Distinguishing Closed Circulations from the Satellite Maps of the Dynamic Topography

<p>An algorithm for distinguishing closed multicore circulations from digital maps of dynamic topography (DT) is described. The algorithm is based on the expansion of circulations over the area from their cores (local maxima/minima of the DT) until the DT thresholds corresponding to these cores are reached. The algorithm is performed in several iterations until the points belonging to the closed circulations are completely exhausted. The algorithm is an exact numerical solution of the problem of determining the value of the DT for a closed loop, the most distant from the core of circulation. The algorithm takes into account the problems of nesting circulations of different signs into each other, the possible intersecting of circulations with different signs on the numerical grid, and the possible existence of islands or floating ice inside the circulations. A method is described for merging smaller DT maps to larger maps with the circulations distinguished from the smaller maps.</p>

On the revealing closed circulations on satellite maps of dynamic topography of the ocean surface

An algorithm for revealing closed multi-core circulations on digital maps of dynamic topography (DT) is described. The algorithm consists in the expansion of eddies over the area from their cores (local maxima/minima of the DT) until the DT sills corresponding to these cores are reached, and is carried out in several iterations until the points belonging to the closed circulations are completely exhausted. The algorithm is an exact numerical solution of the problem of determining the value of the DT for a closed loop, the most distant from the core of circulation. The algorithm takes into account the problems of nesting into each other circulations of a different sign, the possible intersection with each other of the circulation of a different sign on the numerical grid, as well as the possible existence of islands or floating ice inside the circulations. A method is described for gluing smaller DT maps with the circulations revealed on them to larger maps.

Superadiabatic Forces via the Acceleration Gradient in Quantum Many-Body Dynamics

We apply the formally exact quantum power functional framework (J. Chem. Phys. 2015, 143, 174108) to a one-dimensional Hooke’s helium model atom. The physical dynamics are described on the one-body level beyond the density-based adiabatic approximation. We show that gradients of both the microscopic velocity and acceleration field are required to correctly describe the effects due to interparticle interactions. We validate the proposed analytical forms of the superadiabatic force and transport contributions by comparison to one-body data from exact numerical solution of the Schrödinger equation. Superadiabatic contributions beyond the adiabatic approximation are important in the dynamics and they include effective dissipation.

Continuous piecewise linearization method for approximate periodic solution of the relativistic oscillator

This paper presents an approximate periodic solution to the vibration of the relativistic oscillator using a novel analytical method called continuous piecewise linearization method. First, an equivalent conservative equation for the vibration of the relativistic oscillator was derived in a simple straightforward manner that elucidates the physical meaning of the conservative equation. The continuous piecewise linearization method was then applied to derive periodic solutions for the displacement and velocity of the relativistic oscillator based on the conservative equation. The results of the present method were compared with results of published methods and exact numerical solution and the maximum error of the present method was less than 0.002%. The model derivations and the solutions presented in this paper are considerably simple and very accurate and can be used to introduce the relativistic oscillator in relevant undergraduate courses on dynamics. Essentially, knowledge of freshman calculus is sufficient to comprehend and implement the continuous piecewise linearization method for the relativistic oscillator.

The Structured Coalescent and its Approximations

Phylogenetics can be used to elucidate the movement of genes between populations of organisms, using phylogeographic methods. This has been widely done to quantify pathogen movement between different host populations, the migration history of humans, and the geographic spread of languages or the gene flow between species using the location or state of samples alongside sequence data. Phylogenies therefore offer insights into migration processes not available from classic epidemiological or occurrence data alone. Phylogeographic methods have however several known shortcomings. In particular, one of the most widely used methods treats migration the same as mutation, and therefore does not incorporate information about population demography. This may lead to severe biases in estimated migration rates for datasets where sampling is biased across populations. The structured coalescent on the other hand allows us to coherently model the migration and coalescent process, but current implementations struggle with complex datasets due to the need to infer ancestral migration histories. Thus, approximations to the structured coalescent, which integrate over all ancestral migration histories, have been developed. However, the validity and robustness of these approximations remain unclear. We present an exact numerical solution to the structured coalescent that does not require the inference of migration histories. While this solution is computationally unfeasible for large datasets, it clarifies the assumptions of previously developed approximate methods and allows us to provide an improved approximation to the structured coalescent. We have implemented these methods in BEAST2, and we show how these methods compare under different scenarios.

A method of approximate green's function for solving reflection of particles in plane geometry

A method for approximate analytical solution of transport equation for particles in plane geometry is developed by solving Fredholm integral equations. Kernels of these equations are the Green's functions for infinite media treated approximately. Analytical approximation of Green's function is based on decomposition of the functions into terms that are exactly analytically solved and those which are approximately obtained by usual low order DPN approximation. Transport of particles in half-space is treated, and reflection coefficient is determined in the form of an analytical function. Comparison with the exact numerical solution and other approximate methods justified the proposed analytical technique.