A tragedy of the commons (TOC) occurs when individuals acting in their own self-interest deplete commonly held resources, leading to a worse outcome than had they cooperated. Over time, the depletion of resources can change incentives for subsequent actions. Here, we investigate long-term feedback between game and environment across a continuum of incentives in an individual-based framework. We identify payoff-dependent transition rules that lead to oscillatory TOCs in stochastic simulations and the mean field limit. Further extending the stochastic model, we find that spatially explicit interactions can lead to emergent, localized dynamics, including the propagation of cooperative wave fronts and cluster formation of both social context and resources. These dynamics suggest new mechanisms underlying how TOCs arise and how they might be averted.

We present a statistical analysis of the experimental trajectories of colloids in a dilute suspension of the green algae Chlamydomonas reinhardtii. The measured probability density function (pdf) of the displacements of colloids covers 7 orders of magnitude. The pdfs are characterized by non-Gaussian tails for intermediate time intervals, but nevertheless they collapse when scaled with their standard deviation. This diffusive scaling breaks down for longer time intervals and the pdf becomes Gaussian. However, the mean squared displacements of tracer positions are linear over the complete measurement time interval. Experiments are performed for various tracer diameters, swimmer concentrations, and mean swimmer velocities. This allows a rigorous comparison with several theoretical models. We can exclude a description based on an effective temperature and other mean field approaches that describe the irregular motion as a sum of the fluctuating far field of many microswimmers. The data are best described by the microscopic model by J.-L. Thiffeault, Distribution of particle displacements due to swimming microorganisms, Phys. Rev. E 92, 023023 (2015).

Spatial confinement is known to affect molecular organizations of soft matter. We present an important manifestation of this statement for thin films of bent-core smectic liquid crystals. Prior freeze-fracture transmission electron microscopy (FFTEM) studies carried out on nitro-substituted bent-core mesogens ($n\text{−}\mathrm{OPIMB}\text{−}{\mathrm{NO}}_2$) revealed an undulated smectic layer structure with an undulation periodicity of $\sim 8\mathrm{nm}$. We report cryogenic TEM measurements on $\sim 100\mathrm{nm}$ thick $8\text{−}\mathrm{OPIMB}\text{−}{\mathrm{NO}}_2$ films. In contrast to FFTEM results, our studies show only density modulation with periodicity $b=16.2\mathrm{nm}$, and no smectic layer undulation. We show that the discrepancy between the FFTEM and cryogenic transmission electron microscopy (cryo-TEM) results can be attributed to the different sample thicknesses used in the experiments. FFTEM monitors cracked surfaces of a relatively thick ($5–10\mu \mathrm{m}$) frozen sample, whereas cryo-TEM visualizes the volume of a thin ($0.1\mu \mathrm{m}$) film that was quenched from its partially fluid phase. These results have importance in possible photovoltaics and organic electronics applications where submicron thin films are used.

Dispersions of rodlike colloidal particles exhibit a plethora of liquid crystalline states, including nematic, smectic $A$, smectic $B$, and columnar phases. This phase behavior can be explained by presuming the predominance of hard-core volume exclusion between the particles. We show here how the self-organization of rodlike colloids can be controlled by introducing a weak and highly localized directional attractive interaction between one of the ends of the particles. This has been performed by functionalizing the tips of filamentous viruses by means of regioselectively grafting fluorescent dyes onto them, resulting in a hydrophobic patch whose attraction can be tuned by varying the number of bound dye molecules. We show, in agreement with our computer simulations, that increasing the single tip attraction stabilizes the smectic phase at the expense of the nematic phase, leaving all other liquid crystalline phases invariant. For a sufficiently strong tip attraction, the nematic state may be suppressed completely to get a direct isotropic liquid-to-smectic phase transition. Our findings provide insights into the rational design of building blocks for functional structures formed at low densities.

The discontinuous jump in the bulk modulus $B$ at the jamming transition is a consequence of the formation of a critical contact network of spheres that resists compression. We introduce lattice models with underlying undercoordinated compression-resistant spring lattices to which next-nearest-neighbor springs can be added. In these models, the jamming transition emerges as a kind of multicritical point terminating a line of rigidity-percolation transitions. Replacing the undercoordinated lattices with the critical network at jamming yields a faithful description of jamming and its relation to rigidity percolation.

We examine the static dielectric constant of electrolyte solutions with a polar and/or polarizable small-molecule solvent using a classical field-theoretic approach. We compute corrections to the dielectric constant and screening length due to intra- and intermolecular correlations via a renormalized one-loop approximation, accounting for the excluded volume of both solvent and electrolyte. In the salt-free case, we verify the one-loop theory by comparison with full numerical solutions of the field theory. The one-loop theory predicts either a nonlinear dielectric decrement or increment with increasing salt, depending on whether the fluid correlations are dominated by the dipolar or polarizable nature of the solvent. These contrasting regimes of nonlinear dielectric behavior are consistent with experimental trends in high- and low-dielectric constant electrolyte solutions.

The more we learn about the cytoplasm of cells, the more we realize that the cytoplasm is not uniform but instead is highly inhomogeneous. In any inhomogeneous solution, there are concentration gradients, and particles move either up or down these gradients due to a mechanism called diffusiophoresis. I estimate that inside metabolically active cells, the dynamics of particles can be strongly accelerated by diffusiophoresis, provided that they are at least tens of nanometers across. The dynamics of smaller objects, such as single proteins, are largely unaffected.

Fluids in which both time reversal and parity are broken can display a dissipationless viscosity that is odd under each of these symmetries. Here, we show how this odd viscosity has a dramatic effect on topological sound waves in fluids, including the number and spatial profile of topological edge modes. Odd viscosity provides a short-distance cutoff that allows us to define a bulk topological invariant on a compact momentum space. As the sign of odd viscosity changes, a topological phase transition occurs without closing the bulk gap. Instead, at the transition point, the topological invariant becomes ill defined because momentum space cannot be compactified. This mechanism is unique to continuum models and can describe fluids ranging from electronic to chiral active systems.

Microflows constitute an important instrument to control particle dynamics. A prominent example is the sorting of biological cells, which relies on the ability of deformable cells to move transversely to flow lines. A classic result is that soft microparticles migrate in flows through straight microchannels to an attractor at their center. Here, we show that flows through wavy channels fundamentally change the overall picture. They lead to the emergence of a second, coexisting attractor for soft particles. Its emergence and off-center location depends on the boundary modulation and the particle properties. The related cross-stream migration of soft particles is explained by analytical considerations, Stokesian dynamics simulations in unbounded flows, and Lattice-Boltzmann simulations in bounded flows. The novel off-center attractor can be used, for instance, in diagnostics, for separating cells of different size and elasticity, which is often an indicator of their health status.

We report on spontaneous rotational symmetry breaking in a minimal model of complex macromolecules with branches and cycles. The transition takes place as the strength of the self-repulsion is increased. At the transition point, the density distribution transforms from isotropic to anisotropic. We analyze this transition using a variational mean-field theory that combines the Gibbs-Bogolyubov-Feynman inequality with the concept of the Laplacian matrix. The density distribution of the broken symmetry state is shown to be determined by the eigenvalues and eigenvectors of this Laplacian matrix. Physically, this reflects the increasing role of the underlying topological structure in determining the density of the macromolecule when repulsive interactions generate internal tension. Eventually, the variational free energy landscape develops a complex structure with multiple competing minima.

Topological quantum and classical materials can exhibit robust properties that are protected against disorder, for example, for noninteracting particles and linear waves. Here, we demonstrate how to construct topologically protected states that arise from the combination of strong interactions and thermal fluctuations inherent to soft materials or miniaturized mechanical structures. Specifically, we consider fluctuating lines under tension (e.g., polymer or vortex lines), subject to a class of spatially modulated substrate potentials. At equilibrium, the lines acquire a collective tilt proportional to an integer topological invariant called the Chern number. This quantized tilt is robust against substrate disorder, as verified by classical Langevin dynamics simulations. This robustness arises because excitations in this system of thermally fluctuating lines are gapped by virtue of interline interactions. We establish the topological underpinning of this pattern via a mapping that we develop between the interacting-lines system and a hitherto unexplored generalization of Thouless pumping to imaginary time. Our work points to a new class of classical topological phenomena in which the topological signature manifests itself in a structural property observed at finite temperature rather than a transport measurement.

We study the effect of correlations in generation times on the dynamics of population growth of microorganisms. We show that any nonzero correlation that is due to cell-size regulation, no matter how small, induces long-term oscillations in the population growth rate. The population only reaches its steady state when we include the often-neglected variability in the growth rates of individual cells. We discover that the relaxation timescale of the population to its steady state is determined by the distribution of single-cell growth rates and is surprisingly independent of details of the division process such as the noise in the timing of division and the mechanism of cell-size regulation. We validate the predictions of our model using existing experimental data and propose an experimental method to measure single-cell growth variability by observing how long it takes for the population to reach its steady state or balanced growth.

We investigated the dynamics of polymer-grafted gold nanoparticles loaded into polymer melts using x-ray photon correlation spectroscopy. For low molecular weight host matrix polymer chains, normal isotropic diffusion of the gold nanoparticles is observed. For larger molecular weights, anomalous diffusion of the nanoparticles is observed that can be described by ballistic motion and generalized Lévy walks, similar to those often used to discuss the dynamics of jammed systems. Under certain annealing conditions, the diffusion is one-dimensional and related to the direction of heat flow during annealing and is associated with an dynamic alignment of the host polymer chains. Molecular dynamics simulations of a single gold nanoparticle diffusing in a partially aligned polymer network semiquantitatively reproduce the experimental results to a remarkable degree. The results help to showcase how nanoparticles can under certain circumstances move rapidly in polymer networks.

Collections of bidisperse frictionless particles at zero temperature in three dimensions are simulated with a shear-driven dynamics with the aim to compare with the behavior in two dimensions. Contrary to the prevailing picture, and in contrast to results from isotropic jamming from compression or quench, we find that the critical exponents in three dimensions are different from those in two dimensions and conclude that shear-driven jamming in two and three dimensions belong to different universality classes.

Extinction is the ultimate absorbing state of any stochastic birth-death process; hence, the time to extinction is an important characteristic of any natural population. Here we consider logistic and logisticlike systems under the combined effect of demographic and bounded environmental stochasticity. Three phases are identified: an inactive phase where the mean time to extinction $T$ increases logarithmically with the initial population size, an active phase where $T$ grows exponentially with the carrying capacity $N$, and a temporal Griffiths phase, with a power-law relationship between $T$ and $N$. The system supports an exponential phase only when the noise is bounded, in which case the continuum (diffusion) approximation breaks down within the Griffiths phase. This breakdown is associated with a crossover between qualitatively different survival statistics and decline modes. To study the power-law phase we present a new WKB scheme, which is applicable both in the diffusive and in the nondiffusive regime.

Using a large database of 8 million institutional trades executed in the U.S. equity market, we establish a clear crossover between a linear market impact regime and a square-root regime as a function of the volume of the order. Our empirical results are remarkably well explained by a recently proposed dynamical theory of liquidity that makes specific predictions about the scaling function describing this crossover. Allowing at least two characteristic timescales for the liquidity (“fast” and “slow”) enables one to reach quantitative agreement with the data.