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Guy Bunin

Publications and source records attributed to Guy Bunin.

36 records · Page 2Linked to original sources

Environmental engineering is an emergent feature of diverse ecosystems and drives community structure

A central question in ecology is to understand the ecological processes that shape community structure. Niche-based theories have emphasized the important role played by competition for maintaining species diversity. Many of these insights have been derived using MacArthur's consumer resource model (MCRM) or its generalizations. Most theoretical work on the MCRM has focused on small ecosystems with a few species and resources. However theoretical insights derived from small ecosystems many not scale up large ecosystems with many resources and species because large systems with many interacting components often display new emergent behaviors that cannot be understood or deduced from analyzing smaller systems. To address this shortcoming, we develop a sophisticated statistical physics inspired cavity method to analyze MCRM when both the number of species and the number of resources is large. We find that in this limit, species generically and consistently perturb their environments and significantly modify available ecological niches. We show how our cavity approach naturally generalizes niche theory to large ecosystems by accounting for the effect of this emergent environmental engineering on species invasion and ecological stability. Our work suggests that environmental engineering is a generic feature of large, natural ecosystems and must be taken into account when analyzing and interpreting community structure. It also highlights the important role that statistical-physics inspired approaches can play in furthering our understanding of ecology.

q-bio.PE

A model with Darwinian dynamics on a rugged landscape

We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase diagram in terms of the size of the population and the diffusion rate, with a glass phase inside which the dynamics keeps searching for better configurations, and outside which deleterious `mutations' spoil the performance. The phase diagram is analogous to that of dense active matter in terms of temperature and drive.

q-bio.PE

Interaction patterns and diversity in assembled ecological communities

The assembly of ecological communities from a pool of species is central to ecology, but the effect of this process on properties of community interaction networks is still largely unknown. Here, we use a systematic analytical framework to describe how assembly from a species pool gives rise to community network properties that differ from those of the pool: Compared to the pool, the community shows a bias towards higher carrying capacities, weaker competitive interactions and stronger beneficial interactions. Moreover, even if interactions between all pool species are completely random, community networks are more structured, with correlations between interspecies interactions, and between interactions and carrying capacities. Nonetheless, we show that these properties are not sufficient to explain the coexistence of all community species, and that it is a simple relation between interactions and species abundances that is responsible for the diversity within a community.

q-bio.PE

Topological Constraints in Directed Polymer Melts

Polymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of topological constraints on a melt of directed polymers, using simulations of a simple quasi-2D model. We find that fixing the global topology of the melt to be trivial changes the polymer conformations drastically. Polymers of length $L$ wander in the transverse direction only by a distance of order $(\ln L)^ζ$ with $ζ\simeq 1.5$. This is strongly suppressed in comparison with the Brownian $L^{1/2}$ scaling which holds in the absence of the topological constraint. It is also much smaller than the predictions of standard heuristic approaches - in particular the $L^{1/4}$ of a mean-field-like `array of obstacles' model - so our results present a sharp challenge to theory. Dynamics are also strongly affected by the constraints, and a tagged monomer in an infinite system performs logarithmically slow subdiffusion in the transverse direction. To cast light on the suppression of the strands' wandering, we analyse the topological complexity of subregions of the melt: the complexity is also logarithmically small, and is related to the wandering by a power law. We comment on insights the results give for 3D melts, directed and non-directed.

cond-mat.stat-mech

Population aging through survival of the fit and stable

Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates. Individuals reproduce and die with a rate that is a property of each state, not necessarily related to its stability, and the offspring is born on the parent's state. The total population is limited by resources or space, as for example in a chemostat or a Petri dish. Our aim is to show that mutation rate and fitness become more correlated, \emph{even if they are completely uncorrelated for an isolated individual}, underlining the fact that the interaction induced by limitation of resources is by itself efficient for generating collective effects.

physics.bio-ph

Coalescence Model for Crumpled Globules Formed in Polymer Collapse

The rapid collapse of a polymer, due to external forces or changes in solvent, yields a long-lived `crumpled globule.' The conjectured fractal structure shaped by hierarchical collapse dynamics has proved difficult to establish, even with large simulations. To unravel this puzzle, we study a coarse-grained model of in-falling spherical blobs that coalesce upon contact. Distances between pairs of monomers are assigned upon their initial coalescence, and do not `equilibrate' subsequently. Surprisingly, the model reproduces quantitatively the dependence of distance on segment length, suggesting that the slow approach to scaling is related to the wide distribution of blob sizes.

cond-mat.soft

Extending the applicability of Thermal Dynamics to Evolutionary Biology

In the past years, a remarkable mapping has been found between the dynamics of a population of M individuals undergoing random mutations and selection, and that of a single system in contact with a thermal bath with temperature 1/M. This correspondence holds under the somewhat restrictive condition that the population is dominated by a single type at almost all times, punctuated by rare successive mutations. Here we argue that such thermal dynamics will hold more generally, specifically in systems with rugged fitness landscapes. This includes cases with strong clonal interference, where a number of concurrent mutants dominate the population. The problem becomes closely analogous to the experimental situation of glasses subjected to controlled variations of parameters such as temperature, pressure or magnetic fields. Non-trivial suggestions from the field of glasses may be thus proposed for evolutionary systems - including a large part of the numerical simulation procedures - that in many cases would have been counter intuitive without this background.

cond-mat.stat-mech

Singularities in Large Deviation Functionals of Bulk-Driven Transport Models

The large deviation functional of the density field in the weakly asymmetric exclusion process with open boundaries is studied using a combination of numerical and analytical methods. For appropriate boundary conditions and bulk drives the functional becomes non-differentiable. This happens at configurations where instead of a single history, several distinct histories of equal weight dominate their dynamical evolution. As we show, the structure of the singularities can be rather rich. We identify numerically analogues in configuration space of first order phase transition lines ending at a critical point and analogues of tricritical points. First order lines terminating at a critical point appear when there are configurations whose dynamical evolution is controlled by two distinct histories with equal weight. Tricritical point analogues emerge when there are configurations whose dynamical evolution is controlled by three distinct histories with equal weight. A numerical analysis suggests that the structure of the singularities can be described by a Landau like theory. Finally, in the limit of an infinite bulk bias we identify singularities which arise from a competition of s histories, with s arbitrary. In this case we show that all the singularities can be described by a Landau like theory.

cond-mat.stat-mech

Transport-induced correlations in weakly interacting systems

We study spatial correlations in the transport of energy between two baths at different temperatures. To do this, we introduce a minimal model in which energy flows from one bath to another through two subsystems. We show that the transport-induced energy correlations between the two subsystems are of the same order as the energy fluctuations within each subsystem. The correlations can be either positive or negative and we give bounds on their values which are associated with a dynamic energy scale. The different signs originate as a competition between fluctuations generated near the baths, and fluctuations of the current between the two subsystems. This interpretation sheds light on known results for spatially-dependent heat and particle conduction models.

cond-mat.stat-mech

Cusp singularities in boundary-driven diffusive systems

Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be non-differentiable, a phenomenon that is unique to non-equilibrium systems, and discuss the types of models which display such singularities.\ The structure of these singularities is found to generically be a cusp, which can be described by a Landau free energy or, equivalently, by catastrophe theory. Connections with analogous results in systems with finite-dimensional phase spaces are drawn.

cond-mat.stat-mech

Non differentiable large-deviation functionals in boundary-driven diffusive systems

We study the probability of arbitrary density profiles in conserving diffusive fields which are driven by the boundaries. We demonstrate the existence of singularities in the large-deviation functional, the direct analog of the free-energy in non-equilibrium systems. These singularities are unique to non-equilibrium systems and are a direct consequence of the breaking of time-reversal symmetry. This is demonstrated in an exactly-solvable model and also in numerical simulations on a boundary-driven Ising model. We argue that this singular behavior is expected to occur in models where the compressibility has a deep enough minimum. The mechanism is explained using a simple model.

cond-mat.stat-mech

Large deviations in boundary-driven systems: Numerical evaluation and effective large-scale behavior

We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we show that the probability density of a slowly varying configuration can be captured with a small number of long wave-length modes. For a configuration which varies rapidly in space this description can be complemented by a local equilibrium assumption.

cond-mat.stat-mech

Dynamics of Energy Fluctuations in Equilibrating and Driven-Dissipative Systems

When two isolated system are brought in contact, they relax to equilibrium via energy exchange. In another setting, when one of the systems is driven and the other is large, the first system reaches a steady-state which is not described by the Gibbs distribution. Here, we derive expressions for the size of energy fluctuations as a function of time in both settings, assuming that the process is composed of many small steps of energy exchange. In both cases the results depend only on the average energy flows in the system, independent of any other microscopic detail. In the steady-state we also derive an expression relating three key properties: the relaxation time of the system, the energy injection rate, and the size of the fluctuations.

cond-mat.stat-mech

Universal energy fluctuations in thermally isolated driven systems

When an isolated system is brought in contact with a heat bath its final energy is random and follows the Gibbs distribution -- a cornerstone of statistical physics. The system's energy can also be changed by performing non-adiabatic work using a cyclic process. Almost nothing is known about the resulting energy distribution in this setup, which is especially relevant to recent experimental progress in cold atoms, ions traps, superconducting qubits and other systems. Here we show that when the non-adiabatic process comprises of many repeated cyclic processes the resulting energy distribution is universal and different from the Gibbs ensemble. We predict the existence of two qualitatively different regimes with a continuous second order like transition between them. We illustrate our approach performing explicit calculations for both interacting and non-interacting systems.

cond-mat.stat-mech

Frequency-dependent fluctuation-dissipation relations in granular gases

The Green-Kubo relation for two models of granular gases is discussed. In the Maxwell model in any dimension, the effective temperature obtained from the Green-Kubo relation is shown to be frequency independent, and equal to the average kinetic energy, known as the granular temperature. In the second model analyzed, a mean-field granular gas, the collision rate of a particle is taken to be proportional to its velocity. The Green-Kubo relation in the high frequency limit is calculated for this model, and the effective temperature in this limit is shown to be equal to the granular temperature. This result, taken together with previous results, showing a difference between the effective temperature at zero frequency (the Einstein relation) and the granular temperature, shows that the Green-Kubo relation for granular gases is violated.

cond-mat.soft

Towards Unstructured Mesh Generation Using the Inverse Poisson Problem

A novel approach to unstructured quadrilateral mesh generation for planar domains is presented. Away from irregular vertices, the resulting meshes have the properties of nearly conformal grids. The technique is based on a theoretical relation between the present problem, and the inverse Poisson (IP) problem with point sources. An IP algorithm is described, which constructs a point-source distribution, whose sources correspond to the irregular vertices of the mesh. Both the background theory and the IP algorithm address the global nature of the mesh generation problem. The IP algorithm is incorporated in a complete mesh generation scheme, which also includes an algorithm for creating the final mesh. Example results are presented and discussed.

physics.comp-ph

A Continuum Theory for Unstructured Mesh Generation in Two Dimensions

A continuum description of unstructured meshes in two dimensions, both for planar and curved surface domains, is proposed. The meshes described are those which, in the limit of an increasingly finer mesh (smaller cells), and away from irregular vertices, have ideally-shaped cells (squares or equilateral triangles), and can therefore be completely described by two local properties: local cell size and local edge directions. The connection between the two properties is derived by defining a Riemannian manifold whose geodesics trace the edges of the mesh. A function $ϕ$, proportional to the logarithm of the cell size, is shown to obey the Poisson equation, with localized charges corresponding to irregular vertices. The problem of finding a suitable manifold for a given domain is thus shown to exactly reduce to an Inverse Poisson problem on $ϕ$, of finding a distribution of localized charges adhering to the conditions derived for boundary alignment. Possible applications to mesh generation are discussed.

cs.CG

Fluctuation-dissipation relations in driven dissipative systems

Exact theoretical results for the violation of time dependent fluctuation-dissipation relations in driven dissipative systems are presented. The ratio of correlation to delayed response in the stochastic model introduced in [Phys. Rev. Lett. 93, 240601 (2004)] is shown to depend on measurement time. The fluctuation temperature defined by this ratio differs both from the temperature of the environment performing the driving, and from other effective temperatures of the system, such as the average energy (or "granular temperature"). General explanations are given for the time independence of fluctuation temperature for simple measurements or long measurement times.

cond-mat.stat-mech