Discrete Lines Research Articles

Phonon-based mesh optimization for the Monte Carlo on-the-fly thermal scattering temperature fit coefficients

In a series of papers, we have introduced a new sampling method for Monte Carlo codes for the low-energy secondary scattering parameters that greatly reduces data storage requirements. The method is based on the temperature dependence of the energy transfer (beta) and squared momentum transfer (alpha) between a neutron and a target nuclide. Cumulative distribution functions (CDFs) in beta and alpha are constructed for a range of temperatures on a mesh of incident energies in the thermal range and temperature fits are created for beta and alpha at discrete CDF probability lines. The secondary energy and angle distributions generated from the fit coefficients showed good agreement with the standard Monte Carlo sampling. However, some discrepancies still existed because the CDF probability mesh values were selected uniformly and arbitrarily. In this paper, a physics-based approach for optimally selecting the CDF probability meshes for the on-the-fly sampling method is introduced, using bound carbon in graphite as the example nuclide. This approach is based on the structure of the phonon frequency distribution of thermal excitations. From the study, it was determined that low (<0.1) and high (>0.9) beta CDF probabilities are important to the structure of the beta probability density functions (PDFs) while very low (<1×10−4) alpha CDF probabilities are important to the structure of the alpha PDFs. The final meshes contain 200 probability values for both beta and alpha. This results in 14.5MB of total data storage for the on-the-fly coefficients which are used for any temperature realization. This is a significant reduction in data storage from current methods that require around 25MB per temperature.

Multi-wavelength passively Q-switched c-cut Nd:YVO4 self-Raman laser with Cr4+:YAG saturable absorber

A multi-wavelength passively Q-switched self-Raman laser with a c-cut Nd:YVO4 both as laser and Raman medium is reported. With the increasing pump power, the multi-wavelength laser including the fundamental line at 1067.4nm, 1st-Stokes at 1097.9nm, 2nd-Stokes at 1130.1nm, and 3rd-Stokes at 1163.6nm is generated sequentially. At a pump power of 5.0W, the maximum output power of the four discrete lines are 186.8mW, 246.5mW, 158.4mW and 63.6mW, with corresponding optical conversion efficiencies of 3.7%, 4.9%, 3.2% and 1.3% respectively. The total stimulated Raman scattering conversion efficiency is 9.4%. To our best knowledge, this is the first report of the 2nd-Stokes at 1130.1nm and 3rd-Stokes at 1163.6nm.

Derivation of F=FeFp as the continuum limit of crystalline slip

In this paper we provide a proof of the multiplicative kinematic description of crystal elastoplasticity in the setting of large deformations, i.e. F=FeFp, for a two dimensional single crystal. The proof starts by considering a general configuration at the mesoscopic scale, where the dislocations are discrete line defects (points in the two-dimensional description used here) and the displacement field can be considered continuous everywhere in the domain except at the slip surfaces, over which there is a displacement jump. At such scale, as previously shown by two of the authors, there exists unique physically based definitions of the total deformation tensor F and the elastic and plastic tensors Fe and Fp that do not require the consideration of any non-realizable intermediate configuration and do not assume any a priori relation between them of the form F=FeFp. This mesoscopic description is then passed to the continuum limit via homogenization, i.e. by increasing the number of slip surfaces to infinity and reducing the lattice parameter to zero. We show for two-dimensional deformations of initially perfect single crystals that the classical continuum formulation is recovered in the limit with F=FeFp, detFp=1 and G=CurlFp the dislocation density tensor.

Spectropolarimetry of the Type Ib Supernova iPTF 13bvn: revealing the complex explosion geometry of a stripped-envelope core-collapse supernova

We present six epochs of spectropolarimetric observations and one epoch of spectroscopy of the Type Ib SN iPTF 13bvn. The epochs of these observations correspond to $-$10 to $+$61 days with respect to the {\it r}-band light curve maximum. The continuum is intrinsically polarised to the $0.2-0.4\%$ level throughout the observations, implying asphericities of $\sim10\%$ in the shape of the photosphere. We observe significant line polarisation associated with the spectral features of Ca II IR3, He I/Na I D, He I {\lambda}{\lambda}6678, 7065, Fe II {\lambda}4924 and O I {\lambda}7774. We propose that an absorption feature at $\sim 6200\mathrm{\AA}$, usually identified as Si II $\lambda 6355$, is most likely to be high velocity $\mathrm{H\alpha}$ at $-16,400$ $\mathrm{km \; s^{-1}}$. Two distinctly polarised components, separated in velocity, are detected for both He I/Na I D and Ca II IR3, indicating the presence of two discrete line forming regions in the ejecta in both radial velocity space and in the plane of the sky. We use the polarisation of He I $\lambda 5876$ as a tracer of sources of non-thermal excitation in the ejecta; finding that the bulk of the radioactive nickel was constrained to lie interior to $\sim 50-65\%$ of the ejecta radius. The observed polarisation is also discussed in the context of the possible progenitor system of iPTF 13bvn, with our observations favouring the explosion of a star with an extended, distorted envelope rather than a compact Wolf-Rayet star.

Using a derivative-free optimization method for multiple solutions of inverse transport problems

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a mesh adaptive direct search (MADS) algorithm is incorporated into the local phase. Numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.

1D Josephson quantum interference grids: diffraction patterns and dynamics

We investigate the magnetic response of transmission lines with embedded Josephson junctions and thus generating a 1D underdamped array. The measured multi-junction interference patterns are compared with the theoretical predictions for Josephson supercurrent modulations when an external magnetic field couples both to the inter-junction loops and to the junctions themselves. The results provide a striking example of the analogy between Josephson phase modulation and 1D optical diffraction grid. The Fiske resonances in the current-voltage characteristics with voltage spacing , where L is the total physical length of the array, the magnetic flux quantum and the speed of light in the transmission line, demonstrate that the discrete line supports stable dynamic patterns generated by the ac Josephson effect interacting with the cavity modes of the line.

Exact Solutions and Bifurcations of a Modulated Equation in a Discrete Nonlinear Electrical Transmission Line (III)

In this paper, we consider a modulated equation in a discrete nonlinear electrical transmission line. This model is an integrable planar dynamical system having three singular straight lines. By using the theory of singular systems to investigate the dynamical behavior for this system, we obtain bifurcations of phase portraits under different parameter conditions. Corresponding to some special level curves, we derive exact explicit parametric representations of solutions (including smooth solitary wave solutions, peakons, compactons, periodic cusp wave solutions) under different parameter conditions.

Stability analysis of the soliton solutions for the generalized quintic derivative nonlinear Schrödinger equation

The propagation of hydrodynamic wave packets and media with negative refractive index is studied in a quintic derivative nonlinear Schrödinger (DNLS) equation. The quintic DNLS equation describe the wave propagation on a discrete electrical transmission line. We obtain a Lagrangian and the invariant variational principle for quintic DNLS equation. By using a class of ordinary differential equation, we found four types of exact solutions of the quintic DNLS equation, which are kink-type solitary wave solution, antikink-type solitary wave solution, sinusoidal solitary wave solution, bell-type solitary wave solution. By applying the modulation instability to discuss stability analysis of the obtained solutions. Modulation instabilities of continuous waves and localized solutions on a zero background have been investigated.

Exploring Impedance Growth in High Voltage NMC/Graphite Li-Ion Cells Using a Transmission Line Model

A discrete transmission line model (TLM) for the impedance of the positive electrode in a Li-ion cell was studied to investigate causes of impedance increase for Li[Ni0.42Mn0.42Co0.16]O2 (NMC442) positive electrodes operated at high voltage (> 4.4 V vs. Li/Li+). The TLM included contact resistance between the conductive carbon and the active particles (Rc), electrical path resistance through the carbon network (Re), ionic path resistance through the bulk electrolyte (Ri) and transfer resistance/capacitance (Rs, C) through the SEI layers formed on the active particles. It was found that an increase in any of Re, Ri or Rc was necessary to increase the high frequency intercept of the impedance spectra. A limited increase in the spectrum diameter of the TLM was achievable by increasing Re or Ri, but an unlimited increase was only possible by increasing the SEI resistance Rs. Comparison with experiment concluded that the high voltage impedance growth observed in NMC442/graphite cells is primarily due to increases in Rs, while minor increases in Re, Ri or Rc may occur. A brief investigation of inhomogeneous SEI capacitance/resistance produced impedance spectra with a range of heights and asymmetries. This can explain in part the variety of shapes of impedance spectra from real impedance measurements of Li-ion cells.

Observational Discrete Lines for the Detection of Moving Vehicles in Road Traffic Surveillance

Observational Discrete Lines for the Detection of Moving Vehicles in Road Traffic Surveillance

Frequency variability of standing Alfvén waves excited by fast mode resonances in the outer magnetosphere

AbstractCoupled fast mode resonances (cFMRs) in the outer magnetosphere, between the magnetopause and a turning point, are often invoked to explain observed discrete frequency field line resonances. We quantify their frequency variability, applying cFMR theory to a realistic magnetic field model and magnetospheric density profiles observed over almost half a solar cycle. Our calculations show that cFMRs are most likely around dawn, since the plasmaspheric plumes and extended plasmaspheres often found at noon and dusk can preclude their occurrence. The relative spread (median absolute deviation divided by the median) in eigenfrequencies is estimated to be 28%, 72%, and 55% at dawn, noon, and dusk, respectively, with the latter two chiefly due to density. Finally, at dawn we show that the observed bimodal density distribution results in bimodal cFMR frequencies, whereby the secondary peaks are consistent with the so‐called “CMS” frequencies that have previously been attributed to cFMRs.

Influence Of Damping On FRF Of Vehicle Computing Model

Abstract Frequency Response Function (FRF) characterizes the response of dynamic system in frequency domain. Its shape is dependent on the property of analyzed system, especially on damping. The damping neglecting during the calculation of frequency response causes that the Power Response Factors have the character of discrete spectral lines at points of natural frequencies of the vehicle computing model.

Local density approximation for the energy functional of three-dimensional dislocation systems

The elastic energy functional of a system of discrete dislocation lines is well known from dislocation theory. In this paper we demonstrate how the discrete functional can be used to systematically derive approximations which express the elastic energy in terms of dislocation density-like variables which average over the discrete dislocation configurations and represent the dislocation system on scales above the spacing of the individual dislocation lines. We study the simple case of two-dimensional systems of straight dislocation lines before we proceed to derive energy functionals for systems of three-dimensionally curved dislocation lines pertaining to a single, as well as to multiple slip systems. We then illustrate several applications of the theory including Debye screening of dislocations in two and three dimensions, and the derivation of back stress and friction stress terms entering the stress balance from the free energy functionals.

Palindromic language of thin discrete planes

We work on the Réveillès hyperplane P(v,0,ω) with normal vectorv∈Rd, shiftμ=0 and thicknessω∈R. Such a hyperplane is connected as soon as ω is greater than some value Ω(v,0), called the connecting thickness of v with null shift. In the case where v satisfies the so called Kraaikamp and Meester criterion, at the connecting thickness the hyperplane has very specific properties. First of all the adjacency graph of the voxels forms a tree. This tree appeared in many works both in discrete geometry and in discrete dynamical systems. In addition, it is well known that for a finite coding of length n of discrete lines, the number of palindromes in the language is exactly n+1. We extend this notion of language to labeled trees and we compute the number of distinct palindromes. In fact for our voxel adjacency trees with n letters we show that the number of palindromes in the language is also n+1. This result establishes a first link between combinatorics on words, palindromic languages, voxel adjacency trees and connecting thickness of Réveillès hyperplanes. It also provides a better understanding of the combinatorial structure of discrete planes.

Semi-empirical model for fluorescence lines evaluation in diagnostic x-ray beams

Diagnostic x-ray beams are composed of bremsstrahlung and discrete fluorescence lines. The aim of this study is the development of an efficient model for the evaluation of the fluorescence lines. The most important electron ionization models are analyzed and implemented. The model results were compared with experimental data and with other independent spectra presented in the literature. The implemented peak models allow the discrimination between direct and indirect radiation emitted from tungsten anodes. The comparison with the independent literature spectra indicated a good agreement.

Titchener's ⊥ in context 1--delimited, discrete monomotif patterns, line arrangements, and branching patterns.

Three experiments tested the effects of the presence of nontarget ⊥s on Titchener's (1901) ⊥-illusion. Experiment 1 used patterns of four separate ⊥s, Experiment 2 used branching patterns in which four ⊥s were stuck together, and Experiment 3 used patterns of four triangles or four beehive forms for which the ⊥ could be seen as a skeleton. Three independent samples of 12 observers each had to haptically indicate the lengths of target lines and verbally judge the relative lengths of the two lines of target ⊥s. The illusion to judge or indicate the ⊥’s undivided line as longer than its divided line survived throughout except for the branching patterns: here, haptic indications did not differ between the two types of lines. Specific features of these patterns and of the ⊥ itself may be responsible for these effects.

Hybrid dispersive media with controllable wave propagation: A new take on smart materials

In this paper, we report on the wave transmission characteristics of a hybrid one dimensional (1D) medium. The hybrid characteristic is the result of the coupling between a 1D mechanical waveguide in the form of an elastic beam, supporting the propagation of transverse waves and a discrete electrical transmission line, consisting of a series of inductors connected to ground through capacitors. The capacitors correspond to a periodic array of piezoelectric patches that are bonded to the beam and that couple the two waveguides. The coupling leads to a hybrid medium that is characterized by a coincidence condition for the frequency/wavenumber value corresponding to the intersection of the branches of the two waveguides. In the frequency range centered at coincidence, the hybrid medium features strong attenuation of wave motion as a result of the energy transfer towards the electrical transmission line. This energy transfer, and the ensuing attenuation of wave motion, is alike the one obtained through internal resonating units of the kind commonly used in metamaterials. However, the distinct shape of the dispersion curves suggests how this energy transfer is not the result of a resonance and is therefore fundamentally different. This paper presents the numerical investigation of the wave propagation in the considered media, it illustrates experimental evidence of wave transmission characteristics and compares the performance of the considered configuration with that of internal resonating metamaterials. In addition, the ability to conveniently tune the dispersion properties of the electrical transmission line is exploited to adapt the periodicity of the domain and to investigate diatomic periodic configurations that are characterized by a richer dispersion spectrum and broader bandwidth of wave attenuation at coincidence. The medium consisting of mechanical, piezoelectric, and analog electronic elements can be easily interfaced to digital devices to offer a novel approach to smart materials.

Ewald Electrostatics for Mixtures of Point and Continuous Line Charges.

Many charged macro- or supramolecular systems, such as DNA, are approximately rod-shaped and, to the lowest order, may be treated as continuous line charges. However, the standard method used to calculate electrostatics in molecular simulation, the Ewald summation, is designed to treat systems of point charges. We extend the Ewald concept to a hybrid system containing both point charges and continuous line charges. We find the calculated force between a point charge and (i) a continuous line charge and (ii) a discrete line charge consisting of uniformly spaced point charges to be numerically equivalent when the separation greatly exceeds the discretization length. At shorter separations, discretization induces deviations in the force and energy, and point charge-point charge correlation effects. Because significant computational savings are also possible, the continuous line charge Ewald method presented here offers the possibility of accurate and efficient electrostatic calculations.

Characterization of asphalt concrete linear viscoelastic behavior utilizing Havriliak–Negami complex modulus model

This study proposed a new procedure for characterizing linear viscoelastic (LVE) behavior of asphalt concrete using the Havriliak–Negami (HN) complex modulus model and corresponding continuous relaxation spectrum model. To extend its application to modeling retardation behavior of asphalt concrete, the continuous retardation spectrum was analytically derived from the HN model by performing an inverse Fourier–Laplace transform followed by a variable substitution. The two continuous spectra of the HN model allow the accurate construction of all the modulus and compliance function master curves in time and frequency domains as well as the efficient determination of the high-quality discrete relaxation and retardation spectra. The advantages of the proposed approach over existing ones were demonstrated through two different complex modulus test data sets. Also, a simple and practical numerical interconversion method was presented based on the LVE relations between the continuous relaxation and retardation spectra, which can effectively compute one continuous spectrum from the other for any characterization model. Further, for practical considerations, a two-step method for determining reduced master curves with fewer discrete spectrum lines was suggested.

Evaluation of proton inelastic reaction models in Geant4 for prompt gamma production during proton radiotherapy

During proton beam radiotherapy, discrete secondary prompt gamma rays are induced by inelastic nuclear reactions between protons and nuclei in the human body. In recent years, the Geant4 Monte Carlo toolkit has played an important role in the development of a device for real time dose range verification purposes using prompt gamma radiation. Unfortunately the default physics models in Geant4 do not reliably replicate the measured prompt gamma emission. Determining a suitable physics model for low energy proton inelastic interactions will boost the accuracy of prompt gamma simulations. Among the built-in physics models, we found that the precompound model with a modified initial exciton state of 2 (1 particle, 1 hole) produced more accurate discrete gamma lines from the most important elements found within the body such as 16O, 12C and 14N when comparing them with the available gamma production cross section data. Using the modified physics model, we investigated the prompt gamma spectra produced in a water phantom by a 200 MeV pencil beam of protons. The spectra were attained using a LaBr3 detector with a time-of-flight (TOF) window and BGO active shield to reduce the secondary neutron and gamma background. The simulations show that a 2 ns TOF window could reduce 99% of the secondary neutron flux hitting the detector. The results show that using both timing and active shielding can remove up to 85% of the background radiation which includes a 33% reduction by BGO subtraction.