Effective interactions and phase behaviour for a model clay suspension in an electrolyte

Since the early observation of nematic phases of disc-like clay colloids by Langmuir in 1938, the phase behaviour of such systems has resisted theoretical understanding. The main reason is that there is no satisfactory generalization for charged discs of the isotropic DLVO potential describing the effective interactions between a pair of spherical colloids in an electrolyte. In this contribution, we show how to construct such a pair potential, incorporating approximately both the non-linear effects of counter-ion condensation (charge renormalization) and the anisotropy of the charged platelets. The consequences on the phase behaviour of Laponite dispersions (thin discs of 30 nm diameter and 1 nm thickness) are discussed, and investigation into the mesostructure via Monte Carlo simulations are presented.Comment: LaTeX, 12 pages, 11 figure

Quark deconfinement in neutron star cores: The effects of spin-down

We study the role of spin-down in driving quark deconfinement in the high density core of isolated neutron stars. Assuming spin-down to be solely due to magnetic braking, we obtain typical timescales to quark deconfinement for neutron stars that are born with Keplerian frequencies. Employing different equations of state (EOS), we determine the minimum and maximum neutron star masses that will allow for deconfinement via spin-down only. We find that the time to reach deconfinement is strongly dependent on the magnetic field and that this time is least for EOS that support the largest minimum mass at zero spin, unless rotational effects on stellar structure are large. For a fiducial critical density of $5\rho_0$ for the transition to the quark phase ($\rho_0=2.5\times10^{14}$g/cm$^3$ is the saturation density of nuclear matter), we find that neutron stars lighter than $1.5M_{\odot}$ cannot reach a deconfined phase. Depending on the EOS, neutron stars of more than $1.5M_{\odot}$ can enter a quark phase only if they are spinning faster than about 3 milliseconds as observed now, whereas larger spin periods imply that they are either already quark stars or will never become one.Comment: 4 pages, 4 figures, submitted to ApJ

Microscopic Derivation of Non-Markovian Thermalization of a Brownian Particle

In this paper, the first microscopic approach to the Brownian motion is developed in the case where the mass density of the suspending bath is of the same order of magnitude as that of the Brownian (B) particle. Starting from an extended Boltzmann equation, which describes correctly the interaction with the fluid, we derive systematicaly via the multiple time-scale analysis a reduced equation controlling the thermalization of the B particle, i.e. the relaxation towards the Maxwell distribution in velocity space. In contradistinction to the Fokker-Planck equation, the derived new evolution equation is non-local both in time and in velocity space, owing to correlated recollision events between the fluid and particle B. In the long-time limit, it describes a non-markovian generalized Ornstein-Uhlenbeck process. However, in spite of this complex dynamical behaviour, the Stokes-Einstein law relating the friction and diffusion coefficients is shown to remain valid. A microscopic expression for the friction coefficient is derived, which acquires the form of the Stokes law in the limit where the mean-free in the gas is small compared to the radius of particle B.Comment: 28 pages, no figure, submitted to Journal of Statistical Physic

Diffusion in pores and its dependence on boundary conditions

We study the influence of the boundary conditions at the solid liquid interface on diffusion in a confined fluid. Using an hydrodynamic approach, we compute numerical estimates for the diffusion of a particle confined between two planes. Partial slip is shown to significantly influence the diffusion coefficient near a wall. Analytical expressions are derived in the low and high confinement limits, and are in good agreement with numerical results. These calculations indicate that diffusion of tagged particles could be used as a sensitive probe of the solid-liquid boundary conditions.Comment: soumis \`a J.Phys. Cond. Matt. special issue on "Diffusion in Liquids, Polymers, Biophysics and Chemical Dynamics

Correlation between structure and properties in multiferroic La0.7_{0.7}Ca0.3_{0.3}MnO3_3/BaTiO3_3 superlattices

Superlattices composed of ferromagnetics, namely La$_{0.7}$Ca$_{0.3}$MnO$_3$ (LCMO), and ferroelectrics, namely, BaTiO$_3$(BTO) were grown on SrTiO$_3$ at 720$^o$C by pulsed laser deposition process. While the out-of-plane lattice parameters of the superlattices, as extracted from the X-ray diffraction studies, were found to be dependent on the BTO layer thickness, the in-plane lattice parameter is almost constant. The evolution of the strains, their nature, and their distribution in the samples, were examined by the conventional sin$^2\psi$ method. The effects of structural variation on the physical properties, as well as the possible role of the strain on inducing the multiferroism in the superlattices, have also been discussed.Comment: To be published in Journal of Applied Physic

Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models

Recent progress in machine learning has shown how to forecast and, to some extent, learn the dynamics of a model from its output, resorting in particular to neural networks and deep learning techniques. We will show how the same goal can be directly achieved using data assimilation techniques without leveraging on machine learning software libraries, with a view to high-dimensional models. The dynamics of a model are learned from its observation and an ordinary differential equation (ODE) representation of this model is inferred using a recursive nonlinear regression. Because the method is embedded in a Bayesian data assimilation framework, it can learn from partial and noisy observations of a state trajectory of the physical model. Moreover, a space-wise local representation of the ODE system is introduced and is key to coping with high-dimensional models. It has recently been suggested that neural network architectures could be interpreted as dynamical systems. Reciprocally, we show that our ODE representations are reminiscent of deep learning architectures. Furthermore, numerical analysis considerations of stability shed light on the assets and limitations of the method. The method is illustrated on several chaotic discrete and continuous models of various dimensions, with or without noisy observations, with the goal of identifying or improving the model dynamics, building a surrogate or reduced model, or producing forecasts solely from observations of the physical model

On the Maximum Mass of Differentially Rotating Neutron Stars

We construct relativistic equilibrium models of differentially rotating neutron stars and show that they can support significantly more mass than their nonrotating or uniformly rotating counterparts. We dynamically evolve such ``hypermassive'' models in full general relativity and show that there do exist configurations which are dynamically stable against radial collapse and bar formation. Our results suggest that the remnant of binary neutron star coalescence may be temporarily stabilized by differential rotation, leading to delayed collapse and a delayed gravitational wave burst.Comment: 4 pages, 2 figures, uses emulateapj.sty; to appear in ApJ Letter

Slippage of water past superhydrophobic carbon nanotube forests in microchannels

We present in this letter an experimental characterization of liquid flow slippage over superhydrophobic surfaces made of carbon nanotube forests, incorporated in microchannels. We make use of a micro-PIV (Particule Image Velocimetry) technique to achieve the submicrometric resolution on the flow profile necessary for accurate measurement of the surface hydrodynamic properties. We demonstrate boundary slippage on the Cassie superhydrophobic state, associated with slip lengths of a few microns, while a vanishing slip length is found in the Wenzel state, when the liquid impregnates the surface. Varying the lateral roughness scale L of our carbon nanotube forest-based superhydrophobic surfaces, we demonstrate that the slip length varies linearly with L in line with theoretical predictions for slippage on patterned surfaces.Comment: under revie

Innermost stable circular orbits around magnetized rotating massive stars

In 1998, Shibata and Sasaki [Phys. Rev. D 58, 104011 (1998)] presented an approximate analytical formula for the radius of the innermost stable circular orbit (ISCO) of a neutral test particle around a massive, rotating and deformed source. In the present paper, we generalize their expression by including the magnetic dipole moment. We show that our approximate analytical formulas are accurate enough by comparing them with the six-parametric exact solution calculated by Pach\'on et. al. [Phys. Rev. D 73, 104038 (2006)] along with the numerical data presented by Berti and Stergioulas [MNRAS 350, 1416 (2004)] for realistic neutron stars. As a main result, we find that in general, the radius at ISCO exhibits a decreasing behavior with increasing magnetic field. However, for magnetic fields below 100GT the variation of the radius at ISCO is negligible and hence the non-magnetized approximate expression can be used. In addition, we derive approximate analytical formulas for angular velocity, energy and angular momentum of the test particle at ISCO.Comment: 8 pages, 3 figure