4,380 research outputs found
Inverted critical adsorption of polyelectrolytes in confinement
What are the fundamental laws for the adsorption of charged polymers onto
oppositely charged surfaces, for convex, planar, and concave geometries? This
question is at the heart of surface coating applications, various complex
formation phenomena, as well as in the context of cellular and viral
biophysics. It has been a long-standing challenge in theoretical polymer
physics; for realistic systems the quantitative understanding is however often
achievable only by computer simulations. In this study, we present the findings
of such extensive Monte-Carlo in silico experiments for polymer-surface
adsorption in confined domains. We study the inverted critical adsorption of
finite-length polyelectrolytes in three fundamental geometries: planar slit,
cylindrical pore, and spherical cavity. The scaling relations extracted from
simulations for the critical surface charge density -defining the
adsorption-desorption transition-are in excellent agreement with our analytical
calculations based on the ground-state analysis of the Edwards equation. In
particular, we confirm the magnitude and scaling of for the concave
interfaces versus the Debye screening length and the extent of
confinement for these three interfaces for small values. For
large the critical adsorption condition approaches the planar limit.
The transition between the two regimes takes place when the radius of surface
curvature or half of the slit thickness is of the order of . We
also rationalize how gets modified for semi-flexible versus
flexible chains under external confinement. We examine the implications of the
chain length onto critical adsorption-the effect often hard to tackle
theoretically-putting an emphasis on polymers inside attractive spherical
cavities.Comment: 12 pages, 10 figures, RevTe
Relativistic stars with a linear equation of state: analogy with classical isothermal spheres and black holes
We complete our previous investigation concerning the structure and the
stability of "isothermal" spheres in general relativity. This concerns objects
that are described by a linear equation of state so that the
pressure is proportional to the energy density. In the Newtonian limit , this returns the classical isothermal equation of state. We consider
specifically a self-gravitating radiation (q=1/3), the core of neutron stars
(q=1/3) and a gas of baryons interacting through a vector meson field (q=1). We
study how the thermodynamical parameters scale with the size of the object and
find unusual behaviours due to the non-extensivity of the system. We compare
these scaling laws with the area scaling of the black hole entropy. We also
determine the domain of validity of these scaling laws by calculating the
critical radius above which relativistic stars described by a linear equation
of state become dynamically unstable. For photon stars, we show that the
criteria of dynamical and thermodynamical stability coincide. Considering
finite spheres, we find that the mass and entropy as a function of the central
density present damped oscillations. We give the critical value of the central
density, corresponding to the first mass peak, above which the series of
equilibria becomes unstable. Finally, we extend our results to d-dimensional
spheres. We show that the oscillations of mass versus central density disappear
above a critical dimension d_{crit}(q). For Newtonian isothermal stars (q=0) we
recover the critical dimension d_{crit}=10. For the stiffest stars (q=1) we
find d_{crit}=9 and for a self-gravitating radiation (q=1/d) we find
d_{crit}=9.96404372... very close to 10. Finally, we give analytical solutions
of relativistic isothermal spheres in 2D gravity.Comment: A minor mistake in calculation has been corrected in the second
version (v2
Quantum fluids of light
This article reviews recent theoretical and experimental advances in the
fundamental understanding and active control of quantum fluids of light in
nonlinear optical systems. In presence of effective photon-photon interactions
induced by the optical nonlinearity of the medium, a many-photon system can
behave collectively as a quantum fluid with a number of novel features stemming
from its intrinsically non-equilibrium nature. We present a rich variety of
photon hydrodynamical effects that have been recently observed, from the
superfluid flow around a defect at low speeds, to the appearance of a
Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of
topological excitations such as quantized vortices and dark solitons at the
surface of large impenetrable obstacles. While our review is mostly focused on
a class of semiconductor systems that have been extensively studied in recent
years (namely planar semiconductor microcavities in the strong light-matter
coupling regime having cavity polaritons as elementary excitations), the very
concept of quantum fluids of light applies to a broad spectrum of systems,
ranging from bulk nonlinear crystals, to atomic clouds embedded in optical
fibers and cavities, to photonic crystal cavities, to superconducting quantum
circuits based on Josephson junctions. The conclusive part of our article is
devoted to a review of the exciting perspectives to achieve strongly correlated
photon gases. In particular, we present different mechanisms to obtain
efficient photon blockade, we discuss the novel quantum phases that are
expected to appear in arrays of strongly nonlinear cavities, and we point out
the rich phenomenology offered by the implementation of artificial gauge fields
for photons.Comment: Accepted for publication on Rev. Mod. Phys. (in press, 2012
Two-component mixture of charged particles confined in a channel: melting
The melting of a binary system of charged particles confined in a {\it
quasi}-one-dimensional parabolic channel is studied through Monte Carlo
simulations. At zero temperature the particles are ordered in parallel chains.
The melting is anisotropic and different melting temperatures are obtained
according to the spatial direction, and the different types of particles
present in the system. Melting is very different for the single-, two- and
four-chain configurations. A temperature induced structural phase transition is
found between two different four chain ordered states which is absent in the
mono-disperse system. In the mixed regime, where the two types of particles are
only slightly different, melting is almost isotropic and a thermally induced
homogeneous distribution of the distinct types of charges is observed.Comment: To appear in Journal of Physics: condensed matter ; (13 pages, 12
figures
From the Hartree equation to the Vlasov-Poisson system: strong convergence for a class of mixed states
We consider the evolution of fermions interacting through a Coulomb or
gravitational potential in the mean-field limit as governed by the nonlinear
Hartree equation with Coulomb or gravitational interaction. In the limit of
large , we study the convergence in trace norm towards the classical
Vlasov-Poisson equation for a special class of mixed quasi-free states.Comment: 21 pages. Typos corrected, references updated and detailed proof of
Lemma 2.4 adde
Systems of Points with Coulomb Interactions
Large ensembles of points with Coulomb interactions arise in various settings
of condensed matter physics, classical and quantum mechanics, statistical
mechanics, random matrices and even approximation theory, and give rise to a
variety of questions pertaining to calculus of variations, Partial Differential
Equations and probability. We will review these as well as "the mean-field
limit" results that allow to derive effective models and equations describing
the system at the macroscopic scale. We then explain how to analyze the next
order beyond the mean-field limit, giving information on the system at the
microscopic level. In the setting of statistical mechanics, this allows for
instance to observe the effect of the temperature and to connect with
crystallization questions.Comment: 30 pages, to appear as Proceedings of the ICM201
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