We introduce a representative minimal model for phoretically interacting active colloids. Combining kinetic theory, linear stability analyses, and a general relation between self-propulsion and phoretic interactions in autodiffusiophoretic and autothermophoretic Janus colloids collapses the parameter space from six to two dimensionless parameters: area fraction and Péclet number. This collapse arises when the lifetime of the self-generated phoretic fields is not too short, and leads to a universal phase diagram showing that phoretic interactions generically induce pattern formation in typical Janus colloids, even at very low density. The resulting patterns include waves and dynamic aggregates closely resembling the living clusters found in experiments on dilute suspension of Janus colloids.

The mechanical properties of transcription have recently been shown to play a central role in gene expression. However, a full physical characterization of this central biological process is lacking. In this Letter, we introduce a simple description of the basic physical elements of transcription where RNA elongation, RNA polymerase rotation, and DNA supercoiling are coupled. The resulting framework describes the relative amount of RNA polymerase rotation and DNA supercoiling that occurs during RNA elongation. Asymptotic behavior is derived and can be used to experimentally extract unknown mechanical parameters of transcription. Mechanical limits to transcription are incorporated through the addition of a DNA supercoiling-dependent RNA polymerase velocity. This addition can lead to transcriptional stalling and resulting implications for gene expression, chromatin structure and genome organization are discussed.

Learning a task induces connectivity changes in neural circuits, thereby changing their dynamics. To elucidate task-related neural dynamics, we study trained recurrent neural networks. We develop a mean field theory for reservoir computing networks trained to have multiple fixed point attractors. Our main result is that the dynamics of the network’s output in the vicinity of attractors is governed by a low-order linear ordinary differential equation. The stability of the resulting equation can be assessed, predicting training success or failure. As a consequence, networks of rectified linear units and of sigmoidal nonlinearities are shown to have diametrically different properties when it comes to learning attractors. Furthermore, a characteristic time constant, which remains finite at the edge of chaos, offers an explanation of the network’s output robustness in the presence of variability of the internal neural dynamics. Finally, the proposed theory predicts state-dependent frequency selectivity in the network response.

Smectic liquid crystals are characterized by layers that have a preferred uniform spacing and vanishing curvature in their ground state. Dislocations in smectics play an important role in phase nucleation, layer reorientation, and dynamics. Typically modeled as possessing one line singularity, the layer structure of a dislocation leads to a diverging compression strain as one approaches the defect center, suggesting a large, elastically determined melted core. However, it has been observed that for large charge dislocations, the defect breaks up into two disclinations [C. E. Williams, Philos. Mag. 32, 313 (1975)]. Here we investigate the topology of the composite core. Because the smectic cannot twist, transformations between different disclination geometries are highly constrained. We demonstrate the geometric route between them and show that despite enjoying precisely the topological rules of the three-dimensional nematic, the additional structure of line disclinations in three-dimensional smectics localizes transitions to higher-order point singularities.

When a semiflexible chain is confined in a narrow cylindrical tube, the formation of a polymer hairpin is a geometrical conformation that accompanies an exponentially large local free energy and, hence, is a relatively rare event. Numerical solutions of the hairpin distribution functions for persistence-length-to-tube-radius ratios over a wide range are obtained in high precision, by using the Green’s function approach for the wormlike-chain model. The crossover region between the narrow and moderately narrow tubes is critically investigated in terms of the hairpin free energy, global persistence length, mean hairpin-tip distance from the tube axis, and hairpin-plane orientational properties. Accurate representations of the solutions by simple interpolation formulae are suggested.

Experimental measurements of the relaxation kinetics of copolymeric surfactant exchange for micellar systems unexpectedly show a peculiar logarithmic decay. Several authors use polydispersity as an explanation for this behavior. However, in coarse-grained simulations that preserve microscopic details of the surfactants, we find evidence of the same logarithmic behavior. Since we use a strictly monodisperse distribution of chain lengths such a relaxation process cannot be attributed to polydispersity, but has to be caused by an inherent physical process characteristic of this type of system. This is supported by the fact that the decay is specifically logarithmic and not a power law with an exponent inherited from the particular polydispersity distribution of the sample. We suggest that the degeneracy of the energy states of the hydrophobic block in the core, which is broken on leaving the micelle, can qualitatively explain the broad distribution of energy barriers, which gives rise to the observed nonexponential relaxation.

Block copolymer (BCP) melt assembly has been studied for decades, focusing largely on self-organized spatial patterns of periodically ordered segment density. Here, we demonstrate that underlying the well-known composition profiles (i.e., ordered lamella, cylinders, spheres, and networks) are generic and heterogeneous patterns of segment orientation that couple strongly to morphology, even in the absence of specific factors that promote intra or interchain segment alignment. We employ both self-consistent field theory and coarse-grained simulation methods to measure polar and nematic order parameters of segments in a freely jointed chain model of diblock melts. We show that BCP morphologies have a multizone texture, with segments predominantly aligned normal and parallel to interdomain interfaces in the respective brush and interfacial regions of the microdomain. Further, morphologies with anisotropically curved interfaces (i.e., cylinders and networks) exhibit biaxial order that is aligned to the principal curvature axes of the interface.

Adhesion between glass and bromobutyl and polydimethylsiloxane elastomers is investigated. We show that viscoelastic energy dissipation close to the opening (or closing) crack tip, and surface roughness, strongly affect the work of adhesion. We observe strong adhesion hysteresis and we show, in contrast to the Johnson-Kendall-Roberts theory prediction for elastic solids, that this results in a pull-off force, and effective work of adhesion to be dependent on the maximum loading force.

Recent diffraction experiments on metallic glasses have unveiled an unexpected noncubic scaling law between density and average interatomic distance, which led to the speculation of the presence of fractal glass order. Using x-ray tomography we identify here a similar noncubic scaling law in disordered granular packing of spherical particles. We find that the scaling law is directly related to the contact neighbors within the first nearest neighbor shell, and, therefore, is closely connected to the phenomenon of jamming. The seemingly universal scaling exponent around 2.5 arises due to the isostatic condition with a contact number around 6, and we argue that the exponent should not be universal.

Despite the large number of studies on synchronization, the hypothesis that interactions bear a cost for involved individuals has seldom been considered. The introduction of costly interactions leads, instead, to the formulation of a dichotomous scenario in which an individual may decide to cooperate and pay the cost in order to get synchronized with the rest of the population. Alternatively, the same individual can decide to free ride, without incurring any cost, waiting for others to get synchronized to his or her state. Thus, the emergence of synchronization may be seen as the byproduct of an evolutionary game in which individuals decide their behavior according to the benefit-to-cost ratio they accrued in the past. We study the onset of cooperation and synchronization in networked populations of Kuramoto oscillators and report how topology is essential in order for cooperation to thrive. We also display how different classes of topology foster synchronization differently both at microscopic and macroscopic levels.

We describe a new mechanism for Lévy walks, explaining the recently observed superdiffusion of swarming bacteria. The model hinges on several key physical properties of bacteria, such as an elongated cell shape, self-propulsion, and a collectively generated regular vortexlike flow. In particular, chaos and Lévy walking are a consequence of group dynamics. The model explains how cells can fine-tune the geometric properties of their trajectories. Experiments confirm the spectrum of these patterns in fluorescently labeled swarming Bacillus subtilis.

We study the motility of model cells and biomimetic soft objects crawling over a substrate covered with adhesive linkers. The cell exerts traction forces on the substrate through the active periodic motion of molecular complexes to which the linkers bind and unbind stochastically. We first show that the diffusion coefficient of a force dipole (unable by symmetry to perform directed motion) is maximal for a finite ratio of the unbinding to binding rates, highlighting the role of adhesion kinetics on cell translocation. We next show that cells exerting more complex traction force distributions may exhibit directed motion only if the linkers are mechanosensitive, i.e., if the bonds’ lifetime decreases (slip bonds) or increases (catch bonds) under stress. The average migration speed is higher in the catch-bond regime but so are the fluctuations, yielding a biased diffusive motion characterized by a Peclet number smaller than in the slip-bond regime.

Recent magnetic tweezers experiments have reported systematic deviations of the twist response of double-stranded DNA from the predictions of the twistable wormlike chain model. Here we show, by means of analytical results and computer simulations, that these discrepancies can be resolved if a coupling between twist and bend is introduced. We obtain an estimate of $40\pm 10\mathrm{nm}$ for the twist-bend coupling constant. Our simulations are in good agreement with high-resolution, magnetic-tweezers torque data. Although the existence of twist-bend coupling was predicted long ago [J. Marko and E. Siggia, Macromolecules 27, 981 (1994)], its effects on the mechanical properties of DNA have been so far largely unexplored. We expect that this coupling plays an important role in several aspects of DNA statics and dynamics.

We examine the microscopic origin of the tensile response in semicrystalline polymers by performing large-scale molecular dynamics simulations of various chain lengths. We investigate the microscopic rearrangements of the polymers during tensile deformation and show that the intercrystalline chain connections known as tie chains contribute significantly to the elastic and plastic response. These results suggest that the mechanical behavior of semicrystalline polymers is controlled by two interpenetrated networks of entanglements and tie chains.

Densely packed semiflexible polymers with contour length $L$ confined in spheres with radius $R$ of the same order as $L$ cannot exhibit uniform nematic order. Depending on the chain stiffness (which we vary over a wide range), highly distorted structures form with topological defects on the sphere surface. These structures are completely different from previously observed ones of very long chains winding around the inner surface of spheres and from nematic droplets. At high densities, a thin shell of polymers close to the sphere surface exhibits a tennis ball texture due to the confinement-induced gradual bending of polymer bonds. In contrast, when the contour length of the chains is significantly smaller than the radius of the confining sphere, a few bent smectic layers form in the sphere. Molecular dynamics simulations demonstrate these complex structures, and suitable order parameters characterizing them are proposed.

We show how including attraction in interparticle interactions reverses the effect of fluctuations in ordering of a prototypical artificial frustrated system. Buckled colloidal monolayers exhibit the same ground state as the Ising antiferromagnet on a deformable triangular lattice, but it is unclear if ordering in the two systems is driven by the same geometric mechanism. By a real-space expansion we find that, for buckled colloids, bent stripes constitute the stable phase, whereas in the Ising antiferromagnet straight stripes are favored. For generic pair potentials we show that attraction governs this selection mechanism, in a manner that is linked to local packing considerations. This supports the geometric origin of entropy in jammed sphere packings and provides a tool for designing self-assembled colloidal structures.

We demonstrate the continuous translational invariance of the energy of a capillary surface in contact with reconfigurable solid boundaries. We present a theoretical approach to find the energy-invariant equilibria of spherical capillary surfaces in contact with solid boundaries of arbitrary shape and examine the implications of dynamic frictional forces upon a reconfiguration of the boundaries. Experimentally, we realize our ideas by manipulating the position of a droplet in a wedge geometry using lubricant-impregnated solid surfaces, which eliminate the contact-angle hysteresis and provide a test bed for quantifying dissipative losses out of equilibrium. Our experiments show that dissipative energy losses for an otherwise energy-invariant reconfiguration are relatively small, provided that the actuation time scale is longer than the typical relaxation time scale of the capillary surface. We discuss the wider applicability of our ideas as a pathway for liquid manipulation at no potential energy cost in low-pinning, low-friction situations.

We show that real multiplex networks are unexpectedly robust against targeted attacks on high-degree nodes and that hidden interlayer geometric correlations predict this robustness. Without geometric correlations, multiplexes exhibit an abrupt breakdown of mutual connectivity, even with interlayer degree correlations. With geometric correlations, we instead observe a multistep cascading process leading into a continuous transition, which apparently becomes fully continuous in the thermodynamic limit. Our results are important for the design of efficient protection strategies and of robust interacting networks in many domains.