Settling of cohesive sediment: particle-resolved simulations

We develop a physical and computational model for performing fully coupled, particle-resolved Direct Numerical Simulations of cohesive sediment, based on the Immersed Boundary Method. The model distributes the cohesive forces over a thin shell surrounding each particle, thereby allowing for the spatial and temporal resolution of the cohesive forces during particle-particle interactions. The influence of the cohesive forces is captured by a single dimensionless parameter in the form of a cohesion number, which represents the ratio of cohesive and gravitational forces acting on a particle. We test and validate the cohesive force model for binary particle interactions in the Drafting-Kissing-Tumbling (DKT) configuration. The DKT simulations demonstrate that cohesive particle pairs settle in a preferred orientation, with particles of very different sizes preferentially aligning themselves in the vertical direction, so that the smaller particle is drafted in the wake of the larger one. To test this mechanism in a system of higher complexity, we perform large simulations of 1,261 polydisperse settling particles starting from rest. These simulations reproduce several earlier experimental observations by other authors, such as the accelerated settling of sand and silt particles due to particle bonding. The simulations demonstrate that cohesive forces accelerate the overall settling process primarily because smaller grains attach to larger ones and settle in their wakes. For the present cohesion number values, we observe that settling can be accelerated by up to 29%. We propose physically based parametrization of classical hindered settling functions proposed by earlier authors, in order to account for cohesive forces. An investigation of the energy budget shows that the work of the collision forces can substantially modify the relevant energy conversion processes.Comment: 39 page

Some remarks on the geometry of the Standard Map

We define and compute hyperbolic coordinates and associated foliations which provide a new way to describe the geometry of the standard map. We also identify a uniformly hyperbolic region and a complementary 'critical' region containing a smooth curve of tangencies between certain canonical 'stable' foliations.Comment: 25 pages, 11 figure

Statistical Consequences of Devroye Inequality for Processes. Applications to a Class of Non-Uniformly Hyperbolic Dynamical Systems

In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functions, then it holds uniformly in the function spaces. In the last appendix we prove that for the subclass of one-dimensional systems studied in \cite{young} the density of the absolutely continuous invariant measure belongs to a Besov space.Comment: 33 pages; companion of the paper math.DS/0412166; corrected version; to appear in Nonlinearit

Lipoblastoma: Uma entidade clínico-morfológica distinta

Lipoblastoma: Uma entidade clínico-morfológica distint

Invariant manifolds and equilibrium states for non-uniformly hyperbolic horseshoes

In this paper we consider horseshoes containing an orbit of homoclinic tangency accumulated by periodic points. We prove a version of the Invariant Manifolds Theorem, construct finite Markov partitions and use them to prove the existence and uniqueness of equilibrium states associated to H\"older continuous potentials.Comment: 33 pages, 6 figure

Robust exponential decay of correlations for singular-flows

We construct open sets of Ck (k bigger or equal to 2) vector fields with singularities that have robust exponential decay of correlations with respect to the unique physical measure. In particular we prove that the geometric Lorenz attractor has exponential decay of correlations with respect to the unique physical measure.Comment: Final version accepted for publication with added corrections (not in official published version) after O. Butterley pointed out to the authors that the last estimate in the argument in Subsection 4.2.3 of the previous version is not enough to guarantee the uniform non-integrability condition claimed. We have modified the argument and present it here in the same Subsection. 3 figures, 34 page