Search Results (6)

In this contribution, we propose and study long-time behaviors of a new class of N-dimensional delayed Kirchhoff–Carrier-type problems with variable transfer coefficients involving a logarithmic nonlinearity. We take into account the dependence of diffusion and damping coefficients on the position and direction, as well as the presence of different types of delays. This class of nonlocal anisotropic and nonlinear wave-type equations with multiple time-varying mixed delays and dampings, of a fairly general form, containing several arbitrary functions and free parameters, is of the following form: ${\displaystyle \frac{{\partial }^{2}u}{\partial t^2}-{div(\mathcal{K}(\Vert \sigma \nabla u\Vert }_{L^2(\Omega )}^2)A_{\sigma }{(\mathbf{x})\nabla u)+\mathcal{M}(\Vert u\Vert }_{L^2(\Omega )}^2)u-div(\zeta (t)A_{\sigma }(\mathbf{x})\nabla \frac{\partial u}{\partial t})+d_0(t)\frac{\partial u}{\partial t}+{\mathbb{D}}_r(\mathbf{x},t;\frac{\partial u}{\partial t})=\mathbb{G}(u),}$ where $u(\mathbf{x},t)$ is the state function, $\mathcal{M}$ and $\mathcal{K}$ are the nonlocal Kirchhoff operators and the nonlinear operator $\mathbb{G}(u)$ corresponds to a logarithmic source term. The symmetric tensor $A_{\sigma }$ describes the anisotropic behavior and processes of the system, and the operator ${\mathbb{D}}_r$ represents the multiple time-varying mixed delays related to velocity ${\displaystyle \frac{\partial u}{\partial t}}$. Our problem, which encompasses numerous equations already studied in the literature, is relevant to a wide range of practical and concrete applications. It not only considers anisotropy in diffusion, but it also assumes that the strong damping can be totally anisotropic (a phenomenon that has received very little mathematical attention in the literature). We begin with the reformulation of the problem into a nonlinear system coupling a nonlocal wave-type equation with ordinary differential equations, with the help of auxiliary functions. Afterward, we study the local existence and some necessary regularity results of the solutions by using the Faedo–Galerkin approximation, combining some energy estimates and the logarithmic Sobolev inequality. Next, by virtue of the potential well method combined with the Nehari manifold, conditions for global in-time existence are given. Finally, subject to certain conditions, the exponential decay of global solutions is established by applying a perturbed energy method. Many of the obtained results can be extended to the case of other nonlinear source terms. Full article

The low-symmetry Weyl semimetallic Td-phase WTe₂ exhibits both a distinct out-of-plane damping torque (${\tau }_{\mathrm{DL}}$) and exceptional charge–spin interconversion efficiency enabled by strong spin-orbit coupling, positioning it as a prime candidate for spin–orbit torque (SOT) applications in two-dimensional transition metal dichalcogenides. Herein, we report on thickness-dependent unconventional out-of-plane ${\tau }_{\mathrm{DL}}$ in chemically vapor-deposited (CVD) polycrystalline Td-WTe₂ (t)/Ni₈₀Fe₂₀/MgO/Ti (Td-WTN-t) heterostructures. Angle-resolved spin-torque ferromagnetic resonance measurements on the Td-WTN-12 structure showed significant spin Hall conductivities of σ_SH,y = 4.93 × 10³ (ℏ/2e) Ω⁻¹m⁻¹ and σ_SH,z = 0.81 × 10³ (ℏ/2e) Ω⁻¹m⁻¹, highlighting its potential for wafer-scale spin–orbit torque device applications. Additionally, a detailed examination of magnetotransport properties in polycrystalline few-layer Td-WTe₂ films as a function of thickness revealed a marked amplification of the out-of-plane magnetoresistance, which can be ascribed to the anisotropic nature of charge carrier scattering mechanisms within the material. Spin pumping measurements in Td-WTN-t heterostructures further revealed thickness-dependent spin transport properties of Td-WTe₂, with damping analysis yielding an out-of-plane spin diffusion length of λ_SD ≈ 14 nm. Full article

Homogeneous isotropic turbulence (HIT) has been a useful theoretical concept for more than fifty years of theory, modelling, and calculations. Some exact results are revisited in incompressible HIT, with special emphasis on the 4/5 Kolmogorov law. The finite Reynolds number effect (FRN), which yields corrections to that law, is investigated, using both Kármán–Howarth-type equations and a statistical spectral closure of the Eddy-Damped Quasi-Normal Markovian (EDQNM)-type. This discussion offers an opportunity to give an extended review of such spectral closures, from weak turbulence, as in wave turbulence theory, to a strong one. Extensions of the 4/5 or 4/3 Kolmogorov/Monin laws to anisotropic cases, such as stably stratified and MHD turbulence, are briefly touched on. Before addressing more recent work on compressible isotropic turbulence, the simplest case of quasi-incompressible turbulence subjected to externally imposed isotropic compression or dilatation is presented. Rapid distortion theory is found to be a poor model in this isotropic case, in contrast with its relevance in strongly anisotropic flow cases. Accordingly, a fully nonlinear approach based on a rescaling of all fluctuating variables is used, in order to show its interplay with the linear operator. This opens the discussion on the cases of homogeneous incompressible turbulence, where RDT and nonlinear models are relevant, provided that anisotropy is accounted for. Finally, isotropic compressible flows of increasing complexity are considered. Recent studies using weak turbulence theory, modelling, and DNS are discussed. A final unpublished study involves interactions between the solenoidal mode, inherited from incompressible turbulence, and the acoustic and entropic modes, which are specific to the compressible problem. An approach to acoustic wave turbulence, with resonant triads, is revisited on this occasion. Full article

A realizable Eddy Damped Markovian Anisotropic Closure (EDMAC) is presented for the interaction of two-dimensional turbulence and transient waves such as Rossby waves. The structure of the EDMAC ensures that it is as computationally efficient as the eddy damped quasi normal Markovian (EDQNM) closure but, unlike the EDQNM, is guaranteed to be realizable in the presence of transient waves. Jack Herring’s important contributions to laying the foundations of statistical dynamical closure theories of fluid turbulence are briefly reviewed. The topics covered include equilibrium statistical mechanics, Eulerian and quasi-Lagrangian statistical dynamical closure theories, and the statistical dynamics of interactions of turbulence with topography. The impact of Herring’s work is described and placed in the context of related developments. Some of the further works that have built upon Herring’s foundations are discussed. The relationships between theoretical approaches employed in statistical classical and quantum field theories, and their overlap, are outlined. The seminal advances made by the pioneers in strong interaction fluid turbulence theory are put in perspective by comparing related developments in strong interaction quantum field theory. Full article

Real sedimentary media can usually be characterized as transverse isotropy. To reveal wave propagation in the true models and improve the accuracy of migrations and evaluations, we investigated the algorithm of wavefield simulations in an anisotropic viscoelastic medium. The finite difference in the frequency domain (FDFD) has several advantages compared with that in the time domain, e.g., implementing multiple sources, multi-scaled inversion, and introducing attenuation. However, medium anisotropy will lead to the complexity of the wavefield in the calculation. The damping profile of the conventional absorption boundary is only defined in one single direction, which produces instability when the wavefields of strong anisotropy are reflected on that truncated boundary. We applied the multi-axis perfectly matched layer (M-PML) to the wavefield simulations in anisotropic viscoelastic media to overcome this issue, which defines the damping profiles along different axes. In the numerical examples, we simulated seismic wave propagation in three viscous anisotropic media and focused on the wave attenuation in the absorbing layers using time domain snapshots. The M-PML was more effective for wave absorption compared to the conventional perfectly matched layer (PML). In strongly anisotropic media, the PML became unstable, and prominent reflections appeared at truncated boundaries. In contrast, the M-PML remained stable and efficient in the same model. Finally, the modeling of the stratified cross-well model showed the applicability of this proposed algorithm to heterogeneous viscous anisotropic media. The numerical algorithm can analyze wave propagation in viscoelastic anisotropic media. It also provides a reliable forward operator for waveform inversion, wave equation travel-time inversion, and seismic migration in anisotropic viscoelastic media. Full article

Flight feather shafts are outstanding bioinspiration templates due to their unique light weight and their stiff and strong characteristics. As a thin wall of a natural composite beam, the keratinous cortex has evolved anisotropic features to support flight. Here, the anisotropic keratin composition, tensile response, dynamic properties of the cortex, and fracture behaviors of the shafts are clarified. The analysis of Fourier transform infrared (FTIR) spectra indicates that the protein composition of calamus cortex is almost homogeneous. In the middle and distal shafts (rachis), the content of the hydrogen bonds (HBs) and side-chain is the highest within the dorsal cortex and is consistently lower within the lateral wall. The tensile responses, including the properties and dominant damage pattern, are correlated with keratin composition and fiber orientation in the cortex. As for dynamic properties, the storage modulus and damping of the cortex are also anisotropic, corresponding to variation in protein composition and fibrous structure. The fracture behaviors of bent shafts include matrix breakage, fiber dissociation and fiber rupture on compressive dorsal cortex. To clarify, ‘real-time’ damage behaviors, and an integrated analysis between AE signals and fracture morphologies, are performed, indicating that calamus failure results from a straight buckling crack and final fiber rupture. Moreover, in the dorsal and lateral walls of rachis, the matrix breakage initially occurs, and then the propagation of the crack is restrained by ‘ligament-like’ fiber bundles and cross fiber, respectively. Subsequently, the further matrix breakage, interface dissociation and induced fiber rupture in the dorsal cortex result in the final failure. Full article