Geometrical cues play an essential role in neuronal growth. Here, we quantify axonal growth on surfaces with controlled geometries and report a general stochastic approach that quantitatively describes the motion of growth cones. We show that axons display a strong directional alignment on micropatterned surfaces when the periodicity of the patterns matches the dimension of the growth cone. The growth cone dynamics on surfaces with uniform geometry is described by a linear Langevin equation with both deterministic and stochastic contributions. In contrast, axonal growth on surfaces with periodic patterns is characterized by a system of two generalized Langevin equations with both linear and quadratic velocity dependence and stochastic noise. We combine experimental data with theoretical analysis to measure the key parameters of the growth cone motion: angular distributions, correlation functions, diffusion coefficients, characteristics speeds, and damping coefficients. We demonstrate that axonal dynamics displays a crossover from an Ornstein-Uhlenbeck process to a nonlinear stochastic regime when the geometrical periodicity of the pattern approaches the linear dimension of the growth cone. Growth alignment is determined by surface geometry, which is fully quantified by the deterministic part of the Langevin equation. These results provide insight into the role of curvature sensing proteins and their interactions with geometrical cues.

The conformational collapse of polymers in mixtures of two individually good solvents is an intriguing yet puzzling phenomenon termed cononsolvency. In this paper, the concept of the preferential adsorption of the cosolvent is combined with mean-field approaches to elaborate the cononsolvency effect of dimethylformamide (DMF) on the thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) microgels in aqueous solutions. We give a quantitative description concerning the effects of DMF preferential adsorption and partitioning on the reentrant transition of PNIPAM microgels below the lower critical solution temperature (LCST) of PNIPAM. While the DMF cononsolvency incurs the conformational collapse, the affinity of DMF molecules to PNIPAM chains becomes increasingly stronger, which reveals that the conformational collapse is decoupled from the solvent quality of DMF-water mixtures. Considering the chain elasticity, spatial constraints, and surface charge of microgels, we explore the cononsolvency effect on the persistence length quantifying the PNIPAM flexibility. Our analysis elucidates that, depending on chain length and temperature, the DMF cononsolvency-induced collapse of PNIPAM microgels leads to a remarkable increase in the persistent length below LCST, which is comparable to the experimental data regarding suspension mechanical properties of PNIPAM microgels in water above LCST.

Flow and director fields strongly couple with each other in liquid crystalline systems, and herein we discuss the coupling effect in cylindrical and spherical-cap droplets formed by nematic liquid crystal. Applying a temperature gradient to droplets dispersed in a liquid solvent, we observed a crosslike texture in the droplets moved toward the high-temperature side, indicating that the director field was deformed from equilibrium. Additionally, measurement of the flow field revealed that a convective flow was induced in the droplets under temperature gradient. These results suggested that the director deformation in the droplet was induced by convection. By designing a simplified model based on this, we theoretically analyzed the above phenomenon based on Onsager's variational principle. The results show that the phenomenon was well described by a balance of surface energy gradient with viscous and elastic forces.

We present a high accuracy Monte Carlo simulation study of the uniaxial nematic ($N_U$) to isotropic ($I$) phase transition of a lattice dispersion model of uniaxial nematics composed of biaxial molecules. The $N_U\text{−}I$ coexistence curve terminating at the Landau critical point has been determined using the multiple histogram reweighting technique. A close investigation reveals a sharp departure in the nature of the $N_U\text{−}I$ coexistence curve in the temperature-biaxiality parameter phase diagram in comparison to the earlier theoretical (either mean-field or computer simulation) predictions. The coexistence curve shows a change in curvature with increasing value of the degree of molecular biaxiality.

Large-scale coherent structures emerging in two-dimensional flows can be predicted from statistical physics inspired methods consisting in minimizing the global enstrophy while conserving the total energy and circulation in the Euler equations. In many situations, solid obstacles inside the domain may also constrain the flow and have to be accounted for via a minimum enstrophy principle. In this work, we detail this extended variational formulation and its numerical resolution. It is shown from applications to complex geometries containing multiple circular obstacles that the number of solutions is enhanced, allowing many possibilities of bifurcations for the large-scale structures. These phase change phenomena can explain the downstream recombinations of the flow in rod-bundle experiments and simulations.

A shear flow of liquid metal (Galinstan) is driven in an annular channel by counter-rotating traveling magnetic fields imposed at the end caps. When the traveling velocities are large, the flow is turbulent and its azimuthal component displays random reversals. Power spectra of the velocity field exhibit a $1/f^{\alpha }$ power law on several decades and are related to power-law probability distributions $P\left(\tau \right)\sim {\tau }^{-\beta }$ of the waiting times between successive reversals. This $1/f$ type spectrum is observed only when the Reynolds number is large enough. In addition, the exponents $\alpha$ and $\beta$ are controlled by the symmetry of the system; a continuous transition between two different types of Flicker noise is observed as the equatorial symmetry of the flow is broken, in agreement with theoretical predictions.

The dynamics of a nonspherical droplet falling in air is investigated via three-dimensional numerical simulations of the Navier-Stokes and continuity equations. The main focus of this work is to study the effects of the relative influence of surface tension force over the inertial force and the orientation of the droplet. The values of the dimensionless parameters considered in this study are similar to those of a typical falling raindrop. Our results obtained from the numerical simulations for low values of Galilei number agree well with the theoretical predictions in the microgravity condition and in the limit of creeping flow. However, in the inertia-dominated region and for high initial aspect ratio, the droplet undergoes predominant nonlinear oscillations and subsequently breaks up. To the best of our knowledge, none of the previous studies have investigated dynamics of a tilted drop and observed the behavior reported in the present study.

Although the Navier-Stokes equation (NSE) is derived under angular-momentum conservation (AMC), numerical simulation methods often lack it. Here we reveal that AMC violations result from implementation of the degenerated viscous terms of NSE. To maintain AMC, these degenerated terms must be separately integrated in accordance with their stress origins. As observed in particle-based hydrodynamics methods, the violation causes artificial rotations in multicomponent fluids with different viscosities. At the interface between two fluids or with a mobile solid object, AMC must be satisfied, whereas AMC can be neglected in bulk fluids. We also clarify that the condition for constant fluid rotation as a rigid body in a container rotating at a constant speed is not the AMC of the stresses, but the invariance of the viscous forces under a global rotation. To confirm our theory, we simulated the circular laminar flows of single- and binary-component fluids using two-dimensional Lagrangian finite-volume methods. The results show excellent agreement with the analytical predictions for fluids with and without AMC.

Liquid impact on a rigid wall is a common feature in the context of marine structures, as most of them are exposed continuously to breaking waves. In the present paper, a comparison and analysis of the impact load estimates obtained from free surface lattice Boltzmann (LB) simulation with the experimental measurements from available literature have been reported. Initially, two-dimensional simulation of the dam break impact on the wall is performed with two different LB models: BGK-F1: a Bhatnagar-Gross-Krook (BGK) collision operator with the force scheme of Buick and Greated [Phys. Rev. E 61, 5307 (2000)], and MRT-F2: a multiple relaxation time (MRT) operator with the force scheme of Guo et al. [Phys. Rev. E 65, 046308 (2002)]. The pressure estimates obtained from BGK-F1 over MRT-F2 are closer to the measurements, though the other key parameters, such as the waterfront evolution and the free surface profile, have not shown significant variations. Furthermore, the three-dimensional dam break simulation has been performed using BGK-F1 for three test cases: (i) impact on a wall, (ii) impact on a rectangular obstacle, and (iii) impact on a tall tower. In all the test cases, the load estimates are in agreement with the experimental measurements.

The statistical mechanics of a cloud of particles interacting via their gravitational potentials encounters some issues when the Boltzmann-Gibbs statistics is applied. In this work, we consider the alternative statistical framework of Tsallis and analyze the statistical and thermodynamical implications for a self-gravitating gas, obtaining analytical and convergent expressions for the equation of state and specific heat in the ensembles of constant temperature and constant energy. Although our results are comparable in both ensembles, it turns out that only in the ensemble of constant temperature do the thermodynamic quantities depend explicitly on the Tsallis parameter, indicating that the question of ensemble equivalence for Tsallis statistics must be further reviewed.

We investigate a thermally isolated quantum many-body system with an external control represented by a step protocol of a parameter. The propagator at each step of the parameter change is described by thermodynamic quantities under some assumptions. For the time evolution of such systems, we formulate a path integral over the trajectories in the thermodynamic state space. In particular, for quasistatic operations, we derive an effective action of the thermodynamic entropy and its canonically conjugate variable. Then, the symmetry for the uniform translation of the conjugate variable emerges in the path integral. This leads to the entropy as a Noether invariant in quantum mechanics.

We consider a finite-time Otto engine operating on a quantum harmonic oscillator and driven by shortcut-to-adiabaticity (STA) techniques to speed up its cycle. We study its efficiency and power when internal friction, time-averaged work, and work fluctuations are used as quantitative figures of merit, showing that time-averaged efficiency and power are useful cost functions for the characterization of the performance of the engine. We then use the minimum allowed time for validity of STA protocol relation to establish a physically relevant bound to the efficiency at maximum power of the STA-driven cycle.

The coexistence of coherent and incoherent domains, namely the appearance of chimera states, has been studied extensively in many contexts of science and technology since the past decade, though the previous studies are mostly built on the framework of one-dimensional and two-dimensional interaction topologies. Recently, the emergence of such fascinating phenomena has been studied in a three-dimensional (3D) grid formation while considering only the nonlocal interaction. Here we study the emergence and existence of chimera patterns in a three-dimensional network of coupled Stuart-Landau limit-cycle oscillators and Hindmarsh-Rose neuronal oscillators with local (nearest-neighbor) interaction topology. The emergence of different types of spatiotemporal chimera patterns is investigated by taking two distinct nonlinear interaction functions. We provide appropriate analytical explanations in the 3D grid of the network formation and the corresponding numerical justifications are given. We extend our analysis on the basis of the Ott-Antonsen reduction approach in the case of Stuart-Landau oscillators containing infinite numbers of oscillators. Particularly, in the Hindmarsh-Rose neuronal network the existence of nonstationary chimera states is characterized by an instantaneous strength of incoherence and an instantaneous local order parameter. Besides, the condition for achieving exact neuronal synchrony is obtained analytically through a linear stability analysis. The different types of collective dynamics together with chimera states are mapped over a wide range of various parameter spaces.

In population dynamics, mathematical models often contain too many parameters to be easily testable. A way to reliably estimate parameters for a broad range of systems would help us obtain clearer predictions from theory. In this paper, we examine how the allometric scaling of a number of biological quantities with animal mass may be useful to parameterize population dynamical models. Using this allometric scaling, we make predictions about the ratio of prey to predators in real ecosystems, and we attempt to estimate the length of animal population cycles as a function of mass. Our analytical and numerical results turn out to compare reasonably to data from a number of ecosystems. This paves the way for a wider usage of allometric scaling to simplify mathematical models in population dynamics and make testable predictions.

Active work measures how far the local self-forcing of active particles translates into real motion. Using population Monte Carlo methods, we investigate large deviations in the active work for repulsive active Brownian disks. Minimizing the active work generically results in dynamical arrest; in contrast, despite the lack of aligning interactions, trajectories of high active work correspond to a collectively moving, aligned state. We use heuristic and analytic arguments to explain the origin of dynamical phase transitions separating the arrested, typical, and aligned regimes.

Natural and artificial self-propelled systems must manage environmental interactions during movement. In complex environments, these interactions include active collisions, in which propulsive forces create persistent contacts with heterogeneities. Due to the driven and dissipative nature of these systems, such collisions are fundamentally different from those typically studied in classical physics. Here we experimentally and numerically study the effects of active collisions on a laterally undulating sensory-deprived robophysical model, whose dynamics are relevant to self-propelled systems across length scales and environments. Interactions with a single rigid post scatter the robot, and this deflection is dominated by head-post contact. These results motivate a model which reduces the snake to a circular particle with two key features: The collision dynamics are set by internal driving subject to the geometric constraints of the post, and the particle has an effective length equal to the wavelength of the snake. Interactions with a single row of evenly spaced posts (with interpost spacing $d$) produce distributions reminiscent of far-field diffraction patterns: As $d$ decreases, distinct secondary peaks emerge as large deflections become more likely. Surprisingly, we find that the presence of multiple posts does not change the nature of individual collisions; instead, multimodal scattering patterns arise from multiple posts altering the likelihood of individual collisions to occur. As $d$ decreases, collisions near the leading edges of the posts become more probable, and we find that these interactions are associated with larger deflections. Our results, which highlight the surprising dynamics that can occur during active collisions of self-propelled systems, can inform control principles for locomotors in complex terrain and facilitate design of task-capable active matter.

Fluid transport in porous materials is commonly studied in geological samples (soil, sediments, etc.) or idealized systems, but the fluid flow through compacted granular materials, consisting of substantially strained granules, remains relatively unexplored. As a step toward filling this gap, we study a model of liquid transport in packings of deformable elastic shells using finite-element and lattice-Boltzmann methods. We find that the fluid flow abruptly vanishes as the porosity of the material falls below a critical value, and the flow obstruction exhibits features of a percolation transition. We further show that the fluid flow can be captured by a simplified permeability model in which the complex porous material is replaced by a collection of disordered capillaries, which are distributed and shaped by the percolation transition. To that end, we numerically explore the divergence of hydraulic tortuosity ${\tau }_H$ and the decrease of a hydraulic radius $R_h$ as the percolation threshold is approached. We interpret our results in terms of scaling predictions derived from the percolation theory applied to random packings of spheres.

The interactions of bacteria with surfaces have important implications in numerous areas of research, such as bioenergy, biofilm, biofouling, and infection. Recently, several experimental studies have reported that the adhesion of bacteria can be reduced considerably by microscale wall features. To clarify the effect of wall configurations, we numerically investigated the behavior of swimming bacteria near a flat wall with a bump line. The results showed that the effects of bump configuration are significant; a detachment time larger than several seconds can be achieved in certain parameter sets. These results illustrate that the number density of bacteria near the wall may be reduced by appropriately controlling the parameter sets. When background shear flow was imposed, the near-wall bacterium mainly moved towards the vorticity axis. The detachment time of cells increased significantly by adjusting the bump line to have ${45}^{\circ }$ relative to the flow direction. The knowledge obtained in this study is fundamental for understanding the interactions between bacteria and surfaces according to more complex geometries, and is useful for reducing the adhesion of cells to walls.

A gyrokinetic linearized exact (not model) Landau collision operator is derived by transforming the symmetric and conservative Landau form. The formulation obtains the velocity-space flux density and preserves the operator's conservative form as the divergence of this flux density. The operator contains both test-particle and field-particle contributions, and finite Larmor radius effects are evaluated in either Bessel function series or gyrophase integrals. While equivalent to the gyrokinetic Fokker–Planck form with Rosenbluth potentials [B. Li and D. R. Ernst, Phys. Rev. Lett. 106, 195002 (2011)], the gyrokinetic conservative Landau form explicitly preserves the symmetry between test-particle and field-particle contributions, which underlies the conservation laws and the $H$ theorem, and enables discretization with a finite-volume or spectral method to preserve the conservation properties numerically, independent of resolution. The form of the exact linearized field-particle terms differs from those of widely used model operators. We show the finite Larmor radius corrections to the field-particle terms in the exact linearized operator involve Bessel functions of all orders, while present model field-particle terms involve only the first two Bessel functions. This new symmetric and conservative formulation enables the gyrokinetic exact linearized Landau operator to be implemented in gyrokinetic turbulence codes for comparison with present model operators using similar numerical methods.

Nonlinear and low-frequency solitary waves are investigated in the framework of the one-dimensional Hall-magnetohydrodynamic model with finite Larmor effects and two different closure models for the pressures. For a double adiabatic pressure model, the organization of these localized structures in terms of the propagation angle with respect to the ambient magnetic field $\theta$ and the propagation velocity $C$ is discussed. There are three types of regions in the $\theta -C$ plane that correspond to domains where either solitary waves cannot exist, are organized in branches, or have a continuous spectrum. A numerical method valid for the two latter cases, which rigorously proves the existence of the waves, is presented and used to locate many waves, including bright and dark structures. Some of them belong to parametric domains where solitary waves were not found in previous works. The stability of the structures has been investigated by performing a linear analysis of the background plasma state and by means of numerical simulations. They show that the cores of some waves can be robust, but, for the parameters considered in the analysis, the tails are unstable. The substitution of the double adiabatic model by evolution equations for the plasma pressures appears to suppress the instability in some cases and to allow the propagation of the solitary waves during long times.