We construct a pathwise formulation for a multitype age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational representation of the stationary population growth rate; the representation comprises a tradeoff relation between growth effects and a single-cell intrinsic dynamics described by a semi-Markov process. This variational representation leads to a response relation of the stationary population growth rate, in which statistics on a retrospective history work as the response coefficients. These results contribute to predicting and controlling growing populations based on experimentally observed cell-lineage information.

A relationship between the observation of a density anomaly and the underlying crystalline phase diagram is demonstrated. The crystal phase diagram and temperature of maximum density (TMD) lines are calculated over a range of parameter space using a Stillinger-Weber potential. Relationships between the loci of density maxima in the $PT$ plane for the liquid state and the underlying crystalline phase diagram are investigated. Two key potential parameters are systematically varied in order to control the balance between the model two- and three-body interaction terms, and the relative effects of varying the potential parameters analyzed. The respective TMD lines diverge at extreme values with one set of lines showing a reentrant behavior. For each parameter set the TMD lines are extrapolated to $T=0\mathrm{K}$. The corresponding pressures are related to the crystalline phase diagram and are found to lie on or near specific crystal-crystal coexistence lines for a wide range of potential parameters. The density anomaly is observed to vanish corresponding to regions in the crystal phase diagram which lack crystal-crystal coexistence lines potentially offering a new interpretation for the emergence of anomalous behavior.

I provide numerical evidence for the robustness of the Griffiths phase (GP) reported previously in dynamical threshold model simulations on a large human brain network with $N=836733$ connected nodes. The model, with equalized network sensitivity, is extended in two ways: introduction of refractory states or by randomized time-dependent thresholds. The nonuniversal power-law dynamics in an extended control parameter region survives these modifications for a short refractory state and weak disorder. In case of temporal disorder the GP shrinks and for stronger heterogeneity disappears, leaving behind a mean-field type of critical transition. Activity avalanche size distributions below the critical point decay faster than in the original model, but the addition of inhibitory interactions sets it back to the range of experimental values.

The Belousov-Zhabotinsky (BZ) reaction is a famous experimental model for chemical oscillatory reaction and pattern formation. We herein study a diffusive coupled system of two oscillators with global feedback using the photosensitive BZ reaction both experimentally and theoretically. The coupled oscillator showed in-phase and antiphase oscillations depending on the strength of diffusive coupling and light feedback. Moreover, we analyzed our model to locate the bifurcational origin and found the reconnection of the bifurcation branches for antiphase oscillation, which was induced by the competition between global feedback and the diffusion effect.

We show that eigenvector centrality exhibits localization phenomena on networks that can be easily partitioned by the removal of a vertex cut set, the most extreme example being networks with a cut vertex. Three distinct types of localization are identified in these structures. One is related to the well-established hub node localization phenomenon and the other two are introduced and characterized here. We gain insights into these problems by deriving the relationship between eigenvector centrality and Katz centrality. This leads to an interpretation of the principal eigenvector as an approximation to more robust centrality measures which exist in the full span of an eigenbasis of the adjacency matrix.

Bifurcation theory is a powerful tool for studying how the dynamics of a neural network model depends on its underlying neurophysiological parameters. However, bifurcation theory of neural networks has been developed mostly for mean-field limits of infinite-size spin-glass models, for finite-size dynamical systems whose units have a graded, continuous output, and for models with discrete-output neurons that evolve in continuous time. To allow progress on understanding the dynamics of some widely used classes of neural network models with discrete units and finite size, which could not be studied thoroughly with the previous methodology, here we introduced algorithms that perform a semianalytical bifurcation analysis of a finite-size firing-rate neural network model with binary firing rates and discrete-time evolution. In particular, we focus on the case of small networks composed of tens of neurons, to which existing statistical methods are not applicable. Our approach is based on a numerical brute-force search of the stationary and oscillatory solutions of the model, from which we derive analytical expressions of its bifurcation structure by means of the state-to-state transition probability matrix. Our algorithms determine how the network parameters affect the degree of multistability, the emergence and the period of the neural oscillations, and the formation of spontaneous symmetry breaking in the neural populations. While this technique can be applied to networks with arbitrary (generally asymmetric) connectivity matrices, in particular we introduce a highly efficient algorithm for the bifurcation analysis of sparse networks. We also provide some examples of the obtained bifurcation diagrams and a python implementation of the algorithms.

During the interphase in mammalian cells, the position of the centrosome is actively maintained at a small but finite distance away from the nucleus. The perinuclear positioning of the centrosome is crucial for cellular trafficking and progression into mitosis. Although the literature suggests that the contributions of the microtubule-associated forces bring the centrosome to the center of the cell, the position of the centrosome was merely investigated in the absence of the nucleus. Upon performing a coarse-grained simulation study with mathematical analysis, we show that the combined effect of the forces due to the cell cortex and the nucleus facilitate the centrosome positioning. Our study also demonstrates that in the absence of nucleus-based forces, the centrosome collapses on the nucleus due to cortical forces. Depending upon the magnitudes of the cortical forces and the nucleus-based forces, the centrosome appears to stay at various distances away from the nucleus. Such null force regions are found to be stable as well as unstable fixed points. This study uncovers a set of redundant schemes that the cell may adopt to produce the required cortical and nucleus-based forces stabilizing the centrosome at a finite distance away from the nucleus.

We investigate evolutionary dynamics of altruism with long-range interaction on a cycle. The interaction between individuals is described by a simplified version of the prisoner's dilemma (PD) game in which the payoffs are parameterized by $c$, the cost of a cooperative action. In our model, the probabilities of the game interaction and competition decay algebraically with $r_{\mathrm{AB}}$, the distance between two players A and B, but with different exponents: That is, the probability to play the PD game is proportional to $r_{\mathrm{AB}}^{-\alpha }$. If player A is chosen for death, on the other hand, the probability for B to occupy the empty site is proportional to $r_{\mathrm{AB}}^{-\beta }$. In a limiting case of $\beta \to \infty$, where the competition for an empty site occurs between its nearest neighbors only, we analytically find the condition for the proliferation of altruism in terms of $c_{\text{th}}$, a threshold of $c$ below which altruism prevails. For finite $\beta$, we conjecture a formula for $c_{\text{th}}$ as a function of $\alpha$ and $\beta$. We also propose a numerical method to locate $c_{\text{th}}$, according to which we observe excellent agreement with the conjecture even when the selection strength is of considerable magnitude.

An emerging mechanism for intracellular organization is liquid-liquid phase separation (LLPS). Found in both the nucleus and the cytoplasm, liquidlike droplets condense to create compartments that are thought to promote and inhibit specific biochemistry. In this work, a multiphase, Cahn-Hilliard diffuse interface model is used to examine RNA-protein interactions driving LLPS. We create a bivalent system that allows for two different species of protein-RNA complexes and model the competition that arises for a shared binding partner, free protein. With this system we demonstrate that the binding and unbinding of distinct RNA-protein complexes leads to diverse spatial pattern formation and dynamics within droplets. Both the initial formation and transient behavior of spatial patterning are subject to the exchange of free proteins between RNA-protein complexes. This study illustrates that spatiotemporal heterogeneity can emerge within phase-separated biological condensates with simple binding reactions and competition. Intradroplet patterning may influence droplet composition and, subsequently, cellular organization on a larger scale.

A general trait of living cells is their ability to exert contractile stresses on their surroundings and thus respond to substrate rigidity. At the cellular scale, this response affects cell shape, polarity, and ultimately migration. The regulation of cell shape together with rigidity sensing remains largely unknown. In this article we show that both substrate rigidity and cell shape contribute to drive actin organization and cell polarity. Increasing substrate rigidity affects bulk properties of the actin cytoskeleton by favoring long-lived actin stress fibers with increased nematic interactions, whereas cell shape imposes a local alignment of actin fibers at the cell periphery.

Highly concentrated particle suspensions (also called slurries) can undergo a sharp increase in viscosity, or shear thickening, under applied stress. Understanding the fundamental features leading to such rheological change is crucial to optimize flow conditions or to design flow modifiers for slurry processing. While local changes to the particle environment under applied shear can be related to changes in viscosity, there is a broader need to connect the shear thickening transition to the fundamental organization of particle-interaction forces which lead to long-range organization. In particular, at a high volume fraction of particles, recent evidence indicates frictional forces between contacting particles is of importance. Herein, the network of frictional contact forces is analyzed within simulated two-dimensional shear thickening suspensions. Two topological metrics are studied to characterize the response of the contact force network (CFN) under varying applied shear stress. The metrics, geodesic index and the void parameter, reflect complementary aspects of the CFN: One is the connectedness of the contact network and the second is the distribution of spatial areas devoid of particle-particle contacts. Considered in relation to the variation of the viscosity, the topological metrics show that the network grows homogeneously at large scales but with many local regions devoid of contacts, indicating clearly the role of CFN growth in causing the large change in the rheological response at the shear thickening transition.

In relativistic fluid mechanics, positive entropy production is known to be insufficient for guaranteeing stability. Much stronger criteria for thermodynamic admissibility have become available in nonequilibrium thermodynamics. We here perform a linear stability analysis for a model of relativistic hydrodynamics that is based on the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) framework of nonequilibrium thermodynamics. Assuming a quadratic entropy function near equilibrium, we find stability for the entire range of physically meaningful model parameters for relativistic fluid dynamics based on GENERIC. The search for thermodynamic admissibility moreover reveals a fundamental difference between liquids and gases in relativistic fluid dynamics.

The self-diffusion phenomenon in a two-dimensional dusty plasma at extremely strong (effective) magnetic fields is studied experimentally and by means of molecular dynamics simulations. In the experiment the high magnetic field is introduced by rotating the particle cloud and observing the particle trajectories in a corotating frame, which allows reaching effective magnetic fields up to 3000 T. The experimental results confirm the predictions of the simulations: (i) superdiffusive behavior is found at intermediate timescales and (ii) the dependence of the self-diffusion coefficient on the magnetic field is well reproduced.

Chimera states in spatiotemporal dynamical systems have been investigated in physical, chemical, and biological systems, and have been shown to be robust against random perturbations. How do chimera states achieve their robustness? We uncover a self-adaptation behavior by which, upon a spatially localized perturbation, the coherent component of the chimera state spontaneously drifts to an optimal location as far away from the perturbation as possible, exposing only its incoherent component to the perturbation to minimize the disturbance. A systematic numerical analysis of the evolution of the spatiotemporal pattern of the chimera state towards the optimal stable state reveals an exponential relaxation process independent of the spatial location of the perturbation, implying that its effects can be modeled as restoring and damping forces in a mechanical system and enabling the articulation of a phenomenological model. Not only is the model able to reproduce the numerical results, it can also predict the trajectory of drifting. Our finding is striking as it reveals that, inherently, chimera states possess a kind of “intelligence” in achieving robustness through self-adaptation. The behavior can be exploited for the controlled generation of chimera states with their coherent component placed in any desired spatial region of the system.

We show that the dominant mode of alignment plays an important role in dry active nematics, leading to two dynamical subclasses defined by the nature of the instability of the nematic bands that characterize, in these systems, the coexistence phase separating the isotropic and fluctuating nematic states. In addition to the well-known instability inducing long undulations along the band, another stronger instability leading to the breakup of the band in many transversal segments may arise. We elucidate the origin of this strong instability for a realistic model of self-propelled rods and determine the high-order nonlinear terms responsible for it at the hydrodynamic level.

Spatially extended excitable systems can exhibit spiral defect chaos (SDC) during which spiral waves continuously form and disappear. To address how this dynamical state terminates using simulations can be computationally challenging, especially for large systems. To circumvent this limitation, we treat the number of spiral waves as a stochastic population with a corresponding birth-death equation and use techniques from statistical physics to determine the mean episode duration of SDC. Motivated by cardiac fibrillation, during which the heart's electrical activity becomes disorganized and shows fragmenting spiral waves, we use generic models of cardiac electrophysiology. We show that the duration can be computed in minimal computational time and that it depends exponentially on domain size. Therefore, the approach can result in efficient and accurate predictions of mean episode duration which may be extended to more complex geometries and models.

Bacterial movement in confined spaces is routinely encountered either in a natural environment or in artificial structures. Consequently, the ability to understand and predict the behavior of motile bacterial cells in confined geometries is essential to many applications, spanning from the more classical, such as the management complex microbial networks involved in diseases, biomanufacturing, mining, and environment, to the more recent, such as single cell DNA sequencing and computation with biological agents. Fortunately, the development of this understanding can be helped by the decades-long advances in semiconductor microfabrication, which allow the design and the construction of complex confining structures used as test beds for the study of bacterial motility. To this end, here we use microfabricated channels with varying sizes to study the interaction of Escherichia coli with solid confining spaces. It is shown that an optimal channel size exists for which the hydrostatic potential allows the most efficient movement of the cells. The improved understanding of how bacteria move will result in the ability to design better microfluidic structures based on their interaction with bacterial movement.

We numerically examine a two-dimensional system of repulsively interacting particles with dynamics that are governed by both a damping term and a Magnus term. The magnitude of the Magnus term has one value for half of the particles and a different value for the other half of the particles. In the absence of a driving force, the particles form a triangular lattice, while when a driving force is applied, we find that there is a critical drive above which a Magnus-induced disordering transition can occur even if the difference in the Magnus term between the two particle species is as small as one percent. The transition arises due to the different Hall angles of the two species, which causes their motion to decouple at the critical drive. At higher drives, the disordered state can undergo both species and density phase separation into a density-modulated stripe that is oriented perpendicular to the driving direction. We observe several additional phases that occur as a function of drive and Magnus force disparity, including a variety of density-modulated diagonal-laned phases. In general, we find a much richer variety of states compared to systems of oppositely driven overdamped Yukawa particles. We discuss the implications of our work for skyrmion systems, where we predict that even for small skyrmion dispersities, a drive-induced disordering transition can occur along with clustering phases and pattern-forming states.

Turbulence mixing models of different degree of complexity are investigated for Rayleigh-Taylor mixing flows with reference to high-resolution implicit large eddy simulations. The models considered, in order of increasing complexity, comprise the (i) two-equation K-L, (ii) three-equation K-L-a, (iii) four-equation K-L-a-b, and (iv) Besnard-Harlow-Rauenzahn (BHR-2). The above models are implemented in the same numerical framework to minimize the computational uncertainty. The impact of the various approximations represented by the different models is investigated for canonical one-dimensional (1D) Rayleigh-Taylor mixing and for the more complex (2D on average) case of the tilted-rig experiment, aiming to understand the balance between accuracy and complexity. The results provide guidance on the relative merits of various turbulence models over a variety of conditions.