Kink-excitation of N-system under spatio-temporal noise

1998 ◽  
Vol 3 ◽  
pp. 5-17
Author(s):  
R. Bakanas
Keyword(s):  
Differential Equation ◽  
Random Walk ◽  
Gaussian Noise ◽  
Iterative Scheme ◽  
Perturbation Technique ◽  
Electron Gas ◽  
Parabolic Type ◽  
Temporal Noise ◽  
Localized Excitations ◽  
Spatio Temporal

Random walk of the nonlinear localized excitations in a dissipative N-system, i.e., the influence of the irregular perturbations on the kink-shaped excitations in a system characterized by nonlinearities of "N-type", is analyzed. The “evolution” of the randomly walking excitation is described by the onedimensional PDE (partial differential equation) of the parabolic type. The analysis of the considered excitations is performed for the case of the disturbing torque which is randomly distributed in space and time, and makes up the white Gaussian noise. An iterative scheme of perturbation technique is presented to derive the randomly perturbed solutions of the considered evolution equation in a general case of N-system. The average characteristics of the “steady state” of the randomly walking kink-excitations are examined in detail. The explicit expressions that describe the considered random walk are presented for the particular case of the kink-shaped excitations of the free electron gas in semiconductors.

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.

A spatio-temporal noise robust filtering method for separation of 2D incident and reflected irregular waves

2021 ◽  
Vol 237 ◽  
pp. 109544
Author(s):  
Gustavo E. Coelho ◽  
Maria Graça Neves ◽  
António Pascoal ◽  
Álvaro Ribeiro ◽  
Peter Frigaard
Keyword(s):  
Irregular Waves ◽  
Robust Filtering ◽  
Filtering Method ◽  
Temporal Noise ◽  
Spatio Temporal ◽  
Noise Robust

Monotone methods and attractivity results for Volterra integro-partial differential equations

1981 ◽  
Vol 89 (1-2) ◽  
pp. 135-142 ◽  
Author(s):  
Andrea Schiaffino ◽  
Alberto Tesei
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Past History ◽  
Main Tool ◽  
Parabolic Type ◽  
Supremum Norm ◽  
Partial Differential ◽  
Diffusion Effects ◽  
Monotone Methods ◽  
Globally Attractive

SynopsisA Volterra integro-partial differential equation of parabolic type, which describes the time evolution of a population in a bounded habitat, subject both to past history and space diffusion effects, is investigated; general homogeneous boundary conditions are admissible. Under suitable conditions, the unique nontrivial nonnegative equilibrium is shown to be globally attractive in the supremum norm. Monotone methods are the main tool of the proof.

A perturbation solution to the problem of Wien dissociation in weak electrolytes

1978 ◽  
Vol 359 (1698) ◽  
pp. 303-317 ◽  
Keyword(s):  
Differential Equation ◽  
Electric Field ◽  
Applied Electric Field ◽  
Pair Distribution Function ◽  
Infinite System ◽  
Perturbation Technique ◽  
Relative Increase ◽  
Ion Pair ◽  
Legendre Transform ◽  
Weak Electrolytes

The problem of Wien dissociation of a weak electrolyte in the presence of a uniform applied electric field, X , is analysed by using a perturbation technique. The partial differential equation for the ion-pair distribution function is first reduced to an infinite system of ordinary differential equations by taking the Legendre transform . Explicit expressions for the relative increase in the dissociation constant, K ( X )/ K (0), due to the applied electric field, are calculated to second order in the expansion parameter 2 βq , where β is proportional to X and q is the Bjerrum association distance. Further, by induction, the m th term of this expansion is derived. The infinite series obtained in this way for K ( X )/ K (0) is convergent for all values of βq , and when summed, agrees with a formula in terms of an ordinary Bessel function of order one, given by onasager (1934) whose derivation has been published in full.

scholarly journals Mean square rate of convergence for random walk approximation of forward-backward SDEs

2020 ◽  
Vol 52 (3) ◽  
pp. 735-771
Author(s):  
Christel Geiss ◽  
Céline Labart ◽  
Antti Luoto
Keyword(s):  
Differential Equation ◽  
Random Walk ◽  
Rate Of Convergence ◽  
Backward Stochastic Differential Equation ◽  
Stochastic Equations ◽  
Terminal Condition ◽  
Probabilistic Methods ◽  
Mean Square ◽  
Finite Difference Equations ◽  
Backward Sdes

AbstractLet (Y, Z) denote the solution to a forward-backward stochastic differential equation (FBSDE). If one constructs a random walk $B^n$ from the underlying Brownian motion B by Skorokhod embedding, one can show $L_2$-convergence of the corresponding solutions $(Y^n,Z^n)$ to $(Y, Z).$ We estimate the rate of convergence based on smoothness properties, especially for a terminal condition function in $C^{2,\alpha}$. The proof relies on an approximative representation of $Z^n$ and uses the concept of discretized Malliavin calculus. Moreover, we use growth and smoothness properties of the partial differential equation associated to the FBSDE, as well as of the finite difference equations associated to the approximating stochastic equations. We derive these properties by probabilistic methods.

scholarly journals Uniqueness of Iterative Positive Solution to Nonlinear Fractional Differential Equations with Negatively Perturbed Term

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Jingjing Tan ◽  
Meixia Li ◽  
Aixia Pan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Convergence Rate ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Iterative Scheme ◽  
Approximation Error ◽  
Fractional Differential

We prove that there are unique positive solutions for a new kind of fractional differential equation with a negatively perturbed term boundary value problem. Our methods rely on an iterative algorithm which requires constructing an iterative scheme to approximate the solution. This allows us to calculate the estimation of the convergence rate and the approximation error.

scholarly journals The Iterative Scheme and the Convergence Analysis of Unique Solution for a Singular Fractional Differential Equation from the Eco-Economic Complex System’s Co-Evolution Process

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Teng Ren ◽  
Helu Xiao ◽  
Zhongbao Zhou ◽  
Xinguang Zhang ◽  
Lining Xing ◽  
...  
Keyword(s):  
Differential Equation ◽  
Convergence Analysis ◽  
Unique Solution ◽  
Fractional Differential Equation ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Singular Fractional Differential Equation ◽  
Complex Processes ◽  
Fractional Differential ◽  
And Diffusion

In this paper, we focus on a class of singular fractional differential equation, which arises from many complex processes such as the phenomenon and diffusion interaction of the ecological-economic-social complex system. By means of the iterative technique, the uniqueness and nonexistence results of positive solutions are established under the condition concerning the spectral radius of the relevant linear operator. In addition, the iterative scheme that converges to the unique solution is constructed without request of any monotonicity, and the convergence analysis and error estimate of unique solution are obtained. The numerical example and simulation are also given to demonstrate the application of the main results and the effectiveness of iterative process.

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