We propose an experiment combining fluid dynamics and strong magnetic field physics to simulate cosmological scenarios. Our proposed system consists of two immiscible, weakly magnetized fluids moved through a strong gradient magnetic field. The diamagnetic and paramagnetic forces thus generated amount to a time-dependent effective gravity, which allows us to precisely control the propagation speed of interface waves. Perturbations on the interface therefore experience a nonstationary effective metric. In what follows, we demonstrate that our proposed system is capable of simulating a variety of cosmological models. We then present a readily realizable experimental setup which will allow us to capture the essential dynamics of standard inflation, wherein interface perturbations experience a shrinking effective horizon and are shown to transition from oscillatory to frozen and squeezed regimes at horizon crossing.

We study interactions between biological cells that apply anisotropic active mechanical forces on an elastic substrate. We model the cells as thin disks that along their perimeters apply radial, but angle-dependent forces on the substrate. We obtain analytical expressions for the elastic energy stored in the substrate as a function of the distance between the cells, the Fourier modes of applied forces, and their phase angles. We show how the relative phases of the forces applied by the cells can switch the interaction between attractive and repulsive, and relate our results to those for linear force dipoles. For long enough distances, the interaction energy decays in magnitude as a power law of the cell-cell distance with an integer exponent that generally increases with the Fourier modes of the applied forces.

We study pattern formation of skin cancers by means of numerical simulation of a binary system consisting of cancer and healthy cells. We extend the conventional model H for macrophase separations by considering a logistic growth of cancer cells and also a mechanical friction between dermis and epidermis. Importantly, our model exhibits a microphase separation due to the proliferation of cancer cells. By numerically solving the time evolution equations of the cancer composition and its velocity, we show that the phase separation kinetics strongly depends on the cell proliferation rate as well as on the strength of hydrodynamic interactions. A steady-state diagram of cancer patterns is established in terms of these two dynamical parameters and some of the patterns correspond to clinically observed cancer patterns. Furthermore, we examine in detail the time evolution of the average composition of cancer cells and the characteristic length of the microstructures. Our results demonstrate that different sequence of cancer patterns can be obtained by changing the proliferation rate and/or hydrodynamic interactions.

Both stimuli-responsive gels and growing biological tissue can undergo pronounced morphological transitions from two-dimensional (2D) layers into 3D geometries. We derive an analytical model that allows us to quantitatively predict the features of 2D-to-3D shape changes in polymer gels that encompasses different degrees of swelling within the sample. We analyze a particular configuration that emerges from a flat rectangular gel that is divided into two strips (bistrips), where each strip is swollen to a different extent in solution. The final configuration yields double rolls that display a narrow transition layer between two cylinders of constant radii. To characterize the rolls' shapes, we modify the theory of thin incompatible elastic sheets to account for the Flory-Huggins interaction between the gel and the solvent. This modification allows us to derive analytical expressions for the radii, the amplitudes, and the length of the transition layer within a given roll. Our predictions agree quantitatively with available experimental data. In addition, we carry out numerical simulations that account for the complete nonlinear behavior of the gel and show good agreement between the analytical predictions and the numerical results. Our solution sheds light on a stress focusing pattern that forms at the border between two dissimilar soft materials. Moreover, models that provide quantitative predictions on the final morphology in such heterogeneously swelling hydrogels are useful for understanding growth patterns in biology as well as accurately tailoring the structure of gels for various technological applications.

In this work we extend the Caspar-Klug construction to the archaeal viruses, which in recent years have captured the attention of many researchers for their ability to thrive in extreme environments. We assume that the shells of archaeal viruses are composed of hexamers and pentamers—as is true for icosahedral viruses—together with heptamers, necessary to introduce negative Gauss curvature. Following the original work of Caspar and Klug, we first construct models capable of reproducing the shape observed in electron microscopy images of archaeal viruses. Next, using the technique of kirigami, we present a systematic way to formulate archaeal virus templates from regular hexagonal lattices. Finally, we utilize the presented techniques to build finite element models of archaeal virus geometries and investigate their shapes as a function of material properties. In particular, using thin-shell elasticity theory, we describe a buckling transition as a function of a modified Föppl–von Kármán number ${\gamma }^{★}$ and we show how changes in ${\gamma }^{★}$ may initiate the tail formation in the Acidianus two-tailed archaeal virus.

The evolution of self-gravitating systems, and long-range interacting systems more generally, from initial configurations far from dynamical equilibrium is often described as a simple two-phase process: a first phase of violent relaxation bringing it to a quasistationary state in a few dynamical times, followed by a slow adiabatic evolution driven by collisional processes. In this context the complex spatial structure evident, for example, in spiral galaxies is understood either in terms of instabilities of quasistationary states or as a result of dissipative nongravitational interactions. We illustrate here, using numerical simulations, that purely self-gravitating systems evolving from quite simple initial configurations can in fact give rise easily to structures of this kind, of which the lifetime can be large compared to the dynamical characteristic time but short compared to the collisional relaxation timescale. More specifically, for a broad range of nonspherical and nonuniform rotating initial conditions, gravitational relaxation gives rise quite generically to long-lived nonstationary structures of a rich variety, characterized by spiral-like arms, bars, and even ringlike structures in special cases. These structures are a feature of the intrinsically out-of-equilibrium nature of the system's collapse, associated with a part of the system's mass while the bulk is well virialized. They are characterized by predominantly radial motions in their outermost parts, but also incorporate an extended flattened region which rotates coherently about a well-virialized core of triaxial shape with an approximately isotropic velocity dispersion. We characterize the kinematical and dynamical properties of these complex velocity fields and we briefly discuss the possible relevance of these simple toy models to the observed structure of real galaxies, emphasizing the difference between dissipative and dissipationless disk formation.

It is well known that resonance phenomena can destroy adiabatic invariance and cause chaos and mixing. In the present Rapid Communication, we show that a nonlinear wave-particle resonant interaction may do the opposite—generate large-scale coherent structures in phase space. The combined action of the drift due to nonlinear scattering on resonance and trapping (capture) into resonance creates a convection cell-like structure, where the areas of particle acceleration and deceleration are macroscopically separated. At the same time, nonlinear scattering also creates a diffusion that cause mixing on and between the energy levels.

We use a three-component replicator system with healthy cells, sensitive cells, and resistant cells, with a prisoner's dilemma payoff matrix from evolutionary game theory, to model and control the nonlinear dynamical system governing the ecological mechanism of competitive release by which tumors develop chemotherapeutic resistance. The control method we describe is based on nonlinear trajectory design and energy transfer methods first introduced in the orbital mechanics literature for Hamiltonian systems. For continuous therapy, the basin boundaries of attraction associated with the chemo-sensitive population and the chemo-resistant population for increasing values of chemo-concentrations have an intertwined spiral structure with extreme sensitivity to changes in chemo-concentration level as well as sensitivity with respect to resistant mutations. For time-dependent therapies, we introduce an orbit transfer method to construct continuous families of periodic (closed) orbits by switching the chemo-dose at carefully chosen times and appropriate levels to design schedules that are superior to both maximum tolerated dose (MTD) schedules and low-dose metronomic (LDM) schedules, both of which ultimately lead to fixation of sensitive cells or resistant cells. By keeping the three subpopulations of cells in competition with each other indefinitely, we avoid fixation of the cancer cell population and regrowth of a resistant tumor. The method can be viewed as a way to dynamically shape the average population fitness landscape of a tumor to steer the chemotherapeutic response curve. We show that the method is remarkably insensitive to initial conditions and small changes in chemo-dosages, an important criterion for turning the method into an actionable strategy.

We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with the Allee effect, to account for the role of demographic stochasticity. In the mean-field deterministic limit we recover well-known deterministic evolution equations widely employed in population ecology. The mean time to extinction is in general obtained by the Wentzel-Kramers-Brillouin (WKB) approximation for populations with the strong and weak Allee effects. An exact solution for the mean time to extinction can be found via a recursive equation for special cases of the stochastic dynamics. We study the conditions for the validity of the WKB solution and analyze the boundary between the weak and strong Allee effect by comparing exact solutions with numerical simulations.

The spread of an infectious disease can be promoted by previous infections with other pathogens. This cooperative effect can give rise to violent outbreaks, reflecting the presence of an abrupt epidemic transition. As for other diffusive dynamics, the topology of the interaction pattern of the host population plays a crucial role. It was conjectured that a discontinuous transition arises when there are relatively few short loops and many long loops in the contact network. Here we focus on the role of local clustering in determining the nature of the transition. We consider two mutually cooperative pathogens diffusing in the same population: An individual already infected with one disease has an increased probability of getting infected by the other. We look at how a disease obeying the susceptible-infected-removed dynamics spreads on contact networks with tunable clustering. Using numerical simulations we show that for large cooperativity the epidemic transition is always abrupt, with the discontinuity decreasing as clustering is increased. For large clustering strong finite-size effects are present and the discontinuous nature of the transition is manifest only in large networks. We also investigate the problem of influential spreaders for cooperative infections, revealing that both cooperativity and clustering strongly enhance the dependence of the spreading influence on the degree of the initial seed.

We present a simultaneous study of the phase properties of rational breather waves generated in a water wave tank and in an optical fiber platform, namely, the Peregrine soliton and related second-order solution. Our analysis of experimental wave measurements makes use of standard demodulation and filtering techniques in hydrodynamics and more complex phase retrieval techniques in optics to quantitatively confirm analytical and numerical predictions. We clearly highlight a characteristic phase shift that is a multiple of $\pi$ between the central pulsed part and the continuous background of rational breathers at their maximum compression. Moreover, we reveal a large longitudinal phase shift across the point of maximum compression.

We present a model and protocol that enable the generation of extremely stable computer glasses at minimal computational cost. The protocol consists of an instantaneous quench in an augmented potential energy landscape, with particle radii as additional degrees of freedom. We demonstrate how our glasses' mechanical stability, which is readily tunable in our approach, is reflected in both microscopic and macroscopic observables. Our observations indicate that the stability of our computer glasses is at least comparable to that of computer glasses generated by the celebrated Swap Monte Carlo algorithm. Strikingly, some key properties support even qualitatively enhanced stability in our scheme: the density of quasilocalized excitations displays a gap in our most stable computer glasses, whose magnitude scales with the polydispersity of the particles. We explain this observation, which is consistent with the lack of plasticity we observe at small stress. It also suggests that these glasses are depleted from two-level systems, similarly to experimental vapor-deposited ultrastable glasses.

We have developed an experimental platform to generate radiatively heated solid density samples for warm dense matter studies at the OMEGA laser facility. Cylindrical samples of boron and beryllium are isochorically heated by K- and L-shell emission from x-ray converter foils wrapped around the cylinders' radii. X-ray Thomson scattering (XRTS) measures the temperature and the ionization state of the samples as function of time. Temperatures approach 10 eV, and the ionization states are found to be $Z_{\text{B}}=3$ and $Z_{\text{Be}}=2$. Radiation hydrodynamics simulations were performed to confirm a homogeneous plasma state exists in the center of the sample for the duration of the experiment. Results from the study can be extended to improve understanding of radiative heating processes in the warm dense matter regime.

Industrial as well as natural aggregation of fine particles is believed to be associated with electrostatics. Yet like charges repel, so it is unclear how similarly treated particles aggregate. To resolve this apparent contradiction, we analyze conditions necessary to hold aggregates together with electrostatic forces. We find that aggregates of particles charged with the same sign can be held together due to dielectric polarization, we evaluate the effect of aggregate size, and we briefly summarize consequences for practical aggregation.

Density gradient theory has become an important tool for calculating the surface tension of pure components as well as mixtures. The calculation requires knowledge about the so-called influence parameter. Since in most applications this parameter is obtained by fitting results of the density gradient theory to experimental data for surface tensions, the approach lacks predictive power. We propose a predictive density gradient theory based on nonlocal density functional theory (DFT) using the perturbed chain polar statistical associating fluid theory (PCP-SAFT) as equation of state. The formalism can also be applied to other Helmholtz energy functionals based on weighted densities. The predictive density gradient theory (pDGT) is obtained by applying a gradient expansion to the weighted densities of the PCP-SAFT Helmholtz energy functional to second order and expanding the Helmholtz energy density to first order. The resulting model approximates the DFT and can be cast into the form of a density gradient theory. The resulting influence parameter depends on local densities and on temperature. We assess the predictive power of the proposed pDGT to calculate surface tensions of vapor-liquid interfaces of pure components as well as mixtures. The results show that pDGT reduces the computational complexity compared with nonlocal DFT calculations, while largely preserving its accuracy as well as its predictive capability.

In this work we study pedestrian-pedestrian interactions from observational experimental data in diluted pedestrian crowds. While in motion, pedestrians continuously adapt their walking paths trying to preserve mutual comfort distances and to avoid collisions. Leveraging on a high-quality, high-statistics data set, composed of several few millions real-life trajectories acquired from state-of-the-art observational experiments (about 6 months of high-resolution pedestrian tracks acquired in a train station), we develop a quantitative model capable of addressing interactions in the case of binary collision avoidance. We model interactions in terms of both long-range (sight based) and short-range (hard-contact avoidance) forces, which we superimpose on our Langevin model for noninteracting pedestrian motion [Corbetta et al., Phys. Rev. E 95, 032316 (2017)] (here further tested and extended). The model that we propose here features a Langevin dynamics with fast random velocity fluctuations that are superimposed on the slow dynamics of a hidden model variable: the intended walking path. In the case of interactions, social forces may act both on the intended path and on the actual walked path. The model is capable of reproducing quantitatively relevant statistics of the collision avoidance motion, such as the statistics of the side displacement and of the passing speed. Rare occurrences of actual bumping events are also recovered. Furthermore, comparing with large data sets of real-life tracks involves an additional computational challenge so far neglected: identifying automatically, within a database containing very heterogeneous conditions, only the relevant events corresponding to binary avoidance interactions. In order to tackle this challenge, we propose a general approach based on a graph representation of pedestrian trajectories, which allows us to effectively operate complexity reduction for efficient data classification and selection.

In this paper, we present a pedestrian single-file movement experiment that directly captures the characteristics of the interacting pedestrians’ continuous stepping behaviors. We find that the relationship between step length (duration) and spatial headway exhibits piecewise linear behavior: It first increases linearly as the headway increases and then remains constant when the headway exceeds 1.20 m (0.71 m). Three different regimes are observed and defined on the basis of their relationships. The continuous small-step phenomena are found in a strongly constrained regime. We reveal that the relationship between the step duration and the step velocity is nonmonotonous and that the longest duration is seen at a velocity of 1.35 m/s, whereas the relationship between the step length and the step velocity is monotonous and can be well represented by a quartic function. Furthermore, we show that the dependency of the ratio between head displacement and foot displacement in a step on the headway is a piecewise linear relationship. We were interested to find that the ratio is less (greater) than 0.5 when the headway is less (greater) than 1 m. This finding reveals the backward- (forward-) deviating phenomena of the body and can be used to indirectly interpret the differences in some of the results of this paper and previous studies. Finally, we show that step synchronization (asynchronization) is most likely to occur at a headway of 0.76 m (0.51 m). These interesting findings greatly deepen our understanding of basic human stepping behavior.

A solvable model is proposed and analyzed to reveal the mechanism underlying the diffusion enhancement recently reported for a model of molecular motors and predicted to be observed in the biological rotary motor ${\mathrm{F}}_1$-ATPase. It turns out that the diffusion enhancement for the present model can approximately be described by a random walk in which the waiting time for a step to occur is exponentially distributed and it takes nonzero time to proceed forward by the step. It is shown that the diffusion coefficient of such a random walk can significantly be increased when the average waiting time is comparable to the average stepping time.

The embryos of the green alga Volvox carteri are spherical sheets of cells that turn themselves inside out at the close of their development through a program of cell shape changes. This process of inversion is a model for morphogenetic cell sheet deformations; it starts with four lips opening up at the anterior pole of the cell sheet, flipping over, and peeling back to invert the embryo. Experimental studies have revealed that inversion is arrested if some of these cell shape changes are inhibited, but the mechanical basis for these observations has remained unclear. Here, we analyze the mechanics of this inversion by deriving an averaged elastic theory for these lips and we interpret the experimental observations in terms of the mechanics and evolution of inversion.

The combination of bistability and cooperativity plays a crucial role in several biological and artificial micro- and nanosystems. In particular, the exhaustive understanding of the mechanical response of such systems under the effect of thermal fluctuations is essential to elucidate a rich variety of phenomena. Here a linear chain composed of elastic units, which are bistable (folded or unfolded) and coupled through an Ising-like interaction, is selected as a case study. We assess the macroscopic thermoelastic response of this chain in terms of its microscopic description. For small systems, far from the thermodynamic limit, this response depends on the applied isometric or isotensional boundary conditions, which correspond to the Helmholtz or Gibbs ensembles of the statistical mechanics, respectively. The theoretical analysis is conducted through the spin variables approach, based on a set of discrete quantities able to identify the folded or unfolded state of the chain units. Eventually, this technique yields closed-form expressions for the force-extension curves and the average number of unfolded units, as function of the applied fields. In addition, it allows to unveil a critical behavior of such systems, characterizing the operating regions with negative differential stiffness (spinoidal phase).