Search results for "Algebra"
showing 10 items of 4129 documents
Ultra-Wide Band Gap in Two-Dimensional Phononic Crystal with Combined Convex and Concave Holes
2017
A phononic crystal with an ultra‐wide band gap is proposed, whose unit cell consists of a cross‐like concave hole in the center and four square convex holes at the corners. The dispersion relations, modal kinetic energy ratio, and eigenmodes at edges of the band gaps are investigated by using the finite element method. The influence of the geometrical parameters of the convex and concave holes on the band gaps is further analyzed. After optimization, an ultra‐wide band gap with gap‐to‐midgap ratio of 156.0% is achieved, with the filling fraction keeping a relative small value. Numerical results illustrate that the combination of convex and concave holes is a practicable direction for struct…
Experimental and numerical investigation on a new FSW based metal to composite joining technique
2018
Abstract In the last decades, different techniques were proposed to join aluminum sheets with composites materials. Each of them has advantages and weak points over the others and new techniques and patents are continuously developed to overcome these difficulties. In this paper an experimental and numerical investigation on a new Friction Stir Welding based approach to mechanically join AA6082-T6 to self-reinforced polypropylene is presented. The aluminum sheet is pre-holed along both the sides of the weld line and a pinless tool generates the heat and pressure needed to prompt back-extrusion of the composite. New experimental fixtures and hole designs were investigated in order to enhance…
Analytic $JV$ -Characteristics of Ideal Intermediate Band Solar Cells and Solar Cells With Up and Downconverters
2017
The ideal diode equation is regularly used to describe the $\textit {JV}$ -characteristic of single junction solar cells. The connection between the diode equation and fundamental physics is the application of the Boltzmann approximation to describe the fluxes of photons emitted by the cell. In this paper, this approximation is used to derive analytic $\textit {JV}$ -characteristics for three photovoltaic high-efficiency concepts, intermediate band solar cells, and solar cells optically coupled to up and downconverters. These three concepts share the common feature that they allow excitation of electrons between at least three energy levels, which assures a better utilization of the solar s…
Topological two-dimensional Su–Schrieffer–Heeger analog acoustic networks: Total reflection at corners and corner induced modes
2021
In this work, we investigate some aspects of an acoustic analogue of the two-dimensional Su-Schrieffer-Heeger model. The system is composed of alternating cross-section tubes connected in a square network, which in the limit of narrow tubes is described by a discrete model coinciding with the two-dimensional Su-Schrieffer-Heeger model. This model is known to host topological edge waves, and we develop a scattering theory to analyze how these waves scatter on edge structure changes. We show that these edge waves undergo a perfect reflection when scattering on a corner, incidentally leading to a new way of constructing corner modes. It is shown that reflection is high for a broad class of edg…
On the ‘expanded local mode’ approach applied to the methane molecule: isotopic substitution CH2D2←CH4
2011
On the basis of a compilation of the ‘expanded local mode’ model and the general isotopic substitution theory, sets of simple analytical relations between different spectroscopic parameters (harmonic frequencies, ωλ, anharmonic coefficients, x λμ, ro-vibrational coefficients, , different kinds of Fermi- and Coriolis-type interaction parameters) of the CH2D2 molecule are derived. All of them are expressed as simple functions of a few initial spectroscopic parameters of the mother, CH4, molecule. Test calculations with the derived isotopic relations show that, in spite of a total absence of initial information about the CH2D2 species, the numerical results of the calculations have a very good…
Introducing Memory in Coarse-Grained Molecular Simulations
2021
[Image: see text] Preserving the correct dynamics at the coarse-grained (CG) level is a pressing problem in the development of systematic CG models in soft matter simulation. Starting from the seminal idea of simple time-scale mapping, there have been many efforts over the years toward establishing a meticulous connection between the CG and fine-grained (FG) dynamics based on fundamental statistical mechanics approaches. One of the most successful attempts in this context has been the development of CG models based on the Mori–Zwanzig (MZ) theory, where the resulting equation of motion has the form of a generalized Langevin equation (GLE) and closely preserves the underlying FG dynamics. In…
Harmonic morphisms in nonlinear potential theory
1992
This article concerns the following problem: given a family of partial differential operators with similar structure and given a continuous mapping f from an open set Ω in Rn into Rn, then when does f pull back the solutions of one equation in the family to solutions of another equation in that family? This problem is typical in the theory of differential equations when one wants to use a coordinate change to study solutions in a different environment.
Elucidating the Influence of the Activation Energy on Reaction Rates by Simulations Based on a Simple Particle Model
2020
An application for visualizing the dynamic properties of an equimolar binary mixture of isotropic reactive particles is presented. By introducing a user selectable choice for the activation energy, the application is useful to demonstrate qualitatively that the reaction rate depends on the above choice and on temperature. The application is based on a 2D realistic dynamic model where atoms move because of their thermal energies and the trajectories are determined by solving numerically Newton’s laws according to a Molecular Dynamics (MD) scheme. Collisions are monitored as time progresses, and every time the collision energy is larger than the selected activation energy, a reactive event oc…