39 research outputs found
Relaxation times for Hamiltonian systems
Usually, the relaxation times of a gas are estimated in the frame of the
Boltzmann equation. In this paper, instead, we deal with the relaxation problem
in the frame of the dynamical theory of Hamiltonian systems, in which the
definition itself of a relaxation time is an open question. We introduce a
lower bound for the relaxation time, and give a general theorem for estimating
it. Then we give an application to a concrete model of an interacting gas, in
which the lower bound turns out to be of the order of magnitude of the
relaxation times observed in dilute gases.Comment: 26 page
Universal neural field computation
Turing machines and G\"odel numbers are important pillars of the theory of
computation. Thus, any computational architecture needs to show how it could
relate to Turing machines and how stable implementations of Turing computation
are possible. In this chapter, we implement universal Turing computation in a
neural field environment. To this end, we employ the canonical symbologram
representation of a Turing machine obtained from a G\"odel encoding of its
symbolic repertoire and generalized shifts. The resulting nonlinear dynamical
automaton (NDA) is a piecewise affine-linear map acting on the unit square that
is partitioned into rectangular domains. Instead of looking at point dynamics
in phase space, we then consider functional dynamics of probability
distributions functions (p.d.f.s) over phase space. This is generally described
by a Frobenius-Perron integral transformation that can be regarded as a neural
field equation over the unit square as feature space of a dynamic field theory
(DFT). Solving the Frobenius-Perron equation yields that uniform p.d.f.s with
rectangular support are mapped onto uniform p.d.f.s with rectangular support,
again. We call the resulting representation \emph{dynamic field automaton}.Comment: 21 pages; 6 figures. arXiv admin note: text overlap with
arXiv:1204.546
Complementarity in classical dynamical systems
The concept of complementarity, originally defined for non-commuting
observables of quantum systems with states of non-vanishing dispersion, is
extended to classical dynamical systems with a partitioned phase space.
Interpreting partitions in terms of ensembles of epistemic states (symbols)
with corresponding classical observables, it is shown that such observables are
complementary to each other with respect to particular partitions unless those
partitions are generating. This explains why symbolic descriptions based on an
\emph{ad hoc} partition of an underlying phase space description should
generally be expected to be incompatible. Related approaches with different
background and different objectives are discussed.Comment: 18 pages, no figure
Chaos and Quantum-Classical Correspondence via Phase Space Distribution Functions
Quantum-classical correspondence in conservative chaotic Hamiltonian systems
is examined using a uniform structure measure for quantal and classical phase
space distribution functions. The similarities and differences between quantum
and classical time-evolving distribution functions are exposed by both
analytical and numerical means. The quantum-classical correspondence of
low-order statistical moments is also studied. The results shed considerable
light on quantum-classical correspondence.Comment: 16 pages, 5 figures, to appear in Physical Review
Applying search theory to determine the feasibility of eradicating an invasive population in natural environments
The detectability of invasive organisms influences the feasibility of eradicating an infestation. Search theory offers a framework for defining and measuring detectability, taking account of searcher ability, biological factors and the search environment. In this paper, search theory concepts are incorporated into a population model, and the costs of search and control are calculated as functions of the amount of search effort (the decision variable). Simulations are performed on a set of weed scenarios in a natural environment, involving different combinations of plant longevity, seed longevity and plant fecundity. Results provide preliminary estimates of the cost and duration of eradication programs to assist in prioritising weeds for control. The analysis shows that the success of an eradication program depends critically on the detectability of the target plant, the effectiveness of the control method, the labour requirements for search and control, and the germination rate of the plant. Copyright 2007 The Authors Journal compilation 2007 Australian Agricultural and Resource Economics Society Inc. .