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- Subjects
- 82-XX Statistical mechanics, structure of matter
We present an interacting particle system methodology for the numerical solving of the Lyapunov exponent of Feynman–Kac semigroups and for estimating the principal eigenvalue of Schrödinger generators. The continuous or discrete time models studied in this work consists of interacting particles evolving in an environment with soft obstacles related to a potential function . These models are related to genetic algorithms and Moran type particle schemes. Their choice is not unique. We will examine...
We present an interacting particle system
methodology for the numerical solving of the Lyapunov exponent
of Feynman–Kac semigroups and for estimating the principal
eigenvalue of Schrödinger generators. The continuous or discrete time
models studied in this work
consists of N interacting particles evolving in an environment
with soft obstacles related to a potential function V. These
models are related to genetic algorithms and Moran type particle
schemes. Their choice
is not unique. We...
A new numerical scheme called particle-in-wavelets is proposed for the Vlasov-Poisson
equations, and tested in the simplest case of one spatial dimension. The plasma
distribution function is discretized using tracer particles, and the charge distribution
is reconstructed using wavelet-based density estimation. The latter consists in projecting
the Delta distributions corresponding to the particles onto a finite dimensional linear
space spanned by...
The physical properties of particles and phasesare considered in connection with their description by means of the deformation of space-time. The analogy between particle trajectories and phase boundaries is discussed. The geometry and its curvature is related to the Clifford algebraic structure whose construction in terms of the theory of deformation leads to the expected solutions for correlation functions referring to spectroscopy and scattering problems. The stochastic nature of space-time is...
Recent technological advances including brain imaging (higher resolution in space and
time), miniaturization of integrated circuits (nanotechnologies), and acceleration of
computation speed (Moore’s Law), combined with interpenetration between neuroscience,
mathematics, and physics have led to the development of more biologically plausible
computational models and novel therapeutic strategies. Today, mathematical models of
irreversible medical conditions...
We consider the hexagonal circle packing with radius and perturb it by letting the circles move as independent Brownian motions for time . It is shown that, for large enough , if is the point process given by the center of the circles at time , then, as , the critical radius for circles centered at to contain an infinite component converges to that of continuum percolation (which was shown – based on a Monte Carlo estimate – by Balister, Bollobás and Walters to be strictly bigger than...
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