Deterministic continutation of stochastic metastable equilibria via Lyapunov equations and ellipsoids

Numerical continuation methods for deterministic dynamical systems have been one of the most successful tools in applied dynamical systems theory. Continuation techniques have been employed in all branches of the natural sciences as well as in engineering to analyze ordinary, partial and delay differential equations. Here we show that the deterministic continuation algorithm for equilibrium points can be extended to track information about metastable equilibrium points of stochastic differential equations (SDEs). We stress that we do not develop a new technical tool but that we combine results and methods from probability theory, dynamical systems, numerical analysis, optimization and control theory into an algorithm that augments classical equilibrium continuation methods. In particular, we use ellipsoids defining regions of high concentration of sample paths. It is shown that these ellipsoids and the distances between them can be efficiently calculated using iterative methods that take advantage of the numerical continuation framework. We apply our method to a bistable neural competition model and a classical predator-prey system. Furthermore, we show how global assumptions on the flow can be incorporated - if they are available - by relating numerical continuation, Kramers' formula and Rayleigh iteration.Comment: 29 pages, 7 figures [Fig.7 reduced in quality due to arXiv size restrictions]; v2 - added Section 9 on Kramers' formula, additional computations, corrected typos, improved explanation

Climate change, society issues and sustainable agriculture

Despite its prediction 100 years ago by scientists studying CO2, man-made climate change has been officially recognised only in 2007 by the Nobel prize committee. Climate changes since the industrial revolution have already deeply impacted ecosystems. I report major impacts of climate change on waters, terrestrial ecosystems, agriculture, and economy in Europe. The lesson of the climate change story is that humans do not learn from scientists until it really hurts. Furthermore, all society issues cannot be solved anymore using the old, painkiller approach because all issues are now huge, linked, global and fast-developing. In that respect, actual society structures are probably outdated. Here, agronomists are the most advanced scientists to solve society issues because they master the study of complex systems, from the molecule to the global scale. Now more than ever agriculture is a central point to which all society issues are bound. Indeed, humans eat food

On the nonlocal viscosity kernel of mixtures

In this report we investigate the multiscale hydrodynamical response of a liquid as a function of mixture composition. This is done via a series of molecular dynamics simulations where the wave vector dependent viscosity kernel is computed for three mixtures each with 7-15 different compositions. We observe that the nonlocal viscosity kernel is dependent on composition for simple atomic mixtures for all the wave vectors studied here, however, for a model polymer melt mixture the kernel is independent of composition for large wave vectors. The deviation from ideal mixing is also studied. Here it is shown that a Lennard-Jones mixture follows the ideal mixing rule surprisingly well for a large range of wave vectors, whereas for both the Kob-Andersen mixture and the polymer melt large deviations are found. Furthermore, for the polymer melt the deviation is wave vector dependent such that there exists a critical length scale at which the ideal mixing goes from under-estimating to over-estimating the viscosity

First-principles study on field evaporation for silicon atom on Si(001) surface

The simulations of field-evaporation processes for silicon atoms on various Si(001) surfaces are implemented using the first-principles calculations based on the real-space finite-difference method. We find that the atoms which locate on atomically flat Si(001) surfaces and at step edges are easily removed by applying external electric field, and the threshold value of the external electric field for evaporation of atoms on atomically flat Si(001) surfaces, which is predicted between 3.0 and 3.5 V/\AA, is in agreement with the experimental data of 3.8 V/\AA. In this situation, the local field around an evaporating atom does not play a crucial role. This result is instead interpreted in terms of the bond strength between an evaporating atom and surface.Comment: 5 pages and 4 figure

Theorien der Chemie

In der folgenden Reihe von Vorlesungen werde ich Ehre haben, Ihnen einen Ueberblick über die Entwicklung der Theorie in der Chemie zu geben.Material perteneciente a la Biblioteca del Departamento de Física de la Universidad Nacional de La Plata digitalizado en SEDICI.Biblioteca del Departamento de Físic

Lord Rutherford of Nelson, His 1908 Nobel Prize in Chemistry and Why He Didn't Get a Second Prize

"I have dealt with many different transformations with various periods of time, but the quickest that I have met was my own transformation in one moment from a physicist to a chemist." Ernest Rutherford (Nobel Banquet, 1908) This article is about how Ernest Rutherford (1871-1937) got the 1908 Nobel Prize in Chemistry and why he did not get a second Prize for his subsequent outstanding discoveries in physics, specially the discovery of the atomic nucleus and the proton. Who were those who nominated him and who did he nominate for the Nobel Prizes. In order to put the Prize issue into its proper context, I will briefly describe Rutherford's whereabouts. Rutherford, an exceptionally gifted scientist who revolutionized chemistry and physics, was moulded in the finest classical tradition. What were his opinions on some scientific issues such as Einstein's photon, uncertainty relations and the future prospects for atomic energy? What would he have said about the "Theory of Everything"?Comment: Extended version of an invited talk presented at the neutrino conference "Neutrino 2008", Christchurch, New Zealand, 25-31 May 200

Theorien der Chemie

In der folgenden Reihe von Vorlesungen werde ich Ehre haben, Ihnen einen Ueberblick über die Entwicklung der Theorie in der Chemie zu geben.Material perteneciente a la Biblioteca del Departamento de Física de la Universidad Nacional de La Plata digitalizado en SEDICI.Biblioteca del Departamento de Físic

Asymmetries in the Value of Existence

According to asymmetric comparativism, it is worse for a person to exist with a miserable life than not to exist, but it is not better for a person to exist with a happy life than not to exist. My aim in this paper is to explain how asymmetric comparativism could possibly be true. My account of asymmetric comparativism begins with a different asymmetry, regarding the (dis)value of early death. I offer an account of this early death asymmetry, appealing to the idea of conditional goods, and generalize it to explain how asymmetric comparativism could possibly be true. I also address the objection that asymmetric comparativism has unacceptably antinatalist implications