Ballistic Diffusion Research Articles

Stability of β-Nb phase in Zr–Nb alloys under neutron irradiation: Phase field modeling

A phase field approach to study stability of β-Nb precipitates in Zr–Nb alloys is extended by taking into account local rearrangement of point defects and misfit dislocations. Kinetic properties of β-Nb phase formation are discussed at a heat treatment stage. Stability of secondary phase precipitates is studied at different irradiation temperatures and dose rates. It is shown that processes of dissolution/growth of precipitates are governed by the competition of ballistic mixing and thermal diffusion. It is found that at large values of dose rates and low temperatures, precipitates are dissolved due to a major role of ballistic mixing, whereas at low dose rate and elevated temperatures, β-niobium particles grow slowly by an Ostwald ripening scenario up to 1–2 nm due to the dominant role of thermal diffusion. Misfit dislocations sustain the existence of Nb-enriched domains of mixed symmetry. It is shown that growing dislocation loops and dissolving/growing precipitates result in the hardening change up to 0.01% at a dose rate of 10−5dpa/s and temperatures of 550–575 K. Obtained theoretical results are verified by experimental data.

Diffusion of excitations and power-law localization in strongly disordered systems with long-range coupling

We investigate diffusion of excitation in one- and two-dimensional lattices with random on-site energies and deterministic long-range couplings (hopping) inversely proportional to the distance. Three regimes of diffusion are observed in strongly disordered systems: ballistic motion at short time, standard diffusion for intermediate times, and a stationary phase (saturation) at long times. We propose an analytical solution valid in the strong-coupling regime which explains the observed dynamics and relates the ballistic velocity, diffusion coefficient, and asymptotic diffusion range to the system size and disorder strength via simple formulas. We show also that in the long-time asymptotic limit of diffusion from a single site the occupations form a heavy-tailed power-law distribution.

Interfacial Diffusion of Hydrated Ion on Graphene Surface: A Molecular Simulation Study.

Hydration plays an important role in the diffusion and sieving of ions within nanochannels. However, it is hard to quantitatively analyze the contribution of hydration to the diffusion rates due to the complex hydrogen-bond and charge interactions between atoms. Here, we quantitatively investigated the interfacial diffusion rates of a single hydrated ion with different number of water molecules on graphene surface through molecular dynamics simulation. The simulation results show the ballistic diffusion mode by analyzing the mean-square displacement, and the diffusion rates change nonmonotonically with the hydration number. The potential energy profiles with the changing position of the hydrated ion on graphene surface were further analyzed, which shows the dominant factor for interfacial diffusion changing from ion-graphene interaction to water-graphene interaction as the number of water molecules increases. Besides, it was found that the surface hydrophilicity weakened the influence of hydration number on the diffusion rates of hydrated ion. Finally, the diffusion properties of different hydrated ions on graphene surface were investigated, and the hydrated Li+, Na+, and K+ containing three, four, and five water molecules, respectively, show the fastest diffusion rate. This work demonstrates the interfacial diffusion behavior and mechanism of hydrated ions at the molecular level, which can provide valuable guidance in nanosensors, seawater desalination, and other hydrated ion-related fields.

Approximate Solutions of the Model Describing Fluid Flow Using Generalized ρ-Laplace Transform Method and Heat Balance Integral Method

This paper addresses the solution of the incompressible second-grade fluid models. Fundamental qualitative properties of the solution are primarily studied for proving the adequacy of the physical interpretations of the proposed model. We use the Liouville-Caputo fractional derivative with its generalized version that gives more comprehensive physical results in the analysis and investigations. In this work, both the ρ-Laplace homotopy transform method (ρ-LHTM) and the heat balance integral method (HBIM) are successfully combined to solve the fractional incompressible second-grade fluid differential equations. Numerical simulations and their physical interpretations of the mentioned incompressible second-grade fluid model are ensured to illustrate the main findings. It is also proposed that one can recognize the differences in physical analysis of diffusions such as ballistic diffusion, super diffusion, and subdiffusion cases by considering the impact of the orders ρ and φ.

Chaotic dynamics of complex trajectory and its quantum signature* *Project partially supported by the National Natural Science Foundation of China (Grant Nos. 12065009, 11804130, and 11805165) and Zhejiang Provincial Nature Science Foundation, China (Grant No. LY20A050001).

We investigate both the quantum and classical dynamics of a non-Hermitian system via a kicked rotor model with symmetry. For the quantum dynamics, both the mean momentum and mean square of momentum exhibit the staircase growth with time when the system parameter is in the neighborhood of the symmetry breaking point. If the system parameter is much larger than the symmetry breaking point, the accelerator mode results in the directed spreading of the wavepackets as well as the ballistic diffusion in momentum space. For the classical dynamics, the non-Hermitian kicking potential leads to the exponentially-fast increase of classical complex trajectories. As a consequence, the imaginary part of the trajectories exponentially diffuses with time, while the real part exhibits the normal diffusion. Our analytical prediction of the exponential diffusion of imaginary momentum and its breakdown time is in good agreement with numerical results. The quantum signature of the chaotic diffusion of the complex trajectories is reflected by the dynamics of the out-of-time-order correlators (OTOC). In the semiclassical regime, the rate of the exponential increase of the OTOC is equal to that of the exponential diffusion of the complex trajectories.

Analytic description of anomalous diffusion in heterogeneous environments: Fokker-Planck equation without fractional derivatives.

This article presents a one-dimensional model of diffusion in a heterogeneous environment, which qualitatively reflects the transport properties of a polymeric membrane with carbon nanotube areas. We derive the Fokker-Planck equation from a system of stochastic equations using a diffusion regime in polymers and a ballistic diffusion regime in nanotube areas. We demonstrate how the probability density function changes in the presence of nanotubes. The mean-square displacement of nonlinear time dependence is observed, indicating anomalous diffusion. This model explains the mechanism of anomalous diffusion in a ballistic-diffusion regime. Our approach does not suppose any type of distribution and does not use a fractional differentiate apparatus.

Fluctuations in Bacterial Suspensions Driven by Chemotaxis

Stochastic fluctuations in living systems create a spectacular variety of unique states far from equilibrium, which however remains largely unexplored regarding its underlying physics, especially when considering their instinctive responses to environmental stimuli. Here, by utilizing a molecular-dynamics model of bacterial chemotaxis, we present an investigation of tracer statistics in suspensions of chemotactic bacteria. Unlike Brownian motion in conventional media, the tracer particle performs a short-time ballistic but long-time Fickian diffusion with non-Gaussian dynamics. A phenomenological extension of Langevin equation accounts for the observed anomalous behaviors. Moreover, a violation of the Stokes-Einstein relation is identified regarding the size-dependence of particle diffusivity in bacterial suspensions. Our findings uncover the physical nature of stimulus-driven fluctuation statistics in bacterial fluids, and suggest a theoretical framework to deepen the understanding of the nonequilibrium statistical physics of active matter under external stimuli.

Comb Model with Non-Static Stochastic Resetting and Anomalous Diffusion

Nowadays, the stochastic resetting process is an attractive research topic in stochastic process. At the same time, a series of researches on stochastic diffusion in complex structures introduced ways to understand the anomalous diffusion in complex systems. In this work, we propose a non-static stochastic resetting model in the context of comb structure that consists of a structure formed by backbone in x axis and branches in y axis. Then, we find the exact analytical solutions for marginal distribution concerning x and y axis. Moreover, we show the time evolution behavior to mean square displacements (MSD) in both directions. As a consequence, the model revels that until the system reaches the equilibrium, i.e., constant MSD, there is a Brownian diffusion in y direction, i.e., ⟨ ( Δ y ) 2 ⟩ ∝ t , and a crossover between sub and ballistic diffusion behaviors in x direction, i.e., ⟨ ( Δ x ) 2 ⟩ ∝ t 1 2 and ⟨ ( Δ x ) 2 ⟩ ∝ t 2 respectively. For static stochastic resetting, the ballistic regime vanishes. Also, we consider the idealized model according to the memory kernels to investigate the exponential and tempered power-law memory kernels effects on diffusive behaviors. In this way, we expose a rich class of anomalous diffusion process with crossovers among them. The proposal and the techniques applied in this work are useful to describe random walkers with non-static stochastic resetting on comb structure.

Negative friction and mobilities induced by friction fluctuation.

We study the transport phenomena of an inertial Brownian particle in a symmetric potential with periodicity, which is driven by an external time-periodic force and an external constant bias for both cases of the deterministic dynamics and the existence of friction coefficient fluctuations. For the deterministic case, it is shown that for suitable parameters, the existence of certain appropriate friction coefficients can enhance the transport of the particle, which may be interpreted as the negative friction coefficient; additionally, there coexist absolute, differential negative, and giant positive mobilities with increasing friction coefficients in the system. We analyze physical mechanisms hinted behind these findings via basins of attraction. For the existence of friction coefficient fluctuations, it is shown that the fluctuation can enhance or weaken, even eliminate these phenomena. We present the probability distribution of the particle's velocity to interpret these mobilities and the suitable parameters' regimes of these phenomena. In order to further understand the physical mechanism, we also study diffusions corresponding to these mobilities and find that for the small fluctuation, the negative friction appears, and there coexists absolute negative mobility, superdiffusion, and ballistic diffusion, whereas all of them vanish for the large fluctuation. Our findings may extensively exist in materials, including different defects, strains, the number of interfacial hydrogen bonds, the arrangements of ions, or graphite concentrations, which hints at the existence of different friction coefficients.

Self-diffusion of nanoscale particles with hard and soft sphere models

The diffusion of particles in suspension is investigated by a thermostat based on fluctuating hydrodynamics for dynamic simulations of implicit-solvent coarse-grained model which can take into account both hydrodynamic and Brownian effects. Particles with cut-and-shifted Lennard-Jones and Gaussian-core potential are studied. The results show that their diffusion process can be characterized by three regimes: ballistic motion, short-time diffusion and long-time diffusion. We observe that the mean square displacement (MSD) of regime I, ballistic motion, is proportional to t2. For the other two regimes, its MSD is proportional to t with different slopes. Furthermore, we study the diffusion coefficients of spherical particles from MSD at different volume fractions. For the cut-and-shifted Lennard-Jones potential model, we observe the diffusion coefficients decrease monotonously with the increase of volume fraction (0.02–0.3), consistent with the results of the experiment. However, for the Gauss-core potential model, the curve of long-time self-diffusion coefficient as a function of dimensional density (0.001 to 1) appears to be nonmonotonic. It shows that the long-time self-diffusion coefficient decreases monotonically when the dimensional density is below 0.3, and then increases anomalously when the dimensionless density passes through 0.3.

Bose–Einstein condensates in an eightfold symmetric optical lattice**Project supported by the National Natural Science Foundation of China (Grant Nos. 11434011, 11522436, and 11774425), the National Key R&D Program of China (Grants No. 2018YFA0306501), the Beijing Natural Science Foundation, China (Grant No. Z180013), and the Research Funds of Renmin University of China (Grants Nos. 16XNLQ03 and 18XNLQ15).

We investigate the properties of Bose–Einstein condensates (BECs) in a two-dimensional quasi-periodic optical lattice (OL) with eightfold rotational symmetry by numerically solving the Gross–Pitaevskii equation. In a stationary external harmonic trapping potential, we first analyze the evolution of matter-wave interference pattern from periodic to quasi-periodic as the OL is changed continuously from four-fold periodic to eight-fold quasi-periodic. We also investigate the transport properties during this evolution for different interatomic interaction and lattice depth, and find that the BEC crosses over from ballistic diffusion to localization. Finally, we focus on the case of eightfold symmetric lattice and consider a global rotation imposed by the external trapping potential. The BEC shows vortex pattern with eightfold symmetry for slow rotation, becomes unstable for intermediate rotation, and exhibits annular solitons with approximate axial symmetry for fast rotation. These results can be readily demonstrated in experiments using the same configuration as in Phys. Rev. Lett. 122 110404 (2019).

Diffusion behaviors of energy and momentum for 1D single-walled carbon nanotubes

The single-walled carbon nanotube (CNT) is a quasi-1D material with ultra high thermal conductivity. It is known that the heat conduction is closely related with the energy diffusion and the information of heat conduction can be obtained by examining the energy diffusion behavior. The correlated energy distribution CE(i,t) calculated in diffusion process gives the whole spatial distribution of energy spreading at every correlation time which is much better than the traditional heat conduction method where only a number of thermal conductivity is provided. In previous study the anomalous super-diffusion of energy has been reported for CNT via a non-equilibrium diffusion method. Here we apply the more sophisticate equilibrium diffusion method to investigate the energy diffusion behavior in CNT with much longer length up to m with much higher accuracy. At room temperature, the super-diffusion of energy described by the mean square displacement of energy is found to be not far away from ballistic diffusion which is consistent with the experimentally measured ultra high thermal conductivity for CNT. With the equilibrium diffusion method, the diffusion of momentum has also been performed for CNT and ballistic diffusion is found which can be viewed as a support for anomalous super energy diffusion. The momentum diffusion can also give accurate information of sound velocity which is determined as m s−1 at room temperature. In particular, the very weak temperature coefficient of sound velocity can be obtained as m (. The normalized temperature coefficient of sound velocity can be related with the normalized temperature coefficient of Raman frequency shifts experimentally measured as . The obtained value via the momentum diffusion method is consistent with the experimental measurements.

Coexistence of absolute negative mobility and anomalous diffusion

Using extensive numerical studies we demonstrate that absolute negative mobility of a Brownian particle (i.e. the net motion into the direction opposite to a constant biasing force acting around zero bias) does coexist with anomalous diffusion (AD). The latter is characterised in terms of a nonlinear scaling with time of the mean-square deviation of the particle position. Such AD covers ‘coherent’ motion (i.e. the position dynamics x(t) approaches in evolving time a constant dispersion), ballistic diffusion, subdiffusion, superdiffusion and hyperdiffusion. In providing evidence for this coexistence we consider a paradigmatic model of an inertial Brownian particle moving in a one-dimensional symmetric periodic potential being driven by both an unbiased time-periodic force and a constant bias. This very setup allows for various sorts of different physical realisations.

Dynamics of a Particle Moving in One Dimensional Lorentz Lattice Gas

We study the dynamics of a particle moving in one-dimensional Lorentz lattice-gas where particle performs mainly three different kinds of motion {\it viz} ballistic motion, diffusion and confinement. There are two different types of scatterers, {\it viz} reflector and transmitters, randomly placed in the lattice. Reflectors are such that they reverse the particle's velocity direction and transmitters let it pass through. Scatterers also change their character with flipping probability $1-\alpha$, once the particle interacts with a scatterer. Hence the system is defined by two sets of parameters, $r$, which is the initial density of reflector/transmitter and $\alpha$. For $\alpha=0$ and $\alpha=1$ dynamics of the particle is purely deterministic else it is probabilistic. In the pure deterministic case dynamics of the particle is either propagation in one direction or confined between two near-by reflectors present. For the probabilistic case $\alpha \ne 1$ and $\ne 0$, although the dynamics of particle shows anomalous diffusion where dynamics is faster, slower and comparable to normal diffusion on the variation of system parameters $(\alpha, r)$, but the asymptotic behaviour of the particle is normal diffusion. We plot the phase diagram for the asymptotic behaviour, in the plane of $\alpha$ and $r$.

Evolution of periodical surface nanostructures under off-normal gas cluster ion irradiation

Gas cluster ion beam is known as a tool for surface smoothing; at the same time, surface relief formation under oblique beam incidence was reported. We suggested using samples with pre-formed surface pattern to study its evolution caused by ion irradiation and applied this approach to reveal the mechanisms responsible for nanorelief developing under off-normal cluster ion incidence. The role of key processes, which are ballistic diffusion and sputtering depending on the local incidence angle and surface curvature, is discussed. The irradiation conditions as well as the initial patters found to influence on the resulting surface shape.

Anomalous Dynamics of Water in Polyamide Matrix.

Water in polymer matrixes is likely to show anomalous dynamics, a problem that has not been well understood yet. Here, we performed atomistic molecular dynamics simulations to study the water dynamics in a polyamide (PA) matrix, the bulk phase of well-known reverse osmosis membranes. For time-dependent ensemble average, water molecules experienced ballistic diffusion at a shorter time scale, followed by a crossover from subdiffusion to Brownian diffusion at a time scale ∼10 ns, and non-Gaussian diffusion, an indication of anomalous dynamics, sticks on even in the Brownian diffusion region. The anomalous dynamics mainly originates from two distinct motions including small-step continuous diffusion and jumping diffusion. The jumping motion has a mean length of 3.08 ± 0.31 Å and characteristic relaxation time of 0.218 ± 0.040 ns, which dominates the water diffusion in a fully hydrated PA matrix. It comprised low- and high-frequency jumps; the former is almost unchanged, and the latter remarkably increases with the increase of the hydration level. Surrounding neighbors of water strongly affect the jumping frequency, which exponentially or linearly decays with the increase in the number of atoms from the PA matrix. Although the PA matrix is flexible, associated with the water dynamics, the translocation of water is mainly through either tracing the position of neighboring water or jumping into the adjacent accommodation space.

Surfactant-free synthesis and experimental analysis of Mn-doped ZnO–glycerol nanofluids: an ultrasonic and thermal study

A simplistic and environment-friendly approach has been used to prepare surfactant-free Mn-doped ZnO–glycerol nanofluids using high power sonicator. Thermal conductivity of the prepared nanofluids has been measured as a function of temperature and concentration. Maximum thermal conductivity enhancement ~ 32% at 40 °C has been observed with very low nanoparticles loading (2.0 vol% of Mn-doped ZnO-nanoparticles) which is significantly larger than the presently synthesized ZnO–glycerol nanofluids, and that of reported earlier on ZnO-ethylene glycol, and other glycerol-based nanofluids. Our present investigation shows that the thermal conductivity of nanofluids can be increased up to a significant level by changing other physical properties of incorporated nanoparticles than increasing concentration of nanoparticles to a large extent. Various physical phenomena including Brownian motion induced convection effect in conjunction with ballistic diffusion have been proposed for anomalous thermal conductivity enhancement. This may be valuable for various cooling applications and may open avenues for further exploration of efficient heat management with the help of nanosized doped metal oxide suspensions.

Tempered fractional Langevin–Brownian motion with inverse β-stable subordinator

Time-changed stochastic processes have attracted much attention and wide interest due to their extensive applications, especially in financial time series, biology and physics. This paper pays attention to a special stochastic process, tempered fractional Langevin motion, which is non-Markovian and undergoes ballistic diffusion for long times. The corresponding time-changed Langevin system with an inverse β-stable subordinator is discussed in detail, including its diffusion type, moments, Klein–Kramers equation, and the correlation structure. Interestingly, this subordination could result in both subdiffusion and superdiffusion, depending on the value of β. The difference between the subordinated tempered fractional Langevin equation and the subordinated Langevin equation with external biasing force is studied for a deeper understanding of the subordinator. The time-changed tempered fractional Brownian motion by an inverse β-stable subordinator is also considered, as well as the correlation structure of its increments. Some properties of the statistical quantities of the time-changed process are discussed, displaying striking differences compared with the original process.

Bed particle dynamics at entrainment

ABSTRACTThe paper reports a high-resolution experimental study focused on statistical properties of particle trajectories starting with detachment from the bed. This local range of particle motion can either be considered to start from a collision with the bed of an already mobile particle, or from the entrainment of a previously immobile particle. Both approaches are investigated and compared based on the particle diffusion concept. From the point of entrainment, local particle diffusion in all three coordinate directions displays an exponent significantly greater than that of ballistic diffusion. In contrast, particle motion after collision with the bed demonstrates ballistic diffusion in all three coordinate directions. The results highlight clear differences between the diffusion of an already mobile particle and one starting from a position of rest. These differences are attributed to variations in physical mechanisms acting at the initial phase of particle motion after detachment from the bed.

Hydrodynamic dispersion in heterogeneous anisotropic porous media: A simple model for anomalous diffusion emergence

Anomalous transport processes in porous media have become a central physical issue due to the increasing amount of processes and applications where it appears, ranging from contaminant transport in aquifers and oil recovery to anomalous diffusion in biological membranes. In all these cases, the existence of strong heterogeneities and anisotropies make proper physical and mathematical modelling a complicated problem, leading to simplified models where these spatial features and their implications for transport and diffusion are treated separately. In this work we propose a simple model for transport in porous media that includes anisotropy and strong heterogeneities. We show that depending on how strong the medium heterogeneities are, different regimes of superdiffusive transport emerge, going from superdiffusion due to long-range correlations to Lévy walks and ballistic diffusion.