We consider the influence of tetrahedral (octupolar) order on ferromagnetic nematic liquid-crystalline phases. The presence of tetrahedral order leads to broken parity symmetry in an achiral liquid-crystalline system, in addition to broken time-reversal symmetry associated with the existence of a spontaneous magnetization. As a consequence, we find static as well as reversible and irreversible dynamic cross-coupling terms absent in usual ferromagnetic nematics. Several static and dynamic experiments are suggested to detect possible tetrahedral order. We predict that linear gradient terms in the generalized energy involving the ferromagnetic magnetization and the nematic director field lead to chiral domains of ambidextrous helicity. As a characteristic dissipative dynamic cross coupling we point out that the rotation of the magnetization can be driven by temperature and/or concentration gradients. Conversely, heat and concentration currents can be generated by rotations of the magnetization. As a characteristic example for reversible cross-coupling terms we analyze the consequences of the coupling between the molecular field of the nematic director and temperature and concentration gradients.

In this study we give an analytical model for the Young-Laplace equation of two-dimensional (2D) drops under gravity. Inspired by the pioneering work of Landau and Lifshitz [Fluid Mechanics, 2nd ed. (Pergamon Press, Oxford, 1987), pp. 242–243], we derive general analytical expressions of the profile of drops on flat surfaces, which is available for arbitrary contact angles and drop volumes. We then extend the theoretical model to drops on inclined surfaces and reveal that the contact line plays an important role in determining the wetting state of the drops: (1) when the contact line is completely pinning, the rear and front contact angles and the shape of the drop can be uniquely determined by the drop volume, the slope of the inclined surface, and the contact area; (2) when the contact angle hysteresis is taken into consideration, various mathematical solutions of the wetting state exist for a drop of given volume on a given surface, but there is only one wetting state corresponding to a minimum free energy which results from the competition between the capillary force and gravity. Our theory is in excellent agreement with numerical and experimental results.

To better understand the surprising low-frequency vibrational modes in structural glasses, where the density of states $D\left(\omega \right)$ deviates from mean field predictions, we study the spectra of a large ensemble of sparse random matrices where disorder is controlled by the distribution of bond weights and network coordination. We find $D\left(\omega \right)$ has three regimes: a very low-frequency regime that can be predicted analytically using extremal statistics, an intermediate regime with quasilocalized modes, and a plateau in $D\left(\omega \right)$. When there is a finite probability of bond weights approaching zero strength, the intermediate regime displays a scaling consistent with $D\left(\omega \right)\sim {\omega }^4$, independent of network coordination and system size, just as in simulated structural glasses.

Two-dimensional nuclear magnetic resonance measurements are ubiquitous in the literature, with correlations of longitudinal $T_1$ and transverse $T_2$ relaxation times used extensively to characterize porous media. Decomposition of the signal acquired in the time domain to a pseudocontinuous distribution of relaxation times is achieved using numerical inversion. A popular technique to generate a stable solution to this ill-posed problem in the presence of noise is Tikhonov regularization with a non-negativity constraint imposed on the output. However, coupling of the longitudinal and transverse eigenfunctions can generate eigenvalue pairs with apparent $T_2>T_1$ and negative amplitude. Such apparent signal components are encountered in the classic example of Brownstein-Tarr “slow” diffusion in an isolated pore, and in weakly coupled pores governed by different relaxation rates. We show that when negative-amplitude components comprise $\ge 1\%$ of the total signal, the solution achieved by non-negative Tikhonov regularization is sufficiently distorted to prevent robust interpretation. We demonstrate two alternative inversion methods that recover the negative-amplitude components: (1) half-bound Tikhonov regularization assigns a negative amplitude to any peak with apparent $T_2>T_1$, and (2) the optimization problem is expressed as a ${\ell }_2$ regression with ${\ell }_1$ penalization and a solution estimated using a primal-dual algorithm without constraint on the output sign. These methods are applicable to $T_1-T_2$ experiments on porous materials characterized by a hierarchy of length scales, such as biological cells, cement, and limestone.

We study the hydrodynamic behavior of three-dimensional (3D) incompressible collections of self-propelled entities in contact with a momentum sink in a state with nonzero average velocity, hereafter called 3D easy-plane incompressible polar active fluids. We show that the hydrodynamic model for this system belongs to the same universality class as that of an equilibrium system, namely, a special 3D anisotropic magnet. The latter can be further mapped onto yet another equilibrium system, a DNA-lipid mixture in the sliding columnar phase. Through these connections we find a divergent renormalization of the damping coefficients in 3D easy-plane incompressible polar active fluids, and obtain their equal-time velocity correlation functions.

Renewal processes with heavy-tailed power law distributed sojourn times are commonly encountered in physical modeling and so typical fluctuations of observables of interest have been investigated in detail. To describe rare events, the rate function approach from large deviation theory does not hold and new tools must be considered. Here, we investigate the large deviations of the number of renewals, the forward and backward recurrence times, the occupation time, and the time interval straddling the observation time. We show how non-normalized densities describe these rare fluctuations and how moments of certain observables are obtained from these limiting laws. Numerical simulations illustrate our results, showing the deviations from arcsine, Dynkin, Darling-Kac, Lévy, and Lamperti laws.

We study dissipative Langevin dynamics in the path integral formulation using the Martin-Siggia-Rose formalism. The effective action is supersymmetric and we identify the supercharges. In addition we study the transformations generated by superderivatives, which were recently included in the cohomological structure emerging in the dissipative systems. We find that these transformations do not generate Ward identities, which are explicitly broken; however, they lead to universal sum-rule-type identities, which we derive from Schwinger-Dyson equations. We confirm that the above identities hold in an explicit example of the Ornstein-Uhlenbeck process.

We consider a mathematical model of spontaneous mechanical oscillations of hair bundles in bullfrog saccular hair cells. This two-dimensional model describes dynamics of the positions of the bundle tip and molecular motors. The main control parameters of this model are the calcium feedback strength and the maximal force of molecular motors. The dynamics of hair bundles is subject to the random disturbances. We study noise-induced oscillations in the parametric zone where the equilibria are the only attractors of the system. We analyze the probabilistic mechanism of the generation of mixed-mode stochastic oscillations with the help of the stochastic sensitivity functions and confidence domains. The constructive abilities of this mathematical technique in the analysis of the stochastic effects in the hair bundle model are demonstrated.

The influence of lubricated contacts on the stick-slip behavior of a granular system is investigated. Samples of cylindrical shape made of glass spheres confined at a constant pressure and subjected to gradual deformation along their main axis are considered. Under constant axial deformation, the granular compact exhibits a regular stick-slip regime, in which gradual stress loading (stick) is followed by rapid relaxation events or failure (slip). The amplitude of stress drops (slips) and their recurrence time are investigated as a function of the amount of lubricant fluid. In the absence of lubricant, stress drops are very frequent but their amplitude is relatively small. However, the addition of a minute volume of lubricant into the granular packing, increases both the amplitude of stress drops and their recurrence time, following a saturating exponential loading curve with the lubricant volume. We show that the typical volume at which saturation occurs corresponds to the amount of fluid required to completely cover the surface of the spheres, with the thickness of the coat corresponding to the size of the asperities. These results support the idea that, to a certain extent, adding lubricant reduces sliding friction, as well as synchronously mobilizes a set of contacts.

In this paper we employ renormalized viscosity and thermal diffusivity to construct a subgrid-scale model for large eddy simulation (LES) of turbulent thermal convection. For LES, we add ${\nu }_{\mathrm{ren}}\propto {\mathrm{\Pi }}_u^{1/3}{(\pi /\mathrm{\Delta })}^{-4/3}$ to the kinematic viscosity; here ${\mathrm{\Pi }}_u$ is the turbulent kinetic energy flux, and $\mathrm{\Delta }$ is the grid spacing. We take subgrid thermal diffusivity to be same as the subgrid kinematic viscosity. We performed LES of turbulent thermal convection on a ${128}^3$ grid and compare the results with those obtained from direct numerical simulation (DNS) on a ${512}^3$ grid. We started the DNS with random initial condition and forked a LES simulation using the large wave number modes of DNS initial condition. Though the Nusselt number is overestimated in LES as compared to that in DNS, there is a good agreement between the LES and DNS results on the evolution of kinetic energy and entropy, spectra and fluxes of velocity and temperature fields, and the isosurfaces of temperature.

Magnetic reconnection is a fundamental process occurring in many plasma systems. Magnetic field lines break and reconfigure into a lower energy state, converting released magnetic field energy into plasma kinetic energy. Around some of the universe's most energetic objects, such as $\gamma$-ray burst or active galactic nuclei, where the magnetic field energy exceeds the plasma rest mass energy, the most extreme magnetic reconnection in the relativistic regime is theorized. The presented experiments and three-dimensional particle-in-cell modeling recreate in the laboratory the scaled plasma conditions necessary to access the relativistic electron regime and therefore approach conditions around these distant, inaccessible objects. High-power, ultrashort laser pulses focused to high intensity ($I>2.5\times {10}^{18}{\mathrm{Wcm}}^{-2}$) on solid targets produces relativistic temperature electrons within the focal volume. The hot electrons are largely confined to the target surface and form a radial surface current that generates a huge, expanding azimuthal magnetic field. Focusing two laser pulses in close proximity on the target surface leads to oppositely directed magnetic fields being driven together. The fast electron motion due to the magnetic reconnection is inferred using an experimental x-ray imaging technique. The x-ray images enable the measurement of the reconnection layer dimensions and temporal duration. The reconnection rates implied from the aspect ratio of the reconnection layer, $\delta /L\approx 0.3$, was found to be consistent over a range of experimental pulse durations ($40\mathrm{fs}$–$20\mathrm{ps}$) and agreed with the modeling. Further experimental evidence for magnetic reconnection is the formation of a nonthermal electron population shown by the modeling to be accelerated in the reconnection layer.

The relation between the work performed to a system and the change of its free energy during a certain process is important in nonequilibrium statistical mechanics. In particular, the work relation with measurement and feedback control has attracted much attention, because it resolved the paradox concerning Maxwell's demon. Most studies, however, assume that their target systems are isolated or isothermal. In this paper, by considering a nonisothermal system, we generalize the Sagawa-Ueda-Jarzynski relation, which involves measurement and feedback control, and apply it to a realistic model. Furthermore, when the temperature profile is quadratic, we see that the system is governed by Tsallis statistical mechanics. In addition, we show that our formulation provides the generalized version of the second law of information thermodynamics and a set of work relations for isothermal systems.

In most existing pedestrian dynamic models, agents are modeled as sliding or jumping objects. As a kind of bipedal creature, however, this assumption makes it difficult to include some important human walking characteristics in the models, such as the periodicity of stepping, the adjustment of step frequency and step length, and the change of personal space within the same step cycle. To take these characteristics into consideration, a “biped model” is developed to simulate pedestrian locomotion by physical step rather than by time step. The model consists of two components: the stepping simulator and the adjustment of velocity for each step. Simulation results show that the velocity-density relations are consistent with the empirical data. Stable stop-and -go waves are simulated with a critical density. Furthermore, with the considering of biped movement, the lock-step phenomenon is reproduced. The model provides new possibilities to study crowd behavior while considering personal bipedal mechanics.

DNA buckling is the fundamental step for plectoneme nucleation and supercoil dynamics that are critical in the processing of genetic information. Here we systematically quantify DNA buckling dynamics using high-speed magnetic tweezers. Buckling times are $\sim 10–100\mathrm{ms}$ and depend exponentially on both applied force and twist. By deconvolving measured time traces with the instrument response, we reconstruct full two-dimensional extension-twist energy landscapes of the buckling transition that reveal an asymmetry between the pre- and postbuckling states and suggest a highly bent transition state conformation.

The eigenfrequencies of natural eigenmodes of cortical activity are calculated from corticothalamic neural field theory. These correspond to poles of a transcendental transfer function, which is accurately approximated here as a rational function. In this approximation, the least damped frequencies of the lowest order spatial eigenmodes dominate the dynamics and correspond to slow-wave ($\lesssim 1$ Hz) and alpha ($\sim 10$ Hz) resonances. The eigenmodes exhibit standing and rotating wave patterns in which eigenmode beating can give the appearance of sudden changes in dynamics. This provides a physical explanation of sudden transitions that have been argued to occur between artificially discretized brain activity patterns, sometimes termed microstates, and allows the dynamics to be analyzed by replacing these phenomenologically constructed activity patterns with well-defined eigenmodes. An eigenmode interpretation of large-scale brain activity can thus potentially supplant phenomenological approaches and place analysis on a systematic physical footing.

In this paper, the theory for acoustic radiation force exerted by standing surface acoustic waves (SSAWs) is extended to a compressible sphere in inviscid fluids. The conventional theory, developed in plane standing waves, fails to predict the radiation force incident on particles in the SSAW. Our extended formulas reveal that, in the direction normal to the piezoelectric substrate, the acoustic radiation force cannot only push the sphere away, but also pull it back towards the substrate. In the direction parallel to the substrate, both the magnitude of the radiation force and the equilibrium positions for particles can be actively tuned by changing the Rayleigh angle. This is exceedingly meaningful for particle positioning by tilted angle SSAWs and SSAWs. Furthermore, the Rayleigh angle can also be used to actively regulate the resonance point and peak for bubbles acted on by SSAWs. The extended theory can thus be used in the design of SSAWs for manipulating particles and bubbles.

Although turbulence has been conjectured to be important for magnetic reconnection, still very little is known about its role in collisionless plasmas. Previous attempts to quantify the effect of turbulence on reconnection usually prescribed Alfvénic or other low-frequency fluctuations or investigated collisionless kinetic effects in just two-dimensional configurations and antiparallel magnetic fields. In view of this, we analyzed the kinetic turbulence self-generated by three-dimensional guide-field reconnection through force-free current sheets in frequency and wave-number spaces, utilizing 3D particle-in cell code numerical simulations. Our investigations reveal reconnection rates and kinetic turbulence with features similar to those obtained by current in situ spacecraft observations of MMS as well as in the laboratory reconnection experiments MRX, VTF, and VINETA-II. In particular, we found that the kinetic turbulence developing in the course of 3D guide-field reconnection exhibits a broadband power-law spectrum extending beyond the lower-hybrid frequency and up to the electron frequencies. In the frequency space the spectral index of the turbulence appeared to be close to $-2.8$ at the reconnection $X$ line. In the wave-number space it also becomes $-2.8$ as soon as the normalized reconnection rate reaches 0.1. The broadband kinetic turbulence is mainly due to current-streaming and electron-flow-shear instabilities excited in the sufficiently thin current sheets of kinetic reconnection. The growth of the kinetic turbulence corresponds to high reconnection rates which exceed those of fast laminar, nonturbulent reconnection.

The injection of electrons into a laser wakefield accelerator (LWFA) is observed to generate an intense coherent ultra-broadband and ultrashort pulse radiation flash, consistent with the acceleration of electrons from rest to nearly the speed of light in a distance $<\sim 1\mu \mathrm{m}$. Under certain conditions, the radiation occurs at harmonics of the local plasma frequency. The flash is sufficiently bright to induce large nonlinear refractive index shifts in optical materials; we estimate a source brightness temperature of $\sim {10}^{18}\mathrm{K}$. We present measurements of the flash spectra, coherence, pulse duration, polarization, and angular distribution, providing a detailed picture of electron injection dynamics in LWFA. These are characteristic of laser-assisted injection of off-axis electrons, which preserves wake coherence.

We study various properties of the vibrational normal modes for Coulomb-interacting particles in two-dimensional irregular confinement using numerical simulations. By analyzing the participation ratio and spectral statistics, we characterize the vibrational modes for Coulomb clusters as localized, quasilocalized, and delocalized. We also study a correlation function to understand the spatial structure of these different kinds of modes and subsequently extract the associated characteristic length scales. We further demonstrate that, at any given temperature, particles exhibiting larger displacement over a time interval comparable to the structural relaxation time are strongly correlated with the low-frequency quasilocalized modes of the inherent structure corresponding to the initial configuration. Establishing this correlation for Coulomb clusters paves the path to identify the particular feature of the initial configuration that determines the previously observed heterogeneous dynamics of the particles at low temperatures in these systems.

We demonstrate the phenomenon of cumulative inertia in intracellular transport involving multiple motor proteins in human epithelial cells by measuring the empirical survival probability of cargoes on the microtubule and their detachment rates. We found the longer a cargo moves along a microtubule, the less likely it detaches from it. As a result, the movement of cargoes is non-Markovian and involves a memory. We observe memory effects on the scale of up to 2 s. We provide a theoretical link between the measured detachment rate and the superdiffusive Lévy-walk-like cargo movement.