937 research outputs found
Paradoxical diffusion: Discriminating between normal and anomalous random walks
Commonly, normal diffusive behavior is characterized by a linear dependence
of the second central moment on time, , while anomalous
behavior is expected to show a different time dependence, with for
superdiffusive motions. Here we demonstrate that this kind of qualification, if
applied straightforwardly, may be misleading: There are anomalous transport
motions revealing perfectly "normal" diffusive character (), yet being non-Markov and non-Gaussian in nature. We use recently developed
framework \cite[Phys. Rev. E \textbf{75}, 056702 (2007)]{magdziarz2007b} of
Monte Carlo simulations which incorporates anomalous diffusion statistics in
time and space and creates trajectories of such an extended random walk. For
special choice of stability indices describing statistics of waiting times and
jump lengths, the ensemble analysis of paradoxical diffusion is shown to hide
temporal memory effects which can be properly detected only by examination of
formal criteria of Markovianity (fulfillment of the Chapman-Kolmogorov
equation).Comment: 8 pages, 7 figure
Stationary states for underdamped anharmonic oscillators driven by Cauchy noise
Using methods of stochastic dynamics, we have studied stationary states in
the underdamped anharmonic stochastic oscillators driven by Cauchy noise. Shape
of stationary states depend both on the potential type and the damping. If the
damping is strong enough, for potential wells which in the overdamped regime
produce multimodal stationary states, stationary states in the underdamped
regime can be multimodal with the same number of modes like in the overdamped
regime. For the parabolic potential, the stationary density is always unimodal
and it is given by the two dimensional -stable density. For the mixture
of quartic and parabolic single-well potentials the stationary density can be
bimodal. Nevertheless, the parabolic addition, which is strong enough, can
destroy bimodlity of the stationary state.Comment: 9 page
Bimodality and hysteresis in systems driven by confined L\'evy flights
We demonstrate occurrence of bimodality and dynamical hysteresis in a system
describing an overdamped quartic oscillator perturbed by additive white and
asymmetric L\'evy noise. Investigated estimators of the stationary probability
density profiles display not only a turnover from unimodal to bimodal character
but also a change in a relative stability of stationary states that depends on
the asymmetry parameter of the underlying noise term. When varying the
asymmetry parameter cyclically, the system exhibits a hysteresis in the
occupation of a chosen stationary state.Comment: 4 pages, 5 figures, 30 reference
Relational structures for concurrent behaviours
\ua9 2020 The Author(s). Relational structures based on acyclic relations can successfully model fundamental aspects of concurrent systems behaviour. Examples include Elementary Net systems and Mazurkiewicz traces. There are however cases where more general relational structures are needed. In this paper, we present a general model of relational structures which can be used for a broad class of concurrent behaviours. We demonstrate how this general set-up works for combined order structures which are based on two relations, viz. an acyclic ‘before’ relation and a possibly cyclic ‘not later than’ relation
Classifying Invariant Structures of Step Traces
In the study of behaviours of concurrent systems, traces are sets of behaviourally equivalent action sequences. Traces can be represented by causal partial orders. Step traces, on the other hand, are sets of behaviourally equivalent step sequences, each step being a set of simultaneous actions. Step traces can be represented by relational structures comprising non-simultaneity and weak causality. In this paper, we propose a classification of step alphabets as well as the corresponding step traces and relational structures representing them. We also explain how the original trace model fits into the overall framework.Algorithms and the Foundations of Software technolog
Two Algebraic Process Semantics for Contextual Nets
We show that the so-called 'Petri nets are monoids' approach initiated by Meseguer and Montanari can be extended from ordinary place/transition Petri nets to contextual nets by considering suitable non-free monoids of places. The algebraic characterizations of net concurrent computations we provide cover both the collective and the individual token philosophy, uniformly along the two interpretations, and coincide with the classical proposals for place/transition Petri nets in the absence of read-arcs
A Precise Characterisation of Step Traces and Their Concurrent Histories
Step traces are an extension of Mazurkiewicz traces where each equivalence class (trace) consists of sequences of steps instead of sequences of atomic actions. Relations between the actions of the system are defined statically, as parameters of a concurrent step alphabet. By allowing only some of the possible relationships between actions, subclasses of step alphabets can be derived in a natural way. Properties of these classes can then be investigated in terms of invariant structures, i.e., the relational structures that represent the causal invariants that underlie the corresponding step traces.
In this paper, we refine an earlier classification of subclasses of step alphabets and add eight new subclasses to this hierarchy. We divide these eight classes into three families on basis of the absence of a specific behavioural relation and then characterise the corresponding invariant structures
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