Fundamentals in generalized elasticity and dislocation theory of quasicrystals: Green tensor,dislocation key-formulas and dislocation loops

The present work provides fundamental quantities in generalized elasticity and dislocation theory of quasicrystals. In a clear and straightforward manner, the three-dimensional Green tensor of generalized elasticity theory and the extended displacement vector for an arbitrary extended force are derived. Next, in the framework of dislocation theory of quasicrystals, the solutions of the field equations for the extended displacement vector and the extended elastic distortion tensor are given; that is, the generalized Burgers equation for arbitrary sources and the generalized Mura–Willis formula, respectively. Moreover, important quantities of the theory of dislocations as the Eshelby stress tensor, Peach–Koehler force, stress function tensor and the interaction energy are derived for general dislocations. The application to dislocation loops gives rise to the generalized Burgers equation, where the displacement vector can be written as a sum of a line integral plus a purely geometric part. Finally, using the Green tensor, all other dislocation key-formulas for loops, known from the theory of anisotropic elasticity, like the Peach–Koehler stress formula, Mura–Willis equation, Volterra equation, stress function tensor and the interaction energy are derived for quasicrystals.     

Exact solutions of nonlinear fractional differential equations by （G＇/G）-expansion method

In this paper,we use the fractional complex transform and the(G'/G)-expansion method to study the nonlinear fractional differential equations and find the exact solutions.The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie’s modified Riemann–Liouville derivative into its ordinary differential equation.It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations.     

Transport behaviors and mechanisms in cuspidal blockade region for silicon single-hole transistor

The Si single-hole transistor displays the anomalously-extended cuspidal blockade region, which is elongated toward the 45°-tilted direction normal to gate vs. drain bias voltage regions in the Coulomb blockade diagram. This is attributed to the formation of an ultra small Si quantum dot (QD) into the gate-all-around (GAA) stack. Namely, the large one-electron-addition energy (= 447 meV) from the 2-nm-size Si QD enables the clear Coulomb-blockade events at room temperature, and the large voltage gain from the GAA stack allows the cuspidal extension of the blockade region through the renormalization of Coulomb-blockade energies at the adjacent bias points near the initial Coulomb-blockade state.     

Magnetosonic shock waves in dense astrophysical electron–positron–ion plasmas

Multifluid quantum magnetohydrodynamic model (QMHD) is used to investigate small but finite amplitude magnetosonic shock waves in dense) electron–positron–ion (e–p–i) plasmas. The Korteweg–de Vries–Burgers (KdVB) equation is derived by using reductive perturbation method. It is noticed that variations in the positron density modify the profile of magnetosonic shocks in dense e–p–i plasmas significantly. The numerical results are also presented by taking into account the dense plasma parameters from published literature of astrophysical conditions, in compact stars.     

Domain-Wall Dynamics After Photoexcitations Near neutral-Ionic Phase Transitions

Real-time dynamics of domain walls between the neutral and ionic phases just after photoexcitations is studied by fully solving the time-dependent Schrödinger equation for a one-dimensional extended Peierls-Hubbard (PH) model, not by relying on the adiabatic approximation. The unrestricted Hartree-Fock (HF) approximation is used for electrons, and the lattice displacements are treated classically. Three characteristic time scales are observed: rapid oscillation of ionicity owing to the local charge transfer; slow oscillation of lattice displacements; and even slower and collective motion of domain walls. Steady growth of a metastable domain is achieved after complicated competition of micro domains. The relevance to recently measured, time-resolved photoreflectance spectra in TTF-CA is discussed.     

An Initial Boundary-Value Problem in a Half-Strip for the Korteweg–De Vries Equation in Fractional-Order Sobolev Spaces

Abstract

An initial boundary-value problem in a half-strip with one boundary condition for the Korteweg–de Vries equation is considered and results on global well-posedness of this problem are established in Sobolev spaces of various orders, including fractional. Initial and boundary data satisfy natural (or close to natural) conditions, originating from properties of solutions of a corresponding initial-value problem for a linearized KdV equation. An essential part of the study is the investigation of special solutions of a “boundary potential” type for this linearized KdV equation.     

Extended Affine Weyl Groups: Presentation by Conjugation via Integral Collection

We give several necessary and sufficient conditions for the existence of the presentation by conjugation for a non-simply laced extended affine Weyl group. We invent a computational tool by which one can determine simply the existence of the presentation by conjugation for an extended affine Weyl group. As an application, we determine the existence of the presentation by conjugation for a large class of extended affine Weyl groups.     

Nonadditive Strong Commutativity Preserving Maps

The goal of this note is to characterize strong commutativity preserving maps on prime or semiprime rings without the additivity assumption on the maps considered in the literature.     

A Characterization of π-Complemented Algebras

π-complemented algebras are defined as those algebras (not necessarily associative or unital) such that each annihilator ideal is complemented by other annihilator ideal. Let A be a semiprime algebra. We prove that A is π-complemented if, and only if, every idempotent in the extended centroid of A lies in the centroid of A. We also show the existence of a smallest π-complemented subalgebra of the central closure of A containing A. In the case that A is a C*-algebra, this subalgebra turns out to be a norm dense *-subalgebra of the bounded central closure of A. It follows that a C*-algebra is boundedly centrally closed if, and only if, it is π-complemented.