18,269 research outputs found
Fractional Chemotaxis Diffusion Equations
We introduce mesoscopic and macroscopic model equations of chemotaxis with
anomalous subdiffusion for modelling chemically directed transport of
biological organisms in changing chemical environments with diffusion hindered
by traps or macro-molecular crowding. The mesoscopic models are formulated
using Continuous Time Random Walk master equations and the macroscopic models
are formulated with fractional order differential equations. Different models
are proposed depending on the timing of the chemotactic forcing.
Generalizations of the models to include linear reaction dynamics are also
derived. Finally a Monte Carlo method for simulating anomalous subdiffusion
with chemotaxis is introduced and simulation results are compared with
numerical solutions of the model equations. The model equations developed here
could be used to replace Keller-Segel type equations in biological systems with
transport hindered by traps, macro-molecular crowding or other obstacles.Comment: 25page
Fractional chemotaxis diffusion equations
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macromolecular crowding or other obstacles
Fractional Fokker-Planck Equations for Subdiffusion with Space-and-Time-Dependent Forces
We have derived a fractional Fokker-Planck equation for subdiffusion in a
general space-and- time-dependent force field from power law waiting time
continuous time random walks biased by Boltzmann weights. The governing
equation is derived from a generalized master equation and is shown to be
equivalent to a subordinated stochastic Langevin equation.Comment: 5 page
Multiple core hole formation by free-electron laser radiation in molecular nitrogen
We investigate the formation of multiple-core-hole states of molecular
nitrogen interacting with a free-electron laser pulse. We obtain bound and
continuum molecular orbitals in the single-center expansion scheme and use
these orbitals to calculate photo-ionization and Auger decay rates. Using these
rates, we compute the atomic ion yields generated in this interaction. We track
the population of all states throughout this interaction and compute the
proportion of the population which accesses different core-hole states. We also
investigate the pulse parameters that favor the formation of these core-hole
states for 525 eV and 1100 eV photons
Generalised fractional diffusion equations for subdiffusion on arbitrarily growing domains
Many physical phenomena occur on domains that grow in time. When the
timescales of the phenomena and domain growth are comparable, models must
include the dynamics of the domain. A widespread intrinsically slow transport
process is subdiffusion. Many models of subdiffusion include a history
dependence. This greatly confounds efforts to incorporate domain growth. Here
we derive the fractional partial differential equations that govern
subdiffusion on a growing domain, based on a Continuous Time Random Walk. This
requires the introduction of a new, comoving, fractional derivative.Comment: 12 pages, 1 figur
Properties of dense strange hadronic matter with quark degrees of freedom
The properties of strange hadronic matter are studied in the context of the modified quark-meson coupling model using two substantially di erent sets of hyperon-hyperon (Y Y ) interactions. The first set is based on the Nijmegen hard core potential model D with slightly attractive Y Y interactions. The second potential set is based on the recent SU(3) extension of the Nijmegen soft-core potential NSC97 with strongly attractive Y Y interactions which may allow for deeply bound hypernuclear matter. The results show that, for the first potential set, the hyperon does not appear at all in the bulk at any baryon density and for all strangeness fractions. The binding energy curves of the resulting N system vary smoothly with density and the system is stable (or metastable if we include the weak force). However, the situation is drastically changed when using the second set where the hyperons appear in the system at large baryon densities above a critical strangeness fraction. We find strange hadronic matter undergoes a first order phase transition from a N system to a N for strangeness fractions fS > 1.2 and baryonic densities exceeding twice ordinary nuclear matter density. Furthermore, it is found that the system built of N is deeply bound. This phase transition a ects significantly the equation of state which becomes much softer and a substantial drop in energy density and pressure are detected as the phase transition takes place. PACS:21.65.+f, 24.85.+p, 12.39B
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