Phase Separation in Binary Fluid Mixtures with Continuously Ramped Temperature

We consider the demixing of a binary fluid mixture, under gravity, which is steadily driven into a two phase region by slowly ramping the temperature. We assume, as a first approximation, that the system remains spatially isothermal, and examine the interplay of two competing nonlinearities. One of these arises because the supersaturation is greatest far from the meniscus, creating inversion of the density which can lead to fluid motion; although isothermal, this is somewhat like the Benard problem (a single-phase fluid heated from below). The other is the intrinsic diffusive instability which results either in nucleation or in spinodal decomposition at large supersaturations. Experimental results on a simple binary mixture show interesting oscillations in heat capacity and optical properties for a wide range of ramp parameters. We argue that these oscillations arise under conditions where both nonlinearities are important

Shear flow effects on phase separation of entangled polymer blends

We introduce an entanglement model mixing rule for stress relaxation in a polymer blend to a modified Cahn-Hilliard equation of motion for concentration fluctuations in the presence of shear flow. Such an approach predicts both shear-induced mixing and demixing, depending on the relative relaxation times and plateau moduli of the two components

Kramers rate theory of ionization and dissociation of bound states

Calculating the microscopic dissociation rate of a bound state, such as a classical diatomic molecule, has been difficult so far. The problem was that standard theories require an energy barrier over which the bound particle (or state) escapes into the preferred low-energy state. This is not the case when the long-range repulsion responsible for the barrier is either absent or screened (as in Cooper pairs, ionized plasma, or biomolecular complexes). We solve this classical problem by accounting for entropic memory at the microscopic level. The theory predicts dissociation rates for arbitrary potentials and is successfully tested on the example of plasma, where it yields an estimate of ionization in the core of Sun in excellent agreement with experiments. In biology, the new theory accounts for crowding in receptor-ligand kinetics and protein aggregation

Small angle neutron scattering observation of chain retraction after a large step deformation

The process of retraction in entangled linear chains after a fast nonlinear stretch was detected from time-resolved but quenched small angle neutron scattering (SANS) experiments on long, well-entangled polyisoprene chains. The statically obtained SANS data cover the relevant time regime for retraction, and they provide a direct, microscopic verification of this nonlinear process as predicted by the tube model. Clear, quantitative agreement is found with recent theories of contour length fluctuations and convective constraint release, using parameters obtained mainly from linear rheology. The theory captures the full range of scattering vectors once the crossover to fluctuations on length scales below the tube diameter is accounted for

An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation

The classical law of the iterated logarithm (LIL for short)as fundamental limit theorems in probability theory play an important role in the development of probability theory and its applications. Strassen (1964) extended LIL to large classes of functional random variables, it is well known as the invariance principle for LIL which provide an extremely powerful tool in probability and statistical inference. But recently many phenomena show that the linearity of probability is a limit for applications, for example in finance, statistics. As while a nonlinear expectation--- G-expectation has attracted extensive attentions of mathematicians and economists, more and more people began to study the nature of the G-expectation space. A natural question is: Can the classical invariance principle for LIL be generalized under G-expectation space? This paper gives a positive answer. We present the invariance principle of G-Brownian motion for the law of the iterated logarithm under G-expectation

Dumbbell transport and deflection in a spatially periodic potential

We present theoretical results on the deterministic and stochastic motion of a dumbbell carried by a uniform flow through a three-dimensional spatially periodic potential. Depending on parameters like the flow velocity, there are two different kinds of movement: transport along a potential valley and stair-like motion oblique to the potential trenches. The crossover between these two regimes, as well as the deflection angle, depends on the size of the dumbbell. Moreover, thermal fluctuations cause a resonance-like variation in the deflection angle as a function of the dumbbell extension.Comment: 5 pages, 8 figure

Coarse-grained model of entropic allostery

Many signaling functions in molecular biology require proteins to bind to substrates such as DNA in response to environmental signals such as the simultaneous binding to a small molecule. Examples are repressor proteins which may transmit information via a conformational change in response to the ligand binding. An alternative entropic mechanism of "allostery" suggests that the inducer ligand changes the intramolecular vibrational entropy, not just the mean static structure. We present a quantitative, coarse-grained model of entropic allostery, which suggests design rules for internal cohesive potentials in proteins employing this effect. It also addresses the issue of how the signal information to bind or unbind is transmitted through the protein. The model may be applicable to a wide range of repressors and also to signaling in trans-membrane proteins

Molecular observation of contour-length fluctuations limiting topological confinement in polymer melts

In order to study the mechanisms limiting the topological chain confinement in polymer melts, we have performed neutron-spin-echo investigations of the single-chain dynamic-structure factor from polyethylene melts over a large range of chain lengths. While at high molecular weight the reptation model is corroborated, a systematic loosening of the confinement with decreasing chain length is found. The dynamic-structure factors are quantitatively described by the effect of contour-length fluctuations on the confining tube, establishing this mechanism on a molecular level in space and time