Badly approximable numbers and vectors in Cantor-like sets

We show that a large class of Cantor-like sets of R-d, d >= 1, contains uncountably many badly approximable numbers, respectively badly approximable vectors, when d >= 2. An analogous result is also proved for subsets of R-d arising in the study of geodesic flows corresponding to (d+1)-dimensional manifolds of constant negative curvature and finite volume, generalizing the set of badly approximable numbers in R. Furthermore, we describe a condition on sets, which is fulfilled by a large class, ensuring a large intersection with these Cantor-like sets.

Molecular probe dynamics reveals suppression of ice-like regions in strongly confined supercooled water

The structure of the hydrogen bond network is a key element for understanding water's thermodynamic and kinetic anomalies. While ambient water is strongly believed to be a uniform, continuous hydrogen-bonded liquid, there is growing consensus that supercooled water is better described in terms of distinct domains with either a low-density ice-like structure or a high-density disordered one. We evidenced two distinct rotational mobilities of probe molecules in interstitial supercooled water of polycrystalline ice Banerjee D, et al. (2009) ESR evidence for 2 coexisting liquid phases in deeply supercooled bulk water. Proc Natl Acad Sci USA 106: 11448-11453]. Here we show that, by increasing the confinement of interstitial water, the mobility of probe molecules, surprisingly, increases. We argue that loose confinement allows the presence of ice-like regions in supercooled water, whereas a tighter confinement yields the suppression of this ordered fraction and leads to higher fluidity. Compelling evidence of the presence of ice-like regions is provided by the probe orientational entropy barrier which is set, through hydrogen bonding, by the configuration of the surrounding water molecules and yields a direct measure of the configurational entropy of the same. We find that, under loose confinement of supercooled water, the entropy barrier surmounted by the slower probe fraction exceeds that of equilibrium water by the melting entropy of ice, whereas no increase of the barrier is observed under stronger confinement. The lower limit of metastability of supercooled water is discussed.

Subdiffusion in hair bundle dynamics: The role of protein conformational fluctuations

The detection of sound signals in vertebrates involves a complex network of different mechano-sensory elements in the inner ear. An especially important element in this network is the hair bundle, an antenna-like array of stereocilia containing gated ion channels that operate under the control of one or more adaptation motors. Deflections of the hair bundle by sound vibrations or thermal fluctuations transiently open the ion channels, allowing the flow of ions through them, and producing an electrical signal in the process, eventually causing the sensation of hearing. Recent high frequency (0.1-10 kHz) measurements by Kozlov et al. Proc. Natl. Acad. Sci. U. S. A. 109, 2896 (2012)] of the power spectrum and the mean square displacement of the thermal fluctuations of the hair bundle suggest that in this regime the dynamics of the hair bundle are subdiffusive. This finding has been explained in terms of the simple Brownian motion of a filament connecting neighboring stereocilia (the tip link), which is modeled as a viscoelastic spring. In the present paper, the diffusive anomalies of the hair bundle are ascribed to tip link fluctuations that evolve by fractional Brownian motion, which originates in fractional Gaussian noise and is characterized by a power law memory. The predictions of this model for the power spectrum of the hair bundle and its mean square displacement are consistent with the experimental data and the known properties of the tip link. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4768902]

SOI strip waveguide microring resonator for homogeneous biosensing

We report the simulation and analytical results obtained for homogenous or bulk sensing of protein on Siliconon- insulator strip waveguide based microring resonator. The radii of the rings considered are 5 μm and 20 μm; the waveguide dimensions are 300 × 300 nm. A gap of (i) 200 nm and (ii) 300 nm exists between the ring and the bus waveguide. The biomaterial is uniformly distributed over a thickness which exceeds the evanescent field penetration depth of 150 nm. The sensitivities of the resonators are 32.5 nm/RIU and 17.5 nm/RIU (RIU - Refractive index unit) respectively.

QUAD: quality assessment of documents

We propose a set of metrics that evaluate the uniformity, sharpness, continuity, noise, stroke width variance,pulse width ratio, transient pixels density, entropy and variance of components to quantify the quality of a document image. The measures are intended to be used in any optical character recognition (OCR) engine to a priori estimate the expected performance of the OCR. The suggested measures have been evaluated on many document images, which have different scripts. The quality of a document image is manually annotated by users to create a ground truth. The idea is to correlate the values of the measures with the user annotated data. If the measure calculated matches the annotated description,then the metric is accepted; else it is rejected. In the set of metrics proposed, some of them are accepted and the rest are rejected. We have defined metrics that are easily estimatable. The metrics proposed in this paper are based on the feedback of homely grown OCR engines for Indic (Tamil and Kannada) languages. The metrics are independent of the scripts, and depend only on the quality and age of the paper and the printing. Experiments and results for each proposed metric are discussed. Actual recognition of the printed text is not performed to evaluate the proposed metrics. Sometimes, a document image containing broken characters results in good document image as per the evaluated metrics, which is part of the unsolved challenges. The proposed measures work on gray scale document images and fail to provide reliable information on binarized document image.

Guided-wave-based damage detection in a composite T-joint using 3D scanning laser Doppler vibrometer

Composite T-joints are commonly used in modern composite airframe, pressure vessels and piping structures, mainly to increase the bending strength of the joint and prevents buckling of plates and shells, and in multi-cell thin-walled structures. Here we report a detailed study on the propagation of guided ultrasonic wave modes in a composite T-joint and their interactions with delamination in the co-cured co-bonded flange. A well designed guiding path is employed wherein the waves undergo a two step mode conversion process, one is due to the web and joint filler on the back face of the flange and the other is due to the delamination edges close to underneath the accessible surface of the flange. A 3D Laser Doppler Vibrometer is used to obtain the three components of surface displacements/velocities of the accessible face of the flange of the T-joint. The waves are launched by a piezo ceramic wafer bonded on to the back surface of the flange. What is novel in the proposed method is that the location of any change in material/geometric properties can be traced by computing a frequency domain power flow along a scan line. The scan line can be chosen over a grid either during scan or during post-processing of the scan data off-line. The proposed technique eliminates the necessity of baseline data and disassembly of structure for structural interrogation.

Diffusion on a rugged energy landscape with spatial correlations

Rugged energy landscapes find wide applications in diverse fields ranging from astrophysics to protein folding. We study the dependence of diffusion coefficient (D) of a Brownian particle on the distribution width (epsilon) of randomness in a Gaussian random landscape by simulations and theoretical analysis. We first show that the elegant expression of Zwanzig Proc. Natl. Acad. Sci. U.S.A. 85, 2029 (1988)] for D(epsilon) can be reproduced exactly by using the Rosenfeld diffusion-entropy scaling relation. Our simulations show that Zwanzig's expression overestimates D in an uncorrelated Gaussian random lattice - differing by almost an order of magnitude at moderately high ruggedness. The disparity originates from the presence of ``three-site traps'' (TST) on the landscape - which are formed by the presence of deep minima flanked by high barriers on either side. Using mean first passage time formalism, we derive a general expression for the effective diffusion coefficient in the presence of TST, that quantitatively reproduces the simulation results and which reduces to Zwanzig's form only in the limit of infinite spatial correlation. We construct a continuous Gaussian field with inherent correlation to establish the effect of spatial correlation on random walk. The presence of TSTs at large ruggedness (epsilon >> k(B)T) gives rise to an apparent breakdown of ergodicity of the type often encountered in glassy liquids. (C) 2014 AIP Publishing LLC.

Beyond classical dynamic structural plasticity using mesh-free modelling techniques

The problem of modelling the transient response of an elastic-perfectly-plastic cantilever beam, carrying an impulsively loaded tip mass, is,often referred to as the Parkes cantilever problem 25]; The permanent deformation of a cantilever struck transversely at its tip, Proc. R. Soc. A., 288, pp. 462). This paradigm for classical modelling of projectile impact on structures is re-visited and updated using the mesh-free method, smoothed particle hydrodynamics (SPH). The purpose of this study is to investigate further the behaviour of cantilever beams subjected to projectile impact at its tip, by considering especially physically real effects such as plastic shearing close to the projectile, shear deformation, and the variation of the shear strain along the length and across the thickness of the beam. Finally, going beyond macroscopic structural plasticity, a strategy to incorporate physical discontinuity (due to crack formation) in SPH discretization is discussed and explored in the context of tip-severance of the cantilever beam. Consequently, the proposed scheme illustrates the potency for a more refined treatment of penetration mechanics, paramount in the exploration of structural response under ballistic loading. The objective is to contribute to formulating a computational modelling framework within which transient dynamic plasticity and even penetration/failure phenomena for a range of materials, structures and impact conditions can be explored ab initio, this being essential for arriving at suitable tools for the design of armour systems. (C) 2014 Elsevier Ltd. All rights reserved.

Anisotropic isometric fluctuation relations in experiment and theory on a self-propelled rod

The isometric fluctuation relation (IFR) P. I. Hurtado et al., Proc. Natl. Acad. Sci. USA 108, 7704 (2011)] relates the relative probability of current fluctuations of fixed magnitude in different spatial directions. We test its validity in an experiment on a tapered rod, rendered motile by vertical vibration and immersed in a sea of spherical beads. We analyze the statistics of the velocity vector of the rod and show that they depart significantly from the IFR of Hurtado et al. Aided by a Langevin-equation model we show that our measurements are largely described by an anisotropic generalization of the IFR R. Villavicencio et al., Europhys. Lett. 105, 30009 (2014)], with no fitting parameters, but with a discrepancy in the prefactor whose origin may lie in the detailed statistics of the microscopic noise. The experimentally determined large-deviation function of the velocity vector has a kink on a curve in the plane.

Numerical study of laminar, standing hydraulic jumps in a planar geometry

We solve the two-dimensional, planar Navier-Stokes equations to simulate a laminar, standing hydraulic jump using a Volume-of-Fluid method. The geometry downstream of the jump has been designed to be similar to experimental conditions by including a pit at the edge of the platform over which liquid film flows. We obtain jumps with and without separation. Increasing the inlet Froude number pushes the jump downstream and makes the slope of the jump weaker, consistent with experimental observations of circular jumps, and decreasing the Reynolds number brings the jump upstream while making it steeper. We study the effect of the length of the domain and that of a downstream obstacle on the structure and location of the jump. The transient flow which leads to a final steady jump is described for the first time to our knowledge. In the moderate Reynolds number regime, we obtain steady undular jumps with a separated bubble underneath the first few undulations. Interestingly, surface tension leads to shortening of wavelength of these undulations. We show that the undulations can be explained using the inviscid theory of Benjamin and Lighthill (Proc. R. Soc. London, Ser. A, 1954). We hope this new finding will motivate experimental verification.