Related papers: Rayleigh's dissipation function at work
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
This paper is concerned with the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian.…
An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called $\Psi$-fractional calculus. The operational calculus approach has proved useful…
The effective Lagrangian of a test particle, interacting with an ideal gas, is calculated with in the closed time path formalism in the one-loop and the leading order of the particle trajectory. The expansion in the time derivative is…
The fractional diffusion equation is rigorously derived as a scaling limit from a deterministic Rayleigh gas, where particles interact via short range potentials with support of size $\varepsilon$ and the background is distributed in space…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these…
In the Langevin formalism, the delicate balance maintained between the fluctuations in the system and their corresponding dissipation may be upset by the presence of a secondary, space-dependent stochastic force, particularly in the low…
Employing a limiting case of a conjecture for constructing piecewise separable-variables functions, the elements of the Pseudoanalytic Function Theory are used for numerically approaching solutions of the forward Dirichlet boundary value…
The article provides a unitary and complete solution to the fluctuation-dissipation relations for particle hydromechanics in a generic fluid, accounting for the hydrodynamic fluid-particle interactions (including arbitrary memory kernels in…
A unified, fast, and effective approach is developed for numerical calculation of the well-known plasma dispersion function with extensions from Maxwellian distribution to almost arbitrary distribution functions, such as the $\delta$, flat…
We use a stochastic approach to show how Taylor dispersion is affected by kinetic processes of adsorption and desorption onto surfaces. A general theory is developed, from which we derive explicitly the dispersion coefficients of canonical…
A concise method for following the evolving geometry of a moving surface using Lagrangian coordinates is described. All computations can be done in the fixed geometry of the initial surface despite the evolving complexity of the moving…
From characterizing the speed of a thermal system's response to computing natural modes of vibration, eigenvalue analysis is ubiquitous in engineering. In spite of this, eigenvalue problems have received relatively little treatment compared…
The present paper is concerned with the Cauchy-Dirichlet problem for fractional (and non-fractional) nonlinear diffusion equations posed in bounded domains. Main results consist of well-posedness in an energy class with no sign restriction…
We consider the Lagrangian formulation with duplicated variables of dissipative mechanical systems. The application of Noether theorem leads to physical observable quantities which are not conserved, like energy and angular momentum, and…
We consider the fractional Laplace framework and provide models and theorems related to nonlocal diffusion phenomena. Some applications are presented, including: a simple probabilistic interpretation, water waves, crystal dislocations,…
Boundary layers play an important role in controlling convective heat transfer. Their nature varies considerably between different application areas characterized by different boundary conditions, which hampers a uniform treatment. Here, we…
The initial-value problem for the drift-diffusion equation arising from the model of semiconductor device simulations is studied. The dissipation on this equation is given by the fractional Laplacian. When the exponent of the fractional…
The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on…