217 research outputs found
Investigating Crayfish (\u3cem\u3eOrconectes rusticus\u3c/em\u3e) Aggression and How it Varies with Resource Availability
Animals that express agonistic behavior toward one another are prone to recognizing hierarchical status among individuals. Recognizing status has proven to be evolutionarily advantageous for crayfish (Orconectes rusticus) because it allows dominant individuals to maximize resources and permits subordinate individuals to steer clear of potentially costly battles. More specifically, two crayfish experiencing aggression can generally determine who the dominant and subordinate individuals are in a fight. A higher social status within a social hierarchy can allow for increased access to differing resources, such as food, mates, and shelter. In this experiment, we want to see if limiting resources will affect aggression levels in crayfish. To do this, we limited food availability and shelter availability and measured crayfish aggression over several rounds of interaction. While we did not find that resource availability affected crayfish aggression we did find that status does affect crayfish aggression
Enstrophy dissipation in two-dimensional turbulence
Insight into the problem of two-dimensional turbulence can be obtained by an
analogy with a heat conduction network. It allows the identification of an
entropy function associated to the enstrophy dissipation and that fluctuates
around a positive (mean) value. While the corresponding enstrophy network is
highly nonlocal, the direction of the enstrophy current follows from the Second
Law of Thermodynamics. An essential parameter is the ratio of the intensity of driving as a function of
wavenumber , to the dissipation strength , where is the
viscosity. The enstrophy current flows from higher to lower values of ,
similar to a heat current from higher to lower temperature. Our probabilistic
analysis of the enstrophy dissipation and the analogy with heat conduction thus
complements and visualizes the more traditional spectral arguments for the
direct enstrophy cascade. We also show a fluctuation symmetry in the
distribution of the total entropy production which relates the probabilities of
direct and inverse enstrophy cascades.Comment: 8 pages, revtex
Stochastic porous media equations and self-organized criticality: convergence to the critical state in all dimensions
If is the solution to the stochastic porous media equation in
, modelling the self-organized
criticaity and is the critical state, then it is proved that
\int^\9_0m(\cal O\setminus\cal O^t_0)dt<\9, and
\lim_{t\to\9}\int_{\cal O}|X(t)-X_c|d\xi=\ell<\9,\ \mathbb{P}{-a.s.} Here,
is the Lebesgue measure and is the critical region
and a.e.
. If the stochastic Gaussian perturbation has only finitely many
modes (but is still function-valued), \lim_{t\to\9}\int_K|X(t)-X_c|d\xi=0
exponentially fast for all compact with probability one, if
the noise is sufficiently strong. We also recover that in the deterministic
case
Competitive Lotka-Volterra Population Dynamics with Jumps
This paper considers competitive Lotka-Volterra population dynamics with
jumps. The contributions of this paper are as follows. (a) We show stochastic
differential equation (SDE) with jumps associated with the model has a unique
global positive solution; (b) We discuss the uniform boundedness of th
moment with and reveal the sample Lyapunov exponents; (c) Using a
variation-of-constants formula for a class of SDEs with jumps, we provide
explicit solution for 1-dimensional competitive Lotka-Volterra population
dynamics with jumps, and investigate the sample Lyapunov exponent for each
component and the extinction of our -dimensional model.Comment: 25 page
Steady state statistics of driven diffusions
We consider overdamped diffusion processes driven out of thermal equilibrium
and we analyze their dynamical steady fluctuations. We discuss the
thermodynamic interpretation of the joint fluctuations of occupation times and
currents; they incorporate respectively the time-symmetric and the
time-antisymmetric sector of the fluctuations. We highlight the canonical
structure of the joint fluctuations. The novel concept of traffic complements
the entropy production for the study of the occupation statistics. We explain
how the occupation and current fluctuations get mutually coupled out of
equilibrium. Their decoupling close-to-equilibrium explains the validity of
entropy production principles.Comment: rewritten versio
Magnetometry via a double-pass continuous quantum measurement of atomic spin
We argue that it is possible in principle to reduce the uncertainty of an
atomic magnetometer by double-passing a far-detuned laser field through the
atomic sample as it undergoes Larmor precession. Numerical simulations of the
quantum Fisher information suggest that, despite the lack of explicit
multi-body coupling terms in the system's magnetic Hamiltonian, the parameter
estimation uncertainty in such a physical setup scales better than the
conventional Heisenberg uncertainty limit over a specified but arbitrary range
of particle number N. Using the methods of quantum stochastic calculus and
filtering theory, we demonstrate numerically an explicit parameter estimator
(called a quantum particle filter) whose observed scaling follows that of our
calculated quantum Fisher information. Moreover, the quantum particle filter
quantitatively surpasses the uncertainty limit calculated from the quantum
Cramer-Rao inequality based on a magnetic coupling Hamiltonian with only
single-body operators. We also show that a quantum Kalman filter is
insufficient to obtain super-Heisenberg scaling, and present evidence that such
scaling necessitates going beyond the manifold of Gaussian atomic states.Comment: 17 pages, updated to match print versio
Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching
The main aim of this paper is to discuss the almost surely asymptotic stability of the neutral stochastic differential delay equations (NSDDEs) with Markovian switching. Linear NSDDEs with Markovian switching and nonlinear examples will be discussed to illustrate the theory
Maximum likelihood drift estimation for a threshold diffusion
We study the maximum likelihood estimator of the drift parameters of a
stochastic differential equation, with both drift and diffusion coefficients
constant on the positive and negative axis, yet discontinuous at zero. This
threshold diffusion is called drifted Oscillating Brownian motion.For this
continuously observed diffusion, the maximum likelihood estimator coincide with
a quasi-likelihood estimator with constant diffusion term. We show that this
estimator is the limit, as observations become dense in time, of the
(quasi)-maximum likelihood estimator based on discrete observations. In long
time, the asymptotic behaviors of the positive and negative occupation times
rule the ones of the estimators. Differently from most known results in the
literature, we do not restrict ourselves to the ergodic framework: indeed,
depending on the signs of the drift, the process may be ergodic, transient or
null recurrent. For each regime, we establish whether or not the estimators are
consistent; if they are, we prove the convergence in long time of the properly
rescaled difference of the estimators towards a normal or mixed normal
distribution. These theoretical results are backed by numerical simulations
Quantum noise and stochastic reduction
In standard nonrelativistic quantum mechanics the expectation of the energy
is a conserved quantity. It is possible to extend the dynamical law associated
with the evolution of a quantum state consistently to include a nonlinear
stochastic component, while respecting the conservation law. According to the
dynamics thus obtained, referred to as the energy-based stochastic Schrodinger
equation, an arbitrary initial state collapses spontaneously to one of the
energy eigenstates, thus describing the phenomenon of quantum state reduction.
In this article, two such models are investigated: one that achieves state
reduction in infinite time, and the other in finite time. The properties of the
associated energy expectation process and the energy variance process are
worked out in detail. By use of a novel application of a nonlinear filtering
method, closed-form solutions--algebraic in character and involving no
integration--are obtained for both these models. In each case, the solution is
expressed in terms of a random variable representing the terminal energy of the
system, and an independent noise process. With these solutions at hand it is
possible to simulate explicitly the dynamics of the quantum states of
complicated physical systems.Comment: 50 page
Dependent coordinates in path integral measure factorization
The transformation of the path integral measure under the reduction procedure
in the dynamical systems with a symmetry is considered. The investigation is
carried out in the case of the Wiener--type path integrals that are used for
description of the diffusion on a smooth compact Riemannian manifold with the
given free isometric action of the compact semisimple unimodular Lie group. The
transformation of the path integral, which factorizes the path integral
measure, is based on the application of the optimal nonlinear filtering
equation from the stochastic theory. The integral relation between the kernels
of the original and reduced semigroup are obtained.Comment: LaTeX2e, 28 page
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