We study structure formation in systems of classical particles in two dimensions with long-range attractive short-range repulsive two-body interactions and repulsive three-body interactions. Stripe, gossamer, and glass phases are found as a result of nonpairwise interaction.

There are many examples of driven and active matter systems containing particles that exhibit circular motion with different chiralities, such as swimming bacteria near surfaces or certain types of self-driven colloidal particles. Circular motion of passive particles can also be induced with an external rotating drive. Here we examine particles that move in circles and interact with a periodic array of asymmetric L-shaped obstacles. We find a series of dynamical phases as a function of swimming radius, including regimes where the particle motion is rectified, producing a net dc motion. The direction of the rectification varies with the swimming radius, permitting the separation of particles with different swimming radii. Particles with the same swimming radius but different chirality can also move in different directions over the substrate and be separated. The rectification occurs for specific windows of swimming radii corresponding to periodic orbits in which the particles interact one or more times with the barriers per rotation cycle. The rectification effects are robust against the addition of thermal or diffusive effects, and are in some cases even enhanced by these effects.

This paper concerns establishing a theoretical basis and numerical scheme for studying the phase behavior of AB diblock copolymers made of wormlike chains. The general idea of a self-consistent field theory is the combination of the mean-field approach together with a statistical weight that describes the configurational properties of a polymer chain. In recent years, this approach has been extensively used for structural prediction of block copolymers, based on the Gaussian-model description of a polymer chain. The wormlike-chain model has played an important role in the description of polymer systems, covering the semiflexible-to-rod crossover of the polymer properties and the highly stretching regime, which the Gaussian-chain model has difficulties to describe. Although the idea of developing a self-consistent field theory for wormlike chains could be traced back to early development in polymer physics, the solution of such a theory has been limited due to technical difficulties. In particular, a challenge has been to develop a numerical algorithm enabling the calculation of the phase diagram containing three-dimensional structures for wormlike AB diblock copolymers. This paper describes a computational algorithm that combines a number of numerical tricks, which can be used for such a calculation. A phase diagram covering major parameter areas was constructed for the wormlike-chain system and reported by us, where the ratio between the total length and the persistence length of a constituent polymer is suggested as another tuning parameter for the microphase-separated structures; all detailed technical issues are carefully addressed in the current paper.

The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. Given a set of phase oscillators networking with a generic wiring of connections and displaying a generic frequency distribution, we show how combining dynamical local information on frequency mismatches and global information on the graph topology suggests a judicious and yet practical weighting procedure which is able to induce and enhance explosive, irreversible, transitions to synchronization. We report extensive numerical and analytical evidence of the validity and scalability of such a procedure for different initial frequency distributions, for both homogeneous and heterogeneous networks, as well as for both linear and nonlinear weighting functions. We furthermore report on the possibility of parametrically controlling the width and extent of the hysteretic region of coexistence of the unsynchronized and synchronized states.

Yang, Wang, and Motter [Phys. Rev. Lett. 109, 258701 (2012)] analyzed a model for network observability transitions in which a sensor placed on a node makes the node and the adjacent nodes observable. The size of the connected components comprising the observable nodes is a major concern of the model. We analyze this model in random heterogeneous networks with degree correlation. With numerical simulations and analytical arguments based on generating functions, we find that negative degree correlation makes networks more observable. This result holds true both when the sensors are placed on nodes one by one in a random order and when hubs preferentially receive the sensors. Finally, we numerically optimize networks with a fixed degree sequence with respect to the size of the largest observable component. Optimized networks have negative degree correlation induced by the resulting hub-repulsive structure; the largest hubs are rarely connected to each other, in contrast to the rich-club phenomenon of networks.

A neural-network model is proposed as a test bed for the characterization of the chaotic dynamics emerging in a context where the coupling is, on the average, neither excitatory nor inhibitory. The proposed discrete-time model generalizes within a single framework two different setups previously studied in the literature. With the help of theoretical mean field arguments and numerical simulations on GPUs, we characterize the transition and show that the chaotic dynamics is extensive (i.e., that the number of active degrees of freedom is proportional to the network size) from the very beginning. Besides the coupling strength, two parameters play a crucial role: (1) one controls the local dissipation and determines the shape of the initial part of the Lyapunov spectrum as well as the shape of the correlation function; (2) the other, which corresponds to the amplitude of an effective random field, determines the nature of the transition.

The stability of a two-layer film flow of non-Newtonian fluids is studied with a linear temporal approach. Shear-thinning fluids are considered, which follow the four-parameter inelastic Carreau model. A modified Orr-Sommerfeld equation system is obtained, which is solved by using a spectral Tau collocation method based on Chebyshev polynomials. The effects of density and viscosity stratification are considered, as well as the influence of the shear-thinning properties of the fluid. It is found that, when the viscosity is stronger in the upper layer, the base flow and the stability properties are almost not influenced by the change of the shear-thinning properties in this upper layer. In the other situations, the shear-thinning properties have an influence on the different instabilities, the long-wave surface instability and the short- and long-wave interface instabilities.

We focus on the study of a convection problem in a two-dimensional setup in the presence of the O(2) symmetry. The viscosity in the fluid depends on the temperature as it changes its value abruptly in an interval around a temperature of transition. The influence of the viscosity law on the morphology of the plumes is examined for several parameter settings, and a variety of shapes ranging from spout- to mushroom-shaped are found. We explore the impact of the symmetry on the time evolution of this type of fluid, and we find solutions which are greatly influenced by its presence: at a large aspect ratio and high Rayleigh numbers, traveling waves, heteroclinic connections, and chaotic regimes are found. These solutions, which are due to the presence of symmetry, have not been previously described in the context of temperature-dependent viscosities. However, similarities are found with solutions described in other contexts such as flame propagation problems or convection problems with constant viscosity also in the presence of the O(2) symmetry, thus confirming the determining role of the symmetry in the dynamics.

The complex dynamics of a single bubble of a few millimeters in size oscillating inside a narrow fluid-filled gap between two parallel plates is studied using high-speed videography. Two synchronized high-speed cameras were used to observe both the side and front views of the bubble. The front-view images show bubble expansion and collapse with the formation of concentric dark and bright rings. The simultaneous recordings reveal the mechanism behind these rings. The side-view images reveal two different types of collapse behavior of the bubble including a previously unreported collapse phenomenon that is observed as the gap width is changed. At narrow widths, the bubble collapses towards the center of the gap; when the width is increased, the bubble splits before collapsing towards the walls. The bubble dynamics is also observed to be unaffected by the hydrophobic or hydrophilic nature of the plate surface due to the presence of a thin film of liquid between each of the plates and the bubble throughout the bubble lifetime. It is revealed that such systems do not behave as quasi-two-dimensional systems; three-dimensional effects are important.

We show how an appropriate stationary crystalline structure of the magnetic field can induce a partial fragmentation of the accretion disk, generating an axial jet seed composed of hot plasma twisted in a funnel-like structure due to the rotation of the system. The most important feature we outline is the high degree of collimation, naturally following from the basic assumptions underlying the crystalline structure. The presence of nonzero dissipative effects allows the plasma ejection throughout the axial jet seed and the predicted values of the accretion rate are in agreement with observations.

We present an x-ray study of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition by means of angular x-ray cross-correlation analysis. By applying two-point angular-intensity cross-correlation functions to the measured series of diffraction patterns the parameters of bond-orientational (BO) order in hexatic phase were directly determined. The temperature dependence of the positional correlation lengths was analyzed as well. The obtained correlation lengths show larger values for the higher-order Fourier components of BO order. These findings indicate a strong coupling between BO and positional order.

The physical basis of two-state-like folding transitions and the tremendous diversity in folding rates is elucidated by directly simulating the folding kinetics of 52 representative proteins. Relative to the results from a common modeling approach, the diversity of the simulated folding rates can be increased from $\sim {10}^{2.1}$ to the experimental $\sim {10}^{6.0}$ by a modest decrease in the spatial range of the attractive potential. The required theoretical range is consistent with desolvation physics and is notably much more permissive than that needed for two-state-like homopolymer collapse.

We explore the role of the initial state on the onset of thermalization in isolated quantum many-body systems after a quench. The initial state is an eigenstate of an initial Hamiltonian ${\widehat{H}}_I$ and it evolves according to a different final Hamiltonian ${\widehat{H}}_F$. If the initial state has a chaotic structure with respect to ${\widehat{H}}_F$, i.e., if it fills the energy shell ergodically, thermalization is certain to occur. This happens when ${\widehat{H}}_I$ is a full random matrix, because its states projected onto ${\widehat{H}}_F$ are fully delocalized. The results for the observables then agree with those obtained with thermal states at infinite temperature. However, finite real systems with few-body interactions, as the ones considered here, are deprived of fully extended eigenstates, even when described by a nonintegrable Hamiltonian. We examine how the initial state delocalizes as it gets closer to the middle of the spectrum of ${\widehat{H}}_F$, causing the observables to approach thermal averages, be the models integrable or chaotic. Our numerical studies are based on initial states with energies that cover the entire lower half of the spectrum of one-dimensional Heisenberg spin-1/2 systems.

This work analyzes a percolation model on the diamond hierarchical lattice (DHL), where the percolation transition is retarded by the inclusion of a probability of erasing specific connected structures. It has been inspired by the recent interest on the existence of other universality classes of percolation models. The exact scale invariance and renormalization properties of DHL leads to recurrence maps, from which analytical expressions for the critical exponents and precise numerical results in the limit of very large lattices can be derived. The critical exponents $\nu$ and $\beta$ of the investigated model vary continuously as the erasing probability changes. An adequate choice of the erasing probability leads to the result $\nu =\infty$, like in some phase transitions involving vortex formation. The percolation transition is continuous, with $\beta >0$, but $\beta$ can be as small as desired. The modified percolation model turns out to be equivalent to the $Q\to 1$ limit of a Potts model with specific long range interactions on the same lattice.

Understanding the distinctive phase behaviors in random packing due to particle shapes is an important issue in condensed matter physics. In this paper, we investigate the random packing structure of two-dimensional (2D) snowmen via wax-snowman packing experiments and Brownian dynamics simulations. Both experiments and simulations reveal that neighboring snowmen have a strong short-range orientational correlation and consequently locally form particular conformations. A chiral conformation is dominant for high area fractions near the jamming condition ($\phi >0.8$), and the proportion of the chiral conformation increases with $\gamma$. We also found that the attractive interaction does not have a significant impact on the results. The geometry of chirally ordered snowmen causes a mismatch with 2D crystalline symmetries and thus inhibits the development of long-range spatial order, despite the strong orientational correlation between neighbors.

The effects of randomly pinning particles in a model glass-forming fluid are studied, with a focus on the dynamically heterogeneous relaxation in the presence of pinning. We show how four-point dynamical correlations can be analyzed in real space, allowing direct extraction of a length scale that characterizes dynamical heterogeneity. In the presence of pinning, the relaxation time of the glassy system increases by up to two decades, but there is almost no increase in either the four-point correlation length or the strength of the four-point correlations. We discuss the implications of these results for theories of the glass transition.

We investigated a series of nanocomposites, built of the hydrogen-bonded liquid crystal (LC) p-n-heptyloxybenzoic acid (7OBA) and single-walled carbon nanotubes (SWCNTs) by optical microtexture analysis and other complementary methods. The surface orientation strength of the LC cell and the bulk interaction of the dimeric LC molecules with the SWCNTs turn out to mainly govern the type (symmetry), thermal stability, and chirality of the LC states induced in these nanocomposites. As a result, a cascade of phase transitions and phases not typical for pristine 7OBA were observed and additionally confirmed by temperature-dependent Raman spectroscopy and differential scanning calorimetry. The most effective SWCNT concentrations in the LC matrix, ensuring both the necessary conformability between these materials and induction of liquid crystal phases with unique optical and electro-optical properties, were found to be in the range of 0.01–0.007 wt $\%$. Reversal of smectic phases into reentrant nematic states as well as induction of chirality in all LC phases were observed in the SWCNT-7OBA nanocomposite, even though pure 7OBA is typically achiral. However, our most intriguing result is the detection below the reentrant nematic of a triclinic smectic-$C_G$ phase, which is chiral and biaxial, and exhibits bulk ferroelectricity.

Using the intrinsic relationship between the external equitable partition (EEP) and the spectral properties of the graph Laplacian, we characterize convergence and observability properties of consensus dynamics on networks. In particular, we establish the relationship between the original consensus dynamics and the associated consensus of the quotient graph under varied initial conditions, and characterize the asymptotic convergence to the synchronization manifold under nonuniform input signals. We also show that the EEP with respect to a node can reveal nodes in the graph with an increased rate of asymptotic convergence to the consensus value, as characterized by the second smallest eigenvalue of the quotient Laplacian. Finally, we show that the quotient graph preserves the observability properties of the full graph and how the inheritance by the quotient graph of particular aspects of the eigenstructure of the full Laplacian underpins the observability and convergence properties of the system.

We study evolutionary games in a spatial diluted grid environment in which agents strategically interact locally but can also opportunistically move to other positions within a given migration radius. Using the imitation of the best rule for strategy revision, it is shown that cooperation may evolve and be stable in the Prisoner's Dilemma game space for several migration distances but only for small game interaction radius while the Stag Hunt class of games become fully cooperative. We also show that only a few trials are needed for cooperation to evolve, i.e., searching costs are not an issue. When the stochastic Fermi strategy update protocol is used cooperation cannot evolve in the Prisoner's Dilemma if the selection intensity is high in spite of opportunistic migration. However, when imitation becomes more random, fully or partially cooperative states are reached in all games for all migration distances tested and for short to intermediate interaction radii.

Using gauge transformation method, we generate rogue waves for the two-component Bose-Einstein condensates (BECs) governed by the symmetric coupled Gross-Pitaevskii (GP) equations and study their dynamics. We also suggest a mechanism to tame the rogue waves either by manipulating the scattering length through Feshbach resonance or the trapping frequency, a phenomenon not witnessed in the domain of BECs, and we believe that these results may have wider ramifications in the management of rogons.