Transient rectification of Brownian diffusion with asymmetric initial distribution

In an ensemble of non-interacting Brownian particles, a finite systematic average velocity may temporarily develop, even if it is zero initially. The effect originates from a small nonlinear correction to the dissipative force, causing the equation for the first moment of velocity to couple to moments of higher order. The effect may be relevant when a complex system dissociates in a viscous medium with conservation of momentum

A generalization of the cumulant expansion. Application to a scale-invariant probabilistic model

As well known, cumulant expansion is an alternative way to moment expansion to fully characterize probability distributions provided all the moments exist. If this is not the case, the so called escort mean values (or q-moments) have been proposed to characterize probability densities with divergent moments [C. Tsallis et al, J. Math. Phys 50, 043303 (2009)]. We introduce here a new mathematical object, namely the q-cumulants, which, in analogy to the cumulants, provide an alternative characterization to that of the q-moments for the probability densities. We illustrate this new scheme on a recently proposed family of scale-invariant discrete probabilistic models [A. Rodriguez et al, J. Stat. Mech. (2008) P09006; R. Hanel et al, Eur. Phys. J. B 72, 263268 (2009)] having q-Gaussians as limiting probability distributions

Overmerging and M/L ratios in phenomenological galaxy formation models

We show that the discrepancy between the Tully-Fisher relation and the luminosity function predicted by most phenomenological galaxy formation models is mainly due to overmerging of galaxy haloes. We have circumvented this overmerging problem, which is inherent in both the Press-Schechter formalism and dissipationless N-body simulations, by including a specific galaxy halo formation recipe into an otherwise standard N-body code. This numerical technique provides the merger trees which, together with simplified gas dynamics and star formation physics, constitute our implementation of a phenomenological galaxy formation model. Resolving the overmerging problem provides us with the means to match both the I-band Tully-Fisher relation and the B and K band luminosity functions within an EdS sCDM structure formation scenario. It also allows us to include models for chemical evolution and starbursts, which improves the match to observational data and renders the modelling more realistic. We show that the inclusion of chemical evolution into the modelling requires a significant fraction of stars to be formed in short bursts triggered by merging events.Comment: 15 pages, 7 figures, to be published in MNRA

Generalized Fokker-Planck equation, Brownian motion, and ergodicity

Microscopic theory of Brownian motion of a particle of mass $M$ in a bath of molecules of mass $m\ll M$ is considered beyond lowest order in the mass ratio $m/M$. The corresponding Langevin equation contains nonlinear corrections to the dissipative force, and the generalized Fokker-Planck equation involves derivatives of order higher than two. These equations are derived from first principles with coefficients expressed in terms of correlation functions of microscopic force on the particle. The coefficients are evaluated explicitly for a generalized Rayleigh model with a finite time of molecule-particle collisions. In the limit of a low-density bath, we recover the results obtained previously for a model with instantaneous binary collisions. In general case, the equations contain additional corrections, quadratic in bath density, originating from a finite collision time. These corrections survive to order $(m/M)^2$ and are found to make the stationary distribution non-Maxwellian. Some relevant numerical simulations are also presented

Tree Responses to Moderate and Extreme Drought in the Northeastern United States

Climate change is expected to lead to novel drought conditions in the Northeastern United States. Therefore, experimental studies that mimic these conditions are crucial to understand the potential impact on forests. Further, recent large scale dendrochronological studies suggest that spring and summer droughts may immediately impact tree growth while fall droughts may cause delayed impacts on growth the following growing season. Therefore, in this study, we investigated the impacts of six-week-long spring, summer, and fall droughts on the physiology and intra-annual growth on 288 saplings of six tree species native to the Northeastern United States. These species (deciduous broadleaf angiosperms, hereafter “broadleaf”: Acer rubrum L., Betula papyrifera Marsh., Prunus serotina Ehrh.; and coniferous evergreen gymnosperms, hereafter “conifer”: Juniperus virginiana L., Pinus strobus L., and Thuja occidentalis L.) represent different anticipated drought tolerances and projected abundances with climate change according to previous studies. Additionally, we used experimental dry-downs of seventy-one leafy shoots and seventeen xylem segments to assess how structural and physiological adaptations of each species relate to water use during an extreme drought. We observed marked differences in how the growth patterns of these six species responded to seasonal droughts. Spring and summer droughts generally caused height growth rate reductions for all species. Negative impacts on height growth were stronger for trees that had higher water-use and therefore experienced drought sooner. Importantly, some species such as A. rubrum, Pr. serotina, and T. occidentalis were able to compensate for these height growth reductions during spring and summer droughts with more rapid post-drought height growth. We also found that spring and summer droughts for Pr. serotina, Pi. strobus, and T. occidentalis resulted in reductions in diameter growth rates but only post-drought. Interestingly, these three species were not able to compensate for this decrease in diameter growth, which remained low throughout the rest of the growing season. These high-resolution data on intra-annual growth rates of trees in response to seasonal droughts reveal details about the growth phenology that supports and extends our understanding of annual resolution tree ring studies at larger scales. In the benchtop dry-down experiment that simulated an extreme drought, we found that leafy shoots of conifer species dried more slowly than leafy shoots of broadleaf species. In general, conifer species lost water at equal rates between leaves and stems. In contrast, deciduous species lost water very quickly and experienced larger reductions in leaf water content compared to stem water content. We saw evidence of drought-deciduousness in our greenhouse experiment where B. papyrifera was the fastest to dry-down, and in two instances, its cambia remained hydrated enough to re-flush an additional cohort of leaves post-drought. On the other hand, conifers were slow to dry-down in the greenhouse experiment, only experiencing moderate drought by the end of each drought period. The clear division in response between fast-drying broadleaved deciduous angiosperm species and slow-drying needle-leaved evergreen conifers may be partly driven by lower leaf area per shoot of conifer species, which we observed in the simulated extreme drought experiment. In the mixed wood forests common in the northeastern United States, stands may respond to drought in different ways depending on the species present. For example, we observed very different responses to growth and to some extent, recovery, in our species, and in a stand with species showing different responses, competitive dynamics may be altered among these species as the climate continues to change. Acknowledging that tree responses to drought as individuals and as communities may not align will be important moving forward from studies like these, which define drought responses of individual species, to studies which observe drought responses of entire forests

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 $\Omega^{-3/2}$ for reaction systems which do not obey detailed balance and at least accurate to order $\Omega^{-2}$ for systems obeying detailed balance, where $\Omega$ 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 $\Omega^{-1/2}$ and variance estimates accurate to order $\Omega^{-3/2}$. 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

Molecular Discreteness in Reaction-Diffusion Systems Yields Steady States Not Seen in the Continuum Limit

We investigate the effects of spatial discreteness of molecules in reaction-diffusion systems. It is found that discreteness within the so called Kuramoto length can lead to a localization of molecules, resulting in novel steady states that do not exist in the continuous case. These novel states are analyzed theoretically as the fixed points of accelerated localized reactions, an approach that was verified to be in good agreement with stochastic particle simulations. The relevance of this discreteness-induced state to biological intracellular processes is discussed.Comment: 5 pages, 3 figures, revtex

Relaxation of finite perturbations: Beyond the Fluctuation-Response relation

We study the response of dynamical systems to finite amplitude perturbation. A generalized Fluctuation-Response relation is derived, which links the average relaxation toward equilibrium to the invariant measure of the system and points out the relevance of the amplitude of the initial perturbation. Numerical computations on systems with many characteristic times show the relevance of the above relation in realistic cases.Comment: 7 pages, 5 figure

Coarse-graining a restricted solid-on-solid model

A procedure suggested by Vvedensky for obtaining continuum equations as the coarse-grained limit of discrete models is applied to the restricted solid-on-solid model with both adsorption and desorption. Using an expansion of the master equation, discrete Langevin equations are derived; these agree quantitatively with direct simulation of the model. From these, a continuum differential equation is derived, and the model is found to exhibit either Edwards-Wilkinson or Kardar-Parisi-Zhang exponents, as expected from symmetry arguments. The coefficients of the resulting continuum equation remain well-defined in the coarse-grained limit.Comment: Accepted for pubication in PR

Sub-Poissonian atom number fluctuations using light-assisted collisions

We investigate experimentally the number statistics of a mesoscopic ensemble of cold atoms in a microscopic dipole trap loaded from a magneto-optical trap, and find that the atom number fluctuations are reduced with respect to a Poisson distribution due to light-assisted two-body collisions. For numbers of atoms N>2, we measure a reduction factor (Fano factor) of 0.72+/-0.07, which differs from 1 by more than 4 standard deviations. We analyze this fact by a general stochastic model describing the competition between the loading of the trap from a reservoir of cold atoms and multi-atom losses, which leads to a master equation. Applied to our experimental regime, this model indicates an asymptotic value of 3/4 for the Fano factor at large N and in steady state. We thus show that we have reached the ultimate level of reduction in number fluctuations in our system.Comment: 4 pages, 3 figure