Search results for "Mathematica"
showing 10 items of 7971 documents
Path integral solution for non-linear system enforced by Poisson White Noise
2008
Abstract In this paper the response in terms of probability density function of non-linear systems under Poisson White Noise is considered. The problem is handled via path integral (PI) solution that may be considered as a step-by-step solution technique in terms of probability density function. First the extension of the PI to the case of Poisson White Noise is derived, then it is shown that at the limit when the time step becomes an infinitesimal quantity the Kolmogorov–Feller (K–F) equation is fully restored enforcing the validity of the approximations made in obtaining the conditional probability appearing in the Chapman Kolmogorov equation (starting point of the PI). Spectral counterpa…
Probabilistic response of nonlinear systems under combined normal and Poisson white noise via path integral method
2011
In this paper the response in terms of probability density function of nonlinear systems under combined normal and Poisson white noise is considered. The problem is handled via a Path Integral Solution (PIS) that may be considered as a step-by-step solution technique in terms of probability density function. A nonlinear system under normal white noise, Poissonian white noise and under the superposition of normal and Poisson white noise is performed through PIS. The spectral counterpart of the PIS, ruling the evolution of the characteristic functions is also derived. It is shown that at the limit when the time step becomes an infinitesimal quantity an equation ruling the evolution of the pro…
Uniformization with infinitesimally metric measures
2019
We consider extensions of quasiconformal maps and the uniformization theorem to the setting of metric spaces $X$ homeomorphic to $\mathbb R^2$. Given a measure $\mu$ on such a space, we introduce $\mu$-quasiconformal maps $f:X \to \mathbb R^2$, whose definition involves deforming lengths of curves by $\mu$. We show that if $\mu$ is an infinitesimally metric measure, i.e., it satisfies an infinitesimal version of the metric doubling measure condition of David and Semmes, then such a $\mu$-quasiconformal map exists. We apply this result to give a characterization of the metric spaces admitting an infinitesimally quasisymmetric parametrization.
Perturbations of symmetric elliptic Hamiltonians of degree four
2006
AbstractIn this paper four-parameter unfoldings Xλ of symmetric elliptic Hamiltonians of degree four are studied. We prove that in a compact region of the period annulus of X0 the displacement function of Xλ is sign equivalent to its principal part, which is given by a family induced by a Chebychev system; and we describe the bifurcation diagram of Xλ in a full neighborhood of the origin in the parameter space, where at most two limit cycles can exist for the corresponding systems.
Approximate Osher–Solomon schemes for hyperbolic systems
2016
This paper is concerned with a new kind of Riemann solvers for hyperbolic systems, which can be applied both in the conservative and nonconservative cases. In particular, the proposed schemes constitute a simple version of the classical Osher-Solomon Riemann solver, and extend in some sense the schemes proposed in Dumbser and Toro (2011) 19,20. The viscosity matrix of the numerical flux is constructed as a linear combination of functional evaluations of the Jacobian of the flux at several quadrature points. Some families of functions have been proposed to this end: Chebyshev polynomials and rational-type functions. Our schemes have been tested with different initial value Riemann problems f…
Numerical investigations of single mode gyrotron equation
2009
A stationary problem with the integral boundary condition arising in the mathematical modelling of a gyrotron is numerically investigated. The Chebyshev's polynomials of the second kind are used as the tool of calculations. The main result with physical meaning is the possibility to determine the maximal value of electrons efficiency. First published online: 14 Oct 2010
Optimal calculation of the pair correlation function for an orthorhombic system
2012
We present a new computational method to calculate arbitrary pair correlation functions of an orthorombic system in the most efficient way. The algorithm is demonstrated by the calculation of the radial distribution function of shock compressed liquid hydrogen.
Measuring molecular parity nonconservation using nuclear-magnetic-resonance spectroscopy
2017
The weak interaction does not conserve parity and therefore induces energy shifts in chiral enantiomers that should in principle be detectable in molecular spectra. Unfortunately, the magnitude of the expected shifts are small and in spectra of a mixture of enantiomers, the energy shifts are not resolvable. We propose a nuclear magnetic resonance (NMR) experiment in which we titrate the chirality (enantiomeric excess) of a solvent and measure the diasteriomeric splitting in the spectra of a chiral solute in order to search for an anomalous offset due to parity nonconservation (PNC). We present a proof-of-principle experiment in which we search for PNC in the \textsuperscript{13}C resonances…
Geometry of Degeneracy in Potential and Density Space
2022
In a previous work [J. Chem. Phys. 155, 244111 (2021)], we found counterexamples to the fundamental Hohenberg-Kohn theorem from density-functional theory in finite-lattice systems represented by graphs. Here, we demonstrate that this only occurs at very peculiar and rare densities, those where density sets arising from degenerate ground states, called degeneracy regions, touch each other or the boundary of the whole density domain. Degeneracy regions are shown to generally be in the shape of the convex hull of an algebraic variety, even in the continuum setting. The geometry arising between density regions and the potentials that create them is analyzed and explained with examples that, amo…
Density-Functional Theory on Graphs
2021
The principles of density-functional theory are studied for finite lattice systems represented by graphs. Surprisingly, the fundamental Hohenberg–Kohn theorem is found void, in general, while many insights into the topological structure of the density-potential mapping can be won. We give precise conditions for a ground state to be uniquely v-representable and are able to prove that this property holds for almost all densities. A set of examples illustrates the theory and demonstrates the non-convexity of the pure-state constrained-search functional. peerReviewed