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.

Effective Pair Interactions and Structure in Liquid Noble Metals within Wills-Harrison and Bretonnet-Silbert Models

Recently, for calculating the effective pair interactions in liquid transition metals, we have developed an approach which includes the Wills-Harrison and Bretonnet-Silbert models as limit cases. Here, we apply this approach to noble liquid metals. The dependencies of pair potentials and corresponding MD-simulated pair correlation functions in pure liquid Cu, Ag and Au on the portion of the non-diagonal (with respect to the magnet quantum number) d-d-electron couplings in the metal under consideration are studied. The model provides a good agreement with experimental and ab initio data for pair correlation functions, structure factors and velocity autocorrelation functions.

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.

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.

Characterisation of microvessel blood velocity and segment length in the brain using multi-diffusion-time diffusion-weighted MRI

Multi-diffusion-time diffusion-weighted MRI can probe tissue microstructure, but the method has not been widely applied to the microvasculature. At long diffusion-times, blood flow in capillaries is in the diffusive regime, and signal attenuation is dependent on blood velocity ([Formula: see text]) and capillary segment length ([Formula: see text]). It is described by the pseudo-diffusion coefficient ([Formula: see text]) of intravoxel incoherent motion (IVIM). At shorter diffusion-times, blood flow is in the ballistic regime, and signal attenuation depends on [Formula: see text], and not [Formula: see text]. In theory, [Formula: see text] could be estimated using [Formula: see text] and [Formula: see text]. In this study, we compare the accuracy and repeatability of three approaches to estimating [Formula: see text], and therefore [Formula: see text]: the IVIM ballistic model, the velocity autocorrelation model, and the ballistic approximation to the velocity autocorrelation model. Twenty-nine rat datasets from two strains were acquired at 7 T, with [Formula: see text]-values between 0 and 1000 smm−2 and diffusion times between 11.6 and 50 ms. Five rats were scanned twice to assess scan-rescan repeatability. Measurements of [Formula: see text] were validated using corrosion casting and micro-CT imaging. The ballistic approximation of the velocity autocorrelation model had lowest bias relative to corrosion cast estimates of [Formula: see text], and had highest repeatability.

Molecular Dynamics Investigation of Water Behavior Through Nanopores

The transport of fluids through nanoscale pores, channels, and membranes has been of great importance in our daily life. Nanoscale transport is relevant to many applications such as agriculture, energy and environmental fields. Considering these applications, it is important to characterize detailed mechanisms of liquid transport through nanoscale defects and pores on surfaces. Such characterization requires a detailed understanding of the deviation of water behavior and its transport mechanisms in nanoscale from bulk water. Molecular dynamics provide proper means to understand the dynamics and mechanisms of motions of water molecules confined in ultra-small spaces. This work examines the water transport through an individual pore which has a nanoscale dimensions ranging from 1.0 to 1.8 nm from molecular dynamics perspective. The effects of the nanopore dimensions as well as the surface wetting properties on the behavior of confined water are studied. The translational and rotational dynamics of water molecules are characterized by examining velocity autocorrelation functions and the calculation of the density of states, which supports the presence of unusual, solid-like behaviors of water molecules. A good understanding of the transport mechanisms and their origins are crucial to address common challenges in many engineering applications such as energy storage and conversion and could pave the way towards more efficient water-energy systems.

Simple man model in the Heisenberg picture

Describing the ionization of an atom exposed to a strong laser field entails computationally expensive quantum simulations based on the numerical solutions of the time-dependent Shrödinger equation. The well-known Simple Man Model provides a qualitatively accurate description of the ionization process. Here, we propose a quantum generalization of the physical picture given by the Simple Man Model. We describe an approximate solution to the Heisenberg operator equations of motion for an atom in a laser field. We provide justification of this generalization and test its validity by applying it to calculate the coordinate and velocity autocorrelation functions. Both our model and results of the ab initio numerical calculations show distinct types of correlations due to different types of electron’s motion providing insight into the strong field ionization dynamics.