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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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Cited by 16 (0 self)
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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.
Data processing theorems and the second law of thermodynamics
 IEEE Trans. Inform. Theory
, 2011
"... We draw relationships between the generalized data processing theorems of Zakai and Ziv (1973 and 1975) and the dynamical version of the second law of thermodynamics, a.k.a. the Boltzmann H–Theorem, which asserts that the Shannon entropy, H(Xt), pertaining to a finite– state Markov process {Xt}, is ..."
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Cited by 6 (4 self)
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We draw relationships between the generalized data processing theorems of Zakai and Ziv (1973 and 1975) and the dynamical version of the second law of thermodynamics, a.k.a. the Boltzmann H–Theorem, which asserts that the Shannon entropy, H(Xt), pertaining to a finite– state Markov process {Xt}, is monotonically non–decreasing as a function of time t, provided that the steady–state distribution of this process is uniform across the state space (which is the case when the process designates an isolated system). It turns out that both the generalized data processing theorems and the Boltzmann H–Theorem can be viewed as special cases of a more general principle concerning the monotonicity (in time) of a certain generalized information measure applied to a Markov process. This gives rise to a new look at the generalized data processing theorem, which suggests to exploit certain degrees of freedom that may lead to better bounds, for a given choice of the convex function that defines the generalized mutual information. Indeed, we demonstrate an example of a certain setup of joint source–channel coding, where this idea yields an improved lower bound on the distortion, relative to both the 1973 Ziv–Zakai lower bound and the lower bound obtained from the ordinary data processing theorem.
RamanujanFourier series, the WienerKhintchine formula and the distribution of prime pairs
, 1999
"... The WienerKhintchine formula plays a central role in statistical mechanics. It is shown here that the problem of prime pairs is related to autocorrelation and hence to a WienerKhintchine formula. "Experimental" evidence is given for this. c # 1999 Elsevier Science B.V. All rights reserved. PA ..."
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Cited by 4 (2 self)
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The WienerKhintchine formula plays a central role in statistical mechanics. It is shown here that the problem of prime pairs is related to autocorrelation and hence to a WienerKhintchine formula. "Experimental" evidence is given for this. c # 1999 Elsevier Science B.V. All rights reserved. PACS: 05.40+j; 02.30.Nw; 02.10.Lh Keywords: Twin primes; RamanujanFourier series; WienerKhintchine formula 1. Introduction " The WienerKhintchine theorem states a relationship between two important characteristics of a random process: the power spectrum of the process and the correlation function of the process" [1]. One of the outstanding problems in number theory is the problem of prime pairs which asks how primes of the form p and p+h (where h is an even integer) are distributed. One immediately notes that this is a problem of #nding correlation between primes. We make two key observations. First of all there is an arithmetical function (a function de#ned on integers) which traps the...
How Correlation Suppresses Density Fluctuations in the Uniform Electron Gas of 1, 2, Or 3 Dimensions
"... The particle number N fluctuates in a spherical volume fragment\Omega of a uniform electron gas. In an ideal classicalgas or `Hartree' model, the fluctuation is strong, with (\DeltaN\Omega ) 2 = N\Omega : We show in detail how this fluctuation is reduced by exchange in the ideal Fermi gas, and f ..."
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The particle number N fluctuates in a spherical volume fragment\Omega of a uniform electron gas. In an ideal classicalgas or `Hartree' model, the fluctuation is strong, with (\DeltaN\Omega ) 2 = N\Omega : We show in detail how this fluctuation is reduced by exchange in the ideal Fermi gas, and further reduced by Coulomb correlation in the interacting Fermi gas. Besides the mean particle number N\Omega and mean square fluctuation (\DeltaN\Omega ) 2 = (N 2 )\Omega \Gamma (N\Omega ) 2 ; we also examine the full probability distribution P\Omega (N ). The latter is approximately Gaussian, and exactly Gaussian for N\Omega AE 1: More precisely, for any N\Omega it is a Poisson distribution for the ideal classical gas, and a modified Poisson distribution for the ideal or interacting Fermi gases. While most of our results are for nonzero densities and three dimensions, we also consider fluctuations in the lowdensity or strictlycorrelated limit and in the electron gas of o...
Probing a Single Isolated Electron: New Measurements of the Electron Magnetic Moment and the Fine Structure Constant
"... For these measurements one electron is suspended for months at a time within a cylindrical Penning trap [1], a device that was invented long ago just for this purpose. The cylindrical Penning trap provides an electrostatic quadrupole potential for trapping and detecting a single electron [2]. At the ..."
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For these measurements one electron is suspended for months at a time within a cylindrical Penning trap [1], a device that was invented long ago just for this purpose. The cylindrical Penning trap provides an electrostatic quadrupole potential for trapping and detecting a single electron [2]. At the same time, it provides a right,
LINKING THE CIRCLE AND THE SIEVE: RAMANUJAN FOURIER SERIES
, 2006
"... Currently the circle and the sieve methods are the key tools in analytic number theory. In this paper the unifying theme of the two methods is shown to be Ramanujan Fourier series. 1 Introduction. The two well known methods in additive number theory are the circle method and the sieve method. The c ..."
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Currently the circle and the sieve methods are the key tools in analytic number theory. In this paper the unifying theme of the two methods is shown to be Ramanujan Fourier series. 1 Introduction. The two well known methods in additive number theory are the circle method and the sieve method. The circle method is based on using a generating function (See Section 3) and noting along with Ramanujan and Hardy that the rational points on the circle contribute most and then through estimates showing that the contribution from the other points is
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"... back control process. In particular, we find the control fields that ensure the quickest reduction of the entropy (noise). This reduction is related to fluctuations of the controlling part of the Hamiltonian. We also describe the entropyinformation tradeoff: how limitations of the information avai ..."
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back control process. In particular, we find the control fields that ensure the quickest reduction of the entropy (noise). This reduction is related to fluctuations of the controlling part of the Hamiltonian. We also describe the entropyinformation tradeoff: how limitations of the information available on system’s state decrease the speed of the entropy reduction and change the qualitative features of the control process. Note that in contrast to the above works on the Brownian particles control, we shall work with the full Hamiltonian system, and not with a small particle coupled to a large thermal bath. Moreover, we focus on Hamiltonian systems with finite degrees of freedom, though the presented theory applies to macrocopic Hamiltonian systems, e.g., the particle plus the bath. The macroscopic
Entropy of Relativistic MonoAtomic Gas and Temperature Relativistic Transformation in Thermodynamics
"... Abstract: It is demonstrated that the entropy of the ideal monoatomic gas comprising identical spherical atoms is not conserved under the PlanckEinstein like relativistic temperature transformation, as a result of the change in the number of atomic degrees of freedom. This fact supports the idea t ..."
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Abstract: It is demonstrated that the entropy of the ideal monoatomic gas comprising identical spherical atoms is not conserved under the PlanckEinstein like relativistic temperature transformation, as a result of the change in the number of atomic degrees of freedom. This fact supports the idea that there is no universal relativistic temperature transformation.