Nonlocal Damping Research Articles

On weak solutions for a nonlocal model with nonlocal damping term

In this paper, we consider a linear bond-based peridynamic nonlocal evolution problem with the nonlocal viscoelastic damping term, the existence, uniqueness, and continuous dependence upon datum of a weak solution are proved by Galerkin methods. Together with energy inequality, we establish the regularity results of weak solutions in time. In addition, we also briefly analyze the limit behavior of the weak solution as δ→0, and find that its limit function solves the corresponding classical local evolution problem exactly in the sense of distributions. Under more stronger regularity conditions for solutions, the solution of the nonlocal evolution problem strongly converges to the solution of the corresponding classical local problem only in the interior of domain Ω.

Halevi's extension of the Euler-Drude model for plasmonic systems

The nonlocal response of plasmonic materials and nanostructures is often described within a hydrodynamic approach, which is based on the Euler-Drude equation. In this paper, we reconsider this approach within an extension proposed by Halevi [Phys. Rev. B 51, 7497 (1995)]. After discussing the impact of this extended model on the propagation of longitudinal volume modes, we reevaluate within this framework the Mie scattering coefficients for a cylinder and the corresponding plasmon-polariton resonances. Our analysis reveals a nonlocal, collisional, and size-dependent damping term, which influences the resonances in the extinction spectrum. A transfer of the Halevi model into the time domain allows to identify a contribution to the current, which shares similarities with Cattaneo-kind diffusive-wavelike dynamics. After a comparison to other approaches commonly used in the literature, we implement the Halevi model into the discontinuous-Galerkin time-domain finite-element Maxwell solver and identify an oscillatory contribution to the current. Such an implementation of the Halevi model in time domain is of particular importance for applications in nanoplasmonics where nanogap structures and other nanoscale features have to be modeled efficiently and accurately.

Global well-posedness and optimal decay rates for a transmission problem of viscoelastic wave equations with degenerate nonlocal damping

Global well-posedness and optimal decay rates for a transmission problem of viscoelastic wave equations with degenerate nonlocal damping

Unidirectional magnetic coupling induced by chiral interaction and nonlocal damping

We show that an interlayer Dzyaloshinskii-Moriya interaction in combination with nonlocal damping gives rise to unidirectional magnetic coupling. That is, the coupling between two magnetic layers---say, the left and right layer---is such that the dynamics of the left layer leads to the dynamics of the right layer, but not vice versa. We discuss the implications of this result for the magnetic susceptibility of a magnetic bilayer, electrically actuated spin-current transmission, and unidirectional spin-wave packet generation and propagation. Our results may enable a route towards spin-current and spin-wave diodes and further pave the way to design spintronic devices via reservoir engineering.

Asymptotic behavior of the wave equation with nonlocal weak damping, anti-damping and critical nonlinearity

<p style='text-indent:20px;'>In this paper, we prove the existence of the global attractor for the wave equation with nonlocal weak damping, nonlocal anti-damping and critical nonlinearity.</p>

On a beam model with degenerate nonlocal nonlinear damping

<p style='text-indent:20px;'>This paper contains results about the existence, uniqueness and stability of solutions for the damped nonlinear extensible beam equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ u_{tt}+\Delta ^2u-M(\|\nabla u(t)\|^2)\Delta u+\|\Delta u(t)\|^{2\alpha}\,|u_t|^{\gamma}u_t = 0\ \mbox{ in } \ \Omega \times \mathbb{R}^+, $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ \alpha>0 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ \gamma\ge 0 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M3">\begin{document}$ \Omega\subset \mathbb{R}^n $\end{document}</tex-math></inline-formula> is a bounded domain with smooth boundary <inline-formula><tex-math id="M4">\begin{document}$ \Gamma = \partial \Omega $\end{document}</tex-math></inline-formula>, and <inline-formula><tex-math id="M5">\begin{document}$ M $\end{document}</tex-math></inline-formula> is a nonlocal function that represents beam's extensibility term. The novelty of the work is to consider the damping as a product of a degenerate and nonlocal term with a nonlinear function. This work complements the recent article by Cavalcanti et al. [<xref ref-type="bibr" rid="b8">8</xref>] who treated this model with degenerate nonlocal weak (and strong) damping. The main result of the work is to show that for regular initial data the energy associated with the problem proposed goes to zero when <inline-formula><tex-math id="M6">\begin{document}$ t $\end{document}</tex-math></inline-formula> goes to infinity.</p>

The well-posedness and attractor on an extensible beam equation with nonlocal weak damping

<p style='text-indent:20px;'>In this paper, we consider some new results on the well-posedness and the asymptotic behavior of the solutions for a class of extensible beams equation with the nonlocal weak damping and nonlinear source terms. Our contribution is threefold. First, we establish the well-posedness by means of the monotone operator theory with locally Lipschitz perturbation. Then we show that the related solution semigroup <inline-formula><tex-math id="M1">\begin{document}$ \{S_{t}\}_{t\geq0} $\end{document}</tex-math></inline-formula> in phase space <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{H} $\end{document}</tex-math></inline-formula> has a finite-dimensional global attractor <inline-formula><tex-math id="M3">\begin{document}$ \mathcal{A} $\end{document}</tex-math></inline-formula> which has some regularity when the growth exponent of the nonlinearity <inline-formula><tex-math id="M4">\begin{document}$ f(u) $\end{document}</tex-math></inline-formula> is up to the subcritical and critical case, respectively. Finally, we obtain the exponential attractor <inline-formula><tex-math id="M5">\begin{document}$ \mathcal{A}_{exp} $\end{document}</tex-math></inline-formula> of the dynamical system <inline-formula><tex-math id="M6">\begin{document}$ (\mathcal{H}, S_{t}) $\end{document}</tex-math></inline-formula>. These results deepen and extend our previous works([<xref ref-type="bibr" rid="b31">31</xref>], [<xref ref-type="bibr" rid="b30">30</xref>]), where we only considered the existence of the global attractors in the case of degenerate damping.</p>

Hygro-thermo-viscoelastic wave propagation analysis of FGM nanoshells via nonlocal strain gradient fractional time–space theory

Viscoelastic behaviors of nanosize waveguides cannot be determined via simple versions of nonlocal theories if the wavelength is close to the characteristic length of the nanostructure. In such cases, a coupling between small scale and internal damping must be considered. This study is arranged to capture this important issue to provide reliable data about wave propagation responses of viscoelastic functionally graded material (FGM) nanoshells subjected to hygro-thermal loading for the first time. To do so, a tempo-spatially coupled nonlocal strain gradient viscoelasticity framework is introduced for nanoshells located in a hygro-thermally stimulated environment. First-order shear deformation theory (FSDT) is utilized and mixed with Hamilton’s principle to formulate the problem for thin and moderately thick nanoshells. In the context of an analytical solution, the phase velocity of the dispersed waves is calculated. The provided data reveals that conventional size-dependent theories estimate faster damping trends for the phase velocity rather than fractional time–space theory. Also, it is demonstrated that the precision of the previously published data about viscoelastic behaviors of waves scattered in nanostructures is low in small ranges of a nonlocal parameter. This finding is attributed to the coupling between nonlocal and internal damping parameters which was not included in previous studies.

Stability result for a variable-exponent viscoelastic double-Kirchhoff type inverse source problem with nonlocal degenerate damping term

Stability result for a variable-exponent viscoelastic double-Kirchhoff type inverse source problem with nonlocal degenerate damping term

Extremely confined gap plasmon modes: when nonlocality matters

Historically, the field of plasmonics has been relying on the framework of classical electrodynamics, with the local-response approximation of material response being applied even when dealing with nanoscale metallic structures. However, when the confinement of electromagnetic radiation approaches atomic scales, mesoscopic effects are anticipated to become observable, e.g., those associated with the nonlocal electrodynamic surface response of the electron gas. Here, we investigate nonlocal effects in propagating gap surface plasmon modes in ultrathin metal–dielectric–metal planar waveguides, exploiting monocrystalline gold flakes separated by atomic-layer-deposited aluminum oxide. We use scanning near-field optical microscopy to directly access the near-field of such confined gap plasmon modes and measure their dispersion relation via their complex-valued propagation constants. We compare our experimental findings with the predictions of the generalized nonlocal optical response theory to unveil signatures of nonlocal damping, which becomes appreciable for few-nanometer-sized dielectric gaps.

Unconventional Spin Pumping and Magnetic Damping in an Insulating Compensated Ferrimagnet.

Recently, the interest in spin pumping (SP) has escalated from ferromagnets into antiferromagnetic systems, potentially enabling fundamental physics and magnonic applications. Compensated ferrimagnets are considered alternative platforms for bridging ferro- and antiferromagnets, but their SP and the associated magnetic damping have been largely overlooked so far despite their seminal importance for magnonics. Herein, an unconventional SP together with magnetic damping in an insulating compensated ferrimagnet Gd3 Fe5 O12 (GdIG) is reported. Remarkably, the divergence of the nonlocal effective magnetic damping induced by SP close to the compensation temperature in GdIG/Cu/Pt heterostructures is identified unambiguously. Furthermore, the coherent and incoherent spin currents, generated by SP and the spin Seebeck effect, respectively, undergo a distinct direction change with the variation of temperature. The physical mechanisms underlying these observations are self-consistently clarified by the ferrimagnetic counterpart of SP and the handedness-related spin-wave spectra. The findings broaden the conventional paradigm of the ferromagnetic SP model and open new opportunities for exploring the ferrimagnetic magnonic devices.

Attractors and their continuity for an extensible beam equation with rotational inertia and nonlocal energy damping

This paper investigates the well-posedness of global solutions, the existence of global and exponential attractors and their continuity for an extensible beam equation with rotational inertia and nonlocal energy damping in Ω⊂RN: (1−αΔ)utt+Δ2u−ϕ(‖∇u‖2)Δu−M(‖Δu‖2+‖ut‖2)Δut+f(u)=h, where α∈[0,1] is a rotational coefficient. We find a better subcritical index p⁎:=N+2N−4, with N≥5, and show that when the growth exponent p of the nonlinearity f(u) is up to the range: 1≤p≤p⁎, the equation is well-posed. In particular, when 1≤p<p⁎: (i) the related solution semigroup Sα(t) has a global attractor Aα for each α∈[0,1] and the family of {Aα}α∈[0,1] is continuous on α in a residual subset of [0,1], and upper semi-continuous on [0,1]; (ii) Sα(t) has an exponential attractor Aexpα for each α and the family of {Aexpα}α∈[0,1] is Hölder continuous on α. The main contributions of this paper are that: (a) it breaks through the existing growth restriction: 1≤p≤NN−4 on this issue in literature; (b) it gives a new criterion on the continuity (rather than only upper semi-continuity) of the global attractors in a residual subset of the parameter space and its application; (c) it provides a new method to establish the continuity of the exponential attractors for pure hyperbolic model.

Blow-up of solutions to a viscoelastic wave equation with nonlocal damping

&lt;p style='text-indent:20px;'&gt;The viscoelastic wave equation with nonlinear nonlocal weak damping is considered. The local existence of solutions is established. Under arbitrary positive initial energy, a finite-time blow-up result is proved by a new modified concavity method.&lt;/p&gt;

Estimate of the attractive velocity of attractors for some dynamical systems

In this paper, we first prove an abstract theorem on the existence of polynomial attractors and the concrete estimate of their attractive velocity for infinite-dimensional dynamical systems, then apply this theorem to a class of wave equations with nonlocal weak damping and anti-damping in case that the nonlinear term~$f$~is of subcritical growth.

Global attractor for a wave model with nonlocal nonlinear damping

This paper investigates the well-posedness and long-time dynamics of a wave model with nonlocal nonlinear damping: utt−Δu+σ(‖∇u‖2)g(ut)+f(u)=h(x). For a new exponent p⁎=6γγ+1(≥3), where γ∈[1,5) is the growth index of the nonlinear damping term g(ut), it shows that, as the growth exponent p of the nonlinearity f(u) satisfies 2≤p≤p⁎, the problem is well-posed and has a global attractor in the natural energy space H=H01(Ω)×L2(Ω).

Existence of a generalized polynomial attractor for the wave equation with nonlocal weak damping, anti-damping and critical nonlinearity

In this paper, we first establish a criterion based on contractive function for the existence of generalized polynomial attractors. This criterion only involves some rather weak compactness associated with the repeated inferior limit and requires no compactness, which makes it suitable for critical cases. Then by this abstract theorem, we verify the existence of a generalized polynomial attractor and estimate its attractive speed for the wave equation with nonlocal weak damping, anti-damping and critical nonlinearity.

A dissipative logarithmic-type evolution equation: Asymptotic profile and optimal estimates

We introduce a new model of the logarithmic-type of wave-like equation with a nonlocal logarithmic damping mechanism, which is weakly effective compared with the frequently studied fractional damping equations. We consider the Cauchy problem for this new model in Rn, and study the asymptotic profile, optimal decay, and/or blow-up rates of the solutions as t→∞ in the L2-sense. The L operator considered in this study was used to dissipate the solutions of the wave equation investigated by Charão-Ikehata [6] and in the low frequency parameters, the principal part of the equation and the damping term were rather weakly effective compared with the widely studied power-type equations, such as (−Δ)θut with θ∈(0,1].

Annihilation of topological solitons in magnetism with spin-wave burst finale: Role of nonequilibrium electrons causing nonlocal damping and spin pumping over ultrabroadband frequency range

We not only reproduce burst of short-wavelength spin waves (SWs) observed in recent experiment [S. Woo et al., Nat. Phys. 13, 448 (2017)] on magnetic-field-driven annihilation of two magnetic domain walls (DWs) but, furthermore, we predict that this setup additionally generates highly unusual} pumping of electronic spin currents in the absence of any bias voltage. Prior to the instant of annihilation, their power spectrum is ultrabroadband, so they can be converted into rapidly changing in time charge currents, via the inverse spin Hall effect, as a source of THz radiation of bandwidth $\simeq 27$ THz where the lowest frequency is controlled by the applied magnetic field. The spin pumping stems from time-dependent fields introduced into the quantum Hamiltonian of electrons by the classical dynamics of localized magnetic moments (LMMs) comprising the domains. The pumped currents carry spin-polarized electrons which, in turn, exert backaction on LMMs in the form of nonlocal damping which is more than twice as large as conventional local Gilbert damping. The nonlocal damping can substantially modify the spectrum of emitted SWs when compared to widely-used micromagnetic simulations where conduction electrons are completely absent. Since we use fully microscopic (i.e., Hamiltonian-based) framework, self-consistently combining time-dependent electronic nonequilibrium Green functions with the Landau-Lifshitz-Gilbert equation, we also demonstrate that previously derived phenomenological formulas miss ultrabroadband spin pumping while underestimating the magnitude of nonlocal damping due to nonequilibrium electrons.

Energy decay and blow-up of solutions for a viscoelastic equation with nonlocal nonlinear boundary dissipation

In this paper, we consider a nonlinear viscoelastic equation with nonlocal nonlinear boundary damping and two nonlinear source terms (boundary and interior). We obtain the global existence of solution via the potential well method. By introducing suitable Lyapunov functionals, using the multiplier method, and constructing convex differential inequality, we establish an explicit and general decay rate result. This improves previous decay results concerning the problem. We also get a finite time blow-up result of solution with positive initial energy under suitable conditions on the initial data and positive memory function. This is the first result for blow-up of the problem with nonlocal nonlinear boundary damping.

Numerical analysis of a wave equation for lossy media obeying a frequency power law

Abstract We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency-dependent power law. First we prove the existence of a unique solution to this equation with particular attention paid to the handling of the fractional derivative. Then we derive an explicit time-stepping scheme based on the finite element method in space and a combination of convolution quadrature and second-order central differences in time. We conduct a full error analysis of the mixed time discretization and in turn the fully space-time discretized scheme. Error estimates are given for both smooth solutions and solutions with a singularity at $t = 0$ of a type that is typical for equations involving fractional time derivatives. A number of numerical results are presented to support the error analysis.