Browsing by Subject "BROWNIAN-MOTION"

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  • Casteras, Jean-Baptiste; Holopainen, Ilkka; Ripoll, Jaime B. (2019)
    We study the asymptotic Dirichlet problem for A-harmonic equations and for the minimal graph equation on a Cartan-Hadamard manifold M whose sectional curvatures are bounded from below and above by certain functions depending on the distance r = d(., o) to a fixed point o is an element of M. We are, in particular, interested in finding optimal (or close to optimal) curvature upper bounds. In the special case of the Laplace-Beltrami equation we are able to solve the asymptotic Dirichlet problem in dimensions n >= 3 if radial sectional curvatures satisfy -(logr(x))(2 (epsilon) over bar)/r(x)(2 ) outside a compact set for some epsilon > (epsilon) over bar > 0. The upper bound is close to optimal since the nonsolvability is known if K >= -1/(2r(x)(2)log r(x)). Our results (in the non-rotationally symmetric case) improve on the previously known case of the quadratically decaying upper bound.
  • Gurarie, Eliezer; Fleming, Christen H.; Fagan, William F.; Laidre, Kristin L.; Hernandez-Pliego, Jesus; Ovaskainen, Otso (2017)
    Background: Continuous time movement models resolve many of the problems with scaling, sampling, and interpretation that affect discrete movement models. They can, however, be challenging to estimate, have been presented in inconsistent ways, and are not widely used. Methods: We review the literature on integrated Ornstein-Uhlenbeck velocity models and propose four fundamental correlated velocity movement models (CVM's): random, advective, rotational, and rotational-advective. The models are defined in terms of biologically meaningful speeds and time scales of autocorrelation. We summarize several approaches to estimating the models, and apply these tools for the higher order task of behavioral partitioning via change point analysis. Results: An array of simulation illustrate the precision and accuracy of the estimation tools. An analysis of a swimming track of a bowhead whale (Balaena mysticetus) illustrates their robustness to irregular and sparse sampling and identifies switches between slower and faster, and directed vs. random movements. An analysis of a short flight of a lesser kestrel (Falco naumanni) identifies exact moments when switches occur between loopy, thermal soaring and directed flapping or gliding flights. Conclusions: We provide tools to estimate parameters and perform change point analyses in continuous time movement models as an R package (smoove). These resources, together with the synthesis, should facilitate the wider application and development of correlated velocity models among movement ecologists.
  • Boi, S. (2019)
    The Maxey-Riley equation and its simplified versions represent the most widespread tool to investigate dynamics and dispersion of inertial small particles in turbulent flows. The numerical solution of such models is often very challenging, and some of their terms, such as the molecular diffusivity or the Basset history force, are often neglected to reduce the complexity upon suitable approximations. Here, we propose exact results with regard to the rate of transport on large time scales in random shear flows. These can be expediently used as a benchmark to develop and assess algorithms when solving this class of stochastic integrodifferential problems on large time scales.
  • Boi, Simone; Mazzino, Andrea; Muratore-Ginanneschi, Paolo; Olivieri, Stefano (2018)
    One of the cornerstones of turbulent dispersion is the celebrated Taylor's formula. This formula expresses the rate of transport (i.e., the eddy diffusivity) of a tracer as a time integral of the fluid velocity autocorrelation function evaluated along the fluid particle trajectories. Here, we review the hypotheses which permit us to extend Taylor's formula to particles of any inertia. The hypotheses are independent of the details of the inertial particle model. We also show by explicit calculation that the hypotheses encompass cases when memory terms such as Basset's and Faxén's corrections are taken into account in the modeling of inertial particle dynamics.
  • Javanainen, Matti; Ollila, O. H. Samuli; Martinez-Seara, Hector (2020)
    Membrane proteins travel along cellular membranes and reorient themselves to form functional oligomers and proteinlipid complexes. Following the Saffman-Delbruck model, protein-radius sets the rate of this diffusive motion. However, it is unclear how this model, derived for ideal and dilute membranes, performs under crowded conditions of cellular membranes. Here, we study the rotational motion of membrane proteins using molecular dynamics simulations of coarse-grained membranes and 2-dimensional Lennard-Jones fluids with varying levels of crowding. We find that the Saffman-Delbruck model captures the size-dependency of rotational diffusion under dilute conditions where protein-protein interactions are negligible, whereas stronger scaling laws arise under crowding. Together with our recent work on lateral diffusion, our results reshape the description of protein dynamics in native membrane environments: The translational and rotational motions of proteins with small transmembrane domains are rapid, whereas larger proteins or protein complexes display substantially slower dynamics.