104 research outputs found
Dipolar depletion effect on the differential capacitance of carbon based materials
The remarkably low experimental values of the capacitance data of carbon
based materials in contact with water solvent needs to be explained from a
microscopic theory in order to optimize the efficiency of these materials. We
show that this experimental result can be explained by the dielectric screening
deficiency of the electrostatic potential, which in turn results from the
interfacial solvent depletion effect driven by image dipole interactions. We
show this by deriving from the microscopic system Hamiltonian a non-mean-field
dipolar Poisson-Boltzmann equation. This can account for the interaction of
solvent molecules with their electrostatic image resulting from the dielectric
discontinuity between the solvent medium and the substrate. The predictions of
the extended dipolar Poisson-Boltzmann equation for the differential
capacitance are compared with experimental data and good agreement is found
without any fitting parameters
The optimal P3M algorithm for computing electrostatic energies in periodic systems
We optimize Hockney and Eastwood's Particle-Particle Particle-Mesh (P3M)
algorithm to achieve maximal accuracy in the electrostatic energies (instead of
forces) in 3D periodic charged systems. To this end we construct an optimal
influence function that minimizes the RMS errors in the energies. As a
by-product we derive a new real-space cut-off correction term, give a
transparent derivation of the systematic errors in terms of Madelung energies,
and provide an accurate analytical estimate for the RMS error of the energies.
This error estimate is a useful indicator of the accuracy of the computed
energies, and allows an easy and precise determination of the optimal values of
the various parameters in the algorithm (Ewald splitting parameter, mesh size
and charge assignment order).Comment: 31 pages, 3 figure
Clathrate hydrates as a sink of noble gases in Titan's atmosphere
We use a statistical thermodynamic approach to determine the composition of
clathrate hydrates which may form from a multiple compound gas whose
composition is similar to that of Titan's atmosphere. Assuming that noble gases
are initially present in this gas phase, we calculate the ratios of xenon,
krypton and argon to species trapped in clathrate hydrates. We find that these
ratios calculated for xenon and krypton are several orders of magnitude higher
than in the coexisting gas at temperature and pressure conditions close to
those of Titan's present atmosphere at ground level. Furthermore we show that,
by contrast, argon is poorly trapped in these ices. This trapping mechanism
implies that the gas-phase is progressively depleted in xenon and krypton when
the coexisting clathrate hydrates form whereas the initial abundance of argon
remains almost constant. Our results are thus compatible with the deficiency of
Titan's atmosphere in xenon and krypton measured by the {\it Huygens} probe
during its descent on January 14, 2005. However, in order to interpret the
subsolar abundance of primordial Ar also revealed by {\it Huygens}, other
processes that occurred either during the formation of Titan or during its
evolution must be also invoked.Comment: Astronomy & Astrophysics Letters, in pres
Exact aymptotic expansions for the thermodynamics of hydrogen gas in the Saha regime
We consider the hydrogen quantum plasma in the Saha regime, where it almost
reduces to a partially ionized atomic gas. We briefly review the construction
of systematic expansions of thermodynamical functions beyond Saha theory, which
describes an ideal mixture of ionized protons, ionized electrons and hydrogen
atoms in their ground-state. Thanks to the existence of rigorous results, we
first identify the simultaneous low-temperature and low-density limit in which
Saha theory becomes asymptotically exact. Then, we argue that the screened
cluster representation is well suited for calculating corrections, since that
formalism accounts for all screening and recombination phenomena at work in a
more tractable way than other many-body methods. We sketch the corresponding
diagrammatical analysis, which leads to an exact asymptotic expansion for the
equation of state. That scaled low-temperature expansion improves the
analytical knowledge of the phase diagram. It also provides reliable numerical
values over a rather wide range of temperatures and densities, as confirmed by
comparisons to quantum Monte Carlo data.Comment: 10 page
Behavior of Bulky Ferrofluids in the Diluted Low-Coupling Regime: Theory and Simulation
A theoretical formalism to predict the structure factors observed in dipolar soft-sphere fluids based on a virial expansion of the radial distribution function is presented. The theory is able to account for cases with and without externally applied magnetic fields. A thorough comparison of the theoretical results to molecular-dynamics simulations shows a good agreement between theory and numerical simulations when the fraction of particles involved in clustering is low; i.e., the dipolar coupling parameter is λ 2, and the volume fraction is φ 0.25. When magnetic fields are applied to the system, special attention is paid to the study of the anisotropy of the structure factor. The theory reasonably accounts for the structure factors when the Langevin parameter is smaller than 5. © 2010 The American Physical Society.This research has been carried out within the financial support of RFBR Grant No. 08-02-00647 and DFG-RFBR Joint Grants No. HO 1108/12-1 and No. 06-02-04019
Self-consistent equation for an interacting Bose gas
We consider interacting Bose gas in thermal equilibrium assuming a positive
and bounded pair potential such that 0<\int d\br V(r) = a<\infty.
Expressing the partition function by the Feynman-Kac functional integral yields
a classical-like polymer representation of the quantum gas. With Mayer graph
summation techniques, we demonstrate the existence of a self-consistent
relation between the density and the
chemical potential , valid in the range of convergence of Mayer series.
The function is equal to the sum of all rooted multiply connected graphs.
Using Kac's scaling V_{\gamma}(\br)=\gamma^{3}V(\gamma r) we prove that in
the mean-field limit only tree diagrams contribute and function
reduces to the free gas density.
We also investigate how to extend the validity of the self-consistent
relation beyond the convergence radius of Mayer series (vicinity of
Bose-Einstein condensation) and study dominant corrections to mean field. At
lowest order, the form of function is shown to depend on single polymer
partition function for which we derive lower and upper bounds and on the
resummation of ring diagrams which can be analytically performed.Comment: 33 pages, 6 figures, submitted to Phys.Rev.
Charge and Current Sum Rules in Quantum Media Coupled to Radiation
This paper concerns the equilibrium bulk charge and current density
correlation functions in quantum media, conductors and dielectrics, fully
coupled to the radiation (the retarded regime). A sequence of static and
time-dependent sum rules, which fix the values of certain moments of the charge
and current density correlation functions, is obtained by using Rytov's
fluctuational electrodynamics. A technique is developed to extract the
classical and purely quantum-mechanical parts of these sum rules. The sum rules
are critically tested in the classical limit and on the jellium model. A
comparison is made with microscopic approaches to systems of particles
interacting through Coulomb forces only (the non-retarded regime). In contrast
with microscopic results, the current-current correlation function is found to
be integrable in space, in both classical and quantum regimes.Comment: 19 pages, 1 figur
A theoretical investigation into the trapping of noble gases by clathrates on Titan
In this paper, we use a statistical thermodynamic approach to quantify the
efficiency with which clathrates on the surface of Titan trap noble gases. We
consider different values of the Ar, Kr, Xe, CH4, C2H6 and N2 abundances in the
gas phase that may be representative of Titan's early atmosphere. We discuss
the effect of the various parameters that are chosen to represent the
interactions between the guest species and the ice cage in our calculations. We
also discuss the results of varying the size of the clathrate cages. We show
that the trapping efficiency of clathrates is high enough to significantly
decrease the atmospheric concentrations of Xe and, to a lesser extent, of Kr,
irrespective of the initial gas phase composition, provided that these
clathrates are abundant enough on the surface of Titan. In contrast, we find
that Ar is poorly trapped in clathrates and, as a consequence, that the
atmospheric abundance of argon should remain almost constant. We conclude that
the mechanism of trapping noble gases via clathration can explain the
deficiency in primordial Xe and Kr observed in Titan's atmosphere by Huygens,
but that this mechanism is not sufficient to explain the deficiency in Ar.Comment: Accepted for publication in Planetary and Space Scienc
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