Mesoscopic Model for Diffusion-Influenced Reaction Dynamics

A hybrid mesoscopic multi-particle collision model is used to study diffusion-influenced reaction kinetics. The mesoscopic particle dynamics conserves mass, momentum and energy so that hydrodynamic effects are fully taken into account. Reactive and non-reactive interactions with catalytic solute particles are described by full molecular dynamics. Results are presented for large-scale, three-dimensional simulations to study the influence of diffusion on the rate constants of the A+CB+C reaction. In the limit of a dilute solution of catalytic C particles, the simulation results are compared with diffusion equation approaches for both the irreversible and reversible reaction cases. Simulation results for systems where the volume fraction of catalytic spheres is high are also presented, and collective interactions among reactions on catalytic spheres that introduce volume fraction dependence in the rate constants are studied.Comment: 9 pages, 5 figure

The interior structure of Jupiter (Consequences of Pioneer 10 data)

Models of the Jovian interiors based on theoretical equations of state of hydrogen and helium supported by a few experimental points and on observed parameters such as oblateness, gravitational coefficients, heat emission, magnetic fields, are discussed. The models fall into three categories: (1) those that assume a uniform and rather low H2/He ratio throughout the planet; (2) those in which this ratio is solar and thus higher; and (3) those that take into account the lack of complete miscibility of the two elements in the condensed state. It appears now also that within the limits of error the planet is in a hydrostatic equilibrium. The large heat emission and the need for an efficient source of internal heat are confirmed, but the results do not indicate which one of the various possible mechanisms is favored, although new evolutionary models suggest that the primordial heat may be insufficient. A new red spot has been discovered. Finally, the presence of a highly eccentric and inclined magnetic field poses new problems related to the pattern of internal convection and to the possibility of a north-south asymmetry of the interior. Further analysis of the available data may throw additional light on these questions

The interior structure of Jupiter (consequences of Pioneer 10 data)

Models of the Jovian interiors are based on theoretical equations of state of hydrogen and helium supported by a few experimental points and an observed parameter such as oblateness, gravitational coefficients, heat emission, and magnetic fields. The models fall into three categories: (1) those which assume a uniform and rather low H2/He ratio throughout the planet, (2) those in which this ratio is solar and thus higher and (3) those which take into account the lack of complete miscibility of the two elements in the condensed state. Recent values of the observed parameters obtained by Pioneer 10 permit improvements of the first two models but also pose new questions. In the first category of models the new data indicate that the amount of hydrogen has to be increased, while in the solar models which have a heavy core (made of SiO2, MgO, Fe and Ni), the abundance of hydrogen has to be decreased, both changes pointing in the direction of incomplete miscibility present in the third category of models

Gravitational and phase change sources of energy in Jupiter

Gravitational and phase change sources of energy in Jupite

How the asymmetry of internal potential influences the shape of I-V characteristic of nanochannels

Ion transport in biological and synthetic nanochannels is characterized by such phenomena as ion current fluctuations, rectification, and pumping. Recently, it has been shown that the nanofabricated synthetic pores could be considered as analogous to biological channels with respect to their transport characteristics \cite{Apel, Siwy}. The ion current rectification is analyzed. Ion transport through cylindrical nanopores is described by the Smoluchowski equation. The model is considering the symmetric nanopore with asymmetric charge distribution. In this model, the current rectification in asymmetrically charged nanochannels shows a diode-like shape of $I-V$ characteristic. It is shown that this feature may be induced by the coupling between the degree of asymmetry and the depth of internal electric potential well. The role of concentration gradient is discussed

Effects of cluster diffusion on the island density and size distribution in submonolayer island growth

The effects of cluster diffusion on the submonolayer island density and island-size distribution are studied for the case of irreversible growth of compact islands on a 2D substrate. In our model, we assume instantaneous coalescence of circular islands, while the cluster mobility is assumed to exhibit power-law decay as a function of island-size with exponent mu. Results are presented for mu = 1/2, 1, and 3/2 corresponding to cluster diffusion via Brownian motion, correlated evaporation-condensation, and edge-diffusion respectively, as well as for higher values including mu = 2,3, and 6. We also compare our results with those obtained in the limit of no cluster mobility corresponding to mu = infinity. In agreement with theoretical predictions of power-law behavior of the island-size distribution (ISD) for mu < 1, for mu = 1/2 we find Ns({\theta}) ~ s^{-\tau} (where Ns({\theta}) is the number of islands of size s at coverage {\theta}) up to a cross-over island-size S_c. However, the value of {\tau} obtained in our simulations is higher than the mean-field (MF) prediction {\tau} = (3 - mu)/2. Similarly, the value of the exponent {\zeta} corresponding to the dependence of S_c on the average island-size S (e.g. S_c ~ S^{\zeta}) is also significantly higher than the MF prediction {\zeta} = 2/(mu+1). A generalized scaling form for the ISD is also proposed for mu < 1, and using this form excellent scaling is found for mu = 1/2. However, for finite mu >= 1 neither the generalized scaling form nor the standard scaling form Ns({\theta}) = {\theta} /S^2 f(s/S) lead to scaling of the entire ISD for finite values of the ratio R of the monomer diffusion rate to deposition flux. Instead, the scaled ISD becomes more sharply peaked with increasing R and coverage. This is in contrast to models of epitaxial growth with limited cluster mobility for which good scaling occurs over a wide range of coverages.Comment: 12 pages, submitted to Physical Review

Quantum Collapse and the Second Law of Thermodynamics

A heat engine undergoes a cyclic operation while in equilibrium with the net result of conversion of heat into work. Quantum effects such as superposition of states can improve an engine's efficiency by breaking detailed balance, but this improvement comes at a cost due to excess entropy generated from collapse of superpositions on measurement. We quantify these competing facets for a quantum ratchet comprised of an ensemble of pairs of interacting two-level atoms. We suggest that the measurement postulate of quantum mechanics is intricately connected to the second law of thermodynamics. More precisely, if quantum collapse is not inherently random, then the second law of thermodynamics can be violated. Our results challenge the conventional approach of simply quantifying quantum correlations as a thermodynamic work deficit.Comment: 11 pages, 2 figure

Asymptotic behavior of the generalized Becker-D\"oring equations for general initial data

We prove the following asymptotic behavior for solutions to the generalized Becker-D\"oring system for general initial data: under a detailed balance assumption and in situations where density is conserved in time, there is a critical density $\rho_s$ such that solutions with an initial density $\rho_0 \leq \rho_s$ converge strongly to the equilibrium with density $\rho_0$, and solutions with initial density $\rho_0 > \rho_s$ converge (in a weak sense) to the equilibrium with density $\rho_s$. This extends the previous knowledge that this behavior happens under more restrictive conditions on the initial data. The main tool is a new estimate on the tail of solutions with density below the critical density

Nonequilibrium fluctuations in a resistor

In small systems where relevant energies are comparable to thermal agitation, fluctuations are of the order of average values. In systems in thermodynamical equilibrium, the variance of these fluctuations can be related to the dissipation constant in the system, exploiting the Fluctuation-Dissipation Theorem (FDT). In non-equilibrium steady systems, Fluctuations Theorems (FT) additionally describe symmetry properties of the probability density functions (PDFs) of the fluctuations of injected and dissipated energies. We experimentally probe a model system: an electrical dipole driven out of equilibrium by a small constant current $I$, and show that FT are experimentally accessible and valid. Furthermore, we stress that FT can be used to measure the dissipated power $\bar{\cal P}=RI^2$ in the system by just studying the PDFs symmetries.Comment: Juillet 200

Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen

1. Die Gesetze der Koagulationskinetik lassen sich nicht aus dem Studium einer einzigen, indirekt durch Koagulation beeinflussten Größe (Zähigkeit u. dergl.) ableiten, da es ein eindeutiges Koagulationsmass nicht gibt. Relativ einfache Gesetze sind nur für die zeitliche Veränderlichkeit der Anzahlen der Teilchen (oder Aggregate verschiedener Kategorien) zu erwarten. II. Als Grundlage einer mathematischen Koagulationstheorie wird angenommen, dass nach Versetzung einer kolloiden Lösung mit einem Elektrolyten gewisse, die Teilchen umgebende Anziehungsbereiche in Wirkung treten, dass aber die Brownsche Bewegung eines jeden Teilchens unverändert vor sich geht, solange dasselbe sich nicht im Anziehungsbereich eines anderen befindet. Die Art und Grösse jener Anziehungsbereiehe hängt in einer erst näher festzustellenden Weise mit der Elektrolytkonzentration und der dadurch bewirkten Änderung der elektrischen Doppelschicht zusammen. III. Für den Grenzfall "rascher" Koagulation, infolge relativ grossen Elektrolytzusatzes, kann· man annehmen, dass ein jedes Teilchen, sobald sein Mittelpunkt in den Anziehungsbereich eines anderen tritt, für immer mit demselben vereinigt bleibt. Unter Voraussetzung kugelförmiger Anziehungsbereiche und gewisser die Rechnung vereinfachender Annahmen lassen sich damit für die Anzahlen der Teilchenkomplexe bestimmter Art, welche sich aus einem ursprünglich gleichförmigen Kolloid in der Zeit t gebildet haben, Formeln (23) und (24) ableiten, welche das einfachste Schema eines idealen Koagulationsverlaufes darstellen. Dieselben entsprechen in bezug auf die Abhitngigkeit vom Kolloidgehalt der bimolekularen Reaktionskinetik. IV. Diese Formeln stehen mit vorläufigen, von Zsigmondy an koagulierenden Goldlösungen ausgeführten Teilchenzählnngen in genügender Übereinstimmung; es folgt aus ihnen, dass die Grössenordnung der Änziehungssphäre in jenen Fällen ungefähr dem Teilchendurchmesser entspricht, d. h. dass die Teilchen sich beinahe berühren müssen, damit merkliche Anziehung eintrete. V. Durch Einführung der Annahme, dass von den Zusammenstössen der Teilchen nur ein gewisser konstanter Bruchteil eta zur Vereinigung führt, lässt sich obige Koagulationstheorie erweitern, so dass sie auch als einfachstes Schema der langsamen, bei geringem Elektrolytzusatz stattfindenden Koagulation dienen kann. VI. Von diesem Standpunkt aus lassen sich sowohl die Messungen H. Paines, wie auch jene, welche J. Gann bei Verwendung einwertiger anorganischer Koagulatoren angestellt hat, in vollkommen befriedigender Weise interpretieren. Insbesondere erweisen sich die beiden, auf die Abhängigkeit von der Konzentration des Kolloids und des Koagulators bezüglichen Ähnlichkeitsgesetze als gültig. Die bei Verwendung mehrwertiger oder anorganischer Ionen auftretenden Anomalien dürften entweder auf einer Abhängigkeit des eta von der Teilchengrösse oder auf der Veränderung der Konzentration in folge Adsorption des Koagulators beruhen. VII. "Rasche" Koagulation und chemische Reaktionsprozesse bilden entgegengesetzte Extremfälle. Erstere ist ein reines Diffusionsphänomen, bei letzleren bewirkt eine noch unbekannte, mit der Wertigkeit zusammenhängende Ursache, dass nur ein ganz minimaler Teil der Molekularstösse zu chemischer Vereinigung führt