295 research outputs found
Markov evolutions and hierarchical equations in the continuum I. One-component systems
General birth-and-death as well as hopping stochastic dynamics of infinite
particle systems in the continuum are considered. We derive corresponding
evolution equations for correlation functions and generating functionals.
General considerations are illustrated in a number of concrete examples of
Markov evolutions appearing in applications.Comment: 47 page
Selection-mutation balance models with epistatic selection
We present an application of birth-and-death processes on configuration spaces to a generalized mutation4 selection balance model. The model describes the aging of population as a process of accumulation of mu5 tations in a genotype. A rigorous treatment demands that mutations correspond to points in abstract spaces. 6 Our model describes an infinite-population, infinite-sites model in continuum. The dynamical equation which 7 describes the system, is of Kimura-Maruyama type. The problem can be posed in terms of evolution of states 8 (differential equation) or, equivalently, represented in terms of Feynman-Kac formula. The questions of interest 9 are the existence of a solution, its asymptotic behavior, and properties of the limiting state. In the non-epistatic 10 case the problem was posed and solved in [Steinsaltz D., Evans S.N., Wachter K.W., Adv. Appl. Math., 2005, 11 35(1)]. In our model we consider a topological space X as the space of positions of mutations and the influence of epistatic potential
Glauber dynamics in the continuum via generating functionals evolution
We construct the time evolution for states of Glauber dynamics for a spatial
infinite particle system in terms of generating functionals. This is carried
out by an Ovsjannikov-type result in a scale of Banach spaces, leading to a
local (in time) solution which, under certain initial conditions, might be
extended to a global one. An application of this approach to Vlasov-type
scaling in terms of generating functionals is considered as well.Comment: 24 page
Tagged particle process in continuum with singular interactions
By using Dirichlet form techniques we construct the dynamics of a tagged
particle in an infinite particle environment of interacting particles for a
large class of interaction potentials. In particular, we can treat interaction
potentials having a singularity at the origin, non-trivial negative part and
infinite range, as e.g., the Lennard-Jones potential.Comment: 27 pages, proof for conservativity added, tightened presentatio
Feynman integrals for non-smooth and rapidly growing potentials
The Feynman integral for the Schrödinger propagator is constructed as a generalized
function of white noise, for a linear space of potentials spanned by finite
signed measures of bounded support and Laplace transforms of such measures,
i.e., locally singular as well as rapidly growing at infinity. Remarkably, all these
propagators admit a perturbation expansion
A new measurement of the neutron detection efficiency for the NaI Crystal Ball detector
We report on a measurement of the neutron detection efficiency in NaI
crystals in the Crystal Ball detector obtained from a study of single p0
photoproduction on deuterium using the tagged photon beam at the Mainz
Microtron. The results were obtained up to a neutron energy of 400 MeV. They
are compared to previous measurements made more than 15 years ago at the pion
beam at the BNL AGS
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