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.

Structural properties of molten silicates from ab initio molecular-dynamics simulations: Comparison between C a O − A l 2 O 3 − S i O 2 and SiO 2

Abstract: We present the results of first-principles molecular-dynamics simulations of molten silicates, based on the density functional formalism. In particular, the structural properties of a calcium aluminosilicate $[\mathrm{CaO}\ensuremath{-}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}\ensuremath{-}{\mathrm{SiO}}_{2}]$ melt are compared to those of a silica melt. The local structures of the two melts are in good agreement with the experimental understanding of these systems. In the calcium aluminosilicate melt, the number of nonbridging oxygens found is in excess of the number obtained from a simple stoichiometric prediction. In addition, the aluminum avoidance principle, which states that links between ${\mathrm{AlO}}_{4}$ tetrahedra are absent or rare, is found to be violated. Defects such as two-fold rings and five-fold coordinated silicon atoms are found in comparable proportions in both liquids. However, in the calcium aluminosilicate melt, a larger proportion of oxygen atoms are three-fold coordinated. In addition, fivefold coordinated aluminum atoms are observed. Finally evidence of creation and anihilation of nonbridging oxygens is observed, with these oxygens being mostly connected to Si tetrahedra.

An analysis of u.s. stock price behavior using wavelets

Abstract: Using wavelets we re-examine the U.S. stock market price index for any evidence of self-similarity or order that might be revealed at different scales. The wavelet transform localized in time can be used to indicate how the power of the projection of the signal onto the kernel varies with the scale of observation. By comparing how the local power scales vary over time much information about the structure of the data can be obtained. Such evidence is not at all evident from standard analyses of untransformed data, including projections onto a Fourier basis. Wavelets can detect structures in data that are highly localized in time and therefore non-detectable by Fourier transforms. The main conclusion is that while the data are clearly complex, there seems to be some evidence of non-randomness in the data. There is also some limited evidence of quasi-periodicity in the occurrence of large amplitude shocks to the system.

Small-scale universality in fluid turbulence

Abstract: Turbulent flows in nature and technology possess a range of scales. The largest scales carry the memory of the physical system in which a flow is embedded. One challenge is to unravel the universal statistical properties that all turbulent flows share despite their different large-scale driving mechanisms or their particular flow geometries. In the present work, we study three turbulent flows of systematically increasing complexity. These are homogeneous and isotropic turbulence in a periodic box, turbulent shear flow between two parallel walls, and thermal convection in a closed cylindrical container. They are computed by highly resolved direct numerical simulations of the governing dynamical equations. We use these simulation data to establish two fundamental results: (i) at Reynolds numbers Re ∼ 102 the fluctuations of the velocity derivatives pass through a transition from nearly Gaussian (or slightly sub-Gaussian) to intermittent behavior that is characteristic of fully developed high Reynolds number turbulence, and (ii) beyond the transition point, the statistics of the rate of energy dissipation in all three flows obey the same Reynolds number power laws derived for homogeneous turbulence. These results allow us to claim universality of small scales even at low Reynolds numbers. Our results shed new light on the notion of when the turbulence is fully developed at the small scales without relying on the existence of an extended inertial range.

Nonlinear instability of double-humped equilibria

Abstract: Consider a plasma described by the Vlasov-Poisson system in a cube Q with the specular boundary condition. We prove that an equilibrium μ (v), which satisfies the Penrose linear instability condition and which decays like O (|v|−3), is nonlinearly unstable in the C1 norm with a weight function in v.