Ordinary nematic liquid crystals are characterized by having a uniform director field as ground state. In such a state, the director is the same everywhere and no distortion is to be seen at all. We give a definition of uniform distortion which makes precise the intuitive notion of seeing everywhere the same director landscape. We characterize all such distortions and prove that they fall into two families, each described by two scalar parameters. Uniform distortions exhaust R. Meyer's heliconical structures, which, as it has recently been recognized, include the ground state of twist-bend nematics. The generalized elasticity of these new phases is treated with a simple free-energy density, which can be minimized by both uniform and nonuniform distortions, the latter injecting a germ of elastic frustration.

The transport of nanoparticles in confined geometries plays a crucial role in several technological applications ranging from nanopore sensors to filtration membranes. Here we describe a Brownian approach to simulate the motion of a rigid-body nanoparticle of an arbitrary shape under confinement. A quaternion formulation is used for the nanoparticle orientation, and the corresponding overdamped Langevin equation, completed by the proper fluctuation-dissipation relation, is derived. The hydrodynamic mobility matrix is obtained via dissipative particle dynamics simulation equipped with a new method for enforcing the no-slip boundary condition for curved moving solid-liquid interfaces. As an application, we analyzed the motion of a nanoparticle in a cylindrical channel under the action of external fields. We show that both axial effective diffusion and rotational diffusion decrease with confinement.

It is well known that flagellated bacteria swim in circles near surfaces. However, recent experiments have shown that a sulfide-oxidizing bacterium named Thiovulum majus can transition from swimming in circles to a surface bound state where it stops swimming while remaining free to move laterally along the surface. In this bound state, the cell rotates perpendicular to the surface with its flagella pointing away from it. Using numerical simulations and theoretical analysis, we demonstrate the existence of a fluid-structure interaction instability that causes cells with relatively short flagella to become surface bound.

We study the dynamic properties of a thermal autonomous machine made up of two quantum Brownian particles, each of which is in contact with an environment at different temperature and moves on a periodic sinusoidal track. When such tracks are shifted, the center of mass of the system exhibits a nonvanishing velocity, for which we provide an exact expression in the limit of small track undulations. We discuss the role of the broken spatial symmetry in the emergence of directed motion in thermal machines. We then consider the case in which external deterministic forces are applied to the system, and we characterize its steady-state velocity. If the applied external force opposes the system motion, work can be extracted from such a steady-state thermal machine, without any external cyclic protocol. When the two particles are not interacting, our results reduce to those of Fisher and Zwerger [Phys. Rev. B 32, 6190 (1985)] and Aslangul, Pottier, and Saint-James [J. Phys. France 48, 1093 (1987)] for a single particle moving in a periodic tilted potential. We finally use our results for the motor velocity to check the validity of the quantum molecular dynamics algorithm in the nonlinear, nonequilibrium regime.

In many biological systems, motile agents exhibit random motion with short-term directional persistence, together with crowding effects arising from spatial exclusion. We formulate and study a class of lattice-based models for multiple walkers with motion persistence and spatial exclusion in one and two dimensions, and use a mean-field approximation to investigate relevant population-level partial differential equations in the continuum limit. We show that this model of a persistent exclusion process is in general well described by a nonlinear diffusion equation. With reference to results presented in the current literature, our results reveal that the nonlinearity arises from the combination of motion persistence and volume exclusion, with linearity in terms of the canonical diffusion or heat equation being recovered in either the case of persistence without spatial exclusion, or spatial exclusion without persistence. We generalize our results to include systems of multiple species of interacting, motion-persistent walkers, as well as to incorporate a global drift in addition to persistence. These models are shown to be governed approximately by systems of nonlinear advection-diffusion equations. By comparing the prediction of the mean-field approximation to stochastic simulation results, we assess the performance of our results. Finally, we also address the problem of inferring the presence of persistence from simulation results, with a view to application to experimental cell-imaging data.

The propagation of compressional shocks in two-dimensional (2D) dusty plasmas is investigated using MD simulations under various conditions. The shock Hugoniot curves of the relationship between the shock front speed $D$ and the mean particle speed $\overline{v}$ after shocks are obtained and analytically fit to parabolic expressions. As the screening parameter increases, the weaker Yukawa interparticle interaction cause the shock Hugoniot curves to be more linear. Combining the obtained shock Hugoniot curves with the Rankine-Hugoniot jump relations, analytic expressions of pressure and energy after the shocks in 2D Yukawa systems are obtained, which are functions of the observable quantities, like the shock front speed $D$ or the mean particle speed $\overline{v}$ or the specific volume.

In biological organisms, an optimal temperature exists at which the system functioning is maximized or is most effective. To obtain a general and quantitative understanding of the emergence of the optimal temperature is a challenging task. We aim to gain insights into this significant problem in biological physics by addressing the problem of propagation of action potential in myelinated axons. In particular, we construct a Hodgkin-Huxley type of cortical, compartmental model to describe the nodes of Ranvier with coupling between a pair of neighboring compartments characterized by internodal conductance and investigate the effect of temperature on the propagation of the action potential. We conduct direct numerical simulations and develop a physical analysis by taking advantage of the spatially continuous approximation. We find that increasing the temperature requires a larger value of the critical internodal conductance for successful propagation. The striking finding is the spontaneous emergence of an optimal temperature in the sense that, for the propagation of a single action potential at a fixed value of the internodal conductance, the minimum average passage time for one node of Ranvier occurs at this temperature value. A remarkable phenomenon is that the value of the optimal temperature is similar to those of living biological systems observed in experiments.

Laser speckle imaging (LSI) can be used to study dynamic processes in turbid media, such as blood flow. However, it is presently still challenging to obtain meaningful quantitative information from speckle, mainly because speckle is the interferometric summation of multiply scattered light. Consequently, speckle represents a convolution of the local dynamics of the medium. In this paper, we present a computational model for simulating the LSI process, which we aim to use for improving our understanding of the underlying physics. Thereby reliable methods for extracting meaningful information from speckle can be developed. To validate our code, we apply it to a case study resembling blood flow: a cylindrical fluid flow geometry seeded with small spherical particles and modulated with a heartbeat signal. From the simulated speckle pattern, we successfully retrieve the main frequency modes of the original heartbeat signal. By comparing Poiseuille flow to plug flow, we show that speckle boiling causes a small amount of uniform spectral noise. Our results indicate that our computational model is capable of simulating LSI and will therefore be useful in future studies for further developing LSI as a quantitative imaging tool.

We report on a series of experiments in which a grain-sized intruder is pushed by a spring through a two-dimensional granular material composed of photoelastic disks in a Couette geometry. We study the intruder dynamics as a function of packing fraction for two types of supporting substrates: A frictional glass plate and a layer of water for which basal friction forces are negligible. We observe two dynamical regimes: Intermittent flow, in which the intruder moves freely most of the time but occasionally gets stuck, and stick-slip dynamics, in which the intruder advances via a sequence of distinct, rapid events. When basal friction is present, we observe a smooth crossover between the two regimes as a function of packing fraction, and we find that reducing the interparticle friction coefficient causes the stick-slip regime to shift to higher packing fractions. When basal friction is eliminated, we observe intermittent flow at all accessible packing fractions. For all cases, we present results for the statistics of stick events, the intruder velocity, and the force exerted on the intruder by the grains. Our results indicate the qualitative importance of basal friction at high packing fractions and suggest a possible connection between intruder dynamics in a static material and clogging dynamics in granular flows.

Proteins display generic properties that are challenging to explain by direct selection, notably allostery, the capacity to be regulated through long-range effects, and evolvability, the capacity to adapt to new selective pressures. An evolutionary scenario is proposed where proteins acquire these two features indirectly as a by-product of their selection for a more fundamental property, exquisite discrimination, the capacity to bind discriminatively very similar ligands. Achieving this task is shown to typically require proteins to undergo a conformational change. We argue that physical and evolutionary constraints impel this change to be controlled by a group of sites extending from the binding site. Proteins can thus acquire a latent potential for allosteric regulation and evolutionary adaptation because of long-range effects that initially arise as evolutionary spandrels. This scenario accounts for the groups of conserved and coevolving residues observed in multiple sequence alignments. However, we propose that most pairs of coevolving and contacting residues inferred from such alignments have a different origin, related to thermal stability. A physical model is presented that illustrates this evolutionary scenario and its implications. The scenario can be implemented in experiments of protein evolution to directly test its predictions.

We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and conservation laws, we identify several model-independent phenomena, such as a curvature-dependent line tension and local shifts in the binodal concentrations. To shed light on the origin of the phenomenological parameters appearing in the effective free energy, we further construct a lattice-gas model of binary mixtures on nontrivial substrates, based on the curved-space generalization of the two-dimensional Ising model. This allows us to decompose the interaction between the local concentration of the mixture and the substrate curvature into four distinct contributions, as a result of which the phase diagram splits into critical subdiagrams. The resulting free energy landscape can admit, as stable equilibria, strongly inhomogeneous mixed phases, which we refer to as “antimixed” states below the critical temperature. We corroborate our semianalytical findings with phase-field numerical simulations on realistic curved lattices. Despite this work being primarily motivated by recent experimental observations of multicomponent lipid vesicles supported by colloidal scaffolds, our results are applicable to any binary mixture confined on closed surfaces of arbitrary geometry.

We study clustering and percolation phenomena in the Vicsek model, taken here in its capacity of prototypical model for dry aligning active matter. Our results show that the order-disorder transition is not related in any way to a percolation transition, contrary to some earlier claims. We study geometric percolation in each of the phases at play, but we mostly focus on the ordered Toner-Tu phase, where we find that the long-range correlations of density fluctuations give rise to an anisotropic percolation transition.

Haines instabilities are sudden jumps of the fluid interface accompanied by fluid redistribution and a transient pressure response. Haines jumps affect global displacement patterns in porous media, promote fingered invasion, increase fluid trapping, and contribute to hysteretic saturation. Detailed analyses and experimental results show that jumps take place when the pressure-volume response is multivalued across the pore throat, during either advancing or receding tests. This situation emerges in “soft systems” such as liquids with entrapped gas bubbles, compliant substrates, and when multiple menisci interact across the porous networks. Elastic deformations and capillarity combine to form the dimensionless elastocapillary number $N_{\mathrm{ec}}$ for a given pore geometry and fluid mixture: a system with elastocapillary number $N_{\mathrm{ec}}<1$ is prone to Haines instabilities. Therefore, Haines jumps are more likely to occur not only in soft porous systems, but also when the network topology is characterized by pronounced pore constrictions, and the fluids form small contact angles and generate high interfacial tension.

A “self-replicator” is usually understood to be an object of definite form that promotes the conversion of materials in its environment into a nearly identical copy of itself. The challenge of engineering novel, micro- or nanoscale self-replicators has attracted keen interest in recent years, both because exponential amplification is an attractive method for generating high yields of specific products and, also, because self-reproducing entities have the potential to be optimized or adapted through rounds of iterative selection. Substantial steps forward have been achieved both in the engineering of particular self-replicating molecules and in the characterization of the physical basis for possible mechanisms of self-replication. At present, however, there is a need for a theoretical treatment of what physical conditions are most conducive to the emergence of novel self-replicating structures from a reservoir of building blocks on a desired time scale. Here we report progress in addressing this need. By analyzing the kinetics of a toy chemical model, we demonstrate that the emergence of self-replication can be controlled by coarse, tunable features of the chemical system, such as the fraction of fast reactions and the width of the rate constant distribution. We also find that the typical mechanism is dominated by the cooperation of multiple interconnected reaction cycles as opposed to a single isolated cycle. The quantitative treatment presented here may prove useful for designing novel self-replicating chemical systems.

The instability of a thin liquid film on a solid surface is studied both by molecular dynamics simulations (MD) and a stochastic thin-film equation (STF), which models thermal fluctuations with white noise. A linear stability analysis of the STF allows us to derive a power spectrum for the surface fluctuations, which is quantitatively validated against the spectrum observed in MD. Thermal fluctuations are shown to be critical to the dynamics of nanoscale films. Compared to the classical instability mechanism, which is driven by disjoining pressure, fluctuations (a) can massively amplify the instability, (b) cause the fluctuation wavelength that is dominant to evolve in time (a single fastest-growing mode does not exist), and (c) decrease the critical wavelength so that classically stable films can be ruptured.

We investigate the surface adsorption transition of interacting self-avoiding square lattice trails onto a straight boundary line. The character of this adsorption transition depends on the strength of the bulk interaction, which induces a collapse transition of the trails from a swollen to a collapsed phase, separated by a critical state. If the trail is in the critical state, the universality class of the adsorption transition changes; this is known as the special adsorption point. Using flatPERM, a stochastic growth Monte Carlo algorithm, we simulate the adsorption of self-avoiding interacting trails on the square lattice using three different boundary scenarios which differ with respect to the orientation of the boundary and the type of surface interaction. We confirm the expected phase diagram, showing swollen, collapsed, and adsorbed phases in all three scenarios, and confirm universality of the normal adsorption transition at low values of the bulk interaction strength. Intriguingly, we cannot confirm universality of the special adsorption transition. We find different values for the exponents; the most likely explanation is that this is due to the presence of strong corrections to scaling at this point.

Ion channels regulate the flux of ions through cell membranes and play significant roles in many physiological functions. Most of the existing literature focuses on computational approaches based on molecular dynamics simulation or numerical solution of the modified Poisson-Nernst-Planck (PNP) system. In this paper, we present an analytical and computational study of a mathematical model of the KcsA potassium channel, including the effects of ion size (Bikerman model) and solvation energy (Born model). Under equilibrium conditions, we obtain an analytical solution of our modified PNP system, which is used to explain selectivity of KcsA of various ions (${\mathrm{K}}^{+}$, ${\mathrm{Na}}^{+}$, ${\mathrm{Cl}}^{-}$, ${\mathrm{Ca}}^{2+}$, and ${\mathrm{Ba}}^{2+}$) due to negative permanent charges inside the filter region and the effect of ion sizes. Our results show that ${\mathrm{K}}^{+}$ is always selected over ${\mathrm{Na}}^{+}$, as smaller ${\mathrm{Na}}^{+}$ ions have larger solvation energy. As the amount of negative charges in the filter exceeds a critical value, divalent ions (${\mathrm{Ca}}^{2+}$ and ${\mathrm{Ba}}^{2+}$) can enter the filter region and block the KcsA channel. For the nonequilibrium cases, due to difficulties associated with a pure analytical or numerical approach, we use a hybrid analytical-numerical method to solve the modified PNP system. Our predictions of selectivity of KcsA channels and saturation phenomenon of the current-voltage ($I\text{−}V$) curve agree with experimental observations.

The integration of automotive technology with internet connectivity promises to both dramatically improve transportation while simultaneously introducing the potential for new unknown risks. Internet-connected vehicles are like digital data because they can be targeted for malicious hacking. Unlike digital data, however, internet-connected vehicles are cyberphysical systems that physically interact with each other and their environment. As such, the extension of cybersecurity concerns into the cyberphysical domain introduces new possibilities for self-organized phenomena in traffic flow. Here we study a scenario envisioned by cybersecurity experts leading to a large number of internet-connected vehicles being suddenly and simultaneously disabled. We investigate posthack traffic using agent-based simulations and discover the critical relevance of percolation for probabilistically predicting the outcomes on a multilane road in the immediate aftermath of a vehicle-targeted cyberattack. We develop an analytic percolation-based model to rapidly assess road conditions given the density of disabled vehicles and apply it to study the street network of Manhattan (New York City, New York, USA) revealing the city's vulnerability to this particular cyberphysical attack. While a comprehensive investigation of city-scale traffic around hacked vehicles is an extremely complicated problem, we find that the statistical physics of percolation can provide an estimate of the number of vehicles that critically disrupts citywide traffic flow. Our upper-bound estimate represents a quantification of citywide traffic disruptions when multiple vehicles are hacked.

We present direct numerical simulation of heavy inertial particles (dust) immersed in two-dimensional turbulent flow (gas). The dust particles are modeled as monodispersed heavy particles capable of modifying the flow through two-way coupling. By varying the Stokes number ($\text{St}$) and the mass-loading parameter (${\varphi }_{\mathrm{m}}$), we study the clustering phenomenon and the gas phase kinetic energy spectra. We find that the dust-dust correlation dimension ($d_2$) also depends on ${\varphi }_{\mathrm{m}}$. In particular, clustering decreases as mass loading (${\varphi }_{\mathrm{m}}$) is increased. In the kinetic energy spectra of gas we show (i) the emergence of a different scaling regime and that (ii) the scaling exponent in this regime is not universal but a function of both $\text{St}$ and ${\varphi }_{\mathrm{m}}$. Using a scale-by-scale enstrophy budget analysis we show that in this emerged scaling regime, which we call the dust-dissipative range, viscous dissipation due to the gas balances the back-reaction from the dust.

We analyze large deviations of the magnetization in two models of growing clusters. The models have symmetry-breaking transitions, so the typical magnetization of a growing cluster may be either positive or negative, with equal probability. For large clusters, the magnetization obeys a large-deviation principle. We show that the corresponding rate function is zero for values of the magnetization that are intermediate between the two steady state values, which means that fluctuations with these values of the magnetization are much less unlikely than previously thought. We show that their probabilities decay as power laws in the cluster size, instead of the exponential scaling that would be expected from the large-deviation principle. We discuss how this observation is related to dynamical phase coexistence phenomena. We also comment on the typical size of magnetization fluctuations.