Extra Boundary Conditions Research Articles

Boundary Conditions in Case of Spatial Resonance Dispersion

A simple model accounting for the influence of a surface on polariton waves is introduced. From this the extra boundary condition needed in case of a dispersive resonance is derived. The general result is discussed in relation to actual resonances in crystals. The theory of bulk waves and their boundary conditions is extended to include two or more dispersive resonances. The behavior of the measured exciton lines in ZnO agrees well with the computed spectra.

移流型方程式およびプリミティヴ方程式の数値解を求める際, 境界条件によって生ずる誤差

The boundary errors in numerical integrations of hydrodynamical equations are discussed. If the advective type equation is solved on an open domain, adopting centered difference scheme, an extra boundary condition is needed at the outflow point and it brings some errors. It is shown that these errors result from the false reflection of a computational mode wave, synchronized with the incident physical wave. By assuming the situation that in a semi-infinite domain, the incident physical wave and the reflected suprious wave are in balanced state, the rate of reflection of the computational mode is estimated. It was found that if the quantity at the outflow boundary point is extrapolated from the interior of the domain with l-th order continuity, the reflection rate is tan (l+1)(p/2), +where p is the wave number of the incident wave measured in grid unit.The same method of analysis is applied to the examination of boundary conditions of primitive equations. It was revealed that adopting some boundary conditions, the reflection rates of computational mode of gravity wave exceed unity, while a certain condition does not bring artificial reflection at all. Discussions are made about the differences between the Platzman's analyses (1954) and the present results.

A "SELF-CONSISTENT SOLUTION" METHOD FOR DETERMINING THE ELECTRICAL CONDUCTIVITY IN THE SUBSURFACE REGIONS OF THE EARTH

The assumptions on which the so-called magneto-telluric method to determine the subsurface conductivity of the earth is based are examined and it is shown how the method can be revised to get rid of those assumptions which are not necessarily legitimate. The principle of this revised or generalized magneto-telluric method is that the magnetic and telluric field components which observation can provide over the entire surface of the earth are more than sufficient viewed as boundary conditions to determine the electromagnetic field inside the earth with a prescribed conductivity distribution and, therefore, the extra boundary conditions can be consistent with each other only by the correctly prescribed (or chosen) distribution of electrical conductivity. The purely magnetic method to determine the conductivity, which relies on the assumption that the magnetic field in space above the surface of the earth, is a potential field, is also revised to free it of the assumption which, does not hold true unconditionally.

On an Explicit Method for the Solution of a Stefan Problem

The problem has a simple physical interpretation. as given by Evans, Isaacson and Macdonald [6]. Consider a bar of length L, made of a substance which undergoes a change in crystalline structure at a certain critical temperature, which we denote by To. Assume that this change involves a latent heat of recrystallization, and that the cross-section of the bar does not vary along its length. Let the bar be preheated in such a manner that its initial temperature is To throughout, and so that it is originally in the crystalline form corresponding to the lower energy state. If a constant heat source is applied at one end of the bar, recrystallization will occur, and a boundary line will be propagated along the bar separating the recrystallized segment and that portion which remains in its original state. After an appropriate choice of units for temperature, time, heat, and length, the motion of the interface and the temperature of the bar at any time t ? 0 will satisfy (1.1), as long as x(t) is less than the length of the bar. For the sake of convenience, we may assume L = o , for if the bar should ever be completely recrystallized, the question of finding its temperature reduces to a classical, linear, heat flow problem. Problems such as this, involving the solution of a parabolic equation subject to an extra boundary condition (1.le) which defines the position of the unknown boundary, have been treated in the recent literature under the name of Stefan problems [1, 2, 3, 4, 5, 6, 11, 12]. Evans [5], Rubin-