Velocity Fluctuations in Helical Propulsion: How Small Can a Propeller Be

Helical propulsion is at the heart of locomotion strategies utilized by various natural and artificial swimmers. We used experimental observations and a numerical model to study the various fluctuation mechanisms that determine the performance of an externally driven helical propeller as the size of the helix is reduced. From causality analysis, an overwhelming effect of orientational noise at low length scales is observed, which strongly affects the average velocity and direction of motion of a propeller. For length scales smaller than a few micrometers in aqueous media, the operational frequency for the propulsion system would have to increase as the inverse cube of the size, which can be the limiting factor for a helical propeller to achieve locomotion in the desired direction.

On stellated spheres and a tightness criterion for combinatorial manifolds

We introduce k-stellated spheres and consider the class W-k(d) of triangulated d-manifolds, all of whose vertex links are k-stellated, and its subclass W-k*; (d), consisting of the (k + 1)-neighbourly members of W-k(d). We introduce the mu-vector of any simplicial complex and show that, in the case of 2-neighbourly simplicial complexes, the mu-vector dominates the vector of Betti numbers componentwise; the two vectors are equal precisely for tight simplicial complexes. We are able to estimate/compute certain alternating sums of the components of the mu-vector of any 2-neighbourly member of W-k(d) for d >= 2k. As a consequence of this theory, we prove a lower bound theorem for such triangulated manifolds, and we determine the integral homology type of members of W-k*(d) for d >= 2k + 2. As another application, we prove that, when d not equal 2k + 1, all members of W-k*(d) are tight. We also characterize the tight members of W-k*(2k + 1) in terms of their kth Betti numbers. These results more or less answer a recent question of Effenberger, and also provide a uniform and conceptual tightness proof for all except two of the known tight triangulated manifolds. We also prove a lower bound theorem for homology manifolds in which the members of W-1(d) provide the equality case. This generalizes a result (the d = 4 case) due to Walkup and Kuhnel. As a consequence, it is shown that every tight member of W-1 (d) is strongly minimal, thus providing substantial evidence in favour of a conjecture of Kuhnel and Lutz asserting that tight homology manifolds should be strongly minimal. (C) 2013 Elsevier Ltd. All rights reserved.

Modelling the impact of extensive irrigation on the groundwater resources

Drastic groundwater resource depletion due to excessive extraction for irrigation is a major concern in many parts of India. In this study, an attempt was made to simulate the groundwater scenario of the catchment using ArcSWAT. Due to the restriction on the maximum initial storage, the deep aquifer component in ArcSWAT was found to be insufficient to represent the excessive groundwater depletion scenario. Hence, a separate water balance model was used for simulating the deep aquifer water table. This approach is demonstrated through a case study for the Malaprabha catchment in India. Multi-site rainfall data was used to represent the spatial variation in the catchment climatology. Model parameters were calibrated using observed monthly stream flow data. Groundwater table simulation was validated using the qualitative information available from the field. The stream flow was found to be well simulated in the model. The simulated groundwater table fluctuation is also matching reasonably well with the field observations. From the model simulations, deep aquifer water table fluctuation was found very severe in the semi-arid lower parts of the catchment, with some areas showing around 60m depletion over a period of eight years. Copyright (c) 2012 John Wiley & Sons, Ltd.

On existence of periodic solutions for stable interval plants with odd, sector type nonlinearities

In several systems, the physical parameters of the system vary over time or operating points. A popular way of representing such plants with structured or parametric uncertainties is by means of interval polynomials. However, ensuring the stability of such systems is a robust control problem. Fortunately, Kharitonov's theorem enables the analysis of such interval plants and also provides tools for design of robust controllers in such cases. The present paper considers one such case, where the interval plant is connected with a timeinvariant, static, odd, sector type nonlinearity in its feedback path. This paper provides necessary conditions for the existence of self sustaining periodic oscillations in such interval plants, and indicates a possible design algorithm to avoid such periodic solutions or limit cycles. The describing function technique is used to approximate the nonlinearity and subsequently arrive at the results. Furthermore, the value set approach, along with Mikhailov conditions, are resorted to in providing graphical techniques for the derivation of the conditions and subsequent design algorithm of the controller.

EFFICIENT QUANTUM RANDOM NUMBER GENERATION USING QUANTUM INDISTINGUISHABILITY

In this paper, we propose a quantum method for generation of random numbers based on bosonic stimulation. Randomness arises through the path-dependent indeterministic amplification of two competing bosonic modes. We show that the process provides an efficient method for macroscopic extraction of microscopic randomness.

Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications

A series expansion for Heckman-Opdam hypergeometric functions phi(lambda) is obtained for all lambda is an element of alpha(C)*. As a consequence, estimates for phi(lambda) away from the walls of a Weyl chamber are established. We also characterize the bounded hypergeometric functions and thus prove an analogue of the celebrated theorem of Helgason and Johnson on the bounded spherical functions on a Riemannian symmetric space of the noncompact type. The L-P-theory for the hypergeometric Fourier transform is developed for 0 < p < 2. In particular, an inversion formula is proved when 1 <= p < 2. (C) 2013 Elsevier Inc. All rights reserved.

The effect of multisubstitution on the thermoelectric properties of chalcogenide-based Cu2.1Zn0.9Sn1-xInxSe4 (0 <= x <= 0.1)

Quinary chalcogenide compounds Cu2.1Zn0.9Sn1-xInxSe4 (0 <= x <= 0.1) were prepared by melting (1170K) followed by annealing (773 K) for 172 h. Powder X-ray diffraction (XRD) data accompanied by electron probe microanalysis (EPMA) and Raman spectra of all the samples confirmed the formation of a tetragonal kesterite structure with Cu2FeSnS4-type. The thermoelectric properties of all the samples were measured as a function of temperature in the range of 300-780K. The electrical resistivity of all the samples exhibits metallic-like behavior. The positive values of the Seebeck coefficient and the Hall coefficient reveal that holes are the majority charge carriers. The codoping of copper and indium leads to a significant increase of the electrical resistivity and the Seebeck coefficient as a function of temperature above 650 K. The thermal conductivity of all the samples decreases with increasing temperature. Lattice thermal conductivity is not significantly modified as the doping content may infer negligible mass fluctuation scattering for copper/zinc and indium/tin substitution. Even though, the power factors (S-2/rho) of indium-doped samples Cu2.1Zn0.9Sn1-xInxSe4 (x = 0.05, 0.075) are almost the same, the maximum zT = 0.45 at 773K was obtained for Cu2.1Zn0.9Sn0.925In0.075Se4 due to its smaller value of thermal conductivity. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Revisiting the Fourier transform on the Heisenberg group

A recent theorem of S. Alesker, S. Artstein-Avidan and V. Milman characterises the Fourier transform on R-n as essentially the only transform on the space of tempered distributions which interchanges convolutions and pointwise products. In this note we study the image of the Schwartz space on the Heisenberg group under the Fourier transform and obtain a similar characterisation for the Fourier transform on the Heisenberg group.

Upper bound solution for pullout capacity of vertical anchors in sand using finite elements and limit analysis

The horizontal pullout capacity of vertical anchors embedded in sand has been determined by using an upper bound theorem of the limit analysis in combination with finite elements. The numerical results are presented in nondimensional form to determine the pullout resistance for various combinations of embedment ratio of the anchor (H/B), internal friction angle (ϕ) of sand, and the anchor-soil interface friction angle (δ). The pullout resistance increases with increases in the values of embedment ratio, friction angle of sand and anchor-soil interface friction angle. As compared to earlier reported solutions in literature, the present solution provides a better upper bound on the ultimate collapse load.

Two-pion low-energy contribution to the muon g-2 with improved precision from analyticity and unitarity

The two-pion contribution from low energies to the muon magnetic moment anomaly, although small, has a large relative uncertainty since in this region the experimental data on the cross sections are neither sufficient nor precise enough. It is therefore of interest to see whether the precision can be improved by means of additional theoretical information on the pion electromagnetic form factor, which controls the leading-order contribution. In the present paper, we address this problem by exploiting analyticity and unitarity of the form factor in a parametrization-free approach that uses the phase in the elastic region, known with high precision from the Fermi-Watson theorem and Roy equations for pi pi elastic scattering as input. The formalism also includes experimental measurements on the modulus in the region 0.65-0.70 GeV, taken from the most recent e(+)e(-) ->pi(+)pi(-) experiments, and recent measurements of the form factor on the spacelike axis. By combining the results obtained with inputs from CMD2, SND, BABAR, and KLOE, we make the predictions a(mu)(pi pi,LO)2m(pi), 0.30 GeV] = (0.553 +/- 0.004) x 10(-10) and a(mu)(pi pi,LO)0.30 GeV; 0.63 GeV] = (133.083 +/- 0.837) x 10(-10). These are consistent with the other recent determinations and have slightly smaller errors.

Reduced graphene oxide induced phase miscibility in polystyrene-poly(vinyl methyl ether) blends

Graphene oxide and reduced graphene oxide (r-GO) were synthesized by wet chemistry and the effect of r-GO in PS-PVME blends was investigated here with respect to phase miscibility, intermolecular cooperativity in the glass transition region and concentration fluctuation variance by shear rheology and dielectric spectroscopy. The spinodal decomposition temperature (T-s) and correlation length were evaluated from isochronal temperature scans in shear rheology. The r-GO is shown to induce miscibility in the blends, which may lead to increased local heterogeneity in the blends, though the length of cooperatively re-arranged regions (xi) at T-g is more or less unaltered. The evolution of the phase morphology as a function of temperature was assessed using polarized optical microscopy (POM). In the case of the 60/40 PS-PVME blends with 0.25 wt% r-GO, apart from significant refinement in the morphology, retention of the interconnected ligaments of PVME was observed, even in the late stages of phase separation suggesting that the coarsening of the phase morphology has been slowed down in the presence of r-GO. This phenomenon was also supported by AFM. Surface enrichment of PVME, owing to its lower surface tension, in the demixed samples was supported by XPS scans. The interconnected network of PVME has resulted in significantly higher permittivity in the bi-phasic blends, although the concentration of r-GO is below the percolation threshold.

Nonequilibrium noise in electrophoresis: The microion wind

A colloid supported against gravitational settling by means of an imposed electric field behaves, on average, as if it is at equilibrium in a confining potential T. M. Squires, J. Fluid Mech. 443, 403 (2001)]. We show, however, that the effective Langevin equation for the colloid contains a nonequilibrium noise source, proportional to the field, arising from the thermal motion of dissolved ions. The position fluctuations of the colloid show strong, experimentally testable signatures of nonequilibrium behavior, including a highly anisotropic, frequency-dependent ``effective temperature'' obtained from the fluctuation-dissipation ratio.

A simple Kontinuitatssatz

We are interested in several informal statements referred as ``Kontinuitatssatz'' in the recent literature on analytic continuation. The basic (unstated) principle that seems to be in use in these works appears to be a folk theorem. We provide a precise statement of this folk Kontinuitatssatz and give a proof of it.

Proper holomorphic mappings between hyperbolic product manifolds

We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert and Stein, the proof of the full result relies on the interplay of the latter ideas and a finiteness theorem for Riemann surfaces.

Non-equilibrium segmental dynamics driven by multiwall carbon nanotubes in PS/PVME blends

The present paper discusses the effect of multiwall carbon nanotubes (MWNTs) on the structural relaxation and the intermolecular cooperativity in dynamically asymmetric blends of PS/PVME (polystyrene/poly(vinyl methyl ether)). The temperature regime where chain connectivity effects dominate the thermodynamic concentration fluctuation (T/T-g > 0.75, T-g is the glass transition temperature of the blends) was studied using dielectric spectroscopy (DS). Interestingly, in the blends with MWNTs a bimodal distribution of relaxation was obtained in the loss modulus spectra. This plausibly is due to different environments experienced by the faster component (PVME) in the presence of MWNTs. The segmental dynamics of PVME was observed to be significantly slowed down in the presence of MWNTs and an Arrhenius-type behavior, weakly dependent on temperature, is observed at higher frequencies. This non-equilibrium dynamics of PVME is presumed to be originating from interphase regions near the surface of MWNTs. The length scale of the cooperative rearranging region (xi CRR) at T-g, assessed by calorimetric measurements, was observed to be higher in the case of blends with MWNTs. An enhanced molecular level miscibility driven by MWNTs in the blends corroborates with the larger xi CRR and comparatively more number of segments in CRR (in contrast to neat blends) around T-g. The configurational entropy and length scale of the cooperative volume was mapped as a function of temperature in the temperature regime, Tg < T < T-g + 60 K. The blends phase separated by spinodal decomposition which further led to an interconnected PVME network in PS. This further led to materials with very high electrical conductivity upon demixing.