Equations of structural relaxation

In the mode coupling theory of the liquid to glass transition the long time structural relaxation follows from equations solely determined by equilibrium structural parameters. The present extension of these structural relaxation equations to arbitrarily short times on the one hand allows calculations unaffected by model assumptions about the microscopic dynamics and on the other hand supplies new starting points for analytical studies. As a first application, power-law like structural relaxation at a glass-transition singularity is explicitly proven for a special schematic MCT model.Comment: 11 pages, 3 figures; talk given at the Seventh international Workshop on disordered Systems, Molveno, Italy, March 199

Model atmospheres of sub-stellar mass objects

We present an outline of basic assumptions and governing structural equations describing atmospheres of substellar mass objects, in particular the extrasolar giant planets and brown dwarfs. Although most of the presentation of the physical and numerical background is generic, details of the implementation pertain mostly to the code CoolTlusty. We also present a review of numerical approaches and computer codes devised to solve the structural equations, and make a critical evaluation of their efficiency and accuracy.Comment: 31 pages, 10 figure

Autocrat of the Armchair

Structural analysis is a standard tool to identify submodels that can be used to design model based diagnostic tests. Structural approaches typically operate on models described by a set of equations. This work extends such methods to be able to handle models with constraints, e.g. inequality constraints on state variables. The objective is to improve isolability properties of a diagnosis system by extending the class of redundancy relations. An algorithm is developed that identifies which are the constraints and equations that can be used together to derive a new test that can not be found using previous approachesCADIC

Self-duality equations for spherically symmetric SU(2) gauge fields

A model of spherically symmetric SU(2) gauge theory is considered. The self-duality equations are written and it is shown that they are compatible with the Einstein-Yang-Mills equations. It is proven that this property is true for any gauge theory with curved base space-time and having a compact Lie group as structural group.Comment: 8 page

The Use of General Purpose Computer Programs to Derive Equations of Motion for Optimal Isolation Studies

Techniques were developed that utilize general purpose structural analysis computer programs to generate the equations of motion necessary for limiting performance studies. The methodology necessary to couple available general purpose finite element structural programs to a limiting performance capability was developed. Primary emphasis was given to the use of the general purpose program to develop equations of motion in a form that can be used by the limiting performance program

Conditions for the existence of control functions in nonseparable simultaneous equations models

The control function approach (Heckman and Robb (1985)) in a system of linear simultaneous equations provides a convenient procedure to estimate one of the functions in the system using reduced form residuals from the other functions as additional regressors. The conditions on the structural system under which this procedure can be used in nonlinear and nonparametric simultaneous equations has thus far been unknown. In this note, we define a new property of functions called control function separability and show it provides a complete characterization of the structural systems of simultaneous equations in which the control function procedure is valid.

Conditional inference for possibly unidentified structural equations

The possibility that a structural equation may not be identified casts doubt on the measures of estimator precision that are normally used. We argue that the observed identifiability test statistic is directly relevant to the precision with which the structural parameters can be estimated, and hence argue that inference in such models should be conditioned on the observed value of that statistic (or statistics). We examine in detail the effects of conditioning on the properties of the ordinary least squares (OLS) and two-stage least squares (TSLS) estimators for the coefficients of the endogenous variables in a single structural equation. We show that: (a) conditioning has very little impact on the properties of the OLS estimator, but a substantial impact on those of the TSLS estimator; (b) the conditional variance of the TSLS estimator can be very much larger than its unconditional variance (when the identifiability statistic is small), or very much smaller (when the identifiability statistic is large); and (c) conditional mean-square-error comparisons of the two estimators favour the OLS estimator when the sample evidence only weakly supports the identifiablity hypothesis, can favour TSLS slightly when that evidence is moderately favourable, but there is nothing to choose between the two estimators when the data strongly supports the identification hypothesis