Matt Insall

Attraction and Repulsion of Nucleons: Sources of Stellar Energy

The potential energy of a nuclide is enhanced by about 10 MeV per nucleon from the repulsion between like nucleons, and diminished by about 20 MeV per nucleon from the attraction between unlike nucleons. Nuclear stability results mostly from the interplay of these opposing forces, plus Coulomb repulsion of positive charges. Whereas fusion may be the primary mechanism by which first generation stars produce energy, repulsion between like nucleons may cause neutron emission from the collapsed core (neutron star) produced in a terminal supernova explosion and initiate luminosity in second generation stars that accrete on such objects. As noted earlier [1], the scarcity of solar neutrinos, the enrichment of light isotopes in the solar wind, and the presence of abundant short-lived nuclides and interlinked chemical and isotopic heterogeneities in the early solar system might also be explained if the Sun formed in this manner.

Constructing an Interval Temporal Logic for Real-Time System

Abstract This paper presents a modal logic, Interval Temporal Logic, built upon a classical predicate logic L. In the logic system, we consider formulas that can be used to reason about timing properties of systems, in particular, interval formulas and responsiveness assertions. These formulas can be used to describe timing constraints of a system. Hence they can be used to ensure satisfaction of system behavior provided that they are not violated at run-time. A decision procedure is presented to evaluate these formulas. A railroad crossing example is used to illustrate run-time evaluation of interval formulas and responsiveness assertions.

Mathematical analysis of the complete iterative inversion method — I

A gas composed of identical isotropic molecules has a potential energy of interaction between pairs of particles that depends only on their separation distance. The pair potential is encoded in the virial coefficients of the virial equation of state for a gas.The complete iterative inversion method is a technique employed in an attempt to recover the pair potential from the second virial coefficient. Implicit in the complete iterative inversion method is the requirement that various mathematical expressions are meaningful: improper integrals converge, derivatives exist, etc.We provide a mathematical framework in which all these implicit assumptions are valid. We show that the complete iterative inversion method cannot recover the pair potential even if the target potential and the initial estimate are infinitely differentiable.

Some finiteness conditions in lattices—using nonstandard proof methods

We discuss the application of nonstandard methods to local versions of certain lattice notions. In a particular case, we find that imposition of certain local conditions imply a surprising global one, namely boundedness of the given lattice.

Thermal Stress Effect on Fracture Integrity in Enhanced Geothermal Systems

In an enhanced geothermal system (EGS), fluid is injected into pre-existing fractures to be heated up and then pumped out for the electricity generation; injected fluid is cold as compared to surrounding bedrock. The rock-fluid temperature difference induces thermal stress along the fracture wall, and the large thermal stress could damage some of the self-propping asperities and result in a change of the topography and lifespan of the fractures. Although fracture sustainability has been extensively studied, the mechanism of asperity damage due to rock-fluid temperature difference remains unknown. We have constructed a finite-element based three-dimensional model, which uses a hemisphere contact pair to resemble a single self-propping asperity, to investigate the effect of temperature difference on the asperity damage. In the model, the rock mechanical properties are coupled with temperature and stress state of the bedrock. Two trends of asperity deformation with temperature effect are identified: opening zone and closure zone. Closure squeezes asperity further and induces more element damage at bottom. Higher temperature difference damages elements on asperity top whereas has negligible impact on elements at asperity bottom. In other aspect, a higher temperature expands closure zone and degrades elements at the asperity bottom. Accordingly, two potential mechanisms of asperity damage are qualitatively characterized.

General and End Compactifications

The intuitive notion of forming a compactification of a topological space is to “attach” new points to a space to “compactify” it. We use equivalence relations on the remote points of an enlargement of a given topological space to produce the new points. Thus, nonstandard methods are shown to unify the various extant approaches to compactification.

Hyperalgebraic primitive elements for relational algebraic and topological algebraic models

Using nonstandard methods, we generalize the notion of an algebraic primitive element to that of an hyperalgebraic primitive element, and show that under mild restrictions, such elements can be found infinitesimally close to any given element of a topological field.

Point-Valued Mappings of Sets

Let X be a metric space and let CB(X) denote the closed bounded subsets of X with the Hausdorff metric. Given a complete subspace Y of CB(X), two fixed point theorems, analogues of results in [1], are proved, and examples are given to suggest their applicability in practice.

Conjugating polynomials on finite rings

Recall that a function f : R ~ R is a coniueate of a function h : R ~ R if and only if there exists a bijection g : R ~ R such that f = g-1 *h*g . Conjugation is of fundamental importance in topological and differentiable dynamics, and in the case that the ring R is a field, the relationships to dynamics have been studied before by Vivaldi and others (el. IV]). In fact, in this case, the solution of problem 1 is an immediate consequence of Lagrange Interpolation: