Optical solitons of the paraxial wave dynamical model in kerr media and its applications in nonlinear optics

2020 ◽  
Vol 34 (09) ◽  
pp. 2050078
Author(s):  
Muhammad Arshad ◽  
Aly R. Seadawy ◽  
Dianchen Lu ◽  
Farman Ullah Khan
Keyword(s):  
Wave Model ◽  
Dimensionless Time ◽  
Kerr Media ◽  
Expansion Technique ◽  
The Media ◽  
Spatio Temporal ◽  
Mathematical Techniques ◽  
Parameter Values ◽  
Physical Phenomena ◽  
Algebraic Technique

The solitons and other solutions illustrate nondiffractive and nondispersive spatio-temporal localized packets of wave propagating in the media of optical Kerr. In this paper, solitons, elliptic function and other solutions of dimensionless time-dependent paraxial wave model are constructed via employing three mathematical techniques, namely, the improved simple equation technique, [Formula: see text]-expansion technique and modified extended direct algebraic technique. These wave solutions have key applications and help to understand the physical phenomena of this wave model. By giving appropriate parameter values, different types of solitons structures can be depicted graphically. Several precise solutions and computations have proved the straightforwardness, consistency and power of the these techniques.

scholarly journals A Fast Estimator for Binary Choice Models with Spatial, Temporal, and Spatio-Temporal Interdependence

2021 ◽  
pp. 1-7
Author(s):  
Julian Wucherpfennig ◽  
Aya Kachi ◽  
Nils-Christian Bormann ◽  
Philipp Hunziker
Keyword(s):  
Computational Cost ◽  
Choice Models ◽  
Reduced Form ◽  
Binary Choice ◽  
Monte Carlo Experiments ◽  
Binary Choice Models ◽  
Spatio Temporal ◽  
Computationally Intensive ◽  
Pseudo Maximum Likelihood ◽  
Parameter Values

Abstract Binary outcome models are frequently used in the social sciences and economics. However, such models are difficult to estimate with interdependent data structures, including spatial, temporal, and spatio-temporal autocorrelation because jointly determined error terms in the reduced-form specification are generally analytically intractable. To deal with this problem, simulation-based approaches have been proposed. However, these approaches (i) are computationally intensive and impractical for sizable datasets commonly used in contemporary research, and (ii) rarely address temporal interdependence. As a way forward, we demonstrate how to reduce the computational burden significantly by (i) introducing analytically-tractable pseudo maximum likelihood estimators for latent binary choice models that exhibit interdependence across space and time and by (ii) proposing an implementation strategy that increases computational efficiency considerably. Monte Carlo experiments show that our estimators recover the parameter values as good as commonly used estimation alternatives and require only a fraction of the computational cost.

scholarly journals A New Approach for Approximate Solution of ADE: Physical-Based Modeling of Carriers in Doping Region

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 458
Author(s):  
Leobardo Hernandez-Gonzalez ◽  
Jazmin Ramirez-Hernandez ◽  
Oswaldo Ulises Juarez-Sandoval ◽  
Miguel Angel Olivares-Robles ◽  
Ramon Blanco Sanchez ◽  
...  
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Analytic Solution ◽  
Order Differential Equation ◽  
Electric Circuit ◽  
New Approach ◽  
In Doping ◽  
Electric Behavior ◽  
Spatio Temporal ◽  
Physical Phenomena

The electric behavior in semiconductor devices is the result of the electric carriers’ injection and evacuation in the low doping region, N-. The carrier’s dynamic is determined by the ambipolar diffusion equation (ADE), which involves the main physical phenomena in the low doping region. The ADE does not have a direct analytic solution since it is a spatio-temporal second-order differential equation. The numerical solution is the most used, but is inadequate to be integrated into commercial electric circuit simulators. In this paper, an empiric approximation is proposed as the solution of the ADE. The proposed solution was validated using the final equations that were implemented in a simulator; the results were compared with the experimental results in each phase, obtaining a similarity in the current waveforms. Finally, an advantage of the proposed methodology is that the final expressions obtained can be easily implemented in commercial simulators.

scholarly journals Energy current and computing

2018 ◽  
Vol 376 (2134) ◽  
pp. 20170449 ◽  
Author(s):  
Alex Yakovlev
Keyword(s):  
Digital Circuit ◽  
Electrical Networks ◽  
Mathematical Methods ◽  
Power Sources ◽  
Energy Current ◽  
Energy Flows ◽  
State Changes ◽  
Spatio Temporal ◽  
Computational Circuits ◽  
Physical Phenomena

In his seminal Electrical papers , Oliver Heaviside stated ‘We reverse this …' referring to the relationship between energy current and state changes in electrical networks. We explore implications of Heaviside's view upon the state changes in electronic circuits, effectively constituting computational processes. Our vision about energy-modulated computing that can be applicable for electronic systems with energy harvesting is introduced. Examples of analysis of computational circuits as loads on power sources are presented. We also draw inspiration from Heaviside's way of using and advancing mathematical methods from the needs of natural physical phenomena. A vivid example of Heavisidian approach to the use of mathematics is in employing series where they emerge out of the spatio-temporal view upon energy flows. Using series expressions, and types of natural discretization in space and time, we explain the processes of discharging a capacitive transmission line, first, through a constant resistor and, second, through a voltage controlled digital circuit. We show that event-based models, such as Petri nets with an explicit notion of causality inherent in them, can be instrumental in creating bridges between electromagnetics and computing. This article is part of the theme issue ‘Celebrating 125 years of Oliver Heaviside's ‘Electromagnetic Theory’’.

Kinetics and physiological characteristics of autotrophic dentrification by denitrifying sulfur bacteria

2000 ◽  
Vol 42 (3-4) ◽  
pp. 59-68 ◽  
Author(s):  
S.-E. Oh ◽  
K.-S. Kim ◽  
H.-C. Choi ◽  
J. Cho ◽  
I.S. Kim
Keyword(s):  
Gas Production ◽  
Parameter Estimates ◽  
Production Volume ◽  
Autotrophic Denitrification ◽  
Nonlinear Regression Analysis ◽  
Monod Equation ◽  
Sulfur Bacteria ◽  
The Media ◽  
Parameter Values ◽  
Mixotrophic Conditions

To study the kinetics and physiology of autotrophic denitrifying sulfur bacteria, a steady-state anaerobic master culture reactor (MCR) was operated for over six months under a semi-continuous mode and nitrate limiting conditions using nutrient/mineral/buffer (NMB) medium containing thiosulfate and nitrate. Characteristics of the autotropic denitrifier were investigated through the cumulative gas production volume and rate, measured using an anaerobic respirometer, and through the nitrate, nitrite, and sulfate concentrations within the media. The bio-kinetic parameters were obtained based upon the Monod equation using mixed cultures in the MCR. Nonlinear regression analysis was employed using nitrate depletion and biomass production curves. Although this analysis did not yield exact biokinetic parameter estimates, the following ranges for the parameter values were obtained: μmax =0.12-0.2 hr-1; k=0.3-0.4 hr-1; Ks=3-10mg/L; YNO3=0.4-0.5mg Biomass/mg NO3--N. Inhibition of denitrification occurred when the concentrations of NO3--N, and SO42- reached about 660mg/L and 2,000mg/L, respectively. The autotrophic denitrifying sulfur bacteria were observed to be very sensitive to nitrite but relatively tolerant of nitrate, sulfate, and thiosulfate. Under mixotrophic conditions, denitrification by these bacteria occurred autotrophically; even with as high as 2 g COD, autotrophic denitrification was not significantly affected. The optimal pH and temperature for autotrophic denitrification was about 6.5–7.5 and 33–35 °C, respectively.

scholarly journals Global simulations of the atmosphere at 1.45 km grid-spacing with the Integrated Forecasting System

2020 ◽  
Author(s):  
Peter Düben ◽  
Nils Wedi ◽  
Sami Saarinen ◽  
Christian Zeman
Keyword(s):  
Initial Conditions ◽  
Weather Forecast ◽  
Wave Model ◽  
Shallow Convection ◽  
Grid Spacing ◽  
Time Step ◽  
Weather Forecasts ◽  
Forecasting System ◽  
Diabatic Forcing ◽  
Physical Phenomena

<p>Global simulations with 1.45 km grid-spacing are presented that were performed with the Integrated Forecasting System (IFS) of the European Centre for Medium-Range Weather Forecasts (ECMWF). Simulations are uncoupled (without ocean, sea-ice or wave model), using 62 or 137 vertical levels and the full complexity of weather forecast simulations including recent date initial conditions, real-world topography, and state-of-the-art physical parametrizations and diabatic forcing including shallow convection, turbulent diffusion, radiation and five categories for the water substance (vapour, liquid, ice, rain, snow). Simulations are evaluated with regard to computational efficiency and model fidelity. Scaling results are presented that were performed on the fastest supercomputer in Europe - Piz Daint (Top 500, Nov 2018). Important choices for the model configuration at this unprecedented resolution for the IFS are discussed such as the use of hydrostatic and non-hydrostatic equations or the time resolution of physical phenomena which is defined by the length of the time step. </p><p>Our simulations indicate that the IFS model — based on spectral transforms with a semi-implicit, semi-Lagrangian time-stepping scheme in contrast to more local discretization techniques — can provide a meaningful baseline reference for O(1) km global simulations.</p>

Multiple soliton, fusion, breather, lump, mixed kink-lump and periodic solutions to the extended shallow water wave model in (2+1)-dimensions

2020 ◽  
pp. 2150138
Author(s):  
Hajar F. Ismael ◽  
Aly Seadawy ◽  
Hasan Bulut
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Soliton Solutions ◽  
Quadratic Function ◽  
Wave Model ◽  
Simple Method ◽  
Shallow Water Wave ◽  
Hirota Bilinear Form ◽  
The One ◽  
Physical Phenomena

In this paper, we consider the shallow water wave model in the (2+1)-dimensions. The Hirota simple method is applied to construct the new dynamics one-, two-, three-, [Formula: see text]-soliton solutions, complex multi-soliton, fusion, and breather solutions. By using the quadratic function, the one-lump, mixed kink-lump and periodic lump solutions to the model are obtained. The Hirota bilinear form variable of this model is derived at first via logarithmic variable transform. The physical phenomena to this model are explored. The obtained results verify the proposed model.

Variational analysis of spatio-temporal pulse dynamics in dispersive Kerr media

2002 ◽  
Vol 19 (7) ◽  
pp. 1716 ◽  
Author(s):  
Christian Jirauschek ◽  
Uwe Morgner ◽  
Franz X. Kärtner
Keyword(s):  
Variational Analysis ◽  
Pulse Dynamics ◽  
Kerr Media ◽  
Spatio Temporal ◽  
Temporal Pulse

Development of a New Simulation Method for Suspended Sediment Transport in a Tidal River

1988 ◽  
Vol 20 (6-7) ◽  
pp. 103-112 ◽  
Author(s):  
Tohru Futawatari ◽  
Tetsuya Kusuda ◽  
Kenichi Koga ◽  
Hiroyuki Araki ◽  
Teruyuki Umita ◽  
...  
Keyword(s):  
Sediment Transport ◽  
Suspended Sediment ◽  
Simulation Method ◽  
Tidal River ◽  
Suspended Sediment Transport ◽  
One Dimensional ◽  
Dimensional Simulation ◽  
Parameter Values ◽  
Physical Phenomena ◽  
Good Agreement

A one dimensional simulation model of suspended sediment transport in a tidal river was developed with erosion, deposition, and thickening processes of sediments, and inflow from tributaries. This model uses the explicit leapfrog method and its lower end boundary of the river is extended into the sea to close the boundary for calculation. Laboratory experiments were performed to determine erosional and depositional rates of sediments and to study the sediment thickening process in the river under various concentrations of chlorinity and suspended solids. Numerical simulation results with the parameter values obtained experimentally did not show good agreement with observed data. Modifying the parameter values according to physical phenomena was necessary to obtain good agreement in between. After the modification, computation results during a fortnightly cycle explain satisfactorily the sediment transport phenomena in this river.

TURBULENT DIFFUSION OF TEST PARTICLES IN STRONGLY MAGNETIZED PLASMAS

1991 ◽  
Vol 05 (08) ◽  
pp. 1243-1262 ◽  
Author(s):  
MAURIZIO OTTAVIANI ◽  
MARCO PETTINI
Keyword(s):  
Electric Field ◽  
Equations Of Motion ◽  
Charged Particles ◽  
Mean Square Displacement ◽  
Wave Model ◽  
Particle Dynamics ◽  
Suitable Parameter ◽  
Test Particles ◽  
The Mean ◽  
Parameter Values

The motion of charged particles is described in the presence of a strong magnetic field and of an electric field made of three spatial Fourier modes whose amplitudes vary in time. The dynamics of the wave amplitudes is governed by a model of three interacting drift waves. For suitable parameter values of the three-wave model, chaotic solutions are found so that the Eulerian electric field is made of three turbulent modes. The E × B motion is described for charged particles in the guiding center approximation, which brings to nonlinear Hamiltonian equations of motion. The Hamiltonian (that coincides with the electric potential) is explicitly time-dependent through the temporal variation of the mode-amplitudes of the electric field, this fact is at the origin of the intrinsic chaoticity of particle dynamics (lagrangian chaos). Diffusive behaviour of particle trajectories is due to their intrinsic chaoticity and thus it is of non-collisional origin. Some results are reported concerning the particle dynamics when the Eulerian electric field is either quasi-periodically or chaotically varying in time. In particular, one finds different diffusion laws in the two cases (anomalous and classical respectively). The scaling behaviour of the diffusion coefficients (when the mean square displacement grows linearly in time) is reported. A simple stochastic model is also used to account for some of the observed features of particle diffusion.

A STATISTICAL MODEL OF CRIMINAL BEHAVIOR

2008 ◽  
Vol 18 (supp01) ◽  
pp. 1249-1267 ◽  
Author(s):  
M. B. SHORT ◽  
M. R. D'ORSOGNA ◽  
V. B. PASOUR ◽  
G. E. TITA ◽  
P. J. BRANTINGHAM ◽  
...  
Keyword(s):  
Criminal Behavior ◽  
Discrete System ◽  
Continuum Model ◽  
Criminal Activity ◽  
Quantitative Agreement ◽  
Residential Burglary ◽  
Feedback Mechanisms ◽  
Random Walker ◽  
Spatio Temporal ◽  
Parameter Values

Motivated by empirical observations of spatio-temporal clusters of crime across a wide variety of urban settings, we present a model to study the emergence, dynamics, and steady-state properties of crime hotspots. We focus on a two-dimensional lattice model for residential burglary, where each site is characterized by a dynamic attractiveness variable, and where each criminal is represented as a random walker. The dynamics of criminals and of the attractiveness field are coupled to each other via specific biasing and feedback mechanisms. Depending on parameter choices, we observe and describe several regimes of aggregation, including hotspots of high criminal activity. On the basis of the discrete system, we also derive a continuum model; the two are in good quantitative agreement for large system sizes. By means of a linear stability analysis we are able to determine the parameter values that will lead to the creation of stable hotspots. We discuss our model and results in the context of established criminological and sociological findings of criminal behavior.

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