Windings of the 2D free Rouse chain

We study long time dynamical properties of a chain of harmonically bound Brownian particles. This chain is allowed to wander everywhere in the plane. We show that the scaling variables for the occupation times T_j, areas A_j and winding angles \theta_j (j=1,...,n labels the particles) take the same general form as in the usual Brownian motion. We also compute the asymptotic joint laws P({T_j}), P({A_j}), P({\theta_j}) and discuss the correlations occuring in those distributions.Comment: Latex, 17 pages, submitted to J. Phys.

How long does it take to pull an ideal polymer into a small hole?

We present scaling estimates for characteristic times $\tau_{\rm lin}$ and $\tau_{\rm br}$ of pulling ideal linear and randomly branched polymers of $N$ monomers into a small hole by a force $f$. We show that the absorbtion process develops as sequential straightening of folds of the initial polymer configuration. By estimating the typical size of the fold involved into the motion, we arrive at the following predictions: $\tau_{\rm lin}(N) \sim N^{3/2}/f$ and $\tau_{\rm br}(N) \sim N^{5/4}/f$, and we also confirm them by the molecular dynamics experiment.Comment: 4 pages, 3 figure

Statistical Mechanics of the Chinese Restaurant Process: lack of self-averaging, anomalous finite-size effects and condensation

The Pitman-Yor, or Chinese Restaurant Process, is a stochastic process that generates distributions following a power-law with exponents lower than two, as found in a numerous physical, biological, technological and social systems. We discuss its rich behavior with the tools and viewpoint of statistical mechanics. We show that this process invariably gives rise to a condensation, i.e. a distribution dominated by a finite number of classes. We also evaluate thoroughly the finite-size effects, finding that the lack of stationary state and self-averaging of the process creates realization-dependent cutoffs and behavior of the distributions with no equivalent in other statistical mechanical models.Comment: (5pages, 1 figure

Dobinski-type relations and the Log-normal distribution

We consider sequences of generalized Bell numbers B(n), n=0,1,... for which there exist Dobinski-type summation formulas; that is, where B(n) is represented as an infinite sum over k of terms P(k)^n/D(k). These include the standard Bell numbers and their generalizations appearing in the normal ordering of powers of boson monomials, as well as variants of the "ordered" Bell numbers. For any such B we demonstrate that every positive integral power of B(m(n)), where m(n) is a quadratic function of n with positive integral coefficients, is the n-th moment of a positive function on the positive real axis, given by a weighted infinite sum of log-normal distributions.Comment: 7 pages, 2 Figure

Random tree growth by vertex splitting

We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model generalises the preferential attachment model and Ford's $\alpha$-model for phylogenetic trees. We develop a mean field theory for the vertex degree distribution, prove that the mean field theory is exact in some special cases and check that it agrees with numerical simulations in general. We calculate various correlation functions and show that the intrinsic Hausdorff dimension can vary from one to infinity, depending on the parameters of the model.Comment: 47 page

Thirty-eight years of CO<sub>2</sub> fertilization has outpaced growing aridity to drive greening of Australian woody ecosystems

Climate change is projected to increase the imbalance between the supply (precipitation) and atmospheric demand for water (i.e., increased potential evapotranspiration), stressing plants in water-limited environments. Plants may be able to offset increasing aridity because rising CO2 increases water use efficiency. CO2 fertilization has also been cited as one of the drivers of the widespread "greening" phenomenon. However, attributing the size of this CO2 fertilization effect is complicated, due in part to a lack of long-term vegetation monitoring and interannual- to decadalscale climate variability. In this study we asked the question of how much CO2 has contributed towards greening. We focused our analysis on a broad aridity gradient spanning eastern Australia's woody ecosystems. Next we analyzed 38 years of satellite remote sensing estimates of vegetation greenness (normalized difference vegetation index, NDVI) to examine the role of CO2 in ameliorating climate change impacts. Multiple statistical techniques were applied to separate the CO2-attributable effects on greening from the changes in water supply and atmospheric aridity. Widespread vegetation greening occurred despite a warming climate, increases in vapor pressure deficit, and repeated record-breaking droughts and heat waves. Between 1982-2019 we found that NDVI increased (median 11.3 %) across 90.5 % of the woody regions. After masking disturbance effects (e.g., fire), we statistically estimated an 11.7 % increase in NDVI attributable to CO2, broadly consistent with a hypothesized theoretical expectation of an 8.6 % increase in water use efficiency due to rising CO2. In contrast to reports of a weakening CO2 fertilization effect, we found no consistent temporal change in the CO2 effect. We conclude rising CO2 has mitigated the effects of increasing aridity, repeated record-breaking droughts, and record-breaking heat waves in eastern Australia. However, we were unable to determine whether trees or grasses were the primary beneficiary of the CO2-induced change in water use efficiency, which has implications for projecting future ecosystem resilience. A more complete understanding of how CO2-induced changes in water use efficiency affect trees and non-tree vegetation is needed

Examining the evidence for decoupling between photosynthesis and transpiration during heat extremes

Recent experimental evidence suggests that during heat extremes, wooded ecosystems may decouple photosynthesis and transpiration, reducing photosynthesis to near zero but increasing transpiration into the boundary layer. This feedback may act to dampen, rather than amplify, heat extremes in wooded ecosystems. We examined eddy covariance databases (OzFlux and FLUXNET2015) to identify whether there was field-based evidence to support these experimental findings. We focused on two types of heat extremes: (i) the 3 days leading up to a temperature extreme, defined as including a daily maximum temperature &gt;37&thinsp;∘C (similar to the widely used TXx metric), and (ii) heatwaves, defined as 3 or more consecutive days above 35&thinsp;∘C. When focusing on (i), we found some evidence of reduced photosynthesis and sustained or increased latent heat fluxes at seven Australian evergreen wooded flux sites. However, when considering the role of vapour pressure deficit and focusing on (ii), we were unable to conclusively disentangle the decoupling between photosynthesis and latent heat flux from the effect of increasing the vapour pressure deficit. Outside of Australia, the Tier-1 FLUXNET2015 database provided limited scope to tackle this issue as it does not sample sufficient high temperature events with which to probe the physiological response of trees to extreme heat. Thus, further work is required to determine whether this photosynthetic decoupling occurs widely, ideally by matching experimental species with those found at eddy covariance tower sites. Such measurements would allow this decoupling mechanism to be probed experimentally and at the ecosystem scale. Transpiration during heatwaves remains a key issue to resolve, as no land surface model includes a decoupling mechanism, and any potential dampening of the land–atmosphere amplification is thus not included in climate model projections.</p

Extreme value statistics from the Real Space Renormalization Group: Brownian Motion, Bessel Processes and Continuous Time Random Walks

We use the Real Space Renormalization Group (RSRG) method to study extreme value statistics for a variety of Brownian motions, free or constrained such as the Brownian bridge, excursion, meander and reflected bridge, recovering some standard results, and extending others. We apply the same method to compute the distribution of extrema of Bessel processes. We briefly show how the continuous time random walk (CTRW) corresponds to a non standard fixed point of the RSRG transformation.Comment: 24 pages, 5 figure