Simulation of length-preserving motions of flexible one dimensional oObjects using optimization

During the motion of one dimensional flexible objects such as ropes, chains, etc., the assumption of constant length is realistic. Moreover,their motion appears to be naturally minimizing some abstract distance measure, wherein the disturbance at one end gradually dies down along the curve defining the object. This paper presents purely kinematic strategies for deriving length-preserving transformations of flexible objects that minimize appropriate ‘motion’. The strategies involve sequential and overall optimization of the motion derived using variational calculus. Numerical simulations are performed for the motion of a planar curve and results show stable converging behavior for single-step infinitesimal and finite perturbations 1 as well as multi-step perturbations. Additionally, our generalized approach provides different intuitive motions for various problem-specific measures of motion, one of which is shown to converge to the conventional tractrix-based solution. Simulation results for arbitrary shapes and excitations are also included.

An estimate of equilibrium sensitivity of global terrestrial carbon cycle using NCAR CCSM4

Increasing concentrations of atmospheric CO2 influence climate, terrestrial biosphere productivity and ecosystem carbon storage through its radiative, physiological and fertilization effects. In this paper, we quantify these effects for a doubling of CO2 using a low resolution configuration of the coupled model NCAR CCSM4. In contrast to previous coupled climate-carbon modeling studies, we focus on the near-equilibrium response of the terrestrial carbon cycle. For a doubling of CO2, the radiative effect on the physical climate system causes global mean surface air temperature to increase by 2.14 K, whereas the physiological and fertilization on the land biosphere effects cause a warming of 0.22 K, suggesting that these later effects increase global warming by about 10 % as found in many recent studies. The CO2-fertilization leads to total ecosystem carbon gain of 371 Gt-C (28 %) while the radiative effect causes a loss of 131 Gt-C (10 %) indicating that climate warming damps the fertilization-induced carbon uptake over land. Our model-based estimate for the maximum potential terrestrial carbon uptake resulting from a doubling of atmospheric CO2 concentration (285-570 ppm) is only 242 Gt-C. This highlights the limited storage capacity of the terrestrial carbon reservoir. We also find that the terrestrial carbon storage sensitivity to changes in CO2 and temperature have been estimated to be lower in previous transient simulations because of lags in the climate-carbon system. Our model simulations indicate that the time scale of terrestrial carbon cycle response is greater than 500 years for CO2-fertilization and about 200 years for temperature perturbations. We also find that dynamic changes in vegetation amplify the terrestrial carbon storage sensitivity relative to a static vegetation case: because of changes in tree cover, changes in total ecosystem carbon for CO2-direct and climate effects are amplified by 88 and 72 %, respectively, in simulations with dynamic vegetation when compared to static vegetation simulations.

Analytical theory and stability analysis of an elongated nanoscale object under external torque

We consider the rotational motion of an elongated nanoscale object in a fluid under an external torque. The experimentally observed dynamics could be understood from analytical solutions of the Stokes equation, with explicit formulae derived for the dynamical states as a function of the object dimensions and the parameters defining the external torque. Under certain conditions, multiple analytical solutions to the Stokes equations exist, which have been investigated through numerical analysis of their stability against small perturbations and their sensitivity towards initial conditions. These experimental results and analytical formulae are general enough to be applicable to the rotational motion of any isolated elongated object at low Reynolds numbers, and could be useful in the design of non-spherical nanostructures for diverse applications pertaining to microfluidics and nanoscale propulsion technologies.

Solution nuclear magnetic resonance structure of the GATase subunit and structural Basis of the interaction between GATase and ATPPase subunits in a two-subunit-type GMPS from methanocaldococcus jannaschii

The solution structure of the monomeric glutamine amidotransferase (GATase) subunit of the Methanocaldococcus janaschii (Mj) guanosine monophosphate synthetase (GMPS) has been determined using high-resolution nuclear magnetic resonance methods. Gel filtration chromatography and N-15 backbone relaxation studies have shown that the Mj GATase subunit is present in solution as a 21 kDa (188-residue) monomer. The ensemble of 20 lowest-energy structures showed root-mean-square deviations of 0.35 +/- 0.06 angstrom for backbone atoms and 0.8 +/- 0.06 angstrom for all heavy atoms. Furthermore, 99.4% of the backbone dihedral angles are present in the allowed region of the Ramachandran map, indicating the stereochemical quality of the structure. The core of the tertiary structure of the GATase is composed of a seven-stranded mixed beta-sheet that is fenced by five alpha-helices. The Mj GATase is similar in structure to the Pyrococcus horikoshi (Ph) GATase subunit. Nuclear magnetic resonance (NMR) chemical shift perturbations and changes in line width were monitored to identify residues on GATase that were responsible for interaction with magnesium and the ATPPase subunit, respectively. These interaction studies showed that a common surface exists for the metal ion binding as well as for the protein-protein interaction. The dissociation constant for the GATase-Mg2+ interaction has been found to be similar to 1 mM, which implies that interaction is very weak and falls in the fast chemical exchange regime. The GATase-ATPPase interaction, on the other hand, falls in the intermediate chemical exchange regime on the NMR time scale. The implication of this interaction in terms of the regulation of the GATase activity of holo GMPS is discussed.

Magnetohydrodynamic stability of stochastically driven accretion flows

We investigate the evolution of magnetohydrodynamic (or hydromagnetic as coined by Chandrasekhar) perturbations in the presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations and experiments. The mismatch seems to have been resolved, at least in certain regimes, in the presence of a weak magnetic field, revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect, mimicking a small section of an astrophysical accretion disk around a compact object. It is found that such stochastically driven flows exhibit large temporal and spatial autocorrelations and cross-correlations of perturbation and, hence, large energy dissipations of perturbation, which generate instability. Interestingly, autocorrelations and cross-correlations appear independent of background angular velocity profiles, which are Rayleigh stable, indicating their universality. This work initiates our attempt to understand the evolution of three-dimensional hydromagnetic perturbations in rotating shear flows in the presence of stochastic noise.

Spatial Wavelet Approach to Local Matrix Crack Detection in Composite Beams with Ply Level Material Uncertainty

Wavelet coefficients based on spatial wavelets are used as damage indicators to identify the damage location as well as the size of the damage in a laminated composite beam with localized matrix cracks. A finite element model of the composite beam is used in conjunction with a matrix crack based damage model to simulate the damaged composite beam structure. The modes of vibration of the beam are analyzed using the wavelet transform in order to identify the location and the extent of the damage by sensing the local perturbations at the damage locations. The location of the damage is identified by a sudden change in spatial distribution of wavelet coefficients. Monte Carlo Simulations (MCS) are used to investigate the effect of ply level uncertainty in composite material properties such as ply longitudinal stiffness, transverse stiffness, shear modulus and Poisson's ratio on damage detection parameter, wavelet coefficient. In this study, numerical simulations are done for single and multiple damage cases. It is observed that spatial wavelets can be used as a reliable damage detection tool for composite beams with localized matrix cracks which can result from low velocity impact damage.

Microwave, infrared-microwave double resonance, and theoretical studies of C2H4 center dot center dot center dot H2S complex

In this manuscript, rotational spectra of four new isotopologues of the S-H center dot center dot center dot pi bonded C2H4 center dot center dot center dot H2S complex, i.e., C2D4 center dot center dot center dot H2S, C2D4 center dot center dot center dot D2S, C2D4 center dot center dot center dot HDS, and (CCH4)-C-13 center dot center dot center dot H2S have been reported and analyzed. All isotopologues except C2D4 center dot center dot center dot HDS show a four line pattern whereas a doubling of the transition frequencies was observed for C2D4 center dot center dot center dot HDS. These results together with our previous report on the title complex M. Goswami, P. K. Mandal, D. J. Ramdass, and E. Arunan, Chem. Phys. Lett. 393(1-3), 22-27 (2004)] confirm that both subunits (C2H4 and H2S) are involved in large amplitude motions leading to a splitting of each rotational transition to a quartet. Further, the results also confirm that the motions which are responsible for the observed splittings involve both monomers. Molecular symmetry group analysis, considering the interchange of equivalent H atoms in H2S and C2H4 could explain the observed four line pattern and their intensities in the microwave spectrum. In addition, hydride stretching fundamentals of the complex were measured using coherence-converted population transfer Fourier Transform Microwave-infrared (IR-MW double resonance) experiments in the S-H and C-H stretch regions. Changes in the tunneling splittings upon vibrational excitation are consistent with the isotopic dependence of pure rotational transitions. A complexation shift of 2.7-6.5 cm(-1) has been observed in the two fundamental S-H stretching modes of the H2S monomer in the complex. Vibrational pre-dissociation in the bound S-H stretch has been detected whereas the instrument-limited line-shapes in other S-H and C-H stretches indicate slower pre-dissociation rate. Some local perturbations in the vibrational spectra have been observed. Two combination bands have been observed corresponding to both the S-H stretching fundamentals and what appears to be the intermolecular stretching mode at 55 cm(-1). The tunneling splitting involved in the rotation of C2H4 unit has been deduced to be 1.5 GHz from the IR-MW results. In addition, ab initio barrier heights derived for different motions of the monomers support the experimental results and provide further insight into the motions causing the splitting. (C) 2013 AIP Publishing LLC.

Subttractors

We consider extremal limits of the recently constructed ``subtracted geometry''. We show that extremality makes the horizon attractive against scalar perturbations, but radial evolution of such perturbations changes the asymptotics: from a conical-box to flat Minkowski. Thus these are black holes that retain their near-horizon geometry under perturbations that drastically change their asymptotics. We also show that this extremal subtracted solution (''subttractor'') can arise as a boundary of the basin of attraction for flat space attractors. We demonstrate this by using a fairly minimal action (that has connections with STU model) where the equations of motion are integrable and we are able to find analytic solutions that capture the flow from the horizon to the asymptotic region. The subttractor is a boundary between two qualitatively different flows. We expect that these results have generalizations for other theories with charged dilatonic black holes.

Nonlinear thermoacoustics of ducted premixed flames: The influence of perturbation convection speed

When a premixed flame is placed within a duct, acoustic waves induce velocity perturbations at the flame's base. These travel down the flame, distorting its surface and modulating its heat release. This can induce self-sustained thermoacoustic oscillations. Although the phase speed of these perturbations is often assumed to equal the mean flow speed, experiments conducted in other studies and Direct Numerical Simulation (DNS) conducted in this study show that it varies with the acoustic frequency. In this paper, we examine how these variations affect the nonlinear thermoacoustic behaviour. We model the heat release with a nonlinear kinematic G-equation, in which the velocity perturbation is modelled on DNS results. The acoustics are governed by linearised momentum and energy equations. We calculate the flame describing function (FDF) using harmonic forcing at several frequencies and amplitudes. Then we calculate thermoacoustic limit cycles and explain their existence and stability by examining the amplitude-dependence of the gain and phase of the FDF. We find that, when the phase speed equals the mean flow speed, the system has only one stable state. When the phase speed does not equal the mean flow speed, however, the system supports multiple limit cycles because the phase of the FDF changes significantly with oscillation amplitude. This shows that the phase speed of velocity perturbations has a strong influence on the nonlinear thermoacoustic behaviour of ducted premixed flames. (C) 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Jeans instability criterion modified by external tidal field

The well-known Jeans criterion describes the onset of instabilities in an infinite, homogeneous, self-gravitating medium supported by pressure. Most realistic astrophysical systems, however, are not isolated - instead they are under the influence of an external field such as the tidal field due to a neighbour. Here, we do a linear perturbation analysis for a system in an external field and obtain a generalized dispersion relation that depends on the wavenumber, the sound speed and also the magnitude of the tidal field. A typical, disruptive tidal field is shown to make the system more stable against perturbations, and results in a higher effective Jeans wavelength. The minimum mass that can become unstable is then higher (super-Jeans) than the usual Jeans mass. Conversely, in a compressive tidal field, perturbations can grow even when the mass is lower (sub-Jeans). This approach involving the inclusion of tidal field opens up a new way of looking at instabilities in gravitating systems. The treatment is general and the simple analytical form of the modified Jeans criterion obtained makes it easily accessible.

Fractional Hilbert transform extensions and associated analytic signal construction

The analytic signal (AS) was proposed by Gabor as a complex signal corresponding to a given real signal. The AS has a one-sided spectrum and gives rise to meaningful spectral averages. The Hilbert transform (HT) is a key component in Gabor's AS construction. We generalize the construction methodology by employing the fractional Hilbert transform (FrHT), without going through the standard fractional Fourier transform (FrFT) route. We discuss some properties of the fractional Hilbert operator and show how decomposition of the operator in terms of the identity and the standard Hilbert operators enables the construction of a family of analytic signals. We show that these analytic signals also satisfy Bedrosian-type properties and that their time-frequency localization properties are unaltered. We also propose a generalized-phase AS (GPAS) using a generalized-phase Hilbert transform (GPHT). We show that the GPHT shares many properties of the FrHT, in particular, selective highlighting of singularities, and a connection with Lie groups. We also investigate the duality between analyticity and causality concepts to arrive at a representation of causal signals in terms of the FrHT and GPHT. On the application front, we develop a secure multi-key single-sideband (SSB) modulation scheme and analyze its performance in noise and sensitivity to security key perturbations. (C) 2013 Elsevier B.V. All rights reserved.

Network, nodes and nexus: systems approach to multitarget therapeutics

Systems biology is revealing multiple layers of regulatory networks that manifest spatiotemporal variations. Since genes and environment also influence the emergent property of a cell, the biological output requires dynamic understanding of various molecular circuitries. The metabolic networks continually adapt and evolve to cope with the changing milieu of the system, which could also include infection by another organism. Such perturbations of the functional networks can result in disease phenotypes, for instance tuberculosis and cancer. In order to develop effective therapeutics, it is important to determine the disease progression profiles of complex disorders that can reveal dynamic aspects and to develop mutitarget systemic therapies that can help overcome pathway adaptations and redundancy.

Spectral response of a droplet in pulsating external flow field

A droplet introduced in an external convective flow field exhibits significant multimodal shape oscillations depending upon the intensity of the aerodynamic forcing. In this paper, a theoretical model describing the temporal evolution of normal modes of the droplet shape is developed. The fluid is assumed to be weakly viscous and Newtonian. The convective flow velocity, which is assumed to be incompressible and inviscid, is incorporated in the model through the normal stress condition at the droplet surface and the equation of motion governing the dynamics of each mode is derived. The coupling between the external flow and the droplet is approximated to be a one-way process, i.e., the external flow perturbations effect the droplet shape oscillations and the droplet oscillation itself does not influence the external flow characteristics. The shape oscillations of the droplet with different fluid properties under different unsteady flow fields were simulated. For a pulsatile external flow, the frequency spectra of the normal modes of the droplet revealed a dominant response at the resonant frequency, in addition to the driving frequency and the corresponding harmonics. At driving frequencies sufficiently different from the resonant frequency of the prolate-oblate oscillation mode of the droplet, the oscillations are stable. But at resonance the oscillation amplitude grows in time leading to breakup depending upon the fluid viscosity. A line vortex advecting past the droplet, simulated as an isotropic jump in the far field velocity, leads to the resonant excitation of the droplet shape modes if and only if the time taken by the vortex to cross the droplet is less than the resonant period of the P-2 mode of the droplet. A train of two vortices interacting with the droplet is also analysed. It shows clearly that the time instant of introduction of the second vortex with respect to the droplet shape oscillation cycle is crucial in determining the amplitude of oscillation. (C) 2014 AIP Publishing LLC.

Suppression of gravitational instabilities by dominant dark matter halo in low-surface-brightness galaxies

The low-surface-brightness galaxies are gas rich and yet have a low star formation rate; this is a well-known puzzle. The spiral features in these galaxies are weak and difficult to trace, although this aspect has not been studied much. These galaxies are known to be dominated by the dark matter halo from the innermost regions. Here, we do a stability analysis for the galactic disc of UGC 7321, a low-surface-brightness, superthin galaxy, for which the various observational input parameters are available. We show that the disc is stable against local, linear axisymmetric and non-axisymmetric perturbations. The Toomre Q parameter values are found to be large (>> 1) mainly due to the low disc surface density, and the high rotation velocity resulting due to the dominant dark matter halo, which could explain the observed low star formation rate. For the stars-alone case, the disc shows finite swing amplification but the addition of dark matter halo suppresses that amplification almost completely. Even the inclusion of the low-dispersion gas which constitutes a high disc mass fraction does not help in causing swing amplification. This can explain why these galaxies do not show strong spiral features. Thus, the dynamical effect of a halo that is dominant from inner regions can naturally explain why star formation and spiral features are largely suppressed in low-surface-brightness galaxies, making these different from the high-surface-brightness galaxies.

Robust Reentry Guidance of a Reusable Launch Vehicle Using Model Predictive Static Programming

A robust suboptimal reentry guidance scheme is presented for a reusable launch vehicle using the recently developed, computationally efficient model predictive static programming. The formulation uses the nonlinear vehicle dynamics with a spherical and rotating Earth, hard constraints for desired terminal conditions, and an innovative cost function having several components with associated weighting factors that can account for path and control constraints in a soft constraint manner, thereby leading to smooth solutions of the guidance parameters. The proposed guidance essentially shapes the trajectory of the vehicle by computing the necessary angle of attack and bank angle that the vehicle should execute. The path constraints are the structural load constraint, thermal load constraint, bounds on the angle of attack, and bounds on the bank angle. In addition, the terminal constraints include the three-dimensional position and velocity vector components at the end of the reentry. Whereas the angle-of-attack command is generated directly, the bank angle command is generated by first generating the required heading angle history and then using it in a dynamic inversion loop considering the heading angle dynamics. Such a two-loop synthesis of bank angle leads to better management of the vehicle trajectory and avoids mathematical complexity as well. Moreover, all bank angle maneuvers have been confined to the middle of the trajectory and the vehicle ends the reentry segment with near-zero bank angle, which is quite desirable. It has also been demonstrated that the proposed guidance has sufficient robustness for state perturbations as well as parametric uncertainties in the model.