|Date||Speaker, Title, and Abstact||Host|
Levich Institute, CCNY
Issues in the flow of yield-stress liquids: The flow of yield-stress liquids has been studied for nearly one hundred years, but major conceptual issues remain. Yield-stress liquids respond as elastic or viscoelastic solids prior to yielding, and they flow as viscous or viscoelastic liquids after yielding. The primary unresolved issue, at least from a simulation perspective, appears to be the description of the mechanics of the yielding phenomenon itself. Classical descriptions of yield stress fluids assume that yielding is a reversible process that occurs at an invariant surface in stress space, and certain general conclusions regarding flow structure and symmetries in the yielded regime follow. This description is sometimes inadequate to describe real fluids, however, where a thixotropic response caused by disruption of the microstructure following the initiation of flow may result in dissipative motion at stresses below the nominal yield stress.
University of Southern California
Gambler ruin problems, and pricing a barrier option under a jump diffusion model: Suppose there are r gamblers, with gambler i initially having a fortune n(i). In our first model we suppose that at each stage two of the gamblers are chosen to play a game, equally likely to be won by either player, with the winner of the game receiving 1 from the loser. Any gambler whose fortune becomes 0 leaves, and this continues until there is only a single gambler left. We are interested in the mean number of players that involve both players i and j. In our second model we suppose that all remaining players contribute 1 to a pot, which is equally likely to be won by each of them. The problem here is to determine the expected number of games played until one player has all the funds. If time permits, we will also discuss how to efficiently simulate the expected return from an up and in (or up and out) barrier call option under the assumption that the price of the security follows a geometric Brownian motion with random jumps.
Courant Institute for Mathematical Sciences, NYU
Ratchets in fluid transportation and in biological locomotion: I discuss several cases where a broken symmetry - either broken spontaneously or by construction - leads to ratcheting behavior in systems where dynamic boundaries interact with moving fluids. Two examples feature reciprocal forcing combined with geometric anisotropy of boundaries. In one case a solid body can be made to hover, and in another, a fluid is efficiently pumped. I will also discuss the dynamics of a symmetric wing whose “forward flight” follows from a symmetry breaking instability, and how this dynamics is affected by the introduction of more biological realism.
The fluid mechanics of fungal spore ejection, and solutions to the moderate Reynolds number Navier-Stokes equations: To disperse effectively the explosively launched spores of ascomycete fungi must eject through a thin layer of still air surrounding the fruiting body and reach air flows that can take the spores away from the parent fungus. Spores are very small and therefore experience enormous fluid drag. We use a phylogeny of over 110 ascomycete species to compare optimal and real spore shapes and find that spores are shaped to remain within 1 % of the drag minimum. A predicted launch speed is confirmed by high-speed imaging of ejection in Neurospora tetrasperma. The optimal drag shapes themselves exhibit a surprising feature: they are very nearly fore-aft symmetric, despite the fact that the flow field around them is very asymmetric. We use this observation as a basis for constructing a surprisingly accurate linear approximation to steady flows of the Navier Stokes equations that works at least up to Reynolds number of order 100.
The fluid trampoline: Droplets bouncing on a soap film: We present the results of a combined experimental and theoretical investigation of droplets falling onto a horizontal soap film. Both static and vertically vibrated soap films are considered. A quasi-static description of the soap film shape yields a force-displacement relation that allows us to model the film as a nonlinear spring, and yields an accurate criterion for the transition between droplet bouncing and crossing. On the vibrating film, a variety of bouncing behaviors were observed, including simple and complex periodic states, multiperiodicity and chaos. A simple theoretical model is developed that captures the essential physics of the bouncing process, reproducing all observed bouncing states. The system is among the very simplest fluid mechanical chaotic oscillators. The relevance of our model to a seemingly unlikely biological system is discussed.
Chaos: What have we learned? Analysis of experimental data from many physical systems (lasers, chemical reactions, electrical circuits, vibrating strings) has led to a deeper understanding of low-dimensional strange attractors and their perestroikas. They can now be classified. The classification is topological, with four levels of structure. Each is discrete. The signatures that identify these levels can be and have been extracted from experimental data. These advances have raised additional questions that require new mathematics for their resolution.
NJIT Mechanical Engineering
Density relaxation of granular matter: Density relaxation is the phenomenon in which granular solids undergo an increase in bulk density as a result of properly applied external loads. The ability of particulate solids to experience density changes is an inherent property that is not well-understood, and thus it remains a critical impediment in developing predictive models of flowing bulk materials. In this talk, the results of Monte Carlo (MC) and Discrete Element (DM) models of the density relaxation process are discussed, in which a vessel filled with uniform spherical particles is subjected to discrete taps. Both stochastic (MC) and deterministic (DE) models reveal the same dynamical process responsible for density relaxation, namely, the upward progression of organized layers induced by the floor of the vessel as the taps evolve. Furthermore, results suggest that the evolution of bulk density is highly dependent on the microstructure and contact network. Compelling evidence is also found of a tap amplitude that optimizes the evolution of packing density.
City University of Hong Kong
Drawing of viscous threads with temperature-dependent viscosity: The drawing of viscous threads is important in a wide range of industrial applications, and is a primary manufacturing process in the optical fiber and textile industries. Most of the materials used in these processes have viscosities that vary extremely strongly with temperature. We investigate the role played by viscous heating in the drawing of viscous threads. Usually, the effects of viscous heating and inertia are neglected because the parameters that characterize them are typically very small. However, by performing a detailed theoretical analysis, we surprisingly show that even very small amounts of viscous heating can lead to a runaway phenomenon. On the other hand, inertia prevents runaway, and the interplay between viscous heating and inertia results in very complicated dynamics for the system. Even more surprisingly, in the absence of viscous heating, we find that a new type of instability can occur when a thread is heated by a radiative heat source. By analyzing an asymptotic limit of the Navier-Stokes equations we provide a theory that describes the nature of this instability and explains the seemingly counterintuitive behavior.
Defects and epitaxy: using colloids to investigate statistical mechanics phenomena: Colloidal suspensions consist of micron-sized solid particles suspended in a solvent. The particles are Brownian so that the suspension as a whole behaves as a thermal system governed by the laws of statistical mechanics. The thermodynamic nature of these systems has allowed scientists to use colloidal suspensions as models for investigating numerous processes that typically take place on the atomic and nano-scale but are often very difficult to investigate. In this talk I will describe how we use various experimental techniques to investigate the structure and dynamics of these systems and gain an understanding of epitaxial growth, defect nucleation, and defect translation in colloidal crystals.
Department of Mathematical Sciences, NJIT
Determination of interfacial tension for a hydrophobic PDMS-based ferrofluid droplet suspended in glycerol under uniform magnetic fields: Recent interest in ferrofluids has been motivated by biomedical and pharmaceutical applications. Here I investigate the effect of applied magnetic fields on the deformation of a biocompatible hydrophobic ferrofluid drop suspended in a viscous medium. Analytical formulas for ellipsoidal drops and near-spheroidal drops are reviewed and developed for code validation. At low magnetic fields both the experimental and numerical results follow the asymptotic small-deformation theory. At high magnetic fields, experimental drop shapes deviate from numerical results when a constant surface tension value is used. One hypothesis for the difference is the dependence of the interfacial tension on the magnetic field in the experimental data. This idea is investigated computationally by varying the interfacial tension as a function of the applied magnetic field, and by comparing the drop shapes with experimental data until a match is found.
North Dakota State University
Direct Write: Modeling and experiment: Direct Write technology denotes a group of processes which are used to precisely deposit materials onto a substrate in defined locations. In this talk two direct write methods will be presented: (a.) Collimated Aerosol Beam - Direct Write (CAB-DW) and
(b.) STM-controlled capillary-based nanolithography.
University of Nottingham, UK
Instabilities of flows in flexible tubes and channels: A flow driven through a finite-length flexible tube or channel can exhibit a rich array of instabilities. As well as having relevance to blood vessels and lung airways, the mechanisms of instability have been a long-standing conundrum in physiological fluid mechanics. I will describe recent progress towards understanding their origin revealed by a variety of modelling approaches. A spatially one-dimensional model of flexible-channel flow illustrates the relationship between local modes and a global “sloshing” mode. A more accurate two-dimensional model shows how a local flutter mode originates through a novel “weak” critical layer, while also contributing to a global instability. I will also explain how asymptotic methods can be used to predict stability thresholds in a three-dimensional collapsible tube. This is joint work with Jonathan Boyle, Matthias Heil, Peter Stewart, Sarah Waters and Robert Whittaker.
Liquid Crystals Institute, Kent State University
Motors based on shape change: See how they run: Motors are devices that produce motion due to the transfer of energy, but not of momentum, to the device. Recent advances in materials science have allowed the construction of motors where the motion is produced via changes in the shapes of solid objects. In this talk, we consider motors where the shape change is a bend, rather than an elongation or contraction. We analyze in detail the physical mechanisms which bring about the motion, and discuss the origins and path of the momentum current that is generated. We present the results of numerical simulations, and compare these with experimental observations. Some novel approaches to motor design will be discussed.