Interface-induced states at the boundary between a 3D topological insulator and a normal insulator

We show that, when a three-dimensional (3D) narrow-gap semiconductor with inverted band gap (“topological insulator,” TI) is attached to a 3D wide-gap semiconductor with non-inverted band gap (“normal insulator,” NI), two types of bound electron states having different spatial distributions and spin textures arise at the TI/NI interface. Namely, the gapless (“topological”) bound state can be accompanied by the emergence of the gapped (“ordinary”) bound state. We describe these states in the framework of the envelope function method using a variational approach for the energy functional; their existence hinges on the ambivalent character of the constraint for the envelope functions that correspond to the “open” or “natural” boundary conditions at the interface. The properties of the ordinary state strongly depend on the effective interface potential, while the topological state is insensitive to the interface potential variation.     

Code verification for finite volume multiphase scalar equations using the method of manufactured solutions

Code verification answers the question: “Is this code solving the equations correctly?” Validation answers the question: “Is this code solving the correct equations?” Code verification must be performed before attempting validation and is the focus of this paper. Here we present a novel method of applying the method of manufactured solutions (MMS) to finite volume multiphase codes. MMS is a procedure for generating analytic source terms and adding them to the governing equations such that the numerical solution converges to a previously determined analytic (manufactured) solution. This is a powerful method for generating exact benchmark solutions which can test the most general capabilities of a code. We present a series of manufactured solutions (MS) ranging from single-phase to multiphase flows to test all aspects of an example code. The chief obstacle to applying MMS to multiphase flow lies in the discontinuous nature of the material properties at the interface. An extension of the MMS procedure to multiphase flow is presented here using an adaptive marching tetrahedron style algorithm to compute the source terms near the interface. We also present guidelines for the use of the MMS to help locate coding mistakes (i.e. bugs). This is accomplished by the use of progressively simpler MS and material property variations.     

Basic configuration of a single-wall carbon nanotube <Emphasis Type="Italic">Y</Emphasis> junction of <Emphasis Type="Italic">D</Emphasis><Subscript>3<Emphasis Type="Italic">h</Emphasis></Subscript> symmetry: Structure and classification

The structure of single-wall carbon nanotube Y junctions of symmetry D_3h containing topological defects in the form of six heptagons or three octagons located immediately in the junction region of each pair of nanotubes forming the Y junctions is investigated, and their classification is suggested. It is shown that the pairs of heptagons in a Y junction formed by nanotubes of the “zigzag” type can be arranged in two ways and can be transformed into one another by using the (6, 7, 7, 6) ? (7, 6, 7, 6) Stone-Wales transformation and that the octagon and pairs of heptagons in a Y junction formed by nanotubes of the “armchair” type can be transformed into one another by introducing or removing a C₂ cluster. A method for constructing such Y junctions is suggested.     

Supersymmetric extended solitons

It is shown that the recently classified “super p-brane” actions can be considered as effective actions “extended solitons” of supersymmetric field theories for which a Bogomol'nyi-type bound of the form (mass/unit p-volume) ⩾ topological charge is saturated. Such solutions can be found by “double-dimensional oxidation” of the instanton solutions of supersymmetric field theories in d = 1, 2, 4 spacetime dimensions. These provide a field-theoretic of all super p-branes except the d = 10 superstring and the d = 11 supermembrane.     

Irregularly shaped ice aggregates in optical modeling of convectively generated ice clouds

We propose a model of irregular shaped ice particles for satellite and ground-based cloud remote sensing applications. Microphysical observations have shown that ice particles generated in convective clouds tend to have highly irregular structures as a result of aggregation process. To simulate such complex structures, we used spatial Poisson–Voronoi tessellations. Furthermore, we adopted fractal-like shapes that were consistent with the proposed mass-dimension and area ratio-dimension relationships of measured cirrus particles. Single-scattering properties of the modeled “Voronoi aggregates” at visible wavelengths with size parameters up to 2246 were estimated from numerical calculations using the finite-difference time-domain method and the geometrical-optics integral-equation method. The phase functions for randomly oriented Voronoi aggregates showed features with no halos in the forward-scattering direction and a flat angular dependence in the side-to-backscattering directions. These characteristics and resultant asymmetry factors agreed with those of measured ice particles. Moreover, we confirmed the weak size and shape dependences of these scattering properties for the Voronoi aggregates, as well as high backscattering depolarization ratios and low linear polarizations.     

A Quadratic Spline based Interface (QUASI) reconstruction algorithm for accurate tracking of two-phase flows

A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor–corrector operations enforcing function (C⁰) and derivative (C¹) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water.     

A high-resolution mapped grid algorithm for compressible multiphase flow problems

We describe a simple mapped-grid approach for the efficient numerical simulation of compressible multiphase flow in general multi-dimensional geometries. The algorithm uses a curvilinear coordinate formulation of the equations that is derived for the Euler equations with the stiffened gas equation of state to ensure the correct fluid mixing when approximating the equations numerically with material interfaces. A γ-based and a α-based model have been described that is an easy extension of the Cartesian coordinates counterpart devised previously by the author [30]. A standard high-resolution mapped grid method in wave-propagation form is employed to solve the proposed multiphase models, giving the natural generalization of the previous one from single-phase to multiphase flow problems. We validate our algorithm by performing numerical tests in two and three dimensions that show second order accurate results for smooth flow problems and also free of spurious oscillations in the pressure for problems with interfaces. This includes also some tests where our quadrilateral-grid results in two dimensions are in direct comparisons with those obtained using a wave-propagation based Cartesian grid embedded boundary method.     

A linear stability analysis for nonlinear,grey, thermal radiative transfer problems

We present a new linear stability analysis of three time discretizations and Monte Carlo interpretations of the nonlinear, grey thermal radiative transfer (TRT) equations: the widely used “Implicit Monte Carlo” (IMC) equations, the Carter Forest (CF) equations, and the Ahrens–Larsen or “Semi-Analog Monte Carlo” (SMC) equations. Using a spatial Fourier analysis of the 1-D Implicit Monte Carlo (IMC) equations that are linearized about an equilibrium solution, we show that the IMC equations are unconditionally stable (undamped perturbations do not exist) if α, the IMC time-discretization parameter, satisfies 0.5 < α ? 1. This is consistent with conventional wisdom. However, we also show that for sufficiently large time steps, unphysical damped oscillations can exist that correspond to the lowest-frequency Fourier modes. After numerically confirming this result, we develop a method to assess the stability of any time discretization of the 0-D, nonlinear, grey, thermal radiative transfer problem. Subsequent analyses of the CF and SMC methods then demonstrate that the CF method is unconditionally stable and monotonic, but the SMC method is conditionally stable and permits unphysical oscillatory solutions that can prevent it from reaching equilibrium. This stability theory provides new conditions on the time step to guarantee monotonicity of the IMC solution, although they are likely too conservative to be used in practice. Theoretical predictions are tested and confirmed with numerical experiments.     

Approximate reconstruction of torsional potential energy surface based on voronoi tessellation

Torsional modes within a complex molecule containing various functional groups are often strongly coupled so that the harmonic approximation and one-dimensional torsional treatment are inaccurate to evaluate their partition functions. A family of multi-structural approximation methods have been proposed and applied in recent years to deal with the torsional anharmonicity. However, these methods approximate the exact “almost periodic” potential energy as a summation of local periodic functions with symmetric barrier positions and heights. In the present theoretical study, we illustrated that the approximation is inaccurate when torsional modes present non-uniformly distributed local minima. Thereby, we proposed an improved method to reconstruct approximate potential to replace the periodic potential by using information of the local minima and their Voronoi tessellation. First, we established asymmetric barrier heights by introducing two periodicity parameters and assuming that the exact barrier positions are at the boundaries of Voronoi cells. Second, we used multiplicatively weighted Voronoi tessellation to refine the barrier heights and positions by defining a structure-related distance metric. The proposed method has been tested for a few higher-dimensional cases, all of which show promising improved accuracy.     

Quantum bit threads of MERA tensor network in large c limit

The Ryu-Takayanagi (RT) formula plays a large role in the current theory of gauge-gravity duality and emergent geometry phenomena. The recent reinterpretation of this formula in terms of a set of “bit threads” is an interesting effort in understanding holography. In this study, we investigate a quantum generalization of the “bit threads” based on a tensor network, with particular focus on the multi-scale entanglement renormalization ansatz (MERA). We demonstrate that, in the large c limit, isometries of the MERA can be regarded as “sources” (or “sinks”) of the information flow, which extensively modifies the original picture of bit threads by introducing a new variable ρ: density of the isometries. In this modified picture of information flow, the isometries can be viewed as generators of the flow. The strong subadditivity and related properties of the entanglement entropy are also obtained in this new picture. The large c limit implies that classical gravity can emerge from the information flow.     

A model for cluster confinement in one dimensional many-body systems

A variant of the one-dimensional “toy model” for QCD of Horowitz et al. is presented, which uses a density dependent rather than the many-body force originally proposed by Lenz et al. Our approach suggests, already within the RPA framework, the occurrence of a phase transition simulating the one from quark to hadronic matter, similar to the transition foreseen by Horowitz et al. However our force is easy to handle in three dimensions as well, but in such a case, of course, the correspondence between our and the “toy model” remains to be verified.     

High-order unconditionally stable FC-AD solvers for general smooth domains I. Basic elements

We introduce a new methodology for the numerical solution of Partial Differential Equations in general spatial domains: our algorithms are based on the use of the well-known Alternating Direction Implicit (ADI) approach in conjunction with a certain “Fourier continuation” (FC) method for the resolution of the Gibbs phenomenon. Unlike previous alternating direction methods of order higher than one, which can only deliver unconditional stability for rectangular domains, the present high-order algorithms possess the desirable property of unconditional stability for general domains; the computational time required by our algorithms to advance a solution by one time-step, in turn, grows in an essentially linear manner with the number of spatial discretization points used. In this paper we demonstrate the FC-AD methodology through a variety of examples concerning the Heat and Laplace Equations in two and three-dimensional domains with smooth boundaries. Applications of the FC-AD methodology to Hyperbolic PDEs together with a theoretical discussion of the method will be put forth in a subsequent contribution. The numerical examples presented in this text demonstrate the unconditional stability and high-order convergence of the proposed algorithms, as well the very significant improvements they can provide (in one of our examples we demonstrate a one thousand improvement factor) over the computing times required by some of the most efficient alternative general-domain solvers.     

Dual Feynman rules—Topological asymptotic freedom

Feynman-graph rules are formulated for the strong—interaction components of the topological expansion—defined as those graphs all of whose vertices are zero—entropy connected parts. These rules imply a “topological asymptotic freedom” and admit a corresponding perturbative evaluation where the zeroth order exhibits topological supersymmetry.     

Changing topology and nontrivial homotopy

A method is proposed for extending the path integral to a sum over paths which change topology. This is used to show that topological contributions to a field theory path integral arising from nontrivial homotopy on the background space are completely determined in the free theory. The method is applied to extend (“third quantize”) field theory to backgrounds which change topology (e.g. string theory) and to show that topological contributions from nontrivial homotopy of field histories in the target space are completely determined by the field theory on a fixed background.     

Numerical study of 2+1 dimensional sine-Gordon solitons

Numerical studies of the dynamics of sine-Gordon solitons in two spatial dimensions are presented. New results like 4π-break up, “soliton-on-soliton effect”, and scattering at a circular inhomogeneity for line solitons on large-area Josephson junctions are reported. For elliptic ring solitons we find oscillating eccentricity between the major axes in the pulson phase. Colliding non-concentric ring solitons are shown to form larger oval ring solitons or to repel each other. This new effect is qualitatively explained in terms of the 4π-break up for line solitons.     

微液滴动力学特性的耗散粒子动力学模拟

对传统的耗散粒子动力学方法进行了改进.改进的耗散粒子动力学方法采用了包含远程吸引力和近距排斥力的保守力势函数,从而使得用耗散粒子动力学方法模拟多相流动成为可能.应用改进的耗散粒子动力学方法,对微尺度下液滴的形成及液滴在微重力下的大幅度振荡变形进行了数值模拟.计算结果表明,改进的耗散粒子动力学(DPD)方法能够有效地描述微尺度下液滴的动力学特性,对研究复杂流体多相流动有着重要的意义. 关键词： 多相流 微液滴 耗散粒子动力学(DPD)方法 保守力势函数     

One-loop Effective Potential in Higher-dimensional Yang-Mills Theory

We study the effective action in Euclidean Yang-Mills theory with a compact simple gauge group in one-loop approximation assuming a covariantly constant gauge field strength as a background. For groups of higher rank and spacetimes of higher dimensions such field configurations have many independent color components taking values in Cartan subalgebra and many “magnetic fields” in each color component. In our previous investigation it was shown that such background is stable in dimensions higher than four provided the amplitudes of “magnetic fields” do not differ much from each other. In the present paper we exactly calculate the relevant zeta-functions in the case of equal amplitudes of “magnetic fields”. For two “magnetic fields” with equal amplitudes the behavior of the effective action is studied in detail. It is shown that in dimensions d = 4,5,6,7 (8), the perturbative vacuum is metastable, i.e., it is stable in perturbation theory but the effective action is not bounded from below, whereas in dimensions d = 9,10,11 (8) the perturbative vacuum is absolutely stable. In dimensions d = 8 (8) the perturbative vacuum is stable for small values of the coupling constant but becomes unstable for large coupling constant leading to the formation of a non-perturbative stable vacuum with nonvanishing “magnetic fields”. The critical value of the coupling constant and the amplitudes of the vacuum “magnetic fields” are evaluated exactly. PACS numbers: 11.10Kk, 11.15Tk, 11.15.-q, 12.38Aw, 12.38Lg     

Simulating a topological transition in a superconducting phase qubit by fast adiabatic trajectories

The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practically limited due to quantum dissipation. Here we apply the “shortcut to adiabaticity” (STA) protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit. The resulting fast adiabatic trajectories illustrate the change of the bulk Bloch eigenstates in the Su-Schrieffer-Heeger (SSH) model. A sharp transition is experimentally determined for the topological invariant of a winding number. Our experiment helps identify the topological Chern number of a two-dimensional toy model, suggesting the applicability of the fast adiabatic simulation method for topological systems.