2,303 research outputs found
Direct numerical method for counting statistics in stochastic processes
We propose a direct numerical method to calculate the statistics of the
number of transitions in stochastic processes, without having to resort to
Monte Carlo calculations. The method is based on a generating function method,
and arbitrary moments of the probability distribution of the number of
transitions are in principle calculated by solving numerically a system of
coupled differential equations. As an example, a two state model with a
time-dependent transition matrix is considered and the first, second and third
moments of the current are calculated. This calculation scheme is applicable
for any stochastic process with a finite state space, and it would be helpful
to study current statistics in nonequilibrium systems.Comment: 8 pages, 2 figure
The stochastic pump current and the non-adiabatic geometrical phase
We calculate a pump current in a classical two-state stochastic chemical
kinetics by means of the non-adiabatic geometrical phase interpretation. The
two-state system is attached to two particle reservoirs, and under a periodic
perturbation of the kinetic rates, it gives rise to a pump current between the
two-state system and the absorbing states. In order to calculate the pump
current, the Floquet theory for the non-adiabatic geometrical phase is extended
from a Hermitian case to a non-Hermitian case. The dependence of the pump
current on the frequency of the perturbative kinetic rates is explicitly
derived, and a stochastic resonance-like behavior is obtained.Comment: 11 page
A field theoretic approach to master equations and a variational method beyond the Poisson ansatz
We develop a variational scheme in a field theoretic approach to a stochastic
process. While various stochastic processes can be expressed using master
equations, in general it is difficult to solve the master equations exactly,
and it is also hard to solve the master equations numerically because of the
curse of dimensionality. The field theoretic approach has been used in order to
study such complicated master equations, and the variational scheme achieves
tremendous reduction in the dimensionality of master equations. For the
variational method, only the Poisson ansatz has been used, in which one
restricts the variational function to a Poisson distribution. Hence, one has
dealt with only restricted fluctuation effects. We develop the variational
method further, which enables us to treat an arbitrary variational function. It
is shown that the variational scheme developed gives a quantitatively good
approximation for master equations which describe a stochastic gene regulatory
network.Comment: 13 pages, 2 figure
Noncyclic and nonadiabatic geometric phase for counting statistics
We propose a general framework of the geometric-phase interpretation for
counting statistics. Counting statistics is a scheme to count the number of
specific transitions in a stochastic process. The cumulant generating function
for the counting statistics can be interpreted as a `phase', and it is
generally divided into two parts: the dynamical phase and a remaining one. It
has already been shown that for cyclic evolution the remaining phase
corresponds to a geometric phase, such as the Berry phase or Aharonov-Anandan
phase. We here show that the remaining phase also has an interpretation as a
geometric phase even in noncyclic and nonadiabatic evolution.Comment: 12 pages, 1 figur
Population III Gamma Ray Bursts
We discuss a model of Poynting-dominated gamma-ray bursts from the collapse
of very massive first generation (pop. III) stars. From redshifts of order 20,
the resulting relativistic jets would radiate in the hard X-ray range around 50
keV and above, followed after roughly a day by an external shock component
peaking around a few keV. On the same timescales an inverse Compton component
around 75 GeV may be expected, as well as a possible infra-red flash. The
fluences of these components would be above the threshold for detectors such as
Swift and Fermi, providing potentially valuable information on the formation
and properties of what may be the first luminous objects and their black holes
in the high redshift Universe.Comment: 12 pages; Apj, subm. 12/10/2009; accepted 04/12/201
Optimization in the design of a 12 gigahertz low cost ground receiving system for broadcast satellites. Volume 1: System design, performance, and cost analysis
The technical and economical feasibility of using the 12 GHz band for broadcasting from satellites were examined. Among the assigned frequency bands for broadcast satellites, the 12 GHz band system offers the most channels. It also has the least interference on and from the terrestrial communication links. The system design and analysis are carried out on the basis of a decision analysis model. Technical difficulties in achieving low-cost 12 GHz ground receivers are solved by making use of a die cast aluminum packaging, a hybrid integrated circuit mixer, a cavity stabilized Gunn oscillator and other state-of-the-art microwave technologies for the receiver front-end. A working model was designed and tested, which used frequency modulation. A final design for the 2.6 GHz system ground receiver is also presented. The cost of the ground-terminal was analyzed and minimized for a given figure-of-merit (a ratio of receiving antenna gain to receiver system noise temperature). The results were used to analyze the performance and cost of the whole satellite system
Optimization in the design of a 12 gigahertz low cost ground receiving system for broadcast satellites. Volume 2: Antenna system and interference
The antenna characteristics are analyzed of a low cost mass-producible ground station to be used in broadcast satellite systems. It is found that a prime focus antenna is sufficient for a low-cost but not a low noise system. For the antenna feed waveguide systems are the best choice for the 12 GHz band, while printed-element systems are recommended for the 2.6 GHz band. Zoned reflectors are analyzed and appear to be attractive from the standpoint of cost. However, these reflectors suffer a gain reduction of about one db and a possible increase in sidelobe levels. The off-axis gain of a non-auto-tracking station can be optimized by establishing a special illumination function at the reflector aperture. A step-feed tracking system is proposed to provide automatic procedures for searching for peak signal from a geostationary satellite. This system uses integrated circuitry and therefore results in cost saving under mass production. It is estimated that a complete step-track system would cost only $512 for a production quantity of 1000 units per year
Statistical-mechanical iterative algorithms on complex networks
The Ising models have been applied for various problems on information
sciences, social sciences, and so on. In many cases, solving these problems
corresponds to minimizing the Bethe free energy. To minimize the Bethe free
energy, a statistical-mechanical iterative algorithm is often used. We study
the statistical-mechanical iterative algorithm on complex networks. To
investigate effects of heterogeneous structures on the iterative algorithm, we
introduce an iterative algorithm based on information of heterogeneity of
complex networks, in which higher-degree nodes are likely to be updated more
frequently than lower-degree ones. Numerical experiments clarified that the
usage of the information of heterogeneity affects the algorithm in BA networks,
but does not influence that in ER networks. It is revealed that information of
the whole system propagates rapidly through such high-degree nodes in the case
of Barab{\'a}si-Albert's scale-free networks.Comment: 7 pages, 6 figure
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