3,074 research outputs found
Bistability: Requirements on Cell-Volume, Protein Diffusion, and Thermodynamics
Bistability is considered wide-spread among bacteria and eukaryotic cells,
useful e.g. for enzyme induction, bet hedging, and epigenetic switching.
However, this phenomenon has mostly been described with deterministic dynamic
or well-mixed stochastic models. Here, we map known biological bistable systems
onto the well-characterized biochemical Schloegl model, using analytical
calculations and stochastic spatio-temporal simulations. In addition to network
architecture and strong thermodynamic driving away from equilibrium, we show
that bistability requires fine-tuning towards small cell volumes (or
compartments) and fast protein diffusion (well mixing). Bistability is thus
fragile and hence may be restricted to small bacteria and eukaryotic nuclei,
with switching triggered by volume changes during the cell cycle. For large
volumes, single cells generally loose their ability for bistable switching and
instead undergo a first-order phase transition.Comment: 23 pages, 8 figure
Dimension reduction for systems with slow relaxation
We develop reduced, stochastic models for high dimensional, dissipative
dynamical systems that relax very slowly to equilibrium and can encode long
term memory. We present a variety of empirical and first principles approaches
for model reduction, and build a mathematical framework for analyzing the
reduced models. We introduce the notions of universal and asymptotic filters to
characterize `optimal' model reductions for sloppy linear models. We illustrate
our methods by applying them to the practically important problem of modeling
evaporation in oil spills.Comment: 48 Pages, 13 figures. Paper dedicated to the memory of Leo Kadanof
Particle abundance in a thermal plasma: quantum kinetics vs. Boltzmann equation
We study the abundance of a particle species in a thermalized plasma by
introducing a quantum kinetic description based on the non-equilibrium
effective action. A stochastic interpretation of quantum kinetics in terms of a
Langevin equation emerges naturally. We consider a particle species that is
stable in the vacuum and interacts with \emph{heavier} particles that
constitute a thermal bath in equilibrium and define of a fully renormalized
single particle distribution function. The distribution function thermalizes on
a time scale determined by the \emph{quasiparticle} relaxation rate. The
equilibrium distribution function depends on the full spectral density and
features off-shell contributions to the particle abundance. A model of a
bosonic field in interaction with two \emph{heavier} bosonic fields is
studied. We find substantial departures from the Bose-Einstein result both in
the high temperature and the low temperature but high momentum region. In the
latter the abundance is exponentially suppressed but larger than the
Bose-Einstein result. We obtain the Boltzmann equation in renormalized
perturbation theory and highlight the origin of the differences. We argue that
the corrections to the abundance of cold dark matter candidates are
observationally negligible and that recombination erases any possible spectral
distortions of the CMB. However we expect that the enhancement at high
temperature may be important for baryogenesis.Comment: 39 pages, 11 figures. Clarifying remarks. To appear in Physical
Review
Nonlinear effects of dark energy clustering beyond the acoustic scales
We extend the resummation method of Anselmi & Pietroni (2012) to compute the
total density power spectrum in models of quintessence characterized by a
vanishing speed of sound. For standard CDM cosmologies, this
resummation scheme allows predictions with an accuracy at the few percent level
beyond the range of scales where acoustic oscillations are present, therefore
comparable to other, common numerical tools. In addition, our theoretical
approach indicates an approximate but valuable and simple relation between the
power spectra for standard quintessence models and models where scalar field
perturbations appear at all scales. This, in turn, provides an educated guess
for the prediction of nonlinear growth in models with generic speed of sound,
particularly valuable since no numerical results are yet available.Comment: 28 pages, 12 figure
Non-linear Evolution of Baryon Acoustic Oscillations from Improved Perturbation Theory in Real and Redshift Spaces
We study the non-linear evolution of baryon acoustic oscillations in the
matter power spectrum and correlation function from the improved perturbation
theory (PT). Based on the framework of renormalized PT, we apply the {\it
closure approximation} that truncates the infinite series of loop contributions
at one-loop order, and obtain a closed set of integral equations for power
spectrum and non-linear propagator. The resultant integral expressions keep
important non-perturbative properties which can dramatically improve the
prediction of non-linear power spectrum. Employing the Born approximation, we
then derive the analytic expressions for non-linear power spectrum and the
predictions are made for non-linear evolution of baryon acoustic oscillations
in power spectrum and correlation function. A detailed comparison between
improved PT results and N-body simulations shows that a percent-level agreement
is achieved in a certain range in power spectrum and in a rather wider range in
correlation function. Combining a model of non-linear redshift-space
distortion, we also evaluate the power spectrum and correlation function in
correlation function. In contrast to the results in real space, the agreement
between N-body simulations and improved PT predictions tends to be worse, and a
more elaborate modeling for redshift-space distortion needs to be developed.
Nevertheless, with currently existing model, we find that the prediction of
correlation function has a sufficient accuracy compared with the
cosmic-variance errors for future galaxy surveys with volume of a few (Gpc/h)^3
at z>=0.5.Comment: 25 pages, 15 figures, accepted for publication in Phys.Rev.
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