Functional brain networks are often constructed by quantifying correlations between time series of activity of brain regions. Their topological structure includes nodes, edges, triangles, and even higher-dimensional objects. Topological data analysis (TDA) is the emerging framework to process data sets under this perspective. In parallel, topology has proven essential for understanding fundamental questions in physics. Here we report the discovery of topological phase transitions in functional brain networks by merging concepts from TDA, topology, geometry, physics, and network theory. We show that topological phase transitions occur when the Euler entropy has a singularity, which remarkably coincides with the emergence of multidimensional topological holes in the brain network. The geometric nature of the transitions can be interpreted, under certain hypotheses, as an extension of percolation to high-dimensional objects. Due to the universal character of phase transitions and noise robustness of TDA, our findings open perspectives toward establishing reliable topological and geometrical markers for group and possibly individual differences in functional brain network organization.

Gene expression is inherently noisy due to fluctuations occurring at the molecular level. From a top-down perspective, noise has been traditionally decomposed into an intrinsic component that scales inversely with the mean expression level and an extrinsic component that is constant in absence of regulatory changes. Here, we adopt a bottom-up approach to reveal that extrinsic noise, by itself, can follow the aforementioned decomposition, which entails that one component of it can be confounded with intrinsic noise. Analytical expressions of the noise-mean relationship were derived for different scenarios, which were in part supported by numerical simulations.

Clusters of cells can work together in order to follow a signal gradient, chemotaxing even when single cells do not. Cells in different regions of collectively migrating neural crest streams show different gene expression profiles, suggesting that cells may specialize to leader and follower roles. We use a minimal mathematical model to understand when this specialization is advantageous. In our model, leader cells sense the gradient with an accuracy that depends on the kinetics of ligand-receptor binding, while follower cells follow the cluster's direction with a finite error. Intuitively, specialization into leaders and followers should be optimal when a few cells have more information than the rest of the cluster, such as in the presence of a sharp transition in chemoattractant concentration. We do find this—but also find that high levels of specialization can be optimal in the opposite limit of very shallow gradients. We also predict that the best location for leaders may not be at the front of the cluster. In following leaders, clusters may have to choose between speed and flexibility. Clusters with only a few leaders can take orders of magnitude more time to reorient than all-leader clusters.

One of the basic characteristics of a linear dsDNA molecule is its persistence length, typically of order 50 nm. The DNA chain inflicts a large energy penalty if it is bent sharply at that length scale. Viruses of bacteria, known as bacteriophages, typically have a dimension of a few tens of nanometers. Yet, it is known that a bacteriophage actively packages viral DNA inside the capsid and ejects it afterwards. Here, adopting a commonly used polymer model known as the wormlike chain, we answer an idealized question: Placing a linear DNA molecule inside a spherical cavity, what ordered states can we derive from known tools in statistical physics? Solving the model in a rigorous field-theory framework, we report a universal phase diagram for four orientationally ordered and disordered states, in terms of two relevant physical parameters.

The emerging field of self-driven active particles in fluid environments has recently created significant interest in the biophysics and bioengineering communities owing to their promising future for biomedical and technological applications. These microswimmers move autonomously through aqueous media, where under realistic situations they encounter a plethora of external stimuli and confining surfaces with peculiar elastic properties. Based on a far-field hydrodynamic model, we present an analytical theory to describe the physical interaction and hydrodynamic couplings between a self-propelled active microswimmer and an elastic interface that features resistance toward shear and bending. We model the active agent as a superposition of higher-order Stokes singularities and elucidate the associated translational and rotational velocities induced by the nearby elastic boundary. Our results show that the velocities can be decomposed in shear and bending related contributions which approach the velocities of active agents close to a no-slip rigid wall in the steady limit. The transient dynamics predict that contributions to the velocities of the microswimmer due to bending resistance are generally more pronounced than those due to shear resistance. Bending can enhance (suppress) the velocities resulting from higher-order singularities whereas the shear related contribution decreases (increases) the velocities. Most prominently, we find that near an elastic interface of only energetic resistance toward shear deformation, such as that of an elastic capsule designed for drug delivery, a swimming bacterium undergoes rotation of the same sense as observed near a no-slip wall. In contrast to that, near an interface of only energetic resistance toward bending, such as that of a fluid vesicle or liposome, we find a reversed sense of rotation. Our results provide insight into the control and guidance of artificial and synthetic self-propelling active microswimmers near elastic confinements.

We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two-dimensional spherocylinders driven by a uniform steady-state shear strain applied at a fixed finite rate. Energy dissipation occurs via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension and resulting in a Newtonian rheology. We study the resulting pressure $p$ and deviatoric shear stress $\sigma$ of the interacting spherocylinders as a function of packing fraction $\varphi$, strain rate $\dot{\gamma }$, and a parameter $\alpha$ that measures the asphericity of the particles; $\alpha$ is varied to consider the range from nearly circular disks to elongated rods. We consider the direction of anisotropy of the stress tensor, the macroscopic friction $\mu =\sigma /p$, and the divergence of the transport coefficient ${\eta }_p=p/\dot{\gamma }$ as $\varphi$ is increased to the jamming transition ${\varphi }_J$. From a phenomenological analysis of Herschel-Bulkley rheology above jamming, we estimate ${\varphi }_J$ as a function of asphericity $\alpha$ and show that the variation of ${\varphi }_J$ with $\alpha$ is the main cause for differences in rheology as $\alpha$ is varied; when plotted as $\varphi /{\varphi }_J$, rheological curves for different $\alpha$ qualitatively agree. However, a detailed scaling analysis of the divergence of ${\eta }_p$ for our most elongated particles suggests that the jamming transition of spherocylinders may be in a different universality class than that of circular disks. We also compute the number of contacts per particle $Z$ in the system and show that the value at jamming $Z_J$ is a nonmonotonic function of $\alpha$ that is always smaller than the isostatic value. We measure the probability distribution of contacts per unit surface length $\mathcal{P}\left(\vartheta \right)$ at polar angle $\vartheta$ with respect to the spherocylinder spine and find that as $\alpha \to 0$ this distribution seems to diverge at $\vartheta =\pi /2$, giving a finite limiting probability for contacts on the vanishingly small flat sides of the spherocylinder. Finally, we consider the variation of the average contact force as a function of location on the particle surface.

We present the formulation, simulations, and results for multicomponent mutual diffusion coefficients in the warm, dense matter regime. While binary mixtures have received considerable attention for mass transport, far fewer studies have addressed ternary and more complex systems. We therefore explicitly examine ternary systems utilizing the Maxwell-Stefan formulation that relates diffusion to gradients in the chemical potential. Onsager coefficients then connect the macroscopic diffusion to microscopic particle motions, evinced in trajectories characterized by positions and velocities, through various autocorrelation functions (ACFs). These trajectories are generated by molecular dynamics (MD) simulations either through the Born-Oppenheimer approximation, which treats the ions classically and the electrons quantum-mechanically by an orbital-free density-functional theory, or through a classical MD approach with Yukawa pair-potentials, whose effective ionizations and electron screening length derive from quantal considerations. We employ the reference-mean form of the ACFs and determine the center-of-mass coefficients through a simple reference-frame-dependent similarity transformation. The Onsager terms in turn determine the mutual diffusion coefficients. We examine a representative sample of ternary mixtures as a function of density and temperature from those with only light elements (D-Li-C, D-Li-Al) to those with highly asymmetric mass components (D-Li-Cu, D-Li-Ag, H-C-Ag). We also follow trends in the diffusion as a function of number concentration and evaluated the efficacy of various approximations such as the Darken approximation.

Extensive quantum molecular dynamics (QMD) simulations are performed to determine the equation of state, sound velocity, and phase diagram of middle-$Z$ krypton in a warm dense regime where the pressure (P) is up to 300 GPa and the temperature is up to 60 kK. The shock wave experimental data are used to validate the present theoretical models. It is found that, within the regime of the current density ($\rho$) and temperature ($T$), sound velocity can effectively discriminate differences between different theoretical models, and therefore it is more suitable as a benchmark to verify the practicability of models. The QMD-simulated results of the ionic structures and electronic properties imply the occurrence of two kinds of phase transitions, including transition from a solidlike to fluid state and that from an insulator to conductive fluid in this T-P regime. The calculated electrical conductivities confirm that the metallization transition occurs at about 60 GPa and 17.5 kK along the principal Hugoniot. With the help of simulation results and experimental data, a comprehensive phase diagram for krypton is constructed by using the solid-fluid and insulator-metal fluid phase boundaries, which fills the gap of the experimental work [Proc. Natl. Acad. Sci. USA 112, 7925 (2015)]. These results will provide an instructive basis for the experimental investigations of rare gases over a wide T-P range.

We apply a standard nonequilibrium dynamics microscopic analysis of transport coefficients to the smoothed dissipative particle dynamics (SDPD) method of steady-shear flow conditions. Extending the research of Ellero et al. [Phys. Rev. E 82, 046702 (2010)] for smoothed particle hydrodynamics (SPH), we focus, in particular, on velocity and acceleration statistics and on mean-density phenomena. Implicit and explicit fluctuations affect non-Gaussian statistics and effective viscosities whereas only explicit fluctuations affect large-scale dissipation through the fluctuation-dissipation relation. SDPD facilitates the simulation of mesoscopic systems as the resolution scale is defined by the scaling of the random fluctuations. In the kinetic regime, SDPD recovers the behavior of SPH. In the diffusive regime, non-Gaussian behavior occurs, in contrast to SPH. We observe the formation of isotropic randomly oriented structures with high density which are related to the magnitude of thermal fluctuations. It is demonstrated that SDPD produces non-Gaussian acceleration PDF corresponding to that of a turbulent flow field.

A classic three-dimensional spin model, based upon the Baxter-Wu scheme, is presented. It is found, by entropic sampling simulations, that the behavior of the energy and magnetization fourth-order cumulants points to a first-order phase transition. A finite-size procedure was performed, confirming that the system scales with the dimensionality $d=3$, yielding a high-resolution estimate of the transition temperature as $T_c=11.377485\left(29\right)$.

Urban areas experience elevated temperatures due to the urban heat island (UHI) effect. However, temperatures within cities vary considerably and their spatial heterogeneity is not well characterized. Here, we use land surface temperature (LST) of 78 global cities to show that the surface UHI (SUHI) is fractal. We use percentile-based thermal thresholds to identify heat clusters emerging within SUHI and refer to them collectively as intra-urban heat islets. The islets display properties analogous to that of a percolating system as we vary the thermal thresholds. At percolation threshold, the size distribution of these islets in all cities follows a power law, with a scaling exponent ($\beta$) of 1.88 ($\pm 0.23,95\%CI$) and an aggregated perimeter fractal dimension ($D$) of 1.33 ($\pm 0.064,95\%CI$). This commonality indicates that despite the diversity in urban form and function across the world, the urban temperature patterns are different realizations with the same aggregated statistical properties. Furthermore, we observe the convergence of these scaling exponents as the city sizes increase. Therefore, while the effect of diverse urban morphologies is evident in smaller cities, in the mean, the larger cities are alike. Lastly, we calculate the mean islet intensities, i.e., the difference between mean islet temperature and thermal threshold, and show that it follows an exponential distribution, with rate parameter $\lambda$, for all cities. $\lambda$ varied widely across the cities and can be used to quantify the spatial heterogeneity within SUHIs. In conclusion, we present a basis for a unified characterization of urban heat from the spatial scales of an urban block to a megalopolis.

We propose a simple protocol exploiting the thermalization of a storage bipartite system $S$ to extract work from a resource system $R$. The protocol is based on a recent work definition involving only a single bath. A general description of the protocol is provided without specifying the characteristics of $S$. We quantify both the extracted work and the ideal efficiency of the process, also giving maximum bounds for them. Then, we apply the protocol to two cases: two interacting qubits and the Rabi model. In both cases, for very strong couplings, an extraction of work comparable with the bare energies of the subsystems of $S$ is obtained and its peak is reached for finite values of the bath temperature, $T$. We finally show, in the Rabi model at $T=0$, how to transfer the work stored in $S$ to an external device, permitting thus a cyclic implementation of the whole work-extraction protocol. Our proposal makes use of simple operations not needing fine control.

We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum maps, we specify the relationship between the eigenstates and the classical structures, and we quantify their multifractality at different scales. Based on this study, we conjecture that quantum states in such systems are distributed according to a hierarchy of classical structures, but these states are multifractal instead of ergodic at each level of the hierarchy. This is visible for sufficiently long-lived resonance states at scales smaller than the classical structures. Our results can guide experimentalists in order to observe multifractal behavior in open systems.

We present an experimental investigation of the complex dynamics of a modulated relaxation oscillator implemented by using a unipolar junction transistor (UJT) showing the transition to chaos through torus breakdown. In a previous paper a continuous model was introduced for the same system, explaining chaos based on analogy with a memristor. We propose here a new approach based on a piecewise linear model with delay considering a measured parasitic delay effect. The inclusion of this delay, accounting for memory effects, increases the dimensionality of the model, allowing the transition to chaos as observed in the experiment. The piecewise delayed model shows analogies with a two-dimensional leaky integrate-and-fire model used in neurodynamics.

In a highly influential paper twenty years ago, Barabási and Albert [Science 286, 509 (1999)] showed that networks undergoing generic growth processes with preferential attachment evolve towards scale-free structures. In any finite system, the growth eventually stalls and is likely to be followed by a phase of network contraction due to node failures, attacks, or epidemics. Using the master equation formulation and computer simulations, we analyze the structural evolution of networks subjected to contraction processes via random, preferential, and propagating node deletions. We show that the contracting networks converge towards an Erdős-Rényi network structure whose mean degree continues to decrease as the contraction proceeds. This is manifested by the convergence of the degree distribution towards a Poisson distribution and the loss of degree-degree correlations.

We formulate a simple effective model to describe molecular interactions in a lipid monolayer and calculate the line tension between coexisting domains. The model represents lipid molecules in terms of two-dimensional anisotropic particles on the plane of the monolayer. These particles interact through forces that are believed to be relevant for the understanding of fundamental properties of the monolayer: van der Waals interactions originating from lipid chains and dipolar forces between dipole groups in the molecular heads. The model stresses the liquid-crystalline nature of the ordered phase in lipid monolayers and explains coexistence properties between ordered and disordered phases in terms of molecular parameters. Thermodynamic and interfacial properties of the model are analyzed using density-functional theory. In particular, the line tension at the interface between ordered and disordered phases turns out to be highly anisotropic with respect to the angle between the nematic director and the interface separating the coexisting phases. This important feature mainly results from the tilt angle of lipid chains and, to a lesser extent, from dipolar interactions perpendicular to the monolayer. The role of the two dipolar components, parallel and perpendicular to the monolayer, is assessed by comparing with computer simulation results for lipid monolayers.

We investigate the collective dynamics of particles (e.g., microorganisms) interacting via chemotactic gradients. Specifically, we focus on continuum models for chemotaxis that include a damping of the chemical production with increasing local particle density and/or systems where the chemotactic sensitivity is reduced with increasing local concentration of the chemical. Using a recently introduced perturbative method [Phys. Rev. E 98, 020603 (2018)], we show that the onset of particle clustering in these systems is described by the universal Cahn-Hilliard (CH) model. On the one hand, this establishes particle-conserving models for chemotaxis as a further example for the universal class of nonequilibrium demixing phenomena we call active phase separation. On the other hand, the reduction to the CH model allows an analytical determination of suitable parameter ranges wherein, e.g., the transition to spatial density modulations is continuous and/or undesired blow-up solutions can be avoided. A comparison between the numerical solutions of the chemotaxis model and the derived CH model also provides the parameter range where the basic chemotaxis model behaves like other systems showing active phase separation, including the coarsening behavior in two spatial dimensions. Our approach highlights how basic principles of pattern formation theory allow the identification of common basic properties in different chemotaxis models.