4,664 research outputs found

### Towards deterministic equations for Levy walks: the fractional material derivative

Levy walks are random processes with an underlying spatiotemporal coupling.
This coupling penalizes long jumps, and therefore Levy walks give a proper
stochastic description for a particle's motion with broad jump length
distribution. We derive a generalized dynamical formulation for Levy walks in
which the fractional equivalent of the material derivative occurs. Our approach
will be useful for the dynamical formulation of Levy walks in an external force
field or in phase space for which the description in terms of the continuous
time random walk or its corresponding generalized master equation are less well
suited

### Anomalous diffusion in correlated continuous time random walks

We demonstrate that continuous time random walks in which successive waiting
times are correlated by Gaussian statistics lead to anomalous diffusion with
mean squared displacement ~t^{2/3}. Long-ranged correlations of the
waiting times with power-law exponent alpha (0<alpha<=2) give rise to
subdiffusion of the form ~t^{alpha/(1+alpha)}. In contrast correlations
in the jump lengths are shown to produce superdiffusion. We show that in both
cases weak ergodicity breaking occurs. Our results are in excellent agreement
with simulations.Comment: 6 pages, 6 figures. Slightly revised version, accepted to J Phys A as
a Fast Track Communicatio

### On solutions of a class of non-Markovian Fokker-Planck equations

We show that a formal solution of a rather general non-Markovian
Fokker-Planck equation can be represented in a form of an integral
decomposition and thus can be expressed through the solution of the Markovian
equation with the same Fokker-Planck operator. This allows us to classify
memory kernels into safe ones, for which the solution is always a probability
density, and dangerous ones, when this is not guaranteed. The first situation
describes random processes subordinated to a Wiener process, while the second
one typically corresponds to random processes showing a strong ballistic
component. In this case the non-Markovian Fokker-Planck equation is only valid
in a restricted range of parameters, initial and boundary conditions.Comment: A new ref.12 is added and discusse

### Matched pair conical spiral antennas

A matched pair of VHF (220-260 MHz) conical spiral antennas for use in a rocket-tracking interferometer array was designed and tested. While gain, bandwidth, impedance, and pattern measurements met specifications, the phase match between antennas at low elevations was not equal to the design goal

### L\'{e}vy flights as subordination process: first passage times

We obtain the first passage time density for a L\'{e}vy flight random process
from a subordination scheme. By this method, we infer the asymptotic behavior
directly from the Brownian solution and the Sparre Andersen theorem, avoiding
explicit reference to the fractional diffusion equation. Our results
corroborate recent findings for Markovian L\'{e}vy flights and generalize to
broad waiting times.Comment: 4 pages, RevTe

### Black-body furnace Patent

Development of black-body source calibration furnac

### Thermodynamics and Fractional Fokker-Planck Equations

The relaxation to equilibrium in many systems which show strange kinetics is
described by fractional Fokker-Planck equations (FFPEs). These can be
considered as phenomenological equations of linear nonequilibrium theory. We
show that the FFPEs describe the system whose noise in equilibrium funfills the
Nyquist theorem. Moreover, we show that for subdiffusive dynamics the solutions
of the corresponding FFPEs are probability densities for all cases where the
solutions of normal Fokker-Planck equation (with the same Fokker-Planck
operator and with the same initial and boundary conditions) exist. The
solutions of the FFPEs for superdiffusive dynamics are not always probability
densities. This fact means only that the corresponding kinetic coefficients are
incompatible with each other and with the initial conditions

### Optimal target search on a fast folding polymer chain with volume exchange

We study the search process of a target on a rapidly folding polymer (`DNA')
by an ensemble of particles (`proteins'), whose search combines 1D diffusion
along the chain, Levy type diffusion mediated by chain looping, and volume
exchange. A rich behavior of the search process is obtained with respect to the
physical parameters, in particular, for the optimal search.Comment: 4 pages, 3 figures, REVTe

### Dynamics of Interacting Neural Networks

The dynamics of interacting perceptrons is solved analytically. For a
directed flow of information the system runs into a state which has a higher
symmetry than the topology of the model. A symmetry breaking phase transition
is found with increasing learning rate. In addition it is shown that a system
of interacting perceptrons which is trained on the history of its minority
decisions develops a good strategy for the problem of adaptive competition
known as the Bar Problem or Minority Game.Comment: 9 pages, 3 figures; typos corrected, content reorganize

- …