Universal bounds on the electrical and elastic response of two-phase bodies and their application to bounding the volume fraction from boundary measurements

Universal bounds on the electrical and elastic response of two-phase (and multiphase) ellipsoidal or parallelopipedic bodies have been obtained by Nemat-Nasser and Hori. Here we show how their bounds can be improved and extended to bodies of arbitrary shape. Although our analysis is for two-phase bodies with isotropic phases it can easily be extended to multiphase bodies with anisotropic constituents. Our two-phase bounds can be used in an inverse fashion to bound the volume fractions occupied by the phases, and for electrical conductivity reduce to those of Capdeboscq and Vogelius when the volume fraction is asymptotically small. Other volume fraction bounds derived here utilize information obtained from thermal, magnetic, dielectric or elastic responses. One bound on the volume fraction can be obtained by simply immersing the body in a water filled cylinder with a piston at one end and measuring the change in water pressure when the piston is displaced by a known small amount. This bound may be particularly effective for estimating the volume of cavities in a body. We also obtain new bounds utilizing just one pair of (voltage, flux) electrical measurements at the boundary of the body.Comment: 5 figures, 27 page

Euler, Jacobi, and Missions to Comets and Asteroids

Whenever a freely spinning body is found in a complex rotational state, this means that either the body is a recent victim of an impact or a tidal interaction, or is a fragment of a recently disrupted progenitor. Another factor (relevant for comets) is outgassing. Due to impacts, tidal forces and outgassing, the asteroidal and cometary precession must be a generic phenomenon: while some rotators are in the state of visible tumbling, a much larger amount of objects must be performing narrow-cone precession not so easily observable from the Earth. The internal dissipation in a freely precessing top leads to relaxation (gradual damping of the precession) and sometimes to spontaneous changes in the rotation axis. Recently developed theory of dissipative precession of a rigid body reveals that this is a highly nonlinear process: while the body is precessing at an angular rate $\omega$, the precession-caused stresses and strains in the body contain components oscillating at other frequencies. Dependent upon the spin state, those frequencies may be higher or, most remarkably, lower than the precession rate. In many states dissipation at the harmonics is comparable to or even exceeds that at the principal frequency. For this and other reasons, in many spin states the damping of asteroidal and cometary wobble happens faster, by several orders, than believed previously. This makes it possible to measure the precession-damping rate. The narrowing of the precession cone through the period of about a year can be registered by the currently available spacecraft-based observational means. However, in the near-separatrix spin states a precessing rotator can considerably slow down its relaxation.Comment: 21 pages, 1 figur

Forecasting Stock Exchange Data using Group Method of Data Handling Neural Network Approach

The increasing uncertainty of the natural world has motivated computer scientists to seek out the best approach to technological problems. Nature-inspired problem-solving approaches include meta-heuristic methods that are focused on evolutionary computation and swarm intelligence. One of these problems significantly impacting information is forecasting exchange index, which is a serious concern with the growth and decline of stock as there are many reports on loss of financial resources or profitability. When the exchange includes an extensive set of diverse stock, particular concepts and mechanisms for physical security, network security, encryption, and permissions should guarantee and predict its future needs. This study aimed to show it is efficient to use the group method of data handling (GMDH)-type neural networks and their application for the classification of numerical results. Such modeling serves to display the precision of GMDH-type neural networks. Following the US withdrawal from the Joint Comprehensive Plan of Action in April 2018, the behavior of the stock exchange data stream and commend algorithms has not been able to predict correctly and fit in the network satisfactorily. This paper demonstrated that Group Method Data Handling is most likely to improve inductive self-organizing approaches for addressing realistic severe problems such as the Iranian financial market crisis. A new trajectory would be used to verify the consistency of the obtained equations hence the models' validity