Analog Computer Solution of the Electrodiffusion Equation for a Simple Membrane

Onega, Ronald J.

doi:10.1119/1.1986558

Cited by 3 publications

(2 citation statements)

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“…Topic 4, transport in ionic membranes, has received extensive theoretical treatment by solution of the flux equations for various boundary conditions, numbers, charges, and mobilities of species. Recommended are studies by Macdonald (706), Buck (169), Stishkov (1103), Malvadkar and Kostin (725), Barry and Diamond (fixed sites) (76,77), Kobatake (568), Kataoka (548), Arndt, Bond, and Roper (47) and computer solutions by Onega (875). Reviews of electrochemical phenomena are by Teorell (1141) and Franck (323).…”

Section: Some New Departures and Fundamental Problems In Potentiometrymentioning

confidence: 99%

Ion selective electrodes, potentiometry, and potentiometric titrations

Buck¹

1974

Anal. Chem.

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Section: Some New Departures and Fundamental Problems In Potentiometrymentioning

confidence: 99%

Ion selective electrodes, potentiometry, and potentiometric titrations

Buck¹

1974

Anal. Chem.

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“…The use of tabletop models and analog computers in physics, though previously unexplored in the context of quantum vacuum fluctuations, continues to play an important role in contemporary research areas like quantum evolution (32) and quantum information (33). For example, many analog computers have been developed to simulate fluid flow problems (34,35), electromagnetic and acoustic wavefields (36), cell electrolysis (37), and many of the problems governed by Laplace's equations (38). More recently, advances in the field of microwave electromagnetics (which offers unprecedented control over sources and detection of microwaves), have spurred the development of classical electromagnetic analog computations for studying complex quantum problems, including the calculation of the energy levels of Bloch electrons in magnetic fields (39) and the dynamics of certain classes of chaotic quantum systems (32), to name a few.…”

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Theoretical ingredients of a Casimir analog computer

Rodríguez¹,

McCauley²,

Joannopoulos³

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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We derive a correspondence between the contour integration of the Casimir stress tensor in the complex-frequency plane and the electromagnetic response of a physical dissipative medium in a finite real-frequency bandwidth. The consequences of this correspondence are at least threefold: First, the correspondence makes it easier to understand Casimir systems from the perspective of conventional classical electromagnetism, based on real-frequency responses, in contrast to the standard imaginary-frequency point of view based on Wick rotations. Second, it forms the starting point of finite-difference time-domain numerical techniques for calculation of Casimir forces in arbitrary geometries. Finally, this correspondence is also key to a technique for computing quantum Casimir forces at micrometer scales using antenna measurements at tabletop (e.g., centimeter) scales, forming a type of analog computer for the Casimir force. Superficially, relationships between the Casimir force and the classical electromagnetic Green's function are well known, so one might expect that any experimental measurement of the Green's function would suffice to calculate the Casimir force. However, we show that the standard forms of this relationship lead to infeasible experiments involving infinite bandwidth or exponentially growing fields, and a fundamentally different formulation is therefore required.C asimir forces arise due to quantum fluctuations of the electromagnetic field (1-4) and can play a significant role in the physics of neutral, macroscopic bodies at micrometer separations, such as in new generations of micro-electromechanical systems (5, 6). These forces have previously been studied both in delicate experiments at micron and submicron length scales (7-10) and also in theoretical calculations that are only recently becoming feasible for complex nonplanar geometries (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22). Theoretical efforts to predict Casimir forces for geometries very unlike the standard case of parallel plates have begun to yield fruit, having demonstrated a number of interesting results for strong-curvature structures (17,(23)(24)(25)(26)(27)(28)(29). But theoretical challenges still remain, more so in geometries involving multiple bodies and/or multiple length scales (14).In this paper, we describe a correspondence between the calculation of Casimir forces for vacuum-separated objects and a similar electromagnetic-force calculation in which the objects are instead separated by a conducting fluid, as illustrated in Fig. 1. The requirement that the geometry be mapped in this fashion is a practical consideration for any calculation based on the time domain (real frequencies). In fact, it is the theoretical equivalent of a crucial and well-known technique for accurate numerical evaluation of Casimir forces, in which the force integrand is deformed via contour integration and commonly evaluated over the imaginary-frequency axis (2, 14). Our formulation circumvents difficulties with all previous expressions of Casimir...

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Ion selective electrodes, potentiometry, and potentiometric titrations

Buck¹

1972

Anal. Chem.

View full text Add to dashboard Cite

Analog Computer Solution of the Electrodiffusion Equation for a Simple Membrane

Cited by 3 publications

References 0 publications

Ion selective electrodes, potentiometry, and potentiometric titrations

Ion selective electrodes, potentiometry, and potentiometric titrations

Theoretical ingredients of a Casimir analog computer

Ion selective electrodes, potentiometry, and potentiometric titrations

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