Search results for "Boundary value problem"
showing 10 items of 551 documents
Exact analytic expressions for electromagnetic propagation in a finite one-dimensional periodic multilayer
2004
Translation Matrix Formalism has been used to find an exact analytic solution for light propagation in a finite one-dimensional (1-D) periodic stratified structure. This modal approach allows to derive a closed formula for the electric field in every point of the structure, by simply imposing a convenient form for the boundary conditions. As an example it is also shown how to extend this result to gratings featuring defects.
Two-Dimensional Differential Systems with Asymmetric Principal Part
2013
We consider the Sturm–Liouville nonlinear boundary value problem $$\displaystyle\begin{array}{rcl} \left \{\begin{array}{l} x^{\prime} = f(t,y) + u(t,x,y),\\ y^{\prime} = -g(t, x) + v(t, x, y), \end{array} \right.& & {}\\ \begin{array}{l} x(0)\cos \alpha - y(0)\sin \alpha = 0,\\ x(1)\cos \beta - y(1)\sin \beta = 0, \end{array} & & {}\\ \end{array}$$ assuming that the limits \(\lim _{y\rightarrow \pm \infty }\frac{f(t,y)} {y} = f_{\pm }\), \(\lim _{x\rightarrow \pm \infty }\frac{g(t,x)} {x} = g_{\pm }\) exist. Nonlinearities u and v are bounded. The system includes various cases of asymmetric equations (such as the Fucik one). Two classes of multiplicity results are discussed. The first one …
Long Lived Acoustic Vibrational Modes of an Embedded Nanoparticle
2004
Classical continuum elastic calculations show that the acoustic vibrational modes of an embedded nanoparticle can be lightly damped even when the longitudinal plane wave acoustic impedances $Z_o=\rho v_L$ of the nanoparticle and the matrix are the same. It is not necessary for the matrix to be less dense or softer than the nanoparticle in order to have long lived vibrational modes. Continuum boundary conditions do not always accurately reflect the microscropic nature of the interface between nanoparticle and matrix, and a multi-layer model of the interface reveals the possibility of additional reduction of mode damping.
New Boundary-Driven Twist States in Systems with Broken Spatial Inversion Symmetry
2017
A full description of a magnetic sample includes a correct treatment of the boundary conditions (BCs). This is in particular important in thin film systems, where even bulk properties might be modified by the properties of the boundary of the sample. We study generic ferromagnets with broken spatial inversion symmetry and derive the general micromagnetic BCs of a system with Dzyaloshinskii-Moriya interaction (DMI). We demonstrate that the BCs require the full tensorial structure of the third-rank DMI tensor and not just the antisymmetric part, which is usually taken into account. Specifically, we study systems with $C_{\infty v}$ symmetry and explore the consequences of the DMI. Interesting…
DMRG Investigation of Stripe Formation in Doped Hubbard Ladders
2005
Using a parallelized density matrix renormalization group (DMRG) code we demonstrate the potential of the DMRG method by calculating ground-state properties of two-dimensional Hubbard models. For 7 × 6, 11 × 6 and 14 × 6 Hubbard ladders with doped holes and cylindrical boundary conditions (BC), open in x-direction and periodic in the 6-leg y-direction, we comment on recent conjectures about the appearance of stripe-like features in the hole and spin densities. In addition we present results for the half-filled 4 ×4 system with periodic BC, advance to the 6 × 6 case and pinpoint the limits of the current approach.
Coupled plasmonic graphene wires: theoretical study including complex frequencies and field distributions of bright and dark surface plasmons
2020
Theoretical research on localized surface plasmons (LSPs) supported by a structure formed by two parallel dielectric wires with a circular cross section wrapped with a graphene sheet has an impact in the practical realm. Here, LSPs are represented in the form of an infinite series of cylindrical multipole partial waves linked to each of the graphene wires. To obtain the kinematics (complex eigenfrequencies) and dynamic characteristics (field distributions) of the LSPs, we consider the analytic extension to the complex plane of the solution to the boundary value problem. The lower frequency LSP group is formed by four branches, two of them corresponding to bright modes and the others to dark…
Anisotropic interfacial tension, contact angles, and line tensions: A graphics-processing-unit-based Monte Carlo study of the Ising model
2014
As a generic example for crystals where the crystal-fluid interface tension depends on the orientation of the interface relative to the crystal lattice axes, the nearest neighbor Ising model on the simple cubic lattice is studied over a wide temperature range, both above and below the roughening transition temperature. Using a thin film geometry $L_x \times L_y \times L_z$ with periodic boundary conditions along the z-axis and two free $L_x \times L_y$ surfaces at which opposing surface fields $\pm H_{1}$ act, under conditions of partial wetting, a single planar interface inclined under a contact angle $\theta < \pi/2$ relative to the yz-plane is stabilized. In the y-direction, a generaliza…
Properties of the Ising magnet confined in a corner geometry
2007
Abstract The properties of Ising square lattices with nearest neighbor ferromagnetic exchange confined in a corner geometry, are studied by means of Monte Carlo simulations. Free boundary conditions at which boundary magnetic fields ± h are applied, i.e., at the two boundary rows ending at the lower left corner a field + h acts, while at the two boundary rows ending at the upper right corner a field − h acts. For temperatures T less than the critical temperature T c of the bulk, this boundary condition leads to the formation of two domains with opposite orientation of the magnetization direction, separated by an interface which for T larger than the filling transition temperature T f ( h ) …
Contribution of the normal component to the thermal resistance of turbulent liquid helium
2015
Previous results for the velocity profile of the normal component of helium II in counterflow are used to evaluate the viscous contribution to the effective thermal resistance. It turns out that such a contribution becomes considerably higher than the usual Landau estimate, because in the presence of vortices, the velocity profile is appreciably different from the Poiseuille parabolic profile. Thus, a marked increase in the contribution of the normal component to the thermal resistance with respect to the viscous Landau estimate does not necessarily imply that the normal component is turbulent. Furthermore, we examine the influence of a possible slip flow along the walls when the radius of …
Fractional mechanical model for the dynamics of non-local continuum
2009
In this chapter, fractional calculus has been used to account for long-range interactions between material particles. Cohesive forces have been assumed decaying with inverse power law of the absolute distance that yields, as limiting case, an ordinary, fractional differential equation. It is shown that the proposed mathematical formulation is related to a discrete, point-spring model that includes non-local interactions by non-adjacent particles with linear springs with distance-decaying stiffness. Boundary conditions associated to the model coalesce with the well-known kinematic and static constraints and they do not run into divergent behavior. Dynamic analysis has been conducted and both…