12,405 research outputs found
Geometrically derived difference formulae for the numerical integration of trajectory problems
The term 'trajectory problem' is taken to include problems that can arise, for instance, in connection with contour plotting, or in the application of continuation methods, or during phase-plane analysis. Geometrical techniques are used to construct difference methods for these problems to produce in turn explicit and implicit circularly exact formulae. Based on these formulae, a predictor-corrector method is derived which, when compared with a closely related standard method, shows improved performance. It is found that this latter method produces spurious limit cycles, and this behavior is partly analyzed. Finally, a simple variable-step algorithm is constructed and tested
Setting up tunneling conditions by means of Bohmian mechanics
Usually tunneling is established after imposing some matching conditions on
the (time-independent) wave function and its first derivative at the boundaries
of a barrier. Here an alternative scheme is proposed to determine tunneling and
estimate transmission probabilities in time-dependent problems, which takes
advantage of the trajectory picture provided by Bohmian mechanics. From this
theory a general functional expression for the transmission probability in
terms of the system initial state can be reached. This expression is used here
to analyze tunneling properties and estimate transmissions in the case of
initial Gaussian wave packets colliding with ramp-like barriers.Comment: 18 pages, 4 figure
Complex dynamics of elementary cellular automata emerging from chaotic rules
We show techniques of analyzing complex dynamics of cellular automata (CA)
with chaotic behaviour. CA are well known computational substrates for studying
emergent collective behaviour, complexity, randomness and interaction between
order and chaotic systems. A number of attempts have been made to classify CA
functions on their space-time dynamics and to predict behaviour of any given
function. Examples include mechanical computation, \lambda{} and Z-parameters,
mean field theory, differential equations and number conserving features. We
aim to classify CA based on their behaviour when they act in a historical mode,
i.e. as CA with memory. We demonstrate that cell-state transition rules
enriched with memory quickly transform a chaotic system converging to a complex
global behaviour from almost any initial condition. Thus just in few steps we
can select chaotic rules without exhaustive computational experiments or
recurring to additional parameters. We provide analysis of well-known chaotic
functions in one-dimensional CA, and decompose dynamics of the automata using
majority memory exploring glider dynamics and reactions
A Bayesian approach to filter design: detection of compact sources
We consider filters for the detection and extraction of compact sources on a
background. We make a one-dimensional treatment (though a generalization to two
or more dimensions is possible) assuming that the sources have a Gaussian
profile whereas the background is modeled by an homogeneous and isotropic
Gaussian random field, characterized by a scale-free power spectrum. Local peak
detection is used after filtering. Then, a Bayesian Generalized Neyman-Pearson
test is used to define the region of acceptance that includes not only the
amplification but also the curvature of the sources and the a priori
probability distribution function of the sources. We search for an optimal
filter between a family of Matched-type filters (MTF) modifying the filtering
scale such that it gives the maximum number of real detections once fixed the
number density of spurious sources. We have performed numerical simulations to
test theoretical ideas.Comment: 10 pages, 2 figures. SPIE Proceedings "Electronic Imaging II", San
Jose, CA. January 200
Algorithmic quantum simulation of memory effects
We propose a method for the algorithmic quantum simulation of memory effects
described by integrodifferential evolution equations. It consists in the
systematic use of perturbation theory techniques and a Markovian quantum
simulator. Our method aims to efficiently simulate both completely positive and
nonpositive dynamics without the requirement of engineering non-Markovian
environments. Finally, we find that small error bounds can be reached with
polynomially scaling resources, evaluated as the time required for the
simulation
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