2,581 research outputs found
Dark matter density profiles: A comparison of nonextensive theory with N-body simulations
Density profiles of simulated galaxy cluster-sized dark matter haloes are
analysed in the context of a recently introduced nonextensive theory of dark
matter and gas density distributions. Nonextensive statistics accounts for
long-range interactions in gravitationally coupled systems and is derived from
the fundamental concept of entropy generalisation. The simulated profiles are
determined down to radii of ~1% of R_200. The general trend of the relaxed,
spherically averaged profiles is accurately reproduced by the theory. For the
main free parameter kappa, measuring the degree of coupling within the system,
and linked to physical quantities as the heat capacity and the polytropic index
of the self-gravitating ensembles, we find a value of -15. The significant
advantage over empirical fitting functions is provided by the physical content
of the nonextensive approach.Comment: 6 pages, 3 figures, accepted for publication in A&
How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?
The chemical Fokker-Planck equation and the corresponding chemical Langevin
equation are commonly used approximations of the chemical master equation.
These equations are derived from an uncontrolled, second-order truncation of
the Kramers-Moyal expansion of the chemical master equation and hence their
accuracy remains to be clarified. We use the system-size expansion to show that
chemical Fokker-Planck estimates of the mean concentrations and of the variance
of the concentration fluctuations about the mean are accurate to order
for reaction systems which do not obey detailed balance and at
least accurate to order for systems obeying detailed balance,
where is the characteristic size of the system. Hence the chemical
Fokker-Planck equation turns out to be more accurate than the linear-noise
approximation of the chemical master equation (the linear Fokker-Planck
equation) which leads to mean concentration estimates accurate to order
and variance estimates accurate to order . This
higher accuracy is particularly conspicuous for chemical systems realized in
small volumes such as biochemical reactions inside cells. A formula is also
obtained for the approximate size of the relative errors in the concentration
and variance predictions of the chemical Fokker-Planck equation, where the
relative error is defined as the difference between the predictions of the
chemical Fokker-Planck equation and the master equation divided by the
prediction of the master equation. For dimerization and enzyme-catalyzed
reactions, the errors are typically less than few percent even when the
steady-state is characterized by merely few tens of molecules.Comment: 39 pages, 3 figures, accepted for publication in J. Chem. Phy
Statistics of reversible bond dynamics observed in force-clamp spectroscopy
We present a detailed analysis of two-state trajectories obtained from
force-clamp spectroscopy (FCS) of reversibly bonded systems. FCS offers the
unique possibility to vary the equilibrium constant in two-state kinetics, for
instance the unfolding and refolding of biomolecules, over many orders of
magnitude due to the force dependency of the respective rates. We discuss two
different kinds of counting statistics, the event-counting usually employed in
the statistical analysis of two-state kinetics and additionally the so-called
cycle-counting. While in the former case all transitions are counted,
cycle-counting means that we focus on one type of transitions. This might be
advantageous in particular if the equilibrium constant is much larger or much
smaller than unity because in these situations the temporal resolution of the
experimental setup might not allow to capture all transitions of an
event-counting analysis. We discuss how an analysis of FCS data for complex
systems exhibiting dynamic disorder might be performed yielding information
about the detailed force-dependence of the transition rates and about the time
scale of the dynamic disorder. In addition, the question as to which extent the
kinetic scheme can be viewed as a Markovian two-state model is discussed.Comment: 25 pages, 10 figures, Phys. Rev. E, in pres
Field theoretic formulation of a mode-coupling equation for colloids
The only available quantitative description of the slowing down of the
dynamics upon approaching the glass transition has been, so far, the
mode-coupling theory, developed in the 80's by G\"otze and collaborators. The
standard derivation of this theory does not result from a systematic expansion.
We present a field theoretic formulation that arrives at very similar
mode-coupling equation but which is based on a variational principle and on a
controlled expansion in a small dimensioneless parameter. Our approach applies
to such physical systems as colloids interacting via a mildly repulsive
potential. It can in principle, with moderate efforts, be extended to higher
orders and to multipoint correlation functions
Non-equilibrium dynamics of gene expression and the Jarzynski equality
In order to express specific genes at the right time, the transcription of
genes is regulated by the presence and absence of transcription factor
molecules. With transcription factor concentrations undergoing constant
changes, gene transcription takes place out of equilibrium. In this paper we
discuss a simple mapping between dynamic models of gene expression and
stochastic systems driven out of equilibrium. Using this mapping, results of
nonequilibrium statistical mechanics such as the Jarzynski equality and the
fluctuation theorem are demonstrated for gene expression dynamics. Applications
of this approach include the determination of regulatory interactions between
genes from experimental gene expression data
Semi-Analytic Estimates of Lyapunov Exponents in Lower-Dimensional Systems
Recent work has shown that statistical arguments, seemingly well-justified in
higher dimensions, can also be used to derive reasonable, albeit less accurate,
estimates of the largest Lyapunov exponent in lower-dimensional
Hamiltonian systems. This letter explores the detailed assumptions incorporated
into these arguments. The predicted values of are insensitive to most
of these details, which can in any event be relaxed straightforwardly, but {\em
can} depend sensitively on the nongeneric form of the auto-correlation function
characterising the time-dependence of an orbit. This dependence on dynamics
implies a fundamental limitation to the application of thermodynamic arguments
to such lower-dimensional systems.Comment: 6 pages, 3 PostScript figure
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