Valery Ilyin

On the nature of disjoining pressure oscillations in fluid films

The thin fluid films that are in equilibrium with a bulk phase are studied by a computer simulation. A disjoining pressure, whose value oscillates with the change in the distance between two boundary surfaces, is shown to occur in this system. The nature of this phenomenon is associated with the oscillating contribution from the short range repulsive forces.

Direct identification of the glass transition: Growing length scale and the onset of plasticity

Understanding the mechanical properties of glasses remains elusive since the glass transition itself is not fully understood, even in well-studied examples of glass formers in two dimensions. In this context we demonstrate here: i) a direct evidence for a diverging length scale at the glass transition ii) an identification of the glass transition with the disappearance of fluid-like regions and iii) the appearance in the glass state of fluid-like regions when mechanical strain is applied. These fluid-like regions are associated with the onset of plasticity in the amorphous solid. The relaxation times which diverge upon the approach to the glass transition are related quantitatively to the diverging length scale.

Short-range order in cylindrical liquid-filled micropores

A hard-sphere fluid inside an infinitely long circular cylinder with an ideal hard surface is studied by computer simulation. The system is assumed to be in equilibrium with a bulk hard-sphere fluid of fixed number density. The dependence of the structural and transport characteristics on the cylinder radius is determined. A non-monotonic behaviour of the pressure and self-diffusion coefficient dependences is observed.

Randomness-induced redistribution of vibrational frequencies in amorphous solids

Much of the discussion in the literature of the low frequency part of the density of states of amorphous solids was dominated for years by comparing measured or simulated density of states to the classical Debye model. Since this model is hardly appropriate for the materials at hand, this created some amount of confusion regarding the existence and universality of the so- called “Boson Peak” which results from such comparisons. We propose that one should pay attention to the different roles played by different aspects of disorder, the first being disorder in the interaction strengths, the second positional disorder, and the third coordination disorder. These have different effects on the low-frequency part of the density of states. We examine the density of states of a number of tractable models in one and two dimensions, and reach a clearer picture of the softening and redistribution of frequencies in such materials. We discuss the effects of disorder on the elastic moduli and the relation of the latter to frequency softening, reaching the final conclusion that the Boson peak is not universal at all. The study of the density of states of solid materials started with attempts to understand the temperature dependence of the specific heat at low temperatures, say CV ≡ (∂U/∂T )V where U is the energy and T the temperature of the system. This called for a microscopic theory for solids, and the first one was developed by Einstein, assuming that in d dimensions each atom is represented as a d-dimensional harmonic oscillator [1] (in the original paper the case d = 3 was considered). In this article Planck’s quantization assumption, which was originally applied to radiation, was extended to solid vibrations [2]. In the case of dN linear oscillators each with its own frequency ω i, Einstein’s result can be expressed as

The plastic response of magnetoelastic amorphous solids

We address the cross-effects between mechanical strains and magnetic fields on the plastic response of magnetoelastic amorphous solids. It is well known that plasticity in non-magnetic amorphous solids under external strain ? is dominated by the codimension-1 saddle-node bifurcation in which an eigenvalue of the Hessian matrix vanishes at ?P like . This square-root singularity determines much of the statistical physics of elasto-plasticity, and in particular that of the stress-strain curves under athermal-quasistatic conditions. In this letter we discuss the much richer physics that can be expected in magnetic amorphous solids. Firstly, magnetic amorphous solids exhibit codimension-2 plastic instabilities, when an external strain and an external magnetic field are applied simultaneously. Secondly, the phase diagrams promise a rich array of new effects that have been barely studied; this opens up a novel and extremely rich research program for magnetoplastic materials.

Stochastic processes crossing from ballistic to fractional diffusion with memory: exact results.

We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (subdiffusion or superdiffusion) at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exactly respect the two different asymptotics of the diffusion process. Having done so we solve for the probability distribution function (pdf) as a continuous function which evolves inside a ballistically expanding domain. This general solution agrees for long times with the pdf obtained within the continuous random-walk approach, but it is much superior to this solution at shorter times where the effect of the ballistic regime is crucial.

Aging and relaxation in glass-forming systems

We propose that there exists a generic class of glass-forming systems that have competing states (of crystalline order or not) which are locally close in energy to the ground state (which is typically unique). Upon cooling, such systems exhibit patches (or clusters) of these competing states which become locally stable in the sense of having a relatively high local shear modulus. It is in between these clusters where aging, relaxation, and plasticity under strain can take place. We demonstrate explicitly that relaxation events that lead to aging occur where the local shear modulus is low (even negative) and result in an increase in the size of local patches of relative order. We examine the aging events closely from two points of view. On the one hand we show that they are very localized in real space, taking place outside the patches of relative order, and from the other point of view we show that they represent transitions from one local minimum in the potential surface to another. This picture offers a direct relation between structure and dynamics, ascribing the slowing down in glass-forming systems to the reduction in relative volume of the amorphous material which is liquidlike. While we agree with the well-known Adam-Gibbs proposition that the slowing down is due to an entropic squeeze (a dramatic decrease in the number of available configurations), we do not agree with the Adam-Gibbs (or the Volger-Fulcher) formulas that predict an infinite relaxation time at a finite temperature. Rather, we propose that generically there should be no singular crisis at any finite temperature: the relaxation time and the associated correlation length (average cluster size) increase at most superexponentially when the temperature is lowered.

Points at issue in the physics of water and homoeopathy

Abstract The main features of a new model for associated liquids are expounded. The stability of various dissipative structures in water systems is explained by their presence in the earths electromagnetic field and by the stabilizing processes of proton transfer along hydrogen-bonded chains in these structures. A possible connection between processes occurring in dissipative water structures and the radiation characteristics of homoeopathic preparations is shown.

Statistical mechanics of glass formation in molecular liquids with OTP as an example.

We extend our statistical mechanical theory of the glass transition from examples consisting of point particles to molecular liquids with internal degrees of freedom. As before, the fundamental assertion is that supercooled liquids are ergodic, although becoming very viscous at lower temperatures, and are therefore describable in principle by statistical mechanics. The theory is based on analyzing the local neighborhoods of each molecule, and a statistical mechanical weight is assigned to every possible local organization. This results in an approximate theory that is in very good agreement with simulations regarding both thermodynamical and dynamical properties.

Breakdown of nonlinear elasticity in stress-controlled thermal amorphous solids

In recent work it was clarified that amorphous solids under strain control do not possess nonlinear elastic theory in the sense that the shear modulus exists but nonlinear moduli exhibit sample-to-sample fluctuations that grow without bound with the system size. More relevant, however, for experiments are the conditions of stress control. In the present Rapid Communication we show that also under stress control the shear modulus exists, but higher-order moduli show unbounded sample-to-sample fluctuation. The unavoidable consequence is that the characterization of stress-strain curves in experiments should be done with a stress-dependent shear modulus rather than with nonlinear expansions.