Molecular interpretation of the linear relationship between the entropy and the enthalpy of activation of charge transfer reactions in polar liquids

The well-known linear relationship (T?S# =??H# +?, where 1 >? > 0,? > 0) between the entropy (?S#) and the enthalpy (?H#) of activation for reactions in polar liquids is investigated by using a molecular theory. An explicit derivation of this linear relation from first principles is presented for an outersphere charge transfer reaction. The derivation offers microscopic interpretation for the quantities? and?. It has also been possible to make connection with and justify the arguments of Bell put forward many years ago.

Physical interpretation of the Poynting-Robertson effect

Although the prevalent mathematical description of the Poynting-Robertson effect is correct, its physical interpretation is sometimes problematic. By means of a two-parameter model, we revisit the effect in order to get a better physical understanding of it. The principal conclusion is that the motion of a dust in circumsolar orbit is governed only by solar radiation absorption and not by the asymmetry of reemission, even when viewed in the rest-frame of the Sun. (C) 1999 Academic Press.

A thermodynamic interpretation of the zonal arrangement of minerals in the bedded manganese deposits of the Noda tamagawa mine, Japan

Calculated phase relations in the system MnOSi02-C02-02 were used to propose a thermodynamic explanation for the thermal metamorphism of rhodochrosite beds lying between chert strata. The metamorphic MnOS i 0 2 minerals are arranged in order quartz(chert), rhodonite. tephroite and manganosite-hausmannite-pyrochroite rhodonite across the ore bed. The calculation covered temperatures up to 1000 K and pressures up to 5 kb. The zoning was interpreted as the result of a continuous rise in metamorphic temperature. The equilibrium partner of rhodochrosite changed from rhodonite through manganosite. Across the ore bed there are gradients in the chemical potential of MnO and SiO2 but fugacities of volatlle components such as C02. 02 and H20 were probably uniform at any given time and location during formation of the zones. Assuming that the total pressure and the fugacity of C02 were at 1.4 kb and 1.0 1 b. respectively. rhodonite. tephroite and manganosite would have formed at 472. 478 and 629 K.

Challenges in the quantification and interpretation of spike-LFP relationships

Brain signals often show fluctuations in particular frequency bands, which are highly conserved across species and are associated with specific behavioural states. Such rhythmic patterns can be captured in the local field potential (LFP), which is obtained by low-pass filtering the extracellular signal recorded from microelectrodes. However, LFP also captures other neural processes that are associated with spikes, such as synaptic events preceding a spike, low-frequency component of the action potential (spike bleed-through'') and spike afterhyperpolarization, which pose difficulties in the estimation of the amplitude and phase of the rhythm with respect to spikes. Here we discuss these issues and different techniques that have been used to dissociate the rhythm from other neural events in the LFP.

Asymptotic behavior and interpretation of virtual states: The effects of confinement and of basis sets

A real-space high order finite difference method is used to analyze the effect of spherical domain size on the Hartree-Fock (and density functional theory) virtual eigenstates. We show the domain size dependence of both positive and negative virtual eigenvalues of the Hartree-Fock equations for small molecules. We demonstrate that positive states behave like a particle in spherical well and show how they approach zero. For the negative eigenstates, we show that large domains are needed to get the correct eigenvalues. We compare our results to those of Gaussian basis sets and draw some conclusions for real-space, basis-sets, and plane-waves calculations. (C) 2016 AIP Publishing LLC.

A backward particle interpretation of Feynman-Kac formulae

We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals "on-the-fly" as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We provide uniform convergence results with respect to the time horizon parameter as well as functional central limit theorems and exponential concentration estimates. Our results have important consequences for online parameter estimation for non-linear non-Gaussian state-space models. We show how the forward filtering backward smoothing estimates of additive functionals can be computed using a forward only recursion.

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90degrees and 180degrees is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress sigma(infinity) and electric field E-infinity or (sigma(infinity), E-infinity) is replaced by strain e and electric displacement D-infinity or (epsilon(infinity), D-infinity). Mixed conditions (sigma(infinity),D-infinity) and (epsilon(infinity),E-infinity) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with (E-y(infinity),sigma(y)(infinity)) for negative E-y(infinity) and (D-y(infinity), epsilon(y)(infinity)) for positive D-y(infinity) while the mechanical conditions sigma(y)(infinity) or epsilon(y)infinity are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth. (C) 2002 Published by Elsevier Science Ltd.