اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDesign of a mode converter using thin resonant ligaments
170
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The goal of this work is to design an acoustic mode converter. More precisely, the wave number is chosen so that two modes can propagate. We explain how to construct geometries such that the energy of the modes is completely transmitted and additionally the mode 1 is converted into the mode 2 and conversely. To proceed, we work in a symmetric waveguide made of two branches connected by two thin ligaments whose lengths and positions are carefully tuned. The approach is based on asymptotic analysis for thin ligaments around resonance lengths. We also provide numerical results to illustrate the theory.
قيم البحث
اقرأ أيضاً
We consider the propagation of time harmonic acoustic waves in a device with three channels. The wave number is chosen such that only the piston mode can propagate. The main goal of this work is to present a geometry which can serve as an energy dist
ributor. More precisely, the geometry is first designed so that for an incident wave coming from one channel, the energy is almost completely transmitted in the two other channels. Additionally, tuning a bit two geometrical parameters, we can control the ratio of energy transmitted in the two channels. The approach is based on asymptotic analysis for thin slits around resonance lengths. We also provide numerical results to illustrate the theory.
We consider the propagation of acoustic waves in a 2D waveguide unbounded in one direction and containing a compact obstacle. The wavenumber is fixed so that only one mode can propagate. The goal of this work is to propose a method to cloak the obsta
cle. More precisely, we add to the geometry thin outer resonators of width $varepsilon$ and we explain how to choose their positions as well as their lengths to get a transmission coefficient approximately equal to one as if there were no obstacle. In the process we also investigate several related problems. In particular, we explain how to get zero transmission and how to design phase shifters. The approach is based on asymptotic analysis in presence of thin resonators. An essential point is that we work around resonance lengths of the resonators. This allows us to obtain effects of order one with geometrical perturbations of width $varepsilon$. Various numerical experiments illustrate the theory.
In this paper, we study the thin-film limit of the micromagnetic energy functional in the presence of bulk Dzyaloshinskii-Moriya interaction (DMI). Our analysis includes both a stationary $Gamma$-convergence result for the micromagnetic energy, as we
ll as the identification of the asymptotic behavior of the associated Landau-Lifshitz-Gilbert equation. In particular, we prove that, in the limiting model, part of the DMI term behaves like the projection of the magnetic moment onto the normal to the film, contributing this way to an increase in the shape anisotropy arising from the magnetostatic self-energy. Finally, we discuss a convergent finite element approach for the approximation of the time-dependent case and use it to numerically compare the original three-dimensional model with the two-dimensional thin-film limit.
The exact distributed controllability of the semilinear wave equation $y_{tt}-y_{xx} + g(y)=f ,1_{omega}$, assuming that $g$ satisfies the growth condition $vert g(s)vert /(vert svert log^{2}(vert svert))rightarrow 0$ as $vert svert rightarrow infty$
and that $g^primein L^infty_{loc}(mathbb{R})$ has been obtained by Zuazua in the nineties. The proof based on a Leray-Schauder fixed point argument makes use of precise estimates of the observability constant for a linearized wave equation. It does not provide however an explicit construction of a null control. Assuming that $g^primein L^infty_{loc}(mathbb{R})$, that $sup_{a,bin mathbb{R},a eq b} vert g^prime(a)-g^{prime}(b)vert/vert a-bvert^r<infty $ for some $rin (0,1]$ and that $g^prime$ satisfies the growth condition $vert g^prime(s)vert/log^{2}(vert svert)rightarrow 0$ as $vert svert rightarrow infty$, we construct an explicit sequence converging strongly to a null control for the solution of the semilinear equation. The method, based on a least-squares approach guarantees the convergence whatever the initial element of the sequence may be. In particular, after a finite number of iterations, the convergence is super linear with rate $1+r$. This general method provides a constructive proof of the exact controllability for the semilinear wave equation.
Various degenerate diffusion equations exhibit a waiting time phenomenon: Dependening on the flatness of the compactly supported initial datum at the boundary of the support, the support of the solution may not expand for a certain amount of time. We
show that this phenomenon is captured by particular Lagrangian discretizations of the porous medium and the thin-film equations, and we obtain suffcient criteria for the occurrence of waiting times that are consistent with the known ones for the original PDEs. Our proof is based on estimates on the fluid velocity in Lagrangian coordinates. Combining weighted entropy estimates with an iteration technique `a la Stampacchia leads to upper bounds on free boundary propagation. Numerical simulations show that the phenomenon is already clearly visible for relatively coarse discretizations.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
