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...
Stokes equations with penalised slip boundary conditions
Dione, Ibrahima; Tibirna, Cristian; Urquiza, José
2013-07-01
We consider the finite-element approximation of Stokes equations with slip boundary conditions imposed with the penalty method. In the case of a smooth curved boundary, our numerical results suggest that curved finite elements, regularised normal vectors or reduced integration techniques can be used to avoid a Babuska's-type paradox and ensure the convergence of finite-element approximations to the exact solution. Convergence orders with these remedies are also compared.
Modelling classroom conditions with different boundary conditions
DEFF Research Database (Denmark)
Marbjerg, Gerd Høy; Jeong, Cheol-Ho; Brunskog, Jonas
2014-01-01
A model that combines image source modelling and acoustical radiosity with complex boundary condition, thus including phase shifts on reflection has been developed. The model is called PARISM (Phased Acoustical Radiosity and Image Source Model). It has been developed in order to be able to model...... are done using different boundary conditions in order to investigate the influence of phase shifts in reflections, the angle dependence of the reflection coefficient and the scattering coefficient. The focus of the simulations is to investigate the influence of the boundary condition on room acoustic...
Borstnik, Norma Susana Mankoc
2008-01-01
The genuine Kaluza-Klein-like theories--with no fields in addition to gravity--have difficulties with the existence of massless spinors after the compactification of some space dimensions \\cite{witten}. We proposed in previous paper a boundary condition for spinors in d=(1+5) compactified on a flat disk that ensures masslessness of spinors (with all positive half integer charges) in d=(1+3) as well as their chiral coupling to the corresponding background gauge gravitational field. In this paper we study the same toy model, proposing a boundary condition allowing a massless spinor of one handedness and only one charge (1/2) and infinitely many massive spinors of the same charge, allowing disc to be curved. We define the operator of momentum to be Hermitean on the vector space of spinor states--the solutions on a disc with the boundary.
On filter boundary conditions in topology optimization
DEFF Research Database (Denmark)
Clausen, Anders; Andreassen, Erik
2017-01-01
Most research papers on topology optimization involve filters for regularization. Typically, boundary effects from the filters are ignored. Despite significant drawbacks the inappropriate homogeneous Neumann boundary conditions are used, probably because they are trivial to implement. In this paper...
Boundary Conditions of Methamphetamine Craving
Lopez, Richard B.; Onyemekwu, Chukwudi; Hart, Carl L.; Ochsner, Kevin N.; Kober, Hedy
2015-01-01
Methamphetamine use has increased significantly and become a global health concern. Craving is known to predict methamphetamine use and relapse following abstinence. Some have suggested that cravings are automatic, generalized, and uncontrollable, but experimental work addressing these claims is lacking. In two exploratory studies we tested the boundary conditions of methamphetamine craving by asking: (1) is craving specific to users’ preferred route of administration? and (2) can craving be regulated by cognitive strategies? Two groups of methamphetamine users were recruited. In Study 1, participants were grouped by their preferred route of administration (intranasal vs. smoking), and rated their craving in response to photographs and movies depicting methamphetamine use (via the intranasal vs. smoking route). In Study 2, methamphetamine smokers implemented cognitive regulation strategies while viewing photographs depicting methamphetamine smoking. Strategies involved either focusing on the positive aspects of smoking methamphetamine or the negative consequences of doing so – the latter strategy based on treatment protocols for addiction. In Study 1, we found a significant interaction between group and route of administration, such that participants who preferred to smoke methamphetamine reported significantly stronger craving for smoking stimuli, whereas those who preferred the intranasal route reported stronger craving for intranasal stimuli. In Study 2, participants reported significantly lower craving when focusing on the negative consequences associated with methamphetamine use. Taken together, these findings suggest that strength of craving for methamphetamine is moderated by users’ route of administration and can be reduced by cognitive strategies. This has important theoretical, methodological, and clinical implications. PMID:26302338
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....
Green's functions for Neumann boundary conditions
Franklin, Jerrold
2012-01-01
Green's functions for Neumann boundary conditions have been considered in Math Physics and Electromagnetism textbooks, but special constraints and other properties required for Neumann boundary conditions have generally not been noticed or treated correctly. In this paper, we derive an appropriate Neumann Green's function with these constraints and properties incorporated.
Global boundary conditions for the Dirac operator
Falomir, H A
1997-01-01
Ellipticity of boundary value problems is characterized in terms of the Calderon projector. The presence of topological obstructions for the chiral Dirac operator under local boundary conditions in even dimension is discussed. Functional determinants for Dirac operators on manifolds with boundary are considered. The functional determinant for a Dirac operator on a bidimensional disk, in the presence of an Abelian gauge field and subject to global boundary conditions of the type introduced by Atiyah-Patodi-Singer, is evaluated. The relationship with the index theorem is also commented.
Implementation of Boundary Condition to THALES Code
Energy Technology Data Exchange (ETDEWEB)
Jang, Beomjun; Chun, Chong Kuk; Park, Ho Young; Woo, Hae-Seuk [KEPCO Nuclear Fuel, Daejeon (Korea, Republic of)
2016-10-15
The boundary condition of momentum equation of THALES code utilizes the exit pressure boundary to solve the elliptic partial difference momentum equations. This method is the same as the most of the subchannel analysis codes. Other codes such as VIPRE utilize the uniform pressure distribution as outlet boundary condition. In this case, uniform inlet flow rate is assumed. In order to test the core flow field regarding the boundary conditions, analysis was performed for two core conditions. One condition is nominal plant operating condition. In this paper, generic THALES power distribution is used. For nominal operation case, there are no different results depending on the type of outlet pressure boundary condition. But low-power and high-peaking case, density difference for lateral direction becomes large due to high peaking power of core. Since density change causes pressure change, In this case, uniform outlet pressure distribution can't be assumed anymore. Design outlet pressure distribution is measured at nominal core condition. Therefore, design outlet pressure distribution also can't be used due to the difference in core power and flow rate. As a result, it is reasonable that neumann boundary condition is applied in low-power and high peaking core condition including various accident condition.
Symmetries and Boundary Conditions with a Twist
Zawadzki, Krissia; D'Amico, Irene; Oliveira, Luiz N.
2017-10-01
Interest in finite-size systems has risen in the last decades, due to the focus on nanotechnological applications and because they are convenient for numerical treatment that can subsequently be extrapolated to infinite lattices. Independently of the envisioned application, special attention must be given to boundary condition, which may or may not preserve the symmetry of the infinite lattice. Here, we present a detailed study of the compatibility between boundary conditions and conservation laws. The conflict between open boundary conditions and momentum conservation is well understood, but we examine other symmetries, as well: we discuss gauge invariance, inversion, spin, and particle-hole symmetry and their compatibility with open, periodic, and twisted boundary conditions. In the interest of clarity, we develop the reasoning in the framework of the one-dimensional half-filled Hubbard model, whose Hamiltonian displays a variety of symmetries. Our discussion includes analytical and numerical results. Our analytical survey shows that, as a rule, boundary conditions break one or more symmetries of the infinite-lattice Hamiltonian. The exception is twisted boundary condition with the special torsion Θ = πL/2, where L is the lattice size. Our numerical results for the ground-state energy at half-filling and the energy gap for L = 2-7 show how the breaking of symmetry affects the convergence to the L → ∞ limit. We compare the computed energies and gaps with the exact results for the infinite lattice drawn from the Bethe-Ansatz solution. The deviations are boundary-condition dependent. The special torsion yields more rapid convergence than open or periodic boundary conditions. For sizes as small as L = 7, the numerical results for twisted condition are very close to the L → ∞ limit. We also discuss the ground-state electronic density and magnetization at half filling under the three boundary conditions.
Reconstruction of boundary conditions from internal conditions using viability theory
Hofleitner, Aude
2012-06-01
This article presents a method for reconstructing downstream boundary conditions to a HamiltonJacobi partial differential equation for which initial and upstream boundary conditions are prescribed as piecewise affine functions and an internal condition is prescribed as an affine function. Based on viability theory, we reconstruct the downstream boundary condition such that the solution of the Hamilton-Jacobi equation with the prescribed initial and upstream conditions and reconstructed downstream boundary condition satisfies the internal value condition. This work has important applications for estimation in flow networks with unknown capacity reductions. It is applied to urban traffic, to reconstruct signal timings and temporary capacity reductions at intersections, using Lagrangian sensing such as GPS devices onboard vehicles.
Boundary conditions for the gravitational field
Winicour, Jeffrey
2012-06-01
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation of Einstein's equations and a tetrad formulation of the Einstein-Bianchi system. However, a universal approach valid for other formulations is not in hand. In particular, there is no satisfactory boundary theory for the 3+1 formulations which have been highly successful in binary black hole simulation. I discuss the underlying problems that make the initial-boundary-value problem much more complicated than the Cauchy problem. I review the progress that has been made and the important open questions that remain. Science is a differential equation. Religion is a boundary condition. (Alan Turing, quoted in J D Barrow, ‘Theories of Everything’)
Boundary conditions in CO5BOLD
Freytag, Bernd
The declaration of boundary conditions is a crucial step in the setup of a CO5BOLD simulation (and many others) due to the physical nature of the problem, that is reflected in the mathematical description by partial differential equations, discrete versions of which are integrated by the numerical solver(s). While parameters controlling the flux of energy through the computational box are most important for all simulations of convective flows, the detailed specifications describing the behavior of energy, gas and dust densities, velocities, and magnetic fields at or just beyond the boundaries influence the flow, dynamics, and stratification within the box. Recent refinements of the treatment of boundary conditions in CO5BOLD resulted in reliably working implementations of open and closed versions for top, bottom, and ``inner'' boundaries even under conditions with strong velocity fields (waves, shocks, or downdrafts). They are implemented and available in the current version of CO5BOLD - but have to be activated properly with parameters adapted to the type of the star under consideration (by defining for instance the depth of the damping layers for the closed-bottom boundary or by specifying the damping constants for the open-bottom boundary).
Antireflective Boundary Conditions for Deblurring Problems
Directory of Open Access Journals (Sweden)
Marco Donatelli
2010-01-01
Full Text Available This survey paper deals with the use of antireflective boundary conditions for deblurring problems where the issues that we consider are the precision of the reconstruction when the noise is not present, the linear algebra related to these boundary conditions, the iterative and noniterative regularization solvers when the noise is considered, both from the viewpoint of the computational cost and from the viewpoint of the quality of the reconstruction. In the latter case, we consider a reblurring approach that replaces the transposition operation with correlation. For many of the considered items, the anti-reflective algebra coming from the given boundary conditions is the optimal choice. Numerical experiments corroborating the previous statement and a conclusion section end the paper.
parabolic equation with integral boundary condition
Directory of Open Access Journals (Sweden)
M. Denche
2001-01-01
Full Text Available In this paper we study the problem of control by the initial conditions of the heat equation with an integral boundary condition. This problem is ill-posed. Perturbing the final condition we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.
Functional differential inclusions with integral boundary conditions
Directory of Open Access Journals (Sweden)
Mouffak Benchohra
2007-07-01
Full Text Available In this paper, we investigate the existence of solutions for a class of second order functional differential inclusions with integral boundary conditions. By using suitable fixed point theorems, we study the case when the right hand side has convex as well as nonconvex values.
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...
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.
Absorbing boundary conditions for inertial random processes
Energy Technology Data Exchange (ETDEWEB)
Masoliver, J.; Porra, J.M. [Departament de Fisica Fonamental, Universitat de Barcelona, Diagonal, 647, 08028-Barcelona (Spain); Lindenberg, K. [Department of Chemistry and Biochemistry and Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0340 (United States)
1996-12-01
A recent paper by J. Heinrichs [Phys. Rev. E {bold 48}, 2397 (1993)] presents analytic expressions for the first-passage times and the survival probability for a particle moving in a field of random correlated forces. We believe that the analysis there is flawed due to an improper use of boundary conditions. We compare that result, in the white noise limit, with the known exact expression of the mean exit time. {copyright} {ital 1996 The American Physical Society.}
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.
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.
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.
Characteristic Boundary Conditions for ARO-1
1983-05-01
8217--’--’~,oc=~ AEDC-TR-82-28 Characteristic Boundary Conditions for ARO-1 Karl R. Kneile and Donald C. Todd Sverdrup Technology, Inc. and James...REPORT DOCUMENTATION PAGE I i I R E P O R T NUMBER 12 GOVT ACCESSION NO. 3 I AEDC-TR-82-28 4. T I T L E (and Subtitle:, CHARACTERISTIC BOU~DARY...ARO-I program 20. A B S T R A C T ( C ~ t i n ~ ~ reverme side tf n e c o s e a ~ and I d e n t l ~ ~ b lock n u m b o ~ Characteristic
Scalar boundary conditions in hyperscaling violating geometry
Directory of Open Access Journals (Sweden)
Jian-Pin Wu
2016-02-01
Full Text Available We study the possible boundary conditions of scalar field modes in a hyperscaling violation (HV geometry with Lifshitz dynamical exponent z (z≥1 and hyperscaling violation exponent θ (θ≠0. For the case with θ>0, we show that in the parameter range 1≤z≤2, −z+d−12, −z+d−10, which has been addressed in Ref. [1]. Meanwhile, we also carry out the parallel investigation in the case with θ0, only one type is available.
Eigenvalue inequalities for the Laplacian with mixed boundary conditions
Lotoreichik, Vladimir; Rohleder, Jonathan
2017-07-01
Inequalities for the eigenvalues of the (negative) Laplacian subject to mixed boundary conditions on polyhedral and more general bounded domains are established. The eigenvalues subject to a Dirichlet boundary condition on a part of the boundary and a Neumann boundary condition on the remainder of the boundary are estimated in terms of either Dirichlet or Neumann eigenvalues. The results complement several classical inequalities between Dirichlet and Neumann eigenvalues due to Pólya, Payne, Levine and Weinberger, Friedlander, and others.
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 domain wall boundary conditions for the XXZ spin Hamiltonian
DEFF Research Database (Denmark)
Orlando, Domenico; Reffert, Susanne; Reshetikhin, Nicolai
In this note, we derive the spectrum of the infinite quantum XXZ spin chain with domain wall boundary conditions. The eigenstates are constructed as limits of Bethe states for the finite XXZ spin chain with quantum sl(2) invariant boundary conditions.......In this note, we derive the spectrum of the infinite quantum XXZ spin chain with domain wall boundary conditions. The eigenstates are constructed as limits of Bethe states for the finite XXZ spin chain with quantum sl(2) invariant boundary conditions....
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...
Development of a Discrete Mass Inflow Boundary Condition for MFIX
Directory of Open Access Journals (Sweden)
Jordan Musser
2011-02-01
Full Text Available MFIX (Multiphase Flow with Interphase eXchanges is an open source software package developed by the National Energy Technology Laboratory (NETL used for modeling the chemical reactions, heat transfer, and hydrodynamics of fluid-solid systems. Currently, the stable publically available release of MFIX does not include a discrete mass inflow boundary condition (DMIBC for its discrete element method (DEM package. Inflow boundary conditions are useful for simulating systems where particles are consumed through chemical reactions and an incoming feed is necessary to sustain the reaction. To implement the DMIBC an inlet staging area is designated outside the computational domain and particles are passed through the wall region associated with the inlet. Forces incurred on entering particles, generated from collisions with particles already in the system, are ignored whereas, particles already in the system respond to contact forces and react accordingly, moving away from the inlet. This approach prevents any unphysical overlap between new and existing particles. It also ensures that particles entering the system will enter the computational domain regardless of opposing forces. Once an incoming particle is fully within the domain, it reacts appropriately to any and all contact force. This approach for a DMIBC has been implemented and is available within the current development version of MFIX.
The Stochastic Ising Model with the Mixed Boundary Conditions
Directory of Open Access Journals (Sweden)
Wang Jun
2009-01-01
Full Text Available Abstract We estimate the spectral gap of the two-dimensional stochastic Ising model for four classes of mixed boundary conditions. On a finite square, in the absence of an external field, two-sided estimates on the spectral gap for the first class of (weak positive boundary conditions are given. Further, at inverse temperatures , we will show lower bounds of the spectral gap of the Ising model for the other three classes mixed boundary conditions.
Boundary Conditions, Data Assimilation, and Predictability in Coastal Ocean Models
National Research Council Canada - National Science Library
Samelson, Roger M; Allen, John S; Egbert, Gary D; Kindle, John C; Snyder, Chris
2007-01-01
...: The specific objectives of this research are to determine the impact on coastal ocean circulation models of open ocean boundary conditions from Global Ocean Data Assimilation Experiment (GODAE...
Quantum “violation” of Dirichlet boundary condition
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.
Quantum “violation” of Dirichlet boundary condition
Energy Technology Data Exchange (ETDEWEB)
Park, I.Y., E-mail: inyongpark05@gmail.com
2017-02-10
Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the ‘violation’ of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
[Lation in ensuring the sanitary-and-epidemiological well-being under the present conditions].
Filatov, N N; Ivanenko, A V; Khizgiiaev, V I; Safonkina, S G; Beliavskiĭ, A R; Kicha, D I
2009-01-01
The paper describes the basic principles in and approaches to the state regulation in ensuring the sanitary-and-epidemiological well-being. The necessity of enhancing the role of state regulation in ensuring the sanitary-and-epidemiological well-being stems from the intensive development of marketing relations and the complicated realization of the state role in the protection of consumers' rights and human well-being. The investigations provide evidence for the basic tasks of the sanitary-and-epidemiological service of Moscow under the specific conditions of the megalopolis.
Directory of Open Access Journals (Sweden)
Rai Nath Kabindra Rajeev
2009-01-01
Full Text Available In this paper, the solution of the one dimensional moving boundary problem with periodic boundary conditions is obtained with the help of variational iterational method. By using initial and boundary values, the explicit solutions of the equations have been derived, which accelerate the rapid convergence of the series solution. The method performs extremely well in terms of efficiency and simplicity. The temperature distribution and the position of moving boundary are evaluated and numerical results are presented graphically.
Stationary solutions and Neumann boundary conditions in the Sivashinsky equation.
Denet, Bruno
2006-09-01
New stationary solutions of the (Michelson) Sivashinsky equation of premixed flames are obtained numerically in this paper. Some of these solutions, of the bicoalescent type recently described by Guidi and Marchetti, are stable with Neumann boundary conditions. With these boundary conditions, the time evolution of the Sivashinsky equation in the presence of a moderate white noise is controlled by jumps between stationary solutions.
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....
Boundary Conditions and Predictions of Quantum Cosmology
Page, Don N.
2008-09-01
A complete model of the universe needs at least three parts: (1) a complete set of physical variables and dynamical laws for them, (2) the correct solution of the dynamical laws, and (3) the connection with conscious experience. In quantum cosmology, item (1) is often called a 'theory of everything,' and item (2) is the quantum state of the cosmos. Hartle and Hawking have made the 'no-boundary' proposal, that the wavefunction of the universe is given by a path integral over all compact Euclidean 4-dimensional geometries and matter fields that have the 3-dimensional argument of the wavefunction on their one and only boundary. This proposal has had several partial successes, mainly when one takes the zero-loop approximation of summing over a small number of complex extrema of the action. However, it has also been severely challenged by an argument by Susskind.
GenCade Lateral Boundary Conditions
2017-01-01
from marine corals, algae , and other organisms. ................... 18 Figure 5. The Complementary Error Function...Eckstein was Deputy Director of CHL, and José E. Sánchez was Director of CHL. COL Bryan S. Green was ERDC Commander. Dr. Jeffery P. Holland was ERDC... benefit of producing perfect agreement at this boundary during model calibration. However, it would be serendipitous if this procedure also produced
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.
Zhou, Guofeng; Wang, Limin; Wang, Xiaowei; Ge, Wei
2011-12-01
Many investigators have coupled the Lees-Edwards boundary conditions (LEBCs) and suspension methods in the framework of the lattice Boltzmann method to study the pure bulk properties of particle-fluid suspensions. However, these suspension methods are all link-based and are more or less exposed to the disadvantages of violating Galilean invariance. In this paper, we have coupled LEBCs with a node-based suspension method, which is demonstrated to be Galilean invariant in benchmark simulations. We use the coupled algorithm to predict the viscosity of a particle-fluid suspension at very low Reynolds number, and the simulation results are in good agreement with the semiempirical Krieger-Dougherty formula.
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.
Exponential reduction of finite volume effects with twisted boundary conditions
Cherman, Aleksey; Sen, Srimoyee; Wagman, Michael L.; Yaffe, Laurence G.
2017-04-01
Flavor-twisted boundary conditions can be used for exponential reduction of finite volume artifacts in flavor-averaged observables in lattice QCD calculations with S U (Nf) 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 Nc 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.
Boundary conditions for potentials at a plane interface
Energy Technology Data Exchange (ETDEWEB)
Tsai, W.Y.; DeRaad, L.L. Jr.
1985-01-01
For the case of plane interfaces, it is shown that Maxwell's equations can be solved by use of potentials that satisfy a set of decoupled boundary conditions. This is accomplished by exploiting the gauge freedom that is intrinsic to potentials. It is shown that it is always possible to choose a special Lorentz gauge such that the boundary conditions can be restated as the continuity of the vector and scalar potentials as well as the normal derivative of the tangential components of the vector potential. The advantages of this new set of decoupled boundary conditions are demonstrated by three simple examples.
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 solutions...... to this problem exist, most of them have high computational costs, and stability cannot always be ensured. In this work, a solution is proposed based on "mixing modelling strategies"; this involves separating the FDTD mesh and the boundary conditions (a digital filter representation of the impedance...
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
Directory of Open Access Journals (Sweden)
Nieto JuanJ
2009-01-01
Full Text Available This paper deals with some existence results for a boundary value problem involving a nonlinear integrodifferential equation of fractional order with integral boundary conditions. Our results are based on contraction mapping principle and Krasnosel'skiĭ's fixed point theorem.
Directory of Open Access Journals (Sweden)
John Graef
2013-09-01
Full Text Available The authors consider a nonlinear fractional boundary value problem with the Dirichlet boundary condition. An associated Green's function is constructed as a series of functions by applying spectral theory. Criteria for the existence and uniqueness of solutions are obtained based on it.
Refined impedance boundary conditions on a semitransparent periodically loaded structure
Tereshin, O. N.; Dvurechenskii, V. D.
1987-09-01
Improved impedance boundary conditions are presented for a semitransparent periodically loaded structure, i.e., a periodic array of conductors in which reactive loads are inserted. Structures of this sort find application in antenna-feed devices.
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.
Lyapunov Based Estimation of Flight Stability Boundary under Icing Conditions
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Binbin Pei
2017-01-01
Full Text Available Current fight boundary of the envelope protection in icing conditions is usually defined by the critical values of state parameters; however, such method does not take the interrelationship of each parameter and the effect of the external disturbance into consideration. This paper proposes constructing the stability boundary of the aircraft in icing conditions through analyzing the region of attraction (ROA around the equilibrium point. Nonlinear icing effect model is proposed according to existing wind tunnel test results. On this basis, the iced polynomial short period model can be deduced further to obtain the stability boundary under icing conditions using ROA analysis. Simulation results for a series of icing severity demonstrate that, regardless of the icing severity, the boundary of the calculated ROA can be treated as an estimation of the stability boundary around an equilibrium point. The proposed methodology is believed to be a promising way for ROA analysis and stability boundary construction of the aircraft in icing conditions, and it will provide theoretical support for multiple boundary protection of icing tolerant flight.
Time-domain boundary conditions for outdoor ground surfaces
Collier, Sandra L.; Ostashev, Vladimir E.; Wilson, D. Keith; Marlin, David H.
2003-10-01
Finite-difference time-domain techniques are promising for detailed dynamic simulations of sound propagation in complex atmospheric environments. Success of such simulations requires the development of new techniques to accurately handle the reflective and absorptive properties of a porous ground. One method of treating the ground boundary condition in the time domain [Salomons et al., Acta Acust. 88, 483-492 (2002)] is to use modified fluid dynamic equations, where the ground is considered as a porous medium described by its physical properties. However, this approach significantly increases computation time, as the domain must be extended into the ground and a large number of grid points are needed. Standard impedance models for the ground boundary condition are frequency-domain models, which generally are non-causal [Y. H. Berthelot, J. Acoust. Soc. Am. 109, 1736-1739 (2001)]. The development of a time-domain boundary condition from these models requires removing the singularity from the impedance equation when transforming from the frequency domain to the time domain. Alternatively, as the impedance boundary condition is a flux equation, a time-domain boundary condition can be derived from first principles, using the physical properties of the ground. We report on our development of a time-domain ground boundary condition.
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.
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.
DNS of Turbulent Boundary Layers under Highenthalpy Conditions
Duan, Lian; Martín, Pino
2010-11-01
To study real-gas effects and turbulence-chemistry interaction, direct numerical simulations (DNS) of hypersonic boundary layers are conducted under typical hypersonic conditions. We consider the boundary layer on a lifting-body consisting of a flat plate at an angle of attack, which flies at altitude 30km with a Mach number 21. Two different inclined angles, 35^o and 8^o, are considered,representing blunt and slender bodies. Both noncatalytic and supercatalytic wall conditions are considered. The DNS data are studied to assess the validity of Morkovin's hypothesis, the strong Reynolds analogy, as well as the behaviors of turbulence structures under high-enthalpy conditions.Relative to low-enthalpy conditions [1], significant differences in typical scalings are observed. [4pt] [1] L. Duan and I. Beekman and M. P. Mart'in, Direct numerical simulation of hypersonic turbulent boundary layers. Part 2: Effect of temperature, J. Fluid Mech. 655 (2010), 419-445.
Directory of Open Access Journals (Sweden)
Hussein A. H. Salem
2013-01-01
Full Text Available The object of this paper is to investigate the existence of a class of solutions for some boundary value problems of fractional order with integral boundary conditions. The considered problems are very interesting and important from an application point of view. They include two, three, multipoint, and nonlocal boundary value problems as special cases. We stress on single and multivalued problems for which the nonlinear term is assumed only to be Pettis integrable and depends on the fractional derivative of an unknown function. Some investigations on fractional Pettis integrability for functions and multifunctions are also presented. An example illustrating the main result is given.
Boundary-value problems for second-order differential operators with nonlocal boundary conditions
Directory of Open Access Journals (Sweden)
Mohamed Denche
2007-04-01
Full Text Available In this paper, we study a second-order differential operator combining weighting integral boundary condition with another two-point boundary condition. Under certain conditions on the weighting functions, called regular and non regular cases, we prove that the resolvent decreases with respect to the spectral parameter in $L^{p}(0,1$, but there is no maximal decrease at infinity for $p>1$. Furthermore, the studied operator generates in $L^{p}(0,1 $, an analytic semi group for $p=1$ in the regular case, and an analytic semi group with singularities for $p>1$, in both cases, and for $p=1$, in the non regular case only. The obtained results are then used to show the correct solvability of a mixed problem for parabolic partial differential equation with non regular boundary conditions.
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.
Superradiance in the BTZ black hole with Robin boundary conditions
Dappiaggi, Claudio; Ferreira, Hugo R. C.; Herdeiro, Carlos A. R.
2018-03-01
We show the existence of superradiant modes of massive scalar fields propagating in BTZ black holes when certain Robin boundary conditions, which never include the commonly considered Dirichlet boundary conditions, are imposed at spatial infinity. These superradiant modes are defined as those solutions whose energy flux across the horizon is towards the exterior region. Differently from rotating, asymptotically flat black holes, we obtain that not all modes which grow up exponentially in time are superradiant; for some of these, the growth is sourced by a bulk instability of AdS3, triggered by the scalar field with Robin boundary conditions, rather than by energy extraction from the BTZ black hole. Thus, this setup provides an example wherein Bosonic modes with low frequency are pumping energy into, rather than extracting energy from, a rotating black hole.
Vibration Analysis of Annular Sector Plates under Different Boundary Conditions
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Dongyan Shi
2014-01-01
Full Text Available An analytical framework is developed for the vibration analysis of annular sector plates with general elastic restraints along each edge of plates. Regardless of boundary conditions, the displacement solution is invariably expressed as a new form of trigonometric expansion with accelerated convergence. The expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. This work allows a capability of modeling annular sector plates under a variety of boundary conditions and changing the boundary conditions as easily as modifying the material properties or dimensions of the plates. Of equal importance, the proposed approach is universally applicable to annular sector plates of any inclusion angles up to 2π. The reliability and accuracy of the current method are adequately validated through numerical examples.
Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions
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Ciprian G. Gal
2017-01-01
Full Text Available Given a bounded domain Ω⊂RN with a Lipschitz boundary ∂Ω and p,q∈(1,+∞, we consider the quasilinear elliptic equation -Δpu+α1u=f in Ω complemented with the generalized Wentzell-Robin type boundary conditions of the form bx∇up-2∂nu-ρbxΔq,Γu+α2u=g on ∂Ω. In the first part of the article, we give necessary and sufficient conditions in terms of the given functions f, g and the nonlinearities α1, α2, for the solvability of the above nonlinear elliptic boundary value problems with the nonlinear boundary conditions. In other words, we establish a sort of “nonlinear Fredholm alternative” for our problem which extends the corresponding Landesman and Lazer result for elliptic problems with linear homogeneous boundary conditions. In the second part, we give some additional results on existence and uniqueness and we study the regularity of the weak solutions for these classes of nonlinear problems. More precisely, we show some global a priori estimates for these weak solutions in an L∞-setting.
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Paul Eloe
2002-01-01
Full Text Available The method of quasilinearization for nonlinear impulsive differential equations with linear boundary conditions is studied. The boundary conditions include periodic boundary conditions. It is proved the convergence is quadratic.
Function Substitution in Partial Differential Equations: Nonhomogeneous Boundary Conditions
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T. V. Oblakova
2017-01-01
Full Text Available The paper considers a mixed initial-boundary value problem for a parabolic equation with nonhomogeneous boundary conditions. The classical approach to search for analytical solution of such problems in the first phase involves variable substitution, leading to a problem with homogeneous boundary conditions. Reference materials [1] give, as a rule, the simplest types of variable substitutions where new and old unknown functions differ by a term, linear in the spatial variable. The form of this additive term depends on the type of the boundary conditions, but is in no way related to the equation under consideration. Moreover, in the case of the second boundary-value problem, it is necessary to use a quadratic additive, since a linear substitution for this type of conditions may be unavailable. The courseware [2] - [4], usually, ends only with the first boundary-value problem generally formulated.The paper considers 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 substitution for boundary conditions of any type is proved by the example of a non-stationary heat-transfer equation with the heat exchange available with the surrounding medium. In this case, the additive 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 substitution in comparison with the traditional linear (or quadratic one include a much simpler structure of the solution obtained. Just the described approach allows us to obtain a solution with a clearly distinguished stationary component, in case a stationarity occurs, for
Development of the innovative food industry in the conditions of ensuring food security
Berdiev S.
2017-01-01
The purpose of this article is to ensure the safety of food and through the development of innovative food industry and learning to increase the production of food. Work to ensure food security of the Republic of Uzbekistan has its own characteristics and analysis of trends and problems identified in this area. As well as ensuring the safety of food and food industry offer based on the priority directions of scientific and practical recommendations developed.
Boundary conditions for hyperbolic systems of partial differentials equations.
Guaily, Amr G; Epstein, Marcelo
2013-07-01
An easy-to-apply algorithm is proposed to determine the correct set(s) of boundary conditions for hyperbolic systems of partial differential equations. The proposed approach is based on the idea of the incoming/outgoing characteristics and is validated by considering two problems. The first one is the well-known Euler system of equations in gas dynamics and it proved to yield set(s) of boundary conditions consistent with the literature. The second test case corresponds to the system of equations governing the flow of viscoelastic liquids.
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.
Maxwell boundary condition and velocity dependent accommodation coefficient
Energy Technology Data Exchange (ETDEWEB)
Struchtrup, Henning, E-mail: struchtr@uvic.ca [Department of Mechanical Engineering, University of Victoria, Victoria, British Columbia V8W 2Y2 (Canada)
2013-11-15
A modification of Maxwell's boundary condition for the Boltzmann equation is developed that allows to incorporate velocity dependent accommodation coefficients into the microscopic description. As a first example, it is suggested to consider the wall-particle interaction as a thermally activated process with three parameters. A simplified averaging procedure leads to jump and slip boundary conditions for hydrodynamics. Coefficients for velocity slip, temperature jump, and thermal transpiration flow are identified and compared with those resulting from the original Maxwell model and the Cercignani-Lampis model. An extension of the model leads to temperature dependent slip and jump coefficients.
Maxwell boundary condition and velocity dependent accommodation coefficient
Struchtrup, Henning
2013-11-01
A modification of Maxwell's boundary condition for the Boltzmann equation is developed that allows to incorporate velocity dependent accommodation coefficients into the microscopic description. As a first example, it is suggested to consider the wall-particle interaction as a thermally activated process with three parameters. A simplified averaging procedure leads to jump and slip boundary conditions for hydrodynamics. Coefficients for velocity slip, temperature jump, and thermal transpiration flow are identified and compared with those resulting from the original Maxwell model and the Cercignani-Lampis model. An extension of the model leads to temperature dependent slip and jump coefficients.
Non-local boundary conditions and internal gravity wave generation
Bulatov, Vitaly V
2010-01-01
This work focuses on the mathematical modeling of wave dynamics in a stratified medium. Non-local absorbing boundary conditions are considered based on the two following assumptions: (i) a linear theory can be applied at large distances from perturbation sources; and (ii) there are no other sources of wave disturbance outside the mixing zone in the stratified medium. The boundary conditions considered in this paper allowed us to describe the diverging internal gravity waves generated by the mixing region in a stratified medium.
Weak imposition of the slip boundary condition on curved boundaries for Stokes flow
Urquiza, José M.; Garon, André; Farinas, Marie-Isabelle
2014-01-01
We study the finite element approximation of two methods to weakly impose a slip boundary condition for incompressible fluid flows: the Lagrange multiplier method and Nitsche's method. For each method, we can distinguish several formulations depending on the values of some real parameters. In the case of a spatial domain with a polygonal or polyhedral boundary, we prove convergence results of their finite element approximations, extending previous results of Verfürth [33] and we show numerical results confirming them. In the case of a spatial domain with a smooth curved boundary, numerical results show that approximations computed on polygonal domains approximating the original domain may not converge to the exact solution, depending on the values of the aforementioned parameters and on the finite element discretization. These negative results seem to highlight Babuska's like paradox, due to the approximation of the boundary by polygonal ones. In particular, they seem to contradict some of Verfürth's theoretical convergence results.
2010-07-01
... 34 Education 3 2010-07-01 2010-07-01 false How does a grantee ensure that a scholarship recipient understands the terms and conditions of the scholarship before the recipient leaves the teacher preparation... PROGRAM Scholarships § 611.51 How does a grantee ensure that a scholarship recipient understands the terms...
A New Parallel Boundary Condition for Turbulence Simulations in Stellarators
Martin, Mike F.; Landreman, Matt; Dorland, William; Xanthopoulos, Pavlos
2017-10-01
For gyrokinetic simulations of core turbulence, the ``twist-and-shift'' parallel boundary condition (Beer et al., PoP, 1995), which involves a shift in radial wavenumber proportional to the global shear and a quantization of the simulation domain's aspect ratio, is the standard choice. But as this condition was derived under the assumption of axisymmetry, ``twist-and-shift'' as it stands is formally incorrect for turbulence simulations in stellarators. Moreover, for low-shear stellarators like W7X and HSX, the use of a global shear in the traditional boundary condition places an inflexible constraint on the aspect ratio of the domain, requiring more grid points to fully resolve its extent. Here, we present a parallel boundary condition for ``stellarator-symmetric'' simulations that relies on the local shear along a field line. This boundary condition is similar to ``twist-and-shift'', but has an added flexibility in choosing the parallel length of the domain based on local shear consideration in order to optimize certain parameters such as the aspect ratio of the simulation domain.
The No-Slip Boundary Condition in Fluid Mechanics
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 9; Issue 4. The No-Slip Boundary Condition in Fluid Mechanics - 1.The Riddle of Fluid Sticking to the Wall in Flow. Sandeep Prabhakara M D Deshpande. General Article Volume 9 Issue 4 April 2004 pp 50-60 ...
Stress and mixed boundary conditions for two-dimensional ...
Indian Academy of Sciences (India)
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 ...
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...
"Missing" boundary conditions? Discretize first, substitute next, and combine later
Veldman, Arthur E.P.
1990-01-01
A simple approach exists to prevent the need for constructing boundary conditions in situations where they are not explicitly supplied by the original analytical formulation of the problem. An example is the Poisson equation for the pressure in calculations of incompressible flow. Other examples are
Stokes flow with slip and Kuwabara boundary conditions
Indian Academy of Sciences (India)
... 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 ...
Existence of solutions for fractional differential inclusions with boundary conditions
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Dandan Yang
2010-07-01
Full Text Available This article concerns the existence of solutions for fractional-order differential inclusions with boundary-value conditions. The main tools are based on fixed point theorems due to Bohnerblust-Karlin and Leray-Schauder together with a continuous selection theorem for upper semi-continuous multi-valued maps.
Stress and mixed boundary conditions for two-dimensional ...
Indian Academy of Sciences (India)
Abstract. For plate bending and stretching problems in two-dimensional (2D) do- decagonal 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 ...
Mesoscopic Modelling of Heterogeneous Boundary Conditions for Microchannel Flows
Benzi, R.; Biferale, L.; Sbragaglia, M.; Succi, S.; Toschi, F.
2006-01-01
We present a mesoscopic model of the fluid–wall interactions for flows in microchannel geometries. We define a suitable implementation of the boundary conditions for a discrete version of the Boltzmann equations describing a wall-bounded single-phase fluid. We distinguish different slippage
The No-Slip Boundary Condition in Fluid Mechanics
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 9; Issue 5. The No-Slip Boundary Condition in Fluid Mechanics - Solution of the Sticky Problem. Sandeep Prabhakara M D Deshpande. General Article Volume 9 Issue 5 May 2004 pp 61-71 ...
On a stochastic Burgers equation with Dirichlet boundary conditions
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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.
Salesperson improvisation: Antecedents, performance outcomes, and boundary conditions
Yeboah Banin, A.; Boso, N.; Hultman, M.; Souchon, A. L.; Hughes, P; Nemkova, E.
2016-01-01
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. Premised on the idea that not all salesperson behaviors can be pre-scripted and that, increasingly, salespersons must find ways to respond to unexpected but urgent market conditions, this study theorizes the drivers, outcomes and boundary conditions of salesperson improvisation. Using primary data from industrial salespersons, the study examine...
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
Boundary Conditions for a New Type of Design Task
DEFF Research Database (Denmark)
McAloone, Tim C.
2011-01-01
-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...... and knowledge associated with the use of the product is increasingly perceived to be the new design object. But how to organise the design of combined products and services, over expanded time domains and new stakeholder boundaries? The design research community is paying increasing attention to this new design...
Directory of Open Access Journals (Sweden)
Tetiana Bogolib
2016-11-01
Full Text Available The formation of the economy based on knowledge-based innovative economy, new economy, at the present stage of social development is defining the international concept, according to which knowledge play a primary role, and their production is a source of economic growth and competitiveness. The economy is based on knowledge that provides a smart, sustainable and inclusive development. The purpose of the study. Showing that the implementation of the Strategy «Europe 2020», the main directions of the Fourth Industrial Revolution in the Ukraine will be able to provide smart, sustainable, inclusive development of the regions of Ukraine, will help to overcome the crisis and become a source for economic growth. Research methods. In the process of writing were used scientific methods, methods of analysis and synthesis, method of scientific abstraction. The results of the study. Macroeconomic instability has been transformed at the regional level, which led to the deepening of regions differentiation, particularly as it affected old industrial regions, including Donetsk and Luhansk. The crisis of public finances does not allow attracting of financial resources for economic development. As a result of hybrid war, the outflow of foreign investment amounted to 12.6 billion dollars USA. A significant part of the Donetsk and Luhansk regions is completely destroyed. Along with this, it's perfect conditions in order to abandon the old and build new. There are all conditions to implement actively the European strategy «Europe 2020» and the main directions of the Fourth Industrial Revolution to a new stage of economic development, and ensure smart, sustainable and inclusive development of the regions of Ukraine. Conclusions and discussion position. The future of Ukraine and its regions depends on the activity of the Strategy «Europe 2020» and the main directions of the Fourth Industrial Revolution. In Ukraine, in the regions, the main emphasis is on export
On the Derivation of Boundary Conditions for Continuum Dislocation Dynamics
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Thomas Hochrainer
2017-07-01
Full Text Available Continuum dislocation dynamics (CDD is a single crystal strain gradient plasticity theory based exclusively on the evolution of the dislocation state. Recently, we derived a constitutive theory for the average dislocation velocity in CDD in a phase field-type description for an infinite domain. In the current work, so-called rational thermodynamics is employed to obtain thermodynamically consistent boundary conditions for the dislocation density variables of CDD. We find that rational thermodynamics reproduces the bulk constitutive equations as obtained from irreversible thermodynamics. The boundary conditions we find display strong parallels to the microscopic traction conditions derived by Gurtin and Needleman (M.E. Gurtin and A. Needleman, J. Mech. Phys. Solids 53 (2005 1–31 for strain gradient theories based on the Kröner–Nye tensor.
Modeling Groundwater Flow using both Neumann and Dirichlet Boundary Conditions
Zijl, Wouter; El-Rawy, Mustafa; Batelaan, Okke
2013-04-01
In groundwater flow models it is customary to use the recharge rate, obtained from measured precipitation minus run off and evapotranspiration, as the top boundary condition (a Neumann boundary condition). However, as has been emphasized by Tóth (1962; 2009), the topography of the water table offers a better boundary condition (a Dirichlet boundary condition), because it leads to the delineation of flow systems and stagnation zones. However, in practical modeling studies the recharge rates obtained when using the Dirichlet boundary condition may turn out to be unrealistically small or large. To remediate this we have developed an unconventional modeling procedure that is based on both the Neumann and the Dirichlet boundary condition on the phreatic surface. Such a model does not only calculate the heads and fluxes, but also an update of the initially perceived hydraulic conductivities, in such a way that the initially perceived conductivity model is preserved as much as possible. For given grid block conductivities, numerical groundwater models (e.g. MODFLOW) are linear in the heads. However, for given heads the numerical models are not linear in the grid block conductivities. Mohammed et al. (2009) have developed a MODFLOW-compatible numerical model that is linear in the stream functions for given grid block conductivities, while it is also linear in the grid block resistivities (inverse of conductivities) if the heads are given. Unconventional modeling is based on this bi-linearity. Assume we specify a reasonable perception of the hydraulic conductivities and determine the numerical solution with Neumann boundary conditions. The resulting fluxes are then substituted into the stream function model, together with Dirichlet boundary conditions, and the grid block resistivities can then be determined by a standard routine for solving systems of linear algebraic equations. The thus calibrated grid block conductivities do not deviate much from the initially perceived
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.
Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions
Grunau, H.-Ch.; Sweers, G.
1996-01-01
Cranston, Fabes and Zhao ([26], [5]) established the uniform bound sup x; y 2 x 6= y R G1;n (x; z)G1;n (z; y) dz G1;n (x; y) M < 1; (1) where G1;n (x; y) is the Green function for the Laplacian - with Dirichlet boundary conditions on a Lipschitz domain - Rn with n 3 (see [27] for n = 2).
Boundary conditions for simulating large SAW devices using ANSYS.
Peng, Dasong; Yu, Fengqi; Hu, Jian; Li, Peng
2010-08-01
In this report, we propose improved substrate left and right boundary conditions for simulating SAW devices using ANSYS. Compared with the previous methods, the proposed method can greatly reduce computation time. Furthermore, the longer the distance from the first reflector to the last one, the more computation time can be reduced. To verify the proposed method, a design example is presented with device center frequency 971.14 MHz.
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.
On higher-order boundary conditions at elastic-plastic boundaries in strain-gradient plasticity
DEFF Research Database (Denmark)
Niordson, Christian Frithiof
2008-01-01
are suppressed by using a very high artificial hardening modulus. Through numerical studies of pure bending under plane strain conditions, it is shown that this method predicts the build-up of higher order stresses in the pseudo-elastic regime. This has the effect of delaying the onset of incipient yield......A computational method for dealing with higher order boundary conditions on moving elastic-plastic boundaries in strain gradient plasticity is proposed. The basic idea is to skip the notion of a purely elastic regime, and instead introduce a pseudo-elastic regime, where plastic deformations......, as well as extending the plastic zone further toward the neutral axis of the beam, when compared to conventional models. Arguments supporting the present method are presented that rest on both mathematical and physical grounds. The results obtained are compared with other methods for dealing with higher...
Implementation of a Phase-Lagged Boundary Condition for Turbomachinery
Wouden, Alex; Cimbala, John; Lewis, Bryan
2012-11-01
One factor that contributes significantly to the cost of a time-dependent CFD simulation is the size and scope of the computational domain. Common approximations, such as periodic and symmetric boundary conditions, have the advantage of reducing the domain proportional to its periodicity or symmetry. However, turbomachinery applications featuring multiple blade rows render the periodic boundary condition unphysical because the adjacent blade rows are designed with dissimilar blade counts. Though the meshes of adjacent blade rows can be modeled independently and data can be interpolated across a grid interface, applying the standard periodic definition to the coupled faces leads to an over-constrained situation: a failure to reconcile two governing relations imposed on the same cell. A phase-lagged boundary condition (PLBC) relaxes the over-constraint problem and provides a more correct assumption for the resulting flow field. PLBC is available in a limited number of private CFD codes and is only briefly documented in the literature. The present work expands upon its development by implementing PLBC in OpenFOAM®, an open-source CFD software package. Its performance is demonstrated for basic turbomachinery applications through comparisons with full-wheel simulation. This research is funded by a grant from the DOE.
Danoyan Z.N.; Atoyan L.H.
2010-01-01
In the paper reflection problem of an incident bulk ferromagnetic spin-wave is solved. The wave reflects from the ferromagnetic medium surface, when on the surface are given the generalized boundary conditions for magnetization density [4]. Solution of the problem provides a foundation to confirm, that in ferromagnetic medium appears two non-homogeneous accompanying surface waves, besides of the mirror reflected wave. The two surface waves propagation velocities are the same, but coefficients...
On the nonlinear Schrodinger equation with nonzero boundary conditions
Fagerstrom, Emily
integral, provided the initial condition satisfies further conditions. Modulational instability (focusing NLS with symmetric nonzero boundary conditions at infinity.) The focusing NLS equation is considered with potentials that are "box-like" piecewise constant functions. Several results are obtained. In particular, it is shown that there are conditions on the parameters of the potential for which there are no discrete eigenvalues. Thus there is a class of potentials for which the corresponding solutions of the NLS equation have no solitons. Hence, solitons cannot be the medium for the modulational instability. This contradicts a recent conjecture by Zakharov. On the other hand, it is shown for a different class of potentials the scattering problem always has a discrete eigenvalue along the imaginary axis. Thus, there exist arbitrarily small perturbations of the constant potential for which solitons exist, so no area theorem is possible. The existence, number and location of discrete eigenvalues in other situations are studied numerically. Finally, the small-deviation limit of the IST is computed and compared with the direct linearization of the NLS equation around a constant background. From this it is shown that there is an interval of the continuous spectrum on which the eigenvalue is imaginary and the scattering parameter is imaginary. The Jost eigenfunctions corresponding to this interval are the nonlinear analogue of the unstable Fourier modes. Defocusing NLS equation with asymmetric boundary conditions at infinity. The defocusing NLS equation with asymmetric boundary conditions is considered. To do so, first the case of symmetric boundary conditions is revisited. While the IST for this case has been formulated in the literature, it is usually done through the use of a uniformization variable. This was done because the eigenvalues of the scattering problem have branching; the uniformization variable allows one to move from a 2-sheeted Riemann surface to the complex
On Coupled p-Laplacian Fractional Differential Equations with Nonlinear Boundary Conditions
Directory of Open Access Journals (Sweden)
Aziz Khan
2017-01-01
Full Text Available This paper is related to the existence and uniqueness of solutions to a coupled system of fractional differential equations (FDEs with nonlinear p-Laplacian operator by using fractional integral boundary conditions with nonlinear term and also to checking the Hyers-Ulam stability for the proposed problem. The functions involved in the proposed coupled system are continuous and satisfy certain growth conditions. By using topological degree theory some conditions are established which ensure the existence and uniqueness of solution to the proposed problem. Further, certain conditions are developed corresponding to Hyers-Ulam type stability for the positive solution of the considered coupled system of FDEs. Also, from applications point of view, we give an example.
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.
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.
Influence of boundary conditions on fluid flow on hydrophobic surfaces
Simona, Fialová; František, Pochylý; Michal, Havlásek; Jiři, Malík
2017-09-01
The work is focused on the shape of velocity profiles of viscous liquid (water) in contact with hydrophobic surface. A demonstration is done on an example of liquid flow between two parallel plates. The solution is carried out at both the constant and variable viscosity of the liquid near the wall. The slip boundary condition of the liquid on the wall is expressed by the coefficient of adhesion and the shear stress on the wall. As a result, presented are the shapes of the velocity profiles in dependence on the coefficient of adhesion and the slip velocity on the wall. This solution is for laminar flow.
Numerical solutions of telegraph equations with the Dirichlet boundary condition
Ashyralyev, Allaberen; Turkcan, Kadriye Tuba; Koksal, Mehmet Emir
2016-08-01
In this study, the Cauchy problem for telegraph equations in a Hilbert space is considered. Stability estimates for the solution of this problem are presented. The third order of accuracy difference scheme is constructed for approximate solutions of the problem. Stability estimates for the solution of this difference scheme are established. As a test problem to support theoretical results, one-dimensional telegraph equation with the Dirichlet boundary condition is considered. Numerical solutions of this equation are obtained by first, second and third order of accuracy difference schemes.
Magnetospheric conditions near the equatorial footpoints of proton isotropy boundaries
Directory of Open Access Journals (Sweden)
V. A. Sergeev
2015-12-01
Full Text Available Data from a cluster of three THEMIS (Time History of Events and Macroscale Interactions during Substorms spacecraft during February–March 2009 frequently provide an opportunity to construct local data-adaptive magnetospheric models, which are suitable for the accurate mapping along the magnetic field lines at distances of 6–9 Re in the nightside magnetosphere. This allows us to map the isotropy boundaries (IBs of 30 and 80 keV protons observed by low-altitude NOAA POES (Polar Orbiting Environmental Satellites to the equatorial magnetosphere (to find the projected isotropy boundary, PIB and study the magnetospheric conditions, particularly to evaluate the ratio KIB (Rc/rc; the magnetic field curvature radius to the particle gyroradius in the neutral sheet at that point. Special care is taken to control the factors which influence the accuracy of the adaptive models and mapping. Data indicate that better accuracy of an adaptive model is achieved when the PIB distance from the closest spacecraft is as small as 1–2 Re. For this group of most accurate predictions, the spread of KIB values is still large (from 4 to 32, with the median value KIB ~13 being larger than the critical value Kcr ~ 8 expected at the inner boundary of nonadiabatic angular scattering in the current sheet. It appears that two different mechanisms may contribute to form the isotropy boundary. The group with K ~ [4,12] is most likely formed by current sheet scattering, whereas the group having KIB ~ [12,32] could be formed by the resonant scattering of low-energy protons by the electromagnetic ion-cyclotron (EMIC waves. The energy dependence of the upper K limit and close proximity of the latter event to the plasmapause locations support this conclusion. We also discuss other reasons why the K ~ 8 criterion for isotropization may fail to work, as well as a possible relationship between the two scattering mechanisms.
Radiation Boundary Conditions for the Two-Dimensional Wave Equation from a Variational Principle
Broeze, J.; Broeze, Jan; van Daalen, Edwin F.G.; van Daalen, E.F.G.
1992-01-01
A variational principle is used to derive a new radiation boundary condition for the two-dimensional wave equation. This boundary condition is obtained from an expression for the local energy flux velocity on the boundary in normal direction. The wellposedness of the wave equation with this boundary
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.
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.
Stress boundary conditions with the staggered grid: a numerical investigation
Duretz, Thibault; May, Dave
2014-05-01
In this study, we investigate the numerical properties of the finite-difference method employing dynamic boundary conditions (BC). Stress BC's are gaining popularity in the geodynamic modelling community since the use of a free surface (stress-free BC) is required to model the dynamic evolution of topography. Additionnaly, normal stress BC's might also be used to prescribe known lithospheric rheological models as a dynamic forcing. Under this constraints, boundary velocities are not fixed, they thus vary through time in reaction to stress equilibria within the domain. Dynamic BC's were implemented on a regular Cartesian mesh using a standart staggered grid discretisation. The numerical properties of the scheme were quantified by means of a convergence study and error analysis. Integrated errors owing to the numerical method were evaluated using analytical and manufactured full flow-field solutions and associated convergence rates were derived. Finally, we present two lithospheric-scale applications. The first model depicts the topographic evolution of a linear-viscous lithosphere subjected to the rise of a mantle plume, employing a staircase type free surface. The second model shows the pattern of strain localisation in a thermally activated power law crust subjected to normal stress loading.
Sarna, Neeraj; Torrilhon, Manuel
2017-11-01
We define certain criteria, using the characteristic decomposition of the boundary conditions and energy estimates, which a set of stable boundary conditions for a linear initial boundary value problem, involving a symmetric hyperbolic system, must satisfy. We first use these stability criteria to show the instability of the Maxwell boundary conditions proposed by Grad (Commun Pure Appl Math 2(4):331-407, 1949). We then recognise a special block structure of the moment equations which arises due to the recursion relations and the orthogonality of the Hermite polynomials; the block structure will help us in formulating stable boundary conditions for an arbitrary order Hermite discretization of the Boltzmann equation. The formulation of stable boundary conditions relies upon an Onsager matrix which will be constructed such that the newly proposed boundary conditions stay close to the Maxwell boundary conditions at least in the lower order moments.
Baroclinic Planetary Boundary Layer Model: Neutral and Stable Stratification Conditions
Yordanov, D.; Djolov, G.; Syrakov, D.
1998-01-01
The temperature and wind profiles in a baroclinic Planetary Boundary Layer (PBL) are investigated. Assuming stationarity, the turbulent state in the PBL at stable and neutral conditions is uniquely determined by the Rossby number, the external stratification parameter and two external baroclinic parameters. A simple two-layer baroclinic model is developed. It consists of a Surface Layer (SL) and overlying Ekman type layer. The system of dynamic and heat transfer equations is close using the K-theory. In SL the turbulent exchange coefficient is consistent with the results of similarity theory while in the Ekman layer it is constant. The universal functions in the resistance, heat and humidity transfer laws can be deduced from the model. The internal PBL characteristics, necessary for the model calculations, are presented in terms of the external parameters. Favourable agreement of model results with experimental data is demonstrated.
CFD Modeling of Non-Neutral Atmospheric Boundary Layer Conditions
DEFF Research Database (Denmark)
Koblitz, Tilman
cost than e.g. using large-eddy simulations. The developed ABL model is successfully validated using a range of different test cases with increasing complexity. Data from several large scale field campaigns, wind tunnel experiments, and previous numerical simulations is presented and compared against...... model results. A method is developed how to simulate the time-dependant non-neutral ABL flow over complex terrain: a precursor simulation is used to specify unsteady inlet boundary conditions on complex terrain domains. The advantage of the developed RANS model framework is its general applicability....... All implementations in the ABL model are tuning free, and except for standard site specific input parameters, no additional model coefficients need to be specified before the simulation. In summary the results show that the implemented modifications are applicable and reproduce the main flow...
Atom-partitioned multipole expansions for electrostatic potential boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Lee, M., E-mail: michael.s.lee131.civ@mail.mil [Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States); Leiter, K. [Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States); Eisner, C. [Secure Mission Solutions, a Parsons Company (United States); Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States); Knap, J. [Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States)
2017-01-01
Applications such as grid-based real-space density functional theory (DFT) use the Poisson equation to compute electrostatics. However, the expected long tail of the electrostatic potential requires either the use of a large and costly outer domain or Dirichlet boundary conditions estimated via multipole expansion. We find that the oft-used single-center spherical multipole expansion is only appropriate for isotropic mesh domains such as spheres and cubes. In this work, we introduce a method suitable for high aspect ratio meshes whereby the charge density is partitioned into atomic domains and multipoles are computed for each domain. While this approach is moderately more expensive than a single-center expansion, it is numerically stable and still a small fraction of the overall cost of a DFT calculation. The net result is that when high aspect ratio systems are being studied, form-fitted meshes can now be used in lieu of cubic meshes to gain computational speedup.
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.
Directory of Open Access Journals (Sweden)
T. K. Usmanova
2017-01-01
Full Text Available Purpose: the aim of the article is to reveal problems and prospects, formulate economic security within the framework of innovation projects management, plan technologies in the context of integrating economies into the world economy, identify opportunities for forming, organizing, ﬁnancing, managing priority economic directions. The subject is the management of innovative projects to ensure the economic security of Russian regions. The relevance of the chosen topic is due to the study of the features of the current state and the problems of the formation of economic security, the development of innovative design solutions in the context of integrating economies into the world economy. Ensuring the economic security of the regions of Russia directly depends on the introduction of innovative technologies and project management in the sectors of the national economy of Russia. Methods: the methodology of the solution of objectives is based on usage of a method of dialectic research, methods of the economic analysis, forecasting, the situational and systemic analysis, expert evaluations and the analysis of empirical data. Hypothesis. Ensuring an economic safety requires formation of innovative solutions, change of the current legislation within the Strategy of social and economic development in the conditions of integration of economies into the world economy. Results: the practical signiﬁcance of the work is to identify the interrelationship between the development processes of innovative projects that ensure the economic security of the regions of Russia within the framework of regulating the current legislation, forecasting eﬀective economic activity within the framework of the New Industrialization Strategy, selecting optimal project planning models to ensure the country's economic security and competitiveness in the conditions of integration Economies into the world economy. Conclusions and Relevance: in the conditions of integration of
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.
A Two-Dimensional Transverse Magnetic Propagation Model of a Sine Wave Using Mur Boundary Conditions
National Research Council Canada - National Science Library
Korjack, T
1997-01-01
.... The nonreflecting boundary conditions due to Mur were used at the boundary surfaces. Electric field intensity distributions resulted over a progressive time expansion to illustrate the propagation effect over the entire 2-D mesh...
Boundary conditions in the Ginzburg Landau Formulation in heavy ...
African Journals Online (AJOL)
The linearized gap equation is the basis for the microscopic derivation of the second order terms in the Ginzburg-Landau free energy expansion. However, close to the boundary these second order terms do not have the same form, since the kernel is changed due to quasi-particle scattering. In addition, these boundary ...
Boundary conditions for gas flow problems from anisotropic scattering kernels
To, Quy-Dong; Vu, Van-Huyen; Lauriat, Guy; Léonard, Céline
2015-10-01
The paper presents an interface model for gas flowing through a channel constituted of anisotropic wall surfaces. Using anisotropic scattering kernels and Chapman Enskog phase density, the boundary conditions (BCs) for velocity, temperature, and discontinuities including velocity slip and temperature jump at the wall are obtained. Two scattering kernels, Dadzie and Méolans (DM) kernel, and generalized anisotropic Cercignani-Lampis (ACL) are examined in the present paper, yielding simple BCs at the wall fluid interface. With these two kernels, we rigorously recover the analytical expression for orientation dependent slip shown in our previous works [Pham et al., Phys. Rev. E 86, 051201 (2012) and To et al., J. Heat Transfer 137, 091002 (2015)] which is in good agreement with molecular dynamics simulation results. More important, our models include both thermal transpiration effect and new equations for the temperature jump. While the same expression depending on the two tangential accommodation coefficients is obtained for slip velocity, the DM and ACL temperature equations are significantly different. The derived BC equations associated with these two kernels are of interest for the gas simulations since they are able to capture the direction dependent slip behavior of anisotropic interfaces.
Giesler, Marianne; Karsten, Gudrun; Ochsendorf, Falk; Breckwoldt, Jan
2017-01-01
Background: There is general consensus that the organizational and administrative aspects of academic study programs exert an important influence on teaching and learning. Despite this, no comprehensive framework currently exists to describe the conditions that affect the quality of teaching and learning in medical education. The aim of this paper is to systematically and comprehensively identify these factors to offer academic administrators and decision makers interested in improving teaching a theory-based and, to an extent, empirically founded framework on the basis of which improvements in teaching quality can be identified and implemented. Method: Primarily, the issue was addressed by combining a theory-driven deductive approach with an experience based, "best evidence" one during the course of two workshops held by the GMA Committee on Personnel and Organizational Development in Academic Teaching (POiL) in Munich (2013) and Frankfurt (2014). Two models describing the conditions relevant to teaching and learning (Euler/Hahn and Rindermann) were critically appraised and synthesized into a new third model. Practical examples of teaching strategies that promote or hinder learning were compiled and added to the categories of this model and, to the extent possible, supported with empirical evidence. Based on this, a checklist with recommendations for optimizing general academic conditions was formulated. Results: The Frankfurt Model of conditions to ensure Quality in Teaching and Learning covers six categories: organizational structure/medical school culture, regulatory frameworks, curricular requirements, time constraints, material and personnel resources, and qualification of teaching staff. These categories have been supplemented by the interests, motives and abilities of the actual teachers and students in this particular setting. The categories of this model provide the structure for a checklist in which recommendations for optimizing teaching are given
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.
Itu, Lucian; Sharma, Puneet; Suciu, Constantin; Moldoveanu, Florin; Comaniciu, Dorin
2017-03-01
We propose a hierarchical parameter estimation framework for performing patient-specific hemodynamic computations in arterial models, which use structured tree boundary conditions. A calibration problem is formulated at each stage of the hierarchical framework, which seeks the fixed point solution of a nonlinear system of equations. Common hemodynamic properties, like resistance and compliance, are estimated at the first stage in order to match the objectives given by clinical measurements of pressure and/or flow rate. The second stage estimates the parameters of the structured trees so as to match the values of the hemodynamic properties determined at the first stage. A key feature of the proposed method is that to ensure a large range of variation, two different structured tree parameters are personalized for each hemodynamic property. First, the second stage of the parameter estimation framework is evaluated based on the properties of the outlet boundary conditions in a full body arterial model: the calibration method converges for all structured trees in less than 10 iterations. Next, the proposed framework is successfully evaluated on a patient-specific aortic model with coarctation: only six iterations are required for the computational model to be in close agreement with the clinical measurements used as objectives, and overall, there is a good agreement between the measured and computed quantities. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
A simple and efficient outflow boundary condition for the incompressible Navier–Stokes equations
Directory of Open Access Journals (Sweden)
Yibao Li
2017-01-01
Full Text Available Many researchers have proposed special treatments for outlet boundary conditions owing to lack of information at the outlet. Among them, the simplest method requires a large enough computational domain to prevent or reduce numerical errors at the boundaries. However, an efficient method generally requires special treatment to overcome the problems raised by the outlet boundary condition used. For example, mass flux is not conserved and the fluid field is not divergence-free at the outlet boundary. Overcoming these problems requires additional computational cost. In this paper, we present a simple and efficient outflow boundary condition for the incompressible Navier–Stokes equations, aiming to reduce the computational domain for simulating flow inside a long channel in the streamwise direction. The proposed outflow boundary condition is based on the transparent equation, where a weak formulation is used. The pressure boundary condition is derived by using the Navier–Stokes equations and the outlet flow boundary condition. In the numerical algorithm, a staggered marker-and-cell grid is used and temporal discretization is based on a projection method. The intermediate velocity boundary condition is consistently adopted to handle the velocity–pressure coupling. Characteristic numerical experiments are presented to demonstrate the robustness and accuracy of the proposed numerical scheme. Furthermore, the agreement of computational results from small and large domains suggests that our proposed outflow boundary condition can significantly reduce computational domain sizes.
Revisit boundary conditions for the self-adjoint angular flux formulation
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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.
Solution to the one-dimensional telegrapher's equation subject to a backreaction boundary condition
Prüstel, Thorsten; Meier-Schellersheim, Martin
2013-01-01
We discuss solutions of the one-dimensional telegrapher's equation in the presence of boundary conditions. We revisit the case of a radiation boundary condition and obtain an alternative expression for the already known Green's function. Furthermore, we formulate a backreaction boundary condition, which has been widely used in the context of diffusion-controlled reversible reactions, for a one-dimensional telegrapher's equation and derive the corresponding Green's function.
Effective nonlinear Neumann boundary conditions for 1D nonconvex Hamilton-Jacobi equations
Guerand, Jessica
2017-09-01
We study Hamilton-Jacobi equations in [ 0 , + ∞) of evolution type with nonlinear Neumann boundary conditions in the case where the Hamiltonian is not necessarily convex with respect to the gradient variable. In this paper, we give two main results. First, we prove for a nonconvex and coercive Hamiltonian that general boundary conditions in a relaxed sense are equivalent to effective ones in a strong sense. Here, we exhibit the effective boundary conditions while for a quasi-convex Hamiltonian, we already know them (Imbert and Monneau, 2016). Second, we give a comparison principle for a nonconvex and nonnecessarily coercive Hamiltonian where the boundary condition can have constant parts.
Method Suitable for Updating the Boundary Condition of Continuous Beam Bridges
Cao, JianXin; Zheng, Honglan; Liu, Yang
2017-10-01
The boundary support conditions of continuous beam bridges play the great influence on the results of the structural analysis, but it is difficult to accurately model the boundaries owing to the complexity structure of constraint conditions. To address this issue, a parameterized method is proposed to update the boundary support conditions in this study. First, the connection stiffness at boundary is considered as the optimization variable, and then the optimization problem of updating the boundary conditions are described in detail based on the theory of finite element model updating. Second, for verifying the proposed method, a loading test was conducted on an actual three-span continuous beam bridge. With the proposed method, the discrepancy between the measured modal parameters and the analytical results are greatly reduced; therefore, it is shown that the proposed method is effective for updating the boundary support conditions of actual continuous beam bridges.
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Osanyintola, O. F.; Talukdar, P.; Simonson, C. J. [Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Sask. (China)
2006-07-01
In this paper, the moisture buffering capacity of spruce plywood is measured by recording the change in mass of a test specimen when the air relative humidity (RH) is changed between 33% RH and 75% RH. The aim is to represent diurnal cycles in indoor humidity with 33% RH maintained for 16 h and 75% RH maintained for 8 h. Measurements are taken using two different apparatuses, which provide different convective transfer coefficients between the air and the plywood, and the results are compared to a numerical model for validation. The validated numerical model is then used to investigate the effect of initial conditions, boundary conditions and thickness on the moisture buffering capacity of plywood. The results show that the buffering capacity of plywood depends on the initial conditions and thickness of the plywood as well as the surface film coefficient and humidity cycle. (author)
Liu, Zhao; Zheng, Chaorong; Wu, Yue
2017-09-01
Wind profilers have been widely adopted to observe the wind field information in the atmosphere for different purposes. But accuracy of its observation has limitations due to various noises or disturbances and hence need to be further improved. In this paper, the data measured under strong wind conditions, using a 1290-MHz boundary layer profiler (BLP), are quality controlled via a composite quality control (QC) procedure proposed by the authors. Then, through the comparison with the data measured by radiosonde flights (balloon observations), the critical thresholds in the composite QC procedure, including consensus average threshold T 1 and vertical shear threshold T 3 , are systematically discussed. And the performance of the BLP operated under precipitation is also evaluated. It is found that to ensure the high accuracy and high data collectable rate, the optimal range of subsets is determined to be 4 m/s. Although the number of data rejected by the combined algorithm of vertical shear examination and small median test is quite limited, it is proved that the algorithm is quite useful to recognize the outlier with a large discrepancy. And the optimal wind shear threshold T 3 can be recommended as 5 ms -1 /100m. During patchy precipitation, the quality of data measured by the four oblique beams (using the DBS measuring technique) can still be ensured. After the BLP data are quality controlled by the composite QC procedure, the output can show good agreement with the balloon observation.
Questions on solvability of exterior boundary value problems with fractional boundary conditions
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Berikbol Torebek
2016-05-01
Full Text Available In this paper we study questions on solvability of some boundary value problems for the Laplace equation with boundary integro-differential operators in the exterior of a unit ball. We study properties of the given integral - differential operators of fractional order in a class of functions which are harmonic outside a ball. We prove theorems about existence and uniqueness of a solution of the problem. We construct explicit form of the solution of the problem in integral form, by solving the Dirichlet problem.
Experimental verification of free-space singular boundary conditions in an invisibility cloak
Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Chen, Huanyang; Zhang, Baile
2016-04-01
A major issue in invisibility cloaking, which caused intense mathematical discussions in the past few years but still remains physically elusive, is the plausible singular boundary conditions associated with the singular metamaterials at the inner boundary of an invisibility cloak. The perfect cloaking phenomenon, as originally proposed by Pendry et al for electromagnetic waves, cannot be treated as physical before a realistic inner boundary of a cloak is demonstrated. Although a recent demonstration has been done in a waveguide environment, the exotic singular boundary conditions should apply to a general environment as in free space. Here we fabricate a metamaterial surface that exhibits the singular boundary conditions and demonstrate its performance in free space. Particularly, the phase information of waves reflected from this metamaterial surface is explicitly measured, confirming the singular responses of boundary conditions for an invisibility cloak.
Absorption and impedance boundary conditions for phased geometrical-acoustics methods
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, 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...
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.
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2015-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2014-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Directory of Open Access Journals (Sweden)
Giesler, Marianne
2017-10-01
Full Text Available Background: There is general consensus that the organizational and administrative aspects of academic study programs exert an important influence on teaching and learning. Despite this, no comprehensive framework currently exists to describe the conditions that affect the quality of teaching and learning in medical education. The aim of this paper is to systematically and comprehensively identify these factors to offer academic administrators and decision makers interested in improving teaching a theory-based and, to an extent, empirically founded framework on the basis of which improvements in teaching quality can be identified and implemented.Method: Primarily, the issue was addressed by combining a theory-driven deductive approach with an experience based, “best evidence” one during the course of two workshops held by the GMA Committee on Personnel and Organizational Development in Academic Teaching (POiL in Munich (2013 and Frankfurt (2014. Two models describing the conditions relevant to teaching and learning (Euler/Hahn and Rindermann were critically appraised and synthesized into a new third model. Practical examples of teaching strategies that promote or hinder learning were compiled and added to the categories of this model and, to the extent possible, supported with empirical evidence.Based on this, a checklist with recommendations for optimizing general academic conditions was formulated.Results: The covers six categories: and These categories have been supplemented by the interests, motives and abilities of the actual teachers and students in this particular setting. The categories of this model provide the structure for a checklist in which recommendations for optimizing teaching are given.Conclusions: The checklist derived from the Frankfurt Model for ensuring quality in teaching and learning can be used for quality assurance and to improve the conditions under which teaching and learning take place in medical schools.
On one method for solving transient heat conduction problems with asymmetric boundary conditions
Directory of Open Access Journals (Sweden)
Igor V. Kudinov
2016-06-01
Full Text Available Using additional boundary conditions and additional required function in integral method of heat-transfer we obtain approximate analytical solution of transient heat conduction problem for an infinite plate with asymmetric boundary conditions of the first kind. This solution has a simple form of trigonometric polynomial with coefficients exponentially stabilizing in time. With the increase in the count of terms of a polynomial the obtained solution is approaching the exact solution. The introduction of a time-dependent additional required function, setting in the one (point of the boundary points, allows to reduce solving of differential equation in partial derivatives to integration of ordinary differential equation. The additional boundary conditions are found in the form that the required solution would implement the additional boundary conditions and that implementation would be equivalent to executing the original differential equation in boundary points. In this article it is noted that the execution of the original equation at the boundaries of the area only (via the implementation of the additional boundary conditions leads to the execution of the original equation also inside that area. The absence of direct integration of the original equation on the spatial variable allows to apply this method to solving the nonlinear boundary value problems with variable initial conditions and variable physical properties of the environment, etc.
Evaluation of outflow boundary conditions for two-phase lattice Boltzmann equation.
Lou, Qin; Guo, Zhaoli; Shi, Baochang
2013-06-01
Outflow boundary condition (OBC) is a critical issue in computational fluid dynamics. As a type of numerical method for fluid flows, the lattice Boltzmann equation (LBE) method has gained much success in a variety of complex flows, and certain OBCs have been suggested for the LBE in simulating simple single-phase flows. However, very few discussions on the OBCs have been made for the two-phase LBE method. In this work, three types of OBCs that are widely used in the LBE for single-phase flows, i.e., the Neumann boundary condition, the convective boundary condition, and the extrapolation boundary condition, are extended to a two-phase LBE method and their performances are investigated. The comprehensive results of several two-phase flows show that these boundary conditions behave quite differently in the simulations of two-phase flows. Specifically, it is found that the Neumann boundary condition and the extrapolation boundary condition give rather poor predictions, while the type of convective boundary conditions work well, although the choice of the convection velocity has some slight influences on the results. We also apply these OBC schemes to some other two-phase models, and similar observations are found.
Sman, van der R.G.M.
2013-01-01
We have investigated the performance of an alternative wetting boundary condition for complex geometries in a phase field Lattice Boltzmann scheme, which is an alternative to the commonly used formulation by Yeomans and coworkers. Though our boundary condition is much simpler in its implementation,
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.
DEFF Research Database (Denmark)
Jha, Abhinav K.; Zhu, Yansong; Kang, Jin U.
2016-01-01
An integral Neumann-series implementation of the Radiative Transfer Equation that accounts for boundary conditions is proposed to simulate photon transport through tissue for transcranial optical imaging.......An integral Neumann-series implementation of the Radiative Transfer Equation that accounts for boundary conditions is proposed to simulate photon transport through tissue for transcranial optical imaging....
Conditions affecting boundary response to messages out of awareness.
Fisher, S
1976-05-01
Multiple studies evaluated the role of the following parameters in mediating the effects of auditory subliminal inputs upon the body boundary: being made aware that exposure to subliminal stimuli is occurring, nature of the priming preliminary to the input, length of exposure, competing sensory input, use of specialized content messages, tolerance for unrealistic experience, and masculinity-feminity. A test-retest design was typically employed that involved measuring the baseline Barrier score with the Holtzman bolts and then ascertaining the Barrier change when responding to a second series of Holtzman blots at the same time that subliminal input was occurring. Complex results emerged that defined in considerably new detail what facilitates and blocks the boundary-disrupting effects of subliminal messages in men and to a lesser degree in women.
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
The Ritz Method for Boundary Problems with Essential Conditions as Constraints
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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.
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.
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.
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Larysa Yuzevych
2017-09-01
Full Text Available The article develops recommendations for improvement of normative documents concerning the quality of underground metal pipelines (gas pipelines under conditions of fatigue and the impact of an aggressive environment, taking into account cathodic (electrochemical protection. It is established that the basis of information provision of normative documents is the method which includes the following main criteria: the value of the minimum current density of cathode protection; minimum security potential; maximum protective potential, minimal displacement of protective potential; strength criteria of pipe material; criteria of strength of phase layer between the metal and the coating; the strength of the metal in the defect of the insulation coating. It has been found out that the system "metal pipe - insulating dielectric coating" is characterized by such basic procedures as: identification of hazards; various variants of load asymmetry; evaluation of the boundary and optimal values of potentials and currents for the system of cathodic protection of the pipeline. The prospect of further research in this area is determination of the complex indicator of quality and reliability of the linear part of underground main gas pipelines on the basis of research results (submitted information support.
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.)
Large time behavior of solutions to parabolic equations with Neumann boundary conditions
da Lio, Francesca
2008-03-01
In this paper we are interested in the large time behavior as t-->+[infinity] of the viscosity solutions of parabolic equations with nonlinear Neumann type boundary conditions in connection with ergodic boundary problems which have been recently studied by Barles and the author in [G. Barles, F. Da Lio, On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions, Ann. Inst. H. Poincaré Anal. Non Linèaire 22 (5) (2005) 521-541].
Uddin, Mohammed J.; Khan, Waqar A.; Ismail, Ahmed I.
2012-01-01
Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement. PMID:23166688
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.
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.
Scudeler, C.; Paniconi, C.; Pasetto, D.; Putti, M.
2017-03-01
A seepage face is a nonlinear dynamic boundary that strongly affects pressure head distributions, water table fluctuations, and flow patterns. Its handling in hydrological models, especially under complex conditions such as heterogeneity and coupled surface/subsurface flow, has not been extensively studied. In this paper, we compare the treatment of the seepage face as a static (Dirichlet) versus dynamic boundary condition, we assess its resolution under conditions of layered heterogeneity, we examine its interaction with a catchment outlet boundary, and we investigate the effects of surface/subsurface exchanges on seepage faces forming at the land surface. The analyses are carried out with an integrated catchment hydrological model. Numerical simulations are performed for a synthetic rectangular sloping aquifer and for an experimental hillslope from the Landscape Evolution Observatory. The results show that the static boundary condition is not always an adequate stand-in for a dynamic seepage face boundary condition, especially under conditions of high rainfall, steep slope, or heterogeneity; that hillslopes with layered heterogeneity give rise to multiple seepage faces that can be highly dynamic; that seepage face and outlet boundaries can coexist in an integrated hydrological model and both play an important role; and that seepage faces at the land surface are not always controlled by subsurface flow. The paper also presents a generalized algorithm for resolving seepage face outflow that handles heterogeneity in a simple way, is applicable to unstructured grids, and is shown experimentally to be equivalent to the treatment of atmospheric boundary conditions in subsurface flow models.
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.
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...
Exploring the Boundary Conditions of the Redundancy Principle
McCrudden, Matthew T.; Hushman, Carolyn J.; Marley, Scott C.
2014-01-01
This experiment investigated whether study of a scientific text and a visual display that contained redundant text segments would affect memory and transfer. The authors randomly assigned 42 students from a university in the southwestern United States in equal numbers to 1 of 2 conditions: (a) a redundant condition, in which participants studied a…
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.
First-principle proof of the modified collision boundary conditions for the hard-sphere system
Tessarotto, Massimo; Cremaschini, Claudio
2014-05-01
A fundamental issue lying at the foundation of classical statistical mechanics is the determination of the collision boundary conditions that characterize the dynamical evolution of multi-particle probability density functions (PDF) and are applicable to systems of hard-spheres undergoing multiple elastic collisions. In this paper it is proved that, when the deterministic N-body PDF is included in the class of admissible solutions of the Liouville equation, the customary form of collision boundary conditions adopted in previous literature becomes physically inconsistent and must actually be replaced by suitably modified collision boundary conditions.
Simulations of QCD and QED with C* boundary conditions arXiv
Hansen, Martin; Patella, Agostino; Tantalo, Nazario
We present exploratory results from dynamical simulations of QCD in isolation, as well as QCD coupled to QED, with C* boundary conditions. In finite volume, the use of C* boundary conditions allows for a gauge invariant and local formulation of QED without zero modes. In particular we show that the simulations reproduce known results and that masses of charged mesons can be extracted in a completely gauge invariant way. For the simulations we use a modified version of the HiRep code. The primary features of the simulation code are presented and we discuss some details regarding the implementation of C* boundary conditions and the simulated lattice action.
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...
Chemical boundary conditions are a key input to regional-scale photochemical models. In this study, performed during the third phase of the Air Quality Model Evaluation International Initiative (AQMEII3), we perform annual simulations over North America with chemical boundary con...
Crossing the boundary: numerical investigation of water entry conditions
Angelidis, Dionysios; Sotiropoulos, Fotis
2017-11-01
Several engineering and scientific applications involve water impact problems. To accurately capture the dynamics of the cavity formation and the water ejected as a body hits the water, the formidable range of temporal and spatial scales should accurately be resolved with affordable computational cost. We have enhanced the potential of the two-phase flow version of the immersed-boundary adaptive mesh refinement flow solver, developed by our group, to perform high-fidelity two-phase flow calculations on locally refined grids. We employ a level-set method and tackle the computational challenges arise during the explicit solution of a mass-conserving reinitialization equation. In contrast to conventional approaches, we propose a convergence criterion which enables the number of iterations to be self-adjusted based on the values of the distance function. The efficiency of our method is demonstrated by performing two-phase flow calculations including the high-speed water entry of a V-shaped wedge. Our results are found to be in good agreement with experimental measurements and enable us to gain insight into the instability that arises on the onset of the closure phase of the cavity. This material is based upon work supported by the National Science Foundation (CBET-1509071).
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.
Wu, S. T.; Wang, A. H.; Cassibry, J.
2010-09-01
We discuss the self-consistent time-dependent numerical boundary conditions for magnetohydrodynamic (MHD) simulation to study the solar and laboratory plasma dynamics. It is well known that these plasma flows cover from the sub-sonic and sub-Alfvénic to super-sonic and super-Alfvénic region. Mathematically, the set of governing differential equations is transited from elliptical to hyperbolic type. In order to assure self-consistency, characteristic boundary conditions need to be used because the information propagating according to these characteristics will affect the solutions inside the computational domain. To illustrate the importance of the characteristic boundary conditions, two examples are given; one for solar plasma which is to study the energy and magnetic flux from the sub-photosphere to the corona, and the other one concerns laboratory plasma flow for the investigation of sub-Alfvénic inlet boundary conditions of an MHD nozzle flow.
On the symmetry of the boundary conditions of the volume potential
Kal'menov, Tynysbek Sh.; Arepova, Gaukhar; Suragan, Durvudkhan
2017-09-01
It is well known that the volume potential determines the mass or the charge distributed over the domain with density f. The volume potential is extensively used in function theory and embedding theorems. It is also well known that the volume potential gives a solution to an inhomogeneous equation. And it generates a linear self-adjoint operator. It is known that self-adjoint differential operators are generated by boundary conditions. In our previous papers for an arbitrary domain a boundary condition on the volume potential is given. In the past, it was not possible to prove the self-adjointness of these obtained boundary conditions. In the present paper, we prove the symmetry of boundary condition for the volume potential.
Existence of arbitrarily smooth solutions of the LLG equation in 3D with natural boundary conditions
Feischl, Michael; Tran, Thanh
2016-01-01
We prove that the Landau-Lifshitz-Gilbert equation in three space dimensions with homogeneous Neumann boundary conditions admits arbitrarily smooth solutions, given that the initial data is sufficiently close to a constant function.
Directory of Open Access Journals (Sweden)
Yelda Aygar
2012-01-01
Full Text Available Let denote the operator generated in by , , , and the boundary condition , where , , , and , are complex sequences, , , and is an eigenparameter. In this paper we investigated the principal functions corresponding to the eigenvalues and the spectral singularities of .
Effect of a boundary condition on the cylindrical Couette flow of a rarefied gas
Kosuge, Shingo
2014-12-01
The cylindrical Couette flow of a rarefied gas between a rotating inner cylinder and a stationary outer cylinder is investigated on the basis of kinetic theory. We perform a numerical analysis of the (BGK model) Boltzmann equation for a wide range of the Knudsen number and an asymptotic analysis for small Knudsen numbers employing two kinds of kinetic boundary conditions on the cylinders. One is the modified Maxwell-type boundary condition (proposed by S. K. Dadzie and J. G. Méolans) and the other is the Cercignani-Lampis condition, both of which have separate accommodation coefficients associated with the molecular velocity component normal to the boundary and with the tangential component. Our main interest is in the effect of those boundary conditions on the inverted velocity profile. The results show that the onset of the inversion is practically controlled by the tangential accommodation only.
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.
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.
Applying the method of fundamental solutions to harmonic problems with singular boundary conditions
Valtchev, Svilen S.; Alves, Carlos J. S.
2017-07-01
The method of fundamental solutions (MFS) is known to produce highly accurate numerical results for elliptic boundary value problems (BVP) with smooth boundary conditions, posed in analytic domains. However, due to the analyticity of the shape functions in its approximation basis, the MFS is usually disregarded when the boundary functions possess singularities. In this work we present a modification of the classical MFS which can be applied for the numerical solution of the Laplace BVP with Dirichlet boundary conditions exhibiting jump discontinuities. In particular, a set of harmonic functions with discontinuous boundary traces is added to the MFS basis. The accuracy of the proposed method is compared with the results form the classical MFS.
The No-Slip Boundary Condition in Fluid Mechanics
Indian Academy of Sciences (India)
gradient near a wall have to satisfy the no-slip condition at every instant. ... The well known Bernoulli equation giving a relation .... resistance being proportional to the slip velocity itself. leads to infinite stress. But this model was proposed before the. N-S equations were known. The third hypothesis was due to Navier himself.
A Boundary Mixture Approach to Violations of Conditional Independence
Braeken, Johan
2011-01-01
Conditional independence is a fundamental principle in latent variable modeling and item response theory. Violations of this principle, commonly known as local item dependencies, are put in a test information perspective, and sharp bounds on these violations are defined. A modeling approach is proposed that makes use of a mixture representation of…
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.
Wang, Mengjie; Herdeiro, Carlos; Jing, Jiliang
2017-11-01
We study Dirac quasinormal modes of Schwarzschild-anti-de Sitter (Schwarzschild-AdS) black holes, following the generic principle for allowed boundary conditions proposed in [M. Wang, C. Herdeiro, and M. O. P. Sampaio, Phys. Rev. D 92, 124006 (2015)., 10.1103/PhysRevD.92.124006]. After deriving the equations of motion for Dirac fields on the aforementioned background, we impose vanishing energy flux boundary conditions to solve these equations. We find a set of two Robin boundary conditions are allowed. These two boundary conditions are used to calculate Dirac normal modes on empty AdS and quasinormal modes on Schwarzschild-AdS black holes. In the former case, we recover the known normal modes of empty AdS; in the latter case, the two sets of Robin boundary conditions lead to two different branches of quasinormal modes. The impact on these modes of the black hole size, the angular momentum quantum number and the overtone number are discussed. Our results show that vanishing energy flux boundary conditions are a robust principle, applicable not only to bosonic fields but also to fermionic fields.
Semi-transparent boundary conditions in the worldline formalism
Energy Technology Data Exchange (ETDEWEB)
Vinas, S A Franchino; Pisani, P A G, E-mail: safranchino@fisica.unlp.edu.ar, E-mail: pisani@fisica.unlp.edu.ar [IFLP-CONICET/Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, (1900) La Plata (Argentina)
2011-07-22
The interaction of a quantum field with a background containing a Dirac delta function with support on a surface of codimension 1 represents a particular kind of matching conditions on that surface for the field. In this paper, we show that the worldline formalism can be applied to this model. We obtain the asymptotic expansion of the heat kernel corresponding to a scalar field on R{sup d+1} in the presence of an arbitrary regular potential and subject to this kind of matching conditions on a flat surface. We also consider two such surfaces and compute their Casimir attraction due to the vacuum fluctuations of a massive scalar field weakly coupled to the corresponding Dirac deltas.
Rayleigh-Benard convection with time-dependent boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Swift, J.B.; Hohenberg, P.C.
1989-04-15
The 13-mode Lorenz model previously introduced to describe hexagons and rolls in a Rayleigh-Benard cell with periodic modulation of the lower plate is generalized to arbitrary time dependence of both upper and lower plates. Earlier results of Krishnamurti (J. Fluid Mech. 33, 445 (1968); 33, 457 (1968)) for the case of a linear ramp with constant temperature difference are recovered. The conditions for observing hexagons are derived analytically for periodic modulation with different frequencies, amplitudes, and phases at the two plates.
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.
Effects of microscopic boundary conditions on plastic deformations of small-sized single crystals
DEFF Research Database (Denmark)
Kuroda, Mitsutoshi; Tvergaard, Viggo
2009-01-01
for uniaxial plane strain compression of a single crystal block and for uniform pure bending of a single crystal foil. The compressed block has loading surfaces that are penetrable or impenetrable to dislocations. This allows for a study of the two types of higher-order boundaries available, and a significant......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....
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.
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 $h\\in H^{\\frac{2s-1}{4}}(0,T$.
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
The implementation and performance of a new active wave generating‐absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces is presented. This numerical boundary condition AWAVOF is based on an active wave absorption system...... that was first developed in the context of physical wave flume experiments, using a wave paddle. The method applies to regular and irregular waves. Velocities are measured at one location inside the computational domain. The reflected wave train is separated from the incident wave field in front of a structure...... 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...
Exact solution for the fractional cable equation with nonlocal boundary conditions
Bazhlekova, Emilia; Dimovski, Ivan
2013-10-01
The fractional cable equation is studied on a bounded space domain. One of the prescribed boundary conditions is of Dirichlet type, the other is of a general form, which includes the case of nonlocal boundary conditions. In real problems nonlocal boundary conditions are prescribed when the data on the boundary can not be measured directly. We apply spectral projection operators to convert the problem to a system of integral equations in any generalized eigenspace. In this way we prove uniqueness of the solution and give an algorithm for constructing the solution in the form of an expansion in terms of the generalized eigenfunctions and three-parameter Mittag-Leffler functions. Explicit representation of the solution is given for the case of double eigenvalues. We consider some examples and as a particular case we recover a recent result. The asymptotic behavior of the solution is also studied.
Phase-space networks of the six-vertex model under different boundary conditions.
Han, Yilong
2010-04-01
The six-vertex model is mapped to three-dimensional sphere stacks and different boundary conditions corresponding to different containers. The shape of the container provides a qualitative visualization of the boundary effect. Based on the sphere-stacking picture, we map the phase spaces of the six-vertex models to discrete networks. A node in the network represents a state of the system, and an edge between two nodes represents a zero-energy spin flip, which corresponds to adding or removing a sphere. The network analysis shows that the phase spaces of systems with different boundary conditions share some common features. We derived a few formulas for the number and the sizes of the disconnected phase-space subnetworks under the periodic boundary conditions. The sphere stacking provides new challenges in combinatorics and may cast light on some two-dimensional models.
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.
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...
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.
An outgoing energy flux boundary condition for finite difference ICRP antenna models
Energy Technology Data Exchange (ETDEWEB)
Batchelor, D.B.; Carter, M.D.
1992-11-01
For antennas at the ion cyclotron range of frequencies (ICRF) modeling in vacuum can now be carried out to a high level of detail such that shaping of the current straps, isolating septa, and discrete Faraday shield structures can be included. An efficient approach would be to solve for the fields in the vacuum region near the antenna in three dimensions by finite methods and to match this solution at the plasma-vacuum interface to a solution obtained in the plasma region in one dimension by Fourier methods. This approach has been difficult to carry out because boundary conditions must be imposed at the edge of the finite difference grid on a point-by-point basis, whereas the condition for outgoing energy flux into the plasma is known only in terms of the Fourier transform of the plasma fields. A technique is presented by which a boundary condition can be imposed on the computational grid of a three-dimensional finite difference, or finite element, code by constraining the discrete Fourier transform of the fields at the boundary points to satisfy an outgoing energy flux condition appropriate for the plasma. The boundary condition at a specific grid point appears as a coupling to other grid points on the boundary, with weighting determined by a kemel calctdated from the plasma surface impedance matrix for the various plasma Fourier modes. This boundary condition has been implemented in a finite difference solution of a simple problem in two dimensions, which can also be solved directly by Fourier transformation. Results are presented, and it is shown that the proposed boundary condition does enforce outgoing energy flux and yields the same solution as is obtained by Fourier methods.
Bessaih, Hakima
2015-04-01
The evolution Stokes equation in a domain containing periodically distributed obstacles subject to Fourier boundary condition on the boundaries is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the obstacles. We represent the solid obstacles by holes in the fluid domain. The macroscopic (homogenized) equation is derived as another stochastic partial differential equation, defined in the whole non perforated domain. Here, the initial stochastic perturbation on the boundary becomes part of the homogenized equation as another stochastic force. We use the twoscale convergence method after extending the solution with 0 in the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. In order to pass to the limit on the boundary integrals, we rewrite them in terms of integrals in the whole domain. In particular, for the stochastic integral on the boundary, we combine the previous idea of rewriting it on the whole domain with the assumption that the Brownian motion is of trace class. Due to the particular boundary condition dealt with, we get that the solution of the stochastic homogenized equation is not divergence free. However, it is coupled with the cell problem that has a divergence free solution. This paper represents an extension of the results of Duan and Wang (Comm. Math. Phys. 275:1508-1527, 2007), where a reaction diffusion equation with a dynamical boundary condition with a noise source term on both the interior of the domain and on the boundary was studied, and through a tightness argument and a pointwise two scale convergence method the homogenized equation was derived. © American Institute of Mathematical Sciences.
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.
Effect of Boundary Conditions on the Back Face Deformations of Flat UHMWPE Panels
2014-12-01
the experimental results in general, and was computationally more expedient. Delamination is a very common failure mode in composite laminates , and... delaminations in the composites . The calculation showed reasonable agreement with the experimental data for the clamped-corners and free boundary condition...cases for the peak BFD, remaining thickness of the composite and the delamination behavior. The model is useful to assess the size-effects and boundary
Exact controllability for a wave equation with mixed boundary conditions in a non-cylindrical domain
Directory of Open Access Journals (Sweden)
Lizhi Cui
2014-04-01
Full Text Available In this article we study the exact controllability of a one-dimensional wave equation with mixed boundary conditions in a non-cylindrical domain. The fixed endpoint has a Dirichlet-type boundary condition, while the moving end has a Neumann-type condition. When the speed of the moving endpoint is less than the characteristic speed, the exact controllability of this equation is established by Hilbert Uniqueness Method. Moreover, we shall give the explicit dependence of the controllability time on the speed of the moving endpoint.
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.
Winkler boundary conditions for three-point bending tests on 1D nanomaterials
Gangadean, D.; McIlroy, David N.; Faulkner, Brian E.; Aston, D. Eric
2010-06-01
Bending tests with atomic force microscopes (AFM) is a common method for elasticity measurements on 1D nanomaterials. Interpretation of the force and deflection data is necessary to determine the Young's modulus of the tested material and has been done assuming either of two classic boundary conditions that represent two extreme possibilities for the rigidity of the sample-anchor interface. The elasticity results from the two boundary conditions differ by a factor of four. Furthermore, both boundary conditions ignore the effects of deflections in the anchors themselves. The Winkler model for beams on elastic foundations is developed here for three-point bending tests to provide a more realistic representation. Equations for computing sample elasticity are derived from two sets of boundary conditions for the Winkler model. Application of this model to interpret the measurement of mechanical stiffness of a silica nanowire at multiple points in a three-point bending is discussed. With the correct choice of boundary conditions, the Winkler model gives a better fit for the observed stiffness profile than the classical beam models while providing a result that differs from both by a factor of two and is comparable to the bulk elasticity.
Winkler boundary conditions for three-point bending tests on 1D nanomaterials.
Gangadean, D; McIlroy, David N; Faulkner, Brian E; Aston, D Eric
2010-06-04
Bending tests with atomic force microscopes (AFM) is a common method for elasticity measurements on 1D nanomaterials. Interpretation of the force and deflection data is necessary to determine the Young's modulus of the tested material and has been done assuming either of two classic boundary conditions that represent two extreme possibilities for the rigidity of the sample-anchor interface. The elasticity results from the two boundary conditions differ by a factor of four. Furthermore, both boundary conditions ignore the effects of deflections in the anchors themselves. The Winkler model for beams on elastic foundations is developed here for three-point bending tests to provide a more realistic representation. Equations for computing sample elasticity are derived from two sets of boundary conditions for the Winkler model. Application of this model to interpret the measurement of mechanical stiffness of a silica nanowire at multiple points in a three-point bending is discussed. With the correct choice of boundary conditions, the Winkler model gives a better fit for the observed stiffness profile than the classical beam models while providing a result that differs from both by a factor of two and is comparable to the bulk elasticity.
SQUEEZE-E: The Optimal Solution for Molecular Simulations with Periodic Boundary Conditions.
Wassenaar, Tsjerk A; de Vries, Sjoerd; Bonvin, Alexandre M J J; Bekker, Henk
2012-10-09
In molecular simulations of macromolecules, it is desirable to limit the amount of solvent in the system to avoid spending computational resources on uninteresting solvent-solvent interactions. As a consequence, periodic boundary conditions are commonly used, with a simulation box chosen as small as possible, for a given minimal distance between images. Here, we describe how such a simulation cell can be set up for ensembles, taking into account a priori available or estimable information regarding conformational flexibility. Doing so ensures that any conformation present in the input ensemble will satisfy the distance criterion during the simulation. This helps avoid periodicity artifacts due to conformational changes. The method introduces three new approaches in computational geometry: (1) The first is the derivation of an optimal packing of ensembles, for which the mathematical framework is described. (2) A new method for approximating the α-hull and the contact body for single bodies and ensembles is presented, which is orders of magnitude faster than existing routines, allowing the calculation of packings of large ensembles and/or large bodies. 3. A routine is described for searching a combination of three vectors on a discretized contact body forming a reduced base for a lattice with minimal cell volume. The new algorithms reduce the time required to calculate packings of single bodies from minutes or hours to seconds. The use and efficacy of the method is demonstrated for ensembles obtained from NMR, MD simulations, and elastic network modeling. An implementation of the method has been made available online at http://haddock.chem.uu.nl/services/SQUEEZE/ and has been made available as an option for running simulations through the weNMR GRID MD server at http://haddock.science.uu.nl/enmr/services/GROMACS/main.php .
DEFF Research Database (Denmark)
Bieniasz, Leslaw K; Østerby, Ole; Britz, Dieter
1997-01-01
, is based on the forward difference gradient approximation, and may in some cases become numerically unstable. Therefore, we analyse the numerical stability of a number of alternative discretizations that have not yet been used in electrochemical simulations. The discretizations are based on the forward......Mixed boundary conditions with time-dependent coefficients are typical for diffusional initial boundary value problems occurring in electrochemical kinetics. The discretization of such boundary conditions, currently used in connection with the Crank-Nicolson finite difference solution algorithm......, central and backward difference gradient approximations. We show that some variants of the central and backward difference gradient approximations ensure the unconditional stability of the Crank-Nicolson method and can, therefore, be of practical interest. Furthermore, we show that the discretization used...
Boundary condition-selective length dependence of the flexural rigidity of microtubules
Zhang, Jin; Wang, Chengyuan
2017-07-01
Length-dependent flexural rigidity (FR) is observed experimentally for microtubules (MTs) subjected to certain boundary conditions. To shed some light on this unique feature, we have studied the FR of MTs with different boundary conditions. A molecular structural mechanics method is employed to accurately describe the real boundary conditions imposed on MTs in experiments. Some of component protofilaments of MTs are blocked at the ends while others are free. In addition, linked kinesin is treated as an elastic body rather than a rigid body. Our simulations show that for relatively long MTs having a length comparable to those measured in experiments the length-dependent rigidity is detected only for those with fixed-free and fixed-fixed ends, which is consistent with the experimental observation. To capture the physics leading to the above phenomenon, Timoshenko beam model is adopted accounting for both transverse shear effect (TSE) and imperfect boundary effect (IBE). Comparison between TSE and IBE indicates that the boundary condition-selective length-dependence achieved for the FR of relatively long MTs is primarily a result of the influence of IBE rather than TSE.
Energy Technology Data Exchange (ETDEWEB)
Mirzabeigy, Alborz; Madoliat, Reza [Iran University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of); Dabbagh, Vahid [University of Malaya, Kuala Lumpur (Malaysia)
2017-02-15
In this paper, free transverse vibration of two parallel beams connected through Winkler type elastic layer is investigated. Euler- Bernoulli beam hypothesis has been applied and it is assumed that boundary conditions of upper and lower beams are similar while arbitrary without any limitation even for non-ideal boundary conditions. Material properties and cross-section geometry of beams could be different from each other. The motion of the system is described by a homogeneous set of two partial differential equations, which is solved by using the classical Bernoulli-Fourier method. Explicit expressions are derived for the natural frequencies. In order to verify accuracy of results, the problem once again solved using modified Adomian decomposition method. Comparison between results indicates excellent accuracy of proposed formulation for any arbitrary boundary conditions. Derived explicit formulation is simplest method to determine natural frequencies of double-beam systems with high level of accuracy in comparison with other methods in literature.
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.
Fang, Angbo
2008-12-08
Parallel to the highly successful Ericksen-Leslie hydrodynamic theory for the bulk behavior of nematic liquid crystals (NLCs), we derive a set of coupled hydrodynamic boundary conditions to describe the NLC dynamics near NLC-solid interfaces. In our boundary conditions, translational flux (flow slippage) and rotational flux (surface director relaxation) are coupled according to the Onsager variational principle of least energy dissipation. The application of our boundary conditions to the truly bistable π -twist NLC cell reveals a complete picture of the dynamic switching processes. It is found that the thus far overlooked translation-rotation dissipative coupling at solid surfaces can accelerate surface director relaxation and enhance the flow rate. This can be utilized to improve the performance of electro-optical nematic devices by lowering the required switching voltages and reducing the switching times. © 2008 The American Physical Society.
Heat Transfer Boundary Conditions in the RELAP5-3D Code
Energy Technology Data Exchange (ETDEWEB)
Richard A. Riemke; Cliff B. Davis; Richard R. Schultz
2008-05-01
The heat transfer boundary conditions used in the RELAP5-3D computer program have evolved over the years. Currently, RELAP5-3D has the following options for the heat transfer boundary conditions: (a) heat transfer correlation package option, (b) non-convective option (from radiation/conduction enclosure model or symmetry/insulated conditions), and (c) other options (setting the surface temperature to a volume fraction averaged fluid temperature of the boundary volume, obtaining the surface temperature from a control variable, obtaining the surface temperature from a time-dependent general table, obtaining the heat flux from a time-dependent general table, or obtaining heat transfer coefficients from either a time- or temperature-dependent general table). These options will be discussed, including the more recent ones.
Sensitivity of an idealized subtropical gyre to the eastern boundary conditions
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I. Láiz
2001-07-01
Full Text Available The flow pattern of the North Atlantic Subtropical Gyre (NASG is simulated using a highly idealised one-layer quasi-geostrophic wind-driven model. The novel feature of the model is the specification of the eastern boundary conditions. This is an upwelling favourable region with a quasi-permanent southward flowing coastal jet, which is fed by the eastern branch of the Canary Current. The corresponding boundary conditions are non-zero normal flux and constant potential vorticity, the latter being consistent with the generation of anticyclonic vorticity by the coastal jet. We examine the sensitivity of the model to the eastern boundary conditions and compare the results with recent observations for the region.
Reconsidering the boundary conditions for a dynamic, transient mode I crack problem
Leise, Tanya
2008-11-01
A careful examination of a dynamic mode I crack problem leads to the conclusion that the commonly used boundary conditions do not always hold in the case of an applied crack face loading, so that a modification is required to satisfy the equations. In particular, a transient compressive stress wave travels along the crack faces, moving outward from the loading region on the crack face. This does not occur in the quasistatic or steady state problems, and is a special feature of the transient dynamic problem that is important during the time interval immediately following the application of crack face loading. We demonstrate why the usual boundary conditions lead to a prediction of crack face interpenetration, and then examine how to modify the boundary condition for a semi-infinite crack with a cohesive zone. Numerical simulations illustrate the resulting approach.
Fraga Filho, Carlos Alberto Dutra
2017-11-01
The aim of this paper is to present a computational algorithmic implementation of physical reflective boundary conditions and applications, for use in particle methods. It is motivated by the lack of a straightforward study in the literature dedicated to the presentation of this reflective boundary condition, based on Newton's restitution law and the foundations of analytic geometry. Particular attention is given here to the procedures of collision detection and response. The importance of the consistency of input data and an appropriate temporal integration technique for use in the particle method is also discussed. Validation tests are performed, with the results of the algorithm verified using analytical results. Numerical simulations of static and dynamic problems are carried out. The analysis of the numerical results shows that the physical reflective boundary conditions are consistent and that the algorithm has been properly implemented.
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.
Constraint-preserving boundary conditions in the 3+1 first-order approach
Bona, C
2010-01-01
A set of stable energy-momentum constraint-preserving boundary conditions are proposed for the first-order Z4 case. No linear modes appear in the robust stability test. Also, a modified finite-differences stencil for boundary points is presented, which avoids the corner and vertex points even in cartesian-like grids. Moreover, the proposed boundary conditions are tested in a strong field scenario, the Gowdy waves metric, showing that the accumulated amount of energy-momentum constraint violations is of the same order of magnitude than the one generated by either periodic or reflection conditions, which are exact in the Gowdy waves case. As a side result, a new symmetrizer is explicitly given, which extends the parametric domain of symmetric hyperbolicity for the Z4 formalism. The aplication of these results to first-order BSSN-like formalisms is also considered.
(2,2) and (0,4) supersymmetric boundary conditions in 3d N =4 theories and type IIB branes
Chung, Hee-Joong; Okazaki, Tadashi
2017-10-01
The half-BPS boundary conditions preserving N =(2 ,2 ) and N =(0 ,4 ) supersymmetry in 3d N =4 supersymmetric gauge theories are examined. The BPS equations admit decomposition of the bulk supermultiplets into specific boundary supermultiplets of preserved supersymmetry. Nahm-like equations arise in the vector multiplet BPS boundary condition preserving N =(0 ,4 ) supersymmetry, and Robin-type boundary conditions appear for the hypermultiplet coupled to the vector multiplet when N =(2 ,2 ) supersymmetry is preserved. The half-BPS boundary conditions are realized in the brane configurations of type IIB string theory.
Douillet-Grellier, Thomas; Pramanik, Ranjan; Pan, Kai; Albaiz, Abdulaziz; Jones, Bruce D.; Williams, John R.
2017-10-01
This paper develops a method for imposing stress boundary conditions in smoothed particle hydrodynamics (SPH) with and without the need for dummy particles. SPH has been used for simulating phenomena in a number of fields, such as astrophysics and fluid mechanics. More recently, the method has gained traction as a technique for simulation of deformation and fracture in solids, where the meshless property of SPH can be leveraged to represent arbitrary crack paths. Despite this interest, application of boundary conditions within the SPH framework is typically limited to imposed velocity or displacement using fictitious dummy particles to compensate for the lack of particles beyond the boundary interface. While this is enough for a large variety of problems, especially in the case of fluid flow, for problems in solid mechanics there is a clear need to impose stresses upon boundaries. In addition to this, the use of dummy particles to impose a boundary condition is not always suitable or even feasibly, especially for those problems which include internal boundaries. In order to overcome these difficulties, this paper first presents an improved method for applying stress boundary conditions in SPH with dummy particles. This is then followed by a proposal of a formulation which does not require dummy particles. These techniques are then validated against analytical solutions to two common problems in rock mechanics, the Brazilian test and the penny-shaped crack problem both in 2D and 3D. This study highlights the fact that SPH offers a good level of accuracy to solve these problems and that results are reliable. This validation work serves as a foundation for addressing more complex problems involving plasticity and fracture propagation.
Directory of Open Access Journals (Sweden)
G Boroni
2017-03-01
Full Text Available Lattice Boltzmann Method (LBM has shown great potential in fluid simulations, but performance issues and difficulties to manage complex boundary conditions have hindered a wider application. The upcoming of Graphic Processing Units (GPU Computing offered a possible solution for the performance issue, and methods like the Immersed Boundary (IB algorithm proved to be a flexible solution to boundaries. Unfortunately, the implicit IB algorithm makes the LBM implementation in GPU a non-trivial task. This work presents a fully parallel GPU implementation of LBM in combination with IB. The fluid-boundary interaction is implemented via GPU kernels, using execution configurations and data structures specifically designed to accelerate each code execution. Simulations were validated against experimental and analytical data showing good agreement and improving the computational time. Substantial reductions of calculation rates were achieved, lowering down the required time to execute the same model in a CPU to about two magnitude orders.
Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions
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Markus Holzleitner
2016-01-01
Full Text Available We investigate the dependence of the \\(L^1\\to L^{\\infty}\\ dispersive estimates for one-dimensional radial Schrödinger operators on boundary conditions at \\(0\\. In contrast to the case of additive perturbations, we show that the change of a boundary condition at zero results in the change of the dispersive decay estimates if the angular momentum is positive, \\(l\\in (0,1/2\\. However, for nonpositive angular momenta, \\(l\\in (-1/2,0]\\, the standard \\(O(|t|^{-1/2}\\ decay remains true for all self-adjoint realizations.
Mathematical analysis of the Navier-Stokes equations with non standard boundary conditions
Tidriri, M. D.
1995-01-01
One of the major applications of the domain decomposition time marching algorithm is the coupling of the Navier-Stokes systems with Boltzmann equations in order to compute transitional flows. Another important application is the coupling of a global Navier-Stokes problem with a local one in order to use different modelizations and/or discretizations. Both of these applications involve a global Navier-Stokes system with nonstandard boundary conditions. The purpose of this work is to prove, using the classical Leray-Schauder theory, that these boundary conditions are admissible and lead to a well posed problem.
DEFF Research Database (Denmark)
Richards, H.L.; Kolesik, M.; Lindgård, P.-A.
1997-01-01
Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with periodic boundary conditions. In this paper we consider the effe......Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with periodic boundary conditions. In this paper we consider...
Directory of Open Access Journals (Sweden)
Da Silva E Serra Luis
2015-01-01
Full Text Available 2BSvs is one of the most important certification schemes for biofuels worldwide, covering a wide range of feedstock and is currently used in 22 countries by a large number of certified economic operators. 2BSvs covers the complete biofuel industry supply chain from the biomass producer to the final biofuel trader, from production and trading of the raw materials all the way through to biofuel production. 2BSvs has seen regular growth over the last 3 years and the consortium 2BS which manages the scheme, is striving to offer its clients a high level of trust, credibility and support through its professional services with a clear focus on cost-efficiency, and remaining in strict compliance with the requirements of the Directive 2009/28/EC on the promotion of the use of energy from renewable sources. Continuous improvement is at the heart of the management system of the 2BS Consortium, who continually reviews the scheme through regular consultation with industry experts and relevant regulatory bodies so as to ensure that it continues to provide a service that the users and the biofuel market in general can rely on.
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Beatriz Venda
2017-12-01
Full Text Available Nutrition is an important component in the treatment of disease. A correct and balanced food intake before, during, and after treatment can help the patient feel better, maintain weight and nutrient reserves, decrease the risk of infection, increase tolerance to treatment, effect and consequently contribute for better and faster recovery. Oncologic disease (whose incidence rate of new cases of malignant tumors has been increasing regularly, with an increase of 4% of cases in Portugal registered between 2009 and 2010 has repercussions as a harmful experience for well-being and quality of life, not only as a result of the disease itself, but also the treatment. It is in this context that the project "Eat well, live healthy" emerges, whose overall objective aims to provide patients access to a varied menu, balanced and rich from a nutritional point of view. With menus (starter, soup, main course and dessert that promote food intake and ensure good nutritional value, we want patients to know that an adjusted food intake allows them to achieve the energy and protein requirements; reduce and mitigate the side effects of treatment and allow a better recovery, a reduction of hospitalization time and an improved quality of life.
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Syahira Mansur
2014-01-01
Full Text Available The magnetohydrodynamic (MHD boundary layer flow of a nanofluid past a stretching/shrinking sheet with velocity, thermal, and solutal slip boundary conditions is studied. Numerical solutions to the governing equations were obtained using a shooting method. The skin friction coefficient and the local Sherwood number increase as the stretching/shrinking parameter increases. However, the local Nusselt number decreases with increasing the stretching/shrinking parameter. The range of the stretching/shrinking parameter for which the solution exists increases as the velocity slip parameter and the magnetic parameter increase. For the shrinking sheet, the skin friction coefficient increases as the velocity slip parameter and the magnetic parameter increase. For the stretching sheet, it decreases when the velocity slip parameter and the magnetic parameter increase. The local Nusselt number diminishes as the thermal slip parameter increases while the local Sherwood number decreases with increasing the solutal slip parameter. The local Nusselt number is lower for higher values of Lewis number, Brownian motion parameter, and thermophoresis parameter.
Free vibration of functionally graded parabolic and circular panels with general boundary conditions
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Zhang Hong
2017-01-01
Full Text Available The purpose of this content is to investigate the free vibration of functionally graded parabolic and circular panels with general boundary conditions by using the Fourier-Ritz method. The first-order shear deformation theory is adopted to consider the effects of the transverse shear and rotary inertia of the panel structures. The functionally graded panel structures consist of ceramic and metal which are assumed to vary continuously through the thickness according to the power-law distribution, and two types of power-law distributions are considered for the ceramic volume fraction. The improved Fourier series method is applied to construct the new admissible function of the panels to surmount the weakness of the relevant discontinuities with the original displacement and its derivatives at the boundaries while using the traditional Fourier series method. The boundary spring technique is adopted to simulate the general boundary condition. The unknown coefficients appearing in the admissible function are determined by using the Ritz procedure based on the energy functional of the panels. The numerical results show the present method has good convergence, reliability and accuracy. Some new results for functionally graded parabolic and circular panels with different material distributions and boundary conditions are provided, which may serve as benchmark solutions.
Numerical Study of Outlet Boundary Conditions for Unsteady Turbulent Internal Flows Using the NCC
Liu, Nan-Suey; Shih, Tsan-Hsing
2009-01-01
This paper presents the results of studies on the outlet boundary conditions for turbulent internal flow simulations. Several outlet boundary conditions have been investigated by applying the National Combustion Code (NCC) to the configuration of a LM6000 single injector flame tube. First of all, very large eddy simulations (VLES) have been performed using the partially resolved numerical simulation (PRNS) approach, in which both the nonlinear and linear dynamic subscale models were employed. Secondly, unsteady Reynolds averaged Navier- Stokes (URANS) simulations have also been performed for the same configuration to investigate the effects of different outlet boundary conditions in the context of URANS. Thirdly, the possible role of the initial condition is inspected by using three different initial flow fields for both the PRNS/VLES simulation and the URANS simulation. The same grid is used for all the simulations and the number of mesh element is about 0.5 million. The main purpose of this study is to examine the long-time behavior of the solution as determined by the imposed outlet boundary conditions. For a particular simulation to be considered as successful under the given initial and boundary conditions, the solution must be sustainable in a physically meaningful manner over a sufficiently long period of time. The commonly used outlet boundary condition for steady Reynolds averaged Navier-Stokes (RANS) simulation is a fixed pressure at the outlet with all the other dependent variables being extrapolated from the interior. The results of the present study suggest that this is also workable for the URANS simulation of the LM6000 injector flame tube. However, it does not work for the PRNS/VLES simulation due to the unphysical reflections of the pressure disturbances at the outlet boundary. This undesirable situation can be practically alleviated by applying a simple unsteady convection equation for the pressure disturbances at the outlet boundary. The
Accurate and Well-posed Absorbing Boundary Conditions for Anisotropic Media
Savadatti, Siddharth
This dissertation provides (a) an accurate and well-posed local absorbing boundary condition (ABC) for time-dependent modeling of propagating waves in tilted anisotropic acoustic media, (b) an accurate local ABC for time-harmonic modeling of both propagating and evanescent anti-plane and in-plane waves in tilted elliptic anisotropic elastic media, and (c) an accurate local ABC for time-harmonic modeling of in-plane propagating waves in untilted non-elliptic anisotropic elastic media. Such media support wavemodes with opposing signs of phase (cpx) and group (cgx) velocities that have long posed a significant challenge to the design of accurate, well-posed and stable local ABCs. By specifically considering the recently developed local ABC, the perfectly matched discrete layer (PMDL), we show that a careful choice of parameters can result in an effective local ABC for anisotropic media. We first consider a PMDL with real-valued parameters designed to absorb the propagating wavemodes of tilted anisotropic acoustics. Starting with the derivation of the reflection coefficient, we show that the PMDL absorption is based on group (not phase) velocities. The group velocity form of the reflection coefficient is used to derive a sufficient condition for PMDL to accurately absorb all outgoing wavemodes (even those with opposing signs of phase and group velocities, i.e. cpxcgx interior with PMDL, we show that the accuracy condition also ensures well-posedness. We consider next a PMDL with complex-valued parameters designed to absorb both the propagating and evanescent wavemodes of tilted elliptic anisotropic elasticity. By first considering the simpler case of scalar anti-plane shear waves, we show that it is possible to overcome the challenges posed by cpxcgx designed to absorb the propagating wavemodes of untilted non-elliptic anisotropic elasticity. While simple space-time transformations are available to treat the wavemodes with cpxcgx concept of layer grouping along with a
Zhang, Jialin; Chen, Qian; Li, Jiaji; Zuo, Chao
2017-02-01
The transport of intensity equation (TIE) is a powerful tool for direct quantitative phase retrieval in microscopy imaging. However, there may be some problems when dealing with the boundary condition of the TIE. The previous work introduces a hard-edged aperture to the camera port of the traditional bright field microscope to generate the boundary signal for the TIE solver. Under this Neumann boundary condition, we can obtain the quantitative phase without any assumption or prior knowledge about the test object and the setup. In this paper, we will demonstrate the effectiveness of this method based on some experiments in practice. The micro lens array will be used for the comparison of two TIE solvers results based on introducing the aperture or not and this accurate quantitative phase imaging technique allows measuring cell dry mass which is used in biology to follow cell cycle, to investigate cell metabolism, or to address effects of drugs.
Energy Technology Data Exchange (ETDEWEB)
Rauf, A., E-mail: raufamar@ciitsahiwal.edu.pk [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Siddiq, M.K. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Abbasi, F.M. [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Meraj, M.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Ashraf, M. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Shehzad, S.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)
2016-10-15
The present work deals with the steady laminar three-dimensional mixed convective magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid over a bidirectional stretching surface. A uniform magnetic field is applied normal to the flow direction. Similarity variables are implemented to convert the non-linear partial differential equations into ordinary ones. Convective boundary conditions are utilized at surface of the sheet. A numerical technique of Runge–Kutta–Fehlberg (RFK45) is used to obtain the results of velocity, temperature and concentration fields. The physical dimensionless parameters are discussed through tables and graphs. - Highlights: • Mixed convective boundary layer flow of Casson nanofluid is taken into account. • Impact of magnetic field is examined. • Convective heat and mass conditions are imposed. • Numerical solutions are presented and discussed.
Rahimi, Mohammad; Karimi-Varzaneh, Hossein Ali; Böhm, Michael C; Müller-Plathe, Florian; Pfaller, Sebastian; Possart, Gunnar; Steinmann, Paul
2011-04-21
A scheme is described for performing molecular dynamics simulations on polymers under nonperiodic, stochastic boundary conditions. It has been designed to allow later the embedding of a particle domain treated by molecular dynamics into a continuum environment treated by finite elements. It combines, in the boundary region, harmonically restrained particles to confine the system with dissipative particle dynamics to dissipate energy and to thermostat the simulation. The equilibrium position of the tethered particles, the so-called anchor points, are well suited for transmitting deformations, forces and force derivatives between the particle and continuum domains. In the present work the particle scheme is tested by comparing results for coarse-grained polystyrene melts under nonperiodic and regular periodic boundary conditions. Excellent agreement is found for thermodynamic, structural, and dynamic properties.
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Huimin Liu
2017-01-01
Full Text Available This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique.
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Yanmei Sun
2012-01-01
Full Text Available By using the Leggett-Williams fixed theorem, we establish the existence of multiple positive solutions for second-order nonhomogeneous Sturm-Liouville boundary value problems with linear functional boundary conditions. One explicit example with singularity is presented to demonstrate the application of our main results.
On the strongly damped wave equation and the heat equation with mixed boundary conditions
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Aloisio F. Neves
2000-01-01
Full Text Available We study two one-dimensional equations: the strongly damped wave equation and the heat equation, both with mixed boundary conditions. We prove the existence of global strong solutions and the existence of compact global attractors for these equations in two different spaces.
DEFF Research Database (Denmark)
Andersen, Michael; Abel, Sarah Maria Niebe; Erleben, Kenny
2017-01-01
We address the task of computing solutions for a separating fluid-solid wall boundary condition model. We present an embarrassingly parallel, easy to implement, fluid LCP solver.We are able to use greater domain sizes than previous works have shown, due to our new solver. The solver exploits matrix...
On a Mathematical Model with Noncompact Boundary Conditions Describing Bacterial Population
Boulanouar, Mohamed
2013-04-01
In this work, we are concerned with the well-posedness of a mathematical model describing a maturation-velocity structured bacterial population. Each bacterium is distinguished by its degree of maturity and its maturation velocity. The bacterial mitosis is mathematically described by noncompact boundary conditions. We show that the mathematical model is governed by a positive strongly continuous semigroup.
Notes on wave theory in heat conduction: a new boundary condition.
Kronberg, Alexandre E.; Benneker, A.H.; Benneker, A.H.; Westerterp, K.R.
1997-01-01
The physical basis behind the simple hyperbolic heat transport model is discussed. The model equations are interpreted as energy equations for a system in a state of local nonequilibrium. On this basis a new boundary condition for the hyperbolic model is proposed when the temperature of a surface is
DEFF Research Database (Denmark)
Janssen, Hans; Blocken, Bert; Roels, Staf
2007-01-01
While the numerical simulation of moisture transfer inside building components is currently undergoing standardisation, the modelling of the atmospheric boundary conditions has received far less attention. This article analyses the modelling of the wind-driven-rain load on building facades by par...
Boundary lubrication by brushed salivary conditioning films and their degree of glycosylation
Veeregowda, Deepak H; van der Mei, Henderina; de Vries, Jacob; Rutland, Mark W; Valle-Delgado, Juan J; Sharma, Prashant K; Busscher, Hendrik
2012-01-01
Toothbrushing, though aimed at biofilm removal, also affects the lubricative function of adsorbed salivary conditioning films (SCFs). Different modes of brushing (manual, powered, rotary-oscillatory or sonically driven) influence the SCF in different ways. Our objectives were to compare boundary
Impact of boundary conditions on the development of the thermal plume above a sitting human body
DEFF Research Database (Denmark)
Zukowska, Daria; Popiolek, Zbigniew J.; Melikov, Arsen Krikor
2010-01-01
The phenomenon of the thermal plume above a heat source has been reported in the literature as being influenced by a large number of factors. The objective of the present study is to identify the impact of the boundary conditions on the characteristics and development of the thermal plume above...
OpenCL-Based FPGA Accelerator for 3D FDTD with Periodic and Absorbing Boundary Conditions
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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.
Application of impedance boundary conditions to numerical solution of corrugated circular horns
DEFF Research Database (Denmark)
Iskander, K; Shafai, L; Frandsen, Aksel
1982-01-01
An integral equation method is used to formulate the problem of scattering by rotationally symmetric horn antennas. The excitation is assumed to be due to an infinitesimal dipole antenna, while the secondary field is obtained by assuming anisotropic impedance boundary conditions on the horn surface...
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Tengfei Shen
2015-12-01
Full Text Available This paper deals with the multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects. By using critical point theory, a new result is obtained. An example is given to illustrate the main result.
DEFF Research Database (Denmark)
Madsen, Søren; Pinna, Rodney; Randolph, M. F.
2015-01-01
of large-diameter bucket foundations. Since shell structures are generally sensitive to initially imperfect geometries, eigenmode-affine imperfections are introduced in a nonlinear finite-element analysis. The influence of modelling the real lid structure compared to classic boundary conditions...
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Shayma Adil Murad
2011-01-01
Full Text Available 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.
An inherently stable boundary-condition-transfer algorithm for muffler analysis
Kar, T.; Munjal, M. L.
2005-07-01
Wave coupling exists in the wave propagation in multiple interacting ducts within a waveguide. One may use the segmentation approach, decoupling approach, eigenvalue approach, or the matrizant approach to derive the overall transfer matrix for the muffler section with interacting ducts, and then apply the terminal boundary conditions to obtain a two-by-two transfer matrix. In such instances, a boundary condition applied to a vector is given as a linear combination of its components. Spatial dimensions along with parameters like impedance of the perforated interface may yield numerical instability during computation leading to inaccurate prediction of the acoustic performance of mufflers. Here, an inherently stable boundary-condition-transfer approach is discussed to analyze the plane wave propagation in suchlike mufflers and applied to waveguides of variable cross-sectional area. The concept of pseudo boundary conditions applied to the state vector at an intermediate point is outlined. The method is checked for self-consistency and shown to be stable even for extreme geometries.
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Charyyar Ashyralyyev
2015-07-01
Full Text Available This article studies the numerical solution of inverse problems for the multidimensional elliptic equation with Dirichlet-Neumann boundary conditions and Neumann type overdetermination. We present first and second order accuracy difference schemes. The stability and almost coercive stability inequalities for the solution are obtained. Numerical examples with explanation on the implementation illustrate the theoretical results.
Nonlinear parabolic problems with Neumann-type boundary conditions and L^1-data
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Abderrahmane El Hachimi
2007-11-01
$$ \\frac{\\partial u}{\\partial t}-\\triangle_{p}u+\\alpha(u=f \\quad \\text{in } ]0,\\ T[\\times\\Omega, $$ with Neumann-type boundary conditions and initial data in $L^1$. Our approach is based essentially on the time discretization technique by Euler forward scheme.
Nonlinear Fredholm alternative for the p-Laplacian under nonhomogeneous Neumann boundary condition
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Gustavo Ferron Madeira
2016-08-01
Full Text Available The nonlinear Fredholm alternative for the p-Laplacian in higher dimensions is established when nonhomogeneous terms appear in the equation and in the Neumann boundary condition. Further, the geometry of the associated energy functional is described and compared with the Dirichlet counterpart. The proofs require only variational methods.
Menges, J.; Walter, F.; Vogel, B.; Bruch, H.
2011-01-01
Transformational leadership (TFL) climate describes the degree to which leaders throughout an organization engage in TFL behaviors. In this study, we investigate performance linkages, mechanisms, and boundary conditions of TFL climate at the organizational level of analysis. In a sample of 158
Directory of Open Access Journals (Sweden)
Valery Romanovski
2008-12-01
Full Text Available We prove existence results for second-order impulsive differential equations with antiperiodic boundary value conditions in the presence of classical fixed point theorems. We also obtain the expression of Green's function of related linear operator in the space of piecewise continuous functions.
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,...
On The Stabilization of the Linear Kawahara Equation with Periodic Boundary Conditions
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Patricia N. da Silva
2015-03-01
Full Text Available We study the stabilization of global solutions of the linear Kawahara equation (K with periodic boundary conditions under the effect of a localized damping mechanism. The Kawahara equation is a model for small amplitude long waves. Using separation of variables, the Ingham inequality, multiplier techniques and compactness arguments we prove the exponential decay of the solutions of the (K model.
Optimal trajectory generation for generalization of discrete movements with boundary condition
DEFF Research Database (Denmark)
Herzog, Sebastian; Wörgötter, Florentin; Kulvicius, Tomas
2016-01-01
Trajectory generation methods play an important role in robotics since they are essential for the execution of actions. In this paper we present a novel trajectory generation method for generalization of accurate movements with boundary conditions. Our approach originates from optimal control the...
Semilinear Evolution Problems with Ventcel-Type Conditions on Fractal Boundaries
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Maria Rosaria Lancia
2014-01-01
Full Text Available A semilinear parabolic transmission problem with Ventcel's boundary conditions on a fractal interface S or the corresponding prefractal interface Sh is studied. Regularity results for the solution in both cases are proved. The asymptotic behaviour of the solutions of the approximating problems to the solution of limit fractal problem is analyzed.
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Romanovski Valery
2008-01-01
Full Text Available We prove existence results for second-order impulsive differential equations with antiperiodic boundary value conditions in the presence of classical fixed point theorems. We also obtain the expression of Green's function of related linear operator in the space of piecewise continuous functions.
A stable penalty method for the compressible Navier-Stokes equations: I. Open boundary conditions
DEFF Research Database (Denmark)
Hesthaven, Jan; Gottlieb, D.
1996-01-01
The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization...
Grunau, H.-Ch.; Sweers, G.
1995-01-01
Higher order elliptic partial dierential equations with Dirichlet boundary conditions in general do not satisfy a maximum principle. Polyharmonic operators on balls are an exception. Here it is shown that in IR2 small perturbations of polyharmonic operators and of the domain preserve the maximum
Null exact controllability of the parabolic equations with equivalued surface boundary condition
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available This paper is devoted to showing the null exact controllability for a class of parabolic equations with equivalued surface boundary condition. Our method is based on the duality argument and global Carleman-type estimate for a parabolic operator.
In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary Conditions
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Xianjie Shi
2014-01-01
Full Text Available In comparison with the out-of-plane vibrations of annular plates, far less attention has been paid to the in-plane vibrations which may also play a vital important role in affecting the sound radiation from and power flows in a built-up structure. In this investigation, a generalized Fourier series method is proposed for the in-plane vibration analysis of annular plates with arbitrary boundary conditions along each of its edges. Regardless of the boundary conditions, the in-plane displacement fields are invariantly expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. All the unknown expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. Unlike most of the existing studies, the presented method can be readily and universally applied to a wide spectrum of in-plane vibration problems involving different boundary conditions, varying material, and geometric properties with no need of modifying the basic functions or adapting solution procedures. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current solution for predicting the in-plane vibration characteristics of annular plates subjected to different boundary conditions.
Wijnant, Ysbrand H.; Spiering, R.M.E.J.; Blijderveen, M.; de Boer, Andries
2006-01-01
Previous research has shown that viscothermal wave propagation in narrow gaps can efficiently be described by means of the low reduced frequency model. For simple geometries and boundary conditions, analytical solutions are available. For example, Beltman [4] gives the acoustic pressure in the gap
Evidence for Cretaceous-Paleogene boundary bolide “impact winter” conditions from New Jersey, USA
Vellekoop, J.; Esmeray-Senlet, S.; Miller, K.G.; Browning, J.V.; Sluijs, A.; van de Schootbrugge, B.; Sinninghe Damsté, J.S.; Brinkhuis, H.
2016-01-01
Abrupt and short-lived “impact winter” conditions have commonly been implicated as the main mechanism leading to the mass extinction at the Cretaceous-Paleogene (K-Pg) boundary (ca. 66 Ma), marking the end of the reign of the non-avian dinosaurs. However, so far only limited evidence has been
Evidence for Cretaceous-Paleogene boundary bolide "impact winter" conditions from New Jersey, USA
Vellekoop, J.; Esmeray-Senlet, S.; Miller, K.G.; Browning, J.V.; Sluijs, A.; van de Schootbrugge, B.; Sinninghe Damsté, J.S.; Brinkhuis, H.
2016-01-01
Abrupt and short-lived “impact winter” conditions have commonly been implicated as the main mechanism leading to the mass extinction at the Cretaceous-Paleogene (K-Pg) boundary (ca. 66 Ma), marking the end of the reign of the non-avian dinosaurs. However, so far only limited evidence has been
DEFF Research Database (Denmark)
Duggen, Lars; Lopes, Natasha; Willatzen, Morten
2011-01-01
The finite-element method (FEM) is used to simulate the photoacoustic signal in a cylindrical resonant photoacoustic cell. Simulations include loss effects near the cell walls that appear in the boundary conditions for the inhomogeneous Helmholtz equation governing the acoustic pressure. Reasonab...
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Saowaluk Chasreechai
2015-01-01
Full Text Available We study existence and uniqueness results for Caputo fractional sum-difference equations with fractional sum boundary value conditions, by using the Banach contraction principle and Schaefer’s fixed point theorem. Our problem contains different numbers of order in fractional difference and fractional sums. Finally, we present some examples to show the importance of these results.
Damage detection of fatigue cracks under nonlinear boundary condition using subharmonic resonance.
Zhang, Mengyang; Xiao, Li; Qu, Wenzhong; Lu, Ye
2017-05-01
In recent years, the nonlinear ultrasonic technique has been widely utilized for detecting fatigue crack, one of the most common forms of damage. However, one of limitations associated with this technique is that nonlinearities can be produced not only by damage but also by various intrinsic effects such as boundary conditions. The objective of this paper is to demonstrate the application of a nonlinear ultrasonic subharmonic method for detecting fatigue cracks with nonlinear boundary conditions. The fatigue crack was qualitatively modeled as two elastic, frictionless half spaces that enter into contact during vibration and where the contact obeys the basic Hertz contact law. The nonlinear ordinary differential equation drawn from the developed model was solved with the method of multiple scales. The threshold of subharmonic generation was studied. Different threshold behaviors between the nonlinear boundary condition and the fatigue crack were found that can be used to distinguish the source of nonlinear subharmonic features. To evaluate the proposed method, experiments using an aluminum plate with a fatigue crack were conducted to quantitatively verify the subharmonic resonance range. Two surface-bonded piezoelectric transducers were used to generate and receive ultrasonic wave signals. The experimental results demonstrated that the subharmonic component of the sensing signal could be used to detect the fatigue crack and further to distinguish it from inherent nonlinear boundary conditions. Copyright © 2017 Elsevier B.V. All rights reserved.
6d Dirac fermion on a rectangle; scrutinizing boundary conditions, mode functions and spectrum
Fujimoto, Yukihiro; Hasegawa, Kouhei; Nishiwaki, Kenji; Sakamoto, Makoto; Tatsumi, Kentaro
2017-09-01
We classify possible boundary conditions of a 6d Dirac fermion Ψ on a rectangle under the requirement that the 4d Lorentz structure is maintained, and derive the profiles and spectrum of the zero modes and nonzero KK modes under the two specific boundary conditions, (i) 4d-chirality positive components being zero at the boundaries and (ii) internal chirality positive components being zero at the boundaries. In the case of (i), twofold degenerated chiral zero modes appear which are localized towards specific directions of the rectangle pointed by an angle parameter θ. This leads to an implication for a new direction of pursuing the origin of three generations in the matter fields of the standard model, even though triple-degenerated zero modes are not realized in the six dimensions. When such 6d fermions couple with a 6d scalar with a vacuum expectation value, θ contributes to a mass matrix of zero-mode fermions consisting of Yukawa interactions. The emergence of the angle parameter θ originates from a rotational symmetry in the degenerated chiral zero modes on the rectangle extra dimensions since they do not feel the boundaries. In the case of (ii), this rotational symmetry is promoted to the two-dimensional conformal symmetry though no chiral massless zero mode appears. We also discuss the correspondence between our model on a rectangle and orbifold models in some details.
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Máté Tóth
2014-02-01
Full Text Available In 1997 a new Cultural Act was enacted which included, among other things, public library provision. Based on this act the Hungarian library system has been developed systematically through the consecutive strategic plans (Skaliczki, 1999. All projects aimed to push the boundaries of accessibility and to facilitate the realisation of the information society (Caidi, 2006. The 2003-2007 strategic period draws to an end and now we are able to review the tasks accomplished. (Skaliczki, 2003; 2006. The purpose of this article is to present an overview of the strategic development of Hungarian libraries between 1997 and 2007, and to draw up the basic figures regarding to this period. (http://www.ki.oszk.hu/statisztika.html
DEFF Research Database (Denmark)
Villafruela, J.M.; Olmedo, Inés; Ruiz de Adana, M.
2013-01-01
This paper analyses the dispersion of the exhaled contaminants by humans in indoor environments, with special attention to the exhalation jet and its interaction with the indoor airflow pattern in both mixing and displacement ventilation conditions. The way in which three different numerical...... different environmental conditions and to validate whether a steady boundary condition of the exhalation flow may simulate human breathing in an effective and accurate way. The results show a very good agreement of the numerical results obtained for Test a and the experimental data. This fact confirms...... the use of numerical simulation as a powerful tool to predict the contaminant distribution exhaled by a human. The numerical tests with steady boundary conditions for the exhalation flow require a transitory resolution procedure and the predictions provided by these models display some discrepancies...
On a third order parabolic equation with a nonlocal boundary condition
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Abdelfatah Bouziani
2000-01-01
Full Text Available In this paper we demonstrate the existence, uniqueness and continuous dependence of a strong solution upon the data, for a mixed problem which combine classical boundary conditions and an integral condition, such as the total mass, flux or energy, for a third order parabolic equation. We present a functional analysis method based on an a priori estimate and on the density of the range of the operator generated by the studied problem.
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Pysarevskyi Mykola I.
2017-05-01
Full Text Available The article is aimed at the scientific substantiation of the theoretical aspects of formation of an effective mechanism for ensuring the economic security of enterprise in the conditions of raiding. The conceptual approaches to determining the main features of individual elements of the conceptual apparatus, namely, the concepts of «economic security of enterprise» and «raiding» were analyzed. The author’s own definition of ensuring the economic security of enterprise in the conditions of raiding has been formed, which provides an opportunity to develop a complex of organizational and economic measures aimed at maintaining the sustainable functioning and development of enterprise in the current and future periods. Prospect for further research in this direction is a critical analysis of the approaches to assessing threats to the economic security of enterprise in the context of raiding, thus broadening the theoretical basis for an effective response mechanism and establishing a qualitative methodical basis for research. Application of new scientific and methodical approaches to the integrated assessment of the level of economic security in the conditions of raiding will ensure the development and implementation of efficient managerial decisions aimed at establishing a system of preventive measures to address threats to the economic security of enterprise.
Adesanya, S. O.; Oluwadare, E. O.; Falade, J. A.; Makinde, O. D.
2015-12-01
In this paper, the free convective flow of magnetohydrodynamic fluid through a channel with time periodic boundary condition is investigated by taking the effects of Joule dissipation into consideration. Based on simplifying assumptions, the coupled governing equations are reduced to a set of nonlinear boundary valued problem. Approximate solutions are obtained by using semi-analytical Adomian decomposition method. The effect of pertinent parameters on the fluid velocity, temperature distribution, Nusselt number and skin friction are presented graphically and discussed. The result of the computation shows that an increase in the magnetic field intensity has significant influence on the fluid flow.
Gerbi, Stéphane
2013-01-15
The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.
POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
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FAOUZI HADDOUCHI
2015-11-01
Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
Latyshev, A. V.; Yushkanov, A. A.
2013-03-01
The second Stokes problem concerning the behavior of a rarefied gas in the half-space bounded over a plate undergoing harmonic in-plane oscillations is solved analytically using the Bhat-nagar-Gross-Krook equation with Cercignani boundary conditions for gas molecules reflecting from the wall. The distribution function of the gas molecules is constructed. The gas velocity in the half-space and near the wall, the drag force exerted by the gas on the boundary, and the energy dissipation rate per unit area of the oscillating plate are found.
Green's Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions
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Roman Svetlana
2011-01-01
Full Text Available We investigate a second-order discrete problem with two additional conditions which are described by a pair of linearly independent linear functionals. We have found the solution to this problem and presented a formula and the existence condition of Green's function if the general solution of a homogeneous equation is known. We have obtained the relation between two Green's functions of two nonhomogeneous problems. It allows us to find Green's function for the same equation but with different additional conditions. The obtained results are applied to problems with nonlocal boundary conditions.
Kosaka, Atsushi
2012-01-01
We consider a positive solution of the Emden equation with the critical Sobolev exponent on a geodesic ball in S3. In the case of the Dirichlet boundary condition, Bandle and Peletier [2] proved the precise result on the existence of a positive radial solution. We investigate the same equation with the third kind boundary condition and obtain a more general result. Namely we prove that the existence and the nonexistence of solutions depend on the geodesic radius and the boundary condition. Mo...
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Stanislav Lipski
2014-01-01
Full Text Available The availability of suitable land for agricultural activities and the quality of this land are the main factors determining the maximum number of the population of the planet. In the Russian Federation is 8.9 % of the world's arable land. But the natural-climatic conditions of Russia are rather complicated from the point of view of agricultural production. Therefore, the special significance is having the land reclamation and the measures of enhance soil fertility. Meanwhile, the share of reclaimed land in Russia is much lower than by our competitors in the global food market. From 2014 the state is starting the realization of the Federal target program of land reclamation agricultural purposes. The information systems about the land in the period of the agrarian and land transformation and development of a market turnover of land (including agricultural were attending more of legal aspects and of technical side (technology, electronic information exchange rather than on the characteristics of the land as the main means of production. Currently agricultural producers are demanding the land information. But the modern systems, containing information on agricultural lands, are not enough characterizing this land as a productive resource. It is negatively affects the development of agriculture. Now the Ministry of agriculture of Russia develops the proposals on establishment of a special system of monitoring agricultural lands. However, this system is created very slowly.
Effect of boundary conditions on magnetocapacitance effect in a ring-type magnetoelectric structure
Zhang, Juanjuan
2017-12-01
By considering the nonlinear magneto-elastic coupling relationships of magnetostrictive materials, an analytical model is proposed. The resonance frequencies can be accurately predicted by this theoretical model, and they are in good agreement with experimental data. Subsequently, the magnetocapacitance effect in a ring-type magnetoelectric (ME) structure with different boundary conditions is investigated, and it is found that various mechanical boundaries, the frequency, the magnetic field, the geometric size, and the interface bonding significantly affect the capacitance of the ME structure. Further, additional resonance frequencies can be predicted by considering appropriate imperfect interface bonding. Finally, the influence of an external force on the capacitance is studied. The result shows that an external force on the boundary changes the capacitance, but has only a weak influence on the resonance frequency.
Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities
Allen, Rebecca
2016-06-29
We study a multiple relaxation time lattice Boltzmann model for natural convection with moment-based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 108. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy. Copyright © 2016 Inderscience Enterprises Ltd.
Pfeiffer, M.; Munz, C.-D.; Fasoulas, S.
2015-08-01
In a numerical solution of the Maxwell-Vlasov system, the consistency with the charge conservation and divergence conditions has to be kept solving the hyperbolic evolution equations of the Maxwell system, since the vector identity ∇ ṡ (∇ × u →) = 0 and/or the charge conservation of moving particles may be not satisfied completely due to discretization errors. One possible method to force the consistency is the hyperbolic divergence cleaning. This hyperbolic constraint formulation of Maxwell's equations has been proposed previously, coupling the divergence conditions to the hyperbolic evolution equations, which can then be treated with the same numerical method. We pick up this method again and show that electrostatic limit may be obtained by accentuating the divergence cleaning sub-system and converging to steady state. Hence, the electrostatic case can be treated by the electrodynamic code with reduced computational effort. In addition, potential boundary conditions as often given in practical applications can be coupled in a similar way to get appropriate boundary conditions for the field equations. Numerical results are shown for an electric dipole, a parallel-plate capacitor, and a Langmuir wave. The use of potential boundary conditions is demonstrated in an Einzel lens simulation.
Gatsonis, Nikolaos A.; Chamberlin, Ryan E.; Averkin, Sergey N.
2013-01-01
The mathematical and computational aspects of the direct simulation Monte Carlo on unstructured tetrahedral grids (U3DSMC) with a Kinetic-Moment (KM) boundary conditions method are presented. The algorithms for particle injection, particle loading, particle motion, and particle tracking are presented. The KM method applicable to a subsonic or supersonic inflow/outflow boundary, couples kinetic (particle) U3DSMC properties with fluid (moment) properties. The KM method obtains the number density, temperature and mean velocity needed to define the equilibrium, drifting Maxwellian distribution at a boundary. The moment component of KM is based on the local one dimensional inviscid (LODI) boundary conditions method consistent with the 5-moment compressible Euler equations. The kinetic component of KM is based on U3DSMC for interior properties and the equilibrium drifting Maxwellian at the boundary. The KM method is supplemented with a time-averaging procedure, allows for choices in sampling-cell procedures, minimizes fluctuations and accelerates the convergence in subsonic flows. Collision sampling in U3DSMC implements the no-time-counter method and includes elastic and inelastic collisions. The U3DSMC with KM boundary conditions is validated and verified extensively with simulations of subsonic nitrogen flows in a cylindrical tube with imposed inlet pressure and density and imposed outlet pressure. The simulations cover the regime from slip to free-molecular with inlet Knudsen numbers between 0.183 and 18.27 and resulting inlet Mach numbers between 0.037 and 0.027. The pressure and velocity profiles from U3DSMC-KM simulations are compared with analytical solutions obtained from first-order and second-order slip boundary conditions. Mass flow rates from U3DSMC-KM are compared with validated analytical solutions for the entire Knudsen number regime considered. Error and sensitivity analysis is performed and numerical fractional errors are in agreement with theoretical
Conditions for the appearance of boundary modes in topological phases of Heisenberg spin ladders
Robinson, Neil; Atland, Alexander; Egger, Reinhold; Gergs, Nkilas; Konik, Robert; Li, Wei; Schuricht, Dirk; Tsvelik, Alexei; Weichselbaum, Andreas
We consider the problem of delineating the necessary conditions for the appearance of boundary modes in extended SU (2) Heisenberg spin ladders. Specifically, we study Heisenberg ladders with rung exchange, J⊥, and ring exchange, JX, that admit a field theoretic description in terms of Majorana fermions in the continuum limit. In this description there are four Majorana fermions, arranged in a triplet and a singlet. This suggests there are four distinct phases, corresponding to the configurations of the signs of the triplet mt and singlet ms masses. We label these phases as: Haldane (mt > 0 ,ms 0), VBS+ (mt ,ms > 0) and VBS- (mt ,ms VBS+ phase, where all the Majorana fermions have gapless boundary modes. The absence of a gapless boundary mode in the rung singlet phase is surprising; we find that the singlet mode can become gapless if open boundary conditions are replaced with a continuous change in lattice parameters. We suggest a symmetry-allowed modification to the low-energy effective theory which may be responsible for this behavior.
Air Quality and Meteorological Boundary Conditions during the MCMA-2003 Field Campaign
Sosa, G.; Arriaga, J.; Vega, E.; Magaña, V.; Caetano, E.; de Foy, B.; Molina, L. T.; Molina, M. J.; Ramos, R.; Retama, A.; Zaragoza, J.; Martínez, A. P.; Márquez, C.; Cárdenas, B.; Lamb, B.; Velasco, E.; Allwine, E.; Pressley, S.; Westberg, H.; Reyes, R.
2004-12-01
A comprehensive field campaign to characterize photochemical smog in the Mexico City Metropolitan Area (MCMA) was conducted during April 2003. An important number of equipment was deployed all around the urban core and its surroundings to measure gas and particles composition from the various sources and receptor sites. In addition to air quality measurements, meteorology variables were also taken by regular weather meteorological stations, tethered balloons, radiosondes, sodars and lidars. One important issue with regard to the field campaign was the characterization of the boundary conditions in order to feed meteorological and air quality models. Four boundary sites were selected to measure continuously criteria pollutants, VOC and meteorological variables at surface level. Vertical meteorological profiles were measured at three other sites : radiosondes in Tacubaya site were launched every six hours daily; tethered balloons were launched at CENICA and FES-Cuautitlan sites according to the weather conditions, and one sodar was deployed at UNAM site in the south of the city. Additionally to these measurements, two fixed meteorological monitoring networks deployed along the city were available to complement these measurements. In general, we observed that transport of pollutants from the city to the boundary sites changes every day, according to the coupling between synoptic and local winds. This effect were less important at elevated sites such as Cerro de la Catedral and ININ, where synoptic wind were more dominant during the field campaign. Also, local sources nearby boundary sites hide the influence of pollution coming from the city some days, particularly at the La Reforma site.
Path-integral quantum Monte Carlo simulation with open-boundary conditions
Jiang, Zhang; Smelyanskiy, Vadim N.; Boixo, Sergio; Neven, Hartmut
2017-10-01
The tunneling decay event of a metastable state in a fully connected quantum spin model can be simulated efficiently by path-integral quantum Monte Carlo (QMC) [Isakov et al., Phys. Rev. Lett. 117, 180402 (2016), 10.1103/PhysRevLett.117.180402]. This is because the exponential scaling with the number of spins of the thermally assisted quantum tunneling rate and the Kramers escape rate of QMC are identical [Jiang et al., Phys. Rev. A 95, 012322 (2017), 10.1103/PhysRevA.95.012322], a result of a dominant instantonic tunneling path. In Isakov et al., it was also conjectured that the escape rate in open-boundary QMC is quadratically larger than that of conventional periodic-boundary QMC; therefore, open-boundary QMC might be used as a powerful tool to solve combinatorial optimization problems. The intuition behind this conjecture is that the action of the instanton in open-boundary QMC is a half of that in periodic-boundary QMC. Here, we show that this simple intuition—although very useful in interpreting some numerical results—deviates from the actual situation in several ways. Using a fully connected quantum spin model, we derive a set of conditions on the positions and momenta of the end points of the instanton, which remove the extra degrees of freedom due to open boundaries. In comparison, the half-instanton conjecture incorrectly sets the momenta at the end points to zero. We also found that the instantons in open-boundary QMC correspond to quantum tunneling events in the symmetric subspace (maximum total angular momentum) at all temperatures, whereas the instantons in periodic-boundary QMC typically lie in subspaces with lower total angular momenta at finite temperatures. This leads to a lesser-than-quadratic speedup at finite temperatures. The results provide useful insights in utilizing open-boundary QMC to solve hard optimization problems. We also outline the generalization of the instantonic tunneling method to many-qubit systems without permutation
SOLUTION TO THE PROBLEM OF THERMOELASTIC VIBRATION OF A PLATE IN SPECIAL BOUNDARY CONDITIONS
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Egorychev Oleg Aleksandrovich
2012-10-01
Full Text Available Operating conditions of uneven non-stationary heating can cause changes in physical and mechanical properties of materials. The awareness of the value and nature of thermal stresses is needed to perform a comprehensive analysis of structural strength. The authors provide their solution to the problem of identification of natural frequencies of vibrations of rectangular plates, whenever a thermal factor is taken into account. In the introductory section of the paper, the authors provide the equation describing the thermoelastic vibration of a plate and set the initial and boundary conditions. Furthermore, the authors provide a frequency equation derivation for the problem that has an analytical solution available (if all edges are simply supported at zero temperature. The equation derived by the authors has no analytical solution and can be solved only numerically. In the middle of the paper, the authors describe a method of frequency equation derivation for plates exposed to special boundary conditions, if the two opposite edges are simply supported at zero temperature, while the two other edges have arbitrary types of fixation and arbitrary thermal modes. For this boundary condition derived as a general solution, varying fixation of the two edges makes it possible to obtain transcendental trigonometric equations reducible to algebraic frequency equations by using expending in series. Thus, the obtaining frequency equations different from the general solution becomes possible for different types of boundary conditions. The final section of the paper covers the practical testing of the described method for the problem that has an analytical solution (all edges are simply supported at zero temperature as solved above. An approximate equation provided in the research leads to the analytical solution that is already available.
The Impact of Local Microclimate Boundary Conditions on Building Energy Performance
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Anna Laura Pisello
2015-07-01
Full Text Available Local environmental boundaries play an important role in determining microclimate conditions affecting thermal-energy behavior of buildings. In this scenario, the purpose of the present work is to investigate how residential buildings are affected by different local microclimate conditions. To this aim, the continuous microclimate monitoring of (i a rural area; (ii a suburban area; and (iii an urban area is carried out, and the comparative analysis of the different boundary conditions is performed. In particular, the effect of the presence of a large lake in the rural area on building energy demand for heating and cooling is evaluated, both in winter and summer. Coupled degree hour method and numerical analysis are performed in order to predict the energy requirement of buildings subject to local microclimate boundary conditions. The main results show higher air temperature and relative humidity values for the rural area. No significant mitigation effect due to the lake presence is found in urban and suburban areas because of the peculiar wind regime of the region. Additionally, the dynamic thermal-energy simulation shows a decrease of 14% and 25% in the heating consumption and an increase of 58% and 194% in cooling requirements of buildings situated in the rural area around the lake compared to the urban and suburban areas, respectively.
Kyncl, Martin; Pelant, Jaroslav
We work with the system of partial differential equations describing the non-stationary compressible turbulent fluid flow. It is a characteristic feature of the hyperbolic equations, that there is a possible raise of discontinuities in solutions, even in the case when the initial conditions are smooth. The fundamental problem in this area is the solution of the so-called Riemann problem for the split Euler equations. It is the elementary problem of the one-dimensional conservation laws with the given initial conditions (LIC - left-hand side, and RIC - right-hand side). The solution of this problem is required in many numerical methods dealing with the 2D/3D fluid flow. The exact (entropy weak) solution of this hyperbolical problem cannot be expressed in a closed form, and has to be computed by an iterative process (to given accuracy), therefore various approximations of this solution are being used. The complicated Riemann problem has to be further modified at the close vicinity of boundary, where the LIC is given, while the RIC is not known. Usually, this boundary problem is being linearized, or roughly approximated. The inaccuracies implied by these simplifications may be small, but these have a huge impact on the solution in the whole studied area, especially for the non-stationary flow. Using the thorough analysis of the Riemann problem we show, that the RIC for the local problem can be partially replaced by the suitable complementary conditions. We suggest such complementary conditions accordingly to the desired preference. This way it is possible to construct the boundary conditions by the preference of total values, by preference of pressure, velocity, mass flow, temperature. Further, using the suitable complementary conditions, it is possible to simulate the flow in the vicinity of the diffusible barrier. On the contrary to the initial-value Riemann problem, the solution of such modified problems can be written in the closed form for some cases. Moreover
DEFF Research Database (Denmark)
Steskens, Paul Wilhelmus Maria Hermanus; Rode, Carsten; Janssen, Hans
2008-01-01
Current models to predict heat, air and moisture (HAM) conditions in building components assume uniform boundary conditions, both for the temperature and relative humidity of the air in an indoor space as well as for the surface transfer coefficients. Such models cannot accurately predict the HAM...... conditions in the component and on the surface of the component with non-uniform air temperature or relative humidity distributions in an indoor space. Moreover, the heat and moisture surface transfer coefficients strongly depend on the local air velocity, local temperature, water-material interactions...... and water content at the material surface and surface texture of the material. The objective of the present paper is to analyze the influence of the non-uniform local air velocity near the surface of a building component on the HAM conditions in the component. A case study and sensitivity study have been...
Transition of MHD kink-stability properties between line-tied and non-line-tied boundary conditions.
Sun, X; Intrator, T P; Dorf, L; Furno, I; Lapenta, G
2008-05-23
Magnetic flux tubes or flux ropes in plasmas are important in nature and the laboratory. Axial boundary conditions strongly affect flux rope behavior, but this has never been systematically investigated. We experimentally demonstrate for the first time axial boundary conditions that are continuously varied between ideal magnetohydrodynamic (MHD) line-tied (fixed) and non-line-tied (free). In contrast with the usual interpretation that mechanical plasma motion is MHD line-tied to a conducting boundary, we constrain boundary plasma motion to cause the line-tied condition.
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Tristan A Bekinschtein
2011-12-01
Full Text Available Classical (trace conditioning is a specific variant of associative learning in which a neutral stimulus leads to the subsequent prediction of an emotionally charged or noxious stimulus after a temporal gap. When conditioning is concurrent with a distraction task, only participants who can report the relationship (the contingency between stimuli explicitly show associative learning. This suggests that consciousness is a prerequisite for trace conditioning. We review and question three main controversies concerning this view. Firstly, virtually all animals, even invertebrate sea slugs, show this type of learning; secondly, unconsciously perceived stimuli may elicit trace conditioning; and thirdly, some vegetative state patients show trace learning. We discuss and analyze these seemingly contradictory arguments to find the theoretical boundaries of consciousness in classical conditioning. We conclude that trace conditioning remains one of the best measures to test conscious processing in the absence of explicit reports.
Lattice QCD with open boundary conditions and twisted-mass reweighting
Lüscher, Martin
2013-01-01
Lattice QCD simulations at small lattice spacings and quark masses close to their physical values are technically challenging. In particular, the simulations can get trapped in the topological charge sectors of field space or may run into instabilities triggered by accidental near-zero modes of the lattice Dirac operator. As already noted in ref. [1], the first problem is bypassed if open boundary conditions are imposed in the time direction, while the second can potentially be overcome through twisted-mass determinant reweighting [2]. In this paper, we show that twisted-mass reweighting works out as expected in QCD with open boundary conditions and 2+1 flavours of O(a) improved Wilson quarks. Further algorithmic improvements are tested as well and a few physical quantities are computed for illustration.
Performance advantages of CPML over UPML absorbing boundary conditions in FDTD algorithm
Gvozdic, Branko D.; Djurdjevic, Dusan Z.
2017-01-01
Implementation of absorbing boundary condition (ABC) has a very important role in simulation performance and accuracy in finite difference time domain (FDTD) method. The perfectly matched layer (PML) is the most efficient type of ABC. The aim of this paper is to give detailed insight in and discussion of boundary conditions and hence to simplify the choice of PML used for termination of computational domain in FDTD method. In particular, we demonstrate that using the convolutional PML (CPML) has significant advantages in terms of implementation in FDTD method and reducing computer resources than using uniaxial PML (UPML). An extensive number of numerical experiments has been performed and results have shown that CPML is more efficient in electromagnetic waves absorption. Numerical code is prepared, several problems are analyzed and relative error is calculated and presented.
MHD Natural Convection with Convective Surface Boundary Condition over a Flat Plate
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Mohammad M. Rashidi
2014-01-01
Full Text Available We apply the one parameter continuous group method to investigate similarity solutions of magnetohydrodynamic (MHD heat and mass transfer flow of a steady viscous incompressible fluid over a flat plate. By using the one parameter group method, similarity transformations and corresponding similarity representations are presented. A convective boundary condition is applied instead of the usual boundary conditions of constant surface temperature or constant heat flux. In addition it is assumed that viscosity, thermal conductivity, and concentration diffusivity vary linearly. Our study indicates that a similarity solution is possible if the convective heat transfer related to the hot fluid on the lower surface of the plate is directly proportional to (x--1/2 where x- is the distance from the leading edge of the solid surface. Numerical solutions of the ordinary differential equations are obtained by the Keller Box method for different values of the controlling parameters associated with the problem.
Reflected forward-backward SDEs and obstacle problems with boundary conditions
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Jin Ma
2001-01-01
Full Text Available In this paper we study a class of forward-backward stochastic differential equations with reflecting boundary conditions (FBSDER for short. More precisely, we consider the case in which the forward component of the FBSDER is restricted to a fixed, convex region, and the backward component will stay, at each fixed time, in a convex region that may depend on time and is possibly random. The solvability of such FBSDER is studied in a fairly general way. We also prove that if the coefficients are all deterministic and the backward equation is one-dimensional, then the adapted solution of such FBSDER will give the viscosity solution of a quasilinear variational inequality (obstacle problem with a Neumann boundary condition. As an application, we study how the solvability of FBSDERs is related to the solvability of an American game option.
Blow-up analysis for a system of heat equations coupled through a nonlinear boundary condition
DEFF Research Database (Denmark)
Pedersen, M.; Lin, Zhigui
2001-01-01
Consider the system of heat equations uit - Δui = 0 (i = 1 , . . . , k, uk+i := u1) in Ω x (0, T) coupled through nonlinear boundary conditions ∂ui/∂η = up1i+1 on ∂Ω x [0, T). The upper and lower bounds of the blow-up rate is derived. © 2000 Elsevier Science Ltd. All rights reserved.......Consider the system of heat equations uit - Δui = 0 (i = 1 , . . . , k, uk+i := u1) in Ω x (0, T) coupled through nonlinear boundary conditions ∂ui/∂η = up1i+1 on ∂Ω x [0, T). The upper and lower bounds of the blow-up rate is derived. © 2000 Elsevier Science Ltd. All rights reserved....
A Monte Carlo method for solving the one-dimensional telegraph equations with boundary conditions
Acebrón, Juan A.; Ribeiro, Marco A.
2016-01-01
A Monte Carlo algorithm is derived to solve the one-dimensional telegraph equations in a bounded domain subject to resistive and non-resistive boundary conditions. The proposed numerical scheme is more efficient than the classical Kac's theory because it does not require the discretization of time. The algorithm has been validated by comparing the results obtained with theory and the Finite-difference time domain (FDTD) method for a typical two-wire transmission line terminated at both ends with general boundary conditions. We have also tested transmission line heterogeneities to account for wave propagation in multiple media. The algorithm is inherently parallel, since it is based on Monte Carlo simulations, and does not suffer from the numerical dispersion and dissipation issues that arise in finite difference-based numerical schemes on a lossy medium. This allowed us to develop an efficient numerical method, capable of outperforming the classical FDTD method for large scale problems and high frequency signals.
Lazzi Gazzini, S.; Schädler, R.; Kalfas, A. I.; Abhari, R. S.
2017-02-01
It is technically challenging to measure heat fluxes on the rotating components of gas turbines, yet accurate knowledge of local heat loads under engine-representative conditions is crucial for ensuring the reliability of the designs. In this work, quantitative image processing tools were developed to perform fast and accurate infrared thermography measurements on 3D-shaped film-heaters directly deposited on the turbine endwalls. The newly developed image processing method and instrumentation were used to measure the heat load on the rotor endwalls of an axial turbine. A step-transient heat flux calibration technique is applied to measure the heat flux generated locally by the film heater, thus eliminating the need for a rigorously iso-energetic boundary condition. On-board electronics installed on the rotor record the temperature readings of RTDs installed in the substrate below the heaters in order to evaluate the conductive losses in the solid. Full maps of heat transfer coefficient and adiabatic wall temperature are produced for two different operating conditions, demonstrating the sensitivity of the technique to local flow features and variations in heat transfer due to Reynolds number effect.
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Zhang Sheng
2016-01-01
Full Text Available In this paper, variable separation method combined with the properties of Mittag-Leffler function is used to solve a variable-coefficient time fractional advection-dispersion equation with initial and boundary conditions. As a result, a explicit exact solution is obtained. It is shown that the variable separation method can provide a useful mathematical tool for solving the time fractional heat transfer equations.
Czech Academy of Sciences Publication Activity Database
Haslinger, Jaroslav; Kučera, R.; Šátek, V.
2017-01-01
Roč. 22, October 2017 (2017), s. 1-14 ISSN 1081-2865 R&D Projects: GA MŠk LQ1602; GA ČR(CZ) GA17-01747S Institutional support: RVO:68145535 Keywords : Stokes system * threshold slip boundary conditions * solution dependent slip function Subject RIV: BA - General Mathematics Impact factor: 2.953, year: 2016 http://journals.sagepub.com/doi/abs/10.1177/1081286517716222
Initial-boundary value problem with a nonlocal condition for a viscosity equation
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Abdelfatah Bouziani
2002-01-01
Full Text Available This paper deals with the proof of the existence, uniqueness, and continuous dependence of a strong solution upon the data, for an initial-boundary value problem which combine Neumann and integral conditions for a viscosity equation. The proof is based on an energy inequality and on the density of the range of the linear operator corresponding to the abstract formulation of the studied problem.
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Feng Hanying
2011-01-01
Full Text Available The expression and properties of Green's function for a class of nonlinear fractional differential equations with integral boundary conditions are studied and employed to obtain some results on the existence of positive solutions by using fixed point theorem in cones. The proofs are based on the reduction of the problem considered to the equivalent Fredholm integral equation of the second kind. The results significantly extend and improve many known results even for integer-order cases.
Kanguzhin, Baltabek; Tokmagambetov, Niyaz
2013-01-01
We introduce the concepts of the Fourier transform and convolution generated by an arbitrary restriction of the differentiation operator in the space $L_{2}(0,b).$ In contrast to the classical convolution, the introduced convolution explicitly depends on the boundary condition that defines the domain of the operator $L.$ The convolution is closely connected to the inverse operator or to the resolvent. So, we first find a representation for the resolvent, and then introduce the required convol...
Yang, Yongqin; Chen, Shaochun
2010-03-01
A new nonconforming triangular element for the equations of planar linear elasticity with pure traction boundary conditions is considered. By virtue of construction of the element, the discrete version of Korn's second inequality is directly proved to be valid. Convergence rate of the finite element methods is uniformly optimal with respect to [lambda]. Error estimates in the energy norm and L2-norm are O(h2) and O(h3), respectively.
The Kramers problem with accommodative boundary conditions for quantum Fermi gases
Kostikov, A. A.; Latyshev, A. V.; Yushkanov, A. A.
2008-09-01
The Kramers problem of isothermal slip of a quantum Fermi gas with Cercignani boundary conditions is solved analytically. The velocity of isothermal slip is obtained as a function of the accommodation coefficient and the reduced chemical potential—the ratio of the chemical potential to the product of Boltzmann's constant and the absolute temperature. The distribution function of the molecules is presented in explicit form.
Additional Boundary Condition for a Wire Medium Connected to a Metallic Surface
Silveirinha, Mário G.; Fernandes, Carlos A.; Costa, Jorge R.
2007-01-01
WOS:000255793900001 (Nº de Acesso Web of Science) In this work, we demonstrate that the interaction of electromagnetic waves with a microstructured material formed by metallic wires connected to a metallic surface can be described using homogenization methods provided an additional boundary condition (ABC) is considered. The ABC is derived by taking into account the specific microstructure of the wire medium. To illustrate the application of the result, we characterize a substrate formed b...
A Boundary Value Problem with Multivariables Integral Type Condition for Parabolic Equations
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A. L. Marhoune
2009-01-01
Full Text Available We study a boundary value problem with multivariables integral type condition for a class of parabolic equations. We prove the existence, uniqueness, and continuous dependence of the solution upon the data in the functional wieghted Sobolev spaces. Results are obtained by using a functional analysis method based on two-sided a priori estimates and on the density of the range of the linear operator generated by the considered problem.
Masses, decay constants and electromagnetic form-factors with twisted boundary conditions
Bijnens, Johan
2015-01-01
We discuss some of the effects of twisted boundary conditions in finite volume using continuum SU(3) Chiral Perturbation Theory. We point out how broken cubic symmetry affects the definitions of quantities such as form-factors. Using the $\\pi^+$ as an example, we give one loop results for the mass, decay constants and electromagnetic form-factor and illustrate how the relevant Ward identities are satisfied.
Energy Technology Data Exchange (ETDEWEB)
Petracca, S. [Salerno Univ. (Italy)
1996-08-01
Debye potentials, the Lorentz reciprocity theorem, and (extended) Leontovich boundary conditions can be used to obtain simple and accurate analytic estimates of the longitudinal and transverse coupling impedances of (piecewise longitudinally uniform) multi-layered pipes with non simple transverse geometry and/or (spatially inhomogeneous) boundary conditions. (author)
Reyes, Jonathan; Shadwick, B. A.
2016-10-01
Modeling the evolution of a short, intense laser pulse propagating through an underdense plasma is of particular interest in the physics of laser-plasma interactions. Numerical models are typically created by first discretizing the equations of motion and then imposing boundary conditions. Using the variational principle of Chen and Sudan, we spatially discretize the Lagrangian density to obtain discrete equations of motion and a discrete energy conservation law which is exactly satisfied regardless of the spatial grid resolution. Modifying the derived equations of motion (e.g., enforcing boundary conditions) generally ruins energy conservation. However, time-dependent terms can be added to the Lagrangian which force the equations of motion to have the desired boundary conditions. Although some foresight is needed to choose these time-dependent terms, this approach provides a mechanism for energy to exit the closed system while allowing the conservation law to account for the loss. An appropriate time discretization scheme is selected based on stability analysis and resolution requirements. We present results using this variational approach in a co-moving coordinate system and compare such results to those using traditional second-order methods. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY- 1104683.
Vibration analysis of multi-span beam system under arbitrary boundary and coupling conditions
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ZHENG Chaofan
2017-08-01
Full Text Available In order to overcome the difficulties of studying the vibration analysis model of a multi-span beam system under various boundary and coupling conditions, this paper constructs a free vibration analysis model of a multi-span beam system on the basis of the Bernoulli-Euler beam theory. The vibration characteristics of a multi-span beam system under arbitrary boundary supports and elastic coupling conditions are investigated using the current analysis model. Unlike most existing techniques, the beam displacement function is generally sought as an improved Fourier cosine series, and four sine terms are introduced to overcome all the relevant discontinuities or jumps of elastic boundary conditions. On this basis, the unknown series coefficients of the displacement function are treated as the generalized coordinates and solved using the Rayleigh-Ritz method, and the vibration problem of multi-span bean systems is converted into a standard eigenvalue problem concerning the unknown displacement expansion coefficient. By comparing the free vibration characteristics of the proposed method with those of the FEA method, the efficiency and accuracy of the present method are validated, providing a reliable and theoretical basis for multi-span beam system structure in engineering applications.
Energy Technology Data Exchange (ETDEWEB)
Rosnitskiy, P., E-mail: pavrosni@yandex.ru; Yuldashev, P., E-mail: petr@acs366.phys.msu.ru; Khokhlova, V., E-mail: vera@acs366.phys.msu.ru [Physics Faculty, Moscow State University, Leninskie Gory, 119991 Moscow (Russian Federation)
2015-10-28
An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parameters were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.
Musharbash, Eleonora; Nobile, Fabio
2018-02-01
In this paper we propose a method for the strong imposition of random Dirichlet boundary conditions in the Dynamical Low Rank (DLR) approximation of parabolic PDEs and, in particular, incompressible Navier Stokes equations. We show that the DLR variational principle can be set in the constrained manifold of all S rank random fields with a prescribed value on the boundary, expressed in low rank format, with rank smaller then S. We characterize the tangent space to the constrained manifold by means of a Dual Dynamically Orthogonal (Dual DO) formulation, in which the stochastic modes are kept orthonormal and the deterministic modes satisfy suitable boundary conditions, consistent with the original problem. The Dual DO formulation is also convenient to include the incompressibility constraint, when dealing with incompressible Navier Stokes equations. We show the performance of the proposed Dual DO approximation on two numerical test cases: the classical benchmark of a laminar flow around a cylinder with random inflow velocity, and a biomedical application for simulating blood flow in realistic carotid artery reconstructed from MRI data with random inflow conditions coming from Doppler measurements.
Boundary conditions and the generalized metric formulation of the double sigma model
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Chen-Te Ma
2015-09-01
Full Text Available Double sigma model with strong constraints is equivalent to the ordinary sigma model by imposing a self-duality relation. The gauge symmetries are the diffeomorphism and one-form gauge transformation with the strong constraints. We consider boundary conditions in the double sigma model from three ways. The first way is to modify the Dirichlet and Neumann boundary conditions with a fully O(D,D description from double gauge fields. We perform the one-loop β function for the constant background fields to find low-energy effective theory without using the strong constraints. The low-energy theory can also have O(D,D invariance as the double sigma model. The second way is to construct different boundary conditions from the projectors. The third way is to combine the antisymmetric background field with field strength to redefine an O(D,D generalized metric. We use this generalized metric to reconstruct a consistent double sigma model with the classical and quantum equivalence.
Bendine, Kouider; Wankhade, Rajan L.
2017-12-01
Piezoelectric actuators are effectively used to control the response of light weight structures in shape, vibration and buckling. Optimization for the shape control of piezoelectric beam is the recent challenge which requires proper numerical technique to perform. The shape control of a composite beam using surface-bounded piezoelectric actuators has been investigated in the present work. The mathematical model is developed using two-node Timoshenko beam element coupling with the theory of linear piezoelectricity. First-order shear deformation theory is employed in the formulation to consider the effect of shear. In the analysis, the effect of the actuators position for different set of boundary conditions is investigated. For different boundary conditions which include clamped-free-, clamped-clamped- and simply supported beam, optimisation of piezoelectric patch location is investigated. Moreover, a genetic algorithm is adopted and implemented to optimize the required voltage to maintain the desired shape of the beam. This optimization technique is applied to different cases of composite beams with varying the boundary condition.
Importance of boundary conditions for fluctuation-induced forces between colloids at interfaces.
Lehle, Hartwig; Oettel, Martin
2007-01-01
We calculate the effective fluctuation-induced force between spherical or disklike colloids trapped at a flat, fluid interface mediated by thermally excited capillary waves. This Casimir-type force is determined by the partition function of the system which in turn is calculated in a functional integral approach, where the restrictions on the capillary waves imposed by the colloids are incorporated by auxiliary fields. In the long-range regime the fluctuation-induced force is shown to depend sensitively on the boundary conditions imposed at the three-phase contact line between the colloids and the two fluid phases. Separating the colloid fluctuations from the fluctuations of the capillary wave field leads to competing repulsive and attractive contributions, respectively, which give rise to cancellations of the leading terms. In a second approach based on a multipole expansion of the Casimir interaction, these cancellations can be understood from the vanishing of certain multipole moments enforced by the boundary conditions. We also discuss the connection of the different types of boundary conditions to certain external fields acting on the colloids which appear to be realizable by experimental techniques such as the laser tweezer method.
Assessment of a PML Boundary Condition for Simulating an MRI Radio Frequency Coil
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Yunsuo Duan
2008-01-01
Full Text Available Computational methods such as the finite difference time domain (FDTD play an important role in simulating radiofrequency (RF coils used in magnetic resonance imaging (MRI. The choice of absorbing boundary conditions affects the final outcome of such studies. We have used FDTD to assess the Berenger's perfectly matched layer (PML as an absorbing boundary condition for computation of the resonance patterns and electromagnetic fields of RF coils. We first experimentally constructed a high-pass birdcage head coil, measured its resonance pattern, and used it to acquire proton (1H phantom MRI images. We then computed the resonance pattern and B1 field of the coil using FDTD with a PML as an absorbing boundary condition. We assessed the accuracy and efficiency of PML by adjusting the parameters of the PML and comparing the calculated results with measured ones. The optimal PML parameters that produce accurate (comparable to the experimental findings FDTD calculations are then provided for the birdcage head coil operating at 127.72 MHz, the Larmor frequency of 1H at 3 Tesla (T.
Bendine, Kouider; Wankhade, Rajan L.
2017-10-01
Piezoelectric actuators are effectively used to control the response of light weight structures in shape, vibration and buckling. Optimization for the shape control of piezoelectric beam is the recent challenge which requires proper numerical technique to perform. The shape control of a composite beam using surface-bounded piezoelectric actuators has been investigated in the present work. The mathematical model is developed using two-node Timoshenko beam element coupling with the theory of linear piezoelectricity. First-order shear deformation theory is employed in the formulation to consider the effect of shear. In the analysis, the effect of the actuators position for different set of boundary conditions is investigated. For different boundary conditions which include clamped-free-, clamped-clamped- and simply supported beam, optimisation of piezoelectric patch location is investigated. Moreover, a genetic algorithm is adopted and implemented to optimize the required voltage to maintain the desired shape of the beam. This optimization technique is applied to different cases of composite beams with varying the boundary condition.
Directory of Open Access Journals (Sweden)
Pang Fuzhen
2017-01-01
Full Text Available In this paper, a modified Fourier solution based on the first-order shear deformation theory is developed for the free vibration problem of moderately thick composite laminated annular sector plates with general boundary conditions, internal radial line and circumferential arc supports. In this solution approach, regardless of boundary conditions, the displacement and rotation components of the sector plate are written in the form of the trigonometric series expansion in which several auxiliary terms are added to ensure and accelerate the convergence of the series. Each of the unknown coefficients is taken as the generalized coordinate and determined using the Raleigh- Ritz method. The accuracy and reliability of the present solution are validated by the comparison with the results found in the literature, and numerous new results for composite laminated annular sector plates considering various kinds of boundary conditions are presented. Comprehensive studies on the effects of elastic restraint parameters, layout schemes and locations of line/arc supports are also made.New results are obtained for laminated annular sector plates subjected to elastic boundary restraints and arbitrary internal radial line and circumferential arc supports in both directions, and they may serve as benchmark solutions for future researches.
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Petar Glišović
2015-01-01
Full Text Available Although there has been significant progress in the seismic imaging of mantle heterogeneity, the outstanding issue that remains to be resolved is the unknown distribution of mantle temperature anomalies in the distant geological past that give rise to the present-day anomalies inferred by global tomography models. To address this question, we present 3-D convection models in compressible and self-gravitating mantle initialised by different hypothetical temperature patterns. A notable feature of our forward convection modelling is the use of self-consistent coupling of the motion of surface tectonic plates to the underlying mantle flow, without imposing prescribed surface velocities (i.e., plate-like boundary condition. As an approximation for the surface mechanical conditions before plate tectonics began to operate we employ the no-slip (rigid boundary condition. A rigid boundary condition demonstrates that the initial thermally-dominated structure is preserved, and its geographical location is fixed during the evolution of mantle flow. Considering the impact of different assumed surface boundary conditions (rigid and plate-like on the evolution of thermal heterogeneity in the mantle we suggest that the intrinsic buoyancy of seven superplumes is most-likely resolved in the tomographic images of present-day mantle thermal structure. Our convection simulations with a plate-like boundary condition reveal that the evolution of an initial cold anomaly beneath the Java-Indonesian trench system yields a long-term, stable pattern of thermal heterogeneity in the lowermost mantle that resembles the present-day Large Low Shear Velocity Provinces (LLSVPs, especially below the Pacific. The evolution of subduction zones may be, however, influenced by the mantle-wide flow driven by deeply-rooted and long-lived superplumes since Archean times. These convection models also detect the intrinsic buoyancy of the Perm Anomaly that has been identified as a unique
Liu, Hualin; Zhao, Wenwen; Chen, Weifang
2016-11-01
Gas or liquid flow through small channels has become more and more popular due to the micro-electro-mechanical systems (MEMS) fabrication technologies such as micro-motors, electrostatic comb-drive, micro-chromatographs, micro-actuators, micro-turbines and micro-pumps, etc. The flow conditions in and around these systems are always recognized as typical transitional regimes. Under these conditions, the mean free path of gas molecules approaches the characteristic scale of the micro-devices itself, and due to the little collisions the heat and momentum cannot equilibrate between the wall and fluids quickly. Couette flow is a simple and critical model in fluid dynamics which focuses on the mechanism of the heat transfer in shear-driven micro-cavities or micro-channels. Despite numerous work on the numerical solutions of the Couette flow, how to propose stable and accurate slip boundary conditions in rarefied flow conditions still remains to be elucidated. In this paper, converged solutions for steady-state micro Couette flows are obtained by using conventional Burnett equations with a set of modified slip boundary conditions. Instead of using the physical variables at the wall, the modified slip conditions use the variables at the edge of the Knudsen layer based on a physically plausible assumption in literature that Knudsen layer has a thickness only in the order of a mean free path and molecules are likely to travel without collision in this layer. Numerical results for non-dimensional wall shear stress and heat flux are compared with those of the DSMC solutions. Although there are not much improvement in the accuracy by using this modified slip conditions, the modified conditions perform much better than the unmodified slip conditions for numerical stabilization. All results show that the set of conventional Burnett equations with second order modified conditions are proved to be an appropriate model for the micro-Couette flows.
Sheng, Yin; Zhang, Hao; Zeng, Zhigang
2017-10-01
This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.
Nonlinear convection in reaction-diffusion equations under dynamical boundary conditions
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Gaelle Pincet Mailly
2013-01-01
Full Text Available We study the blow-up phenomena for positive solutions of nonlinear reaction-diffusion equations including a nonlinear convection term $partial_t u = Delta u - g(u cdot abla u + f(u$ in a bounded domain of $mathbb{R}^N$ under the dissipative dynamical boundary conditions $sigma partial_t u + partial_u u =0$. Some conditions on g and f are discussed to state if the positive solutions blow up in finite time or not. Moreover, for certain classes of nonlinearities, an upper-bound for the blow-up time can be derived and the blow-up rate can be determined.
Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition
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Stanislav I. POHOZAEV
2004-01-01
Full Text Available We consider the equation Delta u = 0 posed in Q := (0;+inftyimes Omega, Omega:= { x=(x',x_N/ x'in R^{N-1}, x_N >0}, with the dynamical boundary conditionB(t,x',0u_{tt} + A(t,x',0u_t - u_{x_N} geq D(t, x',0|u|^q on Sigma := (0,+infty imes R^{N-1} imes {0} and give conditions on the coeﬃcient functions A(t,x',0; B(t,x',0 and D(t;x',0 for the nonexistence of global solutions.
Real-time gauge/gravity duality and ingoing boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Rees, Balt C. van [ITFA, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)
2009-07-15
In Lorentzian gauge/gravity duality, a proper understanding of initial conditions is essential. I discuss the precise relation between purely ingoing conditions at the horizon for bulk fields and retarded boundary correlation functions, as well as the generalization to higher-point functions. Some open questions can be answered only within the recently developed framework of [K. Skenderis and B. C. van Rees Phys. Rev. Lett. 101 (2008) 081601, (arXiv:0805.0150 [hep-th]), K. Skenderis and B. C. van Rees (arXiv:0812.2909 [hep-th])].
Heat and mass transfer boundary conditions at the surface of a heated sessile droplet
Ljung, Anna-Lena; Lundström, T. Staffan
2017-12-01
This work numerically investigates how the boundary conditions of a heated sessile water droplet should be defined in order to include effects of both ambient and internal flow. Significance of water vapor, Marangoni convection, separate simulations of the external and internal flow, and influence of contact angle throughout drying is studied. The quasi-steady simulations are carried out with Computational Fluid Dynamics and conduction, natural convection and Marangoni convection are accounted for inside the droplet. For the studied conditions, a noticeable effect of buoyancy due to evaporation is observed. Hence, the inclusion of moisture increases the maximum velocities in the external flow. Marangoni convection will, in its turn, increase the velocity within the droplet with up to three orders of magnitude. Results furthermore show that the internal and ambient flow can be simulated separately for the conditions studied, and the accuracy is improved if the internal temperature gradient is low, e.g. if Marangoni convection is present. Simultaneous simulations of the domains are however preferred at high plate temperatures if both internal and external flows are dominated by buoyancy and natural convection. The importance of a spatially resolved heat and mass transfer boundary condition is, in its turn, increased if the internal velocity is small or if there is a large variation of the transfer coefficients at the surface. Finally, the results indicate that when the internal convective heat transport is small, a rather constant evaporation rate may be obtained throughout the drying at certain conditions.
Heat and mass transfer boundary conditions at the surface of a heated sessile droplet
Ljung, Anna-Lena; Lundström, T. Staffan
2017-07-01
This work numerically investigates how the boundary conditions of a heated sessile water droplet should be defined in order to include effects of both ambient and internal flow. Significance of water vapor, Marangoni convection, separate simulations of the external and internal flow, and influence of contact angle throughout drying is studied. The quasi-steady simulations are carried out with Computational Fluid Dynamics and conduction, natural convection and Marangoni convection are accounted for inside the droplet. For the studied conditions, a noticeable effect of buoyancy due to evaporation is observed. Hence, the inclusion of moisture increases the maximum velocities in the external flow. Marangoni convection will, in its turn, increase the velocity within the droplet with up to three orders of magnitude. Results furthermore show that the internal and ambient flow can be simulated separately for the conditions studied, and the accuracy is improved if the internal temperature gradient is low, e.g. if Marangoni convection is present. Simultaneous simulations of the domains are however preferred at high plate temperatures if both internal and external flows are dominated by buoyancy and natural convection. The importance of a spatially resolved heat and mass transfer boundary condition is, in its turn, increased if the internal velocity is small or if there is a large variation of the transfer coefficients at the surface. Finally, the results indicate that when the internal convective heat transport is small, a rather constant evaporation rate may be obtained throughout the drying at certain conditions.
Homogenization of the stochastic Navier–Stokes equation with a stochastic slip boundary condition
Bessaih, Hakima
2015-11-02
The two-dimensional Navier–Stokes equation in a perforated domain with a dynamical slip boundary condition is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the holes. We consider a scaling (ᵋ for the viscosity and 1 for the density) that will lead to a time-dependent limit problem. However, the noncritical scaling (ᵋ, β > 1) is considered in front of the nonlinear term. The homogenized system in the limit is obtained as a Darcy’s law with memory with two permeabilities and an extra term that is due to the stochastic perturbation on the boundary of the holes. The nonhomogeneity on the boundary contains a stochastic part that yields in the limit an additional term in the Darcy’s law. We use the two-scale convergence method after extending the solution with 0 inside the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. Due to the stochastic integral, the pressure that appears in the variational formulation does not have enough regularity in time. This fact made us rely only on the variational formulation for the passage to the limit on the solution. We obtain a variational formulation for the limit that is solution of a Stokes system with two pressures. This two-scale limit gives rise to three cell problems, two of them give the permeabilities while the third one gives an extra term in the Darcy’s law due to the stochastic perturbation on the boundary of the holes.
A Nitsche cut finite element method for the Oseen problem with general Navier boundary conditions
Winter, M.; Schott, B.; Massing, A.; Wall, W. A.
2018-03-01
In this work a Nitsche-based imposition of generalized Navier conditions on cut meshes for the Oseen problem is presented. Other methods from literature dealing with the generalized Navier condition impose this condition by means of substituting the tangential Robin condition in a classical Galerkin way. These methods work fine for a large slip length coefficient but lead to conditioning and stability issues when it approaches zero. We introduce a novel method for the weak imposition of the generalized Navier condition which remains well-posed and stable for arbitrary choice of slip length, including zero. The method proposed here builds on the formulation done by [1]. They impose a Robin condition for the Poisson problem by means of Nitsche's method for an arbitrary combination of the Dirichlet and Neumann parts of the condition. The analysis conducted for the proposed method is done in a similar fashion as in [2], but is done here for a more general type of boundary condition. The analysis proves stability for all flow regimes and all choices of slip lengths. Also an L2-optimal estimate for the velocity error is shown, which was not conducted in the previously mentioned work. A numerical example is carried out for varying slip lengths to verify the robustness and stability of the method with respect to the choice of slip length. Even though proofs and formulations are presented for the more general case of an unfitted grid method, they can easily be reduced to the simpler case of a boundary-fitted grid with the removal of the ghost-penalty stabilization terms.
Influence of boundary conditions on the solution of a hyperbolic thermoelasticity problem
Vitokhin, Evgeniy Yu.; Babenkov, Mikhail B.
2017-03-01
We consider a series of problems with a short laser impact on a thin metal layer accounting various boundary conditions of the first and second kind. The behavior of the material is modeled by the hyperbolic thermoelasticity of Lord-Shulman type. We obtain analytical solutions of the problems in the semi-coupled formulation and numerical solutions in the coupled formulation. Numerical solutions are compared with the analytical ones. The analytical solutions of the semi-coupled problems and numerical solutions of the coupled problems show qualitative match. The solutions of hyperbolic thermoelasticity problems are compared with those obtained in the frame of the classical thermoelasticity. It was determined that the most prominent difference between the classical and hyperbolic solutions arises in the problem with fixed boundaries and constant temperature on them. The smallest differences were observed in the problem with unconstrained, thermally insulated edges. It was shown that a cooling zone is observed if the boundary conditions of the first kind are given for the temperature. Analytical expressions for the velocities of the quasiacoustic and quasithermal fronts as well as the critical value for the attenuation coefficient of the excitation impulse are verified numerically.
Energy dissipation in the Nagel-Schreckenberg model with open boundary condition
Zhang, Wei; Zhang, Wei
2014-01-01
In this paper, we numerically investigate energy dissipation caused by traffic in the Nagel-Schreckenberg (NaSch) model with open boundary conditions (OBC). Boundary results in excess energy dissipation. The effects of the stochastic boundary conditions on energy dissipation are discussed. The behaviors of energy dissipation in different traffic phase are distinct. As an order parameter, energy dissipation rate E d characterizes the phase transition behaviors well. It is shown that there is no true free-flow state in nondeterministic NaSch model with OBC. We refer to this non-true free-flow state as quasi-free-flow (QFF) phase in which there are interactions between vehicles caused by stochastic braking but no backward moving jam exists. In the maximum current phase, E d is minimal thus the social payoff is maximal. Energy dissipation profiles in QFF, jammed and maximum current phase are presented. Theoretical analyses are in good agreement with numerical results for the case v max = 1.
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Ibukun Sarah Oyelakin
2016-06-01
Full Text Available In this paper we report on combined Dufour and Soret effects on the heat and mass transfer in a Casson nanofluid flow over an unsteady stretching sheet with thermal radiation and heat generation. The effects of partial slip on the velocity at the boundary, convective thermal boundary condition, Brownian and thermophoresis diffusion coefficients on the concentration boundary condition are investigated. The model equations are solved using the spectral relaxation method. The results indicate that the fluid flow, temperature and concentration profiles are significantly influenced by the fluid unsteadiness, the Casson parameter, magnetic parameter and the velocity slip. The effect of increasing the Casson parameter is to suppress the velocity and temperature growth. An increase in the Dufour parameter reduces the flow temperature, while an increase in the value of the Soret parameter causes increase in the concentration of the fluid. Again, increasing the velocity slip parameter reduces the velocity profile whereas increasing the heat generation parameter increases the temperature profile. A validation of the work is presented by comparing the current results with existing literature.
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Rais Ahmad
2012-01-01
Full Text Available Guided wave technique is an efficient method for monitoring structural integrity by detecting and forecasting possible damages in distributed pipe networks. Efficient detection depends on appropriate selection of guided wave modes as well as signal processing techniques. Fourier analysis and wavelet analysis are two popular signal processing techniques that provide a flexible set of tools for solving various fundamental problems in science and engineering. In this paper, effective ways of using Fourier and Wavelet analyses on guided wave signals for detecting defects in steel pipes are discussed for different boundary conditions. This research investigates the effectiveness of Fourier transforms and Wavelet analysis in detecting defects in steel pipes. Cylindrical Guided waves are generated by piezo-electric transducers and propagated through the pipe wall boundaries in a pitch-catch system. Fourier transforms of received signals give information regarding the propagating guided wave modes which helps in detecting defects by selecting appropriate modes that are affected by the presence of defects. Continuous wavelet coefficients are found to be sensitive to defects. Several types of mother wavelet functions such as Daubechies, Symlet, and Meyer have been used for the continuous wavelet transform to investigate the most suitable wavelet function for defect detection. This research also investigates the effect of different boundary conditions on wavelet transforms for different mother wavelet functions.
Impacts of boundary condition changes on regional climate projections over West Africa
Kim, Jee Hee; Kim, Yeonjoo; Wang, Guiling
2017-06-01
Future projections using regional climate models (RCMs) are driven with boundary conditions (BCs) typically derived from global climate models. Understanding the impact of the various BCs on regional climate projections is critical for characterizing their robustness and uncertainties. In this study, the International Center for Theoretical Physics Regional Climate Model Version 4 (RegCM4) is used to investigate the impact of different aspects of boundary conditions, including lateral BCs and sea surface temperature (SST), on projected future changes of regional climate in West Africa, and BCs from the coupled European Community-Hamburg Atmospheric Model 5/Max Planck Institute Ocean Model are used as an example. Historical, future, and several sensitivity experiments are conducted with various combinations of BCs and CO2 concentration, and differences among the experiments are compared to identify the most important drivers for RCMs. When driven by changes in all factors, the RegCM4-produced future climate changes include significantly drier conditions in Sahel and wetter conditions along the Guinean coast. Changes in CO2 concentration within the RCM domain alone or changes in wind vectors at the domain boundaries alone have minor impact on projected future climate changes. Changes in the atmospheric humidity alone at the domain boundaries lead to a wetter Sahel due to the northward migration of rain belts during summer. This impact, although significant, is offset and dominated by changes of other BC factors (primarily temperature) that cause a drying signal. Future changes of atmospheric temperature at the domain boundaries combined with SST changes over oceans are sufficient to cause a future climate that closely resembles the projection that accounts for all factors combined. Therefore, climate variability and changes simulated by RCMs depend primarily on the variability and change of temperature aspects of the RCM BCs. Moreover, it is found that the response
Tang, Liang; Cong, Shengyi; Ling, Xianzhang; Ju, Nengpan
2017-01-01
Boundary conditions can significantly affect a slope's behavior under strong earthquakes. To evaluate the importance of boundary conditions for finite element (FE) simulations of a shake-table experiment on the slope response, a validated three-dimensional (3D) nonlinear FE model is presented, and the numerical and experimental results are compared. For that purpose, the robust graphical user-interface "SlopeSAR", based on the open-source computational platform OpenSees, is employed, which simplifies the effort-intensive pre- and post-processing phases. The mesh resolution effect is also addressed. A parametric study is performed to evaluate the influence of boundary conditions on the FE model involving the boundary extent and three types of boundary conditions at the end faces. Generally, variations in the boundary extent produce inconsistent slope deformations. For the two end faces, fixing the y-direction displacement is not appropriate to simulate the shake-table experiment, in which the end walls are rigid and rough. In addition, the influence of the length of the 3D slope's top face and the width of the slope play an important role in the difference between two types of boundary conditions at the end faces (fixing the y-direction displacement and fixing the ( y, z) direction displacement). Overall, this study highlights that the assessment of a comparison between a simulation and an experimental result should be performed with due consideration to the effect of the boundary conditions.
Problem of the boundary condition in quantum cosmology: a simple example
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Zhuk, Alexander
1988-10-01
The quantum cosmological minisuperspace model with a massless scalar field with a potential lambdahi/sup 4/ is investigated. The Hartle-Hawking proposal gives the possibility of picking a particular solution of the Wheeler-DeWitt equation in the space of the imaginary conformal factor a and scalar field phi. An analytic expression for this solution is obtained and an analytic continuation to the space of real ..cap alpha.. and phi is performed. The boundary conditions on the surface a = O, phi=+-infinityare psi(a=O, phi=+-infinity=1. It is shown that near this boundary the psi have exponential behaviour. In the region where the interaction between gravity and the scalar field plays the main role the psi have an oscillation behaviour and this leads to the inflation of the universe. (author).
Sithole, Hloniphile M.; Mondal, Sabyasachi; Sibanda, Precious; Motsa, Sandile S.
2017-11-01
The main focus of this study is on unsteady Maxwell nanofluid flow over a shrinking surface with convective and slip boundary conditions. The objective is to give an evaluation of the impact and significance of Brownian motion and thermophoresis when the nanofluid particle volume fraction flux at the boundary is zero. The transformed equations are solved numerically using the spectral local linearization method. We present an analysis of the residual errors to show the accuracy and convergence of the spectral local linearization method. We explore the effect of magnetic field and thermophoresis parameters on the heat transfer rate. We show, among other results, that an increase in particle Brownian motion leads to a decrease in the concentration profiles but concentration profiles increase with the increasing value of thermophoresis parameter
Reis, Tim
2012-01-01
We present lattice Boltzmann simulations of rarefied flows driven by pressure drops along two-dimensional microchannels. Rarefied effects lead to non-zero cross-channel velocities, nonlinear variations in the pressure along the channel. Both effects are absent in flows driven by uniform body forces. We obtain second-order accuracy for the two components of velocity the pressure relative to asymptotic solutions of the compressible Navier-Stokes equations with slip boundary conditions. Since the common lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier-Maxwell slip boundary conditions that relate the tangential velocity to the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. Our moment formalism is also valuable for analysing the existing boundary conditions. It reveals the origin of numerical slip in the bounce-back other common boundary conditions that impose conditions on the higher moments, not on the local tangential velocity itself. © 2012 American Institute of Physics.
Park, Hyunwook; Pan, Xiaomin; Lee, Changhoon; Choi, Jung-Il
2016-06-01
A novel immersed boundary (IB) method based on an implicit direct forcing (IDF) scheme is developed for incompressible viscous flows. The key idea for the present IDF method is to use a block LU decomposition technique in momentum equations with Taylor series expansion to construct the implicit IB forcing in a recurrence form, which imposes more accurate no-slip boundary conditions on the IB surface. To accelerate the IB forcing convergence during the iterative procedure, a pre-conditioner matrix is introduced in the recurrence formulation of the IB forcing. A Jacobi-type parameter is determined in the pre-conditioner matrix by minimizing the Frobenius norm of the matrix function representing the difference between the IB forcing solution matrix and the pre-conditioner matrix. In addition, the pre-conditioning parameter is restricted due to the numerical stability in the recurrence formulation. Consequently, the present pre-conditioned IDF (PIDF) enables accurate calculation of the IB forcing within a few iterations. We perform numerical simulations of two-dimensional flows around a circular cylinder and three-dimensional flows around a sphere for low and moderate Reynolds numbers. The result shows that PIDF yields a better imposition of no-slip boundary conditions on the IB surfaces for low Reynolds number with a fairly larger time step than IB methods with different direct forcing schemes due to the implicit treatment of the diffusion term for determining the IB forcing. Finally, we demonstrate the robustness of the present PIDF scheme by numerical simulations of flow around a circular array of cylinders, flows around a falling sphere, and two sedimenting spheres in gravity.
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Zhi-Gang Feng
2012-05-31
The simulation of particulate flows for industrial applications often requires the use of two-fluid models, where the solid particles are considered as a separate continuous phase. One of the underlining uncertainties in the use of the two-fluid models in multiphase computations comes from the boundary condition of the solid phase. Typically, the gas or liquid fluid boundary condition at a solid wall is the so called no-slip condition, which has been widely accepted to be valid for single-phase fluid dynamics provided that the Knudsen number is low. However, the boundary condition for the solid phase is not well understood. The no-slip condition at a solid boundary is not a valid assumption for the solid phase. Instead, several researchers advocate a slip condition as a more appropriate boundary condition. However, the question on the selection of an exact slip length or a slip velocity coefficient is still unanswered. Experimental or numerical simulation data are needed in order to determinate the slip boundary condition that is applicable to a two-fluid model. The goal of this project is to improve the performance and accuracy of the boundary conditions used in two-fluid models such as the MFIX code, which is frequently used in multiphase flow simulations. The specific objectives of the project are to use first principles embedded in a validated Direct Numerical Simulation particulate flow numerical program, which uses the Immersed Boundary method (DNS-IB) and the Direct Forcing scheme in order to establish, modify and validate needed energy and momentum boundary conditions for the MFIX code. To achieve these objectives, we have developed a highly efficient DNS code and conducted numerical simulations to investigate the particle-wall and particle-particle interactions in particulate flows. Most of our research findings have been reported in major conferences and archived journals, which are listed in Section 7 of this report. In this report, we will present a
Ruggeri, Fabrizio
2016-05-12
In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given prescribed initial condition. We show how to derive the joint likelihood function for the forward problem, given some measurements of the solution field subject to Gaussian noise. Given Gaussian priors for the time-dependent Dirichlet boundary values, we analytically marginalize the joint likelihood using the linearity of the equation. Our hierarchical Bayesian approach is fully implemented in an example that involves the heat equation. In this example, the thermal diffusivity is the unknown parameter. We assume that the thermal diffusivity parameter can be modeled a priori through a lognormal random variable or by means of a space-dependent stationary lognormal random field. Synthetic data are used to test the inference. We exploit the behavior of the non-normalized log posterior distribution of the thermal diffusivity. Then, we use the Laplace method to obtain an approximated Gaussian posterior and therefore avoid costly Markov Chain Monte Carlo computations. Expected information gains and predictive posterior densities for observable quantities are numerically estimated using Laplace approximation for different experimental setups.
Effects of boundary conditions on bistable behaviour in axisymmetrical shallow shells.
Sobota, P M; Seffen, K A
2017-07-01
Multistable shells are thin-walled structures that have more than one stable state of self-stress. We consider isotropic axisymmetrical shallow shells of arbitrary polynomial shapes using a Föppl-von Kármán analytical model. By employing a Rayleigh-Ritz approach, we identify stable shapes from local minima in the strain energy formulation, and we formally characterize the level of influence of the boundary conditions on the critical geometry for achieving bistable inversion-an effect not directly answered in the literature. Systematic insight is afforded by connecting the boundary to ground through sets of extensional and rotational linear springs. For typical cap-like shells, it is shown that bistability is generally enhanced when the extensional spring stiffness increases and when the rotational spring stiffness decreases, i.e. when boundary movements in-plane are resisted but when their rotations are not; however, for certain other shapes and large in-plane stiffness values, bistability can be enhanced by resisting but not entirely preventing edge rotations. Our predictions are furnished as detailed regime maps of the critical geometry, which are accurately correlated against finite-element analysis. Furthermore, the suitabilities of single degree-of-freedom models, for which solutions are achieved in closed form, are evaluated and compared to our more accurate predictions.
On the numerical solution of the diffusion equation with a nonlocal boundary condition
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Dehghan Mehdi
2003-01-01
Full Text Available Parabolic partial differential equations with nonlocal boundary specifications feature in the mathematical modeling of many phenomena. In this paper, numerical schemes are developed for obtaining approximate solutions to the initial boundary value problem for one-dimensional diffusion equation with a nonlocal constraint in place of one of the standard boundary conditions. The method of lines (MOL semidiscretization approach is used to transform the model partial differential equation into a system of first-order linear ordinary differential equations (ODEs. The partial derivative with respect to the space variable is approximated by a second-order finite-difference approximation. The solution of the resulting system of first-order ODEs satisfies a recurrence relation which involves a matrix exponential function. Numerical techniques are developed by approximating the exponential matrix function in this recurrence relation. We use a partial fraction expansion to compute the matrix exponential function via Pade approximations, which is particularly useful in parallel processing. The algorithm is tested on a model problem from the literature.
Casimir Effect Under Quasi-Periodic Boundary Condition Inspired by Nanotubes
Feng, Chao-Jun; Li, Xin-Zhou; Zhai, Xiang-Hua
2014-01-01
When one studies the Casimir effect, the periodic (anti-periodic) boundary condition is usually taken to mimic a periodic (anti-periodic) structure for a scalar field living in a flat space with a non-Euclidean topology. However, there could be an arbitrary phase difference between the value of the scalar field on one endpoint of the unit structure and that on the other endpoint, such as the structure of nanotubes. Then, in this paper, a periodic condition on the ends of the system with an additional phase factor, which is called the "quasi-periodic" condition, is imposed to investigate the corresponding Casimir effect. And an attractive or repulsive Casimir force is found, whose properties depend on the phase angle value. Especially, the Casimir effect disappears when the phase angle takes a particular value. High dimensional spacetime case is also investigated.
Aeroelastic analysis of versatile thermal insulation (VTI) panels with pinched boundary conditions
Carrera, Erasmo; Zappino, Enrico; Patočka, Karel; Komarek, Martin; Ferrarese, Adriano; Montabone, Mauro; Kotzias, Bernhard; Huermann, Brian; Schwane, Richard
2014-03-01
Launch vehicle design and analysis is a crucial problem in space engineering. The large range of external conditions and the complexity of space vehicles make the solution of the problem really challenging. The problem considered in the present work deals with the versatile thermal insulation (VTI) panel. This thermal protection system is designed to reduce heat fluxes on the LH2 tank during the long coasting phases. Because of the unconventional boundary conditions and the large-scale geometry of the panel, the aeroelastic behaviour of VTI is investigated in the present work. Known available results from literature related to similar problem, are reviewed by considering the effect of various Mach regimes, including boundary layer thickness effects, in-plane mechanical and thermal loads, non-linear effects and amplitude of limit cycle oscillations. A dedicated finite element model is developed for the supersonic regime. The models used for coupling the orthotropic layered structural model with Piston Theory aerodynamic models allow the calculations of flutter conditions in case of curved panels supported in a discrete number of points. An advanced computational aeroelasticity tool is developed using various dedicated commercial softwares (CFX, ZAERO, EDGE). A wind tunnel test campaign is carried out to assess the computational tool in the analysis of this type of problem.
Revisiting the boundary conditions for second-harmonic generation at metal-dielectric interfaces
Nireekshan Reddy, K.; Chen, Parry Y.; Fernández-Domínguez, Antonio I.; Sivan, Yonatan
2017-09-01
We study second-harmonic generation (SHG) arising from surface nonlinearity at a metal-dielectric interface using a spectral decomposition method. Since our method avoids the need to consider the generalized boundary condition across the metal-dielectric interface in the presence of a perpendicular surface source, we retrieve the known discontinuity of the tangential component of the electric field ($E_{\\parallel}^ {2\\omega}$) for a general geometry, based on a purely mathematical argument. Further, we reaffirm the standard convention of the implementation of this condition, namely, that the surface dipole source radiates as if placed outside the metal surface for arbitrary geometries. We also study and explain the spectral dependence of the discontinuity of the tangential component of the electric field at second harmonic. Finally, we note that the default settings of the commercial numerical package COMSOL Multiphysics fail to account for the $E_{\\parallel}^ {2\\omega}$-discontinuity. We provide a simple recipe that corrects the boundary condition within these existing settings.
A Resistive Boundary Condition Enhanced DGTD Scheme for the Transient Analysis of Graphene
Li, Ping
2015-04-24
In this paper, the electromagnetic (EM) features of graphene are characterized by a discontinuous Galerkin timedomain (DGTD) algorithm with a resistive boundary condition (RBC). The atomically thick graphene is equivalently modeled using a RBC by regarding the graphene as an infinitesimally thin conductive sheet. To incorporate RBC into the DGTD analysis, the surface conductivity of the graphene composed of contributions from both intraband and interband terms is firstly approximated by rational basis functions using the fastrelaxation vector-fitting (FRVF) method in the Laplace-domain. Next, through the inverse Laplace transform, the corresponding time-domain matrix equations in integral can be obtained. Finally, these matrix equations are solved by time-domain finite integral technique (FIT). For elements not touching the graphene sheet, however, the well-known Runge-Kutta (RK) method is employed to solve the two first-order time-derivative Maxwell’s equations. The application of the surface boundary condition significantly alleviates the memory consuming and the limitation of time step size required by Courant-Friedrichs-Lewy (CFL) condition. To validate the proposed algorithm, various numerical examples are presented and compared with available references.
Detecting Unsteady Blade Row Interaction in a Francis Turbine using a Phase-Lag Boundary Condition
Wouden, Alex; Cimbala, John; Lewis, Bryan
2013-11-01
For CFD simulations in turbomachinery, methods are typically used to reduce the computational cost. For example, the standard periodic assumption reduces the underlying mesh to a single blade passage in axisymmetric applications. If the simulation includes only a single array of blades with an uniform inlet condition, this assumption is adequate. However, to compute the interaction between successive blade rows of differing periodicity in an unsteady simulation, the periodic assumption breaks down and may produce inaccurate results. As a viable alternative the phase-lag boundary condition assumes that the periodicity includes a temporal component which, if considered, allows for a single passage to be modeled per blade row irrespective of differing periodicity. Prominently used in compressible CFD codes for the analysis of gas turbines/compressors, the phase-lag boundary condition is adapted to analyze the interaction between the guide vanes and rotor blades in an incompressible simulation of the 1989 GAMM Workshop Francis turbine using OpenFOAM. The implementation is based on the ``direct-storage'' method proposed in 1977 by Erdos and Alzner. The phase-lag simulation is compared with available data from the GAMM workshop as well as a full-wheel simulation. Funding provided by DOE Award number: DE-EE0002667.
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Gözde Sarı
2013-01-01
Full Text Available An investigation into the dynamic behavior of a slightly curved resonant microbeam having nonideal boundary conditions is presented. The model accounts for midplane stretching, an applied axial load, and a small AC harmonic force. The ends of the curved microbeam are on immovable simple supports and the microbeam is resting on a nonlinear elastic foundation. The forced vibration response of curved microbeam due to the small AC load is obtained analytically by means of direct application of the method of multiple scales (a perturbation method. The effects of the nonlinear elastic foundation as well as the effect of curvature on the vibrations of the microbeam are examined. It is found that the effect of curvature is of softening type. For sufficiently high values of the coefficients, the elastic foundation and the axial load may suppress the softening behavior resulting in hardening behavior of the nonlinearity. The frequencies and mode shapes obtained are compared with the ideal boundary conditions case and the differences between them are contrasted on frequency-response curves. The frequency response and nonlinear frequency curves obtained may provide a reference for the choice of reasonable resonant conditions, design, and industrial applications of such systems. Results may be beneficial for future experimental and theoretical works on MEMS.
Sirenko, Kostyantyn
2013-07-01
Exact absorbing and periodic boundary conditions allow to truncate grating problems\\' infinite physical domains without introducing any errors. This work presents exact absorbing boundary conditions for 3D diffraction gratings and describes their discretization within a high-order time-domain discontinuous Galerkin finite element method (TD-DG-FEM). The error introduced by the boundary condition discretization matches that of the TD-DG-FEM; this results in an optimal solver in terms of accuracy and computation time. Numerical results demonstrate the superiority of this solver over TD-DG-FEM with perfectly matched layers (PML)-based domain truncation. © 2013 IEEE.
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Verschaeve, Joris C. G.
2011-07-01
The present thesis focuses on two distinct topics of computational fluid dynamics. The first one, treated in part I, focuses on the no-slip boundary conditions for the lattice Boltzmann method, whereas the second one, presented in part II, proposes a high order accurate description of the interface in two-phase flow computations for volume tracking in two dimensions.Part I of the present thesis presents an important issue in the framework of the lattice Boltzmann method, namely no-slip boundary conditions. Since the central object of the lattice Boltzmann method is the particle distribution function, the implementation of the no-slip boundary condition, although straightforward for continuum Navier Stokes solvers, is more involved. Additional physical arguments for the no-slip boundary condition at straight walls are presented. This leads to an alternative formulation of the no-slip boundary condition for the lattice Boltzmann method. This boundary condition is second order accurate with respect to the grid spacing and conserves mass. The origin of numerical instabilities observed for a variety of other boundary conditions is investigated, and it is shown how these can be removed leading to stable boundary conditions. Some arguments unifying different formulations of the no-slip boundary condition are presented. In addition to straight boundary conditions, the question of curved boundary conditions is treated. These represent an elevated level of complexity, since the lattice Boltzmann method is only defined for equidistant Cartesian grids. The curved boundary condition in the present thesis conserves the second order accuracy of the lattice Boltzmann method.Due to the complexity of two-phase flow problems, the majority of numerical methods in this field displays a rather low order of accuracy. In part II of the present thesis, a subproblem of the two-phase flow problem, namely the tracking of the interface is treated. Two different interface descriptions allowing
Analytic theory of curvature effects for wave problems with general boundary conditions
DEFF Research Database (Denmark)
Willatzen, Morten; Gravesen, Jens; Voon, L. C. Lew Yan
2010-01-01
A formalism based on a combination of differential geometry and perturbation theory is used to obtain analytic expressions for confined eigenmode changes due to general curvature effects. In cases of circular-shaped and helix-shaped structures, where alternative analytic solutions can be found......, the perturbative solution is shown to yield the same result. The present technique allows the generalization of earlier results to arbitrary boundary conditions. The power of the method is illustrated using examples based on Maxwell’s and Schrödinger’s equations for applications in photonics and nanoelectronics....
Effects from magnetic boundary conditions in superconducting-magnetic proximity systems
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Thomas E. Baker
2016-05-01
Full Text Available A superconductor-magnetic proximity system displays singlet-triplet pair correlations in the magnetization as a function of inhomogeneities of the magnetic profile. We discuss how the magnetic boundary conditions affects differently the curvature and winding number of rotating magnetizations in the three commonly used structures to generate long range triplet components: an exchange spring, a helical structure and a misaligned magnetic multilayer. We conclude that the choice of the system is dictated by the goal one wishes to achieve in designing a spintronic device but note that only the exchange spring presently offers an experimentally realizable magnetic profile that is tunable.
The Compressible Stokes Flows with No-Slip Boundary Condition on Non-Convex Polygons
Kweon, Jae Ryong
2017-03-01
In this paper we study the compressible Stokes equations with no-slip boundary condition on non-convex polygons and show a best regularity result that the solution can have without subtracting corner singularities. This is obtained by a suitable Helmholtz decomposition: {{{u}}={{w}}+nablaφ_R} with div w = 0 and a potential φ_R. Here w is the solution for the incompressible Stokes problem and φ_R is defined by subtracting from the solution of the Neumann problem the leading two corner singularities at non-convex vertices.
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R. C. Mittal
2014-01-01
Full Text Available We present a technique based on collocation of cubic B-spline basis functions to solve second order one-dimensional hyperbolic telegraph equation with Neumann boundary conditions. The use of cubic B-spline basis functions for spatial variable and its derivatives reduces the problem into system of first order ordinary differential equations. The resulting system subsequently has been solved by SSP-RK54 scheme. The accuracy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and in good agreement with the exact solution.
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M. Stewart
2015-02-01
Full Text Available The determination of the piezoelectric coefficient of thin films using interferometry is hindered by bending contributions. Using finite element analysis (FEA simulations, we show that the Lefki and Dormans approximations using either single or double-beam measurements cannot be used with finite top electrode sizes. We introduce a novel method for characterising piezoelectric thin films which uses a differential measurement over the discontinuity at the electrode edge as an internal reference, thereby eliminating bending contributions. This step height is shown to be electrode size and boundary condition independent. An analytical expression is derived which gives good agreement with FEA predictions of the step height.
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E. Tohidi
2014-01-01
Full Text Available The problem of solving several types of one-dimensional parabolic partial differential equations (PDEs subject to the given initial and nonlocal boundary conditions is considered. The main idea is based on direct collocation and transforming the considered PDEs into their associated algebraic equations. After approximating the solution in the Legendre matrix form, we use Legendre operational matrix of differentiation for representing the mentioned algebraic equations clearly. Three numerical illustrations are provided to show the accuracy of the presented scheme. High accurate results with respect to the Bernstein Tau technique and Sinc collocation method confirm this accuracy.
Energy Technology Data Exchange (ETDEWEB)
Silva, Davi J.M.; Nunes, Carlos E.A.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: davijmsilva@yahoo.com.br, E-mail: ceanunes@yahoo.com.br, E-mail: rcbarros@pq.cnpq.br [Secretaria Municipal de Educacao de Itaborai, RJ (Brazil); Universidade Estacio de Sa (UNESA), Rio de Janeiro, RJ (Brazil); Universidade do Estado do Rio de Janeiro (UERJ), Novra Friburgo, RJ (Brazil). Instituto Politecnico. Departamento de Modelagem Computacional
2017-11-01
Discussed here is the accuracy of approximate albedo boundary conditions for energy multigroup discrete ordinates (S{sub N}) eigenvalue problems in two-dimensional rectangular geometry for criticality calculations in neutron fission reacting systems, such as nuclear reactors. The multigroup (S{sub N}) albedo matrix substitutes approximately the non-multiplying media around the core, e.g., baffle and reflector, as we neglect the transverse leakage terms within these non-multiplying regions. Numerical results to a typical model problem are given to illustrate the accuracy versus the computer running time. (author)
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Inayat Ullah
2013-01-01
Full Text Available A steady two-dimensional axisymmetric flow of an incompressible viscous fluid under the influence of a uniform transverse magnetic field with slip boundary condition is studied. An ordinary nonlinear differential equation is formed by transforming the Navier-Stokes equations using the transformation . Differential transform and optimal homotopy analysis methods have been used to obtain the solutions by varying pertinent flow parameters. By using residuals in each case, the validity of solutions is established. Excellent results are obtained by using the proposed schemes. The influence of different parameters on the flow is shown through graphs.
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Aqlan Mohammed H.
2016-01-01
Full Text Available We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration but also yield some new special cases for specific choices of parameters involved in the problems.
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Nicolae Tarfulea
2009-10-01
Full Text Available We investigate the existence of weak solutions to a class of quasilinear elliptic equations with nonlinear Neumann boundary conditions in exterior domains. Problems of this kind arise in various areas of science and technology. An important model case related to the initial data problem in general relativity is presented. As an application of our main result, we deduce the existence of the conformal factor for the Hamiltonian constraint in general relativity in the presence of multiple black holes. We also give a proof for uniqueness in this case.
Solutions of the Helmholtz equation with boundary conditions for force-free magnetic fields
Rasband, S. N.; Turner, L.
1981-01-01
It is shown that the solution, with one ignorable coordinate, for the Taylor minimum energy state (resulting in a force-free magnetic field) in either a straight cylindrical or a toroidal geometry with arbitrary cross section can be reduced to the solution of either an inhomogeneous Helmholtz equation or a Grad-Shafranov equation with simple boundary conditions. Standard Green's function theory is, therefore, applicable. Detailed solutions are presented for the Taylor state in toroidal and cylindrical domains having a rectangular cross section. The focus is on solutions corresponding to the continuous eigenvalue spectra. Singular behavior at 90 deg corners is explored in detail.
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Nee Alexander
2015-01-01
Full Text Available Mathematical modeling of radiant heating of a closed rectangular area under conditions of convective heat transfer at the external boundaries is passed. The fields of temperature and stream function, illustrating the unsteady nature of the heat transfer were obtained. The extent influence of convective heat transfer at the external boundaries on the circulating flows formation in the gas cavity are shown.
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Ahmed Alsaedi
2016-08-01
Full Text Available In this article, we study a boundary value problem of coupled systems of nonlinear Riemann-Liouvillle fractional integro-differential equations supplemented with nonlocal Riemann-Liouvillle fractional integro-differential boundary conditions. Our results rely on some standard tools of the fixed point theory. An illustrative example is also discussed.
Boundary conditions for General Relativity on AdS{sub 3} and the KdV hierarchy
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Pérez, Alfredo; Tempo, David; Troncoso, Ricardo [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile)
2016-06-20
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 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.
Hu, Pan; Wu, Tao; Wang, Hui-Zhi; Qi, Xin-Zheng; Yao, Jie; Cheng, Xiao-Dong; Chen, Wei; Zhang, Ying-Ze
2017-02-01
To observe the effects of boundary conditions and connect conditions on biomechanics predictions in finite element (FE) pelvic models. Three FE pelvic models were constructed to analyze the effect of boundary conditions and connect conditions in the hip joint: an intact pelvic model assumed contact of the hip joint on both sides (Model I); and a pelvic model assumed the hip joint connecting surfaces fused together with (Model II) or without proximal femurs (Model III). The model was validated by bone surface strains obtained from strain gauges in an in vitro pelvic experiment. Vertical load was applied to the pelvic specimen, and the same load was simulated in the FE model. There was a strong correlation between the FE analysis results of Model I and the experimental results (R 2 = 0.979); meanwhile, the correlation coefficient and the linear regression function increased slightly with increasing load force. Comparing the three models, the stress values in the point near the pubic symphysis in Model III were 48.52 and 39.1% lower, respectively, in comparison with Models I and II. Furthermore, the stress values on the dome region of the acetabulum in Models II and III were 103.61 and 390.53% less than those of Model I. Besides, the posterior acetabular wall stress values of Model II were 197.15 and 305.17% higher than those of Models I and III, respectively. These findings suggest that the effect of the connect condition in the hip joint should not be neglected, especially in studies related to clinical applications. © 2017 Chinese Orthopaedic Association and John Wiley & Sons Australia, Ltd.
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Haichao Li
2017-01-01
Full Text Available The free vibration analysis of moderately thick functionally graded (FG sector plates resting on two-parameter elastic foundation with general boundary conditions is presented via Fourier-Ritz method, which is composed of the modified Fourier series approach and the Ritz procedure. The material properties are assumed to vary continuously along the thickness according to the power-law distribution. The bilayered and single-layered functionally graded sector plates are obtained as the special cases of sandwich plates. The first-order shear deformation theory (FSDT is adopted to construct the theoretical model. Under current framework, regardless of boundary conditions, each displacement and each rotation of plates is represented by the modified Fourier series consisting of a standard Fourier cosine series and several closed-form auxiliary functions introduced to ensure and accelerate the convergence of the series representation. Then, the accurate solutions are obtained by using the Ritz procedure based on the energy function of sector plates. The present method shows good convergence, reliability, and accuracy by comprehensive investigation with some selected classical boundary conditions. Numerous new vibration results for moderately thick FG sandwich sector plates are provided. The effects of the elastic restraint parameters and so forth on free vibration characteristic of sector plates are presented.
Ben-Mansour, R.; Li, H.; Habib, M. A.; Hossain, M. M.
2018-02-01
Global warming has become a worldwide concern due to its severe impacts and consequences on the climate system and ecosystem. As a promising technology proving good carbon capture ability with low-efficiency penalty, Chemical Looping Combustion technology has risen much interest. However, the radiative heat transfer was hardly studied, nor its effects were clearly declared. The present work provides a mathematical model for radiative heat transfer within fuel reactor of chemical looping combustion systems and conducts a numerical research on the effects of boundary conditions, solid particles reflectivity, particles size, and the operating temperature. The results indicate that radiative heat transfer has very limited impacts on the flow pattern. Meanwhile, the temperature variations in the static bed region (where solid particles are dense) brought by radiation are also insignificant. However, the effects of radiation on temperature profiles within free bed region (where solid particles are very sparse) are obvious, especially when convective-radiative (mixed) boundary condition is applied on fuel reactor walls. Smaller oxygen carrier particle size results in larger absorption & scattering coefficients. The consideration of radiative heat transfer within fuel reactor increases the temperature gradient within free bed region. On the other hand, the conversion performance of fuel is nearly not affected by radiation heat transfer within fuel reactor. However, the consideration of radiative heat transfer enhances the heat transfer between the gas phase and solid phase, especially when the operating temperature is low.
Buckling of Nonprismatic Column on Varying Elastic Foundation with Arbitrary Boundary Conditions
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Ahmad A. Ghadban
2017-01-01
Full Text Available Buckling of nonprismatic single columns with arbitrary boundary conditions resting on a nonuniform elastic foundation may be considered as the most generalized treatment of the subject. The buckling differential equation for such columns is extremely difficult to solve analytically. Thus, the authors propose a numerical approach by discretizing the column into a finite number of segments. Each segment has constants E (modulus of elasticity, I (moment of inertia, and β (subgrade stiffness. Next, an exact analytical solution is derived for each prismatic segment resting on uniform elastic foundation. These segments are then assembled in a matrix from which the critical buckling load is obtained. The derived formulation accounts for different end boundary conditions. Validation is performed by benchmarking the present results against analytical solutions found in the literature, showing excellent agreement. After validation, more examples are solved to illustrate the power and flexibility of the proposed method. Overall, the proposed method provides reasonable results, and the examples solved demonstrate the versatility of the developed approach and some of its many possible applications.
Spectroscopy of {sup 12}C within the boundary condition for three-body resonant states
Energy Technology Data Exchange (ETDEWEB)
Kurokawa, Chie [Meme Media Laboratory, Hokkaido University, Sapporo 060-8628 (Japan)]. E-mail: chie@nucl.sci.hokudai.ac.jp; Kato, Kiyoshi [Department of Physics, Faculty of Science, Hokkaido University, Sapporo 060-0810 (Japan)
2007-08-01
The 3{alpha}-cluster structure of excited states in {sup 12}C is investigated by taking into account the correct boundary condition for three-body resonant states. In this study, we adopt the Complex Scaling Method (CSM), which enables us to obtain the resonant states that can be described as square integrable states with the same boundary conditions as those of the bound states, and calculate not only resonance energies but also the total decay widths of the 3{alpha} system. We compare the calculated resonance parameters to the experimental data and also to the previous 3{alpha} model results obtained with a bound state approximation. Our results well explain the many observed levels and give an assurance for the presence of the second 2{sup +} state, which is expected by the 3{alpha} model calculations with the approximations of bound state or two-body scattering. As for the negative-parity states, it is considered that the calculated 4{sup -} state is assigned to the observed E{sub x}=13.4MeV state. Through the calculation of channel amplitudes, the obtained third 0{sup +} state is found to have a s-wave dominant and a more dilute structure compared to the second 0{sup +} state.
Ben-Mansour, R.; Li, H.; Habib, M. A.; Hossain, M. M.
2017-09-01
Global warming has become a worldwide concern due to its severe impacts and consequences on the climate system and ecosystem. As a promising technology proving good carbon capture ability with low-efficiency penalty, Chemical Looping Combustion technology has risen much interest. However, the radiative heat transfer was hardly studied, nor its effects were clearly declared. The present work provides a mathematical model for radiative heat transfer within fuel reactor of chemical looping combustion systems and conducts a numerical research on the effects of boundary conditions, solid particles reflectivity, particles size, and the operating temperature. The results indicate that radiative heat transfer has very limited impacts on the flow pattern. Meanwhile, the temperature variations in the static bed region (where solid particles are dense) brought by radiation are also insignificant. However, the effects of radiation on temperature profiles within free bed region (where solid particles are very sparse) are obvious, especially when convective-radiative (mixed) boundary condition is applied on fuel reactor walls. Smaller oxygen carrier particle size results in larger absorption & scattering coefficients. The consideration of radiative heat transfer within fuel reactor increases the temperature gradient within free bed region. On the other hand, the conversion performance of fuel is nearly not affected by radiation heat transfer within fuel reactor. However, the consideration of radiative heat transfer enhances the heat transfer between the gas phase and solid phase, especially when the operating temperature is low.
Effect of 3D boundary conditions on rift propagation or failure to break.
Le Pourhiet, Laetitia; Watremez, Louise; Delescluse, Matthias
2017-04-01
Oblique rift segments are generally modelled using two type of set-ups. The first one consist of off-set weak notches which are pulled in a cylindrical manner, the second one consist at pulling obliquely on wide weak zone inside which a system of en-echellon grabben can develop. These two set up produce diverging segments of constant age and younger oblique segments which localise after some delays which depends on the offset of the diverging segments and the rheology of the lithosphere. In this study, we propose a different set-up which consist at seeding only one diverging weak segments and at letting the continental rupture propagate through the model in order to assess 1/ how 3D boundary conditions affect the speed on propagation of the continental break-up and 2/ how the structure that form at the front of the propagating break-up affect the propagation it-self. We find that a cylindrical boundary condition or extension in the direction of propagation favour very rapid continental break-up propagation, narrow rift zones and extremely linear diverging segments. On the contrary, when a slight compression is applied in the direction of rift propagation. The propagation is slow and might even stop completely. This slow down in propagation results in an increase of pre-breakup structuration of the margins and can even cause segmentation of final spreading. The numerical models are finally compared to natural examples from the Atlantic and the South China Sea.
Rudyak, V. Yu.; Krakhalev, M. N.; Sutormin, V. S.; Prishchepa, O. O.; Zyryanov, V. Ya.; Liu, J.-H.; Emelyanenko, A. V.; Khokhlov, A. R.
2017-11-01
Polymer-dispersed liquid crystal composites have been a focus of study for a long time for their unique electro-optical properties and manufacturing by "bottom-up" techniques at large scales. In this paper, nematic liquid crystal oblate droplets with conical boundary conditions (CBCs) under the action of electric field were studied by computer simulations and polarized optical microscopy. Droplets with CBCs were shown to prefer an axial-bipolar structure, which combines a pair of boojums and circular disclinations on a surface. In contrast to droplets with degenerate planar boundary conditions (PBCs), hybridization of the two structure types in droplets with CBCs leads to a two-minima energy profile, resulting in an abrupt structure transition and bistable behavior of the system. The nature of the low-energy barrier in droplets with CBCs makes it highly sensitive to external stimuli, such as electric or magnetic fields, temperature, and light. In particular, the value of the electric field of the structure reorientation in droplets with CBCs was found to be a few times smaller than the one for droplets with PBCs, and the droplet state remained stable after switching off the voltage.
Charged hadrons in local finite-volume QED+QCD with C* boundary conditions
Lucini, Biagio; Ramos, Alberto; Tantalo, Nazario
2016-01-01
In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C* boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C* boundary conditions. In particular we learn that a certain class of electrically-charged states can be constructed in this setup in a fully consistent fashion, without relying on gauge fixing. We argue that this class of states covers most of the interesting phenomenological applications in the framework of numerical simulations. We also calculate finite-volume corrections to the mass of stable charg...
Sensitivity of Pliocene climate simulations in MRI-CGCM2.3 to respective boundary conditions
Kamae, Youichi; Yoshida, Kohei; Ueda, Hiroaki
2016-08-01
Accumulations of global proxy data are essential steps for improving reliability of climate model simulations for the Pliocene warming climate. In the Pliocene Model Intercomparison Project phase 2 (PlioMIP2), a part project of the Paleoclimate Modelling Intercomparison Project phase 4, boundary forcing data have been updated from the PlioMIP phase 1 due to recent advances in understanding of oceanic, terrestrial and cryospheric aspects of the Pliocene palaeoenvironment. In this study, sensitivities of Pliocene climate simulations to the newly archived boundary conditions are evaluated by a set of simulations using an atmosphere-ocean coupled general circulation model, MRI-CGCM2.3. The simulated Pliocene climate is warmer than pre-industrial conditions for 2.4 °C in global mean, corresponding to 0.6 °C warmer than the PlioMIP1 simulation by the identical climate model. Revised orography, lakes, and shrunk ice sheets compared with the PlioMIP1 lead to local and remote influences including snow and sea ice albedo feedback, and poleward heat transport due to the atmosphere and ocean that result in additional warming over middle and high latitudes. The amplified higher-latitude warming is supported qualitatively by the proxy evidences, but is still underestimated quantitatively. Physical processes responsible for the global and regional climate changes should be further addressed in future studies under systematic intermodel and data-model comparison frameworks.
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.
Chiruta, Daniel; Linares, Jorge; Miyashita, Seiji; Boukheddaden, Kamel
2014-05-01
In order to explain clearly the role of the open boundary conditions (OBCs) on phase transition in one dimensional system, we consider an Ising model with both short-range (J) and long-range (G) interactions, which has allowed us to study the cooperative nature of spin-crossover (SCO) materials at the nanometer scale. At this end, we developed a transfer-matrix method for one-dimensional (1D) SCO system with free boundary conditions, and we give numerical evidences for how the thermal spin transition curves vary as a function of the physical parameters (J, G) or an applied pressure. Moreover for OBCs case, we have derived the bulk, surface and finite-size contributions to the free energy and we have investigated the variation of these energies as function of J and system size. We have found that the surface free energy behaves like J⟨σ⟩2, where ⟨σ⟩ is the average magnetization per site. Since the properties of the nanometric scale are dramatically influenced by the system's size (N), our analytical outcomes for the size dependence represent a step to achieve new characteristic of the future devices and also a way to find various novel properties which are absent in the bulk materials.
CSIR Research Space (South Africa)
Shatalov, MY
2007-04-01
Full Text Available . The dispersion curves are plotted for propagating waves for non-axisymmetric vibrations of the cylinder. It is shown that the dispersion curves are sensitive to the form of electric boundary conditions...
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Muhammad Tahir
2012-11-01
Full Text Available This article shows the uniqueness of a solution to a Bitsadze system of equations, with a boundary-value problem that has four additional single point conditions. It also shows how to construct the solution.
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Vali Parvaneh
2011-01-01
Full Text Available The effects of boundary conditions and defects on the buckling behavior of SWCNTs are investigated using a structural mechanics model. Due to the application of carbon nanotubes in different fields such as NEMS, where they are subjected to different loading and boundary conditions, an investigation of buckling behavior of nanotubes with different boundary conditions is necessary. Critical buckling loads and the effects of vacancy and Stone-Wales defects were studied for zigzag and armchair nanotubes with various boundary conditions and aspect ratios (length/diameter. The comparison of our results with those of the buckling of shells with cutouts indicates that vacancy defects in carbon nanotubes can most likely be modeled as cutouts of the shells. Finally, a hybrid vacancy defect and Stone-Wales defect are also developed, and their effect on the critical buckling loads is studied.
Vignon-Clementel, Irene; Jansen, K E; Taylor, C A; 10.1080/10255840903413565
2010-01-01
The simulation of blood flow and pressure in arteries requires outflow boundary conditions that incorporate models of downstream domains. We previously described a coupled multidomain method to couple analytical models of the downstream domains with 3D numerical models of the upstream vasculature. This prior work either included pure resistance boundary conditions or impedance boundary conditions based on assumed periodicity of the solution. However, flow and pressure in arteries are not necessarily periodic in time due to heart rate variability, respiration, complex transitional flow or acute physiological changes. We present herein an approach for prescribing lumped parameter outflow boundary conditions that accommodate transient phenomena. We have applied this method to compute haemodynamic quantities in different physiologically relevant cardiovascular models, including patient-specific examples, to study non-periodic flow phenomena often observed in normal subjects and in patients with acquired or congen...
Planck scale boundary conditions in the standard model with singlet scalar dark matter
Energy Technology Data Exchange (ETDEWEB)
Haba, Naoyuki [Graduate School of Science and Engineering, Shimane University, Matsue, Shimane 690-8504 (Japan); Kaneta, Kunio [Kavli IPMU (WPI), The University of Tokyo, Kashiwa, Chiba 277-8568 (Japan); Takahashi, Ryo [Graduate School of Science and Engineering, Shimane University, Matsue, Shimane 690-8504 (Japan)
2014-04-04
We investigate Planck scale boundary conditions on the Higgs sector of the standard model with a gauge singlet scalar dark matter. We will find that vanishing self-coupling and Veltman condition at the Planck scale are realized with the 126 GeV Higgs mass and top pole mass, 172 GeV≲M{sub t}≲173.5 GeV, where a correct abundance of scalar dark matter is obtained with mass of 300 GeV≲m{sub S}≲1 TeV. It means that the Higgs potential is flat at the Planck scale, and this situation can not be realized in the standard model with the top pole mass.
Baroclinic Planetary Boundary-Layer Model for Neutral and Stable Stratification Conditions
Djolov, G. D.; Yordanov, D. L.; Syrakov, D. E.
The temperature and wind profiles in abaroclinic atmospheric boundary layer (ABL) are investigated.Assuming stationary conditions, the turbulent state in the ABL forstable and neutral conditions is uniquely determined by the Rossbynumber, the external stratification parameter and two externalbaroclinic parameters. A simple two-layer baroclinic model isdeveloped. It consists of a surface layer (SL) and overlyingEkman-type layer. The system of dynamic and heat transfer equations isclosed using K-theory. In the SL the turbulent exchangecoefficient is consistent with the results of similarity theorywhile in the Ekman layer it is assumed constant. The universalfunctions in the resistance, heat and humidity transfer laws arededuced from the analytical solutions for the wind and temperatureprofiles. The solutions of the ABL resistance laws for theinternal ABL parameters, necessary for the calculations of the ABLprofiles, are approximated in terms of the external ABLparameters. Favourable agreement of model results with theavailable experimental data is demonstrated.
On the Boundary Condition for Water at a Hydrophobic, Dense Surface
Walther, J. H.; Jaffe, R. L.; Werder, T.; Halicioglu, T.; Koumoutsakos, P.
2002-01-01
We study the no-slip boundary conditions for water at a hydrophobic (graphite) surface using non-equilibrium molecular-dynamics simulations. For the planar Couette flow, we find a slip length of 64 nm at 1 bar and 300 K, decreasing with increasing system pressure to a value of 31 nm at 1000 bar. Changing the properties of the interface to from hydrophobic to strongly hydrophilic reduces the slip to 14 nm. Finally, we study the flow of water past an array of carbon nanotubes mounted in an inline configuration with a spacing of 16.4 x 16.4 nm. For tube diameters of 1.25 and 2.50 nm we find drag coefficients in good agreement with the macroscopic, Navier-Stokes values. For carbon nanotubes, the no-slip condition is valid to within the definition of the position of the interface.
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Handlovičová Angela
2016-01-01
Full Text Available In this paper, the numerical solution to the Helmholtz equation with impedance boundary condition, based on the Finite volume method, is discussed. We used the Robin boundary condition using exterior points. Properties of the weak solution to the Helmholtz equation and numerical solution are presented. Further the numerical experiments, comparing the numerical solution with the exact one, and the computation of the experimental order of convergence are presented.
Tasawar Hayat; Awatif A. Hendi; Jacob A. Gbadeyan; Philip O. Olanrewaju
2011-01-01
In this paper we analyse the effects of internal heat generation, thermal radiation and buoyancy force on the laminar boundary layer about a vertical plate in a uniform stream of fluid under a convective surface boundary condition. In the analysis, we assumed that the left surface of the plate is in contact with a hot fluid whilst a stream of cold fluid flows steadily over the right surface; the heat source decays exponentially outwards from the surface of the plate. The similarity variable m...
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Hua-Cheng Zhou
2016-02-01
Full Text Available This article is devoted to investigating the existence of solutions to fractional multi-point boundary-value problems at resonance in a Hilbert space. More precisely, the dimension of the kernel of the fractional differential operator with the boundary conditions be any positive integer. We point out that the problem is new even when the system under consideration is reduced to a second-order ordinary differential system with resonant boundary conditions. We show that the considered system admits at least a solution by applying coincidence degree theory first introduced by Mawhin. An example is presented to illustrate our results.
Pendlebury, Diane; Gravel, Sylvie; Moran, Michael D.; Lupu, Alexandru
2018-02-01
A regional air quality forecast model, GEM-MACH, is used to examine the conditions under which a limited-area air quality model can accurately forecast near-surface ozone concentrations during stratospheric intrusions. Periods in 2010 and 2014 with known stratospheric intrusions over North America were modelled using four different ozone lateral boundary conditions obtained from a seasonal climatology, a dynamically-interpolated monthly climatology, global air quality forecasts, and global air quality reanalyses. It is shown that the mean bias and correlation in surface ozone over the course of a season can be improved by using time-varying ozone lateral boundary conditions, particularly through the correct assignment of stratospheric vs. tropospheric ozone along the western lateral boundary (for North America). Part of the improvement in surface ozone forecasts results from improvements in the characterization of near-surface ozone along the lateral boundaries that then directly impact surface locations near the boundaries. However, there is an additional benefit from the correct characterization of the location of the tropopause along the western lateral boundary such that the model can correctly simulate stratospheric intrusions and their associated exchange of ozone from stratosphere to troposphere. Over a three-month period in spring 2010, the mean bias was seen to improve by as much as 5 ppbv and the correlation by 0.1 depending on location, and on the form of the chemical lateral boundary condition.
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Nadezhda D. But
2014-09-01
Full Text Available Present article is devoted to the problem of prosecutor participation in the process of ensuring the balance of private and public interests during the supervision over laws on free economic activity execution. Authors noted the existence of need for the formation of the registers of subjects of small and medium business which aren't created so far. According to the authors, for more effective control over the balance of private and public interests the anti-corruption legislation of the Russian Federation, including the Federal Law of July 26, 2006 No. 135-FZ "On the competition protection" should be brought into accord with the international precepts of law and standards. Authors pay special attention to the questions of supervision, including reasons for the fact that during the supervision over the performance of laws in the conditions of the economic activity freedom in sight of prosecutors should be not dispositive, but imperative (regulatory and guarding legal norms. In the sphere of the prosecutor's law-enforcement activity in the conditions of economic activity freedom it is expedient to allocate such activity of prosecutors into the independent supervising subsector as it covers not only economic, but also other spheres of public life (state construction, social questions and many other. In the course of research authors analyze various regulations, opinions of scientists and practice of law application. In the conclusion authors explains opinion that questions listed in the present article need more accurate legislative regulation and realization in the law-enforcement practice.
Characterizing summertime chemical boundary conditions for airmasses entering the US West Coast
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G. G. Pfister
2011-02-01
Full Text Available The objective of this study is to analyze the pollution inflow into California during summertime and how it impacts surface air quality through combined analysis of a suite of observations and global and regional models. The focus is on the transpacific pollution transport investigated by the NASA Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS mission in June 2008. Additional observations include satellite retrievals of carbon monoxide and ozone by the EOS Aura Tropospheric Emissions Spectrometer (TES, aircraft measurements from the MOZAIC program and ozonesondes. We compare chemical boundary conditions (BC from the MOZART-4 global model, which are commonly used in regional simulations, with measured concentrations to quantify both the accuracy of the model results and the variability in pollution inflow. Both observations and model reflect a large variability in pollution inflow on temporal and spatial scales, but the global model captures only about half of the observed free tropospheric variability. Model tracer contributions show a large contribution from Asian emissions in the inflow. Recirculation of local US pollution can impact chemical BC, emphasizing the importance of consistency between the global model simulations used for BC and the regional model in terms of emissions, chemistry and transport. Aircraft measurements in the free troposphere over California show similar concentration ranges, variability and source contributions as free tropospheric air masses over ocean, but caution has to be taken that local pollution aloft is not misinterpreted as inflow. A flight route specifically designed to sample boundary conditions during ARCTAS-CARB showed a prevalence of plumes transported from Asia and thus may not be fully representative for average inflow conditions. Sensitivity simulations with a regional model with altered BCs show that the temporal variability in the pollution inflow does
Investigating effects of boundary conditions on the evaluation of R-factor of un-braced steel frames
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Masood M.M. Irheem
2017-08-01
Full Text Available Design of Structures to resist seismic load depends on the theory of dissipation in elastic of energy that already exists in response modification factor “R-factor”. The main problem in codes gives a constant value for R-factor, since change in boundary conditions of building change in behavior of steel frame structures and that effect on R-factor. This study is an attempt to assess overstrength, ductility and response modification factor of un-braced steel frames under change in boundary conditions as change in the direction of strong axis of column and support type beside to variation in story and bay number to be 9 frame and each frame has 8 different boundary conditions as sum of 72 case for analysis. These frames were analyzed by using nonlinear static “pushover” analysis using SAP2000 program. As a result of this study R-factor does not has a constant value, when change in boundary conditions R-factor directly changes, minimum value of 8 boundary conditions is close to the code value that is mean the code is more conservative and give a large factor of safety. Ductility reduction factor increases with increasing number of story for all boundary conditions, but overstrength has different rule. Response modification factor, overstrength factor and ductility reduction factor decrease when fundamentals period increasing for the studied frames.
Finite-Rate Ablation Boundary Conditions for Carbon-Phenolic Heat-Shield
Chen, Y.-K.; Milos, Frank S.
2003-01-01
A formulation of finite-rate ablation surface boundary conditions, including oxidation, nitridation, and sublimation of carbonaceous material with pyrolysis gas injection, has been developed based on surface species mass conservation. These surface boundary conditions are discretized and integrated with a Navier-Stokes solver. This numerical procedure can predict aerothermal heating, chemical species concentration, and carbonaceous material ablation rate over the heatshield surface of re-entry space vehicles. In this study, the gas-gas and gas-surface interactions are established for air flow over a carbon-phenolic heatshield. Two finite-rate gas-surface interaction models are considered in the present study. The first model is based on the work of Park, and the second model includes the kinetics suggested by Zhluktov and Abe. Nineteen gas phase chemical reactions and four gas-surface interactions are considered in the present model. There is a total of fourteen gas phase chemical species, including five species for air and nine species for ablation products. Three test cases are studied in this paper. The first case is a graphite test model in the arc-jet stream; the second is a light weight Phenolic Impregnated Carbon Ablator at the Stardust re-entry peak heating conditions, and the third is a fully dense carbon-phenolic heatshield at the peak heating point of a proposed Mars Sample Return Earth Entry Vehicle. Predictions based on both finite-rate gas- surface interaction models are compared with those obtained using B' tables, which were created based on the chemical equilibrium assumption. Stagnation point convective heat fluxes predicted using Park's finite-rate model are far below those obtained from chemical equilibrium B' tables and Zhluktov's model. Recession predictions from Zhluktov's model are generally lower than those obtained from Park's model and chemical equilibrium B' tables. The effect of species mass diffusion on predicted ablation rate is also
Towards Dynamic Realism for Solar Wind Boundary Conditions Used in Global Heliospheric Models
Thatcher, L. J.; Mueller, H.; Heiderer, A.
2009-12-01
The two Voyager missions have demonstrated the highly time-dependent nature of the outer heliosphere, and the measurements from IBEX will require, for proper interpretation of the data, theoretical models that incorporate this time-dependence. Our research group uses multifluid HD models of the global heliosphere with idealized, simplified solar wind conditions for the inner boundary of the simulations. For this contribution, solar wind data of the past four solar cycles, taken from NASA's OMNI data set, is used to build a realistic inner boundary data set for our simulations. This data set is time-dependent so as to realistically represent changes in solar wind characteristics through the solar cycle and capture the corresponding transient effects in the heliosphere. We have had preliminary success with our data set, extrapolating OMNI data, which is entirely Sun-Earth directed, to fill the entire ecliptic disc. The success of the results confirmed to us that, with some improvements, our central technique would create a solar win data set sufficiently realistic for heliospheric simulations. To refine the data set, independent analyses and categorization of data will be performed. Four solar wind regimes are envisioned, undisturbed fast and slow wind, ICME wind, and 'other' wind, the catchall category. After we have categorized the entire OMNI data set, our extrapolations will represent the behavior of each regime in a more realistic fashion. Preliminary results for global heliospheric simulations will be presented.
Calculation of the radial electric field with RF sheath boundary conditions in divertor geometry
Gui, B.; Xia, T. Y.; Xu, X. Q.; Myra, J. R.; Xiao, X. T.
2018-02-01
The equilibrium electric field that results from an imposed DC bias potential, such as that driven by a radio frequency (RF) sheath, is calculated using a new minimal two-field model in the BOUT++ framework. Biasing, using an RF-modified sheath boundary condition, is applied to an axisymmetric limiter, and a thermal sheath boundary is applied to the divertor plates. The penetration of the bias potential into the plasma is studied with a minimal self-consistent model that includes the physics of vorticity (charge balance), ion polarization currents, force balance with E× B , ion diamagnetic flow (ion pressure gradient) and parallel electron charge loss to the thermal and biased sheaths. It is found that a positive radial electric field forms in the scrape-off layer and it smoothly connects across the separatrix to the force-balanced radial electric field in the closed flux surface region. The results are in qualitative agreement with the experiments. Plasma convection related to the E× B net flow in front of the limiter is also obtained from the calculation.
Directory of Open Access Journals (Sweden)
Yinhuan Ao
2017-01-01
Full Text Available This paper reported a comprehensive analysis on the diurnal variation of the Atmospheric Boundary Layer (ABL in summer of Badain Jaran Desert and discussed deeply the effect of surface thermal to ABL, including the Difference in Surface-Air Temperature (DSAT, net radiation, and sensible heat, based on limited GPS radiosonde and surface observation data during two intense observation periods of experiments. The results showed that (1 affected by topography of the Tibetan Plateau, the climate provided favorable external conditions for the development of Convective Boundary Layer (CBL, (2 deep CBL showed a diurnal variation of three- to five-layer structure in clear days and five-layer ABL structure often occurred about sunset or sunrise, (3 the diurnal variation of DSAT influenced thickness of ABL through changes of turbulent heat flux, (4 integral value of sensible heat which rapidly converted by surface net radiation had a significant influence on the growth of CBL throughout daytime. The cumulative effect of thick RML dominated the role after CBL got through SBL in the development stage, especially in late summer, and (5 the development of CBL was promoted and accelerated by the variation of wind field and distribution of warm advection in high and low altitude.
Cai, Hongzhu; Hu, Xiangyun; Xiong, Bin; Auken, Esben; Han, Muran; Li, Jianhui
2017-10-01
We implemented an edge-based finite element time domain (FETD) modeling algorithm for simulating controlled-source electromagnetic (CSEM) data. The modeling domain is discretized using unstructured tetrahedral mesh and we consider a finite difference discretization of time using the backward Euler method which is unconditionally stable. We solve the diffusion equation for the electric field with a total field formulation. The finite element system of equation is solved using the direct method. The solutions of electric field, at different time, can be obtained using the effective time stepping method with trivial computation cost once the matrix is factorized. We try to keep the same time step size for a fixed number of steps using an adaptive time step doubling (ATSD) method. The finite element modeling domain is also truncated using a semi-adaptive method. We proposed a new boundary condition based on approximating the total field on the modeling boundary using the primary field corresponding to a layered background model. We validate our algorithm using several synthetic model studies.
Velocity and magnetic field measurements of Taylor plumes in SSX under different boundary conditions
Kaur, Manjit; Brown, M. R.; Han, J.; Shrock, J. E.; Schaffner, D. A.
2016-10-01
The SSX device has been modified by the addition of a 1 m long glass extension for accommodating pulsed theta pinch coils. The Taylor plumes are launched from a magnetized plasma gun and flow to an expansion volume downstream. The time of flight (TOF) measurements of these plumes are carried out using a linear array of Ḃ probes (separated by 10cm). TOF of the plasma plumes from one probe location to the next is determined by direct comparison of the magnetic field structures as well as by carrying out a cross-correlation analysis. With the glass boundary, the typical velocity of the Taylor plumes is found to be 25km /s , accompanied by a fast plasma (>= 50km /s) at the leading edge. Magnetic field embedded in the Taylor plumes is measured in the expansion chamber using a three-dimensional array of Ḃ probes and is found to be 700G . Some flux conservation of the Taylor plumes is provided by using a resistive (soak time 3 μs) and a mesh (soak time 170 μs > discharge time) liner around the glass tube for improving the downstream Taylor state velocity as well as the magnetic field. The results from these different boundary conditions will be presented. Work supported by DOE OFES and ARPA-E ALPHA programs.
On the Energetics of a Damped Beam-Like Equation for Different Boundary Conditions
Directory of Open Access Journals (Sweden)
SAJAD HUSSAIN SANDILO
2017-04-01
Full Text Available In this paper, the energy estimates for a damped linear homogeneous beam-like equation will be considered. The energy estimates will be studied for different BCs (Boundary Conditions for the axially moving continuum. The problem has physical and engineering application. The applications are mostly occurring in models of conveyor belts and band-saw blades. The research study is focused on the Dirichlet, the Neumann and the Robin type of BCs. From physical point of view, the considered mathematical model expounds the transversal vibrations of a moving belt system or moving band-saw blade. It is assumed that a viscous damping parameter and the horizontal velocity are positive and constant. It will be shown in this paper that change in geometry or the physics of the boundaries can affect the stability properties of the system in general and stability depends on the axial direction of the motion. In all cases of the BCs, it will be shown that there is energy decay due to viscous damping parameter and it will also be shown that in some cases there is no conclusion whether the beam energy decreases or increases. The detailed physical interpretation of all terms and expressions is provided and studied in detail.
Thompson, R.S.; Fleming, R.F.
1996-01-01
The general characteristics of global vegetation during the middle Pliocene warm period can be reconstructed from fossil pollen and plant megafossil data. The largest differences between Pliocene vegetation and that of today occurred at high latitudes in both hemispheres, where warming was pronounced relative to today. In the Northern Hemisphere coniferous forests lived in the modern tundra and polar desert regions, whereas in the Southern Hemisphere southern beech apparently grew in coastal areas of Antarctica. Pliocene middle latitude vegetation differed less, although moister-than-modern conditions supported forest and woodland growth in some regions now covered by steppe or grassland. Pliocene tropical vegetation reflects essentially modern conditions in some regions and slightly cooler-than-or warmer-than- modern climates in other areas. Changes in topography induced by tectonics may be responsible for many of the climatic changes since the Pliocene in both middle and lower latitudes. However, the overall latitudinal progression of climatic conditions on land parallels that seen in the reconstruction of middle Pliocene sea-surface temperatures. Pliocene paleovegetational data was employed to construct a 2????2?? global grid of estimated mid-Pliocene vegetational cover for use as boundary conditions for numerical General Circulation Model simulations of middle Pliocene climates. Continental outlines and topography were first modified to represent the Pliocene landscape on the 2????2?? grid. A modern 1????1?? vegetation grid was simplified and mapped on this Pliocene grid, and then modified following general geographic trends evident in the Pliocene paleovegetation data set.
Energy Technology Data Exchange (ETDEWEB)
Pearce, Paul A., E-mail: p.pearce@ms.unimelb.edu.au [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia); Rasmussen, Jørgen, E-mail: j.rasmussen@uq.edu.au [School of Mathematics and Physics, University of Queensland, St Lucia, Brisbane, Queensland 4072 (Australia); Tipunin, Ilya Yu., E-mail: tipunin@gmail.com [TAMM Theory Division, Lebedev Physics Institute, Leninski Pr., 53, Moscow 119991 (Russian Federation)
2014-12-15
For general Temperley–Lieb loop models, including the logarithmic minimal models LM(p,p{sup ′}) with p,p{sup ′} coprime integers, we construct an infinite family of Robin boundary conditions on the strip as linear combinations of Neumann and Dirichlet boundary conditions. These boundary conditions are Yang–Baxter integrable and allow loop segments to terminate on the boundary. Algebraically, the Robin boundary conditions are described by the one-boundary Temperley–Lieb algebra. Solvable critical dense polymers is the first member LM(1,2) of the family of logarithmic minimal models and has loop fugacity β=0 and central charge c=−2. Specialising to LM(1,2) with our Robin boundary conditions, we solve the model exactly on strips of arbitrary finite size N and extract the finite-size conformal corrections using an Euler–Maclaurin formula. The key to the solution is an inversion identity satisfied by the commuting double row transfer matrices. This inversion identity is established directly in the Temperley–Lieb algebra. We classify the eigenvalues of the double row transfer matrices using the physical combinatorics of the patterns of zeros in the complex spectral parameter plane and obtain finitised characters related to spaces of coinvariants of Z{sub 4} fermions. In the continuum scaling limit, the Robin boundary conditions are associated with irreducible Virasoro Verma modules with conformal weights Δ{sub r,s−1/2} =1/(32) (L{sup 2}−4) where L=2s−1−4r, r∈Z, s∈N. These conformal weights populate a Kac table with half-integer Kac labels. Fusion of the corresponding modules with the generators of the Kac fusion algebra is examined and general fusion rules are proposed.
Energy Technology Data Exchange (ETDEWEB)
Fricke, Norman [AGFW - Der Energieeffizienzverband fuer Waerme, Kaelte und KWK e.V., Frankfurt am Main (Germany)
2011-04-15
It is a common misconception that legal regulations of the electricity and gas industry can also be applied to district heating. However, the technical, economic and legal boundary conditions of district heating are quite different. The first part of this article explained the concept of district heating and analyzed its economic boundary conditions. This contribution explains the heat market and its legal boundary conditions.
Free Vibration Analysis of a Rectangular Plate with Kelvin Type Boundary Conditions
Directory of Open Access Journals (Sweden)
R. Kırışık
2007-01-01
Full Text Available The transverse vibrations of a rectangular plate with the Kelvin type boundary conditions at four corners are investigated. The plate is modeled as being attached to four lumped spring-damper systems at the corners. An analytical procedure is proposed based on the modal analysis. The completely free case of the plate is first studied. The expressions for the eigenfrequencies and eigenfunctions of the plate are obtained by utilizing the separation of variables. Then, the case in which the stiffness and the viscous damping as external forces acting at the corners of the plate is studied. Following the modal analysis procedure, the general solution for the equation of motion of the rectangular plate is derived. Some numerical results are presented.
Simon, Andrew E.; Kishk, Ahmed A.
2005-12-01
Geometry description in the finite difference time domain method is a tedious task if the geometry contains fine details, such as the case of corrugated objects. Such fine details constrain the cell size. The corrugated object can be modeled using the asymptotic corrugation boundary condition (ACBC) with a correction due to the width-over-period ratio. The ACBC forces certain field distributions inside the corrugation and allows for the removal of the corrugation teeth to have a homogeneous region with enforced field behavior that represents the actual corrugations. The ACBC approach is found to be accurate when the number of corrugations per wavelength is large (typically around 10 corrugations per wavelength). Computed results using ACBC are in good agreement with detailed simulations, which demonstrates the validity of the asymptotic approximations. Last, a major improvement in the computation time is achieved when using the ACBC to model structures that have a large number of corrugations per wavelength.
Modeling of microdevices for SAW-based acoustophoresis - A study of boundary conditions
DEFF Research Database (Denmark)
Skov, Nils Refstrup; Bruus, Henrik
2016-01-01
We present a finite-element method modeling of acoustophoretic devices consisting of a single, long, straight, water-filled microchannel surrounded by an elastic wall of either borosilicate glass (pyrex) or the elastomer polydimethylsiloxane (PDMS) and placed on top of a piezoelectric transducer...... that actuates the device by surface acoustic waves (SAW). We compare the resulting acoustic fields in these full solid-fluid models with those obtained in reduced fluid models comprising of only a water domain with simplified, approximate boundary conditions representing the surrounding solids. The reduced...... models are found to only approximate the acoustically hard pyrex systems to a limited degree for large wall thicknesses and but not very well for acoustically soft PDMS systems shorter than the PDMS damping length of 3 mm....
General 3D Lumped Thermal Model with Various Boundary Conditions for High Power IGBT Modules
DEFF Research Database (Denmark)
Bahman, Amir Sajjad; Ma, Ke; Blaabjerg, Frede
2016-01-01
Accurate thermal dynamics modeling of high power Insulated Gate Bipolar Transistor (IGBT) modules is important information for the reliability analysis and thermal design of power electronic systems. However, the existing thermal models have their limits to correctly predict these complicated...... thermal behaviors in the IGBTs. In this paper, a new three-dimensional (3D) lumped thermal model is proposed, which can easily be characterized from Finite Element Methods (FEM) based simulation and acquire the thermal distribution in critical points. Meanwhile the boundary conditions including...... the cooling system and power losses are modeled in the 3D thermal model, which can be adapted to different real field applications of power electronic converters. The accuracy of the proposed thermal model is verified by experimental results....
Ding, Xiao-Li; Nieto, Juan J.
2017-11-01
In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.
Directory of Open Access Journals (Sweden)
Josefa Caballero
2014-01-01
Full Text Available We study an existence result for the following coupled system of nonlinear fractional hybrid differential equations with homogeneous boundary conditions D0+α[x(t/f(t,x(t,y(t]=g(t,x(t,y(t,D0+αy(t/f(t,y(t,x(t=g(t,y(t,x(t, 0
Hesselmann, G; Darcy, N; Sterzer, P; Knops, A
2015-01-01
The scope and limits of unconscious processing are a controversial topic of research in experimental psychology. Particularly within the visual domain, a wide range of paradigms have been used to experimentally manipulate perceptual awareness. A recent study reported unconscious numerical processing during continuous flash suppression (CFS), which is a powerful variant of interocular suppression and disrupts the conscious perception of visual stimuli for up to seconds. Since this finding of a distance-dependent priming effect contradicts earlier results showing that interocular suppression abolishes semantic processing, we sought to investigate the boundary conditions of this effect in two experiments. Using statistical analyses and experimental designs that precluded an effect of target numerosity, we found evidence for identity priming, but no conclusive evidence for distance-dependent numerical priming under CFS. Our results suggest that previous conclusions on high-level numerical priming under interocular suppression may have been premature. Copyright © 2014 Elsevier Inc. All rights reserved.
Effect of boundary conditions on piezoelectric buckled beams for vibrational noise harvesting
Cottone, F.; Mattarelli, M.; Vocca, H.; Gammaitoni, L.
2015-11-01
Nonlinear bistable systems have proven to be advantageous for energy harvesting of random and real ambient vibrations. One simple way of implementing a bistable transducer is setting a piezoelectric beam in a post-buckled configuration by axial compression. Besides, hinged or clamped-clamped type of boundary conditions correspond to two different post-buckled shape functions. Here we study, through theoretical analysis and numerical simulations, the efficiency of a hinged and clamped-clamped piezoelectric bridge under band-limited random noise with progressive axial load. Clamped configuration results to harvest 26% more power than hinged around an optimal axial load of 0.05%, while, in the intra-well trapped situation, above 0.1%, the two configurations present no substantial difference. Nevertheless, simulations confirm the advantage of exploiting inter-well oscillations in bistable regime.
A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions
Sun, Xian-He; Zhuang, Yu
1997-01-01
In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.
Scott, Carl D.
1992-01-01
The meaning of catalysis and its relation to aerodynamic heating in nonequilibrium hypersonic flows are discussed. The species equations are described and boundary conditions for them are derived for a multicomponent gas and for a binary gas. Slip effects are included for application of continuum methods to low-density flows. Measurement techniques for determining catalytic wall recombination rates are discussed. Among them are experiments carried out in arc jets as well as flow reactors. Diagnostic methods for determining the atom or molecule concentrations in the flow are included. Results are given for a number of materials of interest to the aerospace community, including glassy coatings such as the RCG coating of the Space Shuttle and for high temperature refractory metals such as coated niobium. Methods of calculating the heat flux to space vehicles in nonequilibrium flows are described. These methods are applied to the Space Shuttle, the planned Aeroassist Flight Experiment, and a hypersonic slender vehicle such as a transatmospheric vehicle.
Characterization of the lubricating action of oils under boundary lubrication conditions
Energy Technology Data Exchange (ETDEWEB)
De Gee, A.W.J.; Lossie, C.M.; Stoop, W. [Univ. of Technology Delft and Univ. of Twente, Amsterdam (Netherlands)]|[TNO Institute of Production and Logistics Research, Apeldoorn (Netherlands)
1995-07-01
Polyalphaolefin (PAO) and polypropylene glycol (PPG)-based lubricants as well as mineral oils were tested to characterize their wear reducing performance under boundary lubrication conditions, using the ISO 7148 test method, which was originally developed for the characterization of bearing materials. This test method has practical value with respect to developing lubricants for use in sliding contacts, such as occur in worm gear drives. It is found that the wear reducing action of PAO-based lubricants is significantly better than that of mineral oils. PPG fluids perform equally well or slightly better than PAOs. Provided that viscosities are in line and additives are compatible, contamination of PAOs with mineral oils has no or only marginal effect on wear reduction.
Kim, Seckyoung Loretta; Yun, Seokhwa
2015-03-01
Considering the importance of coworkers and knowledge sharing in current business environment, this study intends to advance understanding by investigating the effect of coworker knowledge sharing on focal employees' task performance. Furthermore, by taking an interactional perspective, this study examines the boundary conditions of coworker knowledge sharing on task performance. Data from 149 samples indicate that there is a positive relationship between coworker knowledge sharing and task performance, and this relationship is strengthened when general self-efficacy or abusive supervision is low rather than high. Our findings suggest that the recipients' characteristics and leaders' behaviors could be important contingent factors that limit the effect of coworker knowledge sharing on task performance. Implications for theory and practice are discussed. PsycINFO Database Record (c) 2015 APA, all rights reserved.
Dependence on boundary conditions for actuation characteristics of dielectric elastomer actuators
Kollosche, Matthias; Stoyanov, Hristiyan; Ragusch, Hülya; Kofod, Guggi
2010-04-01
We present electro-mechanical characterizations of dielectric elastomer actuators (DEA) prepared from polystyrene- ethylene-butadiene-styrene (SEBS) with comparison to the commonly used VHB 4905 tape. This study discusses effects of boundary conditions, stiffness and voltage ramp rate on the actuation properties of both materials. Measurements on samples in pure-shear configuration were made with variation in both load and applied voltage, to achieve so-called '3D-plots'. A strong dependence of the actuation characteristics on the voltage ramp rate was observed, leading to a large shift in the 'optimum load' for VHB, which was not found for SEBS. This is due to the large difference in visco-elastic behavior between materials.
Thermo-mechanical Analysis of the Dry Clutches under Different Boundary Conditions
Directory of Open Access Journals (Sweden)
O.I. Abdullah
2014-06-01
Full Text Available The high thermal stresses, generated between the contacting surfaces of the clutch system (pressure plate, clutch disc and flywheel due to the frictional heating during the slipping, are considered to be one of the main reasons of clutch failure. A finite element technique has been used to study the transient thermoelastic phenomena of a dry clutch. The effect of the boundary conditions on the contact pressure distribution, the temperature field and the heat flux generated along the frictional surfaces are investigated. Analysis has been completed using two dimensional axisymmetric model that was used to simulate the clutch elements. ANSYS software has been used to perform the numerical calculation in this paper.
Modeling of microdevices for SAW-based acoustophoresis --- a study of boundary conditions
Skov, Nils Refstrup
2016-01-01
We present a finite-element method modeling of acoustophoretic devices consisting of a single, long, straight, water-filled microchannel surrounded by an elastic wall of either borosilicate glass (pyrex) or the elastomer polydimethylsiloxane (PDMS) and placed on top of a piezoelectric transducer that actuates the device by surface acoustic waves (SAW). We compare the resulting acoustic fields in these full solid-fluid models with those obtained in reduced fluid models comprising of only a water domain with simplified, approximate boundary conditions representing the surrounding solids. The reduced models are found to only approximate the acoustically hard pyrex systems to a limited degree for large wall thicknesses and not at all for the acoustically soft PDMS systems.
Isa, Siti Suzilliana Putri Mohamed; Arifin, Norihan Md.; Nazar, Roslinda; Bachok, Norfifah; Ali, Fadzilah Md
2017-12-01
A theoretical study that describes the magnetohydrodynamic mixed convection boundary layer flow with heat transfer over an exponentially stretching sheet with an exponential temperature distribution has been presented herein. This study is conducted in the presence of convective heat exchange at the surface and its surroundings. The system is controlled by viscous dissipation and internal heat generation effects. The governing nonlinear partial differential equations are converted into ordinary differential equations by a similarity transformation. The converted equations are then solved numerically using the shooting method. The results related to skin friction coefficient, local Nusselt number, velocity and temperature profiles are presented for several sets of values of the parameters. The effects of the governing parameters on the features of the flow and heat transfer are examined in detail in this study.
RamReddy, Ch.; Venkata Rao, Ch.
2017-12-01
In this paper, a numerical analysis is performed to investigate the effects of double dispersion and convective boundary condition on natural convection flow over vertical frustum of a cone in a nanofluid saturated non-Darcy porous medium. In addition, Brownian motion and thermophoresis effects have taken into consideration, and the uniform wall nanoparticle condition is replaced with the zero nanoparticle mass flux boundary condition to execute physically applicable results. For this complex problem, the similarity solution does not exist and hence suitable non-similarity transformations are used to transform the governing equations along with the boundary conditions into non-dimensional form. The Bivariate Pseudo-Spectral Local Linearisation Method (BPSLLM) is used to solve the reduced non-similar, coupled partial differential equations. To test the accuracy of proposed method, the error analysis and convergence tests are conducted. The effect of flow influenced parameters on non-dimensional velocity, temperature, nanoparticle volume fraction, regular concentration field as well as on the surface drag, heat transfer, nanoparticle and regular mass transfer rates are analyzed.
Uses of zeta regularization in QFT with boundary conditions: a cosmo-topological Casimir effect
Energy Technology Data Exchange (ETDEWEB)
Elizalde, Emilio [Instituto de Ciencias del Espacio (CSIC) and Institut d' Estudis Espacials de Catalunya (IEEC/CSIC) Campus UAB, Facultat de Ciencies, Torre C5-Parell-2a planta E-08193 Bellaterra, Barcelona (Spain)
2006-05-26
Zeta regularization has proven to be a powerful and reliable tool for the regularization of the vacuum energy density in ideal situations. With the Hadamard complement, it has been shown to provide finite (and meaningful) answers too in more involved cases, as when imposing physical boundary conditions (BCs) in two- and higher-dimensional surfaces (being able to mimic, in a very convenient way, other ad hoc cut-offs, as non-zero depths). Recently, these techniques have been used in calculations of the contribution of the vacuum energy of the quantum fields pervading the universe to the cosmological constant (cc). Naive counting of the absolute contributions of the known fields lead to a value which is off by as much as 120 orders of magnitude, as compared with observational tests, what is known as the cosmological constant problem. This is very difficult to solve and we do not address that question directly. What we have considered-with relative success in several approaches of different nature-is the additional contribution to the cc coming from the non-trivial topology of space or from specific boundary conditions imposed on braneworld models (kind of cosmological Casimir effects). Assuming someone will be able to prove (some day) that the ground value of the cc is zero, as many had suspected until very recently, we will then be left with this incremental value coming from the topology or BCs. We show that this value can have the correct order of magnitude-corresponding to the one coming from the observed acceleration in the expansion of our universe-in a number of quite reasonable models involving small and large compactified scales and/or brane BCs, and supergravitons.
Nelson, P.; Moucha, R.
2014-12-01
Numerical investigations of surface deformation in response to flat slab subduction began with seminal papers by Bird (1988) and Mitrovica et al. (1989). Recently, a number of numerical studies have begun to explore the complexity in the dynamics of flat-slab subduction initiation and continuation, but did not address the corresponding surface deformation (English et al., 2003; Pérez-Campos et al., 2008; Liu et al., 2010; Jones et al., 2011; Arrial and Billen, 2013; Vogt and Gerya, 2014). Herein, we explore the conditions that lead to flat-slab subduction and characterize the resulting surface deformation using a 2D finite-difference marker-in-cell method. We specifically explore how initial model geometry and boundary conditions affect the evolution of the angle at which a slab subducts in the presence/absence of a buoyant oceanic plateau and the resulting surface topography. In our simulations, the surface is tracked through time as an internal erosion/sedimentation surface. The top boundary of the crust is overlaid by a "sticky" (viscous 10^17 Pa.s) water/air layer with correspondingly stratified densities. We apply a coupled surface processes model that solves the sediment transport/diffusion erosion equation at each time step to account for the corresponding crustal mass flux and its effect on crustal deformation. Model results show the initial angle of subduction has a substantial impact on the subduction angle of the slab and hence the evolution of topography. The results also indicate plate velocity and the presence of an oceanic plateau in a forced subduction only have a moderate effect on the angle of subduction.
Fractional instantons and bions in the O(N) model with twisted boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Nitta, Muneto [Department of Physics, and Research and Education Center for Natural Sciences, Keio University,Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan)
2015-03-20
Recently, multiple fractional instanton configurations with zero instanton charge, called bions, have been revealed to play important roles in quantum field theories on compactified spacetime. In two dimensions, fractional instantons and bions have been extensively studied in the ℂP{sup N−1} model and the Grassmann sigma model on ℝ{sup 1}×S{sup 1} with the ℤ{sub N} symmetric twisted boundary condition. Fractional instantons in these models are domain walls with a localized U(1) modulus twisted half along their world volume. In this paper, we classify fractional instantons and bions in the O(N) nonlinear sigma model on ℝ{sup N−2}×S{sup 1} with more general twisted boundary conditions in which arbitrary number of fields change sign. We find that fractional instantons have more general composite structures, that is, a global vortex with an Ising spin (or a half-lump vortex), a half sine-Gordon kink on a domain wall, or a half lump on a “space-filling brane” in the O(3) model (ℂP{sup 1} model) on ℝ{sup 1}×S{sup 1}, and a global monopole with an Ising spin (or a half-Skyrmion monopole), a half sine-Gordon kink on a global vortex, a half lump on a domain wall, or a half Skyrmion on a “space-filling brane” in the O(4) model (principal chiral model or Skyrme model) on ℝ{sup 2}×S{sup 1}. We also construct bion configurations in these models.
Ultrasound-induced lung hemorrhage: Role of acoustic boundary conditions at the pleural surface
O'Brien, William D.; Kramer, Jeffrey M.; Waldrop, Tony G.; Frizzell, Leon A.; Miller, Rita J.; Blue, James P.; Zachary, James F.
2002-02-01
In a previous study [J. Acoust. Soc. Am. 108, 1290 (2000)] the acoustic impedance difference between intercostal tissue and lung was evaluated as a possible explanation for the enhanced lung damage with increased hydrostatic pressure, but the hydrostatic-pressure-dependent impedance difference alone could not explain the enhanced occurrence of hemorrhage. In that study, it was hypothesized that the animal's breathing pattern might be altered as a function of hydrostatic pressure, which in turn might affect the volume of air inspired and expired. The acoustic impedance difference between intercostal tissue and lung would be affected with altered lung inflation, thus altering the acoustic boundary conditions. In this study, 12 rats were exposed to 3 volumes of lung inflation (inflated: approximately tidal volume; half-deflated: half-tidal volume; deflated: lung volume at functional residual capacity), 6 rats at 8.6-MPa in situ peak rarefactional pressure (MI of 3.1) and 6 rats at 16-MPa in situ peak rarefactional pressure (MI of 5.8). Respiration was chemically inhibited and a ventilator was used to control lung volume and respiratory frequency. Superthreshold ultrasound exposures of the lungs were used (3.1-MHz, 1000-Hz PRF, 1.3-μs pulse duration, 10-s exposure duration) to produce lesions. Deflated lungs were more easily damaged than half-deflated lungs, and half-deflated lungs were more easily damaged than inflated lungs. In fact, there were no lesions observed in inflated lungs in any of the rats. The acoustic impedance difference between intercostal tissue and lung is much less for the deflated lung condition, suggesting that the extent of lung damage is related to the amount of acoustic energy that is propagated across the pleural surface boundary.
Dynamic adjustment of climatological ozone boundary conditions for air-quality forecasts
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P. A. Makar
2010-09-01
Full Text Available Ten different approaches for applying lateral and top climatological boundary conditions for ozone have been evaluated using the off-line regional air-quality model AURAMS, driven with meteorology provided by the GEM weather-forecast model. All ten approaches employ the same climatological ozone profiles, but differ in the manner in which they are applied, via the inclusion or exclusion of (i a dynamic adjustment of the climatological ozone profile in response to the model-predicted tropopause height, (ii a sponge zone for ozone on the model top, (iii upward extrapolation of the climatological ozone profile, and (iv different mass consistency corrections. The model performance for each approach was evaluated against North American surface ozone and ozonesonde observations from the BAQS-Met field study period in the summer of 2007. The original daily one-hour maximum surface ozone biases of about +15 ppbv were greatly reduced (halved in some simulations using alternative methodologies. However, comparisons to ozonesonde observations showed that the reduction in surface ozone bias sometimes came at the cost of significant positive biases in ozone concentrations in the free troposphere and upper troposphere. The best overall performance throughout the troposphere was achieved using a methodology that included dynamic tropopause height adjustment, no sponge zone at the model top, extrapolation of ozone when required above the limit of the climatology, and no mass consistency corrections (global mass conservation was still enforced. The simulation using this model version had a one-hour daily maximum surface ozone bias of +8.6 ppbv, with small reductions in model correlation, and the best comparison to ozonesonde profiles. This recommended and original methodologies were compared for two further case studies: a high-resolution simulation of the BAQS-Met measurement intensive, and a study of the downwind region of the Canadian Rockies. Significant
Gao, Guangyao; Fu, Bojie; Zhan, Hongbin; Ma, Ying
2013-05-01
Predicting the fate and movement of contaminant in soils and groundwater is essential to assess and reduce the risk of soil contamination and groundwater pollution. Reaction processes of contaminant often decreased monotonously with depth. Time-dependent input sources usually occurred at the inlet of natural or human-made system such as radioactive waste disposal site. This study presented a one-dimensional convection-dispersion equation (CDE) for contaminant transport in soils with depth-dependent reaction coefficients and time-dependent inlet boundary conditions, and derived its analytical solution. The adsorption coefficient and degradation rate were represented as sigmoidal functions of soil depth. Solute breakthrough curves (BTCs) and concentration profiles obtained from CDE with depth-dependent and constant reaction coefficients were compared, and a constant effective reaction coefficient, which was calculated by arithmetically averaging the depth-dependent reaction coefficient, was proposed to reflect the lumped depth-dependent reaction effect. With the effective adsorption coefficient and degradation rate, CDE could produce similar BTCs and concentration profiles as those from CDE with depth-dependent reactions in soils with moderate chemical heterogeneity. In contrast, the predicted concentrations of CDE with fitted reaction coefficients at a certain depth departed significantly from those of CDE with depth-dependent reactions. Parametric analysis was performed to illustrate the effects of sinusoidally and exponentially decaying input functions on solute BTCs. The BTCs and concentration profiles obtained from the solutions for finite and semi-infinite domain were compared to investigate the effects of effluent boundary condition. The finite solution produced higher concentrations at the increasing limb of the BTCs and possessed a higher peak concentration than the semi-infinite solution which had a slightly long tail. Furthermore, the finite solution gave
Kosuge, Shingo
2015-07-01
The cylindrical Couette flow of a rarefied gas between a rotating inner cylinder and a stationary outer cylinder is investigated under the following two kinds of kinetic boundary conditions. One is the modified Maxwell-type boundary condition proposed by Dadzie and Méolans [J. Math. Phys. 45, 1804 (2004), 10.1063/1.1690491] and the other is the Cercignani-Lampis condition, both of which have separate accommodation coefficients associated with the molecular velocity component normal to the boundary and with the tangential component. An asymptotic analysis of the Boltzmann equation for small Knudsen numbers and a numerical analysis of the Bhatnagar-Gross-Krook model equation for a wide range of the Knudsen number are performed to clarify the effect of each accommodation coefficient as well as of the boundary condition itself on the behavior of the gas, especially on the flow-velocity profile. As a result, the velocity-slip and temperature-jump conditions corresponding to the above kinetic boundary conditions are derived, which are necessary for the fluid-dynamic description of the problem for small Knudsen numbers. The parameter range for the onset of the velocity inversion phenomenon, which is related mainly to the decrease in the tangential momentum accommodation, is also obtained.
Modelling of Edge Insulation Depending on Boundary Conditions for the Ground Level
Stolarska, Agata; Strzałkowski, Jarosław
2017-10-01
The article presents results of CFD software aided simulations of a thermal bridge, existing at the wall–slab on ground connection. Calculations were made for different variants of the edge insulation location. Schemes without any edge insulation, with some vertical insulation, horizontal, diagonal, and diagonal combined with insulation used as formwork under the slab on ground were analysed. Each variant was differentiated with boundary conditions for the ground. Vertical borders of the model in the ground, as well as the lower border were described in the first solution as adiabatic, while in the second case, a variable temperature value, depending on the ground depth, was set. For comparison, additional calculations were conducted for non-stationary conditions, in which the initial temperature of the ground was set to the average annual temperature of air. The calculations were based on the location of Szczecin, for which the outside air temperature was set to -16.0°C. Results obtained from the simulation were then used to determine the thermal bridge parameters, in particular, thermal coupling coefficient and linear thermal transmittance. The effect of the set of boundary conditions is clearly seen. In general, for all the five variants, lower values of heat fluxes and linear thermal transmittances were obtained, when variable temperature in the ground was assumed. From the point of view of energy balance, it is more favourable to use the values of ψg obtained when the ground temperature is taken into account. The data breakdown shows that application of the actual temperature distribution in the ground to a model has a strong effect on distribution of the 0.0°C isotherm. The adiabatic model indicates that the ground under the slab freezes, while the model, which takes into account the temperature of the ground, shows that the ground under the floor has positive temperatures and the 0.0°C isotherm reaches only the edge of the outer wall. Moreover, the
Directory of Open Access Journals (Sweden)
Fu-Dong Ge
2015-01-01
Full Text Available In this paper, by applying the coincidence degree theory which was first introduced by Mawhin, we obtain an existence result for the fractional three-point boundary value problems in $\\mathbb{R}^n$, where the dimension of the kernel of fractional differential operator with the boundary conditions can take any value in $\\{1,2,\\ldots,n\\}$. This is our novelty. Several examples are presented to illustrate the result.
Mardanov, M. J.; Mahmudov, N. I.; Sharifov, Y. A.
2014-01-01
We study a boundary value problem for the system of nonlinear impulsive fractional differential equations of order α (0 < α ≤ 1) involving the two-point and integral boundary conditions. Some new results on existence and uniqueness of a solution are established by using fixed point theorems. Some illustrative examples are also presented. We extend previous results even in the integer case α = 1. PMID:24782675
Charyyar Ashyralyyev; Gulzipa Akyuz; Mutlu Dedeturk
2017-01-01
In this work, we consider an inverse elliptic problem with Bitsadze-Samarskii type multipoint nonlocal and Neumann boundary conditions. We construct the first and second order of accuracy difference schemes (ADSs) for problem considered. We stablish stability and coercive stability estimates for solutions of these difference schemes. Also, we give numerical results for overdetermined elliptic problem with multipoint Bitsadze-Samarskii type nonlocal and Neumann boundary...
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Alsaedi Ahmed
2009-01-01
Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.
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Z. Y. Chen
2016-05-01
Full Text Available The electrocaloric effect (ECE induced by the domain switching of PbTiO3 (PTO nanoparticles under the different electrical boundary conditions is carried out using the phase field model. The toroidal moment of polarization with vortex domain structures decreases to zero taking surface charge compensation into the electrical boundary condition, i.e. intermediate electrical boundary. There exists a critical parameter value 0.25, which decides the single domain and vortex domain structures of ferroelectric nanomaterial at the room temperature. The loops of toroidal moment as a function of the applied curled electric filed are obtained under the different electrical boundary conditions. The various domain structures in ferroelectric nanostructure are discussed in detail. Moreover negative and positive adiabatic temperature changes accompanying with vortex domain structure switching are obtained with the curled electric field under the intermediate electrical boundary. These results indicate that ferroelectric nanostructures can be practical used in field of cooling and heating technology through adjusting the surface electrical boundary.
The boundary condition for vertical velocity and its interdependence with surface gas exchange
Kowalski, Andrew S.
2017-07-01
The law of conservation of linear momentum is applied to surface gas exchanges, employing scale analysis to diagnose the vertical velocity (w) in the boundary layer. Net upward momentum in the surface layer is forced by evaporation (E) and defines non-zero vertical motion, with a magnitude defined by the ratio of E to the air density, as w = E/ρ. This is true even right down at the surface where the boundary condition is w|0 = E/ρ|0 (where w|0 and ρ|0 represent the vertical velocity and density of air at the surface). This Stefan flow velocity implies upward transport of a non-diffusive nature that is a general feature of the troposphere but is of particular importance at the surface, where it assists molecular diffusion with upward gas migration (of H2O, for example) but opposes that of downward-diffusing species like CO2 during daytime. The definition of flux-gradient relationships (eddy diffusivities) requires rectification to exclude non-diffusive transport, which does not depend on scalar gradients. At the microscopic scale, the role of non-diffusive transport in the process of evaporation from inside a narrow tube - with vapour transport into an overlying, horizontal airstream - was described long ago in classical mechanics and is routinely accounted for by chemical engineers, but has been neglected by scientists studying stomatal conductance. Correctly accounting for non-diffusive transport through stomata, which can appreciably reduce net CO2 transport and marginally boost that of water vapour, should improve characterisations of ecosystem and plant functioning.
The boundary condition for vertical velocity and its interdependence with surface gas exchange
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A. S. Kowalski
2017-07-01
Full Text Available The law of conservation of linear momentum is applied to surface gas exchanges, employing scale analysis to diagnose the vertical velocity (w in the boundary layer. Net upward momentum in the surface layer is forced by evaporation (E and defines non-zero vertical motion, with a magnitude defined by the ratio of E to the air density, as w = E/ρ. This is true even right down at the surface where the boundary condition is w|0 = E/ρ|0 (where w|0 and ρ|0 represent the vertical velocity and density of air at the surface. This Stefan flow velocity implies upward transport of a non-diffusive nature that is a general feature of the troposphere but is of particular importance at the surface, where it assists molecular diffusion with upward gas migration (of H2O, for example but opposes that of downward-diffusing species like CO2 during daytime. The definition of flux–gradient relationships (eddy diffusivities requires rectification to exclude non-diffusive transport, which does not depend on scalar gradients. At the microscopic scale, the role of non-diffusive transport in the process of evaporation from inside a narrow tube – with vapour transport into an overlying, horizontal airstream – was described long ago in classical mechanics and is routinely accounted for by chemical engineers, but has been neglected by scientists studying stomatal conductance. Correctly accounting for non-diffusive transport through stomata, which can appreciably reduce net CO2 transport and marginally boost that of water vapour, should improve characterisations of ecosystem and plant functioning.
Qiu, Lei; Yuan, Shenfang; Mei, Hanfei; Fang, Fang
2016-02-26
Structural Health Monitoring (SHM) technology is considered to be a key technology to reduce the maintenance cost and meanwhile ensure the operational safety of aircraft structures. It has gradually developed from theoretic and fundamental research to real-world engineering applications in recent decades. The problem of reliable damage monitoring under time-varying conditions is a main issue for the aerospace engineering applications of SHM technology. Among the existing SHM methods, Guided Wave (GW) and piezoelectric sensor-based SHM technique is a promising method due to its high damage sensitivity and long monitoring range. Nevertheless the reliability problem should be addressed. Several methods including environmental parameter compensation, baseline signal dependency reduction and data normalization, have been well studied but limitations remain. This paper proposes a damage propagation monitoring method based on an improved Gaussian Mixture Model (GMM). It can be used on-line without any structural mechanical model and a priori knowledge of damage and time-varying conditions. With this method, a baseline GMM is constructed first based on the GW features obtained under time-varying conditions when the structure under monitoring is in the healthy state. When a new GW feature is obtained during the on-line damage monitoring process, the GMM can be updated by an adaptive migration mechanism including dynamic learning and Gaussian components split-merge. The mixture probability distribution structure of the GMM and the number of Gaussian components can be optimized adaptively. Then an on-line GMM can be obtained. Finally, a best match based Kullback-Leibler (KL) divergence is studied to measure the migration degree between the baseline GMM and the on-line GMM to reveal the weak cumulative changes of the damage propagation mixed in the time-varying influence. A wing spar of an aircraft is used to validate the proposed method. The results indicate that the crack
Samu, Gergely F.
2017-12-06
The unique optoelectronic properties of lead halide perovskites have triggered a new wave of excitement in materials chemistry during the past five years. Electrochemistry, spectroelectrochemistry, and photoelectrochemistry could be viable tools both for analyzing the optoelectronic features of these materials and to assemble their hybrid architectures (e.g., solar cells). At the same time, the instability of these materials limits the pool of solvents and electrolytes that can be employed in such experiments. The focus of our study is to establish a stability window for electrochemical tests for all-inorganic CsPbBr3 and hybrid organic-inorganic MaPbI3 perovskites. In addition, we aimed to understand the reduction and oxidation events that occur and to assess the damage done during these processes at extreme electrochemical conditions. In this vein, we demonstrated the chemical, structural, and morphological changes of the films in both reductive and oxidative environments. Taking all these results together as a whole, we propose a set of boundary conditions and protocols for how electrochemical experiments with lead halide perovskites should be carried out and interpreted. We believe that the presented results will contribute to the understanding of the electrochemical response of these materials and lead to a standardization of results in the literature so that easier comparisons can be made.
Effects of the current boundary conditions at the plasma-gun gap on density in SSPX
Kolesnikov, Roman; Lodestro, L. L.; Meyer, W. H.
2012-10-01
The Sustained Spheromak Physics Experiment (SSPX) was a toroidal magnetic-confinement device without toroidal magnetic-field coils or a central transformer but which generated core-plasma currents by dynamo processes driven by coaxial plasma-gun injection into a flux-conserving vessel. Record electron temperatures in a spheromak (Te˜500eV) were achieved, and final results of the SSPX program were reported in [1]. Plasma density, which depended strongly on wall conditions, was an important parameter in SSPX. It was observed that density rises with Igun and that confinement improved as the density was lowered. Shortly after the last experiments, a new feature was added to the Corsica code's solver used to reconstruct SSPX equilibria. Motivated by n=0 fields observed in NIMROD simulations of SSPX, an insulating boundary condition was implemented at the plasma-gun gap. Using this option we will perform new reconstructions of SSPX equilibria and look for correlations between the location of the separatrix (which moves up the gun wall and onto the insulating gap as Igun increases) and plasma density and magnetic-flux amplification [2].[4pt] [1] H. S. McLean, APS, DPP, Dallas, TX, 2008.[0pt] [2] E. B. Hooper et al., Nucl. Fusion 47, 1064 (2007).
The influence of upstream boundary conditions on swirling flows undergoing vortex breakdown
Rukes, Lothar; Sieber, Moritz; Oberleithner, Kilian; Paschereit, Oliver
2014-11-01
Swirling jets undergoing vortex breakdown are common in research and technology. In part this is because swirling jets are widely used to anchor the flame position in gas turbines. Recently, the benefit in terms of flashback safety of axial air injection via a center body in the upstream mixing tube of a simplified premixed burner was demonstrated, Reichel (ASME Turbo Expo 2014). However, the presence of a center body alone alters the upstream boundary conditions for the downstream swirling flow. This study investigates how different upstream conditions modify the downstream swirling jet in a more generic setup. A swirling jet facility is used, consisting of a swirler, a pipe, a nozzle and an unconfined part. The focus lies on two large-scale flow features: the precessing vortex core (PVC) and the recirculation bubble. The flow field is measured with Particle Image Velocimetry and proper orthogonal decomposition is conducted to extract the dominant coherent structures. Additionally, a feature tracking approach is used to track the instantaneous shape and position of the recirculation bubble. We find that different center bodies modify the inflow profiles of the unconfined part of the flow in a specific way. This leads to significant differences in the large scale dynamics. Financial support from the German Science Foundation is gratefully acknowledged.
Stück, Arthur
2015-11-01
Inconsistent discrete expressions in the boundary treatment of Navier-Stokes solvers and in the definition of force objective functionals can lead to discrete-adjoint boundary treatments that are not a valid representation of the boundary conditions to the corresponding adjoint partial differential equations. The underlying problem is studied for an elementary 1D advection-diffusion problem first using a node-centred finite-volume discretisation. The defect of the boundary operators in the inconsistently defined discrete-adjoint problem leads to oscillations and becomes evident with the additional insight of the continuous-adjoint approach. A homogenisation of the discretisations for the primal boundary treatment and the force objective functional yields second-order functional accuracy and eliminates the defect in the discrete-adjoint boundary treatment. Subsequently, the issue is studied for aerodynamic Reynolds-averaged Navier-Stokes problems in conjunction with a standard finite-volume discretisation on median-dual grids and a strong implementation of noslip walls, found in many unstructured general-purpose flow solvers. Going out from a base-line discretisation of force objective functionals which is independent of the boundary treatment in the flow solver, two improved flux-consistent schemes are presented; based on either body wall-defined or farfield-defined control-volumes they resolve the dual inconsistency. The behaviour of the schemes is investigated on a sequence of grids in 2D and 3D.
Yang, Yantao; Lohse, Detlef
2016-01-01
Vertically bounded fingering double diffusive convection (DDC) is numerically investigated, focusing on the influences of different velocity boundary conditions, i.e. the no-slip condition which is inevitable in the lab-scale experimental research, and the free-slip condition which is an approximation for the interfaces in many natural environments, such as the oceans. For both boundary conditions the flow is dominated by fingers and the global responses follow the same scaling laws, with enhanced prefactors for the free-slip cases. Therefore, the laboratory experiments with the no-slip boundaries serve as a good model for the finger layers in the ocean. Moreover, in the free-slip case although the tangential shear stress is eliminated at the boundaries, the local dissipation rate in the near-wall region may exceed the value found in the no-slip cases, which is caused by the stronger vertical motions of fingers and sheet structures near the free-slip boundaries. This counter intuitive result might be relevant...
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B. U. Musa
2017-04-01
Full Text Available The C++ programming language was used to implement three-dimensional (3-D finite-difference time-domain (FDTD technique to simulate radiation of high frequency electromagnetic waves in free space. To achieve any meaningful results the computational domain of interest should have to be truncated in some way and this is achieved by applying absorbing boundary conditions. A uniaxial perfectly matched layer (UPML absorbing boundary condition is used in this work. The discretised equations of the UPML in FDTD time stepping scheme were derived and has been successfully implemented using the computer program. Simulation results showed that the UPML behaves as an absorber. This was confirmed by comparing the results with another boundary condition, the Mur ABC.
Energy Technology Data Exchange (ETDEWEB)
Harrington, J.F.; Horseman, S.T. [British Geological Survey, Nottingham (United Kingdom)
2003-01-01
In the current Swedish repository design concept, hydrogen gas can be generated inside a waste canister by anaerobic corrosion of the ferrous metal liner. If the gas generation rate exceeds the diffusion rate of gas molecules in the buffer porewater, gas will accumulate in the void-space of a canister until its pressure becomes large enough for it to enter the bentonite as a discrete gaseous phase. Three long tenn gas injection tests have been performed on cylinders of pre-compacted MX80 bentonite. Two of these tests were undertaken using a custom-designed constant volume and radial flow (CVRF) apparatus. Gas was injected at a centrally located porous filter installed in the clay before hydration. Arrangements were made for gas to flow to three independently monitored sink-filter arrays mounted around the specimen. Axial and radial total stresses and internal porewater pressures were continuously monitored. Breakthrough and peak gas pressures were substantially larger than the sum of the swelling pressure and the external porewater. The third test was performed. using an apparatus which radially constrains the specimen during gas flow. Observed sensitivity of the breakthrough and peak gas pressures to the test boundary conditions suggests that gas entry must be accompanied by dilation of the bentonite fabric. In other words, there is a tendency for the volume of the specimen to increase during this process. The experimental evidence is consistent with the flow of gas along a relatively small number of crack-like pathways which propagate through the clay as gas pressure increases. Gas entry and breakthrough under constant volume boundary conditions causes a substantial increase in the total stress and the internal porewater pressure. It is possible to determine the point at which gas enters the clay by monitoring changes in these parameters. Localisation of gas flow within multiple pathways results, in nonuniform discharge rates at the sinks. When gas injection
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Emran Tohidi
2016-01-01
Full Text Available This article contributes a matrix approach by using Taylor approximation to obtain the numerical solution of one-dimensional time-dependent parabolic partial differential equations (PDEs subject to nonlocal boundary integral conditions. We first impose the initial and boundary conditions to the main problems and then reach to the associated integro-PDEs. By using operational matrices and also the completeness of the monomials basis, the obtained integro-PDEs will be reduced to the generalized Sylvester equations. For solving these algebraic systems, we apply a famous technique in Krylov subspace iterative methods. A numerical example is considered to show the efficiency of the proposed idea.
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Charyyar Ashyralyyev
2017-08-01
Full Text Available In this work, we consider an inverse elliptic problem with Bitsadze-Samarskii type multipoint nonlocal and Neumann boundary conditions. We construct the first and second order of accuracy difference schemes (ADSs for problem considered. We stablish stability and coercive stability estimates for solutions of these difference schemes. Also, we give numerical results for overdetermined elliptic problem with multipoint Bitsadze-Samarskii type nonlocal and Neumann boundary conditions in two and three dimensional test examples. Numerical results are carried out by MATLAB program and brief explanation on the realization of algorithm is given.
Energy Technology Data Exchange (ETDEWEB)
Cercignani, C. [Politecnico di Milano, Milan (Italy)
1996-08-01
Recently R. Illner and the author proved that, under a physically realistic truncation on the collision kernel, the Boltzmann equation in the one-dimensional slab [0,1] with general diffusive boundary conditions at 0 and 1 has a global weak solution in the traditional sense. Here it is proved that when the Maxwellians associated with the boundary conditions at x=0 and x = 1 are the same Maxwellian M{sub w}, then the solution is uniformly bounded and tends to M{sub w} for t {r_arrow}{infinity}.
On initial conditions for a boundary stabilized hybrid Euler–Bernoulli ...
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
elastic structure, Ph.D. thesis (Jadavpur University) (1999). [4] Krall A M, Asymptotic stability of the Euler–Bernoulli beam with boundary control, J. Math. Anal. Appl. 137 (1989) 288–295. [5] Littman W and Markus L, Stabilization of a hybrid system of elasticity by feedback boundary damping, Ann. Mat. Pura Appl. 152 (1988) ...
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Heather Sheridan
Full Text Available In a wide range of problem-solving settings, the presence of a familiar solution can block the discovery of better solutions (i.e., the Einstellung effect. To investigate this effect, we monitored the eye movements of expert and novice chess players while they solved chess problems that contained a familiar move (i.e., the Einstellung move, as well as an optimal move that was located in a different region of the board. When the Einstellung move was an advantageous (but suboptimal move, both the expert and novice chess players who chose the Einstellung move continued to look at this move throughout the trial, whereas the subset of expert players who chose the optimal move were able to gradually disengage their attention from the Einstellung move. However, when the Einstellung move was a blunder, all of the experts and the majority of the novices were able to avoid selecting the Einstellung move, and both the experts and novices gradually disengaged their attention from the Einstellung move. These findings shed light on the boundary conditions of the Einstellung effect, and provide convergent evidence for Bilalić, McLeod, & Gobet (2008's conclusion that the Einstellung effect operates by biasing attention towards problem features that are associated with the familiar solution rather than the optimal solution.
Relaxation processes in 8CB confined in cylindrical pores: homeotropic boundary conditions
Aliev, Fouad; Basu Majumder, Sarmistha
2002-03-01
Dielectric Spectroscopy (DS) and Dynamic Light Scattering (DLS) were applied to investigate relaxation processes in 8CB confined in 2000 Å cylindrical pores of Anopore membranes treated with lecithin. This treatment provides homeotropic boundary conditions for confined 8CB. The homeotropic alignment of molecules facilitates the investigation of the librational mode using DS. The behavior of this mode is totally different from the behavior observed in investigations of relaxation due to reorientation of molecules around their short axis. The temperature dependence of relaxation times of librational mode could not be described by the Arrhenius law. Instead the interpretation of the results obtained in nematic phase might need the involvement of temperature dependence of orientational order parameter. In the smectic-A phase and the supercooled state the temperature dependence of relaxation times is mainly determined by the variations of viscosity. Two well-defined relaxation processes were observed in DLS experiments for confined 8CB in the nematic phase. The first process is qualitatively associated with bulk-like nematic director fluctuations. The second relaxation process (with relaxation time slower than the first one) is most likely due to the fluctuations in layers nearest to the wall surface, which show the onset of smectic-A phase ordering even though the rest of liquid crystal could be in the nematic phase.
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N. Bhardwaj
2008-01-01
Full Text Available In the present paper, asymmetric vibration of polar orthotropic annular circular plates of quadratically varying thickness resting on Winkler elastic foundation is studied by using boundary characteristic orthonormal polynomials in Rayleigh-Ritz method. Convergence of the results is tested and comparison is made with results already available in the existing literature. Numerical results for the first ten frequencies for various values of parameters describing width of annular plate, thickness profile, material orthotropy and foundation constant for all three possible combinations of clamped, simply supported and free edge conditions are shown and discussed. It is found that (a higher elastic property in circumferential direction leads to higher stiffness against lateral vibration; (b Lateral vibration characteristics of F-Fplates is more sensitive towards parametric changes in material orthotropy and foundation stiffness than C-C and S-Splates; (c Effect of quadratical thickness variation on fundamental frequency is more significant in cases of C-C and S-S plates than that of F-Fplates. Thickness profile which is convex relative to plate center-line tends to result in higher stiffness of annular plates against lateral vibration than the one which is concave and (d Fundamental mode of vibration of C-C and S-Splates is axisymmetrical while that of F-Fplates is asymmetrical.
Sheridan, Heather; Reingold, Eyal M
2013-01-01
In a wide range of problem-solving settings, the presence of a familiar solution can block the discovery of better solutions (i.e., the Einstellung effect). To investigate this effect, we monitored the eye movements of expert and novice chess players while they solved chess problems that contained a familiar move (i.e., the Einstellung move), as well as an optimal move that was located in a different region of the board. When the Einstellung move was an advantageous (but suboptimal) move, both the expert and novice chess players who chose the Einstellung move continued to look at this move throughout the trial, whereas the subset of expert players who chose the optimal move were able to gradually disengage their attention from the Einstellung move. However, when the Einstellung move was a blunder, all of the experts and the majority of the novices were able to avoid selecting the Einstellung move, and both the experts and novices gradually disengaged their attention from the Einstellung move. These findings shed light on the boundary conditions of the Einstellung effect, and provide convergent evidence for Bilalić, McLeod, & Gobet (2008)'s conclusion that the Einstellung effect operates by biasing attention towards problem features that are associated with the familiar solution rather than the optimal solution.
Interference by amplitude division with extended sources by paraxial boundary conditions
Liñares, J.; Nistal, M. C.
2014-07-01
We present a wave-optics paraxial approach to the interference by amplitude division produced by plane-parallel films (or plates) and non-plane-parallel films, or by equivalent optical devices such as a Michelson interferometer, when they are illuminated with extended (spatially incoherent) quasi-monochromatic sources. To the best of our knowledge, the most common approaches to the study of interference are based, for simplicity, on the combined use of geometrical optics concepts, such as the optical path length along a ray, together with some wave-optics concepts such as optical phases. However, interference phenomena have been the means by which the wave nature of light has been established and therefore geometrical and wave concepts are so far-off that their simultaneous use can give rise to misleading concepts. Therefore, the primary aim of this work is to provide an analytical homogeneous description of interference by amplitude division using only paraxial spherical waves and boundary conditions at smooth interfaces or discontinuities in such a way that the calculation of the total optical field, interference irradiance, fringe visibility, coherence degree, localization of the interference and so on, can be made in a unified way by taking a fully wave-optics approach. The paraxial regime is enough in most cases and, moreover, interference is generally collected by an optical instrument such as a lens or the eye itself, in which a paraxial approximation is required. This work is particularly aimed at university physics teachers and undergraduate and first year postgraduate students.
Using effective boundary conditions to model fast diffusion on a road in a large field
Li, Huicong; Wang, Xuefeng
2017-10-01
We consider a logistic diffusion equation on the plane consisting of two components, a ‘road’ that is parallel to the x-axis, and a ‘field’, in each of which the diffusion rate differs significantly. Compared to the size of the field, the width δ of the road is assumed to be small. Thus in this diffusion equation multiple scales appear in two places: the spatial variable and the diffusion parameter. Such an equation is not easy to solve numerically, and it is not easy to see the effects of the road. Recently, Berestycki, Roquejoffre and Rossi provide a model which is meant to resolve these issues. In this paper we first use the idea of effective boundary conditions (EBCs) to propose, rigorously, a different model: we study the limit of the solution of the original logistic equation as δ→ 0 , obtaining a limiting model, in which the road now is the x-axis with EBCs imposed on it. This effective problem has no multiple scales and hence should be easier to solve numerically. Moreover, to see the effects of the road, we further investigate the asymptotic propagation speed of the effective model, showing that the road indeed enhances the spreading speed along its direction, provided that the diffusion rate on the road is of order O≤ft(δ-1\\right) .
System-size effects in ionic fluids under periodic boundary conditions
Thompson, Jeff P.; Sanchez, Isaac C.
2016-12-01
We investigate the system-size dependence of the thermodynamic properties of ionic fluids under periodic boundary conditions. Following an approach previously developed in the context of quantum Monte Carlo simulations of many-electron systems, we show that the leading-order finite-size artifact in the Coulomb energy per particle of a classical fluid of N structureless ions at given density and temperature is simply -kBT (2N ) -1 . Analytical approximations for the periodicity-induced size dependence of the excess thermodynamic properties of the fluid in the weak-coupling regime are obtained within the linearized Debye-Hückel theory. Theoretical results are compared with published simulations of the one-component plasma and our own simulations of a primitive-model electrolyte solution. Our work is directly relevant to estimating finite-size corrections in simulations of charged fluids comprising structureless ions embedded in continuous media. We outline in the Appendix how some of our formal results may be generalized to molecular fluids with mobile ions; e.g., electrolyte solutions with explicit solvent.
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.
Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase
Bleher, P M
2005-01-01
The six-vertex model, or the square ice model, with domain wall boundary conditions (DWBC) has been introduced and solved for finite $N$ by Korepin and Izergin. The solution is based on the Yang-Baxter equations and it represents the free energy in terms of an $N\\times N$ Hankel determinant. Paul Zinn-Justin observed that the Izergin-Korepin formula can be re-expressed in terms of the partition function of a random matrix model with a nonpolynomial interaction. We use this observation to obtain the large $N$ asymptotics of the six-vertex model with DWBC in the disordered phase. The solution is based on the Riemann-Hilbert approach and the Deift-Zhou nonlinear steepest descent method. As was noticed by Kuperberg, the problem of enumeration of alternating sign matrices (the ASM problem) is a special case of the the six-vertex model. We compare the obtained exact solution of the six-vertex model with known exact results for the 1, 2, and 3 enumerations of ASMs, and also with the exact solution on the so-called f...
Boundary conditions and formation of pure spin currents in magnetic field
Eliashvili, Merab; Tsitsishvili, George
2017-09-01
Schrödinger equation for an electron confined to a two-dimensional strip is considered in the presence of homogeneous orthogonal magnetic field. Since the system has edges, the eigenvalue problem is supplied by the boundary conditions (BC) aimed in preventing the leakage of matter away across the edges. In the case of spinless electrons the Dirichlet and Neumann BC are considered. The Dirichlet BC result in the existence of charge carrying edge states. For the Neumann BC each separate edge comprises two counterflow sub-currents which precisely cancel out each other provided the system is populated by electrons up to certain Fermi level. Cancelation of electric current is a good starting point for developing the spin-effects. In this scope we reconsider the problem for a spinning electron with Rashba coupling. The Neumann BC are replaced by Robin BC. Again, the two counterflow electric sub-currents cancel out each other for a separate edge, while the spin current survives thus modeling what is known as pure spin current - spin flow without charge flow.
Bifurcation boundary conditions for current programmed PWM DC-DC converters at light loading
Fang, Chung-Chieh
2012-10-01
Three types of bifurcations (instabilities) in the PWM DC-DC converter at light loading under current mode control in continuous-conduction mode (CCM) or discontinuous-conduction mode (DCM) are analysed: saddle-node bifurcation (SNB) in CCM or DCM, border-collision bifurcation during the CCM-DCM transition, and period-doubling bifurcation in CCM. Different bifurcations occur in some particular loading ranges. Bifurcation boundary conditions separating stable regions from unstable regions in the parametric space are derived. A new methodology to analyse the SNB in the buck converter based on the peak inductor current is proposed. The same methodology is applied to analyse the other types of bifurcations and converters. In the buck converter, multiple stable/unstable CCM/DCM steady-state solutions may coexist. Possibility of multiple solutions deserves careful study, because an ignored solution may merge with a desired stable solution and make both disappear. Understanding of SNB can explain some sudden disappearances or jumps of steady-state solutions observed in switching converters.
Set size manipulations reveal the boundary conditions of perceptual ensemble learning.
Chetverikov, Andrey; Campana, Gianluca; Kristjánsson, Árni
2017-10-16
Recent evidence suggests that observers can grasp patterns of feature variations in the environment with surprising efficiency. During visual search tasks where all distractors are randomly drawn from a certain distribution rather than all being homogeneous, observers are capable of learning highly complex statistical properties of distractor sets. After only a few trials (learning phase), the statistical properties of distributions - mean, variance and crucially, shape - can be learned, and these representations affect search during a subsequent test phase (Chetverikov, Campana, & Kristjánsson, 2016). To assess the limits of such distribution learning, we varied the information available to observers about the underlying distractor distributions by manipulating set size during the learning phase in two experiments. We found that robust distribution learning only occurred for large set sizes. We also used set size to assess whether the learning of distribution properties makes search more efficient. The results reveal how a certain minimum of information is required for learning to occur, thereby delineating the boundary conditions of learning of statistical variation in the environment. However, the benefits of distribution learning for search efficiency remain unclear. Copyright © 2017 Elsevier Ltd. All rights reserved.
Spectral boundary conditions and solitonic solutions in a classical Sellmeier dielectric
Energy Technology Data Exchange (ETDEWEB)
Belgiorno, F. [Politecnico di Milano, Dipartimento di Matematica, Milan (Italy); INdAM-GNFM, Rome (Italy); INFN, Milan (Italy); Cacciatori, S.L. [Universita dell' Insubria, Department of Science and High Technology, Como (Italy); INFN, Milan (Italy); Vigano, A. [Universita degli Studi di Milano, Dipartimento di Fisica, Milan (Italy)
2017-06-15
Electromagnetic field interactions in a dielectric medium represent a longstanding field of investigation, both at the classical level and at the quantum one. We propose a 1+1 dimensional toy-model which consists of an half-line filling dielectric medium, with the aim to set up a simplified situation where technicalities related to gauge invariance and, as a consequence, physics of constrained systems are avoided, and still interesting features appear. In particular, we simulate the electromagnetic field and the polarization field by means of two coupled scalar fields φ, ψ, respectively, in a Hopfield-like model. We find that, in order to obtain a physically meaningful behavior for the model, one has to introduce spectral boundary conditions depending on the particle spectrum one is dealing with. This is the first interesting achievement of our analysis. The second relevant achievement is that, by introducing a nonlinear contribution in the polarization field ψ, with the aim of mimicking a third order nonlinearity in a nonlinear dielectric, we obtain solitonic solutions in the Hopfield model framework, whose classical behavior is analyzed too. (orig.)
Trans-boundary air pollution in a city under various atmospheric conditions.
Luo, Ming; Hou, Xiangting; Gu, Yefu; Lau, Ngar-Cheung; Yim, Steve Hung-Lam
2017-11-08
Trans-boundary air pollution (TAP) is a crucial factor affecting air quality, and its contribution may vary over time and differ under various atmospheric conditions. This study firstly applies an integrated statistical scheme to estimate the contributions of TAP and local sources to air pollutants in a city, and then investigate the influences of tropical cyclones (TC) on TAP. Hong Kong is chosen as an example because of its significant and special TAP characteristics. This study focuses on four major air pollutants, namely, respirable and fine suspended particulates (RSP/PM10 and FSP/PM2.5), sulfur dioxide (SO2), and nitrogen dioxide (NO2), from 2002 to 2013. Our results show that, on average, TAP is the major contributor of the annual RSP, FSP, SO2, and NO2 in Hong Kong. We estimate that when a TC is approaching, the increase in pollutant concentration in Hong Kong is mainly due to the increase in TAP contribution by the strengthened northerly wind at higher level of atmosphere (≥900hPa). These changes are accompanied by decreases in precipitation and increases in northerly/north-easterly wind, which may prolong the lifetime of pollutants, enhancing pollutant transport from mainland China to Hong Kong. Copyright © 2017 Elsevier B.V. All rights reserved.
Flow and heat transfer in Sisko fluid with convective boundary condition.
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Rabia Malik
Full Text Available In this article, we have studied the flow and heat transfer in Sisko fluid with convective boundary condition over a nonisothermal stretching sheet. The flow is influenced by non-linearly stretching sheet in the presence of a uniform transverse magnetic field. The partial differential equations governing the problem have been reduced by similarity transformations into the ordinary differential equations. The transformed coupled ordinary differential equations are then solved analytically by using the homotopy analysis method (HAM and numerically by the shooting method. Effects of different parameters like power-law index n, magnetic parameter M, stretching parameter s, generalized Prandtl number Pr and generalized Biot number γ are presented graphically. It is found that temperature profile increases with the increasing value of M and γ whereas it decreases for Pr. Numerical values of the skin-friction coefficient and local Nusselt number are tabulated at various physical situations. In addition, a comparison between the HAM and exact solutions is also made as a special case and excellent agreement between results enhance a confidence in the HAM results.
Luce, Charles H.; Tonina, Daniele; Applebee, Ralph; DeWeese, Timothy
2017-11-01
Two common refrains about using the one-dimensional advection diffusion equation to estimate fluid fluxes and thermal conductivity from temperature time series in streambeds are that the solution assumes that (1) the surface boundary condition is a sine wave or nearly so, and (2) there is no gradient in mean temperature with depth. Although the mathematical posing of the problem in the original solution to the problem might lead one to believe these constraints exist, the perception that they are a source of error is a fallacy. Here we develop a mathematical proof demonstrating the equivalence of the solution as developed based on an arbitrary (Fourier integral) surface temperature forcing when evaluated at a single given frequency versus that derived considering a single frequency from the beginning. The implication is that any single frequency can be used in the frequency-domain solutions to estimate thermal diffusivity and 1-D fluid flux in streambeds, even if the forcing has multiple frequencies. This means that diurnal variations with asymmetric shapes or gradients in the mean temperature with depth are not actually assumptions, and deviations from them should not cause errors in estimates. Given this clarification, we further explore the potential for using information at multiple frequencies to augment the information derived from time series of temperature.
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Dayasindhu Dey
2016-11-01
Full Text Available The Density Matrix Renormalization Group (DMRG is a state-of-the-art numerical technique for a one dimensional quantum many-body system; but calculating accurate results for a system with Periodic Boundary Condition (PBC from the conventional DMRG has been a challenging job from the inception of DMRG. The recent development of the Matrix Product State (MPS algorithm gives a new approach to find accurate results for the one dimensional PBC system. The most efficient implementation of the MPS algorithm can scale as O(p x m^3, where p can vary from 4 to m^2. In this paper, we propose a new DMRG algorithm, which is very similar to the conventional DMRG and gives comparable accuracy to that of MPS. The computation effort of the new algorithm goes as O(m^3 and the conventional DMRG code can be easily modified for the new algorithm. Received: 2 August 2016, Accepted: 12 October 2016; Edited by: K. Hallberg; DOI: http://dx.doi.org/10.4279/PIP.080006 Cite as: D Dey, D Maiti, M Kumar, Papers in Physics 8, 080006 (2016
Bose, Tushar Kanti; Saha, Jayashree
2015-10-01
The realization of a spontaneous macroscopic ferroelectric order in fluids of anisotropic mesogens is a topic of both fundamental and technological interest. Recently we demonstrated that a system of dipolar achiral disklike ellipsoids can exhibit long-searched ferroelectric liquid crystalline phases of dipolar origin. In the present work, extensive off-lattice Monte Carlo simulations are used to investigate the phase behavior of the system under the influences of the electrostatic boundary conditions that restrict any global polarization. We find that the system develops strongly ferroelectric slablike domains periodically arranged in an antiferroelectric fashion. Exploring the phase behavior at different dipole strengths, we find existence of the ferroelectric nematic and ferroelectric columnar order inside the domains. For higher dipole strengths, a biaxial phase is also obtained with a similar periodic array of ferroelectric slabs of antiparallel polarizations. We have studied the depolarizing effects by using both the Ewald summation and the spherical cutoff techniques. We present and compare the results of the two different approaches of considering the depolarizing effects in this anisotropic system. It is explicitly shown that the domain size increases with the system size as a result of considering a longer range of dipolar interactions. The system exhibits pronounced system size effects for stronger dipolar interactions. The results provide strong evidence to the novel understanding that the dipolar interactions are indeed sufficient to produce long-range ferroelectric order in anisotropic fluids.
Grid-size dependence of Cauchy boundary conditions used to simulate stream-aquifer interactions
Mehl, S.; Hill, M.C.
2010-01-01
This work examines the simulation of stream–aquifer interactions as grids are refined vertically and horizontally and suggests that traditional methods for calculating conductance can produce inappropriate values when the grid size is changed. Instead, different grid resolutions require different estimated values. Grid refinement strategies considered include global refinement of the entire model and local refinement of part of the stream. Three methods of calculating the conductance of the Cauchy boundary conditions are investigated. Single- and multi-layer models with narrow and wide streams produced stream leakages that differ by as much as 122% as the grid is refined. Similar results occur for globally and locally refined grids, but the latter required as little as one-quarter the computer execution time and memory and thus are useful for addressing some scale issues of stream–aquifer interactions. Results suggest that existing grid-size criteria for simulating stream–aquifer interactions are useful for one-layer models, but inadequate for three-dimensional models. The grid dependence of the conductance terms suggests that values for refined models using, for example, finite difference or finite-element methods, cannot be determined from previous coarse-grid models or field measurements. Our examples demonstrate the need for a method of obtaining conductances that can be translated to different grid resolutions and provide definitive test cases for investigating alternative conductance formulations.
The CFL condition for spectral approximations to hyperbolic initial-boundary value problems
Gottlieb, David; Tadmor, Eitan
1990-01-01
The stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients are studied. Time is discretized by explicit multi-level or Runge-Kutta methods of order less than or equal to 3 (forward Euler time differencing is included), and spatial discretizations are studied by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. It is proved that these fully explicit spectral approximations are stable provided their time-step, delta t, is restricted by the CFL-like condition, delta t less than Const. N(exp-2), where N equals the spatial number of degrees of freedom. We give two independent proofs of this result, depending on two different choices of approximate L(exp 2)-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the nonperiodic case.
Yuste, A.; Moreno-Cardoner, M.; Sanpera, A.
2017-05-01
Disordered quantum antiferromagnets in two-dimensional compounds have been a focus of interest in the last years due to their exotic properties. However, with very few exceptions, the ground states of the corresponding Hamiltonians are notoriously difficult to simulate making their characterization and detection very elusive, both theoretically and experimentally. Here we propose a method to signal quantum disordered antiferromagnets by doing exact diagonalization in small lattices using random boundary conditions and averaging the observables of interest over the different disorder realizations. We apply our method to study the Heisenberg spin-1/2 model in an anisotropic triangular lattice. In this model, the competition between frustration and quantum fluctuations might lead to some spin-liquid phases as predicted from different methods ranging from spin-wave mean-field theory to 2D-DMRG or PEPS. Our method accurately reproduces the ordered phases expected of the model and signals quantum disordered phases by the presence of a large number of quasidegenerate ground states together with an undefined local order parameter. The method presents a weak dependence on finite-size effects.
On the role of thermal boundary conditions in dynamo scaling laws
Oruba, Ludivine
2016-01-01
In dynamo power-based scaling laws, the power $P$ injected by buoyancy forces is measured by a so-called flux-based Rayleigh number, denoted as ${\\rm Ra}_Q^*$ (see Christensen and Aubert, 2006). Whereas it is widely accepted that this parameter is measured (as opposite to controlled) in dynamos driven by differential heating, the literature is much less clear concerning its nature in the case of imposed heat flux. We clarify this issue by highlighting that in that case, the ${\\rm Ra}_{Q}^*$ parameter becomes controlled only in the limit of large Nusselt numbers (${\\rm Nu} \\gg 1$). We then address the issue of the robustness of the original relation between $P$ and ${\\rm Ra}_Q^*$ with the geometry and the thermal boundary conditions. We show that in the cartesian geometry, as in the spherical geometry with a central mass distribution, this relation is purely linear, in both differential and fixed-flux heating. However, we show that in the geometry commonly studied by geophysicists (spherical with uniform mass ...
EFFECT OF CONVECTIVE BOUNDARY CONDITIONS AT BOTTOM WALL ON NATURAL CONVECTIONS IN A SQUARE CAVITY
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ASWATHA
2013-04-01
Full Text Available Simulations were carried out for natural convection in a square cavity using finite volume based computational procedure with biased quadratic elements to investigate the influence of convective boundary conditions at bottom wall. Parametric study has been carried out for a wide range of Rayleigh number (Ra (103 ≤ Ra ≤ 108, Prandtl number (Pr (0.7 ≤ Pr ≤ 17 and heat transfer coefficient (h (0.1 ≤ h ≤ 104 W/m2 K. It is observed from the present study that the heat transfer is primarily due to conduction for Rayleigh number up to 104. Convection dominant heat transfer is observed at higher Ra values. The intensity of circulation increases with increase in Ra number. The average heat transfer rate at the bottom wall is found to be invariant for all values of heat transfer coefficient for Ra up to 104. The power law correlations between average Nusselt number and Rayleigh numbers are presented for convection dominated regimes.
Hori, K.; Wicht, J.; Dietrich, W.; Christensen, U. R.
2012-12-01
The early dynamos of Earth and Mars probably operated without an inner core being present. They were thus exclusively driven by secular cooling and radiogenic heating, whereas the present geodynamo is thought to be predominantly driven by buoyancy fluxes which arise from the release of latent heat and the compositional enrichment associated with inner core solidification. Dynamo simulations model the secular cooling by volumetric internal buoyancy sources and the inner core-related driving by bottom sources. The impact of the inner core growth on the ancient geodynamo has been discussed extensively but is still controversial. As for Mars, the Mars Global Surveyor detected a strong northern-southern dichotomy in the crustal magnetization. A scenario proposed so far is due to such an ancient dynamo, where thermal heterogeneities at the core mantle boundary (CMB) were imposed by the lower mantle structure. A key issue here is how easily influence of the boundary anomalies emerges. Here we show that the dynamos without inner core solidification are much more sensitive to the CMB heat flows imposed by the lower mantle structure. We compare three-dimensional convection-driven MHD dynamo simulations either driven by homogeneously distributed internal heat sources or by buoyancy sources at the inner core boundary (ICB). Several different boundary heat-flux patterns are used. The effects are found even when boundaries are homogeneous. The impact of the outer boundary condition, fixed temperature or fixed heat flux, is large when convection is predominantly driven by volumetric internal heating. In the dynamos driven by ICB buoyancy sources, the lower boundary condition becomes more important. In both cases, a fixed flux condition promotes larger convective scales than a fixed temperature condition. A dipolar magnetic field can further increase the flow scale. This different sensitivity may also extend to cases when CMB heat flows are laterally inhomogeneous. In the dynamos
Effect of remote field electromagnetic boundary conditions on microwave-induced plasma torches
Jimenez-Diaz, M.; van Dijk, J.; van der Mullen, J. J. A. M.
2011-04-01
A flexible versatile electromagnetic model constructed with the PLASIMO platform is employed to explore electromagnetic features of microwave-induced plasma torches. The bases, formed by a full-vector formulation of the Maxwell equations, provide the possibility to formulate the boundary conditions in a natural way. Together with the use of a direct matrix solver this gives a convergence speed-up of more than a factor of 100 when compared with a scalar formulation on an azimuthal magnetic field that uses an iterative solver. As a result, this electromagnetic model is ready to act in future studies as part of the self-consistent description of plasma-electromagnetic coupling. With the electromagnetic model three types of configuration were studied: the closed, semi-open and open configurations, all three based on the same simplified model plasmas. It is found that the closed configuration, acting as a cavity for which (de)tuning is extremely sensitive for the plasma conditions, is less suitable for applications in which changes in plasma compositions can be expected. The semi-open configuration can be seen as a model for the practice often used in laboratories to place microwave-induced plasma torches in a grid that aims at protecting the environment against microwave electromagnetic radiation. Calculations show that this is good practice provided the radius of this cylindrical grid is in the order of 90 mm. For the most often used configuration, the open version, we found that the power balance as expressed by the coefficients of absorption, transmission and reflection depends on the electron density of the plasma. The reason is that the plasma acts as an antenna, which converts the electromagnetic waves from the coaxial structure to that of the expansion region, and that this antenna function depends on the electron density. The influence of various other antenna elements is investigated as well.
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Rachida El Ouaraini
2015-12-01
Full Text Available The implementation of a regional ensemble data assimilation and forecasting system requires the specification of appropriate perturbations of lateral boundary conditions (LBCs, in order to simulate associated errors. The sensitivity of analysis and 6-h forecast ensemble spread to these perturbations is studied here formally and experimentally by comparing three different LBC configurations for the ensemble data assimilation system of the ALADIN-France limited-area model (LAM. While perturbed initial LBCs are provided by the perturbed LAM analyses in each ensemble, the three ensemble configurations differ with respect to LBCs used at 3- and 6-h forecast ranges, which respectively correspond to: (1 perturbed LBCs provided by the operational global ensemble data assimilation system (GLBC, which is considered as a reference configuration; (2 unperturbed LBCs (ULBC obtained from the global deterministic model; (3 perturbed LBCs obtained by adding random draws of an error covariance model (PLBC to the global deterministic system. A formal analysis of error and perturbation equations is first carried out, in order to provide an insight of the relative effects of observation perturbations and of LBC perturbations at different ranges, in the various ensemble configurations. Horizontal variations of time-averaged ensemble spread are then examined for 6-h forecasts. Despite the use of perturbed initial LBCs, the regional ensemble ULBC is underdispersive not only near the lateral boundaries, but also in approximately one-third of the inner area, due to advection during the data assimilation cycle. This artefact is avoided in PLBC through the additional use of non-zero LBC perturbations at 3- and 6-h ranges, and the sensitivity to the amplitude scaling of the covariance model is illustrated for this configuration. Some aspects of the temporal variation of ensemble spread and associated sensitivities to LBC perturbations are also studied. These results
A Fast Poisson Solver with Periodic Boundary Conditions for GPU Clusters in Various Configurations
Rattermann, Dale Nicholas
Fast Poisson solvers using the Fast Fourier Transform on uniform grids are especially suited for parallel implementation, making them appropriate for portability on graphical processing unit (GPU) devices. The goal of the following work was to implement, test, and evaluate a fast Poisson solver for periodic boundary conditions for use on a variety of GPU configurations. The solver used in this research was FLASH, an immersed-boundary-based method, which is well suited for complex, time-dependent geometries, has robust adaptive mesh refinement/de-refinement capabilities to capture evolving flow structures, and has been successfully implemented on conventional, parallel supercomputers. However, these solvers are still computationally costly to employ, and the total solver time is dominated by the solution of the pressure Poisson equation using state-of-the-art multigrid methods. FLASH improves the performance of its multigrid solvers by integrating a parallel FFT solver on a uniform grid during a coarse level. This hybrid solver could then be theoretically improved by replacing the highly-parallelizable FFT solver with one that utilizes GPUs, and, thus, was the motivation for my research. In the present work, the CPU-utilizing parallel FFT solver (PFFT) used in the base version of FLASH for solving the Poisson equation on uniform grids has been modified to enable parallel execution on CUDA-enabled GPU devices. New algorithms have been implemented to replace the Poisson solver that decompose the computational domain and send each new block to a GPU for parallel computation. One-dimensional (1-D) decomposition of the computational domain minimizes the amount of network traffic involved in this bandwidth-intensive computation by limiting the amount of all-to-all communication required between processes. Advanced techniques have been incorporated and implemented in a GPU-centric code design, while allowing end users the flexibility of parameter control at runtime in
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Lijie Li
2017-01-01
Full Text Available The aim of this paper is to extend the modified Fourier-Ritz approach to evaluate the free vibration of four-parameter functionally graded moderately thick cylindrical, conical, spherical panels and shells of revolution with general boundary conditions. The first-order shear deformation theory is employed to formulate the theoretical model. In the modified Fourier-Ritz approach, the admissible functions of the structure elements are expanded into the improved Fourier series which consist of two-dimensional (2D Fourier cosine series and auxiliary functions to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges regardless of boundary conditions and then solve the natural frequencies by means of the Ritz method. As one merit of this paper, the functionally graded cylindrical, conical, spherical shells are, respectively, regarded as a special functionally graded cylindrical, conical, spherical panels, and the coupling spring technology is introduced to ensure the kinematic and physical compatibility at the common meridian. The excellent accuracy and reliability of the unified computational model are compared with the results found in the literatures.
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Xuemei Zhang
2014-01-01
Full Text Available This paper investigates the expression and properties of Green’s function for a second-order singular boundary value problem with integral boundary conditions and delayed argument -x′′t-atx′t+btxt=ωtft, xαt, t∈0, 1; x′0=0, x1-∫01htxtdt=0, where a∈0, 1, 0, +∞, b∈C0, 1, 0, +∞ and, ω may be singular at t=0 or/and at t=1. Furthermore, several new and more general results are obtained for the existence of positive solutions for the above problem by using Krasnosel’skii’s fixed point theorem. We discuss our problems with a delayed argument, which may concern optimization issues of some technical problems. Moreover, the approach to express the integral equation of the above problem is different from earlier approaches. Our results cover a second-order boundary value problem without deviating arguments and are compared with some recent results.
Yoshida, Hiroaki; Kobayashi, Takayuki; Hayashi, Hidemitsu; Kinjo, Tomoyuki; Washizu, Hitoshi; Fukuzawa, Kenji
2014-07-01
A boundary scheme in the lattice Boltzmann method (LBM) for the convection-diffusion equation, which correctly realizes the internal boundary condition at the interface between two phases with different transport properties, is presented. The difficulty in satisfying the continuity of flux at the interface in a transient analysis, which is inherent in the conventional LBM, is overcome by modifying the collision operator and the streaming process of the LBM. An asymptotic analysis of the scheme is carried out in order to clarify the role played by the adjustable parameters involved in the scheme. As a result, the internal boundary condition is shown to be satisfied with second-order accuracy with respect to the lattice interval, if we assign appropriate values to the adjustable parameters. In addition, two specific problems are numerically analyzed, and comparison with the analytical solutions of the problems numerically validates the proposed scheme.
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Giovanni Pitari
2017-12-01
Full Text Available Two independent chemistry-transport models with troposphere-stratosphere coupling are used to quantify the different components of the radiative forcing (RF from aircraft emissions of NOx, i.e., the University of L'Aquila climate-chemistry model (ULAQ-CCM and the University of Oslo chemistry-transport model (Oslo-CTM3. The tropospheric NOx enhancement due to aircraft emissions produces a short-term O3 increase with a positive RF (+17.3 mW/m2 (as an average value of the two models. This is partly compensated by the CH4 decrease due to the OH enhancement (−9.4 mW/m2. The latter is a long-term response calculated using a surface CH4 flux boundary condition (FBC, with at least 50 years needed for the atmospheric CH4 to reach steady state. The radiative balance is also affected by the decreasing amount of CO2 produced at the end of the CH4 oxidation chain: an average CO2 accumulation change of −2.2 ppbv/yr is calculated on a 50 year time horizon (−1.6 mW/m2. The aviation perturbed amount of CH4 induces a long-term response of tropospheric O3 mostly due to less HO2 and CH3O2 being available for O3 production, compared with the reference case where a constant CH4 surface mixing ratio boundary condition is used (MBC (−3.9 mW/m2. The CH4 decrease induces a long-term response of stratospheric H2O (−1.4 mW/m2. The latter finally perturbs HOx and NOx in the stratosphere, with a more efficient NOx cycle for mid-stratospheric O3 depletion and a decreased O3 production from HO2+NO in the lower stratosphere. This produces a long-term stratospheric O3 loss, with a negative RF (−1.2 mW/m2, compared with the CH4 MBC case. Other contributions to the net NOx RF are those due to NO2 absorption of UV-A and aerosol perturbations (the latter calculated only in the ULAQ-CCM. These comprise: increasing sulfate due to more efficient oxidation of SO2, increasing inorganic and organic nitrates and the net aerosols indirect effect on warm clouds
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Liu Yang
2014-01-01
Full Text Available We consider the existence of infinitely many classical solutions to a class of impulsive differential equations with Dirichlet boundary value condition. Our main tools are based on variant fountain theorems and variational method. We study the case in which the nonlinearity is sublinear. Some recent results are extended and improved.
Veldman, Arthur; Luppes, Roelf; van der Heiden, Hendrik; van der Plas, Peter; Duz, Bulent; Huijsmans, Rene
2014-01-01
To study extreme hydrodynamic wave impact in offshore and coastal engineering, the VOF-based CFD simulation tool ComFLOW is being developed. Recently, much attention has been paid to turbulence modeling, local grid refinement, wave propagation and absorbing boundary conditions. The turbulence model
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Iftikhar Ahmed
2014-04-01
Full Text Available This paper deals with the evolution r-Laplacian equation with absorption and nonlinear boundary condition. By using differential inequality techniques, global existence and blow-up criteria of nonnegative solutions are determined. Moreover, upper bound of the blow-up time for the blow-up solution is obtained.
Bernhard-Oettel, C.; Rigotti, T.; Clinton, M.; de Jong, J.P.
2013-01-01
This study investigates whether temporary contract volition and workers' expectations for contract renewal are boundary conditions to explain differences in temporary workers' job insecurity feelings and well-being. It is hypothesized that (1) low volition through higher job insecurity indirectly
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J. D. Ramírez
2012-01-01
boundary conditions of order , where . We develop results which provide natural monotone sequences or intertwined monotone sequences which converge uniformly and monotonically to coupled minimal and maximal periodic solutions. However, these monotone iterates are solutions of linear initial value problems which are easier to compute.
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Huina Zhang
2014-01-01
Full Text Available This paper studies the existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations of order α,β∈(4,5] with antiperiodic boundary conditions. Our results are based on the nonlinear alternative of Leray-Schauder type and the contraction mapping principle. Two illustrative examples are also presented.
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Guotao Wang
2012-01-01
Full Text Available This paper investigates the existence of solutions for a coupled system of nonlinear fractional differential equations with m-point fractional boundary conditions on an unbounded domain. Some standard fixed point theorems are applied to obtain the main results. The paper concludes with two illustrative examples.
Guotao Wang; Bashir Ahmad; Lihong Zhang
2012-01-01
This paper investigates the existence of solutions for a coupled system of nonlinear fractional differential equations with m-point fractional boundary conditions on an unbounded domain. Some standard fixed point theorems are applied to obtain the main results. The paper concludes with two illustrative examples.
Uranus, H.P.; Hoekstra, Hugo; van Groesen, Embrecht W.C.
2003-01-01
A Galerkin finite element scheme furnished with 1st-order Bayliss-Gunzberger-Turkel-like boundary conditions is formulated to compute both the guided and leaky modes of anisotropic channel waveguides of non-magnetic material with diagonal permitivity tensor. The scheme is formulated using
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Davide Guidetti
2013-12-01
Full Text Available We consider the problem of the reconstruction of the convolution kernel, together with the solution, in a semilinear integrodiential parabolic problem in the case that in the boundary conditions, there appear quite general memory operators.
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Ahmed Dakkak
2015-11-01
Full Text Available This work deals with an indefinite weight one dimensional eigenvalue problem of the p-Laplacian operator subject to Neumann boundary conditions. We are interested in some properties of the spectrum like simplicity, monotonicity and strict monotonicity with respect to the weight. We also aim the study of zeros points of eigenfunctions.
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Giai Giang Vo
2015-01-01
Full Text Available This paper is devoted to the study of a wave equation with a boundary condition of many-point type. The existence of weak solutions is proved by using the Galerkin method. Also, the uniqueness and the stability of solutions are established.
Rahimi, Masoud; Movahedirad, Salman; Shahhosseini, Shahrokh
2017-03-01
Recently, great attention has been paid to predict the acoustic streaming field distribution inside the sonoreactors, induced by high-power ultrasonic wave generator. The focus of this paper is to model an ultrasonic vibrating horn and study the induced flow pattern with a newly developed moving boundary condition. The numerical simulation utilizes the modified cavitation model along with the "mixture" model for turbulent flow (RNG, k-ε), and a moving boundary condition with an oscillating parabolic-logarithmic profile, applied to the horn tip. This moving-boundary provides the situation in which the center of the horn tip vibrates stronger than that of the peripheral regions. The velocity field obtained by computational fluid dynamic was in a reasonably good agreement with the PIV results. The moving boundary model is more accurate since it better approximates the movement of the horn tip in the ultrasonic assisted process. From an optimizing point of view, the model with the new moving boundary is more suitable than the conventional models for design purposes because the displacement magnitude of the horn tip is the only fitting parameter. After developing and validating the numerical model, the model was utilized to predict various quantities such as cavitation zone, pressure field and stream function that are not experimentally feasible to measure. Copyright Â© 2016 Elsevier B.V. All rights reserved.
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Domingo A. Tarzia
2015-01-01
Full Text Available We complete the Solomon-Wilson-Alexiades’s mushy zone model (Solomon, 1982 for the one-phase Lamé-Clapeyron-Stefan problem by obtaining explicit solutions when a convective or heat flux boundary condition is imposed on the fixed face for a semi-infinite material. We also obtain the necessary and sufficient condition on data in order to get the explicit solutions for both cases which is new with respect to the original model. Moreover, when these conditions are satisfied, the two phase-change problems are equivalent to the same problem with a temperature boundary condition on the fixed face and therefore an inequality for the coefficient which characterized one of the two free interfaces of the model is also obtained.
Povstenko, Y.
2013-09-01
The axisymmetric time-fractional diffusion-wave equation with the Caputo derivative of the order 0 function and the values of its normal derivative at the boundary. The fundamental solutions to the Cauchy, source, and boundary problems are investigated. The Laplace transform with respect to time and finite Hankel transform with respect to the radial coordinate are used. The solutions are obtained in terms of Mittag-Leffler functions. The numerical results are illustrated graphically.
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.
Ocean regional circulation model sensitizes to resolution of the lateral boundary conditions
Pham, Van Sy; Hwang, Jin Hwan
2017-04-01
Dynamical downscaling with nested regional oceanographic models is an effective approach for forecasting operationally coastal weather and projecting long term climate on the ocean. Nesting procedures deliver the unwanted in dynamic downscaling due to the differences of numerical grid sizes and updating steps. Therefore, such unavoidable errors restrict the application of the Ocean Regional Circulation Model (ORCMs) in both short-term forecasts and long-term projections. The current work identifies the effects of errors induced by computational limitations during nesting procedures on the downscaled results of the ORCMs. The errors are quantitatively evaluated for each error source and its characteristics by the Big-Brother Experiments (BBE). The BBE separates identified errors from each other and quantitatively assess the amount of uncertainties employing the same model to simulate for both nesting and nested model. Here, we focus on discussing errors resulting from two main matters associated with nesting procedures. They should be the spatial grids' differences and the temporal updating steps. After the diverse cases from separately running of the BBE, a Taylor diagram was adopted to analyze the results and suggest an optimization intern of grid size and updating period and domain sizes. Key words: lateral boundary condition, error, ocean regional circulation model, Big-Brother Experiment. Acknowledgement: This research was supported by grants from the Korean Ministry of Oceans and Fisheries entitled "Development of integrated estuarine management system" and a National Research Foundation of Korea (NRF) Grant (No. 2015R1A5A 7037372) funded by MSIP of Korea. The authors thank the Integrated Research Institute of Construction and Environmental Engineering of Seoul National University for administrative support.
Boundary lubrication by brushed salivary conditioning films and their degree of glycosylation.
Veeregowda, Deepak H; van der Mei, Henny C; de Vries, Joop; Rutland, Mark W; Valle-Delgado, Juan J; Sharma, Prashant K; Busscher, Henk J
2012-10-01
Toothbrushing, though aimed at biofilm removal, also affects the lubricative function of adsorbed salivary conditioning films (SCFs). Different modes of brushing (manual, powered, rotary-oscillatory or sonically driven) influence the SCF in different ways. Our objectives were to compare boundary lubrication of SCFs after different modes of brushing and to explain their lubrication on the basis of their roughness, dehydrated layer thickness, and degree of glycosylation. A pilot study was performed to relate in vitro lubrication with mouthfeel in human volunteers. Coefficient of friction (COF) on 16-h-old SCFs after manual, rotary-oscillatory, and sonically driven brushing was measured using colloidal probe atomic force microscopy (AFM). AFM was also used to assess the roughness of SCFs prior to and after brushing. Dehydrated layer thicknesses and glycosylation of the SCFs were determined using X-ray photoelectron spectroscopy. Mouthfeel after manual and both modes of powered brushing were evaluated employing a split-mouth design. Compared with unbrushed and manually or sonically driven brushed SCFs, powered rotary-oscillatory brushing leads to deglycosylation of the SCF, loss of thickness, and a rougher film. Concurrently, the COF of a powered rotary-oscillatory brushed SCF increased. Volunteers reported a slightly preferred mouthfeel after sonic brushing as compared to powered rotating-oscillating brushing. Deglycosylation and roughness increase the COF on SCFs. Powered rotary-oscillatory brushing can deglycosylate a SCF, leading to a rougher film surface as compared with manual and sonic brushing, decreasing the lubricative function of the SCF. This is consistent with clinical mouthfeel evaluation after different modes of brushing.
Jakkareddy, Pradeep S.; Balaji, C.
2017-02-01
This paper reports the results of an experimental study to estimate the heat flux and convective heat transfer coefficient using liquid crystal thermography and Bayesian inference in a heat generating sphere, enclosed in a cubical Teflon block. The geometry considered for the experiments comprises a heater inserted in a hollow hemispherical aluminium ball, resulting in a volumetric heat generation source that is placed at the center of the Teflon block. Calibrated thermochromic liquid crystal sheets are used to capture the temperature distribution at the front face of the Teflon block. The forward model is the three dimensional conduction equation which is solved within the Teflon block to obtain steady state temperatures, using COMSOL. Match up experiments are carried out for various velocities by minimizing the residual between TLC and simulated temperatures for every assumed loss coefficient, to obtain a correlation of average Nusselt number against Reynolds number. This is used for prescribing the boundary condition for the solution to the forward model. A surrogate model obtained by artificial neural network built upon the data from COMSOL simulations is used to drive a Markov Chain Monte Carlo based Metropolis Hastings algorithm to generate the samples. Bayesian inference is adopted to solve the inverse problem for determination of heat flux and heat transfer coefficient from the measured temperature field. Point estimates of the posterior like the mean, maximum a posteriori and standard deviation of the retrieved heat flux and convective heat transfer coefficient are reported. Additionally the effect of number of samples on the performance of the estimation process has been investigated.
Motion of particles in solar and galactic systems by using Neumann boundary condition
Shenavar, Hossein
2016-12-01
A new equation of motion, which is derived previously by imposing Neumann boundary condition on cosmological perturbation equations (Shenavar in Astrophys. Space Sci., 2016a, doi: 10.1007/s10509-016-2676-5), is investigated. By studying the precession of perihelion, it is shown that the new equation of motion suggests a small, though detectable, correction in orbits of solar system objects. Then a system of particles is surveyed to have a better understanding of galactic structures. Also the general form of the force law is introduced by which the rotation curve and mass discrepancy of axisymmetric disks of stars are derived. In addition, it is suggested that the mass discrepancy as a function of centripetal acceleration becomes significant near a constant acceleration 2c1a0 where c1 is the Neumann constant and a0 = 6.59 ×10^{-10} m/s2 is a fundamental acceleration. Furthermore, it is shown that a critical surface density equal to σ0=a0/G, in which G is the Newton gravitational constant, has a significant role in rotation curve and mass discrepancy plots. Also, the specific form of NFW mass density profile at small radii, ρ∝1/r, is explained too. Finally, the present model will be tested by using a sample of 39 LSB galaxies for which we will show that the rotation curve fittings are generally acceptable. The derived mass to light ratios too are found within the plausible bound except for the galaxy F571-8.
Roy, Amitava; Post, Carol Beth
2011-01-01
A large number of viral capsids, as well as other macromolecular assemblies, have icosahedral structure or structures with other rotational symmetries. This symmetry can be exploited during molecular dynamics (MD) to model in effect the full viral capsid using only a subset of primary atoms plus copies of image atoms generated from rotational symmetry boundary conditions (RSBC). A pure rotational symmetry operation results in both primary and image atoms at short range, and within nonbonded interaction distance of each other, so that nonbonded interactions can not be specified by the minimum image convention and explicit treatment of image atoms is required. As such an unavoidable consequence of RSBC is that the enumeration of nonbonded interactions in regions surrounding certain rotational axes must include both a primary atom and its copied image atom, thereby imposing microscopic symmetry for some forces. We examined the possibility of artifacts arising from this imposed microscopic symmetry of RSBC using two simulation systems: a water shell and human rhinovirus 14 (HRV14) capsid with explicit water. The primary unit was a pentamer of the icosahedron, which has the advantage of direct comparison of icosahedrally equivalent spatial regions, for example regions near a 2-fold symmetry axis with imposed symmetry and a 2-fold axis without imposed symmetry. Analysis of structural and dynamic properties of water molecules and protein atoms found similar behavior near symmetry axes with imposed symmetry and where the minimum image convention fails compared with that in other regions in the simulation system, even though an excluded volume effect was detected for water molecules near the axes with imposed symmetry. These results validate the use of RSBC for icosahedral viral capsids or other rotationally symmetric systems. PMID:22096451
Stoller, Marco; Field, Robert
2017-01-01
In the last decades, membrane processes have gained a significant share of the market for wastewater purification. Although the product (i.e., purified water) is not of high added value, these processes are feasible both technically and from an economic point of view, provided the flux is relatively high and that membrane fouling is strongly inhibited. By controlling membrane fouling, the membrane may work for years without service, thus dramatically reducing operating costs and the need for membrane substitution. There is tension between operating at high permeate fluxes, which enhances fouling but reduces capital costs, and operating at lower fluxes which increases capital costs. Operating batch membrane processes leads to increased difficulties, since the feed fed to the membrane changes as a function of the recovery value. This paper is concerned with the operation of such a process. Membrane process designers should therefore avoid membrane fouling by operating membranes away from the permeate flux point where severe fouling is triggered. The design and operation of membrane purification plants is a difficult task, and the precision to properly describe the evolution of the fouling phenomenon as a function of the operating conditions is a key to success. Many reported works have reported on the control of fouling by operating below the boundary flux. On the other hand, only a few works have successfully sought to exploit super-boundary operating conditions; most super-boundary operations are reported to have led to process failures. In this work, both sub- and super-boundary operating conditions for a batch nanofiltration membrane process used for olive mill wastewater treatment were investigated. A model to identify a priori the point of transition from a sub-boundary to a super-boundary operation during a batch operation was developed, and this will provide membrane designers with a helpful tool to carefully avoid process failures. PMID:28708120
Energy Technology Data Exchange (ETDEWEB)
Fricke, Norman [AGFW Der Energieeffizienzverband fuer Waerme, Kaelte und KWK e.V., Frankfurt am Main (Germany)
2011-03-15
Often, legal regulations governing the electricity and gas industries are thought prematurely to apply to district heating as well. The author shows that the technical and economic boundary conditions of district heating are quite different in many respects. He starts by explaining the concept of district heating and analyzing its economic boundary conditions. The next instalment will follow in the next issue of EuroHeat and Power and will focus on the heat market and its legal boundary conditions.
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Guoyong Jin
2015-01-01
Full Text Available This paper presents elasticity solutions for the vibration analysis of isotropic and orthotropic open shells and plates with arbitrary boundary conditions, including spherical and cylindrical shells and rectangular plates. Vibration characteristics of the shells and plates have been obtained via a unified three-dimensional displacement-based energy formulation represented in the general shell coordinates, in which the displacement in each direction is expanded as a triplicate product of the cosine Fourier series with the addition of certain supplementary terms introduced to eliminate any possible jumps with the original displacement function and its relevant derivatives at the boundaries. All the expansion coefficients are then treated equally as independent generalized coordinates and determined by the Rayleigh-Ritz procedure. To validate the accuracy of the present method and the corresponding theoretical formulations, numerical cases have been compared against the results in the literature and those of 3D FE analysis, with excellent agreements obtained. The effects of boundary conditions, material parameters, and geometric dimensions on the frequencies are discussed as well. Finally, several 3D vibration results of isotropic and orthotropic open spherical and cylindrical shells and plates with different geometry dimensions are presented for various boundary conditions, which may be served as benchmark solutions for future researchers as well as structure designers in this field.
Ye, Xiang; Cai, Qin; Yang, Wei; Luo, Ray
2009-07-22
The wide use of lattice-sum strategies in biomolecular simulations has raised many questions on potential artifacts in these strategies. One interesting question is the artifacts in the counterion distributions of highly charged systems. As one would anticipate, Coulombic interactions under the periodic boundary condition may deviate noticeably from those under the free boundary condition in the highly charged systems, significantly influencing their counterion distributions. On the other hand, the electrostatic screening due to water molecules and mobile ions may effectively damp the possible periodic distortions in Coulombic interactions. Therefore, the magnitude of periodicity-induced artifacts in counterion distributions is not straightforward to dissect without detailed analyses. In this study, we have developed a hybrid explicit counterion/implicit salt representation of mobile ions to address this question. We have chosen a well-studied DNA for easy validation of the minimal hybrid ion representation. Our detailed analysis of continuum ion distributions, explicit ion distributions, radial counterion distribution functions, and sequence-dependent counterion distributions, however, indicates that periodicity artifacts are not apparent at the surface of the tested DNA. Nevertheless, influence of boundary conditions does show up starting at the second solvation shell and becomes apparent at the cell boundary.
Fisher, Travis C.; Carpenter, Mark H.; Nordstroem, Jan; Yamaleev, Nail K.; Swanson, R. Charles
2011-01-01
Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.
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A. Belmiloudi
2014-01-01
Full Text Available The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions J. Numerical simulations illustrate several numerical optimization methods, examples, and realistic cases, in which several interesting phenomena are observed. A large amount of computational effort is required to solve the coupled state equation and the adjoint equation (which is backwards in time, and the algebraic gradient equation (which implements the coupling between the adjoint and control variables. The state and adjoint equations are solved using the finite element method.
Wang, Ya-Guang; Yin, Jierong; Zhu, Shiyong
2017-10-01
In this paper, we will analyze the vanishing viscosity limit of the incompressible Navier-Stokes equations with the Navier slip boundary conditions in a bounded domain of R2. When the slip length is smaller than or equal to the order of viscosity, by using an energy method and developing Kato's approach given in the work of Kato [Math. Sci. Res. Inst. Publ. 2, 85-98 (1984)], we obtain several conditions to guarantee that the solution of the Navier-Stokes equations with the Navier slip boundary conditions goes to the solution of the associated problem of the Euler equations in the energy space L2 uniformly in time, as the viscosity goes to zero.
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Masood Khan
Full Text Available In the present investigation we analyze the impact of magnetic field on the stagnation-point flow of a generalized Newtonian Carreau fluid. The convective surface boundary conditions are considered to investigate the thermal boundary layer. The leading partial differential equations of the current problem are altered to a set of ordinary differential equations by picking local similarity transformations. The developed non-linear ordinary differential equations are then numerically integrated via Runge-Kutta Fehlberg method after changing into initial value problems. This investigation explores that the momentum and thermal boundary layers are significantly influenced by various pertinent parameters like the Hartmann number M, velocity shear ratio parameter α, Weissenberg number We, power law index n, Biot number γ and Prandtl number Pr. The analysis further reveals that the fluid velocity as well as the skin friction is raised by the velocity shear ratio parameter. Moreover, strong values of the Hartmann number correspond to thinning of the momentum boundary layer thickness while quite the opposite is true for the thermal boundary layer thickness. Additionally, it is seen that the numerical computations are in splendid consent with previously reported studies.
Khan, Masood; Hashim; Alshomrani, Ali Saleh
2016-01-01
In the present investigation we analyze the impact of magnetic field on the stagnation-point flow of a generalized Newtonian Carreau fluid. The convective surface boundary conditions are considered to investigate the thermal boundary layer. The leading partial differential equations of the current problem are altered to a set of ordinary differential equations by picking local similarity transformations. The developed non-linear ordinary differential equations are then numerically integrated via Runge-Kutta Fehlberg method after changing into initial value problems. This investigation explores that the momentum and thermal boundary layers are significantly influenced by various pertinent parameters like the Hartmann number M, velocity shear ratio parameter α, Weissenberg number We, power law index n, Biot number γ and Prandtl number Pr. The analysis further reveals that the fluid velocity as well as the skin friction is raised by the velocity shear ratio parameter. Moreover, strong values of the Hartmann number correspond to thinning of the momentum boundary layer thickness while quite the opposite is true for the thermal boundary layer thickness. Additionally, it is seen that the numerical computations are in splendid consent with previously reported studies.
The determination of an unknown boundary condition in a fractional diffusion equation
Rundell, William
2013-07-01
In this article we consider an inverse boundary problem, in which the unknown boundary function ∂u/∂v = f(u) is to be determined from overposed data in a time-fractional diffusion equation. Based upon the free space fundamental solution, we derive a representation for the solution f as a nonlinear Volterra integral equation of second kind with a weakly singular kernel. Uniqueness and reconstructibility by iteration is an immediate result of a priori assumption on f and applying the fixed point theorem. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method. © 2013 Copyright Taylor and Francis Group, LLC.
A Multigrid Algorithm for an Elliptic Problem with a Perturbed Boundary Condition
Bonito, Andrea
2013-01-01
We discuss the preconditioning of systems coupling elliptic operators in Ω⊂Rd, d=2,3, with elliptic operators defined on hypersurfaces. These systems arise naturally when physical phenomena are affected by geometric boundary forces, such as the evolution of liquid drops subject to surface tension. The resulting operators are sums of interior and boundary terms weighted by parameters. We investigate the behavior of multigrid algorithms suited to this context and demonstrate numerical results which suggest uniform preconditioning bounds that are level and parameter independent.
Ouerdane, H.; Apertet, Y.; Goupil, C.; Lecoeur, Ph.
2015-07-01
object of the article is thus to cover some of the milestones of thermodynamics, and show through the illustrative case of thermoelectric generators, our model heat engine, that the shift from Carnot's efficiency to efficienc ies at maximum power explains itself naturally as one considers continuity and boundary conditions carefully; indeed, as an adaptation of Friedrich Nietzche's quote, we may say that the thermodynamic demon is in the details. This article is supplemented with comments by J.M.R. Parrondo and a final reply by the authors.
Morphodynamics, boundary conditions and pattern evolution within a vegetated linear dunefield
Telfer, M. W.; Hesse, P. P.; Perez-Fernandez, M.; Bailey, R. M.; Bajkan, S.; Lancaster, N.
2017-08-01
The controls on the evolution of linear dunefields are poorly understood, despite the potential for reactivation of dunefields, which are currently stabilized by vegetation, under the influence of 21st century climate change. The relative roles of local influences (i.e. boundary conditions) and morphodynamic influences (i.e. emergent properties) remain unclear. Chronostratigraphic and sedimentological analyses were conducted on two pairs of linear dunes exhibiting different spatial patterning in the Strzelecki Desert of central Australia. It was hypothesized that morphodynamic influences, via pattern-coarsening, would mean that dunes from the simpler pattern, defined in terms of the frequency of defects (i.e. junctions and terminations), would be more mature, older landforms. Optically Stimulated Luminescence (OSL) dating of full-depth, regularly-sampled profiles was used to establish accumulation histories for the four dunes, and supported by sedimentological analysis to investigate possible compositional differences and similarities between the dunes. Whilst three of the dunes (the two more simply-patterned dunes, and one of the more complex dunes) have accumulation histories beginning between 100 ka and 150 ka, and document sporadic net accumulation throughout the last interglacial/glacial cycle to the late Holocene, one of the dunes (with relatively complex patterning) reveals that the majority of the dune accumulation (> 7 m) at that site occurred during a relatively short window at 50 ka. There is no clear sedimentological reason for the different behaviour of the younger dune. The data suggest that small-scale and essentially stochastic nature of the aeolian depositional/erosional system can overprint any large-scale morphodynamic controls. The concept of dating landscape change by pattern analysis is thus not supported by this study, and would require very careful interpretation of the scales being considered. This further suggests caution when interpreting