The nature of non-phononic excitations in disordered systems.

The frequency scaling exponent of low-frequency excitations in microscopically small glasses, which do not allow for the existence of waves (phonons), has been in the focus of the recent literature. The density of states g(ω) of these modes obeys an ωs scaling, where the exponent s, ranging between 2 and 5, depends on the quenching protocol. The orgin of these findings remains controversal. Here we show, using heterogeneous-elasticity theory, that in a marginally-stable glass sample g(ω) follows a Debye-like scaling (s = 2), and the associated excitations (type-I) are of random-matrix type. Further, using a generalisation of the theory, we demonstrate that in more stable samples, other, (type-II) excitations prevail, which are non-irrotational oscillations, associated with local frozen-in stresses. The corresponding frequency scaling exponent s is governed by the statistics of small values of the stresses and, therefore, depends on the details of the interaction potential.

Collective behavior and self-organization in neural rosette morphogenesis.

Neural rosettes develop from the self-organization of differentiating human pluripotent stem cells. This process mimics the emergence of the embryonic central nervous system primordium, i.e., the neural tube, whose formation is under close investigation as errors during such process result in severe diseases like spina bifida and anencephaly. While neural tube formation is recognized as an example of self-organization, we still do not understand the fundamental mechanisms guiding the process. Here, we discuss the different theoretical frameworks that have been proposed to explain self-organization in morphogenesis. We show that an explanation based exclusively on stem cell differentiation cannot describe the emergence of spatial organization, and an explanation based on patterning models cannot explain how different groups of cells can collectively migrate and produce the mechanical transformations required to generate the neural tube. We conclude that neural rosette development is a relevant experimental 2D in-vitro model of morphogenesis because it is a multi-scale self-organization process that involves both cell differentiation and tissue development. Ultimately, to understand rosette formation, we first need to fully understand the complex interplay between growth, migration, cytoarchitecture organization, and cell type evolution.

Colloidal transport by light induced gradients of active pressure.

Active fluids, like all other fluids, exert mechanical pressure on confining walls. Unlike equilibrium, this pressure is generally not a function of the fluid state in the bulk and displays some peculiar properties. For example, when activity is not uniform, fluid regions with different activity may exert different pressures on the container walls but they can coexist side by side in mechanical equilibrium. Here we show that by spatially modulating bacterial motility with light, we can generate active pressure gradients capable of transporting passive probe particles in controlled directions. Although bacteria swim faster in the brighter side, we find that bacteria in the dark side apply a stronger pressure resulting in a net drift motion that points away from the low activity region. Using a combination of experiments and numerical simulations, we show that this drift originates mainly from an interaction pressure term that builds up due to the compression exerted by a layer of polarized cells surrounding the slow region. In addition to providing new insights into the generalization of pressure for interacting systems with non-uniform activity, our results demonstrate the possibility of exploiting active pressure for the controlled transport of microscopic objects.

Most probable path of active Ornstein-Uhlenbeck particles.

Using the path integral representation of the nonequilibrium dynamics, we compute the most probable path between arbitrary starting and final points that is followed by an active particle driven by persistent noise. We focus our attention on the case of active particles immersed in harmonic potentials, where the trajectory can be computed analytically. Once we consider the extended Markovian dynamics where the self-propulsive drive evolves according to an Ornstein-Uhlenbeck process, we can compute the trajectory analytically with arbitrary conditions on position and self-propulsion velocity. We test the analytical predictions against numerical simulations and we compare the analytical results with those obtained within approximated equilibriumlike dynamics.

Scaling of the entropy production rate in a φ

In active φ^{4} field theories the nonequilibrium terms play an important role in describing active phase separation; however, they are irrelevant, in the renormalization group sense, at the critical point. Their irrelevance makes the critical exponents the same as those of the Ising universality class. Despite their irrelevance, they contribute to a nontrivial scaling of the entropy production rate at criticality. We consider the nonequilibrium dynamics of a nonconserved scalar field φ (Model A) driven out-of-equilibrium by a persistent noise that is correlated on a finite timescale τ, as in the case of active baths. We perform the computation of the density of entropy production rate σ and we study its scaling near the critical point. We find that similar to the case of active Model A, and although the nonlinearities responsible for nonvanishing entropy production rates in the two models are quite different, the irrelevant parameter τ makes the critical dynamics irreversible.

A single-agent extension of the SIR model describes the impact of mobility restrictions on the COVID-19 epidemic.

Mobility restrictions are successfully used to contain the diffusion of epidemics. In this work we explore their effect on the epidemic growth by investigating an extension of the Susceptible-Infected-Removed (SIR) model in which individual mobility is taken into account. In the model individual agents move on a chessboard with a Lévy walk and, within each square, epidemic spreading follows the standard SIR model. These simple rules allow to reproduce the sub-exponential growth of the epidemic evolution observed during the Covid-19 epidemic waves in several countries and which cannot be captured by the standard SIR model. We show that we can tune the slowing-down of the epidemic spreading by changing the dynamics of the agents from Lévy to Brownian and we investigate how the interplay among different containment strategies mitigate the epidemic spreading. Finally we demonstrate that we can reproduce the epidemic evolution of the first and second COVID-19 waves in Italy using only 3 parameters, i.e , the infection rate, the removing rate, and the mobility in the country. We provide an estimate of the peak reduction due to imposed mobility restrictions, i. e., the so-called flattening the curve effect. Although based on few ingredients, the model captures the kinetic of the epidemic waves, returning mobility values that are consistent with a lock-down intervention during the first wave and milder limitations, associated to a weaker peak reduction, during the second wave.

Alignment interactions drive structural transitions in biological tissues.

Experimental evidence shows that there is a feedback between cell shape and cell motion. How this feedback impacts the collective behavior of dense cell monolayers remains an open question. We investigate the effect of a feedback that tends to align the cell crawling direction with cell elongation in a biological tissue model. We find that the alignment interaction promotes nematic patterns in the fluid phase that eventually undergo a nonequilibrium phase transition into a quasihexagonal solid. Meanwhile, highly asymmetric cells do not undergo the liquid-to-solid transition for any value of the alignment coupling. In this regime, the dynamics of cell centers and shape fluctuation show features typical of glassy systems.

Universality class of the motility-induced critical point in large scale off-lattice simulations of active particles.

We perform large-scale computer simulations of an off-lattice two-dimensional model of active particles undergoing a motility-induced phase separation (MIPS) to investigate the system's critical behaviour close to the critical point of the MIPS curve. By sampling steady-state configurations for large system sizes and performing finite size scaling analysis we provide exhaustive evidence that the critical behaviour of this active system belongs to the Ising universality class. In addition to the scaling observables that are also typical of passive systems, we study the critical behaviour of the kinetic temperature difference between the two active phases. This quantity, which is always zero in equilibrium, displays instead a critical behavior in the active system which is well described by the same exponent of the order parameter in agreement with mean-field theory.

Softness, anomalous dynamics, and fractal-like energy landscape in model cell tissues.

Epithelial cell tissues have a slow relaxation dynamics resembling that of supercooled liquids. Yet, they also have distinguishing features. These include an extended short-time subdiffusive transient, as observed in some experiments and recent studies of model systems, and a sub-Arrhenius dependence of the relaxation time on temperature, as reported in numerical studies. Here we demonstrate that the anomalous glassy dynamics of epithelial tissues originates from the emergence of a fractal-like energy landscape, particles becoming virtually free to diffuse in specific phase space directions up to a small distance. Furthermore, we clarify that the stiffness of the cells tunes this anomalous behavior, tissues of stiff cells having conventional glassy relaxation dynamics.

Narrow-escape time and sorting of active particles in circular domains.

It is now well established that microswimmers can be sorted or segregated fabricating suitable microfluidic devices or using external fields. A natural question is how these techniques can be employed for dividing swimmers of different motility. In this paper, using numerical simulations in the dilute limit, we investigate how motility parameters (time of persistence and velocity) impact the narrow-escape time of active particles from circular domains. We show that the escape time undergoes a crossover between two asymptotic regimes. The control parameters of the crossover is the ratio between the persistence length of the active motion and the typical length scale of the circular domain. We explore the possibility of taking advantage of this finding for sorting active particles by motility parameters.

Information and motility exchange in collectives of active particles.

We examine the interplay of motility and information exchange in a model of run-and-tumble active particles where the particle's motility is encoded as a bit of information that can be exchanged upon contact according to the rules of AND and OR logic gates in a circuit. Motile AND particles become non-motile upon contact with a non-motile particle. Conversely, motile OR particles remain motile upon collision with their non-motile counterparts. AND particles that have become non-motile additionally "reawaken", i.e., recover their motility, at a fixed rate µ, as in the SIS (susceptible, infected, susceptible) model of epidemic spreading, where an infected agent can become healthy again, but keeps no memory of the recent infection, hence it is susceptible to a renewed infection. For µ = 0, both AND and OR particles relax irreversibly to absorbing states of all non-motile or all motile particles, respectively. The relaxation kinetics is, however, faster for OR particles that remain active throughout the process. At finite µ, the AND dynamics is controlled by the interplay between reawakening and collision rates. The system evolves to a state of all motile particles (an absorbing state in the language of absorbing phase transitions) for µ > µc and to a mixed state with coexisting motile and non-motile particles (an active state in the language of absorbing phase transitions) for µ < µc. The final state exhibits a rich structure controlled by motility-induced aggregation. Our work can be relevant to biochemical signaling in motile bacteria, the spreading of epidemics and of social consensus, as well as light-controlled organization of active colloids.

Relation between Heterogeneous Frozen Regions in Supercooled Liquids and Non-Debye Spectrum in the Corresponding Glasses.

Recent numerical studies on glassy systems provide evidence for a population of non-Goldstone modes (NGMs) in the low-frequency spectrum of the vibrational density of states D(ω). Similarly to Goldstone modes (GMs), i.e., phonons in solids, NGMs are soft low-energy excitations. However, differently from GMs, NGMs are localized excitations. Here we first show that the parental temperature T^{*} modifies the GM/NGM ratio in D(ω). In particular, the phonon attenuation is reflected in a parental temperature dependency of the exponent s(T^{*}) in the low-frequency power law D(ω)∼ω^{s(T^{*})}, with 2≤s(T^{*})≤4. Second, by comparing s(T^{*}) with s(p), i.e., the same quantity obtained by pinning a p particle fraction, we suggest that s(T^{*}) reflects the presence of dynamical heterogeneous regions of size ξ^{3}∝p. Finally, we provide an estimate of ξ as a function of T^{*}, finding a mild power law divergence, ξ∼(T^{*}-T_{d})^{-α/3}, with T_{d} the dynamical crossover temperature and α falling in the range α∈[0.8,1.0].

Probing the non-Debye low-frequency excitations in glasses through random pinning.

We investigate the properties of the low-frequency spectrum in the density of states [Formula: see text] of a 3D model glass former. To magnify the non-Debye sector of the spectrum, we introduce a random pinning field that freezes a finite particle fraction to break the translational invariance and shifts all of the vibrational frequencies of the extended modes toward higher frequencies. We show that non-Debye soft localized modes progressively emerge as the fraction p of pinned particles increases. Moreover, the low-frequency tail of [Formula: see text] goes to zero as a power law [Formula: see text], with [Formula: see text] and [Formula: see text] above a threshold fraction [Formula: see text].

Flocking transitions in confluent tissues.

Collective cell migration in dense tissues underlies important biological processes, such as embryonic development, wound healing and cancer invasion. While many aspects of single cell movements are now well established, the mechanisms leading to displacements of cohesive cell groups are still poorly understood. To elucidate the emergence of collective migration in mechanosensitive cells, we examine a self-propelled Voronoi (SPV) model of confluent tissues with an orientational feedback that aligns a cell's polarization with its local migration velocity. While shape and motility are known to regulate a density-independent liquid-solid transition in tissues, we find that aligning interactions facilitate collective motion and promote solidification, with transitions that can be predicted by extending statistical physics tools such as effective temperature to this far-from-equilibrium system. In addition to accounting for recent experimental observations obtained with epithelial monolayers, our model predicts structural and dynamical signatures of flocking, which may serve as gateway to a more quantitative characterization of collective motility.

Effective equilibrium picture in the xy model with exponentially correlated noise.

We study the effect of exponentially correlated noise on the xy model in the limit of small correlation time, discussing the order-disorder transition in the mean field and the topological transition in two dimensions. We map the steady states of the nonequilibrium dynamics into an effective equilibrium theory. In the mean field, the critical temperature increases with the noise correlation time τ, indicating that memory effects promote ordering. This finding is confirmed by numerical simulations. The topological transition temperature in two dimensions remains untouched. However, finite-size effects induce a crossover in the vortices proliferation that is confirmed by numerical simulations.

Memory-less response and violation of the fluctuation-dissipation theorem in colloids suspended in an active bath.

We investigate experimentally and numerically the stochastic dynamics and the time-dependent response of colloids subject to a small external perturbation in a dense bath of motile E. coli bacteria. The external field is a magnetic field acting on a superparamagnetic microbead suspended in an active medium. The measured linear response reveals an instantaneous friction kernel despite the complexity of the bacterial bath. By comparing the mean squared displacement and the response function we detect a clear violation of the fluctuation dissipation theorem.

Pressure in an exactly solvable model of active fluid.

We consider the pressure in the steady-state regime of three stochastic models characterized by self-propulsion and persistent motion and widely employed to describe the behavior of active particles, namely, the Active Brownian particle (ABP) model, the Gaussian colored noise (GCN) model, and the unified colored noise approximation (UCNA) model. Whereas in the limit of short but finite persistence time, the pressure in the UCNA model can be obtained by different methods which have an analog in equilibrium systems, in the remaining two models only the virial route is, in general, possible. According to this method, notwithstanding each model obeys its own specific microscopic law of evolution, the pressure displays a certain universal behavior. For generic interparticle and confining potentials, we derive a formula which establishes a correspondence between the GCN and the UCNA pressures. In order to provide explicit formulas and examples, we specialize the discussion to the case of an assembly of elastic dumbbells confined to a parabolic well. By employing the UCNA we find that, for this model, the pressure determined by the thermodynamic method coincides with the pressures obtained by the virial and mechanical methods. The three methods when applied to the GCN give a pressure identical to that obtained via the UCNA. Finally, we find that the ABP virial pressure exactly agrees with the UCNA and GCN results.

Shape and Displacement Fluctuations in Soft Vesicles Filled by Active Particles.

We investigate numerically the dynamics of shape and displacement fluctuations of two-dimensional flexible vesicles filled with active particles. At low concentration most of the active particles accumulate at the boundary of the vesicle where positive particle number fluctuations are amplified by trapping, leading to the formation of pinched spots of high density, curvature and pressure. At high concentration the active particles cover the vesicle boundary almost uniformly, resulting in fairly homogeneous pressure and curvature, and nearly circular vesicle shape. The change between polarized and spherical shapes is driven by the number of active particles. The center-of-mass of the vesicle performs a persistent random walk with a long time diffusivity that is strongly enhanced for elongated active particles due to orientational correlations in their direction of propulsive motion. In our model shape-shifting induces directional sensing and the cell spontaneously migrate along the polarization direction.