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Shear viscosity of lipid membranes dictates how fast lipids, proteins, and other membrane constituents travel along the membrane and rotate around their principal axis, thus governing the rates of diffusion-limited reactions taking place at membranes. In this framework, the heterogeneity of biomembranes indicates that cells could regulate these rates via varying local viscosities. Unfortunately, experiments to probe membrane viscosity under various conditions are tedious and error prone. Molecular dynamics simulations provide an attractive alternative, especially given that recent theoretical developments enable the elimination of finite-size effects in simulations. Here, we use a variety of different equilibrium methods to extract the shear viscosities of lipid membranes from both coarse-grained and all-atom molecular dynamics simulations. We systematically probe the variables relevant for cellular membranes, namely, membrane protein crowding, cholesterol concentration, and the length and saturation level of lipid acyl chains, as well as temperature. Our results highlight that in their physiologically relevant ranges, protein concentration, cholesterol concentration, and temperature have significantly larger effects on membrane viscosity than lipid acyl chain length and unsaturation level. In particular, the crowding with proteins has a significant effect on the shear viscosity of lipid membranes and thus on the diffusion occurring in the membranes. Our work also provides the largest collection of membrane viscosity values from simulation to date, which can be used by the community to predict the diffusion coefficients or their trends via the Saffman-Delbru..ck description. Additionally, it is worth emphasizing that diffusion coefficients extracted from simulations exploiting periodic boundary conditions must be corrected for the finite-size effects prior to comparison with experiment, for which the present collection of viscosity values can readily be used. Finally, our thorough comparison to experiments suggests that there is room for improvement in the description of bilayer dynamics provided by the present force fields.

Block copolymer melts have been previously used to control the position and alignment of anisotropic nanoparticles. In this work, 2D and 3D mesoscopic simulations are used to explore the phase behavior of block copolymer/nanoparticle systems. The method combines a time-dependent Ginzburg-Landau for the polymer and Brownian dynamics for the anisotropic nanoparticles. Rhomboidal and spheroidal shaped particles are simulated in two and three dimensions, respectively. It is found that the nanoparticle nematic order aligned by the block copolymer domains enhances the lamellar phase of the block copolymer, due to an anisotropy-driven phase transition. Additionally, anisotropic nanoparticles within circular-forming block copolymer leads to a competition between the nematic colloidal ordering and the hexagonally ordered mesophase. At large concentrations, the nematic order dominates, deforming the block copolymer mesophase.

Anti-Brownian electrokinetic trapping is a method for trapping single particles in liquid based on particle position measurements and the application of feedback voltages. To achieve trapping in the axial direction, information on the axial particle position is required. However, existing strategies for determining the axial position that are based on measuring the size of the first diffraction ring, theory fitting, advanced optical setups or pre-determined axial image stacks are impractical for anisotropic particles. In this work, axial electrokinetic trapping of anisotropic particles is realized in devices with planar, transparent electrodes. The trapping algorithm uses Fourier-Bessel decomposition of standard microscopy images and is learning from the correlation between applied voltages and changes in the particle appearance. No previous knowledge on the particle appearance, theory fitting or advanced optical setup is required. The particle motion in the trap and the influence of screening of the electric field on this motion are analyzed. The axial trapping method opens new possibilities for measuring properties of anisotropic or isotropic particles and forces acting on such particles.

The Maxey-Riley equation and its simplified versions represent the most widespread tool to investigate dynamics and dispersion of inertial small particles in turbulent flows. The numerical solution of such models is often very challenging, and some of their terms, such as the molecular diffusivity or the Basset history force, are often neglected to reduce the complexity upon suitable approximations. Here, we propose exact results with regard to the rate of transport on large time scales in random shear flows. These can be expediently used as a benchmark to develop and assess algorithms when solving this class of stochastic integrodifferential problems on large time scales.

Diffusing wave spectroscopy (DWS) is a powerful optical technique suitable to investigate turbid samples in a nondestructive and reproducible way, providing information on the static and dynamic properties of the system. This includes the relative displacement of emulsion droplets over time and changes in the viscoelastic properties. Here, novel and promising cellulose-based oil-in-water (O/W) emulsions were prepared and studied, for the first time, by DWS. Cellulose plays the role of a novel eco-friendly emulsifying agent. The hydrolysis time of cellulose was observed to affect the average size of the emulsion droplets and their stability; the longer the hydrolysis time, the more dispersed and stable the emulsions were found to be. Additionally, a good complementarity between the microrheology (DWS) and macrorheology (mechanical rheometer) data was found. Our work suggests that DWS is a highly attractive method to investigate the stability, aging and microrheology properties of cellulose-based emulsions, providing valuable insights on their microstructure. This technique is thus highly appealing for the characterization and design of novel emulsion formulations. (C) 2018 The Authors. Published by Elsevier Inc. Portuguese Foundation for Science and Technology (FCT) [PTDC/AGR-TEC/4814/2014, 030619 (02/SAICT/2017), IF/01005/2014]; Sodra Skogsagarnas Stiftelse; Stiftelsen Nils och Dorthi Troedssons forskningsfond; Swedish Research Council VR [2015-04290]

Finding the generalized Fokker-Planck Equation (FPE) for the reduced probability density function of a subpart of a given complex system is a classical issue of statistical mechanics. Zwanzig projection perturbation approach to this issue leads to the trouble of resumming a series of commutators of differential operators that we show to correspond to solving the Lie evolution of first order differential operators along the unperturbed Liouvillian of the dynamical system of interest. In this paper, we develop in a systematic way the procedure to formally solve this problem. In particular, here we show which the basic assumptions are, concerning the dynamical system of interest, necessary for the Lie evolution to be a group on the space of first order differential operators, and we obtain the coefficients of the so-evolved operators. It is thus demonstrated that if the Liouvillian of the system of interest is not a first order differential operator, in general, the FPE structure breaks down and the master equation contains all the power of the partial derivatives, up to infinity. Therefore, this work shed some light on the trouble of the ubiquitous emergence of both thermodynamics from microscopic systems and regular regression laws at macroscopic scales. However these results are very general and can be applied also in other contexts that are non-Hamiltonian as, for example, geophysical fluid dynamics, where important events, like El Nino, can be considered as large time scale phenomena emerging from the observation of few ocean degrees of freedom of a more complex system, including the interaction with the atmosphere.

Experimental study on natural convection in a nanofluid-filled differentially heated cavity has been presented. Experiments have been conducted in an octagonal cavity with water and Al2O3/water-based dilute nanofluids of varying concentrations. A Mach Zehnder interferometer has been employed to record the projection data of convective field from four view angles (0, 45, 90 and 135 degrees). The two-dimensional temperature fields determined through the quantitative analysis of the interferometric images have been employed to reconstruct the local field information using the principles of tomography. Results of the three-dimensional reconstructions clearly brought out the mechanisms of possible fluid movement in the differentially-heated cavity and its dependence on nanoparticle concentration. Near wall surface distributions of temperature fields as well as local Nusselt numbers indicated towards possible breakdown of large scale fluid structures into small length scale multiple roll-like circulatory loops at higher volumetric concentrations of dilute nanofluids. Local disturbances thus induced in the fluid layer due to the addition of nanoparticles resulted into better fluid mixing, which in turn led to an enhancement in the heat transfer rates with increasing concentration of nanofluids. Surface plots of Nusselt numbers obtained in the vicinity of the two thermally active walls of the cavity established an overall energy balance in the fluid layer.

One of the cornerstones of turbulent dispersion is the celebrated Taylor's formula. This formula expresses the rate of transport (i.e., the eddy diffusivity) of a tracer as a time integral of the fluid velocity autocorrelation function evaluated along the fluid particle trajectories. Here, we review the hypotheses which permit us to extend Taylor's formula to particles of any inertia. The hypotheses are independent of the details of the inertial particle model. We also show by explicit calculation that the hypotheses encompass cases when memory terms such as Basset's and Faxén's corrections are taken into account in the modeling of inertial particle dynamics. One of the cornerstones of turbulent dispersion is the celebrated Taylor's formula. This formula expresses the rate of transport (i.e., the eddy diffusivity) of a tracer as a time integral of the fluid velocity autocorrelation function evaluated along the fluid particle trajectories. Here, we review the hypotheses which permit us to extend Taylor's formula to particles of any inertia. The hypotheses are independent of the details of the inertial particle model. We also show by explicit calculation that the hypotheses encompass cases when memory terms such as Basset's and Faxén's corrections are taken into account in the modeling of inertial particle dynamics. One of the cornerstones of turbulent dispersion is the celebrated Taylor's formula. This formula expresses the rate of transport (i.e., the eddy diffusivity) of a tracer as a time integral of the fluid velocity autocorrelation function evaluated along the fluid particle trajectories. Here, we review the hypotheses which permit us to extend Taylor's formula to particles of any inertia. The hypotheses are independent of the details of the inertial particle model. We also show by explicit calculation that the hypotheses encompass cases when memory terms such as Basset's and Faxén's corrections are taken into account in the modeling of inertial particle dynamics.

The first-exit time process of an inverse Gaussian L\'evy process is considered. The one-dimensional distribution functions of the process are obtained. They are not infinitely divisible and the tail probabilities decay exponentially. These distribution functions can also be viewed as distribution functions of supremum of the Brownian motion with drift. The density function is shown to solve a fractional PDE and the result is also generalized to tempered stable subordinators. The subordination of this process to the Brownian motion is considered and the underlying PDE of the subordinated process is obtained. The infinite divisibility of the first-exit time of a $\beta$-stable subordinator is also discussed., Comment: 19 pages, 2 figures

Westudy both experimentally and theoretically the dynamics of chemically self-propelled Janus colloids moving atop a two-dimensional crystalline surface. The surface is a hexagonally close-packed monolayer of colloidal particles of the same size as the mobile one. The dynamics of the self-propelled colloid reflects the competition between hindered diffusion due to the periodic surface and enhanced diffusion due to active motion. Which contribution dominates depends on the propulsion strength, which can be systematically tuned by changing the concentration of a chemical fuel. The mean-square displacements (MSDs) obtained from the experiment exhibit enhanced diffusion at long lag times. Our experimental data are consistent with a Langevin model for the effectively two-dimensional translational motion of an active Brownian particle in a periodic potential, combining the confining effects of gravity and the crystalline surface with the free rotational diffusion of the colloid. Approximate analytical predictions are made for the MSD describing the crossover from free Brownian motion at short times to active diffusion at long times. The results are in semi-quantitative agreement with numerical results of a refined Langevin model that treats translational and rotational degrees of freedom on the same footing.

Westudy both experimentally and theoretically the dynamics of chemically self-propelled Janus colloids moving atop a two-dimensional crystalline surface. The surface is a hexagonally close-packed monolayer of colloidal particles of the same size as the mobile one. The dynamics of the self-propelled colloid reflects the competition between hindered diffusion due to the periodic surface and enhanced diffusion due to active motion. Which contribution dominates depends on the propulsion strength, which can be systematically tuned by changing the concentration of a chemical fuel. The mean-square displacements (MSDs) obtained from the experiment exhibit enhanced diffusion at long lag times. Our experimental data are consistent with a Langevin model for the effectively two-dimensional translational motion of an active Brownian particle in a periodic potential, combining the confining effects of gravity and the crystalline surface with the free rotational diffusion of the colloid. Approximate analytical predictions are made for the MSD describing the crossover from free Brownian motion at short times to active diffusion at long times. The results are in semi-quantitative agreement with numerical results of a refined Langevin model that treats translational and rotational degrees of freedom on the same footing.

We investigate computational aspects of basket credit default swap pricing with counterparty credit risk under a multiname contagion model. This model enables us to capture systematic volatility increases in the market triggered by particular bankruptcies. A drawback of this model is its analytical intractability due to a combination of path-dependent coefficients and a path-dependent functional, which furthermore causes potential failure of convergence of numerical approximations under standing assumptions. In this paper, we find sufficient conditions for the desired convergence of functionals associated with approximated solution of certain path-dependent stochastic differential equations.

An Eulerian–Lagrangian model is used to simulate turbulent-forced convection heat transfer in internal flow using dilute nanofluids. For comparison, a single-phase model of the nanofluid which describes a nanofluid as a single-phase fluid with appropriately defined thermophysical properties is also implemented. The Eulerian–Lagrangian model, which requires only the properties of the base fluid and nanoparticles separately, is seen to predict the heat transfer characteristics accurately without resort to any models for the thermophysical properties. The simulations with the single-phase model show that it can very well be used to predict the heat transfer behavior of dilute nanofluids as long as the thermophysical properties are directly those measured experimentally or those predicted from a Brownian motion based model. These approaches are particularly useful for engineering estimation of heat transfer performance of equipment where nanofluids are expected to be used.

Laser interferometry-based forced convective heat transfer experiments in the context of compact channels using nanofluids are reported. Experiments have been carried out under thermally-developing flow conditions for a range of Reynolds numbers. De-ionized water and alumina/water-based dilute nanofluids have been employed as the coolant medium. The nanofluid-based experiments employ three volumetric concentrations of 0.01%, 0.03% and 0.05%. Projection data of the convective fields have been recorded using a Mach-Zehnder interferometer. Phenomena such as thermal boundary layer profiles and thickness of thermal boundary layer have been interpreted based on the infinite fringe setting mode of the interferometer, while the quantitative information in the form of whole-field temperature distributions and heat transfer coefficients have been retrieved from the wedge fringe setting. Effects of increasing Reynolds numbers and volumetric concentrations of nanofluids on thermal boundary layer profiles and the resultant heat transfer rates have been investigated. Results of the experiments carried out at low Reynolds number (Re < 513) reveal that the thermal boundary layer profiles are nearly insensitive to the changes in the concentrations of dilute nanofluids, while a significant enhancement in the heat transfer coefficient is seen as the concentrations of nanofluid is increased. On other hand, at higher Reynolds numbers, increasing concentrations of dilute nanofluids leads to a considerable increase in the thickness of thermal boundary layer that is accompanied with a mild deterioration in the heat transfer rates. Based on the primary findings of the experiments, that are purely non-intrusive in nature, various plausible mechanisms that govern the heat transfer characteristics of dilute nanofluids have been discussed. (C) 2016 Elsevier Inc. All rights reserved.

We prove a Hardy-Stein type identity for the semigroups of symmetric, pure-jump L\'evy processes. Combined with the Burkholder-Gundy inequalities, it gives the $L^p$ two-way boundedness, for $1, Comment: 17 pages

In this article we consider rough differential equations (RDEs) driven by non-geometric rough paths, using the concept of branched rough paths introduced in Gubinelli (2004). We first show that branched rough paths can equivalently be defined as $\gamma$-H\"older continuous paths in some Lie group, akin to geometric rough paths. We then show that every branched rough path can be encoded in a geometric rough path. More precisely, for every branched rough path $\mathbf{X}$ lying above a path $X$, there exists a geometric rough path $\bar{\mathbf{X}}$ lying above an extended path $\bar X$, such that $\bar{\mathbf{X}}$ contains all the information of $\mathbf{X}$. As a corollary of this result, we show that every RDE driven by a non-geometric rough path $\mathbf{X}$ can be rewritten as an extended RDE driven by a geometric rough path $\bar{\mathbf{X}}$. One could think of this as a generalisation of the It\^o-Stratonovich correction formula., Comment: Fixed abstract for display with MathJax

We study the asymptotic Dirichlet problem for A-harmonic equations and for the minimal graph equation on a Cartan-Hadamard manifold M whose sectional curvatures are bounded from below and above by certain functions depending on the distance to a fixed point in M. We are, in particular, interested in finding optimal (or close to optimal) curvature upper bounds., To appear in Communications in Analysis and Geometry

The Generalised Langevin Equation (GLE) method, as developed in Ref. [Phys. Rev. B 89, 134303 (2014)], is used to calculate the dissipative dynamics of systems described at the atomic level. The GLE scheme goes beyond the commonly used bilinear coupling between the central system and the bath, and permits us to have a realistic description of both the dissipative central system and its surrounding bath. We show how to obtain the vibrational properties of a realistic bath and how to convey such properties into an extended Langevin dynamics by the use of the mapping of the bath vibrational properties onto a set of auxiliary variables. Our calculations for a model of a Lennard-Jones solid show that our GLE scheme provides a stable dynamics, with the dissipative/relaxation processes properly described. The total kinetic energy of the central system always thermalises toward the expected bath temperature, with appropriate fluctuation around the mean value. More importantly, we obtain a velocity distribution for the individual atoms in the central system which follows the expected canonical distribution at the corresponding temperature. This confirms that both our GLE scheme and our mapping procedure onto an extended Langevin dynamics provide the correct thermostat. We also examined the velocity autocorrelation functions and compare our results with more conventional Langevin dynamics., accepted for publication in PRB

We study diffusion coefficients of liquid domains by explicitly taking into account the two-layered structure called leaflets of the bilayer membrane. In general, the velocity fields associated with each leaflet are different and the layers sliding past each other cause frictional coupling. We obtain analytical results of diffusion coefficients for a circular liquid domain in a leaflet, and quantitatively study their dependence on the inter-leaflet friction. We also show that the diffusion coefficients diverge in the absence of coupling between the bilayer and solvents, even when the inter-leaflet friction is taken into account. In order to corroborate our theory, the effect of the inter-leaflet friction on the correlated diffusion is examined., Comment: 10 figures

International audience; In the diffusion model of chemical reactions, the encounter (reaction) rate between reactant particles is governed by the Smoluchowski equation, which is a diffusion equation in a field of forces. We consider crowded environments where the particles diffuse through a "liquid" of like particles. Assuming that the liquid-like short-range structure around the reactant gives rise to an effective (osmotic) barrier leads us to map a complicated many-body problem to a one-dimensional problem. This allows us to describe theoretically such complex systems that are encountered in many applications where crowding, intermolecular interactions, and flow are simultaneously present. A particularly important effect is discovered which is due to the interplay between shear and crowding. This effect is responsible for unexpected peaks in the reactivity at low flow intensity which may explain, among other things, the bizarre colloidal stability behavior of concentrated protein suspensions.

We consider excited random walks (ERWs) on integers with a bounded number of i.i.d. cookies per site without the non-negativity assumption on the drifts induced by the cookies. Kosygina and Zerner [KZ08] have shown that when the total expected drift per site, delta, is larger than 1 then ERW is transient to the right and, moreover, for delta>4 under the averaged measure it obeys the Central Limit Theorem. We show that when delta in (2,4] the limiting behavior of an appropriately centered and scaled excited random walk under the averaged measure is described by a strictly stable law with parameter delta/2. Our method also extends the results obtained by Basdevant and Singh [BS08b] for delta in (1,2] under the non-negativity assumption to the setting which allows both positive and negative cookies., 27 pages

We consider a random walk in an i.i.d. non-negative potential on the d-dimensional integer lattice. The walk starts at the origin and is conditioned to hit a remote location y on the lattice. We prove that the expected time under the annealed path measure needed by the random walk to reach y grows only linearly in the distance from y to the origin. In dimension one we show the existence of the asymptotic positive speed., 29 pages

Given a stable L\'{e}vy process $X=(X_t)_{0\le t\le T}$ of index $\alpha\in(1,2)$ with no negative jumps, and letting $S_t=\sup_{0\le s\le t}X_s$ denote its running supremum for $t\in [0,T]$, we consider the optimal prediction problem \[V=\inf_{0\le\tau\le T}\mathsf{E}(S_T-X_{\tau})^p,\] where the infimum is taken over all stopping times $\tau$ of $X$, and the error parameter $p\in(1,\alpha)$ is given and fixed. Reducing the optimal prediction problem to a fractional free-boundary problem of Riemann--Liouville type, and finding an explicit solution to the latter, we show that there exists $\alpha_*\in(1,2)$ (equal to 1.57 approximately) and a strictly increasing function $p_*:(\alpha_*,2)\rightarrow(1,2)$ satisfying $p_*(\alpha_*+)=1$, $p_*(2-)=2$ and $p_*(\alpha), Comment: Published in at http://dx.doi.org/10.1214/10-AOP598 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We present a modified formalization of the 'spine' change of measure approach for branching diffusions in the spirit, of those found in Kyprianou [40] and Lyons et al. [44, 437 41]. We use our formulation to interpret certain 'Gibbs-Boltzmann' weightings of particles and use this to give an intuitive proof of a general 'Many-to-One' result which enables expectations of sums over particles in the branching diffusion to be calculated purely in terms of an expectation of one 'spine' particle. We also exemplify spine proofs of the L-p-convergence (p >= 1) of some key 'additive' martingales for three distinct models of branching diffusions including flew results for a multi-type branching Brownian motion and discussion of left-most particle speeds.

We discuss the recent attempts to generalize dynamical density functional (DDF) theory to situations where the momentum and energy transport, not necessarily associated with mass diffusion, play a role. We consider an assembly of particles described by inertial dynamics and subjected to the influence of a heat-bath. By means of a time multiple timescale analysis we derive the evolution equation for the noise-averaged density field. Remarkably, for large values of the friction parameter and/or the mass of the particles we obtain the same governing equation of DDF, and in addition we are able to compute higher-order corrections.

Formation and motion of copper adatoms and addimers on Ag( 1 1 1) are investigated with low-temperature scanning tunnelling microscopy between 6 and 25 K. Adatoms move between fcc and hcp sites with a strong preference for the fcc site. Adatom motion and dimer rotation change due to the presence of other adatoms or dimers. Furthermore, rotating dimers influence other rotating dimers. These changes are attributed to changes in the diffusion or rotation potential, which are mediated by the electrons in the two-dimensional surface state band.

We studied the coverage dependence of the self-diffusion on the Cu(111) surface using molecular dynamics simulations. The adatoms coalesce to a large island whose migration energy increases with coverage, attaining 0.37 eV above a concentration of 25%. The migration rate of the island's atoms scales with their number as N-1, while step atoms are fast diffusing independent of the cluster size. Detailed trajectory analysis revealed that cluster diffusion occurs via 'step running' of the peripheral atoms that initiate concerted movements of the inner cluster atoms. In addition, adatoms and vacancies are spontaneously created and annihilated on the island's terrace, contributing to the migration of the island. These findings describe the most important processes of cluster diffusion involved in the early stages of growth on this surface. (C) 1999 Elsevier Science B.V. All rights reserved. Surface Science