2,242 research outputs found
Paradoxes of Subdiffusive Infiltration in Disordered Systems
Infiltration of diffusing particles from one material to another where the
diffusion mechanism is either normal or anomalous is a widely observed
phenomena. When the diffusion is anomalous we find interesting behaviors:
diffusion may lead to an averaged net drift from one material to another
even if all particles eventually flow in the opposite direction, or may lead to
a flow without drift. Starting with an underlying continuous time random walk
model we solve diffusion equations describing this problem. Similar drift
against flow is found in the quenched trap model. We argue that such a behavior
is a general feature of diffusion in disordered systems.Comment: 5 pages, 2 figure
Transform of Riccati equation of constant coefficients through fractional procedure
We use a particular fractional generalization of the ordinary differential
equations that we apply to the Riccati equation of constant coefficients. By
this means the latter is transformed into a modified Riccati equation with the
free term expressed as a power of the independent variable which is of the same
order as the order of the applied fractional derivative. We provide the
solutions of the modified equation and employ the results for the case of the
cosmological Riccati equation of FRW barotropic cosmologies that has been
recently introduced by FaraoniComment: 7 pages, 2 figure
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
General Connectivity Distribution Functions for Growing Networks with Preferential Attachment of Fractional Power
We study the general connectivity distribution functions for growing networks
with preferential attachment of fractional power, ,
using the Simon's method. We first show that the heart of the previously known
methods of the rate equations for the connectivity distribution functions is
nothing but the Simon's method for word problem. Secondly, we show that the
case of fractional the -transformation of the rate equation
provides a fractional differential equation of new type, which coincides with
that for PA with linear power, when . We show that to solve such a
fractional differential equation we need define a transidental function
that we call {\it upsilon function}. Most of all
previously known results are obtained consistently in the frame work of a
unified theory.Comment: 10 page
Pinning control of fractional-order weighted complex networks
In this paper, we consider the pinning control problem of fractional-order weighted complex dynamical networks. The well-studied integer-order complex networks are the special cases of the fractional-order ones. The network model considered can represent both directed and undirected weighted networks. First, based on the eigenvalue analysis and fractional-order stability theory, some local stability properties of such pinned fractional-order networks are derived and the valid stability regions are estimated. A surprising finding is that the fractional-order complex networks can stabilize itself by reducing the fractional-order q without pinning any node. Second, numerical algorithms for fractional-order complex networks are introduced in detail. Finally, numerical simulations in scale-free complex networks are provided to show that the smaller fractional-order q, the larger control gain matrix D, the larger tunable weight parameter , the larger overall coupling strength c, the more capacity that the pinning scheme may possess to enhance the control performance of fractional-order complex networks
Detailed balance in Horava-Lifshitz gravity
We study Horava-Lifshitz gravity in the presence of a scalar field. When the
detailed balance condition is implemented, a new term in the gravitational
sector is added in order to maintain ultraviolet stability. The
four-dimensional theory is of a scalar-tensor type with a positive cosmological
constant and gravity is nonminimally coupled with the scalar and its gradient
terms. The scalar field has a double-well potential and, if required to play
the role of the inflation, can produce a scale-invariant spectrum. The total
action is rather complicated and there is no analog of the Einstein frame where
Lorentz invariance is recovered in the infrared. For these reasons it may be
necessary to abandon detailed balance. We comment on open problems and future
directions in anisotropic critical models of gravity.Comment: 10 pages. v2: discussion expanded and improved, section on
generalizations added, typos corrected, references added, conclusions
unchange
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
From non-Brownian Functionals to a Fractional Schr\"odinger Equation
We derive backward and forward fractional Schr\"odinger type of equations for
the distribution of functionals of the path of a particle undergoing anomalous
diffusion. Fractional substantial derivatives introduced by Friedrich and
co-workers [PRL {\bf 96}, 230601 (2006)] provide the correct fractional
framework for the problem at hand. In the limit of normal diffusion we recover
the Feynman-Kac treatment of Brownian functionals. For applications, we
calculate the distribution of occupation times in half space and show how
statistics of anomalous functionals is related to weak ergodicity breaking.Comment: 5 page
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