30,916 research outputs found
Fisher Waves: an individual based stochastic model
The propagation of a beneficial mutation in a spatially extended population
is usually studied using the phenomenological stochastic Fisher-Kolmogorov
(SFKPP) equation. We derive here an individual based, stochastic model founded
on the spatial Moran process where fluctuations are treated exactly. At high
selection pressure, the results of this model are different from the classical
FKPP. At small selection pressure, the front behavior can be mapped into a
Brownian motion with drift, the properties of which can be derived from
microscopic parameters of the Moran model. Finally, we show that the diffusion
coefficient and the noise amplitude of SFKPP are not independent parameters but
are both determined by the dispersal kernel of individuals
Vortexje - An Open-Source Panel Method for Co-Simulation
This paper discusses the use of the 3-dimensional panel method for dynamical
system simulation. Specifically, the advantages and disadvantages of model
exchange versus co-simulation of the aerodynamics and the dynamical system
model are discussed. Based on a trade-off analysis, a set of recommendations
for a panel method implementation and for a co-simulation environment is
proposed. These recommendations are implemented in a C++ library, offered
on-line under an open source license. This code is validated against XFLR5, and
its suitability for co-simulation is demonstrated with an example of a tethered
wing, i.e, a kite. The panel method implementation and the co-simulation
environment are shown to be able to solve this stiff problem in a stable
fashion.Comment: 13 pages, 8 figure
Kinetic theory for scalar fields with nonlocal quantum coherence
We derive quantum kinetic equations for scalar fields undergoing coherent
evolution either in time (coherent particle production) or in space (quantum
reflection). Our central finding is that in systems with certain space-time
symmetries, quantum coherence manifests itself in the form of new spectral
solutions for the dynamical 2-point correlation function. This spectral
structure leads to a consistent approximation for dynamical equations that
describe coherent evolution in presence of decohering collisions. We illustrate
the method by solving the bosonic Klein problem and the bound states for the
nonrelativistic square well potential. We then compare our spectral phase space
definition of particle number to other definitions in the nonequilibrium field
theory. Finally we will explicitly compute the effects of interactions to
coherent particle production in the case of an unstable field coupled to an
oscillating background.Comment: 33 pages, 7 figures, replaced with the version published in JHE
Moment Closure - A Brief Review
Moment closure methods appear in myriad scientific disciplines in the
modelling of complex systems. The goal is to achieve a closed form of a large,
usually even infinite, set of coupled differential (or difference) equations.
Each equation describes the evolution of one "moment", a suitable
coarse-grained quantity computable from the full state space. If the system is
too large for analytical and/or numerical methods, then one aims to reduce it
by finding a moment closure relation expressing "higher-order moments" in terms
of "lower-order moments". In this brief review, we focus on highlighting how
moment closure methods occur in different contexts. We also conjecture via a
geometric explanation why it has been difficult to rigorously justify many
moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in
mathematics, physics, chemistry and quantitative biolog
Stochastic path integral formalism for continuous quantum measurement
We generalize and extend the stochastic path integral formalism and action
principle for continuous quantum measurement introduced in [A. Chantasri, J.
Dressel and A. N. Jordan, Phys. Rev. A {\bf 88}, 042110 (2013)], where the
optimal dynamics, such as the most-likely paths, are obtained by extremizing
the action of the path integral. In this work, we apply exact functional
methods as well as develop a perturbative approach to investigate the
statistical behaviour of continuous quantum measurement, with examples given
for the qubit case. For qubit measurement with zero qubit Hamiltonian, we find
analytic solutions for average trajectories and their variances while
conditioning on fixed initial and final states. For qubit measurement with
unitary evolution, we use the perturbation method to compute expectation
values, variances, and multi-time correlation functions of qubit trajectories
in the short-time regime. Moreover, we consider continuous qubit measurement
with feedback control, using the action principle to investigate the global
dynamics of its most-likely paths, and finding that in an ideal case, qubit
state stabilization at any desired pure state is possible with linear feedback.
We also illustrate the power of the functional method by computing correlation
functions for the qubit trajectories with a feedback loop to stabilize the
qubit Rabi frequency.Comment: 24 pages, 4 figures and 1 tabl
Derivation of mean-field equations for stochastic particle systems
We study stochastic particle systems on a complete graph and derive effective
mean-field rate equations in the limit of diverging system size, which are also
known from cluster aggregation models. We establish the propagation of chaos
under generic growth conditions on particle jump rates, and the limit provides
a master equation for the single site dynamics of the particle system, which is
a non-linear birth death chain. Conservation of mass in the particle system
leads to conservation of the first moment for the limit dynamics, and to
non-uniqueness of stationary distributions. Our findings are consistent with
recent results on exchange driven growth, and provide a connection between the
well studied phenomena of gelation and condensation.Comment: 26 page
Markovian Dynamics on Complex Reaction Networks
Complex networks, comprised of individual elements that interact with each
other through reaction channels, are ubiquitous across many scientific and
engineering disciplines. Examples include biochemical, pharmacokinetic,
epidemiological, ecological, social, neural, and multi-agent networks. A common
approach to modeling such networks is by a master equation that governs the
dynamic evolution of the joint probability mass function of the underling
population process and naturally leads to Markovian dynamics for such process.
Due however to the nonlinear nature of most reactions, the computation and
analysis of the resulting stochastic population dynamics is a difficult task.
This review article provides a coherent and comprehensive coverage of recently
developed approaches and methods to tackle this problem. After reviewing a
general framework for modeling Markovian reaction networks and giving specific
examples, the authors present numerical and computational techniques capable of
evaluating or approximating the solution of the master equation, discuss a
recently developed approach for studying the stationary behavior of Markovian
reaction networks using a potential energy landscape perspective, and provide
an introduction to the emerging theory of thermodynamic analysis of such
networks. Three representative problems of opinion formation, transcription
regulation, and neural network dynamics are used as illustrative examples.Comment: 52 pages, 11 figures, for freely available MATLAB software, see
http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.htm
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