728 research outputs found
ERROR PROPAGATION IN EXTENDED CHAOTIC SYSTEMS
A strong analogy is found between the evolution of localized disturbances in
extended chaotic systems and the propagation of fronts separating different
phases. A condition for the evolution to be controlled by nonlinear mechanisms
is derived on the basis of this relationship. An approximate expression for the
nonlinear velocity is also determined by extending the concept of Lyapunov
exponent to growth rate of finite perturbations.Comment: Tex file without figures- Figures and text in post-script available
via anonymous ftp at ftp://wpts0.physik.uni-wuppertal.de/pub/torcini/jpa_le
Chaotic synchronizations of spatially extended systems as non-equilibrium phase transitions
Two replicas of spatially extended chaotic systems synchronize to a common
spatio-temporal chaotic state when coupled above a critical strength. As a
prototype of each single spatio-temporal chaotic system a lattice of maps
interacting via power-law coupling is considered. The synchronization
transition is studied as a non-equilibrium phase transition, and its critical
properties are analyzed at varying the spatial interaction range as well as the
nonlinearity of the dynamical units composing each system. In particular,
continuous and discontinuous local maps are considered. In both cases the
transitions are of the second order with critical indexes varying with the
exponent characterizing the interaction range. For discontinuous maps it is
numerically shown that the transition belongs to the {\it anomalous directed
percolation} (ADP) family of universality classes, previously identified for
L{\'e}vy-flight spreading of epidemic processes. For continuous maps, the
critical exponents are different from those characterizing ADP, but apart from
the nearest-neighbor case, the identification of the corresponding universality
classes remains an open problem. Finally, to test the influence of
deterministic correlations for the studied synchronization transitions, the
chaotic dynamical evolutions are substituted by suitable stochastic models. In
this framework and for the discontinuous case, it is possible to derive an
effective Langevin description that corresponds to that proposed for ADP.Comment: 12 pages, 5 figures Comments are welcom
Non-Markovian Levy diffusion in nonhomogeneous media
We study the diffusion equation with a position-dependent, power-law
diffusion coefficient. The equation possesses the Riesz-Weyl fractional
operator and includes a memory kernel. It is solved in the diffusion limit of
small wave numbers. Two kernels are considered in detail: the exponential
kernel, for which the problem resolves itself to the telegrapher's equation,
and the power-law one. The resulting distributions have the form of the L\'evy
process for any kernel. The renormalized fractional moment is introduced to
compare different cases with respect to the diffusion properties of the system.Comment: 7 pages, 2 figure
A Comparison of a Direct- and a Plate-counting Technique for the Quantitative Estimation of Soil Micro-organisms
RESP-308
“An unreserved yea‐saying even to suffering”: A skeptical defense of Nietzschean life affirmation
Contact processes with long-range interactions
A class of non-local contact processes is introduced and studied using
mean-field approximation and numerical simulations. In these processes
particles are created at a rate which decays algebraically with the distance
from the nearest particle. It is found that the transition into the absorbing
state is continuous and is characterized by continuously varying critical
exponents. This model differs from the previously studied non-local directed
percolation model, where particles are created by unrestricted Levy flights. It
is motivated by recent studies of non-equilibrium wetting indicating that this
type of non-local processes play a role in the unbinding transition. Other
non-local processes which have been suggested to exist within the context of
wetting are considered as well.Comment: Accepted with minor revisions by Journal of Statistical Mechanics:
Theory and experiment
Extracting the time-dependent transmission rate from infection data via solution of an inverse ODE problem
The transmission rate of many acute infectious diseases varies significantly in time, but the underlying mechanisms are usually uncertain. They may include seasonal changes in the environment, contact rate, immune system response, etc. The transmission rate has been thought difficult to measure directly. We present a new algorithm to compute the time-dependent transmission rate directly from prevalence data, which makes no assumptions about the number of susceptible or vital rates. The algorithm follows our complete and explicit solution of a mathematical inverse problem for SIR-type transmission models. We prove that almost any infection profile can be perfectly fitted by an SIR model with variable transmission rate. This clearly shows a serious danger of overfitting such transmission models. We illustrate the algorithm with historic UK measles data and our observations support the common belief that measles transmission was predominantly driven by school contacts
Travelling waves in a tissue interaction model for skin pattern formation
Tissue interaction plays a major role in many morphogenetic processes, particularly those associated with skin organ primordia. We examine travelling wave solutions in a tissue interaction model for skin pattern formation which is firmly based on the known biology. From a phase space analysis we conjecture the existence of travelling waves with specific wave speeds. Subsequently, analytical approximations to the wave profiles are derived using perturbation methods. We then show numerically that such travelling wave solutions do exist and that they are in good agreement with our analytical results. Finally, the biological implications of our analysis are discussed
Validation and Calibration of Models for Reaction-Diffusion Systems
Space and time scales are not independent in diffusion. In fact, numerical
simulations show that different patterns are obtained when space and time steps
( and ) are varied independently. On the other hand,
anisotropy effects due to the symmetries of the discretization lattice prevent
the quantitative calibration of models. We introduce a new class of explicit
difference methods for numerical integration of diffusion and
reaction-diffusion equations, where the dependence on space and time scales
occurs naturally. Numerical solutions approach the exact solution of the
continuous diffusion equation for finite and , if the
parameter assumes a fixed constant value,
where is an odd positive integer parametrizing the alghorithm. The error
between the solutions of the discrete and the continuous equations goes to zero
as and the values of are dimension
independent. With these new integration methods, anisotropy effects resulting
from the finite differences are minimized, defining a standard for validation
and calibration of numerical solutions of diffusion and reaction-diffusion
equations. Comparison between numerical and analytical solutions of
reaction-diffusion equations give global discretization errors of the order of
in the sup norm. Circular patterns of travelling waves have a maximum
relative random deviation from the spherical symmetry of the order of 0.2%, and
the standard deviation of the fluctuations around the mean circular wave front
is of the order of .Comment: 33 pages, 8 figures, to appear in Int. J. Bifurcation and Chao
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