Isothermal systems of geodesics

Hamiltonian Geodesics in Nonholonomic Differential Systems

Let a smooth manifold M be equipped with a smoothly varying positive definite quadratic form on a distribution-subbundle V of the tangent bundle TM. One assumes that V is completely nonintegrable, equivalently all sections of V together with all brackets between them generate TM at each point of M. Then by the well-known theorem of Rashevski-Chow [3] it is possible to connect any two points (in...

The Isothermal Remanence of Fine Particle Systems

A numerical model based upon the "Stoner-Wohlfarth theory" has been developed to predict Isothermal Remanent Magnetisation (IRM) curves for a system of fine particles with uniaxial anisotropy. This paper reports the predictions of our model for the effects of easy axes alignment on the IRM curve. We have also investigated the effect of the standard deviation after the application of a non-satur...

Modulated Dsc Evaluation of Isothermal Cure & Vitrification for Thermosetting Systems

Geodesics of learned representations

We develop a new method for visualizing and refining the invariances of learned representations. Given two reference images (typically, differing by some transformation), we synthesize a sequence of images lying on a path between them that is of minimal length in the space of a representation (a “representational geodesic”). If the transformation relating the two reference images is an invarian...

Isothermal and Non-isothermal Methods

a comparison was made between the experimental non-isothermal a vs. t curves and those calculated on the basis of a previous isothermal study. It was observed that for low heating rates, when the "thermal lag" is negligible, the dynamic measurements are in good agreement with the isothermal ones. Furthermore, for process (I), two mathematical methods proposed for the interpretation of the non-i...