We study average magnetic field growth in a mirror-symmetrical Kazantsev turbulent flow near the dissipative scales. Our main attention is directed to a subcritical regime, when an exponential decrease of magnetic energy is usually expected. We show that instead of damping, transient energy growth can be obtained, for example, in stochastic processes supported by the large-scale magnetic fields. We calculate the longitudinal correlation functions and demonstrate that they can tend to nonzero stationary solutions, whose localization width is inversely proportional to the square of the magnetic Reynolds numbers and with amplitude depending on the closeness of these numbers to the critical value. We present the local generation effect without any external support, predicted by Zeldovich in 1956. Numerically solving the initial-boundary Kazantsev problem on the nonuniform grids, we simulate this process by implicit schemes and discuss the possible consequences of subcritical growth for dynamo theory.

The process of nuclear excitation by electron capture in plasma environments generated by the interaction of ultrastrong optical lasers with solid-state samples is investigated theoretically. With the help of a plasma model, we perform a comprehensive study of the optimal parameters for the most efficient nuclear excitation and determine the corresponding laser setup requirements. We discern between the low-density plasma regime, modeled by scaling laws, and the high-density regime, for which we perform particle-in-cell calculations. As a nuclear transition case study we consider the 4.85-keV nuclear excitation starting from the long-lived ${}^{93m}\mathrm{Mo}$ isomer. Our results show that the optimal plasma and laser parameters are sensitive to the chosen observable and that measurable rates of nuclear excitation and isomer depletion of ${}^{93m}\mathrm{Mo}$ should be already achievable at laser facilities existing today.

Operator split forcing schemes exploiting a symmetrization principle, i.e., Strang splitting, for cascaded lattice Boltzmann (LB) methods in two- and three-dimensions for fluid flows with impressed local forces are presented. Analogous scheme for the passive scalar transport represented by a convection-diffusion equation with a source term in a novel cascaded LB formulation is also derived. They are based on symmetric applications of the split solutions of the changes on the scalar field or fluid momentum due to the sources or forces over half time steps before and after the collision step. The latter step is effectively represented in terms of the post-collision change of moments at zeroth and first orders, respectively, to represent the effect of the sources on the scalar transport and forces on the fluid flow. Such symmetrized operator split cascaded LB schemes are consistent with the second-order Strang splitting and naturally avoid any discrete effects due to forces or sources by appropriately projecting their effects for higher-order moments. All the force or source implementation steps are performed only in the moment space and they do not require formulations as extra terms and their additional transformations to the velocity space. These result in particularly simpler and efficient schemes to incorporate forces or sources in the cascaded LB methods unlike those considered previously. Numerical study for various benchmark problems in 2D and 3D for fluid flow problems with body forces and scalar transport with sources demonstrate the validity and accuracy, as well as the second-order convergence rate of the symmetrized operator split forcing or source schemes for the cascaded LB methods.

We comment on the findings presented in [Phys. Rev. E 80, 046101 (2009)] concerning the spacing distribution of the spectrum of sparsely connected random networks. We point out that for clustered networks without any connection among them the spacing distribution is not described by Poisson but rather by a superposition of multiple Gaussian orthogonal ensemble (GOE) statistics. Therefore, the spacing distribution for a network having two dense subnetworks with few connections between the two subnetworks follows a transition from two-GOE to a GOE statistics and not as the article suggests a transition from Poisson statistics to the GOE.

Interactions among discrete oscillatory units (e.g., cells) can result in partially synchronized states when some of the units exhibit phase locking and others phase slipping. Such states are typically characterized by a global order parameter that expresses the extent of synchrony in the system. Here we show that such states carry data-rich information of the system behavior, and a local order parameter analysis reveals universal relations through a semicircle representation. The universal relations are derived from thermodynamic limit analysis of a globally coupled Kuramoto-type phase oscillator model. The relations are confirmed with the partially synchronized states in numerical simulations with a model of circadian cells and in laboratory experiments with chemical oscillators. The application of the theory allows direct approximation of coupling strength, the natural frequency of oscillations, and the phase lag parameter without extensive nonlinear fits as well as a self-consistency check for presence of network interactions and higher harmonic components in the phase model.

We modeled the experimentally observed self-assembly of nanoparticles (NPs) into shells with diameters up to 10 $\mu \mathrm{m}$, via segregation from growing nematic domains. Using field-based Monte Carlo simulations, we found the equilibrium configurations of the system by minimizing a free-energy functional that includes effects of excluded-volume interactions among NPs, orientational elasticity, and the isotropic-nematic phase-transition energy. We developed a Gaussian-profile approximation for the liquid crystal (LC) order-parameter field that provides accurate analytical values for the free energy of LC droplets and the associated microshells. This analytical model reveals a first-order transition between equilibrium states with and without microshells, governed mainly by the competition of excluded-volume and phase-transition energies. By contrast, the LC elasticity effects are much smaller and mostly confined to setting the size of the activation barrier for the transition. In conclusion, field-based thermodynamic methods provide a theoretical framework for the self-assembly of NP shells in liquid crystal hosts and suggest that field-based kinetic methods could be useful to simulate and model the time evolution of NP self-assembly coupled to phase separation.

In this paper, we study the effect of the evaporation of adatoms and impurities on the step bunching induced by impurity. Keeping the ratio of the impingement rate of impurities $F_{\mathrm{imp}}$ to that of atoms $F$ constant, we carry out Monte Carlo simulation. In the system with the evaporation of impurities, the growth rate of vicinal face $R$ is proportional to $F$. This relation is the same as that without the evaporation of impurities. When $F$ is small, the vicinal face is unstable. Compared with the system without the evaporation of impurities, the effect of impurities is weakened. In our simulation, step pairing occurs but large bunches are not formed. When we take account of the evaporation of both impurities and adatoms, the vicinal face grows when $F$ is larger than the equilibrium value $F_{\mathrm{eq}}$. $R$ is not proportional to $(F-F_{\mathrm{eq}})$ and large bunches are formed when $F$ is small. In this paper, we also show how the impurity density on surface ${\sigma }_{\mathrm{imp}}$ and that incorporated in solid ${\rho }_{\mathrm{imp}}$ are related to the formation of step bunches.

By means of three-dimensional discrete element simulations, we study the spreading of a granular droplet on a horizontally vibrated plate. Apart from a short transient with a parabolic shape, the droplet adopts a triangular profile during the spreading. The dynamics of the spreading is governed by two distinct regimes: a superdiffusive regime in the early stages driven by surface flow followed by a second one which is subdiffusive and governed by bulk flow. The plate bumpiness is found to alter only the spreading rate but plays a minor role on the shape of the granular droplet and on the scaling laws of the spreading. Importantly, we show that in the subdiffusive regime, the effective friction between the plate and the granular droplet can be interpreted in the framework of the $\mu \left(I\right)$-rheology.

High-$Z$ material mixed into the fuel degrades inertial fusion implosions and can prevent ignition. Mix is often assumed to be dominated by hydrodynamic instabilities, but we report Omega data, using shells with $\sim 150\mathrm{nm}$ deuterated layers to gain unprecedented resolution, which give strong evidence that the dominant mix mechanism is diffusion for these moderate temperature ($\lesssim 6$ keV) and convergence ($\sim 12$) implosions. Small-scale instability-driven or turbulent mix is negligible.

In this paper we study the one-dimensional Kardar-Parisi-Zhang (KPZ) equation with correlated noise by field-theoretic dynamic renormalization-group techniques. We focus on spatially correlated noise where the correlations are characterized by a sinc profile in Fourier space with a certain correlation length $\xi$. The influence of this correlation length on the dynamics of the KPZ equation is analyzed. It is found that its large-scale behavior is controlled by the standard KPZ fixed point, i.e., in this limit the KPZ system forced by sinc noise with arbitrarily large but finite correlation length $\xi$ behaves as if it were excited by pure white noise. A similar result has been found by Mathey et al. [S. Mathey et al., Phys. Rev. E 95, 032117 (2017)] for a spatial noise correlation of Gaussian type ($\sim e^{-x^2/2{\xi }^2}$), using a different method. These two findings together suggest that the KPZ dynamics is universal with respect to the exact noise structure, provided the noise correlation length $\xi$ is finite.

Microtubule rigidity is important for many cellular functions to support extended structures and rearrange materials within the cell. The arrangement of the tubulin dimers within the microtubule can be altered to affect the protofilament number and the lattice type. Prior electron microscopy measurements have shown that when polymerized in the presence of a high concentration of NaCl, microtubules were more likely to be ten protofilaments with altered intertubulin lattice types. Specifically, such high-salt microtubules have a higher percentage of seam defects. Such seams have long been speculated to be a mechanically weak location in the microtubule lattice, yet no experimental evidence supported this claim. We directly measured the persistence length of freely fluctuating filaments made either with high salt or without. We found that the microtubules made with high salt were more flexible, by a factor of 2, compared to those polymerized the same way without salt present. The reduced persistence length of the high-salt microtubules can be accounted for entirely by a smaller cross-sectional radius of these microtubules, implying that the mixed lattice interactions have little effect on the bending rigidity. Our results suggest that the microtubule seam is not weaker than the typical lattice structure as previously speculated from structural studies.

The Helfrich bending energy plays an important role in providing a mechanism for the conformation of a lipid vesicle in theoretical biophysics, which is governed by the principle of energy minimization over configurations of appropriate topological characteristics. We will show that the presence of a quantity called the spontaneous curvature obstructs the existence of a minimizer of the Helfrich energy over the set of embedded ring tori. In addition, despite the well-realized knowledge that lipid vesicles may present themselves in a variety of shapes of complicated topology, there is a lack of topological bounds for the Helfrich energy. To overcome these difficulties, we consider a general scale-invariant anisotropic curvature energy that extends the Canham elastic bending energy developed in modeling a biconcave-shaped red blood cell. We will show that, up to a rescaling of the generating radii, there is a unique minimizer of the energy over the set of embedded ring tori, in the entire parameter regime, which recovers the Willmore minimizer in its Canham isotropic limit. We also show how elevated anisotropy favors energetically a clear transition from spherical-, to ellipsoidal-, and then to biconcave-shaped surfaces, for a lipid vesicle. We then establish some genus-dependent topological lower and upper bounds for the anisotropic energy. Finally, we derive the shape equation of the generalized bending energy, which extends the well-known Helfrich shape equation.

The self-propelled motions of micron-sized nematic liquid crystal droplets in an aqueous surfactant solution have been studied by tracking individual droplets over long time periods. Switching between self-propelled modes is observed as the droplet size decreases at a nearly constant dissolution rate: from random to helical and then straight motion. The velocity of the droplet decreases with its size for straight and helical motions but is independent of size for random motion. The switching between helical and straight motions is found to be governed by the self-propelled velocity, and is confirmed by experiments at various surfactant concentrations. The helical motion appears along with a shifting of a point defect from the self-propelled direction of the droplet. The critical velocity for this shift of the defect position is found to be related with the Ericksen number, which is defined by the ratio of the viscous and elastic stresses. In a thin cell whose thickness is smaller than that of the initial droplet size, the droplets show more complex trajectories, including “figure-8s” and zigzags. The appearance of those characteristic motions is attributed to autochemotaxis of the droplet.

The heterogeneity of local dynamics in disordered systems is behind some key features of glass transition. In order to improve our understanding of the molecular dynamics in disordered systems in the vicinity of the glass transition, different parameters have been proposed to quantitatively describe dynamical heterogeneity. In the case of polymers, free volume models relate the macromolecular mobility to the free or accessible volume. The relationship between dynamic heterogeneity and fluctuations of accessible volume seems straightforward. In the present work, the heterogeneity of local dynamics in polymeric systems is analyzed by computer simulation with the bond fluctuation model. The value of the accessible volume around each polymer chain is evaluated from a snapshot or static structure at each system state, resulting in a distribution of accessible volume that reflects system heterogeneity. The relationship between the average value and the standard deviation of free volume distributions at different temperatures fits a master curve for different systems, regardless of the specific inter- and intramolecular interaction potentials that define each material. The dynamic slowdown around the glass transition is accompanied by a clear evolution of the mean value and shape of the accessible free volume distribution. The relative fluctuation of the dynamically accessible volume has been used as a parameter to quantitatively describe heterogeneity. The fluctuation varies with temperature with remarkable differences between the liquid and glassy states of the systems studied, presenting a peak at the glass transition temperature, which can be interpreted as a reflection of the distribution of local glass transition temperatures.

This paper reports the experimental results of a water droplet spreading on a glass substrate submerged in an oil phase. The radius of the wetted area grows exponentially over time forming two distinct regimes. The early time dynamics of wetting is characterized with the time exponent of 1, referred to as the viscous regime, which is ultimately transitioned to the Tanner's regime with the time exponent of 0.1. It is revealed that an increase in the ambient phase viscosity over three decades considerably slows down the rate of three-phase contact line movement. A scaling law is developed where the three-phase contact line velocity is a function of both spreading radius and mean viscosity, close to the geometric mean of the droplet and ambient fluids’ viscosities. Using the proposed scaling and mean viscosity, all plots of spreading radius for different viscosity ratios collapse to a master curve. Furthermore, several cases with multiple rupture and spreading points, i.e., wetting in a nonideal system, are considered. The growth of an equivalent wetting radius in a multiple point spreading system is predicted by the developed scaling law.

For liquid rubidium the Stokes-Einstein (SE) relation is well fulfilled near the melting point with an effective hydrodynamic diameter, which agrees well with a value from structural investigations. A wealth of thermodynamic and microscopic data exists for a wide range of temperatures for liquid rubidium and hence it represents a good test bed to challenge the SE relation with rising temperature from an experimental point of view. We performed classical molecular dynamics simulations to complement the existing experimental data using a pseudopotential, which describes perfectly the structure and dynamics of liquid rubidium. The derived SE relation from combining experimental shear viscosity data with simulated diffusion coefficients reveals a weak violation at about $1.3T_{\mathrm{melting}}\approx 400$ K. The microscopic relaxation dynamics on nearest neighbor distances from neutron spectroscopy demonstrate distinct changes in the amplitude with rising temperature. The derived average relaxation time for density fluctuations on this length scale shows a non-Arrhenius behavior, with a slope change around $1.5T_{\mathrm{melting}}\approx 450$ K. Combining the simulated macroscopic self-diffusion coefficient with that microscopic average relaxation time, a distinct violation of the SE relation in the same temperature range can be demonstrated. One can conclude that the changes in the collective dynamics, a mirror of the correlated movements of the particles, are at the origin for the violation of the SE relation. The changes in the dynamics can be understood as a transition from a more viscous liquid metal to a more fluid-like liquid above the crossover temperature range of 1.3–1.5 $T_{\mathrm{melting}}$. The decay of the amplitude of density fluctuations in liquid aluminium, lead, and rubidium demonstrates a remarkable agreement and points to a universal thermal crossover in the dynamics of liquid metals.

The relation between Shannon entropy and avoided crossings is investigated in dielectric microcavities. The Shannon entropy of the probability density for eigenfunctions in an open elliptic billiard as well as a closed quadrupole billiard increases as the center of the avoided crossing is approached. These results are opposite to those of atomic physics for electrons. It is found that the collective Lamb shift of the open quantum system and the symmetry breaking in the closed chaotic quantum system have equivalent effects on the Shannon entropy.

We explore traveling waves with oscillatory tails in a bistable piecewise linear reaction-diffusion system of the FitzHugh-Nagumo type with linear cross diffusion. These waves differ fundamentally from the standard simple fronts of the kink type. In contrast to kinks, the waves studied here have a complex shape profile with a front-back-front (a pulse-front) pattern. The characteristic feature of such pulse-front waves is a hybrid type of the speed diagram, which on the one hand reflects the typical dynamical behavior of the fronts in the FitzHugh-Nagumo model, related to the nonequilibrium Ising-Bloch bifurcation, and on the other hand exhibits also the solitary pulse scenario where several waves appear simultaneously with different speeds of propagation. We describe analytically the wave profiles and heteroclinic trajectories in the phase plane and discuss their morphology and transformation. The phenomena of wave formation and propagation are also studied by numerical simulations of the model partial differential equations. These simulations support the view that the pulse-front waves are constructed of fronts and pulses.

We analyze growth mechanisms of complex networks and focus on their validation by measurements. To this end we consider the equation $\mathrm{\Delta }K=A\left(t\right)(K+K_0)\mathrm{\Delta }t$, where $K$ is the node's degree, $\mathrm{\Delta }K$ is its increment, $A\left(t\right)$ is the aging constant, and $K_0$ is the initial attractivity. This equation has been commonly used to validate the preferential attachment mechanism. We show that this equation is undiscriminating and holds for the fitness model [Caldarelli et al., Phys. Rev. Lett. 89, 258702 (2002)] as well. In other words, accepted method of the validation of the microscopic mechanism of network growth does not discriminate between “rich-gets-richer” and “good-gets-richer” scenarios. This means that the growth mechanism of many natural complex networks can be based on the fitness model rather than on the preferential attachment, as it was believed so far. The fitness model yields the long-sought explanation for the initial attractivity $K_0$, an elusive parameter which was left unexplained within the framework of the preferential attachment model. We show that the initial attractivity is determined by the width of the fitness distribution. We also present the network growth model based on recursive search with memory and show that this model contains both the preferential attachment and the fitness models as extreme cases.

Using resonant x-ray scattering techniques, transitional subphases during the electric-field-induced phase transition of a mixture of Se-containing chiral liquid crystals, 80% AS657 and 20% AS620, in a planar-aligned cell geometry were investigated, where the prototypical phase sequence $\mathrm{Sm}{C}_A^{*}-\mathrm{Sm}{C}_{\gamma }^{*}-\mathrm{AF}-\mathrm{Sm}{C}^{*}$ was observed; the transitional subphases were formed during the transition from the three-layer periodicity phase to the ferroelectric phase. In the lower-temperature range where the three-layer $\mathrm{Sm}C{\gamma }^{*}$ phase appeared under the low electric field, nine- and six-layer subphases and a “streak” pattern appeared in sequence after the transition from the $\mathrm{Sm}C{\gamma }^{*}$ phase with increasing applied electric field; the ferroelectric phase was realized. In the higher-temperature range where the four-layer AF phase appeared under a low electric field, the AF phase changed to a three-layer phase at the medium electric field. The twelve-, nine-, and six-layer subphases subsequently appeared in sequence, and finally the ferroelectric phase was generated with increasing electric field. The molecular arrangements of the field-induced subphases, especially the newly found nine-layer periodicity phase, was analyzed. The successive field-induced phase transition of the present results was compared with that of our previous results for pure Se-containing and Br-containing liquid crystals, and the relation to the three-layer ferrielectric phase was discussed.