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Seedless assembly of colloidal crystals by inverted micro-fluidic pumping
2018
We propose a simple seedless approach to assemble millimeter sized monolayer single colloidal crystals with desired orientations at predetermined locations on an unstructured charged substrate. This approach utilizes the millimeter-ranged fluid flow on the bottom glass substrate induced by an ion exchange resin (IEX) fixed on top of the closed sample cell. This fluid flow increases with decreasing height of the sample cell and increasing radius R of the IEX. For a single inverted pump, millimeter sized monolayer single crystals of hexagonal close packing can be obtained. For two closely spaced (D ~ 4R) pumps, the formed crystals have a predefined orientation along the line connecting the tw…
Hiding in plain view: Colloidal self-assembly from polydisperse populations.
2016
We report small-angle x-ray scattering (SAXS) experiments on aqueous dispersions of colloidal silica with a broad monomodal size distribution (polydispersity 18%, size 8 nm). Over a range of volume fractions the silica particles segregate to build first one, then two distinct sets of colloidal crystals. These dispersions thus demonstrate fractional crystallization and multiple-phase (bcc, Laves AB$_2$, liquid) coexistence. Their remarkable ability to build complex crystal structures from a polydisperse population originates from the intermediate-range nature of interparticle forces, and suggests routes for designing self-assembling colloidal crystals from the bottom-up.
Effect of mixing and spatial dimension on the glass transition
2009
We study the influence of composition changes on the glass transition of binary hard disc and hard sphere mixtures in the framework of mode coupling theory. We derive a general expression for the slope of a glass transition line. Applied to the binary mixture in the low concentration limits, this new method allows a fast prediction of some properties of the glass transition lines. The glass transition diagram we find for binary hard discs strongly resembles the random close packing diagram. Compared to 3D from previous studies, the extension of the glass regime due to mixing is much more pronounced in 2D where plasticization only sets in at larger size disparities. For small size disparitie…
On the Distance-Constrained Close Enough Arc Routing Problem
2021
[EN] Arc routing problems consist basically of finding one or several routes traversing a given set of arcs and/or edges that must be serviced. The Close-Enough Arc Routing Problem, or Generalized Directed Rural Postman Problem, does not assume that customers are located at specific arcs, but can be serviced by traversing any arc of a given subset. Real-life applications include routing for meter reading, in which a vehicle equipped with a receiver travels a street network. If the vehicle gets within a certain distance of a meter, the receiver collects its data. Therefore, only a few streets which are close enough to the meters need to be traversed. In this paper we study the generalization…
A Quick Simulation Technique for a Fluid Information Storage Problem
2001
Summary In this paper we present an application of Importance Sampling (IS) for quick simulation of buffer overflow probability in a statistical multiplexer loaded with a number of independent Markov modulated fluid sources. Runtime improvement is deducible from NMCσ2(p) and NISσ2(p*) that characterize the trade-offs between sample size and variance of the estimators of buffer overflow probability experienced in Monte Carlo (MC) and Importance Sampling simulations. By assuming that the same precision is achieved for the two kinds of simulations if σ2(p)=σ2(p*), an approximate closed form expression for the ratio NIS/NMC is derived, and it is minimized with respect to the load of the multipl…
Optimal Local Routing Strategies for Community Structured Time Varying Communication Networks
2017
International audience; In time varying data communication networks (TVCN), traffic congestion, system utility maximization and network performance enhancement are the prominent issues. All these issues can be resolved either by optimizing the network structure or by selecting efficient routing approaches. In this paper, we focus on the design of a time varying network model and propose an algorithm to find efficient user route in this network. Centrality plays a very important role in finding congestion free routes. Indeed, the more a node is central, the more it can be congested by the flow coming from or going to its neighborhood. For that reason, classically, routes are chosen such that…
The geometry of canal surfaces and the length of curves in de Sitter space
2011
Abstract We find the minimal value of the length in de Sitter space of closed space-like curves with non-vanishing non-space-like geodesic curvature vector. These curves are in correspondence with closed almost-regular canal surfaces, and their length is a natural magnitude in conformal geometry. As an application, we get a lower bound for the total conformal torsion of closed space curves.
Prescribing the behaviour of geodesics in negative curvature
2010
Given a family of (almost) disjoint strictly convex subsets of a complete negatively curved Riemannian manifold M, such as balls, horoballs, tubular neighborhoods of totally geodesic submanifolds, etc, the aim of this paper is to construct geodesic rays or lines in M which have exactly once an exactly prescribed (big enough) penetration in one of them, and otherwise avoid (or do not enter too much in) them. Several applications are given, including a definite improvement of the unclouding problem of [PP1], the prescription of heights of geodesic lines in a finite volume such M, or of spiraling times around a closed geodesic in a closed such M. We also prove that the Hall ray phenomenon desc…
Selected Topics on Banach Space Theory
2019
Basic topics on Banach space theory needed for the text are reviewed. Hahn-Banach theorem, Baire’s theorem, uniform boundedness principle, closed graph theorem, weak topologies, Banach-Alaoglu theorem, unconditional basis, Banach sequence spaces, summing operators, factorable operators, cotype, Kahane inequality.
Dynamic response of beams excited by moving oscillators: Approximate analytical solutions for general boundary conditions
2023
In this paper, the dynamic response of an Euler-Bernoulli beam with general boundary conditions (BCs) and subject to a moving oscillator is examined. Notably, novel approximate closed-form expressions are determined for the vertical responses of both the beam and the moving oscillator, specifically considering the effect of damping in these systems, commonly omitted in standard approaches in the literature. In this regard, a modal superposition procedure is adopted and combined with an appropriate expansion-based approach of the dynamic response of the system, which naturally arises considering the oscillator-beam mass ratio to be reasonably small. Further, general boundary conditions are t…