Unidirectional Transport in Electronic and Photonic Weyl Materials by Dirac Mass Engineering

Unidirectional transports have been observed in two-dimensional systems, however, so far they have not been experimentally observed in three-dimensional bulk materials. In this theoretical work we show that the recently discovered Weyl materials provide a platform for unidirectional transports inside bulk materials. With high experimental feasibility, a complex Dirac mass can be generated and manipulated in the photonic Weyl crystals, creating unidirectionally propagating modes observable in transmission experiments. Possible realization in (electronic) Weyl semimetals is also studied. We show in a lattice model that, with a short-range interaction, the desired form of the Dirac mass can be spontaneously generated in a first-order transition.Comment: 9 pages, with supplemental materia

Imaging point sources in heterogeneous environments

Imaging point sources in heterogeneous environments from boundary or far-field measurements has been extensively studied in the past. In most existing results, the environment, represented by the refractive index function in the model equation, is assumed known in the imaging process. In this work, we investigate the impact of environment uncertainty on the reconstruction of point sources inside it. Following the techniques developed by El Badia and El Hajj (C. R. Acad. Sci. Paris, Ser. I, 350 (2012), 1031-1035), we derive stability of reconstructing point sources in heterogeneous media with respect to measurement error as well as smooth changes in the environment, that is, the refractive index. Numerical simulations with synthetic data are presented to further explore the derived stability properties.Comment: 21 pages, 14 figure

Influence of intrinsic decoherence on entanglement teleportation via a Heisenberg XYZ model with different Dzyaloshinskii-Moriya interaction

We investigate the characteristics of entanglement teleportation of a two-qubit Heisenberg XYZ model under different Dzyaloshinskii-Moriya interaction with intrinsic decoherence taken into account. The comparison of the two different Dzyaloshinskii-Moriya interaction, the effects of the initial state and the inputting state on the entanglement teleportation are presented. The results reveal that the dynamics of entanglement is a symmetry function about for the system, whereas it is not for the system. The ferromagnetic case is superior to the antiferromagnetic case for restrain decoherence when using the system. The dependence of entanglement, output entanglement, fidelity on initial state angle all demonstrate periodic. Moreover, we find that seemingly some system are not suitable for teleportation, but they can acquire some best exhibition if we take the proper initial state and inputting state.Comment: 20 pages, 11 figure

Inverse transport problems in quantitative PAT for molecular imaging

Fluorescence photoacoustic tomography (fPAT) is a molecular imaging modality that combines photoacoustic tomography (PAT) with fluorescence imaging to obtain high-resolution imaging of fluorescence distributions inside heterogeneous media. The objective of this work is to study inverse problems in the quantitative step of fPAT where we intend to reconstruct physical coefficients in a coupled system of radiative transport equations using internal data recovered from ultrasound measurements. We derive uniqueness and stability results on the inverse problems and develop some efficient algorithms for image reconstructions. Numerical simulations based on synthetic data are presented to validate the theoretical analysis. The results we present here complement these in [Ren-Zhao, SIAM J. Imag. Sci., 2013] on the same problem but in the diffusive regime

MPO: An Efficient and Low-cost Peer-to-Peer Overlay for Autonomic Communications

The term Autonomic Communication (AC) refers to self-managing systems which are capable of supporting self-configuration, self-healing and self-optimization. However, information reflection and collection, lack of centralized control, non-cooperation and so on are just some of the challenges within AC systems. We have considered these problems in theory and practice and reached the following conclusion; in order to build an ideal system for autonomic communication, there are three key problems to be solved. Motivated by the need for AC, we have designed an efficient and low-cost Peer-to-Peer (P2P) overlay called Maya-Pyramid overlay (MPO) and combined merits of unstructured P2P with those of structured P2P overlays. Differing from the traditional hierarchical P2P (i.e. tree-like structure) overlay, (1) MPO is composed of levels and layers, which uses small world characteristic to improve efficiency, and the maintenance cost is decreased because update and backup only take place in two neighboring levels or layers instead of recursively perform in higher levels. (2) Unlike normal redundant mechanisms for solving the single fault problem: Tri-Information Center (Tri-IC) mechanism is presented in order to improve robustness by alleviating the load of cluster heads in a hierarchical P2P overlay. (3) A source ranking mechanism is proposed in order to discourage free riding and whitewashing and to encourage frequent information exchanges between peers. (4) Inspired by Pastry's ID structure for a structured DHT algorithm, a 3D unique ID structure is presented in the unstructured P2P overlay. This will guarantee anonymity in routing, and will be, not only more efficient because it applies the DHT-like routing algorithm in the unstructured P2P overlay, but also more adaptive to suit AC. Evaluation proved that MPO is robust, highly efficient and of a low-cost.Comment: 37 pages,9 figures,37 reference

An implicit boundary integral method for computing electric potential of macromolecules in solvent

A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics of molecules in solvent. The proposed method used an implicit boundary integral formulation to derived a linear system defined on Cartesian nodes in a narrowband surrounding the closed surface that separate the molecule and the solvent. The needed implicit surfaces is constructed from the given atomic description of the molecules, by a sequence of standard level set algorithms. A fast multipole method is applied to accelerate the solution of the linear system. A few numerical studies involving some standard test cases are presented and compared to other existing results.Comment: 28 page

Backlund transformations for Burgers Equation via localization of residual symmetries

In this paper, we obtained the non-local residual symmetry related to truncated Painlev\'e expansion of Burgers equation. In order to localize the residual symmetry, we introduced new variables to prolong the original Burgers equation into a new system. By using Lie's first theorem, we got the finite transformation for the localized residual symmetry. More importantly, we also localized the linear superposition of multiple residual symmetries to find the corresponding finite transformations. It is interesting to find that the nth Backlund transformation for Burgers equation can be expressed by determinants in a compact way

New interaction solutions of Kadomtsev-Petviashvili equation

The residual symmetry coming from truncated Painleve expansion of KP equation is nonlocal, which is localized in this paper by introducing multiple new dependent variables. By using the standard Lie group approach, the symmetry reduction solutions for KP equation is obtained based on the general form of Lie point symmetry for the prolonged system. In this way, the interaction solutions between solitons and background waves is obtained, which is hard to study by other traditional methods

Dark parameterization approach to Ito equation

The novel coupling Ito systems are obtained with the dark parameterization approach. By solving the coupling equations, the traveling wave solutions are constructed with the mapping and deformation method. Some novel types of exact solutions are constructed with the solutions and symmetries of the usual Ito equation. In the meanwhile, the similarity reduction solutions of the model are also studied with the Lie point symmetry theory

New symmetry reductions related with the residual symmetry of Boussinesq equation

The Backlund transformation related symmetry is nonlocal, which is hardly to apply in constructing solutions for nonlinear equations. In this paper, we first localize nonlocal residual symmetry to Lie point symmetry by introducing multiple new variables and obtain new Baaklund transformation. Then, by solving out the general form of localized the residual symmetry, we reduce the enlarged system by classical symmetry approach and obtain the corresponding reduction solutions as well as related reduction equations. The localization procedure provides a new way to investigate interaction solutions between different waves