Lefschetz Center for Dynamical Systems Seminar
Abstract: When can a function of several variables be written as a finite composition of functions of fewer variables? This is the question of Hilbert's problem XIII. The answer by young V.I. Arnold in the form given by Kolmogorov says: always, by functions of two variables, if we assume continuity. The answer by Vitushkin says: almost never, if we require differentiability.
In chemical engineering, we encounter a related question when we try to identify given input-output networks of coupled reactors from overall input-output data. One individual reactor model, or function, may be known ("white box") or unknown ("black box"). The hybrid model is the composition of such black- and white-box functions. Let black boxes have at most d inputs - typically much less than the total number of inputs to the network. Assuming sufficient, and at times, prohibitive differentiability, we indicate how to uniquely identify all unknown "black-box" functions in the network, from only d-dimensional data on their composition. This addresses the "curse of dimension" in data analysis, and provides extrapolability.
Results are joint work with Stefan Liebscher, Andreas Schuppert, and others.
Brown University
Joint Materials/Solid Mechanics Seminar Series
Abstract: We will discuss mechanisms and techniques to control friction at the atomic scale. The experiments involve an AFM tip sliding on a vibrating surface mounted on a piezo-element. Theoretically, we studied the response of a nano-array of atoms to the mechanical oscillations of their substrate, within a minimalist model of friction. Our motivation is two-fold, namely: (i) understanding the basic mechanisms of frictional response to small periodic and random perturbations; (ii) developing robust control techniques for friction control. Experimental results and numerical simulations of the model suggest that the friction coefficient undergoes a transition to very small values when the amplitude of the vibration reaches a critical threshold. We will also discuss a terminal attractor algorithm to control frictional dynamics of an array of particles towards pre-assigned values of the frictional force. This control technique is robust and significantly reduces the transient time to reach the prescribed behavior.
This research was sponsored by the Division of Materials Sciences and Engineering, U. S. Department of Energy, under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.
Cognitive & Linguistic Sciences Colloquium Series
Refreshments will be served before the talk in Room 124-125 |
Abstract: Over the past 30 years, evidence has accumulated to support the notion that thinking, reasoning and judgement tasks involve two quite distinct kinds of thought process. Heuristic processes appear to be rapid and preconscious and highly contextualised in the light of prior knowledge and belief. Analytic processes are relatively slow and sequential, limited by working memory capacity, and capable of abstract and logical reasoning. Evidence also suggests that these two processes may compete within individuals for control of responding on cognitive tasks.
An important question to consider is where these two distinct processes originate. Stronger forms of dual process theory posit two cognitive systems with differing evolutionary histories. According to this view the implicit or heuristic system is ancient and reflects the operation of a general learning mechanism similar to that found in higher animal species. The analytic system, however, evolved recently and is uniquely human, permitting us alone to engage in abstract and hypothetical thinking. Evidence for this view can be found in the archaeological record as well as in contemporary neuropsychological studies of reasoning. Some theorists argue that as the new brain sits on the old brain, there are effectively two minds competing to control our behavior.
Some interesting problems arise from this analysis. Why is our behavior as consistent and predictable as it is? Why does our consciousness appear to be unitary and why do `we' feel in control? What is the underlying cognitive architecture that allows the two systems to interact and resolve conflict? The talk ends with some speculation about these questions and some pointers to future research priorities.
The Fluids, Thermal and Chemical Processes Group
Of
The Division of Engineering
And
The Center for Fluid Mechanics
Seminar Series
Department of Chemical Engineering and Ophthalmology | |
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Comments: Please Note Change in Day and Time for This Seminar Only
Abstract: Approximately 90% of all ophthalmic drug formulations are applied as eye-drops. While eye-drops are convenient and well accepted by patients, about 95-99% of the drug contained in the drops is lost due to absorption through the conjunctiva or through the tear drainage. A major fraction of the drug eventually enters the blood stream and may cause side effects. The drug loss and the side effects can be minimized by using disposable soft contact lenses for ophthalmic drug delivery. In the past, numerous researchers have investigated the delivery of ophthalmic drugs by using contact lenses soaked in the drug solution. However, due to the small thickness of a contact lens, the soaked lenses can only provide drug delivery for a few hours. The idea pioneered by our group focuses on encapsulating the ophthalmic drug formulations in nanoparticles, and dispersing these drug- laden particles in the lens material during the synthesis. The nanoparticles are designed such that they release drugs for a period of a week, and thus, the nanoparticle-laden contact lenses are suitable for extended drug delivery.
This talk will focus on synthesis, characterization and drug release studies from dispersions of microemulsion drops and DMPC liposomes in poly-2-hydroxyethyl methacrylate (p-HEMA) hydrogels, which are a common contact lens material. The p-HEMA gels loaded with these two types of nanoparticles are transparent and release drugs for a period of about 7 days. Contact lenses made of particle-laden gels are expected to deliver drugs at therapeutic levels for a few days. The delivery rates can be tailored by controlling the particle and the drug loading. The drug release occurs on two different time scales: the initial rapid release is due to the diffusion of the drug that was present in the bulk gel, outside the nanoparticles and the slower release is due to diffusion of the drug that was trapped inside the particles. The talk will also discuss the model for drug release from the nanoparticle-laden gels.
Upon insertion into the eye, the particle-laden lens will slowly release the drug into the pre lens tear film, i.e., the film in between the air and the lens (PLTF) and the post lens film, i.e., the film in between the cornea and the lens (POLTF). The drug released into the PLTF will be lost due to drainage and a fraction of the drug released into the POLTF will also be lost due to mass transfer from the POLTF into the surrounding tear lake. The mass transfer in the post-lens tear film is enhanced by the convective flow, driven by the motion of the contact lens during the blink. A model that couples diffusion of the drug through the contact lens and the dispersive mass transfer in the POLTF will also be presented. This model is helpful in prediction the fraction of the drug released by the contact lens that enters the cornea.
The results of the study show that nanoparticle-laden contact lenses may be able to deliver ophthalmic drugs in an efficient manner for extended periods of time, and thus reduce drug wastage, side effects and improve patient compliance. It may be possible to use this system for both therapeutic drug delivery to eyes and the provision of lubricants that might alleviate eye problems prevalent in extended lens wear.
Scientific Computing Seminar
Abstract: In this talk we show how to construct finite difference central schemes on staggered grids. High-order finite-volume shock-capturing central schemes have been recently developed. Staggered schemes may have better resolution of the corresponding unstaggered schemes of the same order. They are based on high order non oscillatory reconstruction (ENO or WENO), and a suitable ODE solver for the computation of the integral of the flux. Finite difference allows a more natural treatment of the source term, in case of stiff source. Time discretization is of IMEX type, where the flux term is treated explicitly, and the source term is treated implicitly. Some numerical results are presented, which confirm the robustness and accuracy of the method.
PDE Seminar
See Mathematics Colloquium
Department of Mathematics Colloquium
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