A mixed nonlinear time-fractional Rayleigh-Stokes equation

. This paper investigates a nonlinear time-fractional Rayleigh-Stokes equation with mixed nonlinearities containing a power-type function, a logarithmic function and an inverse time-forcing term. Applying Lagrange’s mean value theorem and the compactness of the Sobolev embeddings, we estimate the complex Lipschitz property of mixed nonlinearity. We investigate the local well-posed results (local existence, regularity estimate, continuation) of the solutions in Hilbert scales space. Moreover, the global existence theory affiliated to the finite-time blow-up is considere

Design and analytically full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations

We investigate a general class of electromagnetic devices created with any continuous transformation functions by rigorously calculating the analytical expressions of the electromagnetic field in the whole space. Some interesting phenomena associated with these transformation devices, including the invisibility cloaks, concentrators, and field rotators, are discussed. By carefully choosing the transformation function, we can realize cloaks which are insensitive to perturbations at both the inner and outer boundaries. Furthermore, we find that when the coating layer of the concentrator is realized with left-handed materials, energy will circulate between the coating and the core, and the energy transmits through the core of the concentrator can be much bigger than that transmits through the concentrator. Therefore, such concentrator is also a power flux amplifier. Finally, we propose a spherical field rotator, which functions as not only a wave vector rotator, but also a polarization rotator, depending on the orientations of the spherical rotator with respect to the incident wave direction. The functionality of these novel transformation devices are all successfully confirmed by our analytical full wave method, which also provides an alternate computational efficient validation method in contrast to numerical validation methods.Comment: 22 pages, 3 figure

On a terminal value problem for parabolic reaction–diffusion systems with nonlocal coupled diffusivity terms

In this article, we are interested in investigating the nonlocal nonlinear reaction– diffusion system with final conditions. This problem is called backward in time problem, or terminal value problem which is understood as redefining the previous distributions when the distribution data at the terminal observation are known. There are three main goals presented in this paper. First, we prove that the problem is ill-posed (often called as unstable property) in the sense of Hadamard. Our next propose is to provide a modified quasi-reversibility model to stabilize the ill-posed problem. Using some techniques and tools of Faedo–Galerkin method, we prove the existence of the unique weak solution of the regularized problem. Further, we investigate error estimates between the sought solution and the regularized solution in L2(Ω)− and H1(Ω)− norms. The final aim of this paper is to give some numerical results to demonstrate that our method is useful and effective

On the duality relation for correlation functions of the Potts model

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions, and establish sum rule identities in the form of the M\"obius inversion of a partially ordered set. The strategy of the proof is by first formulating the problem for the more general chiral Potts model. The extension of our consideration to the many-component Potts models is also given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.

Relating multichannel scattering and production amplitudes in a microscopic OZI-based model

Relations between scattering and production amplitudes are studied in a microscopic multichannel model for meson-meson scattering, with coupling to confined quark-antiquark channels. Overlapping resonances and a proper threshold behaviour are treated exactly in the model. Under the spectator assumption, it is found that the two-particle production amplitude shares a common denominator with the elastic scattering amplitude, besides a numerator consisting of a linear combination of all elastic and some inelastic matrix elements. The coefficients in these linear combinations are shown to be generally complex. Finally, the standard operator expressions relating production and scattering amplitudes, viz. A=T/V and Im(A)=T*A, are fulfilled, while in the small-coupling limit the usual isobar model is recovered.Comment: 16 pages, 3 figures, plain LaTeX

Elemental and mineralogical composition of metal-bearing neutralisation sludges, and zinc speciation – A review

Zinc (Zn) in sludges from neutralisation of acidic emissions is a potential environmental pollutant and an element of interest for recovery. Findings regarding the elemental and mineralogical composition of such wastes were aggregated from the literature and examined together for a better understanding of management options, with a focus on Zn. Zn concentrations ranged from 0.006-22% in 46 acid mine drainage sludges, 0.009%-43% in 72 metal-finishing sludges, 0.024%-11.5% in 32 pyrometallurgical sludges, and 1.71-55.7% in 14 Zn production sludges. The main mineralogical characterization technique was X-ray diffraction, which found the dominant minerals to be calcite, gypsum, quartz, and iron oxides, but could not identify considerable proportions of amorphous phases. More than 60 mineral phases were observed. Crystalline Zn compounds identified included oxides, hydroxides, sulfates, sulfides, and metallic Zn; spinel, olivine and carbonate dominated in pyrometallurgical sludges. Zn may also be present in crystalline phases of low concentration, solid solution, and/or amorphous phases, which could be identified and characterised in more detail using other techniques. Overall, it is concluded that Zn occurs in high concentrations and includes phases that have high potential environmental mobility. Zn recovery seems feasible and would also enable harmless disposal of the residual

Nonequilibrium Forces Between Neutral Atoms Mediated by a Quantum Field

We study all known and as yet unknown forces between two neutral atoms, modeled as three dimensional harmonic oscillators, arising from mutual influences mediated by an electromagnetic field but not from their direct interactions. We allow as dynamical variables the center of mass motion of the atom, its internal degrees of freedom and the quantum field treated relativistically. We adopt the method of nonequilibrium quantum field theory which can provide a first principle, systematic and unified description including the intrinsic field fluctuations and induced dipole fluctuations. The inclusion of self-consistent back-actions makes possible a fully dynamical description of these forces valid for general atom motion. In thermal equilibrium we recover the known forces -- London, van der Waals and Casimir-Polder forces -- between neutral atoms in the long-time limit but also discover the existence of two new types of interatomic forces. The first, a `nonequilibrium force', arises when the field and atoms are not in thermal equilibrium, and the second, which we call an `entanglement force', originates from the correlations of the internal degrees of freedom of entangled atoms.Comment: 16 pages, 2 figure