Observation of time-dependent third-order correlations in cavity QED

2011 ◽  
Author(s):  
C. Sames ◽  
M. Koch ◽  
M. Balbach ◽  
H. Chibani ◽  
A. Kubanek ◽  
...  
Keyword(s):  
Cavity Qed ◽  
Time Dependent ◽  
Third Order

scholarly journals Analysis of Large-Amplitude Pulses in Short Time Intervals: Application to Neuron Interactions

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Gianni Mattioli ◽  
Massimo Scalia ◽  
Carlo Cattani
Keyword(s):  
Dynamical System ◽  
Order Approximation ◽  
Nonlinear Dynamical System ◽  
High Amplitude ◽  
Time Dependent ◽  
Third Order ◽  
Time Intervals ◽  
Nonlinear Dynamical ◽  
Short Time ◽  
Third Order Approximation

This paper deals with the analysis of a nonlinear dynamical system which characterizes the axons interaction and is based on a generalization of FitzHugh-Nagumo system. The parametric domain of stability is investigated for both the linear and third-order approximation. A further generalization is studied in presence of high-amplitude (time-dependent) pulse. The corresponding numerical solution for some given values of parameters are analyzed through the wavelet coefficients, showing both the sensitivity to local jumps and some unexpected inertia of neuron's as response to the high-amplitude spike.

On well-posedness of the third-order nonlinear Schrödinger equation with time-dependent coefficients

2015 ◽  
Vol 17 (04) ◽  
pp. 1450031 ◽  
Author(s):  
Xavier Carvajal ◽  
Mahendra Panthee ◽  
Marcia Scialom
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Scaling Limit ◽  
Nonlinear Schrodinger Equation ◽  
Time Dependent ◽  
Well Posedness ◽  
Third Order ◽  
Nonlinear Schrödinger ◽  
The Third

We consider the Cauchy problem associated to the third-order nonlinear Schrödinger equation with time-dependent coefficients. Depending on the nature of the coefficients, we prove local as well as global well-posedness results for given data in L2-based Sobolev spaces. We also address the scaling limit to fast dispersion management and prove that it converges in H1to the solution of the averaged equation.

Third-order differential equations with three-point boundary conditions

2021 ◽  
Vol 19 (1) ◽  
pp. 11-31
Author(s):  
Alberto Cabada ◽  
Nikolay D. Dimitrov
Keyword(s):  
Boundary Conditions ◽  
Fixed Point Theorems ◽  
Nonnegative Function ◽  
Time Dependent ◽  
Point Boundary ◽  
Positive Real ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Positive Real Parameter ◽  
Increasing Functions

Abstract In this paper, a third-order ordinary differential equation coupled to three-point boundary conditions is considered. The related Green’s function changes its sign on the square of definition. Despite this, we are able to deduce the existence of positive and increasing functions on the whole interval of definition, which are convex in a given subinterval. The nonlinear considered problem consists on the product of a positive real parameter, a nonnegative function that depends on the spatial variable and a time dependent function, with negative sign on the first part of the interval and positive on the second one. The results hold by means of fixed point theorems on suitable cones.

Dynamic Analysis of Non-Uniform Beams With Time Dependent Elastic Boundary Conditions

1995 ◽  
Author(s):  
Sen Yung Lee ◽  
Shueei Muh Lin
Keyword(s):  
Boundary Conditions ◽  
Time Dependent ◽  
Polynomial Functions ◽  
Third Order ◽  
The Third ◽  
Elastic Boundary ◽  
Order Degree ◽  
Elastically Restrained ◽  
Fifth Order ◽  
Elastic Boundary Conditions

Abstract The dynamic response of a non-uniform beam with time dependent elastic boundary conditions is studied by generalizing the method of Mindlin-Goodman and utilizing the exact solutions of general elastically restrained non-uniform beams given by Lee and Kuo. The time dependent elastic boundary conditions for the beam are formulated. A general form of change of dependent variable is introduced and the shifting polynomials of the third order degree, instead of the fifth order degree polynomials taken by Mindlin-Goodman, are selected. The physical meaning of these shifting polynomial functions are explored. Finally, the limiting cases are discussed and several examples are given to illustrate the analysis.

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