Perturbation due to a Circumbinary Disc around L4,5 in the Photogravitational Elliptic Restricted Three-Body Problem

The motion is investigated of dust/gas particles in the elliptic restricted three-body problem (ER3BP) in which the less massive primary is an oblate spheroid and the more massive a luminous body surrounded by a circumbinary disk. The paper has investigated both analytically and numerically the effects of oblateness and radiation pressure of the primaries respectively together with the gravitational potential from a disk on the triangular equilibrium L4,5 of the system, all in the elliptic framework of the restricted problem of three bodies. The important result obtained therein is a move towards the line joining the primaries in the presence of any /all perturbation(s). A significant shift away from the origin as the radiation pressure factor decreases and oblateness of the smaller primary increase is also observed. It is also seen that, all aforementioned parameters in the region of stability have destabilizing tendencies resulting in a decrease in the size of the region of stability except the gravitational potential from the disc. The binary system Ruchbah in the constellation Cassiopeiae is an excellent model for the problem, using the analytic results obtained, the locations of the triangular points and the critical mass parameter are computed numerically.

A THREE-STEP INTERPOLATION TECHNIQUE WITH PERTURBATION TERM FOR DIRECT SOLUTION OF THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we developed a new three-step method for numerical solution of third order ordinary differential equations. Interpolation and collocation methods were used by choosing interpolation points at steps points using power series, while collocation points at step points, using a combination of powers series and perturbation terms gotten from the Legendre polynomials, giving rise to a polynomial of degree and equations. All the analysis on the method derived shows that it is zero-stable, convergent and the region of stability is absolutely stable. Numerical examples were provided to test the performance of the method. Results obtained when compared with existing methods in the literature, shows that the method is accurate and efficient

Approximation of the Step-to-Step Dynamics Enables Computationally Efficient and Fast Optimal Control of Legged Robots

Legged robots with point or small feet are nearly impossible to control instantaneously but are controllable over the time scale of one or more steps, also known as step-to-step control. Previous approaches achieve step-to-step control using optimization by (1) using the exact model obtained by integrating the equations of motion, or (2) using a linear approximation of the step-to-step dynamics. The former provides a large region of stability at the expense of a high computational cost while the latter is computationally cheap but offers limited region of stability. Our method combines the advantages of both. First, we generate input/output data by simulating a single step. Second, the input/output data is curve fitted using a regression model to get a closed-form approximation of the step-to-step dynamics. We do this model identification offline. Next, we use the regression model for online optimal control. Here, using the spring-load inverted pendulum model of hopping, we show that both parametric (polynomial and neural network) and non-parametric (gaussian process regression) approximations can adequately model the step-to-step dynamics. We then show this approach can stabilize a wide range of initial conditions fast enough to enable real-time control. Our results suggest that closed-form approximation of the step-to-step dynamics provides a simple accurate model for fast optimal control of legged robots.

Extensive Numerical Results for Integrable Case of Standard Map

In recent years, conservative dynamical systems have become a vivid area of research from the statistical mechanical characterization viewpoint. With this respect, several areapreserving maps have been studied. It has been numerically shown that the probability distribution of the sum of the suitable random variable of these systems can be well approximated by a Gaussian (q-Gaussian) when the initial conditions are randomly selected from the chaotic sea (region of stability islands) in the available phase space. In this study, we will summarize these results and discuss a special case for the standard map, a paradigmatic example of area-preserving maps, for which the map is totally integrable.

Statistical modeling with neural nets: nuclear masses and halflives

Multilayer feedforward neural networks are used to create global models of atomic masses and lifetimes of nuclear states, with the goal of effective prediction of the properties of nuclides outside the region of stability. Innovations in coding and training schemes are used to improve the extrapolation capability of models of the mass table. Studies of nuclear lifetimes have focused on ground states that decay 100% via the β- mode. Results are described which demonstrate that in predictive acuity, statistical approaches to global modeling based on neural networks are potentially competitive with the best phenomenological models based on the traditional methods of theoretical physics.

Pressure-Induced Polymorphism of Caprolactam: A Neutron Diffraction Study

Caprolactam, a precursor to nylon-6 has been investigated as part of our studies into the polymerization of materials at high pressure. Single-crystal X-ray and neutron powder diffraction data have been used to explore the high-pressure phase behavior of caprolactam; two new high pressure solid forms were observed. The transition between each of the forms requires a substantial rearrangement of the molecules and we observe that the kinetic barrier to the conversion can aid retention of phases beyond their region of stability. Form II of caprolactam shows a small pressure region of stability between 0.5 GPa and 0.9 GPa with Form III being stable from 0.9 GPa to 5.4 GPa. The two high-pressure forms have a catemeric hydrogen-bonding pattern compared with the dimer interaction observed in ambient pressure Form I. The interaction between the chains has a marked effect on the directions of maximal compressibility in the structure. Neither of the high-pressure forms can be recovered to ambient pressure and there is no evidence of any polymerization occurring.

Formation parameters of high-pressure minerals in the Dhofar 717 AND 864 chondrite meteorites

This paper presents the results of a Raman spectroscopic study of shock melt veins in L6 chondritic meteorites Dhofar 717 and 864, and conclusions about the PT-parameters recorded in these meteorites after the impact event. The primary minerals of the host chondrite include olivine, orthopyroxene, clinopyroxene, plagioclase, chromite, phosphates, troilite, and kamasite. Shock melt veins up to 1 cm thick contain fragments of the high- pressure minerals ringwoodite, wadsleyite, majorite, akimotoite, jadeite, lingunite, and tuite and quenched melt consisting of majorite, ringwoodite, troilite, and kamasite. The mineral associations of the Dhofar 717 and 864 chondrites indicate high peak PT-parameters of the impact in the region of stability of majorite (>20 GPa and >2500 K) and bridgmanite (>25 GPa and >2500 K). The presence of lingunite also directly indicates a peak pressure in the area of stability of the bridgmanite.

Effect of Thermal Ageing on the Impact and Flexural Damage Behaviour of Carbon Fibre-Reinforced Epoxy Laminates

Most of the composite materials that are used in aerospace structures have been manufactured using a thermostable matrix, as epoxy resin. The region of stability of these polymers is defined by the glass transition temperature (Tg). However, operating temperatures close and above the Tg can cause a variation in the properties of the polymer and consequently, modify the mechanical properties of the composite material. Therefore, it is necessary to understand the failure mechanisms that occur in the material in order to ensure stability and durability. The effect of temperature and time of exposure on the impact and flexural mechanical responses of carbon/epoxy composites are studied in this work. For that purpose, ageing treatments at temperatures below and above the Tg have been considered and then, impact and flexural tests have been performed. It was observed that thermal ageing cause two different effects: at temperatures below the Tg, there is an increase of the maximum strength because of a post-curing effect; however, the mechanical properties decrease at higher temperatures of thermal ageing due to the thermo-oxidation of the epoxy resin and the loss of adhesion in the matrix/fibre interface.

Analytical and numerical approach to defining the stability region of a dynamical system

The paper presents two different approaches to estimating the region of stability of differential equation. Estimation of the region of stability is an essential practice in relation to control of the dynamical system. In this paper the objects of examination are differential equations with quasi-derivation. The equations have features that do not allow the application of classical methods for establishing stability. The goal is to compare the results of an analytic approach using Lyapunov method and computer simulation using a numerical method. The brief description of both methods are introduced and graphical results are presented and compared

FIFTH-ORDER EVOLUTION EQUATION OF GRAVITY–CAPILLARY WAVES

We extend the evolution equation for weak nonlinear gravity–capillary waves by including fifth-order nonlinear terms. Stability properties of a uniform Stokes gravity–capillary wave train is studied using the evolution equation obtained here. The region of stability in the perturbed wave-number plane determined by the fifth-order evolution equation is compared with that determined by third- and fourth-order evolution equations. We find that if the wave number of longitudinal perturbations exceeds a certain critical value, a uniform gravity–capillary wave train becomes unstable. This critical value increases as the wave steepness increases.