Analytical and numerical investigation of structural response of compliant wall materials

Theoretical analysis of an electrostatically driven wall system for a compliant wall drag reduction program is reported. The electrostatic wall system is capable of producing deflections of many orders greater than the thicknesses and at small wavelengths. An intermediate large response theory was used for structural analysis. The theoretical predictions were compared to bench test results, and good agreement between the two was obtained. The effects of aerodynamic loads and perturbation electric fields on the theoretical solutions were considered. It was shown that for very small wavelengths (approximately 2mm) the aerodynamic effects can be estimated using potential theory without loss of accuracy, and the perturbation electric fields do not affect solutions as long as the deflections are less than one percent of the wavelength. Resonance effects for this type of structure were shown to be fairly small

Analytical and numerical investigation of structural response of compliant wall materials

Surface motion of compliant walls in drag reduction experiments was analyzed. The spectrum of surface motion indicates that membranes over deep cavities respond at low frequencies and large wavelengths. The membrane over a deep cavity is therefore found not to yield the desired reponse predicted by the postulated mechanism. The membrane over a thin air gap is found to act as a wavelength chopper, and analysis of the nonlinear response of the compliant surface indicates its possible suitability for compliant wall experiments. Periodic structures are found to lock in the desired wavelengths of motion. Laminated structures are found to be very ineffective as compliant models, except when there is no bonding between the membrane and the backing. Computer programs developed for these analyses are documented

What we don't know about time

String theory has transformed our understanding of geometry, topology and spacetime. Thus, for this special issue of Foundations of Physics commemorating "Forty Years of String Theory", it seems appropriate to step back and ask what we do not understand. As I will discuss, time remains the least understood concept in physical theory. While we have made significant progress in understanding space, our understanding of time has not progressed much beyond the level of a century ago when Einstein introduced the idea of space-time as a combined entity. Thus, I will raise a series of open questions about time, and will review some of the progress that has been made as a roadmap for the future.Comment: 15 pages; Essay for a special issue of Foundations of Physics commemorating "Forty years of string theory

Multi-Boundary Entanglement in Chern-Simons Theory and Link Invariants

We consider Chern-Simons theory for gauge group $G$ at level $k$ on 3-manifolds $M_n$ with boundary consisting of $n$ topologically linked tori. The Euclidean path integral on $M_n$ defines a quantum state on the boundary, in the $n$-fold tensor product of the torus Hilbert space. We focus on the case where $M_n$ is the link-complement of some $n$-component link inside the three-sphere $S^3$. The entanglement entropies of the resulting states define framing-independent link invariants which are sensitive to the topology of the chosen link. For the Abelian theory at level $k$ ($G= U(1)_k$) we give a general formula for the entanglement entropy associated to an arbitrary $(m|n-m)$ partition of a generic $n$-component link into sub-links. The formula involves the number of solutions to certain Diophantine equations with coefficients related to the Gauss linking numbers (mod $k$) between the two sublinks. This formula connects simple concepts in quantum information theory, knot theory, and number theory, and shows that entanglement entropy between sublinks vanishes if and only if they have zero Gauss linking (mod $k$). For $G = SU(2)_k$, we study various two and three component links. We show that the 2-component Hopf link is maximally entangled, and hence analogous to a Bell pair, and that the Whitehead link, which has zero Gauss linking, nevertheless has entanglement entropy. Finally, we show that the Borromean rings have a "W-like" entanglement structure (i.e., tracing out one torus does not lead to a separable state), and give examples of other 3-component links which have "GHZ-like" entanglement (i.e., tracing out one torus does lead to a separable state).Comment: 37 pages, 19 figure

On the existence of supergravity duals to D1--D5 CFT states

We define a metric operator in the 1/2-BPS sector of the D1-D5 CFT, the eigenstates of which have a good semi-classical supergravity dual; the non-eigenstates cannot be mapped to semi-classical gravity duals. We also analyse how the data defining a CFT state manifests itself in the gravity side, and show that it is arranged into a set of multipoles. Interestingly, we find that quantum mechanical interference in the CFT can have observable manifestations in the semi-classical gravity dual. We also point out that the multipoles associated to the normal statistical ensemble fluctuate wildly, indicating that the mixed thermal state should not be associated to a semi-classical geometry.Comment: 22 pages, 2 figures. v2 : references added, typos correcte

Fluorescent nanodiamonds for FRET-based monitoring of a single biological nanomotor FoF1-ATP synthase

Color centers in diamond nanocrystals are a new class of fluorescence markers that attract significant interest due to matchless brightness, photostability and biochemical inertness. Fluorescing diamond nanocrystals containing defects can be used as markers replacing conventional organic dye molecules, quantum dots or autofluorescent proteins. They can be applied for tracking and ultrahigh-resolution localization of the single markers. In addition the spin properties of diamond defects can be utilized for novel magneto-optical imaging (MOI) with nanometer resolution. We develop this technique to unravel the details of the rotary motions and the elastic energy storage mechanism of a single biological nanomotor FoF1-ATP synthase. FoF1-ATP synthase is the enzyme that provides the 'chemical energy currency' adenosine triphosphate, ATP, for living cells. The formation of ATP is accomplished by a stepwise internal rotation of subunits within the enzyme. Previously subunit rotation has been monitored by single-molecule fluorescence resonance energy transfer (FRET) and was limited by the photostability of the fluorophores. Fluorescent nanodiamonds advance these FRET measurements to long time scales.Comment: 10 pages, 4 figure

Cosmological string models from Milne spaces and SL(2,Z) orbifold

The $n+1$-dimensional Milne Universe with extra free directions is used to construct simple FRW cosmological string models in four dimensions, describing expansion in the presence of matter with $p=k \rho$, $k=(4-n)/3n$. We then consider the n=2 case and make SL(2,Z) orbifold identifications. The model is surprisingly related to the null orbifold with an extra reflection generator. The study of the string spectrum involves the theory of harmonic functions in the fundamental domain of SL(2,Z). In particular, from this theory one can deduce a bound for the energy gap and the fact that there are an infinite number of excitations with a finite degeneracy. We discuss the structure of wave functions and give examples of physical winding states becoming light near the singularity.Comment: 14 pages, harvma

EMOTIONAL COMPETENCE OF THE PRINCIPALS OF COLLEGES OF EDUCATION: A CORRELATION STUDY

Descriptive Survey Method has been adopted for the conduct of the study. Emotional Competency Inventory for Teachers (Balasubramanian and Abilash Babu, 2009) has been used to collect the required data from the sample chosen. The inventory contains 20 positive items and 5 negative items. The number of items selected for the inventory falling under four major dimensions viz. Self-Awareness, Self-Management, Social Awareness and Relationship Management. In line with the Stratified Random Sampling Technique, 50 Principals of Colleges of Education from three districts of Tamilnadu state have been chosen for the study. Descriptive, differential and correlation analysis have been undertaken for data analysis adopting appropriate statistical techniques. It is found that there is significant difference at 0.05 level between the means of the scores of the Principals of the Colleges categorized based on their marital status with regard to their scores on Self Awareness, as one of the components of Emotional Competence. The mean value of the unmarried Principals has been found to be greater than that of married Principals. Hence, it is concluded that the unmarried principals possess more of Self-Awareness when compared to their married counter parts. It is also found that there is no significant difference between the means of the Principals of Colleges of Education on the scores of the most of the dimension of emotional competence of the principals irrespective of their sex and marital status as well as the locality and type of the institution. It is also found that there is significant and positive correlation at 0.01 level among different components of Emotional Competence viz. Self-Awareness and Self-Management & Relationship-Management, Self-Management and Social Awareness & Relationship-Management, Social Awareness and Self-Management & Relationship-Management. However, there is no significant relationship between Self-Awareness and Social Awareness, Social Awareness and Relationship Management.  Article visualizations

Arithmetic properties of blocks of consecutive integers

This paper provides a survey of results on the greatest prime factor, the number of distinct prime factors, the greatest squarefree factor and the greatest m-th powerfree part of a block of consecutive integers, both without any assumption and under assumption of the abc-conjecture. Finally we prove that the explicit abc-conjecture implies the Erd\H{o}s-Woods conjecture for each k>2.Comment: A slightly corrected and extended version of a paper which will appear in January 2017 in the book From Arithmetic to Zeta-functions published by Springe