Thermodynamics of d-dimensional hard sphere fluids confined to micropores

We derive an analytical expression of the second virial coefficient of d-dimensional hard sphere fluids confined to slit pores by applying Speedy and Reiss’ interpretation of cavity space. We confirm that this coefficient is identical to the one obtained from the Mayer cluster expansion up to second order with respect to fugacity. The key step of both approaches is to evaluate either the surface area or the volume of the d-dimensional exclusion sphere confined to a slit pore. We, further, present an analytical form of thermodynamic functions such as entropy and pressure tensor as a function of the size of the slit pore. Molecular dynamics simulations are performed for d = 2 and d = 3, and the results are compared with analytically obtained equations of state. They agree satisfactorily in the low density regime, and, for given density, the agreement of the results becomes excellent as the width of the slit pore gets smaller, because the higher order virial coefficients become unimportant

Symmetries of Abelian Orbifolds

Using the Polya Enumeration Theorem, we count with particular attention to C^3/Gamma up to C^6/Gamma, abelian orbifolds in various dimensions which are invariant under cycles of the permutation group S_D. This produces a collection of multiplicative sequences, one for each cycle in the Cycle Index of the permutation group. A multiplicative sequence is controlled by its values on prime numbers and their pure powers. Therefore, we pay particular attention to orbifolds of the form C^D/Gamma where the order of Gamma is p^alpha. We propose a generalization of these sequences for any D and any p.Comment: 75 pages, 13 figures, 30 table

Hierarchical Micro/Nano-Porous Acupuncture Needles Offering Enhanced Therapeutic Properties

Acupuncture as a therapeutic intervention has been widely used for treatment of many pathophysiological disorders. For achieving improved therapeutic effects, relatively thick acupuncture needles have been frequently used in clinical practice with, in turn, enhanced stimulation intensity. However due to the discomforting nature of the larger-diameter acupuncture needles there is considerable interest in developing advanced acupuncture therapeutical techniques that provide more comfort with improved efficacy. So motivated, we have developed a new class of acupuncture needles, porous acupuncture needles (PANs) with hierarchical micro/nano-scale conical pores upon the surface, fabricated via a simple and well known electrochemical process, with surface area approximately 20 times greater than conventional acupuncture needles. The performance of these high-surface-area PANs is evaluated by monitoring the electrophysiological and behavioral responses from the in vivo stimulation of Shenmen (HT7) points in Wistar rats, showing PANs to be more effective in controlling electrophysiological and behavioral responses than conventional acupuncture needles. Comparative analysis of cocaine induced locomotor activity using PANs and thick acupuncture needles shows enhanced performance of PANs with significantly less pain sensation. Our work offers a unique pathway for achieving a comfortable and improved acupuncture therapeutic effect. © The Author(s) 2016.1