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Thermal motion of four liquid lead nanoinclusions attached to fixed dislocation segments joining in a dislocation node in aluminum-based alloy at 485 degrees C is studied in-situ using TEM. The mutual interaction of the inclusions in all pairs is detected demonstrating the collective interaction of the all inclusions. The time-correlated thermal motion of each of the inclusions, and time-correlated thermal motion of the inclusions in all the pairs are indicated. Phase spectra of the time dependencies of the positions of the inclusions on the dislocations obtained using FFT reveal an existence of a common harmonic in their thermal oscillations at low frequencies demonstrating synchronous oscillations of the inclusions. The transition between synchronous and asynchronous dynamics of the thermal oscillations of the inclusions with increasing frequency is observed. The external vibrations introduced by the inclusion attached to the dislocation node are probably the reason for this transition.

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.

Membrane proteins travel along cellular membranes and reorient themselves to form functional oligomers and proteinlipid complexes. Following the Saffman-Delbruck model, protein-radius sets the rate of this diffusive motion. However, it is unclear how this model, derived for ideal and dilute membranes, performs under crowded conditions of cellular membranes. Here, we study the rotational motion of membrane proteins using molecular dynamics simulations of coarse-grained membranes and 2-dimensional Lennard-Jones fluids with varying levels of crowding. We find that the Saffman-Delbruck model captures the size-dependency of rotational diffusion under dilute conditions where protein-protein interactions are negligible, whereas stronger scaling laws arise under crowding. Together with our recent work on lateral diffusion, our results reshape the description of protein dynamics in native membrane environments: The translational and rotational motions of proteins with small transmembrane domains are rapid, whereas larger proteins or protein complexes display substantially slower dynamics.

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.

If $\mathcal{W}$ is the simple random walk on the square lattice $\mathbb{Z}^2$, then $\mathcal{W}$ induces a random walk $\mathcal{W}_G$ on any spanning subgraph $G\subset \mathbb{Z}^2$ of the lattice as follows: viewing $\mathcal{W}$ as a uniformly random infinite word on the alphabet $\{\mathbf{x}, -\mathbf{x}, \mathbf{y}, -\mathbf{y} \}$, the walk $\mathcal{W}_G$ starts at the origin and follows the directions specified by $\mathcal{W}$, only accepting steps of $\mathcal{W}$ along which the walk $\mathcal{W}_G$ does not exit $G$. For any fixed subgraph $G \subset \mathbb{Z}^2$, the walk $\mathcal{W}_G$ is distributed as the simple random walk on $G$, and hence $\mathcal{W}_G$ is almost surely recurrent in the sense that $\mathcal{W}_G$ visits every site reachable from the origin in $G$ infinitely often. This fact naturally leads us to ask the following: does $\mathcal{W}$ almost surely have the property that $\mathcal{W}_G$ is recurrent for \emph{every} subgraph $G \subset \mathbb{Z}^2$? We answer this question negatively, demonstrating that exceptional subgraphs exist almost surely. In fact, we show more to be true: exceptional subgraphs continue to exist almost surely for a countable collection of independent simple random walks, but on the other hand, there are almost surely no exceptional subgraphs for a branching random walk., 19 pages, submitted

The phenomena of nanofluids-based natural convection heat transfer around a heated cylinder have been studied using nonintrusive real-time diagnostics. Experiments have been performed with a horizontally placed heated cylinder immersed in bulk ambient conditions with water and alumina oxide/water-based dilute nanofluids as the working fluids. Volumetric concentrations of alumina nanoparticles have been varied from 0.005 to 0.02%. A classical Mach-Zehnder interferometer has been used to record the line-of-sight projection data of the convective field around the heated cylinder. The strength of thermal gradients prevailing around the surface of the heated cylinder was seen to be clearly affected by the variations in the nanofluid concentration, thus indicating the plausible role of nanoparticles in disrupting the thermal boundary-layer profiles around the cylinder surface. Significant enhancement in the heat transfer coefficient was observed at the highest levels of concentration of the dilute nanofluids employed, whereas the spatially averaged Nusselt numbers around the cylinder surface showed a marginal deterioration at the lower range of volumetric concentrations. With a further increase in nanoparticles concentration, the Nusselt numbers showed an increasing trend, although not as significant as observed in the case of the heat transfer coefficient. Plausible mechanisms responsible for these observations have been delved upon using purely nonintrusive whole field measurements.

We collect recent results on deriving useful response relations also for non-equilibrium systems. The approach is based on dynamical ensembles, determined by an action on trajectory space. (Anti)Symmetry under time-reversal separates two complementary contributions in the response, one entropic the other frenetic. Under time-reversal invariance of the unperturbed reference process, only the entropic term is present in the response, giving the standard fluctuation–dissipation relations in equilibrium. For non-equilibrium reference ensembles, the frenetic term contributes essentially and is responsible for new phenomena. We discuss modifications in the Sutherland-Einstein relation, the occurence of negative differential mobilities and the saturation of response. We also indicate how the Einstein relation between noise and friction gets violated for probes coupled to a non-equilibrium environment. We end with some discussion on the situation for quantum phenomena, but the bulk of the text concerns classical mesoscopic (open) systems. The choice of many simple examples is trying to make the notes pedagogical, to introduce an important area of research in non-equilibrium statistical mechanics.

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.

The present work reports the development and application of a lens-based rainbow schlieren deflectometry technique for non-intrusive investigation of heat transfer characteristics of dilute nanofluids. The experiments have been performed under natural convection regime. Buoyancy-driven convection has been set up in the vicinity of a heated vertical flat plate that is immersed in a quiescent ambient fluid medium with de-ionized water as the base fluid and Al2O3/water-based dilute nanofluids. The experiments have been carried out for three different volumetric concentrations of alumina nanoparticles i.e. 0.01%, 0.02% and 0.03%. The color variant of the classical schlieren technique namely the rainbow schlieren deflectometry has been employed to record the projection data of the temperature gradient field in the test cavity. The optical configuration of the imaging technique employs a specially-designed color filter for generating the desired schlieren effects. The recorded schlieren images are characterized by a gradation of hue distribution that is proportional to the strength of the temperature gradients prevailing in the test section. Results have been discussed in the form of two-dimensional rainbow schlieren images, whole field distribution of temperature gradients in the vicinity of the heated plate and local distribution of heat transfer coefficients as a function of the length of the plate for the varying concentrations of nanofluids. The profiles of local heat transfer coefficients along the length of the heated plate as obtained with nanofluids show a considerable difference when compared with that of the de-ionized water. Significant enhancement in the average values of heat transfer rates is achieved with nanofluids as the ambient fluid medium in comparison with the base fluid. The study clearly reveals the potential of rainbow schlieren deflectometry technique in the context of heat transfer measurements with nanofluids as the working medium. (C) 2016 Elsevier Ltd. All rights reserved.

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]

Heat transfer characteristics of dilute nanofluids under natural convection regime have been experimentally studied. The buoyancy-driven convection has been set-up in a differentially heated cavity containing basefluid (de-ionized water) and Al2O3/water-based dilute nanofluids. Temperature difference has been employed across the two horizontal walls of cavity, the side walls being thermally insulated. Experiments have been performed for four volumetric concentrations (0.01%, 0.02%, 0.03% and 0.04%) of nanofluids. Projection data of the temperature field has been recorded using a Mach-Zehnder interferometer. Results have been presented in the form of interferograms of the convective field, two-dimensional distributions and variations of heat transfer coefficients as a function of nanofluid concentrations and temperature differences. Results of the study reveal a strong dependence of convective field on the concentration of nanofluids. At low Rayleigh numbers, while the heat transfer through central core region of the cavity was predominately through conduction for de-ionized water, significant convective effects were seen in the case of nanofluids. At higher values of driving potential, strong convective movements in the entire fluid layer were observed irrespective of the type of fluid employed. In nanofluid based experiments, well-defined roll-like convective structures were to be seen with an increase in cavity temperature difference. Time-dependent movement of these dominant structures was observed. Spectral analysis of the intensity-time signal revealed an increasing trend in the frequency of oscillation with an increase in the concentration of nanofluid for any given value of AT. The experiments revealed that at higher driving potential, with increasing concentration of nanoparticles, the bigger structures continuously form and break into smaller roll-like structures, thus indicating better mixing in fluid layer, leading to higher heat transfer rates. (C) 2015 Elsevier Ltd. All rights reserved.

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.

Precise low-temperature thermometry is a key requirement for virtually any quantum technological application. Unfortunately, as the temperature $T$ decreases, the errors in its estimation diverge very quickly. In this paper, we determine exactly how quickly this may be. We rigorously prove that the ``conventional wisdom'' of low-$T$ thermometry being exponentially inefficient is limited to local thermometry on translationally invariant systems with short-range interactions, featuring a nonzero gap above the ground state. This result applies very generally to spin and harmonic lattices. On the other hand, we show that a power-law-like scaling is the hallmark of local thermometry on gapless systems. Focusing on thermometry on one node of a harmonic lattice, we obtain valuable physical insight into the switching between the two types of scaling. In particular, we map the problem to an equivalent setup, consisting of a Brownian thermometer coupled to an equilibrium reservoir. This mapping allows us to prove that, surprisingly, the relative error of local thermometry on gapless harmonic lattices does not diverge as $T\ensuremath{\rightarrow}0$; rather, it saturates to a constant. As a useful by-product, we prove that the low-$T$ sensitivity of a harmonic probe arbitrarily strongly coupled to a bosonic reservoir by means of a generic Ohmic interaction, always scales as ${T}^{2}$ for $T\ensuremath{\rightarrow}0$. Our results thus identify the energy gap between the ground and first excited states of the global system as the key parameter in local thermometry, and ultimately provide clues to devising practical thermometric strategies deep in the ultracold regime.

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.

We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig's projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes (NS) description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad-hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory (DFT). The resultant equation has the structure of a dynamical DFT (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating NS equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab-initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium. We believe that the derivation offered here represents the current state of the art in the field.

The present work is concerned with understanding the heat transfer characteristics of dilute nanofluids using laser-based non-intrusive measurement techniques. Experiments have been conducted on a vertical heated flat plate immersed in nanofluids of varying concentrations, with water as the base fluid. Natural convection regime of the heat transfer between the flat plate and the ambient fluid medium is considered. Aluminium oxide (Al2O3) nanoparticles with volume concentrations in the range 0.005-0.02% are dispersed in the basefluid to prepare nanofluids of dilute concentrations. The phenomenon of convective heat transfer between the flat plate and the ambient fluid medium has been mapped using laser interferometry. Real time evolution of thermal boundary layers as a function of concentration of nanofluids has been recorded in order to understand the plausible role of nano particles in the heat transfer enhancement. Recorded interferograms have then been quantitatively analyzed to retrieve the two-dimensional temperature fields in each case and local distributions of heat transfer coefficients have been estimated. Results have been presented in the form of interferometric images of convective field in the vicinity of the flat plate, contours of whole field temperature distribution and local variation of heat transfer coefficient as a function of nanofluid concentration. The thermal boundary layer profiles as recorded using interferometry clearly reveal the effects of varying nanofluid concentration. In quantitative terms, an enhancement of about 21% in the heat transfer coefficient was observed for 0.02% concentration of nanofluid as compared to the base fluid whereas the Nusselt number was seen to deteriorate with increasing concentration of nanofluids. (C) 2014 Elsevier Ltd. All rights reserved.

We study 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 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 mean-square displacement 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.

The theory of rotational diffusion of particles of various symmetry embedded in a liquid crystal host, essential to interpret a variety of spectroscopic observables, has been available for some time, but only for the case of rigid molecules. Here we generalize the treatment and present a theory to describe the rotational diffusion of shape-changing particles dispersed in nematic liquid crystals. The interaction of the particles with the environment is modeled by an effective field potential, while the particles are allowed to assume an arbitrary discrete number of shapes. The transition between shapes is modeled by a Markovian process which is combined with rotational diffusion. Our model is applied to the simple case of a particle that can exchange between three shapes: a rod, a disk, and a sphere. We consider in detail the effect of shape transitions in some selected correlation functions which are relevant for experiments.

[Background] Continuous time movement models resolve many of the problems with scaling, sampling, and interpretation that affect discrete movement models. They can, however, be challenging to estimate, have been presented in inconsistent ways, and are not widely used., [Methods] We review the literature on integrated Ornstein-Uhlenbeck velocity models and propose four fundamental correlated velocity movement models (CVM’s): random, advective, rotational, and rotational-advective. The models are defined in terms of biologically meaningful speeds and time scales of autocorrelation. We summarize several approaches to estimating the models, and apply these tools for the higher order task of behavioral partitioning via change point analysis., [Results] An array of simulation illustrate the precision and accuracy of the estimation tools. An analysis of a swimming track of a bowhead whale (Balaena mysticetus) illustrates their robustness to irregular and sparse sampling and identifies switches between slower and faster, and directed vs. random movements. An analysis of a short flight of a lesser kestrel (Falco naumanni) identifies exact moments when switches occur between loopy, thermal soaring and directed flapping or gliding flights., [Conclusions] We provide tools to estimate parameters and perform change point analyses in continuous time movement models as an R package (smoove). These resources, together with the synthesis, should facilitate the wider application and development of correlated velocity models among movement ecologists., EG, CF, and WF were supported by the US National Science Foundation under grants ABI-1062411 and ABI-1458748; OO and EG were funded in part by Academy of Finland (grants 129636 and 250444) and European Research Council (ERC Starting Grant 205905). EG was additionally funded by the ‘Animals on the Move’ NASA Grant Number NNX15AV92. OO was additionally funded by the Research Council of Norway (Centres of Excellence funding scheme, project number 223257). The bowhead whale data collection was supported by an Office of Naval Research grant to KL. The lesser kestrel study was financed by the Consejería de Innovación, Ciencia y Empresa of the Junta de Andalucía and FEDER funds from the European Union (project ref: P09-RNM-04588). JHP was supported by a JAE-predoc fellowship co-funded by the Spanish National Research Council and the European Social Fund.

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.

We study a notion of local time for a continuous path, defined as a limit of suitable discrete quantities along a general sequence of partitions of the time interval. Our approach subsumes other existing definitions and agrees with the usual (stochastic) local times a.s. for paths of a continuous semimartingale. We establish pathwise version of the It\^o-Tanaka, change of variables and change of time formulae. We provide equivalent conditions for existence of pathwise local time. Finally, we study in detail how the limiting objects, the quadratic variation and the local time, depend on the choice of partitions. In particular, we show that an arbitrary given non-decreasing process can be achieved a.s. by the pathwise quadratic variation of a standard Brownian motion for a suitable sequence of (random) partitions; however, such degenerate behavior is excluded when the partitions are constructed from stopping times., Comment: minor changes

We consider the problem of an overdamped Brownian particle moving in multiscale potential with N + 1 characteristic length scales: the macroscale and N separated microscales. We show that the coarse-grained dynamics is given by an overdamped Langevin equation with respect to the free energy and with a space dependent diffusion tensor, the calculation of which requires the solution of N fully coupled Poisson equations. We study in detail the structure of the bifurcation diagram for one-dimensional problems and we show that the multiscale structure in the potential leads to hysteresis effects and to noise-induced transitions. Furthermore, we obtain an explicit formula for the effective diffusion coefficient for a self-similar separable potential and we investigate the limit of infinitely many small scales., 26 pages

A conditioned hypoelliptic process on a compact manifold, satisfying the strong Hörmander’s condition, is a hypoelliptic bridge. If the Markov generator satisfies the two step strong Hörmander condition, the drift of the conditioned hypoelliptic bridge is integrable on [0,1][0,1] and the hypoelliptic bridge is a continuous semi-martingale.

A thorough experimental investigation of the thermophysical properties (thermal conductivity, viscosity, and specific heat), heat transfer performance, and pressure drop characteristics of aviation turbine fuel (ATF)-based Al2O3, TiO2, and CuO nanofluids was carried out for potential regenerative cooling application in semicryogenic rocket engines. The effects of volume concentration, size, and material of suspended particles, as well as the effect of the temperature of the nanofluid, were investigated. Although an enhanced thermal conductivity led to an increased heat transfer coefficient, the Prandtl number was seen to ha l e a bigger influence on the heat transfer characteristics. In particular, the correlation developed for the Nusselt number showed a much higher influence of the Prandfl number than for single-phase fluids. As a result, the ATF-CuO nanofluid performed the best amongst the three metal oxide nanofluids at a given particle size, concentration, and temperature. The enhancement is seen to improve with temperature, demonstrating the suitability of such a nanofluid at the conditions encountered during the regenerative cooling of the rocket engines (similar to 150 degrees C).

Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. This paper provides explicit strong solutions and stochastic analogues for distributed-order time-fractional diffusion equations on bounded domains, with Dirichlet boundary conditions. Published by Elsevier Inc.

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.

Fluorescence correlation spectroscopy (FCS) was used to measure the translational diffusion of labeled apomyoglobin (tracer) in concentrated solutions of ribonuclease A and human serum albumin (crowders), as a quantitative model system of protein diffusive motions in crowded physiological environments. The ratio of the diffusion coefficient of the tracer protein in the protein crowded solutions and its diffusion coefficient in aqueous solution has been interpreted in terms of local apparent viscosities, a molecular parameter characteristic for each tracer-crowder system. In all protein solutions studied in this work, local translational viscosity values were larger than the solution bulk viscosity, and larger than rotational viscosities estimated for apomyoglobin in the same crowding solutions. Here we propose a method to estimate local apparent viscosities for the tracer translational and rotational diffusion directly from the bulk viscosity of the concentrated protein solutions. As a result of this study, the identification of protein species and the study of hydrodynamic changes and interactions in model crowded protein solutions by means of FCS and time-resolved fluorescence depolarization techniques may be expected to be greatly simplified.

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

Some problems of first-crossing times over two time-dependent boundaries for one-dimensional diffusion processes are considered. The moments of the first-crossing times over each boundary are shown to be the solutions of certain partial differential equations with suitable boundary conditions. For some examples where the boundaries are constant, the results are illustrated graphically.

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

We consider a point particle in one dimension initially confined to a finite spatial region whose state is frequently monitored by projection operators onto that region. In the limit of infinitely frequent monitoring, the state never escapes from the region -- this is the Zeno effect. The aim of this paper is to show how the Zeno effect disappears in the classical limit in this and similar examples. We give a general argument showing that the Zeno effect is suppressed in the presence of a decoherence mechanism which kills interference between histories. We show how this works explicitly by coupling to a decohering environment. Smoothed projectors are required to give the problem proper definition and this implies the existence of a momentum cutoff. We show that the escape rate from the region approaches the classically expected result, and hence the Zeno effect is suppressed, as long as the environmentally-induced fluctuations in momentum are sufficiently large and we establish the associated timescale. We link our results to earlier work on the hbar -->0 limit of the Zeno effect. We illustrate our results by plotting the probability flux lines for the density matrix (which are equivalent to Bohm trajectories in the pure state case). These illustrate both the Zeno and anti-Zeno effects very clearly, and their suppression. Our results are closely related to our earlier paper demonstrating the suppression of quantum-mechanical reflection by decoherence, 45 pages, 8 figures

In this work we study by numerical methods the phase dynamics in ballistic graphene-based short Josephson junctions. The supercurrent through a graphene junction shows a non-sinusoidal phase-dependence, unlike a conventional junction ruled by the well-known d.c. Josephson relation. A superconductor-graphene-superconductor system exhibits superconductive quantum metastable states similar to those present in normal current-biased JJs. We explore the effects of thermal and correlated fluctuations on the escape time from these metastable states, when the system is stimulated by an oscillating bias current. As a first step, the analysis is carried out in the presence of an external Gaussian white noise source, which mimics the random fluctuations of the bias current. Varying the noise intensity, it is possible to analyze the behavior of the escape time from a superconductive metastable state in different temperature regimes. Noise induced phenomena, such as resonant activation and noise induced stability, are observed. The study is extended to the case of a coloured Gaussian noise source, analyzing how the escape time from the metastable state is affected by correlated random fluctuations for different values of the noise correlation time., Comment: 12 pages, 8 figures

We study the decoherence and thermalization dynamics of a nanoscale system coupled nonperturbatively to a fully quantum-mechanical bath. The system is prepared out of equilibrium in a pure state of the complete system. We propose a random matrix model and show analytically that there are two robust temporal regimes in the approach of the system to equilibrium --- an initial Gaussian decay followed by an exponential tail, consistent with numerical results on small interacting lattices [S. Genway, A.F. Ho and D.K.K. Lee, Phys. Rev. Lett. 105, 260402 (2010)]. Furthermore, the system decays towards a Gibbs ensemble in accordance with the eigenstate thermalization hypothesis., 7 pages, 1 figure

The stationary/nonstationary regimes of time series generated by the discrete version of the Ornstein-Uhlenbeck equation are studied by using the detrended fluctuation analysis. Our findings point out to the prevalence of the drift parameter in determining the crossover time between the nonstationary and stationary regimes. The fluctuation functions coincide in the nonstationary regime for a constant diffusion parameter, and in the stationary regime for a constant ratio between the drift and diffusion stochastic forces. In the generalized Ornstein-Uhlenbeck equations, the Hurst exponent H influences the crossover time that increases with the decrease of H. Published by AIP Publishing.

A unified treatment is given of some results of H. Donnelly, P. Li and L. Schwartz concerning the behaviour of heat semigroups on open manifolds with given compactifications, on one hand, and the relationship with the behaviour at infinity of solutions of related stochastic differential equations on the other. A principal tool is the use of certain covers of the manifold: which also gives a non-explosion test. As a corollary we obtain known results about the behaviour of Brownian motions on a complete Riemannian manifold with Ricci curvature decaying at most quadratically in the distance function.

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

The role of sound in the dynamics of mesoscale systems is typically neglected, since frequently the associated time scales are much smaller than all the other time scales of interest. However, for sufficiently small objects embedded in a solvent with a sufficiently small sound velocity, sound can play a crucial role. In particular, behavior resembling viscoelasticity has been theoretically predicted for non-viscoelastic fluids. This effect is due to the interference of the propagation of sound waves caused by the solute particle's motion and hydrodynamic vortex formation. We demonstrate this effect, known as backtracking, in computer simulations employing the method of multiparticle collision dynamics. We systematically study the influence of sound on the dynamics of the solute particle, and find that it disappears in the long-time limit. Thus, we confirm that sonic effects at the single-particle level can be neglected at sufficiently long times., Comment: to appear in The Journal of Physical Chemistry B

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)