Fast evaluation of time domain fields in sub-wavelength source/observer distributions using accelerated Cartesian expansions (ACE)

Time domain integral equation solvers for transient scattering from electrically large objects have benefitted significantly from acceleration techniques like the plane wave time domain (PWTD) algorithm; these techniques reduce the asymptotic CPU and memory cost. However, PWTD breaks down when used in the analysis of structures that have subwavelength features or features whose length scales are orders of magnitude smaller than the smallest wavelength in the incident pulse. Instances of these occurring in electromagnetics range from antenna topologies, to feed structures, etc. In this regime, it is the geometric constraints that dictate the computational complexity, as opposed to the wavelength of interest. In this work, we present an approach for efficient analysis of such sub-wavelength source/observer distributions in time domain. The methodology that we seek to exploit is the recently developed algorithm based on Cartesian expansions for accelerating the computation of potentials of the form R^ν. In this paper, we present an efficient methodology for computing these polynomials for two different scenarios; where the size of the domain spans the distance travelled by light in (i) one time step and (ii) multiple time steps. These algorithms are cast within the framework of both uniform and non-uniform distributions. Results that demonstrate the efficiency and convergence of the proposed algorithm are presented.     

Fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm

The analysis of transient wave scattering from rigid bodies using integral equation-based techniques is computationally intensive: if carried out using classical schemes, the evaluation of the velocity potential on the surface of a three-dimensional scatterer, represented in terms of Ns spatial basis functions for Nt time steps, requires O(NtNs2) operations. The recently developed plane wave time domain (PWTD) algorithm permits the rapid evaluation of transient fields that are generated by bandlimited source distributions. It has been shown that incorporation of the PWTD algorithm into integral equation-based solvers in a two-level setting reduces the computational complexity of a transient analysis to O(NtNs1.5 logNs). In this paper, it is shown that casting the PWTD scheme into a multilevel framework permits the analysis of transient acoustic surface scattering phenomena in O(NtNslog2Ns) operations using O(NtNs) memory. Numerical examples that demonstrate the efficacy of the multilevel implementation are also presented.     

Bidirectional beam propagation method based on the method of lines for the analysis of photonic band gap structures

The bidirectional beam propagation method based on the method of lines is proposed as an innovative and efficient algorithm to investigate the optical properties of photonic band gap (PBG) structures. A few examples illustrate the application of this technique to the modeling of passive, lossy and active one-dimensional and index confined PBG structures. The algorithm results are validated by comparison with those obtained via the transfer matrix method, the mode-matching method and the finite difference time domain method. With respect to these methods, the present algorithm exhibits accurate results with reduced computer resources.     

An implicit parallel multigrid computing scheme to solve coupled thermal-solute phase-field equations for dendrite evolution

An implicit, second-order space and time discretization scheme together with a parallel multigrid method involving a strip grid domain partitioning has been developed to solve fully coupled, nonlinear phase field equations involving solute and heat transport for multiple solidifying dendrites. The computational algorithm has been shown to be stable and monotonously convergent, and allowed time marching steps that were 3–4 orders of magnitude larger than those employed in similar explicit approaches, resulting in an increase of 3–4 orders of magnitude in computing efficiency. Full solute and thermal coupling was achieved for metallic alloys with a realistic, high Lewis number of >10⁴. The parallel multigrid computing scheme is shown to provide a scalable methodology that allowed the efficient use of distributed supercomputing resource to simulate the evolution of tens of complex shaped 2D dendrites in a computational domain containing tens or even hundreds of millions of grid points. The simulations have provided insight into the dynamic interplay of many growing dendrites in a more realistic fully coupled thermal-solute condition, capturing for the first time fine scale features such as dendrite splitting.     

Simple finite-difference algorithm for calculating waveguide modes

Abstact A simple algorithm for solving the finite-difference (FD) equations for the mode eigenvalues and field distributions of a linear waveguide is presented. By applying the discretized Helmholtz operator column-by-column to an index distribution defined on an N x N grid, a matrix whose size is only a few times N x N is obtained. This yields a reduction in computation time and space compared with the other classical FD approaches which involve an N ² x N ² matrix. Our method is tested against problems for which the exact solutions are known, and we find a high degree of accuracy. Despite the existence of fast algorithms for the treatment of the classical N ² x N ² matrix, our new algorithm presents some advantages over existing FD methods of comparable speed, including: the ability to find all the modes and associated field profiles, very high numerical stability, and no numerical approximations in the procedure. In addition, some general optimum expressions for the domain size and density of grid points which are consistent with the desired precision are provided, and apply to any FD method including ours.     

Dynamical approach to spectator fragmentation in Au+Au reactions at 35 MeV/A

The characteristics of fragment emission in peripheral ¹⁹⁷Au+¹⁹⁷Au collisions 35 MeV/A are studied using the two clusterization approaches within framework of quantum molecular dynamics model. Our model calculations using minimum spanning tree (MST) algorithm and advanced clusterization method namely simulated annealing clusterization algorithm (SACA) showed that fragment structure can be realized at an earlier time when spectators contribute significantly toward the fragment production even at such a low incident energy. Comparison of model predictions with experimental data reveals that SACA method can nicely reproduce the fragment charge yields and mean charge of the heaviest fragment. This reflects suitability of SACA method over conventional clusterization techniques to investigate spectator matter fragmentation in low energy domain.     

All optical NOR and NAND gate based on nonlinear photonic crystal ring resonators

In this paper we proposed optical NOR and NAND gates. By combining nonlinear Kerr effect with photonic crystal ring resonators first we designed a structure, whose optical behavior can be controlled via input power intensity. The switching power threshold obtained for this structure equal to 2 kW/μm². For designing the proposed optical logic gates we employed two resonant rings with the same structures, both rings at the logic gates were designed such that their resonant wavelength be at λ = 1550 nm. Every proposed logic gate has one bias and two logic input ports. We used plane wave expansion and finite difference time domain methods for analyzing the proposed structures.     

Efficient determination of Hugoniot states using classical molecular simulation techniques

We present a methodology for the efficient calculation of the shock Hugoniot using standard molecular simulation techniques. The method is an extension of an equation of state methodology proposed by Erpenbeck [1992, Phys. Rev. A, 46, 6406] and is considered as an alternative to other methods that generate Hugoniot properties. We illustrate the methodology for shocked liquid N₂ using two different simulation methods: (a) the reactive Monte Carlo method for a reactive system; and (b) the molecular dynamics method for a non-reactive system. The method is shown to be accurate, stable and generally independent of the algorithm parameters. We find excellent agreement with results calculated by other previous simulation studies. The results show that the methodology provides a simulation tool capable of determining points on the shock Hugoniot from a single simulation in an efficient, straightforward manner. Further applications and extensions of the method are briefly discussed.     

Differential Entropy and Dynamics of Uncertainty

We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L ²(R ⁿ ) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases. PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a     

A Lagrangian fractional step method for the incompressible navier-stokes equations on a periodic domain

In the Lagrangian fractional step method introduced in this paper, the fluid velocity and pressure are defined on a collection of N fluid markers. At each time step, these markers are used to generate a Voronoi diagram, and this diagram is used to construct finite-difference operators corresponding to the divergence, gradient, and Laplacian. The splitting of the Navier-Stokes equations leads to discrete Helmholtz and Poisson problems, which we solve using a two-grid method. The nonlinear convection terms are modeled simply by the displacement of the fluid markers. We have implemented this method on a periodic domain in the planee. We describe an efficient algorithm for the numerical construction of periodic Voronoi diagrams, and we report on numerical results which indicate that the fractional step method is convergent of first order. The overall work per time step is proportional to N log N.     

Ultimate performance of quantum well infrared photodetectors in the tunneling regime

Thanks to their wavelength diversity and to their excellent uniformity, Quantum well infrared photodetectors (QWIP) emerge as potential candidates for astronomical or defense applications in the very long wavelength infrared (VLWIR) spectral domain. However, these applications deal with very low backgrounds and are very stringent on dark current requirements. In this paper, we present the full electro-optical characterization of a 15 μm QWIP, with emphasis on the dark current measurements. Data exhibit striking features, such as a plateau regime in the I(V) curves at low temperature (4–25 K). We show that present theories fail to describe this phenomenon and establish the need for a fully microscopic approach.     

Quantum Principles and Mathematical Computability

Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then outline a quantum mechanical “algorithm” for one of the insoluble problems of mathematics, the Hilbert's tenth and equivalently the Turing halting problem. The key element of this algorithm is the computability and measurability of both the values of physical observables and of the quantum-mechanical probability distributions for these values.     

Group leaders optimization algorithm

We present a new global optimization algorithm in which the influence of the leaders in social groups is used as an inspiration for the evolutionary technique which is designed into a group architecture. To demonstrate the efficiency of the method, a standard suite of single and multi-dimensional optimization functions along with the energies and the geometric structures of Lennard-Jones clusters are given as well as the application of the algorithm on quantum circuit design problems. We show that as an improvement over previous methods, the algorithm scales as N ^2.5 for the Lennard-Jones clusters of N-particles. In addition, an efficient circuit design is shown for a two-qubit Grover search algorithm which is a quantum algorithm providing quadratic speedup over the classical counterpart.     

Raman tensor analysis of (K0.5Na0.5)NbO3–LiSbO3 lead‐free ceramics and its application to study grain/domain orientation

A quantitative polarized Raman analysis of ferroelectric grain/domain orientation in LiSbO₃ (LS‐modified) (K_0.5Na_0.5)NbO₃ (KNN) ceramics is presented, based on the analysis of the complex orientation dependence in space of their Raman‐active modes. Complete sets of Raman tensor elements of A_g, and E_g phonon modes for orthorhombic/tetragonal structures of KNN have been determined. Through this spectroscopic algorithm, quantitative information could be extracted in terms of three Euler angles in space for KNN samples consisting of mixed phases, thus enabling quantitative visualization of the local distribution of grains/domains in the solid angle. As an application of the method, we quantitatively examined the unknown crystallographic grain orientation patterns on the surfaces of pure KNN and of KNN‐0.05LS ceramics. These two samples were useful to clarify a polymorphic phase transition from the orthorhombic to the tetragonal phase taking place in the LS‐modified KNN system. Thus, we demonstrated that polarized Raman spectroscopy is a valuable and efficient tool for nondestructive three‐dimensional assessments of grain/domain orientation in ferroelectric materials with complex polymorphic structures. We believe that the data shown here represent a typical scenario encountered in grain/domain orientation assessments of piezoelectric perovskites. Copyright © 2012 John Wiley & Sons, Ltd.     

Entropy-Based Approach in Selection Exact String-Matching Algorithms

The string-matching paradigm is applied in every computer science and science branch in general. The existence of a plethora of string-matching algorithms makes it hard to choose the best one for any particular case. Expressing, measuring, and testing algorithm efficiency is a challenging task with many potential pitfalls. Algorithm efficiency can be measured based on the usage of different resources. In software engineering, algorithmic productivity is a property of an algorithm execution identified with the computational resources the algorithm consumes. Resource usage in algorithm execution could be determined, and for maximum efficiency, the goal is to minimize resource usage. Guided by the fact that standard measures of algorithm efficiency, such as execution time, directly depend on the number of executed actions. Without touching the problematics of computer power consumption or memory, which also depends on the algorithm type and the techniques used in algorithm development, we have developed a methodology which enables the researchers to choose an efficient algorithm for a specific domain. String searching algorithms efficiency is usually observed independently from the domain texts being searched. This research paper aims to present the idea that algorithm efficiency depends on the properties of searched string and properties of the texts being searched, accompanied by the theoretical analysis of the proposed approach. In the proposed methodology, algorithm efficiency is expressed through character comparison count metrics. The character comparison count metrics is a formal quantitative measure independent of algorithm implementation subtleties and computer platform differences. The model is developed for a particular problem domain by using appropriate domain data (patterns and texts) and provides for a specific domain the ranking of algorithms according to the patterns’ entropy. The proposed approach is limited to on-line exact string-matching problems based on information entropy for a search pattern. Meticulous empirical testing depicts the methodology implementation and purports soundness of the methodology.     

基于直接离散方式的磁化铁氧体材料电磁散射的时域有限差分方法分析

根据磁化铁氧体材料的磁场强度和磁感应强度之间色散的本构关系式,利用时间微分算子/t和jω的时域和频域对应关系,将磁化铁氧体材料频域的本构关系转化为时域的本构关系,然后将时间微分算子/t在时域采用直接离散的方式,得到磁场强度和磁感应强度的时域有限差分迭代式.数值结果表明,该方法易于实现,简单可行,并节约内存. 关键词： 电磁散射 磁化铁氧体 时域有限差分方法 直接离散方法     

Spectral properties of backward stimulated scattering in liquid carbon disulfide

The spectral structure of backward stimulated scattering from a 10 cm-long CS₂-liquid cell is investigated by using Q-switched 10-ns and 532-nm laser pulses with different spectral linewidths. Under a narrow spectral line (∼0.1 cm⁻¹) pump condition, very strong sharp lines near the pump wavelength (λ ₀) position and the first-order stimulated Raman scattering (λ _s1) position can be observed. However, under a wide line (≈1 cm⁻¹) pump condition, only a strong and superbroadening spectral band can be observed mainly in the red-shift side of the pump wavelength. The different spectral features under these two conditions can be explained by a competition between stimulated Brillouin, Raman, and Rayleigh-Kerr scattering. Under both pump conditions, the broadening spectral distributions are not consistent with the predictions given by stimulated Rayleigh-wing scattering theories, but can be interpreted well utilizing the theoretical model of stimulated Rayleigh-Kerr scattering. Zh. éksp. Teor. Fiz. 112, 1563–1573 (November 1997) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

IR Absorption,Raman Scattering,and IR-Vis Sum-Frequency Generation Spectroscopy as Quantitative Probes of Surface Structure

Abstract:Vibrational spectroscopy is a valuable quantitative tool for the determination of structure at surfaces. Various techniques may be applicable and useful, depending on what is available, the transparency of the substrates, the need for in situ probes, and the degree of interfacial specificity required. We examine and compare signals in infrared absorption, Raman scattering, and vibrational sum-frequency generation spectroscopy to the underlying molecular response. In all of these experiments, varying the beam polarizations enables the orientation of specific chemical functional groups to be determined. However, the sensitivity of each technique is directly connected to the manner in which the molecular response manifests itself in the measured signal. Starting with simple distributions of a single vibrational mode, leading up to multiple vibrational bands in more complex orientation distributions, we compare these three techniques in terms of their sensitivity to features of the molecular orientation distribution. This review is aimed at guiding planned experiments when multiple techniques are available for surface structural analysis.     

Efficient Quantum Algorithms for Simulating Sparse Hamiltonians

We present an efficient quantum algorithm for simulating the evolution of a quantum state for a sparse Hamiltonian H over a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a constant number of nonzero entries in each row/column, and ||H|| is bounded by a constant, we may select any positive integer k such that the simulation requires O((log^* n)t ^1+1/2k ) accesses to matrix entries of H. We also show that the temporal scaling cannot be significantly improved beyond this, because sublinear time scaling is not possible.