1,960 research outputs found
Soluble approximation of linear systems in max-plus algebra
summary:We propose an efficient method for finding a Chebyshev-best soluble approximation to an insoluble system of linear equations over max-plus algebra
About Dynamical Systems Appearing in the Microscopic Traffic Modeling
Motivated by microscopic traffic modeling, we analyze dynamical systems which
have a piecewise linear concave dynamics not necessarily monotonic. We
introduce a deterministic Petri net extension where edges may have negative
weights. The dynamics of these Petri nets are well-defined and may be described
by a generalized matrix with a submatrix in the standard algebra with possibly
negative entries, and another submatrix in the minplus algebra. When the
dynamics is additively homogeneous, a generalized additive eigenvalue may be
introduced, and the ergodic theory may be used to define a growth rate under
additional technical assumptions. In the traffic example of two roads with one
junction, we compute explicitly the eigenvalue and we show, by numerical
simulations, that these two quantities (the additive eigenvalue and the growth
rate) are not equal, but are close to each other. With this result, we are able
to extend the well-studied notion of fundamental traffic diagram (the average
flow as a function of the car density on a road) to the case of two roads with
one junction and give a very simple analytic approximation of this diagram
where four phases appear with clear traffic interpretations. Simulations show
that the fundamental diagram shape obtained is also valid for systems with many
junctions. To simulate these systems, we have to compute their dynamics, which
are not quite simple. For building them in a modular way, we introduce
generalized parallel, series and feedback compositions of piecewise linear
concave dynamics.Comment: PDF 38 page
Nonlinear analysis of a simple model of temperature evolution in a satellite
We analyse a simple model of the heat transfer to and from a small satellite
orbiting round a solar system planet. Our approach considers the satellite
isothermal, with external heat input from the environment and from internal
energy dissipation, and output to the environment as black-body radiation. The
resulting nonlinear ordinary differential equation for the satellite's
temperature is analysed by qualitative, perturbation and numerical methods,
which show that the temperature approaches a periodic pattern (attracting limit
cycle). This approach can occur in two ways, according to the values of the
parameters: (i) a slow decay towards the limit cycle over a time longer than
the period, or (ii) a fast decay towards the limit cycle over a time shorter
than the period. In the first case, an exactly soluble average equation is
valid. We discuss the consequences of our model for the thermal stability of
satellites.Comment: 13 pages, 4 figures (5 EPS files
Still on the way to quantizing gravity
I review and discuss some recent developments in non-perturbative approaches
to quantum gravity, with an emphasis on discrete formulations, and those coming
from a classical connection description.Comment: 15 pages, TeX; Invited talk at the 12th Italian Conference on General
Relativity and Gravitational Physics, Roma, September 23-27, 199
Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
We define for quantum many-body systems a quasi-adiabatic continuation of
quantum states. The continuation is valid when the Hamiltonian has a gap, or
else has a sufficiently small low-energy density of states, and thus is away
from a quantum phase transition. This continuation takes local operators into
local operators, while approximately preserving the ground state expectation
values. We apply this continuation to the problem of gauge theories coupled to
matter, and propose a new distinction, perimeter law versus "zero law" to
identify confinement. We also apply the continuation to local bosonic models
with emergent gauge theories. We show that local gauge invariance is
topological and cannot be broken by any local perturbations in the bosonic
models in either continuous or discrete gauge groups. We show that the ground
state degeneracy in emergent discrete gauge theories is a robust property of
the bosonic model, and we argue that the robustness of local gauge invariance
in the continuous case protects the gapless gauge boson.Comment: 15 pages, 6 figure
Dynamical transition in the TASEP with Langmuir kinetics: mean-field theory
We develop a mean-field theory for the totally asymmetric simple exclusion
process (TASEP) with open boundaries, in order to investigate the so-called
dynamical transition. The latter phenomenon appears as a singularity in the
relaxation rate of the system toward its non-equilibrium steady state. In the
high-density (low-density) phase, the relaxation rate becomes independent of
the injection (extraction) rate, at a certain critical value of the parameter
itself, and this transition is not accompanied by any qualitative change in the
steady-state behavior. We characterize the relaxation rate by providing
rigorous bounds, which become tight in the thermodynamic limit. These results
are generalized to the TASEP with Langmuir kinetics, where particles can also
bind to empty sites or unbind from occupied ones, in the symmetric case of
equal binding/unbinding rates. The theory predicts a dynamical transition to
occur in this case as well.Comment: 37 pages (including 16 appendix pages), 6 figures. Submitted to
Journal of Physics
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