Related papers: Evolution profiles and functional equations
The basic mechanics of evolution have been understood since Darwin. But debate continues over whether macroevolutionary phenomena are driven primary by the fitness structure of genotype space or by ecological interaction. In this paper we…
On the example of two-phase continua experiencing stress induced solid-fluid phase transitions we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the…
We consider the nonlinear Schrodinger equation with a logarithmic nonlinearity in a dispersive regime. We show that the presence of the nonlinearity affects the large time behavior of the solution: the dispersion is faster than usual by a…
We review localization with non-Hermitian time evolution as applied to simple models of population biology with spatially varying growth profiles and convection. Convection leads to a constant imaginary vector potential in the…
We prove that if a solution of the discrete time-dependent Schr\"odinger equation with bounded real potential decays fast at two distinct times then the solution is trivial. For the free Shr\"odinger operator and for operators with…
A time dependent variational approach is used to derive the equations of motion for the \lambda \phi^4 model. The simultaneous evolution of the quantum fluctuations and of the classical part of the field is considered in a lattice of 1+1…
In this paper we consider $L^p$-regularity estimates for solutions to stochastic evolution equations, which is called stochastic maximal $L^p$-regularity. Our aim is to find a theory which is analogously to Dore's theory for deterministic…
A simple trick is illustrated, whereby nonlinear evolution equations can be modified so that they feature a lot - or, in some cases, only -- periodic solutions. Several examples (ODEs and PDEs) are exhibited.
Solutions to the wave equation with constant coefficients in $\mathbb{R}^d$ can be represented explicitly in Fourier space. We investigate a reconstruction formula, which provides an approximation of solutions $u(.,t)$ to initial data…
An effective operational approach to quantum mechanics is to focus on the evolution of wave-packets, for which the wave-function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of…
In this note, we give an overview of some results obtained in [3]. This latter work is devoted to the study of the one-dimensional nonlinear Schr{\"o}dinger equation with random initial conditions. Namely, we describe the nonlinear…
A method for numerical approximation of a new class of fractional parabolic stochastic evolution equations is introduced and analysed. This class of equations has recently been proposed as a space-time extension of the SPDE-method in…
An alternative approach - nonequilibrium evolution thermodynamics, is compared with classical Landau approach. A statistical justification of the approach is carried out with help of probability distribution function on an example of a…
Naturally evolving proteins gradually accumulate mutations while continuing to fold to thermodynamically stable native structures. This process of neutral protein evolution is an important mode of genetic change, and forms the basis for the…
We prove existence of strongly continuous evolution systems in L^2 for Schroedinger-type equations with non-Lipschitz coefficients in the principal part. The underlying operator structure is motivated from models of paraxial approximations…
The time derivative (in the sense of distributions) of the solutions to the Evolutionary p-Laplace Equation is proved to be a function in a local Lebesgue space.
Resonances which result from perturbation of embedded eigenvalues are studied by time dependent methods. A general theory is developed, with new and weaker conditions, allowing for perturbations of threshold eigenvalues and relaxed Fermi…
Social evolutionary theory seeks to explain increases in the scale and complexity of human societies, from origins to present. Over the course of the twentieth century, social evolutionary theory largely fell out of favor as a way of…
The Wheeler-DeWitt (WdW) equation does not describe any explicit time evolution of the wave function, and somehow related to this issue, there is no natural way of defining an invariant inner product that provides a viable probability…
We introduce a definition of finite-time curvature evolution along with our recent study on shape coherence in nonautonomous dynamical systems. Comparing to slow evolving curvature preserving the shape, large curvature growth points reveal…