Three-dimensional elliptic solvers for interface problems and applications

Second-order accurate elliptic solvers using Cartesian grids are presented for three-dimensional interface problems in which the coefficients, the source term, the solution and its normal flux may be discontinuous across an interface. One of our methods is designed for general interface problems with variable but discontinuous coefficient. The scheme preserves the discrete maximum principle using constrained optimization techniques. An algebraic multigrid solver is applied to solve the discrete system. The second method is designed for interface problems with piecewise constant coefficient. The method is based on the fast immersed interface method and a fast 3D Poisson solver. The second method has been modified to solve Helmholtz/Poisson equations on irregular domains. An application of our method to an inverse interface problem of shape identification is also presented. In this application, the level set method is applied to find the unknown surface iteratively.     

The compression and stretching of similaritons with nonlinear tunneling in optical fibers

The similarity transformation between the inhomogeneous (n+1)-dimensional generalized nonlinear Schrödinger equation (NLSE) and the constant-coefficient NLSE in optical fibers is constructed with some constraints for the parameters of the medium. The exact balance between the dispersion/diffraction, nonlinearity and the gain/loss produces self-similar waves (similaritons). As an example, we investigate the nonlinear tunneling effect of flat-top similariton. The results show that the effects of dispersion barrier and well for the similariton are similar to that of nonlinear well and barrier, respectively.     

Perturbative BPS algebras in superstring theory

This paper investigates the algebraic structure that exists on perturbative BPS states in the superstring, compactified on the product of a circle and a Calabi-Yau fourfold. This structure was defined in a recent article by Harvey and Moore. It is shown that for a toroidal compactification this algebra is related to a generalized Kac-Moody algebra. The BPS algebra itself is not a Lie algebra. However, it turns out to be possible to construct a Lie algebra with the same graded dimensions, in terms of a half-twisted model. The dimensions of these algebras are related to the elliptic genus of the transverse part of the string algebra. Finally, the construction is applied to an orbifold compactification of the superstring.     

Dynamic Entanglement and Separability Criteria for Quantum Computing Bit States

A theoretical framework is demonstrated to evaluate the degree of entanglement of bit states in quantum computing. Separability of general superposition of Hilbert space unit vectors is discussed, and criteria in amplitude as well as in phase are derived. By these criteria the possibility of different quantum gates such as controlled not (CN), controlled controlled not (CCN), controlled rotation (CR), and controlled phase shift (CPS), to create the entanglement is examined. Furthermore, the selection of measurement mode external to the quantum system is incorporated in the formula using Kronecker delta (δ _kx ), introducing the concept of dynamic entanglement. With this the process of wavefunction collapse upon measurement is understood as the result of the activation of the dynamic entanglement. A firefly in a box model is used to show a pure state of ontological uncertainty, which is in a dynamically entangled state in Hilbert space.     

An improved model for the cantilever NEMS actuator including the surface energy,fringing field and Casimir effects

The influence of the surface energy on the instability of nano-structures under the electrostatic force has been investigated in recent years by different researchers. It appears that in all prior research, the response of all structures becomes softer due to the surface effects. In the present study, the pull-in instability of a NEMS device incorporating the electrostatic force and Casimir intermolecular attraction for different values of the surface parameter is investigated by the Duan–Rach method of determined coefficients (MDC) in order to identify the remarkable effect of the surface energy. Although the obtained results verify the behavior of such structures in presence of the fringing field and the Casimir attraction same as the previous investigations, however the incremental effects of the surface energy cause the aforementioned structures to behave more stiffly in contrast.     

Numerical Complexiton Solutions of Complex KdV Equation

In this paper, we directly extend the applications of the Adomian decomposition method to investigate the complex KdV equation. By choosing different forms of wave functions as the initial values, three new types of realistic numerical solutions： numerical positon, negaton solution, and particularly the numerical analytical complexiton solution are obtained, which can rapidly converge to the exact ones obtained by Lou et al. Numerical simulation figures are used to illustrate the efficiency and accuracy of the proposed method.     

Scintillation advantages of lowest order Bessel–Gaussian beams

For a weak turbulence propagation environment, the scintillation index of the lowest order Bessel–Gaussian beams is formulated. Its triple and single integral versions are presented. Numerical evaluations show that at large source sizes and large width parameters, when compared at the same source size, Bessel–Gaussian beams tend to exhibit lower scintillations than the Gaussian beam scintillations. This advantage is lost however for excessively large width parameters and beyond certain propagation lengths. Large width parameters also cause rises and falls in the scintillation index of off-axis positions toward the edges of the received beam. Comparisons against the fundamental Gaussian beam are made on equal source size and equal power basis. PACS  42.25.Dd; 42.25.Bs; 42.68.Bz; 42.68.-w     

Electronic structure,ferroelectricity and optical properties of CaBi<Subscript>2</Subscript>Ta<Subscript>2</Subscript>O<Subscript>9</Subscript>

Using first-principles calculations based on density-functional theory in its local-density approximation, we investigated the Electronic structure, ferroelectricity and optical properties of CaBi₂Ta₂O₉ (CBT) for the first time. It is found that CBT compound has an indirect band gap of 3.114 eV and the O 2s and 2p states are strongly hybridized with the 6s states of Bi which belong to the (Bi₂O₂)²⁺ planes. The quite strong Ta–O and Bi–O hybridization is the primary source for ferroelectricity. Our results imply that the interaction between Bi and O is highly covalent. The anisotropy occurs mainly above 4 eV in the optical properties. The different optical properties have been discussed.