Random Flight Model Research Articles

Nonequilibrium statistical physics beyond the ideal heat bath approximation.

Important models of nonequilibrium statistical physics (NESP) are limited by a commonly used, but often unrecognized, near-equilibrium approximation. Fokker-Planck and Langevin equations, the Einstein and random-flight diffusion models, and the Schnakenberg model of biochemical networks suppose that fluctuations are due to an ideal equilibrium bath. But far from equilibrium, this perfect bath concept does not hold. A more principled approach should derive the rate fluctuations from an underlying dynamical model, rather than assuming a particular form. Here, using maximum caliber as the underlying principle, we derive corrections for NESP processes in an imperfect-but more realistic-environment, corrections which become particularly important for a system driven strongly away from equilibrium. Beyond characterizing a heat bath by the single equilibrium property of its temperature, the bath's speed and size must also be used to characterize the bath's ability to handle fast or large fluctuations.

Hysteresis and Surface Shear Stresses During Snow-Particle Aeolian Transportation

Surface shear stresses produced by wind and particle collision play a key role in aerodynamic entrainment and splash processes. The fluid shear stress at the surface during aeolian transport has been researched for decades; however, the equilibrium property reported in the literature, numerical simulations, and experiments is inconsistent. To discuss this discrepancy, this study investigates fluid and particle shear stresses at the surface during the aeolian transport of snow particles using a two-dimensional random-flight model of drifting snow. The simulations are performed for various friction velocities on a loose snow bed. By varying the wind conditions in stages, the transport hysteresis is confirmed, and the impact threshold is estimated from the particle transport rate (0.206,hbox {m,s}^{-1}). The friction velocity at the surface during transport decreases marginally with an increase in wind speed caused by the impact threshold, revealing that our results do not contradict Owen’s second hypothesis. The total shear stress, which is calculated by summing the fluid and particle shear stresses, is vertically uniform in the equilibrium state; thus, the increase in the particle shear stress decreases the fluid shear stress at the surface. The equilibrium property of the fluid shear stress near the surface changes significantly with height (from a decreasing trend to an increasing trend) because the particle shear stress decreases rapidly in the height range of 1–10 mm. Our findings suggest that it is difficult to accurately measure the fluid shear stress in the surface vicinity using anemometers, and a new methodology is needed.

An ensemble trajectory prediction model for maritime search and rescue and oil spill based on sub-grid velocity model

An important part of establishing a prediction model for maritime search and rescue and oil spill drift is to quantify the uncertainty in particle motion simulation. A regional Sub-grid velocity model based on drifting buoy data is proposed to simulate the unsolved velocity which is composed of turbulence and advection simulation errors (TASE) in the ocean model. Contrary to most of the traditional drift trajectory prediction models, the presented method divided the experimental area into 69 custom grids. The standard deviation of TASE velocity, TASE time scale, and TASE diffusion coefficients of each grid were obtained by using the fitting velocity difference of buoy velocity, current velocity and wind velocity, and autocorrelation analysis of time series. Two Sub-grid velocity models, the random flight model and the random walk model, were built respectively and were combined with the Lagrangian particle tracking model to simulate the drifting buoy trajectory. In the process of Lagrange particle tracking, fourth-order Runge-Kutta was used to interpolate the velocity and kernel density estimate method was used to calculate the predicted range of 95% confidence interval for evaluation and validation. The experimental results of several different settings indicated that the prediction performance of the random flight model was better than that of the random walk model when the TASE diffusion coefficient was determined by this method, and the prediction performance of models with different diffusion coefficients is better than that of models with the same diffusion coefficient. This work also proved the value of using the trajectory data of drifting buoys to build a Sub-grid velocity model for trajectory prediction.

Dispersion of passive tracers from long-range HF radar systems along the east coast of Korea

We have conducted a virtual surface layer dispersion experiment using the long-range High Frequency radar (HFR) measurements off the east coast of Korea, and investigated the spreading characteristics of the surface waters in the vicinity of two cities, YoungDuk and UlJin for three days of experiments utilizing with random flight model (Markovian stochastic model). The diffusion coefficient was estimated as (Kx , Ky ) = (192, 251) m 2 /s with zonal and meridional dispersions ( σ² u, σ²υ ) = (0.0013, 0.017) m/s and turbulence time scales (Tu , Tv ) = (4, 4) hours derived from exponential fitting of lagged autocorrelation of difference between the HFR-derived and surface drifter-derived currents. During the experiment period, the centroid of the spatial particle distribution moved northward 80 km from the initial position following the East Korea Warm Current (EKWC) and its area became more than 500 times than the initial area. The trajectory and distribution of the surface particles are dependent on the EKWC and diffusion coefficient. Long-term and real-time continuous monitoring system of HFR needs to be combined into national system to improve search and rescue (SAR), and prevent coastal disasters (e.g., oil spill, marine litter) for risk management.

Unfolding and Refolding of Protein by a Combination of Ionic and Nonionic Surfactants.

The interaction of protein and surfactant yields protein–surfactant complexes which have a wide range of applications in the cosmetics, foods, and pharmaceutical industries among others. Ionic and nonionic surfactants are known to interact differently with the protein. The interplay of electrostatic and hydrophobic interactions governs the resultant structure of protein–surfactant complexes. The present study enlightens the paramount role of the hydrophobic interaction, tuned by the hydrophobic tail length of ionic surfactants, in the unfolding of anionic bovine serum albumin (BSA) protein. The unfolding of BSA in the presence of four different tail-length cationic surfactants, that is, C10TAB, C12TAB, C14TAB, and C16TAB, has been investigated by small-angle neutron scattering and dynamic light scattering. All cationic surfactants unfold the protein at a certain concentration range. The propensity of protein unfolding increases with increasing the hydrophobic tail length. The denatured structure of BSA upon addition of cationic surfactants is characterized by the random flight model representing a beads-on-a-string chain-like complex. The unfolded protein binds the surfactant micelles in the protein–surfactant cluster. The micelles get elongated with the increasing concentration of cationic surfactants, whereas the number of micelles per cluster is decreased. In the final stage, the protein–surfactant cluster merges to one large micelle with unfolded protein wrapping the micelle surface. The pathway of protein unfolding is described in terms of the changes in the micellar size, the number of micelles formed per cluster, the separation between the micelles in the cluster, the aggregation number of micelles, and the number of proteins per cluster. The protein–surfactant interaction is further examined in the presence of a nonionic surfactant, that is, C12E10. The nonionic surfactant significantly suppresses the interaction of BSA protein with ionic surfactants by forming mixed micelles. As a result of the mixed micelles formation by ionic–nonionic surfactants, the ionic surfactant moves out from the unfolded BSA protein, and this enables the protein to refold back to its native structure. The propensity of mixed micelle-driven refolding of proteins is significantly changed with changing the tail length of the ionic surfactant.

Scavenging and recombination kinetics in a radiation spur: The successive ordered scavenging events

This study describes stochastic models to investigate the successive ordered scavenging events in a spur of four radicals, a model system based on a radiation spur. Three simulation models have been developed to obtain the probabilities of the ordered scavenging events: (i) a Monte Carlo random flight (RF) model, (ii) hybrid simulations in which the reaction rate coefficient is used to generate scavenging times for the radicals and (iii) the independent reaction times (IRT) method. The results of these simulations are found to be in agreement with one another. In addition, a detailed master equation treatment is also presented, and used to extract simulated rate coefficients of the ordered scavenging reactions from the RF simulations. These rate coefficients are transient, the rate coefficients obtained for subsequent reactions are effectively equal, and in reasonable agreement with the simple correction for competition effects that has recently been proposed.

Spatiotemporal Structure of Aeolian Particle Transport on Flat Surface

We conduct numerical simulations based on a model of blowing snow to reveal the long-term properties and equilibrium state of aeolian particle transport from $10^{-5} \hspace{0.5 ex} \mathrm{m}$ to $10 \hspace{0.5 ex} \mathrm{m}$ above the flat surface. The numerical results are as follows. (i) Time-series data of particle transport are divided into development, relaxation, and equilibrium phases, which are formed by rapid wind response below $10 \hspace{0.5 ex} \mathrm{cm}$ and gradual wind response above $10 \hspace{0.5 ex} \mathrm{cm}$. (ii) The particle transport rate at equilibrium is expressed as a power function of friction velocity, and the index of 2.35 implies that most particles are transported by saltation. (iii) The friction velocity below $100 \hspace{0.5 ex} \mu\mathrm{m}$ remains roughly constant and lower than the fluid threshold at equilibrium. (iv) The mean particle speed above $300 \hspace{0.5 ex} \mu\mathrm{m}$ is less than the wind speed, whereas that below $300 \hspace{0.5 ex} \mu\mathrm{m}$ exceeds the wind speed because of descending particles. (v) The particle diameter increases with height in the saltation layer, and the relationship is expressed as a power function. Through comparisons with the previously reported random-flight model, we find a crucial problem that empirical splash functions cannot reproduce particle dynamics at a relatively high wind speed.

The free path in a high velocity random flight process associated to a Lorentz gas in an external field

We investigate the asymptotic behavior of the free path of a variable density random flight model in an external field as the initial velocity of the particle goes to infinity. The random flight models we study arise naturally as the Boltzmann-Grad limit of a random Lorentz gas in the presence of an external field. By analyzing the time duration of the free path, we obtain exact forms for the asymptotic mean and variance of the free path in terms of the external field and the density of scatterers. As a consequence, we obtain a diffusion approximation for the joint process of the particle observed at reflection times and the amount of time spent in free flight.

Statistic thermodynamic analysis of fructans – Part 2: Chain configuration parameters of non-branched and branched fructans – Branching structure and molar mass distribution of branched fructans

Applying statistical thermodynamic models for chain configurations in combination with linkage analysis, molar mass distribution and small angle X-ray scattering data allow the unambiguous structural elucidation of branched fructans. The radius of gyration of fructans can be accurately predicted by applying a random flight model with bond angle restrictions. The structural factor g has been calculated and correlated with experimental data only allowing a comb shaped structure for branched fructans. A formula for calculating the molar mass distribution of comb shaped branched fructans is proposed. Amalgamation of experimental and theoretical data prove a regular comb shape structure for the branched fructans of U. maritima, L. bulbiferum and A. tequilana.

Conformational properties of high molecular weight heteropolysaccharide isolated from seeds of Artemisia sphaerocephala Krasch

The conformational properties of a high molecular weight polysaccharide (60P) extracted from Artemisia sphaerocephala Krasch (ASK) were investigated. The Mw and Rg of 60P were obtained using both static light scattering and HPSEC techniques, which were 590 kDa and 56 nm, respectively. Dynamic light scattering measurement indicated that 0.5 M NaOH solvents exhibited the ability to reduce/eliminate aggregates of 60P. 60P in 0.5 M NaOH showed strong concentration dependence, but minimal angular dependence. The average structure parameter ρ (Rg/Rh) value of 1.75 indicated that 60P exhibited a random coil conformation in 0.5 M NaOH solution. The conformational parameters (derived from Rg vs Mw and Rh vs Mw) from HPSEC also suggested a random coil conformation of 60P in 0.1 M NaNO3 solution (eluent for HPSEC). The characteristic ratio and the persistence length obtained from the random flight model and wormlike cylinder model both indicated a semi-flexible structure of 60P.

Efficient estimators with sample observations generated by independent planar random flights

In this paper we consider observations from independent planar random flights. The random flight model represents a random motion at finite speed of a particle with changes of direction governed by a Poisson process with parameter λ > 0 . We introduce and study the asymptotic behavior of the maximum likelihood and Bayesian estimator for λ in order to obtain the asymptotic efficiency in Hájek–Le Cam sense of the considered estimators.

Characterization of synthetic copolymers by interaction polymer chromatography: Separation by microstructure

Gradient elution of synthetic polymers has been studied both theoretically and experimentally using normal and reversed-phase HPLC systems. An accurate equation describing the gradient elution of polymer-homologous series in the context of continuous random-flight model of a flexible polymer chain interacting with attractive surface of the porous material has been derived and experimentally verified against a series of narrow polystyrene standards. Both the theory and the experiment predict the existence of molar mass-independent gradient elution at critical point of adsorption (CPA). The extension of the theory to synthetic copolymers predicts the existence of the CPA for statistical copolymers and describes its dependence on chemical composition and microstructure (blockiness) of the polymer chains. One of the important theoretical conclusions is that blockiness always increases the retention, so that blockier polymer chains elute later than their more random counterparts with the same chemical composition. This prediction has been confirmed experimentally using block and statistical styrene-methylmethacrylate copolymers. Block copolymers do not have CPA and always elute between critical points of the corresponding homopolymers. The retention depends on the polymer molar mass and increases with the length of the blocks from a stronger absorbing monomer. These findings provide theoretical and experimental bases for separation of statistical and block copolymers by chemical composition and microstructure of polymer chains.

Fluids density functional theory studies of supramolecular polymers at a hard surface

We have applied a fluids density functional theory based on that of Yu and Wu [J. Chem. Phys. 116, 7094 (2002)] to treat reversible supramolecular polymers near a hard surface. This approach combines a hard-sphere fluids density functional theory with the first-order thermodynamic perturbation theory of Wertheim. The supramolecular polymers are represented in the theory by hard-spheres with two associating sites. We explore the effects of the bonding scheme, monomer concentration, and association energy upon the equilibrium chain sizes and the depletion lengths. This study is performed on simple systems containing two-site monomers and binary mixtures of two-site monomers combined with end stopper monomers which have only a single association site. Our model has correct behavior in the dilute and overlap regimes and the bulk results can be easily connected to simpler random-flight models. We find that there is a nonmonotonic behavior of the depletion length of the polymers as a function of concentration and that this depletion length can be controlled through the concentration of end stoppers. These results are applicable to the study of colloidal dispersions in supramolecular polymer solutions.

The hydrodynamic and conformational properties of denatured proteins in dilute solutions

Published data on the characterization of unfolded proteins in dilute solutions in aqueous guanidine hydrochloride are analyzed to show that the data are not fit by either the random flight or wormlike chain models for linear chains. The analysis includes data on the intrinsic viscosity, root-mean-square radius of gyration, from small-angle X-ray scattering, and hydrodynamic radius, from the translational diffusion coefficient. It is concluded that residual structure consistent with that deduced from nuclear magnetic resonance on these solutions can explain the dilute solution results in a consistent manner through the presence of ring structures, which otherwise have an essentially flexible coil conformation. The ring structures could be in a state of continual flux and rearrangement. Calculation of the radius of gyration for the random-flight model gives a similar reduction of this measure for chains joined at their endpoints, or those containing loop with two dangling ends, each one-fourth the total length of the chain. This relative insensitivity to the details of the ring structure is taken to support the behavior observed across a range of proteins.

Erratum: “Efficient chain moves for Monte Carlo simulations of a wormlike DNA model: Excluded volume, supercoils, site juxtapositions, knots, and comparisons with random-flight and lattice models” [J. Chem. Phys. 128, 145104 (2008)

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Efficient chain moves for Monte Carlo simulations of a wormlike DNA model: Excluded volume, supercoils, site juxtapositions, knots, and comparisons with random-flight and lattice models

We develop two classes of Monte Carlo moves for efficient sampling of wormlike DNA chains that can have significant degrees of supercoiling, a conformational feature that is key to many aspects of biological function including replication, transcription, and recombination. One class of moves entails reversing the coordinates of a segment of the chain along one, two, or three axes of an appropriately chosen local frame of reference. These transformations may be viewed as a generalization, to the continuum, of the Madras-Orlitsky-Shepp algorithm for cubic lattices. Another class of moves, termed T+/-2, allows for interconversions between chains with different lengths by adding or subtracting two beads (monomer units) to or from the chain. Length-changing moves are generally useful for conformational sampling with a given site juxtaposition, as has been shown in previous lattice studies. Here, the continuum T+/-2 moves are designed to enhance their acceptance rate in supercoiled conformations. We apply these moves to a wormlike model in which excluded volume is accounted for by a bond-bond repulsion term. The computed autocorrelation functions for the relaxation of bond length, bond angle, writhe, and branch number indicate that the new moves lead to significantly more efficient sampling than conventional bead displacements and crankshaft rotations. A close correspondence is found in the equilibrium ensemble between the map of writhe computed for pair of chain segments and the map of site juxtapositions or self-contacts. To evaluate the more coarse-grained freely jointed chain (random-flight) and cubic lattice models that are commonly used in DNA investigations, twisting (torsional) potentials are introduced into these models. Conformational properties for a given superhelical density sigma may then be sampled by computing the writhe and using White's formula to relate the degree of twisting to writhe and sigma. Extensive comparisons of contact patterns and knot probabilities of the more coarse-grained models with the wormlike model show that the behaviors of the random-flight model are similar to that of DNA molecules in a solution environment with high ionic strengths, whereas the behaviors of the cubic lattice model with excluded volume are akin to that of DNA molecules under low ionic strengths.

Particle growth behavior of poly(methyl methacrylate) nanoparticles synthesized by the reversible addition fragmentation transfer living radical polymerization reaction

PMMA nanoparticles with highly mono-dispersed size distribution were prepared using the RAFT living radical emulsion polymerization technique. A novel sur-iniferter for the RAFT reaction, DTBA, was synthesized and its chemical structure was identified using several spectroscopic techniques. The relationship between the particle size and the molecular weight of the polymer was investigated measuring the rate of growth of each during formation of particles, and was well explained by the simple random flight molecular conformation model. The particle size increased up to a certain value with decreasing sur-iniferter concentration and then leveled off, because the surface charge density of the growing particles was not high enough to stabilize the particles in aqueous medium above that value. The core-shell type di-block copolymer nanoparticles were also successfully prepared via RAFT reaction.

Lagrangian numerical simulations of canopy air flow effects on maize pollen dispersal

A three-dimensional Lagrangian random flight model was constructed for numerical simulations of maize pollen dispersion. The model simulates the paths of tracer particles which are interpreted as individual pollen grains, with particle motion determined by the mean flow and a stochastic turbulent velocity. The Lagrangian approach was chosen because it can be extended to complex flow regimes. The capacity of the model to simulate measured patterns of pollen deposition was tested by comparing simulations to measurements for a small maize canopy isolated within a large field of soybeans near Ames, Iowa, USA in August 2003. For this application, measurements from a single point meteorological observation were used to generate a surface layer wind profile over the maize canopy and surrounding soybean field. The method used to construct the wind field included development of internal boundary layers as the airflow passed from one canopy surface to another. The dispersion model produced spatial patterns of particle deposition that included the sharp near-source deposition gradient consistent with observations. The model tended to over-predict particle deposition near the source field and under-predict deposition at greater distances. Inclusion of the effect of the roughness difference between the maize canopy and the surrounding soybean canopy on the flow field was found to be essential for simulation accuracy. Agreement with observations improved considerably by including an approximation for vertical motions induced by changes in surface cover. These results indicate that the Lagrangian random flight model provides a realistic simulation of pollen dispersal from an isolated maize canopy. A more complete hydrodynamic model should be explored to better represent the influence of surface inhomogeneities on winds and turbulence.

Solution and Conformational Properties of Wheat β-d-Glucans Studied by Light Scattering and Viscometry

The solution properties of wheat beta-glucan were investigated by light scattering and viscometric methods. The hydrodynamic radius (R(h)), weight average molecular weight (M(w)), radius of gyration (R(g)), and the second virial coefficient (A(2)) of wheat beta-glucan were determined by both dynamic and static light scattering methods, whereas the critical concentrations (c) of the solution were derived from [eta] via viscometric method. The structure sensitive parameters, rho (1.52-1.62), the conformation parameter nu (0.62), and the Mark-Houwink-Sakurada exponents alpha (0.78) confirmed the random coil conformation of wheat beta-glucan in 0.5 M NaOH solution. The characteristic ratio (4.97) was obtained by the random flight model, and the statistical segment length (8.83 nm) was derived from the wormlike cylinder model. It was found that the wormlike cylinder model could explain the chain stiffness better than the random flight model, which suggested an extended random coil conformation of wheat beta-glucan in 0.5 M NaOH solution. The study also revealed that the structure feature of wheat beta-glucan; that is, the higher trisaccharide-to-tetrasaccharide ratio contributed to the stiffer chain conformation compared with other cereal beta-glucans.

Turbulence characteristics and dispersion in a forest—tests of Thomson's random-flight model

A dispersion experiment, where the tracer SF 6 was released from line sources, was carried out within a young pine forest. Line sources made of silicone tubes were installed at different heights and distances from a tower. Vertical concentration profiles were measured on the tower and the samples were analysed with a gas chromatograph. The measured concentration profiles were compared to those calculated using Thomson's random-flight model. To provide input information to the model on turbulence, the turbulence characteristics were measured at four different heights with sonic anemometers. Data are presented for standard deviations of the velocity components, the momentum flux, the Lagrangian time scale and the mean horizontal wind velocity, depending on height and thermal stability. The derived turbulence characteristics resemble previous results in the literature; but are still stand specific. Satisfactory agreement was obtained between the measured and simulated SF 6 concentration profiles. However, the model clearly underestimates the concentrations in the upper part of the stand. The results should add more confidence to the continued use of Thomson's model and are useful for planning better dispersion experiments.