Related papers: Hill's Equation with Random Forcing Parameters: Th…
Motivated by a class of orbit problems in astrophysics, this paper considers solutions to Hill's equation with forcing strength parameters that vary from cycle to cycle. The results are generalized to include period variations from cycle to…
This paper derives expressions for the growth rates for the random 2 x 2 matrices that result from solutions to the random Hill's equation. The parameters that appear in Hill's equation include the forcing strength and oscillation…
Hill's equations arise in a wide variety of physical problems, and are specified by a natural frequency, a periodic forcing function, and a forcing strength parameter. This classic problem is generalized here in two ways: [A] to Random…
Consider a difference equation which takes the k-th largest output of m functions of the previous m terms of the sequence. If the functions are also allowed to change periodically as the difference equation evolves this is analogous to a…
For the Dunkl operator $\Lambda_\alpha$ $(\alpha > -1/2)$ on the space of entire functions on the complex space C, the critical rate of growth for the integral means $M_p(f,r)$ of their hypercyclic functions $f$ is obtained. The rate of…
We study the elliptic equation with a line Dirac delta function as the source term subject to the Dirichlet boundary condition in a two-dimensional domain. Such a line Dirac measure causes different types of solution singularities in the…
We address the question of representativeness of a single long unstable periodic orbit for properties of the chaotic attractor it is embedded in. Y. Saiki and M. Yamada [Phys. Rev. E 79, 015201(R) (2009)] have recently suggested the…
Cosmic inflation provides a compelling framework for explaining several observed features of our Universe, but its viability depends on an efficient reheating phase that converts the inflaton's energy into Standard Model particles. This…
In this article we discuss the Dirac equation in the presence of an attractive cylindrical \delta-shell potential V(\rho)=-a\delta(\rho-\rho_0), where \rho is the radial coordinate and a>0. We present a detailed discussion on the boundary…
We show how the linear delta expansion, as applied to the slow-roll transition in quantum mechanics, can be recast in the closed time-path formalism. This results in simpler, explicit expressions than were obtained in the Schr\"odinger…
A time-changed discretization for the Dirac equation is proposed. More precisely, we consider a Dirac equation with discrete space and continuous time perturbed by a time-dependent diffusion term $\sigma^2Ht^{2H-1}$ that seamlessly…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…
The dynamics of a light fermion bound to a heavy one is expected to be described by the Dirac equation with an external potential. The potential breaks translation invariance, whereas the bound state momentum is well defined. Boosting the…
A thorough analysis is presented of the class of central fields of force that exhibit: (i) dimensional transmutation and (ii) rotational invariance. Using dimensional regularization, the two-dimensional delta-function potential and the…
We analyze the time evolution of a one-dimensional quantum system with an attractive delta function potential whose strength is subjected to a time periodic (zero mean) parametric variation. We show that for generic forcing which includes…
Quantum dynamics of a Dirac particle in a 1D box with moving wall is studied. Dirac equation with time-dependent boundary condition is mapped onto that with static one, but with time-dependent mass. Exact analytical solution of such…
We consider several mathematical issues regarding models that simulate forces exerted by cells. Since the size of cells is much smaller than the size of the domain of computation, one often considers point forces, modelled by Dirac Delta…
The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation…
Complex dynamical systems may exhibit multiple steady states, including time-periodic limit cycles, where the final trajectory depends on initial conditions. With tuning of parameters, limit cycles can proliferate or merge at an exceptional…