Estimation of Kalman filter model parameters from an ensemble of tests

A methodology for estimating initial mean and covariance parameters in a Kalman filter model from an ensemble of nonidentical tests is presented. In addition, the problem of estimating time constants and process noise levels is addressed. Practical problems such as developing and validating inertial instrument error models from laboratory test data or developing error models of individual phases of a test are generally considered

Convex Functions and Spacetime Geometry

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial data set $(\Sigma, h_{ij}, K_{ij})$ admitting a suitably defined convex function. We show how the existence of a convex function on a spacetime places restrictions on the properties of the spacetime geometry.Comment: 26 pages, latex, 7 figures, improved version. some claims removed, references adde

Pion double charge exchange on 4He

The doubly differential cross sections for the $^4$He$(\pi^+,\pi^-) 4p$ reaction were calculated using both a two-nucleon sequential single charge exchange model and an intranuclear cascade code. Final state interactions between the two final protons which were the initial neutrons were included in both methods. At incident pion energies of 240 and 270 MeV the low-energy peak observed experimentally in the energy spectrum of the final pions can be understood only if the contribution of pion production is included. The calculated cross sections are compared with data.Comment: 25 pages, 9 figure

Generalized Phase Rules

For a multi-component system, general formulas are derived for the dimension of a coexisting region in the phase diagram in various state spaces.Comment: In the revised manuscript, physical meanings of D's are explained by adding three figures. 10 pages, 3 figure

Low-energy Antiproton Interaction with Helium

An ab initio potential for the interaction of the neutral helium atom with antiprotons and protons is calculated using the Born-Oppenheimer approximation. Using this potential, the annihilation cross section for antiprotons in the energy range 0.01 microvolt to 1 eV is calculated.Comment: 13 pages, 7 figures, LaTe

Grand potential in thermodynamics of solid bodies and surfaces

Using the chemical potential of a solid in a dissolved state or the corresponding component of the chemical potential tensor at equilibrium with the solution, a new concept of grand thermodynamic potential for solids has been suggested. This allows generalizing the definition of Gibbs' quantity $\sigma$ (surface work often called the solid-fluid interfacial free energy) at a planar surface as an excess grand thermodynamic potential per unit surface area that (1) does not depend on the dividing surface location and (2) is common for fluids and solids.Comment: 6 page

Performance Analysis of the Spaceborne Laser Ranging System

The 'spaceborne laser ranging system' is a proposed short pulse laser on board an orbiting spacecraft. It measures the distances between the spacecraft and many laser retroreflectors (targets) deployed on the earth's surface. The precision of these range measurements was assumed to be about plus or minus 2 cm. These measurements were then used together with the orbital dynamics of the spacecraft to derive the intersite vector between the laser ground targets. The errors associated with this vector were on the order of 1 to 2 cm. The baseline distances determined range from 25 km to 1200 km. By repeating the measurements of the intersite vector, strain and strain rate errors were estimated. The realizable precision for intersite distance determination was estimated to be on the order of 0.5 cm at 300 km and about 1.5 cm at 1200 km. The corresponding inaccuracies for the intersite distances were larger, than is 1 cm and 3.5 cm respectively. The corresponding precision in the vertical direction was 1 cm and 3 cm

Wall-liquid and wall-crystal interfacial free energies via thermodynamic integration: A molecular dynamics simulation study

A method is proposed to compute the interfacial free energy of a Lennard-Jones system in contact with a structured wall by molecular dynamics simulation. Both the bulk liquid and bulk face-centered-cubic crystal phase along the (111) orientation are considered. Our approach is based on a thermodynamic integration scheme where first the bulk Lennard-Jones system is reversibly transformed to a state where it interacts with a structureless flat wall. In a second step, the flat structureless wall is reversibly transformed into an atomistic wall with crystalline structure. The dependence of the interfacial free energy on various parameters such as the wall potential, the density and orientation of the wall is investigated. The conditions are indicated under which a Lennard-Jones crystal partially wets a flat wall.Comment: 15 pages, 11 figure

Exact Solution of the Infinite-Range Quantum Mattis Model

We have solved the quantum version of the Mattis model with infinite-range interactions. A variational approach gives the exact solution for the infinite-range system, in spite of the non-commutative nature of the quantum spin components; this implies that quantum effects are not predominant in determining the macroscopic properties of the system. Nevertheless, the model has a surprisingly rich phase behaviour, exhibiting phase diagrams with tricritical, three-phase and critical end points.Comment: 14 pages, 11 figure

It's OK not to be OK: Shared Reflections from two PhD Parents in a Time of Pandemic

Adopting an intersectional feminist lens, we explore our identities as single and co‐parents thrust into the new reality of the UK COVID‐19 lockdown. As two PhD students, we present shared reflections on our intersectional and divergent experiences of parenting and our attempts to protect our work and families during a pandemic. We reflect on the social constructions of ‘masculinities’ and ‘emphasized femininities’ as complicated influence on our roles as parents. Finally, we highlight the importance of time and self‐care as ways of managing our shared realities during this uncertain period. Through sharing reflections, we became closer friends in mutual appreciation and solidarity as we learned about each other’s struggles and vulnerabilities