scholarly journals Exact analytic solutions for nonlinear waves in cold plasmas

2008 ◽  
Vol 74 (4) ◽  
pp. 569-573 ◽  
Author(s):  
G. ROWLANDS ◽  
G. BRODIN ◽  
L. STENFLO
Keyword(s):  
Wave Breaking ◽  
Electron Plasma ◽  
Analytic Solutions ◽  
Field Amplitude ◽  
Cold Electron ◽  
Electric Field Amplitude ◽  
New Class ◽  
Exact Analytic Solutions ◽  
Lagrangian Variables ◽  
Cold Plasmas

AbstractLarge amplitude plasma oscillations are studied in a cold electron plasma. Using Lagrangian variables, a new class of exact analytical solutions is found. It turns out that the electric field amplitude is limited either by wave breaking or by the condition that the electron density always has to stay positive. The range of possible amplitudes is determined analytically.

CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

scholarly journals Exact analytical solutions of continuously graded models of flat lenses based on transformation optics

2017 ◽  
Vol 30 (4) ◽  
pp. 639-646 ◽  
Author(s):  
Mariana Dalarsson ◽  
Raj Mittra
Keyword(s):  
Magnetic Fields ◽  
Longitudinal Direction ◽  
Middle Layer ◽  
Analytic Solutions ◽  
Transformation Optics ◽  
Confluent Hypergeometric Functions ◽  
Graded Index ◽  
Exact Analytic Solutions ◽  
Electric And Magnetic Fields ◽  
Physical Insight

We present a study of exact analytic solutions for electric and magnetic fields in continuously graded flat lenses designed utilizing transformation optics. The lenses typically consist of a number of layers of graded index dielectrics in both the radial and longitudinal directions, where the central layer in the longitudinal direction primarily contributes to a bulk of the phase transformation, while other layers act as matching layers and reduce the reflections at the interfaces of the middle layer. Such lenses can be modeled as compact composites with continuous permittivity (and if needed) permeability functions which asymptotically approach unity at the boundaries of the composite cylinder. We illustrate the proposed procedures by obtaining the exact analytic solutions for the electric and magnetic fields for one simple special class of composite designs with radially graded parameters. To this purpose we utilize the equivalence between the Helmholtz equation of our graded flat lens and the quantum-mechanical radial Schr?dinger equation with Coulomb potential, furnishing the results in the form of Kummer confluent hypergeometric functions. Our approach allows for a better physical insight into the operation of our transformation optics-based graded lenses and opens a path toward novel designs and approaches.

scholarly journals New Soliton Solutions for the Higher-Dimensional Non-Local Ito Equation

2021 ◽  
Vol 10 (1) ◽  
pp. 374-384
Author(s):  
Mustafa Inc ◽  
E. A. Az-Zo’bi ◽  
Adil Jhangeer ◽  
Hadi Rezazadeh ◽  
Muhammad Nasir Ali ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Solution Process ◽  
Soliton Solutions ◽  
Analytic Solutions ◽  
Bright Solitons ◽  
Exact Analytic Solutions ◽  
Higher Dimensional ◽  
Non Local ◽  
Free Parameters ◽  
Ito Equation

Abstract In this article, (2+1)-dimensional Ito equation that models waves motion on shallow water surfaces is analyzed for exact analytic solutions. Two reliable techniques involving the simplest equation and modified simplest equation algorithms are utilized to find exact solutions of the considered equation involving bright solitons, singular periodic solitons, and singular bright solitons. These solutions are also described graphically while taking suitable values of free parameters. The applied algorithms are effective and convenient in handling the solution process for Ito equation that appears in many phenomena.

Scaling Behavior of Dynamic Hysteresis in Hard PZT Bulk Ceramics under Influence of Compressive Stress

2008 ◽  
Vol 55-57 ◽  
pp. 281-284 ◽  
Author(s):  
N. Wongdamnern ◽  
Athipong Ngamjarurojana ◽  
Supon Ananta ◽  
Yongyut Laosiritaworn ◽  
Rattikorn Yimnirun
Keyword(s):  
Energy Dissipation ◽  
Electric Field ◽  
Mechanical Stress ◽  
Compressive Stress ◽  
Power Law ◽  
Field Amplitude ◽  
Electric Field Amplitude ◽  
Bulk Ceramic ◽  
Compressive Stresses ◽  
The Difference

Effects of electric field-amplitude and mechanical stress on hysteresis area were investigated in partially depoled hard PZT bulk ceramic. At any compressive stress, the hysteresis area was found to depend on the field-amplitude with a same set of exponents to the power-law scaling. Consequently, inclusion of compressive stresses into the power-law was also obtained in the form of < A – Aσ=0 > α E05.1σ1.19 which indicated the difference of the energy dissipation between the under-stress and stress-free conditions.

scholarly journals A new class of discontinuous solar wind solutions

2020 ◽  
Vol 496 (2) ◽  
pp. 1023-1034
Author(s):  
Bidzina M Shergelashvili ◽  
Velentin N Melnik ◽  
Grigol Dididze ◽  
Horst Fichtner ◽  
Günter Brenn ◽  
...  
Keyword(s):  
Solar Wind ◽  
External Source ◽  
Analytic Solutions ◽  
Governing Equations ◽  
Discontinuous Solutions ◽  
One Dimensional ◽  
Heating Source ◽  
New Class ◽  
Localized Heating ◽  
Physical Quantities

ABSTRACT A new class of one-dimensional solar wind models is developed within the general polytropic, single-fluid hydrodynamic framework. The particular case of quasi-adiabatic radial expansion with a localized heating source is considered. We consider analytical solutions with continuous Mach number over the entire radial domain while allowing for jumps in the flow velocity, density, and temperature, provided that there exists an external source of energy in the vicinity of the critical point that supports such jumps in physical quantities. This is substantially distinct from both the standard Parker solar wind model and the original nozzle solutions, where such discontinuous solutions are not permissible. We obtain novel sample analytic solutions of the governing equations corresponding to both slow and fast winds.

The evolution process of nonlinear cold-electron-plasma oscillations against fixed periodic ion density cavities

2019 ◽  
Vol 26 (2) ◽  
pp. 022112 ◽  
Author(s):  
Hui Xu ◽  
Fu-fang Su ◽  
Xiang-mu Kong ◽  
Yu Sun ◽  
Rui-ning Jin ◽  
...  
Keyword(s):  
Electron Plasma ◽  
Evolution Process ◽  
Cold Electron ◽  
Plasma Oscillations ◽  
Ion Density
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