The diffusive epidemic process is a paradigmatic example of an absorbing state phase transition in which healthy and infected individuals spread with different diffusion constants. Using stochastic activity spreading simulations in combination with finite-size scaling analyses we reveal two qualitatively different processes that characterize the critical dynamics: subdiffusive propagation of infection clusters and diffusive fluctuations in the healthy population. This suggests the presence of a strong-coupling regime and sheds new light on a long-standing debate about the theoretical classification of the system.

We analyze the stability of biological membrane tubes, with and without a base flow of lipids. Membrane dynamics are completely specified by two dimensionless numbers: the well-known Föppl–von Kármán number $\mathrm{\Gamma }$ and the recently introduced Scriven–Love number $\text{S}\mathrm{L}$, respectively quantifying the base tension and base flow speed. For unstable tubes, the growth rate of a local perturbation depends only on $\mathrm{\Gamma }$, whereas $\text{S}\mathrm{L}$ governs the absolute versus convective nature of the instability. Furthermore, nonlinear simulations of unstable tubes reveal an initially localized disturbance result in propagating fronts, which leave a thin atrophied tube in their wake. Depending on the value of $\mathrm{\Gamma }$, the thin tube is connected to the unperturbed regions via oscillatory or monotonic shape transitions—reminiscent of recent experimental observations on the retraction and atrophy of axons. We elucidate our findings through a weakly nonlinear analysis, which shows membrane dynamics may be approximated by a model of the class of extended Fisher–Kolmogorov equations. Our study sheds light on the pattern selection mechanism in axonal shapes by recognizing the existence of two Lifshitz points, at which the front dynamics undergo steady-to-oscillatory bifurcations.

Contraction of the cytokinetic ring during cell division leads to physical partitioning of a eukaryotic cell into two daughter cells. This involves flows of actin filaments and myosin motors in the growing membrane interface at the midplane of the dividing cell. Assuming boundary driven alignment of the actomyosin filaments at the inner edge of the interface, we explore how the resulting active stresses influence the flow. Using the continuum gel theory framework, we obtain exact axisymmetric solutions of the dynamical equations. These solutions are consistent with experimental observations on closure rate. Using these solutions, we perform linear stability analysis for the contracting ring under nonaxisymmetric deformations. Our analysis shows that few low wave number modes, which are unstable during onset of the constriction, later on become stable when the ring shrinks to smaller radii, which is a generic feature of actomyosin ring closure. Our theory also captures how the effective tension in the ring decreases with its radius, causing significant slowdown in the contraction process at later times.

We find that a porous piezoelectric medium stabilizes electrodeposition and suppresses dendrite. The effect is 6 orders of magnitude larger than mechanical blocking. We develop a theory integrating electrochemistry, piezoelectricity, and mechanics. A piezoelectric overpotential is derived, which reveals a fundamental relation to surface charge density, dielectric property of the medium, electrolyte concentration and diffusivity, and the reaction coefficient. The simulations show that piezoelectric medium suppresses electrodeposition on any protrusion, leading to a flat, dendrite-free surface.

We report the formation of “ripple” patterns by the sequential superposition of nonorthogonal surface waves excited by the spontaneous buckling of polymeric bilayers. Albeit of a different nature and micron scale compared to the familiar sedimentary ripples caused by gentle wave oscillations, we find commonalities in their topography, defects, and bifurcations. The patterns are rationalized in terms of a defect density that depends on the relative angle between generations, and a constant in-plane bending angle that depends on skin thickness. A minimal wave summation model enables the design of ripple and checkerboard surfaces by tuning material properties and fabrication process.

We explore the relationship between the nonequilibrium generation of myosin-induced active stress within the $F$-actin cytoskeleton and the pressure-volume relationship of cellular aggregates as models of simple tissues. We find that due to active stress, aggregate surface tension depends upon its size. As a result, both pressure and cell number density depend on size and violate equilibrium assumptions. However, the relationship between them resembles an equilibrium equation of state with an effective temperature. This suggests that bulk and surface properties of aggregates balance to yield a constant average work performed by each cell on their environment in regulating tissue size. These results describe basic physical principles that govern the size of cell aggregates.

Turbulent vortex structures emerging in bacterial active fluids can be organized into regular vortex lattices by weak geometrical constraints such as obstacles. Here we show, using a continuum-theoretical approach, that the formation and destruction of these patterns exhibit features of a continuous second-order equilibrium phase transition, including long-range correlations, divergent susceptibility, and critical slowing down. The emerging vorticity field can be mapped onto a two-dimensional (2D) Ising model with antiferromagnetic nearest-neighbor interactions by coarse graining. The resulting effective temperature is found to be proportional to the strength of the nonlinear advection in the continuum model.

The vibrational eigenmodes of dumbbell-shaped polystyrene nanoparticles are recorded by Brillouin light spectroscopy (BLS), and the full experimental spectra are calculated theoretically. Different from spheres with a degeneracy of ($2l+1$), with $l$ being the angular momentum quantum number, the eigenmodes of dumbbells are either singly or doubly degenerate owing to their axial symmetry. The BLS spectrum reveals a new, low-frequency peak, which is attributed to the out-of-phase vibration of the two lobes of the dumbbell. The quantization of acoustic modes in these molecule-shaped dumbbell particles evolves from the primary colloidal spheres as the separation between the two lobes increases.

We use numerical simulations and linear stability analysis to study an active nematic layer where the director is allowed to point out of the plane. Our results highlight the difference between extensile and contractile systems. Contractile stress suppresses the flows perpendicular to the layer and favors in-plane orientations of the director. By contrast extensile stress promotes instabilities that can turn the director out of the plane, leaving behind a population of distinct, in-plane regions that continually elongate and divide. This supports extensile forces as a mechanism for the initial stages of layer formation in living systems, and we show that a planar drop with extensile (contractile) activity grows into three dimensions (remains in two dimensions). The results also explain the propensity of disclination lines in three dimensional active nematics to be of twist type in extensile or wedge type in contractile materials.

The effective interactions between the constituents of driven soft matter generically defy Newton’s third law. Combining theory and numerical simulations, we establish that six classes of mechanics with no counterparts in equilibrium systems emerge in elastic crystals challenged by nonreciprocal interactions. Going beyond linear deformations, we reveal that interactions violating Newton’s third law generically turn otherwise quiescent dislocations into motile singularities which steadily glide though periodic lattices.

Stochastic protein accumulation up to some concentration threshold sets the timing of many cellular physiological processes. Here we obtain the exact distribution of first threshold crossing times of protein concentration, in either Laplace or time domain, and its associated cumulants: mean, variance, and skewness. The distribution is asymmetric, and its skewness nonmonotonically varies with the threshold. We study lysis times of E. coli cells for holin gene mutants of bacteriophage-$\lambda$ and find a good match with theory. Mutants requiring higher holin thresholds show more skewed lysis time distributions as predicted. The theory also predicts a linear relationship between infection delay time and host doubling time for lytic viruses, that has recently been experimentally observed.

Multivalent associative proteins with strong complementary interactions play a crucial role in phase separation of intracellular liquid condensates. We study the internal dynamics of such “bond-network” condensates comprising two complementary proteins via scaling analysis and molecular dynamics. We find that when stoichiometry is balanced, relaxation slows down dramatically due to a scarcity of alternative binding partners following bond breakage. This microscopic slow-down strongly affects the bulk diffusivity, viscosity, and mixing, which provides a means to experimentally test this prediction.

We calculate the diffusion coefficient of an active tracer in a schematic crowded environment, represented as a lattice gas of passive particles with hardcore interactions. Starting from the master equation of the problem, we put forward a closure approximation that goes beyond trivial mean field and provides the diffusion coefficient for an arbitrary density of crowders in the system. We show that our approximation is accurate for a very wide range of parameters, and that it correctly captures numerous nonequilibrium effects, which are the signature of the activity in the system. In addition to the determination of the diffusion coefficient of the tracer, our approach allows us to characterize the perturbation of the environment induced by the displacement of the active tracer. Finally, we consider the asymptotic regimes of low and high densities, in which the expression of the diffusion coefficient of the tracer becomes explicit, and which we argue to be exact.

Chromosomes in the nucleus assemble into hierarchies of 3D domains that, during interphase, share essential features with a knot-free condensed polymer known as the fractal globule (FG). The FG-like chromosome likely affects macromolecular transport, yet its characteristics remain poorly understood. Using computer simulations and scaling analysis, we show that the 3D folding and macromolecular size of the chromosomes determine their transport characteristics. Large-scale subdiffusion occurs at a critical particle size where the network of accessible volumes is critically connected. Condensed chromosomes have connectivity networks akin to simple Bernoulli bond percolation clusters, regardless of the polymer models. However, even if the network structures are similar, the tracer’s walk dimension varies. It turns out that the walk dimension depends on the network topology of the accessible volume and dynamic heterogeneity of the tracer’s hopping rate. We find that the FG structure has a smaller walk dimension than other random geometries, suggesting that the FG-like chromosome structure accelerates macromolecular diffusion and target-search.