The three dimensional motion and stability of a rotating space station: Cable-counterweight configuration

The three dimensional equations of motion for a cable connected space station--counterweight system are developed using a Lagrangian formulation. The system model employed allows for cable and end body damping and restoring effects. The equations are then linearized about the equilibrium motion and nondimensionalized. To first degree, the out-of-plane equations uncouple from the inplane equations. Therefore, the characteristic polynomials for the in-plane and out-of-plane equations are developed and treated separately. From the general in-plane characteristic equation, necessary conditions for stability are obtained. The Routh-Hurwitz necessary and sufficient conditions for stability are derived for the general out-of-plane characteristic equation. Special cases of the in-plane and out-of-plane equations (such as identical end masses, and when the cable is attached to the centers of mass of the two end bodies) are then examined for stability criteria

Matter waves in a gravitational field: An index of refraction for massive particles in general relativity

We consider the propagation of massive-particle de Broglie waves in a static, isotropic metric in general relativity. We demonstrate the existence of an index of refraction that governs the waves and that has all the properties of a classical index of refraction. We confirm our interpretation with a WKB solution of the general-relativistic Klein-Gordon equation. Finally, we make some observations on the significance of the optical action.Comment: 20 pages, latex, ps and pdf. To appear in Am.J.Phys September, 200

Task Persistence: A Potential Mediator of the Income-Achievement Gap

Background: The pervasive gap in achievement among impoverished children has been investigated primarily in terms of parental investments, specifically parent to child speech and other forms of cognitive stimulation (e.g., toys, print materials). This research extends that literature by considering the role of a non-cognitive factor, namely task persistence, in the income-achievement gap. Using task persistence as the hypothesized mediator, duration of childhood in poverty is used to predict two educational variables - perceived academic competence and educational attainment. Although bivariate relationships between each of the variables have been demonstrated in past research, a full model linking task persistence with the income-achievement gap has not been investigated thus far. Methods: Using multiple waves of longitudinal data, duration of childhood poverty (ages 0-9) is used to predict both perceived academic competence (age 17) and educational attainment (age 23) with task persistence (average of ages 9, 13, 17) as a mediator. Results: With task persistence included in each model, the relationships between duration of childhood in poverty and both perceived academic competence and educational attainment are significantly reduced, confirming a mediational influence of task persistence. Conclusions: As hypothesized, task persistence statistically mediates the relationship between duration of childhood in poverty and educational outcomes. The implications of these findings on school success and intergenerational poverty are addressed, as well as suggestions for future research

The structure and composition of exhumed faults, and their implications for seismic processes

Field studies of faults exhumed from seismogenic depths provide useful data to constrain seismologic models of fault zone processes and properties. Data collected on the San Andreas Fault in the San Gabriel Mountains has shown that large-displacement faults consist of one to several very narrow slip zones embedded in a cataclastically deformed sheared region several meters thick. However these faults have not been buried to depths greater than 5 km. Fault zones in the Sierra Nevada, California allow us to study the microstructures resulting from the deformation mechanisms active at seismogenic depths. Syn-fault mineralization shows that these left-lateral strike-slip faults formed at 5-12 km depth. Detailed microstructural analyses of the small faults reveal that they evolved from cooling joints filled by chlorite, epidote and quartz. These joints were then reactivated to form shear faults with accompanying brittle fracture and cataclastic deformation, ultimately developing very fined-grained cataclasites and ultracataclasites. The shear-induced microstructures are developed on faults with as little as several mm of slip showing that narrow slip-surfaces develop early in the lifetime of these faults. Subsequent slip has little effect on the microstructures. The inferred similarity of deformation mechanisms in faults 10 m to 10 km long indicates that basic slip processes on the faults are scale invariant, and may be a cause for the inferred constant b-value for small earthquakes. Analysis of map-scale fault linkages and terminations indicate that linkage zones are up to 400 m wide and 1 km long, and consist of altered and fractured rocks with numerous through-going slip surfaces. Terminations are regions of numerous splay faults that have cumulative offsets approaching those of the main faults. The slip distribution and structure of the terminations and linkage zones suggest that seismic slip may propagate into these zones of enhanced toughness, and that through-going slip can occur when a sufficient linkage of faults in the zone allow slip to be transmitted

Construction of the factorized steady state distribution in models of mass transport

For a class of one-dimensional mass transport models we present a simple and direct test on the chipping functions, which define the probabilities for mass to be transferred to neighbouring sites, to determine whether the stationary distribution is factorized. In cases where the answer is affirmative, we provide an explicit method for constructing the single-site weight function. As an illustration of the power of this approach, previously known results on the Zero-range process and Asymmetric random average process are recovered in a few lines. We also construct new models, namely a generalized Zero-range process and a binomial chipping model, which have factorized steady states.Comment: 6 pages, no figure

Planetary and Light Motions From Newtoinian Theory: An Amusing Exercise

We attempt to see how closely we can formally obtain the planetary and light path equations of General Relativity by employing certain operations on the familiar Newtonian equation. This article is intended neither as an alternative to nor as a tool for grasping Einstein's General Relativity. Though the exercise is understandable by readers at large, it is especially recommended to the teachers of Relativity for an appreciative understanding of its peculiarity as well as its pedagogical value in the teaching of differential equations.Comment: 7 page

Factorised Steady States in Mass Transport Models on an Arbitrary Graph

We study a general mass transport model on an arbitrary graph consisting of $L$ nodes each carrying a continuous mass. The graph also has a set of directed links between pairs of nodes through which a stochastic portion of mass, chosen from a site-dependent distribution, is transported between the nodes at each time step. The dynamics conserves the total mass and the system eventually reaches a steady state. This general model includes as special cases various previously studied models such as the Zero-range process and the Asymmetric random average process. We derive a general condition on the stochastic mass transport rules, valid for arbitrary graph and for both parallel and random sequential dynamics, that is sufficient to guarantee that the steady state is factorisable. We demonstrate how this condition can be achieved in several examples. We show that our generalized result contains as a special case the recent results derived by Greenblatt and Lebowitz for $d$-dimensional hypercubic lattices with random sequential dynamics.Comment: 17 pages 1 figur