A hybrid method for the parallel computation of Green’s functions

Quantum transport models for nanodevices using the non-equilibrium Green’s function method require the repeated calculation of the block tridiagonal part of the Green’s and lesser Green’s function matrices. This problem is related to the calculation of the inverse of a sparse matrix. Because of the large number of times this calculation needs to be performed, this is computationally very expensive even on supercomputers. The classical approach is based on recurrence formulas which cannot be efficiently parallelized. This practically prevents the solution of large problems with hundreds of thousands of atoms. We propose new recurrences for a general class of sparse matrices to calculate Green’s and lesser Green’s function matrices which extend formulas derived by Takahashi and others. We show that these recurrences may lead to a dramatically reduced computational cost because they only require computing a small number of entries of the inverse matrix. Then, we propose a parallelization strategy for block tridiagonal matrices which involves a combination of Schur complement calculations and cyclic reduction. It achieves good scalability even on problems of modest size.     

An approximate block Newton method for coupled iterations of nonlinear solvers: Theory and conjugate heat transfer applications

A new, approximate block Newton (ABN) method is derived and tested for the coupled solution of nonlinear models, each of which is treated as a modular, black box. Such an approach is motivated by a desire to maintain software flexibility without sacrificing solution efficiency or robustness. Though block Newton methods of similar type have been proposed and studied, we present a unique derivation and use it to sort out some of the more confusing points in the literature. In particular, we show that our ABN method behaves like a Newton iteration preconditioned by an inexact Newton solver derived from subproblem Jacobians. The method is demonstrated on several conjugate heat transfer problems modeled after melt crystal growth processes. These problems are represented by partitioned spatial regions, each modeled by independent heat transfer codes and linked by temperature and flux matching conditions at the boundaries common to the partitions. Whereas a typical block Gauss–Seidel iteration fails about half the time for the model problem, quadratic convergence is achieved by the ABN method under all conditions studied here. Additional performance advantages over existing methods are demonstrated and discussed.     

Dynamically tessellating algorithm for analysis of pore size distribution in particle agglomerates

We describe a novel physical application of the OctTree data structure [P. Meagher, Comput. Graphics Image Process 19(2) (1982) 129–147] in a dynamically tessellating algorithm, in conjunction with an object-oriented, constructive solid geometry library (DOC), to efficiently determine pore size distributions in large multi-particle systems. We apply the DOC library to investigate the evolving dynamics of pore formation in multi-particle systems, such as a mixture of smooth hard cubes and spheres and a collection of frictional soft spheres. We demonstrate that the algorithm is able to provide insight into the effect of structural changes on the porosity network; for example, during the uniaxial compaction of soft spheres, we find the number density of pores increases while the mean volume of the pores decreases. This trend is responsible for a shift in the distribution of the pore volumes to favour smaller volumes. We anticipate that the DOC method will have wider applications in the area of granular materials for studying the changes in pore structure in both experimental and numerical systems as a complement to the analysis of particle packing.     

Optimization with extremal dynamics for the traveling salesman problem

By mapping the optimization problems to physical systems, the paper presents a general-purpose stochastic optimization method with extremal dynamics. It is built up with the traveling salesman problem (TSP) being a typical NP-complete problem. As self-organized critical processes of extremal dynamics, the optimization dynamics successively updates the states of those cities with high energy. Consequently, a near-optimal solution can be quickly obtained through the optimization processes combining the two phases of greedy searching and fluctuated explorations (ergodic walk near the phase transition). The computational results demonstrate that the proposed optimization method may provide much better performance than other optimization techniques developed from statistical physics, such as simulated annealing (SA). Since the proposed fundamental solution is based on the principles and micromechanisms of computational systems, it can provide systematic viewpoints and effective computational methods on a wide spectrum of combinatorial and physical optimization problems.     

Maximizing band gaps in two-dimensional photonic crystals by using level set methods

The optimal design of photonic band gaps for two-dimensional square lattices is considered. We use the level set method to represent the interface between two materials with two different dielectric constants. The interface is moved by a generalized gradient ascent method. The biggest gap of GaAs in air that we found is 0.4418 for TM (transverse magnetic field) and 0.2104 for TE (transverse electric field).     

A simple GUI for modeling the optical properties of single metal nanoparticles

We present a graphical user interface, based on the modified long-wavelength approximation, to compute the optical properties of single metal nanoparticles of ellipsoidal geometry (spheres, rods, and disks). The user-friendly interface allows one to readily gauge the accuracy of results obtained using the modified long-wavelength approximation. For spherical particles, up to 10-nm diameter, we confirm that our approach yields an exact correspondence with Mie theory, and gives an approximation error of less than 15% for gold (silver) particles with diameters approaching 40 nm (26 nm). Results are shown to be sensitive to the source data for the optical constants for a given material. The modular nature of the simulation platform provides a quick and intuitive guide for optical characterization experiments.     

Semi-spectral Chebyshev method in quantum mechanics

Traditionally, finite differences and finite element methods have been by many regarded as the basic tools for obtaining numerical solutions in a variety of quantum mechanical problems emerging in atomic, nuclear and particle physics, astrophysics, quantum chemistry, etc. In recent years, however, an alternative technique based on the semi-spectral methods has focused considerable attention. The purpose of this work is first to provide the necessary tools and subsequently examine the efficiency of this method in quantum mechanical applications. Restricting our interest to time-independent two-body problems, we obtained the continuous and discrete spectrum solutions of the underlying Schrödinger or Lippmann-Schwinger equations in both, the coordinate and momentum space. In all of the numerically studied examples we had no difficulty in achieving the machine accuracy and the semi-spectral method showed exponential convergence combined with excellent numerical stability.     

Magnetic separation from superparamagnetic particle suspensions

We investigate the magnetophoretic separation of magnetic microparticles from a non-dilute flow in a microfluidic channel and their subsequent field-induced aggregation under the influence of an externally applied magnetic force. This force induces dipolar interactions between the particles that aid in their separation from the flow. Existing analytical models for dilute suspensions cannot be extended to non-dilute suspensions in which interparticle magnetic interactions play an important role. We therefore conduct a parametric investigation of the mechanics of this problem in a microcapillary flow through simulations and experimental visualization. When a magnetic field is applied, the magnetic microparticles form an aggregate on the channel wall that is influenced by the competition between the holding magnetic force and the aggregate-depleting flow shear force. Microparticle collection in the aggregate increases linearly with increasing magnetic field strength and is characterized by distinct buildup and washaway phases. The collected microparticle volume fraction in an aggregate is found to depend on a single dimensional group that depends upon characteristic system parameters.     

An improved ray approximation method to design the single-mode 3-D optical waveguide

A novel method is developed to analyze a single-mode 3-D optical waveguide based on the ray-approximation method, which we call the improved ray approximation method. The effect of the optical parameters (wavelength, refractive-index and refractive-index difference) on the optimum design is investigated for a strong single-mode 3-D optical waveguide. This is simple and effective for the optimum design of the optical waveguide using the method. This will be helpful for the design of waveguide devices.     

Optimal block-tridiagonalization of matrices for coherent charge transport

Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms require the tight-binding Hamiltonian to be in the form of a block-tridiagonal matrix. Here, we develop a matrix reordering algorithm based on graph partitioning techniques that yields the optimal block-tridiagonal form for quantum transport. The reordered Hamiltonian can lead to significant performance gains in transport calculations, and allows to apply conventional two-terminal algorithms to arbitrarily complex geometries, including multi-terminal structures. The block-tridiagonalization algorithm can thus be the foundation for a generic quantum transport code, applicable to arbitrary tight-binding systems. We demonstrate the power of this approach by applying the block-tridiagonalization algorithm together with the recursive Green’s function algorithm to various examples of mesoscopic transport in two-dimensional electron gases in semiconductors and graphene.     

Sharp interface immersed-boundary/level-set method for wave–body interactions

A sharp interface Cartesian grid method for the large-eddy simulation of two-phase turbulent flows interacting with moving bodies is presented. The overall approach uses a sharp interface immersed boundary formulation and a level-set/ghost–fluid method for solid–fluid and fluid–fluid interface treatments, respectively. A four-step fractional-step method is used for velocity–pressure coupling, and a Lagrangian dynamic Smagorinsky subgrid-scale model is adopted for large-eddy simulations. A simple contact angle boundary condition treatment that conforms to the immersed boundary formulation is developed. A variety of test cases of different scales ranging from bubble dynamics, water entry and exit, landslide-generated waves, to ship hydrodynamics are performed for validation. Extensions for high Reynolds number ship flows using wall-layer models are also considered.     

Lattice Boltzmann Simulation for the Optimized Surface Pattern in a Micro-Channel

Based on the Bhatangar-Gross-Krook （BGK） models, numerical simulation using the lattice Boltzmann model is performed to investigate the optimized surface pattern in a micro-channel. In order to simulate the practical situation correctly, a slip/no-slip boundary condition is applied with making several assumptions. To assess the validity and efficiency of the model, one benchmark problem with considering the surface patterns is studied. Numerical results show the value of rms velocity Vrms increases with the increasing ratio β and larger Reynolds number Re, higher fluctuation of the rms oscillating velocity. Furthermore, the results show that a good mixing effect can be obtained when Re is large enough and the ratio β is about 1.618,which is the appropriate choice, i.e. the well known golden section phenomenon.     

Solving the Schrödinger equation for a charged particle in a magnetic field using the finite difference time domain method

We extend our finite difference time domain method for numerical solution of the Schrödinger equation to cases where eigenfunctions are complex-valued. Illustrative numerical results for an electron in two dimensions, subject to a confining potential V(x,y), in a constant perpendicular magnetic field demonstrate the accuracy of the method.     

Silicon nanowire and polyethylene superhydrophobic surfaces for discrete magnetic microfluidics

A microfluidic method to manipulate small drops of water is studied on two different superhydrophobic surfaces. Using this digital magnetofluidic method, water drops containing paramagnetic carbonyl-iron microparticles were displaced on silicon nanowire (Si NW) and low-density polyethylene (LDPE) superhydrophobic surfaces using magnetic fields. Horizontal, vertical, or upside-down drop movement is made possible by the action of capillary forces induced by paramagnetic particles aligning and following a magnetic field, indicating that three-dimensional digital microfluidics is possible. Also, both Si NW and LDPE superhydrophobic surfaces combine surface chemistry with nano and microscale surface roughness to make drop movement possible. Si NW superhydrophobic surfaces were prepared using vapor-liquid-solid growth systems followed by coating with a perfluorinated hydrocarbon. LDPE superhydrophobic surfaces were prepared by growing polyethylene crystals on a polyethylene substrate through careful rate control.     

Fabrication of xenogeneic bone-derived hydroxyapatite thin film by aerosol deposition method

Xenogeneic bone-derived hydroxyapatite (HA) was coated on Ti-6Al-4V substrate using aerosol deposition (AD) system. HA precursor powder was derived from bovine bone for the deposition. In aerosol system, submicron particles of HA were mixed with a carrier gas to form an aerosol flow in the aerosol chamber. The aerosol flow was through a tube to a nozzle, and then ejected into a deposition chamber. The effect of the beam incident angle on the HA film formation was investigated. The incident angle of the beam was changed from 0° to 60°. Homogeneous HA film with the thickness of 1-2 μm was fabricated by flattering of particles shape for the incident angle of 60°.     

Metal and polymer melt jet formation by the high-power laser ablation

The laser-induced metal and polymer melt jets are studied experimentally. Two classes of physical phenomena of interest are: first, the process of explosive phase change of laser induced surface ablation and second, the hydrodynamic jetting of liquid melts ejected from a beamed spot. We focus on the dynamic link between these two distinct physical phenomena in a framework of forming and patterning of metallic and polymer jets using a high-power Nd:YAG laser. The microexplosion of ablative spot on a target first forms a pocket of hot liquid melt and then it is followed by a sudden volume change of gas-liquid mixture leading to a pressure-induced spray jet ejection into surrounding medium.     

Destruction of the family of steady states in the planar problem of Darcy convection

We consider natural convection of an incompressible fluid in a porous medium described by the planar Darcy equation. For some boundary conditions, Darcy problem may have non-unique solutions in form of a continuous family of steady states. We are interested in the situation when these boundary conditions are violated. The resulting destruction of the family of steady states is studied via computer experiments based on a mimetic finite-difference approach. Convection in a rectangular enclosure is considered under different perturbations of boundary conditions (heat sources, infiltration). Two scenario of the family of equilibria are found: the transformation to a limit cycle and the formation of isolated convective patterns.     

Multiparty quantum secret sharing based on the improved Boström-Felbinger protocol

Based on the famous quantum secure direct communication protocol (i.e., the Boström-Felbinger protocol) [Phys. Rev. Lett. 89 (2002) 187902] and its improvements, we propose a scheme of multiparty quantum secret sharing of classical messages (QSSCM), in which no subset of all the classical message receivers is sufficient to extract the sender’s secret classical messages but all the parties cooperate together. Then we take advantage of this multiparty QSSCM scheme to establish a scheme of multiparty secret sharing of quantum information (SSQI), in which the unknown quantum state in the sender’s qubit can be reconstructed in one receiver’s qubit if and only if all the quantum information receivers collaborate together.