Generation of 1/f noise from a broken-symmetry model for the arbitrary absolute pitch of musical melodies.

PubMed

Grant, Martin; Faghihi, Niloufar

2017-11-01

A model is presented to generate power spectrum noise with intensity proportional to 1/f  as a function of frequency f. The model arises from a broken-symmetry variable, which corresponds to absolute pitch, where fluctuations occur in an attempt to restore that symmetry, influenced by interactions in the creation of musical melodies.

A systematic study of finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2014-09-01

We study systematically finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.

XLWrap - Querying and Integrating Arbitrary Spreadsheets with SPARQL

NASA Astrophysics Data System (ADS)

Langegger, Andreas; Wöß, Wolfram

In this paper a novel approach is presented for generating RDF graphs of arbitrary complexity from various spreadsheet layouts. Currently, none of the available spreadsheet-to-RDF wrappers supports cross tables and tables where data is not aligned in rows. Similar to RDF123, XLWrap is based on template graphs where fragments of triples can be mapped to specific cells of a spreadsheet. Additionally, it features a full expression algebra based on the syntax of OpenOffice Calc and various shift operations, which can be used to repeat similar mappings in order to wrap cross tables including multiple sheets and spreadsheet files. The set of available expression functions includes most of the native functions of OpenOffice Calc and can be easily extended by users of XLWrap.

Rapid calculation of acoustic fields from arbitrary continuous-wave sources.

PubMed

Treeby, Bradley E; Budisky, Jakub; Wise, Elliott S; Jaros, Jiri; Cox, B T

2018-01-01

A Green's function solution is derived for calculating the acoustic field generated by phased array transducers of arbitrary shape when driven by a single frequency continuous wave excitation with spatially varying amplitude and phase. The solution is based on the Green's function for the homogeneous wave equation expressed in the spatial frequency domain or k-space. The temporal convolution integral is solved analytically, and the remaining integrals are expressed in the form of the spatial Fourier transform. This allows the acoustic pressure for all spatial positions to be calculated in a single step using two fast Fourier transforms. The model is demonstrated through several numerical examples, including single element rectangular and spherically focused bowl transducers, and multi-element linear and hemispherical arrays.

Optical Imaging and Radiometric Modeling and Simulation

NASA Technical Reports Server (NTRS)

Ha, Kong Q.; Fitzmaurice, Michael W.; Moiser, Gary E.; Howard, Joseph M.; Le, Chi M.

2010-01-01

OPTOOL software is a general-purpose optical systems analysis tool that was developed to offer a solution to problems associated with computational programs written for the James Webb Space Telescope optical system. It integrates existing routines into coherent processes, and provides a structure with reusable capabilities that allow additional processes to be quickly developed and integrated. It has an extensive graphical user interface, which makes the tool more intuitive and friendly. OPTOOL is implemented using MATLAB with a Fourier optics-based approach for point spread function (PSF) calculations. It features parametric and Monte Carlo simulation capabilities, and uses a direct integration calculation to permit high spatial sampling of the PSF. Exit pupil optical path difference (OPD) maps can be generated using combinations of Zernike polynomials or shaped power spectral densities. The graphical user interface allows rapid creation of arbitrary pupil geometries, and entry of all other modeling parameters to support basic imaging and radiometric analyses. OPTOOL provides the capability to generate wavefront-error (WFE) maps for arbitrary grid sizes. These maps are 2D arrays containing digital sampled versions of functions ranging from Zernike polynomials to combination of sinusoidal wave functions in 2D, to functions generated from a spatial frequency power spectral distribution (PSD). It also can generate optical transfer functions (OTFs), which are incorporated into the PSF calculation. The user can specify radiometrics for the target and sky background, and key performance parameters for the instrument s focal plane array (FPA). This radiometric and detector model setup is fairly extensive, and includes parameters such as zodiacal background, thermal emission noise, read noise, and dark current. The setup also includes target spectral energy distribution as a function of wavelength for polychromatic sources, detector pixel size, and the FPA s charge diffusion modulation transfer function (MTF).

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hoek, J.

A set of programs to calculate algebraically the generating functional (free energy) of a gauge system with arbitrary external sources on a lattice has been developed. It makes use of the strong coupling expansion. For theories with the standard Tr(UUU/sup dagger/U/sup dagger/) action results have been obtained up to fourth order.

Digital processing with single electrons for arbitrary waveform generation of current

NASA Astrophysics Data System (ADS)

Okazaki, Yuma; Nakamura, Shuji; Onomitsu, Koji; Kaneko, Nobu-Hisa

2018-03-01

We demonstrate arbitrary waveform generation of current using a GaAs-based single-electron pump. In our experiment, a digital processing algorithm known as delta-sigma modulation is incorporated into single-electron pumping to generate a density-modulated single-electron stream, by which we demonstrate the generation of arbitrary waveforms of current including sinusoidal, square, and triangular waves with a peak-to-peak amplitude of approximately 10 pA and an output bandwidth ranging from dc to close to 1 MHz. The developed current generator can be used as the precise and calculable current reference required for measurements of current noise in low-temperature experiments.

Arbitrary nonlinearity is sufficient to represent all functions by neural networks - A theorem

NASA Technical Reports Server (NTRS)

Kreinovich, Vladik YA.

1991-01-01

It is proved that if we have neurons implementing arbitrary linear functions and a neuron implementing one (arbitrary but smooth) nonlinear function g(x), then for every continuous function f(x sub 1,..., x sub m) of arbitrarily many variables, and for arbitrary e above 0, we can construct a network that consists of g-neurons and linear neurons, and computes f with precision e.

Estimation of Image Sensor Fill Factor Using a Single Arbitrary Image

PubMed Central

Wen, Wei; Khatibi, Siamak

2017-01-01

Achieving a high fill factor is a bottleneck problem for capturing high-quality images. There are hardware and software solutions to overcome this problem. In the solutions, the fill factor is known. However, this is an industrial secrecy by most image sensor manufacturers due to its direct effect on the assessment of the sensor quality. In this paper, we propose a method to estimate the fill factor of a camera sensor from an arbitrary single image. The virtual response function of the imaging process and sensor irradiance are estimated from the generation of virtual images. Then the global intensity values of the virtual images are obtained, which are the result of fusing the virtual images into a single, high dynamic range radiance map. A non-linear function is inferred from the original and global intensity values of the virtual images. The fill factor is estimated by the conditional minimum of the inferred function. The method is verified using images of two datasets. The results show that our method estimates the fill factor correctly with significant stability and accuracy from one single arbitrary image according to the low standard deviation of the estimated fill factors from each of images and for each camera. PMID:28335459

An intrinsic algorithm for parallel Poisson disk sampling on arbitrary surfaces.

PubMed

Ying, Xiang; Xin, Shi-Qing; Sun, Qian; He, Ying

2013-09-01

Poisson disk sampling has excellent spatial and spectral properties, and plays an important role in a variety of visual computing. Although many promising algorithms have been proposed for multidimensional sampling in euclidean space, very few studies have been reported with regard to the problem of generating Poisson disks on surfaces due to the complicated nature of the surface. This paper presents an intrinsic algorithm for parallel Poisson disk sampling on arbitrary surfaces. In sharp contrast to the conventional parallel approaches, our method neither partitions the given surface into small patches nor uses any spatial data structure to maintain the voids in the sampling domain. Instead, our approach assigns each sample candidate a random and unique priority that is unbiased with regard to the distribution. Hence, multiple threads can process the candidates simultaneously and resolve conflicts by checking the given priority values. Our algorithm guarantees that the generated Poisson disks are uniformly and randomly distributed without bias. It is worth noting that our method is intrinsic and independent of the embedding space. This intrinsic feature allows us to generate Poisson disk patterns on arbitrary surfaces in IR(n). To our knowledge, this is the first intrinsic, parallel, and accurate algorithm for surface Poisson disk sampling. Furthermore, by manipulating the spatially varying density function, we can obtain adaptive sampling easily.

The cosmic microwave background radiation power spectrum as a random bit generator for symmetric- and asymmetric-key cryptography.

PubMed

Lee, Jeffrey S; Cleaver, Gerald B

2017-10-01

In this note, the Cosmic Microwave Background (CMB) Radiation is shown to be capable of functioning as a Random Bit Generator, and constitutes an effectively infinite supply of truly random one-time pad values of arbitrary length. It is further argued that the CMB power spectrum potentially conforms to the FIPS 140-2 standard. Additionally, its applicability to the generation of a (n × n) random key matrix for a Vernam cipher is established.

Elliptic surface grid generation in three-dimensional space

NASA Technical Reports Server (NTRS)

Kania, Lee

1992-01-01

A methodology for surface grid generation in three dimensional space is described. The method solves a Poisson equation for each coordinate on arbitrary surfaces using successive line over-relaxation. The complete surface curvature terms were discretized and retained within the nonhomogeneous term in order to preserve surface definition; there is no need for conventional surface splines. Control functions were formulated to permit control of grid orthogonality and spacing. A method for interpolation of control functions into the domain was devised which permits their specification not only at the surface boundaries but within the interior as well. An interactive surface generation code which makes use of this methodology is currently under development.

Multivariate η-μ fading distribution with arbitrary correlation model

NASA Astrophysics Data System (ADS)

Ghareeb, Ibrahim; Atiani, Amani

2018-03-01

An extensive analysis for the multivariate ? distribution with arbitrary correlation is presented, where novel analytical expressions for the multivariate probability density function, cumulative distribution function and moment generating function (MGF) of arbitrarily correlated and not necessarily identically distributed ? power random variables are derived. Also, this paper provides exact-form expression for the MGF of the instantaneous signal-to-noise ratio at the combiner output in a diversity reception system with maximal-ratio combining and post-detection equal-gain combining operating in slow frequency nonselective arbitrarily correlated not necessarily identically distributed ?-fading channels. The average bit error probability of differentially detected quadrature phase shift keying signals with post-detection diversity reception system over arbitrarily correlated and not necessarily identical fading parameters ?-fading channels is determined by using the MGF-based approach. The effect of fading correlation between diversity branches, fading severity parameters and diversity level is studied.

Hardware simulator for optical correlation spectroscopy with Gaussian statistics and arbitrary correlation functions.

PubMed

Molteni, Matteo; Weigel, Udo M; Remiro, Francisco; Durduran, Turgut; Ferri, Fabio

2014-11-17

We present a new hardware simulator (HS) for characterization, testing and benchmarking of digital correlators used in various optical correlation spectroscopy experiments where the photon statistics is Gaussian and the corresponding time correlation function can have any arbitrary shape. Starting from the HS developed in [Rev. Sci. Instrum. 74, 4273 (2003)], and using the same I/O board (PCI-6534 National Instrument) mounted on a modern PC (Intel Core i7-CPU, 3.07GHz, 12GB RAM), we have realized an instrument capable of delivering continuous streams of TTL pulses over two channels, with a time resolution of Δt = 50ns, up to a maximum count rate of 〈I〉 ∼ 5MHz. Pulse streams, typically detected in dynamic light scattering and diffuse correlation spectroscopy experiments were generated and measured with a commercial hardware correlator obtaining measured correlation functions that match accurately the expected ones.

mrpy: Renormalized generalized gamma distribution for HMF and galaxy ensemble properties comparisons

NASA Astrophysics Data System (ADS)

Murray, Steven G.; Robotham, Aaron S. G.; Power, Chris

2018-02-01

mrpy calculates the MRP parameterization of the Halo Mass Function. It calculates basic statistics of the truncated generalized gamma distribution (TGGD) with the TGGD class, including mean, mode, variance, skewness, pdf, and cdf. It generates MRP quantities with the MRP class, such as differential number counts and cumulative number counts, and offers various methods for generating normalizations. It can generate the MRP-based halo mass function as a function of physical parameters via the mrp_b13 function, and fit MRP parameters to data in the form of arbitrary curves and in the form of a sample of variates with the SimFit class. mrpy also calculates analytic hessians and jacobians at any point, and allows the user to alternate parameterizations of the same form via the reparameterize module.

A dense array stimulator to generate arbitrary spatio-temporal tactile stimuli

PubMed Central

Killebrew, Justin H.; Bensmaïa, Sliman J.; Dammann, John F.; Denchev, Peter; Hsiao, Steven S.; Craig, James C.

2007-01-01

The generation and presentation of tactile stimuli presents a unique challenge. Unlike vision and audition, in which standard equipment such as monitors and audio systems can be used for most experiments, tactile stimuli and/or stimulators often have to be tailor-made for a given study. Here, we present a novel tactile stimulator designed to present arbitrary spatio-temporal stimuli to the skin. The stimulator consists of 400 pins, arrayed over a 1 cm2 area, each under independent computer control. The dense array allows for an unprecedented number of stimuli to be presented within an experimental session (e.g., up to 1200 stimuli per minute) and for stimuli to be generated adaptively. The stimulator can be used in a variety of modes and can deliver indented and scanned patterns as well as stimuli defined by mathematical spatio-temporal functions (e.g., drifting sinusoids). We describe the hardware and software of the system, and discuss previous and prospective applications. PMID:17134760

General kinetic solution for the Biermann battery with an associated pressure anisotropy generation

NASA Astrophysics Data System (ADS)

Schoeffler, K. M.; Silva, L. O.

2018-01-01

Fully kinetic analytic calculations of an initially Maxwellian distribution with arbitrary density and temperature gradients exhibit the development of temperature anisotropies and magnetic field growth associated with the Biermann battery. The calculation, performed by taking a small order expansion of the ratio of the Debye length to the gradient scale, predicts anisotropies and magnetic fields as a function of space given an arbitrary temperature and density profile. These predictions are shown to qualitatively match the values measured from particle-in-cell simulations, where the development of the Weibel instability occurs at the same location and with a wavenumber aligned with the predicted temperature anisotropy.

Fully Automated Single-Zone Elliptic Grid Generation for Mars Science Laboratory (MSL) Aeroshell and Canopy Geometries

NASA Technical Reports Server (NTRS)

kaul, Upender K.

2008-01-01

A procedure for generating smooth uniformly clustered single-zone grids using enhanced elliptic grid generation has been demonstrated here for the Mars Science Laboratory (MSL) geometries such as aeroshell and canopy. The procedure obviates the need for generating multizone grids for such geometries, as reported in the literature. This has been possible because the enhanced elliptic grid generator automatically generates clustered grids without manual prescription of decay parameters needed with the conventional approach. In fact, these decay parameters are calculated as decay functions as part of the solution, and they are not constant over a given boundary. Since these decay functions vary over a given boundary, orthogonal grids near any arbitrary boundary can be clustered automatically without having to break up the boundaries and the corresponding interior domains into various zones for grid generation.

Fast generation of three-dimensional computational boundary-conforming periodic grids of C-type. [for turbine blades and propellers

NASA Technical Reports Server (NTRS)

Dulikravich, D. S.

1982-01-01

A fast computer program, GRID3C, was developed to generate multilevel three dimensional, C type, periodic, boundary conforming grids for the calculation of realistic turbomachinery and propeller flow fields. The technique is based on two analytic functions that conformally map a cascade of semi-infinite slits to a cascade of doubly infinite strips on different Riemann sheets. Up to four consecutively refined three dimensional grids are automatically generated and permanently stored on four different computer tapes. Grid nonorthogonality is introduced by a separate coordinate shearing and stretching performed in each of three coordinate directions. The grids are easily clustered closer to the blade surface, the trailing and leading edges and the hub or shroud regions by changing appropriate input parameters. Hub and duct (or outer free boundary) have different axisymmetric shapes. A vortex sheet of arbitrary thickness emanating smoothly from the blade trailing edge is generated automatically by GRID3C. Blade cross sectional shape, chord length, twist angle, sweep angle, and dihedral angle can vary in an arbitrary smooth fashion in the spanwise direction.

Model Checking a Self-Stabilizing Distributed Clock Synchronization Protocol for Arbitrary Digraphs

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.

2011-01-01

This report presents the mechanical verification of a self-stabilizing distributed clock synchronization protocol for arbitrary digraphs in the absence of faults. This protocol does not rely on assumptions about the initial state of the system, other than the presence of at least one node, and no central clock or a centrally generated signal, pulse, or message is used. The system under study is an arbitrary, non-partitioned digraph ranging from fully connected to 1-connected networks of nodes while allowing for differences in the network elements. Nodes are anonymous, i.e., they do not have unique identities. There is no theoretical limit on the maximum number of participating nodes. The only constraint on the behavior of the node is that the interactions with other nodes are restricted to defined links and interfaces. This protocol deterministically converges within a time bound that is a linear function of the self-stabilization period.

Finite BRST-BFV transformations for dynamical systems with second-class constraints

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2015-06-01

We study finite field-dependent BRST-BFV transformations for dynamical systems with first- and second-class constraints within the generalized Hamiltonian formalism. We find explicitly their Jacobians and the form of a solution to the compensation equation necessary for generating an arbitrary finite change of gauge-fixing functionals in the path integral.

The Hurwitz Enumeration Problem of Branched Covers and Hodge Integrals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Yun S.

We use algebraic methods to compute the simple Hurwitz numbers for arbitrary source and target Riemann surfaces. For an elliptic curve target, we reproduce the results previously obtained by string theorists. Motivated by the Gromov-Witten potentials, we find a general generating function for the simple Hurwitz numbers in terms of the representation theory of the symmetric group S{sub n}. We also find a generating function for Hodge integrals on the moduli space {bar M}{sub g,2} of Riemann surfaces with two marked points, similar to that found by Faber and Pandharipande for the case of one marked point.

DAC-board based X-band EPR spectrometer with arbitrary waveform control

NASA Astrophysics Data System (ADS)

Kaufmann, Thomas; Keller, Timothy J.; Franck, John M.; Barnes, Ryan P.; Glaser, Steffen J.; Martinis, John M.; Han, Songi

2013-10-01

We present arbitrary control over a homogenous spin system, demonstrated on a simple, home-built, electron paramagnetic resonance (EPR) spectrometer operating at 8-10 GHz (X-band) and controlled by a 1 GHz arbitrary waveform generator (AWG) with 42 dB (i.e. 14-bit) of dynamic range. Such a spectrometer can be relatively easily built from a single DAC (digital to analog converter) board with a modest number of stock components and offers powerful capabilities for automated digital calibration and correction routines that allow it to generate shaped X-band pulses with precise amplitude and phase control. It can precisely tailor the excitation profiles "seen" by the spins in the microwave resonator, based on feedback calibration with experimental input. We demonstrate the capability to generate a variety of pulse shapes, including rectangular, triangular, Gaussian, sinc, and adiabatic rapid passage waveforms. We then show how one can precisely compensate for the distortion and broadening caused by transmission into the microwave cavity in order to optimize corrected waveforms that are distinctly different from the initial, uncorrected waveforms. Specifically, we exploit a narrow EPR signal whose width is finer than the features of any distortions in order to map out the response to a short pulse, which, in turn, yields the precise transfer function of the spectrometer system. This transfer function is found to be consistent for all pulse shapes in the linear response regime. In addition to allowing precise waveform shaping capabilities, the spectrometer presented here offers complete digital control and calibration of the spectrometer that allows one to phase cycle the pulse phase with 0.007° resolution and to specify the inter-pulse delays and pulse durations to ⩽250 ps resolution. The implications and potential applications of these capabilities will be discussed.

Thermal conductivity, electrical resistivity, and thermopower of aerospace alloys from 4 to 300 K. 6: Fe-22Cr-13Ni-5Mn stainless steel

NASA Technical Reports Server (NTRS)

Hust, J. G.; Sparks, L. L.

1971-01-01

The equipment and techniques for determining the thermal conductivity, electrical resistivity Lorenz ratio, and thermopower characteristics of Fe-22Cr-13Ni-5Mn stainless steel are discussed. The dimensions of the specimen and its preparation are described. The experimental data are represented by arbitrary functions over the entire range and smooth tables are generated from these functions.

Amplitude Modulator Chassis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Erbert, G

2009-09-01

The Amplitude Modulator Chassis (AMC) is the final component in the MOR system and connects directly to the PAM input through a 100-meter fiber. The 48 AMCs temporally shape the 48 outputs of the MOR using an arbitrary waveform generator coupled to an amplitude modulator. The amplitude modulation element is a two stage, Lithium Niobate waveguide device, where the intensity of the light passing through the device is a function of the electrical drive applied. The first stage of the modulator is connected to a programmable high performance Arbitrary Waveform Generator (AWG) consisting of 140 impulse generators space 250 psmore » apart. An arbitrary waveform is generated by independently varying the amplitude of each impulse generator and then summing the impulses together. In addition to the AWG a short pulse generator is also connected to the first stage of the modulator to provide a sub 100-ps pulse used for timing experiments. The second stage of the modulator is connect to a square pulse generator used to further attenuate any pre or post pulse light passing through the first stage of the modulator. The fast rise and fall time of the square pulse generator is also used to produce fast rise and fall times of the AWG by clipping the AWG pulse. For maximum extinction, a pulse bias voltage is applied to each stage of the modulator. A pulse voltage is applied as opposed to a DC voltage to prevent charge buildup on the modulator. Each bias voltage is adjustable to provide a minimum of 50-dB extinction. The AMC is controlled through ICCS to generate the desired temporal pulse shape. This process involves a closed-loop control algorithm, which compares the desired temporal waveform to the produced optical pulse, and iterates the programming of the AWG until the two waveforms agree within an allowable tolerance.« less

High-order time-marching reinitialization for regional level-set functions

NASA Astrophysics Data System (ADS)

Pan, Shucheng; Lyu, Xiuxiu; Hu, Xiangyu Y.; Adams, Nikolaus A.

2018-02-01

In this work, the time-marching reinitialization method is extended to compute the unsigned distance function in multi-region systems involving arbitrary number of regions. High order and interface preservation are achieved by applying a simple mapping that transforms the regional level-set function to the level-set function and a high-order two-step reinitialization method which is a combination of the closest point finding procedure and the HJ-WENO scheme. The convergence failure of the closest point finding procedure in three dimensions is addressed by employing a proposed multiple junction treatment and a directional optimization algorithm. Simple test cases show that our method exhibits 4th-order accuracy for reinitializing the regional level-set functions and strictly satisfies the interface-preserving property. The reinitialization results for more complex cases with randomly generated diagrams show the capability our method for arbitrary number of regions N, with a computational effort independent of N. The proposed method has been applied to dynamic interfaces with different types of flows, and the results demonstrate high accuracy and robustness.

A computer graphics based model for scattering from objects of arbitrary shapes in the optical region

NASA Technical Reports Server (NTRS)

Goel, Narendra S.; Rozehnal, Ivan; Thompson, Richard L.

1991-01-01

A computer-graphics-based model, named DIANA, is presented for generation of objects of arbitrary shape and for calculating bidirectional reflectances and scattering from them, in the visible and infrared region. The computer generation is based on a modified Lindenmayer system approach which makes it possible to generate objects of arbitrary shapes and to simulate their growth, dynamics, and movement. Rendering techniques are used to display an object on a computer screen with appropriate shading and shadowing and to calculate the scattering and reflectance from the object. The technique is illustrated with scattering from canopies of simulated corn plants.

Automated generation of influence functions for planar crack problems

NASA Technical Reports Server (NTRS)

Sire, Robert A.; Harris, David O.; Eason, Ernest D.

1989-01-01

A numerical procedure for the generation of influence functions for Mode I planar problems is described. The resulting influence functions are in a form for convenient evaluation of stress-intensity factors for complex stress distributions. Crack surface displacements are obtained by a least-squares solution of the Williams eigenfunction expansion for displacements in a cracked body. Discrete values of the influence function, evaluated using the crack surface displacements, are curve fit using an assumed functional form. The assumed functional form includes appropriate limit-behavior terms for very deep and very shallow cracks. Continuous representation of the influence function provides a convenient means for evaluating stress-intensity factors for arbitrary stress distributions by numerical integration. The procedure is demonstrated for an edge-cracked strip and a radially cracked disk. Comparisons with available published results demonstrate the accuracy of the procedure.

Conditional generation of an arbitrary superposition of coherent states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Takeoka, Masahiro; Sasaki, Masahide

2007-06-15

We present a scheme to conditionally generate an arbitrary superposition of a pair of coherent states from a squeezed vacuum by means of the modified photon subtraction where a coherent state ancilla and two on/off type detectors are used. We show that, even including realistic imperfections of the detectors, our scheme can generate a target state with a high fidelity. The amplitude of the generated states can be amplified by conditional homodyne detections.

Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights

PubMed Central

Nicola, Wilten; Tripp, Bryan; Scott, Matthew

2016-01-01

A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF). The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks. PMID:26973503

Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights.

PubMed

Nicola, Wilten; Tripp, Bryan; Scott, Matthew

2016-01-01

A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF). The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks.

Synthesis of arbitrary pulse waveforms in QCL-seeded ns-pulse CO₂ laser for optimization of an LPP EUV source.

PubMed

Nowak, Krzysztof M; Kurosawa, Yoshiaki; Suganuma, Takashi; Kawasuji, Yasufumi; Nakarai, Hiroaki; Saito, Takashi; Fujimoto, Junichi; Mizoguchi, Hakaru

2016-07-01

One of the unique features of the quantum-cascade-laser-seeded, nanosecond-pulse CO₂ laser, invented for the purpose of generation of extreme UV by laser-produced-plasma, is a robust synthesis of arbitrary pulse waveforms. In the present Letter we report on experimental results that are, to our best knowledge, the first demonstration of such functionality obtainable from nanosecond-pulse CO₂ laser technology. An online pulse duration adjustment within 10-40 ns was demonstrated, and a few exemplary pulse waveforms were synthesized, such as "tophat," "tailspike," and "leadspike" shapes. Such output characteristics may be useful to optimize the performance of LPP EUV source.

Photonic Generation and Detection of Arbitrary MMW Waveform for High-Resolution MMW Radar Imaging

DTIC Science & Technology

2014-12-06

20ft ~ 2cm Destribution A: Approved for public release. Distribution is unlimited. Fig. 1. The system setup for our MMW arbitrary waveform generation...IOA(AOARD) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) AOARD-134088 12. DISTRIBUTION/AVAILABILITY STATEMENT Destribution A: Approved for public...traveling carrier photodiode (NBUTC-PD), advanced optical pulse shaper system , and ultrafast TDS system to demonstrate the photonic generation and detection

Generation of an arbitrary concatenated Greenberger-Horne-Zeilinger state with single photons

NASA Astrophysics Data System (ADS)

Chen, Shan-Shan; Zhou, Lan; Sheng, Yu-Bo

2017-02-01

The concatenated Greenberger-Horne-Zeilinger (C-GHZ) state is a new kind of logic-qubit entangled state, which may have extensive applications in future quantum communication. In this letter, we propose a protocol for constructing an arbitrary C-GHZ state with single photons. We exploit the cross-Kerr nonlinearity for this purpose. This protocol has some advantages over previous protocols. First, it only requires two kinds of cross-Kerr nonlinearities to generate single phase shifts  ±θ. Second, it is not necessary to use sophisticated m-photon Toffoli gates. Third, this protocol is deterministic and can be used to generate an arbitrary C-GHZ state. This protocol may be useful in future quantum information processing based on the C-GHZ state.

Transient potentials in dendritic systems of arbitrary geometry.

PubMed

Butz, E G; Cowan, J D

1974-09-01

A simple graphical calculus is developed that generates analytic solutions for membrane potential transforms at any point on the dendritic tree of neurons with arbitrary dendritic geometries, in response to synaptic "current" inputs. Such solutions permit the computation of transients in neurons with arbitrary geometry and may facilitate analysis of the role of dendrites in such cells.

Free boundary skin current MHD (magnetohydrodynamic) equilibria

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reusch, M.F.

1988-02-01

Function theoretic methods in the complex plane are used to develop simple parametric hodograph formulae which generate sharp boundary equilibria of arbitrary shape. The related method of Gorenflo and Merkel is discussed. A numerical technique for the construction of solutions, based on one of the methods is presented. A study is made of the bifurcations of an equilibrium of general form. 28 refs., 9 figs.

Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integrals

NASA Astrophysics Data System (ADS)

Patel, Hiren H.

2017-09-01

This article summarizes new features and enhancements of the first major update of Package-X. Package-X 2.0 can now generate analytic expressions for arbitrarily high rank dimensionally regulated tensor integrals with up to four distinct propagators, each with arbitrary integer weight, near an arbitrary even number of spacetime dimensions, giving UV divergent, IR divergent, and finite parts at (almost) any real-valued kinematic point. Additionally, it can generate multivariable Taylor series expansions of these integrals around any non-singular kinematic point to arbitrary order. All special functions and abbreviations output by Package-X 2.0 support Mathematica's arbitrary precision evaluation capabilities to deal with issues of numerical stability. Finally, tensor algebraic routines of Package-X have been polished and extended to support open fermion chains both on and off shell. The documentation (equivalent to over 100 printed pages) is accessed through Mathematica's Wolfram Documentation Center and contains information on all Package-X symbols, with over 300 basic usage examples, 3 project-scale tutorials, and instructions on linking to FEYNCALC and LOOPTOOLS. Program files doi:http://dx.doi.org/10.17632/yfkwrd4d5t.1 Licensing provisions: CC by 4.0 Programming language: Mathematica (Wolfram Language) Journal reference of previous version: H. H. Patel, Comput. Phys. Commun 197, 276 (2015) Does the new version supersede the previous version?: Yes Summary of revisions: Extension to four point one-loop integrals with higher powers of denominator factors, separate extraction of UV and IR divergent parts, testing for power IR divergences, construction of Taylor series expansions of one-loop integrals, numerical evaluation with arbitrary precision arithmetic, manipulation of fermion chains, improved tensor algebraic routines, and much expanded documentation. Nature of problem: Analytic calculation of one-loop integrals in relativistic quantum field theory. Solution method: Passarino-Veltman reduction formula, Denner-Dittmaier reduction formulae, and additional algorithms described in the manuscript. Restrictions: One-loop integrals are limited to those involving no more than four denominator factors.

On-chip generation of Einstein-Podolsky-Rosen states with arbitrary symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gräfe, Markus; Heilmann, René; Nolte, Stefan

We experimentally demonstrate a method for integrated-optical generation of two-photon Einstein-Podolsky-Rosen states featuring arbitrary symmetries. In our setting, we employ detuned directional couplers to impose a freely tailorable phase between the two modes of the state. Our results allow to mimic the quantum random walk statistics of bosons, fermions, and anyons, particles with fractional exchange statistics.

Solving the Hamilton-Jacobi equation for general relativity

NASA Astrophysics Data System (ADS)

Parry, J.; Salopek, D. S.; Stewart, J. M.

1994-03-01

We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly invariant under reparametrizations of the spatial coordinates (``gauge invariant''). At each order we solve the Hamiltonian constraint using a conformal transformation of the three-metric as well as a line integral in superspace. This gives a recursion relation for the generating functional which then may be solved to arbitrary order simply by functionally differentiating previous orders. At fourth order in spatial gradients we demonstrate solutions for irrotational dust as well as for a scalar field. We explicitly evolve the three-metric to the same order. This method can be used to derive the Zel'dovich approximation for general relativity.

Arbitrary waveform modulated pulse EPR at 200 GHz

NASA Astrophysics Data System (ADS)

Kaminker, Ilia; Barnes, Ryan; Han, Songi

2017-06-01

We report here on the implementation of arbitrary waveform generation (AWG) capabilities at ∼200 GHz into an Electron Paramagnetic Resonance (EPR) and Dynamic Nuclear Polarization (DNP) instrument platform operating at 7 T. This is achieved with the integration of a 1 GHz, 2 channel, digital to analog converter (DAC) board that enables the generation of coherent arbitrary waveforms at Ku-band frequencies with 1 ns resolution into an existing architecture of a solid state amplifier multiplier chain (AMC). This allows for the generation of arbitrary phase- and amplitude-modulated waveforms at 200 GHz with >150 mW power. We find that the non-linearity of the AMC poses significant difficulties in generating amplitude-modulated pulses at 200 GHz. We demonstrate that in the power-limited regime of ω1 < 1 MHz phase-modulated pulses were sufficient to achieve significant improvements in broadband (>10 MHz) spin manipulation in incoherent (inversion), as well as coherent (echo formation) experiments. Highlights include the improvement by one order of magnitude in inversion bandwidth compared to that of conventional rectangular pulses, as well as a factor of two in improvement in the refocused echo intensity at 200 GHz.

Transient Potentials in Dendritic Systems of Arbitrary Geometry

PubMed Central

Butz, Edward G.; Cowan, Jack D.

1974-01-01

A simple graphical calculus is developed that generates analytic solutions for membrane potential transforms at any point on the dendritic tree of neurons with arbitrary dendritic geometries, in response to synaptic “current” inputs. Such solutions permit the computation of transients in neurons with arbitrary geometry and may facilitate analysis of the role of dendrites in such cells. PMID:4416699

Rapidly reconfigurable high-fidelity optical arbitrary waveform generation in heterogeneous photonic integrated circuits.

PubMed

Feng, Shaoqi; Qin, Chuan; Shang, Kuanping; Pathak, Shibnath; Lai, Weicheng; Guan, Binbin; Clements, Matthew; Su, Tiehui; Liu, Guangyao; Lu, Hongbo; Scott, Ryan P; Ben Yoo, S J

2017-04-17

This paper demonstrates rapidly reconfigurable, high-fidelity optical arbitrary waveform generation (OAWG) in a heterogeneous photonic integrated circuit (PIC). The heterogeneous PIC combines advantages of high-speed indium phosphide (InP) modulators and low-loss, high-contrast silicon nitride (Si₃N₄) arrayed waveguide gratings (AWGs) so that high-fidelity optical waveform syntheses with rapid waveform updates are possible. The generated optical waveforms spanned a 160 GHz spectral bandwidth starting from an optical frequency comb consisting of eight comb lines separated by 20 GHz channel spacing. The Error Vector Magnitude (EVM) values of the generated waveforms were approximately 16.4%. The OAWG module can rapidly and arbitrarily reconfigure waveforms upon every pulse arriving at 2 ns repetition time. The result of this work indicates the feasibility of truly dynamic optical arbitrary waveform generation where the reconfiguration rate or the modulator bandwidth must exceed the channel spacing of the AWG and the optical frequency comb.

Dispersion in a thermal plasma including arbitrary degeneracy and quantum recoil.

PubMed

Melrose, D B; Mushtaq, A

2010-11-01

The longitudinal response function for a thermal electron gas is calculated including two quantum effects exactly, degeneracy, and the quantum recoil. The Fermi-Dirac distribution is expanded in powers of a parameter that is small in the nondegenerate limit and the response function is evaluated in terms of the conventional plasma dispersion function to arbitrary order in this parameter. The infinite sum is performed in terms of polylogarithms in the long-wavelength and quasistatic limits, giving results that apply for arbitrary degeneracy. The results are applied to the dispersion relations for Langmuir waves and to screening, reproducing known results in the nondegenerate and completely degenerate limits, and generalizing them to arbitrary degeneracy.

Central command generated prior to arbitrary motor execution induces muscle vasodilatation at the beginning of dynamic exercise.

PubMed

Ishii, Kei; Matsukawa, Kanji; Liang, Nan; Endo, Kana; Idesako, Mitsuhiro; Asahara, Ryota; Kadowaki, Akito; Wakasugi, Rie; Takahashi, Makoto

2016-06-15

The purpose of this study was to examine the role of central command, generated prior to arbitrary motor execution, in cardiovascular and muscle blood flow regulation during exercise. Thirty two subjects performed 30 s of two-legged cycling or 1 min of one-legged cycling (66 ± 4% and 35% of the maximal exercise intensity, respectively), which was started arbitrarily or abruptly by a verbal cue (arbitrary vs. cued start). We measured the cardiovascular variables during both exercises and the relative changes in oxygenated-hemoglobin concentration (Oxy-Hb) of noncontracting vastus lateralis muscles as index of tissue blood flow and femoral blood flow to nonexercising leg during one-legged cycling. Two-legged cycling with arbitrary start caused a decrease in total peripheral resistance (TPR), which was smaller during the exercise with cued start. The greater reduction of TPR with arbitrary start was also recognized at the beginning of one-legged cycling. Oxy-Hb of noncontracting muscle increased by 3.6 ± 1% (P < 0.05) during one-legged cycling with arbitrary start, whereas such increase in Oxy-Hb was absent with cued start. The increases in femoral blood flow and vascular conductance of nonexercising leg were evident (P < 0.05) at 10 s from the onset of one-legged cycling with arbitrary start, whereas those were smaller or absent with cued start. It is likely that when voluntary exercise is started arbitrarily, central command is generated prior to motor execution and then contributes to muscle vasodilatation at the beginning of exercise. Such centrally induced muscle vasodilatation may be weakened and/or masked in the case of exercise with cued start. Copyright © 2016 the American Physiological Society.

Heating a plasma by a broadband stream of fast electrons: Fast ignition, shock ignition, and Gbar shock wave applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gus’kov, S. Yu., E-mail: guskov@sci.lebedev.ru; Nicolai, Ph.; Ribeyre, X.

2015-09-15

An exact analytic solution is found for the steady-state distribution function of fast electrons with an arbitrary initial spectrum irradiating a planar low-Z plasma with an arbitrary density distribution. The solution is applied to study the heating of a material by fast electrons of different spectra such as a monoenergetic spectrum, a step-like distribution in a given energy range, and a Maxwellian spectrum, which is inherent in laser-produced fast electrons. The heating of shock- and fast-ignited precompressed inertial confinement fusion (ICF) targets as well as the heating of a target designed to generate a Gbar shock wave for equation ofmore » state (EOS) experiments by laser-produced fast electrons with a Maxwellian spectrum is investigated. A relation is established between the energies of two groups of Maxwellian fast electrons, which are responsible for generation of a shock wave and heating the upstream material (preheating). The minimum energy of the fast and shock igniting beams as well as of the beam for a Gbar shock wave generation increases with the spectral width of the electron distribution.« less

Using Arden Syntax for the Generation of Intelligent Intensive Care Discharge Letters.

PubMed

Kraus, Stefan; Castellanos, Ixchel; Albermann, Matthias; Schuettler, Christina; Prokosch, Hans-Ulrich; Staudigel, Martin; Toddenroth, Dennis

2016-01-01

Discharge letters are an important means of communication between physicians and nurses from intensive care units and their colleagues from normal wards. The patient data management system (PDMS) used at our local intensive care units provides an export tool to create discharge letters by inserting data items from electronic medical records into predefined templates. Local intensivists criticized the limitations of this tool regarding the identification and the further processing of clinically relevant data items for a flexible creation of discharge letters. As our PDMS supports Arden Syntax, and the demanded functionalities are well within the scope of this standard, we set out to investigate the suitability of Arden Syntax for the generation of discharge letters. To provide an easy-to-understand facility for integrating data items into document templates, we created an Arden Syntax interface function which replaces the names of previously defined variables with their content in a way that permits arbitrary custom formatting by clinical users. Our approach facilitates the creation of flexible text sections by conditional statements, as well as the integration of arbitrary HTML code and dynamically generated graphs. The resulting prototype enables clinical users to apply the full set of Arden Syntax language constructs to identify and process relevant data items in a way that far exceeds the capabilities of the PDMS export tool. The generation of discharge letters is an uncommon area of application for Arden Syntax, considerably differing from its original purpose. However, we found our prototype well suited for this task and plan to evaluate it in clinical production after the next major release change of our PDMS.

Symbolic computation of equivalence transformations and parameter reduction for nonlinear physical models

NASA Astrophysics Data System (ADS)

Cheviakov, Alexei F.

2017-11-01

An efficient systematic procedure is provided for symbolic computation of Lie groups of equivalence transformations and generalized equivalence transformations of systems of differential equations that contain arbitrary elements (arbitrary functions and/or arbitrary constant parameters), using the software package GeM for Maple. Application of equivalence transformations to the reduction of the number of arbitrary elements in a given system of equations is discussed, and several examples are considered. The first computational example of generalized equivalence transformations where the transformation of the dependent variable involves an arbitrary constitutive function is presented. As a detailed physical example, a three-parameter family of nonlinear wave equations describing finite anti-plane shear displacements of an incompressible hyperelastic fiber-reinforced medium is considered. Equivalence transformations are computed and employed to radically simplify the model for an arbitrary fiber direction, invertibly reducing the model to a simple form that corresponds to a special fiber direction, and involves no arbitrary elements. The presented computation algorithm is applicable to wide classes of systems of differential equations containing arbitrary elements.

Generation of electron Airy beams.

PubMed

Voloch-Bloch, Noa; Lereah, Yossi; Lilach, Yigal; Gover, Avraham; Arie, Ady

2013-02-21

Within the framework of quantum mechanics, a unique particle wave packet exists in the form of the Airy function. Its counterintuitive properties are revealed as it propagates in time or space: the quantum probability wave packet preserves its shape despite dispersion or diffraction and propagates along a parabolic caustic trajectory, even though no force is applied. This does not contradict Newton's laws of motion, because the wave packet centroid propagates along a straight line. Nearly 30 years later, this wave packet, known as an accelerating Airy beam, was realized in the optical domain; later it was generalized to an orthogonal and complete family of beams that propagate along parabolic trajectories, as well as to beams that propagate along arbitrary convex trajectories. Here we report the experimental generation and observation of the Airy beams of free electrons. These electron Airy beams were generated by diffraction of electrons through a nanoscale hologram, which imprinted on the electrons' wavefunction a cubic phase modulation in the transverse plane. The highest-intensity lobes of the generated beams indeed followed parabolic trajectories. We directly observed a non-spreading electron wavefunction that self-heals, restoring its original shape after passing an obstacle. This holographic generation of electron Airy beams opens up new avenues for steering electronic wave packets like their photonic counterparts, because the wave packets can be imprinted with arbitrary shapes or trajectories.

Functional contributions and interactions between the human hippocampus and subregions of the striatum during arbitrary associative learning and memory

PubMed Central

Mattfeld, Aaron T.; Stark, Craig E. L.

2015-01-01

The hippocampus and striatum are thought to have different functional roles in learning and memory. It is unknown under what experimental conditions their contributions are dissimilar or converge, and the extent to which they interact over the course of learning. In order to evaluate both the functional contributions of as well as the interactions between the human hippocampus and striatum, the present study used high-resolution functional magnetic resonance imaging (fMRI) and variations of a conditional visuomotor associative learning task that either taxed arbitrary associative learning (Experiment 1) or stimulus-response learning (Experiment 2). In the first experiment we observed changes in activity in the hippocampus and anterior caudate that reflect differences between the two regions consistent with distinct computational principles. In the second experiment we observed activity in the putamen that reflected content specific representations during the learning of arbitrary conditional visuomotor associations. In both experiments the hippocampus and ventral striatum demonstrated dynamic functional coupling during the learning of new arbitrary associations, but not during retrieval of well-learned arbitrary associations using control variants of the tasks that did not preferentially tax one system versus the other. These findings suggest that both the hippocampus and subregions of the dorsal striatum contribute uniquely to the learning of arbitrary associations while the hippocampus and ventral striatum interact over the course of learning. PMID:25560298

Invariant Functions, Symmetries and Primary Branch Solutions of First Order Autonomous Systems

NASA Astrophysics Data System (ADS)

Lou, Sen-Yue; Yao, Ruo-Xia

2017-07-01

An invariant function (IF) is defined as a multiplier of a symmetry that means a symmetry multiplied by an IF is still a symmetry. Primary branch solutions of arbitrary first order scalar systems can be obtained by means of the IF and its related symmetry approach. Especially, one recursion operator and some sets of infinitely many high order symmetries are also explicitly given for arbitrary (1+1)-dimensional first order autonomous systems. Because of the intrusion of the arbitrary function, various implicit special exact solutions can be found by fixing the arbitrary functions and selecting different seed solutions. Supported by the National Natural Science Foundations of China under Grant Nos. 11435005, 11471004, 11175092, and 11205092, Shanghai Knowledge Service Platform for Trustworthy Internet of Things No. ZF1213 and K. C. Wong Magna Fund in Ningbo University

Transport Coefficients from Large Deviation Functions

NASA Astrophysics Data System (ADS)

Gao, Chloe; Limmer, David

2017-10-01

We describe a method for computing transport coefficients from the direct evaluation of large deviation function. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based importance sampling. Equilibrium fluctuations of molecular currents are characterized by their large deviation functions, which is a scaled cumulant generating function analogous to the free energy. A diffusion Monte Carlo algorithm is used to evaluate the large deviation functions, from which arbitrary transport coefficients are derivable. We find significant statistical improvement over traditional Green-Kubo based calculations. The systematic and statistical errors of this method are analyzed in the context of specific transport coefficient calculations, including the shear viscosity, interfacial friction coefficient, and thermal conductivity.

Probability function of breaking-limited surface elevation. [wind generated waves of ocean

NASA Technical Reports Server (NTRS)

Tung, C. C.; Huang, N. E.; Yuan, Y.; Long, S. R.

1989-01-01

The effect of wave breaking on the probability function of surface elevation is examined. The surface elevation limited by wave breaking zeta sub b(t) is first related to the original wave elevation zeta(t) and its second derivative. An approximate, second-order, nonlinear, non-Gaussian model for zeta(t) of arbitrary but moderate bandwidth is presented, and an expression for the probability density function zeta sub b(t) is derived. The results show clearly that the effect of wave breaking on the probability density function of surface elevation is to introduce a secondary hump on the positive side of the probability density function, a phenomenon also observed in wind wave tank experiments.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, H.

In this dissertation we study a procedure which restarts a Markov process when the process is killed by some arbitrary multiplicative functional. The regenerative nature of this revival procedure is characterized through a Markov renewal equation. An interesting duality between the revival procedure and the classical killing operation is found. Under the condition that the multiplicative functional possesses an intensity, the generators of the revival process can be written down explicitly. An intimate connection is also found between the perturbation of the sample path of a Markov process and the perturbation of a generator (in Kato's sense). The applications ofmore » the theory include the study of the processes like piecewise-deterministic Markov process, virtual waiting time process and the first entrance decomposition (taboo probability).« less

Photonic generation of low phase noise arbitrary chirped microwave waveforms with large time-bandwidth product.

PubMed

Xie, Weilin; Xia, Zongyang; Zhou, Qian; Shi, Hongxiao; Dong, Yi; Hu, Weisheng

2015-07-13

We present a photonic approach for generating low phase noise, arbitrary chirped microwave waveforms based on heterodyne beating between high order correlated comb lines extracted from frequency-agile optical frequency comb. Using the dual heterodyne phase transfer scheme, extrinsic phase noises induced by the separate optical paths are efficiently suppressed by 42-dB at 1-Hz offset frequency. Linearly chirped microwave waveforms are achieved within 30-ms temporal duration, contributing to a large time-bandwidth product. The linearity measurement leads to less than 90 kHz RMS frequency error during the entire chirp duration, exhibiting excellent linearity for the microwave and sub-THz waveforms. The capability of generating arbitrary waveforms up to sub-THz band with flexible temporal duration, long repetition period, broad bandwidth, and large time-bandwidth product is investigated and discussed.

Electron beam deflection control system of a welding and surface modification installation

NASA Astrophysics Data System (ADS)

Koleva, E.; Dzharov, V.; Gerasimov, V.; Tsvetkov, K.; Mladenov, G.

2018-03-01

In the present work, we examined the patterns of the electron beam motion when controlling the transverse with respect to the axis of the beam homogeneous magnetic field created by the coils of the deflection system the electron gun. During electron beam processes, the beam motion is determined the process type (welding, surface modification, etc.), the technological mode, the design dimensions of the electron gun and the shape of the processed samples. The electron beam motion is defined by the cumulative action of two cosine-like control signals generated by a functional generator. The signal control is related to changing the amplitudes, frequencies and phases (phase differences) of the generated voltages. We realized the motion control by applying a graphical user interface developed by us and an Arduino Uno programmable microcontroller. The signals generated were calibrated using experimental data from the available functional generator. The free and precise motion on arbitrary trajectories determines the possible applications of an electron beam process to carrying out various scientific research tasks in material processing.

Numerical generation of two-dimensional grids by the use of Poisson equations with grid control at boundaries

NASA Technical Reports Server (NTRS)

Sorenson, R. L.; Steger, J. L.

1980-01-01

A method for generating boundary-fitted, curvilinear, two dimensional grids by the use of the Poisson equations is presented. Grids of C-type and O-type were made about airfoils and other shapes, with circular, rectangular, cascade-type, and other outer boundary shapes. Both viscous and inviscid spacings were used. In all cases, two important types of grid control can be exercised at both inner and outer boundaries. First is arbitrary control of the distances between the boundaries and the adjacent lines of the same coordinate family, i.e., stand-off distances. Second is arbitrary control of the angles with which lines of the opposite coordinate family intersect the boundaries. Thus, both grid cell size (or aspect ratio) and grid cell skewness are controlled at boundaries. Reasonable cell size and shape are ensured even in cases wherein extreme boundary shapes would tend to cause skewness or poorly controlled grid spacing. An inherent feature of the Poisson equations is that lines in the interior of the grid smoothly connect the boundary points (the grid mapping functions are second order differentiable).

Position-specific automated processing of V3 env ultra-deep pyrosequencing data for predicting HIV-1 tropism

PubMed Central

Jeanne, Nicolas; Saliou, Adrien; Carcenac, Romain; Lefebvre, Caroline; Dubois, Martine; Cazabat, Michelle; Nicot, Florence; Loiseau, Claire; Raymond, Stéphanie; Izopet, Jacques; Delobel, Pierre

2015-01-01

HIV-1 coreceptor usage must be accurately determined before starting CCR5 antagonist-based treatment as the presence of undetected minor CXCR4-using variants can cause subsequent virological failure. Ultra-deep pyrosequencing of HIV-1 V3 env allows to detect low levels of CXCR4-using variants that current genotypic approaches miss. However, the computation of the mass of sequence data and the need to identify true minor variants while excluding artifactual sequences generated during amplification and ultra-deep pyrosequencing is rate-limiting. Arbitrary fixed cut-offs below which minor variants are discarded are currently used but the errors generated during ultra-deep pyrosequencing are sequence-dependant rather than random. We have developed an automated processing of HIV-1 V3 env ultra-deep pyrosequencing data that uses biological filters to discard artifactual or non-functional V3 sequences followed by statistical filters to determine position-specific sensitivity thresholds, rather than arbitrary fixed cut-offs. It allows to retain authentic sequences with point mutations at V3 positions of interest and discard artifactual ones with accurate sensitivity thresholds. PMID:26585833

Position-specific automated processing of V3 env ultra-deep pyrosequencing data for predicting HIV-1 tropism.

PubMed

Jeanne, Nicolas; Saliou, Adrien; Carcenac, Romain; Lefebvre, Caroline; Dubois, Martine; Cazabat, Michelle; Nicot, Florence; Loiseau, Claire; Raymond, Stéphanie; Izopet, Jacques; Delobel, Pierre

2015-11-20

HIV-1 coreceptor usage must be accurately determined before starting CCR5 antagonist-based treatment as the presence of undetected minor CXCR4-using variants can cause subsequent virological failure. Ultra-deep pyrosequencing of HIV-1 V3 env allows to detect low levels of CXCR4-using variants that current genotypic approaches miss. However, the computation of the mass of sequence data and the need to identify true minor variants while excluding artifactual sequences generated during amplification and ultra-deep pyrosequencing is rate-limiting. Arbitrary fixed cut-offs below which minor variants are discarded are currently used but the errors generated during ultra-deep pyrosequencing are sequence-dependant rather than random. We have developed an automated processing of HIV-1 V3 env ultra-deep pyrosequencing data that uses biological filters to discard artifactual or non-functional V3 sequences followed by statistical filters to determine position-specific sensitivity thresholds, rather than arbitrary fixed cut-offs. It allows to retain authentic sequences with point mutations at V3 positions of interest and discard artifactual ones with accurate sensitivity thresholds.

Grid generation in three dimensions by Poisson equations with control of cell size and skewness at boundary surfaces

NASA Technical Reports Server (NTRS)

Sorenson, R. L.; Steger, J. L.

1983-01-01

An algorithm for generating computational grids about arbitrary three-dimensional bodies is developed. The elliptic partial differential equation (PDE) approach developed by Steger and Sorenson and used in the NASA computer program GRAPE is extended from two to three dimensions. Forcing functions which are found automatically by the algorithm give the user the ability to control mesh cell size and skewness at boundary surfaces. This algorithm, as is typical of PDE grid generators, gives smooth grid lines and spacing in the interior of the grid. The method is applied to a rectilinear wind-tunnel case and to two body shapes in spherical coordinates.

An accurate method for evaluating the kernel of the integral equation relating lift to downwash in unsteady potential flow

NASA Technical Reports Server (NTRS)

Desmarais, R. N.

1982-01-01

The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the nonelementary integrals in the kernel by exponential functions and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. The method can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.

Free boundary skin current magnetohydrodynamic equilibria

NASA Astrophysics Data System (ADS)

Reusch, Michael F.

1988-10-01

Function theoretic methods in the complex plane are used to develop simple parametric hodograph formulas that generate sharp boundary equilibria of arbitrary shape. The related method of Gorenflo [Z. Angew. Math. Phys. 16, 279 (1965)] and Merkel (Ph.D. thesis, University of Munich, 1965) is discussed. A numerical technique for the construction of solutions, based on one of the methods, is presented. A study is made of the bifurcations of an equilibrium of general form.

Application of neural networks with orthogonal activation functions in control of dynamical systems

NASA Astrophysics Data System (ADS)

Nikolić, Saša S.; Antić, Dragan S.; Milojković, Marko T.; Milovanović, Miroslav B.; Perić, Staniša Lj.; Mitić, Darko B.

2016-04-01

In this article, we present a new method for the synthesis of almost and quasi-orthogonal polynomials of arbitrary order. Filters designed on the bases of these functions are generators of generalised quasi-orthogonal signals for which we derived and presented necessary mathematical background. Based on theoretical results, we designed and practically implemented generalised first-order (k = 1) quasi-orthogonal filter and proved its quasi-orthogonality via performed experiments. Designed filters can be applied in many scientific areas. In this article, generated functions were successfully implemented in Nonlinear Auto Regressive eXogenous (NARX) neural network as activation functions. One practical application of the designed orthogonal neural network is demonstrated through the example of control of the complex technical non-linear system - laboratory magnetic levitation system. Obtained results were compared with neural networks with standard activation functions and orthogonal functions of trigonometric shape. The proposed network demonstrated superiority over existing solutions in the sense of system performances.

An ultrasound transient elastography system with coded excitation.

PubMed

Diao, Xianfen; Zhu, Jing; He, Xiaonian; Chen, Xin; Zhang, Xinyu; Chen, Siping; Liu, Weixiang

2017-06-28

Ultrasound transient elastography technology has found its place in elastography because it is safe and easy to operate. However, it's application in deep tissue is limited. The aim of this study is to design an ultrasound transient elastography system with coded excitation to obtain greater detection depth. The ultrasound transient elastography system requires tissue vibration to be strictly synchronous with ultrasound detection. Therefore, an ultrasound transient elastography system with coded excitation was designed. A central component of this transient elastography system was an arbitrary waveform generator with multi-channel signals output function. This arbitrary waveform generator was used to produce the tissue vibration signal, the ultrasound detection signal and the synchronous triggering signal of the radio frequency data acquisition system. The arbitrary waveform generator can produce different forms of vibration waveform to induce different shear wave propagation in the tissue. Moreover, it can achieve either traditional pulse-echo detection or a phase-modulated or a frequency-modulated coded excitation. A 7-chip Barker code and traditional pulse-echo detection were programmed on the designed ultrasound transient elastography system to detect the shear wave in the phantom excited by the mechanical vibrator. Then an elasticity QA phantom and sixteen in vitro rat livers were used for performance evaluation of the two detection pulses. The elasticity QA phantom's results show that our system is effective, and the rat liver results show the detection depth can be increased more than 1 cm. In addition, the SNR (signal-to-noise ratio) is increased by 15 dB using the 7-chip Barker coded excitation. Applying 7-chip Barker coded excitation technique to the ultrasound transient elastography can increase the detection depth and SNR. Using coded excitation technology to assess the human liver, especially in obese patients, may be a good choice.

Arbitrary waveform generator to improve laser diode driver performance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fulkerson, Jr, Edward Steven

2015-11-03

An arbitrary waveform generator modifies the input signal to a laser diode driver circuit in order to reduce the overshoot/undershoot and provide a "flat-top" signal to the laser diode driver circuit. The input signal is modified based on the original received signal and the feedback from the laser diode by measuring the actual current flowing in the laser diode after the original signal is applied to the laser diode.

Polarization-multiplexed plasmonic phase generation with distributed nanoslits.

PubMed

Lee, Seung-Yeol; Kim, Kyuho; Lee, Gun-Yeal; Lee, Byoungho

2015-06-15

Methods for multiplexing surface plasmon polaritons (SPPs) have been attracting much attention due to their potentials for plasmonic integrated systems, plasmonic holography, and optical tweezing. Here, using closely-distanced distributed nanoslits, we propose a method for generating polarization-multiplexed SPP phase profiles which can be applied for implementing general SPP phase distributions. Two independent types of SPP phase generation mechanisms - polarization-independent and polarization-reversible ones - are combined to generate fully arbitrary phase profiles for each optical handedness. As a simple verification of the proposed scheme, we experimentally demonstrate that the location of plasmonic focus can be arbitrary designed, and switched by the change of optical handedness.

Simulation of a Single-Element Lean-Direct Injection Combustor Using Arbitrary Polyhedral Mesh

NASA Technical Reports Server (NTRS)

Wey, Thomas; Liu, Nan-Suey

2012-01-01

This paper summarizes procedures of generating the arbitrary polyhedral mesh as well as presents sample results from its application to the numerical solution of a single-element LDI combustor using a preliminary version of the new OpenNCC.

Automatic numerical evaluation of vacancy-mediated transport for arbitrary crystals: Onsager coefficients in the dilute limit using a Green function approach

NASA Astrophysics Data System (ADS)

Trinkle, Dallas R.

2017-10-01

A general solution for vacancy-mediated diffusion in the dilute-vacancy/dilute-solute limit for arbitrary crystal structures is derived from the master equation. A general numerical approach to the vacancy lattice Green function reduces to the sum of a few analytic functions and numerical integration of a smooth function over the Brillouin zone for arbitrary crystals. The Dyson equation solves for the Green function in the presence of a solute with arbitrary but finite interaction range to compute the transport coefficients accurately, efficiently and automatically, including cases with very large differences in solute-vacancy exchange rates. The methodology takes advantage of the space group symmetry of a crystal to reduce the complexity of the matrix inversion in the Dyson equation. An open-source implementation of the algorithm is available, and numerical results are presented for the convergence of the integration error of the bare vacancy Green function, and tracer correlation factors for a variety of crystals including wurtzite (hexagonal diamond) and garnet.

Generalized serial search code acquisition - The equivalent circular state diagram approach

NASA Technical Reports Server (NTRS)

Polydoros, A.; Simon, M. K.

1984-01-01

A transform-domain method for deriving the generating function of the acquisition process resulting from an arbitrary serial search strategy is presented. The method relies on equivalent circular state diagrams, uses Mason's formula from flow-graph theory, and employs a minimum number of required parameters. The transform-domain approach is briefly described and the concept of equivalent circular state diagrams is introduced and exploited to derive the generating function and resulting mean acquisition time for three particular cases of interest, the continuous/center Z search, the broken/center Z search, and the expanding window search. An optimization of the latter technique is performed whereby the number of partial windows which minimizes the mean acquisition time is determined. The numerical results satisfy certain intuitive predictions and provide useful design guidelines for such systems.

Generation of arbitrary vector fields based on a pair of orthogonal elliptically polarized base vectors.

PubMed

Xu, Danfeng; Gu, Bing; Rui, Guanghao; Zhan, Qiwen; Cui, Yiping

2016-02-22

We present an arbitrary vector field with hybrid polarization based on the combination of a pair of orthogonal elliptically polarized base vectors on the Poincaré sphere. It is shown that the created vector field is only dependent on the latitude angle 2χ but is independent on the longitude angle 2ψ on the Poincaré sphere. By adjusting the latitude angle 2χ, which is related to two identical waveplates in a common path interferometric arrangement, one could obtain arbitrary type of vector fields. Experimentally, we demonstrate the generation of such kind of vector fields and confirm the distribution of state of polarization by the measurement of Stokes parameters. Besides, we investigate the tight focusing properties of these vector fields. It is found that the additional degree of freedom 2χ provided by arbitrary vector field with hybrid polarization allows one to control the spatial structure of polarization and to engineer the focusing field.

Wigner functions on non-standard symplectic vector spaces

NASA Astrophysics Data System (ADS)

Dias, Nuno Costa; Prata, João Nuno

2018-01-01

We consider the Weyl quantization on a flat non-standard symplectic vector space. We focus mainly on the properties of the Wigner functions defined therein. In particular we show that the sets of Wigner functions on distinct symplectic spaces are different but have non-empty intersections. This extends previous results to arbitrary dimension and arbitrary (constant) symplectic structure. As a by-product we introduce and prove several concepts and results on non-standard symplectic spaces which generalize those on the standard symplectic space, namely, the symplectic spectrum, Williamson's theorem, and Narcowich-Wigner spectra. We also show how Wigner functions on non-standard symplectic spaces behave under the action of an arbitrary linear coordinate transformation.

Aperiodic Volume Optics

NASA Astrophysics Data System (ADS)

Gerke, Tim D.

Presented in this thesis is an investigation into aperiodic volume optical devices. The three main topics of research and discussion are the aperiodic volume optical devices that we call computer-generated volume holograms (CGVH), defects within periodic 3D photonic crystals, and non-periodic, but ordered 3D quasicrystals. The first of these devices, CGVHs, are designed and investigated numerically and experimentally. We study the performance of multi-layered amplitude computer-generated volume holograms in terms of efficiency and angular/frequency selectivity. Simulation results show that such aperiodic devices can increase diffraction efficiency relative to periodic amplitude volume holograms while maintaining angular and wavelength selectivity. CGVHs are also designed as voxelated volumes using a new projection optimization algorithm. They are investigated using a volumetric diffraction simulation and a standard 3D beam propagation technique as well as experimentally. Both simulation and experiment verify that the structures function according to their design. These represent the first diffractive structures that have the capacity for generating arbitrary transmission and reflection wave fronts and that provide the ability for multiplexing arbitrary functionality given different illumination conditions. Also investigated and discussed in this thesis are 3D photonic crystals and quasicrystals. We demonstrate that these devices can be fabricated using a femtosecond laser direct writing system that is particularly appropriate for fabrication of such arbitrary 3D structures. We also show that these devices can provide 3D partial bandgaps which could become complete bandgaps if fabricated using high index materials or by coating lower index materials with high index metals. Our fabrication method is particularly suited to the fabrication of engineered defects within the periodic or quasi-periodic systems. We demonstrate the potential for fabricating defects within periodic and quasi-periodic systems for the manipulation of light in the IR regime. The general thesis of this document is that aperiodic three-dimensional structures provide additional degrees of freedom that can be utilized to improve on the performance of periodic volume devices. The results we will discuss suggest that, under certain circumstances, a departure from the Bragg paradigm provides enhanced volume diffraction properties.

Energy bounds in designer gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Amsel, Aaron J.; Marolf, Donald

We consider asymptotically anti-de Sitter gravity coupled to tachyonic scalar fields with mass at or slightly above the Breitenlohner-Freedman bound in d{>=}4 spacetime dimensions. The boundary conditions in these ''designer gravity'' theories are defined in terms of an arbitrary function W. We give a general argument that the Hamiltonian generators of asymptotic symmetries for such systems will be finite, and proceed to construct these generators using the covariant phase space method. The direct calculation confirms that the generators are finite and shows that they take the form of the pure gravity result plus additional contributions from the scalar fields. Bymore » comparing the generators to the spinor charge, we derive a lower bound on the gravitational energy when W has a global minimum and the Breitenlohner-Freedman bound is not saturated.« less

Open groups of constraints. Integrating arbitrary involutions

NASA Astrophysics Data System (ADS)

Batalin, Igor; Marnelius, Robert

1998-11-01

A new type of quantum master equation is presented which is expressed in terms of a recently introduced quantum antibracket. The equation involves only two operators: an extended nilpotent BFV-BRST charge and an extended ghost charge. It is proposed to determine the generalized quantum Maurer-Cartan equations for arbitrary open groups. These groups are the integration of constraints in arbitrary involutions. The only condition for this is that the constraint operators may be embedded in an odd nilpotent operator, the BFV-BRST charge. The proposal is verified at the quasigroup level. The integration formulas are also used to construct a generating operator for quantum antibrackets of operators in arbitrary involutions.

Photonic arbitrary waveform generation applicable to multiband UWB communications.

PubMed

Bolea, Mario; Mora, José; Ortega, Beatriz; Capmany, José

2010-12-06

A novel photonic structure for arbitrary waveform generation (AWG) is proposed based on the electrooptical intensity modulation of a broadband optical signal which is transmitted by a dispersive element and the optoelectrical processing is realized by combining an interferometric structure with balanced photodetection. The generated waveform can be fully reconfigured through the control of the optical source power spectrum and the interferometric structure. The use of balanced photodetection permits to remove the baseband component of the generated signal which is relevant in certain applications. We have theoretically described and experimentally demonstrated the feasibility of the system by means of the generation of different pulse shapes. Specifically, the proposed structure has been applicable to generate Multiband UWB signaling formats regarding to the FCC requirements in order to show the flexibility of the system.

Arbitrary digital pulse sequence generator with delay-loop timing

NASA Astrophysics Data System (ADS)

Hošák, Radim; Ježek, Miroslav

2018-04-01

We propose an idea of an electronic multi-channel arbitrary digital sequence generator with temporal granularity equal to two clock cycles. We implement the generator with 32 channels using a low-cost ARM microcontroller and demonstrate its capability to produce temporal delays ranging from tens of nanoseconds to hundreds of seconds, with 24 ns timing granularity and linear scaling of delay with respect to the number of delay loop iterations. The generator is optionally synchronized with an external clock source to provide 100 ps jitter and overall sequence repeatability within the whole temporal range. The generator is fully programmable and able to produce digital sequences of high complexity. The concept of the generator can be implemented using different microcontrollers and applied for controlling of various optical, atomic, and nuclear physics measurement setups.

DecisionMaker software and extracting fuzzy rules under uncertainty

NASA Technical Reports Server (NTRS)

Walker, Kevin B.

1992-01-01

Knowledge acquisition under uncertainty is examined. Theories proposed in deKorvin's paper 'Extracting Fuzzy Rules Under Uncertainty and Measuring Definability Using Rough Sets' are discussed as they relate to rule calculation algorithms. A data structure for holding an arbitrary number of data fields is described. Limitations of Pascal for loops in the generation of combinations are also discussed. Finally, recursive algorithms for generating all possible combination of attributes and for calculating the intersection of an arbitrary number of fuzzy sets are presented.

Enhancing robustness and immunization in geographical networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang Liang; Department of Physics, Lanzhou University, Lanzhou 730000; Yang Kongqing

2007-03-15

We find that different geographical structures of networks lead to varied percolation thresholds, although these networks may have similar abstract topological structures. Thus, strategies for enhancing robustness and immunization of a geographical network are proposed. Using the generating function formalism, we obtain an explicit form of the percolation threshold q{sub c} for networks containing arbitrary order cycles. For three-cycles, the dependence of q{sub c} on the clustering coefficients is ascertained. The analysis substantiates the validity of the strategies with analytical evidence.

The eigenvalue problem in phase space.

PubMed

Cohen, Leon

2018-06-30

We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c-function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi-representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Generation of five phase-locked harmonics in the continuous wave regime and its potential application to arbitrary optical waveform synthesis

NASA Astrophysics Data System (ADS)

Suhaimi, N. Sheeda; Ohae, C.; Gavara, T.; Nakagawa, K.; Hong, F.-L.; Katsuragawa, M.

2017-08-01

We have successfully generated a new broadband coherent light source in the continuous wave (CW) regime which is an ensemble of multi-harmonic radiations (2403, 1201, 801, 600 and 480 nm) by implementing a frequency dividing technology. The system is uniquely designed that all the harmonics are generated and propagate coaxially which gives the advantage of robustly maintaining the phase coherence among the harmonics. The highlight is its huge potential for the arbitrary optical waveform synthesis in the CW regime which has not been performed yet due to the limitation of the existing light source.

Arbitrary Dicke-State Control of Symmetric Rydberg Ensembles

NASA Astrophysics Data System (ADS)

Deutsch, Ivan

2017-04-01

We study the production of arbitrary superpositions of Dicke states via optimal control. We show that N atomic hyperfine qubits, interacting symmetrically via the Rydberg blockade, are well described by the Jaynes-Cummings Model (JCM), familiar in cavity QED. In this isomorphism, the presence or absence of a collective Rydberg excitation plays the role of the two-level system and the number of symmetric excitations of the hyperfine qubits plays the role of the bosonic excitations of the JCM. This system is fully controllable through the addition of phase-modulated microwaves that drive transitions between the Rydberg-dressed states. In the weak dressing regime, this results in a single-axis twisting Hamiltonian, plus time-dependent rotations of the collective spin. For strong dressing we control the entire Jaynes-Cummings ladder. Using optimal control, we design microwave waveforms that can generate arbitrary states in the symmetric subspace. This includes cat states, Dicke states, and spin squeezed states. With currently feasible parameters, it is possible to generate arbitrary symmetric states of _10 hyperfine qubits in 1 microsec, assuming a fast microwave phase switching time. The same control can be achieved with a ``dressed-ground control'' scheme, which reduces the demands for fast phase switching at the expense of increased total control time. More generally, we can achieve control on larger ensembles of qubits by designing waveforms that are bandwidth limited within the coherence time of the system. We use this to study general questions of the ``quantum speed limit'' and information content in a waveform that is needed to generate arbitrary quantum states.

Quantum optical signatures in strong-field laser physics: Infrared photon counting in high-order-harmonic generation.

PubMed

Gonoskov, I A; Tsatrafyllis, N; Kominis, I K; Tzallas, P

2016-09-07

We analytically describe the strong-field light-electron interaction using a quantized coherent laser state with arbitrary photon number. We obtain a light-electron wave function which is a closed-form solution of the time-dependent Schrödinger equation (TDSE). This wave function provides information about the quantum optical features of the interaction not accessible by semi-classical theories. With this approach we can reveal the quantum optical properties of high harmonic generation (HHG) process in gases by measuring the photon statistics of the transmitted infrared (IR) laser radiation. This work can lead to novel experiments in high-resolution spectroscopy in extreme-ultraviolet (XUV) and attosecond science without the need to measure the XUV light, while it can pave the way for the development of intense non-classical light sources.

Matrix models and stochastic growth in Donaldson-Thomas theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Szabo, Richard J.; Tierz, Miguel; Departamento de Analisis Matematico, Facultad de Ciencias Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid

We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kaehler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used tomore » show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.« less

Building validation tools for knowledge-based systems

NASA Technical Reports Server (NTRS)

Stachowitz, R. A.; Chang, C. L.; Stock, T. S.; Combs, J. B.

1987-01-01

The Expert Systems Validation Associate (EVA), a validation system under development at the Lockheed Artificial Intelligence Center for more than a year, provides a wide range of validation tools to check the correctness, consistency and completeness of a knowledge-based system. A declarative meta-language (higher-order language), is used to create a generic version of EVA to validate applications written in arbitrary expert system shells. The architecture and functionality of EVA are presented. The functionality includes Structure Check, Logic Check, Extended Structure Check (using semantic information), Extended Logic Check, Semantic Check, Omission Check, Rule Refinement, Control Check, Test Case Generation, Error Localization, and Behavior Verification.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Collins, Benjamin S.

The Futility package contains the following: 1) Definition of the size of integers and real numbers; 2) A generic Unit test harness; 3) Definitions for some basic extensions to the Fortran language: arbitrary length strings, a parameter list construct, exception handlers, command line processor, timers; 4) Geometry definitions: point, line, plane, box, cylinder, polyhedron; 5) File wrapper functions: standard Fortran input/output files, Fortran binary files, HDF5 files; 6) Parallel wrapper functions: MPI, and Open MP abstraction layers, partitioning algorithms; 7) Math utilities: BLAS, Matrix and Vector definitions, Linear Solver methods and wrappers for other TPLs (PETSC, MKL, etc), preconditioner classes;more » 8) Misc: random number generator, water saturation properties, sorting algorithms.« less

Wave Field Synthesis of moving sources with arbitrary trajectory and velocity profile.

PubMed

Firtha, Gergely; Fiala, Péter

2017-08-01

The sound field synthesis of moving sound sources is of great importance when dynamic virtual sound scenes are to be reconstructed. Previous solutions considered only virtual sources moving uniformly along a straight trajectory, synthesized employing a linear loudspeaker array. This article presents the synthesis of point sources following an arbitrary trajectory. Under high-frequency assumptions 2.5D Wave Field Synthesis driving functions are derived for arbitrary shaped secondary source contours by adapting the stationary phase approximation to the dynamic description of sources in motion. It is explained how a referencing function should be chosen in order to optimize the amplitude of synthesis on an arbitrary receiver curve. Finally, a finite difference implementation scheme is considered, making the presented approach suitable for real-time applications.

Population-Specific Use of the Same Tool-Assisted Alarm Call between Two Wild Orangutan Populations (Pongopygmaeus wurmbii) Indicates Functional Arbitrariness

PubMed Central

Lameira, Adriano R.; Hardus, Madeleine E.; Nouwen, Kim J. J. M.; Topelberg, Eva; Delgado, Roberto A.; Spruijt, Berry M.; Sterck, Elisabeth H. M.; Knott, Cheryl D.; Wich, Serge A.

2013-01-01

Arbitrariness is an elementary feature of human language, yet seldom an object of comparative inquiry. While arbitrary signals for the same function are relatively frequent between animal populations across taxa, the same signal with arbitrary functions is rare and it remains unknown whether, in parallel with human speech, it may involve call production in animals. To investigate this question, we examined a particular orangutan alarm call – the kiss-squeak – and two variants – hand and leaf kiss-squeaks. In Tuanan (Central Kalimantan, Indonesia), the acoustic frequency of unaided kiss-squeaks is negatively related to body size. The modified variants are correlated with perceived threat and are hypothesized to increase the perceived body size of the sender, as the use of a hand or leaves lowers the kiss-squeak’s acoustic frequency. We examined the use of these variants in the same context in another orangutan population of the same sub-species and with partially similar habitat at Cabang Panti (West Kalimantan, Indonesia). Identical analyses of data from this site provided similar results for unaided kiss-squeaks but dissimilar results for hand and leaf kiss-squeaks. Unaided kiss-squeaks at Cabang Panti were emitted as commonly and showed the same relationship to body size as in Tuanan. However, at Cabang Panti, hand kiss-squeaks were extremely rare, while leaf-use neither conveyed larger body size nor was related to perceived threat. These findings indicate functional discontinuity between the two sites and therefore imply functional arbitrariness of leaf kiss-squeaks. These results show for the first time the existence of animal signals involving call production with arbitrary function. Our findings are consistent with previous studies arguing that these orangutan call variants are socially learned and reconcile the role of gestures and calls within evolutionary theories based on common ancestry for speech and music. PMID:23861981

Population-specific use of the same tool-assisted alarm call between two wild orangutan populations (Pongo pygmaeus wurmbii) indicates functional arbitrariness [corrected].

PubMed

Lameira, Adriano R; Hardus, Madeleine E; Nouwen, Kim J J M; Topelberg, Eva; Delgado, Roberto A; Spruijt, Berry M; Sterck, Elisabeth H M; Knott, Cheryl D; Wich, Serge A

2013-01-01

Arbitrariness is an elementary feature of human language, yet seldom an object of comparative inquiry. While arbitrary signals for the same function are relatively frequent between animal populations across taxa, the same signal with arbitrary functions is rare and it remains unknown whether, in parallel with human speech, it may involve call production in animals. To investigate this question, we examined a particular orangutan alarm call - the kiss-squeak - and two variants - hand and leaf kiss-squeaks. In Tuanan (Central Kalimantan, Indonesia), the acoustic frequency of unaided kiss-squeaks is negatively related to body size. The modified variants are correlated with perceived threat and are hypothesized to increase the perceived body size of the sender, as the use of a hand or leaves lowers the kiss-squeak's acoustic frequency. We examined the use of these variants in the same context in another orangutan population of the same sub-species and with partially similar habitat at Cabang Panti (West Kalimantan, Indonesia). Identical analyses of data from this site provided similar results for unaided kiss-squeaks but dissimilar results for hand and leaf kiss-squeaks. Unaided kiss-squeaks at Cabang Panti were emitted as commonly and showed the same relationship to body size as in Tuanan. However, at Cabang Panti, hand kiss-squeaks were extremely rare, while leaf-use neither conveyed larger body size nor was related to perceived threat. These findings indicate functional discontinuity between the two sites and therefore imply functional arbitrariness of leaf kiss-squeaks. These results show for the first time the existence of animal signals involving call production with arbitrary function. Our findings are consistent with previous studies arguing that these orangutan call variants are socially learned and reconcile the role of gestures and calls within evolutionary theories based on common ancestry for speech and music.

Dynamic generation of light states with discrete symmetries

NASA Astrophysics Data System (ADS)

Cordero, S.; Nahmad-Achar, E.; Castaños, O.; López-Peña, R.

2018-01-01

A dynamic procedure is established within the generalized Tavis-Cummings model to generate light states with discrete point symmetries, given by the cyclic group Cn. We consider arbitrary dipolar coupling strengths of the atoms with a one-mode electromagnetic field in a cavity. The method uses mainly the matter-field entanglement properties of the system, which can be extended to any number of three-level atoms. An initial state constituted by the superposition of two states with definite total excitation numbers, |ψ〉 M1,and |ψ〉 M 2, is considered. It can be generated by the proper selection of the time of flight of an atom passing through the cavity. We demonstrate that the resulting Husimi function of the light is invariant under cyclic point transformations of order n =| M1-M2| .

Dynamic Mesh Adaptation for Front Evolution Using Discontinuous Galerkin Based Weighted Condition Number Mesh Relaxation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Greene, Patrick T.; Schofield, Samuel P.; Nourgaliev, Robert

2016-06-21

A new mesh smoothing method designed to cluster mesh cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered elds, such as amore » volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness to arbitrary Lagrangian Eulerian (ALE) methods.« less

Plethystic vertex operators and boson-fermion correspondences

NASA Astrophysics Data System (ADS)

Fauser, Bertfried; Jarvis, Peter D.; King, Ronald C.

2016-10-01

We study the algebraic properties of plethystic vertex operators, introduced in (2010 J. Phys. A: Math. Theor. 43 405202), underlying the structure of symmetric functions associated with certain generalized universal character rings of subgroups of the general linear group, defined to stabilize tensors of Young symmetry type characterized by a partition of arbitrary shape π. Here we establish an extension of the well-known boson-fermion correspondence involving Schur functions and their associated (Bernstein) vertex operators: for each π, the modes generated by the plethystic vertex operators and their suitably constructed duals, satisfy the anticommutation relations of a complex Clifford algebra. The combinatorial manipulations underlying the results involve exchange identities exploiting the Hopf-algebraic structure of certain symmetric function series and their plethysms.

Identities of almost Stable Group Representations

NASA Astrophysics Data System (ADS)

Vovsi, S. M.; Khung Shon, Nguen

1988-02-01

It is proved that almost stable group representations over a field have a finite basis of identities. Moreover, a variety generated by an arbitrary almost stable representation is Specht and all of its subvarieties have a finite uniformly bounded basis rank. In particular, the identities of an arbitrary representation of a finite group are finitely based.Bibliography: 17 titles.

Model Checking A Self-Stabilizing Synchronization Protocol for Arbitrary Digraphs

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.

2012-01-01

This report presents the mechanical verification of a self-stabilizing distributed clock synchronization protocol for arbitrary digraphs in the absence of faults. This protocol does not rely on assumptions about the initial state of the system, other than the presence of at least one node, and no central clock or a centrally generated signal, pulse, or message is used. The system under study is an arbitrary, non-partitioned digraph ranging from fully connected to 1-connected networks of nodes while allowing for differences in the network elements. Nodes are anonymous, i.e., they do not have unique identities. There is no theoretical limit on the maximum number of participating nodes. The only constraint on the behavior of the node is that the interactions with other nodes are restricted to defined links and interfaces. This protocol deterministically converges within a time bound that is a linear function of the self-stabilization period. A bounded model of the protocol is verified using the Symbolic Model Verifier (SMV) for a subset of digraphs. Modeling challenges of the protocol and the system are addressed. The model checking effort is focused on verifying correctness of the bounded model of the protocol as well as confirmation of claims of determinism and linear convergence with respect to the self-stabilization period.

Turning and Radius Deviation Correction for a Hexapod Walking Robot Based on an Ant-Inspired Sensory Strategy

PubMed Central

Guo, Tong; Liu, Qiong; Zhu, Qianwei; Zhao, Xiangmo; Jin, Bo

2017-01-01

In order to find a common approach to plan the turning of a bio-inspired hexapod robot, a locomotion strategy for turning and deviation correction of a hexapod walking robot based on the biological behavior and sensory strategy of ants. A series of experiments using ants were carried out where the gait and the movement form of ants was studied. Taking the results of the ant experiments as inspiration by imitating the behavior of ants during turning, an extended turning algorithm based on arbitrary gait was proposed. Furthermore, after the observation of the radius adjustment of ants during turning, a radius correction algorithm based on the arbitrary gait of the hexapod robot was raised. The radius correction surface function was generated by fitting the correction data, which made it possible for the robot to move in an outdoor environment without the positioning system and environment model. The proposed algorithm was verified on the hexapod robot experimental platform. The turning and radius correction experiment of the robot with several gaits were carried out. The results indicated that the robot could follow the ideal radius and maintain stability, and the proposed ant-inspired turning strategy could easily make free turns with an arbitrary gait. PMID:29168742

Turning and Radius Deviation Correction for a Hexapod Walking Robot Based on an Ant-Inspired Sensory Strategy.

PubMed

Zhu, Yaguang; Guo, Tong; Liu, Qiong; Zhu, Qianwei; Zhao, Xiangmo; Jin, Bo

2017-11-23

Abstract : In order to find a common approach to plan the turning of a bio-inspired hexapod robot, a locomotion strategy for turning and deviation correction of a hexapod walking robot based on the biological behavior and sensory strategy of ants. A series of experiments using ants were carried out where the gait and the movement form of ants was studied. Taking the results of the ant experiments as inspiration by imitating the behavior of ants during turning, an extended turning algorithm based on arbitrary gait was proposed. Furthermore, after the observation of the radius adjustment of ants during turning, a radius correction algorithm based on the arbitrary gait of the hexapod robot was raised. The radius correction surface function was generated by fitting the correction data, which made it possible for the robot to move in an outdoor environment without the positioning system and environment model. The proposed algorithm was verified on the hexapod robot experimental platform. The turning and radius correction experiment of the robot with several gaits were carried out. The results indicated that the robot could follow the ideal radius and maintain stability, and the proposed ant-inspired turning strategy could easily make free turns with an arbitrary gait.

Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia S.

2012-11-01

The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order. Throughout the survey, we illustrate the parallels in the relationships: Laplace type integral transforms - special functions as kernels - operators of generalized integration and differentiation generated by special functions - special functions as solutions of related differential equations. The role of the so-called Special Functions of Fractional Calculus is emphasized.

The generation of arbitrary order, non-classical, Gauss-type quadrature for transport applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spence, Peter J., E-mail: peter.spence@awe.co.uk

A method is presented, based upon the Stieltjes method (1884), for the determination of non-classical Gauss-type quadrature rules, and the associated sets of abscissae and weights. The method is then used to generate a number of quadrature sets, to arbitrary order, which are primarily aimed at deterministic transport calculations. The quadrature rules and sets detailed include arbitrary order reproductions of those presented by Abu-Shumays in [4,8] (known as the QR sets, but labelled QRA here), in addition to a number of new rules and associated sets; these are generated in a similar way, and we label them the QRS quadraturemore » sets. The method presented here shifts the inherent difficulty (encountered by Abu-Shumays) associated with solving the non-linear moment equations, particular to the required quadrature rule, to one of the determination of non-classical weight functions and the subsequent calculation of various associated inner products. Once a quadrature rule has been written in a standard form, with an associated weight function having been identified, the calculation of the required inner products is achieved using specific variable transformations, in addition to the use of rapid, highly accurate quadrature suited to this purpose. The associated non-classical Gauss quadrature sets can then be determined, and this can be done to any order very rapidly. In this paper, instead of listing weights and abscissae for the different quadrature sets detailed (of which there are a number), the MATLAB code written to generate them is included as Appendix D. The accuracy and efficacy (in a transport setting) of the quadrature sets presented is not tested in this paper (although the accuracy of the QRA quadrature sets has been studied in [12,13]), but comparisons to tabulated results listed in [8] are made. When comparisons are made with one of the azimuthal QRA sets detailed in [8], the inherent difficulty in the method of generation, used there, becomes apparent, with the highest order tabulated sets showing unexpected anomalies. Although not in an actual transport setting, the accuracy of the sets presented here is assessed to some extent, by using them to approximate integrals (over an octant of the unit sphere) of various high order spherical harmonics. When this is done, errors in the tabulated QRA sets present themselves at the highest tabulated orders, whilst combinations of the new QRS quadrature sets offer some improvements in accuracy over the original QRA sets. Finally, in order to offer a quick, visual understanding of the various quadrature sets presented, when combined to give product sets for the purposes of integrating functions confined to the surface of a sphere, three-dimensional representations of points located on an octant of the unit sphere (as in [8,12]) are shown.« less

Wigner Functions for Arbitrary Quantum Systems.

PubMed

Tilma, Todd; Everitt, Mark J; Samson, John H; Munro, William J; Nemoto, Kae

2016-10-28

The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an ensemble of spins. Here we present a general and consistent framework for constructing Wigner functions exploiting the underlying symmetries in the physical system at hand. The Wigner function can be used to fully describe any quantum system of arbitrary dimension or ensemble size.

ACIRF user's guide: Theory and examples

NASA Astrophysics Data System (ADS)

Dana, Roger A.

1989-12-01

Design and evaluation of radio frequency systems that must operate through ionospheric disturbances resulting from high altitude nuclear detonations requires an accurate channel model. This model must include the effects of high gain antennas that may be used to receive the signals. Such a model can then be used to construct realizations of the received signal for use in digital simulations of trans-ionospheric links or for use in hardware channel simulators. The FORTRAN channel model ACIRF (Antenna Channel Impulse Response Function) generates random realizations of the impulse response function at the outputs of multiple antennas. This user's guide describes the FORTRAN program ACIRF (version 2.0) that generates realizations of channel impulse response functions at the outputs of multiple antennas with arbitrary beamwidths, pointing angles, and relatives positions. This channel model is valid under strong scattering conditions when Rayleigh fading statistics apply. Both frozen-in and turbulent models for the temporal fluctuations are included in this version of ACIRF. The theory of the channel model is described and several examples are given.

Review on Photonic Generation of Chirp Arbitrary Microwave Waveforms for Remote Sensing Application

NASA Astrophysics Data System (ADS)

Raghuwanshi, Sanjeev Kumar; Srivastav, Akash; Athokpam, Bidhanshel Singh

2017-12-01

A novel technique to generate an arbitrary chirped waveform by harnessing features of lithium niobate (LiNb O_3) Mach-Zehnder modulator is proposed and demonstrated. The most important application of chirped microwave waveform is that, it improves the range resolution of radar. Microwave photonics system provides high bandwidth capabilities of fiber-optic systems and also contains the ability to provide interconnect transmission properties, which are virtually independent of length. The low-loss wide bandwidth capability of optoelectronic systems makes them attractive for the transmission and processing of microwave signals, while the development of high-capacity optical communication systems has required the use of microwave techniques in optical transmitters and receivers. These two strands have led to the development of the research area of microwave photonics. So, it should be consider that microwave photonics as the field that studies the interaction between microwave and optical waves for applications such as communications, radars, sensors and instrumentations. In this paper, we have thoroughly reviewed the arbitrary chirped microwave generation techniques by using photonics technology.

Optical arbitrary waveform generation based on multi-wavelength semiconductor fiber ring laser

NASA Astrophysics Data System (ADS)

Li, Peili; Ma, Xiaolu; Shi, Weihua; Xu, Enming

2017-09-01

A new scheme of generating optical arbitrary waveforms based on multi-wavelength semiconductor fiber ring laser (SFRL) is proposed. In this novel scheme, a wide and flat optical frequency comb (OFC) is provided directly by multi-wavelength SFRL, whose central frequency and comb spacing are tunable. OFC generation, de-multiplexing, amplitude and phase modulation, and multiplexing are implementing in an intensity and phase tunable comb filter, as induces the merits of high spectral coherence, satisfactory waveform control and low system loss. By using the mode couple theory and the transfer matrix method, the theoretical model of the scheme is established. The impacts of amplitude control, phase control, number of spectral line, and injection current of semiconductor optical amplifier (SOA) on the waveform similarity are studied using the theoretical model. The results show that, amplitude control and phase control error should be smaller than 1% and 0.64% respectively to achieve high similarity. The similarity of the waveform is improved with the increase of the number of spectral line. When the injection current of SOA is in a certain range, the optical arbitrary waveform reaches a high similarity.

Representing Functions in n Dimensions to Arbitrary Accuracy

NASA Technical Reports Server (NTRS)

Scotti, Stephen J.

2007-01-01

A method of approximating a scalar function of n independent variables (where n is a positive integer) to arbitrary accuracy has been developed. This method is expected to be attractive for use in engineering computations in which it is necessary to link global models with local ones or in which it is necessary to interpolate noiseless tabular data that have been computed from analytic functions or numerical models in n-dimensional spaces of design parameters.

The Two-Dimensional Gabor Function Adapted to Natural Image Statistics: A Model of Simple-Cell Receptive Fields and Sparse Structure in Images.

PubMed

Loxley, P N

2017-10-01

The two-dimensional Gabor function is adapted to natural image statistics, leading to a tractable probabilistic generative model that can be used to model simple cell receptive field profiles, or generate basis functions for sparse coding applications. Learning is found to be most pronounced in three Gabor function parameters representing the size and spatial frequency of the two-dimensional Gabor function and characterized by a nonuniform probability distribution with heavy tails. All three parameters are found to be strongly correlated, resulting in a basis of multiscale Gabor functions with similar aspect ratios and size-dependent spatial frequencies. A key finding is that the distribution of receptive-field sizes is scale invariant over a wide range of values, so there is no characteristic receptive field size selected by natural image statistics. The Gabor function aspect ratio is found to be approximately conserved by the learning rules and is therefore not well determined by natural image statistics. This allows for three distinct solutions: a basis of Gabor functions with sharp orientation resolution at the expense of spatial-frequency resolution, a basis of Gabor functions with sharp spatial-frequency resolution at the expense of orientation resolution, or a basis with unit aspect ratio. Arbitrary mixtures of all three cases are also possible. Two parameters controlling the shape of the marginal distributions in a probabilistic generative model fully account for all three solutions. The best-performing probabilistic generative model for sparse coding applications is found to be a gaussian copula with Pareto marginal probability density functions.

Detailed noise statistics for an optically preamplified direct detection receiver

NASA Astrophysics Data System (ADS)

Danielsen, Soeren Lykke; Mikkelsen, Benny; Durhuus, Terji; Joergensen, Carsten; Stubkjaer, Kristian E.

We describe the exact statistics of an optically preamplified direct detection receiver by means of the moment generating function. The theory allows an arbitrary shaped electrical filter in the receiver circuit. The moment generating function (MGF) allows for a precise calculation of the error rate by using the inverse Fast Fourier transform (FFT). The exact results are compared with the usual Gaussian approximation (GA), the saddlepoint approximation (SAP) and the modified Chernoff bound (MCB). This comparison shows that the noise is not Gaussian distributed for all values of the optical amplifier gain. In the region from 20-30 dB gain, calculations shows that the GA underestimates the receiver sensitivity while the SAP is very close to the results of our exact model. Using the MGF derived in the article we then find the optimal bandwidth of the electrical filter in the receiver circuit and calculate the sensitivity degradation due to inter symbol interference (ISI).

GEMPAK: An arbitrary aircraft geometry generator

NASA Technical Reports Server (NTRS)

Stack, S. H.; Edwards, C. L. W.; Small, W. J.

1977-01-01

A computer program, GEMPAK, has been developed to aid in the generation of detailed configuration geometry. The program was written to allow the user as much flexibility as possible in his choices of configurations and the detail of description desired and at the same time keep input requirements and program turnaround and cost to a minimum. The program consists of routines that generate fuselage and planar-surface (winglike) geometry and a routine that will determine the true intersection of all components with the fuselage. This paper describes the methods by which the various geometries are generated and provides input description with sample input and output. Also included are descriptions of the primary program variables and functions performed by the various routines. The FORTRAN program GEMPAK has been used extensively in conjunction with interfaces to several aerodynamic and plotting computer programs and has proven to be an effective aid in the preliminary design phase of aircraft configurations.

An electric generator using living Torpedo electric organs controlled by fluid pressure-based alternative nervous systems

PubMed Central

Tanaka, Yo; Funano, Shun-ichi; Nishizawa, Yohei; Kamamichi, Norihiro; Nishinaka, Masahiro; Kitamori, Takehiko

2016-01-01

Direct electric power generation using biological functions have become a research focus due to their low cost and cleanliness. Unlike major approaches using glucose fuels or microbial fuel cells (MFCs), we present a generation method with intrinsically high energy conversion efficiency and generation with arbitrary timing using living electric organs of Torpedo (electric rays) which are serially integrated electrocytes converting ATP into electric energy. We developed alternative nervous systems using fluid pressure to stimulate electrocytes by a neurotransmitter, acetylcholine (Ach), and demonstrated electric generation. Maximum voltage and current were 1.5 V and 0.64 mA, respectively, with a duration time of a few seconds. We also demonstrated energy accumulation in a capacitor. The current was far larger than that using general cells other than electrocytes (~pA level). The generation ability was confirmed against repetitive cycles and also after preservation for 1 day. This is the first step toward ATP-based energy harvesting devices. PMID:27241817

An electric generator using living Torpedo electric organs controlled by fluid pressure-based alternative nervous systems

NASA Astrophysics Data System (ADS)

Tanaka, Yo; Funano, Shun-Ichi; Nishizawa, Yohei; Kamamichi, Norihiro; Nishinaka, Masahiro; Kitamori, Takehiko

2016-05-01

Direct electric power generation using biological functions have become a research focus due to their low cost and cleanliness. Unlike major approaches using glucose fuels or microbial fuel cells (MFCs), we present a generation method with intrinsically high energy conversion efficiency and generation with arbitrary timing using living electric organs of Torpedo (electric rays) which are serially integrated electrocytes converting ATP into electric energy. We developed alternative nervous systems using fluid pressure to stimulate electrocytes by a neurotransmitter, acetylcholine (Ach), and demonstrated electric generation. Maximum voltage and current were 1.5 V and 0.64 mA, respectively, with a duration time of a few seconds. We also demonstrated energy accumulation in a capacitor. The current was far larger than that using general cells other than electrocytes (~pA level). The generation ability was confirmed against repetitive cycles and also after preservation for 1 day. This is the first step toward ATP-based energy harvesting devices.

Spinning AdS loop diagrams: two point functions

NASA Astrophysics Data System (ADS)

Giombi, Simone; Sleight, Charlotte; Taronna, Massimo

2018-06-01

We develop a systematic approach to evaluating AdS loop amplitudes with spinning legs based on the spectral (or "split") representation of bulk-to-bulk propagators, which re-expresses loop diagrams in terms of spectral integrals and higher-point tree diagrams. In this work we focus on 2pt one-loop Witten diagrams involving totally symmetric fields of arbitrary mass and integer spin. As an application of this framework, we study the contribution to the anomalous dimension of higher-spin currents generated by bubble diagrams in higher-spin gauge theories on AdS.

Solutions to an advanced functional partial differential equation of the pantograph type

PubMed Central

Zaidi, Ali A.; Van Brunt, B.; Wake, G. C.

2015-01-01

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained. PMID:26345391

Solutions to an advanced functional partial differential equation of the pantograph type.

PubMed

Zaidi, Ali A; Van Brunt, B; Wake, G C

2015-07-08

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained.

Shaded-Color Picture Generation of Computer-Defined Arbitrary Shapes

NASA Technical Reports Server (NTRS)

Cozzolongo, J. V.; Hermstad, D. L.; Mccoy, D. S.; Clark, J.

1986-01-01

SHADE computer program generates realistic color-shaded pictures from computer-defined arbitrary shapes. Objects defined for computer representation displayed as smooth, color-shaded surfaces, including varying degrees of transparency. Results also used for presentation of computational results. By performing color mapping, SHADE colors model surface to display analysis results as pressures, stresses, and temperatures. NASA has used SHADE extensively in sign and analysis of high-performance aircraft. Industry should find applications for SHADE in computer-aided design and computer-aided manufacturing. SHADE written in VAX FORTRAN and MACRO Assembler for either interactive or batch execution.

OncoSimulR: genetic simulation with arbitrary epistasis and mutator genes in asexual populations.

PubMed

Diaz-Uriarte, Ramon

2017-06-15

OncoSimulR implements forward-time genetic simulations of biallelic loci in asexual populations with special focus on cancer progression. Fitness can be defined as an arbitrary function of genetic interactions between multiple genes or modules of genes, including epistasis, restrictions in the order of accumulation of mutations, and order effects. Mutation rates can differ among genes, and can be affected by (anti)mutator genes. Also available are sampling from simulations (including single-cell sampling), plotting the genealogical relationships of clones and generating and plotting fitness landscapes. Implemented in R and C ++, freely available from BioConductor for Linux, Mac and Windows under the GNU GPL license. Version 2.5.9 or higher available from: http://www.bioconductor.org/packages/devel/bioc/html/OncoSimulR.html . GitHub repository at: https://github.com/rdiaz02/OncoSimul. ramon.diaz@iib.uam.es. Supplementary data are available at Bioinformatics online. © The Author 2017. Published by Oxford University Press.

The crack-inclusion interaction problem

NASA Technical Reports Server (NTRS)

Liu, X.-H.; Erdogan, F.

1986-01-01

The general plane elastostatic problem of interaction between a crack and an inclusion is considered. The Green's functions for a pair of dislocations and a pair of concentrated body forces are used to generate the crack and the inclusion. Integral equations are obtained for a line crack and an elastic line inclusion having an arbitrary relative orientation and size. The nature of stress singularity around the end points of rigid and elastic inclusions is described and three special cases of this intersection problem are studied. The problem is solved for an arbitrary uniform stress state away from the crack-inclusion region. The nonintersecting crack-inclusion problem is considered for various relative size, orientation, and stiffness parameters, and the stress intensity factors at the ends of the inclusion and the crack are calculated. For the crack-inclusion intersection case, special stress intensity factors are defined and are calculated for various values of the parameters defining the relative size and orientation of the crack and the inclusion and the stiffness of the inclusion.

The crack-inclusion interaction problem

NASA Technical Reports Server (NTRS)

Xue-Hui, L.; Erdogan, F.

1984-01-01

The general plane elastostatic problem of interaction between a crack and an inclusion is considered. The Green's functions for a pair of dislocations and a pair of concentrated body forces are used to generate the crack and the inclusion. Integral equations are obtained for a line crack and an elastic line inclusion having an arbitrary relative orientation and size. The nature of stress singularity around the end points of rigid and elastic inclusions is described and three special cases of this intersection problem are studied. The problem is solved for an arbitrary uniform stress state away from the crack-inclusion region. The nonintersecting crack-inclusion problem is considered for various relative size, orientation, and stiffness parameters, and the stress intensity factors at the ends of the inclusion and the crack are calculated. For the crack-inclusion intersection case, special stress intensity factors are defined and are calculated for various values of the parameters defining the relative size and orientation of the crack and the inclusion and the stiffness of the inclusion.

Fully reconfigurable photonic microwave transversal filter based on digital micromirror device and continuous-wave, incoherent supercontinuum source.

PubMed

Lee, Ju Han; Chang, You Min; Han, Young-Geun; Lee, Sang Bae; Chung, Hae Yang

2007-08-01

The combined use of a programmable, digital micromirror device (DMD) and an ultrabroadband, cw, incoherent supercontinuum (SC) source is experimentally demonstrated to fully explore various aspects on the reconfiguration of a microwave filter transfer function by creating a range of multiwavelength optical filter shapes. Owing to both the unique characteristic of the DMD that an arbitrary optical filter shape can be readily produced and the ultrabroad bandwidth of the cw SC source that is 3 times larger than that of Er-amplified spontaneous emission, a multiwavelength optical beam pattern can be generated with a large number of wavelength filter taps apodized by an arbitrary amplitude window. Therefore various types of high-quality microwave filter can be readily achieved through the spectrum slicing-based photonic microwave transversal filter scheme. The experimental demonstration is performed in three aspects: the tuning of a filter resonance bandwidth at a fixed resonance frequency, filter resonance frequency tuning at a fixed resonance frequency, and flexible microwave filter shape reconstruction.

Decoding brain activity using a large-scale probabilistic functional-anatomical atlas of human cognition

PubMed Central

Jones, Michael N.

2017-01-01

A central goal of cognitive neuroscience is to decode human brain activity—that is, to infer mental processes from observed patterns of whole-brain activation. Previous decoding efforts have focused on classifying brain activity into a small set of discrete cognitive states. To attain maximal utility, a decoding framework must be open-ended, systematic, and context-sensitive—that is, capable of interpreting numerous brain states, presented in arbitrary combinations, in light of prior information. Here we take steps towards this objective by introducing a probabilistic decoding framework based on a novel topic model—Generalized Correspondence Latent Dirichlet Allocation—that learns latent topics from a database of over 11,000 published fMRI studies. The model produces highly interpretable, spatially-circumscribed topics that enable flexible decoding of whole-brain images. Importantly, the Bayesian nature of the model allows one to “seed” decoder priors with arbitrary images and text—enabling researchers, for the first time, to generate quantitative, context-sensitive interpretations of whole-brain patterns of brain activity. PMID:29059185

Analytic solution of the Spencer-Lewis angular-spatial moments equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Filippone, W.L.

A closed-form solution for the angular-spatial moments of the Spencer-Lewis equation is presented that is valid for infinite homogeneous media. From the moments, the electron density distribution as a function of position and path length (energy) is reconstructed for several sample problems involving plane isotropic sources of electrons in aluminium. The results are in excellent agreement with those determined numerically using the streaming ray method. The primary use of the closed form solution will most likely be to generate accurate electron transport benchmark solutions. In principle, the electron density as a function of space, path length, and direction can bemore » determined for planar sources of arbitrary angular distribution.« less

Arbitrariness is not enough: towards a functional approach to the genetic code.

PubMed

Lacková, Ľudmila; Matlach, Vladimír; Faltýnek, Dan

2017-12-01

Arbitrariness in the genetic code is one of the main reasons for a linguistic approach to molecular biology: the genetic code is usually understood as an arbitrary relation between amino acids and nucleobases. However, from a semiotic point of view, arbitrariness should not be the only condition for definition of a code, consequently it is not completely correct to talk about "code" in this case. Yet we suppose that there exist a code in the process of protein synthesis, but on a higher level than the nucleic bases chains. Semiotically, a code should be always associated with a function and we propose to define the genetic code not only relationally (in basis of relation between nucleobases and amino acids) but also in terms of function (function of a protein as meaning of the code). Even if the functional definition of meaning in the genetic code has been discussed in the field of biosemiotics, its further implications have not been considered. In fact, if the function of a protein represents the meaning of the genetic code (the sign's object), then it is crucial to reconsider the notion of its expression (the sign) as well. In our contribution, we will show that the actual model of the genetic code is not the only possible and we will propose a more appropriate model from a semiotic point of view.

Semi-analytical solution for the generalized absorbing boundary condition in molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Lee, Chung-Shuo; Chen, Yan-Yu; Yu, Chi-Hua; Hsu, Yu-Chuan; Chen, Chuin-Shan

2017-07-01

We present a semi-analytical solution of a time-history kernel for the generalized absorbing boundary condition in molecular dynamics (MD) simulations. To facilitate the kernel derivation, the concept of virtual atoms in real space that can conform with an arbitrary boundary in an arbitrary lattice is adopted. The generalized Langevin equation is regularized using eigenvalue decomposition and, consequently, an analytical expression of an inverse Laplace transform is obtained. With construction of dynamical matrices in the virtual domain, a semi-analytical form of the time-history kernel functions for an arbitrary boundary in an arbitrary lattice can be found. The time-history kernel functions for different crystal lattices are derived to show the generality of the proposed method. Non-equilibrium MD simulations in a triangular lattice with and without the absorbing boundary condition are conducted to demonstrate the validity of the solution.

Direct Synthesis of Microwave Waveforms for Quantum Computing

NASA Astrophysics Data System (ADS)

Raftery, James; Vrajitoarea, Andrei; Zhang, Gengyan; Leng, Zhaoqi; Srinivasan, Srikanth; Houck, Andrew

Current state of the art quantum computing experiments in the microwave regime use control pulses generated by modulating microwave tones with baseband signals generated by an arbitrary waveform generator (AWG). Recent advances in digital analog conversion technology have made it possible to directly synthesize arbitrary microwave pulses with sampling rates of 65 gigasamples per second (GSa/s) or higher. These new ultra-wide bandwidth AWG's could dramatically simplify the classical control chain for quantum computing experiments, presenting potential cost savings and reducing the number of components that need to be carefully calibrated. Here we use a Keysight M8195A AWG to study the viability of such a simplified scheme, demonstrating randomized benchmarking of a superconducting qubit with high fidelity.

Generation of tunable radially polarized array beams by controllable coherence

NASA Astrophysics Data System (ADS)

Wang, Jing; Zhang, Jipeng; Zhu, Shijun; Li, Zhenhua

2017-05-01

In this paper, a new method for converting a single radial polarization beam into an arbitrary radially polarized array (RPA) beam such as a radial or rectangular symmetry array in the focal plane by modulating a periodic correlation structure is introduced. The realizability conditions for such source and the beam condition for radiation generated by such source are derived. It is illustrated that both the amplitude and the polarization are controllable by means of initial correlation structure and coherence parameter. Furthermore, by designing the source correlation structure, a tunable NUST-shaped RPA beam is demonstrated, which can find widespread applications in micro-nano engineering. Such a method for generation of arbitrary vector array beams is useful in beam shaping and optical tweezers.

The exact fundamental solution for the Benes tracking problem

NASA Astrophysics Data System (ADS)

Balaji, Bhashyam

2009-05-01

The universal continuous-discrete tracking problem requires the solution of a Fokker-Planck-Kolmogorov forward equation (FPKfe) for an arbitrary initial condition. Using results from quantum mechanics, the exact fundamental solution for the FPKfe is derived for the state model of arbitrary dimension with Benes drift that requires only the computation of elementary transcendental functions and standard linear algebra techniques- no ordinary or partial differential equations need to be solved. The measurement process may be an arbitrary, discrete-time nonlinear stochastic process, and the time step size can be arbitrary. Numerical examples are included, demonstrating its utility in practical implementation.

Generation of arbitrary order Bessel beams via 3D printed axicons at the terahertz frequency range.

PubMed

Wei, Xuli; Liu, Changming; Niu, Liting; Zhang, Zhongqi; Wang, Kejia; Yang, Zhengang; Liu, Jinsong

2015-12-20

We present the generation of arbitrary order Bessel beams at 0.3 THz through the implementation of suitably designed axicons based on 3D printing technology. The helical axicons, which possess thickness gradients in both radial and azimuthal directions, can convert the incident Gaussian beam into a high-order Bessel beam with spiral phase structure. The evolution of the generated Bessel beams are characterized experimentally with a three-dimensional field scanner. Moreover, the topological charges carried by the high-order Bessel beams are determined by the fork-like interferograms. This 3D-printing-based Bessel beam generation technique is useful not only for THz imaging systems with zero-order Bessel beams but also for future orbital-angular-momentum-based THz free-space communication with higher-order Bessel beams.

On-Demand Microwave Generator of Shaped Single Photons

NASA Astrophysics Data System (ADS)

Forn-Díaz, P.; Warren, C. W.; Chang, C. W. S.; Vadiraj, A. M.; Wilson, C. M.

2017-11-01

We demonstrate the full functionality of a circuit that generates single microwave photons on demand, with a wave packet that can be modulated with a near-arbitrary shape. We achieve such a high tunability by coupling a superconducting qubit near the end of a semi-infinite transmission line. A dc superconducting quantum interference device shunts the line to ground and is employed to modify the spatial dependence of the electromagnetic mode structure in the transmission line. This control allows us to couple and decouple the qubit from the line, shaping its emission rate on fast time scales. Our decoupling scheme is applicable to all types of superconducting qubits and other solid-state systems and can be generalized to multiple qubits as well as to resonators.

On the symmetry of the boundary conditions of the volume potential

NASA Astrophysics Data System (ADS)

Kal'menov, Tynysbek Sh.; Arepova, Gaukhar; Suragan, Durvudkhan

2017-09-01

It is well known that the volume potential determines the mass or the charge distributed over the domain with density f. The volume potential is extensively used in function theory and embedding theorems. It is also well known that the volume potential gives a solution to an inhomogeneous equation. And it generates a linear self-adjoint operator. It is known that self-adjoint differential operators are generated by boundary conditions. In our previous papers for an arbitrary domain a boundary condition on the volume potential is given. In the past, it was not possible to prove the self-adjointness of these obtained boundary conditions. In the present paper, we prove the symmetry of boundary condition for the volume potential.

Matrix elements of explicitly correlated Gaussian basis functions with arbitrary angular momentum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Joyce, Tennesse; Varga, Kálmán

2016-05-14

A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with arbitrary angular momentum is presented. The calculations are checked on several excited states of three and four electron systems. The presented formalism can be used as unified framework for high accuracy calculations of properties of small atoms and molecules.

The generation of gravitational waves. III - Derivation of bremsstrahlung formulae

NASA Technical Reports Server (NTRS)

Kovacs, S. J.; Thorne, K. S.

1977-01-01

Formulas are derived describing the gravitational waves produced by a stellar encounter of the following type. The two stars have stationary (i.e., nonpulsating) nearly Newtonian structures with arbitrary relative masses; they fly past each other with an arbitrary relative velocity; and their impact parameter is sufficiently large that they gravitationally deflect each other through an angle that is small as compared with 90 deg.

Covariant Derivatives and the Renormalization Group Equation

NASA Astrophysics Data System (ADS)

Dolan, Brian P.

The renormalization group equation for N-point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has components given by the β functions of the theory. It is argued that this simple picture requires modification whenever any one of the points at which the amplitude is evaluated becomes close to any other. This modification necessitates the introduction of a connection on the space of couplings and new terms appear in the renormalization group equation involving covariant derivatives of the β function and the curvature associated with the connection. It is shown how the connection is related to the operator product expansion coefficients, but there remains an arbitrariness in its definition.

Elementary Green function as an integral superposition of Gaussian beams in inhomogeneous anisotropic layered structures in Cartesian coordinates

NASA Astrophysics Data System (ADS)

Červený, Vlastislav; Pšenčík, Ivan

2017-08-01

Integral superposition of Gaussian beams is a useful generalization of the standard ray theory. It removes some of the deficiencies of the ray theory like its failure to describe properly behaviour of waves in caustic regions. It also leads to a more efficient computation of seismic wavefields since it does not require the time-consuming two-point ray tracing. We present the formula for a high-frequency elementary Green function expressed in terms of the integral superposition of Gaussian beams for inhomogeneous, isotropic or anisotropic, layered structures, based on the dynamic ray tracing (DRT) in Cartesian coordinates. For the evaluation of the superposition formula, it is sufficient to solve the DRT in Cartesian coordinates just for the point-source initial conditions. Moreover, instead of seeking 3 × 3 paraxial matrices in Cartesian coordinates, it is sufficient to seek just 3 × 2 parts of these matrices. The presented formulae can be used for the computation of the elementary Green function corresponding to an arbitrary direct, multiply reflected/transmitted, unconverted or converted, independently propagating elementary wave of any of the three modes, P, S1 and S2. Receivers distributed along or in a vicinity of a target surface may be situated at an arbitrary part of the medium, including ray-theory shadow regions. The elementary Green function formula can be used as a basis for the computation of wavefields generated by various types of point sources (explosive, moment tensor).

The point-characteristic function, wavefronts, and caustic of a spherical wave refracted by an arbitrary smooth surface.

PubMed

Marciano-Melchor, Magdalena; Navarro-Morales, Esperanza; Román-Hernández, Edwin; Santiago-Santiago, José Guadalupe; Silva-Ortigoza, Gilberto; Silva-Ortigoza, Ramón; Suárez-Xique, Román

2012-06-01

The aim of this paper is to obtain expressions for the k-function, the wavefront train, and the caustic associated with the light rays refracted by an arbitrary smooth surface after being emitted by a point light source located at an arbitrary position in a three-dimensional homogeneous optical medium. The general results are applied to a parabolic refracting surface. For this case, we find that when the point light source is off the optical axis, the caustic locally has singularities of the hyperbolic umbilic type, while the refracted wavefront, at the caustic region, locally has singularities of the cusp ridge and swallowtail types.

A first class constraint generates not a gauge transformation, but a bad physical change: The case of electromagnetism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pitts, J. Brian, E-mail: jbp25@cam.ac.uk

In Dirac–Bergmann constrained dynamics, a first-class constraint typically does not alone generate a gauge transformation. By direct calculation it is found that each first-class constraint in Maxwell’s theory generates a change in the electric field E{sup →} by an arbitrary gradient, spoiling Gauss’s law. The secondary first-class constraint p{sup i},{sub i}=0 still holds, but being a function of derivatives of momenta (mere auxiliary fields), it is not directly about the observable electric field (a function of derivatives of A{sub μ}), which couples to charge. Only a special combination of the two first-class constraints, the Anderson–Bergmann–Castellani gauge generator G, leaves E{supmore » →} unchanged. Likewise only that combination leaves the canonical action invariant—an argument independent of observables. If one uses a first-class constraint to generate instead a canonical transformation, one partly strips the canonical coordinates of physical meaning as electromagnetic potentials, vindicating the Anderson–Bergmann Lagrangian orientation of interesting canonical transformations. The need to keep gauge-invariant the relation q-dot −(δH)/(δp) =−E{sub i}−p{sup i}=0 supports using the gauge generator and primary Hamiltonian rather than the separate first-class constraints and the extended Hamiltonian. Partly paralleling Pons’s criticism, it is shown that Dirac’s proof that a first-class primary constraint generates a gauge transformation, by comparing evolutions from identical initial data, cancels out and hence fails to detect the alterations made to the initial state. It also neglects the arbitrary coordinates multiplying the secondary constraints inside the canonical Hamiltonian. Thus the gauge-generating property has been ascribed to the primaries alone, not the primary–secondary team G. Hence the Dirac conjecture about secondary first-class constraints as generating gauge transformations rests upon a false presupposition about primary first-class constraints. Clarity about Hamiltonian electromagnetism will be useful for an analogous treatment of GR. - Highlights: • A first-class constraint changes the electric field E, spoiling Gauss’s law. • A first-class constraint does not leave the action invariant or preserve q,0−dH/dp. • The gauge generator preserves E,q,0−dH/dp, and the canonical action. • The error in proofs that first-class primaries generating gauge is shown. • Dirac’s conjecture about secondary first-class constraints is blocked.« less

New Computational Approach to Electron Transport in Irregular Graphene Nanostructures

NASA Astrophysics Data System (ADS)

Mason, Douglas; Heller, Eric; Prendergast, David; Neaton, Jeffrey

2009-03-01

For novel graphene devices of nanoscale-to-macroscopic scale, many aspects of their transport properties are not easily understood due to difficulties in fabricating devices with regular edges. Here we develop a framework to efficiently calculate and potentially screen electronic transport properties of arbitrary nanoscale graphene device structures. A generalization of the established recursive Green's function method is presented, providing access to arbitrary device and lead geometries with substantial computer-time savings. Using single-orbital nearest-neighbor tight-binding models and the Green's function-Landauer scattering formalism, we will explore the transmission function of irregular two-dimensional graphene-based nanostructures with arbitrary lead orientation. Prepared by LBNL under contract DE-AC02-05CH11231 and supported by the U.S. Dept. of Energy Computer Science Graduate Fellowship under grant DE-FG02-97ER25308.

Three-dimensional zonal grids about arbitrary shapes by Poisson's equation

NASA Technical Reports Server (NTRS)

Sorenson, Reese L.

1988-01-01

A method for generating 3-D finite difference grids about or within arbitrary shapes is presented. The 3-D Poisson equations are solved numerically, with values for the inhomogeneous terms found automatically by the algorithm. Those inhomogeneous terms have the effect near boundaries of reducing cell skewness and imposing arbitrary cell height. The method allows the region of interest to be divided into zones (blocks), allowing the method to be applicable to almost any physical domain. A FORTRAN program called 3DGRAPE has been written to implement the algorithm. Lastly, a method for redistributing grid points along lines normal to boundaries will be described.

Dynamic optical arbitrary waveform generation with amplitude controlled by interference of two FBG arrays.

PubMed

Zhang, Ailing; Li, Changxiu

2012-10-08

In this paper, a novel structure of dynamic optical arbitrary waveform generation (O-AWG) with amplitude controlled by interference of two fiber Bragg grating (FBG) arrays is proposed. The FBG array consists of several FBGs and fiber stretchers (FSs). The amplitude is controlled by FSs through interference of two FBG arrays. The phase is controlled by FSs simultaneously. As a result, optical pulse trains with various waveforms as well as pulse trains with nonuniform pulse intensity, pulse spacing and pulse width in each period are obtained via FSs adjustment to change the phase shift of signal in each array.

Opto-VLSI-based photonic true-time delay architecture for broadband adaptive nulling in phased array antennas.

PubMed

Juswardy, Budi; Xiao, Feng; Alameh, Kamal

2009-03-16

This paper proposes a novel Opto-VLSI-based tunable true-time delay generation unit for adaptively steering the nulls of microwave phased array antennas. Arbitrary single or multiple true-time delays can simultaneously be synthesized for each antenna element by slicing an RF-modulated broadband optical source and routing specific sliced wavebands through an Opto-VLSI processor to a high-dispersion fiber. Experimental results are presented, which demonstrate the principle of the true-time delay unit through the generation of 5 arbitrary true-time delays of up to 2.5 ns each. (c) 2009 Optical Society of America

The emission function of ground-based light sources: State of the art and research challenges

NASA Astrophysics Data System (ADS)

Solano Lamphar, Héctor Antonio

2018-05-01

To understand the night sky radiance generated by the light emissions of urbanised areas, different researchers are currently proposing various theoretical approaches. The distribution of the radiant intensity as a function of the zenith angle is one of the most unknown properties on modelling skyglow. This is due to the collective effects of the artificial radiation emitted from the ground-based light sources. The emission function is a key property in characterising the sky brightness under arbitrary conditions, therefore it is required by modellers, environmental engineers, urban planners, light pollution researchers, and experimentalists who study the diffuse light of the night sky. As a matter of course, the emission function considers the public lighting system, which is in fact the main generator of the skyglow. Still, another class of light-emitting devices are gaining importance since their overuse and the urban sprawl of recent years. This paper will address the importance of the emission function in modelling skyglow and the factors involved in its characterization. On this subject, the author's intention is to organise, integrate, and evaluate previously published research in order to state the progress of current research toward clarifying this topic.

Pattern Formation and Complexity Emergence

NASA Astrophysics Data System (ADS)

Berezin, Alexander A.

2001-03-01

Success of nonlinear modelling of pattern formation and self-organization encourages speculations on informational and number theoretical foundations of complexity emergence. Pythagorean "unreasonable effectiveness of integers" in natural processes is perhaps extrapolatable even to universal emergence "out-of-nothing" (Leibniz, Wheeler). Because rational numbers (R = M/N) are everywhere dense on real axis, any digital string (hence any "book" from "Library of Babel" of J.L.Borges) is "recorded" infinitely many times in arbitrary many rationals. Furthermore, within any arbitrary small interval there are infinitely many Rs for which (either or both) integers (Ms and Ns) "carry" any given string of any given length. Because any iterational process (such as generation of fractal features of Mandelbrot Set) is arbitrary closely approximatable with rational numbers, the infinite pattern of integers expresses itself in generation of complexity of the world, as well as in emergence of the world itself. This "tunnelling" from Platonic World ("Platonia" of J.Barbour) to a real (physical) world is modern recast of Leibniz's motto ("for deriving all from nothing there suffices a single principle").

Demonstration of Current Profile Shaping using Double Dog-Leg Emittance Exchange Beam Line at Argonne Wakefield Accelerator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ha, Gwanghui; Cho, Moo-Hyun; Conde, Manoel

Emittance exchange (EEX) based longitudinal current profile shaping is the one of the promising current profile shaping technique. This method can generate high quality arbitrary current profiles under the ideal conditions. The double dog-leg EEX beam line was recently installed at the Argonne Wakefield Accelerator (AWA) to explore the shaping capability and confirm the quality of this method. To demonstrate the arbitrary current profile generation, several different transverse masks are applied to generate different final current profiles. The phase space slopes and the charge of incoming beam are varied to observe and suppress the aberrations on the ideal profile. Wemore » present current profile shaping results, aberrations on the shaped profile, and its suppression.« less

Digital EPR with an arbitrary waveform generator and direct detection at the carrier frequency

PubMed Central

Tseitlin, Mark; Quine, Richard W.; Rinard, George A.; Eaton, Sandra S.; Eaton, Gareth R.

2011-01-01

A digital EPR spectrometer was constructed by replacing the traditional bridge with an arbitrary waveform generator (AWG) to produce excitation patterns and a high-speed digitizer for direct detection of the spin system response at the carrier frequency. Digital down-conversion produced baseband signals in quadrature with very precise orthogonality. Real-time resonator tuning was performed by monitoring the Fourier transforms of signals reflected from the resonator during frequency sweeps generated by the AWG. The capabilities of the system were demonstrated by rapid magnetic field scans at 256 MHz carrier frequency, and FID and spin echo experiments at 1 and 10 GHz carrier frequencies. For the rapid scan experiments the leakage through a cross-loop resonator was compensated by adjusting the amplitude and phase of a sinusoid at the carrier frequency that was generated with another AWG channel. PMID:21968420

Polarization singularity indices in Gaussian laser beams

NASA Astrophysics Data System (ADS)

Freund, Isaac

2002-01-01

Two types of point singularities in the polarization of a paraxial Gaussian laser beam are discussed in detail. V-points, which are vector point singularities where the direction of the electric vector of a linearly polarized field becomes undefined, and C-points, which are elliptic point singularities where the ellipse orientations of elliptically polarized fields become undefined. Conventionally, V-points are characterized by the conserved integer valued Poincaré-Hopf index η, with generic value η=±1, while C-points are characterized by the conserved half-integer singularity index IC, with generic value IC=±1/2. Simple algorithms are given for generating V-points with arbitrary positive or negative integer indices, including zero, at arbitrary locations, and C-points with arbitrary positive or negative half-integer or integer indices, including zero, at arbitrary locations. Algorithms are also given for generating continuous lines of these singularities in the plane, V-lines and C-lines. V-points and C-points may be transformed one into another. A topological index based on directly measurable Stokes parameters is used to discuss this transformation. The evolution under propagation of V-points and C-points initially embedded in the beam waist is studied, as is the evolution of V-dipoles and C-dipoles.

Concise calculation of the scaling function, exponents, and probability functional of the Edwards-Wilkinson equation with correlated noise

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Y.; Pang, N.; Halpin-Healy, T.

1994-12-01

The linear Langevin equation proposed by Edwards and Wilkinson [Proc. R. Soc. London A 381, 17 (1982)] is solved in closed form for noise of arbitrary space and time correlation. Furthermore, the temporal development of the full probability functional describing the height fluctuations is derived exactly, exhibiting an interesting evolution between two distinct Gaussian forms. We determine explicitly the dynamic scaling function for the interfacial width for any given initial condition, isolate the early-time behavior, and discover an invariance that was unsuspected in this problem of arbitrary spatiotemporal noise.

Analytical results for a stochastic model of gene expression with arbitrary partitioning of proteins

NASA Astrophysics Data System (ADS)

Tschirhart, Hugo; Platini, Thierry

2018-05-01

In biophysics, the search for analytical solutions of stochastic models of cellular processes is often a challenging task. In recent work on models of gene expression, it was shown that a mapping based on partitioning of Poisson arrivals (PPA-mapping) can lead to exact solutions for previously unsolved problems. While the approach can be used in general when the model involves Poisson processes corresponding to creation or degradation, current applications of the method and new results derived using it have been limited to date. In this paper, we present the exact solution of a variation of the two-stage model of gene expression (with time dependent transition rates) describing the arbitrary partitioning of proteins. The methodology proposed makes full use of the PPA-mapping by transforming the original problem into a new process describing the evolution of three biological switches. Based on a succession of transformations, the method leads to a hierarchy of reduced models. We give an integral expression of the time dependent generating function as well as explicit results for the mean, variance, and correlation function. Finally, we discuss how results for time dependent parameters can be extended to the three-stage model and used to make inferences about models with parameter fluctuations induced by hidden stochastic variables.

Modern control techniques in active flutter suppression using a control moment gyro

NASA Technical Reports Server (NTRS)

Buchek, P. M.

1974-01-01

Development of organized synthesis techniques, using concepts of modern control theory was studied for the design of active flutter suppression systems for two and three-dimensional lifting surfaces, utilizing a control moment gyro (CMG) to generate the required control torques. Incompressible flow theory is assumed, with the unsteady aerodynamic forces and moments for arbitrary airfoil motion obtained by using the convolution integral based on Wagner's indicial lift function. Linear optimal control theory is applied to find particular optimal sets of gain values which minimize a quadratic performance function. The closed loop system's response to impulsive gust disturbances and the resulting control power requirements are investigated, and the system eigenvalues necessary to minimize the maximum value of control power are determined.

Generalized skew-symmetric interfacial probability distribution in reflectivity and small-angle scattering analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Zhang; Chen, Wei

Generalized skew-symmetric probability density functions are proposed to model asymmetric interfacial density distributions for the parameterization of any arbitrary density profiles in the `effective-density model'. The penetration of the densities into adjacent layers can be selectively controlled and parameterized. A continuous density profile is generated and discretized into many independent slices of very thin thickness with constant density values and sharp interfaces. The discretized profile can be used to calculate reflectivities via Parratt's recursive formula, or small-angle scattering via the concentric onion model that is also developed in this work.

A method for estimating the rolling moment due to spin rate for arbitrary planform wings

NASA Technical Reports Server (NTRS)

Poppen, W. A., Jr.

1985-01-01

The application of aerodynamic theory for estimating the force and moments acting upon spinning airplanes is of interest. For example, strip theory has been used to generate estimates of the aerodynamic characteristics as a function of spin rate for wing-dominated configurations for angles of attack up to 90 degrees. This work, which had been limited to constant chord wings, is extended here to wings comprised of tapered segments. Comparison of the analytical predictions with rotary balance wind tunnel results shows that large discrepancies remain, particularly for those angles-of-attack greater than 40 degrees.

Generalized skew-symmetric interfacial probability distribution in reflectivity and small-angle scattering analysis

DOE PAGES

Jiang, Zhang; Chen, Wei

2017-11-03

Generalized skew-symmetric probability density functions are proposed to model asymmetric interfacial density distributions for the parameterization of any arbitrary density profiles in the `effective-density model'. The penetration of the densities into adjacent layers can be selectively controlled and parameterized. A continuous density profile is generated and discretized into many independent slices of very thin thickness with constant density values and sharp interfaces. The discretized profile can be used to calculate reflectivities via Parratt's recursive formula, or small-angle scattering via the concentric onion model that is also developed in this work.

Analysis of high-aspect-ratio jet-flap wings of arbitrary geometry

NASA Technical Reports Server (NTRS)

Lissaman, P. B. S.

1973-01-01

An analytical technique to compute the performance of an arbitrary jet-flapped wing is developed. The solution technique is based on the method of Maskell and Spence in which the well-known lifting-line approach is coupled with an auxiliary equation providing the extra function needed in jet-flap theory. The present method is generalized to handle straight, uncambered wings of arbitrary planform, twist, and blowing (including unsymmetrical cases). An analytical procedure is developed for continuous variations in the above geometric data with special functions to exactly treat discontinuities in any of the geometric and blowing data. A rational theory for the effect of finite wing thickness is introduced as well as simplified concepts of effective aspect ratio for rapid estimation of performance.

Efficient quantum algorithm for computing n-time correlation functions.

PubMed

Pedernales, J S; Di Candia, R; Egusquiza, I L; Casanova, J; Solano, E

2014-07-11

We propose a method for computing n-time correlation functions of arbitrary spinorial, fermionic, and bosonic operators, consisting of an efficient quantum algorithm that encodes these correlations in an initially added ancillary qubit for probe and control tasks. For spinorial and fermionic systems, the reconstruction of arbitrary n-time correlation functions requires the measurement of two ancilla observables, while for bosonic variables time derivatives of the same observables are needed. Finally, we provide examples applicable to different quantum platforms in the frame of the linear response theory.

Advanced satellite communication system

NASA Technical Reports Server (NTRS)

Staples, Edward J.; Lie, Sen

1992-01-01

The objective of this research program was to develop an innovative advanced satellite receiver/demodulator utilizing surface acoustic wave (SAW) chirp transform processor and coherent BPSK demodulation. The algorithm of this SAW chirp Fourier transformer is of the Convolve - Multiply - Convolve (CMC) type, utilizing off-the-shelf reflective array compressor (RAC) chirp filters. This satellite receiver, if fully developed, was intended to be used as an on-board multichannel communications repeater. The Advanced Communications Receiver consists of four units: (1) CMC processor, (2) single sideband modulator, (3) demodulator, and (4) chirp waveform generator and individual channel processors. The input signal is composed of multiple user transmission frequencies operating independently from remotely located ground terminals. This signal is Fourier transformed by the CMC Processor into a unique time slot for each user frequency. The CMC processor is driven by a waveform generator through a single sideband (SSB) modulator. The output of the coherent demodulator is composed of positive and negative pulses, which are the envelopes of the chirp transform processor output. These pulses correspond to the data symbols. Following the demodulator, a logic circuit reconstructs the pulses into data, which are subsequently differentially decoded to form the transmitted data. The coherent demodulation and detection of BPSK signals derived from a CMC chirp transform processor were experimentally demonstrated and bit error rate (BER) testing was performed. To assess the feasibility of such advanced receiver, the results were compared with the theoretical analysis and plotted for an average BER as a function of signal-to-noise ratio. Another goal of this SBIR program was the development of a commercial product. The commercial product developed was an arbitrary waveform generator. The successful sales have begun with the delivery of the first arbitrary waveform generator.

Computing arbitrary defect structures on arbitrary lattices on arbitrary geometries from arbitrary energies

NASA Astrophysics Data System (ADS)

Allen, Brian; Travesset, Alex

2004-03-01

Dislocations and disclinations play a fundamental role in the properties of two dimensional crystals. In this talk, it will be shown that a general computational framework can be developed by combining previous work of Seung and Nelson* and modern advances in objected oriented design. This allows separating the problem into independent classes such as: geometry (sphere, plane, torus..), lattice (triangular, square, etc..), type of defect (dislocation, disclinations, etc..), boundary conditions, type of order (crystalline, hexatic) or energy functional. As applications, the ground state of crystals in several geometries will be discussed. Experimental examples with colloidal particles will be shown. *S. Seung and D. Nelson, Phys. Rev. A 38, 1005 (1988)

Rational BRDF.

PubMed

Pacanowski, Romain; Salazar Celis, Oliver; Schlick, Christophe; Granier, Xavier; Poulin, Pierre; Cuyt, Annie

2012-11-01

Over the last two decades, much effort has been devoted to accurately measuring Bidirectional Reflectance Distribution Functions (BRDFs) of real-world materials and to use efficiently the resulting data for rendering. Because of their large size, it is difficult to use directly measured BRDFs for real-time applications, and fitting the most sophisticated analytical BRDF models is still a complex task. In this paper, we introduce Rational BRDF, a general-purpose and efficient representation for arbitrary BRDFs, based on Rational Functions (RFs). Using an adapted parametrization, we demonstrate how Rational BRDFs offer 1) a more compact and efficient representation using low-degree RFs, 2) an accurate fitting of measured materials with guaranteed control of the residual error, and 3) efficient importance sampling by applying the same fitting process to determine the inverse of the Cumulative Distribution Function (CDF) generated from the BRDF for use in Monte-Carlo rendering.

Is selective attention the basis for selective imitation in infants? An eye-tracking study of deferred imitation with 12-month-olds.

PubMed

Kolling, Thorsten; Oturai, Gabriella; Knopf, Monika

2014-08-01

Infants and children do not blindly copy every action they observe during imitation tasks. Research demonstrated that infants are efficient selective imitators. The impact of selective perceptual processes (selective attention) for selective deferred imitation, however, is still poorly described. The current study, therefore, analyzed 12-month-old infants' looking behavior during demonstration of two types of target actions: arbitrary versus functional actions. A fully automated remote eye tracker was used to assess infants' looking behavior during action demonstration. After a 30-min delay, infants' deferred imitation performance was assessed. Next to replicating a memory effect, results demonstrate that infants do imitate significantly more functional actions than arbitrary actions (functionality effect). Eye-tracking data show that whereas infants do not fixate significantly longer on functional actions than on arbitrary actions, amount of fixations and amount of saccades differ between functional and arbitrary actions, indicating different encoding mechanisms. In addition, item-level findings differ from overall findings, indicating that perceptual and conceptual item features influence looking behavior. Looking behavior on both the overall and item levels, however, does not relate to deferred imitation performance. Taken together, the findings demonstrate that, on the one hand, selective imitation is not explainable merely by selective attention processes. On the other hand, notwithstanding this reasoning, attention processes on the item level are important for encoding processes during target action demonstration. Limitations and future studies are discussed. Copyright © 2014 Elsevier Inc. All rights reserved.

Synthesis of focused beam with controllable arbitrary homogeneous polarization using engineered vectorial optical fields.

PubMed

Rui, Guanghao; Chen, Jian; Wang, Xiaoyan; Gu, Bing; Cui, Yiping; Zhan, Qiwen

2016-10-17

The propagation and focusing properties of light beams continue to remain a research interest owning to their promising applications in physics, chemistry and biological sciences. One of the main challenges to these applications is the control of polarization distribution within the focal volume. In this work, we propose and experimentally demonstrate a method for generating a focused beam with arbitrary homogeneous polarization at any transverse plane. The required input field at the pupil plane of a high numerical aperture objective lens can be found analytically by solving an inverse problem with the Richard-Wolf vectorial diffraction method, and can be experimentally created with a vectorial optical field generator. Focused fields with various polarizations are successfully generated and verified using a Stokes parameter measurement to demonstrate the capability and versatility of proposed technique.

General description of circularly symmetric Bessel beams of arbitrary order

NASA Astrophysics Data System (ADS)

Wang, Jia Jie; Wriedt, Thomas; Lock, James A.; Mädler, Lutz

2016-11-01

A general description of circularly symmetric Bessel beams of arbitrary order is derived in this paper. This is achieved by analyzing the relationship between different descriptions of polarized Bessel beams obtained using different approaches. It is shown that a class of circularly symmetric Davis Bessel beams derived using the Hertz vector potentials possesses the same general functional dependence as the aplanatic Bessel beams generated using the angular spectrum representation (ASR). This result bridges the gap between different descriptions of Bessel beams and leads to a general description of circularly symmetric Bessel beams, such that the Davis Bessel beams and the aplanatic Bessel beams are merely the two simplest cases of an infinite number of possible circularly symmetric Bessel beams. Additionally, magnitude profiles of the electric and magnetic fields, the energy density and the Poynting vector are displayed for Bessel beams in both paraxial and nonparaxial cases. The results presented in this paper provide a fresh perspective on the description of Bessel beams and cast some insights into the light scattering and light-matter interactions problems in practice.

Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation

DOE PAGES

Greene, Patrick T.; Schofield, Samuel P.; Nourgaliev, Robert

2017-01-27

A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fractionmore » or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Lastly, dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.« less

A New Merit Function for Evaluating the Flaw Tolerance of Composite Laminates. Pt. 2; Arbitrary Size Holes and Center Cracks

NASA Technical Reports Server (NTRS)

Mikulas, Martin M., Jr.; Sumpter, Rod

1999-01-01

In a previous paper, a new merit function for determining the strength performance of flawed composite laminates was presented. This previous analysis was restricted to circular hole flaws that were large enough that failure could be predicted using the laminate stress concentration factor. In this paper, the merit function is expanded to include the flaw cases of an arbitrary size circular hole or a center crack. Failure prediction for these cases is determined using the point stress criterion. An example application of the merit function is included for a wide range of graphite/epoxy laminates.

A New Merit Function for Evaluating the Flaw Tolerance of Composite Laminates. Part 2; Arbitrary Size Holes and Center Cracks

NASA Technical Reports Server (NTRS)

Martin, Mikulas M., Jr.; Sumpter, Rod

2000-01-01

In a previous paper, a new merit function for determining the strength performance of flawed composite laminates was presented. This previous analysis was restricted to circular hole flaws that were large enough that failure could be predicted using the laminate stress concentration factor. In this paper, the merit function is expanded to include the flaw cases of an arbitrary size circular hole or center crack. Failure prediction for these cases is determined using the point stress criterion. An example application of the merit function is included for a wide range of graphite/epoxy laminates.

A New Merit Function for Evaluating the Flaw Tolerance of Composite Laminates. Part 2; Arbitrary Size Holes and Center Cracks

NASA Technical Reports Server (NTRS)

Mikulas, Martin M., Jr.; Sumpter, Rod

1997-01-01

In a previous paper, a new merit function for determining the strength performance of flawed composite laminates was presented. This previous analysis was restricted to circular hole flaws that were large enough that failure could be predicted using the laminate stress concentration factor. In this paper, the merit function is expanded to include the flaw cases of an arbitrary size circular hole or a center crack. Failure prediction for these cases is determined using the point stress criterion. An example application of the merit function is included for a wide range of graphite/epoxy laminates.

Probabilistic treatment of the uncertainty from the finite size of weighted Monte Carlo data

NASA Astrophysics Data System (ADS)

Glüsenkamp, Thorsten

2018-06-01

Parameter estimation in HEP experiments often involves Monte Carlo simulation to model the experimental response function. A typical application are forward-folding likelihood analyses with re-weighting, or time-consuming minimization schemes with a new simulation set for each parameter value. Problematically, the finite size of such Monte Carlo samples carries intrinsic uncertainty that can lead to a substantial bias in parameter estimation if it is neglected and the sample size is small. We introduce a probabilistic treatment of this problem by replacing the usual likelihood functions with novel generalized probability distributions that incorporate the finite statistics via suitable marginalization. These new PDFs are analytic, and can be used to replace the Poisson, multinomial, and sample-based unbinned likelihoods, which covers many use cases in high-energy physics. In the limit of infinite statistics, they reduce to the respective standard probability distributions. In the general case of arbitrary Monte Carlo weights, the expressions involve the fourth Lauricella function FD, for which we find a new finite-sum representation in a certain parameter setting. The result also represents an exact form for Carlson's Dirichlet average Rn with n > 0, and thereby an efficient way to calculate the probability generating function of the Dirichlet-multinomial distribution, the extended divided difference of a monomial, or arbitrary moments of univariate B-splines. We demonstrate the bias reduction of our approach with a typical toy Monte Carlo problem, estimating the normalization of a peak in a falling energy spectrum, and compare the results with previously published methods from the literature.

lsjk—a C++ library for arbitrary-precision numeric evaluation of the generalized log-sine functions

NASA Astrophysics Data System (ADS)

Kalmykov, M. Yu.; Sheplyakov, A.

2005-10-01

Generalized log-sine functions Lsj(k)(θ) appear in higher order ɛ-expansion of different Feynman diagrams. We present an algorithm for the numerical evaluation of these functions for real arguments. This algorithm is implemented as a C++ library with arbitrary-precision arithmetics for integer 0⩽k⩽9 and j⩾2. Some new relations and representations of the generalized log-sine functions are given. Program summaryTitle of program:lsjk Catalogue number:ADVS Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVS Program obtained from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing terms: GNU General Public License Computers:all Operating systems:POSIX Programming language:C++ Memory required to execute:Depending on the complexity of the problem, at least 32 MB RAM recommended No. of lines in distributed program, including testing data, etc.:41 975 No. of bytes in distributed program, including testing data, etc.:309 156 Distribution format:tar.gz Other programs called:The CLN library for arbitrary-precision arithmetics is required at version 1.1.5 or greater External files needed:none Nature of the physical problem:Numerical evaluation of the generalized log-sine functions for real argument in the region 0<θ<π. These functions appear in Feynman integrals Method of solution:Series representation for the real argument in the region 0<θ<π Restriction on the complexity of the problem:Limited up to Lsj(9)(θ), and j is an arbitrary integer number. Thus, all function up to the weight 12 in the region 0<θ<π can be evaluated. The algorithm can be extended up to higher values of k(k>9) without modification Typical running time:Depending on the complexity of problem. See text below.

Arbitrary Symmetric Running Gait Generation for an Underactuated Biped Model.

PubMed

Dadashzadeh, Behnam; Esmaeili, Mohammad; Macnab, Chris

2017-01-01

This paper investigates generating symmetric trajectories for an underactuated biped during the stance phase of running. We use a point mass biped (PMB) model for gait analysis that consists of a prismatic force actuator on a massless leg. The significance of this model is its ability to generate more general and versatile running gaits than the spring-loaded inverted pendulum (SLIP) model, making it more suitable as a template for real robots. The algorithm plans the necessary leg actuator force to cause the robot center of mass to undergo arbitrary trajectories in stance with any arbitrary attack angle and velocity angle. The necessary actuator forces follow from the inverse kinematics and dynamics. Then these calculated forces become the control input to the dynamic model. We compare various center-of-mass trajectories, including a circular arc and polynomials of the degrees 2, 4 and 6. The cost of transport and maximum leg force are calculated for various attack angles and velocity angles. The results show that choosing the velocity angle as small as possible is beneficial, but the angle of attack has an optimum value. We also find a new result: there exist biped running gaits with double-hump ground reaction force profiles which result in less maximum leg force than single-hump profiles.

Arbitrary Symmetric Running Gait Generation for an Underactuated Biped Model

PubMed Central

Esmaeili, Mohammad; Macnab, Chris

2017-01-01

This paper investigates generating symmetric trajectories for an underactuated biped during the stance phase of running. We use a point mass biped (PMB) model for gait analysis that consists of a prismatic force actuator on a massless leg. The significance of this model is its ability to generate more general and versatile running gaits than the spring-loaded inverted pendulum (SLIP) model, making it more suitable as a template for real robots. The algorithm plans the necessary leg actuator force to cause the robot center of mass to undergo arbitrary trajectories in stance with any arbitrary attack angle and velocity angle. The necessary actuator forces follow from the inverse kinematics and dynamics. Then these calculated forces become the control input to the dynamic model. We compare various center-of-mass trajectories, including a circular arc and polynomials of the degrees 2, 4 and 6. The cost of transport and maximum leg force are calculated for various attack angles and velocity angles. The results show that choosing the velocity angle as small as possible is beneficial, but the angle of attack has an optimum value. We also find a new result: there exist biped running gaits with double-hump ground reaction force profiles which result in less maximum leg force than single-hump profiles. PMID:28118401

Generation of sequence signatures from DNA amplification fingerprints with mini-hairpin and microsatellite primers.

PubMed

Caetano-Anollés, G; Gresshoff, P M

1996-06-01

DNA amplification fingerprinting (DAF) with mini-hairpins harboring arbitrary "core" sequences at their 3' termini were used to fingerprint a variety of templates, including PCR products and whole genomes, to establish genetic relationships between plant tax at the interspecific and intraspecific level, and to identify closely related fungal isolates and plant accessions. No correlation was observed between the sequence of the arbitrary core, the stability of the mini-hairpin structure and DAF efficiency. Mini-hairpin primers with short arbitrary cores and primers complementary to simple sequence repeats present in microsatellites were also used to generate arbitrary signatures from amplification profiles (ASAP). The ASAP strategy is a dual-step amplification procedure that uses at least one primer in each fingerprinting stage. ASAP was able to reproducibly amplify DAF products (representing about 10-15 kb of sequence) following careful optimization of amplification parameters such as primer and template concentration. Avoidance of primer sequences partially complementary to DAF product termini was necessary in order to produce distinct fingerprints. This allowed the combinatorial use of oligomers in nucleic acid screening, with numerous ASAP fingerprinting reactions based on a limited number of primer sequences. Mini-hairpin primers and ASAP analysis significantly increased detection of polymorphic DNA, separating closely related bermudagrass (Cynodon) cultivars and detecting putatively linked markers in bulked segregant analysis of the soybean (Glycine max) supernodulation (nitrate-tolerant symbiosis) locus.

Trivial constraints on orbital-free kinetic energy density functionals

NASA Astrophysics Data System (ADS)

Luo, Kai; Trickey, S. B.

2018-03-01

Approximate kinetic energy density functionals (KEDFs) are central to orbital-free density functional theory. Limitations on the spatial derivative dependencies of KEDFs have been claimed from differential virial theorems. We identify a central defect in the argument: the relationships are not true for an arbitrary density but hold only for the minimizing density and corresponding chemical potential. Contrary to the claims therefore, the relationships are not constraints and provide no independent information about the spatial derivative dependencies of approximate KEDFs. A simple argument also shows that validity for arbitrary v-representable densities is not restored by appeal to the density-potential bijection.

Decomposition of the polynomial kernel of arbitrary higher spin Dirac operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eelbode, D., E-mail: David.Eelbode@ua.ac.be; Raeymaekers, T., E-mail: Tim.Raeymaekers@UGent.be; Van der Jeugt, J., E-mail: Joris.VanderJeugt@UGent.be

2015-10-15

In a series of recent papers, we have introduced higher spin Dirac operators, which are generalisations of the classical Dirac operator. Whereas the latter acts on spinor-valued functions, the former acts on functions taking values in arbitrary irreducible half-integer highest weight representations for the spin group. In this paper, we describe how the polynomial kernel spaces of such operators decompose in irreducible representations of the spin group. We will hereby make use of results from representation theory.

Universal sequence map (USM) of arbitrary discrete sequences

PubMed Central

2002-01-01

Background For over a decade the idea of representing biological sequences in a continuous coordinate space has maintained its appeal but not been fully realized. The basic idea is that any sequence of symbols may define trajectories in the continuous space conserving all its statistical properties. Ideally, such a representation would allow scale independent sequence analysis – without the context of fixed memory length. A simple example would consist on being able to infer the homology between two sequences solely by comparing the coordinates of any two homologous units. Results We have successfully identified such an iterative function for bijective mappingψ of discrete sequences into objects of continuous state space that enable scale-independent sequence analysis. The technique, named Universal Sequence Mapping (USM), is applicable to sequences with an arbitrary length and arbitrary number of unique units and generates a representation where map distance estimates sequence similarity. The novel USM procedure is based on earlier work by these and other authors on the properties of Chaos Game Representation (CGR). The latter enables the representation of 4 unit type sequences (like DNA) as an order free Markov Chain transition table. The properties of USM are illustrated with test data and can be verified for other data by using the accompanying web-based tool:http://bioinformatics.musc.edu/~jonas/usm/. Conclusions USM is shown to enable a statistical mechanics approach to sequence analysis. The scale independent representation frees sequence analysis from the need to assume a memory length in the investigation of syntactic rules. PMID:11895567

Cutting-edge Kinetic Physics with Parker Solar Probe and Solar Orbiter: The Arbitrary Linear Plasma Solver (ALPS)

NASA Astrophysics Data System (ADS)

Verscharen, D.; Klein, K. G.; Chandran, B. D. G.; Stevens, M. L.; Salem, C. S.; Bale, S. D.

2017-12-01

The Arbitrary Linear Plasma Solver (ALPS) is a parallelized numerical code that solves the dispersion relation in a hot (even relativistic) magnetized plasma with an arbitrary number of particle species with arbitrary gyrotropic equilibrium distribution functions for any direction of wave propagation with respect to the background field. In this way, ALPS retains generality and overcomes the shortcomings of previous (bi-)Maxwellian solvers for the plasma dispersion relations. The unprecedented high-resolution particle and field data products from Parker Solar Probe (PSP) and Solar Orbiter (SO) will require novel theoretical tools. ALPS is one such tool, and its use will make possible new investigations into the role of non-Maxwellian distributions in the near-Sun solar wind. It can be applied to numerous high-velocity-resolution systems, ranging from current space missions to numerical simulations. We will briefly discuss the ALPS algorithm and demonstrate its functionality based on previous solar-wind measurements. We will then highlight our plans for future applications of ALPS to PSP and SO observations.

Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Peng; Ji, Wei; Wei, Bing-Yan

Arbitrary vector beams (VBs) are realized by the designed polarization converters and corresponding vector-photoaligned q-plates. The polarization converter is a specific twisted nematic cell with one substrate homogeneously aligned and the other space-variantly aligned. By combining a polarization-sensitive alignment agent with a dynamic micro-lithography system, various categories of liquid crystal polarization converters are demonstrated. Besides, traditional radially/azimuthally polarized light, high-order and multi-ringed VBs, and a VB array with different orders are generated. The obtained converters are further utilized as polarization masks to implement vector-photoaligning. The technique facilitates both the volume duplication of these converters and the generation of another promisingmore » optical element, the q-plate, which is suitable for the generation of VBs for coherent lasers. The combination of proposed polarization converters and correspondingly fabricated q-plates would drastically enhance the capability of polarization control and may bring more possibilities for the design of photonic devices.« less

Flexible approach to vibrational sum-frequency generation using shaped near-infrared light

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chowdhury, Azhad U.; Liu, Fangjie; Watson, Brianna R.

We describe a new approach that expands the utility of vibrational sum-frequency generation (vSFG) spectroscopy using shaped near-infrared (NIR) laser pulses. Here, we demonstrate that arbitrary pulse shapes can be specified to match experimental requirements without the need for changes to the optical alignment. In this way, narrowband NIR pulses as long as 5.75 ps are readily generated, with a spectral resolution of about 2.5 cm -1, an improvement of approximately a factor of 3 compared to a typical vSFG system. Moreover, the utility of having complete control over the NIR pulse characteristics is demonstrated through nonresonant background suppression frommore » a metallic substrate by generating an etalon waveform in the pulse shaper. The flexibility afforded by switching between arbitrary NIR waveforms at the sample position with the same instrument geometry expands the type of samples that can be studied without extensive modifications to existing apparatuses or large investments in specialty optics.« less

Flexible approach to vibrational sum-frequency generation using shaped near-infrared light

DOE PAGES

Chowdhury, Azhad U.; Liu, Fangjie; Watson, Brianna R.; ...

2018-04-23

We describe a new approach that expands the utility of vibrational sum-frequency generation (vSFG) spectroscopy using shaped near-infrared (NIR) laser pulses. Here, we demonstrate that arbitrary pulse shapes can be specified to match experimental requirements without the need for changes to the optical alignment. In this way, narrowband NIR pulses as long as 5.75 ps are readily generated, with a spectral resolution of about 2.5 cm -1, an improvement of approximately a factor of 3 compared to a typical vSFG system. Moreover, the utility of having complete control over the NIR pulse characteristics is demonstrated through nonresonant background suppression frommore » a metallic substrate by generating an etalon waveform in the pulse shaper. The flexibility afforded by switching between arbitrary NIR waveforms at the sample position with the same instrument geometry expands the type of samples that can be studied without extensive modifications to existing apparatuses or large investments in specialty optics.« less

Characterizing the propagation evolution of wave patterns and vortex structures in astigmatic transformations of Hermite-Gaussian beams

NASA Astrophysics Data System (ADS)

Chen, Y. F.; Chang, C. C.; Lee, C. Y.; Tung, J. C.; Liang, H. C.; Huang, K. F.

2018-01-01

Theoretical wave functions are analytically derived to characterize the propagation evolution of the Hermite-Gaussian (HG) beams transformed by a single-lens astigmatic mode converter with arbitrary angle. The derived wave functions are related to the combination of the rotation transform and the antisymmetric fractional Fourier transform. The derived formula is systematically validated by using an off-axis diode-pumped solid-state laser to generate various high-order HG beams for mode conversions. In addition to validation, the creation and evolution of vortex structures in the transformed HG beams are numerically manifested. The present theoretical analyses can be used not only to characterize the evolution of the transformed beams but to design the optical vortex beams with various forms.

Relaxation time estimation in surface NMR

DOEpatents

Grunewald, Elliot D.; Walsh, David O.

2017-03-21

NMR relaxation time estimation methods and corresponding apparatus generate two or more alternating current transmit pulses with arbitrary amplitudes, time delays, and relative phases; apply a surface NMR acquisition scheme in which initial preparatory pulses, the properties of which may be fixed across a set of multiple acquisition sequence, are transmitted at the start of each acquisition sequence and are followed by one or more depth sensitive pulses, the pulse moments of which are varied across the set of multiple acquisition sequences; and apply processing techniques in which recorded NMR response data are used to estimate NMR properties and the relaxation times T.sub.1 and T.sub.2* as a function of position as well as one-dimensional and two-dimension distributions of T.sub.1 versus T.sub.2* as a function of subsurface position.

The large-scale correlations of multicell densities and profiles: implications for cosmic variance estimates

NASA Astrophysics Data System (ADS)

Codis, Sandrine; Bernardeau, Francis; Pichon, Christophe

2016-08-01

In order to quantify the error budget in the measured probability distribution functions of cell densities, the two-point statistics of cosmic densities in concentric spheres is investigated. Bias functions are introduced as the ratio of their two-point correlation function to the two-point correlation of the underlying dark matter distribution. They describe how cell densities are spatially correlated. They are computed here via the so-called large deviation principle in the quasi-linear regime. Their large-separation limit is presented and successfully compared to simulations for density and density slopes: this regime is shown to be rapidly reached allowing to get sub-percent precision for a wide range of densities and variances. The corresponding asymptotic limit provides an estimate of the cosmic variance of standard concentric cell statistics applied to finite surveys. More generally, no assumption on the separation is required for some specific moments of the two-point statistics, for instance when predicting the generating function of cumulants containing any powers of concentric densities in one location and one power of density at some arbitrary distance from the rest. This exact `one external leg' cumulant generating function is used in particular to probe the rate of convergence of the large-separation approximation.

Statistics of primordial density perturbations from discrete seed masses

NASA Technical Reports Server (NTRS)

Scherrer, Robert J.; Bertschinger, Edmund

1991-01-01

The statistics of density perturbations for general distributions of seed masses with arbitrary matter accretion is examined. Formal expressions for the power spectrum, the N-point correlation functions, and the density distribution function are derived. These results are applied to the case of uncorrelated seed masses, and power spectra are derived for accretion of both hot and cold dark matter plus baryons. The reduced moments (cumulants) of the density distribution are computed and used to obtain a series expansion for the density distribution function. Analytic results are obtained for the density distribution function in the case of a distribution of seed masses with a spherical top-hat accretion pattern. More generally, the formalism makes it possible to give a complete characterization of the statistical properties of any random field generated from a discrete linear superposition of kernels. In particular, the results can be applied to density fields derived by smoothing a discrete set of points with a window function.

BLUES function method in computational physics

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Müller-Nedebock, Kristian K.

2018-04-01

We introduce a computational method in physics that goes ‘beyond linear use of equation superposition’ (BLUES). A BLUES function is defined as a solution of a nonlinear differential equation (DE) with a delta source that is at the same time a Green’s function for a related linear DE. For an arbitrary source, the BLUES function can be used to construct an exact solution to the nonlinear DE with a different, but related source. Alternatively, the BLUES function can be used to construct an approximate piecewise analytical solution to the nonlinear DE with an arbitrary source. For this alternative use the related linear DE need not be known. The method is illustrated in a few examples using analytical calculations and numerical computations. Areas for further applications are suggested.

Tree-level correlations in the strong field regime

NASA Astrophysics Data System (ADS)

Gelis, François

2017-09-01

We consider the correlation function of an arbitrary number of local observables in quantum field theory, in situations where the field amplitude is large. Using a quasi-classical approximation (valid for a highly occupied initial mixed state, or for a coherent initial state if the classical dynamics has instabilities), we show that at tree level these correlations are dominated by fluctuations at the initial time. We obtain a general expression of the correlation functions in terms of the classical solution of the field equation of motion and its derivatives with respect to its initial conditions, that can be arranged graphically as the sum of labeled trees where the nodes are the individual observables, and the links are pairs of derivatives acting on them. For 3-point (and higher) correlation functions, there are additional tree-level terms beyond the quasi-classical approximation, generated by fluctuations in the bulk.

Response functions of free mass gravitational wave antennas

NASA Technical Reports Server (NTRS)

Estabrook, F. B.

1985-01-01

The work of Gursel, Linsay, Spero, Saulson, Whitcomb and Weiss (1984) on the response of a free-mass interferometric antenna is extended. Starting from first principles, the earlier work derived the response of a 2-arm gravitational wave antenna to plane polarized gravitational waves. Equivalent formulas (generalized slightly to allow for arbitrary elliptical polarization) are obtained by a simple differencing of the '3-pulse' Doppler response functions of two 1-arm antennas. A '4-pulse' response function is found, with quite complicated angular dependences for arbitrary incident polarization. The differencing method can as readily be used to write exact response functions ('3n+1 pulse') for antennas having multiple passes or more arms.

Impact of self-healing capability on network robustness

NASA Astrophysics Data System (ADS)

Shang, Yilun

2015-04-01

A wide spectrum of real-life systems ranging from neurons to botnets display spontaneous recovery ability. Using the generating function formalism applied to static uncorrelated random networks with arbitrary degree distributions, the microscopic mechanism underlying the depreciation-recovery process is characterized and the effect of varying self-healing capability on network robustness is revealed. It is found that the self-healing capability of nodes has a profound impact on the phase transition in the emergence of percolating clusters, and that salient difference exists in upholding network integrity under random failures and intentional attacks. The results provide a theoretical framework for quantitatively understanding the self-healing phenomenon in varied complex systems.

Impact of self-healing capability on network robustness.

PubMed

Shang, Yilun

2015-04-01

A wide spectrum of real-life systems ranging from neurons to botnets display spontaneous recovery ability. Using the generating function formalism applied to static uncorrelated random networks with arbitrary degree distributions, the microscopic mechanism underlying the depreciation-recovery process is characterized and the effect of varying self-healing capability on network robustness is revealed. It is found that the self-healing capability of nodes has a profound impact on the phase transition in the emergence of percolating clusters, and that salient difference exists in upholding network integrity under random failures and intentional attacks. The results provide a theoretical framework for quantitatively understanding the self-healing phenomenon in varied complex systems.

Full counting statistics of a charge pump in the Coulomb blockade regime

NASA Astrophysics Data System (ADS)

Andreev, A. V.; Mishchenko, E. G.

2001-12-01

We study full charge counting statistics (FCCS) of a charge pump based on a nearly open single electron transistor. The problem is mapped onto an exactly soluble problem of a nonequilibrium g=1/2 Luttinger liquid with an impurity. We obtain an analytic expression for the generating function of the transmitted charge for an arbitrary pumping strength. Although this model contains fractionally charged excitations only integer transmitted charges can be observed. In the weak pumping limit FCCS correspond to a Poissonian transmission of particles with charge e*=e/2 from which all events with odd numbers of transferred particles are excluded.

Multi-dimensional Rankings, Program Termination, and Complexity Bounds of Flowchart Programs

NASA Astrophysics Data System (ADS)

Alias, Christophe; Darte, Alain; Feautrier, Paul; Gonnord, Laure

Proving the termination of a flowchart program can be done by exhibiting a ranking function, i.e., a function from the program states to a well-founded set, which strictly decreases at each program step. A standard method to automatically generate such a function is to compute invariants for each program point and to search for a ranking in a restricted class of functions that can be handled with linear programming techniques. Previous algorithms based on affine rankings either are applicable only to simple loops (i.e., single-node flowcharts) and rely on enumeration, or are not complete in the sense that they are not guaranteed to find a ranking in the class of functions they consider, if one exists. Our first contribution is to propose an efficient algorithm to compute ranking functions: It can handle flowcharts of arbitrary structure, the class of candidate rankings it explores is larger, and our method, although greedy, is provably complete. Our second contribution is to show how to use the ranking functions we generate to get upper bounds for the computational complexity (number of transitions) of the source program. This estimate is a polynomial, which means that we can handle programs with more than linear complexity. We applied the method on a collection of test cases from the literature. We also show the links and differences with previous techniques based on the insertion of counters.

Construction of multiple trade-offs to obtain arbitrary singularities of adaptive dynamics.

PubMed

Kisdi, Éva

2015-04-01

Evolutionary singularities are central to the adaptive dynamics of evolving traits. The evolutionary singularities are strongly affected by the shape of any trade-off functions a model assumes, yet the trade-off functions are often chosen in an ad hoc manner, which may unjustifiably constrain the evolutionary dynamics exhibited by the model. To avoid this problem, critical function analysis has been used to find a trade-off function that yields a certain evolutionary singularity such as an evolutionary branching point. Here I extend this method to multiple trade-offs parameterized with a scalar strategy. I show that the trade-off functions can be chosen such that an arbitrary point in the viability domain of the trait space is a singularity of an arbitrary type, provided (next to certain non-degeneracy conditions) that the model has at least two environmental feedback variables and at least as many trade-offs as feedback variables. The proof is constructive, i.e., it provides an algorithm to find trade-off functions that yield the desired singularity. I illustrate the construction of trade-offs with an example where the virulence of a pathogen evolves in a small ecosystem of a host, its pathogen, a predator that attacks the host and an alternative prey of the predator.

Toward autonomous spacecraft

NASA Technical Reports Server (NTRS)

Fogel, L. J.; Calabrese, P. G.; Walsh, M. J.; Owens, A. J.

1982-01-01

Ways in which autonomous behavior of spacecraft can be extended to treat situations wherein a closed loop control by a human may not be appropriate or even possible are explored. Predictive models that minimize mean least squared error and arbitrary cost functions are discussed. A methodology for extracting cyclic components for an arbitrary environment with respect to usual and arbitrary criteria is developed. An approach to prediction and control based on evolutionary programming is outlined. A computer program capable of predicting time series is presented. A design of a control system for a robotic dense with partially unknown physical properties is presented.

Quantitative phase retrieval with arbitrary pupil and illumination

DOE PAGES

Claus, Rene A.; Naulleau, Patrick P.; Neureuther, Andrew R.; ...

2015-10-02

We present a general algorithm for combining measurements taken under various illumination and imaging conditions to quantitatively extract the amplitude and phase of an object wave. The algorithm uses the weak object transfer function, which incorporates arbitrary pupil functions and partially coherent illumination. The approach is extended beyond the weak object regime using an iterative algorithm. Finally, we demonstrate the method on measurements of Extreme Ultraviolet Lithography (EUV) multilayer mask defects taken in an EUV zone plate microscope with both a standard zone plate lens and a zone plate implementing Zernike phase contrast.

Automatic Molecular Design using Evolutionary Techniques

NASA Technical Reports Server (NTRS)

Globus, Al; Lawton, John; Wipke, Todd; Saini, Subhash (Technical Monitor)

1998-01-01

Molecular nanotechnology is the precise, three-dimensional control of materials and devices at the atomic scale. An important part of nanotechnology is the design of molecules for specific purposes. This paper describes early results using genetic software techniques to automatically design molecules under the control of a fitness function. The fitness function must be capable of determining which of two arbitrary molecules is better for a specific task. The software begins by generating a population of random molecules. The population is then evolved towards greater fitness by randomly combining parts of the better individuals to create new molecules. These new molecules then replace some of the worst molecules in the population. The unique aspect of our approach is that we apply genetic crossover to molecules represented by graphs, i.e., sets of atoms and the bonds that connect them. We present evidence suggesting that crossover alone, operating on graphs, can evolve any possible molecule given an appropriate fitness function and a population containing both rings and chains. Prior work evolved strings or trees that were subsequently processed to generate molecular graphs. In principle, genetic graph software should be able to evolve other graph representable systems such as circuits, transportation networks, metabolic pathways, computer networks, etc.

Nonlinear Wavefront Control with All-Dielectric Metasurfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Lei; Kruk, Sergey; Koshelev, Kirill

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less

Nonlinear Wavefront Control with All-Dielectric Metasurfaces.

PubMed

Wang, Lei; Kruk, Sergey; Koshelev, Kirill; Kravchenko, Ivan; Luther-Davies, Barry; Kivshar, Yuri

2018-06-13

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront of parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Our nonlinear metasurfaces produce phase gradients over a full 0-2π phase range with a 92% diffraction efficiency.

Nonlinear Wavefront Control with All-Dielectric Metasurfaces

DOE PAGES

Wang, Lei; Kruk, Sergey; Koshelev, Kirill; ...

2018-05-11

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less

Noise Characterization of Erbium-Doped Fiber Amplifiers and Avalanche Photodiodes in Optical Communication Systems.

NASA Astrophysics Data System (ADS)

Kahraman, Gokalp

We examine the performance of optical communication systems using erbium-doped fiber amplifiers (OFAs) and avalanche photodiodes (APDs) including nonlinear and transient effects in the former and transient effects in the latter. Transient effects become important as these amplifiers are operated at very high data rates. Nonlinear effects are important for high gain amplifiers. In most studies of noise in these devices, the temporal and nonlinear effects have been ignored. We present a quantum theory of noise in OFAs including the saturation of the atomic population inversion and the pump depletion. We study the quantum-statistical properties of pulse amplification. The generating function of the output photon number distribution (PND) is determined as a function of time during the course of the pulse with an arbitrary input PND assumed. Under stationary conditions, we determine the Kolmogorov equation obeyed by the PND. The PND at the output is determined for arbitrary input distributions. The effect of the counting time and the filter bandwidth used by the detection circuit is determined. We determine the gain, the noise figure, and the sensitivity of receivers using OFAs as preamplifiers, including the effect of backward amplified spontaneous emission (ASE). Backward ASE degrades the noise figure and the sensitivity by depleting the population inversion at the input side of the fiber and thus increasing the noise during signal amplification. We show that the sensitivity improves with the bit rate at low rates but degrades at high rates. We provide a stochastic model that describes the time dynamics in a double-carrier multiplication (DCM) APD. A discrete stochastic model for the electron/hole motion and multiplication is defined on a spatio-temporal lattice and used to derive recursive equations for the mean, the variance, and the autocorrelation of the impulse response as functions of time. The power spectral density of the photocurrent produced in response to a Poisson-distributed stream of photons of uniform rate is evaluated. A method is also developed for solving the coupled transport equations that describe the electron and hole currents in a DCM-APD of arbitrary structure.

Virtual reality based adaptive dose assessment method for arbitrary geometries in nuclear facility decommissioning.

PubMed

Liu, Yong-Kuo; Chao, Nan; Xia, Hong; Peng, Min-Jun; Ayodeji, Abiodun

2018-05-17

This paper presents an improved and efficient virtual reality-based adaptive dose assessment method (VRBAM) applicable to the cutting and dismantling tasks in nuclear facility decommissioning. The method combines the modeling strength of virtual reality with the flexibility of adaptive technology. The initial geometry is designed with the three-dimensional computer-aided design tools, and a hybrid model composed of cuboids and a point-cloud is generated automatically according to the virtual model of the object. In order to improve the efficiency of dose calculation while retaining accuracy, the hybrid model is converted to a weighted point-cloud model, and the point kernels are generated by adaptively simplifying the weighted point-cloud model according to the detector position, an approach that is suitable for arbitrary geometries. The dose rates are calculated with the Point-Kernel method. To account for radiation scattering effects, buildup factors are calculated with the Geometric-Progression formula in the fitting function. The geometric modeling capability of VRBAM was verified by simulating basic geometries, which included a convex surface, a concave surface, a flat surface and their combination. The simulation results show that the VRBAM is more flexible and superior to other approaches in modeling complex geometries. In this paper, the computation time and dose rate results obtained from the proposed method were also compared with those obtained using the MCNP code and an earlier virtual reality-based method (VRBM) developed by the same authors. © 2018 IOP Publishing Ltd.

Nonlinear differential equations for the wavefront surface at arbitrary Hartmann-plane distances.

PubMed

Téllez-Quiñones, Alejandro; Malacara-Doblado, Daniel; Flores-Hernández, Ricardo; Gutiérrez-Hernández, David A; León-Rodríguez, Miguel

2016-03-20

In the Hartmann test, a wave aberration function W is estimated from the information of the spot diagram drawn in an observation plane. The distance from a reference plane to the observation plane, the Hartmann-plane distance, is typically chosen as z=f, where f is the radius of a reference sphere. The function W and the transversal aberrations {X,Y} calculated at the plane z=f are related by two well-known linear differential equations. Here, we propose two nonlinear differential equations to denote a more general relation between W and the transversal aberrations {U,V} calculated at any arbitrary Hartmann-plane distance z=r. We also show how to directly estimate the wavefront surface w from the information of {U,V}. The use of arbitrary r values could improve the reliability of the measurements of W, or w, when finding difficulties in adequate ray identification at z=f.

Ionization waves of arbitrary velocity driven by a flying focus

NASA Astrophysics Data System (ADS)

Palastro, J. P.; Turnbull, D.; Bahk, S.-W.; Follett, R. K.; Shaw, J. L.; Haberberger, D.; Bromage, J.; Froula, D. H.

2018-03-01

A chirped laser pulse focused by a chromatic lens exhibits a dynamic, or flying, focus in which the trajectory of the peak intensity decouples from the group velocity. In a medium, the flying focus can trigger an ionization front that follows this trajectory. By adjusting the chirp, the ionization front can be made to travel at an arbitrary velocity along the optical axis. We present analytical calculations and simulations describing the propagation of the flying focus pulse, the self-similar form of its intensity profile, and ionization wave formation. The ability to control the speed of the ionization wave and, in conjunction, mitigate plasma refraction has the potential to advance several laser-based applications, including Raman amplification, photon acceleration, high-order-harmonic generation, and THz generation.

Large deviation principle at work: Computation of the statistical properties of the exact one-point aperture mass

NASA Astrophysics Data System (ADS)

Reimberg, Paulo; Bernardeau, Francis

2018-01-01

We present a formalism based on the large deviation principle (LDP) applied to cosmological density fields, and more specifically to the arbitrary functional of density profiles, and we apply it to the derivation of the cumulant generating function and one-point probability distribution function (PDF) of the aperture mass (Map ), a common observable for cosmic shear observations. We show that the LDP can indeed be used in practice for a much larger family of observables than previously envisioned, such as those built from continuous and nonlinear functionals of density profiles. Taking advantage of this formalism, we can extend previous results, which were based on crude definitions of the aperture mass, with top-hat windows and the use of the reduced shear approximation (replacing the reduced shear with the shear itself). We were precisely able to quantify how this latter approximation affects the Map statistical properties. In particular, we derive the corrective term for the skewness of the Map and reconstruct its one-point PDF.

GENIE(++): A Multi-Block Structured Grid System

NASA Technical Reports Server (NTRS)

Williams, Tonya; Nadenthiran, Naren; Thornburg, Hugh; Soni, Bharat K.

1996-01-01

The computer code GENIE++ is a continuously evolving grid system containing a multitude of proven geometry/grid techniques. The generation process in GENIE++ is based on an earlier version. The process uses several techniques either separately or in combination to quickly and economically generate sculptured geometry descriptions and grids for arbitrary geometries. The computational mesh is formed by using an appropriate algebraic method. Grid clustering is accomplished with either exponential or hyperbolic tangent routines which allow the user to specify a desired point distribution. Grid smoothing can be accomplished by using an elliptic solver with proper forcing functions. B-spline and Non-Uniform Rational B-splines (NURBS) algorithms are used for surface definition and redistribution. The built in sculptured geometry definition with desired distribution of points, automatic Bezier curve/surface generation for interior boundaries/surfaces, and surface redistribution is based on NURBS. Weighted Lagrance/Hermite transfinite interpolation methods, interactive geometry/grid manipulation modules, and on-line graphical visualization of the generation process are salient features of this system which result in a significant time savings for a given geometry/grid application.

GRID3O- FAST GENERATION OF MULTILEVEL, THREE-DIMENSIONAL BOUNDARY-CONFORMING O-TYPE COMPUTATIONAL GRIDS

NASA Technical Reports Server (NTRS)

Dulikravich, D. S.

1994-01-01

A fast algorithm has been developed for accurately generating boundary-conforming, three-dimensional consecutively refined computational grids applicable to arbitrary wing-body and axial turbomachinery geometries. This algorithm has been incorporated into the GRID3O computer program. The method employed in GRID3O is based on using an analytic function to generate two-dimensional grids on a number of coaxial axisymmetric surfaces positioned between the centerbody and the outer radial boundary. These grids are of the O-type and are characterized by quasi-orthogonality, geometric periodicity, and an adequate resolution throughout the flow field. Because the built-in nonorthogonal coordinate stretching and shearing cause the grid lines leaving the blade or wing trailing-edge to end at downstream infinity, use of the generated grid simplifies the numerical treatment of three-dimensional trailing vortex sheets. The GRID3O program is written in FORTRAN IV for batch execution and has been implemented on an IBM 370 series computer with a central memory requirement of approximately 450K of 8 bit bytes. The GRID3O program was developed in 1981.

Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation.

PubMed

Chen, Rui-Pin; Chen, Zhaozhong; Chew, Khian-Hooi; Li, Pei-Gang; Yu, Zhongliang; Ding, Jianping; He, Sailing

2015-05-29

A caustic vector vortex optical field is experimentally generated and demonstrated by a caustic-based approach. The desired caustic with arbitrary acceleration trajectories, as well as the structured states of polarization (SoP) and vortex orders located in different positions in the field cross-section, is generated by imposing the corresponding spatial phase function in a vector vortex optical field. Our study reveals that different spin and orbital angular momentum flux distributions (including opposite directions) in different positions in the cross-section of a caustic vector vortex optical field can be dynamically managed during propagation by intentionally choosing the initial polarization and vortex topological charges, as a result of the modulation of the caustic phase. We find that the SoP in the field cross-section rotates during propagation due to the existence of the vortex. The unique structured feature of the caustic vector vortex optical field opens the possibility of multi-manipulation of optical angular momentum fluxes and SoP, leading to more complex manipulation of the optical field scenarios. Thus this approach further expands the functionality of an optical system.

Integrand reduction for two-loop scattering amplitudes through multivariate polynomial division

NASA Astrophysics Data System (ADS)

Mastrolia, Pierpaolo; Mirabella, Edoardo; Ossola, Giovanni; Peraro, Tiziano

2013-04-01

We describe the application of a novel approach for the reduction of scattering amplitudes, based on multivariate polynomial division, which we have recently presented. This technique yields the complete integrand decomposition for arbitrary amplitudes, regardless of the number of loops. It allows for the determination of the residue at any multiparticle cut, whose knowledge is a mandatory prerequisite for applying the integrand-reduction procedure. By using the division modulo Gröbner basis, we can derive a simple integrand recurrence relation that generates the multiparticle pole decomposition for integrands of arbitrary multiloop amplitudes. We apply the new reduction algorithm to the two-loop planar and nonplanar diagrams contributing to the five-point scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity in four dimensions, whose numerator functions contain up to rank-two terms in the integration momenta. We determine all polynomial residues parametrizing the cuts of the corresponding topologies and subtopologies. We obtain the integral basis for the decomposition of each diagram from the polynomial form of the residues. Our approach is well suited for a seminumerical implementation, and its general mathematical properties provide an effective algorithm for the generalization of the integrand-reduction method to all orders in perturbation theory.

A dose assessment method for arbitrary geometries with virtual reality in the nuclear facilities decommissioning

NASA Astrophysics Data System (ADS)

Chao, Nan; Liu, Yong-kuo; Xia, Hong; Ayodeji, Abiodun; Bai, Lu

2018-03-01

During the decommissioning of nuclear facilities, a large number of cutting and demolition activities are performed, which results in a frequent change in the structure and produce many irregular objects. In order to assess dose rates during the cutting and demolition process, a flexible dose assessment method for arbitrary geometries and radiation sources was proposed based on virtual reality technology and Point-Kernel method. The initial geometry is designed with the three-dimensional computer-aided design tools. An approximate model is built automatically in the process of geometric modeling via three procedures namely: space division, rough modeling of the body and fine modeling of the surface, all in combination with collision detection of virtual reality technology. Then point kernels are generated by sampling within the approximate model, and when the material and radiometric attributes are inputted, dose rates can be calculated with the Point-Kernel method. To account for radiation scattering effects, buildup factors are calculated with the Geometric-Progression formula in the fitting function. The effectiveness and accuracy of the proposed method was verified by means of simulations using different geometries and the dose rate results were compared with that derived from CIDEC code, MCNP code and experimental measurements.

Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter.

PubMed

Zhuang, Leimeng; Khan, Muhammad Rezaul; Beeker, Willem; Leinse, Arne; Heideman, René; Roeloffzen, Chris

2012-11-19

We propose and demonstrate a novel wideband microwave photonic fractional Hilbert transformer implemented using a ring resonator-based optical all-pass filter. The full programmability of the ring resonator allows variable and arbitrary fractional order of the Hilbert transformer. The performance analysis in both frequency and time domain validates that the proposed implementation provides a good approximation to an ideal fractional Hilbert transformer. This is also experimentally verified by an electrical S₂₁ response characterization performed on a waveguide realization of a ring resonator. The waveguide-based structure allows the proposed Hilbert transformer to be integrated together with other building blocks on a photonic integrated circuit to create various system-level functionalities for on-chip microwave photonic signal processors. As an example, a circuit consisting of a splitter and a ring resonator has been realized which can perform on-chip phase control of microwave signals generated by means of optical heterodyning, and simultaneous generation of in-phase and quadrature microwave signals for a wide frequency range. For these functionalities, this simple and on-chip solution is considered to be practical, particularly when operating together with a dual-frequency laser. To our best knowledge, this is the first-time on-chip demonstration where ring resonators are employed to perform phase control functionalities for optical generation of microwave signals by means of optical heterodyning.

NASA Ames three-dimensional potential flow analyses system (POTFAN) boundary condition code (BCDN), version 1

NASA Technical Reports Server (NTRS)

Davis, J. E.; Medan, R. T.

1977-01-01

This segment of the POTFAN system is used to generate right hand sides (boundary conditions) of the system of equations associated with the flow field under consideration. These specified flow boundary conditions are encountered in the oblique derivative boundary value problem (boundary value problem of the third kind) and contain the Neumann boundary condition as a special case. Arbitrary angle of attack and/or sideslip and/or rotation rates may be specified, as well as an arbitrary, nonuniform external flow field and the influence of prescribed singularity distributions.

Entanglement detection in the vicinity of arbitrary Dicke states.

PubMed

Duan, L-M

2011-10-28

Dicke states represent a class of multipartite entangled states that can be generated experimentally with many applications in quantum information. We propose a method to experimentally detect genuine multipartite entanglement in the vicinity of arbitrary Dicke states. The detection scheme can be used to experimentally quantify the entanglement depth of many-body systems and is easy to implement as it requires measurement of only three collective spin operators. The detection criterion is strong as it heralds multipartite entanglement even in cases where the state fidelity goes down exponentially with the number of qubits.

Numerical analysis method for linear induction machines.

NASA Technical Reports Server (NTRS)

Elliott, D. G.

1972-01-01

A numerical analysis method has been developed for linear induction machines such as liquid metal MHD pumps and generators and linear motors. Arbitrary phase currents or voltages can be specified and the moving conductor can have arbitrary velocity and conductivity variations from point to point. The moving conductor is divided into a mesh and coefficients are calculated for the voltage induced at each mesh point by unit current at every other mesh point. Combining the coefficients with the mesh resistances yields a set of simultaneous equations which are solved for the unknown currents.

A New Approach for Proving or Generating Combinatorial Identities

ERIC Educational Resources Information Center

Gonzalez, Luis

2010-01-01

A new method for proving, in an immediate way, many combinatorial identities is presented. The method is based on a simple recursive combinatorial formula involving n + 1 arbitrary real parameters. Moreover, this formula enables one not only to prove, but also generate many different combinatorial identities (not being required to know them "a…

Arbitrary grammars generating context-free languages

NASA Technical Reports Server (NTRS)

Baker, B. S.

1972-01-01

If G is a grammar such that in each noncontext-free rule of G, the right side contains a string of terminals longer than any terminal string appearing between two nonterminals in the left side; then the language generated by G is context-free. Six previous results follow as simple corollaries of this theorem.

Method to study complex systems of mesons in lattice QCD

DOE PAGES

Detmold, William; Savage, Martin J.

2010-07-30

Correlation functions involving many hadrons allow finite density systems to be explored with Lattice QCD. Recently, systems with up to 12more » $$\\pi^+$$'s or $K^+$'s have been studied to determine the the $3$-$$\\pi^+$$ and $3$-$K^+$ interactions and the corresponding chemical potential has been determined as a function of density in each case. We derive recursion relations between correlation functions that allow us to extend this work to systems of arbitrary numbers of mesons and to systems containing arbitrary different types of mesons such as $$\\pi^+$$'s, $K^+$'s, $D^0$'s and $B^+$'s. These relations allow for the study of finite-density systems in arbitrary volumes, and the study of high-density systems. Systems comprised of up to N=12 m mesons can be explored with Lattice QCD calculations utilizing $m$ different sources for the quark propagators. As the recursion relations require only a small, N-independent, number of operations to derive the N+1 meson contractions from the N meson contractions, they are compuationally feasible.« less

Iterative simulated quenching for designing irregular-spot-array generators.

PubMed

Gillet, J N; Sheng, Y

2000-07-10

We propose a novel, to our knowledge, algorithm of iterative simulated quenching with temperature rescaling for designing diffractive optical elements, based on an analogy between simulated annealing and statistical thermodynamics. The temperature is iteratively rescaled at the end of each quenching process according to ensemble statistics to bring the system back from a frozen imperfect state with a local minimum of energy to a dynamic state in a Boltzmann heat bath in thermal equilibrium at the rescaled temperature. The new algorithm achieves much lower cost function and reconstruction error and higher diffraction efficiency than conventional simulated annealing with a fast exponential cooling schedule and is easy to program. The algorithm is used to design binary-phase generators of large irregular spot arrays. The diffractive phase elements have trapezoidal apertures of varying heights, which fit ideal arbitrary-shaped apertures better than do trapezoidal apertures of fixed heights.

Numerical integration of discontinuous functions: moment fitting and smart octree

NASA Astrophysics Data System (ADS)

Hubrich, Simeon; Di Stolfo, Paolo; Kudela, László; Kollmannsberger, Stefan; Rank, Ernst; Schröder, Andreas; Düster, Alexander

2017-11-01

A fast and simple grid generation can be achieved by non-standard discretization methods where the mesh does not conform to the boundary or the internal interfaces of the problem. However, this simplification leads to discontinuous integrands for intersected elements and, therefore, standard quadrature rules do not perform well anymore. Consequently, special methods are required for the numerical integration. To this end, we present two approaches to obtain quadrature rules for arbitrary domains. The first approach is based on an extension of the moment fitting method combined with an optimization strategy for the position and weights of the quadrature points. In the second approach, we apply the smart octree, which generates curved sub-cells for the integration mesh. To demonstrate the performance of the proposed methods, we consider several numerical examples, showing that the methods lead to efficient quadrature rules, resulting in less integration points and in high accuracy.

Flexible coherent control of plasmonic spin-Hall effect.

PubMed

Xiao, Shiyi; Zhong, Fan; Liu, Hui; Zhu, Shining; Li, Jensen

2015-09-29

The surface plasmon polariton is an emerging candidate for miniaturizing optoelectronic circuits. Recent demonstrations of polarization-dependent splitting using metasurfaces, including focal-spot shifting and unidirectional propagation, allow us to exploit the spin degree of freedom in plasmonics. However, further progress has been hampered by the inability to generate more complicated and independent surface plasmon profiles for two incident spins, which work coherently together for more flexible and tunable functionalities. Here by matching the geometric phases of the nano-slots on silver to specific superimpositions of the inward and outward surface plasmon profiles for the two spins, arbitrary spin-dependent orbitals can be generated in a slot-free region. Furthermore, motion pictures with a series of picture frames can be assembled and played by varying the linear polarization angle of incident light. This spin-enabled control of orbitals is potentially useful for tip-free near-field scanning microscopy, holographic data storage, tunable plasmonic tweezers, and integrated optical components.

Léon Rosenfeld's general theory of constrained Hamiltonian dynamics

NASA Astrophysics Data System (ADS)

Salisbury, Donald

Léon Rosenfeld published in Annalen der Physik in 1930 a groundbreaking paper showing how to construct a Hamiltonian formalism for Lagrangian theories which admitted an underlying local gauge symmetry. The theory included both ``internal'' transformations such as the U(1) symmetry group of electromagnetism, and ``external'' symmetries typified by Einstein's general theory of relativity. His comprehensive analysis predated by two decades the formalism known as the Dirac-Bergmann approach, and I will present evidence that each of these giants were to some extent influenced by Rosenfeld's theory. Of particular significance is Rosenfeld's incorporation of arbitrary functions into the phase space generator of temporal evolution, and his construction of the phase space generator of symmetry transformations. The existing Hamiltonian formalisms have of course played a central role both in the demonstration of the renormalizability of Yang-Mills theories and current efforts in constructing a quantum theory of gravity.

Three-dimensional broadband acoustic illusion cloak for sound-hard boundaries of curved geometry

PubMed Central

Kan, Weiwei; Liang, Bin; Li, Ruiqi; Jiang, Xue; Zou, Xin-ye; Yin, Lei-lei; Cheng, Jianchun

2016-01-01

Acoustic illusion cloaks that create illusion effects by changing the scattered wave have many potential applications in a variety of scenarios. However, the experimental realization of generating three-dimensional (3D) acoustic illusions under detection of broadband signals still remains challenging despite the paramount importance for practical applications. Here we report the design and experimental demonstration of a 3D broadband cloak that can effectively manipulate the scattered field to generate the desired illusion effect near curved boundaries. The designed cloak simply comprises positive-index anisotropic materials, with parameters completely independent of either the cloaked object or the boundary. With the ability of manipulating the scattered field in 3D space and flexibility of applying to arbitrary geometries, our method may take a major step toward the real world application of acoustic cloaks and offer the possibilities of building advanced acoustic devices with versatile functionalities. PMID:27833141

Generalized parallel-perspective stereo mosaics from airborne video.

PubMed

Zhu, Zhigang; Hanson, Allen R; Riseman, Edward M

2004-02-01

In this paper, we present a new method for automatically and efficiently generating stereoscopic mosaics by seamless registration of images collected by a video camera mounted on an airborne platform. Using a parallel-perspective representation, a pair of geometrically registered stereo mosaics can be precisely constructed under quite general motion. A novel parallel ray interpolation for stereo mosaicing (PRISM) approach is proposed to make stereo mosaics seamless in the presence of obvious motion parallax and for rather arbitrary scenes. Parallel-perspective stereo mosaics generated with the PRISM method have better depth resolution than perspective stereo due to the adaptive baseline geometry. Moreover, unlike previous results showing that parallel-perspective stereo has a constant depth error, we conclude that the depth estimation error of stereo mosaics is in fact a linear function of the absolute depths of a scene. Experimental results on long video sequences are given.

Dynamic non-reciprocal meta-surfaces with arbitrary phase reconfigurability based on photonic transition in meta-atoms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shi, Yu; Fan, Shanhui, E-mail: shanhui@stanford.edu

2016-01-11

We introduce a distinct class of dynamic non-reciprocal meta-surfaces with arbitrary phase-reconfigurability. This meta-surface consists of an array of meta-atoms, each of which is subject to temporal refractive index modulation, which induces photonic transitions between the states of the meta-atom. We show that arbitrary phase profile for the outgoing wave can be achieved by controlling the phase of the modulation at each meta-atom. Moreover, such dynamic meta-surfaces exhibit non-reciprocal response without the need for magneto-optical effects. The use of photonic transition significantly enhances the tunability and the possible functionalities of meta-surfaces.

Geometry of quantum state manifolds generated by the Lie algebra operators

NASA Astrophysics Data System (ADS)

Kuzmak, A. R.

2018-03-01

The Fubini-Study metric of quantum state manifold generated by the operators which satisfy the Heisenberg Lie algebra is calculated. The similar problem is studied for the manifold generated by the so(3) Lie algebra operators. Using these results, we calculate the Fubini-Study metrics of state manifolds generated by the position and momentum operators. Also the metrics of quantum state manifolds generated by some spin systems are obtained. Finally, we generalize this problem for operators of an arbitrary Lie algebra.

Ultralow-phase-noise millimetre-wave signal generator assisted with an electro-optics-modulator-based optical frequency comb

PubMed Central

Ishizawa, A.; Nishikawa, T.; Goto, T.; Hitachi, K.; Sogawa, T.; Gotoh, H.

2016-01-01

Low-noise millimetre-wave signals are valuable for digital sampling systems, arbitrary waveform generation for ultra-wideband communications, and coherent radar systems. However, the phase noise of widely used conventional signal generators (SGs) will increase as the millimetre-wave frequency increases. Our goal has been to improve commercially available SGs so that they provide a low-phase-noise millimetre-wave signal with assistance from an electro-optics-modulator-based optical frequency comb (EOM-OFC). Here, we show that the phase noise can be greatly reduced by bridging the vast frequency difference between the gigahertz and terahertz ranges with an EOM-OFC. The EOM-OFC serves as a liaison that magnifies the phase noise of the SG. With the EOM-OFC used as a phase noise “booster” for a millimetre-wave signal, the phase noise of widely used SGs can be reduced at an arbitrary frequency f (6 ≦ f ≦ 72 GHz). PMID:27185040

Generation of Optical Vortices by Nonlinear Inverse Thomson Scattering at Arbitrary Angle Interactions

NASA Astrophysics Data System (ADS)

Taira, Yoshitaka; Katoh, Masahiro

2018-06-01

We theoretically verify that optical vortices carrying orbital angular momentum are generated in various astrophysical situations via nonlinear inverse Thomson scattering. Arbitrary angle collisions between relativistic electrons and circularly polarized strong electromagnetic waves are treated. We reveal that the higher harmonic components of scattered photons carry well-defined orbital angular momentum under a specific condition that the Lorentz factor of the electron is much larger than the field strength parameter of the electromagnetic wave. Our study indicates that optical vortices in a wide frequency range from radio waves to gamma-rays are naturally generated in environments where high-energy electrons interact with circularly polarized strong electromagnetic waves at various interaction angles. Optical vortices should be a new multi-messenger member carrying information concerning the physical circumstances of their sources, e.g., the magnetic and radiation fields. Moreover, their interactions with matter via their orbital angular momenta may play an important role in the evolution of matter in the universe.

High-speed pulse-shape generator, pulse multiplexer

DOEpatents

Burkhart, Scott C.

2002-01-01

The invention combines arbitrary amplitude high-speed pulses for precision pulse shaping for the National Ignition Facility (NIF). The circuitry combines arbitrary height pulses which are generated by replicating scaled versions of a trigger pulse and summing them delayed in time on a pulse line. The combined electrical pulses are connected to an electro-optic modulator which modulates a laser beam. The circuit can also be adapted to combine multiple channels of high speed data into a single train of electrical pulses which generates the optical pulses for very high speed optical communication. The invention has application in laser pulse shaping for inertial confinement fusion, in optical data links for computers, telecommunications, and in laser pulse shaping for atomic excitation studies. The invention can be used to effect at least a 10.times. increase in all fiber communication lines. It allows a greatly increased data transfer rate between high-performance computers. The invention is inexpensive enough to bring high-speed video and data services to homes through a super modem.

Classical and quantum aspects of Yang-Baxter Wess-Zumino models

NASA Astrophysics Data System (ADS)

Demulder, Saskia; Driezen, Sibylle; Sevrin, Alexander; Thompson, Daniel C.

2018-03-01

We investigate the integrable Yang-Baxter deformation of the 2d Principal Chiral Model with a Wess-Zumino term. For arbitrary groups, the one-loop β-functions are calculated and display a surprising connection between classical and quantum physics: the classical integrability condition is necessary to prevent new couplings being generated by renormalisation. We show these theories admit an elegant realisation of Poisson-Lie T-duality acting as a simple inversion of coupling constants. The self-dual point corresponds to the Wess-Zumino-Witten model and is the IR fixed point under RG. We address the possibility of having supersymmetric extensions of these models showing that extended supersymmetry is not possible in general.

Advance finite element modeling of rotor blade aeroelasticity

NASA Technical Reports Server (NTRS)

Straub, F. K.; Sangha, K. B.; Panda, B.

1994-01-01

An advanced beam finite element has been developed for modeling rotor blade dynamics and aeroelasticity. This element is part of the Element Library of the Second Generation Comprehensive Helicopter Analysis System (2GCHAS). The element allows modeling of arbitrary rotor systems, including bearingless rotors. It accounts for moderately large elastic deflections, anisotropic properties, large frame motion for maneuver simulation, and allows for variable order shape functions. The effects of gravity, mechanically applied and aerodynamic loads are included. All kinematic quantities required to compute airloads are provided. In this paper, the fundamental assumptions and derivation of the element matrices are presented. Numerical results are shown to verify the formulation and illustrate several features of the element.

Simplified computational methods for elastic and elastic-plastic fracture problems

NASA Technical Reports Server (NTRS)

Atluri, Satya N.

1992-01-01

An overview is given of some of the recent (1984-1991) developments in computational/analytical methods in the mechanics of fractures. Topics covered include analytical solutions for elliptical or circular cracks embedded in isotropic or transversely isotropic solids, with crack faces being subjected to arbitrary tractions; finite element or boundary element alternating methods for two or three dimensional crack problems; a 'direct stiffness' method for stiffened panels with flexible fasteners and with multiple cracks; multiple site damage near a row of fastener holes; an analysis of cracks with bonded repair patches; methods for the generation of weight functions for two and three dimensional crack problems; and domain-integral methods for elastic-plastic or inelastic crack mechanics.

Effects of dust size distribution on dust acoustic waves in two-dimensional unmagnetized dusty plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

He Guangjun; Duan Wenshan; Tian Duoxiang

2008-04-15

For unmagnetized dusty plasma with many different dust grain species containing both hot isothermal electrons and ions, both the linear dispersion relation and the Kadomtsev-Petviashvili equation for small, but finite amplitude dust acoustic waves are obtained. The linear dispersion relation is investigated numerically. Furthermore, the variations of amplitude, width, and propagation velocity of the nonlinear solitary wave with an arbitrary dust size distribution function are studied as well. Moreover, both the power law distribution and the Gaussian distribution are approximately simulated by using appropriate arbitrary dust size distribution functions.

Digital simulation of two-dimensional random fields with arbitrary power spectra and non-Gaussian probability distribution functions.

PubMed

Yura, Harold T; Hanson, Steen G

2012-04-01

Methods for simulation of two-dimensional signals with arbitrary power spectral densities and signal amplitude probability density functions are disclosed. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In most cases the method provides satisfactory results and can thus be considered an engineering approach. Several illustrative examples with relevance for optics are given.

New 2D dilaton gravity for nonsingular black holes

NASA Astrophysics Data System (ADS)

Kunstatter, Gabor; Maeda, Hideki; Taves, Tim

2016-05-01

We construct a two-dimensional action that is an extension of spherically symmetric Einstein-Lanczos-Lovelock (ELL) gravity. The action contains arbitrary functions of the areal radius and the norm squared of its gradient, but the field equations are second order and obey Birkhoff’s theorem. In complete analogy with spherically symmetric ELL gravity, the field equations admit the generalized Misner-Sharp mass as the first integral that determines the form of the vacuum solution. The arbitrary functions in the action allow for vacuum solutions that describe a larger class of interesting nonsingular black hole spacetimes than previously available.

Noninvasive measurement of dynamic correlation functions

NASA Astrophysics Data System (ADS)

Uhrich, Philipp; Castrignano, Salvatore; Uys, Hermann; Kastner, Michael

2017-08-01

The measurement of dynamic correlation functions of quantum systems is complicated by measurement backaction. To facilitate such measurements we introduce a protocol, based on weak ancilla-system couplings, that is applicable to arbitrary (pseudo)spin systems and arbitrary equilibrium or nonequilibrium initial states. Different choices of the coupling operator give access to the real and imaginary parts of the dynamic correlation function. This protocol reduces disturbances due to the early-time measurements to a minimum, and we quantify the deviation of the measured correlation functions from the theoretical, unitarily evolved ones. Implementations of the protocol in trapped ions and other experimental platforms are discussed. For spin-1 /2 models and single-site observables we prove that measurement backaction can be avoided altogether, allowing for the use of ancilla-free protocols.

Ionization waves of arbitrary velocity driven by a flying focus

DOE Office of Scientific and Technical Information (OSTI.GOV)

Palastro, J. P.; Turnbull, D.; Bahk, S. -W.

A chirped laser pulse focused by a chromatic lens exhibits a dynamic, or flying, focus in which the trajectory of the peak intensity decouples from the group velocity. In a medium, the flying focus can trigger an ionization front that follows this trajectory. By adjusting the chirp, the ionization front can be made to travel at an arbitrary velocity along the optical axis. For this study, we present analytical calculations and simulations describing the propagation of the flying focus pulse, the self-similar form of its intensity profile, and ionization wave formation. The ability to control the speed of the ionizationmore » wave and, in conjunction, mitigate plasma refraction has the potential to advance several laser-based applications, including Raman amplification, photon acceleration, high-order-harmonic generation, and THz generation.« less

Ionization waves of arbitrary velocity driven by a flying focus

DOE PAGES

Palastro, J. P.; Turnbull, D.; Bahk, S. -W.; ...

2018-03-01

A chirped laser pulse focused by a chromatic lens exhibits a dynamic, or flying, focus in which the trajectory of the peak intensity decouples from the group velocity. In a medium, the flying focus can trigger an ionization front that follows this trajectory. By adjusting the chirp, the ionization front can be made to travel at an arbitrary velocity along the optical axis. For this study, we present analytical calculations and simulations describing the propagation of the flying focus pulse, the self-similar form of its intensity profile, and ionization wave formation. The ability to control the speed of the ionizationmore » wave and, in conjunction, mitigate plasma refraction has the potential to advance several laser-based applications, including Raman amplification, photon acceleration, high-order-harmonic generation, and THz generation.« less

Design and Testing of a Fast, 50 kV Solid-State Kicker Pulser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cook, E G; Hickman, B C; Lee, B S

2002-06-24

The ability to extract particle beam bunches from a ring accelerator in arbitrary order can greatly extend an accelerator's capabilities and applications. A prototype solid-state kicker pulser capable of generating asynchronous bursts of 50 kV pulses has been designed and tested into a 50{Omega} load. The pulser features fast rise and fall times and is capable of generating an arbitrary pattern of pulses with a maximum burst frequency exceeding 5 MHz If required, the pulse-width of each pulse in the burst is independently adjustable. This kicker modulator uses multiple solid-state modules stacked in an inductive-adder configuration where the energy ismore » switched into each section of the adder by a parallel array of MOSFETs. Test data, capabilities, and limitations of the prototype pulser are described.« less

Realisation of a holographic microlaser scalpel using a digital micromirror device

NASA Astrophysics Data System (ADS)

Zwick, Susanne; Warber, Michael; Haist, Tobias; Osten, Wolfgang

2007-06-01

Modern spatial light modulators (SLM) enable the generation of more or less arbitrary light fields in three dimensions. Such light fields can be used for different future applications in the field of biomedical optics. One example is the processing/cutting of biological material on a microscopic scale. By displaying computer generated holograms by suitable SLMs it is possible to ablate complex structures into three-dimensional objects without scanning with very high accuracy on a microscopic scale. To effectively cut biological materials by light, pulsed ultraviolet light is preferable. We will present a combined setup of a holographic laser scalpel using a digital micromirror device (DMD) and holographic optical tweezers using a liquid crystal display (LCD). The setup enables to move and cut or process micro-scaled objects like biological cells or tissue in three dimensions with high accuracy and without any mechanical movements just by changing the hologram displayed by the SLMs. We will show that holograms can be used to compensate aberrations implemented by the DMD or other optical components of the setup. Also we can generate arbitrary light fields like stripes, circles or arbitrary curves. Additionally we will present results for the fast optimization of holograms for the system. In particular we will show results obtained by implementing iterative Fourier transform based algorithms on a standard consumer graphics board (Nvidia 8800GLX). By this approach we are able to compute more than 360 complex 2D FFTs (512 × 512 pixels) per second with floating point precision.

Measuring system for the determination of nonlinear elastic and electromechanical properties in solids

NASA Astrophysics Data System (ADS)

Straube, U.; Beige, H.

1999-03-01

An arbitrary waveform generator was introduced to produce pulse bursts with improved time jitter for the generation of ultrasound pulses. The problem of pulse amplification was solved using a ceramic power triode driven by a power FET amplifier. The construction of these special amplifier stages is mainly considered in this paper.

Cooperative Control for A Hybrid Rehabilitation System Combining Functional Electrical Stimulation and Robotic Exoskeleton

PubMed Central

Zhang, Dingguo; Ren, Yong; Gui, Kai; Jia, Jie; Xu, Wendong

2017-01-01

Functional electrical stimulation (FES) and robotic exoskeletons are two important technologies widely used for physical rehabilitation of paraplegic patients. We developed a hybrid rehabilitation system (FEXO Knee) that combined FES and an exoskeleton for swinging movement control of human knee joints. This study proposed a novel cooperative control strategy, which could realize arbitrary distribution of torque generated by FES and exoskeleton, and guarantee harmonic movements. The cooperative control adopted feedfoward control for FES and feedback control for exoskeleton. A parameter regulator was designed to update key parameters in real time to coordinate FES controller and exoskeleton controller. Two muscle groups (quadriceps and hamstrings) were stimulated to generate active torque for knee joint in synchronization with torque compensation from exoskeleton. The knee joint angle and the interactive torque between exoskeleton and shank were used as feedback signals for the control system. Central pattern generator (CPG) was adopted that acted as a phase predictor to deal with phase confliction of motor patterns, and realized synchronization between the two different bodies (shank and exoskeleton). Experimental evaluation of the hybrid FES-exoskeleton system was conducted on five healthy subjects and four paraplegic patients. Experimental results and statistical analysis showed good control performance of the cooperative control on torque distribution, trajectory tracking, and phase synchronization. PMID:29311798

Cooperative Control for A Hybrid Rehabilitation System Combining Functional Electrical Stimulation and Robotic Exoskeleton.

PubMed

Zhang, Dingguo; Ren, Yong; Gui, Kai; Jia, Jie; Xu, Wendong

2017-01-01

Functional electrical stimulation (FES) and robotic exoskeletons are two important technologies widely used for physical rehabilitation of paraplegic patients. We developed a hybrid rehabilitation system (FEXO Knee) that combined FES and an exoskeleton for swinging movement control of human knee joints. This study proposed a novel cooperative control strategy, which could realize arbitrary distribution of torque generated by FES and exoskeleton, and guarantee harmonic movements. The cooperative control adopted feedfoward control for FES and feedback control for exoskeleton. A parameter regulator was designed to update key parameters in real time to coordinate FES controller and exoskeleton controller. Two muscle groups (quadriceps and hamstrings) were stimulated to generate active torque for knee joint in synchronization with torque compensation from exoskeleton. The knee joint angle and the interactive torque between exoskeleton and shank were used as feedback signals for the control system. Central pattern generator (CPG) was adopted that acted as a phase predictor to deal with phase confliction of motor patterns, and realized synchronization between the two different bodies (shank and exoskeleton). Experimental evaluation of the hybrid FES-exoskeleton system was conducted on five healthy subjects and four paraplegic patients. Experimental results and statistical analysis showed good control performance of the cooperative control on torque distribution, trajectory tracking, and phase synchronization.

Comparison of Four Mixed Layer Mesoscale Parameterizations and the Equation for an Arbitrary Tracer

NASA Technical Reports Server (NTRS)

Canuto, V. M.; Dubovikov, M. S.

2011-01-01

In this paper we discuss two issues, the inter-comparison of four mixed layer mesoscale parameterizations and the search for the eddy induced velocity for an arbitrary tracer. It must be stressed that our analysis is limited to mixed layer mesoscales since we do not treat sub-mesoscales and small turbulent mixing. As for the first item, since three of the four parameterizations are expressed in terms of a stream function and a residual flux of the RMT formalism (residual mean theory), while the fourth is expressed in terms of vertical and horizontal fluxes, we needed a formalism to connect the two formulations. The standard RMT representation developed for the deep ocean cannot be extended to the mixed layer since its stream function does not vanish at the ocean's surface. We develop a new RMT representation that satisfies the surface boundary condition. As for the general form of the eddy induced velocity for an arbitrary tracer, thus far, it has been assumed that there is only the one that originates from the curl of the stream function. This is because it was assumed that the tracer residual flux is purely diffusive. On the other hand, we show that in the case of an arbitrary tracer, the residual flux has also a skew component that gives rise to an additional bolus velocity. Therefore, instead of only one bolus velocity, there are now two, one coming from the curl of the stream function and other from the skew part of the residual flux. In the buoyancy case, only one bolus velocity contributes to the mean buoyancy equation since the residual flux is indeed only diffusive.

Bounds on the number of hidden neurons in three-layer binary neural networks.

PubMed

Zhang, Zhaozhi; Ma, Xiaomin; Yang, Yixian

2003-09-01

This paper investigates an important problem concerning the complexity of three-layer binary neural networks (BNNs) with one hidden layer. The neuron in the studied BNNs employs a hard limiter activation function with only integer weights and an integer threshold. The studies are focused on implementations of arbitrary Boolean functions which map from [0, 1]n into [0, 1]. A deterministic algorithm called set covering algorithm (SCA) is proposed for the construction of a three-layer BNN to implement an arbitrary Boolean function. The SCA is based on a unit sphere covering (USC) of the Hamming space (HS) which is chosen in advance. It is proved that for the implementation of an arbitrary Boolean function of n-variables (n > or = 3) by using SCA, [3L/2] hidden neurons are necessary and sufficient, where L is the number of unit spheres contained in the chosen USC of the n-dimensional HS. It is shown that by using SCA, the number of hidden neurons required is much less than that by using a two-parallel hyperplane method. In order to indicate the potential ability of three-layer BNNs, a lower bound on the required number of hidden neurons which is derived by using the method of estimating the Vapnik-Chervonenkis (VC) dimension is also given.

Localized states in an arbitrarily bent quantum wire (bend-imitating approach)

NASA Astrophysics Data System (ADS)

Vakhnenko, Oleksity O.

1996-02-01

The bend-imitating matching technique is proposed to simplify the quantum mechanical treatment of singly and multiply bent 2D quantum wires of constant width, arbitrary bending angles, arbitrary bending radii and arbitrary distances between the bends. The spectrum of one-electron localized states and its dependence on the bending angle and the bending radius in a singly bent wire is explicitly calculated. Doubly bent wires are shown to possess doubly split localized states. The splitting energies as a function of the distance between the bends and the bending angles and bending radii have also been obtained. A similar description of bent 3D quantum wires and bent optical fibers is expected to be possible.

Rarefied gas flow through two-dimensional nozzles

NASA Technical Reports Server (NTRS)

De Witt, Kenneth J.; Jeng, Duen-Ren; Keith, Theo G., Jr.; Chung, Chan-Hong

1989-01-01

A kinetic theory analysis is made of the flow of a rarefied gas from one reservoir to another through two-dimensional nozzles with arbitrary curvature. The Boltzmann equation simplified by a model collision integral is solved by means of finite-difference approximations with the discrete ordinate method. The physical space is transformed by a general grid generation technique and the velocity space is transformed to a polar coordinate system. A numerical code is developed which can be applied to any two-dimensional passage of complicated geometry for the flow regimes from free-molecular to slip. Numerical values of flow quantities can be calculated for the entire physical space including both inside the nozzle and in the outside plume. Predictions are made for the case of parallel slots and compared with existing literature data. Also, results for the cases of convergent or divergent slots and two-dimensional nozzles with arbitrary curvature at arbitrary knudsen number are presented.

The Construction of 3-d Neutral Density for Arbitrary Data Sets

NASA Astrophysics Data System (ADS)

Riha, S.; McDougall, T. J.; Barker, P. M.

2014-12-01

The Neutral Density variable allows inference of water pathways from thermodynamic properties in the global ocean, and is therefore an essential component of global ocean circulation analysis. The widely used algorithm for the computation of Neutral Density yields accurate results for data sets which are close to the observed climatological ocean. Long-term numerical climate simulations, however, often generate a significant drift from present-day climate, which renders the existing algorithm inaccurate. To remedy this problem, new algorithms which operate on arbitrary data have been developed, which may potentially be used to compute Neutral Density during runtime of a numerical model.We review existing approaches for the construction of Neutral Density in arbitrary data sets, detail their algorithmic structure, and present an analysis of the computational cost for implementations on a single-CPU computer. We discuss possible strategies for the implementation in state-of-the-art numerical models, with a focus on distributed computing environments.

Arbitrary-Order Conservative and Consistent Remapping and a Theory of Linear Maps: Part II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ullrich, Paul A.; Devendran, Dharshi; Johansen, Hans

2016-04-01

The focus on this series of articles is on the generation of accurate, conservative, consistent, and (optionally) monotone linear offline maps. This paper is the second in the series. It extends on the first part by describing four examples of 2D linear maps that can be constructed in accordance with the theory of the earlier work. The focus is again on spherical geometry, although these techniques can be readily extended to arbitrary manifolds. The four maps include conservative, consistent, and (optionally) monotone linear maps (i) between two finite-volume meshes, (ii) from finite-volume to finite-element meshes using a projection-type approach, (iii)more » from finite-volume to finite-element meshes using volumetric integration, and (iv) between two finite-element meshes. Arbitrary order of accuracy is supported for each of the described nonmonotone maps.« less

Inertial nonvacuum states viewed from the Rindler frame

NASA Astrophysics Data System (ADS)

Lochan, Kinjalk; Padmanabhan, T.

2015-02-01

The appearance of the inertial vacuum state in Rindler frame has been extensively studied in the literature, both from the point of view of quantum field theory developed using Rindler foliation and using the response of an Unruh-Dewitt detector. In comparison, less attention has been devoted to the study of inertial nonvacuum states when viewed from the Rindler frame. We provide a comprehensive study of this issue in this paper. We first present a general formalism describing the characterization of arbitrary inertial state (i) when described using an arbitrary foliation and (ii) using the response of an Unruh-DeWitt detector moving along an arbitrary trajectory. This allows us to calculate the mean number of particles in an arbitrary inertial state, when the QFT is described using an arbitrary foliation of spacetime or when the state is probed by a detector moving along an arbitrary trajectory. We use this formalism to explicitly compute the results for the Rindler frame and uniformly accelerated detectors. Any arbitrary inertial state will always have a thermal component in the Rindler frame with additional contributions arising from the nonvacuum nature. We classify the nature of the additional contributions in terms of functions characterizing the inertial state. We establish that for all physically well-behaved normalizable inertial states, the correction terms decrease rapidly with the energy of the Rindler mode so that the high frequency limit is dominated by the thermal noise in any normalizable inertial state. However, inertial states which are not strictly normalizable like, for example, the one-particle state with definite momentum, lead to a constant contribution at all high frequencies in the Rindler frame. We show that a similar behavior arises in the response of the Unruh-DeWitt detector as well. In the case of the detector response, we provide a physical interpretation for the constant contribution at high frequencies in terms of total detection rate of comoving inertial detectors. We also describe two different approaches for defining a transition rate for the Unruh-DeWitt detector, when the two-point function lacks the time translation invariance, and discuss several features of different definitions of transition rates. The implications are discussed.

Modulation of the pupil function of microscope objective lens for multifocal multi-photon microscopy using a spatial light modulator

NASA Astrophysics Data System (ADS)

Matsumoto, Naoya; Okazaki, Shigetoshi; Takamoto, Hisayoshi; Inoue, Takashi; Terakawa, Susumu

2014-02-01

We propose a method for high precision modulation of the pupil function of a microscope objective lens to improve the performance of multifocal multi-photon microscopy (MMM). To modulate the pupil function, we adopt a spatial light modulator (SLM) and place it at the conjugate position of the objective lens. The SLM can generate an arbitrary number of spots to excite the multiple fluorescence spots (MFS) at the desired positions and intensities by applying an appropriate computer-generated hologram (CGH). This flexibility allows us to control the MFS according to the photobleaching level of a fluorescent protein and phototoxicity of a specimen. However, when a large number of excitation spots are generated, the intensity distribution of the MFS is significantly different from the one originally designed due to misalignment of the optical setup and characteristics of the SLM. As a result, the image of a specimen obtained using laser scanning for the MFS has block noise segments because the SLM could not generate a uniform MFS. To improve the intensity distribution of the MFS, we adaptively redesigned the CGH based on the observed MFS. We experimentally demonstrate an improvement in the uniformity of a 10 × 10 MFS grid using a dye solution. The simplicity of the proposed method will allow it to be applied for calibration of MMM before observing living tissue. After the MMM calibration, we performed laser scanning with two-photon excitation to observe a real specimen without detecting block noise segments.

Ideal solar cell equation in the presence of photon recycling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lan, Dongchen, E-mail: d.lan@unsw.edu.au; Green, Martin A., E-mail: m.green@unsw.edu.au

Previous derivations of the ideal solar cell equation based on Shockley's p-n junction diode theory implicitly assume negligible effects of photon recycling. This paper derives the equation in the presence of photon recycling that modifies the values of dark saturation and light-generated currents, using an approach applicable to arbitrary three-dimensional geometries with arbitrary doping profile and variable band gap. The work also corrects an error in previous work and proves the validity of the reciprocity theorem for charge collection in such a more general case with the previously neglected junction depletion region included.

Some remarks on elastic crack-tip stress fields.

NASA Technical Reports Server (NTRS)

Rice, J. R.

1972-01-01

It is shown that if the displacement field and stress intensity factor are known as functions of crack length for any symmetrical load system acting on a linear elastic body in plane strain, then the stress intensity factor for any other symmetrical load system whatsoever on the same body may be directly determined. The result is closely related to Bueckner's (1970) weight function, through which the stress intensity factor is expressed as a sum of work-like products between applied forces and values of the weight function at their points of application. An example of the method is given wherein the solution for a crack in a remotely uniform stress field is used to generate the expression for the stress intensity factor due to an arbitrary traction distribution on the faces of a crack. A corresponding theory is developed in an appendix for three-dimensional crack problems, although this appears to be directly useful chiefly for problems in which there is axial symmetry.

Numerical solution of the Navier-Stokes equations for blunt nosed bodies in supersonic flows

NASA Technical Reports Server (NTRS)

Warsi, Z. U. A.; Devarayalu, K.; Thompson, J. F.

1978-01-01

A time dependent, two dimensional Navier-Stokes code employing the method of body fitted coordinate technique was developed for supersonic flows past blunt bodies of arbitrary shapes. The bow shock ahead of the body is obtained as part of the solution, viz., by shock capturing. A first attempt at mesh refinement in the shock region was made by using the forcing function in the coordinate generating equations as a linear function of the density gradients. The technique displaces a few lines from the neighboring region into the shock region. Numerical calculations for Mach numbers 2 and 4.6 and Reynolds numbers from 320 to 10,000 were performed for a circular cylinder with and without a fairing. Results of Mach number 4.6 and Reynolds number 10,000 for an isothermal wall temperature of 556 K are presented in detail.

Design of a reading test for low-vision image warping

NASA Astrophysics Data System (ADS)

Loshin, David S.; Wensveen, Janice; Juday, Richard D.; Barton, R. Shane

1993-08-01

NASA and the University of Houston College of Optometry are examining the efficacy of image warping as a possible prosthesis for at least two forms of low vision -- maculopathy and retinitis pigmentosa. Before incurring the expense of reducing the concept to practice, one would wish to have confidence that a worthwhile improvement in visual function would result. NASA's Programmable Remapper (PR) can warp an input image onto arbitrary geometric coordinate systems at full video rate, and it has recently been upgraded to accept computer- generated video text. We have integrated the Remapper with an SRI eye tracker to simulate visual malfunction in normal observers. A reading performance test has been developed to determine if the proposed warpings yield an increase in visual function; i.e., reading speed. We describe the preliminary experimental results of this reading test with a simulated central field defect with and without remapped images.

Design of a reading test for low vision image warping

NASA Technical Reports Server (NTRS)

Loshin, David S.; Wensveen, Janice; Juday, Richard D.; Barton, R. S.

1993-01-01

NASA and the University of Houston College of Optometry are examining the efficacy of image warping as a possible prosthesis for at least two forms of low vision - maculopathy and retinitis pigmentosa. Before incurring the expense of reducing the concept to practice, one would wish to have confidence that a worthwhile improvement in visual function would result. NASA's Programmable Remapper (PR) can warp an input image onto arbitrary geometric coordinate systems at full video rate, and it has recently been upgraded to accept computer-generated video text. We have integrated the Remapper with an SRI eye tracker to simulate visual malfunction in normal observers. A reading performance test has been developed to determine if the proposed warpings yield an increase in visual function; i.e., reading speed. We will describe the preliminary experimental results of this reading test with a simulated central field defect with and without remapped images.

Statistical dynamo theory: Mode excitation.

PubMed

Hoyng, P

2009-04-01

We compute statistical properties of the lowest-order multipole coefficients of the magnetic field generated by a dynamo of arbitrary shape. To this end we expand the field in a complete biorthogonal set of base functions, viz. B= summation operator_{k}a;{k}(t)b;{k}(r) . The properties of these biorthogonal function sets are treated in detail. We consider a linear problem and the statistical properties of the fluid flow are supposed to be given. The turbulent convection may have an arbitrary distribution of spatial scales. The time evolution of the expansion coefficients a;{k} is governed by a stochastic differential equation from which we infer their averages a;{k} , autocorrelation functions a;{k}(t)a;{k *}(t+tau) , and an equation for the cross correlations a;{k}a;{l *} . The eigenfunctions of the dynamo equation (with eigenvalues lambda_{k} ) turn out to be a preferred set in terms of which our results assume their simplest form. The magnetic field of the dynamo is shown to consist of transiently excited eigenmodes whose frequency and coherence time is given by Ilambda_{k} and -1/Rlambda_{k} , respectively. The relative rms excitation level of the eigenmodes, and hence the distribution of magnetic energy over spatial scales, is determined by linear theory. An expression is derived for |a;{k}|;{2}/|a;{0}|;{2} in case the fundamental mode b;{0} has a dominant amplitude, and we outline how this expression may be evaluated. It is estimated that |a;{k}|;{2}/|a;{0}|;{2} approximately 1/N , where N is the number of convective cells in the dynamo. We show that the old problem of a short correlation time (or first-order smoothing approximation) has been partially eliminated. Finally we prove that for a simple statistically steady dynamo with finite resistivity all eigenvalues obey Rlambda_{k}<0 .

Strong Measurements Give a Better Direct Measurement of the Quantum Wave Function.

PubMed

Vallone, Giuseppe; Dequal, Daniele

2016-01-29

Weak measurements have thus far been considered instrumental in the so-called direct measurement of the quantum wave function [4J. S. Lundeen, Nature (London) 474, 188 (2011).]. Here we show that a direct measurement of the wave function can be obtained by using measurements of arbitrary strength. In particular, in the case of strong measurements, i.e., those in which the coupling between the system and the measuring apparatus is maximum, we compared the precision and the accuracy of the two methods, by showing that strong measurements outperform weak measurements in both for arbitrary quantum states in most cases. We also give the exact expression of the difference between the original and reconstructed wave function obtained by the weak measurement approach; this will allow one to define the range of applicability of such a method.

On the formulation of the aerodynamic characteristics in aircraft dynamics

NASA Technical Reports Server (NTRS)

Tobak, M.; Schiff, L. B.

1976-01-01

The theory of functionals is used to reformulate the notions of aerodynamic indicial functions and superposition. Integral forms for the aerodynamic response to arbitrary motions are derived that are free of dependence on a linearity assumption. Simplifications of the integral forms lead to practicable nonlinear generalizations of the linear superpositions and stability derivative formulations. Applied to arbitrary nonplanar motions, the generalization yields a form for the aerodynamic response that can be compounded of the contributions from a limited number of well-defined characteristic motions, in principle reproducible in the wind tunnel. Further generalizations that would enable the consideration of random fluctuations and multivalued aerodynamic responses are indicated.

Boundary control by displacement at one end of a string and the integral condition on the other

NASA Astrophysics Data System (ADS)

Attaev, Anatoly Kh.

2017-09-01

For a one-dimensional wave equation we study the problem of finding such boundary controls that makes a string move from an arbitrary specified initial state to an arbitrary specified final state. The control is applied at the left end of the string while the nonlocal displacement is at the right end. Necessary and sufficient conditions are established for the functions determining the initial and final state of the string. An explicit analytical form of the boundary control is obtained as well as the minimum time T = l for this control. In case when T = l - ɛ, 0 < ɛ < l, i.e. T < l it is shown the initial values u(x, 0) = ϕ(x) and ut (x, 0) = ψ(x) cannot be set arbitrary. Moreover, if ɛ < l/2, hence the functions ϕ(x) and ψ(x) are linearly dependent on any segment of finite length either in the segment [0, ɛ], or in [l-ɛ, l]. Suppose ɛ ≥ l/2, then functions ϕ(x) and ψ(x) are linearly dependent on any segment of finite length in the segment [0, l].

Numerical analysis of the accuracy of bivariate quantile distributions utilizing copulas compared to the GUM supplement 2 for oil pressure balance uncertainties

NASA Astrophysics Data System (ADS)

Ramnath, Vishal

2017-11-01

In the field of pressure metrology the effective area is Ae = A0 (1 + λP) where A0 is the zero-pressure area and λ is the distortion coefficient and the conventional practise is to construct univariate probability density functions (PDFs) for A0 and λ. As a result analytical generalized non-Gaussian bivariate joint PDFs has not featured prominently in pressure metrology. Recently extended lambda distribution based quantile functions have been successfully utilized for summarizing univariate arbitrary PDF distributions of gas pressure balances. Motivated by this development we investigate the feasibility and utility of extending and applying quantile functions to systems which naturally exhibit bivariate PDFs. Our approach is to utilize the GUM Supplement 1 methodology to solve and generate Monte Carlo based multivariate uncertainty data for an oil based pressure balance laboratory standard that is used to generate known high pressures, and which are in turn cross-floated against another pressure balance transfer standard in order to deduce the transfer standard's respective area. We then numerically analyse the uncertainty data by formulating and constructing an approximate bivariate quantile distribution that directly couples A0 and λ in order to compare and contrast its accuracy to an exact GUM Supplement 2 based uncertainty quantification analysis.

Functional Data Approximation on Bounded Domains using Polygonal Finite Elements.

PubMed

Cao, Juan; Xiao, Yanyang; Chen, Zhonggui; Wang, Wenping; Bajaj, Chandrajit

2018-07-01

We construct and analyze piecewise approximations of functional data on arbitrary 2D bounded domains using generalized barycentric finite elements, and particularly quadratic serendipity elements for planar polygons. We compare approximation qualities (precision/convergence) of these partition-of-unity finite elements through numerical experiments, using Wachspress coordinates, natural neighbor coordinates, Poisson coordinates, mean value coordinates, and quadratic serendipity bases over polygonal meshes on the domain. For a convex n -sided polygon, the quadratic serendipity elements have 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, rather than the usual n ( n + 1)/2 basis functions to achieve quadratic convergence. Two greedy algorithms are proposed to generate Voronoi meshes for adaptive functional/scattered data approximations. Experimental results show space/accuracy advantages for these quadratic serendipity finite elements on polygonal domains versus traditional finite elements over simplicial meshes. Polygonal meshes and parameter coefficients of the quadratic serendipity finite elements obtained by our greedy algorithms can be further refined using an L 2 -optimization to improve the piecewise functional approximation. We conduct several experiments to demonstrate the efficacy of our algorithm for modeling features/discontinuities in functional data/image approximation.

Relations between 18-month-olds' gaze pattern and target action performance: a deferred imitation study with eye tracking.

PubMed

Óturai, Gabriella; Kolling, Thorsten; Knopf, Monika

2013-12-01

Deferred imitation studies are used to assess infants' declarative memory performance. These studies have found that deferred imitation performance improves with age, which is usually attributed to advancing memory capabilities. Imitation studies, however, are also used to assess infants' action understanding. In this second research program it has been observed that infants around the age of one year imitate selectively, i.e., they imitate certain kinds of target actions and omit others. In contrast to this, two-year-olds usually imitate the model's exact actions. 18-month-olds imitate more exactly than one-year-olds, but more selectively than two-year-olds, a fact which makes this age group especially interesting, since the processes underlying selective vs. exact imitation are largely debated. The question, for example, if selective attention to certain kinds of target actions accounts for preferential imitation of these actions in young infants is still open. Additionally, relations between memory capabilities and selective imitation processes, as well as their role in shaping 18-month-olds' neither completely selective, nor completely exact imitation have not been thoroughly investigated yet. The present study, therefore, assessed 18-month-olds' gaze toward two types of actions (functional vs. arbitrary target actions) and the model's face during target action demonstration, as well as infants' deferred imitation performance. Although infants' fixation times to functional target actions were not longer than to arbitrary target actions, they imitated the functional target actions more frequently than the arbitrary ones. This suggests that selective imitation does not rely on selective gaze toward functional target actions during the demonstration phase. In addition, a post hoc analysis of interindividual differences suggested that infants' attention to the model's social-communicative cues might play an important role in exact imitation, meaning the imitation of both functional and arbitrary target actions. Copyright © 2013 Elsevier Inc. All rights reserved.

Photonic Arbitrary Waveform Generation Technology

DTIC Science & Technology

2006-06-01

locked external- cavity semiconductor diode ring laser “, Optics Letters, Vol. 27, No. 9 , 719-721, (2002). [22] S. Gee, F. Quinlan, S. Ozharar... optical pulses that one is accustomed to. Modelocked semiconductor lasers are used to generate a set of phase locked optical frequencies on a periodic...The corresponding optical spectrum of the laser consists of a comb of periodically spaced, phase - locked

Bandwidth scalable, coherent transmitter based on the parallel synthesis of multiple spectral slices using optical arbitrary waveform generation.

PubMed

Geisler, David J; Fontaine, Nicolas K; Scott, Ryan P; He, Tingting; Paraschis, Loukas; Gerstel, Ori; Heritage, Jonathan P; Yoo, S J B

2011-04-25

We demonstrate an optical transmitter based on dynamic optical arbitrary waveform generation (OAWG) which is capable of creating high-bandwidth (THz) data waveforms in any modulation format using the parallel synthesis of multiple coherent spectral slices. As an initial demonstration, the transmitter uses only 5.5 GHz of electrical bandwidth and two 10-GHz-wide spectral slices to create 100-ns duration, 20-GHz optical waveforms in various modulation formats including differential phase-shift keying (DPSK), quaternary phase-shift keying (QPSK), and eight phase-shift keying (8PSK) with only changes in software. The experimentally generated waveforms showed clear eye openings and separated constellation points when measured using a real-time digital coherent receiver. Bit-error-rate (BER) performance analysis resulted in a BER < 9.8 × 10(-6) for DPSK and QPSK waveforms. Additionally, we experimentally demonstrate three-slice, 4-ns long waveforms that highlight the bandwidth scalable nature of the optical transmitter. The various generated waveforms show that the key transmitter properties (i.e., packet length, modulation format, data rate, and modulation filter shape) are software definable, and that the optical transmitter is capable of acting as a flexible bandwidth transmitter.

Surface acoustic wave micromotor with arbitrary axis rotational capability

NASA Astrophysics Data System (ADS)

Tjeung, Ricky T.; Hughes, Mark S.; Yeo, Leslie Y.; Friend, James R.

2011-11-01

A surface acoustic wave (SAW) actuated rotary motor is reported here, consisting of a millimeter-sized spherical metal rotor placed on the surface of a lead zirconate titanate piezoelectric substrate upon which the SAW is made to propagate. At the design frequency of 3.2 MHz and with a fixed preload of 41.1 μN, the maximum rotational speed and torque achieved were approximately 1900 rpm and 5.37 μN-mm, respectively, producing a maximum output power of 1.19 μW. The surface vibrations were visualized using laser Doppler vibrometry and indicate that the rotational motion arises due to retrograde elliptical motions of the piezoelectric surface elements. Rotation about orthogonal axes in the plane of the substrate has been obtained by using orthogonally placed interdigital electrodes on the substrate to generate SAW impinging on the rotor, offering a means to generate rotation about an arbitrary axis in the plane of the substrate.

Agile high resolution arbitrary waveform generator with jitterless frequency stepping

DOEpatents

Reilly, Peter T. A.; Koizumi, Hideya

2010-05-11

Jitterless transition of the programmable clock waveform is generated employing a set of two coupled direct digital synthesis (DDS) circuits. The first phase accumulator in the first DDS circuit runs at least one cycle of a common reference clock for the DDS circuits ahead of the second phase accumulator in the second DDS circuit. As a phase transition through the beginning of a phase cycle is detected from the first phase accumulator, a first phase offset word and a second phase offset word for the first and second phase accumulators are calculated and loaded into the first and second DDS circuits. The programmable clock waveform is employed as a clock input for the RAM address controller. A well defined jitterless transition in frequency of the arbitrary waveform is provided which coincides with the beginning of the phase cycle of the DDS output signal from the second DDS circuit.

Automatic generation of efficient array redistribution routines for distributed memory multicomputers

NASA Technical Reports Server (NTRS)

Ramaswamy, Shankar; Banerjee, Prithviraj

1994-01-01

Appropriate data distribution has been found to be critical for obtaining good performance on Distributed Memory Multicomputers like the CM-5, Intel Paragon and IBM SP-1. It has also been found that some programs need to change their distributions during execution for better performance (redistribution). This work focuses on automatically generating efficient routines for redistribution. We present a new mathematical representation for regular distributions called PITFALLS and then discuss algorithms for redistribution based on this representation. One of the significant contributions of this work is being able to handle arbitrary source and target processor sets while performing redistribution. Another important contribution is the ability to handle an arbitrary number of dimensions for the array involved in the redistribution in a scalable manner. Our implementation of these techniques is based on an MPI-like communication library. The results presented show the low overheads for our redistribution algorithm as compared to naive runtime methods.

Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam.

PubMed

Li, Xiangping; Lan, Tzu-Hsiang; Tien, Chung-Hao; Gu, Min

2012-01-01

The interplay between light polarization and matter is the basis of many fundamental physical processes and applications. However, the electromagnetic wave nature of light in free space sets a fundamental limit on the three-dimensional polarization orientation of a light beam. Although a high numerical aperture objective can be used to bend the wavefront of a radially polarized beam to generate the longitudinal polarization state in the focal volume, the arbitrary three-dimensional polarization orientation of a beam has not been achieved yet. Here we present a novel technique for generating arbitrary three-dimensional polarization orientation by a single optically configured vectorial beam. As a consequence, by applying this technique to gold nanorods, orientation-unlimited polarization encryption with ultra-security is demonstrated. These results represent a new landmark of the orientation-unlimited three-dimensional polarization control of the light-matter interaction.

Time-dependent solutions for a stochastic model of gene expression with molecule production in the form of a compound Poisson process.

PubMed

Jędrak, Jakub; Ochab-Marcinek, Anna

2016-09-01

We study a stochastic model of gene expression, in which protein production has a form of random bursts whose size distribution is arbitrary, whereas protein decay is a first-order reaction. We find exact analytical expressions for the time evolution of the cumulant-generating function for the most general case when both the burst size probability distribution and the model parameters depend on time in an arbitrary (e.g., oscillatory) manner, and for arbitrary initial conditions. We show that in the case of periodic external activation and constant protein degradation rate, the response of the gene is analogous to the resistor-capacitor low-pass filter, where slow oscillations of the external driving have a greater effect on gene expression than the fast ones. We also demonstrate that the nth cumulant of the protein number distribution depends on the nth moment of the burst size distribution. We use these results to show that different measures of noise (coefficient of variation, Fano factor, fractional change of variance) may vary in time in a different manner. Therefore, any biological hypothesis of evolutionary optimization based on the nonmonotonic dependence of a chosen measure of noise on time must justify why it assumes that biological evolution quantifies noise in that particular way. Finally, we show that not only for exponentially distributed burst sizes but also for a wider class of burst size distributions (e.g., Dirac delta and gamma) the control of gene expression level by burst frequency modulation gives rise to proportional scaling of variance of the protein number distribution to its mean, whereas the control by amplitude modulation implies proportionality of protein number variance to the mean squared.

Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2018-02-01

In order to accelerate the spherical harmonic synthesis and/or analysis of arbitrary function on the unit sphere, we developed a pair of procedures to transform between a truncated spherical harmonic expansion and the corresponding two-dimensional Fourier series. First, we obtained an analytic expression of the sine/cosine series coefficient of the 4 π fully normalized associated Legendre function in terms of the rectangle values of the Wigner d function. Then, we elaborated the existing method to transform the coefficients of the surface spherical harmonic expansion to those of the double Fourier series so as to be capable with arbitrary high degree and order. Next, we created a new method to transform inversely a given double Fourier series to the corresponding surface spherical harmonic expansion. The key of the new method is a couple of new recurrence formulas to compute the inverse transformation coefficients: a decreasing-order, fixed-degree, and fixed-wavenumber three-term formula for general terms, and an increasing-degree-and-order and fixed-wavenumber two-term formula for diagonal terms. Meanwhile, the two seed values are analytically prepared. Both of the forward and inverse transformation procedures are confirmed to be sufficiently accurate and applicable to an extremely high degree/order/wavenumber as 2^{30} {≈ } 10^9. The developed procedures will be useful not only in the synthesis and analysis of the spherical harmonic expansion of arbitrary high degree and order, but also in the evaluation of the derivatives and integrals of the spherical harmonic expansion.

Universal bounds on current fluctuations.

PubMed

Pietzonka, Patrick; Barato, Andre C; Seifert, Udo

2016-05-01

For current fluctuations in nonequilibrium steady states of Markovian processes, we derive four different universal bounds valid beyond the Gaussian regime. Different variants of these bounds apply to either the entropy change or any individual current, e.g., the rate of substrate consumption in a chemical reaction or the electron current in an electronic device. The bounds vary with respect to their degree of universality and tightness. A universal parabolic bound on the generating function of an arbitrary current depends solely on the average entropy production. A second, stronger bound requires knowledge both of the thermodynamic forces that drive the system and of the topology of the network of states. These two bounds are conjectures based on extensive numerics. An exponential bound that depends only on the average entropy production and the average number of transitions per time is rigorously proved. This bound has no obvious relation to the parabolic bound but it is typically tighter further away from equilibrium. An asymptotic bound that depends on the specific transition rates and becomes tight for large fluctuations is also derived. This bound allows for the prediction of the asymptotic growth of the generating function. Even though our results are restricted to networks with a finite number of states, we show that the parabolic bound is also valid for three paradigmatic examples of driven diffusive systems for which the generating function can be calculated using the additivity principle. Our bounds provide a general class of constraints for nonequilibrium systems.

Laser ablation synthesis of arsenic-phosphide Asm Pn clusters from As-P mixtures. Laser desorption ionisation with quadrupole ion trap time-of-flight mass spectrometry: The mass spectrometer as a synthesizer.

PubMed

Kubáček, Pavel; Prokeš, Lubomír; Pamreddy, Annapurna; Peña-Méndez, Eladia María; Conde, José Elias; Alberti, Milan; Havel, Josef

2018-05-30

Only a few arsenic phosphides are known. A high potential for the generation of new compounds is offered by Laser Ablation Synthesis (LAS) and when Laser Desorption Ionization (LDI) is coupled with simultaneous Time-Of-Flight Mass Spectrometry (TOFMS), immediate identification of the clusters can be achieved. LAS was used for the generation of arsenic phosphides via laser ablation of phosphorus-arsenic mixtures while quadrupole ion trap time-of-flight mass spectrometry (QIT-TOFMS) was used to acquire the mass spectra. Many new As m P n ± clusters (479 binary and 369 mono-elemental) not yet described in the literature were generated in the gas phase and their stoichiometry determined. The likely structures for some of the observed clusters arbitrary selected (20) were computed by density functional theory (DFT) optimization. LAS is an advantageous approach for the generation of new As m P n clusters, while mass spectrometry was found to be an efficient technique for the determination of cluster stoichiometry. The results achieved might inspire the synthesis of new materials. Copyright © 2018 John Wiley & Sons, Ltd.

Software For Graphical Representation Of A Network

NASA Technical Reports Server (NTRS)

Mcallister, R. William; Mclellan, James P.

1993-01-01

System Visualization Tool (SVT) computer program developed to provide systems engineers with means of graphically representing networks. Generates diagrams illustrating structures and states of networks defined by users. Provides systems engineers powerful tool simplifing analysis of requirements and testing and maintenance of complex software-controlled systems. Employs visual models supporting analysis of chronological sequences of requirements, simulation data, and related software functions. Applied to pneumatic, hydraulic, and propellant-distribution networks. Used to define and view arbitrary configurations of such major hardware components of system as propellant tanks, valves, propellant lines, and engines. Also graphically displays status of each component. Advantage of SVT: utilizes visual cues to represent configuration of each component within network. Written in Turbo Pascal(R), version 5.0.

Nonclassicality of Photon-Added Displaced Thermal State via Quantum Phase-Space Distributions

NASA Astrophysics Data System (ADS)

Zhang, Ran; Meng, Xiang-Guo; Du, Chuan-Xun; Wang, Ji-Suo

2018-02-01

We introduce a new kind of nonclassical mixed state generated by adding arbitrary photons to a displaced thermal state, i.e., the photon-added displaced thermal state (PADTS), and obtain the normalization factor, which is simply related to two-variable Hermite polynomials. We also discuss the nonclassicality of the PADTS by considering quantum phase-space distributions. The results indicate that the value of the photon count statistics is maximum when the number of detected photons is equal to the number of added photons, and that the photon-added operation has a similar modulation effect with increasing displacement. Moreover, the negative volume of the Wigner function for the PADTS takes a maximal value for a specific photon-added number.

General solution of a cosmological model induced from higher dimensions using a kinematical constraint

NASA Astrophysics Data System (ADS)

Akarsu, Özgür; Dereli, Tekin; Katırcı, Nihan; Sheftel, Mikhail B.

2015-05-01

In a recent study Akarsu and Dereli (Gen. Relativ. Gravit. 45:1211, 2013) discussed the dynamical reduction of a higher dimensional cosmological model which is augmented by a kinematical constraint characterized by a single real parameter, correlating and controlling the expansion of both the external (physical) and internal spaces. In that paper explicit solutions were found only for the case of three dimensional internal space (). Here we derive a general solution of the system using Lie group symmetry properties, in parametric form for arbitrary number of internal dimensions. We also investigate the dynamical reduction of the model as a function of cosmic time for various values of and generate parametric plots to discuss cosmologically relevant results.

Computer simulation of random variables and vectors with arbitrary probability distribution laws

NASA Technical Reports Server (NTRS)

Bogdan, V. M.

1981-01-01

Assume that there is given an arbitrary n-dimensional probability distribution F. A recursive construction is found for a sequence of functions x sub 1 = f sub 1 (U sub 1, ..., U sub n), ..., x sub n = f sub n (U sub 1, ..., U sub n) such that if U sub 1, ..., U sub n are independent random variables having uniform distribution over the open interval (0,1), then the joint distribution of the variables x sub 1, ..., x sub n coincides with the distribution F. Since uniform independent random variables can be well simulated by means of a computer, this result allows one to simulate arbitrary n-random variables if their joint probability distribution is known.

WebVR: an interactive web browser for virtual environments

NASA Astrophysics Data System (ADS)

Barsoum, Emad; Kuester, Falko

2005-03-01

The pervasive nature of web-based content has lead to the development of applications and user interfaces that port between a broad range of operating systems and databases, while providing intuitive access to static and time-varying information. However, the integration of this vast resource into virtual environments has remained elusive. In this paper we present an implementation of a 3D Web Browser (WebVR) that enables the user to search the internet for arbitrary information and to seamlessly augment this information into virtual environments. WebVR provides access to the standard data input and query mechanisms offered by conventional web browsers, with the difference that it generates active texture-skins of the web contents that can be mapped onto arbitrary surfaces within the environment. Once mapped, the corresponding texture functions as a fully integrated web-browser that will respond to traditional events such as the selection of links or text input. As a result, any surface within the environment can be turned into a web-enabled resource that provides access to user-definable data. In order to leverage from the continuous advancement of browser technology and to support both static as well as streamed content, WebVR uses ActiveX controls to extract the desired texture skin from industry strength browsers, providing a unique mechanism for data fusion and extensibility.

True orbit simulation of piecewise linear and linear fractional maps of arbitrary dimension using algebraic numbers

NASA Astrophysics Data System (ADS)

Saito, Asaki; Yasutomi, Shin-ichi; Tamura, Jun-ichi; Ito, Shunji

2015-06-01

We introduce a true orbit generation method enabling exact simulations of dynamical systems defined by arbitrary-dimensional piecewise linear fractional maps, including piecewise linear maps, with rational coefficients. This method can generate sufficiently long true orbits which reproduce typical behaviors (inherent behaviors) of these systems, by properly selecting algebraic numbers in accordance with the dimension of the target system, and involving only integer arithmetic. By applying our method to three dynamical systems—that is, the baker's transformation, the map associated with a modified Jacobi-Perron algorithm, and an open flow system—we demonstrate that it can reproduce their typical behaviors that have been very difficult to reproduce with conventional simulation methods. In particular, for the first two maps, we show that we can generate true orbits displaying the same statistical properties as typical orbits, by estimating the marginal densities of their invariant measures. For the open flow system, we show that an obtained true orbit correctly converges to the stable period-1 orbit, which is inherently possessed by the system.

A "Healthy-Contingencies" Behavioral Intervention

ERIC Educational Resources Information Center

St. Peter, Claire C.; Marsteller, Tonya M.

2017-01-01

Interventions based on functional analyses may result in better treatment outcomes than those using arbitrary reinforcers. However, functional analyses may be impractical in some situations, or an immediate intervention may be necessary while a functional analysis is being conducted. In these situations, delivering the social reinforcers most…

Position dependent mass Schroedinger equation and isospectral potentials: Intertwining operator approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Midya, Bikashkali; Roy, B.; Roychoudhury, R.

2010-02-15

Here, we have studied first- and second-order intertwining approaches to generate isospectral partner potentials of position dependent (effective) mass Schroedinger equation. The second-order intertwiner is constructed directly by taking it as second-order linear differential operator with position dependent coefficients, and the system of equations arising from the intertwining relationship is solved for the coefficients by taking an ansatz. A complete scheme for obtaining general solution is obtained, which is valid for any arbitrary potential and mass function. The proposed technique allows us to generate isospectral potentials with the following spectral modifications: (i) to add new bound state(s), (ii) to removemore » bound state(s), and (iii) to leave the spectrum unaffected. To explain our findings with the help of an illustration, we have used point canonical transformation to obtain the general solution of the position dependent mass Schrodinger equation corresponding to a potential and mass function. It is shown that our results are consistent with the formulation of type A N-fold supersymmetry [T. Tanaka, J. Phys. A 39, 219 (2006); A. Gonzalez-Lopez and T. Tanaka, J. Phys. A 39, 3715 (2006)] for the particular cases N=1 and N=2, respectively.« less

Effective field theory dimensional regularization

NASA Astrophysics Data System (ADS)

Lehmann, Dirk; Prézeau, Gary

2002-01-01

A Lorentz-covariant regularization scheme for effective field theories with an arbitrary number of propagating heavy and light particles is given. This regularization scheme leaves the low-energy analytic structure of Greens functions intact and preserves all the symmetries of the underlying Lagrangian. The power divergences of regularized loop integrals are controlled by the low-energy kinematic variables. Simple diagrammatic rules are derived for the regularization of arbitrary one-loop graphs and the generalization to higher loops is discussed.

The general solution to the classical problem of finite Euler Bernoulli beam

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Amba-Rao, C. L.

1977-01-01

An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.

Arbitrary and semantic associations in subjective memory impairment and amnestic mild cognitive impairment among Taiwanese individuals: A cross-sectional study.

PubMed

Chang, Hsin-Te; Chen, Ta-Fu; Cheng, Ting-Wen; Lai, Ya-Mei; Hua, Mau-Sun

2018-05-01

Researchers have recently proposed a preclinical stage of dementia of Alzheimer's type (DAT), referred to as subjective memory impairment (SMI), with the aim of developing methods for the early detection of DAT and subsequent intervention. It has been proposed that the objective memory functions of individuals with SMI are normal; however, arbitrary and semantic associations are both used to describe the processes of memory. No previous studies have investigated these processes among individuals with SMI. Cross-sectional analysis was used to compare the memory function of individuals with SMI, amnestic mild cognitive impairment (aMCI), or DAT. One hundred and eighty-three participants were recruited from the Memory Clinic of National Taiwan University Hospital and communities in northern Taiwan, including individuals with no memory complaints (HC, n = 30) and individuals with SMI (n = 61), aMCI-single domain (n = 24), aMCI-multiple domain (n = 33), or DAT (n = 35). The Word Sequence Learning Test (WSLT) was used to assess the formation of arbitrary associations and the Logical Memory subtest of the Wechsler Memory Scale-Third Edition was used to assess the formation of semantic associations. Compared to the HC group, the SMI group performed poorly only on the WSLT, whereas the other groups performed poorly on both of the memory tasks. This study demonstrated that SMI individuals tend to perform poorly in the formation of arbitrary associations. Our findings suggest that tasks requiring arbitrary associations may provide greater sensitivity in the detection cognitive changes associated with preclinical DAT. Copyright © 2017. Published by Elsevier B.V.

Delamination Analysis of a Multilayered Two-Dimensional Functionally Graded Cantilever Beam

NASA Astrophysics Data System (ADS)

Rizov, V.

2017-11-01

Delamination fracture behaviour of a multilayered two-dimensional functionally graded cantilever beam is analyzed in terms of the strain energy release rate. The beam is made of an arbitrary number of layers. Perfect adhesion is assumed between layers. Each layer has individual thickness and material properties. Besides, the material is two-dimensional functionally graded in the cross-section of each layer. There is a delamination crack located arbitrary between layers. The beam is loaded by a bending moment applied at the free end of the lower crack arm. The upper crack arm is free of stresses. The solution to strain energy release rate derived is applied to investigate the influence of the crack location and the material gradient on the delamination fracture. The results obtained can be used to optimize the multilayered two-dimensional functionally graded beam structure with respect to the delamination fracture behaviour.

The role of symmetry in the regulation of brain dynamics

NASA Astrophysics Data System (ADS)

Tang, Evelyn; Giusti, Chad; Cieslak, Matthew; Grafton, Scott; Bassett, Danielle

Synchronous neural processes regulate a wide range of behaviors from attention to learning. Yet structural constraints on these processes are far from understood. We draw on new theoretical links between structural symmetries and the control of synchronous function, to offer a reconceptualization of the relationships between brain structure and function in human and non-human primates. By classifying 3-node motifs in macaque connectivity data, we find the most prevalent motifs can theoretically ensure a diversity of function including strict synchrony as well as control to arbitrary states. The least prevalent motifs are theoretically controllable to arbitrary states, which may not be desirable in a biological system. In humans, regions with high topological similarity of connections (a continuous notion related to symmetry) are most commonly found in fronto-parietal systems, which may account for their critical role in cognitive control. Collectively, our work underscores the role of symmetry and topological similarity in regulating dynamics of brain function.

3D automatic Cartesian grid generation for Euler flows

NASA Technical Reports Server (NTRS)

Melton, John E.; Enomoto, Francis Y.; Berger, Marsha J.

1993-01-01

We describe a Cartesian grid strategy for the study of three dimensional inviscid flows about arbitrary geometries that uses both conventional and CAD/CAM surface geometry databases. Initial applications of the technique are presented. The elimination of the body-fitted constraint allows the grid generation process to be automated, significantly reducing the time and effort required to develop suitable computational grids for inviscid flowfield simulations.

Open Group Transformations

NASA Astrophysics Data System (ADS)

Batalin, Igor; Marnelius, Robert

Open groups whose generators are in arbitrary involutions may be quantized within a ghost extended framework in terms of a nilpotent BFV-BRST charge operator. Previously we have shown that generalized quantum Maurer-Cartan equations for arbitrary open groups may be extracted from the quantum connection operators and that they also follow from a simple quantum master equation involving an extended nilpotent BFV-BRST charge and a master charge. Here we give further details of these results. In addition we establish the general structure of the solutions of the quantum master equation. We also construct an extended formulation whose properties are determined by the extended BRST charge in the master equation.

Nonreciprocal lasing in topological cavities of arbitrary geometries

NASA Astrophysics Data System (ADS)

Bahari, Babak; Ndao, Abdoulaye; Vallini, Felipe; El Amili, Abdelkrim; Fainman, Yeshaiahu; Kanté, Boubacar

2017-11-01

Resonant cavities are essential building blocks governing many wave-based phenomena, but their geometry and reciprocity fundamentally limit the integration of optical devices. We report, at telecommunication wavelengths, geometry-independent and integrated nonreciprocal topological cavities that couple stimulated emission from one-way photonic edge states to a selected waveguide output with an isolation ratio in excess of 10 decibels. Nonreciprocity originates from unidirectional edge states at the boundary between photonic structures with distinct topological invariants. Our experimental demonstration of lasing from topological cavities provides the opportunity to develop complex topological circuitry of arbitrary geometries for the integrated and robust generation and transport of photons in classical and quantum regimes.

Quantum noise and squeezing in optical parametric oscillator with arbitrary output coupling

NASA Technical Reports Server (NTRS)

Prasad, Sudhakar

1993-01-01

The redistribution of intrinsic quantum noise in the quadratures of the field generated in a sub-threshold degenerate optical parametric oscillator exhibits interesting dependences on the individual output mirror transmittances, when they are included exactly. We present a physical picture of this problem, based on mirror boundary conditions, which is valid for arbitrary transmittances. Hence, our picture applies uniformly to all values of the cavity Q factor representing, in the opposite extremes, both perfect oscillator and amplifier configurations. Beginning with a classical second-harmonic pump, we shall generalize our analysis to the finite amplitude and phase fluctuations of the pump.

Quantum mechanics in noninertial reference frames: Relativistic accelerations and fictitious forces

NASA Astrophysics Data System (ADS)

Klink, W. H.; Wickramasekara, S.

2016-06-01

One-particle systems in relativistically accelerating reference frames can be associated with a class of unitary representations of the group of arbitrary coordinate transformations, an extension of the Wigner-Bargmann definition of particles as the physical realization of unitary irreducible representations of the Poincaré group. Representations of the group of arbitrary coordinate transformations become necessary to define unitary operators implementing relativistic acceleration transformations in quantum theory because, unlike in the Galilean case, the relativistic acceleration transformations do not themselves form a group. The momentum operators that follow from these representations show how the fictitious forces in noninertial reference frames are generated in quantum theory.

GPU based contouring method on grid DEM data

NASA Astrophysics Data System (ADS)

Tan, Liheng; Wan, Gang; Li, Feng; Chen, Xiaohui; Du, Wenlong

2017-08-01

This paper presents a novel method to generate contour lines from grid DEM data based on the programmable GPU pipeline. The previous contouring approaches often use CPU to construct a finite element mesh from the raw DEM data, and then extract contour segments from the elements. They also need a tracing or sorting strategy to generate the final continuous contours. These approaches can be heavily CPU-costing and time-consuming. Meanwhile the generated contours would be unsmooth if the raw data is sparsely distributed. Unlike the CPU approaches, we employ the GPU's vertex shader to generate a triangular mesh with arbitrary user-defined density, in which the height of each vertex is calculated through a third-order Cardinal spline function. Then in the same frame, segments are extracted from the triangles by the geometry shader, and translated to the CPU-side with an internal order in the GPU's transform feedback stage. Finally we propose a "Grid Sorting" algorithm to achieve the continuous contour lines by travelling the segments only once. Our method makes use of multiple stages of GPU pipeline for computation, which can generate smooth contour lines, and is significantly faster than the previous CPU approaches. The algorithm can be easily implemented with OpenGL 3.3 API or higher on consumer-level PCs.

Dispersion characteristics of anisotropic unmagnetized ultra-relativistic transverse plasma wave with arbitrary electron degeneracy

NASA Astrophysics Data System (ADS)

Sarfraz, M.; Farooq, H.; Abbas, G.; Noureen, S.; Iqbal, Z.; Rasheed, A.

2018-03-01

Thermal momentum space anisotropy is ubiquitous in many astrophysical and laboratory plasma environments. Using Vlasov-Maxwell's model equations, a generalized polarization tensor for a collisionless ultra-relativistic unmagnetized electron plasma is derived. In particular, the tensor is obtained by considering anisotropy in the momentum space. The integral of moments of Fermi-Dirac distribution function in terms of Polylog functions is used for describing the border line plasma systems (T/e TF e ≈1 ) comprising arbitrary electron degeneracy, where Te and TF e, are thermal and Fermi temperatures, respectively. Furthermore, the effects of variation in thermal momentum space anisotropy on the electron equilibrium number density and the spectrum of electromagnetic waves are analyzed.

Radiative transfer in multilayered random medium with laminar structure - Green's function approach

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.

1986-01-01

For a multilayered random medium with a laminar structure a Green's function approach is introduced to obtain the emitted intensity due to an arbitrary point source. It is then shown that the approach is applicable to both active and passive remote sensing. In active remote sensing, the computed radar backscattering cross section for the multilayered medium includes the effects of both volume multiple scattering and surface multiple scattering at the layer boundaries. In passive remote sensing, the brightness temperature is obtained for arbitrary temperature profiles in the layers. As an illustration the brightness temperature and reflectivity are calculated for a bounded layer and compared with results in the literature.

High-fidelity modeling and impact footprint prediction for vehicle breakup analysis

NASA Astrophysics Data System (ADS)

Ling, Lisa

For decades, vehicle breakup analysis had been performed for space missions that used nuclear heater or power units in order to assess aerospace nuclear safety for potential launch failures leading to inadvertent atmospheric reentry. Such pre-launch risk analysis is imperative to assess possible environmental impacts, obtain launch approval, and for launch contingency planning. In order to accurately perform a vehicle breakup analysis, the analysis tool should include a trajectory propagation algorithm coupled with thermal and structural analyses and influences. Since such a software tool was not available commercially or in the public domain, a basic analysis tool was developed by Dr. Angus McRonald prior to this study. This legacy software consisted of low-fidelity modeling and had the capability to predict vehicle breakup, but did not predict the surface impact point of the nuclear component. Thus the main thrust of this study was to develop and verify the additional dynamics modeling and capabilities for the analysis tool with the objectives to (1) have the capability to predict impact point and footprint, (2) increase the fidelity in the prediction of vehicle breakup, and (3) reduce the effort and time required to complete an analysis. The new functions developed for predicting the impact point and footprint included 3-degrees-of-freedom trajectory propagation, the generation of non-arbitrary entry conditions, sensitivity analysis, and the calculation of impact footprint. The functions to increase the fidelity in the prediction of vehicle breakup included a panel code to calculate the hypersonic aerodynamic coefficients for an arbitrary-shaped body and the modeling of local winds. The function to reduce the effort and time required to complete an analysis included the calculation of node failure criteria. The derivation and development of these new functions are presented in this dissertation, and examples are given to demonstrate the new capabilities and the improvements made, with comparisons between the results obtained from the upgraded analysis tool and the legacy software wherever applicable.

Flexible coherent control of plasmonic spin-Hall effect

PubMed Central

Xiao, Shiyi; Zhong, Fan; Liu, Hui; Zhu, Shining; Li, Jensen

2015-01-01

The surface plasmon polariton is an emerging candidate for miniaturizing optoelectronic circuits. Recent demonstrations of polarization-dependent splitting using metasurfaces, including focal-spot shifting and unidirectional propagation, allow us to exploit the spin degree of freedom in plasmonics. However, further progress has been hampered by the inability to generate more complicated and independent surface plasmon profiles for two incident spins, which work coherently together for more flexible and tunable functionalities. Here by matching the geometric phases of the nano-slots on silver to specific superimpositions of the inward and outward surface plasmon profiles for the two spins, arbitrary spin-dependent orbitals can be generated in a slot-free region. Furthermore, motion pictures with a series of picture frames can be assembled and played by varying the linear polarization angle of incident light. This spin-enabled control of orbitals is potentially useful for tip-free near-field scanning microscopy, holographic data storage, tunable plasmonic tweezers, and integrated optical components. PMID:26415636

Digital computer programs for generating oblique orthographic projections and contour plots

NASA Technical Reports Server (NTRS)

Giles, G. L.

1975-01-01

User and programer documentation is presented for two programs for automatic plotting of digital data. One of the programs generates oblique orthographic projections of three-dimensional numerical models and the other program generates contour plots of data distributed in an arbitrary planar region. A general description of the computational algorithms, user instructions, and complete listings of the programs is given. Several plots are included to illustrate various program options, and a single example is described to facilitate learning the use of the programs.

Controlling the carrier-envelope phase of Raman-generated periodic waveforms.

PubMed

Hsieh, Zhi-Ming; Lai, Chien-Jen; Chan, Han-Sung; Wu, Sih-Ying; Lee, Chao-Kuei; Chen, Wei-Jan; Pan, Ci-Ling; Yee, Fu-Goul; Kung, A H

2009-05-29

We demonstrate control of the carrier-envelope phase of ultrashort periodic waveforms that are synthesized from a Raman-generated optical frequency comb. We generated the comb by adiabatically driving a molecular vibrational coherence with a beam at a fundamental frequency plus its second harmonic. Heterodyne measurements show that full interpulse phase locking of the comb components is realized. The results set the stage for the synthesis of periodic arbitrary waveforms in the femtosecond and subfemtosecond regimes with full control.

Spectroscopy of the Schwarzschild black hole at arbitrary frequencies.

PubMed

Casals, Marc; Ottewill, Adrian

2012-09-14

Linear field perturbations of a black hole are described by the Green function of the wave equation that they obey. After Fourier decomposing the Green function, its two natural contributions are given by poles (quasinormal modes) and a largely unexplored branch cut in the complex frequency plane. We present new analytic methods for calculating the branch cut on a Schwarzschild black hole for arbitrary values of the frequency. The branch cut yields a power-law tail decay for late times in the response of a black hole to an initial perturbation. We determine explicitly the first three orders in the power-law and show that the branch cut also yields a new logarithmic behavior T(-2ℓ-5)lnT for late times. Before the tail sets in, the quasinormal modes dominate the black hole response. For electromagnetic perturbations, the quasinormal mode frequencies approach the branch cut at large overtone index n. We determine these frequencies up to n(-5/2) and, formally, to arbitrary order. Highly damped quasinormal modes are of particular interest in that they have been linked to quantum properties of black holes.

Extension of Murray's law using a non-Newtonian model of blood flow.

PubMed

Revellin, Rémi; Rousset, François; Baud, David; Bonjour, Jocelyn

2009-05-15

So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate. MODELING: In the present paper, Murray's law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murray's law remains valid (i.e. SigmaR(c) = cste with c = 3 is verified and is independent of n, the dimensionless index in the viscosity equation; R being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of c may be calculated depending on the value of n. We find that c varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to c = 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature. It is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid.

Algebraic aspects of the driven dynamics in the density operator and correlation functions calculation for multi-level open quantum systems

NASA Astrophysics Data System (ADS)

Bogolubov, Nikolai N.; Soldatov, Andrey V.

2017-12-01

Exact and approximate master equations were derived by the projection operator method for the reduced statistical operator of a multi-level quantum system with finite number N of quantum eigenstates interacting with arbitrary external classical fields and dissipative environment simultaneously. It was shown that the structure of these equations can be simplified significantly if the free Hamiltonian driven dynamics of an arbitrary quantum multi-level system under the influence of the external driving fields as well as its Markovian and non-Markovian evolution, stipulated by the interaction with the environment, are described in terms of the SU(N) algebra representation. As a consequence, efficient numerical methods can be developed and employed to analyze these master equations for real problems in various fields of theoretical and applied physics. It was also shown that literally the same master equations hold not only for the reduced density operator but also for arbitrary nonequilibrium multi-time correlation functions as well under the only assumption that the system and the environment are uncorrelated at some initial moment of time. A calculational scheme was proposed to account for these lost correlations in a regular perturbative way, thus providing additional computable terms to the correspondent master equations for the correlation functions.

Numerical and experimental study of curved and planar frequency selective surfaces with arbitrary illumination. M.S. Thesis - Maryland Univ., 1989

NASA Technical Reports Server (NTRS)

Caroglanian, Armen

1991-01-01

A frequency selective surface (FSS) composed of apertures in a metallic sheet is known as the inductive FSS. The infinite inductive FSS theory is derived and the aperture fields are solved by a spectral domain formulation with method of moments solution. Both full domain and subsectional basis functions are studied. A locally planar technique (LPT) is used to determine the forward scattered field from a generally shaped inductive FSS with arbitrary illumination.

An Elementary Algorithm to Evaluate Trigonometric Functions to High Precision

ERIC Educational Resources Information Center

Johansson, B. Tomas

2018-01-01

Evaluation of the cosine function is done via a simple Cordic-like algorithm, together with a package for handling arbitrary-precision arithmetic in the computer program Matlab. Approximations to the cosine function having hundreds of correct decimals are presented with a discussion around errors and implementation.

Viscoelastic Timoshenko Beams with Occasionally Constant Relaxation Functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tatar, Nasser-eddine, E-mail: tatarn@kfupm.edu.sa

2012-08-15

For a prescribed desirable arbitrary decay suitable viscoelastic materials are determined through their relaxation functions. It is shown that if we wish to have a decay of order {gamma}(t) then the kernels should be of the same order. That is their product with this function should be summable.

Compact universal logic gates realized using quantization of current in nanodevices.

PubMed

Zhang, Wancheng; Wu, Nan-Jian; Yang, Fuhua

2007-12-12

This paper proposes novel universal logic gates using the current quantization characteristics of nanodevices. In nanodevices like the electron waveguide (EW) and single-electron (SE) turnstile, the channel current is a staircase quantized function of its control voltage. We use this unique characteristic to compactly realize Boolean functions. First we present the concept of the periodic-threshold threshold logic gate (PTTG), and we build a compact PTTG using EW and SE turnstiles. We show that an arbitrary three-input Boolean function can be realized with a single PTTG, and an arbitrary four-input Boolean function can be realized by using two PTTGs. We then use one PTTG to build a universal programmable two-input logic gate which can be used to realize all two-input Boolean functions. We also build a programmable three-input logic gate by using one PTTG. Compared with linear threshold logic gates, with the PTTG one can build digital circuits more compactly. The proposed PTTGs are promising for future smart nanoscale digital system use.

Foundations of a mathematical theory of darwinism.

PubMed

Batty, Charles J K; Crewe, Paul; Grafen, Alan; Gratwick, Richard

2014-08-01

This paper pursues the 'formal darwinism' project of Grafen, whose aim is to construct formal links between dynamics of gene frequencies and optimization programmes, in very abstract settings with general implications for biologically relevant situations. A major outcome is the definition, within wide assumptions, of the ubiquitous but problematic concept of 'fitness'. This paper is the first to present the project for mathematicians. Within the framework of overlapping generations in discrete time and no social interactions, the current model shows links between fitness maximization and gene frequency change in a class-structured population, with individual-level uncertainty but no uncertainty in the class projection operator, where individuals are permitted to observe and condition their behaviour on arbitrary parts of the uncertainty. The results hold with arbitrary numbers of loci and alleles, arbitrary dominance and epistasis, and make no assumptions about linkage, linkage disequilibrium or mating system. An explicit derivation is given of Fisher's Fundamental Theorem of Natural Selection in its full generality.

On A Problem Of Propagation Of Shock Waves Generated By Explosive Volcanic Eruptions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gusev, V. A.; Sobissevitch, A. L.

2008-06-24

Interdisciplinary study of flows of matter and energy in geospheres has become one of the most significant advances in Earth sciences. It is carried out by means of direct quantitative estimations based on detailed analysis of geological and geophysical observations and experimental data. The actual contribution is the interdisciplinary study of nonlinear acoustics and physical volcanology dedicated to shock wave propagation in a viscous and inhomogeneous medium. The equations governing evolution of shock waves with an arbitrary initial profile and an arbitrary cross-section of a beam are obtained. For the case of low viscous medium, the asymptotic solution meant tomore » calculate a profile of a shock wave in an arbitrary point has been derived. The analytical solution of the problem on propagation of shock pulses from atmosphere into a two-phase fluid-saturated geophysical medium is analysed. Quantitative estimations were carried out with respect to experimental results obtained in the course of real explosive volcanic eruptions.« less

Potential flow about arbitrary biplane wing sections

NASA Technical Reports Server (NTRS)

Garrick, I E

1937-01-01

A rigorous treatment is given of the problem of determining the two-dimensional potential flow around arbitrary biplane cellules. The analysis involves the use of elliptic functions and is sufficiently general to include the effects of such elements as the section shapes, the chord ratio, gap, stagger, and decalage, which elements may be specified arbitrarily. The flow problem is resolved by making use of the methods of conformal representation. Thus the solution of the problem of transforming conformally two arbitrary contours into two circles is expressed by a pair of simultaneous integral equations, for which a method of numerical solution is outlined. As an example of the numerical process, the pressure distribution over certain arrangements of the NACA 4412 airfoil in biplane combinations is presented and compared with the monoplane pressure distribution.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rehman, Nasir, E-mail: nasirzainy1@hotmail.com; Shashiashvili, Malkhaz

The classical Garman-Kohlhagen model for the currency exchange assumes that the domestic and foreign currency risk-free interest rates are constant and the exchange rate follows a log-normal diffusion process.In this paper we consider the general case, when exchange rate evolves according to arbitrary one-dimensional diffusion process with local volatility that is the function of time and the current exchange rate and where the domestic and foreign currency risk-free interest rates may be arbitrary continuous functions of time. First non-trivial problem we encounter in time-dependent case is the continuity in time argument of the value function of the American put optionmore » and the regularity properties of the optimal exercise boundary. We establish these properties based on systematic use of the monotonicity in volatility for the value functions of the American as well as European options with convex payoffs together with the Dynamic Programming Principle and we obtain certain type of comparison result for the value functions and corresponding exercise boundaries for the American puts with different strikes, maturities and volatilities.Starting from the latter fact that the optimal exercise boundary curve is left continuous with right-hand limits we give a mathematically rigorous and transparent derivation of the significant early exercise premium representation for the value function of the American foreign exchange put option as the sum of the European put option value function and the early exercise premium.The proof essentially relies on the particular property of the stochastic integral with respect to arbitrary continuous semimartingale over the predictable subsets of its zeros. We derive from the latter the nonlinear integral equation for the optimal exercise boundary which can be studied by numerical methods.« less

Hamiltonian structure of real Monge - Ampère equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1996-06-01

The variational principle for the real homogeneous Monge - Ampère equation in two dimensions is shown to contain three arbitrary functions of four variables. There exist two different specializations of this variational principle where the Lagrangian is degenerate and furthermore contains an arbitrary function of two variables. The Hamiltonian formulation of these degenerate Lagrangian systems requires the use of Dirac's theory of constraints. As in the case of most completely integrable systems the constraints are second class and Dirac brackets directly yield the Hamiltonian operators. Thus the real homogeneous Monge - Ampère equation in two dimensions admits two classes of infinitely many Hamiltonian operators, namely a family of local, as well as another family non-local Hamiltonian operators and symplectic 2-forms which depend on arbitrary functions of two variables. The simplest non-local Hamiltonian operator corresponds to the Kac - Moody algebra of vector fields and functions on the unit circle. Hamiltonian operators that belong to either class are compatible with each other but between classes there is only one compatible pair. In the case of real Monge - Ampère equations with constant right-hand side this compatible pair is the only pair of Hamiltonian operators that survives. Then the complete integrability of all these real Monge - Ampère equations follows by Magri's theorem. Some of the remarkable properties we have obtained for the Hamiltonian structure of the real homogeneous Monge - Ampère equation in two dimensions turn out to be generic to the real homogeneous Monge - Ampère equation and the geodesic flow for the complex homogeneous Monge - Ampère equation in arbitrary number of dimensions. Hence among all integrable nonlinear evolution equations in one space and one time dimension, the real homogeneous Monge - Ampère equation is distinguished as one that retains its character as an integrable system in multiple dimensions.

Irreducible representations of finitely generated nilpotent groups

DOE Office of Scientific and Technical Information (OSTI.GOV)

Beloshapka, I V; Gorchinskiy, S O

2016-01-31

We prove that irreducible complex representations of finitely generated nilpotent groups are monomial if and only if they have finite weight, which was conjectured by Parshin. Note that we consider (possibly infinite-dimensional) representations without any topological structure. In addition, we prove that for certain induced representations, irreducibility is implied by Schur irreducibility. Both results are obtained in a more general form for representations over an arbitrary field. Bibliography: 21 titles.

The Electrolyte Genome project: A big data approach in battery materials discovery

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qu, Xiaohui; Jain, Anubhav; Rajput, Nav Nidhi

2015-06-01

We present a high-throughput infrastructure for the automated calculation of molecular properties with a focus on battery electrolytes. The infrastructure is largely open-source and handles both practical aspects (input file generation, output file parsing, and information management) as well as more complex problems (structure matching, salt complex generation, and failure recovery). Using this infrastructure, we have computed the ionization potential (IP) and electron affinities (EA) of 4830 molecules relevant to battery electrolytes (encompassing almost 55,000 quantum mechanics calculations) at the B3LYP/6-31+G(*) level. We describe automated workflows for computing redox potential, dissociation constant, and salt-molecule binding complex structure generation. We presentmore » routines for automatic recovery from calculation errors, which brings the failure rate from 9.2% to 0.8% for the QChem DFT code. Automated algorithms to check duplication between two arbitrary molecules and structures are described. We present benchmark data on basis sets and functionals on the G2-97 test set; one finding is that a IP/EA calculation method that combines PBE geometry optimization and B3LYP energy evaluation requires less computational cost and yields nearly identical results as compared to a full B3LYP calculation, and could be suitable for the calculation of large molecules. Our data indicates that among the 8 functionals tested, XYGJ-OS and B3LYP are the two best functionals to predict IP/EA with an RMSE of 0.12 and 0.27 eV, respectively. Application of our automated workflow to a large set of quinoxaline derivative molecules shows that functional group effect and substitution position effect can be separated for IP/EA of quinoxaline derivatives, and the most sensitive position is different for IP and EA. Published by Elsevier B.V« less

EzGal: A Flexible Interface for Stellar Population Synthesis Models

NASA Astrophysics Data System (ADS)

Mancone, Conor L.; Gonzalez, Anthony H.

2012-06-01

We present EzGal, a flexible Python program designed to easily generate observable parameters (magnitudes, colors, and mass-to-light ratios) for arbitrary input stellar population synthesis (SPS) models. As has been demonstrated by various authors, for many applications the choice of input SPS models can be a significant source of systematic uncertainty. A key strength of EzGal is that it enables simple, direct comparison of different model sets so that the uncertainty introduced by choice of model set can be quantified. Its ability to work with new models will allow EzGal to remain useful as SPS modeling evolves to keep up with the latest research (such as varying IMFs). EzGal is also capable of generating composite stellar population models (CSPs) for arbitrary input star-formation histories and reddening laws, and it can be used to interpolate between metallicities for a given model set. To facilitate use, we have created an online interface to run EzGal and quickly generate magnitude and mass-to-light ratio predictions for a variety of star-formation histories and model sets. We make many commonly used SPS models available from the online interface, including the canonical Bruzual & Charlot models, an updated version of these models, the Maraston models, the BaSTI models, and the Flexible Stellar Population Synthesis (FSPS) models. We use EzGal to compare magnitude predictions for the model sets as a function of wavelength, age, metallicity, and star-formation history. From this comparison we quickly recover the well-known result that the models agree best in the optical for old solar-metallicity models, with differences at the level. Similarly, the most problematic regime for SPS modeling is for young ages (≲2 Gyr) and long wavelengths (λ ≳ 7500 Å), where thermally pulsating AGB stars are important and scatter between models can vary from 0.3 mag (Sloan i) to 0.7 mag (Ks). We find that these differences are not caused by one discrepant model set and should therefore be interpreted as general uncertainties in SPS modeling. Finally, we connect our results to a more physically motivated example by generating CSPs with a star-formation history matching the global star-formation history of the universe. We demonstrate that the wavelength and age dependence of SPS model uncertainty translates into a redshift-dependent model uncertainty, highlighting the importance of a quantitative understanding of model differences when comparing observations with models as a function of redshift.

Programmable controlled mode-locked fiber laser using a digital micromirror device.

PubMed

Liu, Wu; Fan, Jintao; Xie, Chen; Song, Youjian; Gu, Chenlin; Chai, Lu; Wang, Chingyue; Hu, Minglie

2017-05-15

A digital micromirror device (DMD)-based arbitrary spectrum amplitude shaper is incorporated into a large-mode-area photonic crystal fiber laser cavity. The shaper acts as an in-cavity programmable filter and provides large tunable dispersion from normal to anomalous. As a result, mode-locking is achieved in different dispersion regimes with watt-level high output power. By programming different filter profiles on the DMD, the laser generates femtosecond pulse with a tunable central wavelength and controllable bandwidth. Under conditions of suitable cavity dispersion and pump power, design-shaped spectra are directly obtained by varying the amplitude transfer function of the filter. The results show the versatility of the DMD-based in-cavity filter for flexible control of the pulse dynamics in a mode-locked fiber laser.

Collective Yu-Shiba-Rusinov states in magnetic clusters at superconducting surfaces

NASA Astrophysics Data System (ADS)

Körber, Simon; Trauzettel, Björn; Kashuba, Oleksiy

2018-05-01

We study the properties of collective Yu-Shiba-Rusinov (YSR) states generated by multiple magnetic adatoms (clusters) placed on the surface of a superconductor. For magnetic clusters with equal distances between their constituents, we demonstrate the formation of effectively spin-unpolarized YSR states with subgap energies independent of the spin configuration of the magnetic impurities. We solve the problem analytically for arbitrary spin structure and analyze both spin-polarized (dispersive energy levels) and spin-unpolarized (pinned energy levels) solutions. While the energies of the spin-polarized solutions can be characterized solely by the net magnetic moment of the cluster, the wave functions of the spin-unpolarized solutions effectively decouple from it. This decoupling makes them stable against thermal fluctuation and detectable in scanning tunneling microscopy experiments.

Discrimination of shot-noise-driven Poisson processes by external dead time - Application of radioluminescence from glass

NASA Technical Reports Server (NTRS)

Saleh, B. E. A.; Tavolacci, J. T.; Teich, M. C.

1981-01-01

Ways in which dead time can be used to constructively enhance or diminish the effects of point processes that display bunching in the shot-noise-driven doubly stochastic Poisson point process (SNDP) are discussed. Interrelations between photocount bunching arising in the SNDP and the antibunching character arising from dead-time effects are investigated. It is demonstrated that the dead-time-modified count mean and variance for an arbitrary doubly stochastic Poisson point process can be obtained from the Laplace transform of the single-fold and joint-moment-generating functions for the driving rate process. The theory is in good agreement with experimental values for radioluminescence radiation in fused silica, quartz, and glass, and the process has many applications in pulse, particle, and photon detection.

L-hop percolation on networks with arbitrary degree distributions and its applications

NASA Astrophysics Data System (ADS)

Shang, Yilun; Luo, Weiliang; Xu, Shouhuai

2011-09-01

Site percolation has been used to help understand analytically the robustness of complex networks in the presence of random node deletion (or failure). In this paper we move a further step beyond random node deletion by considering that a node can be deleted because it is chosen or because it is within some L-hop distance of a chosen node. Using the generating functions approach, we present analytic results on the percolation threshold as well as the mean size, and size distribution, of nongiant components of complex networks under such operations. The introduction of parameter L is both conceptually interesting because it accommodates a sort of nonindependent node deletion, which is often difficult to tackle analytically, and practically interesting because it offers useful insights for cybersecurity (such as botnet defense).

Problems and methods of calculating the Legendre functions of arbitrary degree and order

NASA Astrophysics Data System (ADS)

Novikova, Elena; Dmitrenko, Alexander

2016-12-01

The known standard recursion methods of computing the full normalized associated Legendre functions do not give the necessary precision due to application of IEEE754-2008 standard, that creates a problems of underflow and overflow. The analysis of the problems of the calculation of the Legendre functions shows that the problem underflow is not dangerous by itself. The main problem that generates the gross errors in its calculations is the problem named the effect of "absolute zero". Once appeared in a forward column recursion, "absolute zero" converts to zero all values which are multiplied by it, regardless of whether a zero result of multiplication is real or not. Three methods of calculating of the Legendre functions, that removed the effect of "absolute zero" from the calculations are discussed here. These methods are also of interest because they almost have no limit for the maximum degree of Legendre functions. It is shown that the numerical accuracy of these three methods is the same. But, the CPU calculation time of the Legendre functions with Fukushima method is minimal. Therefore, the Fukushima method is the best. Its main advantage is computational speed which is an important factor in calculation of such large amount of the Legendre functions as 2 401 336 for EGM2008.

Automated aberration correction of arbitrary laser modes in high numerical aperture systems.

PubMed

Hering, Julian; Waller, Erik H; Von Freymann, Georg

2016-12-12

Controlling the point-spread-function in three-dimensional laser lithography is crucial for fabricating structures with highest definition and resolution. In contrast to microscopy, aberrations have to be physically corrected prior to writing, to create well defined doughnut modes, bottlebeams or multi foci modes. We report on a modified Gerchberg-Saxton algorithm for spatial-light-modulator based automated aberration compensation to optimize arbitrary laser-modes in a high numerical aperture system. Using circularly polarized light for the measurement and first-guess initial conditions for amplitude and phase of the pupil function our scalar approach outperforms recent algorithms with vectorial corrections. Besides laser lithography also applications like optical tweezers and microscopy might benefit from the method presented.

Boundary Conditions for Infinite Conservation Laws

NASA Astrophysics Data System (ADS)

Rosenhaus, V.; Bruzón, M. S.; Gandarias, M. L.

2016-12-01

Regular soliton equations (KdV, sine-Gordon, NLS) are known to possess infinite sets of local conservation laws. Some other classes of nonlinear PDE possess infinite-dimensional symmetries parametrized by arbitrary functions of independent or dependent variables; among them are Zabolotskaya-Khokhlov, Kadomtsev-Petviashvili, Davey-Stewartson equations and Born-Infeld equation. Boundary conditions were shown to play an important role for the existence of local conservation laws associated with infinite-dimensional symmetries. In this paper, we analyze boundary conditions for the infinite conserved densities of regular soliton equations: KdV, potential KdV, Sine-Gordon equation, and nonlinear Schrödinger equation, and compare them with boundary conditions for the conserved densities obtained from infinite-dimensional symmetries with arbitrary functions of independent and dependent variables.

Spherical type integrable classical systems in a magnetic field

NASA Astrophysics Data System (ADS)

Marchesiello, A.; Šnobl, L.; Winternitz, P.

2018-04-01

We show that four classes of second order spherical type integrable classical systems in a magnetic field exist in the Euclidean space {E}3 , and construct the Hamiltonian and two second order integrals of motion in involution for each of them. For one of the classes the Hamiltonian depends on four arbitrary functions of one variable. This class contains the magnetic monopole as a special case. Two further classes have Hamiltonians depending on one arbitrary function of one variable and four or six constants, respectively. The magnetic field in these cases is radial. The remaining system corresponds to a constant magnetic field and the Hamiltonian depends on two constants. Questions of superintegrability—i.e. the existence of further integrals—are discussed.

ABJM Wilson loops in arbitrary representations

NASA Astrophysics Data System (ADS)

Hatsuda, Yasuyuki; Honda, Masazumi; Moriyama, Sanefumi; Okuyama, Kazumi

2013-10-01

We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.

Two-Point Resistance of a Non-Regular Cylindrical Network with a Zero Resistor Axis and Two Arbitrary Boundaries

NASA Astrophysics Data System (ADS)

Tan, Zhi-Zhong

2017-03-01

We study a problem of two-point resistance in a non-regular m × n cylindrical network with a zero resistor axis and two arbitrary boundaries by means of the Recursion-Transform method. This is a new problem never solved before, the Green’s function technique and the Laplacian matrix approach are invalid in this case. A disordered network with arbitrary boundaries is a basic model in many physical systems or real world systems, however looking for the exact calculation of the resistance of a binary resistor network is important but difficult in the case of the arbitrary boundaries, the boundary is like a wall or trap which affects the behavior of finite network. In this paper we obtain a general resistance formula of a non-regular m × n cylindrical network, which is composed of a single summation. Further, the current distribution is given explicitly as a byproduct of the method. As applications, several interesting results are derived by making special cases from the general formula. Supported by the Natural Science Foundation of Jiangsu Province under Grant No. BK20161278

Preprocessing for Eddy Dissipation Rate and TKE Profile Generation

NASA Technical Reports Server (NTRS)

Zak, J. Allen; Rodgers, William G., Jr.; McKissick, Burnell T. (Technical Monitor)

2001-01-01

The Aircraft Vortex Spacing System (AVOSS), a set of algorithms to determine aircraft spacing according to wake vortex behavior prediction, requires turbulence profiles to appropriately determine arrival and departure aircraft spacing. The ambient atmospheric turbulence profile must always be produced, even if the result is an arbitrary (canned) profile. The original turbulence profile code was generated By North Carolina State University and used in a non-real-time environment in the past. All the input parameters could be carefully selected and screened prior to input. Since this code must run in real-time using actual measurements in the field as input, it became imperative to begin a data checking and screening process as part of the real-time implementation. The process described herein is a step towards ensuring that the best possible turbulence profile is always provided to AVOSS. Data fill-ins, constant profiles and arbitrary profiles are used only as a last resort, but are essential to ensure uninterrupted application of AVOSS.

Three-dimensional rearrangement of single atoms using actively controlled optical microtraps.

PubMed

Lee, Woojun; Kim, Hyosub; Ahn, Jaewook

2016-05-02

We propose and demonstrate three-dimensional rearrangements of single atoms. In experiments performed with single ⁸⁷Rb atoms in optical microtraps actively controlled by a spatial light modulator, we demonstrate various dynamic rearrangements of up to N = 9 atoms including rotation, 2D vacancy filling, guiding, compactification, and 3D shuffling. With the capability of a phase-only Fourier mask to generate arbitrary shapes of the holographic microtraps, it was possible to place single atoms at arbitrary geometries of a few μm size and even continuously reconfigure them by conveying each atom. For this purpose, we loaded a series of computer-generated phase masks in the full frame rate of 60 Hz of the spatial light modulator, so the animation of phase mask transformed the holographic microtraps in real time, driving each atom along the assigned trajectory. Possible applications of this method of transformation of single atoms include preparation of scalable quantum platforms for quantum computation, quantum simulation, and quantum many-body physics.

Development of multi-component explosive lenses for arbitrary phase velocity generation

NASA Astrophysics Data System (ADS)

Loiseau, Jason; Huneault, Justin; Petel, Oren; Goroshin, Sam; Frost, David; Higgins, Andrew; Zhang, Fan

2013-06-01

The combination of explosives with different detonation velocities and lens-like geometric shaping is a well-established technique for producing structured detonation waves. This technique can be extended to produce nearly arbitrary detonation phase velocities for the purposes of sequentially imploding pressurized tubes or driving Mach disks through high-density metalized explosives. The current study presents the experimental development of accelerating, multi-component lenses designed using simple geometric optics and idealized front curvature. The fast explosive component is either Composition C4 (VOD = 8 km/s) or Primasheet 1000 (VOD = 7 km/s), while the slow component varies from heavily amine-diluted nitromethane (amine mass fraction exceeding 20%) to packed metal and glass particle beds wetted with amine-sensitized nitromethane. The applicability of the geometric optic analog to such highly heterogeneous explosives is also investigated. The multi-layered lens technique is further developed as a means of generating a directed mass and momentum flux of metal particles via Mach-disk formation and jetting in circular and oval planar lenses.

A stationary phase solution for mountain waves with application to mesospheric mountain waves generated by Auckland Island

NASA Astrophysics Data System (ADS)

Broutman, Dave; Eckermann, Stephen D.; Knight, Harold; Ma, Jun

2017-01-01

A relatively general stationary phase solution is derived for mountain waves from localized topography. It applies to hydrostatic, nonhydrostatic, or anelastic dispersion relations, to arbitrary localized topography, and to arbitrary smooth vertically varying background temperature and vector wind profiles. A simple method is introduced to compute the ray Jacobian that quantifies the effects of horizontal geometrical spreading in the stationary phase solution. The stationary phase solution is applied to mesospheric mountain waves generated by Auckland Island during the Deep Propagating Gravity Wave Experiment. The results are compared to a Fourier solution. The emphasis is on interpretations involving horizontal geometrical spreading. The results show larger horizontal geometrical spreading for nonhydrostatic waves than for hydrostatic waves in the region directly above the island; the dominant effect of horizontal geometrical spreading in the lower ˜30 km of the atmosphere, compared to the effects of refraction and background density variation; and the enhanced geometrical spreading due to directional wind in the approach to a critical layer in the mesosphere.

Integrated Kerr comb-based reconfigurable transversal differentiator for microwave photonic signal processing

NASA Astrophysics Data System (ADS)

Xu, Xingyuan; Wu, Jiayang; Shoeiby, Mehrdad; Nguyen, Thach G.; Chu, Sai T.; Little, Brent E.; Morandotti, Roberto; Mitchell, Arnan; Moss, David J.

2018-01-01

An arbitrary-order intensity differentiator for high-order microwave signal differentiation is proposed and experimentally demonstrated on a versatile transversal microwave photonic signal processing platform based on integrated Kerr combs. With a CMOS-compatible nonlinear micro-ring resonator, high quality Kerr combs with broad bandwidth and large frequency spacings are generated, enabling a larger number of taps and an increased Nyquist zone. By programming and shaping individual comb lines' power, calculated tap weights are realized, thus achieving a versatile microwave photonic signal processing platform. Arbitrary-order intensity differentiation is demonstrated on the platform. The RF responses are experimentally characterized, and systems demonstrations for Gaussian input signals are also performed.

Development of an in-fiber white-light interferometric distance sensor for absolute measurement of arbitrary small distances.

PubMed

Majumdar, Ayan; Huang, Haiying

2008-05-20

The fabrication, implementation, and evaluation of an in-fiber white-light interferometric distance sensor that is capable of measuring the absolute value of an arbitrary small distance are presented. Taking advantage of the mode-coupling effect of a long-period fiber grating, an additional cavity distance is added to the optical path difference of the distance sensor; therefore, it can generate a sufficient number of fringes for distance demodulation even if the free-space cavity distance is very small. It is experimentally verified that the distance sensor is capable of measuring small distances that are beyond the capability of a Fabry-Perot interferometric distance sensor.

Laplace-Runge-Lenz vector for arbitrary spin

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nikitin, A. G.

2013-12-15

A countable set of superintegrable quantum mechanical systems is presented which admit the dynamical symmetry with respect to algebra so(4). This algebra is generated by the Laplace-Runge-Lenz vector generalized to the case of arbitrary spin. The presented systems describe neutral particles with non-trivial multipole momenta. Their spectra can be found algebraically like in the case of hydrogen atom. Solutions for the systems with spins 1/2 and 1 are presented explicitly, solutions for spin 3/2 can be expressed via solutions of an ordinary differential equation of first order. A more extended version of this paper including detailed calculations is published asmore » an e-print arXiv:1308.4279.« less

Program manual for ASTOP, an Arbitrary space trajectory optimization program

NASA Technical Reports Server (NTRS)

Horsewood, J. L.

1974-01-01

The ASTOP program (an Arbitrary Space Trajectory Optimization Program) designed to generate optimum low-thrust trajectories in an N-body field while satisfying selected hardware and operational constraints is presented. The trajectory is divided into a number of segments or arcs over which the control is held constant. This constant control over each arc is optimized using a parameter optimization scheme based on gradient techniques. A modified Encke formulation of the equations of motion is employed. The program provides a wide range of constraint, end conditions, and performance index options. The basic approach is conducive to future expansion of features such as the incorporation of new constraints and the addition of new end conditions.

Quantum mechanics in noninertial reference frames: Relativistic accelerations and fictitious forces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Klink, W.H., E-mail: william-klink@uiowa.edu; Wickramasekara, S., E-mail: wickrama@grinnell.edu

2016-06-15

One-particle systems in relativistically accelerating reference frames can be associated with a class of unitary representations of the group of arbitrary coordinate transformations, an extension of the Wigner–Bargmann definition of particles as the physical realization of unitary irreducible representations of the Poincaré group. Representations of the group of arbitrary coordinate transformations become necessary to define unitary operators implementing relativistic acceleration transformations in quantum theory because, unlike in the Galilean case, the relativistic acceleration transformations do not themselves form a group. The momentum operators that follow from these representations show how the fictitious forces in noninertial reference frames are generated inmore » quantum theory.« less

Brownian dynamics simulation of rigid particles of arbitrary shape in external fields.

PubMed

Fernandes, Miguel X; de la Torre, José García

2002-12-01

We have developed a Brownian dynamics simulation algorithm to generate Brownian trajectories of an isolated, rigid particle of arbitrary shape in the presence of electric fields or any other external agents. Starting from the generalized diffusion tensor, which can be calculated with the existing HYDRO software, the new program BROWNRIG (including a case-specific subprogram for the external agent) carries out a simulation that is analyzed later to extract the observable dynamic properties. We provide a variety of examples of utilization of this method, which serve as tests of its performance, and also illustrate its applicability. Examples include free diffusion, transport in an electric field, and diffusion in a restricting environment.

Biological adaptations for functional features of language in the face of cultural evolution.

PubMed

Christiansen, Morten H; Reali, Florencia; Chater, Nick

2011-04-01

Although there may be no true language universals, it is nonetheless possible to discern several family resemblance patterns across the languages of the world. Recent work on the cultural evolution of language indicates the source of these patterns is unlikely to be an innate universal grammar evolved through biological adaptations for arbitrary linguistic features. Instead, it has been suggested that the patterns of resemblance emerge because language has been shaped by the brain, with individual languages representing different but partially overlapping solutions to the same set of nonlinguistic constraints. Here, we use computational simulations to investigate whether biological adaptation for functional features of language, deriving from cognitive and communicative constraints, may nonetheless be possible alongside rapid cultural evolution. Specifically, we focus on the Baldwin effect as an evolutionary mechanism by which previously learned linguistic features might become innate through natural selection across many generations of language users. The results indicate that cultural evolution of language does not necessarily prevent functional features of language from becoming genetically fixed, thus potentially providing a particularly informative source of constraints on cross-linguistic resemblance patterns.

Isolated Attosecond Pulse Generation without the Need to Stabilize the Carrier-Envelope Phase of Driving Lasers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gilbertson, Steve; Khan, Sabih D.; Wu Yi

2010-08-27

Single isolated attosecond pulses can be extracted from a pulse train with an ultrafast gate in the generation target. By setting the gate width sufficiently narrow with the generalized double optical gating, we demonstrate that single isolated attosecond pulses can be generated with any arbitrary carrier-envelope phase value of the driving laser. The carrier-envelope phase only affects the photon flux, not the pulse duration or contrast. Our results show that isolated attosecond pulses can be generated using carrier-envelope phase unstabilized 23 fs pulses directly from chirped pulse amplifiers.

Partition-free theory of time-dependent current correlations in nanojunctions in response to an arbitrary time-dependent bias

NASA Astrophysics Data System (ADS)

Ridley, Michael; MacKinnon, Angus; Kantorovich, Lev

2017-04-01

Working within the nonequilibrium Green's function formalism, a formula for the two-time current correlation function is derived for the case of transport through a nanojunction in response to an arbitrary time-dependent bias. The one-particle Hamiltonian and the wide-band limit approximation are assumed, enabling us to extract all necessary Green's functions and self-energies for the system, extending the analytic work presented previously [Ridley et al., Phys. Rev. B 91, 125433 (2015), 10.1103/PhysRevB.91.125433]. We show that our expression for the two-time correlation function generalizes the Büttiker theory of shot and thermal noise on the current through a nanojunction to the time-dependent bias case including the transient regime following the switch-on. Transient terms in the correlation function arise from an initial state that does not assume (as is usually done) that the system is initially uncoupled, i.e., our approach is partition free. We show that when the bias loses its time dependence, the long-time limit of the current correlation function depends on the time difference only, as in this case an ideal steady state is reached. This enables derivation of known results for the single-frequency power spectrum and for the zero-frequency limit of this power spectrum. In addition, we present a technique which facilitates fast calculations of the transient quantum noise, valid for arbitrary temperature, time, and voltage scales. We apply this formalism to a molecular wire system for both dc and ac biases, and find a signature of the traversal time for electrons crossing the wire in the time-dependent cross-lead current correlations.

Light field rendering with omni-directional camera

NASA Astrophysics Data System (ADS)

Todoroki, Hiroshi; Saito, Hideo

2003-06-01

This paper presents an approach to capture visual appearance of a real environment such as an interior of a room. We propose the method for generating arbitrary viewpoint images by building light field with the omni-directional camera, which can capture the wide circumferences. Omni-directional camera used in this technique is a special camera with the hyperbolic mirror in the upper part of a camera, so that we can capture luminosity in the environment in the range of 360 degree of circumferences in one image. We apply the light field method, which is one technique of Image-Based-Rendering(IBR), for generating the arbitrary viewpoint images. The light field is a kind of the database that records the luminosity information in the object space. We employ the omni-directional camera for constructing the light field, so that we can collect many view direction images in the light field. Thus our method allows the user to explore the wide scene, that can acheive realistic representation of virtual enviroment. For demonstating the proposed method, we capture image sequence in our lab's interior environment with an omni-directional camera, and succesfully generate arbitray viewpoint images for virual tour of the environment.

Generation of synthetic image sequences for the verification of matching and tracking algorithms for deformation analysis

NASA Astrophysics Data System (ADS)

Bethmann, F.; Jepping, C.; Luhmann, T.

2013-04-01

This paper reports on a method for the generation of synthetic image data for almost arbitrary static or dynamic 3D scenarios. Image data generation is based on pre-defined 3D objects, object textures, camera orientation data and their imaging properties. The procedure does not focus on the creation of photo-realistic images under consideration of complex imaging and reflection models as they are used by common computer graphics programs. In contrast, the method is designed with main emphasis on geometrically correct synthetic images without radiometric impact. The calculation process includes photogrammetric distortion models, hence cameras with arbitrary geometric imaging characteristics can be applied. Consequently, image sets can be created that are consistent to mathematical photogrammetric models to be used as sup-pixel accurate data for the assessment of high-precision photogrammetric processing methods. In the first instance the paper describes the process of image simulation under consideration of colour value interpolation, MTF/PSF and so on. Subsequently the geometric quality of the synthetic images is evaluated with ellipse operators. Finally, simulated image sets are used to investigate matching and tracking algorithms as they have been developed at IAPG for deformation measurement in car safety testing.

Optimization of contrast resolution by genetic algorithm in ultrasound tissue harmonic imaging.

PubMed

Ménigot, Sébastien; Girault, Jean-Marc

2016-09-01

The development of ultrasound imaging techniques such as pulse inversion has improved tissue harmonic imaging. Nevertheless, no recommendation has been made to date for the design of the waveform transmitted through the medium being explored. Our aim was therefore to find automatically the optimal "imaging" wave which maximized the contrast resolution without a priori information. To overcome assumption regarding the waveform, a genetic algorithm investigated the medium thanks to the transmission of stochastic "explorer" waves. Moreover, these stochastic signals could be constrained by the type of generator available (bipolar or arbitrary). To implement it, we changed the current pulse inversion imaging system by including feedback. Thus the method optimized the contrast resolution by adaptively selecting the samples of the excitation. In simulation, we benchmarked the contrast effectiveness of the best found transmitted stochastic commands and the usual fixed-frequency command. The optimization method converged quickly after around 300 iterations in the same optimal area. These results were confirmed experimentally. In the experimental case, the contrast resolution measured on a radiofrequency line could be improved by 6% with a bipolar generator and it could still increase by 15% with an arbitrary waveform generator. Copyright © 2016 Elsevier B.V. All rights reserved.

High frequency direct drive generation using white noise sources

NASA Astrophysics Data System (ADS)

Frazier, S.; Sebacher, K.; Lawry, D.; Prather, W.; Hoffer, G.

1994-12-01

Damped sinusoid direct drive injection on interconnecting cable bundles between subsystems has long been used as a technique for determining susceptibility to electromagnetic transients in military weapon systems. Questions arise, however, about the adequacy of this method of individually injected, single sinusoids in assuring subsystem strength against broad band threats. This issue has recently been raised in the latest revision of MIL-STD-461 that requires subsystems exhibit no malfunctions when subjected to a repetitive square wave pulse with fast rise and fall time (CS115). An extension to this approach would be to test subsystems using arbitrary waveforms. In recent years arbitrary waveform generators (AWG's) have been used to duplicate, with a high degree of fidelity, the waveforms measured on cable bundles in a system illuminated by fields in a system-level EMP simulator. However, the operating speeds of present AWG's do not allow the extension of this approach to meet new threats such as MIL-STD-2169A. A novel alternative approach for generation of the required signals, being developed in a cooperative effort between the Naval Air Warfare Center and Phillips Laboratory, is the use of white noise signals conditioned in such a manner to produce the desired direct drive waveforms.

Propagation of waves from an arbitrary shaped surface-A generalization of the Fresnel diffraction integral

NASA Astrophysics Data System (ADS)

Feshchenko, R. M.; Vinogradov, A. V.; Artyukov, I. A.

2018-04-01

Using the method of Laplace transform the field amplitude in the paraxial approximation is found in the two-dimensional free space using initial values of the amplitude specified on an arbitrary shaped monotonic curve. The obtained amplitude depends on one a priori unknown function, which can be found from a Volterra first kind integral equation. In a special case of field amplitude specified on a concave parabolic curve the exact solution is derived. Both solutions can be used to study the light propagation from arbitrary surfaces including grazing incidence X-ray mirrors. They can find applications in the analysis of coherent imaging problems of X-ray optics, in phase retrieval algorithms as well as in inverse problems in the cases when the initial field amplitude is sought on a curved surface.

Fast RBF OGr for solving PDEs on arbitrary surfaces

NASA Astrophysics Data System (ADS)

Piret, Cécile; Dunn, Jarrett

2016-10-01

The Radial Basis Functions Orthogonal Gradients method (RBF-OGr) was introduced in [1] to discretize differential operators defined on arbitrary manifolds defined only by a point cloud. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent complex geometries in any spatial dimension. A large limitation of the RBF-OGr method was its large computational complexity, which greatly restricted the size of the point cloud. In this paper, we apply the RBF-Finite Difference (RBF-FD) technique to the RBF-OGr method for building sparse differentiation matrices discretizing continuous differential operators such as the Laplace-Beltrami operator. This method can be applied to solving PDEs on arbitrary surfaces embedded in ℛ3. We illustrate the accuracy of our new method by solving the heat equation on the unit sphere.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berezhiani, Lasha; Khoury, Justin; Wang, Junpu, E-mail: lashaber@gmail.com, E-mail: jkhoury@sas.upenn.edu, E-mail: jwang217@jhu.edu

Single-field perturbations satisfy an infinite number of consistency relations constraining the squeezed limit of correlation functions at each order in the soft momentum. These can be understood as Ward identities for an infinite set of residual global symmetries, or equivalently as Slavnov-Taylor identities for spatial diffeomorphisms. In this paper, we perform a number of novel, non-trivial checks of the identities in the context of single field inflationary models with arbitrary sound speed. We focus for concreteness on identities involving 3-point functions with a soft external mode, and consider all possible scalar and tensor combinations for the hard-momentum modes. In allmore » these cases, we check the consistency relations up to and including cubic order in the soft momentum. For this purpose, we compute for the first time the 3-point functions involving 2 scalars and 1 tensor, as well as 2 tensors and 1 scalar, for arbitrary sound speed.« less

On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations

NASA Astrophysics Data System (ADS)

Doha, E. H.

2002-02-01

An analytical formula expressing the ultraspherical coefficients of an expansion for an infinitely differentiable function that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion of the function is stated in a more compact form and proved in a simpler way than the formula suggested by Phillips and Karageorghis (27 (1990) 823). A new formula expressing explicitly the integrals of ultraspherical polynomials of any degree that has been integrated an arbitrary number of times of ultraspherical polynomials is given. The tensor product of ultraspherical polynomials is used to approximate a function of more than one variable. Formulae expressing the coefficients of differentiated expansions of double and triple ultraspherical polynomials in terms of the original expansion are stated and proved. Some applications of how to use ultraspherical polynomials for solving ordinary and partial differential equations are described.

Theory of a peristaltic pump for fermionic quantum fluids

NASA Astrophysics Data System (ADS)

Romeo, F.; Citro, R.

2018-05-01

Motivated by the recent developments in fermionic cold atoms and in nanostructured systems, we propose the model of a peristaltic quantum pump. Differently from the Thouless paradigm, a peristaltic pump is a quantum device that generates a particle flux as the effect of a sliding finite-size microlattice. A one-dimensional tight-binding Hamiltonian model of this quantum machine is formulated and analyzed within a lattice Green's function formalism on the Keldysh contour. The pump observables, as, e.g., the pumped particles per cycle, are studied as a function of the pumping frequency, the width of the pumping potential, the particles mean free path, and system temperature. The proposed analysis applies to arbitrary peristaltic potentials acting on fermionic quantum fluids confined to one dimension. These confinement conditions can be realized in nanostructured systems or, in a more controllable way, in cold atoms experiments. In view of the validation of the theoretical results, we describe the outcomes of the model considering a fermionic cold atoms system as a paradigmatic example.

The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey's h Transformation as a Special Case

PubMed Central

Goerg, Georg M.

2015-01-01

I present a parametric, bijective transformation to generate heavy tail versions of arbitrary random variables. The tail behavior of this heavy tail Lambert  W × F X random variable depends on a tail parameter δ ≥ 0: for δ = 0, Y ≡ X, for δ > 0 Y has heavier tails than X. For X being Gaussian it reduces to Tukey's h distribution. The Lambert W function provides an explicit inverse transformation, which can thus remove heavy tails from observed data. It also provides closed-form expressions for the cumulative distribution (cdf) and probability density function (pdf). As a special case, these yield analytic expression for Tukey's h pdf and cdf. Parameters can be estimated by maximum likelihood and applications to S&P 500 log-returns demonstrate the usefulness of the presented methodology. The R package LambertW implements most of the introduced methodology and is publicly available on CRAN. PMID:26380372

Apodized Pupil Lyot Coronagraphs for Arbitrary Apertures. II. Theoretical Properties and Application to Extremely Large Telescopes

NASA Astrophysics Data System (ADS)

Soummer, Rémi; Pueyo, Laurent; Ferrari, André; Aime, Claude; Sivaramakrishnan, Anand; Yaitskova, Natalia

2009-04-01

We study the application of Lyot coronagraphy to future Extremely Large Telescopes (ELTs), showing that Apodized Pupil Lyot Coronagraphs enable high-contrast imaging for exoplanet detection and characterization with ELTs. We discuss the properties of the optimal pupil apodizers for this application (generalized prolate spheroidal functions). The case of a circular aperture telescope with a central obstruction is considered in detail, and we discuss the effects of primary mirror segmentation and secondary mirror support structures as a function of the occulting mask size. In most cases where inner working distance is critical, e.g., for exoplanet detection, these additional features do not alter the solutions derived with just the central obstruction, although certain applications such as quasar-host galaxy coronagraphic observations could benefit from designs that explicitly accomodate ELT spider geometries. We illustrate coronagraphic designs for several ELT geometries including ESO/OWL, the Thirty Mirror Telescope, the Giant Magellan Telescope, and describe numerical methods for generating these designs.

Reanimating the arm and hand with intraspinal microstimulation

NASA Astrophysics Data System (ADS)

Zimmermann, Jonas B.; Seki, Kazuhiko; Jackson, Andrew

2011-10-01

To date, there is no effective therapy for spinal cord injury, and many patients could benefit dramatically from at least partial restoration of arm and hand function. Despite a substantial body of research investigating intraspinal microstimulation (ISMS) in frogs, rodents and cats, little is known about upper-limb responses to cervical stimulation in the primate. Here, we show for the first time that long trains of ISMS delivered to the macaque spinal cord can evoke functional arm and hand movements. Complex movements involving coordinated activation of multiple muscles could be elicited from a single electrode, while just two electrodes were required for independent control of reaching and grasping. We found that the motor responses to ISMS were described by a dual exponential model that depended only on stimulation history. We demonstrate that this model can be inverted to generate stimulus trains capable of eliciting arbitrary, graded motor responses, and could be used to restore volitional movements in a closed-loop brain-machine interface.

A novel beamformer design method for medical ultrasound. Part I: Theory.

PubMed

Ranganathan, Karthik; Walker, William F

2003-01-01

The design of transmit and receive aperture weightings is a critical step in the development of ultrasound imaging systems. Current design methods are generally iterative, and consequently time consuming and inexact. We describe a new and general ultrasound beamformer design method, the minimum sum squared error (MSSE) technique. The MSSE technique enables aperture design for arbitrary beam patterns (within fundamental limitations imposed by diffraction). It uses a linear algebra formulation to describe the system point spread function (psf) as a function of the aperture weightings. The sum squared error (SSE) between the system psf and the desired or goal psf is minimized, yielding the optimal aperture weightings. We present detailed analysis for continuous wave (CW) and broadband systems. We also discuss several possible applications of the technique, such as the design of aperture weightings that improve the system depth of field, generate limited diffraction transmit beams, and improve the correlation depth of field in translated aperture system geometries. Simulation results are presented in an accompanying paper.

Role of Möbius constants and scattering functions in Cachazo-He-Yuan scalar amplitudes

NASA Astrophysics Data System (ADS)

Lam, C. S.; Yao, York-Peng

2016-05-01

The integration over the Möbius variables leading to the Cachazo-He-Yuan double-color n -point massless scalar amplitude are carried out one integral at a time. Möbius invariance dictates the final amplitude to be independent of the three Möbius constants σr,σs,σt, but their choice affects integrations and the intermediate results. The effect of the Möbius constants, which will be held finite but otherwise arbitrary, the two sets of colors, and the scattering functions on each integration is investigated. A general systematic way to carry out the n -3 integrations is explained, each exposing one of the n -3 propagators of a single Feynman diagram. Two detailed examples are shown to illustrate the procedure, one a five-point amplitude, and the other a nine-point amplitude. Our procedure does not generate intermediate spurious poles, in contrast to what is common by choosing Möbius constants at 0, 1, and ∞ .

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fox, John

A 4.2 GS/sec. beam excitation system with accelerator synchronization and power stages is described. The system is capable of playing unique samples (32 samples/bunch) for 15,000 turns on selected bunch(es) in the SPS in syn- chronism with the injection and acceleration cycle. The purpose of the system is to excite internal modes of single-bunch vertical motion, and study the bunch dynamics in the presence of developing Electron cloud or TMCI effects. The system includes a synchronized master oscillator, SPS timing functions, an FPGA based arbitrary waveform generator, 4.2 GS/sec. D/A system and four 80W 20-1000 MHz amplifiers driving a taperedmore » stripline pickup/kicker. A software GUI allows specification of various modulation signals, selection of bunches and turns to excite, while a remote control interface allows simple control/monitoring of the RF power stages located in the tunnel. The successful use of this system for SPS MD measurements in 2011 is a vital proof-of-principle for wideband feedback using similar functions to correct the beam motion.« less

Structure of polarization singularities of a light beam at triple frequency generated in isotropic medium by singularly polarized beam.

PubMed

Grigoriev, K S; Ryzhikov, P S; Cherepetskaya, E B; Makarov, V A

2017-10-16

The components of electric field of the third harmonic beam, generated in isotropic medium with cubic nonlinearity by a monochromatic light beam carrying polarization singularity of an arbitrary type, are found analytically. The relation between C-points characteristics in the fundamental and signal beams are determined, as well as the impact of the phase mismatch on the shape of the C-lines.

Nonlinear dispersion-based incoherent photonic processing for microwave pulse generation with full reconfigurability.

PubMed

Bolea, Mario; Mora, José; Ortega, Beatriz; Capmany, José

2012-03-12

A novel all-optical technique based on the incoherent processing of optical signals using high-order dispersive elements is analyzed for microwave arbitrary pulse generation. We show an approach which allows a full reconfigurability of a pulse in terms of chirp, envelope and central frequency by the proper control of the second-order dispersion and the incoherent optical source power distribution, achieving large values of time-bandwidth product.

Variable-speed wind power system with improved energy capture via multilevel conversion

DOEpatents

Erickson, Robert W.; Al-Naseem, Osama A.; Fingersh, Lee Jay

2005-05-31

A system and method for efficiently capturing electrical energy from a variable-speed generator are disclosed. The system includes a matrix converter using full-bridge, multilevel switch cells, in which semiconductor devices are clamped to a known constant DC voltage of a capacitor. The multilevel matrix converter is capable of generating multilevel voltage wave waveform of arbitrary magnitude and frequencies. The matrix converter can be controlled by using space vector modulation.

Next-generation digital information storage in DNA.

PubMed

Church, George M; Gao, Yuan; Kosuri, Sriram

2012-09-28

Digital information is accumulating at an astounding rate, straining our ability to store and archive it. DNA is among the most dense and stable information media known. The development of new technologies in both DNA synthesis and sequencing make DNA an increasingly feasible digital storage medium. We developed a strategy to encode arbitrary digital information in DNA, wrote a 5.27-megabit book using DNA microchips, and read the book by using next-generation DNA sequencing.

NASA Ames potential flow analysis (POTFAN) geometry program (POTGEM), version 1

NASA Technical Reports Server (NTRS)

Medan, R. T.; Bullock, R. B.

1976-01-01

A computer program known as POTGEM is reported which has been developed as an independent segment of a three-dimensional linearized, potential flow analysis system and which is used to generate a panel point description of arbitrary, three-dimensional bodies from convenient engineering descriptions consisting of equations and/or tables. Due to the independent, modular nature of the program, it may be used to generate corner points for other computer programs.

Dynamical generation of noiseless quantum subsystems

PubMed

Viola; Knill; Lloyd

2000-10-16

We combine dynamical decoupling and universal control methods for open quantum systems with coding procedures. By exploiting a general algebraic approach, we show how appropriate encodings of quantum states result in obtaining universal control over dynamically generated noise-protected subsystems with limited control resources. In particular, we provide a constructive scheme based on two-body Hamiltonians for performing universal quantum computation over large noiseless spaces which can be engineered in the presence of arbitrary linear quantum noise.

Generating Textures for Arbitrary Surfaces Using Reaction-Diffusion

DTIC Science & Technology

1990-01-01

Review and Classification," Computer Aided Design, Vol. 20, No. 1, pp. 27-38 (January/February 1988). [ Hubel and Wiesel 79] Hubel , David H. and...columns found in mammals [ Hubel and Wiesel 791. Complex Patterns This section shows how we can generate more complex patterns using reaction-diffusion by... Torsten N. Wiesel , "Brain Mechanisms of Vision," Scientific American, Vol. 241, No. 3, pp. 150-162 (September 1979). [Hunding 90] Hunding, Axel, Stuart A

A direct temporal domain approach for ultrafast optical signal processing and its implementation using planar lightwave circuits

NASA Astrophysics Data System (ADS)

Xia, Bing

Ultrafast optical signal processing, which shares the same fundamental principles of electrical signal processing, can realize numerous important functionalities required in both academic research and industry. Due to the extremely fast processing speed, all-optical signal processing and pulse shaping have been widely used in ultrafast telecommunication networks, photonically-assisted RFlmicro-meter waveform generation, microscopy, biophotonics, and studies on transient and nonlinear properties of atoms and molecules. In this thesis, we investigate two types of optical spectrally-periodic (SP) filters that can be fabricated on planar lightwave circuits (PLC) to perform pulse repetition rate multiplication (PRRM) and arbitrary optical waveform generation (AOWG). First, we present a direct temporal domain approach for PRRM using SP filters. We show that the repetition rate of an input pulse train can be multiplied by a factor N using an optical filter with a free spectral range that does not need to be constrained to an integer multiple of N. Furthermore, the amplitude of each individual output pulse can be manipulated separately to form an arbitrary envelope at the output by optimizing the impulse response of the filter. Next, we use lattice-form Mach-Zehnder interferometers (LF-MZI) to implement the temporal domain approach for PRRM. The simulation results show that PRRM with uniform profiles, binary-code profiles and triangular profiles can be achieved. Three silica based LF-MZIs are designed and fabricated, which incorporate multi-mode interference (MMI) couplers and phase shifters. The experimental results show that 40 GHz pulse trains with a uniform envelope pattern, a binary code pattern "1011" and a binary code pattern "1101" are generated from a 10 GHz input pulse train. Finally, we investigate 2D ring resonator arrays (RRA) for ultraf ast optical signal processing. We design 2D RRAs to generate a pair of pulse trains with different binary-code patterns simultaneously from a single pulse train at a low repetition rate. We also design 2D RRAs for AOWG using the modified direct temporal domain approach. To demonstrate the approach, we provide numerical examples to illustrate the generation of two very different waveforms (square waveform and triangular waveform) from the same hyperbolic secant input pulse train. This powerful technique based on SP filters can be very useful for ultrafast optical signal processing and pulse shaping.

A Numerical Investigation of Two-Different Drosophila Forward Flight Modes

NASA Astrophysics Data System (ADS)

Sahin, Mehmet; Dilek, Ezgi; Erzincanli, Belkis

2016-11-01

The parallel large-scale unstructured finite volume method based on an Arbitrary Lagrangian-Eulerian (ALE) formulation has been applied in order to investigate the near wake structure of Drosophila in forward flight. DISTENE MeshGems-Hexa algorithm based on the octree method is used to generate the all hexahedral mesh for the wing-body combination. The mesh deformation algorithm is based on the indirect radial basis function (RBF) method at each time level while avoiding remeshing in order to enhance numerical robustness. The large-scale numerical simulations are carried out for a flapping Drosophila in forward flight. In the first case, the wing tip-path plane is tilted forward to generate forward force. In the second case, paddling wing motion is used to generate the forward fore. The λ2-criterion proposed by Jeong and Hussain (1995) is used for investigating the time variation of the Eulerian coherent structures in the near wake. The present simulations reveal highly detailed near wake topology for a hovering Drosophila. This is very useful in terms of understanding physics in biological flights which can provide a very useful tool for designing bio-inspired MAVs.

Generation of anisotropy in turbulent flows subjected to rapid distortion

NASA Astrophysics Data System (ADS)

Clark, Timothy T.; Kurien, Susan; Rubinstein, Robert

2018-01-01

A computational tool for the anisotropic time-evolution of the spectral velocity correlation tensor is presented. We operate in the linear, rapid distortion limit of the mean-field-coupled equations. Each term of the equations is written in the form of an expansion to arbitrary order in the basis of irreducible representations of the SO(3) symmetry group. The computational algorithm for this calculation solves a system of coupled equations for the scalar weights of each generated anisotropic mode. The analysis demonstrates that rapid distortion rapidly but systematically generates higher-order anisotropic modes. To maintain a tractable computation, the maximum number of rotational modes to be used in a given calculation is specified a priori. The computed Reynolds stress converges to the theoretical result derived by Batchelor and Proudman [Quart. J. Mech. Appl. Math. 7, 83 (1954), 10.1093/qjmam/7.1.83] if a sufficiently large maximum number of rotational modes is utilized; more modes are required to recover the solution at later times. The emergence and evolution of the underlying multidimensional space of functions is presented here using a 64-mode calculation. Alternative implications for modeling strategies are discussed.

Computational Systems for Multidisciplinary Applications

NASA Technical Reports Server (NTRS)

Soni, Bharat; Haupt, Tomasz; Koomullil, Roy; Luke, Edward; Thompson, David

2002-01-01

In this paper, we briefly describe our efforts to develop complex simulation systems. We focus first on four key infrastructure items: enterprise computational services, simulation synthesis, geometry modeling and mesh generation, and a fluid flow solver for arbitrary meshes. We conclude by presenting three diverse applications developed using these technologies.

Research and realization of signal simulation on virtual instrument

NASA Astrophysics Data System (ADS)

Zhao, Qi; He, Wenting; Guan, Xiumei

2010-02-01

In the engineering project, arbitrary waveform generator controlled by software interface is needed by simulation and test. This article discussed the program using the SCPI (Standard Commands For Programmable Instruments) protocol and the VISA (Virtual Instrument System Architecture) library to control the Agilent signal generator (Agilent N5182A) by instrument communication over the LAN interface. The program can conduct several signal generations such as CW (continuous wave), AM (amplitude modulation), FM (frequency modulation), ΦM (phase modulation), Sweep. As the result, the program system has good operability and portability.

Geometrical Method for the Calculation of Spherical Harmonics up to an Arbitrary Degree and Order

NASA Astrophysics Data System (ADS)

Svehla, D.

2009-12-01

We introduce a novel method for the computation and rotation of spherical harmonics, Legendre polynomials and associated Legendre functions without making use of recursive relations. This novel geometrical approach allows calculation of spherical harmonics without any numerical instability up to an arbitrary degree and order, i.e. up to a degree and order 1e6 and beyond. It is shown, that spherical harmonics can be treated as vectors in Hilbert hyperspace leading to the unitary hermitian rotation matrices with geometric properties.

On the arbitrary l-wave solutions of the deformed hyperbolic manning-rosen potential including an improved approximation to the orbital centrifugal term

NASA Astrophysics Data System (ADS)

Xu, Chun-Long; Zhang, Min-Cang

2017-01-01

The arbitrary l-wave solutions to the Schrödinger equation for the deformed hyperbolic Manning-Rosen potential is investigated analytically by using the Nikiforov-Uvarov method, the centrifugal term is treated with an improved Greene and Aldrich's approximation scheme. The wavefunctions depend on the deformation parameter q, which is expressed in terms of the Jocobi polynomial or the hypergeometric function. The bound state energy is obtained, and the discrete spectrum is shown to be independent of the deformation parameter q.

[ital N]-string vertices in string field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bordes, J.; Abdurrahman, A.; Anton, F.

1994-03-15

We give the general form of the vertex corresponding to the interaction of an arbitrary number of strings. The technique employed relies on the comma'' representation of string field theory where string fields and interactions are represented as matrices and operations between them such as multiplication and trace. The general formulation presented here shows that the interaction vertex of [ital N] strings, for any arbitrary [ital N], is given as a function of particular combinations of matrices corresponding to the change of representation between the full string and the half string degrees of freedom.

Matriarch: A Python Library for Materials Architecture.

PubMed

Giesa, Tristan; Jagadeesan, Ravi; Spivak, David I; Buehler, Markus J

2015-10-12

Biological materials, such as proteins, often have a hierarchical structure ranging from basic building blocks at the nanoscale (e.g., amino acids) to assembled structures at the macroscale (e.g., fibers). Current software for materials engineering allows the user to specify polypeptide chains and simple secondary structures prior to molecular dynamics simulation, but is not flexible in terms of the geometric arrangement of unequilibrated structures. Given some knowledge of a larger-scale structure, instructing the software to create it can be very difficult and time-intensive. To this end, the present paper reports a mathematical language, using category theory, to describe the architecture of a material, i.e., its set of building blocks and instructions for combining them. While this framework applies to any hierarchical material, here we concentrate on proteins. We implement this mathematical language as an open-source Python library called Matriarch. It is a domain-specific language that gives the user the ability to create almost arbitrary structures with arbitrary amino acid sequences and, from them, generate Protein Data Bank (PDB) files. In this way, Matriarch is more powerful than commercial software now available. Matriarch can be used in tandem with molecular dynamics simulations and helps engineers design and modify biologically inspired materials based on their desired functionality. As a case study, we use our software to alter both building blocks and building instructions for tropocollagen, and determine their effect on its structure and mechanical properties.

Evaluation of realistic layouts for next generation on-scalp MEG: spatial information density maps.

PubMed

Riaz, Bushra; Pfeiffer, Christoph; Schneiderman, Justin F

2017-08-01

While commercial magnetoencephalography (MEG) systems are the functional neuroimaging state-of-the-art in terms of spatio-temporal resolution, MEG sensors have not changed significantly since the 1990s. Interest in newer sensors that operate at less extreme temperatures, e.g., high critical temperature (high-T c ) SQUIDs, optically-pumped magnetometers, etc., is growing because they enable significant reductions in head-to-sensor standoff (on-scalp MEG). Various metrics quantify the advantages of on-scalp MEG, but a single straightforward one is lacking. Previous works have furthermore been limited to arbitrary and/or unrealistic sensor layouts. We introduce spatial information density (SID) maps for quantitative and qualitative evaluations of sensor arrays. SID-maps present the spatial distribution of information a sensor array extracts from a source space while accounting for relevant source and sensor parameters. We use it in a systematic comparison of three practical on-scalp MEG sensor array layouts (based on high-T c SQUIDs) and the standard Elekta Neuromag TRIUX magnetometer array. Results strengthen the case for on-scalp and specifically high-T c SQUID-based MEG while providing a path for the practical design of future MEG systems. SID-maps are furthermore general to arbitrary magnetic sensor technologies and source spaces and can thus be used for design and evaluation of sensor arrays for magnetocardiography, magnetic particle imaging, etc.

Generation of quantum entangled states in nonlinear plasmonic structures and metamaterials (Presentation Recording)

NASA Astrophysics Data System (ADS)

Poddubny, Alexander N.; Sukhorukov, Andrey A.

2015-09-01

The practical development of quantum plasmonic circuits incorporating non-classical interference [1] and sources of entangled states calls for a versatile quantum theoretical framework which can fully describe the generation and detection of entangled photons and plasmons. However, majority of the presently used theoretical approaches are typically limited to the toy models assuming loss-less and nondispersive elements or including just a few resonant modes. Here, we present a rigorous Green function approach describing entangled photon-plasmon state generation through spontaneous wave mixing in realistic metal-dielectric nanostructures. Our approach is based on the local Huttner-Barnett quantization scheme [2], which enables problem formulation in terms of a Hermitian Hamiltonian where the losses and dispersion are fully encoded in the electromagnetic Green functions. Hence, the problem can be addressed by the standard quantum mechanical perturbation theory, overcoming mathematical difficulties associated with other quantization schemes. We derive explicit expressions with clear physical meaning for the spatially dependent two-photon detection probability, single-photon detection probability and single-photon density matrix. In the limiting case of low-loss nondispersive waveguides our approach reproduces the previous results [3,4]. Importantly, our technique is far more general and can quantitatively describe generation and detection of spatially-entangled photons in arbitrary metal-dielectric structures taking into account actual losses and dispersion. This is essential to perform the design and optimization of plasmonic structures for generation and control of quantum entangled states. [1] J.S. Fakonas, H. Lee, Y.A. Kelaita and H.A. Atwater, Nature Photonics 8, 317(2014) [2] W. Vogel and D.-G. Welsch, Quantum Optics, Wiley (2006). [3] D.A. Antonosyan, A.S. Solntsev and A.A. Sukhorukov, Phys. Rev. A 90 043845 (2014) [4] L.-G. Helt, J.E. Sipe and M.J. Steel, arXiv: 1407.4219

Dielectric function and plasmons in graphene: A self-consistent-field calculation within a Markovian master equation formalism

DOE PAGES

Karimi, F.; Davoody, A. H.; Knezevic, I.

2016-05-12

We introduce a method for calculating the dielectric function of nanostructures with an arbitrary band dispersion and Bloch wave functions. The linear response of a dissipative electronic system to an external electromagnetic field is calculated by a self-consistent-field approach within a Markovian master equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations. The SCF-MMEF accurately accounts for several concurrent scattering mechanisms. The method captures interband electron-hole-pair generation, as well as the interband and intraband electron scattering with phonons and impurities. We employ the SCF-MMEF to calculate the dielectric function, complex conductivity, and loss function for supported graphene. From the loss-function maximum,more » we obtain plasmon dispersion and propagation length for different substrate types [nonpolar diamondlike carbon (DLC) and polar SiO 2 and hBN], impurity densities, carrier densities, and temperatures. Plasmons on the two polar substrates are suppressed below the highest surface phonon energy, while the spectrum is broad on the nonpolar DLC. Plasmon propagation lengths are comparable on polar and nonpolar substrates and are on the order of tens of nanometers, considerably shorter than previously reported. As a result, they improve with fewer impurities, at lower temperatures, and at higher carrier densities.« less

Eshelby's problem of polygonal inclusions with polynomial eigenstrains in an anisotropic magneto-electro-elastic full plane

PubMed Central

Lee, Y.-G.; Zou, W.-N.; Pan, E.

2015-01-01

This paper presents a closed-form solution for the arbitrary polygonal inclusion problem with polynomial eigenstrains of arbitrary order in an anisotropic magneto-electro-elastic full plane. The additional displacements or eigendisplacements, instead of the eigenstrains, are assumed to be a polynomial with general terms of order M+N. By virtue of the extended Stroh formulism, the induced fields are expressed in terms of a group of basic functions which involve boundary integrals of the inclusion domain. For the special case of polygonal inclusions, the boundary integrals are carried out explicitly, and their averages over the inclusion are also obtained. The induced fields under quadratic eigenstrains are mostly analysed in terms of figures and tables, as well as those under the linear and cubic eigenstrains. The connection between the present solution and the solution via the Green's function method is established and numerically verified. The singularity at the vertices of the arbitrary polygon is further analysed via the basic functions. The general solution and the numerical results for the constant, linear, quadratic and cubic eigenstrains presented in this paper enable us to investigate the features of the inclusion and inhomogeneity problem concerning polynomial eigenstrains in semiconductors and advanced composites, while the results can further serve as benchmarks for future analyses of Eshelby's inclusion problem. PMID:26345141

Enhanced equivalence class formation by the delay and relational functions of meaningful stimuli.

PubMed

Arntzen, Erik; Nartey, Richard K; Fields, Lanny

2015-05-01

Undergraduates in six groups of 10 attempted to form three 3-node 5-member equivalence classes (A → B → C → D → E) under the simultaneous protocol. In five of six groups, all stimuli were abstract shapes; in the PIC group, C stimuli were pictures with the remainder being abstract shapes. Before class formation, participants in the Identity-S and Identity-D groups were given preliminary training to form identity conditional discriminations with the C stimuli using simultaneous and 6 s delayed matching-to-sample procedures, respectively. In the Arbitrary-S and Arbitrary-D groups, before class formation, arbitrary conditional discriminations were formed between C and X stimuli using simultaneous and 6 s delayed matching-to-sample procedures, respectively. With no preliminary training, classes in the PIC and ABS groups were formed by 80% and 0% of participants, respectively. After preliminary training, class formation (yield) increased with delay, regardless of relational type. For each of the two delays, yield was slightly greater after forming arbitrary- instead of identity-relations. Yield was greatest, however, when a class contained a meaningful stimulus (PIC). During failed class formation, probes produced experimenter-defined relations, participant-defined relations, and unsystematic responding; delay, but not the relation type in preliminary training influenced relational and indeterminate responding. These results suggest how meaningful stimuli enhance equivalence class formation. © Society for the Experimental Analysis of Behavior.

Vlasov Treatment of Coherent Synchrotron Radiation from Arbitrary Planar Orbits

DOE Office of Scientific and Technical Information (OSTI.GOV)

Warnock, R

2004-09-22

We study the influence of coherent synchrotron radiation (CSR) on particle bunches traveling on arbitrary planar orbits between parallel conducting plates. The plates represent shielding due to the vacuum chamber. The vertical distribution of charge is an arbitrary fixed function. Our goal is to follow the time evolution of the phase space distribution by solving the Vlasov-Maxwell equations in the time domain. This provides simulations with lower numerical noise than the macroparticle method, and allows one to study such issues as emittance degradation and microbunching due to CSR in bunch compressors. The fields excited by the bunch are computed inmore » the laboratory frame from a new formula that leads to much simpler computations than the usual retarded potentials or Lienard-Wiechert potentials. The nonlinear Vlasov equation, formulated in the interaction picture, is integrated in the beam frame by approximating the Perron-Frobenius operator. The distribution function is represented by B-splines, in a scheme preserving positivity and normalization of the distribution. For application to a chicane bunch compressor we take steps to deal with energy chirp, an initial near-perfect correlation of energy with position in the bunch.« less

Automated geometric optimization for robotic HIFU treatment of liver tumors.

PubMed

Williamson, Tom; Everitt, Scott; Chauhan, Sunita

2018-05-01

High intensity focused ultrasound (HIFU) represents a non-invasive method for the destruction of cancerous tissue within the body. Heating of targeted tissue by focused ultrasound transducers results in the creation of ellipsoidal lesions at the target site, the locations of which can have a significant impact on treatment outcomes. Towards this end, this work describes a method for the optimization of lesion positions within arbitrary tumors, with specific anatomical constraints. A force-based optimization framework was extended to the case of arbitrary tumor position and constrained orientation. Analysis of the approximate reachable treatment volume for the specific case of treatment of liver tumors was performed based on four transducer configurations and constraint conditions derived. Evaluation was completed utilizing simplified spherical and ellipsoidal tumor models and randomly generated tumor volumes. The total volume treated, lesion overlap and healthy tissue ablated was evaluated. Two evaluation scenarios were defined and optimized treatment plans assessed. The optimization framework resulted in improvements of up to 10% in tumor volume treated, and reductions of up to 20% in healthy tissue ablated as compared to the standard lesion rastering approach. Generation of optimized plans proved feasible for both sub- and intercostally located tumors. This work describes an optimized method for the planning of lesion positions during HIFU treatment of liver tumors. The approach allows the determination of optimal lesion locations and orientations, and can be applied to arbitrary tumor shapes and sizes. Copyright © 2018 Elsevier Ltd. All rights reserved.

Amortization does not enhance the max-Rains information of a quantum channel

NASA Astrophysics Data System (ADS)

Berta, Mario; Wilde, Mark M.

2018-05-01

Given an entanglement measure E, the entanglement of a quantum channel is defined as the largest amount of entanglement E that can be generated from the channel, if the sender and receiver are not allowed to share a quantum state before using the channel. The amortized entanglement of a quantum channel is defined as the largest net amount of entanglement E that can be generated from the channel, if the sender and receiver are allowed to share an arbitrary state before using the channel. Our main technical result is that amortization does not enhance the entanglement of an arbitrary quantum channel, when entanglement is quantified by the max-Rains relative entropy. We prove this statement by employing semi-definite programming (SDP) duality and SDP formulations for the max-Rains relative entropy and a channel’s max-Rains information, found recently in Wang et al (arXiv:1709.00200). The main application of our result is a single-letter, strong converse, and efficiently computable upper bound on the capacity of a quantum channel for transmitting qubits when assisted by positive-partial-transpose preserving (PPT-P) channels between every use of the channel. As the class of local operations and classical communication (LOCC) is contained in PPT-P, our result establishes a benchmark for the LOCC-assisted quantum capacity of an arbitrary quantum channel, which is relevant in the context of distributed quantum computation and quantum key distribution.

A Ku band pulsed electron paramagnetic resonance spectrometer using an arbitrary waveform generator for quantum control experiments at millikelvin temperatures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yap, Yung Szen, E-mail: yungszen@utm.my; Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor; Tabuchi, Yutaka

2015-06-15

We present a 17 GHz (Ku band) arbitrary waveform pulsed electron paramagnetic resonance spectrometer for experiments down to millikelvin temperatures. The spectrometer is located at room temperature, while the resonator is placed either in a room temperature magnet or inside a cryogen-free dilution refrigerator; the operating temperature range of the dilution unit is from ca. 10 mK to 8 K. This combination provides the opportunity to perform quantum control experiments on electron spins in the pure-state regime. At 0.6 T, spin echo experiments were carried out using γ-irradiated quartz glass from 1 K to 12.3 mK. With decreasing temperatures, wemore » observed an increase in spin echo signal intensities due to increasing spin polarizations, in accordance with theoretical predictions. Through experimental data fitting, thermal spin polarization at 100 mK was estimated to be at least 99%, which was almost pure state. Next, to demonstrate the ability to create arbitrary waveform pulses, we generate a shaped pulse by superposing three Gaussian pulses of different frequencies. The resulting pulse was able to selectively and coherently excite three different spin packets simultaneously—a useful ability for analyzing multi-spin system and for controlling a multi-qubit quantum computer. By applying this pulse to the inhomogeneously broadened sample, we obtain three well-resolved excitations at 8 K, 1 K, and 14 mK.« less

Three-photon states in nonlinear crystal superlattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Antonosyan, D. A.; Kryuchkyan, G. Yu.; Institute for Physical Researches, National Academy of Sciences Ashtarak-2, 0203 Ashtarak

2011-04-15

It has been a longstanding goal in quantum optics to realize controllable sources generating joint multiphoton states, particularly photon triplet with arbitrary spectral characteristics. We demonstrate that such sources can be realized via cascaded parametric down-conversion (PDC) in superlattice structures of nonlinear and linear segments. We consider a scheme that involves two parametric processes--{omega}{sub 0{yields}{omega}1}+{omega}{sub 2}, {omega}{sub 2{yields}{omega}1}+{omega}{sub 1} under pulsed pump--and investigate the spontaneous creation of a photon triplet as well as the generation of high-intensity mode in intracavity three-photon splitting. We show the preparation of Greenberger-Horne-Zeilinger polarization-entangled states in cascaded type-II and type-I PDC in the framework ofmore » considering the dual-grid structure that involves two periodically poled crystals. We demonstrate the method of compensation of the dispersive effects in nonlinear segments by appropriately chosen linear dispersive segments of superlattice for preparation of the heralded joint states of two polarized photons. In the case of intracavity three-photon splitting, we concentrate on the investigation of photon-number distributions, third-order photon-number correlation function, as well as the Wigner functions. These quantities are observed both for short interaction time intervals and the over-transient regime, when dissipative effects are essential.« less

Vehicular road influence areas

NASA Astrophysics Data System (ADS)

Huertas, María E.; Huertas, José I.; Valencia, Alexander

2017-02-01

Vehicle operation over paved and unpaved roads is an emission source that significantly contributes to air pollution. Emissions are derived from vehicle exhaust pipes and re-suspension of particulate matter generated by wind erosion and tire to road surface interactions. Environmental authorities require a methodology to evaluate road impact areas, which enable managers to initiate counter-measures, particularly under circumstances where historic meteorological and/or air quality data is unavailable. The present study describes an analytical and experimental work developed to establish a simplified methodology to estimate the area influenced by vehicular roads. AERMOD was chosen to model pollutant dispersion generated by two roads of common attributes (straight road over flat terrain) under the effects of several arbitrary chosen weather conditions. The resulting pollutant concentration vs. Distance curves collapsed into a single curve when concentration and distance were expressed as dimensionless numbers and this curve can be described by a beta distribution function. This result implied that average concentration at a given distance was proportional to emission intensity and that it showed minor sensitivity to meteorological conditions. Therefore, road influence was defined by the area adjacent to the road limited by distance at which the beta distribution function equaled the limiting value specified by the national air quality standard for the pollutant under consideration.

Atom probe trajectory mapping using experimental tip shape measurements.

PubMed

Haley, D; Petersen, T; Ringer, S P; Smith, G D W

2011-11-01

Atom probe tomography is an accurate analytical and imaging technique which can reconstruct the complex structure and composition of a specimen in three dimensions. Despite providing locally high spatial resolution, atom probe tomography suffers from global distortions due to a complex projection function between the specimen and detector which is different for each experiment and can change during a single run. To aid characterization of this projection function, this work demonstrates a method for the reverse projection of ions from an arbitrary projection surface in 3D space back to an atom probe tomography specimen surface. Experimental data from transmission electron microscopy tilt tomography are combined with point cloud surface reconstruction algorithms and finite element modelling to generate a mapping back to the original tip surface in a physically and experimentally motivated manner. As a case study, aluminium tips are imaged using transmission electron microscopy before and after atom probe tomography, and the specimen profiles used as input in surface reconstruction methods. This reconstruction method is a general procedure that can be used to generate mappings between a selected surface and a known tip shape using numerical solutions to the electrostatic equation, with quantitative solutions to the projection problem readily achievable in tens of minutes on a contemporary workstation. © 2011 The Authors Journal of Microscopy © 2011 Royal Microscopical Society.

On the composition of an arbitrary collection of SU(2) spins: an enumerative combinatoric approach

NASA Astrophysics Data System (ADS)

Gyamfi, J. A.; Barone, V.

2018-03-01

The whole enterprise of spin compositions can be recast as simple enumerative combinatoric problems. We show here that enumerative combinatorics (Stanley 2011 Enumerative Combinatorics (Cambridge Studies in Advanced Mathematics vol 1) (Cambridge: Cambridge University Press)) is a natural setting for spin composition, and easily leads to very general analytic formulae—many of which hitherto not present in the literature. Based on it, we propose three general methods for computing spin multiplicities; namely, (1) the multi-restricted composition, (2) the generalized binomial and (3) the generating function methods. Symmetric and anti-symmetric compositions of SU(2) spins are also discussed, using generating functions. Of particular importance is the observation that while the common Clebsch-Gordan decomposition—which considers the spins as distinguishable—is related to integer compositions, the symmetric and anti-symmetric compositions (where one considers the spins as indistinguishable) are obtained considering integer partitions. The integers in question here are none other than the occupation numbers of the Holstein-Primakoff bosons. The pervasiveness of q-analogues in our approach is a testament to the fundamental role they play in spin compositions. In the appendix, some new results in the power series representation of Gaussian polynomials (or q-binomial coefficients)—relevant to symmetric and antisymmetric compositions—are presented.

On the Problem of Deformed Spherical Systems in Modified Newtonian Dynamics

NASA Astrophysics Data System (ADS)

Ko, Chung-Ming

2016-04-01

Based on Newtonian dynamics, observations show that the luminous masses of astrophysical objects that are the size of a galaxy or larger are not enough to generate the measured motions which they supposedly determine. This is typically attributed to the existence of dark matter, which possesses mass but does not radiate (or absorb radiation). Alternatively, the mismatch can be explained if the underlying dynamics is not Newtonian. Within this conceptual scheme, Modified Newtonian Dynamics (MOND) is a successful theoretical paradigm. MOND is usually expressed in terms of a nonlinear Poisson equation, which is difficult to analyze for arbitrary matter distributions. We study the MONDian gravitational field generated by slightly non-spherically symmetric mass distributions based on the fact that both Newtonian and MONDian fields are conservative (which we refer to as the compatibility condition). As the non-relativistic version of MOND has two different formulations (AQUAL and QuMOND) and the compatibility condition can be expressed in two ways, there are four approaches to the problem in total. The method involves solving a suitably defined linear deformation potential, which generally depends on the choice of MOND interpolation function. However, for some specific form of the deformation potential, the solution is independent of the interpolation function.

AMPX: a modular code system for generating coupled multigroup neutron-gamma libraries from ENDF/B

DOE Office of Scientific and Technical Information (OSTI.GOV)

Greene, N.M.; Lucius, J.L.; Petrie, L.M.

1976-03-01

AMPX is a modular system for producing coupled multigroup neutron-gamma cross section sets. Basic neutron and gamma cross-section data for AMPX are obtained from ENDF/B libraries. Most commonly used operations required to generate and collapse multigroup cross-section sets are provided in the system. AMPX is flexibly dimensioned; neutron group structures, and gamma group structures, and expansion orders to represent anisotropic processes are all arbitrary and limited only by available computer core and budget. The basic processes provided will (1) generate multigroup neutron cross sections; (2) generate multigroup gamma cross sections; (3) generate gamma yields for gamma-producing neutron interactions; (4) combinemore » neutron cross sections, gamma cross sections, and gamma yields into final ''coupled sets''; (5) perform one-dimensional discrete ordinates transport or diffusion theory calculations for neutrons and gammas and, on option, collapse the cross sections to a broad-group structure, using the one-dimensional results as weighting functions; (6) plot cross sections, on option, to facilitate the ''evaluation'' of a particular multigroup set of data; (7) update and maintain multigroup cross section libraries in such a manner as to make it not only easy to combine new data with previously processed data but also to do it in a single pass on the computer; and (8) output multigroup cross sections in convenient formats for other codes. (auth)« less

An automatic generation of non-uniform mesh for CFD analyses of image-based multiscale human airway models

NASA Astrophysics Data System (ADS)

Miyawaki, Shinjiro; Tawhai, Merryn H.; Hoffman, Eric A.; Lin, Ching-Long

2014-11-01

The authors have developed a method to automatically generate non-uniform CFD mesh for image-based human airway models. The sizes of generated tetrahedral elements vary in both radial and longitudinal directions to account for boundary layer and multiscale nature of pulmonary airflow. The proposed method takes advantage of our previously developed centerline-based geometry reconstruction method. In order to generate the mesh branch by branch in parallel, we used the open-source programs Gmsh and TetGen for surface and volume meshes, respectively. Both programs can specify element sizes by means of background mesh. The size of an arbitrary element in the domain is a function of wall distance, element size on the wall, and element size at the center of airway lumen. The element sizes on the wall are computed based on local flow rate and airway diameter. The total number of elements in the non-uniform mesh (10 M) was about half of that in the uniform mesh, although the computational time for the non-uniform mesh was about twice longer (170 min). The proposed method generates CFD meshes with fine elements near the wall and smooth variation of element size in longitudinal direction, which are required, e.g., for simulations with high flow rate. NIH Grants R01-HL094315, U01-HL114494, and S10-RR022421. Computer time provided by XSEDE.

Biotechnological mass production of DNA origami

NASA Astrophysics Data System (ADS)

Praetorius, Florian; Kick, Benjamin; Behler, Karl L.; Honemann, Maximilian N.; Weuster-Botz, Dirk; Dietz, Hendrik

2017-12-01

DNA nanotechnology, in particular DNA origami, enables the bottom-up self-assembly of micrometre-scale, three-dimensional structures with nanometre-precise features. These structures are customizable in that they can be site-specifically functionalized or constructed to exhibit machine-like or logic-gating behaviour. Their use has been limited to applications that require only small amounts of material (of the order of micrograms), owing to the limitations of current production methods. But many proposed applications, for example as therapeutic agents or in complex materials, could be realized if more material could be used. In DNA origami, a nanostructure is assembled from a very long single-stranded scaffold molecule held in place by many short single-stranded staple oligonucleotides. Only the bacteriophage-derived scaffold molecules are amenable to scalable and efficient mass production; the shorter staple strands are obtained through costly solid-phase synthesis or enzymatic processes. Here we show that single strands of DNA of virtually arbitrary length and with virtually arbitrary sequences can be produced in a scalable and cost-efficient manner by using bacteriophages to generate single-stranded precursor DNA that contains target strand sequences interleaved with self-excising ‘cassettes’, with each cassette comprising two Zn2+-dependent DNA-cleaving DNA enzymes. We produce all of the necessary single strands of DNA for several DNA origami using shaker-flask cultures, and demonstrate end-to-end production of macroscopic amounts of a DNA origami nanorod in a litre-scale stirred-tank bioreactor. Our method is compatible with existing DNA origami design frameworks and retains the modularity and addressability of DNA origami objects that are necessary for implementing custom modifications using functional groups. With all of the production and purification steps amenable to scaling, we expect that our method will expand the scope of DNA nanotechnology in many areas of science and technology.

Mapping gravitational-wave backgrounds using methods from CMB analysis: Application to pulsar timing arrays

NASA Astrophysics Data System (ADS)

Gair, Jonathan; Romano, Joseph D.; Taylor, Stephen; Mingarelli, Chiara M. F.

2014-10-01

We describe an alternative approach to the analysis of gravitational-wave backgrounds, based on the formalism used to characterize the polarization of the cosmic microwave background. In contrast to standard analyses, this approach makes no assumptions about the nature of the background and so has the potential to reveal much more about the physical processes that generated it. An arbitrary background can be decomposed into modes whose angular dependence on the sky is given by gradients and curls of spherical harmonics. We derive the pulsar timing overlap reduction functions for the individual modes, which are given by simple combinations of spherical harmonics evaluated at the pulsar locations. We show how these can be used to recover the components of an arbitrary background, giving explicit results for both isotropic and anisotropic uncorrelated backgrounds. We also find that the response of a pulsar timing array to curl modes is identically zero, so half of the gravitational-wave sky will never be observed using pulsar timing, no matter how many pulsars are included in the array. An isotropic, unpolarized and uncorrelated background can be accurately represented using only three modes, and so a search of this type will be only slightly more complicated than the standard cross-correlation search using the Hellings and Downs overlap reduction function. However, by measuring the components of individual modes of the background and checking for consistency with isotropy, this approach has the potential to reveal much more information. Each individual mode on its own describes a background that is correlated between different points on the sky. A measurement of the components that indicates the presence of correlations in the background on large angular scales would suggest startling new physics.

Biotechnological mass production of DNA origami.

PubMed

Praetorius, Florian; Kick, Benjamin; Behler, Karl L; Honemann, Maximilian N; Weuster-Botz, Dirk; Dietz, Hendrik

2017-12-06

DNA nanotechnology, in particular DNA origami, enables the bottom-up self-assembly of micrometre-scale, three-dimensional structures with nanometre-precise features. These structures are customizable in that they can be site-specifically functionalized or constructed to exhibit machine-like or logic-gating behaviour. Their use has been limited to applications that require only small amounts of material (of the order of micrograms), owing to the limitations of current production methods. But many proposed applications, for example as therapeutic agents or in complex materials, could be realized if more material could be used. In DNA origami, a nanostructure is assembled from a very long single-stranded scaffold molecule held in place by many short single-stranded staple oligonucleotides. Only the bacteriophage-derived scaffold molecules are amenable to scalable and efficient mass production; the shorter staple strands are obtained through costly solid-phase synthesis or enzymatic processes. Here we show that single strands of DNA of virtually arbitrary length and with virtually arbitrary sequences can be produced in a scalable and cost-efficient manner by using bacteriophages to generate single-stranded precursor DNA that contains target strand sequences interleaved with self-excising 'cassettes', with each cassette comprising two Zn 2+ -dependent DNA-cleaving DNA enzymes. We produce all of the necessary single strands of DNA for several DNA origami using shaker-flask cultures, and demonstrate end-to-end production of macroscopic amounts of a DNA origami nanorod in a litre-scale stirred-tank bioreactor. Our method is compatible with existing DNA origami design frameworks and retains the modularity and addressability of DNA origami objects that are necessary for implementing custom modifications using functional groups. With all of the production and purification steps amenable to scaling, we expect that our method will expand the scope of DNA nanotechnology in many areas of science and technology.

Global stability and exact solution of an arbitrary-solute nonlinear cellular mass transport system.

PubMed

Benson, James D

2014-12-01

The prediction of the cellular state as a function of extracellular concentrations and temperatures has been of interest to physiologists for nearly a century. One of the most widely used models in the field is one where mass flux is linearly proportional to the concentration difference across the membrane. These fluxes define a nonlinear differential equation system for the intracellular state, which when coupled with appropriate initial conditions, define the intracellular state as a function of the extracellular concentrations of both permeating and nonpermeating solutes. Here we take advantage of a reparametrization scheme to extend existing stability results to a more general setting and to a develop analytical solutions to this model for an arbitrary number of extracellular solutes. Copyright © 2014 Elsevier Inc. All rights reserved.

Efficient scheme for parametric fitting of data in arbitrary dimensions.

PubMed

Pang, Ning-Ning; Tzeng, Wen-Jer; Kao, Hisen-Ching

2008-07-01

We propose an efficient scheme for parametric fitting expressed in terms of the Legendre polynomials. For continuous systems, our scheme is exact and the derived explicit expression is very helpful for further analytical studies. For discrete systems, our scheme is almost as accurate as the method of singular value decomposition. Through a few numerical examples, we show that our algorithm costs much less CPU time and memory space than the method of singular value decomposition. Thus, our algorithm is very suitable for a large amount of data fitting. In addition, the proposed scheme can also be used to extract the global structure of fluctuating systems. We then derive the exact relation between the correlation function and the detrended variance function of fluctuating systems in arbitrary dimensions and give a general scaling analysis.

Adaptive Fuzzy Control Design for Stochastic Nonlinear Switched Systems With Arbitrary Switchings and Unmodeled Dynamics.

PubMed

Li, Yongming; Sui, Shuai; Tong, Shaocheng

2017-02-01

This paper deals with the problem of adaptive fuzzy output feedback control for a class of stochastic nonlinear switched systems. The controlled system in this paper possesses unmeasured states, completely unknown nonlinear system functions, unmodeled dynamics, and arbitrary switchings. A state observer which does not depend on the switching signal is constructed to tackle the unmeasured states. Fuzzy logic systems are employed to identify the completely unknown nonlinear system functions. Based on the common Lyapunov stability theory and stochastic small-gain theorem, a new robust adaptive fuzzy backstepping stabilization control strategy is developed. The stability of the closed-loop system on input-state-practically stable in probability is proved. The simulation results are given to verify the efficiency of the proposed fuzzy adaptive control scheme.

Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel

1997-01-01

This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.

Photochemical preparation of sub-wavelength heterogeneous laser-induced periodic surface structures.

PubMed

Kim, Hee-Cheol; Reinhardt, Hendrik; Hillebrecht, Pierre; Hampp, Norbert A

2012-04-17

Laser-induced periodic surface structures (LIPSS) are a phenomenon caused by interaction of light with solid surfaces. We present a photochemical concept which uses LIPSS-related light intensity patterns for the generation of heterogeneous nanostructures. The process facilitates arbitrary combinations of substrate and LIPSS-pattern materials. An efficient method for the generation of organometallic hybrid-nanowire arrays on porous anodic aluminum oxide is demonstrated. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning.

PubMed

Gorban, A N; Mirkes, E M; Zinovyev, A

2016-12-01

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L 1 norm or even sub-linear potentials corresponding to quasinorms L p (0

Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic half-space

DOE PAGES

Fabrikant, I.; Karapetian, E.; Kalinin, S. V.

2017-12-09

Here, we consider the problem of an arbitrary shaped rigid punch pressed against the boundary of a transversely isotropic half-space and interacting with an arbitrary flat crack or inclusion, located in the plane parallel to the boundary. The set of governing integral equations is derived for the most general conditions, namely the presence of both normal and tangential stresses under the punch, as well as general loading of the crack faces. In order to verify correctness of the derivations, two different methods were used to obtain governing integral equations: generalized method of images and utilization of the reciprocal theorem. Bothmore » methods gave the same results. Axisymmetric coaxial case of interaction between a rigid inclusion and a flat circular punch both centered along the z-axis is considered as an illustrative example. Most of the final results are presented in terms of elementary functions.« less

Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic half-space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fabrikant, I.; Karapetian, E.; Kalinin, S. V.

Here, we consider the problem of an arbitrary shaped rigid punch pressed against the boundary of a transversely isotropic half-space and interacting with an arbitrary flat crack or inclusion, located in the plane parallel to the boundary. The set of governing integral equations is derived for the most general conditions, namely the presence of both normal and tangential stresses under the punch, as well as general loading of the crack faces. In order to verify correctness of the derivations, two different methods were used to obtain governing integral equations: generalized method of images and utilization of the reciprocal theorem. Bothmore » methods gave the same results. Axisymmetric coaxial case of interaction between a rigid inclusion and a flat circular punch both centered along the z-axis is considered as an illustrative example. Most of the final results are presented in terms of elementary functions.« less

Exact stochastic unraveling of an optical coherence dynamics by cumulant expansion

NASA Astrophysics Data System (ADS)

Olšina, Jan; Kramer, Tobias; Kreisbeck, Christoph; Mančal, Tomáš

2014-10-01

A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space with respect to the coupling between the excited states of the molecule. The trajectories are weighted by a complex decoherence factor based on the second-order cumulant expansion of the environmental evolution. The method can be used with an arbitrary environment characterized by a general correlation function and arbitrary coupling strength. It is formally exact for harmonic environments, and it can be used with arbitrary temperature. Time evolution of an optically excited Frenkel exciton dimer representing a molecular exciton interacting with a charge transfer state is calculated by the proposed method. We calculate the evolution of the optical coherence elements of the density matrix and linear absorption spectrum, and compare them with the predictions of standard simulation methods.

Quantum spin dynamics with pairwise-tunable, long-range interactions

PubMed Central

Hung, C.-L.; González-Tudela, Alejandro; Cirac, J. Ignacio; Kimble, H. J.

2016-01-01

We present a platform for the simulation of quantum magnetism with full control of interactions between pairs of spins at arbitrary distances in 1D and 2D lattices. In our scheme, two internal atomic states represent a pseudospin for atoms trapped within a photonic crystal waveguide (PCW). With the atomic transition frequency aligned inside a band gap of the PCW, virtual photons mediate coherent spin–spin interactions between lattice sites. To obtain full control of interaction coefficients at arbitrary atom–atom separations, ground-state energy shifts are introduced as a function of distance across the PCW. In conjunction with auxiliary pump fields, spin-exchange versus atom–atom separation can be engineered with arbitrary magnitude and phase, and arranged to introduce nontrivial Berry phases in the spin lattice, thus opening new avenues for realizing topological spin models. We illustrate the broad applicability of our scheme by explicit construction for several well-known spin models. PMID:27496329

Time reversal of arbitrary photonic temporal modes via nonlinear optical frequency conversion

NASA Astrophysics Data System (ADS)

Raymer, Michael G.; Reddy, Dileep V.; van Enk, Steven J.; McKinstrie, Colin J.

2018-05-01

Single-photon wave packets can carry quantum information between nodes of a quantum network. An important general operation in photon-based quantum information systems is ‘blind’ reversal of a photon’s temporal wave packet envelope, that is, the ability to reverse an envelope without knowing the temporal state of the photon. We present an all-optical means for doing so, using nonlinear-optical frequency conversion driven by a short pump pulse. The process used may be sum-frequency generation or four-wave Bragg scattering. This scheme allows for quantum operations such as a temporal-mode parity sorter. We also verify that the scheme works for arbitrary states (not only single-photon ones) of an unknown wave packet.

The nonlinear gyroresonance interaction between energetic electrons and coherent VLF waves propagating at an arbitrary angle with respect to the earth's magnetic field

NASA Technical Reports Server (NTRS)

Bell, T. F.

1984-01-01

A theory is presented of the nonlinear gyroresonance interaction that takes place in the magnetosphere between energetic electrons and coherent VLF waves propagating in the whistler mode at an arbitrary angle psi with respect to the earth's magnetic field B-sub-0. Particularly examined is the phase trapping (PT) mechanism believed to be responsible for the generation of VLF emissions. It is concluded that near the magnetic equatorial plane gradients of psi may play a very important part in the PT process for nonducted waves. Predictions of a higher threshold value for PT for nonducted waves generally agree with experimental data concerning VLF emission triggering by nonducted waves.

SPIDYAN, a MATLAB library for simulating pulse EPR experiments with arbitrary waveform excitation.

PubMed

Pribitzer, Stephan; Doll, Andrin; Jeschke, Gunnar

2016-02-01

Frequency-swept chirp pulses, created with arbitrary waveform generators (AWGs), can achieve inversion over a range of several hundreds of MHz. Such passage pulses provide defined flip angles and increase sensitivity. The fact that spectra are not excited at once, but single transitions are passed one after another, can cause new effects in established pulse EPR sequences. We developed a MATLAB library for simulation of pulse EPR, which is especially suited for modeling spin dynamics in ultra-wideband (UWB) EPR experiments, but can also be used for other experiments and NMR. At present the command line controlled SPin DYnamics ANalysis (SPIDYAN) package supports one-spin and two-spin systems with arbitrary spin quantum numbers. By providing the program with appropriate spin operators and Hamiltonian matrices any spin system is accessible, with limits set only by available memory and computation time. Any pulse sequence using rectangular and linearly or variable-rate frequency-swept chirp pulses, including phase cycling can be quickly created. To keep track of spin evolution the user can choose from a vast variety of detection operators, including transition selective operators. If relaxation effects can be neglected, the program solves the Liouville-von Neumann equation and propagates spin density matrices. In the other cases SPIDYAN uses the quantum mechanical master equation and Liouvillians for propagation. In order to consider the resonator response function, which on the scale of UWB excitation limits bandwidth, the program includes a simple RLC circuit model. Another subroutine can compute waveforms that, for a given resonator, maintain a constant critical adiabaticity factor over the excitation band. Computational efficiency is enhanced by precomputing propagator lookup tables for the whole set of AWG output levels. The features of the software library are discussed and demonstrated with spin-echo and population transfer simulations. Copyright © 2016 Elsevier Inc. All rights reserved.

A Monte Carlo modeling on charging effect for structures with arbitrary geometries

NASA Astrophysics Data System (ADS)

Li, C.; Mao, S. F.; Zou, Y. B.; Li, Yong Gang; Zhang, P.; Li, H. M.; Ding, Z. J.

2018-04-01

Insulating materials usually suffer charging effects when irradiated by charged particles. In this paper, we present a Monte Carlo study on the charging effect caused by electron beam irradiation for sample structures with any complex geometry. When transporting in an insulating solid, electrons encounter elastic and inelastic scattering events; the Mott cross section and a Lorentz-type dielectric function are respectively employed to describe such scatterings. In addition, the band gap and the electron–long optical phonon interaction are taken into account. The electronic excitation in inelastic scattering causes generation of electron–hole pairs; these negative and positive charges establish an inner electric field, which in turn induces the drift of charges to be trapped by impurities, defects, vacancies etc in the solid, where the distributions of trapping sites are assumed to have uniform density. Under charging conditions, the inner electric field distorts electron trajectories, and the surface electric potential dynamically alters secondary electron emission. We present, in this work, an iterative modeling method for a self-consistent calculation of electric potential; the method has advantages in treating any structure with arbitrary complex geometry, in comparison with the image charge method—which is limited to a quite simple boundary geometry. Our modeling is based on: the combination of the finite triangle mesh method for an arbitrary geometry construction; a self-consistent method for the spatial potential calculation; and a full dynamic description for the motion of deposited charges. Example calculations have been done to simulate secondary electron yield of SiO2 for a semi-infinite solid, the charging for a heterostructure of SiO2 film grown on an Au substrate, and SEM imaging of a SiO2 line structure with rough surfaces and SiO2 nanoparticles with irregular shapes. The simulations have explored interesting interlaced charge layer distribution underneath the nanoparticle surface and the mechanism by which it is produced.

Miniature L-Band Radar Transceiver

NASA Technical Reports Server (NTRS)

McWatters, Dalia; Price, Douglas; Edelstein, Wendy

2007-01-01

A miniature L-band transceiver that operates at a carrier frequency of 1.25 GHz has been developed as part of a generic radar electronics module (REM) that would constitute one unit in an array of many identical units in a very-large-aperture phased-array antenna. NASA and the Department of Defense are considering the deployment of such antennas in outer space; the underlying principles of operation, and some of those of design, also are applicable on Earth. The large dimensions of the antennas make it advantageous to distribute radio-frequency electronic circuitry into elements of the arrays. The design of the REM is intended to implement the distribution. The design also reflects a requirement to minimize the size and weight of the circuitry in order to minimize the weight of any such antenna. Other requirements include making the transceiver robust and radiation-hard and minimizing power demand. Figure 1 depicts the functional blocks of the REM, including the L-band transceiver. The key functions of the REM include signal generation, frequency translation, amplification, detection, handling of data, and radar control and timing. An arbitrary-waveform generator that includes logic circuitry and a digital-to-analog converter (DAC) generates a linear-frequency-modulation chirp waveform. A frequency synthesizer produces local-oscillator signals used for frequency conversion and clock signals for the arbitrary-waveform generator, for a digitizer [that is, an analog-to-digital converter (ADC)], and for a control and timing unit. Digital functions include command, timing, telemetry, filtering, and high-rate framing and serialization of data for a high-speed scientific-data interface. The aforementioned digital implementation of filtering is a key feature of the REM architecture. Digital filters, in contradistinction to analog ones, provide consistent and temperature-independent performance, which is particularly important when REMs are distributed throughout a large array. Digital filtering also enables selection among multiple filter parameters as required for different radar operating modes. After digital filtering, data are decimated appropriately in order to minimize the data rate out of an antenna panel. The L-band transceiver (see Figure 2) includes a radio-frequency (RF)-to-baseband down-converter chain and an intermediate- frequency (IF)-to-RF up-converter chain. Transmit/receive (T/R) switches enable the use of a single feed to the antenna for both transmission and reception. The T/R switches also afford a built-in test capability by enabling injection of a calibration signal into the receiver chain. In order of decreasing priority, components of the transceiver were selected according to requirements of radiation hardness, then compactness, then low power. All of the RF components are radiation-hard. The noise figure (NF) was optimized to the extent that (1) a low-noise amplifier (LNA) (characterized by NF < 2 dB) was selected but (2) the receiver front-end T/R switches were selected for a high degree of isolation and acceptably low loss, regardless of the requirement to minimize noise.

Two-point resistance of an m × n resistor network with an arbitrary boundary and its application in RLC network

NASA Astrophysics Data System (ADS)

Zhi-Zhong, Tan

2016-05-01

A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform (RT) method, a problem that has never been resolved before, for the Green’s function technique and the Laplacian matrix approach are inapplicable to it. To have the exact solution of resistance is important but it is difficult to obtain under the condition of arbitrary boundary. Our result is directly expressed in a single summation and mainly composed of characteristic roots, which contain both finite and infinite cases. Further, the current distribution is given explicitly as a byproduct of the method. Our framework can be effectively applied to RLC networks. As an application to the LC network, we find that our formulation leads to the occurrence of resonances at h 1 = 1 - cos ϕ i - sin ϕ i cot n ϕ i . This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits. Project supported by the Prophase Preparatory Project of Natural Science Foundation of Nantong University, China (Grant No. 15ZY16).

Kurtosis parameter K of arbitrary electromagnetic beams propagating through non-Kolmogorov turbulence

NASA Astrophysics Data System (ADS)

Xu, Yonggen; Dan, Youquan; Yu, Jiayi; Cai, Yangjian

2017-10-01

General analytical formulae for the kurtosis parameters K (K parameters) of the arbitrary electromagnetic (AE) beams propagating through non-Kolmogorov turbulence are derived, and according to the unified theory of polarization and coherence, the effect of degree of polarization (DOP) of an electromagnetic beam on the K parameter is studied. The analytical formulae can be given by the second-order moments and fourth-order moments of the Wigner distribution function for AE beams at source plane, the two turbulence quantities relating to the spatial power spectrum, and the propagation distance. Our results can also be extended to the arbitrary beams and the arbitrary spatial power spectra of Kolmogorov turbulence or non-Kolmogorov turbulence. Taking the stochastic electromagnetic Gaussian Schell-model (SEGSM) beam as an example, the numerical examples indicate that the K parameters of a SEGSM beam in non-Kolmogorov turbulence depend on propagation distance, the beam parameters and turbulence parameters. The K parameter of a SEGM beam is more sensitive to effect of turbulence with smaller inner scale and generalized exponent parameter. A non-polarized light has the strongest ability of resisting turbulence (ART), however, a fully polarized SEGSM beam has the poorest ART.

Off-shell renormalization in Higgs effective field theories

NASA Astrophysics Data System (ADS)

Binosi, Daniele; Quadri, Andrea

2018-04-01

The off-shell one-loop renormalization of a Higgs effective field theory possessing a scalar potential ˜ {({Φ}^{\\dagger}Φ -υ^2/2)}^N with N arbitrary is presented. This is achieved by renormalizing the theory once reformulated in terms of two auxiliary fields X 1,2, which, due to the invariance under an extended Becchi-Rouet-Stora-Tyutin symmetry, are tightly constrained by functional identities. The latter allow in turn the explicit derivation of the mapping onto the original theory, through which the (divergent) multi-Higgs amplitude are generated in a purely algebraic fashion. We show that, contrary to naive expectations based on the loss of power counting renormalizability, the Higgs field undergoes a linear Standard Model like redefinition, and evaluate the renormalization of the complete set of Higgs self-coupling in the N → ∞ case.

Wave-packet continuum-discretization approach to ion-atom collisions including rearrangement: Application to differential ionization in proton-hydrogen scattering

NASA Astrophysics Data System (ADS)

Abdurakhmanov, I. B.; Bailey, J. J.; Kadyrov, A. S.; Bray, I.

2018-03-01

In this work, we develop a wave-packet continuum-discretization approach to ion-atom collisions that includes rearrangement processes. The total scattering wave function is expanded using a two-center basis built from wave-packet pseudostates. The exact three-body Schrödinger equation is converted into coupled-channel differential equations for time-dependent expansion coefficients. In the asymptotic region these time-dependent coefficients represent transition amplitudes for all processes including elastic scattering, excitation, ionization, and electron capture. The wave-packet continuum-discretization approach is ideal for differential ionization studies as it allows one to generate pseudostates with arbitrary energies and distribution. The approach is used to calculate the double differential cross section for ionization in proton collisions with atomic hydrogen. Overall good agreement with experiment is obtained for all considered cases.

Genomically Encoded Analog Memory with Precise In vivo DNA Writing in Living Cell Populations

PubMed Central

Farzadfard, Fahim; Lu, Timothy K.

2014-01-01

Cellular memory is crucial to many natural biological processes and for sophisticated synthetic-biology applications. Existing cellular memories rely on epigenetic switches or recombinases, which are limited in scalability and recording capacity. Here, we use the DNA of living cell populations as genomic ‘tape recorders’ for the analog and distributed recording of long-term event histories. We describe a platform for generating single-stranded DNA (ssDNA) in vivo in response to arbitrary transcriptional signals. When co-expressed with a recombinase, these intracellularly expressed ssDNAs target specific genomic DNA addresses, resulting in precise mutations that accumulate in cell populations as a function of the magnitude and duration of the inputs. This platform could enable long-term cellular recorders for environmental and biomedical applications, biological state machines, and enhanced genome engineering strategies. PMID:25395541

Node degree distribution in spanning trees

NASA Astrophysics Data System (ADS)

Pozrikidis, C.

2016-03-01

A method is presented for computing the number of spanning trees involving one link or a specified group of links, and excluding another link or a specified group of links, in a network described by a simple graph in terms of derivatives of the spanning-tree generating function defined with respect to the eigenvalues of the Kirchhoff (weighted Laplacian) matrix. The method is applied to deduce the node degree distribution in a complete or randomized set of spanning trees of an arbitrary network. An important feature of the proposed method is that the explicit construction of spanning trees is not required. It is shown that the node degree distribution in the spanning trees of the complete network is described by the binomial distribution. Numerical results are presented for the node degree distribution in square, triangular, and honeycomb lattices.

Autonomous exploration and mapping of unknown environments

NASA Astrophysics Data System (ADS)

Owens, Jason; Osteen, Phil; Fields, MaryAnne

2012-06-01

Autonomous exploration and mapping is a vital capability for future robotic systems expected to function in arbitrary complex environments. In this paper, we describe an end-to-end robotic solution for remotely mapping buildings. For a typical mapping system, an unmanned system is directed to enter an unknown building at a distance, sense the internal structure, and, barring additional tasks, while in situ, create a 2-D map of the building. This map provides a useful and intuitive representation of the environment for the remote operator. We have integrated a robust mapping and exploration system utilizing laser range scanners and RGB-D cameras, and we demonstrate an exploration and metacognition algorithm on a robotic platform. The algorithm allows the robot to safely navigate the building, explore the interior, report significant features to the operator, and generate a consistent map - all while maintaining localization.

Communication: Fitting potential energy surfaces with fundamental invariant neural network

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shao, Kejie; Chen, Jun; Zhao, Zhiqiang

A more flexible neural network (NN) method using the fundamental invariants (FIs) as the input vector is proposed in the construction of potential energy surfaces for molecular systems involving identical atoms. Mathematically, FIs finitely generate the permutation invariant polynomial (PIP) ring. In combination with NN, fundamental invariant neural network (FI-NN) can approximate any function to arbitrary accuracy. Because FI-NN minimizes the size of input permutation invariant polynomials, it can efficiently reduce the evaluation time of potential energy, in particular for polyatomic systems. In this work, we provide the FIs for all possible molecular systems up to five atoms. Potential energymore » surfaces for OH{sub 3} and CH{sub 4} were constructed with FI-NN, with the accuracy confirmed by full-dimensional quantum dynamic scattering and bound state calculations.« less

Scattering matrix of arbitrary tight-binding Hamiltonians

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ramírez, C., E-mail: carlos@ciencias.unam.mx; Medina-Amayo, L.A.

2017-03-15

A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kinds of fundamental structures is given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated.

GENESUS: a two-step sequence design program for DNA nanostructure self-assembly.

PubMed

Tsutsumi, Takanobu; Asakawa, Takeshi; Kanegami, Akemi; Okada, Takao; Tahira, Tomoko; Hayashi, Kenshi

2014-01-01

DNA has been recognized as an ideal material for bottom-up construction of nanometer scale structures by self-assembly. The generation of sequences optimized for unique self-assembly (GENESUS) program reported here is a straightforward method for generating sets of strand sequences optimized for self-assembly of arbitrarily designed DNA nanostructures by a generate-candidates-and-choose-the-best strategy. A scalable procedure to prepare single-stranded DNA having arbitrary sequences is also presented. Strands for the assembly of various structures were designed and successfully constructed, validating both the program and the procedure.

Realistic generation of natural phenomena based on video synthesis

NASA Astrophysics Data System (ADS)

Wang, Changbo; Quan, Hongyan; Li, Chenhui; Xiao, Zhao; Chen, Xiao; Li, Peng; Shen, Liuwei

2009-10-01

Research on the generation of natural phenomena has many applications in special effects of movie, battlefield simulation and virtual reality, etc. Based on video synthesis technique, a new approach is proposed for the synthesis of natural phenomena, including flowing water and fire flame. From the fire and flow video, the seamless video of arbitrary length is generated. Then, the interaction between wind and fire flame is achieved through the skeleton of flame. Later, the flow is also synthesized by extending the video textures using an edge resample method. Finally, we can integrate the synthesized natural phenomena into a virtual scene.

Stochastic transfer of polarized radiation in finite cloudy atmospheric media with reflective boundaries

NASA Astrophysics Data System (ADS)

Sallah, M.

2014-03-01

The problem of monoenergetic radiative transfer in a finite planar stochastic atmospheric medium with polarized (vector) Rayleigh scattering is proposed. The solution is presented for an arbitrary absorption and scattering cross sections. The extinction function of the medium is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. The joint probability distribution function of these Gaussian random variables is used to calculate the ensemble-averaged quantities, such as reflectivity and transmissivity, for an arbitrary correlation function. A modified Gaussian probability distribution function is also used to average the solution in order to exclude the probable negative values of the optical variable. Pomraning-Eddington approximation is used, at first, to obtain the deterministic analytical solution for both the total intensity and the difference function used to describe the polarized radiation. The problem is treated with specular reflecting boundaries and angular-dependent externally incident flux upon the medium from one side and with no flux from the other side. For the sake of comparison, two different forms of the weight function, which introduced to force the boundary conditions to be fulfilled, are used. Numerical results of the average reflectivity and average transmissivity are obtained for both Gaussian and modified Gaussian probability density functions at the different degrees of polarization.

Rapid convergence of optimal control in NMR using numerically-constructed toggling frames

NASA Astrophysics Data System (ADS)

Coote, Paul; Anklin, Clemens; Massefski, Walter; Wagner, Gerhard; Arthanari, Haribabu

2017-08-01

We present a numerical method for rapidly solving the Bloch equation for an arbitrary time-varying spin-1/2 Hamiltonian. The method relies on fast, vectorized computations such as summation and quaternion multiplication, rather than slow computations such as matrix exponentiation. A toggling frame is constructed in which the Hamiltonian is time-invariant, and therefore has a simple analytical solution. The key insight is that constructing this frame is faster than solving the system dynamics in the original frame. Rapidly solving the Bloch equations for an arbitrary Hamiltonian is particularly useful in the context of NMR optimal control. Optimal control theory can be used to design pulse shapes for a range of tasks in NMR spectroscopy. However, it requires multiple simulations of the Bloch equations at each stage of the algorithm, and for each relevant set of parameters (e.g. chemical shift frequencies). This is typically time consuming. We demonstrate that by working in an appropriate toggling frame, optimal control pulses can be generated much faster. We present a new alternative to the well-known GRAPE algorithm to continuously update the toggling-frame as the optimal pulse is generated, and demonstrate that this approach is extremely fast. The use and benefit of rapid optimal pulse generation is demonstrated for 19F fragment screening experiments.

An unstructured mesh arbitrary Lagrangian-Eulerian unsteady incompressible flow solver and its application to insect flight aerodynamics

NASA Astrophysics Data System (ADS)

Su, Xiaohui; Cao, Yuanwei; Zhao, Yong

2016-06-01

In this paper, an unstructured mesh Arbitrary Lagrangian-Eulerian (ALE) incompressible flow solver is developed to investigate the aerodynamics of insect hovering flight. The proposed finite-volume ALE Navier-Stokes solver is based on the artificial compressibility method (ACM) with a high-resolution method of characteristics-based scheme on unstructured grids. The present ALE model is validated and assessed through flow passing over an oscillating cylinder. Good agreements with experimental results and other numerical solutions are obtained, which demonstrates the accuracy and the capability of the present model. The lift generation mechanisms of 2D wing in hovering motion, including wake capture, delayed stall, rapid pitch, as well as clap and fling are then studied and illustrated using the current ALE model. Moreover, the optimized angular amplitude in symmetry model, 45°, is firstly reported in details using averaged lift and the energy power method. Besides, the lift generation of complete cyclic clap and fling motion, which is simulated by few researchers using the ALE method due to large deformation, is studied and clarified for the first time. The present ALE model is found to be a useful tool to investigate lift force generation mechanism for insect wing flight.

Diffuse interface simulation of bubble rising process: a comparison of adaptive mesh refinement and arbitrary lagrange-euler methods

NASA Astrophysics Data System (ADS)

Wang, Ye; Cai, Jiejin; Li, Qiong; Yin, Huaqiang; Yang, Xingtuan

2018-06-01

Gas-liquid two phase flow exists in several industrial processes and light-water reactors (LWRs). A diffuse interface based finite element method with two different mesh generation methods namely, the Adaptive Mesh Refinement (AMR) and the Arbitrary Lagrange Euler (ALE) methods is used to model the shape and velocity changes in a rising bubble. Moreover, the calculating speed and mesh generation strategies of AMR and ALE are contrasted. The simulation results agree with the Bhagat's experiments, indicating that both mesh generation methods can simulate the characteristics of bubble accurately. We concluded that: the small bubble rises as elliptical with oscillation, whereas a larger bubble (11 mm > d > 7 mm) rises with a morphology between the elliptical and cap type with a larger oscillation. When the bubble is large (d > 11 mm), it rises up as a cap type, and the amplitude becomes smaller. Moreover, it takes longer to achieve the stable shape from the ellipsoid to the spherical cap type with the increase of the bubble diameter. The results also show that for smaller diameter case, the ALE method uses fewer grids and has a faster calculation speed, but the AMR method can solve the case of a large geometry deformation efficiently.

Distributed processing method for arbitrary view generation in camera sensor network

NASA Astrophysics Data System (ADS)

Tehrani, Mehrdad P.; Fujii, Toshiaki; Tanimoto, Masayuki

2003-05-01

Camera sensor network as a new advent of technology is a network that each sensor node can capture video signals, process and communicate them with other nodes. The processing task in this network is to generate arbitrary view, which can be requested from central node or user. To avoid unnecessary communication between nodes in camera sensor network and speed up the processing time, we have distributed the processing tasks between nodes. In this method, each sensor node processes part of interpolation algorithm to generate the interpolated image with local communication between nodes. The processing task in camera sensor network is ray-space interpolation, which is an object independent method and based on MSE minimization by using adaptive filtering. Two methods were proposed for distributing processing tasks, which are Fully Image Shared Decentralized Processing (FIS-DP), and Partially Image Shared Decentralized Processing (PIS-DP), to share image data locally. Comparison of the proposed methods with Centralized Processing (CP) method shows that PIS-DP has the highest processing speed after FIS-DP, and CP has the lowest processing speed. Communication rate of CP and PIS-DP is almost same and better than FIS-DP. So, PIS-DP is recommended because of its better performance than CP and FIS-DP.

A robust, efficient equidistribution 2D grid generation method

NASA Astrophysics Data System (ADS)

Chacon, Luis; Delzanno, Gian Luca; Finn, John; Chung, Jeojin; Lapenta, Giovanni

2007-11-01

We present a new cell-area equidistribution method for two- dimensional grid adaptation [1]. The method is able to satisfy the equidistribution constraint to arbitrary precision while optimizing desired grid properties (such as isotropy and smoothness). The method is based on the minimization of the grid smoothness integral, constrained to producing a given positive-definite cell volume distribution. The procedure gives rise to a single, non-linear scalar equation with no free-parameters. We solve this equation numerically with the Newton-Krylov technique. The ellipticity property of the linearized scalar equation allows multigrid preconditioning techniques to be effectively used. We demonstrate a solution exists and is unique. Therefore, once the solution is found, the adapted grid cannot be folded due to the positivity of the constraint on the cell volumes. We present several challenging tests to show that our new method produces optimal grids in which the constraint is satisfied numerically to arbitrary precision. We also compare the new method to the deformation method [2] and show that our new method produces better quality grids. [1] G.L. Delzanno, L. Chac'on, J.M. Finn, Y. Chung, G. Lapenta, A new, robust equidistribution method for two-dimensional grid generation, in preparation. [2] G. Liao and D. Anderson, A new approach to grid generation, Appl. Anal. 44, 285--297 (1992).

Perspectives of shaped pulses for EPR spectroscopy

NASA Astrophysics Data System (ADS)

Spindler, Philipp E.; Schöps, Philipp; Kallies, Wolfgang; Glaser, Steffen J.; Prisner, Thomas F.

2017-07-01

This article describes current uses of shaped pulses, generated by an arbitrary waveform generator, in the field of EPR spectroscopy. We show applications of sech/tanh and WURST pulses to dipolar spectroscopy, including new pulse schemes and procedures, and discuss the more general concept of optimum-control-based pulses for applications in EPR spectroscopy. The article also describes a procedure to correct for experimental imperfections, mostly introduced by the microwave resonator, and discusses further potential applications and limitations of such pulses.

Numerical Solution of the Three-Dimensional Navier-Stokes Equation.

DTIC Science & Technology

1982-03-01

compressible, viscous fluid in an arbitrary geometry. We wish to use a grid generating scheme so we assume that the geometry of the physical problem given in...bian J of the mapping are provided. (For work on grid generating schemes see [4], [5] or [6).) Hence we must solve the following system of equations...these limitations the data structure used in the ILLIAC code is to partition the grid into 8 x 8 x 8 blocks. A row of these blocks in a given

Techniques for Microwave Near-Field Quantum Control of Trapped Ions

DTIC Science & Technology

2013-01-31

counts. Each DDS (Analog Devices AD9858) can generate signals at frequencies to 400 MHz with a frequency resolution of 0.233 Hz and phase resolution...fast, two- channel DAC is used to generate arbitrary waveforms with a 50-MHz update rate, a voltage range from −10 V to 10 V, and a resolution of 0.305...mV. This DAC is programed via USB and triggered by the data acquisition FPGA . We use three DDS modules as sources for three frequency octupling

Generation of multiphoton Greenberger-Horne-Zeilinger state and its two kinds of teleportation

NASA Astrophysics Data System (ADS)

Song, Jia-Min; Chang, Di; Huang, Yong-Chang

2012-02-01

We propose a comprehensive experimental scheme to generate and teleport GHZ states of any number of photons as well as to accomplish the process of open-destination teleportation of a single photon's arbitrary state. The equipment and techniques which are used in our scheme are all feasible under current technology. Moreover, we make a direct extension of the above cases and investigate the open-destination teleportation of any M-photon general GHZ states with a brief diagram.

Invasion Percolation and Global Optimization

NASA Astrophysics Data System (ADS)

Barabási, Albert-László

1996-05-01

Invasion bond percolation (IBP) is mapped exactly into Prim's algorithm for finding the shortest spanning tree of a weighted random graph. Exploring this mapping, which is valid for arbitrary dimensions and lattices, we introduce a new IBP model that belongs to the same universality class as IBP and generates the minimal energy tree spanning the IBP cluster.

A New Framework of Happiness Survey and Evaluation of National Wellbeing

ERIC Educational Resources Information Center

Zhou, Haiou

2012-01-01

Happiness surveys based on self-reporting may generate unreliable data due to respondents' imperfect retrospection, vulnerability to context and arbitrariness in measuring happiness. To overcome these problems, this paper proposes to combine a happiness evaluation method developed by Ng (Soc Indic Res, 38:1-29, 1996) with the day reconstruction…

Non-classical State via Superposition of Two Opposite Coherent States

NASA Astrophysics Data System (ADS)

Ren, Gang; Du, Jian-ming; Yu, Hai-jun

2018-04-01

We study the non-classical properties of the states generated by superpositions of two opposite coherent states with the arbitrary relative phase factors. We show that the relative phase factors plays an important role in these superpositions. We demonstrate this result by discussing their squeezing properties, quantum statistical properties and fidelity in principle.

Two-Volt Josephson Arbitrary Waveform Synthesizer Using Wilkinson Dividers.

PubMed

Flowers-Jacobs, Nathan E; Fox, Anna E; Dresselhaus, Paul D; Schwall, Robert E; Benz, Samuel P

2016-09-01

The root-mean-square (rms) output voltage of the NIST Josephson arbitrary waveform synthesizer (JAWS) has been doubled from 1 V to a record 2 V by combining two new 1 V chips on a cryocooler. This higher voltage will improve calibrations of ac thermal voltage converters and precision voltage measurements that require state-of-the-art quantum accuracy, stability, and signal-to-noise ratio. We achieved this increase in output voltage by using four on-chip Wilkinson dividers and eight inner-outer dc blocks, which enable biasing of eight Josephson junction (JJ) arrays with high-speed inputs from only four high-speed pulse generator channels. This approach halves the number of pulse generator channels required in future JAWS systems. We also implemented on-chip superconducting interconnects between JJ arrays, which reduces systematic errors and enables a new modular chip package. Finally, we demonstrate a new technique for measuring and visualizing the operating current range that reduces the measurement time by almost two orders of magnitude and reveals the relationship between distortion in the output spectrum and output pulse sequence errors.

Three-dimensional mid-air acoustic manipulation by ultrasonic phased arrays.

PubMed

Ochiai, Yoichi; Hoshi, Takayuki; Rekimoto, Jun

2014-01-01

The essence of levitation technology is the countervailing of gravity. It is known that an ultrasound standing wave is capable of suspending small particles at its sound pressure nodes. The acoustic axis of the ultrasound beam in conventional studies was parallel to the gravitational force, and the levitated objects were manipulated along the fixed axis (i.e. one-dimensionally) by controlling the phases or frequencies of bolted Langevin-type transducers. In the present study, we considered extended acoustic manipulation whereby millimetre-sized particles were levitated and moved three-dimensionally by localised ultrasonic standing waves, which were generated by ultrasonic phased arrays. Our manipulation system has two original features. One is the direction of the ultrasound beam, which is arbitrary because the force acting toward its centre is also utilised. The other is the manipulation principle by which a localised standing wave is generated at an arbitrary position and moved three-dimensionally by opposed and ultrasonic phased arrays. We experimentally confirmed that expanded-polystyrene particles of 0.6 mm, 1 mm, and 2 mm in diameter could be manipulated by our proposed method.

Three-Dimensional Mid-Air Acoustic Manipulation by Ultrasonic Phased Arrays

PubMed Central

Ochiai, Yoichi; Hoshi, Takayuki; Rekimoto, Jun

2014-01-01

The essence of levitation technology is the countervailing of gravity. It is known that an ultrasound standing wave is capable of suspending small particles at its sound pressure nodes. The acoustic axis of the ultrasound beam in conventional studies was parallel to the gravitational force, and the levitated objects were manipulated along the fixed axis (i.e. one-dimensionally) by controlling the phases or frequencies of bolted Langevin-type transducers. In the present study, we considered extended acoustic manipulation whereby millimetre-sized particles were levitated and moved three-dimensionally by localised ultrasonic standing waves, which were generated by ultrasonic phased arrays. Our manipulation system has two original features. One is the direction of the ultrasound beam, which is arbitrary because the force acting toward its centre is also utilised. The other is the manipulation principle by which a localised standing wave is generated at an arbitrary position and moved three-dimensionally by opposed and ultrasonic phased arrays. We experimentally confirmed that expanded-polystyrene particles of 0.6 mm, 1 mm, and 2 mm in diameter could be manipulated by our proposed method. PMID:24849371

Prediction and generation of binary Markov processes: Can a finite-state fox catch a Markov mouse?

NASA Astrophysics Data System (ADS)

Ruebeck, Joshua B.; James, Ryan G.; Mahoney, John R.; Crutchfield, James P.

2018-01-01

Understanding the generative mechanism of a natural system is a vital component of the scientific method. Here, we investigate one of the fundamental steps toward this goal by presenting the minimal generator of an arbitrary binary Markov process. This is a class of processes whose predictive model is well known. Surprisingly, the generative model requires three distinct topologies for different regions of parameter space. We show that a previously proposed generator for a particular set of binary Markov processes is, in fact, not minimal. Our results shed the first quantitative light on the relative (minimal) costs of prediction and generation. We find, for instance, that the difference between prediction and generation is maximized when the process is approximately independently, identically distributed.

A recursively formulated first-order semianalytic artificial satellite theory based on the generalized method of averaging. Volume 1: The generalized method of averaging applied to the artificial satellite problem

NASA Technical Reports Server (NTRS)

Mcclain, W. D.

1977-01-01

A recursively formulated, first-order, semianalytic artificial satellite theory, based on the generalized method of averaging is presented in two volumes. Volume I comprehensively discusses the theory of the generalized method of averaging applied to the artificial satellite problem. Volume II presents the explicit development in the nonsingular equinoctial elements of the first-order average equations of motion. The recursive algorithms used to evaluate the first-order averaged equations of motion are also presented in Volume II. This semianalytic theory is, in principle, valid for a term of arbitrary degree in the expansion of the third-body disturbing function (nonresonant cases only) and for a term of arbitrary degree and order in the expansion of the nonspherical gravitational potential function.

Separation of variables in the special diagonal Hamilton-Jacobi equation: Application to the dynamical problem of a particle constrained on a moving surface

NASA Technical Reports Server (NTRS)

Blanchard, D. L.; Chan, F. K.

1973-01-01

For a time-dependent, n-dimensional, special diagonal Hamilton-Jacobi equation a necessary and sufficient condition for the separation of variables to yield a complete integral of the form was established by specifying the admissible forms in terms of arbitrary functions. A complete integral was then expressed in terms of these arbitrary functions and also the n irreducible constants. As an application of the results obtained for the two-dimensional Hamilton-Jacobi equation, analysis was made for a comparatively wide class of dynamical problems involving a particle moving in Euclidean three-dimensional space under the action of external forces but constrained on a moving surface. All the possible cases in which this equation had a complete integral of the form were obtained and these are tubulated for reference.

Two-spinor description of massive particles and relativistic spin projection operators

NASA Astrophysics Data System (ADS)

Isaev, A. P.; Podoinitsyn, M. A.

2018-04-01

On the basis of the Wigner unitary representations of the covering group ISL (2 , C) of the Poincaré group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the Dirac-Pauli-Fierz equations. In the framework of the two-spinor formalism we construct spin-vectors of polarizations and obtain conditions that fix the corresponding relativistic spin projection operators (Behrends-Fronsdal projection operators). With the help of these conditions we find explicit expressions for relativistic spin projection operators for integer spins (Behrends-Fronsdal projection operators) and then find relativistic spin projection operators for half integer spins. These projection operators determine the numerators in the propagators of fields of relativistic particles. We deduce generalizations of the Behrends-Fronsdal projection operators for arbitrary space-time dimensions D > 2.

Calculation of the Poisson cumulative distribution function

NASA Technical Reports Server (NTRS)

Bowerman, Paul N.; Nolty, Robert G.; Scheuer, Ernest M.

1990-01-01

A method for calculating the Poisson cdf (cumulative distribution function) is presented. The method avoids computer underflow and overflow during the process. The computer program uses this technique to calculate the Poisson cdf for arbitrary inputs. An algorithm that determines the Poisson parameter required to yield a specified value of the cdf is presented.

Shape Sensing Using a Multi-Core Optical Fiber Having an Arbitrary Initial Shape in the Presence of Extrinsic Forces

NASA Technical Reports Server (NTRS)

Rogge, Matthew D. (Inventor); Moore, Jason P. (Inventor)

2014-01-01

Shape of a multi-core optical fiber is determined by positioning the fiber in an arbitrary initial shape and measuring strain over the fiber's length using strain sensors. A three-coordinate p-vector is defined for each core as a function of the distance of the corresponding cores from a center point of the fiber and a bending angle of the cores. The method includes calculating, via a controller, an applied strain value of the fiber using the p-vector and the measured strain for each core, and calculating strain due to bending as a function of the measured and the applied strain values. Additionally, an apparent local curvature vector is defined for each core as a function of the calculated strain due to bending. Curvature and bend direction are calculated using the apparent local curvature vector, and fiber shape is determined via the controller using the calculated curvature and bend direction.

The role of axis embedding on rigid rotor decomposition analysis of variational rovibrational wave functions.

PubMed

Szidarovszky, Tamás; Fábri, Csaba; Császár, Attila G

2012-05-07

Approximate rotational characterization of variational rovibrational wave functions via the rigid rotor decomposition (RRD) protocol is developed for Hamiltonians based on arbitrary sets of internal coordinates and axis embeddings. An efficient and general procedure is given that allows employing the Eckart embedding with arbitrary polyatomic Hamiltonians through a fully numerical approach. RRD tables formed by projecting rotational-vibrational wave functions into products of rigid-rotor basis functions and previously determined vibrational eigenstates yield rigid-rotor labels for rovibrational eigenstates by selecting the largest overlap. Embedding-dependent RRD analyses are performed, up to high energies and rotational excitations, for the H(2) (16)O isotopologue of the water molecule. Irrespective of the embedding chosen, the RRD procedure proves effective in providing unambiguous rotational assignments at low energies and J values. Rotational labeling of rovibrational states of H(2) (16)O proves to be increasingly difficult beyond about 10,000 cm(-1), close to the barrier to linearity of the water molecule. For medium energies and excitations the Eckart embedding yields the largest RRD coefficients, thus providing the largest number of unambiguous rotational labels.

Simplified expressions that incorporate finite pulse effects into coherent two-dimensional optical spectra.

PubMed

Do, Thanh Nhut; Gelin, Maxim F; Tan, Howe-Siang

2017-10-14

We derive general expressions that incorporate finite pulse envelope effects into a coherent two-dimensional optical spectroscopy (2DOS) technique. These expressions are simpler and less computationally intensive than the conventional triple integral calculations needed to simulate 2DOS spectra. The simplified expressions involving multiplications of arbitrary pulse spectra with 2D spectral response function are shown to be exactly equal to the conventional triple integral calculations of 2DOS spectra if the 2D spectral response functions do not vary with population time. With minor modifications, they are also accurate for 2D spectral response functions with quantum beats and exponential decay during population time. These conditions cover a broad range of experimental 2DOS spectra. For certain analytically defined pulse spectra, we also derived expressions of 2D spectra for arbitrary population time dependent 2DOS spectral response functions. Having simpler and more efficient methods to calculate experimentally relevant 2DOS spectra with finite pulse effect considered will be important in the simulation and understanding of the complex systems routinely being studied by using 2DOS.

Multispectral simulation environment for modeling low-light-level sensor systems

NASA Astrophysics Data System (ADS)

Ientilucci, Emmett J.; Brown, Scott D.; Schott, John R.; Raqueno, Rolando V.

1998-11-01

Image intensifying cameras have been found to be extremely useful in low-light-level (LLL) scenarios including military night vision and civilian rescue operations. These sensors utilize the available visible region photons and an amplification process to produce high contrast imagery. It has been demonstrated that processing techniques can further enhance the quality of this imagery. For example, fusion with matching thermal IR imagery can improve image content when very little visible region contrast is available. To aid in the improvement of current algorithms and the development of new ones, a high fidelity simulation environment capable of producing radiometrically correct multi-band imagery for low- light-level conditions is desired. This paper describes a modeling environment attempting to meet these criteria by addressing the task as two individual components: (1) prediction of a low-light-level radiance field from an arbitrary scene, and (2) simulation of the output from a low- light-level sensor for a given radiance field. The radiance prediction engine utilized in this environment is the Digital Imaging and Remote Sensing Image Generation (DIRSIG) model which is a first principles based multi-spectral synthetic image generation model capable of producing an arbitrary number of bands in the 0.28 to 20 micrometer region. The DIRSIG model is utilized to produce high spatial and spectral resolution radiance field images. These images are then processed by a user configurable multi-stage low-light-level sensor model that applies the appropriate noise and modulation transfer function (MTF) at each stage in the image processing chain. This includes the ability to reproduce common intensifying sensor artifacts such as saturation and 'blooming.' Additionally, co-registered imagery in other spectral bands may be simultaneously generated for testing fusion and exploitation algorithms. This paper discusses specific aspects of the DIRSIG radiance prediction for low- light-level conditions including the incorporation of natural and man-made sources which emphasizes the importance of accurate BRDF. A description of the implementation of each stage in the image processing and capture chain for the LLL model is also presented. Finally, simulated images are presented and qualitatively compared to lab acquired imagery from a commercial system.

Diffusive Cosmic-Ray Acceleration at Shock Waves of Arbitrary Speed with Magnetostatic Turbulence. I. General Theory and Correct Nonrelativistic Speed Limit

NASA Astrophysics Data System (ADS)

Schlickeiser, R.; Oppotsch, J.

2017-12-01

The analytical theory of diffusive acceleration of cosmic rays at parallel stationary shock waves of arbitrary speed with magnetostatic turbulence is developed from first principles. The theory is based on the diffusion approximation to the gyrotropic cosmic-ray particle phase-space distribution functions in the respective rest frames of the up- and downstream medium. We derive the correct cosmic-ray jump conditions for the cosmic-ray current and density, and match the up- and downstream distribution functions at the position of the shock. It is essential to account for the different particle momentum coordinates in the up- and downstream media. Analytical expressions for the momentum spectra of shock-accelerated cosmic rays are calculated. These are valid for arbitrary shock speeds including relativistic shocks. The correctly taken limit for nonrelativistic shock speeds leads to a universal broken power-law momentum spectrum of accelerated particles with velocities well above the injection velocity threshold, where the universal power-law spectral index q≃ 2-{γ }1-4 is independent of the flow compression ratio r. For nonrelativistic shock speeds, we calculate for the first time the injection velocity threshold, settling the long-standing injection problem for nonrelativistic shock acceleration.

Cyclotron resonant scattering feature simulations. II. Description of the CRSF simulation process

NASA Astrophysics Data System (ADS)

Schwarm, F.-W.; Ballhausen, R.; Falkner, S.; Schönherr, G.; Pottschmidt, K.; Wolff, M. T.; Becker, P. A.; Fürst, F.; Marcu-Cheatham, D. M.; Hemphill, P. B.; Sokolova-Lapa, E.; Dauser, T.; Klochkov, D.; Ferrigno, C.; Wilms, J.

2017-05-01

Context. Cyclotron resonant scattering features (CRSFs) are formed by scattering of X-ray photons off quantized plasma electrons in the strong magnetic field (of the order 1012 G) close to the surface of an accreting X-ray pulsar. Due to the complex scattering cross-sections, the line profiles of CRSFs cannot be described by an analytic expression. Numerical methods, such as Monte Carlo (MC) simulations of the scattering processes, are required in order to predict precise line shapes for a given physical setup, which can be compared to observations to gain information about the underlying physics in these systems. Aims: A versatile simulation code is needed for the generation of synthetic cyclotron lines. Sophisticated geometries should be investigatable by making their simulation possible for the first time. Methods: The simulation utilizes the mean free path tables described in the first paper of this series for the fast interpolation of propagation lengths. The code is parallelized to make the very time-consuming simulations possible on convenient time scales. Furthermore, it can generate responses to monoenergetic photon injections, producing Green's functions, which can be used later to generate spectra for arbitrary continua. Results: We develop a new simulation code to generate synthetic cyclotron lines for complex scenarios, allowing for unprecedented physical interpretation of the observed data. An associated XSPEC model implementation is used to fit synthetic line profiles to NuSTAR data of Cep X-4. The code has been developed with the main goal of overcoming previous geometrical constraints in MC simulations of CRSFs. By applying this code also to more simple, classic geometries used in previous works, we furthermore address issues of code verification and cross-comparison of various models. The XSPEC model and the Green's function tables are available online (see link in footnote, page 1).

Interactions between Mathematics and Physics: The History of the Concept of Function--Teaching with and about Nature of Mathematics

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-01-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another…

Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver

DOE PAGES

Vincenti, H.; Vay, J. -L.

2015-11-22

Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the result. Such modifications for instance occur when Perfectly Matched Layers (PMLs) are used at simulation domain boundaries to simulate open media. Another example is the use of arbitrary order Maxwell solver with domain decomposition technique that may under some condition involve stencil truncations at subdomain boundaries, resulting in small spurious errors that do eventually build up. In each case, a careful evaluation of the characteristics and magnitude of themore » errors resulting from these approximations, and their impact at any frequency and angle, requires detailed analytical and numerical studies. To this end, we present a general analytical approach that enables the evaluation of numerical discretization errors of fully three-dimensional arbitrary order finite-difference Maxwell solver, with arbitrary modification of the local stencil in the simulation domain. The analytical model is validated against simulations of domain decomposition technique and PMLs, when these are used with very high-order Maxwell solver, as well as in the infinite order limit of pseudo-spectral solvers. Results confirm that the new analytical approach enables exact predictions in each case. It also confirms that the domain decomposition technique can be used with very high-order Maxwell solver and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.« less

Normal order and extended Wick theorem for a multiconfiguration reference wave function

NASA Astrophysics Data System (ADS)

Kutzelnigg, Werner; Mukherjee, Debashis

1997-07-01

A generalization of normal ordering and of Wick's theorem with respect to an arbitrary reference function Φ as some generalized "physical vacuum" is formulated in a different (but essentially equivalent) way than that suggested previously by one of the present authors. Guiding principles are that normal order operators with respect to any reference state must be expressible as linear combinations of those with respect to the genuine vacuum, that the vacuum expectation value of a normal order operator must vanish (with respect to the vacuum to which it is in normal order), and that the well-known formalism for a single Slater determinant as physical vacuum must be contained as a special case. The derivation is largely based on the concepts of "Quantum Chemistry in Fock space," which means that particle-number-conserving operators (excitation operators) play a central role. Nevertheless, the contraction rules in the frame of a generalized Wick theorem are derived, that hold for non-particle-number-conserving operators as well. The contraction rules are formulated and illustrated in terms of diagrams. The contractions involve the "residual n-particle density matrices" λ, which are the irreducible (non-factorizable) parts of the conventional n-particle density matrices γ, in the sense of a cumulant expansion for the density. A spinfree formulation is presented as well. The expression of the Hamiltonian in normal order with respect to a multiconfiguration reference function leads to a natural definition of a generalized Fock operator. MC-SCF-theory is easily worked out in this context. The paper concludes with a discussion of the excited configurations and the first-order interacting space, that underlies a perturbative coupled cluster type correction to the MCSCF function for an arbitrary reference function, and with general implications of the new formalism, that is related to "internally contracted multireference configuration interaction." The present generalization of normal ordering is not only valid for arbitrary reference functions, but also if the reference state is an ensemble state.

Synthesis of Arbitrary Quantum Circuits to Topological Assembly: Systematic, Online and Compact.

PubMed

Paler, Alexandru; Fowler, Austin G; Wille, Robert

2017-09-05

It is challenging to transform an arbitrary quantum circuit into a form protected by surface code quantum error correcting codes (a variant of topological quantum error correction), especially if the goal is to minimise overhead. One of the issues is the efficient placement of magic state distillation sub circuits, so-called distillation boxes, in the space-time volume that abstracts the computation's required resources. This work presents a general, systematic, online method for the synthesis of such circuits. Distillation box placement is controlled by so-called schedulers. The work introduces a greedy scheduler generating compact box placements. The implemented software, whose source code is available at www.github.com/alexandrupaler/tqec, is used to illustrate and discuss synthesis examples. Synthesis and optimisation improvements are proposed.

Simulation model of fatigue crack opening/closing phenomena for predicting RPG load under arbitrary stress distribution field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Toyosada, M.; Niwa, T.

1995-12-31

In this paper, Newman`s calculation model is modified to solve his neglected effect of the change of stress distribution ahead of a crack, and to leave elastic plastic materials along the crack surface because of the compatibility of Dugdale model. In addition to above treatment, the authors introduce plastic shrinkage at an immediate generation of new crack surfaces due to emancipation of internal force with the magnitude of yield stress level during unloading process in the model. Moreover, the model is expanded to arbitrary stress distribution field. By using the model, RPG load is simulated for a center notched specimenmore » under constant amplitude loading with various stress ratios and decreased maximum load while keeping minimum load.« less

A simple method for finding explicit analytic transition densities of diffusion processes with general diploid selection.

PubMed

Song, Yun S; Steinrücken, Matthias

2012-03-01

The transition density function of the Wright-Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright-Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation-selection balance.

A cryptographic hash function based on chaotic network automata

NASA Astrophysics Data System (ADS)

Machicao, Jeaneth; Bruno, Odemir M.

2017-12-01

Chaos theory has been used to develop several cryptographic methods relying on the pseudo-random properties extracted from simple nonlinear systems such as cellular automata (CA). Cryptographic hash functions (CHF) are commonly used to check data integrity. CHF “compress” arbitrary long messages (input) into much smaller representations called hash values or message digest (output), designed to prevent the ability to reverse the hash values into the original message. This paper proposes a chaos-based CHF inspired on an encryption method based on chaotic CA rule B1357-S2468. Here, we propose an hybrid model that combines CA and networks, called network automata (CNA), whose chaotic spatio-temporal outputs are used to compute a hash value. Following the Merkle and Damgård model of construction, a portion of the message is entered as the initial condition of the network automata, so that the rest parts of messages are iteratively entered to perturb the system. The chaotic network automata shuffles the message using flexible control parameters, so that the generated hash value is highly sensitive to the message. As demonstrated in our experiments, the proposed model has excellent pseudo-randomness and sensitivity properties with acceptable performance when compared to conventional hash functions.

A Simple Method for Finding Explicit Analytic Transition Densities of Diffusion Processes with General Diploid Selection

PubMed Central

Song, Yun S.; Steinrücken, Matthias

2012-01-01

The transition density function of the Wright–Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright–Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation–selection balance. PMID:22209899

An analytical computation of magnetic field generated from a cylinder ferromagnet

NASA Astrophysics Data System (ADS)

Taniguchi, Tomohiro

2018-04-01

An analytical formulation to compute a magnetic field generated from an uniformly magnetized cylinder ferromagnet is developed. Exact solutions of the magnetic field generated from the magnetization pointing in an arbitrary direction are derived, which are applicable both inside and outside the ferromagnet. The validities of the present formulas are confirmed by comparing them with demagnetization coefficients estimated in earlier works. The results will be useful for designing practical applications, such as high-density magnetic recording and microwave generators, where nanostructured ferromagnets are coupled to each other through the dipole interactions and show cooperative phenomena such as synchronization. As an example, the magnetic field generated from a spin torque oscillator for magnetic recording based on microwave assisted magnetization reversal is studied.

A massive Feynman integral and some reduction relations for Appell functions

NASA Astrophysics Data System (ADS)

Shpot, M. A.

2007-12-01

New explicit expressions are derived for the one-loop two-point Feynman integral with arbitrary external momentum and masses m12 and m22 in D dimensions. The results are given in terms of Appell functions, manifestly symmetric with respect to the masses mi2. Equating our expressions with previously known results in terms of Gauss hypergeometric functions yields reduction relations for the involved Appell functions that are apparently new mathematical results.

Generation of Synthetic Spike Trains with Defined Pairwise Correlations

PubMed Central

Niebur, Ernst

2008-01-01

Recent technological advances as well as progress in theoretical understanding of neural systems have created a need for synthetic spike trains with controlled mean rate and pairwise cross-correlation. This report introduces and analyzes a novel algorithm for the generation of discretized spike trains with arbitrary mean rates and controlled cross correlation. Pairs of spike trains with any pairwise correlation can be generated, and higher-order correlations are compatible with common synaptic input. Relations between allowable mean rates and correlations within a population are discussed. The algorithm is highly efficient, its complexity increasing linearly with the number of spike trains generated and therefore inversely with the number of cross-correlated pairs. PMID:17521277

Pseudopotential theoretical study of the alkali metals under arbitrary pressure: Density, bulk modulus, and shear moduli

NASA Astrophysics Data System (ADS)

Rasky, Daniel J.; Milstein, Frederick

1986-02-01

Milstein and Hill previously derived formulas for computing the bulk and shear moduli, κ, μ, and μ', at arbitrary pressures, for cubic crystals in which interatomic interaction energies are modeled by pairwise functions, and they carried out the moduli computations using the complete family of Morse functions. The present study extends their work to a pseudopotential description of atomic binding. Specifically: (1) General formulas are derived for determining these moduli under hydrostatic loading within the framework of a pseudopotential model. (2) A two-parameter pseudopotential model is used to describe atomic binding of the alkali metals, and the two parameters are determined from experimental data (the model employs the Heine-Abarenkov potential with the Taylor dielectric function). (3) For each alkali metal (Li, Na, K, Rb, and Cs), the model is used to compute the pressure-versus-volume behavior and, at zero pressure, the binding energy, the density, and the elastic moduli and their pressure derivatives; the theoretical behavior is found to be in excellent agreement with experiment. (4) Calculations are made of κ, μ, and μ' of the bcc alkali metals over wide ranges of hydrostatic compression and expansion. (5) The pseudopotential results are compared with those of arbitrary-central-force models (wherein κ-(2/3)μ=μ'+2P) and with the specific Morse-function results. The pressures, bulk moduli, and zero-pressure shear moduli (as determined for the Morse and pseudopotential models) are in excellent agreement, but important differences appear in the shear moduli under high compressions. The computations in the present paper are for the bcc metals; a subsequent paper will extend this work to include both the bcc and fcc structures, at compressions and expansions where elastic stability or lattice cohesion is, in practice, lost.

Performance characteristics of a batch service queueing system with functioning server failure and multiple vacations

NASA Astrophysics Data System (ADS)

Niranjan, S. P.; Chandrasekaran, V. M.; Indhira, K.

2018-04-01

This paper examines bulk arrival and batch service queueing system with functioning server failure and multiple vacations. Customers are arriving into the system in bulk according to Poisson process with rate λ. Arriving customers are served in batches with minimum of ‘a’ and maximum of ‘b’ number of customers according to general bulk service rule. In the service completion epoch if the queue length is less than ‘a’ then the server leaves for vacation (secondary job) of random length. After a vacation completion, if the queue length is still less than ‘a’ then the server leaves for another vacation. The server keeps on going vacation until the queue length reaches the value ‘a’. The server is not stable at all the times. Sometimes it may fails during functioning of customers. Though the server fails service process will not be interrupted.It will be continued for the current batch of customers with lower service rate than the regular service rate. The server will be repaired after the service completion with lower service rate. The probability generating function of the queue size at an arbitrary time epoch will be obtained for the modelled queueing system by using supplementary variable technique. Moreover various performance characteristics will also be derived with suitable numerical illustrations.

Efficient Modeling of Gravity Fields Caused by Sources with Arbitrary Geometry and Arbitrary Density Distribution

NASA Astrophysics Data System (ADS)

Wu, Leyuan

2018-01-01

We present a brief review of gravity forward algorithms in Cartesian coordinate system, including both space-domain and Fourier-domain approaches, after which we introduce a truly general and efficient algorithm, namely the convolution-type Gauss fast Fourier transform (Conv-Gauss-FFT) algorithm, for 2D and 3D modeling of gravity potential and its derivatives due to sources with arbitrary geometry and arbitrary density distribution which are defined either by discrete or by continuous functions. The Conv-Gauss-FFT algorithm is based on the combined use of a hybrid rectangle-Gaussian grid and the fast Fourier transform (FFT) algorithm. Since the gravity forward problem in Cartesian coordinate system can be expressed as continuous convolution-type integrals, we first approximate the continuous convolution by a weighted sum of a series of shifted discrete convolutions, and then each shifted discrete convolution, which is essentially a Toeplitz system, is calculated efficiently and accurately by combining circulant embedding with the FFT algorithm. Synthetic and real model tests show that the Conv-Gauss-FFT algorithm can obtain high-precision forward results very efficiently for almost any practical model, and it works especially well for complex 3D models when gravity fields on large 3D regular grids are needed.

Hybrid space-airborne bistatic SAR geometric resolutions

NASA Astrophysics Data System (ADS)

Moccia, Antonio; Renga, Alfredo

2009-09-01

Performance analysis of Bistatic Synthetic Aperture Radar (SAR) characterized by arbitrary geometric configurations is usually complex and time-consuming since system impulse response has to be evaluated by bistatic SAR processing. This approach does not allow derivation of general equations regulating the behaviour of image resolutions with varying the observation geometry. It is well known that for an arbitrary configuration of bistatic SAR there are not perpendicular range and azimuth directions, but the capability to produce an image is not prevented as it depends only on the possibility to generate image pixels from time delay and Doppler measurements. However, even if separately range and Doppler resolutions are good, bistatic SAR geometries can exist in which imaging capabilities are very poor when range and Doppler directions become locally parallel. The present paper aims to derive analytical tools for calculating the geometric resolutions of arbitrary configuration of bistatic SAR. The method has been applied to a hybrid bistatic Synthetic Aperture Radar formed by a spaceborne illuminator and a receiving-only airborne forward-looking Synthetic Aperture Radar (F-SAR). It can take advantage of the spaceborne illuminator to dodge the limitations of monostatic FSAR. Basic modeling and best illumination conditions have been detailed in the paper.

Development of the apparatus for measuring magnetic properties of electrical steel sheets in arbitrary directions under compressive stress normal to their surface

NASA Astrophysics Data System (ADS)

Maeda, Yoshitaka; Urata, Shinya; Nakai, Hideo; Takeuchi, Yuuya; Yun, Kyyoul; Yanase, Shunji; Okazaki, Yasuo

2017-05-01

In designing motors, one must grasp the magnetic properties of electrical steel sheets considering actual conditions in motors. Especially important is grasping the stress dependence of magnetic power loss. This paper describes a newly developed apparatus to measure two-dimensional (2-D) magnetic properties (properties under the arbitrary alternating and the rotating flux conditions) of electrical steel sheets under compressive stress normal to the sheet surface. The apparatus has a 2-D magnetic excitation circuit to generate magnetic fields in arbitrary directions in the evaluation area. It also has a pressing unit to apply compressive stress normal to the sheet surface. During measurement, it is important to apply uniform stress throughout the evaluation area. Therefore, we have developed a new flux density sensor using needle probe method. It is composed of thin copper foils sputtered on electrical steel sheets. By using this sensor, the stress can be applied to the surface of the specimen without influence of this sensor. This paper described the details of newly developed apparatus with this sensor, and measurement results of iron loss by using are shown.

Transformation of the Discriminative and Eliciting Functions of Generalized Relational Stimuli

ERIC Educational Resources Information Center

Dougher, Michael J.; Hamilton, Derek; Fink, Brandi; Harrington, Jennifer

2007-01-01

In three experiments, match-to-sample procedures were used with undergraduates to establish arbitrary relational functions for three abstract visual stimuli. In the presence of samples A, B, and C, participants were trained to select the smallest, middle, and largest member, respectively, of a series of three-comparison arrays. In Experiment 1,…

Hippocampus Is Required for Paired Associate Memory with Neither Delay Nor Trial Uniqueness

ERIC Educational Resources Information Center

Yoon, Jinah; Seo, Yeran; Kim, Jangjin; Lee, Inah

2012-01-01

Cued retrieval of memory is typically examined with delay when testing hippocampal functions, as in delayed matching-to-sample tasks. Equally emphasized in the literature, on the other hand, is the hippocampal involvement in making arbitrary associations. Paired associate memory tasks are widely used for examining this function. However, the two…

Particle dynamics around time conformal regular black holes via Noether symmetries

NASA Astrophysics Data System (ADS)

Jawad, Abdul; Umair Shahzad, M.

The time conformal regular black hole (RBH) solutions which are admitting the time conformal factor e𝜖g(t), where g(t) is an arbitrary function of time and 𝜖 is the perturbation parameter are being considered. The approximate Noether symmetries technique is being used for finding the function g(t) which leads to t α. The dynamics of particles around RBHs are also being discussed through symmetry generators which provide approximate energy as well as angular momentum of the particles. In addition, we analyze the motion of neutral and charged particles around two well known RBHs such as charged RBH using Fermi-Dirac distribution and Kehagias-Sftesos asymptotically flat RBH. We obtain the innermost stable circular orbit and corresponding approximate energy and angular momentum. The behavior of effective potential, effective force and escape velocity of the particles in the presence/absence of magnetic field for different values of angular momentum near horizons are also being analyzed. The stable and unstable regions of particle near horizons due to the effect of angular momentum and magnetic field are also explained.

Back in the saddle: large-deviation statistics of the cosmic log-density field

NASA Astrophysics Data System (ADS)

Uhlemann, C.; Codis, S.; Pichon, C.; Bernardeau, F.; Reimberg, P.

2016-08-01

We present a first principle approach to obtain analytical predictions for spherically averaged cosmic densities in the mildly non-linear regime that go well beyond what is usually achieved by standard perturbation theory. A large deviation principle allows us to compute the leading order cumulants of average densities in concentric cells. In this symmetry, the spherical collapse model leads to cumulant generating functions that are robust for finite variances and free of critical points when logarithmic density transformations are implemented. They yield in turn accurate density probability distribution functions (PDFs) from a straightforward saddle-point approximation valid for all density values. Based on this easy-to-implement modification, explicit analytic formulas for the evaluation of the one- and two-cell PDF are provided. The theoretical predictions obtained for the PDFs are accurate to a few per cent compared to the numerical integration, regardless of the density under consideration and in excellent agreement with N-body simulations for a wide range of densities. This formalism should prove valuable for accurately probing the quasi-linear scales of low-redshift surveys for arbitrary primordial power spectra.

A formal model of asynchronous communication and its use in mechanically verifying a biphase mark protocol

NASA Technical Reports Server (NTRS)

Moore, J. Strother

1992-01-01

In this paper we present a formal model of asynchronous communication as a function in the Boyer-Moore logic. The function transforms the signal stream generated by one processor into the signal stream consumed by an independently clocked processor. This transformation 'blurs' edges and 'dilates' time due to differences in the phases and rates of the two clocks and the communications delay. The model can be used quantitatively to derive concrete performance bounds on asynchronous communications at ISO protocol level 1 (physical level). We develop part of the reusable formal theory that permits the convenient application of the model. We use the theory to show that a biphase mark protocol can be used to send messages of arbitrary length between two asynchronous processors. We study two versions of the protocol, a conventional one which uses cells of size 32 cycles and an unconventional one which uses cells of size 18. We conjecture that the protocol can be proved to work under our model for smaller cell sizes and more divergent clock rates but the proofs would be harder.

Decorating surfaces with bidirectional texture functions.

PubMed

Zhou, Kun; Du, Peng; Wang, Lifeng; Matsushita, Yasuyuki; Shi, Jiaoying; Guo, Baining; Shum, Heung-Yeung

2005-01-01

We present a system for decorating arbitrary surfaces with bidirectional texture functions (BTF). Our system generates BTFs in two steps. First, we automatically synthesize a BTF over the target surface from a given BTF sample. Then, we let the user interactively paint BTF patches onto the surface such that the painted patches seamlessly integrate with the background patterns. Our system is based on a patch-based texture synthesis approach known as quilting. We present a graphcut algorithm for BTF synthesis on surfaces and the algorithm works well for a wide variety of BTF samples, including those which present problems for existing algorithms. We also describe a graphcut texture painting algorithm for creating new surface imperfections (e.g., dirt, cracks, scratches) from existing imperfections found in input BTF samples. Using these algorithms, we can decorate surfaces with real-world textures that have spatially-variant reflectance, fine-scale geometry details, and surfaces imperfections. A particularly attractive feature of BTF painting is that it allows us to capture imperfections of real materials and paint them onto geometry models. We demonstrate the effectiveness of our system with examples.

Clinical records anonymisation and text extraction (CRATE): an open-source software system.

PubMed

Cardinal, Rudolf N

2017-04-26

Electronic medical records contain information of value for research, but contain identifiable and often highly sensitive confidential information. Patient-identifiable information cannot in general be shared outside clinical care teams without explicit consent, but anonymisation/de-identification allows research uses of clinical data without explicit consent. This article presents CRATE (Clinical Records Anonymisation and Text Extraction), an open-source software system with separable functions: (1) it anonymises or de-identifies arbitrary relational databases, with sensitivity and precision similar to previous comparable systems; (2) it uses public secure cryptographic methods to map patient identifiers to research identifiers (pseudonyms); (3) it connects relational databases to external tools for natural language processing; (4) it provides a web front end for research and administrative functions; and (5) it supports a specific model through which patients may consent to be contacted about research. Creation and management of a research database from sensitive clinical records with secure pseudonym generation, full-text indexing, and a consent-to-contact process is possible and practical using entirely free and open-source software.

Analytic H I-to-H2 Photodissociation Transition Profiles

NASA Astrophysics Data System (ADS)

Bialy, Shmuel; Sternberg, Amiel

2016-05-01

We present a simple analytic procedure for generating atomic (H I) to molecular ({{{H}}}2) density profiles for optically thick hydrogen gas clouds illuminated by far-ultraviolet radiation fields. Our procedure is based on the analytic theory for the structure of one-dimensional H I/{{{H}}}2 photon-dominated regions, presented by Sternberg et al. Depth-dependent atomic and molecular density fractions may be computed for arbitrary gas density, far-ultraviolet field intensity, and the metallicity-dependent H2 formation rate coefficient, and dust absorption cross section in the Lyman-Werner photodissociation band. We use our procedure to generate a set of {{H}} {{I}}{-}{to}{-}{{{H}}}2 transition profiles for a wide range of conditions, from the weak- to strong-field limits, and from super-solar down to low metallicities. We show that if presented as functions of dust optical depth, the {{H}} {{I}} and {{{H}}}2 density profiles depend primarily on the Sternberg “α G parameter” (dimensionless) that determines the dust optical depth associated with the total photodissociated {{H}} {{I}} column. We derive a universal analytic formula for the {{H}} {{I}}{-}{to}{-}{{{H}}}2 transition points as a function of just α G. Our formula will be useful for interpreting emission-line observations of H I/{{{H}}}2 interfaces, for estimating star formation thresholds, and for sub-grid components in hydrodynamics simulations.

Acoustic scattering by arbitrary distributions of disjoint, homogeneous cylinders or spheres.

PubMed

Hesford, Andrew J; Astheimer, Jeffrey P; Waag, Robert C

2010-05-01

A T-matrix formulation is presented to compute acoustic scattering from arbitrary, disjoint distributions of cylinders or spheres, each with arbitrary, uniform acoustic properties. The generalized approach exploits the similarities in these scattering problems to present a single system of equations that is easily specialized to cylindrical or spherical scatterers. By employing field expansions based on orthogonal harmonic functions, continuity of pressure and normal particle velocity are directly enforced at each scatterer using diagonal, analytic expressions to eliminate the need for integral equations. The effect of a cylinder or sphere that encloses all other scatterers is simulated with an outer iterative procedure that decouples the inner-object solution from the effect of the enclosing object to improve computational efficiency when interactions among the interior objects are significant. Numerical results establish the validity and efficiency of the outer iteration procedure for nested objects. Two- and three-dimensional methods that employ this outer iteration are used to measure and characterize the accuracy of two-dimensional approximations to three-dimensional scattering of elevation-focused beams.

Variational extension of the mean spherical approximation to arbitrary dimensions

NASA Astrophysics Data System (ADS)

Velázquez, Esov S.; Blum, Lesser; Frisch, Harry L.

1997-10-01

We generalize a variational principle for the mean spherical approximation for a system of charged hard spheres in 3D to arbitrary dimensions. We first construct a free energy variational trial function from the Debye-Hückel excess charging internal energy at a finite concentration and an entropy obtained at the zero-concentration limit by thermodynamic integration. In three dimensions the minimization of this expression with respect to the screening parameter leads to the mean spherical approximation, usually obtained by solution of the Ornstein-Zernike equation. This procedure, which interpolates naturally between the zero concentration/coupling limit and the high-concentration/ coupling limit, is extended to arbitrary dimensions. We conjecture that this result is also equivalent to the MSA as originally defined, although a technical proof of this point is left for the future. The Onsager limit T ΔS MSA / ΔE MSA → 0 for infinite concentration/coupling is satisfied for all d ≠ 2, while for d=2 this limit is 1.

Radiation and scattering by thin-wire structures in the complex frequency domain. [electromagnetic theory for thin-wire antennas

NASA Technical Reports Server (NTRS)

Richmond, J. H.

1974-01-01

Piecewise-sinusoidal expansion functions and Galerkin's method are employed to formulate a solution for an arbitrary thin-wire configuration in a homogeneous conducting medium. The analysis is performed in the real or complex frequency domain. In antenna problems, the solution determines the current distribution, impedance, radiation efficiency, gain and far-field patterns. In scattering problems, the solution determines the absorption cross section, scattering cross section and the polarization scattering matrix. The electromagnetic theory is presented for thin wires and the forward-scattering theorem is developed for an arbitrary target in a homogeneous conducting medium.

A method for computing the kernel of the downwash integral equation for arbitrary complex frequencies

NASA Technical Reports Server (NTRS)

Desmarais, R. N.; Rowe, W. S.

1984-01-01

For the design of active controls to stabilize flight vehicles, which requires the use of unsteady aerodynamics that are valid for arbitrary complex frequencies, algorithms are derived for evaluating the nonelementary part of the kernel of the integral equation that relates unsteady pressure to downwash. This part of the kernel is separated into an infinite limit integral that is evaluated using Bessel and Struve functions and into a finite limit integral that is expanded in series and integrated termwise in closed form. The developed series expansions gave reliable answers for all complex reduced frequencies and executed faster than exponential approximations for many pressure stations.

Stochastic associative memory

NASA Astrophysics Data System (ADS)

Baumann, Erwin W.; Williams, David L.

1993-08-01

Artificial neural networks capable of learning and recalling stochastic associations between non-deterministic quantities have received relatively little attention to date. One potential application of such stochastic associative networks is the generation of sensory 'expectations' based on arbitrary subsets of sensor inputs to support anticipatory and investigate behavior in sensor-based robots. Another application of this type of associative memory is the prediction of how a scene will look in one spectral band, including noise, based upon its appearance in several other wavebands. This paper describes a semi-supervised neural network architecture composed of self-organizing maps associated through stochastic inter-layer connections. This 'Stochastic Associative Memory' (SAM) can learn and recall non-deterministic associations between multi-dimensional probability density functions. The stochastic nature of the network also enables it to represent noise distributions that are inherent in any true sensing process. The SAM architecture, training process, and initial application to sensor image prediction are described. Relationships to Fuzzy Associative Memory (FAM) are discussed.

Research on bulbous bow optimization based on the improved PSO algorithm

NASA Astrophysics Data System (ADS)

Zhang, Sheng-long; Zhang, Bao-ji; Tezdogan, Tahsin; Xu, Le-ping; Lai, Yu-yang

2017-08-01

In order to reduce the total resistance of a hull, an optimization framework for the bulbous bow optimization was presented. The total resistance in calm water was selected as the objective function, and the overset mesh technique was used for mesh generation. RANS method was used to calculate the total resistance of the hull. In order to improve the efficiency and smoothness of the geometric reconstruction, the arbitrary shape deformation (ASD) technique was introduced to change the shape of the bulbous bow. To improve the global search ability of the particle swarm optimization (PSO) algorithm, an improved particle swarm optimization (IPSO) algorithm was proposed to set up the optimization model. After a series of optimization analyses, the optimal hull form was found. It can be concluded that the simulation based design framework built in this paper is a promising method for bulbous bow optimization.

Constraints on rapidity-dependent initial conditions from charged-particle pseudorapidity densities and two-particle correlations

NASA Astrophysics Data System (ADS)

Ke, Weiyao; Moreland, J. Scott; Bernhard, Jonah E.; Bass, Steffen A.

2017-10-01

We study the initial three-dimensional spatial configuration of the quark-gluon plasma (QGP) produced in relativistic heavy-ion collisions using centrality and pseudorapidity-dependent measurements of the medium's charged particle density and two-particle correlations. A cumulant-generating function is first used to parametrize the rapidity dependence of local entropy deposition and extend arbitrary boost-invariant initial conditions to nonzero beam rapidities. The model is then compared to p +Pb and Pb + Pb charged-particle pseudorapidity densities and two-particle pseudorapidity correlations and systematically optimized using Bayesian parameter estimation to extract high-probability initial condition parameters. The optimized initial conditions are then compared to a number of experimental observables including the pseudorapidity-dependent anisotropic flows, event-plane decorrelations, and flow correlations. We find that the form of the initial local longitudinal entropy profile is well constrained by these experimental measurements.

Integration of the Rotation of an Earth-like Body as a Perturbed Spherical Rotor

NASA Astrophysics Data System (ADS)

Ferrer, Sebastián; Lara, Martin

2010-05-01

For rigid bodies close to a sphere, we propose an analytical solution that is free from elliptic integrals and functions, and can be fundamental for application to perturbed problems. After reordering the Hamiltonian as a perturbed spherical rotor, the Lie-series solution is generated up to an arbitrary order. Using the inertia parameters of different solar system bodies, the comparison of the approximate series solution with the exact analytical one shows that the precision reached with relatively low orders is at the same level of the observational accuracy for the Earth and Mars. Thus, for instance, the periodic errors of the mathematical solution are confined to the microarcsecond level with a simple second-order truncation for the Earth. On the contrary, higher orders are required for the mathematical solution to reach a precision at the expected level of accuracy of proposed new theories for the rotational dynamics of the Moon.

Analysis of bulk arrival queueing system with batch size dependent service and working vacation

NASA Astrophysics Data System (ADS)

Niranjan, S. P.; Indhira, K.; Chandrasekaran, V. M.

2018-04-01

This paper concentrates on single server bulk arrival queue system with batch size dependent service and working vacation. The server provides service in two service modes depending upon the queue length. The server provides single service if the queue length is at least `a'. On the other hand the server provides fixed batch service if the queue length is at least `k' (k > a). Batch service is provided with some fixed batch size `k'. After completion of service if the queue length is less than `a' then the server leaves for working vacation. During working vacation customers are served with lower service rate than the regular service rate. Service during working vacation also contains two service modes. For the proposed model probability generating function of the queue length at an arbitrary time will be obtained by using supplementary variable technique. Some performance measures will also be presented with suitable numerical illustrations.

Approximating the Generalized Voronoi Diagram of Closely Spaced Objects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Edwards, John; Daniel, Eric; Pascucci, Valerio

2015-06-22

We present an algorithm to compute an approximation of the generalized Voronoi diagram (GVD) on arbitrary collections of 2D or 3D geometric objects. In particular, we focus on datasets with closely spaced objects; GVD approximation is expensive and sometimes intractable on these datasets using previous algorithms. With our approach, the GVD can be computed using commodity hardware even on datasets with many, extremely tightly packed objects. Our approach is to subdivide the space with an octree that is represented with an adjacency structure. We then use a novel adaptive distance transform to compute the distance function on octree vertices. Themore » computed distance field is sampled more densely in areas of close object spacing, enabling robust and parallelizable GVD surface generation. We demonstrate our method on a variety of data and show example applications of the GVD in 2D and 3D.« less

Demonstration of temperature imaging by H₂O absorption spectroscopy using compressed sensing tomography.

PubMed

An, Xinliang; Brittelle, Mack S; Lauzier, Pascal T; Gord, James R; Roy, Sukesh; Chen, Guang-Hong; Sanders, Scott T

2015-11-01

This paper introduces temperature imaging by total-variation-based compressed sensing (CS) tomography of H2O vapor absorption spectroscopy. A controlled laboratory setup is used to generate a constant two-dimensional temperature distribution in air (a roughly Gaussian temperature profile with a central temperature of 677 K). A wavelength-tunable laser beam is directed through the known distribution; the beam is translated and rotated using motorized stages to acquire complete absorption spectra in the 1330-1365 nm range at each of 64 beam locations and 60 view angles. Temperature reconstructions are compared to independent thermocouple measurements. Although the distribution studied is approximately axisymmetric, axisymmetry is not assumed and simulations show similar performance for arbitrary temperature distributions. We study the measurement error as a function of number of beams and view angles used in reconstruction to gauge the potential for application of CS in practical test articles where optical access is limited.

Selected Aspects of Markovian and Non-Markovian Quantum Master Equations

NASA Astrophysics Data System (ADS)

Lendi, K.

A few particular marked properties of quantum dynamical equations accounting for general relaxation and dissipation are selected and summarized in brief. Most results derive from the universal concept of complete positivity. The considerations mainly regard genuinely irreversible processes as characterized by a unique asymptotically stationary final state for arbitrary initial conditions. From ordinary Markovian master equations and associated quantum dynamical semigroup time-evolution, derivations of higher order Onsager coefficients and related entropy production are discussed. For general processes including non-faithful states a regularized version of quantum relative entropy is introduced. Further considerations extend to time-dependent infinitesimal generators of time-evolution and to a possible description of propagation of initial states entangled between open system and environment. In the coherence-vector representation of the full non-Markovian equations including entangled initial states, first results are outlined towards identifying mathematical properties of a restricted class of trial integral-kernel functions suited to phenomenological applications.

All-atom calculation of protein free-energy profiles

NASA Astrophysics Data System (ADS)

Orioli, S.; Ianeselli, A.; Spagnolli, G.; Faccioli, P.

2017-10-01

The Bias Functional (BF) approach is a variational method which enables one to efficiently generate ensembles of reactive trajectories for complex biomolecular transitions, using ordinary computer clusters. For example, this scheme was applied to simulate in atomistic detail the folding of proteins consisting of several hundreds of amino acids and with experimental folding time of several minutes. A drawback of the BF approach is that it produces trajectories which do not satisfy microscopic reversibility. Consequently, this method cannot be used to directly compute equilibrium observables, such as free energy landscapes or equilibrium constants. In this work, we develop a statistical analysis which permits us to compute the potential of mean-force (PMF) along an arbitrary collective coordinate, by exploiting the information contained in the reactive trajectories calculated with the BF approach. We assess the accuracy and computational efficiency of this scheme by comparing its results with the PMF obtained for a small protein by means of plain molecular dynamics.

Programmable Oscillator

NASA Technical Reports Server (NTRS)

Quirk, Kevin J.; Patawaran, Ferze D.; Nguyen, Danh H.; Lee, Clement G.; Nguyen, Huy

2011-01-01

A programmable oscillator is a frequency synthesizer with an output phase that tracks an arbitrary function. An offset, phase-locked loop circuit is used in combination with an error control feedback loop to precisely control the output phase of the oscillator. To down-convert the received signal, several stages of mixing may be employed with the compensation for the time-base distortion of the carrier occurring at any one of those stages. In the Goldstone Solar System Radar (GSSR), the compensation occurs in the mixing from an intermediate frequency (IF), whose value is dependent on the station and band, to a common IF used in the final stage of down-conversion to baseband. The programmable oscillator (PO) is used in the final stage of down-conversion to generate the IF, along with a time-varying phase component that matches the time-base distortion of the carrier, thus removing it from the final down-converted signal.

A low power, area efficient fpga based beamforming technique for 1-D CMUT arrays.

PubMed

Joseph, Bastin; Joseph, Jose; Vanjari, Siva Rama Krishna

2015-08-01

A low power area efficient digital beamformer targeting low frequency (2MHz) 1-D linear Capacitive Micromachined Ultrasonic Transducer (CMUT) array is developed. While designing the beamforming logic, the symmetry of the CMUT array is well exploited to reduce the area and power consumption. The proposed method is verified in Matlab by clocking an Arbitrary Waveform Generator(AWG). The architecture is successfully implemented in Xilinx Spartan 3E FPGA kit to check its functionality. The beamforming logic is implemented for 8, 16, 32, and 64 element CMUTs targeting Application Specific Integrated Circuit (ASIC) platform at Vdd 1.62V for UMC 90nm technology. It is observed that the proposed architecture consumes significantly lesser power and area (1.2895 mW power and 47134.4 μm(2) area for a 64 element digital beamforming circuit) compared to the conventional square root based algorithm.

Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks.

PubMed

Chen, Boshan; Chen, Jiejie

2015-08-01

We study the global asymptotic ω-periodicity for a fractional-order non-autonomous neural networks. Firstly, based on the Caputo fractional-order derivative it is shown that ω-periodic or autonomous fractional-order neural networks cannot generate exactly ω-periodic signals. Next, by using the contraction mapping principle we discuss the existence and uniqueness of S-asymptotically ω-periodic solution for a class of fractional-order non-autonomous neural networks. Then by using a fractional-order differential and integral inequality technique, we study global Mittag-Leffler stability and global asymptotical periodicity of the fractional-order non-autonomous neural networks, which shows that all paths of the networks, starting from arbitrary points and responding to persistent, nonconstant ω-periodic external inputs, asymptotically converge to the same nonconstant ω-periodic function that may be not a solution. Copyright © 2015 Elsevier Ltd. All rights reserved.

Theory and simulation of photogeneration and transport in Si-SiOx superlattice absorbers

PubMed Central

2011-01-01

Si-SiOx superlattices are among the candidates that have been proposed as high band gap absorber material in all-Si tandem solar cell devices. Owing to the large potential barriers for photoexited charge carriers, transport in these devices is restricted to quantum-confined superlattice states. As a consequence of the finite number of wells and large built-in fields, the electronic spectrum can deviate considerably from the minibands of a regular superlattice. In this article, a quantum-kinetic theory based on the non-equilibrium Green's function formalism for an effective mass Hamiltonian is used for investigating photogeneration and transport in such devices for arbitrary geometry and operating conditions. By including the coupling of electrons to both photons and phonons, the theory is able to provide a microscopic picture of indirect generation, carrier relaxation, and inter-well transport mechanisms beyond the ballistic regime. PMID:21711827

Synthetic Biology Platform for Sensing and Integrating Endogenous Transcriptional Inputs in Mammalian Cells.

PubMed

Angelici, Bartolomeo; Mailand, Erik; Haefliger, Benjamin; Benenson, Yaakov

2016-08-30

One of the goals of synthetic biology is to develop programmable artificial gene networks that can transduce multiple endogenous molecular cues to precisely control cell behavior. Realizing this vision requires interfacing natural molecular inputs with synthetic components that generate functional molecular outputs. Interfacing synthetic circuits with endogenous mammalian transcription factors has been particularly difficult. Here, we describe a systematic approach that enables integration and transduction of multiple mammalian transcription factor inputs by a synthetic network. The approach is facilitated by a proportional amplifier sensor based on synergistic positive autoregulation. The circuits efficiently transduce endogenous transcription factor levels into RNAi, transcriptional transactivation, and site-specific recombination. They also enable AND logic between pairs of arbitrary transcription factors. The results establish a framework for developing synthetic gene networks that interface with cellular processes through transcriptional regulators. Copyright © 2016 The Author(s). Published by Elsevier Inc. All rights reserved.

Typical performance of approximation algorithms for NP-hard problems

NASA Astrophysics Data System (ADS)

Takabe, Satoshi; Hukushima, Koji

2016-11-01

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with the presentation of a theoretical framework. Herein, three approximation algorithms are examined: linear-programming relaxation, loopy-belief propagation, and the leaf-removal algorithm. The former two algorithms are analyzed using a statistical-mechanical technique, whereas the average-case analysis of the last one is conducted using the generating function method. These algorithms have a threshold in the typical performance with increasing average degree of the random graph, below which they find true optimal solutions with high probability. Our study reveals that there exist only three cases, determined by the order of the typical performance thresholds. In addition, we provide some conditions for classification of the graph ensembles and demonstrate explicitly some examples for the difference in thresholds.

Synthetic biology. Genomically encoded analog memory with precise in vivo DNA writing in living cell populations.

PubMed

Farzadfard, Fahim; Lu, Timothy K

2014-11-14

Cellular memory is crucial to many natural biological processes and sophisticated synthetic biology applications. Existing cellular memories rely on epigenetic switches or recombinases, which are limited in scalability and recording capacity. In this work, we use the DNA of living cell populations as genomic "tape recorders" for the analog and distributed recording of long-term event histories. We describe a platform for generating single-stranded DNA (ssDNA) in vivo in response to arbitrary transcriptional signals. When coexpressed with a recombinase, these intracellularly expressed ssDNAs target specific genomic DNA addresses, resulting in precise mutations that accumulate in cell populations as a function of the magnitude and duration of the inputs. This platform could enable long-term cellular recorders for environmental and biomedical applications, biological state machines, and enhanced genome engineering strategies. Copyright © 2014, American Association for the Advancement of Science.

Motion of kinesin in a viscoelastic medium

NASA Astrophysics Data System (ADS)

Knoops, Gert; Vanderzande, Carlo

2018-05-01

Kinesin is a molecular motor that transports cargo along microtubules. The results of many in vitro experiments on kinesin-1 are described by kinetic models in which one transition corresponds to the forward motion and subsequent binding of the tethered motor head. We argue that in a viscoelastic medium like the cytosol of a cell this step is not Markov and has to be described by a nonexponential waiting time distribution. We introduce a semi-Markov kinetic model for kinesin that takes this effect into account. We calculate, for arbitrary waiting time distributions, the moment generating function of the number of steps made, and determine from this the average velocity and the diffusion constant of the motor. We illustrate our results for the case of a waiting time distribution that is Weibull. We find that for realistic parameter values, viscoelasticity decreases the velocity and the diffusion constant, but increases the randomness (or Fano factor).

A Hidden Markov Model Approach for Simultaneously Estimating Local Ancestry and Admixture Time Using Next Generation Sequence Data in Samples of Arbitrary Ploidy

PubMed Central

Nielsen, Rasmus

2017-01-01

Admixture—the mixing of genomes from divergent populations—is increasingly appreciated as a central process in evolution. To characterize and quantify patterns of admixture across the genome, a number of methods have been developed for local ancestry inference. However, existing approaches have a number of shortcomings. First, all local ancestry inference methods require some prior assumption about the expected ancestry tract lengths. Second, existing methods generally require genotypes, which is not feasible to obtain for many next-generation sequencing projects. Third, many methods assume samples are diploid, however a wide variety of sequencing applications will fail to meet this assumption. To address these issues, we introduce a novel hidden Markov model for estimating local ancestry that models the read pileup data, rather than genotypes, is generalized to arbitrary ploidy, and can estimate the time since admixture during local ancestry inference. We demonstrate that our method can simultaneously estimate the time since admixture and local ancestry with good accuracy, and that it performs well on samples of high ploidy—i.e. 100 or more chromosomes. As this method is very general, we expect it will be useful for local ancestry inference in a wider variety of populations than what previously has been possible. We then applied our method to pooled sequencing data derived from populations of Drosophila melanogaster on an ancestry cline on the east coast of North America. We find that regions of local recombination rates are negatively correlated with the proportion of African ancestry, suggesting that selection against foreign ancestry is the least efficient in low recombination regions. Finally we show that clinal outlier loci are enriched for genes associated with gene regulatory functions, consistent with a role of regulatory evolution in ecological adaptation of admixed D. melanogaster populations. Our results illustrate the potential of local ancestry inference for elucidating fundamental evolutionary processes. PMID:28045893

User's Manual for FEMOM3DR. Version 1.0

NASA Technical Reports Server (NTRS)

Reddy, C. J.

1998-01-01

FEMoM3DR is a computer code written in FORTRAN 77 to compute radiation characteristics of antennas on 3D body using combined Finite Element Method (FEM)/Method of Moments (MoM) technique. The code is written to handle different feeding structures like coaxial line, rectangular waveguide, and circular waveguide. This code uses the tetrahedral elements, with vector edge basis functions for FEM and triangular elements with roof-top basis functions for MoM. By virtue of FEM, this code can handle any arbitrary shaped three dimensional bodies with inhomogeneous lossy materials; and due to MoM the computational domain can be terminated in any arbitrary shape. The User's Manual is written to make the user acquainted with the operation of the code. The user is assumed to be familiar with the FORTRAN 77 language and the operating environment of the computers on which the code is intended to run.

From spinning conformal blocks to matrix Calogero-Sutherland models

NASA Astrophysics Data System (ADS)

Schomerus, Volker; Sobko, Evgeny

2018-04-01

In this paper we develop further the relation between conformal four-point blocks involving external spinning fields and Calogero-Sutherland quantum mechanics with matrix-valued potentials. To this end, the analysis of [1] is extended to arbitrary dimensions and to the case of boundary two-point functions. In particular, we construct the potential for any set of external tensor fields. Some of the resulting Schrödinger equations are mapped explicitly to the known Casimir equations for 4-dimensional seed conformal blocks. Our approach furnishes solutions of Casimir equations for external fields of arbitrary spin and dimension in terms of functions on the conformal group. This allows us to reinterpret standard operations on conformal blocks in terms of group-theoretic objects. In particular, we shall discuss the relation between the construction of spinning blocks in any dimension through differential operators acting on seed blocks and the action of left/right invariant vector fields on the conformal group.

Anti-plane eigenstrain problem of an inclusion of arbitrary shape in an anisotropic bimaterial with a semi-infinite interface crack

NASA Astrophysics Data System (ADS)

Wang, Xu; Schiavone, Peter

2018-02-01

We consider an Eshelby inclusion of arbitrary shape with uniform anti-plane eigenstrains embedded in one of two bonded dissimilar anisotropic half planes containing a semi-infinite interface crack situated along the negative real axis. Using two consecutive conformal mappings, the upper and lower halves of the physical plane are first mapped onto two separate quarters of the image plane. The corresponding boundary value problem is then analyzed in this image plane rather than in the original physical plane. Corresponding analytic functions in all three phases of the composite are derived via the construction of an auxiliary function and repeated application of analytic continuation across the real and imaginary axes in the image plane. As a result, the local stress intensity factor is then obtained explicitly. Perhaps most interestingly, we find that the satisfaction of a particular condition makes the inclusion (stress) invisible to the crack.

Induced drag ideal efficiency factor of arbitrary lateral-vertical wing forms

NASA Technical Reports Server (NTRS)

Deyoung, J.

1980-01-01

A relatively simple equation is presented for estimating the induced drag ideal efficiency factor e for arbitrary cross sectional wing forms. This equation is based on eight basic but varied wing configurations which have exact solutions. The e function which relates the basic wings is developed statistically and is a continuous function of configuration geometry. The basic wing configurations include boxwings shaped as a rectangle, ellipse, and diamond; the V-wing; end-plate wing; 90 degree cruciform; circle dumbbell; and biplane. Example applications of the e equations are made to many wing forms such as wings with struts which form partial span rectangle dumbbell wings; bowtie, cruciform, winglet, and fan wings; and multiwings. Derivations are presented in the appendices of exact closed form solutions found of e for the V-wing and 90 degree cruciform wing and for an asymptotic solution for multiwings.

A study of the nonlinear aerodynamics of bodies in nonplanar motion. Ph.D. Thesis - Stanford Univ., Calif.; [numerical analysis of aerodynamic force and moment systems during large amplitude, arbitrary motions

NASA Technical Reports Server (NTRS)

Schiff, L. B.

1974-01-01

Concepts from the theory of functionals are used to develop nonlinear formulations of the aerodynamic force and moment systems acting on bodies in large-amplitude, arbitrary motions. The analysis, which proceeds formally once the functional dependence of the aerodynamic reactions upon the motion variables is established, ensures the inclusion, within the resulting formulation, of pertinent aerodynamic terms that normally are excluded in the classical treatment. Applied to the large-amplitude, slowly varying, nonplanar motion of a body, the formulation suggests that the aerodynamic moment can be compounded of the moments acting on the body in four basic motions: steady angle of attack, pitch oscillations, either roll or yaw oscillations, and coning motion. Coning, where the nose of the body describes a circle around the velocity vector, characterizes the nonplanar nature of the general motion.

High-order noise filtering in nontrivial quantum logic gates.

PubMed

Green, Todd; Uys, Hermann; Biercuk, Michael J

2012-07-13

Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of noncommuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics.

Algebraic grid generation for coolant passages of turbine blades with serpentine channels and pin fins

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Roelke, R. J.; Steinthorsson, E.

1991-01-01

In order to study numerically details of the flow and heat transfer within coolant passages of turbine blades, a method must first be developed to generate grid systems within the very complicated geometries involved. In this study, a grid generation package was developed that is capable of generating the required grid systems. The package developed is based on an algebraic grid generation technique that permits the user considerable control over how grid points are to be distributed in a very explicit way. These controls include orthogonality of grid lines next to boundary surfaces and ability to cluster about arbitrary points, lines, and surfaces. This paper describes that grid generation package and shows how it can be used to generate grid systems within complicated-shaped coolant passages via an example.

Vibration characteristics of functionally graded carbon nanotube reinforced composite rectangular plates on Pasternak foundation with arbitrary boundary conditions and internal line supports

NASA Astrophysics Data System (ADS)

Zhong, Rui; Wang, Qingshan; Tang, Jinyuan; Shuai, Cijun; Liang, Qian

2018-02-01

This paper presents the first known vibration characteristics of moderately thick functionally graded carbon nanotube reinforced composite rectangular plates on Pasternak foundation with arbitrary boundary conditions and internal line supports on the basis of the firstorder shear deformation theory. Different distributions of single walled carbon nanotubes (SWCNTs) along the thickness are considered. Uniform and other three kinds of functionally graded distributions of carbon nanotubes along the thickness direction of plates are studied. The solutions carried out using an enhanced Ritz method mainly include the following three points: Firstly, create the Lagrange energy function by the energy principle; Secondly, as the main innovation point, the modified Fourier series are chosen as the basic functions of the admissible functions of the plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges; Lastly, solve the natural frequencies as well as the associated mode shapes by means of the Ritz-variational energy method. In this study, the influences of the volume fraction of CNTs, distribution type of CNTs, boundary restrain parameters, location of the internal line supports, foundation coefficients on the natural frequencies and mode shapes of the FG-CNT reinforced composite rectangular plates are presented.

Nanosecond pulse shaping at 780 nm with fiber-based electro-optical modulators and a double-pass tapered amplifier

DOE PAGES

Rogers, III, C. E.; Gould, P. L.

2016-02-01

Here, we describe a system for generating frequency-chirped and amplitude-shaped pulses on time scales from sub-nanosecond to ten nanoseconds. The system starts with cw diode-laser light at 780 nm and utilizes fiber-based electro-optical phase and intensity modulators, driven by an arbitrary waveform generator, to generate the shaped pulses. These pulses are subsequently amplified to several hundred mW with a tapered amplifier in a delayed double-pass configuration. Frequency chirps up to 5 GHz in 2 ns and pulse widths as short as 0.15 ns have been realized.