Search results for "boundary"
showing 10 items of 1626 documents
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.
Approximate Modeling of Spherical Membrane
2010
Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical systems, using revised periodic boundary conditions adapted to spherical symmetry. Method reduces computational costs by orders of magnitude, and is applicable for both solid and liquid membranes, provided the curvature is sufficiently small. We demonstrate the method by calculating the bending and Gaussian curvature moduli of single- and multi-layer graphene. Method works with any interaction (ab initio, classical interactions), with any approach (molecular …
Self-similarity and scaling of thermal shock fractures
2013
The problem of crack pattern formation due to thermal shock loading at the surface of half-space is solved numerically using two-dimensional boundary element method. The results of numerical simulations with 100-200 random simultaneously growing and interacting cracks are used to obtain scaling relations for crack length and spacing. The numerical results predict that such process of pattern formation with quasi-static crack growth is not stable and at some point the excess energy leads to unstable propagation of one of the longest crack. The onset of instability has also been determined from numerical results.
Revised periodic boundary conditions: Fundamentals, electrostatics, and the tight-binding approximation
2011
Many nanostructures today are low-dimensional and flimsy, and therefore get easily distorted. Distortion-induced symmetry-breaking makes conventional, translation-periodic simulations invalid, which has triggered developments for new methods. Revised periodic boundary conditions (RPBC) is a simple method that enables simulations of complex material distortions, either classically or quantum-mechanically. The mathematical details of this easy-to-implement approach, however, have not been discussed before. Therefore, in this paper we summarize the underlying theory, present the practical details of RPBC, especially related to a non-orthogonal tight-binding formulation, discuss selected featur…
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…
Limits of lateral expansion in two-dimensional materials with line defects
2021
The flexibility of two-dimensional (2D) materials enables static and dynamic ripples that are known to cause lateral contraction, shrinking of the material boundary. However, the limits of 2D materials' \emph{lateral expansion} are unknown. Therefore, here we discuss the limits of intrinsic lateral expansion of 2D materials that are modified by compressive line defects. Using thin sheet elasticity theory and sequential multiscale modeling, we find that the lateral expansion is inevitably limited by the onset of rippling. The maximum lateral expansion $\chi_{max}\approx 2.1\cdot t^2\sigma_d$, governed by the elastic thickness $t$ and the defect density $\sigma_d$, remains typically well belo…
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…
The Impact of a Finite Waveguide Work Function on Resonant Tunneling
2021
To describe electron transport in a waveguide, we assume that the electron wave functions vanish at the waveguide boundary. This means that, being in the waveguide, an electron can not cross the waveguide boundary because of the infinite potential barrier. In reality, the assumption has never been fulfilled: generally, electrons can penetrate through the waveguide boundary and go some distance away from the waveguide. Therefore, we have to clarify how this phenomenon affects the resonant tunneling.
Unified model of fractal conductance fluctuations for diffusive and ballistic semiconductor devices
2006
We present an experimental comparison of magnetoconductance fluctuations measured in the ballistic, quasiballistic, and diffusive scattering regimes of semiconductor devices. In contradiction to expectations, we show that the spectral content of the magnetoconductance fluctuations exhibits an identical fractal behavior for these scattering regimes and that this behavior is remarkably insensitive to device boundary properties. We propose a unified model of fractal conductance fluctuations in the ballistic, quasiballistic, and diffusive transport regimes, in which the generic fractal behavior is generated by a subtle interplay between boundary and material-induced chaotic scattering events.