33,826 research outputs found
Memory-Controlled Diffusion
Memory effects require for their incorporation into random-walk models an
extension of the conventional equations. The linear Fokker-Planck equation for
the probability density is generalized to include non-linear and
non-local spatial-temporal memory effects. The realization of the memory
kernels are restricted due the conservation of the basic quantity . A
general criteria is given for the existence of stationary solutions. In case
the memory kernel depends on polynomially the transport is prevented. Owing
to the delay effects a finite amount of particles remains localized and the
further transport is terminated. For diffusion with non-linear memory effects
we find an exact solution in the long-time limit. Although the mean square
displacement shows diffusive behavior, higher order cumulants exhibits
differences to diffusion and they depend on the memory strength
Macroscopic description of particle systems with non-local density-dependent diffusivity
In this paper we study macroscopic density equations in which the diffusion
coefficient depends on a weighted spatial average of the density itself. We
show that large differences (not present in the local density-dependence case)
appear between the density equations that are derived from different
representations of the Langevin equation describing a system of interacting
Brownian particles. Linear stability analysis demonstrates that under some
circumstances the density equation interpreted like Ito has pattern solutions,
which never appear for the Hanggi-Klimontovich interpretation, which is the
other one typically appearing in the context of nonlinear diffusion processes.
We also introduce a discrete-time microscopic model of particles that confirms
the results obtained at the macroscopic density level.Comment: 4 pages, 3 figure
Iowa Farm Values Up in 1955
Farm expansion, social security and capital gains overbalance drouth, lower hog prices
Truncation effects in superdiffusive front propagation with L\'evy flights
A numerical and analytical study of the role of exponentially truncated
L\'evy flights in the superdiffusive propagation of fronts in
reaction-diffusion systems is presented. The study is based on a variation of
the Fisher-Kolmogorov equation where the diffusion operator is replaced by a
-truncated fractional derivative of order where
is the characteristic truncation length scale. For there is no
truncation and fronts exhibit exponential acceleration and algebraic decaying
tails. It is shown that for this phenomenology prevails in the
intermediate asymptotic regime where
is the diffusion constant. Outside the intermediate asymptotic regime,
i.e. for , the tail of the front exhibits the tempered decay
, the acceleration is transient, and
the front velocity, , approaches the terminal speed as , where it is assumed that
with denoting the growth rate of the
reaction kinetics. However, the convergence of this process is algebraic, , which is very slow compared to the exponential
convergence observed in the diffusive (Gaussian) case. An over-truncated regime
in which the characteristic truncation length scale is shorter than the length
scale of the decay of the initial condition, , is also identified. In
this extreme regime, fronts exhibit exponential tails, ,
and move at the constant velocity, .Comment: Accepted for publication in Phys. Rev. E (Feb. 2009
The 10 to the 8th power bit solid state spacecraft data recorder
The results are summarized of a program to demonstrate the feasibility of Bubble Domain Memory Technology as a mass memory medium for spacecraft applications. The design, fabrication and test of a partially populated 10 to the 8th power Bit Data Recorder using 100 Kbit serial bubble memory chips is described. Design tradeoffs, design approach and performance are discussed. This effort resulted in a 10 to the 8th power bit recorder with a volume of 858.6 cu in and a weight of 47.2 pounds. The recorder is plug reconfigurable, having the capability of operating as one, two or four independent serial channel recorders or as a single sixteen bit byte parallel input recorder. Data rates up to 1.2 Mb/s in a serial mode and 2.4 Mb/s in a parallel mode may be supported. Fabrication and test of the recorder demonstrated the basic feasibility of Bubble Domain Memory technology for such applications. Test results indicate the need for improvement in memory element operating temperature range and detector performance
Interplanetary propulsion using inertial fusion
Inertial fusion can be used to power spacecraft within the solar system and beyond. Such spacecraft have the potential for short-duration manned-mission performance exceeding other technologies. We are conducting a study to assess the systems aspects of inertial fusion as applied to such missions, based on the conceptual engine design of Hyde (1983) we describe the required systems for an entirely new spacecraft design called VISTA that is based on the use of DT fuel. We give preliminary design details for the power conversion and power conditioning systems for manned missions to Mars of total duration of about 100 days. Specific mission performance results will be published elsewhere, after the study has been completed
Thermal gravity, black holes and cosmological entropy
Taking seriously the interpretation of black hole entropy as the logarithm of
the number of microstates, we argue that thermal gravitons may undergo a phase
transition to a kind of black hole condensate. The phase transition proceeds
via nucleation of black holes at a rate governed by a saddlepoint configuration
whose free energy is of order the inverse temperature in Planck units. Whether
the universe remains in a low entropy state as opposed to the high entropy
black hole condensate depends sensitively on its thermal history. Our results
may clarify an old observation of Penrose regarding the very low entropy state
of the universe.Comment: 5 pages, 2 figures, RevTex. v4: to appear in Phys. Rev.
Density Matrix Renormalization for Model Reduction in Nonlinear Dynamics
We present a novel approach for model reduction of nonlinear dynamical
systems based on proper orthogonal decomposition (POD). Our method, derived
from Density Matrix Renormalization Group (DMRG), provides a significant
reduction in computational effort for the calculation of the reduced system,
compared to a POD. The efficiency of the algorithm is tested on the one
dimensional Burgers equations and a one dimensional equation of the Fisher type
as nonlinear model systems.Comment: 12 pages, 12 figure
New conditional symmetries and exact solutions of nonlinear reaction-diffusion-convection equations. II
In the first part of this paper math-ph/0612078, a complete description of
Q-conditional symmetries for two classes of reaction-diffusion-convection
equations with power diffusivities is derived. It was shown that all the known
results for reaction-diffusion equations with power diffusivities follow as
particular cases from those obtained in math-ph/0612078 but not vise versa. In
the second part the symmetries obtained in are successfully applied for
constructing exact solutions of the relevant equations. In the particular case,
new exact solutions of nonlinear reaction-diffusion-convection (RDC) equations
arising in application and their natural generalizations are found
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