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AC Electrokinetics: A Review of Forces in Microelectrode Structures
 Journal of Physics D: Applied Physics
, 1998
"... Abstract. Ac electrokinetics is concerned with the study of the movement and behaviour of particles in suspension when they are subjected to ac electrical fields. The development of new microfabricated electrode structures has meant that particles down to the size of macromolecules have been manipul ..."
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Abstract. Ac electrokinetics is concerned with the study of the movement and behaviour of particles in suspension when they are subjected to ac electrical fields. The development of new microfabricated electrode structures has meant that particles down to the size of macromolecules have been manipulated, but on this scale forces other than electrokinetic affect particles behaviour. The high electrical fields, which are required to produce sufficient force to move a particle, result in heat dissipation in the medium. This in turn produces thermal gradients, which may give rise to fluid motion through buoyancy, and electrothermal forces. In this paper, the frequency dependency and magnitude of electrothermally induced fluid flow are discussed. A new type of fluid flow is identified for low frequencies (up to 500 kHz). Our preliminary observations indicate that it has its origin in the action of a tangential electrical field on the diffuse double layer of the microfabricated electrodes. The effects of Brownian motion, diffusion and the buoyancy force are discussed in the context of the controlled manipulation of submicrometre particles. The orders of magnitude of the various forces experienced by a submicrometre latex particle in a model electrode structure are calculated. The results are compared with experiment and the relative influence of each type of force on the overall behaviour of particles is described. 1.
Interpreting the Quantum
, 1997
"... This paper is a commentary on the foundational significance of the CliftonBubHalvorson theorem characterizing quantum theory in terms of three informationtheoretic constraints. I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of informa ..."
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This paper is a commentary on the foundational significance of the CliftonBubHalvorson theorem characterizing quantum theory in terms of three informationtheoretic constraints. I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of information transfer, as opposed to a theory about the mechanics of nonclassical waves or particles, (2) given the informationtheoretic constraints, any mechanical theory of quantum phenomena that includes an account of the measuring instruments that reveal these phenomena must be empirically equivalent to a quantum theory, and (3) assuming the informationtheoretic constraints are in fact satisfied in our world, no mechanical theory of quantum phenomena that includes an account of measurement interactions can be acceptable, and the appropriate aim of physics at the fundamental level then becomes the representation and manipulation of information.
Endoplasmic filaments generate the motive force for rotational streaming in Nitella. Doctoral Thesis
, 1973
"... The streaming endoplasm of characean cells has been shown to contain previously unreported endoplasmic filaments along which bending waves are observed under the light microscope using special techniques. The bending waves are similar to those propagated along sperm tails causing propulsion of sperm ..."
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The streaming endoplasm of characean cells has been shown to contain previously unreported endoplasmic filaments along which bending waves are observed under the light microscope using special techniques. The bending waves are similar to those propagated along sperm tails causing propulsion of sperm. In Nitella there is reason to believe that nearly all of the filaments are anchored in the cortex and that their beating propels the endoplasm in which they are suspended. This hypothesis is supported by calculations in which typical and average wave parameters have been inserted into the classical hydrodynamic equations derived for sperm tail bending waves. These calculations come within an order of magnitude of predicting the velocity of streaming and they show that waves of the character described, propagated along an estimated 52 m of endoplasmic filaments per cell, must generate a total motive force per cell within less than an order of magnitude of the forces measured experimentally by others. If we assume that undulating filaments produce the force driving the endoplasm, then the method described for measuring the motive force could lead to a lower than actual value for the motive force, since both centrifugation and vacuolar perfusion would reverse the orientation of some filaments. Observations of the initiation of particle translation in association with the filaments suggest that particle transport and wave propagation, which occur at the same velocity, may both be dependent on the same process. The possibility that some form of contractility provides the motive force for filament flection and particle transport is discussed.
A Short History of Stochastic Integration and Mathematical Finance The early years, 1880 – 1970
, 2003
"... The history of stochastic integration and the modelling of risky asset prices both begin with Brownian motion, so let us begin there too. The earliest attempts to model Brownian motion mathematically can be traced to three sources, each of which knew nothing about the others: the first was that of T ..."
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The history of stochastic integration and the modelling of risky asset prices both begin with Brownian motion, so let us begin there too. The earliest attempts to model Brownian motion mathematically can be traced to three sources, each of which knew nothing about the others: the first was that of T. N. Thiele of Copenhagen, who effectively created a model of Brownian motion while studying time series in 1880 [77]. 2; the second was that of L. Bachelier of Paris, who created a model of Brownian motion while deriving the dynamic behavior of the Paris stock market, in 1900 (see, [1], [2], [11]); and the third was that of A. Einstein, who proposed a model of the motion of small particles suspended in a liquid, in an attempt to convince other physicists of the molecular nature of matter, in 1905 [19](See [61] for a discussion of Einstein’s model and his motivations.) Of these three models, those of Thiele and Bachelier had little impact for a long time, while that of Einstein was immediately influential. We go into a little detail about what happened to Bachelier, since he is now seen by many as the founder of modern Mathematical Finance. Ignorant of the work of Thiele (which was little appreciated in its day) and preceding the work of Einstein, Bachelier attempted
Applications to Mathematical Finance
, 2001
"... We give an introduction to the theory of Mathematical Finance with special emphasis on the applications of Banach space theory. The introductary section presents on an informal and intuitive level some of the basic ideas of Mathematical Finance, in particular the notions of “No Arbitrage ” and “equi ..."
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We give an introduction to the theory of Mathematical Finance with special emphasis on the applications of Banach space theory. The introductary section presents on an informal and intuitive level some of the basic ideas of Mathematical Finance, in particular the notions of “No Arbitrage ” and “equivalent martingale measures”. In section two we formalize these ideas in a mathematically rigorous way and then develop in the subsequent four sections some of the basic themes. Of course, in this short handbookcontribution we are not able to give a comprehensive overview of the whole field of Mathematical Finance; we only concentrate on those issues where Banach space theory plays an important role. 1 1
MEMORY FUNCTION FOR COLLECTIVE DIFFUSION OF INTERACTING BROWNIAN PARTICLES
"... in accordance with the requirements ..."
How applied mathematics became pure
 Review of Symbolic Logic
"... Abstract. This paper traces the evolution of thinking on how mathematics relates to the world— from the ancients, through the beginnings of mathematized science in Galileo and Newton, to the rise of pure mathematics in the nineteenth century. The goal is to better understand the role of mathematics ..."
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Abstract. This paper traces the evolution of thinking on how mathematics relates to the world— from the ancients, through the beginnings of mathematized science in Galileo and Newton, to the rise of pure mathematics in the nineteenth century. The goal is to better understand the role of mathematics in contemporary science. My goal here is to explore the relationship between pure and applied mathematics and then, eventually, to draw a few morals for both. In particular, I hope to show that this relationship has not been static, that the historical rise of pure mathematics has coincided with a gradual shift in our understanding of how mathematics works in application to the world. In some circles today, it is held that historical developments of this sort simply represent changes in fashion, or in social arrangements, governments, power structures, or some such thing, but I resist the full force of this way of thinking, clinging to the old school notion that we have gradually learned more about the world over time, that our opinions on these matters have improved, and that seeing how we reached the point we now occupy may help us avoid falling back into old philosophies that are now no longer viable. In that spirit, it seems to me that once we focus on the general question of how mathematics relates to science, one
Steady state thermodynamics
, 2004
"... We propose a thermodynamic formalism that is expected to apply to a large class of nonequilibrium steady states including a heat conducting fluid, a sheared fluid, and an electrically conducting fluid. We call our theory steady state thermodynamics (SST) after Oono and Paniconi’s original proposal. ..."
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We propose a thermodynamic formalism that is expected to apply to a large class of nonequilibrium steady states including a heat conducting fluid, a sheared fluid, and an electrically conducting fluid. We call our theory steady state thermodynamics (SST) after Oono and Paniconi’s original proposal. The construction of SST is based on a careful examination of how the basic notions in thermodynamics should be modified in nonequilibrium steady states. We define all thermodynamic quantities through operational procedures, which can be (in principle) realized experimentally. Based on SST thus constructed, we make some nontrivial predictions, including an extension of Einstein’s formula on density fluctuation, an extension of the minimum work principle, the existence of a new osmotic pressure of a purely nonequilibrium origin, and a shift of coexistence temperature. All these predictions may be checked experimentally to test SST for its quantitative validity. Contents
Sensor placement optimization under uncertainty for structural health monitoring systems of hot aerospace structures
"... iii ACKNOWLEDGEMENTS It is with great sincerity that I thank my mentor and advisor – Dr. Sankaran Mahadevan – for his constant support throughout my career at Vanderbilt University. I thank him for his encouragement, constructive criticism, and belief in my abilities. I thank him especially for his ..."
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iii ACKNOWLEDGEMENTS It is with great sincerity that I thank my mentor and advisor – Dr. Sankaran Mahadevan – for his constant support throughout my career at Vanderbilt University. I thank him for his encouragement, constructive criticism, and belief in my abilities. I thank him especially for his patience during the countless hours we spent working together. I also wish to thank the members of my committee, Dr. P.K. Basu, Dr. Gautam Biswas, and Dr. Mark Ellingham, for their advice and great attitude toward working with me.
FLOW FOCUSING IN MICROFLUIDIC DEVICES
"... This paper presents numerical analysis of the hydrodynamic flow focusing in rectangular microchannels. The low Reynolds number pressure driven flow in symmetric system of crossed channels with three inlets and one outlet is investigated. The numerical model is used to elucidate the origin of broaden ..."
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This paper presents numerical analysis of the hydrodynamic flow focusing in rectangular microchannels. The low Reynolds number pressure driven flow in symmetric system of crossed channels with three inlets and one outlet is investigated. The numerical model is used to elucidate the origin of broadening of the focused flow sheet observed experimentally close to the side walls of the outlet channel. It is found that the observed broadening is mainly due to the residual flow inertia and can be totally eliminated if flow Reynolds number is less than one. 1.