Relation between dry granular flow regimes and morphology of deposits: formation of levees in pyroclastic deposits

Experiments on dry granular matter flowing down an inclined plane are performed in order to study the dynamics of dense pyroclastic flows. The plane is rough, and always wider than the flow, focusing this study on the case of laterally unconfined (free boundary) flows.We found that several flow regimes exist depending on the input fluxand on the inclination of the plane. Each flow regime corresponds to a particular morphology of the associated deposit. In one of these regimes, the flow reaches a steady state, and the deposit exhibits a levee/channel morphology similar to those observed on small pyroclastic flow deposits. The levees result from the combination between lateral static zones on each border of the flow and the drainage of the central part of the flow after the supply stops. Particle segregation featuresare created during the flow, corresponding to those observed on the deposits of pyroclastic flows. Moreover, the measurements of the deposit morphology (thickness of the channel, height of the levees, width of the deposit) are quantitatively related to parameters of the dynamics of the flow (flux, velocity, height of the flow), leading to a way of studying the flow dynamics from only measurements of the deposit. Some attempts to make extensions to natural cases are discussed through experiments introducing the polydispersity of the particle sizes and the particle segregation process

Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that diffusion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarising their densely packed and heterogeneous structures. The most familiar phenomenon is a power-law increase of the MSD, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations, non-gaussian distributions of the displacements, heterogeneous diffusion, and immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarise some widely used theoretical models: gaussian models like FBM and Langevin equations for visco-elastic media, the CTRW model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Emphasis is put on the spatio-temporal properties of the transport in terms of 2-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even for identical MSDs. Then, we review the theory underlying common experimental techniques in the presence of anomalous transport: single-particle tracking, FCS, and FRAP. We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where model systems mimic physiological crowding conditions. Finally, computer simulations play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.Comment: review article, to appear in Rep. Prog. Phy

Rational BV-algebra in String Topology

Let $M$ be a 1-connected closed manifold and $LM$ be the space of free loops on $M$. In \cite{C-S} M. Chas and D. Sullivan defined a structure of BV-algebra on the singular homology of $LM$, H_\ast(LM; \bk). When the field of coefficients is of characteristic zero, we prove that there exists a BV-algebra structure on \hH^\ast(C^\ast (M); C^\ast (M)) which carries the canonical structure of Gerstenhaber algebra. We construct then an isomorphism of BV-algebras between \hH^\ast (C^\ast (M); C^\ast (M)) and the shifted H_{\ast+m} (LM; {\bk}). We also prove that the Chas-Sullivan product and the BV-operator behave well with the Hodge decomposition of $H_\ast (LM)$

String topology on Gorenstein spaces

The purpose of this paper is to describe a general and simple setting for defining $(g,p+q)$-string operations on a Poincar\'e duality space and more generally on a Gorenstein space. Gorenstein spaces include Poincar\'e duality spaces as well as classifying spaces or homotopy quotients of connected Lie groups. Our presentation implies directly the homotopy invariance of each $(g,p+q)$-string operation as well as it leads to explicit computations.Comment: 30 pages and 2 figure

Localization phenomena in models of ion-conducting glass formers

The mass transport in soft-sphere mixtures of small and big particles as well as in the disordered Lorentz gas (LG) model is studied using molecular dynamics (MD) computer simulations. The soft-sphere mixture shows anomalous small-particle diffusion signifying a localization transition separate from the big-particle glass transition. Switching off small-particle excluded volume constraints slows down the small-particle dynamics, as indicated by incoherent intermediate scattering functions. A comparison of logarithmic time derivatives of the mean-squared displacements reveals qualitative similarities between the localization transition in the soft-sphere mixture and its counterpart in the LG. Nevertheless, qualitative differences emphasize the need for further research elucidating the connection between both models.Comment: to appear in Eur. Phys. J. Special Topic

Funnel control for a moving water tank

We study tracking control for a moving water tank system, which is modelled using the Saint-Venant equations. The output is given by the position of the tank and the control input is the force acting on it. For a given reference signal, the objective is to achieve that the tracking error evolves within a prespecified performance funnel. Exploiting recent results in funnel control we show that it suffices to show that the operator associated with the internal dynamics of the system is causal, locally Lipschitz continuous and maps bounded functions to bounded functions. To show these properties we consider the linearized Saint-Venant equations in an abstract framework and show that it corresponds to a regular well-posed linear system, where the inverse Laplace transform of the transfer function defines a measure with bounded total variation.Comment: 11 page