1,617 research outputs found
-theory of damped wave equations with stabilisation
The aim of this note is to extend the energy decay estimates from [J. Wirth,
J. Differential Equations 222 (2006) 487--514] to a broader class of
time-dependent dissipation including very fast oscillations. This is achieved
using stabilisation conditions on the coefficient in the spirit of [F.
Hirosawa, Math. Ann. 339/4 (2007) 819--839].Comment: 13 page
Magnonic Quadrupole Topological Insulator in Antiskyrmion Crystals
When the crystalline symmetries that protect a higher-order topological phase
are not preserved at the boundaries of the sample, gapless hinge modes or
in-gap corner states cannot be stabilized. Therefore, careful engineering of
the sample termination is required. Similarly, magnetic textures, whose quantum
fluctuations determine the supported magnonic excitations, tend to relax to new
configurations that may also break crystalline symmetries when boundaries are
introduced. Here we uncover that antiskyrmion crystals provide an
experimentally accessible platform to realize a magnonic topological quadrupole
insulator, whose hallmark signature are robust magnonic corner states.
Furthermore, we show that tuning an applied magnetic field can trigger the
self-assembly of antiskyrmions carrying a fractional topological charge along
the sample edges. Crucially, these fractional antiskyrmions restore the
symmetries needed to enforce the emergence of the magnonic corner states. Using
the machinery of nested Wilson loops, adapted to magnonic systems supported by
noncollinear magnetic textures, we demonstrate the quantization of the bulk
quadrupole moment, edge dipole moments, and corner charges
The influence of oscillations on energy estimates for damped wave models with time-dependent propagation speed and dissipation
The aim of this paper is to derive higher order energy estimates for
solutions to the Cauchy problem for damped wave models with time-dependent
propagation speed and dissipation. The model of interest is \begin{equation*}
u_{tt}-\lambda^2(t)\omega^2(t)\Delta u +\rho(t)\omega(t)u_t=0, \quad
u(0,x)=u_0(x), \,\, u_t(0,x)=u_1(x). \end{equation*} The coefficients
and are shape functions and
is an oscillating function. If and
is an "effective" dissipation term, then energy
estimates are proved in [2]. In contrast, the main goal of the present paper is
to generalize the previous results to coefficients including an oscillating
function in the time-dependent coefficients. We will explain how the interplay
between the shape functions and oscillating behavior of the coefficient will
influence energy estimates.Comment: 37 pages, 2 figure
Global solvability for semi-discrete Kirchhoff equation
In this paper, we consider the global solvability and energy conservation for
initial value problem of nonlinear semi-discrete wave equation of Kirchhoff
type, which is a discretized model of Kirchhoff equation
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