A perfect probe: Resonance of underdamped scaled Brownian motion

We numerically investigate the resonance of the underdamped scaled Brownian motion in a bistable system for both cases of a single particle and interacting particles. Through the velocity autocorrelation function (VACF) and mean squared displacement (MSD) of a single particle, we find that for the steady state, diffusions are ballistic at short times and then become normal for most of parameter regimes. However, for certain parameter regimes, both VACF and MSD suggest that the transition between superdiffusion and subdiffusion takes place at intermediate times, and diffusion becomes normal at long times. Via the power spectrum density corresponding to the transitions, we find that there exists a nontrivial resonance. For interacting particles, we find that the interaction between the probe particle and other particles can lead to the resonance, too. Thus we theoretically propose the system with the Brownian particle as a probe, which can detect the temperature of the system and identify the number of the particles or the types of different coupling strengths in the system. The probe is potentially useful for detecting microscopic and nanometer-scale particles and for identifying cancer cells or healthy ones.

On longitudinal and transversal diffusion of carbon nanotubes

In this work, the anisotropy of diffusion of carbon nanotubes in water was studied by the molecular dynamics method. Two models of nanotubes were used, their lengths varied from 4 to 31 nanometers. The first model is a nanotube with armchair chirality, the second is connected solid nanoscale rods. The behavior of various components of the velocity autocorrelation function of the nanotubes center of mass has been studied. It was established that the transverse component of this function has a negative region and a minimum point, in contrast to the average autocorrelation function, which decays monotonically. It is shown that the diffusion coefficients in the longitudinal and transverse directions can differ several times; the method proposed in this work was used to determine them. The effect of anisotropy increases with an increase in the ratio of the characteristic sizes of the nanotube. Using the Stokes - Einstein formula, the effective hydrodynamic radii of nanotubes have been determined. In all cases, the effective radius is significantly less than the tube length.

Velocity autocorrelation function and self-diffusion coefficient in large molecular dynamics models of liquid argon and water

Autocorrelation function of the particle velocity Z(t) is calculated using the molecular dynamics method in the models of liquid argon and water. The large size of the models (more than a hundred thousand particles) allowed us to trace these functions up to 50 picoseconds in argon and up to 10 picoseconds in water, and to achieve a calculation accuracy sufficient for analytical analysis of their shape. The difference in the determination of the self-diffusion coefficient using Einstein's law and the integral of Z(t) (Green-Kubo integral) is analyzed and it is shown to be 3% at best when t is of the order of several picoseconds. The asymptote of the function Z(t) in argon is close to the power law αt–3/2 predicted by hydrodynamics, but with an amplitude that depends on the time interval under consideration. In water, the asymptote of Z(t) has nothing in common with that in argon: it has α < 0 and the exponent is close to -5/2, and not to -3/2.

Kinetics and Thermodynamics of Fe-X (X= Al, Cr, Mn, Ti, B, and C) Melts under High Pressure

The kinetic properties such as diffusivity and viscosity of the metal melt are the foundations to reveal the structure evolutions and the glass formation abilities during solidification of the investigated alloy, thus, to control the microstructures, defects and properties of materials. In this work, ab initio molecular dynamics simulations were utilized to investigate the kinetic and thermodynamic properties and the structural relaxations of Fe-X (X = 10-15 wt% Al, Cr, Mn and Ti, or 1-2wt% B and C) melts under various temperature and external pressure, which are in line with the interested concentration range of multi-component Fe-based alloys. The kinetics and structural relaxations are characterized by mean squared displacement, velocity autocorrelation function and self-intermediate scattering function. The thermodynamics properties including entropy and heat capacity are calculated by combining the vibrational and electronic contributions based on vibrational and electronic density of states. The predicted kinetics and thermodynamics properties under high temperature and pressure agree well with the experimental and theoretical results while the connection among structural relaxations and diffusion are revealed based on the Stokes-Einstein relation and the Hall-Wolynes (HW) relation. This work provides an insight into the structure-property relationships of metal melts, which are essential in the development of advanced multi-component Fe-based alloys.

Improving estimates of the growth rate using galaxy–velocity correlations: a simulation study

ABSTRACT We present an improved framework for estimating the growth rate of large-scale structure, using measurements of the galaxy–velocity cross-correlation in configuration space. We consider standard estimators of the velocity autocorrelation function, ψ1 and ψ2, the two-point galaxy correlation function, ξgg, and introduce a new estimator of the galaxy–velocity cross-correlation function, ψ3. By including pair counts measured from random catalogues of velocities and positions sampled from distributions characteristic of the true data, we find that the variance in the galaxy–velocity cross-correlation function is significantly reduced. Applying a covariance analysis and χ2 minimization procedure to these statistics, we determine estimates and errors for the normalized growth rate fσ8 and the parameter β = f/b, where b is the galaxy bias factor. We test this framework on mock hemisphere data sets for redshift z &lt; 0.1 with realistic velocity noise constructed from the l-picola simulation code, and find that we are able to recover the fiducial value of fσ8 from the joint combination of ψ1 + ψ2 + ψ3 + ξgg, with 15 per cent accuracy from individual mocks. We also recover the fiducial fσ8 to within 1σ regardless of the combination of correlation statistics used. When we consider all four statistics together we find that the statistical uncertainty in our measurement of the growth rate is reduced by $59{{\ \rm per\ cent}}$ compared to the same analysis only considering ψ2, by $53{{\ \rm per\ cent}}$ compared to the same analysis only considering ψ1, and by $52{{\ \rm per\ cent}}$ compared to the same analysis jointly considering ψ1 and ψ2.

Impulse response function for Brownian motion

Motivated from the central role of the mean-square displacement and its second time-derivative – that is the velocity autocorrelation function in the description of Brownian motion, we revisit the physical meaning of its first time-derivative.

Diffusion Spectrum of Polymer Melt Measured by Varying Magnetic Field Gradient Pulse Width in PGSE NMR

The translational motion of polymers is a complex process and has a big impact on polymer structure and chemical reactivity. The process can be described by the segment velocity autocorrelation function or its diffusion spectrum, which exhibit several characteristic features depending on the observational time scale—from the Brownian delta function on a large time scale, to complex details in a very short range. Several stepwise, more-complex models of translational dynamics thus exist—from the Rouse regime over reptation motion to a combination of reptation and tube-Rouse motion. Accordingly, different methods of measurement are applicable, from neutron scattering for very short times to optical methods for very long times. In the intermediate regime, nuclear magnetic resonance (NMR) is applicable—for microseconds, relaxometry, and for milliseconds, diffusometry. We used a variation of the established diffusometric method of pulsed gradient spin-echo NMR to measure the diffusion spectrum of a linear polyethylene melt by varying the gradient pulse width. We were able to determine the characteristic relaxation time of the first mode of the tube-Rouse motion. This result is a deviation from a Rouse model of polymer chain displacement at the crossover from a square-root to linear time dependence, indicating a new long-term diffusion regime in which the dynamics of the tube are also described by the Rouse model.

Analysis of Random Dynamics of Cell Segmented by a Modified Active Contour Method

To understand the dynamics of a living system, the analysis of particular and/or cellular dynamics has been performed based on shape-based center point detection. After collecting sequential time-lapse images of cellular dynamics, the trajectory of a moving object is determined from the set of center points of the cell analyzed from each image. The accuracy of trajectory is significant in understanding the stochastic nature of the dynamics of biological objects. In this study, to localize a cellular object in time-lapse images, three different localization methods, namely radial symmetry, circular Hough transform, and modified active contour, were considered. To analyze the accuracy of cellular dynamics, several statistical parameters such as mean square displacement and velocity autocorrelation function were employed, and localization error derived from these was reported for each localization method. In particular, through denoising using a Poisson noise filter, improved localization characteristics could be achieved. The modified active contour with denoising reduced localization error significantly, and thus allowed for accurate estimation of the statistical parameters of cellular dynamics.

Effect of Self-Oscillation on Escape Dynamics of Classical and Quantum Open Systems

We study the effect of self-oscillation on the escape dynamics of classical and quantum open systems by employing the system-plus-environment-plus-interaction model. For a damped free particle (system) with memory kernel function expressed by Zwanzig (J. Stat. Phys. 9, 215 (1973)), which is originated from a harmonic oscillator bath (environment) of Debye type with cut-off frequency wd, ergodicity breakdown is found because the velocity autocorrelation function oscillates in cosine function for asymptotic time. The steady escape rate of such a self-oscillated system from a metastable potential exhibits nonmonotonic dependence on wd, which denotes that there is an optimal cut-off frequency makes it maximal. Comparing results in classical and quantum regimes, the steady escape rate of a quantum open system reduces to a classical one with wd decreasing gradually, and quantum fluctuation indeed enhances the steady escape rate. The effect of a finite number of uncoupled harmonic oscillators N on the escape dynamics of a classical open system is also discussed.