Presence Of Boundary Conditions Research Articles

Homotopy Analysis Solution to Thermal Radiation Effects on MHD Boundary Layer Flow and Heat Transfer Towards an Inclined Plate with Convective Boundary Conditions

This paper investigates the Magnetohydrodynamic flow and heat transfer towards a stationary/moving plate with convective boundary conditions in presence of thermal radiation. The governing equations are simplified by similarity transformations which are then solved by homotopy analysis method (HAM). Effects of emerging parameters such as Prandtl number, local Grashof number, Magnetic parameter, Radiation parameter and the Biot number on the velocity field and temperature field are plotted and discussed. It is found that the temperature of the stationary flat plate is higher than the temperature of the moving flat plate. The obtained results are compared with other results obtain in previous works so that the high accuracy of the present result is apparent.

An unsteady double-diffusive natural convection in an inclined enclosures filled with porous medium with non-uniform boundary conditions in presence of thermal radiation

An unsteady double-diffusive natural convection in an inclined enclosures filled with porous medium with non-uniform boundary conditions in presence of thermal radiation

On the compatibility equations of nonlinear and linear elasticity in the presence of boundary conditions

We use Hodge-type orthogonal decompositions for studying the compatibility equations of the displacement gradient and the linear strain with prescribed boundary displacements. We show that the displacement gradient is compatible if and only if for any equilibrated virtual first Piola–Kirchhoff stress tensor field, the virtual work done by the displacement gradient is equal to the virtual work done by the prescribed boundary displacements. This condition is very similar to the classical compatibility equations for the linear strain. Since these compatibility equations for linear and nonlinear strains involve infinite-dimensional spaces and consequently are not easy to use in practice, we derive alternative compatibility equations, which are written in terms of some finite-dimensional spaces and are more useful in practice. Using these new compatibility equations, we present some non-trivial examples that show that compatible strains may become incompatible in the presence of prescribed boundary displacements.

Boundary conditions and the Wigner equation solution

We consider the existence and uniqueness of the solution of the Wigner equation in the presence of boundary conditions. The equation, describing electron transport in nanostructures, is analyzed in terms of the Neumann series expansion of the corresponding integral form, obtained with the help of classical particle trajectories. It is shown that the mathematical aspects of the solution can not be separated from the physical attributes of the problem. In the presented analysis these two sides of the problem mutually interplay, which is of importance for understanding of the peculiarities of Wigner-quantum transport. The problem is first formulated as the long time limit of a general evolution process posed by initial and boundary conditions. Then the Wigner equation is reformulated as a second kind of a Fredholm integral equation which is of Volterra type with respect to the time variable. The analysis of the convergence of the corresponding Neumann series, sometimes called Liouville---Neumann series, relies on the assumption for reasonable local conditions obeyed by the kernel.

Energy level shifts of a uniformly accelerated atom in the presence of boundary conditions

We discuss the radiative level shifts of an atom moving with uniform acceleration near an infinite reflecting plate. We first consider the case of a two-level system interacting with a massless scalar field in the vacuum state. The acceleration of the two-level atom is supposed in a direction parallel to the conducting plate. We evaluate the contribution of vacuum fluctuations and of the radiation reaction field to the energy shift of the atomic levels, and discuss their behaviour as a function of the atomic acceleration and of the atom-plate distance. Then, we investigate the more general case of an hydrogen atom accelerating near a perfectly reflecting plate and interacting with the electromagnetic field in the vacuum state.

Casimir-Polder interatomic potential between two atoms at finite temperature and in the presence of boundary conditions

We evaluate the Casimir-Polder potential between two atoms in the presence of an infinite perfectly conducting plate and at nonzero temperature. In order to calculate the potential, we use a method based on equal-time spatial correlations of the electric field, already used to evaluate the effect of boundary conditions on interatomic potentials. This method also gives a transparent physical picture of the role of a finite temperature and boundary conditions on the Casimir-Polder potential. We obtain an analytical expression of the potential both in the near and far zones, and consider several limiting cases of interest, according to the values of the parameters involved, such as atom-atom distance, atoms-wall distance, and temperature.

Field fluctuations near a conducting plate and Casimir-Polder forces in the presence of boundary conditions

We consider vacuum fluctuations of the quantum electromagnetic field in the presence of an infinite and perfectly conducting plate. We evaluate how the change of vacuum fluctuations due to the plate modifies the Casimir-Polder potential between two atoms placed near the plate. We use two different methods to evaluate the Casimir-Polder potential in the presence of the plate. They also give new insights on the role of boundary conditions in the Casimir-Polder interatomic potential, as well as indications for possible generalizations to more complicated boundary conditions.

Existence result for a third-order ODE with nonlinear boundary conditions in presence of a sign-type Nagumo control

In this work we provide an existence and location result for the third-order nonlinear differential equation u ‴ ( t ) = f ( t , u ( t ) , u ′ ( t ) , u ″ ( t ) ) , where f : [ a , b ] × R 3 → R is a continuous function, and two types of boundary conditions: u ( a ) = A , ϕ ( u ′ ( b ) , u ″ ( b ) ) = 0 , u ″ ( a ) = B , or u ( a ) = A , ψ ( u ′ ( a ) , u ″ ( a ) ) = 0 , u ″ ( b ) = C , with ϕ , ψ : R 2 → R continuous functions, monotonous in the second variable and A , B , C ∈ R . We assume that f satisfies a sign-type Nagumo condition which allows an asymmetric unbounded behaviour on the nonlinearity. The arguments used concern Leray–Schauder degree theory and lower and upper solutions technique.

The Roles of the Horizontal Component of the Earth's Angular Velocity in Nonhydrostatic Linear Models

Abstract Roles of the horizontal component of the earth's rotation, which is neglected traditionally in atmospheric and oceanographic models, are studied through the normal mode analysis of a compressible and stratified model on a tangent plane in the domain that is periodic in the zonal and meridional directions but bounded at the top and bottom. As expected, there exist two distinct kinds of acoustic and buoyancy oscillations that are modified by the earth's rotation. When the cos(latitude) Coriolis terms are included, there exists another kind of wave oscillation whose frequencies are very close to the inertial frequency, 2Ω sin(latitude), where Ω is the earth's angular velocity. The objective of this article is to clarify the circumstance in which a distinct kind of wave oscillation emerges whose frequencies are very close to the inertial frequency. Because this particular kind of normal mode appears only due to the presence of boundary conditions in the vertical, it may be appropriate to call these w...

Symmetry breaking boundary conditions and WZW orbifolds

Symmetry breaking boundary conditions for WZW theories are discussed. We derive explicit formulae for the reflection coefficients in the presence of boundary conditions that preserve only an orbifold subalgebra with respect to an involutive automorphism of the chiral algebra. The characters and modular transformations of the corresponding orbifold theories are computed. Both inner and outer automorphisms are treated.

Anomalous diffusion in presence of boundary conditions

Anomalous diffusion in presence of a (fractal) boundary is investigated. Asymptotic behaviour of the survival probability and current through an absorbing boundary are exactly calculated in specific examples. They agree with recent findings related with anomalous Warburg impedance experiments. The autocorrelation function for sites near the boundary is carefully discussed; in presence of reflecting boundary conditions it can be different from the (spatial) average of the autocorrelation at variance with the normal diffusion case. Interesting issues from a methodological point of view are discussed in the renormalization groups analysis. Scaling arguments are given relating various exponents

Electric energy and forces in the presence of boundary conditions

Energy and forces in boundary value problems of electrostatics are considered. It is well known that when boundary conditions can be simulated by electrical images, care must be taken in evaluating forces from energy. In this article, it is shown how the energy has to be corrected, in the general case, in order to be used as a force potential. Physical meaning of this correction is analyzed.

Finite element analysis of the stability of multilayer elastomeric bearings

The stability of multilayer elastomeric bearings is considered within the framework of two-dimensional finite elasticity. For this purpose, simple constitutive equations which generalize those of a transversally isotropic linear elastic solid are considered. A finite element formulation is discussed which is capable of accounting for very general boundary conditions. For moderate deflections and classical boundary conditions this formulation leads to numerical results in close correspondence with those obtained by Haringx's one-dimensional treatment. It is shown that the presence of boundary conditions in the form of unilateral constraints explains a softening effect which has been experimentally observed during the testing of this type of composite column. Experimental results are also presented which indicate that this softening effect is not produced by a form of material instability. These experimental results provide further justification for the simple constitutive model adopted.