Holomorphic Solutions of a Class of 3-D Propagated Wave Dynamical Equations Indicated by a Complex Conformable Calculus

2021 ◽  
Vol 7 (7) ◽  
pp. 23-30
Keyword(s):  
Dynamical Equations ◽  
Conformable Calculus

Application of Modified Bloch Waves to Image Analysis of Extended Linear Defects

1974 ◽  
Vol 32 ◽  
pp. 402-403
Author(s):  
S. Nakahara ◽  
D. M. Maher
Keyword(s):  
Image Analysis ◽  
Computational Approach ◽  
Dislocation Loops ◽  
Plane Wave Expansion ◽  
Dynamical Equations ◽  
Bloch Waves ◽  
Linear Defects ◽  
Imperfect Crystal ◽  
Localized Defects ◽  
Defective Crystals

Since Head first demonstrated the advantages of computer displayed theoretical intensities from defective crystals, computer display techniques have become important in image analysis. However the computational methods employed resort largely to numerical integration of the dynamical equations of electron diffraction. As a consequence, the interpretation of the results in terms of the defect displacement field and diffracting variables is difficult to follow in detail. In contrast to this type of computational approach which is based on a plane-wave expansion of the excited waves within the crystal (i.e. Darwin representation ), Wilkens assumed scattering of modified Bloch waves by an imperfect crystal. For localized defects, the wave amplitudes can be described analytically and this formulation has been used successfully to predict the black-white symmetry of images arising from small dislocation loops.

New Solutions of Dynamical Equations of Ideal Plasticity

2019 ◽  
Vol 13 (4) ◽  
pp. 740-745
Author(s):  
S. I. Senashov ◽  
I. L. Savostyanova
Keyword(s):  
Ideal Plasticity ◽  
Dynamical Equations

scholarly journals A brief review of E theory

2016 ◽  
Vol 31 (26) ◽  
pp. 1630043 ◽  
Author(s):  
Peter West
Keyword(s):  
Infinite Number ◽  
Equations Of Motion ◽  
Space Time ◽  
Unified Theory ◽  
Dynamical Equations ◽  
Supergravity Theory ◽  
Maximal Supergravity ◽  
Abdus Salam ◽  
Strings And Branes ◽  
Time Lead

I begin with some memories of Abdus Salam who was my PhD supervisor. After reviewing the theory of nonlinear realisations and Kac–Moody algebras, I explain how to construct the nonlinear realisation based on the Kac–Moody algebra [Formula: see text] and its vector representation. I explain how this field theory leads to dynamical equations which contain an infinite number of fields defined on a space–time with an infinite number of coordinates. I then show that these unique dynamical equations, when truncated to low level fields and the usual coordinates of space–time, lead to precisely the equations of motion of 11-dimensional supergravity theory. By taking different group decompositions of [Formula: see text] we find all the maximal supergravity theories, including the gauged maximal supergravities, and as a result the nonlinear realisation should be thought of as a unified theory that is the low energy effective action for type II strings and branes. These results essentially confirm the [Formula: see text] conjecture given many years ago.

scholarly journals NanoLEDs for energy-efficient and gigahertz-speed spike-based sub-λ neuromorphic nanophotonic computing

Nanophotonics ◽  
2020 ◽  
Vol 9 (13) ◽  
pp. 4149-4162 ◽  
Author(s):  
Bruno Romeira ◽  
José M. L. Figueiredo ◽  
Julien Javaloyes
Keyword(s):  
Neural Networks ◽  
Energy Efficient ◽  
High Speed ◽  
Dynamic Properties ◽  
Optical Computing ◽  
Differential Conductance ◽  
Rate Equations ◽  
Dynamical Equations ◽  
Electrical Modulation ◽  
High Bandwidth

AbstractEvent-activated biological-inspired subwavelength (sub-λ) photonic neural networks are of key importance for future energy-efficient and high-bandwidth artificial intelligence systems. However, a miniaturized light-emitting nanosource for spike-based operation of interest for neuromorphic optical computing is still lacking. In this work, we propose and theoretically analyze a novel nanoscale nanophotonic neuron circuit. It is formed by a quantum resonant tunneling (QRT) nanostructure monolithic integrated into a sub-λ metal-cavity nanolight-emitting diode (nanoLED). The resulting optical nanosource displays a negative differential conductance which controls the all-or-nothing optical spiking response of the nanoLED. Here we demonstrate efficient activation of the spiking response via high-speed nonlinear electrical modulation of the nanoLED. A model that combines the dynamical equations of the circuit which considers the nonlinear voltage-controlled current characteristic, and rate equations that takes into account the Purcell enhancement of the spontaneous emission, is used to provide a theoretical framework to investigate the optical spiking dynamic properties of the neuromorphic nanoLED. We show inhibitory- and excitatory-like optical spikes at multi-gigahertz speeds can be achieved upon receiving exceptionally low (sub-10 mV) synaptic-like electrical activation signals, lower than biological voltages of 100 mV, and with remarkably low energy consumption, in the range of 10–100 fJ per emitted spike. Importantly, the energy per spike is roughly constant and almost independent of the incoming modulating frequency signal, which is markedly different from conventional current modulation schemes. This method of spike generation in neuromorphic nanoLED devices paves the way for sub-λ incoherent neural elements for fast and efficient asynchronous neural computation in photonic spiking neural networks.

Impact of Consistent Semi-Lagrangian Trajectory Calculations on Numerical Weather Prediction Performance

2017 ◽  
Vol 145 (10) ◽  
pp. 4127-4150 ◽  
Author(s):  
Syed Zahid Husain ◽  
Claude Girard
Keyword(s):  
Numerical Weather Prediction ◽  
Numerical Experiments ◽  
Prediction Models ◽  
Weather Prediction ◽  
Forecast Accuracy ◽  
Multiscale Model ◽  
Dynamical Equations ◽  
Numerical Weather ◽  
Trajectory Calculation ◽  
Trajectory Calculations

Inconsistencies may arise in numerical weather prediction models—that are based on semi-Lagrangian advection—when the governing dynamical and the kinematic trajectory equations are discretized in a dissimilar manner. This study presents consistent trajectory calculation approaches, both in the presence and absence of off-centering in the discretized dynamical equations. Both uniform and differential off-centering in the discretized dynamical equations have been considered. The proposed consistent trajectory calculations are evaluated using numerical experiments involving a nonhydrostatic two-dimensional theoretical mountain case and hydrostatic global forecasts. The experiments are carried out using the Global Environmental Multiscale model. Both the choice of the averaging method for approximating the velocity integral in the discretized trajectory equations and the interpolation scheme for calculating the departure positions are found to be important for consistent trajectory calculations. Results from the numerical experiments confirm that the proposed consistent trajectory calculation approaches not only improve numerical consistency, but also improve forecast accuracy.

scholarly journals Data Assimilation with Gaussian Mixture Models Using the Dynamically Orthogonal Field Equations. Part I: Theory and Scheme

2013 ◽  
Vol 141 (6) ◽  
pp. 1737-1760 ◽  
Author(s):  
Thomas Sondergaard ◽  
Pierre F. J. Lermusiaux
Keyword(s):  
Data Assimilation ◽  
Mixture Models ◽  
Gaussian Mixture Models ◽  
Expectation Maximization Algorithm ◽  
Planck Equation ◽  
Information Criterion ◽  
Gaussian Mixture ◽  
Field Equations ◽  
Dynamical Equations ◽  
Prior Probabilities

Abstract This work introduces and derives an efficient, data-driven assimilation scheme, focused on a time-dependent stochastic subspace that respects nonlinear dynamics and captures non-Gaussian statistics as it occurs. The motivation is to obtain a filter that is applicable to realistic geophysical applications, but that also rigorously utilizes the governing dynamical equations with information theory and learning theory for efficient Bayesian data assimilation. Building on the foundations of classical filters, the underlying theory and algorithmic implementation of the new filter are developed and derived. The stochastic Dynamically Orthogonal (DO) field equations and their adaptive stochastic subspace are employed to predict prior probabilities for the full dynamical state, effectively approximating the Fokker–Planck equation. At assimilation times, the DO realizations are fit to semiparametric Gaussian Mixture Models (GMMs) using the Expectation-Maximization algorithm and the Bayesian Information Criterion. Bayes’s law is then efficiently carried out analytically within the evolving stochastic subspace. The resulting GMM-DO filter is illustrated in a very simple example. Variations of the GMM-DO filter are also provided along with comparisons with related schemes.

scholarly journals CONSTRAINTS IN QUANTUM GEOMETRODYNAMICS

2004 ◽  
Vol 19 (10) ◽  
pp. 1609-1638 ◽  
Author(s):  
ADRIAN P. GENTLE ◽  
NATHAN D. GEORGE ◽  
ARKADY KHEYFETS ◽  
WARNER A. MILLER
Keyword(s):  
Quantum Gravity ◽  
General Setting ◽  
Square Root ◽  
Dynamical Equations ◽  
Dynamic Content ◽  
Quantization Formalism ◽  
Canonical Quantum Gravity ◽  
First Time ◽  
Quantum Geometrodynamics ◽  
Canonical Quantum

We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3-geometries treats the constraints as the sole carriers of the dynamic content of the theory, thus rendering the traditional dynamical equations obsolete. Quantization of the constraints in both the Dirac and ADM square root Hamiltonian approaches leads to the well known problems of time evolution. These problems of time are of both an interpretational and technical nature. In contrast, the geometrodynamic quantization procedure on the superspace of the true dynamical variables separates the issues of quantization from the enforcement of the constraints. The resulting theory takes into account states that are off-shell with respect to the constraints, and thus avoids the problems of time. We develop, for the first time, the geometrodynamic quantization formalism in a general setting and show that it retains all essential features previously illustrated in the context of homogeneous cosmologies.

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