Holography and the C-Theorem

We review the geometric definition of C-function in the context of field theories that admit a holographic gravity dual.Comment: Contribution to the proceedings of the TMR 2000 Paris Conferenc

Testing the Equivalence Principle using Atomic Vacuum Energy Shifts

We consider possible tests of the Einstein Equivalence Principle for quantum-mechanical vacuum energies by evaluating the Lamb shift transition in a class of non-metric theories of gravity described by the \tmu formalism. We compute to lowest order the associated red shift and time dilation parameters, and discuss how (high-precision) measurements of these quantities could provide new information on the validity of the equivalence principle.Comment: 4 pages, latex, epsf, 1 figur

Temporal Behavior of the Individual Soft Microparticles: Understanding the Detection by Particle Impact Electrochemistry

Emerging progress of the Particle Impact Electrochemistry (PIE) technique has opened a novel field of detection and characterization of many analyte particles. 1 PIE comprises detection of changes in current when collisions of individual micro or nanoparticles are linked with an electrochemical event at the surface of an ultramicroelectrode (UME). 2 Being a rapid, low cost, and analyzing of one analyte at a time, PIE is widely used to characterize the shape, size distribution, and catalytic activity of nanoparticles. 2-5 To explore the scope of PIE for the detection of soft microparticles (absence of crystalline structure), ferrocene (Fc) trapped toluene-in-water emulsion droplets was used as a model with ultramicroelectrode. Droplets were analyzed by tracking the oxidation of Fc inside the droplet in the presence of an ionic liquid acting as emulsifier and conductivity enhancer. The droplet diameter was determined electrochemically using Faraday’s law. PIE was able to characterize the polydisperse size distribution of the droplets successfully. A 3D lattice random walk simulation indicated the stochastic nature of the droplet motion. Unlike nanoparticles, the droplets have slow kinetics and the collision dynamics associated with adsorption on the electrode surface. The adsorbing droplet generated similar spike-like electrical signals in real-time experiments that follow the bulk electrolysis model. These findings will facilitate the characterization of polydisperse microparticles including bacteria, which also adsorb and have similar size and density as the droplets in this work. Finally, because electrolysis time spans from hundreds of milliseconds to a second, single events of such duration are detectable with present-day instrumentation in contrast to non-adsorbing nanoparticles that have nanosecond collisions.https://scholarscompass.vcu.edu/gradposters/1057/thumbnail.jp

Surface holonomy and gauge 2-group

Just as point objects are parallel transported along curves, giving holonomies, string-like objects are parallel transported along surfaces, giving surface holonomies. Composition of these surfaces correspond to products in a category theoretic generalization of the gauge group, called a 2-group. I consider two different ways of constructing surface holonomies, one by using a pair of one and two form connections, and another by using a pair of one-form connections. Both procedures result in the structure of a 2-group.Comment: 8pp, RevTeX4, Submitted upon invitation to IJGMM