Three-dimensional surface wrinkling of soft cylindrical tissues induced by differential growth is explored. Differential volumetric growth can cause their morphological stability, leading to the formation of hexagonal and labyrinth wrinkles. During postbuckling, multiple bifurcations and morphological transitions may occur as a consequence of continuous growth in the surface layer. The physical mechanisms underpinning the morphological evolution are examined from the viewpoint of energy. Surface curvature is found to play a regulatory role in the pattern evolution. This study may not only help understand the morphogenesis of soft biological tissues, but also inspire novel routes for creating desired surface patterns of soft materials.

Until now, no simple symmetries have been detected in complex networks. Here we show that in growing multiplex networks the symmetries of multilayer structures can be exploited by their dynamical rules, forming supersymmetric multiplex networks described by coupled Bose-Einstein and Fermi-Dirac quantum statistics. The supersymmetric multiplex is formed by layers which are scale-free networks and can display a Bose-Einstein condensation of the links. To characterize the complexity of the supersymmetric multiplex using quantum information tools, we extend the definition of the network entanglement entropy to the layers of any multiplex network. Interestingly, we observe a very simple relation between the entanglement entropies of the layers of the supersymmetric multiplex network and the entropy rate of the same multiplex network. This relation therefore connects the classical nonequilibrium growing dynamics of the supersymmetric multiplex network with its quantum information static characteristics.

Understanding and quantifying the dynamics of disordered out-of-equilibrium models is an important problem in many branches of science. Using the dynamic cavity method on time trajectories, we construct a general procedure for deriving the dynamic message-passing equations for a large class of models with unidirectional dynamics, which includes the zero-temperature random-field Ising model, the susceptible-infected-recovered model, and rumor spreading models. We show that unidirectionality of the dynamics is the key ingredient that makes the problem solvable. These equations are applicable to single instances of the corresponding problems with arbitrary initial conditions and are asymptotically exact for problems defined on locally treelike graphs. When applied to real-world networks, they generically provide a good analytic approximation of the real dynamics.

The dynamics of static and traveling breathers in two-species Bose-Einstein condensates in a one-dimensional optical lattice is modelled within the tight-binding approximation. Two coupled discrete nonlinear Schrödinger equations describe the interaction of the condensates in two cases of relevance: a mixture of two ytterbium isotopes and a mixture of ${}^{87}\mathrm{Rb}$ and ${}^{41}\mathrm{K}$. Depending on their initial separation, interaction between static breathers of different species can lead to the formation of symbiotic structures and transform one of the breathers from a static into a traveling one. Collisions between traveling and static discrete breathers composed of different species are separated into four distinct regimes ranging from totally elastic when the interspecies interaction is highly attractive to mutual destruction when the interaction is sufficiently large and repulsive. We provide an explanation of the collision features in terms of the interspecies coupling and the negative effective mass of the discrete breathers.

An optoelectronic oscillator exhibiting a large delay in its feedback loop is studied both experimentally and theoretically. We show that multiple square-wave oscillations may coexist for the same values of the parameters (multirhythmicity). Depending on the sign of the phase shift, these regimes admit either periods close to an integer fraction of the delay or periods close to an odd integer fraction of twice the delay. These periodic solutions emerge from successive Hopf bifurcation points and stabilize at a finite amplitude following a scenario similar to Eckhaus instability in spatially extended systems. We find quantitative agreements between experiments and numerical simulations. The linear stability of the square waves is substantiated analytically by determining the stable fixed points of a map.

We study the validity of the eigenstate thermalization hypothesis (ETH) and its role for the occurrence of initial-state independent (ISI) equilibration in closed quantum many-body systems. Using the concept of dynamical typicality, we present an extensive numerical analysis of energy exchange in integrable and nonintegrable spin-$1/2$ systems of large size outside the range of exact diagonalization. In the case of nonintegrable systems, our finite-size scaling shows that the ETH becomes valid in the thermodynamic limit and can serve as the underlying mechanism for ISI equilibration. In the case of integrable systems, however, indication of ISI equilibration has been observed despite the violation of the ETH. We establish a connection between this observation and the need of choosing a proper parameter within the ETH.

For thermoelectric power generation in a multiterminal geometry, strong numerical evidence for a universal bound as a function of the magnetic-field induced asymmetry of the nondiagonal Onsager coefficients is presented. This bound implies, inter alia, that the power vanishes at least linearly when the maximal efficiency is approached. In particular, this result rules out that Carnot efficiency can be reached at finite power, which an analysis based on the second law only would, in principle, allow.

We investigate the diffusion of a rigid rodlike object in a two-dimensional disordered host medium, which consists of static pointlike sources of force. The points are distributed with long-range spatial correlation and interact with the rod via a repulsive potential. The time dependence of the rod's center-of-mass mean-squared displacement and its rotational mean-squared displacement are obtained for various degrees of long-range spatial correlation and rod's lengths. These transport characteristics are compared to those obtained in previous studies for the case of homogeneous distribution of force points. It is shown that existence of long-range correlation among force points makes the center of mass diffusion anomalous.

We examine the structure and dynamics of small isolated $N$-particle clusters interacting via short-ranged Morse potentials. “Ideally prepared ensembles” obtained via exact enumeration studies of sticky hard-sphere packings serve as reference states allowing us to identify key statistical-geometrical properties and to quantitatively characterize how nonequilibrium ensembles prepared by thermal quenches at different rates $\dot{T}$ differ from their equilibrium counterparts. Studies of equilibrium dynamics show nontrivial temperature dependence: nonexponential relaxation indicates both glassy dynamics and differing stabilities of degenerate clusters with different structures. Our results should be useful for extending recent experimental studies of small colloidal clusters to examine both equilibrium relaxation dynamics at fixed $T$ and a variety of nonequilibrium phenomena.

We study the connection between sliding friction and the phase behavior of a simple rigid bead-necklace model of a liquid crystal (LC) lubricant layer confined between two parallel plates. The dynamics is dependent on competing LC ordering mechanisms, including the direction of sliding, and an applied (electric) field. Together with temperature and an applied pressure, determining whether the lubricant is in a fluidlike isotropic state or in a layered in-plane nematic state, such ordering is found to control the frictional properties of the lubricant. Our extensive molecular dynamics simulations reveal in a detailed manner how friction can be controlled via applied fields. The results are expected to help in designing novel strategies to develop lubricants with dynamically controllable properties.

We develop an off-lattice (continuum) model to describe the adsorption of neutral polymer chains and polyelectrolytes to surfaces. Our continuum description allows taking excluded volume interactions between polymer chains and ions directly into account. To implement those interactions, we use a modified hard-sphere equation of state, adapted for mixtures of connected beads. Our model is applicable to neutral, charged, and ionizable surfaces and polymer chains alike and accounts for polarizability effects of the adsorbed layer and chemical interactions between polymer chains and the surface. We compare our model predictions to data of a classical system for polymer adsorption: neutral poly($N$-vinylpyrrolidone) (PVP) on silica surfaces. The model shows that PVP adsorption on silica is driven by surface hydrogen bonding with an effective maximum binding energy of about $1.3k_{\mathrm{B}}T$ per PVP segment at low $p\mathrm{H}$. As the $p\mathrm{H}$ increases, the Si-OH groups become increasingly dissociated, leading to a lower capacity for H bonding and simultaneous counterion accumulation and volume exclusion close to the surface. Together these effects result in a characteristic adsorption isotherm, with the adsorbed amount dropping sharply at a critical $p\mathrm{H}$. Using this model for adsorption data on silica surfaces cleaned by either a piranha solution or an ${\mathrm{O}}_2$ plasma, we find that the former have a significantly higher density of silanol groups.

Biochemical reactions in crowded fluids differ significantly from those in dilute solutions. Both, excluded-volume interactions with surrounding macromolecules (“crowders”) and an enhanced rebinding of reaction partners due to crowding-induced viscoelasticity and subdiffusion have been hypothesized to shift chemical equilibria towards the associated state. We have explored the impact of both cues in an experimentally tunable system by monitoring the steady-state fraction of open DNA hairpins in crowded fluids with varying viscoelastic characteristics but similar occupied volume fractions. As a result, we observed an increased fraction of closed DNA hairpins in viscoelastic crowded fluids. Our observations compare favorably to a simple statistical model that considers both facets of crowding, while preferential interactions between crowders and DNA hairpins appear to have little influence.

A community detection algorithm is considered to have a resolution limit if the scale of the smallest modules that can be resolved depends on the size of the analyzed subnetwork. The resolution limit is known to prevent some community detection algorithms from accurately identifying the modular structure of a network. In fact, any global objective function for measuring the quality of a two-level assignment of nodes into modules must have some sort of resolution limit or an external resolution parameter. However, it is yet unknown how the resolution limit affects the so-called map equation, which is known to be an efficient objective function for community detection. We derive an analytical estimate and conclude that the resolution limit of the map equation is set by the total number of links between modules instead of the total number of links in the full network as for modularity. This mechanism makes the resolution limit much less restrictive for the map equation than for modularity; in practice, it is orders of magnitudes smaller. Furthermore, we argue that the effect of the resolution limit often results from shoehorning multilevel modular structures into two-level descriptions. As we show, the hierarchical map equation effectively eliminates the resolution limit for networks with nested multilevel modular structures.

We derive adaptive time-delayed feedback controllers that stabilize fixed points and periodic orbits. First, we develop an adaptive controller for stabilization of a steady state by applying the speed-gradient method to an appropriate goal function and prove global asymptotic stability of the resulting system. For an example we show that the advantage of the adaptive controller over the nonadaptive one is in a smaller controller gain. Second, we propose adaptive time-delayed algorithms for stabilization of periodic orbits. Their efficiency is confirmed by local stability analysis. Numerical examples demonstrate the applicability of the proposed controllers.

We study a nonlinear Langevin equation describing the dynamic variable $X\left(t\right)$, the mean field (order parameter) of a finite size complex network at criticality. The conditions under which the autocorrelation function of $X$ shows any direct connection with criticality are discussed. We find that if the network is prepared in a state far from equilibrium, $X\left(0\right)=1$, the autocorrelation function is characterized by evident signs of critical slowing down as well as by significant aging effects, while the preparation $X\left(0\right)=0$ does not generate evident signs of criticality on $X\left(t\right)$, in spite of the fact that the same initial state makes the fluctuating variable $\eta \left(t\right)\equiv sgn\left(X\right(t\left)\right)$ yield significant aging effects. These latter effects arise because the dynamics of $\eta \left(t\right)$ are directly dependent on crucial events, namely the re-crossings of the origin, which undergo a significant aging process with the preparation $X\left(0\right)=0$. The time scale dominated by temporal complexity, aging, and ergodicity breakdown of $\eta \left(t\right)$ is properly evaluated by adopting the method of stochastic linearization which is used to explain the exponential-like behavior of the equilibrium autocorrelation function of $X\left(t\right)$.

To understand the dynamics of real-world networks, we investigate a mathematical model of the interplay between the dynamics of random walkers on a weighted network and the link weights driven by a resource carried by the walkers. Our numerical studies reveal that, under suitable conditions, the co-evolving dynamics lead to the emergence of stationary power-law distributions of the resource and link weights, while the resource quantity at each node ceaselessly changes with time. We analyze the network organization as a deterministic dynamical system and find that the system exhibits multistability, with numerous fixed points, limit cycles, and chaotic states. The chaotic behavior of the system leads to the continual changes in the microscopic network dynamics in the absence of any external random noises. We conclude that the intrinsic interplay between the states of the nodes and network reformation constitutes a major factor in the vicissitudes of real-world networks.

We test two isothermal-isobaric mixing rules, respectively based on excess-pressure and total-pressure equilibration, applied to the equation of state of a dense plasma. While the equation of state is generally known for pure species, that of arbitrary mixtures is not available so that the validation of accurate mixing rules, that implies resorting to first-principles simulations, is very useful. Here we consider the case of a plastic with composition ${\mathrm{C}}_2{\mathrm{H}}_3$ and we implement two complementary ab initio approaches adapted to the dense plasma domain: quantum molecular dynamics, limited to low temperature by its computational cost, and orbital-free molecular dynamics, that can be implemented at high temperature. The temperature and density range considered is 1–10 eV and 0.6–10 ${\mathrm{g}/\mathrm{cm}}^3$ for quantum molecular dynamics, and 5–1000 eV and 1–10 ${\mathrm{g}/\mathrm{cm}}^3$ for orbital-free molecular dynamics. Simulations for the full ${\mathrm{C}}_2{\mathrm{H}}_3$ mixture are the benchmark against which to assess the mixing rules, and both pressure and internal energy are compared. We find that the mixing rule based on excess-pressure equilibration is overall more accurate than that based on total-pressure equilibration; except for quantum molecular dynamics and a thermodynamic domain characterized by very low or negative excess pressures, it gives pressures which are generally within statistical error or within 1% of the exact ones. Besides, its superiority is amplified in the calculation of a principal Hugoniot.

Models with mixed origins of anomalous subdiffusion have been considered important for understanding transport in biological systems. Here one such mixed model, the quenched-trap model (QTM) on fractal lattices, is investigated. It is shown that both ensemble- and time-averaged mean-square displacements (MSDs) show subdiffusion with different scaling exponents, i.e., this system shows weak ergodicity breaking. Moreover, time-averaged MSD exhibits aging and converges to a random variable following the modified Mittag-Leffler distribution. It is also shown that the QTM on a fractal lattice cannot be reduced to the continuous-time random walks if the spectral dimension of the fractal lattice is less than 2.

We show that the mixed phase space dynamics of a typical smooth Hamiltonian system universally leads to a sustained exponential growth of energy at a slow periodic variation of parameters. We build a model for this process in terms of geometric Brownian motion with a positive drift, and relate it to the steady entropy increase after each period of the parameters variation.

Microscopic models of realistic thermodynamic systems usually involve a number of parameters, not all of equal macroscopic relevance. We examine a decorated $(1+3)$ Ising spin chain containing two microscopic parameters: a stiff parameter $K$ mediating the long-range interactions, and a sloppy $J$ operating within local spin groups. We show that $K$ dominates the macroscopic behavior, with varying $J$ having only a weak effect, except in regions where $J$ brings about transitions between phases through its conditioning of the local spin groups with which $K$ interacts. We calculate the heat capacity $C_H$, the magnetic susceptibility ${\chi }_T$, and the thermodynamic curvature $R$. For large $|J/K|$, we identify four magnetic phases: ferromagnetic, antiferromagnetic, and two ferrimagnetic, according to the signs of $K$ and $J$. We argue that for characterizing these phases, the strongest picture is offered by the thermodynamic geometric invariant $R$, proportional to the correlation length $\xi$. This picture has correspondences to other cases, such as fluids.