Randomness and Irreversiblity in Quantum Mechanics: A Worked Example for a Statistical Theory.

The randomness of some irreversible quantum phenomena is a central question because irreversible phenomena break quantum coherence and thus yield an irreversible loss of information. The case of quantum jumps observed in the fluorescence of a single two-level atom illuminated by a quasi-resonant laser beam is a worked example where statistical interpretations of quantum mechanics still meet some difficulties because the basic equations are fully deterministic and unitary. In such a problem with two different time scales, the atom makes coherent optical Rabi oscillations between the two states, interrupted by random emissions (quasi-instantaneous) of photons where coherence is lost. To describe this system, we already proposed a novel approach, which is completed here. It amounts to putting a probability on the density matrix of the atom and deducing a general "kinetic Kolmogorov-like" equation for the evolution of the probability. In the simple case considered here, the probability only depends on a single variable θ describing the state of the atom, and p(θ,t) yields the statistical properties of the atom under the joint effects of coherent pumping and random emission of photons. We emphasize that p(θ,t) allows the description of all possible histories of the atom, as in Everett's many-worlds interpretation of quantum mechanics. This yields solvable equations in the two-level atom case.

Cutting and Slicing Weak Solids.

Dicing soft solids with a sharp knife is quicker and smoother if the blade is sliding rapidly parallel to its edge in addition to the normal squeezing motion. We explain this common observation with a consistent theory suited for soft gels and departing from the standard theories of elastic fracture mechanics relied on for a century. The gel is assumed to fail locally when submitted to stresses exceeding a threshold σ_{1}. The changes in its structure generate a liquid layer coating the blade and transmitting the stress through viscous forces. The driving parameters are the ratio U/W of the normal to the tangential velocity of the blade, and the characteristic length ηW/σ_{1}, with η the viscosity of the liquid layer. The existence of a maximal value of U/W for a steady regime explains the crucial role of the tangential velocity for slicing biological and other soft materials.

Scaling laws in turbulence.

Following the idea that dissipation in turbulence at high Reynolds number is dominated by singular events in space-time and described by solutions of the inviscid Euler equations, we draw the conclusion that in such flows, scaling laws should depend only on quantities appearing in the Euler equations. This excludes viscosity or a turbulent length as scaling parameters and constrains drastically possible analytical pictures of this limit. We focus on the drag law deduced by Newton for a projectile moving quickly in a fluid at rest. Inspired by this Newton's drag force law (proportional to the square of the speed of the moving object in the limit of large Reynolds numbers), which is well verified in experiments when the location of the detachment of the boundary layer is defined, we propose an explicit relationship between the Reynolds stress in the turbulent wake and quantities depending on the velocity field (averaged in time but depending on space). This model takes the form of an integrodifferential equation for the velocity which is eventually solved for a Poiseuille flow in a circular pipe.

The shape of hanging elastic cylinders.

Deformations of heavy elastic cylinders with their axis in the direction of earth's gravity field are investigated. The specimens, made of polyacrylamide hydrogels, are attached from their top circular cross section to a rigid plate. An equilibrium configuration results from the interplay between gravity that tends to deform the cylinders downwards under their own weight, and elasticity that resists these distortions. The corresponding steady state exhibits fascinating shapes which are measured with lab-based micro-tomography. For any given initial radius to height ratio, the deformed cylinders are no longer axially symmetric beyond a critical value of a control parameter that depends on the volume force, the height and the elastic modulus: self-similar wrinkling hierarchies develop, and dimples appear at the bottom surface of the shallowest samples. We show that these patterns are the consequences of elastic instabilities.

New Drop Fluidics Enabled by Magnetic-Field-Mediated Elastocapillary Transduction.

This research introduces a new drop fluidics that uses a deformable and stretchable elastomeric film as the platform instead of the commonly used rigid supports. Such a soft film impregnated with magnetic particles can be modulated with an external electromagnetic field that produces a vast array of topographical landscapes with varying surface curvature, which, in conjunction with capillarity, can direct and control the motion of water droplets efficiently and accurately. When a thin layer of oil is present on this film that is deformed locally, a centrosymmetric wedge is formed. A water droplet placed on this oil-laden film becomes asymmetrically deformed, thus producing a gradient of Laplace pressure within the droplet and setting it in motion. A simple theory is presented that accounts for the droplet speed in terms of such geometric variables as the volume of the droplet and the thickness of the oil film covering the soft elastomeric film as well as material variables such as the viscosity of the oil and the interfacial tension of the oil-water interfaces. Following the verification of the theoretical result using well-controlled model systems, we demonstrate how the electromagnetically controlled elastocapillary force can be used to manipulate the motion of single and/or multiple droplets on the surface of the elastomeric film and how elementary operations such as drop fusion and thermally addressed chemical transformation can be carried out in aqueous droplets. It is expected that the resulting drop fluidics would be suitable for the digital control of drop motion by simply switching on and off the electromagnetic fields applied at different positions underneath the elastomeric film in a Boolean sequence. We anticipate that this method of directing and manipulating water droplets is poised for application in various biochemical reaction engineering situations, an example of which is the polymerase chain reaction (PCR).

Interview with Yves Pomeau, Boltzmann Medallist 2016 : The universality of statistical physics interpretation is ever more obvious.

During the StatPhys Conference on 20th July 2016 in Lyon, France, Yves Pomeau and Daan Frenkel will be awarded the most important prize in the field of Statistical Mechanics: the 2016 Boltzmann Medal, named after the Austrian physicist and philosopher Ludwig Boltzmann. The award recognises Pomeau's key contributions to the Statistical Physics of non-equilibrium phenomena in general. And, in particular, for developing our modern understanding of fluid mechanics, instabilities, pattern formation and chaos. He is recognised as an outstanding theorist bridging disciplines from applied mathematics to statistical physics with a profound impact on the neighbouring fields of turbulence and mechanics. In the article Sabine Louët interviews Pomeau, who is an Editor for the European Physical Journal Special Topics. He shares his views and tells how he experienced the rise of Statistical Mechanics in the past few decades. He also touches upon the need to provide funding to people who have the rare ability to discover new things and ideas, and not just those who are good at filling in grant application forms.

Gravity driven instability in elastic solid layers.

We demonstrate the instability of the free surface of a soft elastic solid facing downwards. Experiments are carried out using a gel of constant density ρ, shear modulus µ, put in a rigid cylindrical dish of depth h. When turned upside down, the free surface of the gel undergoes a normal outgoing acceleration g. It remains perfectly flat for ρgh/µ<α* with α*≃6, whereas a steady pattern spontaneously appears in the opposite case. This phenomenon results from the interplay between the gravitational energy and the elastic energy of deformation, which reduces the Rayleigh waves celerity and vanishes it at the threshold.

Supernovae: an example of complexity in the physics of compressible fluids.

Because the collapse of massive stars occurs in a few seconds, while the stars evolve on billions of years, the supernovae are typical complex phenomena in fluid mechanics with multiple time scales. We describe them in the light of catastrophe theory, assuming that successive equilibria between pressure and gravity present a saddle-center bifurcation. In the early stage we show that the loss of equilibrium may be described by a generic equation of the Painlevé I form. This is confirmed by two approaches, first by the full numerical solutions of the Euler-Poisson equations for a particular pressure-density relation, secondly by a derivation of the normal form of the solutions close to the saddle-center. In the final stage of the collapse, just before the divergence of the central density, we show that the existence of a self-similar collapsing solution compatible with the numerical observations imposes that the gravity forces are stronger than the pressure ones. This situation differs drastically in its principle from the one generally admitted where pressure and gravity forces are assumed to be of the same order. Moreover it leads to different scaling laws for the density and the velocity of the collapsing material. The new self-similar solution (based on the hypothesis of dominant gravity forces) which matches the smooth solution of the outer core solution, agrees globally well with our numerical results, except a delay in the very central part of the star, as discussed. Whereas some differences with the earlier self-similar solutions are minor, others are very important. For example, we find that the velocity field becomes singular at the collapse time, diverging at the center, and decreasing slowly outside the core, whereas previous works described a finite velocity field in the core which tends to a supersonic constant value at large distances. This discrepancy should be important for explaining the emission of remnants in the post-collapse regime. Finally we describe the post-collapse dynamics, when mass begins to accumulate in the center, also within the hypothesis that gravity forces are dominant.

Solid drops: large capillary deformations of immersed elastic rods.

Under the effect of surface tension, a blob of liquid adopts a spherical shape when immersed in another fluid. We demonstrate experimentally that soft, centimeter-size elastic solids can exhibit a similar behavior: when immersed into a liquid, a gel having a low elastic modulus undergoes large, reversible deformations. We analyze three fundamental types of deformations of a slender elastic solid driven by surface stress, depending on the shape of its cross section: a circular elastic cylinder shortens in the longitudinal direction and stretches transversally; the sharp edges of a square based prism get rounded off as its cross sections tend to become circular; and a slender, triangular based prism bends. These experimental results are compared to analysis and nonlinear simulations of neo-Hookean solids deformed by surface tension and are found to be in good agreement with each other.

Room temperature water Leidenfrost droplets.

We experimentally investigate the Leidenfrost effect at pressures ranging from 1 to 0.05 atmospheric pressure. As a direct consequence of the Clausius­Clapeyron phase diagram of water, the droplet temperature can be at ambient temperature in a non-sophisticated lab environment. Furthermore, the lifetime of the Leidenfrost droplet is significantly increased in this low pressure environment. The temperature and pressure dependence of the evaporation rate is successfully tested against a recently proposed model. These results may pave the way for reaching efficient Leidenfrost micro-fluidic and milli-fluidic applications.

Take off of small Leidenfrost droplets.

We put in evidence the unexpected behavior of Leidenfrost droplets at the later stage of their evaporation. We predict and observe that, below a critical size Rl, the droplets spontaneously take off due to the breakdown of the lubrication regime. We establish the theoretical relation between the droplet radius and its elevation. We predict that the vapor layer thickness increases when the droplets become smaller. A satisfactory agreement is found between the model and the experimental results performed on droplets of water and of ethanol.

Capillarity driven instability of a soft solid.

We report the observation of a Plateau instability in a thin filament of solid gel with a very small elastic modulus. A longitudinal undulation of the surface of the cylinder reduces its area thereby triggering capillary instability, but is counterbalanced by elastic forces following the deformation. This competition leads to a nontrivial instability threshold for a solid cylinder. The ratio of surface tension to elastic modulus defines a characteristic length scale. The onset of linear instability is when the radius of the cylinder is one-sixth of this length scale, in agreement with theory presented here.

Boltzmann-type collision operators for Bogoliubov excitations of Bose-Einstein condensates: A unified framework.

Starting from the Bogoliubov diagonalization for the Hamiltonian of a weakly interacting Bose gas under the presence of a Bose-Einstein condensate, we derive the kinetic equation for the Bogoliubov excitations. Without dropping any of the commutators, we find three collisional processes. One of them describes the 1↔2 interactions between the condensate and the excited atoms. The other two describe the 2↔2 and 1↔3 interactions between the excited atoms themselves.

Shock waves from the inhomogeneous Boltzmann equation.

We revisit the problem on the inner structure of shock waves in simple gases modelized by the Boltzmann kinetic equation. In a paper by Pomeau [Y. Pomeau, Transp. Theory Stat. Phys. 16, 727 (1987)10.1080/00411458708204311], a self-similarity approach was proposed for infinite total cross section resulting from a power-law interaction, but this self-similar form does not have finite energy. Motivated by the work of Pomeau [Y. Pomeau, Transp. Theory Stat. Phys. 16, 727 (1987)10.1080/00411458708204311] and Bobylev and Cercignani [A. V. Bobylev and C. Cercignani, J. Stat. Phys. 106, 1039 (2002)10.1023/A:1014037804043], we started the research on the rigorous study of the solutions of the spatial homogeneous Boltzmann equation, focusing on those which do not have finite energy. However, infinite energy solutions do not have physical meaning in the present framework of kinetic theory of gases with collisions conserving the total kinetic energy. In the present work, we provide a correction to the self-similar form, so that the solutions are more physically sound in the sense that the energy is no longer infinite and that the perturbation brought by the shock does not grow at large distances of it on the cold side in the soft potential case.

Anisotropic cellular forces support mechanical integrity of the Stratum Corneum barrier.

The protective function of biological surfaces that are exposed to the exterior of living organisms is the result of a complex arrangement and interaction of cellular components. This is the case for the most external cornified layer of skin, the stratum corneum (SC). This layer is made of corneocytes, the elementary 'flat bricks' that are held together through adhesive junctions. Despite the well-known protective role of the SC under high mechanical stresses and rapid cell turnover, the subtleties regarding the adhesion and mechanical interaction among the individual corneocytes are still poorly known. Here, we explore the adhesion of single corneocytes at different depths of the SC, by pulling them using glass microcantilevers, and measuring their detachment forces. We measured their interplanar adhesion between SC layers, and their peripheral adhesion among cells within a SC layer. Both adhesions increased considerably with depth. At the SC surface, with respect to adhesion, the corneocyte population exhibited a strong heterogeneity, where detachment forces differed by more than one order of magnitude for corneocytes located side by side. The measured detachment forces indicated that in the upper-middle layers of SC, the peripheral adhesion was stronger than the interplanar one. We conclude that the stronger peripheral adhesion of corneocytes in the SC favors an efficient barrier which would be able to resist strong stresses.

Softening of edges of solids by surface tension.

Surface tension tends to minimize the area of interfaces between pieces of matter in different thermodynamic phases, be they in the solid or the liquid state. This can be relevant for the macroscopic shape of very soft solids and lead to a roughening of initially sharp edges. We calculate this effect for a Neo-Hookean elastic solid, with assumptions corresponding to actual experiments, namely the case where an initially sharp edge is rounded by the effect of surface tension felt when the fluid surrounding the soft solid (and so surface tension) is changed at the solid/liquid boundary. We consider two opposite limits where the analysis can be carried to the end, the one of a shallow angle and the one of a very sharp angle. Both cases yield a discontinuity of curvature in the state with surface tension although the initial state had a discontinuous slope.

Prediction of catastrophes: an experimental model.

Catastrophes of all kinds can be roughly defined as short-duration, large-amplitude events following and followed by long periods of "ripening." Major earthquakes surely belong to the class of "catastrophic" events. Because of the space-time scales involved, an experimental approach is often difficult, not to say impossible, however desirable it could be. Described in this article is a "laboratory" setup that yields data of a type that is amenable to theoretical methods of prediction. Observations are made of a critical slowing down in the noisy signal of a solder wire creeping under constant stress. This effect is shown to be a fair signal of the forthcoming catastrophe in two separate dynamical models. The first is an "abstract" model in which a time-dependent quantity drifts slowly but makes quick jumps from time to time. The second is a realistic physical model for the collective motion of dislocations (the Ananthakrishna set of equations for unstable creep). Hope thus exists that similar changes in the response to noise could forewarn catastrophes in other situations, where such precursor effects should manifest early enough.

Shape of an elastic loop strongly bent by surface tension: experiments and comparison with theory.

When a very flexible wire is dipped into a soapy solution, it collapses onto itself. We consider the regions of high curvature where the wire folds back onto itself, enclosing a capillary film. The shapes of these end loops are measured in experiments using soap films and compared to a known similarity solution. The sizes of these structures provide a simple and reliable way to measure surface tension.

Optical solitons as quantum objects.

The intensity of classical bright solitons propagating in linearly coupled identical fibers can be distributed either in a stable symmetric state at strong coupling or in a stable asymmetric state if the coupling is small enough. In the first case, if the initial state is not the equilibrium state, the intensity may switch periodically from fiber to fiber, while in the second case the asymmetrical state remains forever, with most of its energy in either fiber. The latter situation makes a state of propagation with two exactly reciprocal realizations. In the quantum case, such a situation does not exist as an eigenstate because of the quantum tunneling between the two fibers. Such a tunneling is a purely quantum phenomenon without counterpart in the classical theory. We estimate the rate of tunneling by quantizing a simplified dynamics derived from the original Lagrangian equations with test functions. This tunneling could be within reach of the experiments, particularly if the quantum coherence of the soliton can be maintained over a sufficient amount of time.

Coexistence of ordinary elasticity and superfluidity in a model of a defect-free supersolid.

The mechanical behavior of a supersolid is studied in the framework of a fully explicit model derived from the Gross-Pitaevskii equation without assuming any defect or vacancy. A set of coupled nonlinear partial differential equations plus boundary conditions is derived. The conditions of mechanical equilibrium are studied under external constraints such as steady rotation and external stress. Our model explains the experimentally observed paradoxical behavior: a nonclassical rotational inertia fraction in the limit of small rotation speed but a solidlike elastic response to small stress or an external force field.