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.

The Production and Dissipation of Compensated Thermohaline Variance by Mesoscale Stirring

Abstract: Temperature–salinity profiles from the region studied in the North Atlantic Tracer Release Experiment (NATRE) show large isopycnal excursions at depths just below the thermocline. It is proposed here that these thermohaline filaments result from the mesoscale stirring of large-scale temperature and salinity gradients by geostrophic turbulence, resulting in a direct cascade of thermohaline variance to small scales. This hypothesis is investigated as follows: Measurements from NATRE are used to generate mean temperature, salinity, and shear profiles. The mean stratification and shear are used as the background state in a high-resolution horizontally homogeneous quasigeostrophic model. The mean state is baroclinically unstable, and the model produces a vigorous eddy field. Temperature and salinity are stirred laterally in each density layer by the geostrophic velocity and vertical advection is by the ageostrophic velocity. The simulated temperature–salinity diagram exhibits fluctuations at depths ju...

Asymptotic Solution of the Dirac Equation

Abstract: The WKB method is applied to solve the Dirac equation and the modified Dirac equation appropriate to a spin-\textonehalf{} particle with an anomalous magnetic moment. The solution consists of a phase factor multiplied by a spinor amplitude which is a power series in Planck's constant. The phase is a solution of the Hamilton-Jacobi equation of relativistic mechanics for a spinless particle without electric or magnetic moments. Each term in the spinor amplitude satisfies an ordinary differential equation along the relativistic trajectories. The equation for the leading amplitude yields an equation for the polarization four-vector which is identical with that derived classically by Bargmann, Michel, and Telegdi. It also yields the law of conservation of probability in a tube of trajectories. In addition, it gives rise to an equation for a supplementary phase factor. By using the classical Hamilton-Jacobi function, the law of probability conservation, the polarization four-vector and the supplementary phase factor, the leading term in the solution of the Dirac or modified Dirac equation can be constructed. This solution should be useful when the wavelength of the particle is small compared to the characteristic distance associated with the electromagnetic potential through which the particle moves. When applied to the bound states of a particle without an anomalous moment in a spherically symmetric electrostatic potential, it yields the same results as are usually obtained by separation of variables and use of the ordinary WKB method. The advantage of the present method is that it applies equally well to nonseparable problems.

Stretch-coil transition and transport of fibers in cellular flows.

Abstract: It is shown that a slender elastic fiber moving in a Stokesian fluid can be susceptible to a buckling instability---termed the ``stretch-coil'' instability---when moving in the neighborhood of a hyperbolic stagnation point of the flow. When the stagnation point is part of an extended cellular flow, it is found that immersed fibers can move as random walkers across time-independent closed-streamline flow. It is also found that the flow is segregated into transport regions around hyperbolic stagnation points and their manifolds, and closed entrapment regions around elliptic points.

An Automatic Technique for Selection of Data Representations in SETL Programs

Abstract: Publisher Summary This chapter highlights an automatic technique for selection of data representations in SETL programs. SETL is a very-high-level programming language supporting set-theoretic syntax and semantics. It allows algorithms to be programmed rapidly and succinctly without requiring data-structure declarations to be supplied. The chapter describes a new technique for automatic selection of appropriate data representations during compile time for programs with omitted declarations. It also presents an efficient data representation selection algorithm, whose complexity is comparable with those of the fastest known general data-flow algorithms of Tarjan and Reif. The level of a programming language is determined by the power of its semantic primitives, which influence the ease and speed of programming in the language profoundly. The chapter also describes how the SETL compiler chooses data structure implementations. SETL supports logical quantifiers and the abstract data type set as the prominent high-level features of the language. Programmers are intended to use these features as much as possible and leave more specific data structure and control structure decisions to the SETL compiler. Most other very high-level languages start by incorporating these same features. SETL is a very-high-level programming language supporting set-theoretic syntax and semantics. It allows algorithms to be programmed rapidly and succinctly without requiring data-structure declarations to be supplied. Such declarations can be manually specified later, without recoding the program, to improve the efficiency of program execution. We describe a new technique for automatic selection of appropriate data representations during compile time for programs with omitted declarations and present an efficient data representation selection algorithm, whose complexity is comparable with those of the fastest known general data-flow algorithms of Tarjan and Reif.