Courant Institute of Mathematical Sciences

About: Courant Institute of Mathematical Sciences is a education organization based out in New York, New York, United States. It is known for research contribution in the topics: Nonlinear system & Boundary value problem. The organization has 2414 authors who have published 7759 publications receiving 439773 citations. The organization is also known as: CIMS & New York University Department of Mathematics.

Computer Simulation of the Time Evolution of a Quenched Model Alloy in the Nucleation Region

Abstract: The time evolution of the structure function and of the cluster (or grain) distribution following quenching in a model binary alloy with a small concentration of minority atoms is obtained from computer simulations. The structure function $\overline{S}(k,t)$ obeys a simple scaling relation, $\overline{S}(k,t)={K}^{\ensuremath{-}3}F(\frac{k}{K})$ with $K(t)\ensuremath{\propto}{t}^{\ensuremath{-}a}$, $a\ensuremath{\cong}0.25$, during the latter and larger part of the evolution. During the same period, the mean cluster size grows approximately linearly with time.

Modern potentials and the properties of condensed /sup 4/He

Abstract: The Green's-function Monte Carlo method has been used to calculate the properties of the ground-state $^{4}\mathrm{He}$ with several modern potentials. One potential, dubbed HFDHE2, by Aziz et al., gave very good agreement with the experimental equation of state in both the liquid and crystal phases. Other properties such as the structure factor and the momentum distribution also compare well with the experiment. In both phases, perturbative estimates of the three-body Axilrod-Teller potential were computed. When they are added to the two-body energies, the total energy is no longer in agreement with experiment. Further investigation on the nature of three-body interactions in the $^{4}\mathrm{He}$ may be necessary to elucidate this problem.

On a variational formula for the principal eigenvalue for operators with maximum principle

Abstract: In this paper a variational formula is obtained for the principal eigenvalue for operators with maximum principle. This variational formula does not require the operators to be self-adjoint. But if they are self-adjoint this formula reduces to the classical Rayleigh-Ritz formula.

Free oscillations in a climate model with ice-sheet dynamics

Abstract: A study of stable periodic solutions to a simple nonlinear model of the ocean-atmosphere-ice system is presented. The model has two dependent variables: ocean-atmosphere temperature and latitudinal extent of the ice cover. No explicit dependence on latitude is considered in the model. Hence all variables depend only on time and the model consists of a coupled set of nonlinear ordinary differential equations. The globally averaged ocean-atmosphere temperature in the model is governed by the radiation balance. The reflectivity to incoming solar radiation, i.e., the planetary albedo, includes separate contributions from sea ice and from continental ice sheets. The major physical mechanisms active in the model are (1) albedo-temperature feedback, (2) continental ice-sheet dynamics and (3) precipitation-rate variations. The model has three-equilibrium solutions, two of which are linearly unstable, while one is linearly stable. For some choices of parameters, the stability picture changes and sustained, finite-amplitude oscillations obtain around the previously stable equilibrium solution. The physical interpretation of these oscillations points to the possibility of internal mechanisms playing a role in glaciation cycles.