Various Kinds Of Boundary Conditions Research Articles

Stability of a circular epitaxial island

The morphological stability of a single, epitaxially growing, circular adatom island with a radially symmetric adatom distribution is studied using a Burton–Cabrera–Frank type island dynamics model. Various kinds of boundary conditions for the adatom density that include the thermodynamic equilibrium value, line tension, and attachment–detachment kinetics, and different velocity formulas with or without the one-dimensional “surface” diffusion are examined. Rigorous analysis shows that the circular island is always stable if its normalized area A is larger than a critical value. If A is less than such a critical value, and if neither the line tension nor surface diffusion is present, then there exists a critical wavenumber k c = k c( A) such that the island is only stable for wavenumbers less than k c. When the line tension or surface diffusion is present, small islands are always stable. In particular, the Bales–Zangwill instability for straight steps due to the kinetic asymmetry does not exist for small circular islands.

複合管路系内流体過渡現象の数値的モード近似法に基づく実用的で高精度なシミュレーション法の開発 第２報 多様な境界条件に適用できる汎用ＳＭＡ法の開発

In the previous paper, the authors proposed a new simulation technique called the “system modal approximation” method (SMA method for short) for fluid transients in compound pipeline systems, which was able to predict fast and accurately, and verified superiority of this technique to other existing methods. There, however, detailed considerations were limited to the case whose transfer functions of output/input were of the form of pressure/pressure and flow-rate/flow-rate. This paper enhances the analytical functions of the SMA method so as to be widely applicable to compound pipeline systems with various kinds of boundary conditions. Specifically, the calculation methods of time response of the wanted output variables at any points are newly proposed for the case (i) whose transfer functions of output/input are of the form of pressure/flow-rate and flow-rate/pressure, and (ii) whose boundary conditions are given by the relation between pressure and flow-rate. For fluid transients in three kinds of compound pipeline systems, simulation results based on the methods mentioned above are compared with both the solutions from the method of characteristics and experimental results, and then the usefulness of the generalized SMA method is verified.

Compromise of localized graviton with a small cosmological constant in Randall–Sundrum scenario

A new mechanism which leads to a linearized massless graviton localized on the brane is found in the $AdS$/CFT setting, {\it i.e.} in a single copy of $AdS_5$ spacetime with a singular brane on the boundary, within the Randall-Sundrum brane-world scenario. With an help of a recent development in path-integral techniques, a one-parameter family of propagators for linearized gravity is obtained analytically, in which a parameter $\xi$ reflects various kinds of boundary conditions that arise as a result of the half-line constraint. In the case of a Dirichlet boundary condition ($\xi = 0$) the graviton localized on the brane can be massless {\it via} coupling constant renormalization. Our result supports a conjecture that the usual Randall-Sundrum scenario is a regularized version of a certain underlying theory.

Stability analysis of single-phase thermosyphon loops by finite-difference numerical methods

In this paper, examples of the application of finite-difference numerical methods in the analysis of stability of single-phase natural circulation loops are reported. The problem is addressed here for its relevance to thermal-hydraulic system code applications, with the aim to point out the effects of truncation error on stability prediction. The methodology adopted for analyzing in a systematic way the effect of various finite-difference discretization can be considered the numerical analogue of the usual techniques adopted for PDE stability analysis. Three different single-phase loop configurations are considered involving various kinds of boundary conditions. In one of these cases, an original dimensionless form of the governing equations is proposed, adopting the Reynolds number as a flow variable. This allows for an appropriate consideration of transition between laminar and turbulent regimes, which is not possible with other dimensionless forms, thus enlarging the range of validity of model assumptions.

Analysis of Lateral Vibration of Plates Using Analytic Solutions Discretized on Boundaries. 2nd Report. Application of Collocation Method to Various Kinds of Boundary Conditions.

Although the collocation method is the simplest among various methods of discretization, it is generally thought to be insufficient in accuracy. However, the accuracy of numerical analysis depends on the kind of function used in the solution. In this paper, the collocation method is examined in analyses of the lateral vibrations of square, trapezoidal and elliptic plates. The boundary conditions treated here are clamped, simply supported, free and combinations of the aforementioned. A general solution of the governing equation is expressed in terms of the Bessel and modified Bessel functions. Comparison of the calculated natural frequencies with the exact values or the approximate values which have been obtained so far shows very good agreement. This means that the collocation method can be applied widely in plate vibration analyses.

Residual Cutting Method for Elliptic Boundary Value Problems. Application to Poisson's Equation.

A new, efficient and accurate numerical method which consists of perturbed residual equation and residual L2 norm minimization is proposed for boundary value problems of elliptic partial differential equations. For example, Neumann, Dirichlet and mixed boundary value problems in a three dimensional Poisson's equation for the pressure in curved duct flow and cascade flow, are solved. Numerical results demonstrate the effectiveness, robustness and a high convergence rate of this method. Residual Cutting Method is expected to be the numerical solution method applicable to a wide range of partial differential equations with various kinds of boundary conditions.

Eulerian-Lagrangian localized adjoint methods for a nonlinear advection-diffusion equation

Eulerian-Lagrangian localized adjoint methods (ELLAM) are developed for the nonlinear Buckley-Leverett equation, which is characterized by degenerate diffusion and sharpening near-shock solutions. The ELLAM methodology employs space-time finite elements with edges oriented along flow paths, and space-time test functions that satisfy a local adjoint condition. This combination extends Eulearian-Lagrangian concepts in a systematic mass-conservative fashion to problems with general boundary conditions. Various kinds of boundary conditions are considered, and a local time-stepping procedure is developed for a no-flow outlet condition that leads to a boundary layer. Numerical experiments illustrate the potential of these methods.

Active Wave Control of a Flexible Beam. On the Power Flow Control.

This paper deals with the active vibration control of a flexible beam with various kinds of boundary conditions. It is the purpose of this paper to investigate the relationship between the power flow and the vibrational energy accumulated in the beam. First, from the viewpoint of the conventional feedforward control method, the role of the power flow to suppress the vibrational energy is discussed. Next, by using a transfer matrix method, this paper derives the control law of the active sink method whose principle has been presented in the previous paper. Then, it is shown that all the vibration modes of a beam with arbitrary boundary conditions are suppressed by the active sink method. It is also shown that the power flow due to the active sink method is different from that of an infinite beam. Furthermore, this paper points out that there exist notches in the frequency characteristics of the power flow, and these are independent of vibration modes. Finally, an experiment is carried out to verify the existence of the active sink.

Noise spectra resulting from diffusion processes in a cylindrical geometry

A discussion is presented of noise spectra resulting from diffusion in a cylindrical domain D s with volume sources and sinks in the domain, subject to various kinds of boundary conditions at the surface of D s , including the case that D s is part of an infinite domain D. This applies to various physical processes, e.g.: (i) fluctuations caused by diffusion and recombination at the walls in a gaseous plasma; (ii) carrier fluctuations in a solid involving diffusion, surface recombination and volume recombination; (iii) temperature or energy fluctuations in cylindrical bars with spontaneous radiation at the boundaries; (iv) problems involving contact noise. The spectral densities are derived from the relevant Green's functions. For the infinite domain an extension of the Macfarlane-Burgess spectrum is obtained, which yields spectra such as are often observed in insulators with a small photoconductive layer (CdS in band-band absorption). The finite domain case leads to three kinds of spectra (diffusion-limited, surface-limited and volume-limited) analogous to the one dimensional solutions obtained before. The details of these spectra, especially the characteristic break points, are discussed.