Inertial spin Hall effect in non-commutative space

In the present Letter the study of inertial spin current (that appears in an accelerated frame of reference) is extended to Non-Commutative (NC) space. In the Hamiltonian framework, the Dirac Hamiltonian in an accelerating frame is computed in the low energy regime by exploiting the Foldy–Wouthuysen scheme. The NC θ-effect appears from the replacement of normal products and commutators by Moyal ?-products and ?-commutators. In particular, the commutator between the external magnetic vector potential and the potential induced by acceleration becomes non-trivial. Expressions for θ-corrected inertial spin current and conductivity are derived explicitly. We have provided yet another way of experimentally measuring θ. The θ bound is obtained from the out of plane spin polarization, which is experimentally observable.     

Dynamics of bound vector solitons induced by stochastic perturbations: Soliton breakup and soliton switching

We respectively investigate breakup and switching of the Manakov-typed bound vector solitons (BVSs) induced by two types of stochastic perturbations: the homogenous and nonhomogenous. Symmetry-recovering is discovered for the asymmetrical homogenous case, while soliton switching is found to relate with the perturbation amplitude and soliton coherence. Simulations show that soliton switching in the circularly-polarized light system is much weaker than that in the Manakov and linearly-polarized systems. In addition, the homogenous perturbations can enhance the soliton switching in both of the Manakov and non-integrable (linearly- and circularly-polarized) systems. Our results might be helpful in interpreting dynamics of the BVSs with stochastic noises in nonlinear optics or with stochastic quantum fluctuations in Bose–Einstein condensates.     

ESTIMATIONS OF THE CONSTANTS IN INVERSE INEQUALITIES FOR FINITE ELEMENT FUNCTIONS

In this paper, we estimate the constants in the inverse inequalities for the finite ele- ment functions. Furthermore, we obtain the least upper bounds of the constants in inverse inequalities for the low-order finite element functions. Such explicit estimates of the con- stants can be used as computable error bounds for the finite element method.     

Inequivalent Quantization in the Field of a Ferromagnetic Wire

We argue that it is possible to bind neutral atom (NA) to the ferromagnetic wire (FW) by inequivalent quantization of the Hamiltonian. We follow the well known von Neumann’s method of self-adjoint extensions (SAE) to get this inequivalent quantization, which is characterized by a parameter Σ∈ℝ(mod2π). There exists a single bound state for the coupling constant η ²∈[0,1). Although this bound state should not occur due to the existence of classical scale symmetry in the problem. But since quantization procedure breaks this classical symmetry, bound state comes out as a scale in the problem leading to scaling anomaly. We also discuss the strong coupling region η ²<0, which supports bound state making the problem re-normalizable.     

具有Kratzer型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态

给出了具有Kratzer型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解.     

Novel test method to estimate bound rubber formation of silica-filled solution styrene-butadiene rubber compounds

Bound rubber formation was investigated in detail by applying various extraction temperatures (at room temperature, 90°C, and 180°C) and novel treatment methods (ammonia bubbling and sonication). Bound rubbers could be divided into three major components of core shell, primary layer including tightly primary layer and occluded rubber, and secondary layer including connecting filament. Bound rubber content of the core shell was measured by four successive procedures of extraction at room temperature, ammonia bubbling, extraction at 180°C and sonication. Bound rubber content of the tightly primary layer was measured by three successive procedures of extraction at 90°C, ammonia bubbling and sonication. Bound rubber content of the primary layer was measured by two successive procedures of extraction at 90°C and sonication.     

Weakly (and not so weakly) bound states of a relativistic particle in one dimension

We present the first exact calculation of the energy of the bound state of a one dimensional Dirac massive particle in weak short-range arbitrary potentials, using perturbation theory to fourth order (the analogous result for two dimensional systems with confinement along one direction and arbitrary mass is also calculated to second order). We show that the non-perturbative extension obtained using Padé approximants can provide remarkably good approximations even for deep wells, in certain range of physical parameters. As an example, we discuss the case of two gaussian wells, comparing numerical and analytical results, predicted by our formulas.     

Variation of the Payne Effect in Natural Rubber Reinforced by Graft-Modified Carbon Black

Carbon black (CB) was modified by liquid grafting and used for natural rubber (NR) reinforcement. Payne effects during NR reinforcement by the graft-modified carbon black (GCB) were analyzed in this paper. The results showed a proportional relationship between filler content and the Payne effect. Rubber compounds with GCB presented weaker Payne effects than their non-modified counterparts. Qualitative analysis of the correlation between filler network structure and filler content was conducted according to the relationship between bound rubber of a rubber compound and shear modulus. The impact of the storage period on the Payne effect was further studied, and the results demonstrated that the longer the storage period of the rubber compound, the stronger the Payne effect tended to be. The mechanisms by which the Payne effects were manifested differed according to the content of the filler in the rubber.     

Bound states for a Coulomb-type potential induced by the interaction between a moving electric quadrupole moment and a magnetic field

We discuss the arising of bound states solutions of the Schrödinger equation due to the presence of a Coulomb-type potential induced by the interaction between a moving electric quadrupole moment and a magnetic field. Furthermore, we study the influence of the Coulomb-type potential on the harmonic oscillator by showing a quantum effect characterized by the dependence of the angular frequency on the quantum numbers of the system, whose meaning is that not all values of the angular frequency are allowed.