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.

Cloaking via change of variables in electric impedance tomography

Abstract: A recent paper by Pendry et al (2006 Science 312 1780?2) used the coordinate invariance of Maxwell's equations to show how a region of space can be 'cloaked'?in other words, made inaccessible to electromagnetic sensing?by surrounding it with a suitable (anisotropic and heterogenous) dielectric shield. Essentially the same observation was made several years earlier by Greenleaf et al (2003 Math. Res. Lett. 10 685?93, 2003 Physiol. Meas. 24 413?9) in the closely related setting of electric impedance tomography. These papers, though brilliant, have two shortcomings: (a) the cloaks they consider are rather singular; and (b) the analysis by Greenleaf, Lassas and Uhlmann does not apply in space dimension n = 2. The present paper provides a fresh treatment that remedies these shortcomings in the context of electric impedance tomography. In particular, we show how a regular near-cloak can be obtained using a nonsingular change of variables, and we prove that the change-of-variable-based scheme achieves perfect cloaking in any dimension n ? 2.

On the maslov index

Abstract: In this paper we give four definitions of Maslov index and show that they all satisfy the same system of axioms and hence are equivalent to each other. Moreover, relationships of several symplectic and differential geometric, analytic, and topological invariants (including triple Maslov indices, eta invariants, spectral flow and signatures of quadratic forms) to the Maslov index are developed and formulae relating them are given. The broad presentation is designed with a view to applications both in geometry and in analysis. © 1994 John Wiley & Sons, Inc.

Structure and dynamics of OH-(aq)

Abstract: Topological defects in aqueous solution in the form of H+(aq) and OH-(aq) ions undergo anomalously fast transport via the structural Grotthuss diffusion mechanism. However, while the microscopic details of this process are well understood for H+(aq), the corresponding picture for OH-(aq) remains unresolved. Mechanistic scenarios proposed previously are critically reviewed with the help of the presolvation concept, which provides a unifying framework for understanding charge migration mechanisms in hydrogen-bonded networks. It is argued that OH-(aq) features a nonclassical, in the Lewis sense, hypercoordinated solvation structure. The resulting mechanism deviates substantially from the traditional “mirror image” picture. Within the presolvation concept, it can also be suggested why alternative scenarios are inconsistent with experimental data.

Arrangements and Their Applications

Abstract: The arrangement of a finite collection of geometric objects is the decomposition of the space into connected cells induced by them. We survey combinatorial and algorithmic properties of arrangements of arcs in the plane and of surface patches in higher dimensions. We present many applications of arrangements to problems in motion planning, visualization, range searching, molecular modeling, and geometric optimization. Some results involving planar arrangements of arcs have been presented in Chapter 1 of this Handbook, and are extended in this chapter to higher dimensions.