The active Brownian particle (ABP) model is widely used to describe the dynamics of active matter systems, such as Janus microswimmers. In particular, the analytical expression for an ABP's mean-squared displacement (MSD) is useful as it provides a means to describe the essential physics of a self-propelled, spherical Brownian particle. However, the truncated or “short-time” form of the MSD equation is typically fitted, which can lead to significant problems in parameter estimation. Furthermore, heteroscedasticity and the often statistically dependent observations of an ABP's MSD lead to a situation where standard ordinary least-squares regression leads to biased estimates and unreliable confidence intervals. Instead, we propose here to revert to always fitting the full expression of an ABP's MSD at short timescales, using bootstrapping to construct confidence intervals of the fitted parameters. Additionally, after comparison between different fitting strategies, we propose to extract the physical parameters of an ABP using its mean logarithmic squared displacement. These steps improve the estimation of an ABP's physical properties and provide more reliable confidence intervals, which are critical in the context of a growing interest in the interactions of microswimmers with confining boundaries and the influence on their motion.

Icicles that have grown from slightly impure water develop ripples around their circumference. The ripples have a near-universal wavelength and are thought to be the result of a morphological instability. Using laboratory-grown icicles and various species of impurities, including fluorescent dye, we show that a certain fraction of the impurities remain trapped inside the icicle, forming inclusions within the ice. The inclusions are organized into chevron patterns aligned with the peaks of the ripples. Within the chevrons, a substructure of crescent-shaped structures is observed. We also examine the crystal grain structure of laboratory icicles with and without impurities. We present the first detailed study of these growth patterns in the interior of icicles and discuss their implications for the mechanism of the ripple-forming instability.

The jamming transition is ubiquitous. It is present in granular matter, foams, colloids, structural glasses, and many other systems. Yet, it defines a critical point whose properties still need to be fully understood. Recently, a major breakthrough came about when the replica formalism was extended to build a mean-field theory that provides an exact description of the jamming transition of spherical particles in the infinite-dimensional limit. While such theory explains the jamming critical behavior of both soft and hard spheres, investigating the transition in finite-dimensional systems poses very difficult and different problems, in particular from the numerical point of view. Soft particles are modeled by continuous potentials; thus, their jamming point can be reached through efficient energy minimization algorithms. In contrast, the latter methods are inapplicable to hard-sphere (HS) systems since the interaction energy among the particles is always zero by construction. To overcome these difficulties, here we recast the jamming of hard spheres as a constrained optimization problem and introduce the CALiPPSO algorithm, capable of readily producing jammed HS packings without including any effective potential. This algorithm brings a HS configuration of arbitrary dimensions to its jamming point by solving a chain of linear optimization problems. We show that there is a strict correspondence between the force balance conditions of jammed packings and the properties of the optimal solutions of CALiPPSO, whence we prove analytically that our packings are always isostatic and in mechanical equilibrium. Furthermore, using extensive numerical simulations, we show that our algorithm is able to probe the complex structure of the free-energy landscape, finding qualitative agreement with mean-field predictions. We also characterize the algorithmic complexity of CALiPPSO and provide an open-source implementation of it.

Linkages are mechanical devices constructed from rigid bars and freely rotating joints studied both for their utility in engineering and as mathematical idealizations in a number of physical systems. Recently, there has been a resurgence of interest in designing linkages in the physics community due to the concurrent developments of mechanical metamaterials, topological mechanics, and the discovery of anomalous rigidity in fiber networks and vertex models. These developments raise a natural question: to what extent can the motion of a linkage or mechanical structure be designed? Here, we describe a method to design the topology of the configuration space of a linkage by first identifying the manifold of critical points, then perturbing around such critical configurations. Unlike other methods, our methods are tractable and provide a simple visual toolkit for mechanism design. We demonstrate our procedure by designing a mechanism to gate the propagation of a soliton in a Kane-Lubensky chain of interconnected rotors.

In a system of interacting thin rigid rods of equal length $2\ell$ on a two-dimensional grid of lattice spacing $a$, we show that there are multiple phase transitions as the coupling strength $\kappa =\ell /a$ and the temperature are varied. There are essentially two classes of transitions. One corresponds to the Ising-type spontaneous symmetry-breaking transition and the second belongs to less-studied phase transitions of geometrical origin. The latter class of transitions appears at fixed values of $\kappa$ irrespective of the temperature, whereas the critical coupling for the spontaneous symmetry-breaking transition depends on it. By varying the temperature, the phase boundaries may cross each other, leading to a rich phase behavior with infinitely many phases. Our results are based on Monte Carlo simulations on the square lattice and a fixed-point analysis of a functional flow equation on a Bethe lattice.

In this article, we study the dynamics of marking in football matches. To do this, we survey and analyze a database containing the trajectories of players from both teams on the field of play during three professional games. We describe the dynamics through the construction of temporal bipartite networks of proximity. Based on the introduced concept of proximity, the nodes are the players, and the links are defined between opponents that are close enough to each other at a given moment. By studying the evolution of the heterogeneity parameter of the networks during the game, we characterize a scaling law for the average shape of the fluctuations, unveiling the emergence of complexity in the system. Moreover, we propose a simple model to simulate the players' motion in the field from where we obtained the evolution of a synthetic proximity network. We show that the model captures with a remarkable agreement the complexity of the empirical case, hence it proves to be helpful to elucidate the underlying mechanisms responsible for the observed phenomena.

Molecular sorting is a fundamental process that allows eukaryotic cells to distill and concentrate specific chemical factors in appropriate cell membrane subregions, thus endowing them with different chemical identities and functional properties. A phenomenological theory of this molecular distillation process has recently been proposed [M. Zamparo, D. Valdembri, G. Serini, I. V. Kolokolov, V. V. Lebedev, L. Dall'Asta, and A. Gamba, Phys. Rev. Lett. 126, 088101 (2021)], based on the idea that molecular sorting emerges from the combination of (a) phase separation driven formation of sorting domains and (b) domain-induced membrane bending, leading to the production of submicrometric lipid vesicles enriched in the sorted molecules. In this framework, a natural parameter controlling the efficiency of molecular distillation is the critical size of phase separated domains. In the experiments, sorting domains appear to fall into two classes: unproductive domains, characterized by short lifetimes and low probability of extraction, and productive domains, that evolve into vesicles that ultimately detach from the membrane system. It is tempting to link these two classes to the different fates predicted by classical phase separation theory for subcritical and supercritical phase separated domains. Here, we discuss the implication of this picture in the framework of the previously introduced phenomenological theory of molecular sorting. Several predictions of the theory are verified by numerical simulations of a lattice-gas model. Sorting is observed to be most efficient when the number of sorting domains is close to a minimum. To help in the analysis of experimental data, an operational definition of the critical size of sorting domains is proposed. Comparison with experimental results shows that the statistical properties of productive and unproductive domains inferred from experimental data are in agreement with those predicted from numerical simulations of the model, compatibly with the hypothesis that molecular sorting is driven by a phase separation process.

We study the moving phase of two-dimensional (2D) incompressible polar active fluids in the presence of both quenched and annealed disorder. We show that long-range polar order persists even in this defect-ridden two-dimensional system. We obtain the large-distance, long-time scaling laws of the velocity fluctuations using three distinct dynamic renormalization group schemes. These are an uncontrolled one-loop calculation in exactly two dimensions, and two $d=(d_c-\epsilon )$ expansions to $O\left(\epsilon \right)$, obtained by two different analytic continuations of our 2D model to higher spatial dimensions: a “hard” continuation which has $d_c=\frac{7}{3}$, and a “soft” continuation with $d_c=\frac{5}{2}$. Surprisingly, the quenched and annealed parts of the velocity correlation function have the same anisotropy exponent and the relaxational and propagating parts of the dispersion relation have the same dynamic exponent in the nonlinear theory even though they are distinct in the linearized theory. This is due to anomalous hydrodynamics. Furthermore, all three renormalization schemes yield very similar values for the universal exponents, and therefore we expect the numerical values that we predict for them to be highly accurate.

Hard-core lattice-gas models are minimal models to study entropy-driven phase transitions. In the $k$-nearest-neighbor lattice gas, a particle excludes all sites up to the $k\mathrm{th}$ next-nearest neighbors from being occupied by another particle. As $k$ increases from one, it extrapolates from nearest-neighbor exclusion to the hard-sphere gas. In this paper we study the model on the triangular lattice for $k\le 7$ using a flat histogram algorithm that includes cluster moves. Earlier studies focused on $k\le 3$. We show that for $4\le k\le 7$, the system undergoes a single phase transition from a low-density fluid phase to a high-density sublattice-ordered phase. Using partition function zeros and nonconvexity properties of the entropy, we show that the transitions are discontinuous. The critical chemical potential, coexistence densities, and critical pressure are determined accurately.

When surface-active molecules are released at a liquid interface, their spreading dynamics is controlled by Marangoni flows. Though such Marangoni spreading was investigated in different limits, exact solutions remain very few. Here we consider the spreading of an insoluble surfactant along the interface of a deep fluid layer. For two-dimensional Stokes flows, it was recently shown that the nonlinear transport problem can be exactly mapped to a complex Burgers equation [D. Crowdy, SIAM J. Appl. Math. 81, 2526 (2021)]. We first present a very simple derivation of this equation. We then provide fully explicit solutions and find that varying the initial surfactant distribution—pulse, hole, or periodic—results in distinct spreading behaviors. By obtaining the fundamental solution, we also discuss the influence of surface diffusion. We identify situations where spreading can be described as an effective diffusion process but observe that this approximation is not generally valid. Finally, the case of a three-dimensional flow with axial symmetry is briefly considered. Our findings should provide reference solutions for Marangoni spreading that may be tested experimentally with fluorescent or photoswitchable surfactants.

Aperiodic (quasicrystalline) tilings, such as Penrose's tiling, can be built up from, e.g., kites and darts, squares and equilateral triangles, rhombi- or shield-shaped tiles, and can have a variety of different symmetries. However, almost all quasicrystals occurring in soft matter are of the dodecagonal type. Here we investigate a class of aperiodic tilings with hexagonal symmetry that are based on rectangles and two types of equilateral triangles. We show how to design soft-matter systems of particles interacting via pair potentials containing two length scales that form aperiodic stable states with two different examples of rectangle-triangle tilings. One of these is the bronze-mean tiling, while the other is a generalization. Our work points to how more general (beyond dodecagonal) quasicrystals can be designed in soft matter.

Two boundary lines are frequently discussed in the literature, separating state regions dominated by repulsion or attraction. The Fisher-Widom line indicates where the longest-range decay of the total pair correlation function crosses from monotonic to exponentially damped oscillatory. In the context of thermodynamic metric geometry, such a transition exists where the Ricci curvature scalar vanishes, $R=0$. To establish a possible relation between these two lines, $R$ is worked out for four simple fluids. The truncated and shifted Lennard-Jones, a colloid-like and the square-well potential are analyzed to investigate the influence of the repulsive nature on the location of the $R=0$ line. For the longer-ranged Lennard-Jones potential, the influence of the cutoff radius on the $R=0$ line is studied. The results are compared with literature data on the Fisher-Widom line. Since such data are rare for the longer-ranged Lennard-Jones potential, dedicated simulations are carried out to determine the number of zeros of the total correlation function, which may provide approximate information about the position of the Fisher-Widom line. An increase of the repulsive strength toward hard sphere interaction leads to the disappearance of the $R=0$ line in the fluid phase. A rising attraction range results in the nonexistence of the Fisher-Widom line, while it has little effect on the $R=0$ line as long as it is present in the fluid state.

Helical-shaped magnetotactic bacteria provide a rare opportunity to precisely measure both the translational and rotational friction coefficients of micron-sized chiral particles. The possibility to align these cells with a uniform magnetic field allows clearly separating diffusion along and perpendicular to their longitudinal axis. Meanwhile, their corkscrew shape allows detecting rotations around their longitudinal axis, after which orientation correlation analysis can be used to retrieve rotational diffusion coefficients in the two principal directions. Using light microscopy, we measured the four principal friction coefficients of deflagellated Magnetospirillum magneticum cells, and compared our results to that expected for cylinders of comparable size. We show that for rotational motions, the overall dimensions of the cell body are what matters most, while the exact body shape has a larger influence on translational motions. To obtain a full characterization of the friction matrix of these elongated chiral particles, we also quantified the coupling between the rotation around and translation along the longitudinal axis of the cell. Our results suggest that for this bacterial species cell body rotation could significantly contribute to cellular propulsion.

Aerotaxis is the ability of motile cells to navigate toward oxygen. A key question is the dependence of the aerotactic velocity with the local oxygen concentration $c$. Here we combine simultaneous bacteria tracking and local oxygen concentration measurements using Ruthenium encapsulated in micelles to characterize the aerotactic response of Burkholderia contaminans, a motile bacterium ubiquitous in the environment. In our experiments, an oxygen gradient is produced by the bacterial respiration in a sealed glass capillary permeable to oxygen at one end, producing a bacterial band traveling toward the oxygen source. We compute the aerotactic response $\chi \left(c\right)$ both at the population scale, from the drift velocity in the bacterial band, and at the bacterial scale, from the angular modulation of the run times. Both methods are consistent with a power-law $\chi \propto c^{-2}$, in good agreement with existing models based on the biochemistry of bacterial membrane receptors.

Living systems are fundamentally irreversible, breaking detailed balance and establishing an arrow of time. But how does the evident arrow of time for a whole system arise from the interactions among its multiple elements? We show that the local evidence for the arrow of time, which is the entropy production for thermodynamic systems, can be decomposed. First, it can be split into two components: an independent term reflecting the dynamics of individual elements and an interaction term driven by the dependencies among elements. Adapting tools from nonequilibrium physics, we further decompose the interaction term into contributions from pairs of elements, triplets, and higher-order terms. We illustrate our methods on models of cellular sensing and logical computations, as well as on patterns of neural activity in the retina as it responds to visual inputs. We find that neural activity can define the arrow of time even when the visual inputs do not, and that the dominant contribution to this breaking of detailed balance comes from interactions among pairs of neurons.

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existing literature concerned with the low-rank (i.e., constant-rank) regime. We first consider a class of rotationally invariant matrix denoising problems whose mutual information and minimum mean-square error are computable using techniques from random matrix theory. Next, we analyze the more challenging models of dictionary learning. To do so we introduce a combination of the replica method from statistical mechanics together with random matrix theory, coined spectral replica method. This allows us to derive variational formulas for the mutual information between hidden representations and the noisy data of the dictionary learning problem, as well as for the overlaps quantifying the optimal reconstruction error. The proposed method reduces the number of degrees of freedom from $\mathrm{\Theta }\left(N^2\right)$ matrix entries to $\mathrm{\Theta }\left(N\right)$ eigenvalues (or singular values), and yields Coulomb gas representations of the mutual information which are reminiscent of matrix models in physics. The main ingredients are a combination of large deviation results for random matrices together with a replica symmetric decoupling ansatz at the level of the probability distributions of eigenvalues (or singular values) of certain overlap matrices and the use of Harish-Chandra-Itzykson-Zuber spherical integrals.

Autologous chemotaxis, in which cells secrete and detect molecules to determine the direction of fluid flow, is thwarted at high cell density because molecules from other cells interfere with a given cell's signal. Using a minimal model of autologous chemotaxis, we determine the cell density at which sensing fails, and we find that it agrees with experimental observations of metastatic cancer cells. To understand this agreement, we derive a physical limit to autologous chemotaxis in terms of the cell density, the Péclet number, and the lengthscales of the cell and its environment. Surprisingly, in an environment that is uniformly oversaturated in the signaling molecule, we find that not only can sensing fail, but it can be reversed, causing backwards cell motion. Our results get to the heart of the competition between chemical and mechanical cellular sensing, and they shed light on a sensory strategy employed by cancer cells in dense tumor environments.

Despite the success achieved by the analysis of supervised learning algorithms in the framework of statistical mechanics, reinforcement learning has remained largely untouched by physicists. Here we move towards closing the gap by analyzing the dynamics of the policy gradient algorithm. For a convex problem, namely the $k$-armed bandit, we show that the learning dynamics obeys a drift-diffusion motion described by a Langevin equation, the coefficients of which can be tuned by the learning rate. We explore the striking similarity between our Langevin equation and the Kimura equation, describing genotypes evolution. Furthermore, we propose a mapping between a nonconvex reinforcement learning setting describing multiple joints of a robotic arm and a disordered system, namely a $p$-spin glass. This mapping enables us to show how the learning rate acts as an effective temperature and thus is capable of smoothing rough landscapes, corroborating what is displayed by the drift-diffusive description and paving the way for physics-inspired algorithmic optimization based on annealing procedures in disordered systems.

Thermal forces drive several nonequilibrium phenomena able to set a fluid in motion without pressure gradients. Although the most celebrated effect is thermophoresis, also known as Ludwig-Soret effect, probably the simplest example where thermal forces are at play is thermo-osmosis: The motion of a confined fluid exclusively due to the presence of a temperature gradient. We present a concise but complete derivation of the microscopic theory of thermo-osmosis based on linear response theory. This approach is applied to a simple fluid confined in a slab geometry, mimicking the flow through a pore in a membrane separating two fluid reservoirs at different temperatures. We consider both the case of an open channel, where the fluid can flow freely, and that of a closed channel, where mass transport is inhibited and a pressure drop sets in at the boundaries. Quantitative results require the evaluation of generalized transport coefficients, but a preliminary check on a specific prediction of the theory has been successfully performed via nonequilibrium molecular dynamics simulations.

We apply periodic control to realize a quantum thermal transistor, which we term as the Floquet quantum thermal transistor. Periodic modulation allows us to control the heat flows and achieve large amplification factors even for fixed bath temperatures. Importantly, this transistor effect persists in the cutoff region, where traditional quantum thermal transistors operating in the absence of periodic modulation, fail to act as viable heat modulation devices.