Optimal estimates of the diffusion coefficient of a single Brownian trajectory

Modern developments in microscopy and image processing are revolutionizing areas of physics, chemistry and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal of single particle tracking is to determine the interaction between the particle and its environment. The price paid for having a direct visualization of a single particle is a consequent lack of statistics. Here we address the optimal way of extracting diffusion constants from single trajectories for pure Brownian motion. It is shown that the maximum likelihood estimator is much more efficient than the commonly used least squares estimate. Furthermore we investigate the effect of disorder on the distribution of estimated diffusion constants and show that it increases the probability of observing estimates much smaller than the true (average) value.Comment: 8 pages, 5 figure

Natural attenuation of Fukushima-derived radiocesium in soils due to its vertical and lateral migration

Processes of vertical and lateral migration lead to gradual reduction in contamination of catchment soil, particularly its top layer. The reduction can be considered as natural attenuation. This, in turn, results in a gradual decrease of radiocesium activity concentrations in the surface runoff and river water, in both dissolved and particulate forms. The purpose of this research is to study the dynamics of Fukushima-derived radiocesium in undisturbed soils and floodplain deposits exposed to erosion and sedimentation during floods. Combined observations of radiocesium vertical distribution in soil and sediment deposition on artificial lawn-grass mats on the Niida River floodplain allowed us to estimate both annual mean sediment accumulation rates and maximum sedimentation rates corresponding to an extreme flood event during Tropical Storm Etau, 6-11 September 2015. Dose rates were reduced considerably for floodplain sections with high sedimentation because the top soil layer with high radionuclide contamination was eroded and/or buried under cleaner fresh sediments produced mostly due to bank erosion and sediments movements. Rate constants of natural attenuation on the sites of the Takase River and floodplain of Niida River was found to be in range 0.2-0.4 year-1. For the site in the lower reach of the Niida River, collimated shield dose readings from soil surfaces slightly increased during the period of observation from February to July 2016. Generally, due to more precipitation, steeper slopes, higher temperatures and increased biological activities in soils, self-purification of radioactive contamination in Fukushima associated with vertical and lateral radionuclide migration is faster than in Chernobyl. In many cases, monitored natural attenuation along with appropriate restrictions seems to be optimal option for water remediation in Fukushima contaminated areas

Formation of quasi-periodic nano- and microstructures on silicon surface under IR and UV femtosecond laser pulses

Quasi-periodic nano- and microstructures have been formed on silicon surface using IR ( λ ≈ 744 nm) and UV ( λ ≈ 248 nm) femtosecond laser pulses. The influence of the incident laser fluence and the number of pulses on the structured surface topology has been investigatedyesBelgorod State Universit

Alternative proof for the localization of Sinai's walk

We give an alternative proof of the localization of Sinai's random walk in random environment under weaker hypothesis than the ones used by Sinai. Moreover we give estimates that are stronger than the one of Sinai on the localization neighborhood and on the probability for the random walk to stay inside this neighborhood

Effect of thickness on the piezoelectric properties of LiNbO3 films

The results were obtained using the equipment of Research and Education Center and the Center of collective use “Nanotechnology” of Southern Federal University

Transverse spin dynamics in a spin-polarized Fermi liquid

The linear equations for transverse spin dynamics in weakly polarised degenerate Fermi liquid with arbitrary relationship between temperature and polarization are derived from Landau-Silin phenomenological kinetic equation with general form of two-particle collision integral. The temperature and polarization dependence of the spin current relaxation time is established. It is found in particular that at finite polarization transverse spin wave damping has a finite value at T=0. The analogy between temperature dependences of spin waves attenuation and ultrasound absorption in degenerate Fermi liquid at arbitrary temperature is presented. We also discuss spin-polarized Fermi liquid in the general context of the Fermi-liquid theory and compare it with "Fermi liquid" with spontaneous magnetization.Comment: 10 page

Iterative algorithm versus analytic solutions of the parametrically driven dissipative quantum harmonic oscillator

We consider the Brownian motion of a quantum mechanical particle in a one-dimensional parabolic potential with periodically modulated curvature under the influence of a thermal heat bath. Analytic expressions for the time-dependent position and momentum variances are compared with results of an iterative algorithm, the so-called quasiadiabatic propagator path integral algorithm (QUAPI). We obtain good agreement over an extended range of parameters for this spatially continuous quantum system. These findings indicate the reliability of the algorithm also in cases for which analytic results may not be available a priori.Comment: 15 pages including 11 figures, one reference added, minor typos correcte

Hydration dynamics at fluorinated protein surfaces

Water-protein interactions dictate many processes crucial to protein function including folding, dynamics, interactions with other biomolecules, and enzymatic catalysis. Here we examine the effect of surface fluorination on water-protein interactions. Modification of designed coiled-coil proteins by incorporation of 5,5,5-trifluoroleucine or (4S)-2-amino-4-methylhexanoic acid enables systematic examination of the effects of side-chain volume and fluorination on solvation dynamics. Using ultrafast fluorescence spectroscopy, we find that fluorinated side chains exert electrostatic drag on neighboring water molecules, slowing water motion at the protein surface

Localization of thermal packets and metastable states in Sinai model

We consider the Sinai model describing a particle diffusing in a 1D random force field. As shown by Golosov, this model exhibits a strong localization phenomenon for the thermal packet: the disorder average of the thermal distribution of the relative distance y=x-m(t), with respect to the (disorder-dependent) most probable position m(t), converges in the limit of infinite time towards a distribution P(y). In this paper, we revisit this question of the localization of the thermal packet. We first generalize the result of Golosov by computing explicitly the joint asymptotic distribution of relative position y=x(t)-m(t) and relative energy u=U(x(t))-U(m(t)) for the thermal packet. Next, we compute in the infinite-time limit the localization parameters Y_k, representing the disorder-averaged probabilities that k particles of the thermal packet are at the same place, and the correlation function C(l) representing the disorder-averaged probability that two particles of the thermal packet are at a distance l from each other. We moreover prove that our results for Y_k and C(l) exactly coincide with the thermodynamic limit of the analog quantities computed for independent particles at equilibrium in a finite sample of length L. Finally, we discuss the properties of the finite-time metastable states that are responsible for the localization phenomenon and compare with the general theory of metastable states in glassy systems, in particular as a test of the Edwards conjecture.Comment: 17 page

Random Walks, Reaction-Diffusion, and Nonequilibrium Dynamics of Spin Chains in One-dimensional Random Environments

Sinai's model of diffusion in one-dimension with random local bias is studied by a real space renormalization group which yields asymptotically exact long time results. The distribution of the position of a particle and the probability of it not returning to the origin are obtained, as well as the two-time distribution which exhibits "aging" with $\frac{\ln t}{\ln t'}$ scaling and a singularity at $\ln t =\ln t'$. The effects of a small uniform force are also studied. Extension to motion of many domain walls yields non-equilibrium time dependent correlations for the 1D random field Ising model with Glauber dynamics and "persistence" exponents of 1D reaction-diffusion models with random forces.Comment: 5 pages, 1 figures, RevTe