The turbulent hydromagnetic dynamo is a process of magnetic field amplification by a chaotic flow of an electrically conducting fluid, responsible for generation of the magnetic fields of planets and stars. Here we demonstrate a curious effect of the Lorentz force, which can act to intensify the magnetic fields, counterintuitively in light of the Lenz law according to which the Lorentz force acts to retard motions and saturate the dynamo-induced magnetic field. However, the net effect of its small-scale fluctuations in a turbulent flow is far from obvious and it is shown that it can lead to amplification rather than saturation of the magnetic energy through creation of negative turbulent diffusivity.

Low-frequency Raman spectroscopy was used to study the dynamic response on a nanometer scale of aqueous suspensions of two-component lipid vesicles. Binary mixtures of saturated phospholipid (1,2-dipalmitoyl-sn-glycero-3-phosphocholine, DPPC) and cholesterol are interesting for possible coexistence of solidlike and liquid-ordered phases, while the phase coexistence was not reported for unsaturated phospholipid (1,2-dioleoyl-sn-glycero-3-phosphocholine, DOPC) and cholesterol mixtures. The DOPC-DPPC mixtures represent the well-documented case of coexisting domains of solidlike and liquid-disordered phases. These three series of lipid mixtures are studied here. A broad peak with the maximum in the range of $30–50\mathrm{c}{\mathrm{m}}^{–1}$ and a narrow peak near $10\mathrm{c}{\mathrm{m}}^{–1}$ are observed in the Raman susceptibility of the binary mixtures and attributed to the acousticlike vibrational density of states and layer modes, respectively. Parameters of the broad and narrow peaks are sensitive to lateral and conformational hydrocarbon chain ordering. It was also demonstrated that the low-frequency Raman susceptibility of multicomponent lipid bilayers allows one to determine the phase state of lipid bilayers and distinguish the homogeneous distribution of molecular complexes from coexisting domains with sizes above several nanometers. Thus, the low-frequency Raman spectroscopy provides unique information in studying phase coexistence in lipid bilayers.

Vital for a variety of industries, colloids also serve as an excellent model to probe phase transitions at the individual particle level. Despite extensive studies, origins of the glass transition in hard-sphere colloids discovered about 30 y ago remain elusive. Results of our numerical simulations and asymptotic analysis suggest that cessation of long-time particle diffusivity does not suppress crystallization of a metastable liquid-phase hard-sphere colloid. Once a crystallite forms, its growth is then controlled by the particle diffusion in the depletion zone surrounding the crystallite. Using simulations, we evaluate the solid-liquid interface mobility from data on colloidal crystallization in terrestrial and microgravity experiments and demonstrate that there is no drastic difference between the respective mobility values. The insight into the effect of vanishing particle mobility and particle sedimentation on crystallization of colloids will help engineer colloidal materials with controllable structure.

The response, pathways, and memory effects of cyclically driven complex media can be captured by hysteretic elements called hysterons. Here we demonstrate the profound impact of hysteron interactions on pathways and memory. Specifically, while the Preisach model of independent hysterons features a restricted class of pathways which always satisfy return point memory, we show that three interacting hysterons generate more than 15 000 transition graphs, with most violating return point memory and having features completely distinct from the Preisach model. Exploring these opens a route to designer pathways and information processing in complex matter.

A theoretical derivation of slip boundary conditions for single-species gas and binary gas mixture based on two typical gas-surface scattering kernels is presented. If the Maxwell model is assumed, then the derived slip boundary conditions are consistent with the previous conclusions. Considering the limitation of the Maxwell model in describing the complexity of gas-surface scattering behavior, we further perform theoretical analyses based on the Cercignani-Lampis-Lord (CLL) model, where separate accommodation coefficients in the tangential and normal directions are defined. Our results demonstrate that for both single-species gas and binary gas mixture, the velocity slip predicted by the CLL model is only dependent on the tangential accommodation coefficient, while the temperature jump determined by the CLL model is related to the accommodation coefficients in both tangential and normal directions. To account for the collision effect in the Knudsen layer, we propose to add correction terms to the theoretical models, and the corrected slip coefficients agree well with the previous numerical results obtained by solving Boltzmann equation for single-species gas. Moreover, the slip boundary conditions for binary gas mixture based on the CLL model are determined theoretically for the first time. Since at most situations the tangential and normal accommodation coefficients are not equal, the temperature jump boundary condition based on the CLL model is expected to give more accurate predictions about temperature distribution and heat flux at the boundaries, particularly for hypersonic gas flows with strong nonequilibrium effect.

The nonlinear evolution of mixing layer in cylindrical Rayleigh-Taylor (RT) turbulence is studied theoretically and numerically. The scaling laws including the hyperbolic cosine growth for outward mixing layer and the cosine growth for inward mixing layer of the cylindrical RT turbulence are proposed for the first time and verified reliably by direct numerical simulation of the Navier-Stokes equations. It is identified that the scaling laws for the cylindrical RT turbulence transcend the classical power law for the planar RT turbulence and can be recovered to the quadratic growth as cylindrical geometry effect vanishes. Further, characteristic time- and length scales are reasonably obtained based on the scaling laws to reveal the self-similar evolution features for the cylindrical RT turbulence.

The structure of the sheath and the current exchange of two-dimensional electron-emitting objects with elliptic cross section immersed at rest in Maxwellian plasmas are investigated with an energy-conserving stationary Vlasov-Poisson solver free of statistical noise. The parameter domains for current collection within the orbital-motion-limited (OML) regime and current emission in space-charge-limited (SCL) conditions were studied by varying the characteristic dimension of the ellipse, its eccentricity, and the emission level. The analysis reveals the correlations between the onset of the non-OML and SCL regimes and the local curvature of the ellipse. As compared to nonemitting ellipses, electron emission broadens the parameter domain for OML current collection for ions and reduces considerably the current drop for non-OML conditions. Under identical plasma environments, elliptic bodies are more prone to operate under non-OML and SCL conditions than cylinders. Their emitted current in SCL conditions can be computed accurately from well-known results for cylinders if appropriate dimensionless variables and an equivalent radius are used. The role of the eccentricity, which acts as an integrability-breaking parameter, on the filamentation of the distribution function of the attracted species is studied.

A compressible Cahn-Hilliard fluid model is derived from the kinetic theory of dense gas mixtures. The fluid model involves a van der Waals and Cahn-Hilliard gradient energy, a generalized Korteweg's tensor, a generalized Dunn and Serrin heat flux, and Cahn-Hilliard–type diffusive fluxes. Starting from the BBGKY hierarchy for gas mixtures, a Chapman-Enskog method is used—with a proper scaling of the generalized Boltzmann equations—as well as higher-order Taylor expansions of pair distribution functions. A Euler and van der Waals model is obtained at zeroth order, while the Cahn-Hilliard fluid model is obtained at first order, involving viscous, heat, and diffusive fluxes. The Cahn-Hilliard extra terms are associated with intermolecular forces and pair interaction potentials.

Confined systems are usually treated as integer dimensional systems, like two dimensional (2D), 1D, and 0D, by considering extreme confinement conditions in one or more directions. This approach costs piecewise representations, some limitations in confinement interval, and the deviations from the true behaviors, especially when the confinement is neither strong nor weak. In this study, fractional integral representation (FIR) is proposed as a methodology to calculate the infinite summations in statistical thermodynamics for any dimension and confinement values. FIR directly incorporates the dimension as a control variable into calculation procedures and allows us to get solutions valid for the whole confinement and dimension scales, including the fractional ones. We define the dimension of a summation and used it in the proposed FIR to calculate the partition function. The first and the higher-order FIR are introduced and high accuracy results are achieved. FIR is then extended for a generalized function to calculate thermodynamic properties directly from their fundamental expressions based on infinite sums. By using the proposed FIR approach, the thermodynamic properties of a noninteracting Maxwell-Boltzmann gas confined in an elongated rectangular domain are determined. The excess quantities induced by confinement are examined for different confinement scenarios. FIR successfully predicts the true behavior of thermodynamic properties for the whole range of confinement and dimension scales. Defining and controlling the dimension allows designing new types of thermodynamic cycles. Besides the infinite-well potential for the confinement of particles with quadratic and linear dispersion relations, quadratic and quartic confining potentials are also considered to show the success of FIR. The proposed method not only incorporates the dimension into the calculation procedures but also constitutes an application of fractional calculus in statistical thermodynamics. FIR has many potential applications especially for Bose-Einstein condensation phenomenon which inherently contains dimensional transitions.

We study continuations of topological edge states in the Su-Schrieffer-Heeger model with on-site cubic (Kerr) nonlinearity, which is a 1D nonlinear photonic topological insulator (TI). Based on the topology of the underlying spatial dynamical system, we establish the existence of nonlinear edge states (edge solitons) for all positive energies in the topological band gap. We discover that these edge solitons are stable at any energy when the ratio between the weak and strong couplings is below a critical value. Above the critical coupling ratio, there are energy intervals where the edge solitons experience an oscillatory instability. Though our paper focuses on a photonic system, we also discuss the broader relevance of our methods and results to 1D nonlinear mechanical TIs.

Recently, it has been shown that the long coiled-coil membrane tether protein early endosome antigen 1 (EEA1) switches from a rigid to a flexible conformation upon binding of a signaling protein to its free end. This flexibility switch represents a motorlike activity, allowing EEA1 to generate a force that moves vesicles closer to the membrane they will fuse with. It was hypothesized that the binding-induced signal could propagate along the coiled coil and lead to conformational changes through the localized domains of the protein chain that deviate from a perfect coiled-coil structure. To elucidate, if upon binding of a single protein the corresponding mechanical signal could propagate through the whole 200-nm-long chain, we propose a simplified description of the coiled coil as a one-dimensional Frenkel-Kontorova chain. Using numerical simulations, we find that an initial perturbation of the chain can propagate along its whole length in the presence of thermal fluctuations. This may enable the change of the configuration of the entire molecule and thereby affect its stiffness. Our work sheds light on intramolecular communication and force generation in long coiled-coil proteins.

Several studies on brain signals suggested that bottom-up and top-down influences are exerted through distinct frequency bands among visual cortical areas. It was recently shown that theta and gamma rhythms subserve feedforward, whereas the feedback influence is dominated by the alpha-beta rhythm in primates. A few theoretical models for reproducing these effects have been proposed so far. Here we show that a simple but biophysically plausible two-network motif composed of spiking-neuron models and chemical synapses can exhibit feedforward and feedback influences through distinct frequency bands. Different from previous studies, this kind of model allows us to study directed influences not only at the population level, by using a proxy for the local field potential, but also at the cellular level, by using the neuronal spiking series.

The bioactivity of nanoparticles (NPs) crucially depends on their ability to cross biological membranes. A fundamental understanding of cell-NP interaction is hence essential to improve the performance of the NP-based biomedical applications. Although extensive studies of cellular uptake have converged upon the idea that the uptake process is mainly regulated by the elastic deformation of the cell membrane or NP, recent experimental observations indicate the ligand density as another critical factor in modulating NP uptake into cells. In this study, we propose a theoretical model of the wrapping of an elastic vesicle NP by a finite lipid membrane to depict the relevant energetic and morphological evolutions during the wrapping process driven by forming receptor-ligand bonds. In this model, the deformations of the membrane and the vesicle NP are assumed to follow the continuum Canham-Helfrich framework, whereas the change of configurational entropy of receptors is described from statistical thermodynamics. Results show that the ligand density strongly affects the binding energy and configurational entropy of free receptors, thereby altering the morphology of the vesicle-membrane system in the steady wrapping state. For the wrapping process by the finite lipid membrane, we also find that there exists optimal ligand density for the maximum wrapping degree. These predictions are consistent with relevant experimental observations reported in the literature. We have further observed that there are transitions of various wrapping phases (no wrapping, partial wrapping, and full wrapping) in terms of ligand density, membrane tension, and molecular binding energy. In particular, the ligand and receptor shortage regimes for the small and high ligand density are, respectively, identified. These results may provide guidelines for the rational design of nanocarriers for drug delivery.

In this paper we analytically derive the exact closed dynamical equations for a liquid with short-ranged interactions in large spatial dimensions using the same statistical mechanics tools employed to analyze Brownian motion. Our derivation greatly simplifies the original path-integral-based route to these equations and provides insight into the physical features associated with high-dimensional liquids and glass formation. Most importantly, our construction provides a route to the exact dynamical analysis of important related dynamical problems, as well as a means to devise cluster generalizations of the exact solution in infinite dimensions. This latter fact opens the door to the construction of increasingly accurate theories of vitrification in three-dimensional liquids.

We look at the wetting of a pure fluid in contact with a charged flat surface. In the bulk, the fluid is a classical van der Waals fluid containing dissociated ions. The presence of wall and ions leads to strong dielectrophoretic and electrophoretic forces that increase the fluid's density at the wall. We calculate the fluid's profiles analytically and numerically and obtain the energy integrals. The critical surface potential for prewetting is obtained. In the phase diagrams, the line of first-order transition meets a second-order transition line at a critical point whose temperature can be higher or lower than the bulk critical temperature. The results are relevant to droplet nucleation around charged particles in the atmosphere and could possibly explain deviations from expected nucleation rates.

Resonances with electromagnetic whistler-mode waves are the primary driver for the formation and dynamics of energetic electron fluxes in various space plasma systems, including shock waves and planetary radiation belts. The basic and most elaborated theoretical framework for the description of the integral effect of multiple resonant interactions is the quasilinear theory, which operates through electron diffusion in velocity space. The quasilinear diffusion rate scales linearly with the wave intensity, $D_{\mathrm{QL}}\sim B_w^2$, which should be small enough to satisfy the applicability criteria of this theory. Spacecraft measurements, however, often detect whistle-mode waves sufficiently intense to resonate with electrons nonlinearly. Such nonlinear resonant interactions imply effects of phase trapping and phase bunching, which may quickly change the electron fluxes in a nondiffusive manner. Both regimes of electron resonant interactions (diffusive and nonlinear) are well studied, but there is no theory quantifying the transition between these two regimes. In this paper we describe the integral effect of nonlinear electron interactions with whistler-mode waves in terms of the timescale of electron distribution relaxation, $\sim 1/D_{\mathrm{NL}}$. We determine the scaling of $D_{\mathrm{NL}}$ with wave intensity $B_w^2$ and other main wave characteristics, such as wave-packet size. The comparison of $D_{\mathrm{QL}}$ and $D_{\mathrm{NL}}$ provides the range of wave intensity and wave-packet sizes where the electron distribution evolves at the same rates for the diffusive and nonlinear resonant regimes. The obtained results are discussed in the context of energetic electron dynamics in the Earth's radiation belt.

The thermodynamic uncertainty relation (TUR) provides a stricter bound for entropy production (EP) than that of the thermodynamic second law. This stricter bound can be utilized to infer the EP and derive other tradeoff relations. Though the validity of the TUR has been verified in various stochastic systems, its application to general Langevin dynamics has not been successfully unified, especially for underdamped Langevin dynamics, where odd parity variables in time-reversal operation such as velocity get involved. Previous TURs for underdamped Langevin dynamics are neither experimentally accessible nor reduced to the original form of the overdamped Langevin dynamics in the zero-mass limit. Here, we find a TUR for underdamped Langevin dynamics with an arbitrary time-dependent protocol, which is operationally accessible when all mechanical forces are controllable. We show that the original TUR is a consequence of our underdamped TUR in the zero-mass limit. This indicates that the TUR formulation presented here can be regarded as the universal form of the TUR for general Langevin dynamics.

We report quantitative imaging experiments describing the three-dimensional (3D) bursting cascade of droplets from a liquid melt reacting with the oxygen of air which explode sequentially to produce ever smaller fragments. The 3D space-time resolved trajectories of the fragmenting drops reveal an arborescent structure of branchings defining the cascade steps, each random in direction and shortening along the cascade, in a way we determine. The phenomenon is a unique and prototypical illustration of the so-called Richardson regime, namely, an accelerated cascade towards smaller scales. The phenomenon, which coincides with the early time dispersion period of a Brownian motion, featuring here ever shrinking steps, is well captured by a Langevin dynamics.

We perform a detailed study of heat transport in one-dimensional long-ranged anharmonic oscillator systems, such as the long-ranged Fermi-Pasta-Ulam-Tsingou model. For these systems, the long-ranged anharmonic potential decays with distance as a power law, controlled by an exponent $\delta \ge 0$. For such a nonintegrable model, one of the recent results that has captured quite some attention is the puzzling ballisticlike transport observed for $\delta =2$, reminiscent of integrable systems. Here, we first employ the reverse nonequilibrium molecular dynamics simulations to look closely at the $\delta =2$ transport in three long-ranged models and point out a few problematic issues with this simulation method. Next, we examine the process of energy relaxation, and find that relaxation can be appreciably slow for $\delta =2$ in some situations. We invoke the concept of nonlinear localized modes of excitation, also known as discrete breathers, and demonstrate that the slow relaxation and the ballisticlike transport properties can be consistently explained in terms of a novel depinning of the discrete breathers that makes them highly mobile at $\delta =2$. Finally, in the presence of quartic pinning potentials we find that the long-ranged model exhibits Fourier (diffusive) transport at $\delta =2$, as one would expect from short-ranged interacting systems with broken momentum conservation. Such a diffusive regime is not observed for harmonic pinning.

Novel technologies are revealing that chromosomes have a complex three-dimensional organization within the cell nucleus that serves functional purposes. Models from polymer physics have been developed to quantitively understand the molecular principles controlling their structure and folding mechanisms. Here, by using massive molecular-dynamics simulations we show that classical scaling laws combined with finite-size effects of a simple polymer model can effectively explain the scaling behavior that chromatin exhibits at the topologically associating domains level, as revealed by experimental observations. Model results are then validated against recently published high-resolution in situ Hi-C data.