The microscopic dynamics of protons (${\mathrm{H}}^{+}$) in poly(ethylene oxide) (PEO) have been investigated through a study of implanted positive muons (${\mathrm{Mu}}^{+}$), which can be considered a light proton analog. The exponential decay of the muon spin polarization in zero magnetic field indicated that ${\mathrm{Mu}}^{+}$ hopping is in the fast fluctuation limit between 140 and 310 K and the relaxation rate was found to be sensitive to the glass transition. ${\mathrm{Mu}}^{+}$ dynamics in PEO was monitored via the relaxation of the muon spin polarization in a transverse field of 10 mT. Activated hopping of ${\mathrm{Mu}}^{+}$ was observed above the glass transition temperature with an activation barrier of $122\pm 1$ meV. The temperature dependence of the diamagnetic muon polarization in PEO can be explained by diffusion of radiolytic electrons.

Open-porous deformable particles, often envisaged as sponges, are ubiquitous in biological and industrial systems (e.g., casein micelles in dairy products and microgels in cosmetics). The rich behavior of these suspensions is owing to the elasticity of the supporting network of the particle, and the viscosity of permeating solvent. Therefore, the rate-dependent size change of these particles depends on their structure, i.e., the permeability. This work aims at investigating the effect of the particle-size dynamics and the underlying particle structure, i.e., the particle permeability, on the transient and long-time behavior of suspensions of spongy particles in the absence of applied deformation, using the dynamic two-scale model developed by Hütter et al. [Farad. Discuss. 158, 407 (2012)]. In the high-density limit, the transient behavior is found to be accelerated by the particle-size dynamics, even at average size changes as small as $1\%$. The accelerated dynamics is evidenced by (i) the higher short-time diffusion coefficient as compared to elastic-particle systems and (ii) the accelerated formation of the stable fcc crystal structure. Furthermore, after long times, the particle-size dynamics of spongy particles is shown to result in lower stationary values of the energy and normal stresses as compared to elastic-particle systems. This dependence of the long-time behavior of these systems on the permeability, that essentially is a transport coefficient and hence must not affect the equilibrium properties, confirms that full equilibration has not been reached.

The motion of a single ellipsoidal particle in simple shear flow can provide valuable insights toward understanding suspension flows with nonspherical particles. Previously, extensive studies have been performed on the ellipsoidal particle with rotational symmetry, a so-called spheroid. The nearly prolate ellipsoid (one major and two minor axes of almost equal size) is known to perform quasiperiodic or even chaotic orbits in the absence of inertia. With small particle inertia, the particle is also known to drift toward this irregular motion. However, it is not previously understood what effects from fluid inertia could be, which is of highest importance for particles close to neutral buoyancy. Here, we find that fluid inertia is acting strongly to suppress the chaotic motion and only very weak fluid inertia is sufficient to stabilize a rotation around the middle axis. The mechanism responsible for this transition is believed to be centrifugal forces acting on fluid, which is dragged along with the rotational motion of the particle. With moderate fluid inertia, it is found that nearly prolate triaxial particles behave similarly to the perfectly spheroidal particles. Finally, we also are able to provide predictions about the stable rotational states for the general triaxial ellipsoid in simple shear with weak inertia.

We apply our extended Kirkwood-Riseman theory to compute the translation, rotation, and coupling friction tensors and the scalar rotational friction coefficient for an aerosol fractal aggregate in the transition flow regime. The method can be used for particles consisting of spheres in contact. Our approach considers only the linear velocity of the primary spheres in a rotating aggregate and ignores rotational and coupling interactions between spheres. We show that this simplified approach is within approximately 40% of the true value for any particle for Knudsen numbers between 0.01 and 100. The method is especially accurate (i.e., within about 5%) near the free-molecule regime, where there is little interaction between the particle and the flow field, and for particles with low fractal dimension ($\lesssim 2)$ consisting of many spheres, where the average distance between spheres is large and translational interaction effects dominate. Our results suggest that there is a universal relationship between the rotational friction coefficient and an aggregate Knudsen number, defined as the ratio of continuum to free-molecule rotational friction coefficients.

The first nonequilibrium effect experienced by gaseous flows in contact with solid surfaces is the slip-flow regime. While the classical hydrodynamic description holds valid in bulk, at boundaries the fluid-wall interactions must consider slip. In comparison to the standard no-slip Dirichlet condition, the case of slip formulates as a Robin-type condition for the fluid tangential velocity. This makes its numerical modeling a challenging task, particularly in complex geometries. In this work, this issue is handled with the lattice Boltzmann method (LBM), motivated by the similarities between the closure relations of the reflection-type boundary schemes equipping the LBM equation and the slip velocity condition established by slip-flow theory. Based on this analogy, we derive, as central result, the structure of the LBM boundary closure relation that is consistent with the second-order slip velocity condition, applicable to planar walls. Subsequently, three tasks are performed. First, we clarify the limitations of existing slip velocity LBM schemes, based on discrete analogs of kinetic theory fluid-wall interaction models. Second, we present improved slip velocity LBM boundary schemes, constructed directly at discrete level, by extending the multireflection framework to the slip-flow regime. Here, two classes of slip velocity LBM boundary schemes are considered: (i) linear slip schemes, which are local but retain some calibration requirements and/or operation limitations, (ii) parabolic slip schemes, which use a two-point implementation but guarantee the consistent prescription of the intended slip velocity condition, at arbitrary plane wall discretizations, further dispensing any numerical calibration procedure. Third and final, we verify the improvements of our proposed slip velocity LBM boundary schemes against existing ones. The numerical tests evaluate the ability of the slip schemes to exactly accommodate the steady Poiseuille channel flow solution, over distinct wall slippage conditions, namely, no-slip, first-order slip, and second-order slip. The modeling of channel walls is discussed at both lattice-aligned and non-mesh-aligned configurations: the first case illustrates the numerical slip due to the incorrect modeling of slippage coefficients, whereas the second case adds the effect of spurious boundary layers created by the deficient accommodation of bulk solution. Finally, the slip-flow solutions predicted by LBM schemes are further evaluated for the Knudsen's paradox problem. As conclusion, this work establishes the parabolic accuracy of slip velocity schemes as the necessary condition for the consistent LBM modeling of the slip-flow regime.

Cells exhibit qualitatively different behaviors on substrates with different rigidities. The fact that cells are more polarized on the stiffer substrate motivates us to construct a two-dimensional cell with the distribution of focal adhesions dependent on substrate rigidities. This distribution affects the forces exerted by the cell and thereby determines its motion. Our model reproduces the experimental observation that the persistence time is higher on the stiffer substrate. This stiffness-dependent persistence will lead to durotaxis, the preference in moving towards stiffer substrates. This propensity is characterized by the durotaxis index first defined in experiments. We derive and validate a two-dimensional corresponding Fokker-Planck equation associated with our model. Our approach highlights the possible role of the focal adhesion arrangement in durotaxis.

The linear stability of viscous Keplerian flow around a gravitating center is studied using the rheological granular fluid model. The linear rheological instability triggered by the interplay of the shear rheology and Keplerian differential rotation of incompressible dense granular fluids is found. Instability sets in in granular fluids, where the viscosity parameter grows faster than the square of the local shear rate (strain rate) at constant pressure. Found instability can play a crucial role in the dynamics of dense planetary rings and granular flows in protoplanetary disks.

We investigate a kinetic Ising model with several single-spin-flip dynamics (including Metropolis and heat bath) on quenched and annealed random regular graphs. As expected, on the quenched structures all proposed algorithms reproduce the same results since the conditions for the detailed balance and the Boltzmann distribution in an equilibrium are satisfied. However, on the annealed graphs the situation is far less clear—the network annealing disturbs the equilibrium moving the system away from it. Consequently, distinct dynamics lead to different steady states. We show that some algorithms are more resistant to the annealed disorder, which causes only small quantitative changes in the model behavior. On the other hand, there are dynamics for which the influence of annealing on the system is significant, and qualitative changes arise like switching the type of phase transition from a continuous to a discontinuous one. We try to identify features of the proposed dynamics which are responsible for the above phenomenon.

The transitionless tracking (TT) algorithm enables the exact tracking of quantum adiabatic dynamics in an arbitrary short time by adding a counterdiabatic Hamiltonian to the original adiabatic Hamiltonian. By applying Husimi's method originally developed for a quantum parametric oscillator (QPO) to the transitionless QPO achieved using the TT algorithm, we obtain the transition probability generating function with a time-dependent parameter constituted with solutions of the corresponding classical parametric oscillator (CPO). By obtaining the explicit solutions of this CPO using the phase-amplitude method, we find that the time-dependent parameter can be reduced to the frequency ratio between the Hamiltonians without and with the counterdiabatic Hamiltonian, from which we can easily characterize the result achieved by the TT algorithm. We illustrate our theory by showing the trajectories of the CPO on the classical phase space, which elucidate the effect of the counterdiabatic Hamiltonian of the QPO.

We investigate the relation between the classical ergodicity and the quantum eigenstate thermalization in the fully connected Ising ferromagnets. In the case of spin-1/2, an expectation value of an observable in a single-energy eigenstate coincides with the long-time average in the underlying classical dynamics, which is a consequence of the Wentzel-Kramers-Brillouin approximation. In the case of spin-1, the underlying classical dynamics is not necessarily ergodic. In that case, it turns out that, in the thermodynamic limit, the statistics of the expectation values of an observable in the energy eigenstates coincides with the statistics of the long-time averages in the underlying classical dynamics starting from random initial states sampled uniformly from the classical phase space. This feature seems to be a general property in semiclassical systems, and the result presented here is crucial in discussing equilibration, thermalization, and dynamical transitions of such systems.

To explore energy transfer in the nonequilibrium spin-boson model (NESB) from weak to strong system-bath coupling regimes, we propose a polaron-transformed nonequilibrium Green's function (NEGF) method. By combining the polaron transformation, we are able to treat the system-bath coupling nonperturbatively, thus in direct contrast to conventionally used NEGF methods which take the system-bath coupling as a perturbation. The Majorana-fermion representation is further utilized to evaluate terms in the Dyson series. This method not only allows us to deal with weak as well as strong coupling regimes but also enables an investigation on the role of bias in the energy transfer. As an application of the method, we study an Ohmic NESB. For an unbiased spin system, our energy current result smoothly bridges predictions of two benchmarks, namely, the quantum master equation and the nonequilibrium noninteracting blip approximation, a considerable improvement over existing theories. In case of a biased spin system, we found a bias-induced nonmonotonic behavior of the energy conductance in the intermediate coupling regime, resulting from the resonant character of the energy transfer. This finding may offer a nontrivial quantum control knob over energy transfer at the nanoscale.

The kink solution in the long Josephson junction is studied. The perturbation scheme of constructing the fluxon solution in curved junction is formulated. The prediction from the perturbation scheme is compared with the prediction that follows from the numerical studies of the complete field model.

In recent years several local extrema-based methodologies have been proposed to investigate either the nonlinear or the nonstationary time series for scaling analysis. In the present work, we study systematically the distribution of the local extrema for both synthesized scaling processes and turbulent velocity data from experiments. The results show that for the fractional Brownian motion (fBm) without intermittency correction the measured extremal-point-density (EPD) agrees well with a theoretical prediction. For a multifractal random walk (MRW) with the lognormal statistics, the measured EPD is independent of the intermittency parameter $\mu$, suggesting that the intermittency correction does not change the distribution of extremal points but changes the amplitude. By introducing a coarse-grained operator, the power-law behavior of these scaling processes is then revealed via the measured EPD for different scales. For fBm the scaling exponent $\xi \left(H\right)$ is found to be $\xi \left(H\right)=H$, where $H$ is Hurst number, while for MRW $\xi \left(\mu \right)$ shows a linear relation with the intermittency parameter $\mu$. Such EPD approach is further applied to the turbulent velocity data obtained from a wind tunnel flow experiment with the Taylor scale $\lambda$-based Reynolds number ${\text{Re}}_{\lambda }=720$, and a turbulent boundary layer with the momentum thickness $\theta$ based Reynolds number ${\text{Re}}_{\theta }=810$. A scaling exponent $\xi \simeq 0.37$ is retrieved for the former case. For the latter one, the measured EPD shows clearly four regimes, which agrees well with the corresponding sublayer structures inside the turbulent boundary layer.

The ultimate goal of exploring complex networks is to control them. As such, controllability of complex networks has been intensively investigated. Despite recent advances in studying the impact of a network's topology on its controllability, a comprehensive understanding of the synergistic impact of network topology and dynamics on controllability is still lacking. Here, we explore the controllability of flow-conservation networks, trying to identify the minimal number of driver nodes that can guide the network to any desirable state. We develop a method to analyze the controllability on flow-conservation networks based on exact controllability theory, transforming the original analysis on adjacency matrix to Laplacian matrix. With this framework, we systematically investigate the impact of some key factors of networks, including link density, link directionality, and link polarity, on the controllability of these networks. We also obtain the analytical equations by investigating the network's structural properties approximatively and design the efficient tools. Finally, we consider some real networks with flow dynamics, finding that their controllability is significantly different from that predicted by only considering the topology. These findings deepen our understanding of network controllability with flow-conservation dynamics and provide a general framework to incorporate real dynamics in the analysis of network controllability.

We investigate opinion spreading by a threshold model in a situation in which the influence of people is heterogeneously distributed. We assume that there is a coupling between the influence of an individual (measured by the out-degree) and the threshold for accepting a new opinion or habit. We find that if the coupling is strongly positive, the final state of the system will be a mix of different opinions. Otherwise, it will converge to a consensus state. This phenomenon cannot simply be explained as a phase transition, but it is a combined effect of mechanisms and their relative dominance in different regions of parameter space.

The ligand-receptor-mediated contacts of small sub-100-nm-sized lipid vesicles (or nanoparticles) with the cellular membrane are of interest in the contexts of cell-to-cell communication, endocytosis of membrane-coated virions, and drug (RNA) delivery. In all these cases, the interior of vesicles is filled by biologically relevant content. Despite the diversity of such systems, the corresponding ligand-receptor interaction possesses universal features. One of them is that the vesicle-membrane contacts can be accompanied by the redistribution of ligands and receptors between the contact and contact-free regions. In particular, the concentrations of ligands and receptors may become appreciably higher in the contact regions and their composition may there be different compared to that in the suspended state in the solution. A statistical model presented herein describes the corresponding distribution of various ligands and receptors and allows one to calculate the related change of the free energy with variation of the vesicle-engulfment extent. The results obtained are used to clarify the necessary conditions for the vesicle-assisted pathway of drug delivery.

We study marginally compact macromolecular trees that are created by means of two different fractal generators. In doing so, we assume Gaussian statistics for the vectors connecting nodes of the trees. Moreover, we introduce bond-bond correlations that make the trees locally semiflexible. The symmetry of the structures allows an iterative construction of full sets of eigenmodes (notwithstanding the additional interactions that are present due to semiflexibility constraints), enabling us to get physical insights about the trees' behavior and to consider larger structures. Due to the local stiffness, the self-contact density gets drastically reduced.

We explore the growth of two-dimensional quasicrystals, i.e., aperiodic structures that possess long-range order, from two seeds at various distances and with different orientations by using dynamical phase-field crystal calculations. We compare the results to the growth of periodic crystals from two seeds. There, a domain border consisting of dislocations is observed in case of large distances between the seed and large angles between their orientation. Furthermore, a domain border is found if the seeds are placed at a distance that does not fit to the periodic lattice. In the case of the growth of quasicrystals, we only observe domain borders for large distances and different orientations. Note that all distances do inherently not match to a perfect domain wall-free quasicrystalline structure. Nevertheless, we find dislocation-free growth for all seeds at a small enough distance and for all seeds that approximately have the same orientation. In periodic structures, the stress that occurs due to incommensurate distances between the seeds results in phononic strain fields or, in the case of too large stresses, in dislocations. In contrast, in quasicrystals an additional phasonic strain field can occur and suppress dislocations. Phasons are additional degrees of freedom that are unique to quasicrystals. As a consequence, the additional phasonic strain field helps to distribute the stress and facilitates the growth of dislocation-free quasicrystals from multiple seeds. In contrast, in the periodic case the growth from multiple seeds most likely leads to a structure with multiple domains. Our work lays the theoretical foundations for growing perfect quasicrystals from different seeds and is therefore relevant for many applications.

Molecular dynamics simulations are used to investigate the structural properties of a two-dimensional ensemble of magnetic rods, which are modeled as aligned single dipolar beads. The obtained self-assembled configurations can be characterized as (1) clusters, (2) percolated, and (3) ordered structures, and their structural properties are investigated in detail. By increasing the aspect ratio of the magnetic rods, we show that the percolation transition is suppressed due to the reduced mobility of the rods in two dimensions. Such a behavior is opposite to the one observed in three dimensions. A magnetic bulk phase is found with local ferromagnetic order and an unusual nonmonotonic behavior of the nematic order is observed.

The stability of the horizontal interface of two immiscible viscous fluids in a Hele-Shaw cell subject to gravity and horizontal vibrations is studied. The problem is reduced to the generalized Hill equation, which is solved analytically by the multiple scale method and numerically. The long-wave instability, the resonance (parametric resonance) excitation of waves at finite frequencies of vibrations (for the first three resonances), and the limit of high-frequency vibrations are studied analytically under the assumption of small amplitudes of vibrations and small viscosity. For finite amplitudes of vibrations, finite wave numbers, and finite viscosity, the study is performed numerically. The influence of the specific natural control parameters and physical parameters of the system on its instability threshold is discussed. The results provide extension to other results [J. Bouchgl, S. Aniss, and M. Souhar, Phys. Rev. E 88, 023027 (2013)], where the authors considered a similar problem but took into account viscosity in the basic state and did not consider it in the equations for perturbations.