One of the most successful ways to model the multitude of electron and photon processes in plasmas is the approach used in collisional radiative (CR) codes. The accuracy of CR codes depends largely on the accuracy of the rates of each process. These rates are generally well approximated in hot, classical plasmas. However, in degenerate plasmas quantum effects can influence these rates and must be accounted for. Previous approaches have developed corrections to the classical rates using the free-electron-gas (FEG) approximation. Here, we use electronic structures beyond the FEG approximation and show how the collisional rates are affected by degeneracy in aluminum and iron plasmas. We find that the FEG is a good approximation for aluminum, whereas more complex electronic structures that include $d$ orbitals, such as iron, deviate from the FEG approximation. This results in different degeneracy corrections to the collisional rates relative to those for the FEG. Although the general trend of the corrections to degenerate plasmas is captured by assuming an FEG, we show that more complex electronic structures can result in deviations, even outside the degenerate regime. This study further advances the treatment of free-electron quantum effects in collisional radiative models.

The so-called Jagla fluid is well known to exhibit, in addition to the usual gas-liquid critical point, also a liquid-liquid critical point, as well as a density anomaly. This makes it an interesting toy model for water, for which a liquid-liquid critical point is considered to exist but so far eludes experimental verification due to crystallization occurring in the corresponding metastable, deeply supercooled state. With the Jagla fluid being understood quite well in bulk—mostly via simulation studies—the focus of the present study is to describe the spatially inhomogeneous fluid in terms of classical density-functional theory (DFT) with the aim to be able to control its phase behavior on changing the shape or the nature of the confinement of the fluid. This information might contribute to guide potential experimental tests of the liquid-liquid critical point of actual water. We first determine the bulk phase diagram for the Jagla fluid by using thermodynamical perturbation theory. In doing so we explain why the perturbation theories of Barker and Henderson as well as of Weeks, Chandler, and Anderson fail to describe the Jagla fluid. We then continue to construct a perturbative DFT based on our bulk model, which shows significant improvement over the standard mean-field DFT valid at high temperatures. But ultimately the perturbative DFT breaks down at state points close to the binodal line and at low temperatures. This prevents us from achieving the original aim to study a highly confined, inhomogeneous Jagla fluid close to its liquid-liquid binodal.

We study the off-diagonal matrix elements of observables that break the translational symmetry of a spin-chain Hamiltonian, and as such connect energy eigenstates from different total quasimomentum sectors. We consider quantum-chaotic and interacting integrable points of the Hamiltonian, and focus on average energies at the center of the spectrum. In the quantum-chaotic model, we find that there is eigenstate thermalization; specifically, the matrix elements are Gaussian distributed with a variance that is a smooth function of $\omega =E_{\alpha }-E_{\beta }$ ($E_{\alpha }$ are the eigenenergies) and scales as $1/D$ ($D$ is the Hilbert space dimension). In the interacting integrable model, we find that the matrix elements exhibit a skewed log-normal-like distribution and have a variance that is also a smooth function of $\omega$ that scales as $1/D$. We study in detail the low-frequency behavior of the variance of the matrix elements to unveil the regimes in which it exhibits diffusive or ballistic scaling. We show that in the quantum-chaotic model the behavior of the variance is qualitatively similar for matrix elements that connect eigenstates from the same versus different quasimomentum sectors. We also show that this is not the case in the interacting integrable model for observables whose translationally invariant counterpart does not break integrability if added as a perturbation to the Hamiltonian.

How the internal degree of freedom of particles influences self-organization is explored by considering cluster formation in many-particle systems. We analyze a general class of dynamical systems in which the interactions between particles depend on their spatial distance and the difference of their internal states. In particular, we analyze a three-particle system in which two types of steady patterns exist, namely, (i) a regular triangle (two-dimensional cluster) and (ii) a straight line (one-dimensional cluster). The results show that the linear pattern can be stable when the internal degree of freedom exists, while it is always unstable when the dynamics depend only on the spatial distance. Based on this analysis, we can understand why this difference occurs. If the internal states can cause asymmetry of the interactions, this can enable the particles to remain in a one-dimensional cluster.

We study the phase space objects that control the transport in a classical Hamiltonian model for a chemical reaction. This model has been proposed to study the yield of products in an ultracold exothermic reaction. In this model, two features determine the evolution of the system: a Van der Waals force and a short-range force associated with the many-body interactions. In the previous work, small random periodic changes in the direction of the momentum were used to simulate the short-range many-body interactions. In the present work, random Gaussian bumps have been added to the Van der Waals potential energy to simulate the short-range effects between the particles in the system. We compare both variants of the model and explain their differences and similarities from a phase space perspective. To visualize the structures that direct the dynamics in the phase space, we construct a natural Lagrangian descriptor for Hamiltonian systems based on the Maupertuis action $S_0={\int }_{{\mathbf{q}}_i}^{{\mathbf{q}}_f}\mathbf{p}·d\mathbf{q}$.

Structural changes in a network representation of a system, due to different experimental conditions, different connectivity across layers, or to its time evolution, can provide insight on its organization, function, and on how it responds to external perturbations. The deeper understanding of how gene networks cope with diseases and treatments is maybe the most incisive demonstration of the gains obtained through this differential network analysis point of view, which led to an explosion of new numeric techniques in the last decade. However, where to focus one's attention, or how to navigate through the differential structures in the context of large networks, can be overwhelming even for a few experimental conditions. In this paper, we propose a theory and a methodological implementation for the characterization of shared “structural roles” of nodes simultaneously within and between networks. Inspired by recent methodological advances in chaotic phase synchronization analysis, we show how the information about the shared structures of a set of networks can be split and organized in an automatic fashion, in scenarios with very different (i) community sizes, (ii) total number of communities, and (iii) even for a large number of 100 networks compared using numerical benchmarks generated by a stochastic block model. Then, we investigate how the network size, number of networks, and mean size of communities influence the method performance in a series of Monte Carlo experiments. To illustrate its potential use in a more challenging scenario with real-world data, we show evidence that the method can still split and organize the structural information of a set of four gene coexpression networks obtained from two cell types $\times$ two treatments (interferon-$\beta$ stimulated or control). Aside from its potential use as for automatic feature extraction and preprocessing tool, we discuss that another strength of the method is its “story-telling”-like characterization of the information encoded in a set of networks, which can be used to pinpoint unexpected shared structure, leading to further investigations and providing new insights. Finally, the method is flexible to address different research-field-specific questions, by not restricting what scientific-meaningful characteristic (or relevant feature) of a node shall be used.

The analysis of games and sports as complex systems can give insights into the dynamics of human competition and has been proven useful in soccer, basketball, and other professional sports. In this paper, we present a model for dodgeball, a popular sport in U.S. schools, and analyze it using an ordinary differential equation (ODE) compartmental model and stochastic agent-based game simulations. The ODE model reveals a rich landscape with different game dynamics occurring depending on the strategies used by the teams, which can in some cases be mapped to scenarios in competitive species models. Stochastic agent-based game simulations confirm and complement the predictions of the deterministic ODE models. In some scenarios, game victory can be interpreted as a noise-driven escape from the basin of attraction of a stable fixed point, resulting in extremely long games when the number of players is large. Using the ODE and agent-based models, we construct a strategy to increase the probability of winning.

Sequences of nucleotides (for DNA and RNA) or amino acids (for proteins) are central objects in biology. Among the most important computational problems is that of sequence alignment, i.e., arranging sequences from different organisms in such a way to identify similar regions, to detect evolutionary relationships between sequences, and to predict biomolecular structure and function. This is typically addressed through profile models, which capture position specificities like conservation in sequences but assume an independent evolution of different positions. Over recent years, it has been well established that coevolution of different amino-acid positions is essential for maintaining three-dimensional structure and function. Modeling approaches based on inverse statistical physics can catch the coevolution signal in sequence ensembles, and they are now widely used in predicting protein structure, protein-protein interactions, and mutational landscapes. Here, we present DCAlign, an efficient alignment algorithm based on an approximate message-passing strategy, which is able to overcome the limitations of profile models, to include coevolution among positions in a general way, and to be therefore universally applicable to protein- and RNA-sequence alignment without the need of using complementary structural information. The potential of DCAlign is carefully explored using well-controlled simulated data, as well as real protein and RNA sequences.

In this study, a constitutive model is proposed to describe the necking behavior of double network (DN) gels based on statistical micromechanics of interpenetrating polymer networks. Accordingly, the constitutive response of DN gels in large deformations has been divided into three zones, i.e., prenecking, necking, and postnecking. The behavior of the DN gel is dominated by the behavior of the first and the second networks in each stage. In a previous study, we described how the destruction of the first network can govern the inelastic effects during the prenecking stage. Here, we elucidate the role of the second network to govern the material behavior in the necking and postnecking stages. To incorporate the effect of necking, the material behavior at each zone is described through the competition of three mechanisms that control the rearrangement of the two networks. Here, we challenge a general simplifying assumption in the modeling of DN gels, which considers the second network to be fully elastic. The recent experimental observations show the reduction of energy dissipation in the first network after necking initiation due to the localization of the damage in an active zone. Thus, we assumed that the chains of the second network contribute to the energy dissipation of the matrix by keeping the connection between the fragments of the first network. The proposed model has been validated in all three stages against different sets of experimental data on the uniaxial cyclic tensile behavior of DN gels. Moreover, the initiation and propagation of necking instability have been comprehensively illustrated through a finite-element implementation of the proposed model.

We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As a result, for overdamped particles, both an external random force field and disorder in the self-propulsion speed induce ballistic behavior adding to the ballistic regime of an active particle with sharp self-propulsion speed. Spatial correlations in the force and motility landscape contribute only to the cubic and higher-order powers in time for the MSD. Finally, for inertial particles two superballistic regimes are found where the scaling exponent of the MSD with time is $\alpha =3$ and $\alpha =4$. We confirm our theoretical predictions by computer simulations. Moreover, they are verifiable in experiments on self-propelled colloids in random environments.

Supercooled liquids display dynamics that are inherently heterogeneous in space. This essentially means that at temperatures below the melting point, particle dynamics in certain regions of the liquid can be orders of magnitude faster than other regions. Often dubbed dynamical heterogeneity, this behavior has fascinated researchers involved in the study of glass transition for over two decades. A fundamentally important question in all glass transition studies is whether one can connect the growing relaxation time to a concomitantly growing length scale. In this paper, we go beyond the realm of ordinary glass forming liquids and study the origin of a growing dynamical length scale $\xi$ in a self-propelled “active” glass former. This length scale, which is constructed using structural correlations, agrees well with the average size of the clusters of slow-moving particles that are formed as the liquid becomes spatially heterogeneous. We further report that the concomitantly growing $\alpha$-relaxation time exhibits a simple scaling law, ${\tau }_{\alpha }\sim \text{exp}(\mu \xi /T_{\text{eff}})$, with $\mu$ as an effective chemical potential, $T_{\text{eff}}$ as the effective temperature, and $\mu \xi$ as the growing free energy barrier for cluster rearrangements. The findings of our study are valid over four decades of persistence times, and hence they could be very useful in understanding the slow dynamics of a generic active liquid such as an active colloidal suspension, or a self-propelled granular medium.

In this paper, we study the flow of angular grains in a split-bottom Couette cell. Grains departing from a spherical shape result in collective flow fields that form a heap on the free surface. Here we extend on previous observations in split-bottom cells, exploring a wider range of flows within the inertial regime and finding a richness collection of behaviours. Surface height profiles and velocity profiles are accurately measured with digital image analysis. These measurements allow the characterization of the flow regimes within the cell and the heap morphology. We show that the known flow regimes in split-bottom geometries, like the universal and wall-collapsed regimes, can also be observed in moderately high inertial flows, extending the range for studying universal shear banding. The heap morphology is amplified by the flow inertia, with a partial collapse when the cell comes to a halt. Moreover, at high angular velocities, flows under low confinement will spread radially outwards, while flows under high confinement will develop localized particle ejections. Our results complement the observation of free-surface deformations of flows of nonspherical grains. These observations suggest a need for considering deformable free surface boundary conditions in the simulation of angular grains during shear, with repercussions in the characterization and prediction of natural mass flows.

Cell membranes show an intricate organization of lipids and membrane proteins into domains with distinct composition and hydrophobic thickness. Using mechanosensitive ion channels as a model system, we employ the membrane elasticity theory of lipid-protein interactions together with the Landau-Ginzburg theory of lipid domain formation to quantify protein-induced lipid bilayer thickness deformations in lipid bilayers with heterogeneous hydrophobic thickness. We show that protein-induced lipid bilayer thickness deformations yield, without any assumptions about preferential interactions between particular lipid and protein species, organization of lipids and membrane proteins according to their preferred hydrophobic thickness, and couple the conformational states of membrane proteins to the local membrane composition. Our calculations suggest that protein-induced lipid bilayer thickness deformations endow proteins in cell membranes with diverse and controlled mechanical environments that, in turn, allow targeted regulation of membrane proteins.

The first passage search of a diffusing target (prey) by multiple searchers (predators) in confinement is an important problem in the stochastic process literature. While the analogous problem in open space has been studied in some detail, a systematic study in confined space is still lacking. In this paper, we study the first passage times for this problem in one, two, and three dimensions. Due to confinement, the survival probability of the target takes a form $\sim e^{-t/\tau }$ at large times $t$. The characteristic capture timescale $\tau$ associated with the rare capture events are rather challenging to measure. We use a computational algorithm that allows us to estimate $\tau$ with high accuracy. We study in detail the behavior of $\tau$ as a function of the system parameters, namely, the number of searchers $N$, the relative diffusivity $r$ of the target with respect to the searcher, and the system size. We find that $\tau$ deviates from the $\sim 1/N$ scaling seen in the case of a static target, and this deviation varies continuously with $r$ and the spatial dimensions.

Key aspects of glasses are controlled by the presence of excitations in which a group of particles can rearrange. Surprisingly, recent observations indicate that their density is dramatically reduced and their size decreases as the temperature of the supercooled liquid is lowered. Some theories predict these excitations to cause a gap in the spectrum of quasilocalized modes of the Hessian that grows upon cooling, while others predict a pseudogap $D_L\left(\omega \right)\sim {\omega }^{\alpha }$. To unify these views and observations, we generate glassy configurations of controlled gap magnitude ${\omega }_c$ at temperature $T=0$, using so-called breathing particles, and study how such gapped states respond to thermal fluctuations. We find that (i) the gap always fills up at finite $T$ with $D_L\left(\omega \right)\approx A_4\left(T\right){\omega }^4$ and $A_4\sim exp(-E_a/T)$ at low $T$, (ii) $E_a$ rapidly grows with ${\omega }_c$, in reasonable agreement with a simple scaling prediction $E_a\sim {\omega }_c^4$ and (iii) at larger ${\omega }_c$ excitations involve fewer particles, as we rationalize, and eventually become stringlike. We propose an interpretation of mean-field theories of the glass transition, in which the modes beyond the gap act as an excitation reservoir, from which a pseudogap distribution is populated with its magnitude rapidly decreasing at lower $T$. We discuss how this picture unifies the rarefaction as well as the decreasing size of excitations upon cooling, together with a stringlike relaxation occurring near the glass transition.

We study the large scale behavior of a collection of hard core run and tumble particles on a one-dimensional lattice with periodic boundary conditions. Each particle has persistent motion in one direction decided by an associated spin variable until the direction of spin is reversed. We map the run and tumble model to a mass transfer model with fluctuating directed bonds. We calculate the steady-state single-site mass distribution in the mass model within a mean field approximation for larger spin-flip rates and by analyzing an appropriate coalescence-fragmentation model for small spin-flip rates. We also calculate the hydrodynamic coefficients of diffusivity and conductivity for both large and small spin-flip rates and show that the Einstein relation is violated in both regimes. We also show how the nongradient nature of the process can be taken into account in a systematic manner to calculate the hydrodynamic coefficients.

We found evidence of dynamic scaling in the spreading of Madin-Darby canine kidney (MDCK) cell monolayer, which can be characterized by the Hurst exponent $\alpha =0.86$ and the growth exponent $\beta =0.73$, and theoretically and experimentally clarified the mechanism that governs the contour shape dynamics. Dynamic scaling refers to the roughness of the surface scales, both spatially and temporally. During the spreading of the monolayer, it is known that so-called leader cells generate the driving force and lead the other cells. Our time-lapse observations of cell behavior showed that these leader cells appeared at the early stage of the spreading and formed the monolayer protrusion. Informed by these observations, we developed a simple mathematical model that included differences in cell motility, cell-cell adhesion, and random cell movement. The model reproduced the quantitative characteristics obtained from the experiment, such as the spreading speed, the distribution of the increment, and the dynamic scaling law. Analysis of the model equation shows that the model can reproduce different scaling laws from $(\alpha =0.5,\beta =0.25)$ to $(\alpha =0.9,\beta =0.75)$, where the exponents $\alpha$ and $\beta$ are determined by two dimensionless quantities determined by the microscopic cell behavior. From the analytical result, parameter estimation from the experimental results was achieved. The monolayer on the collagen-coated dishes showed a different scaling law, $\alpha =0.74,\beta =0.68$, suggesting that cell motility increased ninefold. This result was consistent with the assay of the single-cell motility. Our study demonstrated that the dynamics of the contour of the monolayer were explained by the simple model, and we propose a mechanism that exhibits the dynamic scaling property.

We report observational evidence of Lagrangian chaotic saddles in plasmas, given by the intersections of finite-time unstable and stable manifolds, using an $\approx 22\mathrm{h}$ sequence of spacecraft images of the horizontal velocity field of solar photosphere. A set of 29 persistent objective vortices with lifetimes varying from 28.5 to 298.3 min are detected by computing the Lagrangian averaged vorticity deviation. The unstable manifold of the Lagrangian chaotic saddles computed for $\approx 11\mathrm{h}$ exhibits twisted folding motions indicative of recurring vortices in a magnetic mixed-polarity region. We show that the persistent objective vortices are formed in the gap regions of Lagrangian chaotic saddles at supergranular junctions.

We study the dynamics of a bulk deterministic Floquet model, the Rule 201 synchronous one-dimensional reversible cellular automaton (RCA201). The system corresponds to a deterministic, reversible, and discrete version of the PXP model, whereby a site flips only if both its nearest neighbors are unexcited. We show that the RCA201 (Floquet-PXP) model exhibits ballistic propagation of interacting quasiparticles—or solitons—corresponding to the domain walls between nontrivial threefold vacuum states. Starting from the quasiparticle picture, we find the exact matrix product state form of the nonequilibrium stationary state for a range of boundary conditions, including both periodic and stochastic. We discuss further implications of the integrability of the model.