.
Energy Technology Data Exchange (ETDEWEB)
Sharapov, T F [Bashkir State Pedagogical University, Ufa (Russian Federation)
2014-10-31
We consider an elliptic operator in a multidimensional domain with frequently changing boundary conditions in the case when the homogenized operator contains the Dirichlet boundary condition. We prove the uniform resolvent convergence of the perturbed operator to the homogenized operator and obtain estimates for the rate of convergence. A complete asymptotic expansion is constructed for the resolvent when it acts on sufficiently smooth functions. Bibliography: 41 titles.
Skewon-Axion Medium and Soft-and-Hard/DB Boundary Condition
Lindell, Ismo V
2012-01-01
The class of skewon-axion media can be defined in a simple and natural manner applying four-dimensional differential-form representation of electromagnetic fields and media. It has been recently shown that an interface of a uniaxial skewon-axion medium acts as a DB boundary requiring vanishing normal components of the D and B vectors. In the present paper a more general skewon-axion medium is considered. It is shown that a planar interface of such a medium acts as a boundary generalizing both soft-and-hard (SH) and DB boundary conditions to SHDB conditions. Reflection of a plane wave from a planar SHDB boundary is studied. It is shown that for the two eigenpolarizations the boundary can be replaced by equivalent PEC or PMC boundaries. The theory is tested with a numerical example.
Numerical simulation of Neumann boundary condition in the thermal lattice Boltzmann model
Chen, Q.; Zhang, X. B.; Zhang, J. F.
2014-03-01
In this paper, a bilinear interpolation finite-difference scheme is proposed to handle the Neumann boundary condition with nonequilibrium extrapolation method in the thermal lattice Boltzmann model. The temperature value at the boundary point is obtained by the finite-difference approximation, and then used to determine the wall temperature via an extrapolation. Our method can deal with the boundaries with complex geometries, motions and gradient boundary conditions. Several simulations are performed to examine the capacity of this proposed boundary method. The numerical results agree well with the analytical solutions. When compared with a representative boundary method, an improved performance is observed. The results also show that the proposed scheme together with nonequilibrium extrapolation method has second-order accuracy.
Free boundary conditions and the AdS{sub 3}/CFT{sub 2} correspondence
Energy Technology Data Exchange (ETDEWEB)
Apolo, Luis; Porrati, Massimo [Center for Cosmology and Particle Physics, Department of Physics, New York University,4 Washington Place, New York, NY 10003 (United States)
2014-03-26
We show that recently proposed free boundary conditions for AdS{sub 3} are dual to two-dimensional quantum gravity in certain fixed gauges. In particular, we note that an appropriate identification of the generator of Virasoro transformations leads to a vanishing total central charge in agreement with the theory at the boundary. We argue that this identification is necessary to match the bulk and boundary generators of Virasoro transformations and for consistency with the constraint equations.
Free boundary conditions and the AdS$_3$/CFT$_2$ correspondence
Apolo, Luis
2014-01-01
We show that the recently proposed free boundary conditions for AdS$_3$ are dual to two-dimensional quantum gravity in certain fixed gauges. In particular, we note that an appropriate identification of the generator of Virasoro transformations leads to a vanishing total central charge in agreement with the theory at the boundary. We argue that this identification is necessary to match the bulk and boundary generators of Virasoro transformations and for consistency with the constraint equations.
Surface boundary conditions for the numerical solution of the Euler equations
Dadone, A.; Grossman, B.
1993-01-01
We consider the implementation of boundary conditions at solid walls in inviscid Euler solutions by upwind, finite-volume methods. We review some current methods for the implementation of surface boundary conditions and examine their behavior for the problem of an oblique shock reflecting off a planar surface. We show the importance of characteristic boundary conditions for this problem and introduce a method of applying the classical flux-difference splitting of Roe as a characteristic boundary condition. Consideration of the equivalent problem of the intersection of two (equal and opposite) oblique shocks was very illuminating on the role of surface boundary conditions for an inviscid flow and led to the introduction of two new boundary-condition procedures, denoted as the symmetry technique and the curvature-corrected symmetry technique. Examples of the effects of the various surface boundary conditions considered are presented for the supersonic blunt body problem and the subcritical compressible flow over a circular cylinder. Dramatic advantages of the curvature-corrected symmetry technique over the other methods are shown, with regard to numerical entropy generation, total pressure loss, drag and grid convergence.
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 th...
Gowdy waves as a test-bed for constraint-preserving boundary conditions
Bona, C
2010-01-01
Gowdy waves, one of the standard 'apples with apples' tests, is proposed as a test-bed for constraint-preserving boundary conditions in the non-linear regime. As an illustration, energy-constraint preservation is separately tested in the Z4 framework. Both algebraic conditions, derived from energy estimates, and derivative conditions, deduced from the constraint-propagation system, are considered. The numerical errors at the boundary are of the same order than those at the interior points.
He, Yubao; Yin, Hang; Huang, Hongyan; Yu, Daren
2017-08-01
Based on the sharp forward of shock train and taking the forthcoming unstart for a background, the dynamic characteristics for sharp opening procedure of boundary-layer suction slot are investigated numerically using the dynamic mesh technique. Results indicate that the climbing path of shock train with the complex background waves exhibits a sharp and slow forward state at different time. The compression waves in the primary shock sweep the trailing edge of the separation bubble, and the recirculation within the shock train is communicated with the separation bubble, which reveals that the flow is in a critical state and is about to be unstart at the subsequent time. Furthermore, the dynamic pattern for sharp opening procedure of boundary-layer suction slot can be classified into four distinct stages, namely, the formation of the jet plume without suction mass loss, the formation of the barrier shock with suction mass loss characterized by gradient increase and subsequent two oscillations, the evolution of the barrier shock and jet plume with suction mass loss that ramps up via a series of discrete step increases, and the formation of the stable structure accompanied by the linear suction mass loss.
Collins, Courtney J; Strutwolf, Jörg; Arrigan, Damien W M
2011-04-01
In this work, the modulation of the diffusion potential formed at the microfluidic aqueous-aqueous boundary by a pharmaceutical substance is presented. Co-flowing aqueous streams in a microchannel were used to form the stable boundary between the streams. Measurement of the open circuit potential between two silver/silver chloride electrodes enabled the diffusion potential at the boundary to be determined, which is concentration dependent. Experimental results for protonated propranolol as well as tetrapropylammonium are presented. This concept may be useful as a strategy for the detection of drug substances.
Time-dependent density functional theory with twist-averaged boundary conditions
Schuetrumpf, B; Reinhard, P -G
2016-01-01
Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, 3D coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a box. For finite quantum systems (atoms, molecules, nuclei), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. These artifacts can be practically cured by introducing absorbing boundary conditions (ABC) through an absorbing potential in a certain boundary region sufficiently far from the described system. But also the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust) suffer artifacts from a finite computational box. In this regime, twist- averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we exte...
Araneda, Bernardo
2016-01-01
The static region outside the event horizon of an asymptotically anti de Sitter black hole has a conformal timelike boundary $\\mathscr{I}$, the evolution from initial data of linear fields satisfying hyperbolic equations is a well posed problem only after imposing boundary conditions at $\\mathscr{I}$. Boundary conditions preserving the action of the background isometry group on the solution space are limited to the homogeneous Dirichlet, Neumann or Robin types. We study, scalar and Maxwell fields and gravitational perturbations on asymptotically AdS black holes arising in Einstein and Lovelock theories. A decomposition in modes transforms the field equations into a set of wave equations with time independent potentials for auxiliary fields in the $x<0$ half of 1+1 Minkowski spacetime. We study systematically these equations for the case of potentials not diverging at the boundary and prove that there is always an instability if Robin boundary conditions with large $\\gamma$ (the quotient between the derivat...
How to determine a boundary condition for diffusion at a thin membrane from experimental data
Kosztołowicz, Tadeusz; WÄ sik, Sławomir; Lewandowska, Katarzyna D.
2017-07-01
We present a method of deriving a boundary condition for diffusion at a thin membrane from experimental data. Based on experimental results obtained for normal diffusion of ethanol in water, we show that the derived boundary condition at a membrane contains a term with a Riemann-Liouville fractional time derivative of order 1/2 . Such a form of the boundary condition shows that a transfer of particles through a thin membrane is a "long-memory process." The presented method is an example that an important part of the mathematical model of physical processes may be derived directly from experimental data.
Kolomenskiy, Dmitry; Schneider, Kai
2014-01-01
We study the properties of an approximation of the Laplace operator with Neumann boundary conditions using volume penalization. For the one-dimensional Poisson equation we compute explicitly the exact solution of the penalized equation and quantify the penalization error. Numerical simulations using finite differences allow then to assess the discretisation and penalization errors. The eigenvalue problem of the penalized Laplace operator with Neumann boundary conditions is also studied. As examples in two space dimensions, we consider a Poisson equation with Neumann boundary conditions in rectangular and circular domains.
Institute of Scientific and Technical Information of China (English)
Ze－NingWang; Qiang－TaiZhou
1994-01-01
Numerical solutions for fully developed laminar flow in internally finned tubes with trapezoidal and triangular fin profiles were given with Finite Elemant Method(FEM):The heat transfer charactieristics were obtained and compared under the boundary conditions of uniform heat flux,univform wall tepmerature,and the third boundary condition with finite wall thermal conductivity considered.The numerical results show that boundary conditions have pronounced effects on the temperature field.Furthermore,a new mechanism on the heat transfer augmentation of internally finned tubes is proposed.
Effects of microscopic boundary conditions on plastic deformations of small-sized single crystals
DEFF Research Database (Denmark)
Kuroda, Mitsutoshi; Tvergaard, Viggo
2009-01-01
The finite deformation version of the higher-order gradient crystal plasticity model proposed by the authors is applied to solve plane strain boundary value problems, in order to obtain an understanding of the effect of the higher-order boundary conditions. Numerical solutions are carried out...... effect of higher-order boundary conditions on the overall deformation mode of the block is observed. The bent foil has free surfaces through which dislocations can go out of the material, and we observe a strong size-dependent mechanical response resulting from the surface condition assumed....
DIFFERENT ROOF BEHAVIOUR UNDER DIFFERENT UPPER MINING BOUNDARY CONDITION IN DATONG
Institute of Scientific and Technical Information of China (English)
康立勋
1997-01-01
Understanding roof behaviour and immediate roof failure patterns of Iongwall face is a prerequisite for establishing correct roof control theory and appplying effective roof control measures. Roof behaviour and immediate roof failure pattern have a close relationship with upper mining boundary conditions of Iongwall face. According to actual situation of Datong Mining Area, upper mining boundary conditions of Iongwall face have been classified into 5 types in this paper. Roof behaviour and immediate roof failure pattern under each upper mining boundary condition are discussed in details.
R-matrix theory with Dirichlet boundary conditions for integrable electron waveguides
Energy Technology Data Exchange (ETDEWEB)
Lee, Hoshik [Department of Physics, College of William and Mary, Williamsburg, VA 23187 (United States); Reichl, L E, E-mail: hoshik.lee@wm.ed, E-mail: reichl@physics.utexas.ed [Center for Complex Quantum Systems, University of Texas at Austin, Austin, TX 78712 (United States)
2010-10-08
R-matrix theory is used to compute transmission properties of a T-shaped electron waveguide and an electron waveguide-based rotation gate by using Dirichlet boundary conditions for reaction region basis states, even at interfaces with external leads. Such boundary conditions have been known to cause R-matrix convergence problems. We show that an R-matrix obtained using Dirichlet boundary conditions can be convergent for some cases. We also show that R-matrix theory can efficiently reproduce results that were obtained using far more computationally demanding methods such as mode matching techniques, tight-binding Green's function methods or the finite element methods.
Ramos, I C
2015-01-01
We present the adaptation to non--free boundary conditions of a pseudospectral method based on the (complex) Fourier transform. The method is applied to the numerical integration of the Oberbeck--Boussinesq equations in a Rayleigh--B\\'enard cell with no-slip boundary conditions for velocity and Dirichlet boundary conditions for temperature. We show the first results of a 2D numerical simulation of dry air convection at high Rayleigh number ($R\\sim10^9$). These results are the basis for the later study, by the same method, of wet convection in a solar still.
Calkins, Michael A; Julien, Keith; Nieves, David; Driggs, Derek; Marti, Philippe
2015-01-01
The influence of fixed temperature and fixed heat flux thermal boundary conditions on rapidly rotating convection in the plane layer geometry is investigated for the case of stress-free mechanical boundary conditions. It is shown that whereas the leading order system satisfies fixed temperature boundary conditions implicitly, a double boundary layer structure is necessary to satisfy the fixed heat flux thermal boundary conditions. The boundary layers consist of a classical Ekman layer adjacent to the solid boundaries that adjust viscous stresses to zero, and a layer in thermal wind balance just outside the Ekman layers adjusts the temperature such that the fixed heat flux thermal boundary conditions are satisfied. The influence of these boundary layers on the interior geostrophically balanced convection is shown to be asymptotically weak, however. Upon defining a simple rescaling of the thermal variables, the leading order reduced system of governing equations are therefore equivalent for both boundary condit...
Bagchi, Arunabha; ten Brummelhuis, P.G.J.; ten Brummelhuis, P.G.J.
1990-01-01
A method to estimate simultaneously states and parameters of a discrete-time hyperbolic system with noisy boundary conditions is presented. This method is based on maximization of a likelihood (ML) function. The ML function leads to a two-point boundary value problem of considerable complexity.
Lie and Conditional Symmetries of a Class of Nonlinear (1 + 2-Dimensional Boundary Value Problems
Directory of Open Access Journals (Sweden)
Roman Cherniha
2015-08-01
Full Text Available A new definition of conditional invariance for boundary value problems involving a wide range of boundary conditions (including initial value problems as a special case is proposed. It is shown that other definitions worked out in order to find Lie symmetries of boundary value problems with standard boundary conditions, followed as particular cases from our definition. Simple examples of direct applicability to the nonlinear problems arising in applications are demonstrated. Moreover, the successful application of the definition for the Lie and conditional symmetry classification of a class of (1 + 2-dimensional nonlinear boundary value problems governed by the nonlinear diffusion equation in a semi-infinite domain is realised. In particular, it is proven that there is a special exponent, k ≠ —2, for the power diffusivity uk when the problem in question with non-vanishing flux on the boundary admits additional Lie symmetry operators compared to the case k ≠ —2. In order to demonstrate the applicability of the symmetries derived, they are used for reducing the nonlinear problems with power diffusivity uk and a constant non-zero flux on the boundary (such problems are common in applications and describing a wide range of phenomena to (1 + 1-dimensional problems. The structure and properties of the problems obtained are briefly analysed. Finally, some results demonstrating how Lie invariance of the boundary value problem in question depends on the geometry of the domain are presented.
Janssen, R.H.H.; Vilà-Guerau de Arellano, J.; Ganzeveld, L.N.; Kabat, P.; Jimenez, J.L.; Farmer, D.K.; Heerwaarden, van C.C.; Mammarella, I.
2012-01-01
We study the combined effects of land surface conditions, atmospheric boundary layer dynamics and chemistry on the diurnal evolution of biogenic secondary organic aerosol in the atmospheric boundary layer, using a model that contains the essentials of all these components. First, we evaluate the mod
Institute of Scientific and Technical Information of China (English)
Sun Hye PARK
2014-01-01
In this paper, we investigate the influence of boundary dissipation on the de-cay property of solutions for a transmission problem of Kirchhoff type wave equation with boundary memory condition. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of relaxation function.
REGULARITY THEORY FOR SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. This type of problem is motivated by stochastic differential games. The Neumann case corresponds to stochastic differential equations with reflection on boundary of the domain.
Boundary conditions for General Relativity on AdS3 and the KdV hierarchy
Pérez, Alfredo; Tempo, David; Troncoso, Ricardo
2016-06-01
It is shown that General Relativity with negative cosmological constant in three spacetime dimensions admits a new family of boundary conditions being labeled by a nonnegative integer k. Gravitational excitations are then described by "boundary gravitons" that fulfill the equations of the k-th element of the KdV hierarchy. In particular, k = 0 corresponds to the Brown-Henneaux boundary conditions so that excitations are described by chiral movers. In the case of k = 1, the boundary gravitons fulfill the KdV equation and the asymptotic symmetry algebra turns out to be infinite-dimensional, abelian and devoid of central extensions. The latter feature also holds for the remaining cases that describe the hierarchy ( k > 1). Our boundary conditions then provide a gravitational dual of two noninteracting left and right KdV movers, and hence, boundary gravitons possess anisotropic Lifshitz scaling with dynamical exponent z = 2 k + 1. Remarkably, despite spacetimes solving the field equations are locally AdS, they possess anisotropic scaling being induced by the choice of boundary conditions. As an application, the entropy of a rotating BTZ black hole is precisely recovered from a suitable generalization of the Cardy formula that is compatible with the anisotropic scaling of the chiral KdV movers at the boundary, in which the energy of AdS spacetime with our boundary conditions depends on z and plays the role of the central charge. The extension of our boundary conditions to the case of higher spin gravity and its link with different classes of integrable systems is also briefly addressed.
Towards an effective non-reflective boundary condition for computational aeroacoustics
Gill, James; Fattah, Ryu; Zhang, Xin
2017-03-01
A generic, non-reflective zonal transverse characteristic boundary condition is described for computational aeroacoustics, which shows superior performance to existing non-reflective boundary conditions for two-dimensional linearized Euler simulations. The new condition is based on a characteristic non-reflective method, and also contains optimised use of transverse characteristic terms and a zonal forcing region. The performance of the new method and several existing non-reflective acoustic boundary conditions is quantitatively compared using a plane wave test case. The performance of buffer zone, perfectly matched layer, far-field, and characteristic non-reflective methods is compared, following an optimisation of the tuneable parameters in each method to give best performance. The study uses a high-order linearised Euler equation solver to assess non-reflective boundary conditions with a variety of cases. The performance is compared for downstream travelling acoustic waves with varying frequency and incident angle, and at various Mach numbers. The current study includes a more comprehensive evaluation than previous studies which used constant values of tuneable parameters or qualitative assessment methods. The new zonal transverse characteristic boundary condition is shown to give improved performance in comparison to the other tested outflow boundary conditions for two-dimensional linearized Euler simulations, and is also shown to give good performance when used as an inflow condition.
Zarepour, Misagh; Amirhosein Hosseini, Seyed
2016-08-01
This study presents an examination of nonlinear free vibration of a nanobeam under electro-thermo-mechanical loading with elastic medium and various boundary conditions, especially the elastic boundary condition. The nanobeam is modeled as an Euler-Bernoulli beam. The von Kármán strain-displacement relationship together with Hamilton’s principle and Eringen’s theory are employed to derive equations of motion. The nonlinear free vibration frequency is obtained for simply supported (S-S) and elastic supported (E-E) boundary conditions. E-E boundary condition is a general and actual form of boundary conditions and it is chosen because of more realistic behavior. By applying the differential transform method (DTM), the nanobeam’s natural frequencies can be easily obtained for the two different boundary conditions mentioned above. Performing a precise study led to investigation of the influences of nonlocal parameter, temperature change, spring constants (either for elastic medium or boundary condition) and imposed electric potential on the nonlinear free vibration characteristics of nanobeam. The results for S-S and E-E nanobeams are compared with each other. In order to validate the results, some comparisons are presented between DTM results and open literature to show the accuracy of this new approach. It has been discovered that DTM solves the equations with minimum calculation cost.
Geomagnetic Secular Variation Prediction with Thermal Heterogeneous Boundary Conditions
Kuang, Weijia; Tangborn, Andrew; Jiang, Weiyuan
2011-01-01
It has long been conjectured that thermal heterogeneity at the core-mantle boundary (CMB) affects the geodynamo substantially. The observed two pairs of steady and strong magnetic flux lobes near the Polar Regions and the low secular variation in the Pacific over the past 400 years (and perhaps longer) are likely the consequences of this CMB thermal heterogeneity. There are several studies on the impact of the thermal heterogeneity with numerical geodynamo simulations. However, direct correlation between the numerical results and the observations is found very difficult, except qualitative comparisons of certain features in the radial component of the magnetic field at the CMB. This makes it difficult to assess accurately the impact of thermal heterogeneity on the geodynamo and the geomagnetic secular variation. We revisit this problem with our MoSST_DAS system in which geomagnetic data are assimilated with our geodynamo model to predict geomagnetic secular variations. In this study, we implement a heterogeneous heat flux across the CMB that is chosen based on the seismic tomography of the lowermost mantle. The amplitude of the heat flux (relative to the mean heat flux across the CMB) varies in the simulation. With these assimilation studies, we will examine the influences of the heterogeneity on the forecast accuracies, e.g. the accuracies as functions of the heterogeneity amplitude. With these, we could be able to assess the model errors to the true core state, and thus the thermal heterogeneity in geodynamo modeling.
Ground Boundary Conditions for Thermal Convection Over Horizontal Surfaces at High Rayleigh Numbers
Hanjalić, K.; Hrebtov, M.
2016-07-01
We present "wall functions" for treating the ground boundary conditions in the computation of thermal convection over horizontal surfaces at high Rayleigh numbers using coarse numerical grids. The functions are formulated for an algebraic-flux model closed by transport equations for the turbulence kinetic energy, its dissipation rate and scalar variance, but could also be applied to other turbulence models. The three-equation algebraic-flux model, solved in a T-RANS mode ("Transient" Reynolds-averaged Navier-Stokes, based on triple decomposition), was shown earlier to reproduce well a number of generic buoyancy-driven flows over heated surfaces, albeit by integrating equations up to the wall. Here we show that by using a set of wall functions satisfactory results are found for the ensemble-averaged properties even on a very coarse computational grid. This is illustrated by the computations of the time evolution of a penetrative mixed layer and Rayleigh-Bénard (open-ended, 4:4:1 domain) convection, using 10 × 10 × 100 and 10 × 10 × 20 grids, compared also with finer grids (e.g. 60 × 60 × 100), as well as with one-dimensional treatment using 1 × 1 × 100 and 1 × 1 × 20 nodes. The approach is deemed functional for simulations of a convective boundary layer and mesoscale atmospheric flows, and pollutant transport over realistic complex hilly terrain with heat islands, urban and natural canopies, for diurnal cycles, or subjected to other time and space variations in ground conditions and stratification.
Benincasa, T.; Donado Escobar, L. D.; Moroşanu, C.
2016-08-01
This paper is concerned with an optimal control problem (P) (both distributed control as well as boundary control) for the nonlinear phase-field (Allen-Cahn) equation, involving a regular potential and dynamic boundary condition. A family of approximate optimal control problems (Pɛ) is introduced and results for the existence of an optimal control for problems (P) and (Pɛ) are proven. Furthermore, the convergence result of the optimal solution of problem (Pɛ) to the optimal solution of problem (P) is proved. Besides the existence of an optimal control in problem (Pɛ), necessary optimality conditions (Pontryagin's principle) as well as a conceptual gradient-type algorithm to approximate the optimal control, were established in the end.
Basu, S.; Holtslag, A.A.M.; Wiel, van de B.J.H.; Moene, A.F.; Steeneveld, G.J.
2008-01-01
In single column and large-eddy simulation studies of the atmospheric boundary layer, surface sensible heat flux is often used as a boundary condition. In this paper, we delineate the fundamental shortcomings of such a boundary condition in the context of stable boundary layer modelling and simulati
High order local absorbing boundary conditions for acoustic waves in terms of farfield expansions
Villamizar, Vianey; Acosta, Sebastian; Dastrup, Blake
2017-03-01
We devise a new high order local absorbing boundary condition (ABC) for radiating problems and scattering of time-harmonic acoustic waves from obstacles of arbitrary shape. By introducing an artificial boundary S enclosing the scatterer, the original unbounded domain Ω is decomposed into a bounded computational domain Ω- and an exterior unbounded domain Ω+. Then, we define interface conditions at the artificial boundary S, from truncated versions of the well-known Wilcox and Karp farfield expansion representations of the exact solution in the exterior region Ω+. As a result, we obtain a new local absorbing boundary condition (ABC) for a bounded problem on Ω-, which effectively accounts for the outgoing behavior of the scattered field. Contrary to the low order absorbing conditions previously defined, the error at the artificial boundary induced by this novel ABC can be easily reduced to reach any accuracy within the limits of the computational resources. We accomplish this by simply adding as many terms as needed to the truncated farfield expansions of Wilcox or Karp. The convergence of these expansions guarantees that the order of approximation of the new ABC can be increased arbitrarily without having to enlarge the radius of the artificial boundary. We include numerical results in two and three dimensions which demonstrate the improved accuracy and simplicity of this new formulation when compared to other absorbing boundary conditions.
Generalized adjoint consistent treatment of wall boundary conditions for compressible flows
Hartmann, Ralf; Leicht, Tobias
2015-11-01
In this article, we revisit the adjoint consistency analysis of Discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations with application to the Reynolds-averaged Navier-Stokes and k- ω turbulence equations. Here, particular emphasis is laid on the discretization of wall boundary conditions. While previously only one specific combination of discretizations of wall boundary conditions and of aerodynamic force coefficients has been shown to give an adjoint consistent discretization, in this article we generalize this analysis and provide a discretization of the force coefficients for any consistent discretization of wall boundary conditions. Furthermore, we demonstrate that a related evaluation of the cp- and cf-distributions is required. The freedom gained in choosing the discretization of boundary conditions without loosing adjoint consistency is used to devise a new adjoint consistent discretization including numerical fluxes on the wall boundary which is more robust than the adjoint consistent discretization known up to now. While this work is presented in the framework of Discontinuous Galerkin discretizations, the insight gained is also applicable to (and thus valuable for) other discretization schemes. In particular, the discretization of integral quantities, like the drag, lift and moment coefficients, as well as the discretization of local quantities at the wall like surface pressure and skin friction should follow as closely as possible the discretization of the flow equations and boundary conditions at the wall boundary.
New boundary conditions from January; Vieles neu ab Januar
Energy Technology Data Exchange (ETDEWEB)
Wiedemann, Karsten
2011-12-15
The biogas industry now has to cope with changed public funding conditions. Manufacturers of biogas plant are trying out microsize plants and direct marketing models in an attempt to invite customers. But it is to be expected that few new customers will be acquired.
Regular and Irregular Boundary Conditions in the AdS/CFT Correspondence
Mück, W
1999-01-01
We expand on Klebanov and Witten's recent proposal for formulating the AdS/CFT correspondence using irregular boundary conditions. The proposal is shown to be correct to any order in perturbation theory.
Invariance of decay rate with respect to boundary conditions in thermoelastic Timoshenko systems
Alves, M. S.; Jorge Silva, M. A.; Ma, T. F.; Muñoz Rivera, J. E.
2016-06-01
This paper is mainly concerned with the polynomial stability of a thermoelastic Timoshenko system recently introduced by Almeida Júnior et al. (Z Angew Math Phys 65(6):1233-1249, 2014) that proved, in the general case when equal wave speeds are not assumed, different polynomial decay rates depending on the boundary conditions, namely, optimal rate {t^{-1/2}} for mixed Dirichlet-Neumann boundary condition and rate {t^{-1/4}} for full Dirichlet boundary condition. Here, our main achievement is to prove the same polynomial decay rate {t^{-1/2}} (corresponding to the optimal one) independently of the boundary conditions, which improves the existing literature on the subject. As a complementary result, we also prove that the system is exponentially stable under equal wave speeds assumption. The technique employed here can probably be applied to other kind of thermoelastic systems.
Brahim Tellab; Kamel Haouam
2016-01-01
In this paper, we investigate the existence and uniqueness of solutions for second order nonlinear fractional differential equation with integral boundary conditions. Our result is an application of the Banach contraction principle and the Krasnoselskii fixed point theorem.
Shayma Adil Murad; Hussein Jebrail Zekri; Samir Hadid
2011-01-01
We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.
PRESBC: pressure boundary conditions for the K-FIX code. Supplement III
Energy Technology Data Exchange (ETDEWEB)
Travis, J.R.; Rivard, W.C.
1980-07-01
Recommended pressure boundary condition modifications are described for the computer code K-FIX, which has been published in the report LA-NUREG-6623 and released to the National Energy Software Center in April 1977.
Corrected second-order slip boundary condition for fluid flows in nanochannels.
Zhang, Hongwu; Zhang, Zhongqiang; Zheng, Yonggang; Ye, Hongfei
2010-06-01
A corrected second-order slip boundary condition is proposed to solve the Navier-Stokes equations for fluid flows confined in parallel-plate nanochannels. Compared with the classical second-order slip boundary condition proposed by Beskok and Karniadakis, the corrected slip boundary condition is not only dependent on the Knudsen number and the tangential momentum accommodation coefficient, but also dependent on the relative position of the slip surface in the Knudsen layer. For the fluid flows in slip-flow regime with the Knudsen number less than 0.3, Couette cell is investigated using molecular-dynamics simulations to verify Newtonian flow behaviors by examining the constitutive relationship between shear stress and strain rate. By comparing the velocity profiles of Poiseuille flows predicted from the Navier-Stokes equations with the corrected slip boundary condition with that from molecular-dynamics simulations, it is found that the flow behaviors in our models can be effectively captured.
Simulating thermal boundary conditions of spin-lattice models with weighted averages
Wang, Wenlong
2016-07-01
Thermal boundary conditions have played an increasingly important role in revealing the nature of short-range spin glasses and is likely to be relevant also for other disordered systems. Diffusion method initializing each replica with a random boundary condition at the infinite temperature using population annealing has been used in recent large-scale simulations. However, the efficiency of this method can be greatly suppressed because of temperature chaos. For example, most samples have some boundary conditions that are completely eliminated from the population in the process of annealing at low temperatures. In this work, I study a weighted average method to solve this problem by simulating each boundary conditions separately and collect data using weighted averages. The efficiency of the two methods is studied using both population annealing and parallel tempering, showing that the weighted average method is more efficient and accurate.
A Kind of Discrete Non-Reflecting Boundary Conditions for Varieties of Wave Equations
Institute of Scientific and Technical Information of China (English)
Xiu-min Shao; Zhi-ling Lan
2002-01-01
In this paper, a new kind of discrete non-reflecting boundary conditions is developed. It can be used for a variety of wave equations such as the acoustic wave equation, the isotropic and anisotropic elastic wave equations and the equations for wave propagation in multi-phase media and so on. In this kind of boundary conditions, the composition of all artificial reflected waves, but not the individual reflected ones, is considered and eliminated. Thus, it has a uniform formula for different wave equations. The velocity CA of the composed reflected wave is determined in the way to make the reflection coefficients minimal, the value of which depends on equations. In this paper, the construction of the boundary conditions is illustrated and CA is found, numerical results are presented to illustrate the effectiveness of the boundary conditions.
Structure and vibrational spectra of a model of a-Si:H with periodic boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Winer, K.; Wooten, F.
1983-08-01
A ball-and -stick model of a-Si:H with periodic boundary conditions has been constructed. A computer replica of the structure has been relaxed and the density, radial distribution function and vibrational spectra calculated.
Directory of Open Access Journals (Sweden)
Abdelfatah Bouziani
2010-01-01
the weak solvability of parabolic integrodifferential equations with a nonclassical boundary conditions. The investigation is made by means of approximation by the Rothes method which is based on a semidiscretization of the given problem with respect to the time variable.
Eigenvalue Problem for Nonlinear Fractional Differential Equations with Integral Boundary Conditions
Directory of Open Access Journals (Sweden)
Guotao Wang
2014-01-01
Full Text Available By employing known Guo-Krasnoselskii fixed point theorem, we investigate the eigenvalue interval for the existence and nonexistence of at least one positive solution of nonlinear fractional differential equation with integral boundary conditions.
THE DYNAMICS OF SINE-GORDON SYSTEM WITH DIRICHLET BOUNDARY CONDITION
Institute of Scientific and Technical Information of China (English)
Liu Yingdong; Li Zhengyuan
2000-01-01
We prove the existence of the global attractor of Sine-Gordon system with Dirichlet boundary condition and show the attractor is the unique steady state when the damping constant and the diffusion constant are sufficiently large.
An analysis of boundary condition effects on the thermomechanical modeling of the FSW process
Guedoiri, A.; Moufki, A.; Favier, V.; Zahrouni, H.
2011-01-01
The aim of the present work is to study the influence of thermal boundary conditions on the simulation of friction stir welding process "FSW". Generally, dimensions of the workpieces to be welded are very large and a very small zone surrounding the welding tool is modeled for the thermomechanical study of the process. This area, named box, should be small enough to reduce the computation time and large enough to minimize effects of boundary conditions. It is well known that during welding, the mixing zone is closed arround the tool; it is easily identified by analyzing the velocity field which is complex in contact interface with the tool and which tends rapidly to the tool traverse speed far from the tool. In the thermal analysis, the boundary conditions are not obvious since they depend on the welding parameters, on the workpiece dimensions and on its vicinity. We propose in this study a numerical strategy for determining the thermal boundary conditions on the box.
Directory of Open Access Journals (Sweden)
Li Ming
2013-03-01
Full Text Available In this study, a single beam model has been developed to analyze the thermal vibration of Single-Walled Carbon Nanotubes (SWCNT. The nonlocal elasticity takes into account the effect of small size into the formulation and the boundary condition. With exact solution of the dynamic governing equations, the thermal-vibrational characteristics of a cantilever SWCNT are obtained. Influence of nonlocal small scale effects, temperature change and vibration modes of the CNT on the frequency are investigated. The present study shows that the additional boundary conditions from small scale do not change natural frequencies at different temperature change. Thus for simplicity, one can apply the local boundary condition to replace the small scale boundary condition.
Institute of Scientific and Technical Information of China (English)
Ling DING; Chunlei TANG
2013-01-01
The existence and multiplicity of positive solutions are studied for a class of quasilinear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.
Blow-up estimates for semilinear parabolic systems coupled in an equation and a boundary condition
Institute of Scientific and Technical Information of China (English)
王明新
2001-01-01
This paper deals with the blow-up rate estimates of solutions for semilinear parabolic systems coupled in an equation and a boundary condition. The upper and lower bounds of blow-up rates have been obtained.
Asymptotic behavior of solutions to nonlinear parabolic equation with nonlinear boundary conditions
Directory of Open Access Journals (Sweden)
Diabate Nabongo
2008-01-01
Full Text Available We show that solutions of a nonlinear parabolic equation of second order with nonlinear boundary conditions approach zero as t approaches infinity. Also, under additional assumptions, the solutions behave as a function determined here.
Institute of Scientific and Technical Information of China (English)
M.Yakit ONGUN
2007-01-01
In this paper we consider the nonselfadjoint (dissipative) Schr(o)dinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator,and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schr(o)dinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schr(o)dinger boundary value problem are given.
Institute of Scientific and Technical Information of China (English)
M.Yakit; ONGUN
2007-01-01
In this paper we consider the nonselfadjoint (dissipative) Schrodinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator, and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schrodinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schrodinger boundary value problem are given.
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.
Gasymov, E. A.; Guseinova, A. O.; Gasanova, U. N.
2016-07-01
One of the methods for solving mixed problems is the classical separation of variables (the Fourier method). If the boundary conditions of the mixed problem are irregular, this method, generally speaking, is not applicable. In the present paper, a generalized separation of variables and a way of application of this method to solving some mixed problems with irregular boundary conditions are proposed. Analytical representation of the solution to this irregular mixed problem is obtained.
A Novel Absorbing Boundary Condition for the Frequency-DependentFinite-Difference Time-Domain Method
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A new absorbing boundary condition (ABC) for frequency-dependent finite-difference time-domain algorithm for the arbitrary dispersive media is presented. The concepts of the digital systems are introduced to the (FD)2TD method. On the basis of digital filter designing and vector algebra, the absorbing boundary condition under arbitrary angle of incidence are derived. The transient electromagnetic problems in two-dimensions and three-dimensions are calculated and the validity of the ABC is verified.
Boundary Conditions for Translation-Invariant Gibbs Measures of the Potts Model on Cayley Trees
Gandolfo, D.; Rahmatullaev, M. M.; Rozikov, U. A.
2017-06-01
We consider translation-invariant splitting Gibbs measures (TISGMs) for the q-state Potts model on a Cayley tree of order two. Recently a full description of the TISGMs was obtained, and it was shown in particular that at sufficiently low temperatures their number is 2q-1. In this paper for each TISGM μ we explicitly give the set of boundary conditions such that limiting Gibbs measures with respect to these boundary conditions coincide with μ.
Boundary conditions on faster-than-light transportation systems
Bennett, Gary L.; Knowles, H. B.
1993-01-01
In order to be consistent with current physical theories, any proposal of a faster-than light (FTL) transportation system must satisfy several critical conditions. It must predict the mass, space, and time dimensional changes predicted by relativity physics when velocity falls below the speed of light. It must also not violate causality, and remain consistent with quantum physics in the limit of microscopic systems. It is also essential that the proposal conserve energy.
Continuous matrix product states with periodic boundary conditions and an application to atomtronics
Draxler, Damian; Haegeman, Jutho; Verstraete, Frank; Rizzi, Matteo
2017-01-01
We introduce a time evolution algorithm for one-dimensional quantum field theories with periodic boundary conditions. This is done by applying the Dirac-Frenkel time-dependent variational principle to the set of translational invariant continuous matrix product states with periodic boundary conditions. Moreover, the ansatz is accompanied with additional boundary degrees of freedom to study quantum impurity problems. The algorithm allows for a cutoff in the spectrum of the transfer matrix and thus has an efficient computational scaling. In particular we study the prototypical example of an atomtronic system—an interacting Bose gas rotating in a ring shaped trap in the presence of a localized barrier potential.
A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions
Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.
2014-01-01
We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.
The Second Stokes Problem with Specular - Diffusive Boundary Conditions in Kinetic Theory
Akimova, V A; Yushkanov, A A
2012-01-01
The second Stokes problem with specular - diffusive boundary conditions of the kinetic theory is considered. The new method of the decision of the boundary problems of the kinetic theory is applied. The method allows to receive the decision with any degree of accuracy. At the basis of a method lays the idea of representation of a boundary condition on distribution function in the form of a source in the kinetic equation. By means of integrals Fourier the kinetic equation with a source is reduced to the integral equation of Fredholm type of the second kind. The decision is received in the form of Neumann's series.
Factor analysis of small business conditions of boundary region
Directory of Open Access Journals (Sweden)
Леся Михайлівна Газуда
2015-05-01
Full Text Available In terms of border-zone and capabilities of direct implementation of foreign economic cooperation with the Member States of the European Union is necessary to intensify the development of priority economic activities in Zakarpattia region. Background and specific characteristics of small business development in the region are considered in the article. It is conducted the multivariate correlation and regression analysis of conditions of regional small business development for the main indicators, including the volume of sales, the gross regional product, the economically active population, capital investment, exports and imports
Bai, Xiao-Dong; Zhang, Mei; Xiong, Jun; Yang, Guo-Jian; Deng, Fu-Guo
2015-01-01
We investigate the formation of discrete breathers (DBs) and the dynamics of the mixture of two-species Bose-Einstein condensates (BECs) in open boundary optical lattices using the discrete nonlinear Schrödinger equations. The results show that the coupling of intra- and interspecies interaction can lead to the existence of pure single-species DBs and symbiotic DBs (i.e., two-species DBs). Furthermore, we find that there is a selective distillation phenomenon in the dynamics of the mixture of two-species BECs. One can selectively distil one species from the mixture of two-species BECs and can even control dominant species fraction by adjusting the intra- and interspecies interaction in optical lattices. Our selective distillation mechanism may find potential application in quantum information storage and quantum information processing based on multi-species atoms. PMID:26597592
The role of boundary and initial conditions for dynamical seasonal predictability
Directory of Open Access Journals (Sweden)
T. J. Reichler
2003-01-01
Full Text Available The importance of initial state and boundary forcing for atmospheric predictability is explored on global to regional spatial scales and on daily to seasonal time scales. A general circulation model is used to conduct predictability experiments with different combinations of initial and boundary conditions. The experiments are verified under perfect model assumptions as well as against observational data. From initial conditions alone, there is significant instantaneous forecast skill out to 2 months. Different initial conditions show different predictability using the same kind of boundary forcing. Even on seasonal time scales, using observed atmospheric initial conditions leads to a substantial increase in overall skill, especially during periods with weak tropical forcing. The impact of boundary forcing on predictability is detectable after 10 days and leads to measurable instantaneous forecast skill at very long lead times. Over the Northern Hemisphere, it takes roughly 4 weeks for boundary conditions to reach the same effect on predictability as initial conditions. During events with strong tropical forcing, these time scales are somewhat shorter. Over the Southern Hemisphere, there is a strongly enhanced influence of initial conditions during summer. We conclude that the long term memory of initial conditions is important for seasonal forecasting.
Bouncing Dirac particles: compatibility between MIT boundary conditions and Thomas precession
Nicolaevici, Nistor
2016-01-01
We consider the reflection of a Dirac plane wave on a perfectly reflecting plane described by chiral MIT boundary conditions and determine the rotation of the spin in the reflected component of the wave. We solve the analogous problem for a classical particle using the evolution of the spin defined by the Thomas precession and make a comparison with the quantum result. We find that the rotation axes of the spin in the two problems coincide only for a vanishing chiral angle, in which case the rotation angles coincide in the nonrelativistic limit, and also remain remarkably close in the relativistic regime. The result shows that in the nonrelativistic limit the interaction between the spin and a reflecting surface with nonchiral boundary conditions is completely contained in the Thomas precession effect, in conformity with the fact that these boundary conditions are equivalent to an infinite repulsive scalar potential outside the boundary. By contrast, in the ultrarelativistic limit the rotation angle in the qu...
An energy absorbing far-field boundary condition for the elastic wave equation
Energy Technology Data Exchange (ETDEWEB)
Petersson, N A; Sjogreen, B
2008-07-15
The authors present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional to shear wave speed. They prove stability for a second order accurate finite-difference discretization of the elastic wave equation in three space dimensions together with a discretization of the proposed non-reflecting boundary condition. The stability proof is based on a discrete energy estimate and is valid for heterogeneous materials. The proof includes all six boundaries of the computational domain where special discretizations are needed at the edges and corners. The stability proof holds also when a free surface boundary condition is imposed on some sides of the computational domain.
Jin, Guoyong; Su, Zhu
2015-01-01
This book develops a uniform accurate method which is capable of dealing with vibrations of laminated beams, plates and shells with arbitrary boundary conditions including classical boundaries, elastic supports and their combinations. It also provides numerous solutions for various configurations including various boundary conditions, laminated schemes, geometry and material parameters, which fill certain gaps in this area of reach and may serve as benchmark solutions for the readers. For each case, corresponding fundamental equations in the framework of classical and shear deformation theory are developed. Following the fundamental equations, numerous free vibration results are presented for various configurations including different boundary conditions, laminated sequences and geometry and material properties. The proposed method and corresponding formulations can be readily extended to static analysis.
Performance of Numerical Boundary Condition based on Active Wave Absorption System
DEFF Research Database (Denmark)
Trouch, P.; Rouck, J. de; Frigaard, Peter
2001-01-01
that was first developed in the context of physical wave flume experiments, using a wave paddle. The method applies to regular and irregular waves. Velocities are measured at one location inside the computational domain. The reflected wave train is separated from the incident wave field in front of a structure......The implementation and performance of a new active wave generating‐absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces is presented. This numerical boundary condition AWAVOF is based on an active wave absorption system...... by means of digital filtering and subsequent superposition of the measured velocity signals. The incident wave signal is corrected, so that the reflected wave is effectively absorbed at the boundary. The effectiveness of the active wave generating‐absorbing boundary condition is proved using numerical...
Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions
Directory of Open Access Journals (Sweden)
Ahmet Batal
2016-08-01
Full Text Available In this article, we study the initial boundary value problem for nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions $$ u_x(0,t+\\lambda|u(0,t|^ru(0,t=0,\\quad \\lambda\\in\\mathbb{R}-\\{0\\},\\; r> 0. $$ We discuss the local well-posedness when the initial data $u_0=u(x,0$ belongs to an $L^2$-based inhomogeneous Sobolev space $H^s(\\mathbb{R}_+$ with $s\\in (\\frac{1}{2},\\frac{7}{2}-\\{\\frac{3}{2}\\}$. We deal with the nonlinear boundary condition by first studying the linear Schrodinger equation with a time-dependent inhomogeneous Neumann boundary condition $u_x(0,t=h(t$ where $h\\in H^{\\frac{2s-1}{4}}(0,T$.
Directory of Open Access Journals (Sweden)
Syahira Mansur
2016-10-01
Full Text Available The unsteady boundary layer flow of a nanofluid past a stretching/shrinking sheet with a convective surface boundary condition is studied. The effects of the unsteadiness parameter, stretching/shrinking parameter, convective parameter, Brownian motion parameter and thermophoresis parameter on the local Nusselt number are investigated. Numerical solutions to the governing equations are obtained using a shooting method. The results for the local Nusselt number are presented for different values of the governing parameters. The local Nusselt number decreases as the stretching/shrinking parameter increases. The local Nusselt number is consistently higher for higher values of the convective parameter but lower for higher values of the unsteadiness parameter, Brownian motion parameter and thermophoresis parameter.
On the Nature of Boundary Conditions for Flows with Moving Free Surfaces
Renardy, Michael; Renardy, Yuriko
1991-04-01
We consider small perturbations of plane parallel flow between a wall and a moving free surface. The problem is posed on a rectangle with inflow and outflow boundaries. The usual boundary conditions are posed at the wall and the free surface, and the fluid satisfies the Navier-Stokes equations. We examine the nature of boundary conditions which can be imposed at the inflow and outflow boundaries in order to yield a well-posed problem. This question turns out to be more delicate than is generally appreciated. Depending on the precise situation and on the regularity required of the solution, boundary conditions at just one or both endpoints of the free surface need to be imposed. For example, we show that if the velocities at te inflow and outflow boundaries are prescribed, then the position of the free surface at the inflow boundary can be prescribed, but not at the outflow if an H1-solution is desired. Numerical simulations with the FIDAP package are used to illustrate our analytical results.
Institute of Scientific and Technical Information of China (English)
于艳梅; 杨根仓; 赵达文; 吕衣礼
2002-01-01
By the phase-field approach, the dendritic growth in binary alloy melt was simulated respectively using two types of temperature boundary conditions, i.e., the constant temperature boundary by which the boundary temperature was fixed at the initial temperature, and Zero-Neumann temperature boundary. The influences of the temperature boundary conditions on numerical results are investigated. How to choose appropriate temperature boundary conditions is proposed. The results show that: 1) when the computation region is limited to a changeless size, the Zero-Neumann and constant temperature boundary conditions lead to the different dendritic growth behaviors, and the Zero-Neumann condition is preferable to the constant temperature condition; 2) when the computation region is enlarged continually with the computational time according to the increasing thermal diffusion scale, the two types of temperature boundary conditions achieve the consistent tip velocities and tip radii, and they both are appropriate choices.
DEFF Research Database (Denmark)
Svec, Oldrich; Skoček, Jan
2013-01-01
The ability of the Lattice Boltzmann method, as the fluid dynamics solver, to properly simulate macroscopic Navier’s slip boundary condition is investigated. An approximate equation relating the Lattice Boltzmann variable slip boundary condition with the macroscopic Navier’s slip boundary condition...
Energy Technology Data Exchange (ETDEWEB)
Graf von der Pahlen, J.; Tsiklauri, D. [School of Physics and Astronomy, Queen Mary University of London, London E1 4NS (United Kingdom)
2014-01-15
Works of Tsiklauri and Haruki [Phys. Plasmas 15, 102902 (2008); 14, 112905 (2007)] are extended by inclusion of the out-of-plane magnetic (guide) field. In particular, magnetic reconnection during collisionless, stressed X-point collapse for varying out-of-plane guide-fields is studied using a kinetic, 2.5D, fully electromagnetic, relativistic particle-in-cell numerical code. For zero guide-field, cases for both open and closed boundary conditions are investigated, where magnetic flux and particles are lost and conserved, respectively. It is found that reconnection rates, out-of-plane currents and density in the X-point increase more rapidly and peak sooner in the closed boundary case, but higher values are reached in the open boundary case. The normalized reconnection rate is fast: 0.10-0.25. In the open boundary case it is shown that an increase of guide-field yields later onsets in the reconnection peak rates, while in the closed boundary case initial peak rates occur sooner but are suppressed. The reconnection current changes similarly with increasing guide-field; however for low guide-fields the reconnection current increases, giving an optimal value for the guide-field between 0.1 and 0.2 times the in-plane field in both cases. Also, in the open boundary case, it is found that for guide-fields of the order of the in-plane magnetic field, the generation of electron vortices occurs. Possible causes of the vortex generation, based on the flow of decoupled particles in the diffusion region and localized plasma heating, are discussed. Before peak reconnection onset, oscillations in the out-of-plane electric field at the X-point are found, ranging in frequency from approximately 1 to 2 ω{sub pe} and coinciding with oscillatory reconnection. These oscillations are found to be part of a larger wave pattern in the simulation domain. Mapping the out-of-plane electric field along the central lines of the domain over time and applying a 2D Fourier transform reveal that
Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions
Hodge, Steve L.; Zorumski, William E.; Watson, Willie R.
1995-01-01
The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.
Fluid flow in nanopores: An examination of hydrodynamic boundary conditions
Sokhan, V. P.; Nicholson, D.; Quirke, N.
2001-08-01
Steady-state Poiseuille flow of a simple fluid in carbon slit pores under a gravity-like force is simulated using a realistic empirical many-body potential model for carbon. In this work we focus on the small Knudsen number regime, where the macroscopic equations are applicable, and simulate different wetting conditions by varying the strength of fluid-wall interactions. We show that fluid flow in a carbon pore is characterized by a large slip length even in the strongly wetting case, contrary to the predictions of Tolstoi's theory. When the surface density of wall atoms is reduced to values typical of a van der Waals solid, the streaming velocity profile vanishes at the wall, in accordance with earlier findings. From the velocity profiles we have calculated the slip length and by analyzing temporal profiles of the velocity components of particles colliding with the wall we obtained values of the Maxwell coefficient defining the fraction of molecules thermalized by the wall.
Importance of Hydrogeological Conditions on Open-loop Geothermal System
Park, D.; Bae, G.; Kim, S.; Lee, K.
2013-12-01
The open-loop geothermal system has been known as an eco-friendly, energy-saving, and cost-efficient alternative for the cooling and heating of buildings with directly using the relatively stable temperature of groundwater. Thus, hydrogeological properties of aquifer, such as hydraulic conductivity and storage, must be important in the system application. The study site is located near Han-river, Korea, and because of the well-developed alluvium it might be a typical site appropriate to this system requiring an amount of groundwater. In this study, the first objective of numerical experiments was to find the best distributions of pumping and injection wells suitable to the hydrogeological conditions of the site for the efficient and sustainable system operation. The aquifer has a gravel layer at 15m depth below the ground surface and the river and the agricultural field, which may be a potential contaminant source, are located at the west and east sides, respectively. Under the general conditions that the regional groundwater flows from the east to the river, the locally reversed well distribution, locating the pumping well at upgradient and the injection well at downgradient of the regional flow, was most sustainable. The gravel layer with high hydraulic conductivity caused a little drawdown despite of an amount of pumping and allowed to stably reinject the used groundwater in all the cases, but it provided a passage transferring the injected heat to the pumping well quickly, particularly in the cases locating the injection well at the upgradient. This thermal interference was more severe in the cases of the short distance between the wells. The high conductive layer is also a reason that the seasonal role conversion of wells for the aquifer thermal energy storage was ineffective in this site. Furthermore, the well distribution vertical to the regional groundwater flow was stable, but not best, and, thus, it may be a good choice in the conditions that the regional
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.
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.
Existence and Asymptotic Behavior of the Wave Equation with Dynamic Boundary Conditions
Energy Technology Data Exchange (ETDEWEB)
Graber, Philip Jameson, E-mail: pjg9g@virginia.edu [University of Virginia, Department of Mathematics (United States); Said-Houari, Belkacem, E-mail: belkacem.saidhouari@kaust.edu.sa [King Abdullah University of Science and Technology (KAUST), Division of Mathematical and Computer Sciences and Engineering (Saudi Arabia)
2012-08-15
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.
Effects of Boundary Condition and Helix Angle On Meshing Performance of TI Worm Gearing
Institute of Scientific and Technical Information of China (English)
SUN Yue-hai; DUAN Lu-qian; WANG Shu-ren; ZHANG Ce
2006-01-01
To exactly describe the contact state and contact area oftooth surface oftoroidalinvolute(TI) worm gearing.the authors introduced boundary condition into contact line analysis.With helix angle chosen as parameter,the criterion for the existence of meshing boundary line on the surface of TI worm gearing is derived.Results show that there can be four situations for meshing boundary line on the tooth surface of gear.namely,inexistence of meshing boundary line.a unique line,two lines,and two coincident lines.If the helix angle is equal to or slightly smaller than the bigger angle,which makes two meshing boundary lines superpose,a preferable meshing performance is obtained.Computer simulation proves the validity Of the above conclusion.
Realistic boundary conditions for stochastic simulations of reaction-diffusion processes
Erban, R; Erban, Radek
2006-01-01
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic partial-differential equations or stochastic simulation algorithms. The latter provide a more detailed and precise picture, and several stochastic simulation algorithms have been proposed in recent years. Such models typically give the same description of the reaction-diffusion processes far from the boundary of the simulated domain, but the behaviour close to a reactive boundary (e.g. a membrane with receptors) is unfortunately model-dependent. In this paper, we study four different approaches to stochastic modelling of reaction-diffusion problems and show the correct choice of the boundary condition for each model. The reactive boundary is treated as partially reflective, which means that some molecules hitting the boundary are adsorbed (e.g. bound to the receptor) and some molecul...
Energy Technology Data Exchange (ETDEWEB)
Follin, S. [Golder Grundteknik, Uppsala (Sweden)
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.
Green's function of the heat equation with periodic and antiperiodic boundary conditions
Imanbaev, Nurlan; Erzhanov, Nurzhan
2016-12-01
In this work a non-local initial-boundary value problem for a non-homogeneous one-dimensional heat equation is con-sidered. The domain under consideration is a rectangle. The classical initial condition with respect to t is put. A non-local periodic boundary condition with respect to a spatial variable x is put. It is well-known that a solution of problem can be constructed in the form of convergent orthonormal series according to eigenfunctions of a spectral problem for an operator of multiple differentiation with periodic boundary conditions. Therefore Green's function can be also written in the form of an infinite series with respect to trigonometric functions (Fourier series). For classical first and second initial-boundary value problems there also exists a second representation of the Green's function by Jacobi function. In this paper we find the representation of the Green's function of the non-local initial-boundary value problem with periodic boundary conditions in the form of series according to exponents.
Sheloput, Tatiana; Agoshkov, Valery
2017-04-01
The problem of modeling water areas with `liquid' (open) lateral boundaries is discussed. There are different known methods dealing with open boundaries in limited-area models, and one of the most efficient is data assimilation. Although this method is popular, there are not so many articles concerning its implementation for recovering boundary functions. However, the problem of specifying boundary conditions at the open boundary of a limited area is still actual and important. The mathematical model of the Baltic Sea circulation, developed in INM RAS, is considered. It is based on the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations. The splitting method that is used for time approximation in the model allows to consider the data assimilation problem as a sequence of linear problems. One of such `simple' temperature (salinity) assimilation problem is investigated in the study. Using well known techniques of study and solution of inverse problems and optimal control problems [1], we propose an iterative solution algorithm and we obtain conditions for existence of the solution, for unique and dense solvability of the problem and for convergence of the iterative algorithm. The investigation shows that if observations satisfy certain conditions, the proposed algorithm converges to the solution of the boundary control problem. Particularly, it converges when observational data are given on the `liquid' boundary [2]. Theoretical results are confirmed by the results of numerical experiments. The numerical algorithm was implemented to water area of the Baltic Sea. Two numerical experiments were carried out in the Gulf of Finland: one with the application of the assimilation procedure and the other without. The analyses have shown that the surface temperature field in the first experiment is close to the observed one, while the result of the second experiment misfits. Number of iterations depends on the regularisation parameter, but
Poisson-Nernst-Planck model with Chang-Jaffe, diffusion, and ohmic boundary conditions
Lelidis, I.; Macdonald, J. Ross; Barbero, G.
2016-01-01
Using the linear Poisson-Nernst-Planck impedance-response continuum model, we investigate the possible equivalences of three different types of boundary conditions previously proposed to model the electrode behavior of an electrolytic cell in the shape of a slab. We show analytically that the boundary conditions proposed long ago by Chang-Jaffe are fully equivalent to the ohmic boundary conditions only if the positive and negative ions have the same mobility, or when only ions of a single polarity are mobile. In the case where the ions have different and non-zero mobilities, we fit exact impedance spectra created for ohmic boundary conditions by using the Chang-Jaffe Poisson-Nernst-Planck response model, one that is dominated by diffusion effects. These fits yield conditions for essentially exact or approximate numerical correspondence for the complex impedance between the two models even in the unequal mobility case. Finally, diffusion type boundary conditions are shown to be fully equivalent to the ohmic one. Some limiting cases of the model parameters are investigated.
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2012-06-01
Full Text Available We study boundary value problems of nonlinear fractional differential equations and inclusions of order $q in (m-1, m]$, $m ge 2$ with multi-strip boundary conditions. Multi-strip boundary conditions may be regarded as the generalization of multi-point boundary conditions. Our problem is new in the sense that we consider a nonlocal strip condition of the form: $$ x(1=sum_{i=1}^{n-2}alpha_i int^{eta_i}_{zeta_i} x(sds, $$ which can be viewed as an extension of a multi-point nonlocal boundary condition: $$ x(1=sum_{i=1}^{n-2}alpha_i x(eta_i. $$ In fact, the strip condition corresponds to a continuous distribution of the values of the unknown function on arbitrary finite segments $(zeta_i,eta_i$ of the interval $[0,1]$ and the effect of these strips is accumulated at $x=1$. Such problems occur in the applied fields such as wave propagation and geophysics. Some new existence and uniqueness results are obtained by using a variety of fixed point theorems. Some illustrative examples are also discussed.
Institute of Scientific and Technical Information of China (English)
Cheng-Qi Sun; Kai-Xin Liu; You-Shi Hong
2012-01-01
The paper studies the axisymmetric compressive buckling behavior of multi-walled carbon nanotubes (MWNTs) under different boundary conditions based on continuum mechanics model.A buckling condition is derived for determining the critical buckling load and associated buckling mode of MWNTs,and numerical results are worked out for MWNTs with different aspect ratios under fixed and simply supported boundary conditions.It is shown that the critical buckling load of MWNTs is insensitive to boundary conditions,except for nanotubes with smaller radii and very small aspect ratio.The associated buckling modes for different layers of MWNTs are in-phase,and the buckling displacement ratios for different layers are independent of the boundary conditions and the length of MWNTs.Moreover,for simply supported boundary conditions,the critical buckling load is compared with the corresponding one for axial compressive buckling,which indicates that the critical buckling load for axial compressive buckling can be well approximated by the corresponding one for axisymmetric compressive buckling.In particular,for axial compressive buckling of double-walled carbon nanotubes,an analytical expression is given for approximating the critical buckling load.The present investigation may be of some help in further understanding the mechanical properties of MWNTs.
Paleoenvironmental conditions across the Jurassic-Cretaceous boundary in central-eastern Mexico
Martínez-Yáñez, Mario; Núñez-Useche, Fernando; López Martínez, Rafael; Gardner, Rand D.
2017-08-01
The Padni section of central-eastern Mexico is characterized by pelagic, organic-rich carbonates and shales dated in this study by calpionellid biostratigraphy to the late Tithonian-late Berriasian time interval. Microfacies, pyrite framboid size, spectrometric gamma-ray and mineralogical data are herein integrated in order to reconstruct the paleoenvironmental change during the Jurassic-Cretaceous boundary. Deposits of the late Tithonian-early Berriasian are characterized by laminated, organic-rich facies with abundant radiolarian, tiny pyrite framboids and low Th/U ratios. They are linked to upwelling in a semi-restricted basin, high marine productivity and anoxic bottom waters. The early incursions of Tethyan oceanic waters into the proto-Gulf of Mexico occurred during late Tithonian as attested the appearance of calpionellids. Short and intermittent accumulations of saccocomids during early Berriasian suggest episodes of sporadic connection between the Tethys, the proto-Atlantic and the Pacific ocean during sea-level rise events. A full and stable connection between the Tethys and proto-Gulf of Mexico was established until the late Berriasian. This event is supported by the presence of open marine and bioturbated facies with a framboid population typical of dysoxic conditions, higher Th/U ratios and a decreasing pattern of the total organic carbon content. In addition to highlighting the replenishment of the oxygen supply to the basin, this facies also points to a younger age for the finalization of the Yucatán Block rotation and the end of the Gulf of Mexico opening. Deposition of the studied section occurred mostly during a Tithonian-Berriasian arid phase reported in other Tethyan and Atlantic regions. The similarity between the discrete segments of the standard gamma-ray curve defined in the studied outcrop and those reported from subsurface implies their regional continuity allowing their use for correlation purposes.
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.
Wissocq, Gauthier; Gourdain, Nicolas; Malaspinas, Orestis; Eyssartier, Alexandre
2017-02-01
This paper reports the investigations done to adapt the Characteristic Boundary Conditions (CBC) to the Lattice-Boltzmann formalism for high Reynolds number applications. Three CBC formalisms are implemented and tested in an open source LBM code: the baseline local one-dimension inviscid (BL-LODI) approach, its extension including the effects of the transverse terms (CBC-2D) and a local streamline approach in which the problem is reformulated in the incident wave framework (LS-LODI). Then all implementations of the CBC methods are tested for a variety of test cases, ranging from canonical problems (such as 2D plane and spherical waves and 2D vortices) to a 2D NACA profile at high Reynolds number (Re =105), representative of aeronautic applications. The LS-LODI approach provides the best results for pure acoustics waves (plane and spherical waves). However, it is not well suited to the outflow of a convected vortex for which the CBC-2D associated with a relaxation on density and transverse waves provides the best results. As regards numerical stability, a regularized adaptation is necessary to simulate high Reynolds number flows. The so-called regularized FD (Finite Difference) adaptation, a modified regularized approach where the off-equilibrium part of the stress tensor is computed thanks to a finite difference scheme, is the only tested adaptation that can handle the high Reynolds computation.
Solution of the quantum initial value problem with transparent boundary conditions
Puga, A.; Miller, B. N.
2013-01-01
Many systems of interest at the forefront of technological development, for example, in quantum computation, consist of weakly interacting elements that obey quantum mechanics. A challenge for modern theoretical physics is to develop a systematic methodology for approaching these "open" quantum systems. In particular, applied mathematicians have formulated the method of transparent boundary conditions (TBCs) to model interacting quantum systems of infinite extent. Here, we consider a particular application of TBCs to the escape of a particle from a one-dimensional infinite well when one of the bounding barriers is extinguished. We analytically obtain the exact time-dependent wave function by a Green's function method and then show that a numerical solution based on the TBC method is in excellent agreement. This work was motivated by an experiment carried out at the University of Texas on escape from a gravitational wedge billiard. Physicists have used billiards to understand and explore both classical and quantum chaos. Although the original experiment was carried out in the classical regime, current work is probing lower temperatures, where a quantum mechanical formulation is required.
Biondini, Gino; Fagerstrom, Emily; Prinari, Barbara
2016-10-01
We formulate the inverse scattering transform (IST) for the defocusing nonlinear Schrödinger (NLS) equation with fully asymmetric non-zero boundary conditions (i.e., when the limiting values of the solution at space infinities have different non-zero moduli). The theory is formulated without making use of Riemann surfaces, and instead by dealing explicitly with the branched nature of the eigenvalues of the associated scattering problem. For the direct problem, we give explicit single-valued definitions of the Jost eigenfunctions and scattering coefficients over the whole complex plane, and we characterize their discontinuous behavior across the branch cut arising from the square root behavior of the corresponding eigenvalues. We pose the inverse problem as a Riemann-Hilbert Problem on an open contour, and we reduce the problem to a standard set of linear integral equations. Finally, for comparison purposes, we present the single-sheet, branch cut formulation of the inverse scattering transform for the initial value problem with symmetric (equimodular) non-zero boundary conditions, as well as for the initial value problem with one-sided non-zero boundary conditions, and we also briefly describe the formulation of the inverse scattering transform when a different choice is made for the location of the branch cuts.
Institute of Scientific and Technical Information of China (English)
LAI Yuanming; ZHANG Mingyi; LIU Zhiqiang; YU Wenbing
2006-01-01
The heat convection of fluid inside the ballast layer and ripped-rock layer, which are regarded as porous media in railway embankment, is a process of heat and mass transfer. At present,the ripped-rock embankment, as a new type of embankment structure, has widely been used in the construction of Qinghai-Tibetan railway. However, because its ripped-rock layer is almost open in two bilateral boundaries and closed at top and bottom, and air can flow into/out of the ballast layer and ripped-rock layer, the convection and transfer heat patterns are very complicated in the embankment.Therefore, based on the temperature and geology conditions of the Qinghai-Tibetan Plateau, a numerical approach of the unsteady two-dimensional continuity, momentum (non-Darcy flow) and energy equations of heat convection for incompressible fluid in porous media is provided to analyze the velocity and temperature characteristics of the ripped-rock embankment with different embankment heights under open boundary condition for the coming 50 years in this paper. The calculated results indicate that, due to the influence of the outside wind, the convective heat transfer mainly relies on the forced convection in the open ripped-rock embankment. Even if the air temperature will be warmed up by 2.6℃ in the coming 50 years, it still has a better cooling effect on the underlying soils and a low temperature frozen-soil core is formed in the permafrost below it if the embankment is constructed in the regions whose present mean annual air temperature is -4.0℃. Furthermore, the cooling effect of high ripped-rock embankment is better than that of low embankment. This is because the wider bottom of high embankment has a more influence dimension on the underlying frozen soil. However,cardinal winds on the Qinghai-Tibetan Plateau disturb its convection pattern, so that an asymmetric temperature distribution occurs under high embankment and it is possible to induce a transverse uneven deformation of
Institute of Scientific and Technical Information of China (English)
Ling Huang; Chi-Wang Shu; Mengping Zhang
2008-01-01
High order fast sweeping methods have been developed recently in the literature to solve static Hamilton-Jacobi equations efficiently. Comparing with the first order fast sweeping methods, the high order fast sweeping methods are more accurate, but they often require additional numerical boundary treatment for several grid points near the boundary because of the wider numerical stencil. It is particularly important to treat the points near the inflow boundary accurately, as the information would flow into the computational domain and would affect global accuracy. In the literature, the numerical solution at these boundary points are either fixed with the exact solution, which is not always feasible, or computed with a first order discretization, which could reduce the global accuracy. In this paper, we discuss two strategies to handle the inflow boundary conditions. One is based on the numerical solutions of a first order fast sweeping method with several different mesh sizes near the boundary and a Richardson extrapolation, the other is based on a Lax-Wendroff type procedure to repeatedly utilizing the PDE to write the normal spatial derivatives to the inflow boundary in terms of the tangential derivatives, thereby obtaining high order solution values at the grid points near the inflow boundary. We explore these two approaches using the fast sweeping high order WENO scheme in [18] for solving the static Eikonal equation as a representative example. Numerical examples are given to demonstrate the performance of these two approaches.
Lee, Chung-Shuo; Chen, Yan-Yu; Yu, Chi-Hua; Hsu, Yu-Chuan; Chen, Chuin-Shan
2017-02-01
We present a semi-analytical solution of a time-history kernel for the generalized absorbing boundary condition in molecular dynamics (MD) simulations. To facilitate the kernel derivation, the concept of virtual atoms in real space that can conform with an arbitrary boundary in an arbitrary lattice is adopted. The generalized Langevin equation is regularized using eigenvalue decomposition and, consequently, an analytical expression of an inverse Laplace transform is obtained. With construction of dynamical matrices in the virtual domain, a semi-analytical form of the time-history kernel functions for an arbitrary boundary in an arbitrary lattice can be found. The time-history kernel functions for different crystal lattices are derived to show the generality of the proposed method. Non-equilibrium MD simulations in a triangular lattice with and without the absorbing boundary condition are conducted to demonstrate the validity of the solution.
Institute of Scientific and Technical Information of China (English)
Guo Zhenhua; He Wen
2011-01-01
In this paper, we study a one-dimensional motion of viscous gas near vacuum. We are interested in the case that the gas is in contact with the vacuum at a finite interval. This is a free boundary problem for the one-dimensional isentropic Navier-Stokes equations, and the free boundaries are the interfaces separating the gas from vacuum, across which the density changes discontinuosly. Smoothness of the solutions and the uniqueness of the weak solutions are also discussed. The present paper extends results in Luo-Xin-Yang [12] to the jump boundary conditions case.
Unified approach to split absorbing boundary conditions for nonlinear Schrödinger equations.
Zhang, Jiwei; Xu, Zhenli; Wu, Xiaonan
2008-08-01
An efficient method is proposed for numerical solutions of nonlinear Schrödinger equations on an unbounded domain. Through approximating the kinetic energy term by a one-way equation and uniting it with the potential energy equation, absorbing boundary conditions are designed to truncate the unbounded domain, which are in nonlinear form and can perfectly absorb waves outgoing from the boundaries of the truncated computational domain. The stability of the induced initial boundary value problem defined on the computational domain is examined by a normal mode analysis. Numerical examples are given to illustrate the stable and tractable advantages of the method.
Boundary conditions for multistep finite-difference methods for time-dependent equations
Gottlieb, D.; Turkel, E.
1978-01-01
The stability and accuracy of various boundary treatments are analyzed for the two-step Richtmyer and MacCormack methods. Special attention is paid to ways of imposing the extra boundary conditions after the first step of the two-step process. The theory of Kreiss is used to study stability properties for both scalar and vector equations. The theory of Skollermo is used to compare accuracies of the various methods. Computations were also performed on both wavelike equations and on systems that approach a steady state. Several suggestions are given for more reliable boundary treatments.
Directory of Open Access Journals (Sweden)
Tairone Paiva Leão
2011-02-01
Full Text Available An accurate estimation of hydraulic fluxes in the vadose zone is essential for the prediction of water, nutrient and contaminant transport in natural systems. The objective of this study was to simulate the effect of variation of boundary conditions on the estimation of hydraulic properties (i.e. water content, effective unsaturated hydraulic conductivity and hydraulic flux in a one-dimensional unsaturated flow model domain. Unsaturated one-dimensional vertical water flow was simulated in a pure phase clay loam profile and in clay loam interlayered with silt loam distributed according to the third iteration of the Cantor Bar fractal object Simulations were performed using the numerical model Hydrus 1D. The upper and lower pressure heads were varied around average values of -55 cm for the near-saturation range. This resulted in combinations for the upper and lower constant head boundary conditions, respectively, of -50 and -60 cm, -40 and -70 cm, -30 and -80 cm, -20 and -90 cm, and -10 and -100 cm. For the drier range the average head between the upper and lower boundary conditions was set to -550 cm, resulting in the combinations -500 and -600 cm, -400 and -700 cm, -300 and -800 cm, -200 and -900 cm, and -100 and -1,000 cm, for upper and lower boundary conditions, respectively. There was an increase in water contents, fluxes and hydraulic conductivities with the increase in head difference between boundary conditions. Variation in boundary conditions in the pure phase and interlayered one-dimensional profiles caused significant deviations in fluxes, water contents and hydraulic conductivities compared to the simplest case (a head difference between the upper and lower constant head boundaries of 10 cm in the wetter range and 100 cm in the drier range.
Influence of Boundary Conditions on Yielding in a Soft Glassy Material
Gibaud, Thomas; Barentin, Catherine; Manneville, Sébastien
2008-12-01
The yielding behavior of a sheared Laponite suspension is investigated within a 1 mm gap under two different boundary conditions. No-slip conditions, ensured by using rough walls, lead to shear localization as already reported in various soft glassy materials. When apparent wall slip is allowed using a smooth geometry, the sample breaks up into macroscopic solid pieces that get slowly eroded by the surrounding fluidized material up to the point where the whole sample is fluid. Such a drastic effect of boundary conditions on yielding suggests the existence of some macroscopic characteristic length that could be connected to cooperativity effects in jammed materials under shear.
NON-STATIONARY STOKES FLOWS UNDER LEAK BOUNDARY CONDITIONS OF FRICTION TYPE
Institute of Scientific and Technical Information of China (English)
Hiroshi Fujita
2001-01-01
This paper is concerned with the initial value problem for non-stationary Stokes flows,under a certain non-linear boundary condition which can be called the leak boundarycondition of friction type. Theoretically, our main purpose is to show the strong solvability(i.e.,the unique existence of the L2-strong solution) of this initial value problem by meansof the non-linear semi-group theory originated with Y. Komura. The method of analysiscan be applied to other boundary or interface conditions of friction type. It should benoted that the result yields a sound basis of simulation methods for evolution problemsinvolving these conditions.
Sliding fluids: Dewetting experiments reveal the solid/liquid boundary condition
Energy Technology Data Exchange (ETDEWEB)
Baeumchen, Oliver; Lessel, Matthias; Fetzer, Renate; Seemann, Ralf; Jacobs, Karin, E-mail: k.jacobs@physik.uni-saarland.d [Department of Experimental Physics, Saarland University, D-66041 Saarbruecken (Germany)
2010-03-01
Nanoscale liquid polymer films are ideal candidates to probe the solid/liquid boundary condition: Prepared on hydrophobized Si wafer, the films are not stable, they dewet. The dewetting induces a flow without applying an external force. Probing the dynamics of the dewetting film and the morphology of the liquid front, we can deduce the slip length. A variation of the type of hydrophobic coating (silane or Teflon (registered)) of the Si wafer enables us to tune the boundary condition from a no-slip to a nearly full-slip condition. For a short introduction to the topic, we offer a phenomenological approach and supply multimedia files.
Tjernström, Michael; Sotiropoulou, Georgia; Sedlar, Joseph; Achtert, Peggy; Brooks, Barbara; Brooks, Ian; Persson, Ola; Prytherch, John; Salsbury, Dominic; Shupe, Matthew; Johnston, Paul; Wolfe, Dan
2016-04-01
With more open water present in the Arctic summer, an understanding of atmospheric processes over open-water and sea-ice surfaces as summer turns into autumn and ice starts forming becomes increasingly important. The Arctic Clouds in Summer Experiment (ACSE) was conducted in a mix of open water and sea ice in the eastern Arctic along the Siberian shelf during late summer and early autumn 2014, providing detailed observations of the seasonal transition, from melt to freeze. Measurements were taken over both ice-free and ice-covered surfaces, offering an insight to the role of the surface state in shaping the lower troposphere and the boundary-layer conditions as summer turned into autumn. During summer, strong surface inversions persisted over sea ice, while well-mixed boundary layers capped by elevated inversions were frequent over open-water. The former were often associated with advection of warm air from adjacent open-water or land surfaces, whereas the latter were due to a positive buoyancy flux from the warm ocean surface. Fog and stratus clouds often persisted over the ice, whereas low-level liquid-water clouds developed over open water. These differences largely disappeared in autumn, when mixed-phase clouds capped by elevated inversions dominated in both ice-free and ice-covered conditions. Low-level-jets occurred ~20-25% of the time in both seasons. The observations indicate that these jets were typically initiated at air-mass boundaries or along the ice edge in autumn, while in summer they appeared to be inertial oscillations initiated by partial frictional decoupling as warm air was advected in over the sea ice. The start of the autumn season was related to an abrupt change in atmospheric conditions, rather than to the gradual change in solar radiation. The autumn onset appeared as a rapid cooling of the whole atmosphere and the freeze up followed as the warm surface lost heat to the atmosphere. While the surface type had a pronounced impact on boundary
I=2 $\\pi\\pi$ scattering using G-parity boundary condition
Kim, Changhoan
2003-01-01
To make the $\\pi\\pi$ state with non-zero relative momentum as the leading exponential, we impose anti-periodic boundary condition on the pion, which is implemented by imposing G-parity or H-parity on the quark fields at the boundary. With this, we calculate the I=2 $\\pi\\pi$ phase shift from lattice simulation by using L\\"uscher's formula.
Directory of Open Access Journals (Sweden)
Alexander M. Alekseenko
2008-01-01
the existence of the solution is proved using the properties of the reduced system. A treatment is proposed for the full nonlinear BSSN system to construct constraint-preserving boundary conditions without invoking the second order in time reduction. Energy estimates on the principal part of the BSSN system (which is first order in temporal and second order in spatial derivatives are obtained. Generalizations to the case of nonhomogeneous boundary data are proposed.
Energy Technology Data Exchange (ETDEWEB)
Li Xicheng; Xu Mingyu [Institute of Applied Mathematics, School of Mathematics and System Science, Shandong University, Jinan 250100 (China); Wang Shaowei [Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China)], E-mail: xichengli@yahoo.com.cn
2008-04-18
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.
He, Cong
2011-01-01
In this paper, we are concerned with the Cauchy problem on the one-dimensional Landau equation with $\\gamma\\geq -2$\\ with specular boundary condition and the time asymptotic behavior toward to a given local Maxwellian under some initial conditions. A time decay rate is also obtained. The method include energy method, micro-macro decomposition and the properties of Burnett functions.
Stress and mixed boundary conditions for two-dimensional dodecagonal quasi-crystal plates
Indian Academy of Sciences (India)
Yan Gao; Si-Peng Xu; Bao-Sheng Zhao
2007-05-01
For plate bending and stretching problems in two-dimensional (2D) dodecagonal quasi-crystal (QC) media, the reciprocal theorem and the general solution for QCs are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all order. The method developed by Gregory and Wan is used to generate necessary conditions which the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the plate; these decaying state conditions are obtained explicitly for axisymmetric bending and stretching of a circular plate when stress or mixed conditions are imposed on the plate edge. They are then used for the correct formulation of boundary conditions for the interior solution. For the stress data, our boundary conditions coincide with those obtained in conventional forms of plate theories. More importantly, appropriate boundary conditions with a set of mixed edge-data are obtained for the ﬁrst time. Furthermore, the corresponding necessary conditions for transversely isotropic elastic plate are obtained directly, and their isotropic elastic counterparts are also obtained.
Blow-up estimates for semilinear parabolic systems coupled in an equation and a boundary condition
Institute of Scientific and Technical Information of China (English)
WANG; Mingxin(
2001-01-01
［1］Wang, S., Wang, M. X., Xie, C. H., Reaction-diffusion systems with nonlinear boundary conditions, Z. angew. Math.Phys., 1997, 48(6): 994－1001.［2］Fila, M., Quittner, P., The blow-up rate for a semilinear parabolic system, J. Math. Anal. Appl., 1999, 238: 468－476.［3］Hu, B., Remarks on the blow-up estimate for solutions of the heat equation with a nonlinear boundary condition, Differential Integral Equations, 1996, 9(5): 891－901.［4］Hu, B. , Yin, H. M., The profile near blow-up time for solution of the heat equation with a nonlinear boundary condition,Trans. of Amer. Math. Soc., 1994, 346: 117－135.［5］Amann, H., Parabolic equations and nonlinear boundary conditions, J. of Diff. Eqns., 1988, 72: 201－269.［6］Deng, K., Blow-up rates for parabolic systems, Z. angew. Math. Phys. ,1996, 47: 132－143.［7］Fila, M., Levine, H. A., On critical exponents for a semilinear parabolic system coupled in an equation and a boundary condition, J. Math. Anal. Appl., 1996, 204: 494－521.
Boundary conditions for General Relativity on AdS$_{3}$ and the KdV hierarchy
Pérez, Alfredo; Troncoso, Ricardo
2016-01-01
It is shown that General Relativity with negative cosmological constant in three spacetime dimensions admits a new family of boundary conditions being labeled by a nonnegative integer $k$. Gravitational excitations are then described by "boundary gravitons" that fulfill the equations of the $k$-th element of the KdV hierarchy. In particular, $k=0$ corresponds to the Brown-Henneaux boundary conditions so that excitations are described by chiral movers. In the case of $k=1$, the boundary gravitons fulfill the KdV equation and the asymptotic symmetry algebra turns out to be infinite-dimensional, abelian and devoid of central extensions. The latter feature also holds for the remaining cases that describe the hierarchy ($k>1$). Our boundary conditions then provide a gravitational dual of two noninteracting left and right KdV movers, and hence, boundary gravitons possess anisotropic Lifshitz scaling with dynamical exponent $z=2k+1$. Remarkably, despite spacetimes solving the field equations are locally AdS, they po...
Dubail, J.; Santachiara, R.; Emig, T.
2017-03-01
Systems as diverse as binary mixtures and inclusions in biological membranes, and many more, can be described effectively by interacting spins. When the critical fluctuations in these systems are constrained by boundary conditions, critical Casimir forces (CCF) emerge. Here we analyze CCF between boundaries with alternating boundary conditions in two dimensions, employing conformal field theory (CFT). After presenting the concept of boundary changing operators, we specifically consider two different boundary configurations for a strip of critical Ising spins: (I) alternating equi-sized domains of up and down spins on both sides of the strip, with a possible lateral shift, and (II) alternating domains of up and down spins of different size on one side and homogeneously fixed spins on the other side of the strip. Asymptotic results for the CCF at small and large distances are derived. We introduce a novel modified Szegö formula for determinants of real antisymmetric block Toeplitz matrices to obtain the exact CCF and the corresponding scaling functions at all distances. We demonstrate the existence of a surface renormalization group flow between universal force amplitudes of different magnitude and sign. The Casimir force can vanish at a stable equilibrium position that can be controlled by parameters of the boundary conditions. Lateral Casimir forces assume a universal simple cosine form at large separations.
Improved outer boundary conditions for Einstein's field equations
Energy Technology Data Exchange (ETDEWEB)
Buchman, Luisa T [Center for Relativity, University of Texas at Austin, 1 University Station C1606, Austin, TX 78712-1081 (United States); Sarbach, Olivier C A [Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Edificio C-3, Cd. Universitaria, C P 58040 Morelia, Michoacan (Mexico)
2007-06-21
In a recent article, we constructed a hierarchy B{sub L} of outer boundary conditions for Einstein's field equations with the property that, for a spherical outer boundary, it is perfectly absorbing for linearized gravitational radiation up to a given angular momentum number L. In this paper, we generalize B{sub L} so that it can be applied to fairly general foliations of spacetime by space-like hypersurfaces and general outer boundary shapes and further, we improve B{sub L} in two steps: (i) we give a local boundary condition C{sub L}which is perfectly absorbing including first-order contributions in 2M/R of curvature corrections for quadrupolar waves (where M is the mass of the spacetime and R is a typical radius of the outer boundary) and which significantly reduces spurious reflections due to backscatter, and (ii) we give a non-local boundary condition D{sub L} which is exact when first-order corrections in 2M/R for both curvature and backscatter are considered, for quadrupolar radiation.
Ganeshan, Manisha; Wu, Dong L.
2016-10-01
The increasing ice-free area during late summer has transformed the Arctic to a climate system with more dynamic boundary layer (BL) clouds and seasonal sea ice growth. The open-ocean sensible heat flux, a crucial mechanism of excessive ocean heat loss to the atmosphere during the fall freeze season, is speculated to play an important role in the recently observed cloud cover increase and BL instability. However, lack of observations and understanding of the resilience of the proposed mechanisms, especially in relation to meteorological and interannual variability, has left a poorly constrained BL parameterization scheme in Arctic climate models. In this study, we use multi-year Japanese cruise-ship observations from R/V Mirai over the open Arctic Ocean to characterize the surface sensible heat flux (SSHF) during early fall and investigate its contribution to BL turbulence. It is found that mixing by SSHF is favored during episodes of high surface wind speed and is also influenced by the prevailing cloud regime. The deepest BLs and maximum ocean-atmosphere temperature difference are observed during cold air advection (associated with the stratocumulus regime), yet, contrary to previous speculation, the efficiency of sensible heat exchange is low. On the other hand, the SSHF contributes significantly to BL mixing during the uplift (low pressure) followed by the highly stable (stratus) regime. Overall, it can explain ˜ 10 % of the open-ocean BL height variability, whereas cloud-driven (moisture and radiative) mechanisms appear to be the other dominant source of convective turbulence. Nevertheless, there is strong interannual variability in the relationship between the SSHF and the BL height which can be intensified by the changing occurrence of Arctic climate patterns, such as positive surface wind speed anomalies and more frequent conditions of uplift. This study highlights the need for comprehensive BL observations like the R/V Mirai for better understanding and
Ganeshan, Manisha; Wu, Dongliang
2016-01-01
The increasing ice-free area during late summer has transformed the Arctic to a climate system with more dynamic boundary layer (BL) clouds and seasonal sea ice growth. The open-ocean sensible heat flux, a crucial mechanism of excessive ocean heat loss to the atmosphere during the fall freeze season, is speculated to play an important role in the recently observed cloud cover increase and BL instability. However, lack of observations and understanding of the resilience of the proposed mechanisms, especially in relation to meteorological and interannual variability, has left a poorly constrained BL parameterization scheme in Arctic climate models. In this study, we use multiyear Japanese cruise-ship observations from RV Mirai over the open Arctic Ocean to characterize the surface sensible heat flux (SSHF) during early fall and investigate its contribution to BL turbulence. It is found that mixing by SSHF is favored during episodes of high surface wind speed and is also influenced by the prevailing cloud regime. The deepest BLs and maximum ocean-atmosphere temperature difference are observed during cold air advection (associated with the stratocumulus regime), yet, contrary to previous speculation, the efficiency of sensible heat exchange is low. On the other hand, the SSHF contributes significantly to BL mixing during the uplift (low pressure) followed by the highly stable (stratus) regime. Overall, it can explain 10 of the open ocean BL height variability, whereas cloud-driven (moisture and radiative) mechanisms appear to be the other dominant source of convective turbulence. Nevertheless, there is strong interannual variability in the relationship between the SSHF and the BL height which can be intensified by the changing occurrence of Arctic climate patterns, such as positive surface wind speed anomalies and more frequent conditions of uplift. This study highlights the need for comprehensive BL observations like the RV Mirai for better understanding and
Nemnes, G. A.; Palici, Alexandra; Manolescu, A.
2016-11-01
Transparent boundary conditions for the time-dependent Schrödinger equation are implemented using the R-matrix method. The employed scattering formalism is suitable for describing open quantum systems and provides the framework for the time-dependent coherent transport. Transmission and reflection of wave functions at the edges of a finite quantum system are essential for an accurate and efficient description of the time-dependent processes on large time scales. We detail the computational method and point out the numerical advantages stemming from the open system approach based on the R-matrix formalism. The approach is used here to describe time-dependent transport across nanostructured interfaces relevant for photovoltaic applications.
DEFF Research Database (Denmark)
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 solutio...
Institute of Scientific and Technical Information of China (English)
YAN Jing-hua(闫敬华); Detlev Majewski
2003-01-01
Based on the real case of a frontal precipitation process affecting South China, 27 controlled numerical experiments was made for the effects of hydrostatic and non-hydrostatic effects, different driving models, combinations of initial/boundary conditions, updates of lateral values and initial time levels of forecast, on model predictions. Features about the impact of initial/boundary conditions on mesoscale numerical weather prediction (NWP) model are analyzed and discussed in detail. Some theoretically and practically valuable conclusions aredrawn. It is found that the overall tendency of mesoscale NWP models is governed by its driving model, with the initial conditions showing remarkable impacts on mesoscale models for the first 10 hours of the predictions while leaving lateral boundary conditions to take care the period beyond; the latter affect the inner area of mesoscale predictions mainly through the propagation and movement of weather signals (waves) of different time scales; initial values of external model parameters such as soil moisture content may affect predictions of more longer time validity, while fast signals may be filtered away and only information with time scale 4 times as large as or more than the updated period of boundary values may be introduced, through lateral boundary, to mesoscale models, etc. Someresults may be taken as important guidance on mesoscale model and its data assimilation developments of the future.
GaN-based heterostructures: electric-static equilibrium and boundary conditions
Institute of Scientific and Technical Information of China (English)
Zhang Jin-Feng; Hao Yue
2006-01-01
In the GaN-based heterostructures, this paper reports that the strong electric fields induced by polarization effects at the structure boundaries complicate the electric-static equilibrium and the boundary conditions. The basic requirements of electric-static equilibrium for the heterostructure systems are discussed first, and it is deduced that in the application of the coupled Schr(o)dinger-Poisson model to the heterostructures of electric-static equilibrium state,zero external electric field guarantees the overall electric neutrality, and there is no need to introduce the charge balance equation. Then the relation between the screening of the polar charges in GaN-based heterostructures and the possible boundary conditions of the Poisson equation is analysed, it is shown that the various boundary conditions are equivalent to each other, and the surface charge, which can be used in studying the screening of the polar charges, can be precisely solved even if only the conduction band energy is correctly known at the surface. Finally, through the calculations on an AlGaN/GaN heterostructure with typical structure parameters by the coupled Schr(o)dinger-Poisson model under the various boundary conditions, the correctness of the above analyses are validated.
Su, Zhu; Jin, Guoyong; Ye, Tiangui
2016-06-01
The paper presents a unified solution for free and transient vibration analyses of a functionally graded piezoelectric curved beam with general boundary conditions within the framework of Timoshenko beam theory. The formulation is derived by means of the variational principle in conjunction with a modified Fourier series which consists of standard Fourier cosine series and supplemented functions. The mechanical and electrical properties of functionally graded piezoelectric materials (FGPMs) are assumed to vary continuously in the thickness direction and are estimated by Voigt’s rule of mixture. The convergence, accuracy and reliability of the present formulation are demonstrated by comparing the present solutions with those from the literature and finite element analysis. Numerous results for FGPM beams with different boundary conditions, geometrical parameters as well as material distributions are given. Moreover, forced vibration of the FGPM beams subjected to dynamic loads and general boundary conditions are also investigated.
Pseudoscalar mesons in a finite cubic volume with twisted boundary conditions
Colangelo, Gilberto; Vaghi, Alessio
2016-07-01
We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We first apply chiral perturbation theory in the p-regime and calculate the corrections for masses, decay constants, pseudoscalar coupling constants and form factors at next-to-leading order. We show that the Feynman-Hellmann theorem and the relevant Ward-Takahashi identity are satisfied. We then derive asymptotic formulae à la Lüscher for twisted boundary conditions. We show that chiral Ward identities for masses and decay constants are satisfied by the asymptotic formulae in finite volume as a consequence of infinite-volume Ward identities. Applying asymptotic formulae in combination with chiral perturbation theory we estimate corrections beyond next-to-leading order for twisted boundary conditions.
Twist-averaged boundary conditions for nuclear pasta Hartree-Fock calculations
Schuetrumpf, B
2015-01-01
Background: Nuclear pasta phases, present in the inner crust of neutron stars, are associated with nucleonic matter at sub-saturation densities arranged in regular shapes. Those complex phases, residing in a layer which is approximately 100 m thick, impact many features of neutron stars. Theoretical quantum-mechanical simulations of nuclear pasta are usually carried out in finite 3D boxes assuming periodic boundary conditions (PBC). The resulting solutions are affected by spurious finite-size effects. Purpose: In order to remove spurious finite-size effects, it is convenient to employ twist-averaged boundary conditions (TABC) used in condensed matter, nuclear matter, and lattice QCD applications. In this work, we study the effectiveness of TABC in the context of pasta phases simulations within nuclear density functional theory. Methods: We perform Skyrme-Hartree-Fock calculations in three dimensions by implementing Bloch boundary conditions. The TABC averages are obtained by means of Gauss-Legendre integratio...
Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions
Directory of Open Access Journals (Sweden)
Danxia Wang
2015-01-01
Full Text Available Simultaneously, considering the viscous effect of material, damping of medium, and rotational inertia, we study a kind of more general Kirchhoff-type extensible beam equation utt-uxxtt+uxxxx-σ(∫0l(ux2dxuxx-ϕ(∫0l(ux2dxuxxt=q(x, in [0,L]×R+ with the structural damping and the rotational inertia term. Little attention is paid to the longtime behavior of the beam equation under nonlinear boundary conditions. In this paper, under nonlinear boundary conditions, we prove not only the existence and uniqueness of global solutions by prior estimates combined with some inequality skills, but also the existence of a global attractor by the existence of an absorbing set and asymptotic compactness of corresponding solution semigroup. In addition, the same results also can be proved under the other nonlinear boundary conditions.
Feshchenko, R M
2016-01-01
In this paper exact 1D transparent boundary conditions (TBC) for the 2D parabolic wave equation with a linear or a quadratic dependence of the dielectric permittivity on the transversal coordinate are reported. Unlike the previously derived TBCs they contain only elementary functions. The obtained boundary conditions can be used to numerically solve the 2D parabolic equation describing the propagation of light in weakly bent optical waveguides and fibers including waveguides with variable curvature. They also are useful when solving the equivalent 1D Schr\\"odinger equation with a potential depending linearly or quadratically on the coordinate. The prospects and problems of discretization of the derived transparent boundary conditions are discussed.