The task of solving (9.41) is very formidable, but may be simplified considerably if the friction constant is large enough. In this case, the particle momenta reach equilibrium values appreciably more quickly than the particle configurations and the Fokker–Planck equation in phase space can be ...
The Freundlich equation states that, at a constant temperature, the amount of adsorbate bound per unit weight of adsorbent, Qe (adsorption efficiency of the adsorbent) is a logarithmic function of the residual concentration in the fluid phase at equilibrium, Ce. At low-solute concentrations, the ...
This article is devoted to the study of a nonlinear Schrödinger equation with an x-periodic and t-quasi-periodic quintic nonlinear term. It is proved that the equation admits small-amplitude, linearly stable, real analytic, and quasi-periodic solution
Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state space dimension of these equations, numerical simulations are computationally expens...
Experimentally, the main challenge in implementing the fractional quantum phenomenology is to find a physical setting featuring Lévy flights with arbitrary LI, which would impart a fractional-phase shift to the particle’s wave function, and thus realize the FSE. An alternative is to use a condens...
1. Find the velocity v as a function of t. 2. FiA particle passes through the point P = (-5,1,1) at time t = 2, moving with constant velocity v(t) = %3C0, -4, -5%3E. Find a parametric equation for ...
The Chaffee–Infante (CI) equation is a nonlinear equation that may be used to predict the complex dynamics of soliton propagation in a nonlinear optical medium. In this study, we elucidate soliton solutions of the CI equation by stochastic differential equations (SDEs) with the Wiener process....
Interestingly, we find that the empirical expression18,19 $$R=\alpha {E}_{0}^{p}$$ (21) behaves similarly to our solution. Here, α is a material dependent constant and p depends on the proton velocity which typical ranges from 1.5 to 2. As can be seen in Fig. 5, in the ...
Use the given initial conditions to find values for the constants A and B. Substituting y = 0 when t = 0 into y = e−0.6t (A cos(0.8t) + B sin(0.8t)) + sin(t) then 0=e0(A cos(0) + B sin(0)) + sin(0)⇔0 = A. To use ...
systems.” Newton’s law gives the equation of motion θ¨+sinθ=0, where θ parametrizes the position of the bob in terms of the angle the pendulum makes with the vertical axis, as it rotates about its pivot (the length has been normalized so as to match the gravitational constant). ...