The exact solution for the free induction decay in a quasi-one-dimensional system in a multi-pulse NMR experiment

The exact solution for the free induction decay in a one-dimensional system in the multi-pulse experiment is obtained at both high and low temperatures in the approximation of nearest neighbor interactions. The experimental investigation is performed on a quasi-one-dimensional system of ¹⁹F nuclear spins in a single crystal of fluorapatite. The theoretical results are in a good agreement with the obtained experimental data.     

Global existence and decay estimate of solutions to magneto-micropolar fluid equations

We are concerned with magneto-micropolar fluid equations (1.3)–(1.4). The global existence of solutions to the Cauchy problem is investigated under certain conditions. Precisely, for the magneto-micropolar-Navier–Stokes (MMNS) system, we obtain global existence and large time behavior of solutions near a constant states in ${\mathbb{R}}^3$. Appealing to a refined pure energy method, we first obtain a global existence theorem by assuming that the $H^3$ norm of the initial data is small, but the higher order derivatives can be arbitrary large. If the initial data belongs to homogeneous Sobolev norms ${\dot{H}}^{?s}$ $(0\le s<\frac{3}{2})$ or homogeneous Besov norms ${\dot{B}}_{2,\infty }^{?s}$ $(0<s\le \frac{3}{2})$, we obtain the optimal decay rates of the solutions and its higher order derivatives. As an immediate byproduct, we also obtain the usual $L^p?L^2$ $(1\le p\le 2)$ type of the decay rates without requiring that the $L^p$ norm of initial data is small. At last, we derive a weak solution to (1.3)–(1.4) in ${\mathbb{R}}^2$ with large initial data.     

Decay rates for the energy of a singular nonlocal viscoelastic system

This work deals with decay rates for the energy of an initial boundary value problem with a nonlocal boundary condition for a system of nonlinear singular viscoelastic equations. We prove the decay rates for the energy of a singular one‐dimensional viscoelastic system with a nonlinear source term and nonlocal boundary condition of relaxation kernels described by the inequality $g_i^{\prime }\left(t\right)\le ?H\left(g_i\left(t\right)\right),\left(i=1,2\right)$ for all t ≥ 0, with H convex.     

Backing effects on the underwater acoustic absorption of a viscoelastic slab with locally resonant scatterers

Backing effects on the underwater acoustic absorption of a viscoelastic polymer slab embedded with locally resonant scatterers are reported. The polymer slab is embedded with two layers of locally resonant scatterers, i.e. Al spheres coated by soft silicon rubber. Theoretical absorption coefficients of the polymer slab under different backings using a layer multiple scattering method show good agreement with the experimental results, which supports unambiguously the experimental observation. Then relations between the resonance modes and the low-frequency absorption peaks of the composite slab are clarified to address the absorption mechanisms. It shows that the mass of the steel backing affects evidently the low-frequency absorption, the absorption peak shifts to lower frequency range while increasing the backing mass.     

New decay results in linear thermoelastodynamics

This paper is concerned with the linear theory of thermoelastodynamics for the class of homogeneous and isotropic media with a semi‐strongly elliptic elasticity tensor. For this class of materials, some results about the spatial behavior of solutions for the initial‐boundary value problem are obtained by using an appropriate family of surface integral measures.     

The matrix method for black hole quasinormal modes

We provide a comprehensive survey of possible applications of the matrix method for black hole quasinormal modes. The proposed algorithm can generally be applied to various background metrics, and in particular, it accommodates both analytic and numerical forms of the tortoise coordinates, as well as black hole spacetimes. We give a detailed account of different types of black hole metrics, master equations, and the corresponding boundary conditions. Besides, we argue that the method can readily be applied to cases where the master equation is a system of coupled equations. By adjusting the number of interpolation points, the present method provides a desirable degree of precision, in reasonable balance with its efficiency. The method is flexible and can easily be adopted to various distinct physical scenarios.     

Optimal decay rate of the two-fluid incompressible Navier–Stokes–Fourier–Poisson system with Ohm’s law

This paper is to investigate the optimal $L^p$ ($p\ge 2$) time decay rate of global solutions to the two-fluid incompressible Navier–Stokes–Fourier–Poisson system with Ohm’s law. The result shows that the time decay rate of this system achieves the same as that of the incompressible Navier–Stokes equation, in other words, the coupling of the self-consistent Poisson equation does not change the decay rate of the incompressible Navier–Stokes equation. This phenomenon is interesting, compared to the compressible Navier–Stokes equation, whose time decay rate decreases when it is coupled with the self-consistent Poisson equation.