4,111 research outputs found
The exit-time problem for a Markov jump process
The purpose of this paper is to consider the exit-time problem for a
finite-range Markov jump process, i.e, the distance the particle can jump is
bounded independent of its location. Such jump diffusions are expedient models
for anomalous transport exhibiting super-diffusion or nonstandard normal
diffusion. We refer to the associated deterministic equation as a
volume-constrained nonlocal diffusion equation. The volume constraint is the
nonlocal analogue of a boundary condition necessary to demonstrate that the
nonlocal diffusion equation is well-posed and is consistent with the jump
process. A critical aspect of the analysis is a variational formulation and a
recently developed nonlocal vector calculus. This calculus allows us to pose
nonlocal backward and forward Kolmogorov equations, the former equation
granting the various moments of the exit-time distribution.Comment: 15 pages, 7 figure
Probing the properties of convective cores through g modes: high-order g modes in SPB and gamma Doradus stars
In main sequence stars the periods of high-order gravity modes are sensitive
probes of stellar cores and, in particular, of the chemical composition
gradient that develops near the outer edge of the convective core. We present
an analytical approximation of high-order g modes that takes into account the
effect of the mu gradient near the core. We show that in main-sequence models,
similarly to the case of white dwarfs, the periods of high-order gravity modes
are accurately described by a uniform period spacing superposed to an
oscillatory component. The periodicity and amplitude of such component are
related, respectively, to the location and sharpness of the mu gradient.
We investigate the properties of high-order gravity modes for stellar models
in a mass domain between 1 and 10 Msun, and the effects of the stellar mass,
evolutionary state, and extra-mixing processes on period spacing features. In
particular, we show that for models of a typical SPB star, a chemical mixing
that could likely be induced by the slow rotation observed in these stars, is
able to significantly change the g-mode spectra of the equilibrium model.
Prospects and challenges for the asteroseismology of gamma Doradus and SPB
stars are also discussed.Comment: 18 pages, 29 figures, accepted for publication in MNRA
A mathematical model for breath gas analysis of volatile organic compounds with special emphasis on acetone
Recommended standardized procedures for determining exhaled lower respiratory
nitric oxide and nasal nitric oxide have been developed by task forces of the
European Respiratory Society and the American Thoracic Society. These
recommendations have paved the way for the measurement of nitric oxide to
become a diagnostic tool for specific clinical applications. It would be
desirable to develop similar guidelines for the sampling of other trace gases
in exhaled breath, especially volatile organic compounds (VOCs) which reflect
ongoing metabolism. The concentrations of water-soluble, blood-borne substances
in exhaled breath are influenced by: (i) breathing patterns affecting gas
exchange in the conducting airways; (ii) the concentrations in the
tracheo-bronchial lining fluid; (iii) the alveolar and systemic concentrations
of the compound. The classical Farhi equation takes only the alveolar
concentrations into account. Real-time measurements of acetone in end-tidal
breath under an ergometer challenge show characteristics which cannot be
explained within the Farhi setting. Here we develop a compartment model that
reliably captures these profiles and is capable of relating breath to the
systemic concentrations of acetone. By comparison with experimental data it is
inferred that the major part of variability in breath acetone concentrations
(e.g., in response to moderate exercise or altered breathing patterns) can be
attributed to airway gas exchange, with minimal changes of the underlying blood
and tissue concentrations. Moreover, it is deduced that measured end-tidal
breath concentrations of acetone determined during resting conditions and free
breathing will be rather poor indicators for endogenous levels. Particularly,
the current formulation includes the classical Farhi and the Scheid series
inhomogeneity model as special limiting cases.Comment: 38 page
New developments in Functional and Fractional Differential Equations and in Lie Symmetry
Delay, difference, functional, fractional, and partial differential equations have many applications in science and engineering. In this Special Issue, 29 experts co-authored 10 papers dealing with these subjects. A summary of the main points of these papers follows:Several oscillation conditions for a first-order linear differential equation with non-monotone delay are established in Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays, whereas a sharp oscillation criterion using the notion of slowly varying functions is established in A Sharp Oscillation Criterion for a Linear Differential Equation with Variable Delay. The approximation of a linear autonomous differential equation with a small delay is considered in Approximation of a Linear Autonomous Differential Equation with Small Delay; the model of infection diseases by Marchuk is studied in Around the Model of Infection Disease: The Cauchy Matrix and Its Properties. Exact solutions to fractional-order Fokker–Planck equations are presented in New Exact Solutions and Conservation Laws to the Fractional-Order Fokker–Planck Equations, and a spectral collocation approach to solving a class of time-fractional stochastic heat equations driven by Brownian motion is constructed in A Collocation Approach for Solving Time-Fractional Stochastic Heat Equation Driven by an Additive Noise. A finite difference approximation method for a space fractional convection-diffusion model with variable coefficients is proposed in Finite Difference Approximation Method for a Space Fractional Convection–Diffusion Equation with Variable Coefficients; existence results for a nonlinear fractional difference equation with delay and impulses are established in On Nonlinear Fractional Difference Equation with Delay and Impulses. A complete Noether symmetry analysis of a generalized coupled Lane–Emden–Klein–Gordon–Fock system with central symmetry is provided in Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays, and new soliton solutions of a fractional Jaulent soliton Miodek system via symmetry analysis are presented in New Soliton Solutions of Fractional Jaulent-Miodek System with Symmetry Analysis
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