Analytical thermal study on nonlinear fundamental heat transfer cases using a novel computational technique

In this paper a novel computational technique called Parameterized Perturbation Method (PPM) is used to obtain the solutions of nonlinear fundamental heat conduction equations. Three well known problems in the area of heat transfer are addressed to be solved. An analytical investigation is carried out for: (a) the temperature distribution in a fin with a temperature-dependent thermal conductivity, (b) the cooling of the lumped system with variable specific heat, and (c) the temperature distribution of a convective-radiative fin. The validity of the results of PPM solution was verified via comparison with numerical results obtained using a fourth order Runge-Kutta method. These comparisons revealed that PPM is a powerful approach for solving these problems. Also, the results showed that the main attributions of this method are very straightforward calculations and low computational burden compared to previous analytical and numerical approaches.

Refugium for surface life on Snowball Earth in a nearly enclosed sea? A numerical solution for sea-glacier invation through a narrow strait

Abstract Where photosynthetic eukaryotic organisms survived during the Snowball Earth events of the Neoproterozoic remains unclear. Our previous research tested whether a narrow arm of the ocean, similar to the modern Red Sea, could have been a refugium for photosynthetic eukaryotes during the Snowball Earth. Using an analytical ice-flow model, we demonstrated that a limited range of climate conditions could restrict sea-glacier flow sufficiently to allow an arm of the sea to remain partially free from sea-glacier penetration, a necessary condition for it to act as a refugium. Here we expand on the previous study, using a numerical ice-flow model, with the ability to capture additional physics, to calculate sea-glacier penetration, and to explore the effect of a channel with a narrow entrance. The climatic conditions are made selfconsistent by linking sublimation rate to surface temperature. As expected, the narrow entrance allows parts of the nearly enclosed sea to remain safe from sea-glacier penetration for a wider range of climate conditions.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

An Efficient and Verifiable Solution to the Millionaire Problem

A new solution to the millionaire problem is designed on the base of two new techniques: zero test and batch equation. Zero test is a technique used to test whether one or more ciphertext contains a zero without revealing other information. Batch equation is a technique used to test equality of multiple integers. Combination of these two techniques produces the only known solution to the millionaire problem that is correct, private, publicly verifiable and efficient at the same time.