The Diurnal Temperature Wave with a Coefficient of Diffusivity Which Varies Periodically with Time and Exponentially with Height

The article of record as published may be found at http://dx.doi.org/10.1175/1520-0469(1958)0152.0.CO;2The partial differential equation for heat diffusion is numerically integrated by the Runge-Kutta method. Solutions are·obtained for the diurnal temperature variation with a bounded coefficient of eddy diffusivity which varies periodically with time and exponentially with height. The surface wave is represented by the sum of a diurnal and a semidiurnal harmonic wave. The results may be interpreted to apply over a fairly broad range of diffusivity values and height. With appropriate choices of the various parameters, reasonably good agreement is obtained between theoretical and observational values of amplitude reduction and phase lag as functions of height and time

Use of long-range weather forecasts in ship routing

Naval Air Systems Command (AIR 051) under the administration of Naval Weather Research Facility Norfolk, VA.http://archive.org/details/useoflongrangewe09hal

Continuous monitoring devices and seizure patterns by glucose, time and lateralized seizure onset.

Objectives: To investigate if glucose levels influence seizure patterns. Materials and methods: In a patient with RNS/NeuroPace implanted bi-temporally and type 1 diabetes mellitus, seizure event times and onset locations were matched to continuous tissue glucose. Results: Left focal seizure (LFS, n = 22) glucoses averaged 169 mg/dL, while right focal seizure (RFS, n = 23) glucoses averaged 131 mg/dL (p = 0.03). LFS occurred at mean time 17:02 while RFS occurred at 04:23. LFS spread to the contralateral side (n = 19) more than RFS (n = 2). Conclusion: Seizure onset laterality and spread vary with glucose and time of seizure

Fast finite difference solvers for singular solutions of the elliptic Monge-Amp\`ere equation

The elliptic Monge-Ampere equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, elasticity, geometric optics, image processing and image registration. Solutions can be singular, in which case standard numerical approaches fail. In this article we build a finite difference solver for the Monge-Ampere equation, which converges even for singular solutions. Regularity results are used to select a priori between a stable, provably convergent monotone discretization and an accurate finite difference discretization in different regions of the computational domain. This allows singular solutions to be computed using a stable method, and regular solutions to be computed more accurately. The resulting nonlinear equations are then solved by Newton's method. Computational results in two and three dimensions validate the claims of accuracy and solution speed. A computational example is presented which demonstrates the necessity of the use of the monotone scheme near singularities.Comment: 23 pages, 4 figures, 4 tables; added arxiv links to references, added coment