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.

Anomalous hydrodynamic drafting of interacting flapping flags.

Abstract: In aggregates of objects moving through a fluid, bodies downstream of a leader generally experience reduced drag force. This conventional drafting holds for objects of fixed shape, but interactions of deformable bodies in a flow are poorly understood, as in schools of fish. In our experiments on "schooling" flapping flags, we find that it is the leader of a group who enjoys a significant drag reduction (of up to 50%), while the downstream flag suffers a drag increase. This counterintuitive inverted drag relationship is rationalized by dissecting the mutual influence of shape and flow in determining drag. Inverted drafting has never been observed with rigid bodies, apparently due to the inability to deform in response to the altered flow field of neighbors.

Homogenization of elliptic systems with Neumann boundary conditions

Abstract: The main purpose of this work is to study uniform regularity estimates for a family of elliptic operators $\{\mathcal{L}_\varepsilon, \varepsilon>0\}$, arising in the theory of homogenization, with rapidly oscillating periodic coefficients. We establish sharp $W^{1,p}$ estimates, Lipschitz estimates, and nontangential maximal function estimates, which are uniform in the parameter $\varepsilon$, on solutions with Neumann boundary conditions in $C^{1,\alpha}$ domains.

New Monte Carlo method for the self-avoiding walk

Abstract: We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We findμ=2.63820 ± 0.00004 ± 0.00030γ=1.352 ± 0.006 ± 0.025νv=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length ≈ 166, using 340 hours CPU time on a CDC Cyber 170–730. We compare our results to previous work and indicate some directions for future research.

Bogoliubov Spectrum of Interacting Bose Gases

Abstract: We study the large-N limit of a system of N bosons interacting with a potential of intensity 1/N. When the ground state energy is to the first order given by Hartree's theory, we study the next order, predicted by Bogoliubov's theory. We show the convergence of the lower eigenvalues and eigenfunctions towards that of the Bogoliubov Hamiltonian (up to a convenient unitary transform). We also prove the convergence of the free energy when the system is sufficiently trapped. Our results are valid in an abstract setting, our main assumptions being that the Hartree ground state is unique and non-degenerate, and that there is complete Bose-Einstein condensation on this state. Using our method we then treat two applications: atoms with ''bosonic'' electrons on one hand, and trapped 2D and 3D Coulomb gases on the other hand.

Connecting solvation shell structure to proton transport kinetics in hydrogen-bonded networks via population correlation functions.

Abstract: A theory based on population correlation functions is introduced for connecting solvation topologies and microscopic mechanisms to transport kinetics of charge defects in hydrogen-bonded networks. The theory is tested on the hydrated proton by extracting a comprehensive set of relaxation times, lifetimes, and rates from ab initio molecular dynamics simulations and comparing to recent femtosecond experiments. When applied to the controversial case of the hydrated hydroxide ion, the theory predicts that only one out of three proposed transport models is consistent with known experimental data.