This research examines the effect of undergraduate course letter grades on future course selection and major choice. Using a Regression-Discontinuity design, we exploit the fact that the probability of earning a particular letter grade jumps discontinuously around letter grade cutoffs. This variation in letter grades allows us to isolate the impact of letter grades on major choice and course se...

This paper discusses a new family of sixth-order continuously imbedded Runge-Kutta-Sarafyan methods and a mathematical software package DKLAG6 for the numerical solution of systems of functional differential equations with state-dependent delays. The methods used are based on piecewise polynomial approximants which are used for error estimation and stepsize selection, to handle the necessary in...

In this paper, periodic motions in a periodically excited, Duffing oscillator with a time-delayed displacement are investigated through the Fourier series, and the stability and bifurcation of such periodic motions are discussed through eigenvalue analysis. The time-delayed displacement is from the feedback control of displacement. The analytical bifurcation trees of period-1 motions to chaos i...

A numerical solution is given to the problem of a weak R type ionization front approaching a contact discontinuity across which the density increases. During the interaction it is found that there are three possible configurations produced; the weak-R type ionization front becomes (a) weak-R type but slower for QI/QO < 1.15, (b) strong-D type for 1.15 < QI/QO < 3.4 or (c) weak-D type for QI/QO ...

In recent years the threshold of black hole formation in spherically symmetric gravitational collapse has been studied for a variety of matter models. In this paper the corresponding issue is investigated for a matter model significantly different from those considered so far in this context. We study the transition from dispersion to black hole formation in the collapse of collisionless matter...

Using Stroh's formalism and conformal mapping, Green's functions are obtained in closed-form for an in®nite thermopiezoelectric plate with an elliptic hole induced by temperature discontinuity. The Green's function satis®es freetraction-charge as well as thermal-insulated conditions along the hole boundary. Based on the Green's function, a system of singular integral equations for the unknown t...

Recently, a novel multi-scale modelling approach for damage and fracture problems was presented. This method departs from classical computational homogenization (FE) and evolves to a discontinuity enriched scheme upon the localization detection. Rotating boundary conditions allow for microscale localization bands to develop. The formulation of the macroscopic cohesive discontinuity enables the ...

Several techniques exist for index reduction and consistent initialization of higher index DAEs. Many such techniques change the original set of equations by differentiation, substitution, and/or introduction of new variables. This paper introduces substitute equations as a new language element. By means of a substitute equation, the value of a continuous variable or its time derivative is spec...

In the present paper, the numerical calculation of transonic equilibria, first introduced with the FLOW code in Guazzotto et al. [Phys. Plasmas 11, 604 (2004)], is critically reviewed. In particular, the necessity and effect of imposing explicit jump conditions at the transonic discontinuity are investigated. It is found that “standard” (low-b, large aspect ratio) transonic equilibria satisfy t...

This paper describes a new method for computing the stability of nonsmooth periodic orbits of piecewise-smooth dynamical systems with delay. Stability computations for piecewise-smooth dynamical systems without delay have previously been performed using discontinuity mappings to ‘correct’ the linearized periodmap. However, this approach is less convenient for systems with delays due to the infi...