Kinetically constrained models are lattice-gas models that are used for describing glassy systems. By construction, their equilibrium state is trivial and there are no equal-time correlations between the occupancy of different sites. We drive such models out of equilibrium by connecting them to two reservoirs of different densities, and we measure the response of the system to this perturbation. We find that under the proper coarse-graining, the behavior of these models may be expressed by a nonlinear diffusion equation, with a model- and density-dependent diffusion coefficient. We find a simple approximation for the diffusion coefficient, and we show that the relatively mild discrepancy between the approximation and our numerical results arises due to non-negligible correlations that appear as the system is driven out of equilibrium, even when the density gradient is infinitesimally small. Similar correlations appear when such kinetically constrained models are driven out of equilibrium by applying a uniform external force. We suggest that these correlations are the reason for the same discrepancy between the approximate diffusion coefficient and the numerical results for a broader group of models—nongradient lattice-gas models—for which kinetically constrained models are arguably the simplest example thereof.

Mixing in smoothly deforming systems is achieved by repeated stretching and folding of material, and has been widely studied. However, for the classes of materials that also admit discontinuous deformation, the theory of mixing based on the assumption of smooth deformation does not apply. Discontinuous deformation provides additional topological freedom for material transport and results in different Lagrangian coherent structures forbidden in smoothly deforming systems. We uncover the impact of discontinuous deformation on mixing rates, showing that mixing can be either enhanced or impeded depending on the local stability of the underlying smooth map.

Bacteria such as Vibrio alginolyticus swim through a fluid by utilizing the rotational motion of their helical flagellum driven by a rotary motor. The flagellar motor is embedded in the cell body and turns either clockwise (CW) or counterclockwise (CCW), which may lead to straight forward or backward swimming, or reorientation of the cell. In this paper we investigate the dynamics of the helical flagellum by adopting the Kirchhoff rod theory in which the flagellum is described as a space curve associated with orthonormal triads that measure the degree of bending and twisting of the rod. The hydrodynamic interaction with the flagellum is described by the regularized Stokes formulation. We focus on two different types of instabilities: (1) whirling instability of a rotating helical filament in the absence of a hook and (2) buckling instability of a flagellum in the presence of a compliant hook that links the flagellar filament to the rotary motor. Our simulation results show that the helical filament without a hook displays three regimes of dynamical motions: stable twirling, unstable whirling, and stable overwhirling motions depending on the physical parameters, such as rotational frequency and elastic properties of the flagellum. The helical filament with a hook experiences buckling instability when the motor switches the direction of rotation and the elastic properties of the hook change. Variations of physical parameter values of the hook such as the bending modulus and the length make an impact on the buckling angle, which may subsequently affect the reorientation of the cell.

Molecular motors and cytoskeletal filaments work collectively most of the time under opposing forces. This opposing force may be due to cargo carried by motors or resistance coming from the cell membrane pressing against the cytoskeletal filaments. Some recent studies have shown that the collective maximum force (stall force) generated by multiple cytoskeletal filaments or molecular motors may not always be just a simple sum of the stall forces of the individual filaments or motors. To understand this excess or deficit in the collective force, we study a broad class of models of both cytoskeletal filaments and molecular motors. We argue that the stall force generated by a group of filaments or motors is additive, that is, the stall force of $N$ number of filaments (motors) is $N$ times the stall force of one filament (motor), when the system is reversible at stall. Conversely, we show that this additive property typically does not hold true when the system is irreversible at stall. We thus present a novel and unified understanding of the existing models exhibiting such non-addivity, and generalise our arguments by developing new models that demonstrate this phenomena. We also propose a quantity similar to thermodynamic efficiency to easily predict this deviation from stall-force additivity for filament and motor collectives.

The response properties of excitable systems driven by colored noise are of great interest, but are usually mathematically only accessible via approximations. For this reason, dichotomous noise, a rare example of a colored noise leading often to analytically tractable problems, has been extensively used in the study of stochastic systems. Here, we calculate exact expressions for the power spectrum and the susceptibility of a leaky integrate-and-fire neuron driven by asymmetric dichotomous noise. While our results are in excellent agreement with simulations, they also highlight a limitation of using dichotomous noise as a simple model for more complex fluctuations: Both power spectrum and susceptibility exhibit an undamped periodic structure, the origin of which we discuss in detail.

Completely open systems can exchange heat, work, and matter with the environment. While energy, volume, and number of particles fluctuate under completely open conditions, the equilibrium states of the system, if they exist, can be specified using the temperature, pressure, and chemical potential as control parameters. The unconstrained ensemble is the statistical ensemble describing completely open systems and the replica energy is the appropriate free energy for these control parameters from which the thermodynamics must be derived. It turns out that macroscopic systems with short-range interactions cannot attain equilibrium configurations in the unconstrained ensemble, since temperature, pressure, and chemical potential cannot be taken as a set of independent variables in this case. In contrast, we show that systems with long-range interactions can reach states of thermodynamic equilibrium in the unconstrained ensemble. To illustrate this fact, we consider a modification of the Thirring model and compare the unconstrained ensemble with the canonical and grand-canonical ones: The more the ensemble is constrained by fixing the volume or number of particles, the larger the space of parameters defining the equilibrium configurations.

We establish a link between the phenomenon of Taylor dispersion and the theory of empirical distributions. Using this connection, we derive, upon applying the theory of large deviations, an alternative and much more precise description of the long-time regime for Taylor dispersion.

While Flory theories [J. Isaacson and T. C. Lubensky, J. Physique Lett. 41, 469 (1980); M. Daoud and J. F. Joanny, J. Physique 42, 1359 (1981); A. M. Gutin et al., Macromolecules 26, 1293 (1993)] provide an extremely useful framework for understanding the behavior of interacting, randomly branching polymers, the approach is inherently limited. Here we use a combination of scaling arguments and computer simulations to go beyond a Gaussian description. We analyze distribution functions for a wide variety of quantities characterizing the tree connectivities and conformations for the four different statistical ensembles, which we have studied numerically in [A. Rosa and R. Everaers, J. Phys. A: Math. Theor. 49, 345001 (2016) and J. Chem. Phys. 145, 164906 (2016)]: (a) ideal randomly branching polymers, (b) $2d$ and $3d$ melts of interacting randomly branching polymers, (c) $3d$ self-avoiding trees with annealed connectivity, and (d) $3d$ self-avoiding trees with quenched ideal connectivity. In particular, we investigate the distributions (i) $p_N\left(n\right)$ of the weight, $n$, of branches cut from trees of mass $N$ by severing randomly chosen bonds; (ii) $p_N\left(l\right)$ of the contour distances, $l$, between monomers; (iii) $p_N\left(\vec{r}\right)$ of spatial distances, $\vec{r}$, between monomers, and (iv) $p_N\left(\vec{r}\right|l)$ of the end-to-end distance of paths of length $l$. Data for different tree sizes superimpose, when expressed as functions of suitably rescaled observables $\vec{x}=\vec{r}/\sqrt{\langle r^2\left(N\right)\rangle }$ or $x=l/\langle l\left(N\right)\rangle$. In particular, we observe a generalized Kramers relation for the branch weight distributions (i) and find that all the other distributions (ii–iv) are of Redner-des Cloizeaux type, $q\left(\vec{x}\right)=C{\left|x\right|}^{\theta }exp\left(-{\left(K\right|x\left|\right)}^t\right)$. We propose a coherent framework, including generalized Fisher-Pincus relations, relating most of the RdC exponents to each other and to the contact and Flory exponents for interacting trees.

Origami folded cylinders (origami bellows) have found increasingly sophisticated applications in space flight and medicine. In spite of this interest, a general understanding of the mechanics of an origami folded cylinder has been elusive. With a newly developed set of geometrical tools, we have found an analytic solution for all possible cylindrical rigid-face states of both Miura-ori and triangular tessellations. Although an idealized bellows in both of these families may have two allowed rigid-face configurations over a well-defined region, the corresponding physical device, limited by nonzero material thickness and forced to balance hinge and plate-bending energy, often cannot stably maintain a stowed configuration. We have identified the parameters that control this emergent bistability, and we have demonstrated the ability to design and fabricate bellows with tunable deployability.

We study a minimal model of a crawling eukaryotic cell with a chemical polarity controlled by a reaction-diffusion mechanism describing Rho GTPase dynamics. The size, shape, and speed of the cell emerge from the combination of the chemical polarity, which controls the locations where actin polymerization occurs, and the physical properties of the cell, including its membrane tension. We find in our model both highly persistent trajectories, in which the cell crawls in a straight line, and turning trajectories, where the cell transitions from crawling in a line to crawling in a circle. We discuss the controlling variables for this turning instability and argue that turning arises from a coupling between the reaction-diffusion mechanism and the shape of the cell. This emphasizes the surprising features that can arise from simple links between cell mechanics and biochemistry. Our results suggest that similar instabilities may be present in a broad class of biochemical descriptions of cell polarity.

The matching problem is a notorious combinatorial optimization problem that has attracted for many years the attention of the statistical physics community. Here we analyze the Euclidean version of the problem, i.e., the optimal matching problem between points randomly distributed on a $d$-dimensional Euclidean space, where the cost to minimize depends on the points' pairwise distances. Using Mayer's cluster expansion we write a formal expression for the replicated action that is suitable for a saddle point computation. We give the diagrammatic rules for each term of the expansion, and we analyze in detail the one-loop diagrams. A characteristic feature of the theory, when diagrams are perturbatively computed around the mean field part of the action, is the vanishing of the mass at zero momentum. In the non-Euclidean case of uncorrelated costs instead, we predict and numerically verify an anomalous scaling for the sub-sub-leading correction to the asymptotic average cost.

After establishing stochastic thermodynamics for underdamped Langevin systems in contact with multiple reservoirs, we derive its overdamped limit using timescale separation techniques. The overdamped theory is different from the naive theory that one obtains when starting from overdamped Langevin or Fokker-Planck dynamics and only coincides with it in the presence of a single reservoir. The reason is that the coarse-grained fast momentum dynamics reaches a nonequilibrium state, which conducts heat in the presence of multiple reservoirs. The underdamped and overdamped theory are both shown to satisfy fundamental fluctuation theorems. Their predictions for the heat statistics are derived analytically for a Brownian particle on a ring in contact with two reservoirs and subjected to a nonconservative force and are shown to coincide in the long-time limit.

The dislocation and disclination density defining the structure of a crystal constrained on a general curved background is computed analytically in the thermodynamic limit, when the number of particles is arbitrarily large. It is shown that the minimum of the elastic energy, where strains are optimally close to zero, can be formulated in terms of a connection (a rule on how to parallel transport vectors), which allows to provide an explicit solution in the thermodynamic limit that consists of disclinations surrounded by scars (grain boundaries with variable spacing). The approach allows to compute the interaction potential. For a sphere, a full characterization of the scars is provided, and it is shown that the potential of interaction among disclinations “dressed” by scars is inversely proportional to the sinus of the geodesic distance and that the ground state consists of 12 dressed disclinations that display icosahedral symmetry. The case of a torus is also considered. More generally, the thermodynamic solution implements a “perfect screening” condition, where defects completely screen the Gaussian curvature. Implications for the problem of melting are discussed.

We introduce a growing network model, the copying model, in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When $p<\frac{1}{2}$, this algorithm generates sparse networks, in which the average node degree is finite. A power-law degree distribution also arises, with a nonuniversal exponent whose value is determined by a transcendental equation in $p$. In the sparse regime, the network is “normal,” e.g., the relative fluctuations in the number of links are asymptotically negligible. For $p\ge \frac{1}{2}$, the emergent networks are dense (the average degree increases with the number of nodes $N$), and they exhibit intriguing structural behaviors. In particular, the $N$ dependence of the number of $m$ cliques (complete subgraphs of $m$ nodes) undergoes $m-1$ transitions from normal to progressively more anomalous behavior at an $m$-dependent critical values of $p$. Different realizations of the network, which start from the same initial state, exhibit macroscopic fluctuations in the thermodynamic limit: absence of self-averaging. When linking to second neighbors of the target node can occur, the number of links asymptotically grows as $N^2$ as $N\to \infty$, so that the network is effectively complete as $N\to \infty$.

We demonstrate an equivalence between two widely used methods of community detection in networks, the method of modularity maximization and the method of maximum likelihood applied to the degree-corrected stochastic block model. Specifically, we show an exact equivalence between maximization of the generalized modularity that includes a resolution parameter and the special case of the block model known as the planted partition model, in which all communities in a network are assumed to have statistically similar properties. Among other things, this equivalence provides a mathematically principled derivation of the modularity function, clarifies the conditions and assumptions of its use, and gives an explicit formula for the optimal value of the resolution parameter.

Long-ranged correlations generically exist in nonequilibrium fluid systems. In the case of a nonequilibrium steady state caused by a temperature gradient, the correlations are especially long-ranged and strong. The anomalous light scattering predicted to exist in these systems is well-confirmed by numerous experiments. Recently, the Casimir force or pressure due to these fluctuations or correlations has been discussed in great detail. In this paper, the notion of a Casimir work is introduced, and an alternative way to measure the nonequilibrium Casimir force is suggested. In particular, the nonequilibrium Casimir force is related to nonequilibrium heat, and not, as in equilibrium, to a volume derivative of an average energy. The nonequilibrium work fluctuations are determined and shown to be very anomalous compared to equilibrium work fluctuations. The nonequilibrium work distribution is also computed, and it is contrasted with work distributions in systems with short-range correlations. Again, there is a striking difference in the two cases. Formal theories of work and work distributions in nonequilibrium steady states are not explicit enough to illustrate any of these interesting features.

Localized fragmentation is an important phenomenon associated with the formation of shear bands and faults in granular media. It can be studied by empirical observation, by laboratory experiment, or by numerical simulation. Here we investigate the spatial structure and statistics of fragmentation using discrete element simulations of the strain-controlled uniaxial compression of cylindrical samples of different finite size. As the system approaches failure, damage localizes in a narrow shear band or synthetic fault “gouge” containing a large number of poorly sorted noncohesive fragments on a broad bandwidth of scales, with properties similar to those of natural and experimental faults. We determine the position and orientation of the central fault plane, the width of the shear band, and the spatial and mass distribution of fragments. The relative width of the shear band decreases as a power law of the system size, and the probability distribution of the angle of the central fault plane converges to around 30 degrees, representing an internal coefficient of friction of 0.7 or so. The mass of fragments is power law distributed, with an exponent that does not depend on scale, and is near that inferred for experimental and natural fault gouges. The fragments are in general angular, with a clear self-affine geometry. The consistency of this model with experimental and field results confirms the critical roles of preexisting heterogeneity, elastic interactions, and finite system size to grain size ratio on the development of shear bands and faults in porous media.

The effective interaction between two planar walls immersed in a fluid is investigated by use of density functional theory in the supercritical region of the phase diagram. A hard core Yukawa model of fluid is studied with special attention to the critical region. To achieve this goal a formulation of the weighted density approximation coupled with the hierarchical reference theory, able to deal with critical long wavelength fluctuations, is put forward and compared with other approaches. The effective interaction between the walls is seen to change character on lowering the temperature: The strong oscillations induced by layering of the molecules, typical of the depletion mechanism in hard core systems, are gradually smoothed and, close to the critical point, a long range attractive tail emerges leading to a scaling form which agrees with the expectations based on the critical Casimir effect. Strong corrections to scaling are seen to affect the results up to very small reduced temperatures. By use of the Derjaguin approximation, this investigation has natural implications for the aggregation of colloidal particles in critical solvents.

The universal asymptotic amplitude ratio between the gyration radius and the hydrodynamic radius of self-avoiding walks is estimated by high-resolution Monte Carlo simulations. By studying chains of length of up to $N=2^{25}\approx 34\times {10}^6$ monomers, we find that the ratio takes the value $R_{\mathrm{G}}/R_{\mathrm{H}}=1.5803940\left(45\right)$, which is several orders of magnitude more accurate than the previous state of the art. This is facilitated by a sampling scheme which is quite general and which allows for the efficient estimation of averages of a large class of observables. The competing corrections to scaling for the hydrodynamic radius are clearly discernible. We also find improved estimates for other universal properties that measure the chain dimension. In particular, a method of analysis which eliminates the leading correction to scaling results in a highly accurate estimate for the Flory exponent of $\nu =0.58759700\left(40\right)$.

In this paper we propose a Monte Carlo method for generating finite-domain marginals of critical distributions of statistical models in infinite volume. The algorithm corrects the problem of the long-range effects of boundaries associated to generating critical distributions on finite lattices. It uses the advantage of scale invariance combined with ideas of the renormalization group in order to construct a type of “holographic” boundary condition that encodes the presence of an infinite volume beyond it. We check the quality of the distribution obtained in the case of the planar Ising model by comparing various observables with their infinite-plane prediction. We accurately reproduce planar two-, three-, and four-point of spin and energy operators. We also define a lattice stress-energy tensor, and numerically obtain the associated conformal Ward identities and the Ising central charge.