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.

Local stability of a gravitating filament: a dispersion relation

Filamentary structures are ubiquitous in astrophysics and are observed at various scales. On a cosmological scale, matter is usually distributed along filaments, and filaments are also typical features of the interstellar medium. Within a cosmic filament, matter can contract and form galaxies, whereas an interstellar gas filament can clump into a series of bead-like structures that can then turn into stars. To investigate the growth of such instabilities, we derive a local dispersion relation for an idealized self-gravitating filament and study some of its properties. Our idealized picture consists of an infinite self-gravitating and rotating cylinder with pressure and density related by a polytropic equation of state. We assume no specific density distribution, treat matter as a fluid, and use hydrodynamics to derive the linearized equations that govern the local perturbations. We obtain a dispersion relation for axisymmetric perturbations and study its properties in the (kR, kz) phase space, where kR and kz are the radial and longitudinal wavenumbers, respectively. While the boundary between the stable and unstable regimes is symmetrical in kR and kz and analogous to the Jeans criterion, the most unstable mode displays an asymmetry that could constrain the shape of the structures that form within the filament. Here the results are applied to a fiducial interstellar filament, but could be extended for other astrophysical systems, such as cosmological filaments and tidal tails.

A Kaluza-Klein subtractor

We generalize the results of arXiv : 1212.1875 and arXiv : 1212.6919 on attraction basins and their boundaries to the case of a specific class of rotating black holes,namely the ergo-free branch of extremal black holes in Kaluza-Klein theory. We find that exact solutions that span the attraction basin can be found even in the rotating case by appealing to certain symmetries of the equations of motion. They are characterized by two asymptotic parameters that generalize those of the non-rotating case, and the boundaries of the basin are spinning versions of the (generalized) subtractor geometry. We also give examples to illustrate that the shape of the attraction basin can drastically change depending on the theory.

Life Estimation of Electrothermally Stressed Epoxy Nanocomposites

Accelerated electrothermal aging tests were conducted at a constant temperature of 60 degrees C and at different stress levels of 6 kV/mm, 7 kV/mm and 8 kV/mm on unfilled epoxy and epoxy filled with 5 wt% of nano alumina. The leakage current through the samples were continuously monitored and the variation in tan delta values with aging duration was monitored to predict the impending failure and the time to failure of the samples. It is observed that the time to failure of epoxy alumina nanocomposite samples is significantly higher as compared to the unfilled epoxy. Data from the experiments has been analyzed graphically by plotting the Weibull probability and theoretically by the linear least square regression analysis. The characteristic life obtained from the least square regression analysis has been used to plot the inverse power law curve. From the inverse power law curve, the life of the epoxy insulation with and without nanofiller loading at a stress level of 3 kV/mm, i.e. within the midrange of the design stress level of rotating machine insulation, has been obtained by extrapolation. It is observed that the life of epoxy alumina nanocomposite of 5 wt% filler loading is nine times higher than that of the unfilled epoxy.

Desingularization of the Milne Universe

Resolution of cosmological singularities is an important problem in any full theory of quantum gravity. The Milne orbifold is a cosmology with a big-bang/big-crunch singularity, but being a quotient of flat space it holds potential for resolution in string theory. It is known, however, that some perturbative string amplitudes diverge in the Milne geometry. Here we show that flat space higher spin theories can effect a simple resolution of the Milne singularity when one embeds the latter in 2 + 1 dimensions. We explain how to reconcile this with the expectation that non-perturbative string effects are required for resolving Milne. Along the way, we introduce a Grassmann realization of the inonfi-Wigner contraction to export much of the AdS technology to -our flat space computation. (C) 2014 The Authors. Published by Elsevier BAT.

Maximum mass of stable magnetized highly super-Chandrasekhar white dwarfs: stable solutions with varying magnetic fields

We address the issue of stability of recently proposed significantly super-Chandrasekhar white dwarfs. We present stable solutions of magnetostatic equilibrium models for super-Chandrasekhar white dwarfs pertaining to various magnetic field profiles. This has been obtained by self-consistently including the effects of the magnetic pressure gradient and total magnetic density in a general relativistic framework. We estimate that the maximum stable mass of magnetized white dwarfs could be more than 3 solar mass. This is very useful to explain peculiar, overluminous type Ia supernovae which do not conform to the traditional Chandrasekhar mass-limit.

A DYNAMO MODEL OF MAGNETIC ACTIVITY IN SOLAR-LIKE STARS WITH DIFFERENT ROTATIONAL VELOCITIES

We attempt to provide a quantitative theoretical explanation for the observations that Ca II H/K emission and X-ray emission from solar-like stars increase with decreasing Rossby number (i.e., with faster rotation). Assuming that these emissions are caused by magnetic cycles similar to the sunspot cycle, we construct flux transport dynamo models of 1M(circle dot) stars rotating with different rotation periods. We first compute the differential rotation and the meridional circulation inside these stars from a mean-field hydrodynamics model. Then these are substituted in our dynamo code to produce periodic solutions. We find that the dimensionless amplitude f(m) of the toroidal flux through the star increases with decreasing rotation period. The observational data can be matched if we assume the emissions to go as the power 3-4 of f(m). Assuming that the Babcock-Leighton mechanism saturates with increasing rotation, we can provide an explanation for the observed saturation of emission at low Rossby numbers. The main failure of our model is that it predicts an increase of the magnetic cycle period with increasing rotation rate, which is the opposite of what is found observationally. Much of our calculations are based on the assumption that the magnetic buoyancy makes the magnetic flux tubes rise radially from the bottom of the convection zone. Taking into account the fact that the Coriolis force diverts the magnetic flux tubes to rise parallel to the rotation axis in rapidly rotating stars, the results do not change qualitatively.

The generalized Onsager model for a binary gas mixture

The Onsager model for the secondary flow field in a high-speed rotating cylinder is extended to incorporate the difference in mass of the two species in a binary gas mixture. The base flow is an isothermal solid-body rotation in which there is a balance between the radial pressure gradient and the centrifugal force density for each species. Explicit expressions for the radial variation of the pressure, mass/mole fractions, and from these the radial variation of the viscosity, thermal conductivity and diffusion coefficient, are derived, and these are used in the computation of the secondary flow. For the secondary flow, the mass, momentum and energy equations in axisymmetric coordinates are expanded in an asymptotic series in a parameter epsilon = (Delta m/m(av)), where Delta m is the difference in the molecular masses of the two species, and the average molecular mass m(av) is defined as m(av) = (rho(w1)m(1) + rho(w2)m(2))/rho(w), where rho(w1) and rho(w2) are the mass densities of the two species at the wall, and rho(w) = rho(w1) + rho(w2). The equation for the master potential and the boundary conditions are derived correct to O(epsilon(2)). The leading-order equation for the master potential contains a self-adjoint sixth-order operator in the radial direction, which is different from the generalized Onsager model (Pradhan & Kumaran, J. Fluid Mech., vol. 686, 2011, pp. 109-159), since the species mass difference is included in the computation of the density, viscosity and thermal conductivity in the base state. This is solved, subject to boundary conditions, to obtain the leading approximation for the secondary flow, followed by a solution of the diffusion equation for the leading correction to the species mole fractions. The O(epsilon) and O(epsilon(2)) equations contain inhomogeneous terms that depend on the lower-order solutions, and these are solved in a hierarchical manner to obtain the O(epsilon) and O(epsilon(2)) corrections to the master potential. A similar hierarchical procedure is used for the Carrier-Maslen model for the end-cap secondary flow. The results of the Onsager hierarchy, up to O(epsilon(2)), are compared with the results of direct simulation Monte Carlo simulations for a binary hard-sphere gas mixture for secondary flow due to a wall temperature gradient, inflow/outflow of gas along the axis, as well as mass and momentum sources in the flow. There is excellent agreement between the solutions for the secondary flow correct to O(epsilon(2)) and the simulations, to within 15 %, even at a Reynolds number as low as 100, and length/diameter ratio as low as 2, for a low stratification parameter A of 0.707, and when the secondary flow velocity is as high as 0.2 times the maximum base flow velocity, and the ratio 2 Delta m/(m(1) + m(2)) is as high as 0.5. Here, the Reynolds number Re = rho(w)Omega R-2/mu, the stratification parameter A = root m Omega R-2(2)/(2k(B)T), R and Omega are the cylinder radius and angular velocity, m is the molecular mass, rho(w) is the wall density, mu is the viscosity and T is the temperature. The leading-order solutions do capture the qualitative trends, but are not in quantitative agreement.

Low-frequency modes in an equatorial shallow-water model with moisture gradients

Motivated by observations of the mean state of tropical precipitable water (PW), a moist, first baroclinic mode, shallow-water system on an equatorial beta-plane with a background saturation profile that depends on latitude and longitude is studied. In the presence of a latitudinal moisture gradient, linear analysis of the non-rotating problem reveals large-scale, symmetric, eastward and westward propagating unstable modes. The introduction of a zonal moisture gradient breaks the east-west symmetry of the unstable modes. The effects of rotation are then included by numerically solving the resulting eigenvalue problem on an equatorial beta-plane. With a purely meridional moisture gradient, the system supports large-scale, low-frequency, eastward and westward moving neutral modes. Some of the similarities, and some of the discrepancies of these modes with intraseasonal tropical waves are pointed out. Finally, a zonal moisture gradient in the presence of rotation renders some of the aforementioned neutral modes unstable. In particular, according to observations of large-scale, low-frequency tropical variability, it is seen that regions where the background saturation profile increases (decreases) to the east favour eastward (westward) moving moist modes.

Molecular topology of three ring nematogens from C-13-H-1 dipolar couplings

Molecules in their liquid crystalline phase undergo rotational motion about the long axis of the molecule and the shape adopted by the rotating molecule plays an important role in influencing the mesophase morphology. In this context, obtaining the topology and the relative orientation of the different sub-units are important steps. For studying the liquid crystalline phase, C-13 NMR spectroscopy is a convenient method and for certain specifically designed nematogens, 2-dimensional separated local field (2D-SLF) NMR spectroscopy provides a particularly simple and straightforward means of arriving at the molecular topology. We demonstrate this approach on two three ring based nematogens designed with a phenyl or a thiophene ring at one of the termini. From the C-13-H-1 dipolar couplings of the terminal carbon obtained using the 2D-SLF NMR technique, the order parameter of the local symmetry axis of the terminal phenyl ring as well as of the long molecular axis could be easily estimated. For the thiophene nematogen, the lack of symmetry of the thiophene moiety necessitates some additional computational steps. The results indicate that the thiophene unit has its local ordering axis oriented away from the long molecular axis by a small angle, consistent with a bent structure expected in view of the thiophene geometry. The experiment also demonstrates the ability of 2D-SLF NMR to provide high resolution spectra by separation of several overlapped resonances in terms of their C-13-H-1 dipolar couplings. The results are consistent with a rod-like topology of the core of the investigated mesogens. The investigation demonstrates the potential of 2D-SLF NMR C-13 spectroscopy for obtaining atomistic level information and its utility for topological studies of different mesogens.

Ag nanoparticles-anchored reduced graphene oxide catalyst for oxygen electrode reaction in aqueous electrolytes and also a non-aqueous electrolyte for Li-O-2 cells

Silver nanoparticles-anchored reduced graphene oxide (Ag-RGO) is prepared by simultaneous reduction of graphene oxide and Ag+ ions in an aqueous medium by ethylene glycol as the reducing agent. Ag particles of average size of 4.7 nm were uniformly distributed on the RGO sheets. Oxygen reduction reaction (ORR) is studied on Ag-RGO catalyst in both aqueous and non-aqueous electrolytes by using cyclic voltammetry and rotating disk electrode techniques. As the interest in non-aqueous electrolyte is to study the catalytic performance of Ag-RGO for rechargeable Li-O-2 cells, these cells are assembled and characterized. Li-O-2 cells with Ag-RGO as the oxygen electrode catalyst are subjected to charge-discharge cycling at several current densities. A discharge capacity of 11 950 mA h g(-1) (11.29 mA h cm(-2)) is obtained initially at low current density. Although there is a decrease in the capacity on repeated discharge-charge cycling initially, a stable capacity is observed for about 30 cycles. The results indicate that Ag-RGO is a suitable catalyst for rechargeable Li-O-2 cells.

Turbulent electrical activity at sharp-edged inexcitable obstacles in a model for human cardiac tissue

Wave propagation around various geometric expansions, structures, and obstacles in cardiac tissue may result in the formation of unidirectional block of wave propagation and the onset of reentrant arrhythmias in the heart. Therefore, we investigated the conditions under which reentrant spiral waves can be generated by high-frequency stimulation at sharp-edged obstacles in the ten Tusscher-Noble-Noble-Panfilov (TNNP) ionic model for human cardiac tissue. We show that, in a large range of parameters that account for the conductance of major inward and outward ionic currents of the model fast inward Na+ current (INa), L-type slow inward Ca2+ current (I-CaL), slow delayed-rectifier current (I-Ks), rapid delayed-rectifier current (I-Kr), inward rectifier K+ current (I-K1)], the critical period necessary for spiral formation is close to the period of a spiral wave rotating in the same tissue. We also show that there is a minimal size of the obstacle for which formation of spirals is possible; this size is similar to 2.5 cm and decreases with a decrease in the excitability of cardiac tissue. We show that other factors, such as the obstacle thickness and direction of wave propagation in relation to the obstacle, are of secondary importance and affect the conditions for spiral wave initiation only slightly. We also perform studies for obstacle shapes derived from experimental measurements of infarction scars and show that the formation of spiral waves there is facilitated by tissue remodeling around it. Overall, we demonstrate that the formation of reentrant sources around inexcitable obstacles is a potential mechanism for the onset of cardiac arrhythmias in the presence of a fast heart rate.

The role of buoyancy in polarity reversals of the geodynamo

We investigate polarity reversals in the geodynamo using a rotating, convection-driven dynamo model. As the flow in rapidly rotating convection is dominated by columns aligned with the axis of rotation, the focus is on the dynamics of columnar vortices. By studying the growth of a seed magnetic field to a stable axial dipole field, we show that the magnetic field acts in ways that significantly enhance the relative helicity between cyclonic and anticyclonic vortices. This flow asymmetry is the hallmark of a dipolar dynamo. Strong buoyancy, on the other hand, offsets the effect of the magnetic field, establishing parity between positive and negative vortices. As the dipole field is deprived of the helicity required to support itself, the dynamo is pushed into a reversing state. This is a likely regime for polarity reversals in the Earth's core. The integral lengthscale at which buoyancy injects energy is not significantly different from the convective flow lengthscale, which implies that buoyancy does not feed vortices at the small scales where non-linear inertia is present. The lengthscale at which the Lorentz force acts in the reversing dynamo is small, which may allow the passive presence of non-linear inertia in the small scales.

A Brushless Wound Rotor Induction Generator for Variable Speed Microhydel Plants Without Ballast Load

A new generator topology for microhydel power plants, capable of unsupervised operation, is proposed. While conventional microhydel plants operate at constant speed with switched ballast loads, the proposed generator, based on the wound rotor induction machine, operates at variable speed and does away with the need for ballast loads. This increases reliability and substantially decreases system costs and setup times. The proposed generator has a simplified decoupled control structure with stator-referenced voltage control similar to a conventional synchronous generator, and rotor-side frequency control that is facilitated by rotating electronics mounted on the rotor. While this paper describes an isolated plant, the topology can also be tailored for distributed generation enabling conversion of the available hydraulic power into useful electrical power when the grid is present, and supplying local loads in the event of grid outage.

Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation

We carry out an extensive numerical study of the dynamics of spiral waves of electrical activation, in the presence of periodic deformation (PD) in two-dimensional simulation domains, in the biophysically realistic mathematical models of human ventricular tissue due to (a) ten-Tusscher and Panfilov (the TP06 model) and (b) ten-Tusscher, Noble, Noble, and Panfilov (the TNNPO4 model). We first consider simulations in cable-type domains, in which we calculate the conduction velocity theta and the wavelength lambda of a plane wave; we show that PD leads to a periodic, spatial modulation of theta and a temporally periodic modulation of lambda; both these modulations depend on the amplitude and frequency of the PD. We then examine three types of initial conditions for both TP06 and TNNPO4 models and show that the imposition of PD leads to a rich variety of spatiotemporal patterns in the transmembrane potential including states with a single rotating spiral (RS) wave, a spiral-turbulence (ST) state with a single meandering spiral, an ST state with multiple broken spirals, and a state SA in which all spirals are absorbed at the boundaries of our simulation domain. We find, for both TP06 and TNNPO4 models, that spiral-wave dynamics depends sensitively on the amplitude and frequency of PD and the initial condition. We examine how these different types of spiral-wave states can be eliminated in the presence of PD by the application of low-amplitude pulses by square- and rectangular-mesh suppression techniques. We suggest specific experiments that can test the results of our simulations.