Mathematical Physics (MP)http://hdl.handle.net/20.500.11824/162019-04-09T23:31:49Z2019-04-09T23:31:49ZStochastic spatial models in ecology: a statistical physics approachPigolotti S.Cencini M.Molina-Garcia D.Muñoz M.A.http://hdl.handle.net/20.500.11824/9552019-03-27T02:00:13Z2017-11-21T00:00:00ZStochastic spatial models in ecology: a statistical physics approach
Pigolotti S.; Cencini M.; Molina-Garcia D.; Muñoz M.A.
Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them
by looking at how different measures of biodiversity change across spatial scales. Ecological neutral
theory has provided simple predictions accounting for general empirical patterns in communities of
competing species. However, while neutral theory in well-mixed ecosystems is mathematically well
understood, spatial models still present several open problems, limiting the quantitative understanding of spatial biodiversity. In this review, we discuss the state of the art in spatial neutral theory.
We emphasize the connection between spatial ecological models and the physics of non-equilibrium
phase transitions and how concepts developed in statistical physics translate in population dynamics, and vice versa. We focus on non-trivial scaling laws arising at the critical dimension D=2
of spatial neutral models, and their relevance for biological populations inhabiting two-dimensional
environments. We conclude by discussing models incorporating non-neutral effects in the form of
spatial and temporal disorder, and analyze how their predictions deviate from those of purely neutral
theories.
2017-11-21T00:00:00ZFractional kinetics in random/complex mediaPagnini G.http://hdl.handle.net/20.500.11824/9492019-03-14T02:00:19Z2019-01-01T00:00:00ZFractional kinetics in random/complex media
Pagnini G.
In this chapter, we consider a randomly-scaled Gaussian process and discuss a number of applications to model fractional diffusion. Actually, this approach can be understood as a Gaussian diffusion in a medium characterized by a population of scales. This interpretation supports the idea that fractional diffusion emerges from standard diffusion occurring in a complex medium.
2019-01-01T00:00:00ZFractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundariesGuggenberger T.Pagnini G.Vojta T.Metzler R.http://hdl.handle.net/20.500.11824/9482019-03-14T02:00:14Z2019-02-01T00:00:00ZFractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries
Guggenberger T.; Pagnini G.; Vojta T.; Metzler R.
Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite interval with reflecting boundary conditions. The probability density function of this reflected FBM at long times converges to a stationary distribution showing distinct deviations from the fully flat distribution of amplitude 1/L in an interval of length L found for reflected normal Brownian motion. While for superdiffusion, corresponding to a mean squared displacement (MSD) with 1 < α < 2, the probability density function is lowered in the centre of the interval and rises towards the boundaries, for subdiffusion (0 < α < 1) this behaviour is reversed and the particle density is depleted close to the boundaries. The MSD in these cases at long times converges to a stationary value, which is, remarkably, monotonically increasing with the anomalous diffusion exponent α. Our a priori surprising results may have interesting consequences for the application of FBM for processes such as molecule or tracer diffusion in the confines of living biological cells or organelles, or other viscoelastic environments such as dense liquids in microfluidic chambers.
2019-02-01T00:00:00ZSurrogate-based uncertainty and sensitivity analysis for bacterial invasion in multi-species biofilm modelingTrucchia A.Mattei M.R.Luongo V.Frunzo L.Rochoux M.C.http://hdl.handle.net/20.500.11824/9452019-03-12T02:00:14Z2019-01-01T00:00:00ZSurrogate-based uncertainty and sensitivity analysis for bacterial invasion in multi-species biofilm modeling
Trucchia A.; Mattei M.R.; Luongo V.; Frunzo L.; Rochoux M.C.
In this work, we present a probabilistic analysis of a detailed one-dimensional biofilm model that explicitly accounts for planktonic bacterial invasion in a multi-species biofilm. The objective is (1) to quantify and understand how the uncertainty in the parameters of the invasion submodel impacts the biofilm model predictions (here the microbial species volume fractions); and (2) to spot which parameters are the most important factors enhancing the biofilm model response. An emulator (or “surrogate”) of the biofilm model is trained using a limited experimental design of size N=216 and corresponding to a Halton’s low-discrepancy sequence in order to optimally cover the uncertain space of dimension d=3 (corresponding to the three scalar parameters newly introduced in the invasion submodel). A comparison of different types of emulator (generalized Polynomial Chaos expansion – gPC, Gaussian process model – GP) is carried out; results show that the best performance (measured in terms of the Q2 predictive coefficient) is obtained using a Least-Angle Regression (LAR) gPC-type expansion, where a sparse polynomial basis is constructed to reduce the problem size and where the basis coordinates are computed using a regularized least-square minimization. The resulting LAR gPC-expansion is found to capture the growth in complexity of the biofilm structure due to niche formation. Sobol’ sensitivity indices show the relative prevalence of the maximum colonization rate of autotrophic bacteria on biofilm composition in the invasion submodel. They provide guidelines for orienting future sensitivity analysis including more sources of variability, as well as further biofilm model developments.
2019-01-01T00:00:00Z