Discovering Clusters in Motion Time-Series Data

A new approach is proposed for clustering time-series data. The approach can be used to discover groupings of similar object motions that were observed in a video collection. A finite mixture of hidden Markov models (HMMs) is fitted to the motion data using the expectation-maximization (EM) framework. Previous approaches for HMM-based clustering employ a k-means formulation, where each sequence is assigned to only a single HMM. In contrast, the formulation presented in this paper allows each sequence to belong to more than a single HMM with some probability, and the hard decision about the sequence class membership can be deferred until a later time when such a decision is required. Experiments with simulated data demonstrate the benefit of using this EM-based approach when there is more "overlap" in the processes generating the data. Experiments with real data show the promising potential of HMM-based motion clustering in a number of applications.Office of Naval Research (N000140310108, N000140110444); National Science Foundation (IIS-0208876, CAREER Award 0133825

Quasi-one dimensional fluids that exhibit higher dimensional behavior

Fluids confined within narrow channels exhibit a variety of phases and phase transitions associated with their reduced dimensionality. In this review paper, we illustrate the crossover from quasi-one dimensional to higher effective dimensionality behavior of fluids adsorbed within different carbon nanotubes geometries. In the single nanotube geometry, no phase transitions can occur at finite temperature. Instead, we identify a crossover from a quasi-one dimensional to a two dimensional behavior of the adsorbate. In bundles of nanotubes, phase transitions at finite temperature arise from the transverse coupling of interactions between channels.Comment: 8 pages, 5 figures, presented at CMT3

Helium mixtures in nanotube bundles

An analogue to Raoult's law is determined for the case of a 3He-4He mixture adsorbed in the interstitial channels of a bundle of carbon nanotubes. Unlike the case of He mixtures in other environments, the ratio of the partial pressures of the coexisting vapor is found to be a simple function of the ratio of concentrations within the nanotube bundle.Comment: 3 pages, no figures, submitted to Phys. Rev. Let

A macroscopic device described by a Boltzmann-like distribution

Equilibrium thermodynamic phenomena such as the Maxwell-Boltzmann distribution of molecular velocities are rare in systems of macroscopic particles interacting by mechanical collisions. This paper reports a system composed of millimeter-sized polymer objects that under mechanical agitation exhibits a “discretization” of the configurations of the system, and has a distribution of the probabilities of these configurations that is analogous to a Boltzmann distribution. The system is composed of spheres and a three-link chain on a bounded horizontal surface, shaken with an aperiodic but not completely random horizontal motion. Experiments were performed at different strengths of agitation (quantified by the frequency of agitation, f, at constant amplitude) and densities of spheres (quantified by the filling ratio, FR). The chain was typically found in one of three conformations—extended, single folded, and double folded— because, under collisions with the spheres, adjacent links were stable mechanically only when fully extended or fully folded. The probabilities of the different conformations of the chain could be described by a Boltzmann distribution in which the “temperature” depended on f and the “energies” of conformations on FR. The predictions of the Boltzmann formula using empirically determined “temperatures” and “energies” agreed with measurements within two experimental standard deviations in 47 out of 48 experiments.Chemistry and Chemical Biolog

The Magnitude of Lift Forces Acting on Drops and Bubbles in Liquids Flowing Inside Microchannels

Hydrodynamic lift forces offer a convenient way to manipulate particles in microfluidic applications, but there is little quantitative information on how non-inertial lift mechanisms act and compete with each other in the confined space of microfluidic channels. This paper reports measurements of lift forces on nearly spherical drops and bubbles, with diameters from one quarter to one half of the width of the channel, flowing in microfluidic channels, under flow conditions characterized by particle capillary numbers CaP = 0.0003–0.3 and particle Reynolds numbers ReP = 0.0001–0.1. For CaP < 0.01 and ReP < 0.01 the measured lift forces were much larger than predictions of deformation-induced and inertial lift forces found in the literature, probably due to physicochemical hydrodynamic effects at the interface of drops and bubbles, such as the presence of surfactants. The measured forces could be fit with good accuracy using an empirical formula given herein. The empirical formula describes the power-law dependence of the lift force on hydrodynamic parameters (velocity and viscosity of the carrier phase; sizes of channel and drop or bubble), and includes a numerical lift coefficient that depends on the fluids used. The empirical formula using an average lift coefficient of [similar]500 predicted, within one order of magnitude, all lift force measurements in channels with cross-sectional dimensions below 1 mm.Chemistry and Chemical Biolog

Sheathless hydrodynamic positioning of buoyant drops and bubbles inside microchannels

Particles, bubbles, and drops carried by a fluid in a confined environment such as a pipe can be subjected to hydrodynamic lift forces, i.e., forces that are perpendicular to the direction of the flow. We investigated the positioning effect of lift forces acting on buoyant drops and bubbles suspended in a carrier fluid and flowing in a horizontal microchannel. We report experiments on drops of water in fluorocarbon liquid, and on bubbles of nitrogen in hydrocarbon liquid and silicone oil, inside microchannels with widths on the order of 0.1–1 mm. Despite their buoyancy, drops and bubbles could travel without contacting with the walls of channels; the most important parameters for reaching this flow regime in our experiments were the viscosity and the velocity of the carrier fluid, and the sizes of drops and bubbles. The dependencies of the transverse position of drops and bubbles on these parameters were investigated. At steady state, the trajectories of drops and bubbles approached the center of the channel for drops and bubbles almost as large as the channel, carried by rapidly flowing viscous liquids; among our experiments, these flow conditions were characterized by larger capillary numbers and smaller Reynolds numbers. Analytical models of lift forces developed for the flow of drops much smaller than the width of the channel failed to predict their transverse position, while computational fluid dynamic simulations of the experiments agreed better with the experimental measurements. The degrees of success of these predictions indicate the importance of confinement on generating strong hydrodynamic lift forces. We conclude that, inside microfluidic channels, it is possible to support and position buoyant drops and bubbles simply by flowing a single-stream (i.e., “sheathless”) carrier liquid that has appropriate velocity and hydrodynamic properties.Chemistry and Chemical Biolog