Embracing Integrability in Stellar and Planetary Dynamics

Hamiltonian systems in stellar and planetary dynamics are typically near integrable. For example, Solar System planets are almost in two-body orbits, and in simulations of the Galaxy, the orbits of stars seem regular. For such systems, sophisticated numerical methods can be developed through integrable approximations. Following this theme, we discuss three distinct problems. We start by considering numerical integration techniques for planetary systems. Perturbation methods (that utilize the integrability of the two-body motion) are preferred over conventional "blind" integration schemes. We introduce perturbation methods formulated with Cartesian variables. In our numerical comparisons, these are superior to their conventional counterparts, but, by definition, lack the energy-preserving properties of symplectic integrators. However, they are exceptionally well suited for relatively short-term integrations in which moderately high positional accuracy is required. The next exercise falls into the category of stability questions in solar systems. Traditionally, the interest has been on the orbital stability of planets, which have been quantified, e.g., by Liapunov exponents. We offer a complementary aspect by considering the protective effect that massive gas giants, like Jupiter, can offer to Earth-like planets inside the habitable zone of a planetary system. Our method produces a single quantity, called the escape rate, which characterizes the system of giant planets. We obtain some interesting results by computing escape rates for the Solar System. Galaxy modelling is our third and final topic. Because of the sheer number of stars (about 10^11 in Milky Way) galaxies are often modelled as smooth potentials hosting distributions of stars. Unfortunately, only a handful of suitable potentials are integrable (harmonic oscillator, isochrone and Stäckel potential). This severely limits the possibilities of finding an integrable approximation for an observed galaxy. A solution to this problem is torus construction; a method for numerically creating a foliation of invariant phase-space tori corresponding to a given target Hamiltonian. Canonically, the invariant tori are constructed by deforming the tori of some existing integrable toy Hamiltonian. Our contribution is to demonstrate how this can be accomplished by using a Stäckel toy Hamiltonian in ellipsoidal coordinates.

Studies in biogas technology. Part IV. A novel biogas plant incorporating a solar water-heater and solar still

A reduction in the heat losses from the top of the gas holder of a biogas plant has been achieved by the simple device of a transparent cover. The heat losses thus prevented have been deployed to heat a water pond formed on the roof of the gas holder. This solar-heated water is mixed with the organic input for ‘ hot-charging ’ of the biogas plant. A thermal analysis of such a solar water-heater ‘ piggy-backing ’ on the gas holder of a biogas plant has been carried out.To test whether the advantages indicated by the thermal analysis can be realised in practice, a biogas plant of the ASTRA design was modified to incorporate a roof-top solar water-heater. The operation of such a modified plant, even under ‘ worst case ’ onditions, shows a significant improvement in the gas yield compared to the unmodified plant. Hence, the innovation reported here may lead to drastic reductions in the sizes and therefore costs of biogas plants. By making the transparent cover assume a tent-shape, the roof-top solar heater can serve the additional function of a solar still to yield distilled water. The biogas plant-cum-solar water-heater-cum-solar still described here is an example of a spatially integrated hybrid device which is extremely cost-effective.

Solar rechargeable battery—principle and materials

A brief survey of the historical development of a photoelectrochemical solar cell is given. The principle and future of solar chargeable battery is compared with a wet and a dry type photovoltaic cell. A solar chargeable battery, with or without a membrane and with an aqueous solution or with solid-state electrolytes is discussed. A new unique type of configuration “Sharon-Schottky” junction solar cell is described which can be used either as a charger for any secondary batteries or could be used for photoelectrolysis of water. All these configurations and their relative merits are discussed. A review on the various semiconductors and types of solar chargeable batteries is made. Finally, a conclusion is drawn for future direction of research for developing an economically viable photoelectrochemical (PEC) solar cell based on either the principle of a solar charger (to charge a Ni---Cd battery or lead—acid battery) and/or solar chargeable battery with or without without a membrane. Some new innovative ideas for the preparation of materials is discussed. The entire discussion is geared towards answering a relevant question: what has gone wrong to result in the stagnation and failure in commercialization of a PEC based solar cell?

Stress and strength analysis of pin joints in laminated anisotropic plates

Mechanical joints in composites can be tailored to achieve improved performance and better life by appropriately selecting the laminate parameters. In order to gain the best advantage of this possibility of tailoring the laminate, it is necessary to understand the influence of laminate parameters on the behaviour of joints in composites. Most of the earlier studies in this direction were based on simplified assumptions regarding load transfer at the pin-plate interface and such studies were only carried out on orthotropic and quasi-isotropic laminates. In the present study, a more rigorous analysis is carried out to study pin joints in laminates with anisotropic properties. Two types of laminates with (0/ + ?4/90)s and (0/ ± ?2/90)s layups made out of graphite epoxy T300/5208 material system are considered. The analysis mainly concentrates on clearance fit in which the pin is of smaller diameter compared to the hole. The main aspect of the analysis of pin joints is the changing contact between the pin and the plate with increasing load levels. The analysis is carried out by an iterative finite element technique and a computationally efficient routine is developed for this purpose. Numerical studies indicate that the location and magnitude of the peak stresses along the hole boundary are functions of fibre angle and the overall anisotropic properties. It is also shown that the conventional assumption of cosine distribution for the contact pressure between pin and the plate in the analysis lead to underestimation of bearing failure load and overestimation of shear and tensile failure loads in typical (0/905)s cross-ply laminates.

Psi-angle dependence of geminal proton–carbonyl-13C coupling constants in peptides. A theoretical investigation†

Theoretical calculations of the geminal carbonyl-13C- proton coupling constant, 2J(C′H), in α-amino acids have been carried out using Dirac Vector model and Penney-Dirac bond order formulations. The results indicate that the couplings are dependent on the backbone torsion angle psi (ψ) of the amino acid residues in peptides. The meagre available experimental data seem to support the theoretical findings.

Polarization studies in electromagnetic scattering by small Solar-system particles

In remote-sensing studies, particles that are comparable to the wavelength exhibit characteristic features in electromagnetic scattering, especially in the degree of linear polarization. These features vary with the physical properties of the particles, such as shape, size, refractive index, and orientation. In the thesis, the direct problem of computing the unknown scattered quantities using the known properties of the particles and the incident radiation is solved at both optical and radar spectral regions in a unique way. The internal electromagnetic fields of wavelength-scale particles are analyzed by using both novel and established methods to show how the internal fields are related to the scattered fields in the far zone. This is achieved by using the tools and methods that were developed specifically to reveal the internal field structure of particles and to study the mechanisms that relate the structure to the scattering characteristics of those particles. It is shown that, for spherical particles, the internal field is a combination of a forward propagating wave with the apparent wavelength determined by the refractive index of the particle, and a standing wave pattern with the apparent wavelength the same as for the incident wave. Due to the surface curvature and dielectric nature of the particle, the incident wave front undergoes a phase shift, and the resulting internal wave is focused mostly at the forward part of the particle similar to an optical lens. This focusing is also seen for irregular particles. It is concluded that, for both spherical and nonspherical particles, the interference at the far field between the partial waves that originate from these concentrated areas in the particle interior, is responsible for the specific polarization features that are common for wavelength-scale particles, such as negative values and local extrema in the degree of linear polarization, asymmetry of the phase function, and enhancement of intensity near the backscattering direction. The papers presented in this thesis solve the direct problem for particles with both simple and irregular shapes to demonstrate that these interference mechanisms are common for all dielectric wavelength-scale particles. Furthermore, it is shown that these mechanisms can be applied to both regolith particles in the optical wavelengths and hydrometeors at microwave frequencies. An advantage from this kind of study is that it does not matter whether the observation is active (e.g., polarimetric radar) or passive (e.g., optical telescope). In both cases, the internal field is computed for two mutually perpendicular incident polarizations, so that the polarization characteristics can then be analyzed according to the relation between these fields and the scattered far field.

A Comparative Study of the Effect of Metallic Au and ReO3 Nanoparticles on the Performance of Silicon Solar Cells

The influence of gold (similar to 35 nm diameter) as well as ReO3 (similar to 17 nm diameter) nanoparticles placed atop silicon photovoltaic devices on absorption and photocurrent generation has been investigated. The nanoparticles improve the power transmission into the semiconductor and consequently, the photocurrent response at wavelengths corresponding to plasmon absorption. An increase in short circuit current up to 4.5% under simulated solar irradiation was observed with the ReO3 nanoparticles, while the gold nanoparticles showed enhancements up to 6.5%. The increase in photocurrent is observed at wavelengths corresponding to the maxima in the surface plasmon resonance absorption spectra. (C) 2010 The Japan Society of Applied Physics

Hybrid Solar Cooking

In the existing traditional solar cookers, the cooking is performed near the collector which may be at an inconvenient location for cooking purposes. This paper proposes a hybrid solar cooking system where the solar energy is brought to the kitchen. The energy source is a combination of the solar thermal energy and the Liquefied Petroleum Gas (LPG) that is very common in kitchens. The solar thermal energy is transferred to the kitchen by means of a circulating fluid like oil. The transfer of solar heat is a two fold process wherein the energy from the collector is transferred first to an intermediate energy storage tank and then the energy is subsequently transferred from the tank to the cooking load. There are three parameters that are controlled in order to maximize the energy transfer from the collector to the load viz. the fluid flow rate from collector to tank, fluid flow rate from tank to load and the diameter of the pipes. The entire system is modeled using the bond graph approach. This paper discusses the implementation of such a system.

Wigner distribution for angle coordinates in quantum mechanics

The method of Wigner distribution functions, and the Weyl correspondence between quantum and classical variables, are extended from the usual kind of canonically conjugate position and momentum operators to the case of an angle and angular momentum operator pair. The sense in which one has a description of quantum mechanics using classical phase‐space language is much clarified by this extension.

Performance of a small solar pond in the tropics

The performance of the 240 m2 solar pond in Bangalore is discussed. The problems of erosion of gradient zone and formation of internal convective zones is highlighted. The technique of passive salt addition is shown to be a viable alternative for salt recycling. Different techniques of heat extraction are discussed and the use of an immersed copper heat exchanger is shown to be most convenient. A two-zone model for prediction of the seasonal structure of the solar pond performance is proposed. The model is shown to simulate the seasonal structure of the observed variation of the temperature in the storage zone.

Locating the seat of the solar dynamo

The hypothesis that the solar dynamo operates in a thin layer at the bottom of the convection zone is addressed. Recent work on the question whether the magnetic flux can be made to emerge at sunspot latitudes is reviewed. It is concluded that this hypothesis can fit the observational facts only if there is turbulence with a length scale of a few hundred kilometers in and around the dynamo region.

An Investigation Of Alkali Aluminosilicate Glasses By Si-29 And Al-27 Magic-Angle-Spinning Nmr-Spectroscopy

Alkali aluminosilicate glasses prepared by the gel and the melt routes have been investigated by Si-29 and Al-27 MAS NMR spectroscopy. It is found that Al has a tetrahedral coordination in the gel glasses modified with equivalent proportions of alkalis unlike in a pure aluminosilicate glass where Al has both four and six coordinations. Silicon is present as Q4 units in all the 5M2O 5Al2O3 9OSiO2 ( M = Li, Na and K) gel glasses studied whereas it is present in Q2 or Q3 species in the lithium aluminosilicate glasses of compositions 40Li2O x Al2O3 (1-x)SiO2 (1 less-than-or-equal-to x less-than-or-equal-to 15) and xLi2O 10Al2O3 (1-x)SiO2 (20 less-than-or-equal-to x less-than-or-equal-to 40). The combination of Q2 and Q3 is also found in certain sodium aluminosilicate glasses, but they change to Q2 and Q1 as the concentration of SiO2 decreases.

Influence of Inclination Angle and Machining Direction on Friction and Transfer Layer Formation

In the present investigation, unidirectional grinding marks were created on a set of steel plates. Sliding experiments were then conducted with the prepared steel plates using Al-Mg alloy pins and an inclined pin-on-plate sliding tester. The goals of the experiments were to ascertain the influence of inclination angle and grinding mark direction on friction and transfer layer formation during sliding contact. The inclination angle of the plate was held at 0.2 deg, 0.6 deg, 1 deg, 1.4 deg, 1.8 deg, 2.2 deg, and 2.6 deg in the tests. The pins were slid both perpendicular and parallel to the grinding marks direction. The experiments were conducted under both dry and lubricated conditions on each plate in an ambient environment. Results showed that the coefficient of friction and the formation of transfer layer depend on the grinding marks direction and inclination angle of the hard surfaces. For a given inclination angle, under both dry and lubricated conditions, the coefficient of friction and transfer layer formation were found to be greater when the pins slid perpendicular to the unidirectional grinding marks than when the pins slid parallel to the grinding marks. In addition, a stick-slip phenomenon was observed under lubricated conditions at the highest inclination angle for sliding perpendicular to the grinding marks direction. This phenomenon could be attributed to the extent of plane strain conditions taking place at the asperity level during sliding. DOI: 10.1115/1.4002604]

Solar pond technology

Solar pond technology has made substantial progress in the last fifteen years. This paper reviews the basic principles of solar ponds and the problems encountered in their operation and maintenance. The factors which influence the technical and economic viability of solar ponds for thermal applications and power generation have been discussed.