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

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

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

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

Rates and Intermediates in Ser26 Mutants of Benzoylformate Decarboxylase

poster abstractBenzoylformate decarboxylase (BFDC), a thiamine diphosphate dependent enzyme, catalyzes decarboxylation of benzoylformate to benzaldehyde and CO2. The BFDC reaction proceeds through at least four individual chemical steps and, recently, NMR spectroscopy has been used to measure the ratios of intermediates in the overall reaction. This method permits calculation of rate constants for formation of the first intermediate, mandelylThDP (k2) and its subsequent decarboxylation (k3), as well as the combined breakdown of the enamine and product release (k4). As part of a study of the contributions of the active site residues, Ser26, His70 and His281, to the individual catalytic steps several Ser26 variants were expressed and purified. Initially, the variants were characterized using steady-state kinetics. Subsequently, the enzymes were mixed with benzoylformate and the mixture immediately acid quenched to trap intermediates of the reaction. NMR spectroscopy was used to identify and quantitate individual catalytic intermediates. Rate constants for the formation of these intermediates were then determined and compared to those of the wild-type enzyme. Here we report those results and discuss their implications for the role of Ser26 in the BFDC reaction mechanism

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

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

Unfolding dynamics of proteins under applied force

Understanding the mechanisms of protein folding is a major challenge that is being addressed effectively by collaboration between researchers in the physical and life sciences. Recently, it has become possible to mechanically unfold proteins by pulling on their two termini using local force probes such as the atomic force microscope. Here, we present data from experiments in which synthetic protein polymers designed to mimic naturally occurring polyproteins have been mechanically unfolded. For many years protein folding dynamics have been studied using chemical denaturation, and we therefore firstly discuss our mechanical unfolding data in the context of such experiments and show that the two unfolding mechanisms are not the same, at least for the proteins studied here. We also report unexpected observations that indicate a history effect in the observed unfolding forces of polymeric proteins and explain this in terms of the changing number of domains remaining to unfold and the increasing compliance of the lengthening unstructured polypeptide chain produced each time a domain unfolds

High and low molecular weight crossovers in the longest relaxation time dependence of linear cis-1,4 polyisoprene by dielectric relaxations

The dielectric relaxation of cis-1,4 Polyisoprene [PI] is sensitive not only to the local and segmental dynamics but also to the larger scale chain (end-to-end) fluctuations. We have performed a careful dielectric investigation on linear PI with various molecular weights in the range of 1 to 320 kg/mol. The broadband dielectric spectra of all samples were measured isothermally at the same temperature to avoid utilizing shift factors. For the low and medium molecular weight range, the comparisons were performed at 250 K to access both the segmental relaxation and normal mode peaks inside the available frequency window (1 mHz–10 MHz). In this way, we were able to observe simultaneously the effect of molecular mass on the segmental dynamics—related with the glass transition process—and on the end-to-end relaxation time of PI and thus decouple the direct effect of molecular weight on the normal mode from that due to the effect on the monomeric friction coefficient. The latter effect is significant for low molecular weight (M w < 33 kg/mol), i.e., in the range where the crossover from Rouse dynamics to entanglement limited flow occurs. Despite the conductivity contribution at low frequency, careful experiments allowed us to access to the normal mode signal for molecular weights as high as M w = 320 kg/mol, i.e., into the range of high molecular weights where the pure reptation behavior could be valid, at least for the description of the slowest chain modes. The comparison between the dielectric relaxations of PI samples with medium and high molecular weight was performed at 320 K. We found two crossovers in the molecular weight dependence of the longest relaxation time, the first around a molecular weight of 6.5 ± 0.5 kg/mol corresponding to the end of the Rouse regime and the second around 75 ± 10 kg/mol. Above this latter value, we find a power law compatible with exponent 3 as predicted by the De Gennes theory

Dynamic photoinhibition exhibited by red coralline algae in the Red Sea

Background Red coralline algae are critical components of tropical reef systems, and their success and development is, at least in part, dependent on photosynthesis. However, natural variability in the photosynthetic characteristics of red coralline algae is poorly understood. This study investigated diurnal variability in encrusting Porolithon sp. and free-living Lithophyllum kotschyanum. Measured parameters included: photosynthetic characteristics, pigment composition, thallus reflectance and intracellular concentrations of dimethylsulphoniopropionate (DMSP), an algal antioxidant that is derived from methionine, an indirect product of photosynthesis. L. kotschyanum thalli were characterised by a bleached topside and a pigmented underside. Results Minimum saturation intensity and intracellular DMSP concentrations in Porolithon sp. were characterised by significant diurnal patterns in response to the high-light regime. A smaller diurnal pattern in minimum saturation intensity in the topside of L. kotschyanum was also evident. The overall reflectance of the topside of L. kotschyanum also exhibited a diurnal pattern, becoming increasingly reflective with increasing ambient irradiance. The underside of L. kotschyanum, which is shaded from ambient light exposure, exhibited a much smaller diurnal variability. Conclusions This study highlights a number of dynamic photoinhibition strategies adopted by coralline algae, enabling them to tolerate, rather than be inhibited by, the naturally high irradiance of tropical reef systems; a factor that may become more important in the future under global change projections. In this context, this research has significant implications for tropical reef management planning and conservation monitoring, which, if natural variability is not taken into account, may become flawed. The information provided by this research may be used to inform future investigations into the contribution of coralline algae to reef accretion, ecosystem service provision and palaeoenvironmental reconstruction