List of publications
Note: each reference is a hyperlink pointing, via a DOI, to the corresponding article at the publisher's site. If you would like have the full text (PDF file) of an article of mine that is not already provided below, please ask me.
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Ice and clathrates

Cage occupancies in nitrogen clathrate hydrates from Monte Carlo simulations
V. Ballenegger
J. Phys. Chem. C
123
1675716765
(2019)
👁AbstractComparisons of Gibbs ensemble Monte Carlo simulations with experimental data for the cage occupancies in N2 clathrate hydrates are performed to assess the accuracy of such simulations, to refine the effective potentials employed, and to help interpret recently measured large cage over small cage occupancy ratios. Different sets of interaction potentials for N2N2, N2H2O and H2OH2O interactions are considered. Some of them fail to reproduce the known experimental fact that some large cages are doubly occupied at 273 K and high pressures. The best agreement between simulations and experiments is obtained when using a new NO interaction potential derived in this work by averaging an abinitio potential energy surface for the N2H2O dimer.
HAL

Sensitivity of predicted gas hydrate occupancies on treatment of intermolecular interactions
C. Thomas, S. Picaud, V. Ballenegger, and O. Mousis
J. Chem. Phys.
132
104510
(2010)
👁AbstractThe sensitivity of gas hydrate occupancies predicted on the basis
of van der WaalsPlatteeuw theory is investigated, as a function
of the intermolecular guestwater interaction potential model, and
of the number of water molecules taken into account. Simple analytical
correction terms that account for the interactions with the water
molecules beyond the cutoff distance are introduced, and shown to
improve significantly the convergence rate, and hence the efficiency
of the computation of the Langmuir constants. The predicted cage
occupancies in pure methane and pure carbon dioxide clathrates, calculated
using different recent guestwater pair potentials models derived
from ab initio calculations, can vary significantly depending on
the model. That sensitivity becomes especially strong in the case
of multiple guest clathrates. It is shown that the abundances of
coenclathrated molecules in multiple guest clathrate hydrates potentially
formed on the surface of Mars can vary by more than two orders of
magnitude depending on the model. These results underline the strong
need for experimental data on pure and multiple guest clathrate hydrates,
in particular in the temperature and pressure range that are relevant
in extreme environment conditions, to discriminate among the theoretical
models.

Variability of the methane trapping in martian subsurface clathrate hydrates
C. Thomas, O. Mousis, S. Picaud, and V. Ballenegger
Planet. Space Sci.
57
4247
(2009)
👁AbstractRecent observations have evidenced traces of methane (CH(4)) heterogeneously
distributed in the martian atmosphere. However, because the lifetime
of CH(4) in the atmosphere of Mars is estimated to be around 300600
years on the basis of photochemistry, its release from a subsurface
reservoir or an active primary source of methane have been invoked
in the recent literature. Among the existing scenarios, it has been
proposed that clathrate hydrates located in the near subsurface of
Mars could be at the origin of the small quantities of the detected
CH(4). Here, we accurately determine the composition of these clathrate
hydrates, as a function of temperature and gas phase composition,
by using a hybrid statistical thermodynamic model based on experimental
data. Compared to the other recent works, our model allows us to
calculate the composition of clathrate hydrates formed from a more
plausible composition of the martian atmosphere by considering its
main compounds, i.e. carbon dioxide, nitrogen and argon, together
with methane. Besides, because there is no low temperature restriction
in our model, we are able to determine the composition of clathrate
hydrates formed at temperatures corresponding to the extreme ones
measured in the polar caps. Our results show that methane enriched
clathrate hydrates could be stable in the subsurface of Mars only
if a primitive CH(4)rich atmosphere has existed or if a subsurface
source of CH(4) has been (or is still) present.

Clathration of volatiles in the solar nebula and implications for the origin of titan's atmosphere
O. Mousis, J. I. Lunine, C. Thomas, M. Pasek, U. Marbaeuf, Y. Alibert, V. Ballenegger, D. Cordier, Y. Ellinger, F. Pauzat, and S. Picaud
Astrophys. J.
691
17801786
(2009)
👁AbstractWe describe a scenario of Titan's formation matching the constraints
imposed by its current atmospheric composition. Assuming that the
abundances of all elements, including oxygen, are solar in the outer
nebula, we show that the icy planetesimals were agglomerated in the
feeding zone of Saturn from a mixture of clathrates with multiple
guest species, socalled stochiometric hydrates such as ammonia hydrate,
and pure condensates. We also use a statistical thermodynamic approach
to constrain the composition of multiple guest clathrates formed
in the solar nebula. We then infer that krypton and xenon, that are
expected to condense in the 2030 K temperature range in the solar
nebula, are trapped in clathrates at higher temperatures than 50
K. Once formed, these ices either were accreted by Saturn or remained
embedded in its surrounding subnebula until they found their way
into the regular satellites growing around Saturn. In order to explain
the carbon monoxide and primordial argon deficiencies of Titan's
atmosphere, we suggest that the satellite was formed from icy planetesimals
initially produced in the solar nebula and that were partially devolatilized
at a temperature not exceeding similar to 50 K during their migration
within Saturn's subnebula. The observed deficiencies of Titan's atmosphere
in krypton and xenon could result from other processes that may have
occurred both prior to or after the completion of Titan. Thus, krypton
and xenon may have been sequestrated in the form of XH(3)(+) complexes
in the solar nebula gas phase, causing the formation of noble gaspoor
planetesimals ultimately accreted by Titan. Alternatively, krypton
and xenon may have also been trapped efficiently in clathrates located
on the satellite's surface or in its atmospheric haze. We finally
discuss the subsequent observations that would allow us to determine
which of these processes is the most likely.

A theoretical investigation into the trapping of noble gases by clathrates on Titan
C. Thomas, S. Picaud, O. Mousis, and V. Ballenegger
Planet. Space Sci.
56
16071617
(2008)
👁AbstractIn 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, CH(4),
C(2)H(6) and N(2) 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.

Clathrate hydrates as a sink of noble gases in Titan's atmosphere
C. Thomas, O. Mousis, V. Ballenegger, and S. Picaud
Astron. Astrophys.
474
L17L20
(2007)
👁AbstractWe 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 gasphase 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 Huygens probe during its descent on January
14, 2005. However, in order to interpret the subsolar abundance of
primordial Ar also revealed by Huygens, other processes that occurred
either during the formation of Titan or during its evolution must
be also invoked.

Molecular dynamics study of diffusion of formaldehyde in ice
V. Ballenegger, S. Picaud, and C. Toubin
Chem. Phys. Lett.
432
7883
(2006)
👁AbstractWe report a Molecular Dynamics simulation study of the diffusion process
of formaldehyde (CH2O) in protondisordered ice Ih at atmospheric
pressure, in the temperature range 200273 K. CH2O molecules diffuse
in ice predominantly by jumping between B sites (bondbreaking mechanism),
but substitutional diffusion can also be observed. At 260 K, the
diffusion constant is predicted to be 4 x 10(7) cm(2)/S with the
TIP4PEw water model, and 3 x 10(7) cm(2)/S with the TIP4P/Ice water
model.
ParticleMesh Ewald and P3M methods

Communication: On the origin of the surface term in the Ewald formula
V. Ballenegger
J. Chem. Phys.
140
161102
(2014)
👁Abstract{A transparent derivation of the Ewald formula for the electrostatic
energy of a periodic threedimensional system of point charges is
presented. The problem of the conditional convergence of the lattice sum
is dealt with by separating off, in a physically natural and
mathematically simple way, longrange nonabsolutely integrable
contributions in the series. The general expression, for any summation
order, of the surface (or dipole) term emerges very directly from those
longrange contributions. (C) 2014 AIP Publishing LLC.}

How to Convert SPME to P3M: Influence Functions and Error Estimates
V. Ballenegger, J. J. Cerda, and C. Holm
J. Chem. Theory Comput.
8
936947
(2012)
👁AbstractWe demonstrate explicitly how the two seemingly different particle
mesh Ewald methods, the smooth particle mesh Ewald (SPME) and the
particle particle particle mesh (P3M), can be mathematically transformed
into each other. This allows us in particular to convert the error
estimate of the P3M method in the energyconserving scheme (also
known as "P3M with analytic differentiation") into an error estimate
for the SPME method, via a simple change of the lattice Green function.
Our error estimate is valid for any values of the SPME parameters
(mesh size, spline interpolation order, Ewald splitting parameter,
realspace cutoff distance), including odd orders of splines. The
problem with the selfforces is avoided thanks to an analytical formula
that allows to subtract them directly within the particle mesh calculation.
Plots of the accuracy of the SPME forces are provided for a wide
range of parameter values. The main use of the error estimate is
to allow simulation program to scan quickly the multidimensional
parameter space to find the best set of parameters to achieve a target
accuracy at the smallest computational cost. As a byproduct, we show
how a SPME code can be transformed into a P3M version by changing
a few lines of code. We demonstrate also that the P3M lattice Green
function can be approximated by a closed farm expression, computable
onthefly, that provides essentially the same accuracy as the full
function.

Removal of spurious selfinteractions in particlemesh methods
V. Ballenegger, J. J. Cerda, and C. Holm
Comput. Phys. Commun.
182
19191923
(2011)
👁AbstractWe derive an analytic formula for subtracting the spurious selfforces
in particlemesh methods that use the analytical differentiation
scheme, such as the Smooth Particle Mesh Ewald (SPME) method and
the ParticleParticle ParticleMesh (P3M) method with analytical
differentiation. The impact of the selfforces on the accuracy of
the particlemesh methods is investigated, and it is shown that subtracting
them can improve the accuracy of the calculation for some choices
of the method's parameters. It is also suggested to subtract exactly
the approximate, meshcomputed, selfenergy of each particle, replacing
them by the exact value. Subtracting in this way the selfenergy
and selfforce of each particle not only improves the accuracy, but
also reduces the violation of momentum and energy conservation in
particlemesh methods with analytical differentiation.

Particleparticle particlemesh method for dipolar interactions: On error estimates and efficiency of schemes with analytical differentiation and mesh interlacing
J. J. Cerda, V. Ballenegger, and C. Holm
J. Chem. Phys.
135
184110
(2011)
👁AbstractThe interlaced and noninterlaced versions of the dipolar particleparticle
particlemesh (P(3)M) method implemented using the analytic differentiation
scheme (ADP(3)M) are presented together with their respective error
estimates for the calculation of the forces, torques, and energies.
Expressions for the optimized lattice Green functions, and for the
Madelung selfforces, selftorques and selfenergies are given. The
applicability of the theoretical error estimates are thoroughly tested
and confirmed in several numerical examples. Our results show that
the accuracy of the calculations can be improved substantially when
the approximate (mesh computed) Madelung selfinteractions are subtracted.
Furthermore, we show that the interlaced dipolar ADP(3)M method
delivers a significantly higher accuracy (which corresponds approximately
to using a twice finer mesh) than the conventional method, allowing
thereby to reduce the mesh size with respect to the noninterlaced
version for a given accuracy. In addition, we present similar expressions
for the dipolar ikdifferentiation interlaced scheme, and we perform
a comparison with the AD interlaced scheme. Rough tests for the relative
speed of the dipolar P(3)M method using ikdifferentiation and the
interlaced/noninterlaced AD schemes show that when FFT computing
time is the bottleneck, usually when working at high precisions,
the interlaced ADscheme can be several times faster than the other
two schemes. For calculations with a low accuracy requirement, the
interlaced version can perform worse than the ik and the noninterlaced
AD schemes.

Simulations of nonneutral slab systems with longrange electrostatic interactions in twodimensional periodic boundary conditions
V. Ballenegger, A. Arnold, and J. J. Cerda
J. Chem. Phys.
131
094107
(2009)
👁AbstractWe introduce a regularization procedure to define electrostatic energies
and forces in a slab system of thickness h that is periodic in two
dimensions and carries a net charge. The regularization corresponds
to a neutralization of the system by two charged walls and can be
viewed as the extension to the twodimensional (2D)+h geometry of
the neutralization by a homogeneous background in the standard threedimensional
Ewald method. The energies and forces can be computed efficiently
by using advanced methods for systems with 2D periodicity, such as
MMM2D or P3M/ELC, or by introducing a simple backgroundcharge correction
to the YehBerkowitz approach of slab systems. The results are checked
against direct lattice sum calculations on simple systems. We show,
in particular, that the Madelung energy of a 2D square charge lattice
in a uniform compensating background is correctly reproduced to high
accuracy. A molecular dynamics simulation of a sodium ion close to
an air/water interface is performed to demonstrate that the method
does indeed provide consistent longrange electrostatics. The mean
force on the ion reduces at large distances to the imagecharge interaction
predicted by macroscopic electrostatics. This result is used to determine
precisely the position of the macroscopic dielectric interface with
respect to the true molecular surface.

The optimal P3M algorithm for computing electrostatic energies in periodic systems
V. Ballenegger, J. J. Cerda, O. Lenz, and C. Holm
J. Chem. Phys.
128
034109
(2008)
👁AbstractWe optimize Hockney and Eastwood's particleparticle particlemesh
algorithm to achieve maximal accuracy in the electrostatic energies
(instead of forces) in threedimensional periodic charged systems.
To this end we construct an optimal influence function that minimizes
the rootmeansquare (rms) errors of the energies. As a byproduct
we derive a new realspace cutoff 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).

P3M algorithm for dipolar interactions
J. J. Cerda, V. Ballenegger, O. Lenz, and C. Holm
J. Chem. Phys.
129
234104
(2008)
👁AbstractAn extension to the (PM)M3 algorithm for electrostatic interactions
is presented that allows to efficiently compute dipolar interactions
in periodic boundary conditions. Theoretical estimates for the rootmeansquare
error of the forces, torques, and the energy are derived. The applicability
of the estimates is tested and confirmed in several numerical examples.
A comparison of the computational performance of the new algorithm
to a standard dipolarEwald summation methods shows a performance
crossover from the Ewald method to the dipolar (PM)M3 method for
as few as 300 dipolar particles. In larger systems, the new algorithm
represents a substantial improvement in performance with respect
to the dipolar standard Ewald method. Finally, a test comparing pointdipolebased
and chargedpair based models shows that pointdipolebased models
exhibit a better performance than chargedpair based models.
Thermodynamics of (weakly quantum) partially ionized gases

The screened cluster equation of state for hydrogenhelium mixtures: Atomic, molecular, and ionic contributions from first principles
Ballenegger V., Alastuey A. and Wendland D.
Contrib. Plasm. Phys.
58
114121
(2018)
👁Abstract{We present a method that provides reliable equations of state for
partially ionized gases at moderate densities. The gas is described
within the physical picture in terms of a quantum plasma made with
nuclei and electrons interacting via the Coulomb potential. The method
relies on the screened cluster representation derived elsewhere and is
obtained by resummations of Mayerlike diagrammatics for the equivalent
classical gas of loops. The contributions to the thermodynamics of
atoms, molecules, or ions are described by cluster functions built with
simple diagrams involving a few elementary particles and screened
interactions. All quantum and collective mechanisms at work are embedded
in these cluster functions, which can be computed numerically by
sampling the corresponding path integrals. The usefulness and accuracy
of this formalism is illustrated by considering a hydrogenhelium
mixture under solar interior conditions. As a byproduct of our
calculations, we also exhibit the density dependence of the twobody
cluster function analogous to the second virial coefficient in a
hydrogen gas.}

Quantum screened interactions in moderately dense plasmas and atomic contributions to thermodynamics
V. Ballenegger, D. Wendland, and A. Alastuey
Contrib. Plasm. Phys.
57
106125
(2017)
👁AbstractThe screened Coulomb interaction φ through which particles interact in the path integral description of quantum plasmas is studied analytically and numerically. This interaction, which is a key ingredient in quantum Mayer diagrams, is closely related to the random‐phase approximation potential known from finite‐temperature many‐body perturbation theory. An efficient way to compute numerically φ and its contributions in quantum Mayer diagrams under weak degeneracy conditions is proposed. Two key contributions to the thermodynamics of a moderately dense hydrogen plasma are studied using this method: polarization of the plasma and the electron– proton cluster function which accounts for the contributions from hydrogen atoms at finite density and finite temperature. The calculations include effects from dynamical screening and from shifts as well as broadening of spectral lines. When κ λ≪1, with κ the inverse Debye screening length and λ the electronic thermal de Broglie wavelength, a simple fast‐to‐evaluate approximation for φ can be used without loss of accuracy. The error induced on the electron– proton cluster function by the common approximation of replacing φ by a statically screened Debye potential is assessed for κ λ in the range 0⩽κ λ⩽0.5.

Comment on ``Direct linear term in the equation of state of plasmas''
A. Alastuey, V. Ballenegger, and W. Ebeling
Physical Review E
92
(2015)
👁AbstractIn a recent paper [Phys. Rev. E 91, 013108 (2015)], Kraeft et al. criticize known exact results on the equation of state of quantum plasmas, which have been obtained independently by several authors. They argue about a difference in the definition of the direct twobody function Q(x), which appears in virial expansions of thermodynamical quantities, but Q(x) is not a measurable quantity in itself. Differences in definitions of intermediate quantities are irrelevant, and only differences in physical quantities are meaningful. Beyond Kraeft et al.'s broad statement that there is no agreement at order ρ^5/2 in the virial equation for the pressure, we show that their published results for this quantity are in fact in perfect agreement with previous existing expressions.
HAL

Quantum partition functions of composite particles in a hydrogenhelium plasma via path integral Monte Carlo
D. Wendland, V. Ballenegger, and A. Alastuey
J. Chem. Phys.
141
(2014)
👁Abstract{We compute two and threebody cluster functions that describe
contributions of composite entities, like hydrogen atoms, ions H,
H2(+), and helium atoms, and also chargecharge and atomcharge
interactions, to the equation of state of a hydrogenhelium mixture at
low density. A cluster function has the structure of a truncated virial
coefficient and behaves, at low temperatures, like a usual partition
function for the composite entity. Our path integral Monte Carlo
calculations use importance sampling to sample efficiently the cluster
partition functions even at low temperatures where bound state
contributions dominate. We also employ a new and efficient adaptive
discretization scheme that allows one not only to eliminate Coulomb
divergencies in discretized path integrals, but also to direct the
computational effort where particles are close and thus strongly
interacting. The numerical results for the twobody function agree with
the analytically known quantum second virial coefficient. The threebody
cluster functions are compared at low temperatures with familiar
partition functions for composite entities. (C) 2014 AIP Publishing LLC.}

Atomic Ionization and Molecular Dissociation in a Hydrogen Gas within the Physical Picture
A. Alastuey and V. Ballenegger
Contrib. Plasm. Phys.
52
9599
(2012)
👁AbstractWe study a hydrogen gas at low densities within the physical picture.
Recombination processes leading to the formation of atoms and molecules
are properly taken into account via the wellknown Ebeling function
and a new fourbody partition function. Our method provides a reliable
equation of state which covers the plasma, atomic and molecular phases

The divergent atomic partition function or how to assign correct statistical weights to bound states
V. Ballenegger
Ann. Phys.
524
103105
(2012)
👁Abstract

Thermodynamics of atomic and ionized hydrogen: Analytical results versus equationofstate tables and Monte Carlo data
A. Alastuey and V. Ballenegger
Phys. Rev. E
86
066402
(2012)
👁AbstractWe compute thermodynamical properties of a lowdensity hydrogen gas
within the physical picture, in which the system is described as
a quantum electronproton plasma interacting via the Coulomb potential.
Our calculations are done using the exact scaled lowtemperature
(SLT) expansion, which provides a rigorous extension of the wellknown
virial expansionvalid in the fully ionized phaseinto the Saha regime
where the system is partially or fully recombined into hydrogen atoms.
After recalling the SLT expansion of the pressure [A. Alastuey et
al., J. Stat. Phys. 130, 1119 (2008)], we obtain the SLT expansions
of the chemical potential and of the internal energy, up to order
exp(EH/kT) included (EH similar or equal to 13.6 eV). Those
truncated expansions describe the first five nonideal corrections
to the ideal Saha law. They account exactly, up to the considered
order, for all effects of interactions and thermal excitations, including
the formation of bound states (atom H, ions H and H2(+), molecule
H2, ... ) and atomcharge and atomatom interactions. Among the
five leading corrections, three are easy to evaluate, while the remaining
ones involve welldefined internal partition functions for the molecule
H2 and ions H and H2(+), for which no closedform analytical formula
exist currently. We provide accurate lowtemperature approximations
for those partition functions by using known values of rotational
and vibrational energies. We compare then the predictions of the
SLT expansion, for the pressure and the internal energy, with, on
the one hand, the equationofstate tables obtained within the opacity
program at Livermore (OPAL) and, on the other hand, data of path
integral quantum Monte Carlo (PIMC) simulations. In general, a good
agreement is found. At low densities, the simple analytical SLT formulas
reproduce the values of the OPAL tables up to the last digit in a
large range of temperatures, while at higher densities (rho similar
to 10(2) g/cm(3)), some discrepancies among the SLT, OPAL, and PIMC
results are observed.
HAL

Pressure of a Partially Ionized Hydrogen Gas: Numerical Results from Exact Low Temperature Expansions
A. Alastuey and V. Ballenegger
Contrib. Plasm. Phys.
50
4653
(2010)
👁AbstractWe consider a partially ionized hydrogen gas at low densities, where
it reduces almost to an ideal mixture made with hydrogen atoms in
their groundstate, ionized protons and ionized electrons. By performing
systematic lowtemperature expansions within the physical picture,
in which the system is described as a quantum electronproton plasma
interacting via the Coulomb potential, exact formulae for the first
five leading corrections to the ideal Saha equation of state have
been derived [A. Alastuey, V. Ballenegger et al., J. Stat. Phys.
130, 1119 (2008)]. Those corrections account for all effects of interactions
and thermal excitations up to order exp(E(H)/kT) included, where
E(H) similar or equal to 13.6 eV is the ground state energy of the
hydrogen atom. Among the five leading corrections, three are easy
to evaluate, while the remaining ones involve suitably truncated
internal partition functions of H(2) molecules and H() and H(2)(+)
ions, for which no analytical formulae are available in closed form.
We estimate those partitions functions at finite temperature via
a simple phenomenology based on known values of rotational and vibrational
energies. This allows us to compute numerically the leading deviations
to the Saha pressure along several isotherms and isochores. Our values
are compared with those of the OPAL tables (for pure hydrogen) calculated
within the ACTEX method.
HAL

Exact asymptotic expansions for the thermodynamics of hydrogen gas in the Saha regime
A. Alastuey and V. Ballenegger
J. Phys. A  Math. Theor.
42
214031
(2009)
👁AbstractWe 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
lowtemperature and lowdensity 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 manybody methods. We sketch the
corresponding diagrammatical analysis, which leads to an exact asymptotic
expansion for the equation of state. That scaled lowtemperature
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.
HAL

Exact results for thermodynamics of the hydrogen plasma: Lowtemperature expansions beyond Saha theory
A. Alastuey, V. Ballenegger, F. Cornu, and P. A. Martin
J. Stat. Phys.
130
11191176
(2008)
👁AbstractWe study hydrogen in the Saha regime, within the physical picture
in terms of a quantum protonelectron plasma. Long ago, Saha showed
that, at sufficiently low densities and low temperatures, the system
behaves almost as an ideal mixture made with hydrogen atoms in their
groundstate, ionized protons and ionized electrons. More recently,
that result has been rigorously proved in some scaling limit where
both temperature and density vanish. In that Saha regime, we derive
exact lowtemperature expansions for the pressure and internal energy,
where density rho is rescaled in units of a temperaturedependent
density rho* which controls the crossover between full ionization
(rho << rho*) and full atomic recombination (rho >>rho*). Each term
reduces to a function of rho/rho* times temperaturedependent functions
which decay exponentially fast when temperature T vanishes. Scaled
expansions are ordered with respect to the corresponding decay rates.
Leading terms do reduce to ideal contributions obtained within Saha
theory. We consistently compute all corrections which are exponentially
smaller by a factor exp(beta E (H) ) at most, where E (H) is the
negative groundstate energy of a hydrogen atom and beta=1/(k (B)
T). They include all effects arising from both the Coulomb potential
and the quantum nature of the particles: excitations of atoms H,
formation of molecules H2, ions H2(+) and H, thermal and pressure
ionization, plasma polarization, screening, interactions between
atoms and ionized charges, etc. Scaled lowtemperature expansions
can be viewed as partial resummations of usual virial expansions
up to arbitrary high orders in the density.

Dielectric versus conductive behaviour in quantum gases: exact results for the hydrogen plasma
V. Ballenegger and P. A. Martin
Physica A
328
97144
(2003)
👁AbstractWe study the electrical susceptibility of a hydrogen gas at equilibrium,
partially ionized by thermal excitations. The gas is described as
a quantum plasma of point protons and electrons, interacting via
the Coulomb potential. Using the newly developed diagrammatical technique
of screened cluster expansions, we calculate exactly the wavenumberdependent
susceptibility in the atomic limit, where most charges are bound
into hydrogen atoms. A transition from conductive to dielectric behaviour
occurs when the wavelength is decreased well below the Debye screening
length. The standard formula for the dielectric function of an ideal
gas of hydrogen atoms is recovered in an appropriate scaling limit.
The derivation treats all effects arising from the Coulomb interaction
(screening, binding, polarization) in a fully coherent way, without
intermediate approximation nor modelization.

Screened cluster expansions for partially ionized gases
A. Alastuey, V. Ballenegger, F. Cornu, and P. A. Martin
J. Stat. Phys.
113
455503
(2003)
👁AbstractWe consider a partially ionized gas at thermal equilibrium, in the
Saha regime. The system is described in terms of a quantum plasma
of nuclei and electrons. In this framework, the Coulomb interaction
is the source of a large variety of phenomena occurring at different
scales: recombination, screening, diffraction, etc. In this paper,
we derive a cluster expansion adequate for a coherent treatment of
those phenomena. The expansion is obtained by combining the path
integral representation of the quantum gas with familiar Mayer diagrammatics.
In this formalism, graphs have a clear physical interpretation: vertices
are associated with recombined chemical species, while bonds describe
their mutual interactions. The diagrammatical rules account exactly
for all effects in the medium. Applications to thermodynamics, van
der Waals forces and dielectric versus conductive behaviour will
be presented in forthcoming papers.

Quantum Coulomb systems: some exact results in the atomic limit
V. Ballenegger and P. A. Martin
Physica A
306
5967
(2002)
👁AbstractWe review a number of exact results concerning the recombined electronproton
gas. The recombination problem can be formulated in precise terms
in the atomic limit. In this limit one lets the density and the temperature
tend to zero in a coupled way so that the resulting energyentropy
balance favors the formation of certain chemical species. This enables
to develop a clear understanding of the dielectric versus conducting
behavior in the system. In particular, we give a first principle
derivation of the dielectric constant of the dilute atomic gas without
presupposing the existence of atoms. The analysis relies on the path
integral representation of the Coulomb gas together with Mayer diagrammatic
techniques.

Quantum Mayer graphs for Coulomb systems and the analog of the Debye potential
V. Ballenegger, P. A. Martin, and A. Alastuey
J. Stat. Phys.
108
169211
(2002)
👁AbstractWithin the FeynmanKac path integral representation, the equilibrium
quantities of a quantum plasma can be represented by Mayer graphs.
The well known Coulomb divergencies that appear in these series are
eliminated by partial resummations. In this paper, we propose a resummation
scheme based on the introduction of a single effective potential
phi that is the quantum analog of the Debye potential. A low density
analysis of phi shows that it reduces, at short distances, to the
bare Coulomb interaction between the charges (which is able to lead
to bound states). At scale of the order of the Debye screening length
kappa(D)(1), phi approaches the classical Debye potential and, at
large distances, it decays as a dipolar potential (this large distance
behaviour is due to the quantum nature of the particles). The prototype
graphs that result from the resummation obey the same diagrammatical
rules as the classical graphs of the AbeMeeron series. We give several
applications that show the usefulness of phi to account for Coulombic
effects at all distances in a coherent way.
Dielectric fluids and magnetic filaments

Semiflexible magnetic filaments near attractive flat surfaces: a Langevin dynamics study
P. A. Sanchez, J. J. Cerda, V. Ballenegger, T. Sintes, O. Piro, and C. Holm
Soft Matter
7
18091818
(2011)
👁AbstractThe adsorption of stiff magnetic filaments close to an attractive
surface is studied thoroughly via extensive Langevin dynamics simulations
(LD). Magnetic filaments are represented by a coarsegrained beadspring
model where each bead bears a point dipole located at its center
and the excluded volume interaction is introduced via a softcore
repulsive potential. We find strong evidence for the existence of
two transitions as the temperature is lowered. First, the system
undergoes a continuum phase transition from the desorbed to the adsorbed
state. This transition is followed by a second structural transition
that takes place when the filaments are already adsorbed. The adsorption
transition is found to be very similar to the one observed for stiff
nonmagnetic polymer chains [Sintes et al., Macromolecules 2001,
34, 13521357] where the chain bending interaction plays a similar
role as the magnetic component of the present case. However, the
tendency of the magnetic chains to stretch is reversed by a further
reduction in temperature and the chains tend to form closed adsorbed
loops leading to a second structural transition. A representation
of the phase diagram for the adsorption of magnetic filaments is
determined here for the first time. We also present a novel way to
determine the temperature at which the chain is adsorbed that is
based on the analysis of the change in the number of trains, tails
and loops developed by the polymer chain during the adsorption process.

Study of the structure factor anisotropy and long range correlations of ferrofluids in the dilute lowcoupling regime
J. J. Cerda, E. Elfimova, V. Ballenegger, E. Krutikova, A. Ivanov, and C. Holm
J. Magn. Magn. Mater.
323
12461253
(2011)
👁AbstractDipolar softsphere (DSS) fluids in the dilute lowcoupling regime
are studied via Molecular Dynamic simulations and the extension of
a theoretical formalism previously used for dipolar hard spheres
in which new terms for the virial expansion of the radial distribution
function corresponding to the threeparticle contribution are presented
and tested for the zero and nonzero magnetic field case. A thorough
comparison with simulations shows that the extended formalism is
able to account for the structure factors of DSS with and without
externally applied magnetic fields in the dilute lowcoupling regime:
quantitative agreement between theory and simulations is found for
dipolar coupling parameters lambda less than or similar to 2, and
volume fraction phi less than or similar to 0.25. When lambda>1 the
new added term to the virial expansion is observed to play a crucial
role in order to match quantitatively theory and simulations at zero
field. In the presence of an external magnetic field our tests show
that further improvements are needed and only new terms with Langevin
function dependences can significatively contribute to improve the
predictions for the dilute lowcoupling regime. Numerical simulations
show that despite that the ferrofluids considered here are in the
dilute lowcoupling regime, when an external field is applied, important
correlations along the parallel direction to the field and depletion
phenomena along the perpendicular direction are observed in the averaged
density surrounding a particle.

Behavior of bulky ferrofluids in the diluted lowcoupling regime: Theory and simulation
J. J. Cerda, E. Elfimova, V. Ballenegger, E. Krutikova, A. Ivanov, and C. Holm
Phys. Rev. E
81
011501
(2010)
👁AbstractA theoretical formalism to predict the structure factors observed
in dipolar softsphere 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 moleculardynamics
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 lambda less than or similar to
2, and the volume fraction is phi less than or similar to 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.

Dipolar fluctuations in the bulk and at interfaces
V. Ballenegger, R. Blaak, and J. P. Hansen
Lect. Notes Phys.
704
4563
(2006)
👁AbstractThe dielectric response of classical polar fluids is by now well understood
for bulk systems, where the permittivity can be calculated by a variety
of methods within the linear response regime. Near interfaces or
inhomogeneities, one may attempt to describe the dielectric response
of the fluid using a local dielectric tensor epsilon(r), for which
an explicit expression can be derived from linear response theory.
This chapter describes the limitations of this approach, exemplified
by Molecular Dynamics simulations of polar fluids confined to a slit
or a spherical cavity.

Dielectric permittivity profiles of confined polar fluids
V. Ballenegger and J. P. Hansen
J. Chem. Phys.
122
114711
(2005)
👁AbstractThe dielectric response of a simple model of,a polar fluid near neutral
interfaces is examined by a combination of linear response theory
and extensive molecular dynamics simulations. Fluctuation expressions
for a local permittivity tensor is an element of(r) are derived for
planar and spherical geometries, based on the assumption of a purely
local relationship between polarization and electric field. While
the longitudinal component of e exhibits strong oscillations on the
molecular scale near interfaces, the transverse component becomes
ill defined and unphysical, indicating nonlocality in the dielectric
response. Both components go over to the correct bulk permittivity
beyond a few molecular diameters. Upon approaching interfaces from
the bulk, the permittivity tends to increase, rather than decrease
as commonly assumed, and this behavior is confirmed for a simple
model of water near a hydrophobic surface. An unexpected finding
of the present analysis is the formation of "electrostatic double
layers" signaled by a dramatic overscreening of an externally applied
field inside the polar fluid close to an interface. The local electric
field is of opposite sign to the external field and of significantly
larger amplitude within the first layer of polar molecules.

Structure and dielectric properties of polar fluids with extended dipoles: results from numerical simulations
V. Ballenegger and J. P. Hansen
Mol. Phys.
102
599609
(2004)
👁AbstractThe strengths and shortcomings of the point dipole model for polar
fluids of spherical molecules are illustrated by considering the
physically more relevant case of extended dipoles formed by two opposite
charges +/q separated by a distance d (dipole moment mu = qd). Extensive
molecular dynamics simulations on a highdensity dipolar fluid are
used to analyse the dependence of the pair structure, dielectric
constant epsilon and dynamics as a function of the ratio d/sigma
(sigma is the molecular diameter), for a fixed dipole moment mu.
The point dipole model is found to agree well with the extended dipole
model up to d/sigma similar or equal to 0.3. Beyond that ratio, epsilon
shows a nontrivial variation with d/sigma. When d/sigma > 0.6, a
transition is observed towards a hexagonal columnar phase; the corresponding
value of the dipole moment is found to be substantially lower than
the value of the point dipole required to drive a similar transition.

Local dielectric permittivity near an interface
V. Ballenegger and J. P. Hansen
Europhys. Lett.
63
381387
(2003)
👁AbstractA statistical mechanics expression is derived for the spacedependent
dielectric permittivity of a polar solvent near an interface. The
asymptotic behaviour of this local permittivity is calculated in
the lowdensity limit, near a planar interface. The potential of
mean force between two ions is shown to agree with the prediction
of macroscopic electrostatics for large separations parallel to the
interface.

Onsager model for a variable dielectric permittivity near an interface
R. Finken, V. Ballenegger, and J. P. Hansen
Mol. Phys.
101
25592568
(2003)
👁AbstractUsing a generalization of an Onsager type approach, we are able to
predict a dielectric permittivity profile of an inhomogeneous dipolar
fluid in the presence of a dielectric interface. The reaction and
cavity fields are calculated semianalytically using bispherical
coordinates. An asymptotic expression for the local permittivity
is derived as a function of distance from the interface.

Statistical mechanics of dipolar fluids: dielectric constant and sample shape
A. Alastuey and V. Ballenegger
Physica A
279
268286
(2000)
👁AbstractWe give a new proof that the constitutive relation of macroscopic
electrostatics holds in a dipolar fluid with a sample shape independent
dielectric constant. Our approach is based on a BGYlike hierarchy
equation which allows us to calculate the canonical onebody density
function up to linear order in the electric field, in the thermodynamic
limit. The dielectric constant comes out as an integral over a 3point
correlation function of the infinite unperturbed (unpolarized) system,
from which one can recover the wellknown formula for epsilon in
terms of the 2point direct correlation function.

The EwaldOseen extinction theorem and extinction lengths
V. C. Ballenegger and T. A. Weber
Am. J. Phys.
67
599605
(1999)
👁AbstractWe give an elementary demonstration of the extinction theorem for
electromagnetic waves at normal incidence on a plane surface of a
medium. We stress that the extinction of the incident wave nd its
replacement with a wave of index of refraction n takes place throughout
the medium rather than in the surface layers. Although the extinction
theorem is usually thought to apply only to dielectrics, we extend
the theorem to include conductors. We use the macroscopic fields
in which the contributions of the oscillating dipoles in a dielectric
or the induced currents in a conductor are already summed. Our elementary
derivation of the extinction theorem should be readily accessible
to advanced undergraduates since it depends only on the superposition
principle and the solution of the wave equation. An analogy is made
between this extinction and the cancellation of the electric field
inside a conductor placed in a static electric field. We also study
the more advanced case of propagation of radiation in a dilute random
medium in which the wavelength is small relative to the interparticle
distance and find that an analogous extinction of the incident wave
takes place. Furthermore, for the dilute random medium, we estimate
the length into the medium for which a large fraction, (11/e), of
the incident radiation has interacted with the particles making up
the medium. This length is much larger than any lengths associated
with the extinction theorem itself.
MyArticles.bib
Theses

Traitement exact de la longue portée des interactions coulombiennes dans les systèmes chargés : développements méthodologiques et applications
V. Ballenegger
Habilitation thesis
(2013)
👁Abstract
Ce mémoire d'habilitation à diriger des recherches expose mes travaux portant sur des systèmes chargés classiques et quantiques. Ces travaux utilisent des méthodes de Mécanique statistique et ont pour caractéristique commune le fait qu'une description précise des effets dus à la longue portée des interactions de Coulomb est à chaque fois nécessaire pour capturer correctement certains effets physiques.
Dans la première partie, nous considérons un plasma quantique d'électrons et de protons à l'équilibre thermodynamique. En utilisant la représentation du système en terme d'intégrales de chemin et des développements diagrammatiques de Mayer, il est possible d'obtenir une représentation exacte des propriétés d'équilibre du système en termes de diagrammes bien définis qui permettent de décrire, à basse densité, simultanément et exactement les effets quantiques, en particulier la formation d'états liés, et les effets d'écran dus à la longue portée du potentiel de Coulomb. Cette approche évite d'introduire une régularisation arbitraire des fonctions de partition atomique et moléculaires, et évite également l'emploi de potentiels d'interaction effectifs semiempiriques entre charges ionisées, atomes et molécules. Ce formalisme est utilisé pour obtenir une équation d'état d'un gaz d'hydrogène partiellement ionisé qui est asymptotiquement exacte dans le régime de Saha. Les prédictions de cette équation d'état sont comparées avec celles d'autres approches couramment employées dans la littérature.
La seconde partie de ce mémoire porte en grande part sur des techniques de calculs efficaces et sans troncation des interactions coulombiennes dans les simulations numériques de systèmes chargés en conditions aux bords périodiques. Après une preuve originale et simple du terme de surface pour le potentiel électrostatique dans la méthode d'Ewald, des améliorations et extensions des méthodes de type particulegrille sont proposées (estimateur d'erreur pour la méthode Smooth Particle Mesh Ewald, méthode ParticleParticle ParticleMesh pour interactions dipolaires, soustraction des selfforces, calcul des énergies et forces dans le cas d'un système tridimensionnel périodique en deux dimensions et portant une charge globale non nulle). Des résultats de simulations de Dynamique moléculaire sont finalement présentés, portant notamment sur la permittivité diélectrique de fluides polaires au voisinage d'une interface.

Etude des phénomènes d'écran et de polarisastion dans un plasma quantique par la méthode des graphes de Mayer
V. Ballenegger
Ph.D. thesis
(2002)
👁Abstract
Cette thèse est dédiée à l'étude des effets d'écran et de polarisation dans un plasma quantique d'électrons et de protons, lorsque ce système est essentiellement un gaz dilué d'atomes d'hydrogène. Cette phase atomique est obtenue en considérant une limite couplée de basse densité et de basse température, dans laquelle la recombinaison des charges sous forme d'atomes est favorisée. Nous étudions la susceptibilité électrique de ce plasma à l'aide d'un développement en fugacit\'es de cette fonction basé sur les séries diagrammatiques de Mayer. Ce développement  qui n'est pas perturbatif visàvis de la charge électrique ni de la constante de Planck  permet de tenir compte systématiquement, à basse densité, de tous les phénomènes induits par les interactions coulombiennes, dont la formation d'états liés et les effets d'écran. Nous mettons en particulier en évidence un régime o\`u la susceptibilité du plasma mesure l'effet d'écran diélectrique d\^u à la polarisabilité des atomes d'hydrogène.
Nous abordons également dans cette thèse la problématique des effets de bords qui interviennent dans la polarisation d'un corps diélectrique de taille finie, lorsque ce dernier est soumis à un champ électrique statique. Le corps diélectrique est modélisé par un fluide dipolaire classique confiné dans une certaine région, et nous calculons sa polarisation moyenne par la mécanique statistique. Nous montrons qu'en limite thermodynamique, cette polarisation vérifie bien la loi locale de l'électrostatique macroscopique, avec une constante diélectrique qui est une propriété de volume du fluide, indépendante de la forme du diélectrique.

Aspects microscopiques de la phénoménologie des diélectriques pour un modèle classique de fluide dipolaire
V. Ballenegger
Master thesis
(1998)