Particle diffusion is a fundamental process in various systems, so its effective manipulation is crucially important. For this purpose, here we design a basic structure composed of two moving rings with equal-but-opposite velocities and a stationary intermediate layer, which can realize multiple functions to control particle diffusion. On the one hand, the intermediate layer allows particle exchange between the two moving rings, which gives birth to an exceptional point of velocity. As a result, a geometric phase appears for a loop evolution of velocity containing the exceptional point. On the other hand, the two moving rings also enhance the effective diffusivity of the intermediate layer, which helps design a bilayer particle-diffusion cloak. The present cloak only requires homogeneous parameters and simple structures, and meanwhile, its on and off can be flexibly controlled by velocity. These results broaden the scope of geometric phase and provide hints for designing particle-diffusion metamaterials.

Reexamining algebraic curves found in the eight-vertex model, we propose an asymptotic form of the correlation functions for off-critical systems possessing rotational and mirror symmetries of the square lattice, i.e., the $C_{4v}$ symmetry. In comparison with the use of the Ornstein-Zernike form, it is efficient to investigate the correlation length with its directional dependence (or anisotropy). We investigate the $Q$-state Potts model on the square lattice. Monte Carlo (MC) simulations are performed using the infinite-size algorithm by Evertz and von der Linden. Fitting the MC data with the asymptotic form above the critical temperature, we reproduce the exact solution of the the anisotropic correlation length (ACL) of the Ising model $(Q=2)$ within a five-digit accuracy. For $Q=3$ and 4, we obtain numerical evidence that the asymptotic form is applicable to their correlation functions and the ACLs. Furthermore, we successfully apply it to the bond percolation problem which corresponds to the $Q\to 1$ limit. From the calculated ACLs, the equilibrium crystal shapes (ECSs) are derived via duality and Wulff's construction. Regarding $Q$ as a continuous variable, we find that the ECS of the $Q$-state Potts model is essentially the same as those of the Ising models on the Union Jack and 4-8 lattices, which are represented in terms of a simple algebraic curve of genus 1.

The Bose-Einstein condensates in a finite depth potential well provide an ideal platform to study the quantum escape dynamics. In this paper, the ground state, tunneling, and diffusion dynamics of the spin-orbit coupling (SOC) of Bose-Einstein condensates with two pseudospin components in a shallow trap are studied analytically and numerically. The phase transition between the plane-wave phase and zero-momentum phase of the ground state is obtained. Furthermore, the stability of the ground state is discussed, and the stability diagram in the parameter space is provided. The bound state (in which condensates are stably trapped in the potential well), the quasibound state (in which condensates tunnel through the well), and the unstable state (in which diffusion occurs) are revealed. We find that the finite depth potential well has an important effect on the phase transition of the ground state, and, interestingly, SOC can stabilize the system against the diffusion and manipulate the tunneling and diffusion dynamics. In particular, spatial anisotropic tunneling and diffusion dynamics of the two pseudospin components induced by SOC in quasibound and unstable states are observed. We provide an effective model and method to study and control the quantum tunneling and diffusion dynamics.

If interaction partners in social dilemma games are not selected randomly from the population but are instead determined by a network of contacts, it has far reaching consequences for the evolutionary dynamics. Selecting partners randomly leads to a well-mixed population, where pattern formation is essentially impossible. This rules out important mechanisms that can facilitate cooperation, most notably network reciprocity. In contrast, if interactions are determined by a lattice or a network, then the population is said to be structured, where cooperators can form compact clusters that protect them from invading defectors. Between these two extremes, however, there is ample middle ground that can be brought about by the consideration of temporal networks, mobility, or other coevolutionary processes. The question that we here seek to answer is, when does mixing on a lattice actually lead to well-mixed conditions? To that effect, we use the public goods game on a square lattice, and we consider nearest-neighbor and random mixing with different frequencies, as well as a mix of both mixing protocols. Not surprisingly, we find that nearest-neighbor mixing requires a higher frequency than random mixing to arrive at the well-mixed limit. The differences between the two mixing protocols are most expressed at intermediate mixing frequencies, whilst at very low and very high mixing frequencies the two almost converge. We also find a near universal exponential growth of the average size of cooperator clusters as their fraction increases from zero to one, regardless of whether this increase is due to increasing the multiplication factor of the public goods, decreasing the frequency of mixing, or gradually shifting the mixing from random to nearest neighbors.

The small-angle neutron scattering (SANS) on the chicken erythrocyte nuclei demonstrates the bifractal nature of the chromatin structural organization. Use of the contrast variation (${\mathrm{D}}_2\mathrm{O}-{\mathrm{H}}_2\mathrm{O}$) in SANS measurements reveals the differences in the DNA and protein arrangements inside the chromatin substance. It is the DNA that serves as a framework that constitutes the bifractal behavior showing the mass fractal properties with $D=2.22$ at a smaller scale and the logarithmic fractal behavior with $D\approx 3$ at a larger scale. The protein spatial organization shows the mass fractal properties with $D\approx 2.34$ throughout the whole nucleus. The borderline between two fractal levels can be significantly shifted toward smaller scales by centrifugation of the nuclei disposed on the dry substrate, since nuclei suffer from mechanical stress transforming them to a disklike shape. The height of this disk measured by atomic force microscopy (AFM) coincides closely with the fractal borderline, thus characterizing two types of the chromatin with the soft (at larger scale) and rigid (at smaller scale) properties. The combined SANS and AFM measurements demonstrate the stress induced switch of the DNA fractal properties from the rigid, but loosely packed, mass fractal to the soft, but densely packed, logarithmic fractal.

We investigate coarsening dynamics in the two-dimensional, incompressible Toner-Tu equation. We show that coarsening proceeds via vortex merger events, and the dynamics crucially depend on the Reynolds number $\text{Re}$. For low $\text{Re}$, the coarsening process has similarities to Ginzburg-Landau dynamics. On the other hand, for high $\text{Re}$, coarsening shows signatures of turbulence. In particular, we show the presence of an enstrophy cascade from the intervortex separation scale to the dissipation scale.

Memory effect in weakly aligned surface stabilized ferroelectric liquid crystal (SSFLC) material has been investigated by electro-optical and dielectric spectroscopy in three configurations of alignment: antiparallel, $90^{\circ }$ twisted, and unaligned planar samples. It has been observed that two types of molecular dynamics exist in antiparallel rubbed cell in which memory effect is observed for longer duration than in other samples. One dielectric relaxation process is near the surface of the electrode and a second is in the bulk of the SSFLC. Both the molecular dynamics contribute in the switching process and affect the memory phenomenon in surface stabilized geometries. However, a single dielectric process is observed in twisted geometry in which the sample is showing shorter memory effect than in antiparallel and this is compared with unaligned samples also having cell thickness less than the pitch value of FLC. In an unaligned sample, a single dielectric process is observed and the smaple does not show memory effect at all. The investigation is significant to understand the anomalies occurring in memory observations in various geometries.

Experiments performed in DECLIC-DSI on board the International Space Station evidenced oscillatory modes during the directional solidification of a bulk sample of succinonitrile-based transparent alloy. The interferometric data acquired during a reference experiment, $V_p=1$ $\mu \mathrm{m}/\mathrm{s}$ and $G=19 \mathrm{K}/\mathrm{cm}$, allowed us to reconstruct the cell shape and thus measure the cell tip position, radius, and growth velocity evolution, in order to quantify the dynamics of the oscillating cells. This study completes our previous reports [Bergeon et al., Phys. Rev. Lett. 110, 226102 (2013); Tourret et al., Phys. Rev. E 92, 042401 (2015); Pereda et al., Phys. Rev. E 95, 012803 (2017)] with, to our knowledge, the first complete monitoring of the geometric cell tip characteristics variations in bulk samples. The evolution of the shape, velocity, and position of the tip of the oscillating cells is associated with an evolution of the concentration field, inaccessible experimentally but mediating the diffusive interactions between the cells. The experimental results are supported by 3D phase-field simulations which evidence the existence of transversal solute fluxes between neighboring cells that play a fundamental role in the oscillation dynamics. The dynamics of oscillation of an individual cell is analyzed using a theoretical model based on classical equations of solidification through the calculation of the phase relationships between oscillation of the different tip characteristics.

In this contribution, we investigate the fundamental mechanism of plasticity in a model two-dimensional network glass. The glass is generated by using a Monte Carlo bond-switching algorithm and subjected to athermal simple shear deformation, followed by subsequent unloading at selected deformation states. This enables us to investigate the topological origin of reversible and irreversible atomic-scale rearrangements. It is shown that some events that are triggered during loading recover during unloading, while some do not. Thus, two kinds of elementary plastic events are observed, which can be linked to the network topology of the model glass.

Flagella are hairlike appendages attached to microorganisms that allow the organisms to traverse their fluid environment. The algae Volvox are spherical swimmers with thousands of individual flagella on their surface, and their coordination is not fully understood. In this work, a previously developed minimal model of flagella synchronization is extended to the outer surface of a sphere submerged in a fluid. Each beating flagellum tip is modeled as a small sphere, elastically bound to a circular orbit just above the spherical surface and a regularized image system for Stokes flow outside of a sphere is used to enforce the no-slip condition. Biologically relevant distributions of rotors results in a rapidly developing and robust symplectic metachronal wave traveling from the anterior to the posterior of the spherical Volvox body.

Significant advances have recently been made in modeling chaotic systems with the reservoir computing approach, especially for prediction. We find that although state prediction of the trained reservoir computer will gradually deviate from the actual trajectory of the original system, the associated geometric features remain invariant. Specifically, we show that the typical geometric metrics including the correlation dimension, the multiscale entropy, and the memory effect are nearly identical between the trained reservoir computer and its learned chaotic systems. We further demonstrate this fact on a broad range of chaotic systems ranging from discrete and continuous chaotic systems to hyperchaotic systems. Our findings suggest that the successfully reservoir computer may be topologically conjugate to an observed dynamical system.

Traditional origami starts from flat surfaces, leading to crease patterns consisting of Euclidean vertices. However, Euclidean vertices are limited in their folding motions, are degenerate, and suffer from misfolding. Here we show how non-Euclidean 4-vertices overcome these limitations by lifting this degeneracy, and that when the elasticity of the hinges is taken into account, non-Euclidean 4-vertices permit higher order multistability. We harness these advantages to design an origami inverter that does not suffer from misfolding and to physically realize a tristable vertex.

We investigate a disordered cluster Ising antiferromagnet in the presence of a transverse field. By adopting a replica cluster mean-field framework, we analyze the role of quantum fluctuations in a model with competing short-range antiferromagnetic and intercluster disordered interactions. The model exhibits paramagnetic (PM), antiferromagnetic (AF), and cluster spin-glass (CSG) phases, which are separated by thermal and quantum phase transitions. A scenario of strong competition between AF and CSG unveils a number of interesting phenomena induced by quantum fluctuations, including a quantum PM state and quantum driven criticality. The latter occurs when the thermally driven PM-AF discontinuous phase transition becomes continuous at strong transverse fields. Analogous phenomena have been reported in a number of systems, but a description of underlying mechanisms is still required. Our results indicate that quantum driven criticality can be found in a highly competitive regime of disordered antiferromagnets, which is in consonance with recent findings in spin models with competing interactions.

Power-law behaviors are common in many disciplines, especially in network science. Real-world networks, like disease spreading among people, are more likely to be interconnected communities, and show richer power-law behaviors than isolated networks. In this paper, we look at the system of two communities which are connected by bridge links between a fraction $r$ of bridge nodes, and study the effect of bridge nodes to the final state of the Susceptible-Infected-Recovered model by mapping it to link percolation. By keeping a fixed average connectivity, but allowing different transmissibilities along internal and bridge links, we theoretically derive different power-law asymptotic behaviors of the total fraction of the recovered $R$ in the final state as $r$ goes to zero, for different combinations of internal and bridge link transmissibilities. We also find crossover points where $R$ follows different power-law behaviors with $r$ on both sides when the internal transmissibility is below but close to its critical value for different bridge link transmissibilities. All of these power-law behaviors can be explained through different mechanisms of how finite clusters in each community are connected into the giant component of the whole system, and enable us to pick effective epidemic strategies and to better predict their impacts.

In bipartite networks, community structures are restricted to being disassortative, in that nodes of one type are grouped according to common patterns of connection with nodes of the other type. This makes the stochastic block model (SBM), a highly flexible generative model for networks with block structure, an intuitive choice for bipartite community detection. However, typical formulations of the SBM do not make use of the special structure of bipartite networks. Here we introduce a Bayesian nonparametric formulation of the SBM and a corresponding algorithm to efficiently find communities in bipartite networks which parsimoniously chooses the number of communities. The biSBM improves community detection results over general SBMs when data are noisy, improves the model resolution limit by a factor of $\sqrt{2}$, and expands our understanding of the complicated optimization landscape associated with community detection tasks. A direct comparison of certain terms of the prior distributions in the biSBM and a related high-resolution hierarchical SBM also reveals a counterintuitive regime of community detection problems, populated by smaller and sparser networks, where nonhierarchical models outperform their more flexible counterpart.

It is well known that suspensions of particles in a viscous fluid can affect the rheology significantly, producing a pronounced non-Newtonian response even in dilute suspension. However, it is unclear a priori which particle shapes lead to this behavior. We present two simple symmetry conditions on the shape which are sufficient for a dilute suspension to be Newtonian for all strain sizes and one sufficient for Newtonian behavior for small strains. We also construct a class of shapes out of thin, rigid rods not found by the symmetry argument which share this property for small strains.

Phase transitions in active fluids attracted significant attention within the last decades. Recent results show [L. Chen et al., New J. Phys. 17, 042002 (2015)] that an order-disorder phase transition in incompressible active fluids belongs to a new universality class. In this work, we further investigate this type of phase transition and focus on the effect of long-range interactions. This is achieved by introducing a nonlocal shear stress into the hydrodynamic description, which leads to superdiffusion of the velocity field, and can be viewed as a result of the active particles performing Lévy walks. The universal properties in the critical region are derived by performing a perturbative renormalization group analysis of the corresponding response functional within the one-loop approximation. We show that the effect of nonlocal shear stress decreases the upper critical dimension of the model, and can lead to the irrelevance of the active fluid self-advection with the resulting model belonging to an unusual long-range Model A universality class not reported before, to our knowledge. Moreover, when the degree of nonlocality is sufficiently high all nonlinearities become irrelevant and the mean-field description is valid in any spatial dimension.

Recently, the importance of higher-order interactions in the physics of quantum systems and nanoparticle assemblies has prompted the exploration of new classes of networks that grow through geometrically constrained simplex aggregation. Based on the model of chemically tunable self-assembly of simplexes [Šuvakov et al., Sci. Rep. 8, 1987 (2018)], here we extend the model to allow the presence of a defect edge per simplex. Using a wide distribution of simplex sizes (from edges, triangles, tetrahedrons, etc., up to 10-cliques) and various chemical affinity parameters, we investigate the magnitude of the impact of defects on the self-assembly process and the emerging higher-order networks. Their essential characteristics are treelike patterns of defect bonds, hyperbolic geometry, and simplicial complexes, which are described using the algebraic topology method. Furthermore, we demonstrate how the presence of patterned defects can be used to alter the structure of the assembly after the growth process is complete. In the assemblies grown under different chemical affinities, we consider the removal of defect bonds and analyze the progressive changes in the hierarchical architecture of simplicial complexes and the hyperbolicity parameters of the underlying graphs. Within the framework of cooperative self-assembly of nanonetworks, these results shed light on the use of defects in the design of complex materials. They also provide a different perspective on the understanding of extended connectivity beyond pairwise interactions in many complex systems.

Electrokinetics is the science of the physical phenomena appearing at the solid-liquid interface of dispersed particles subjected to external fields. Techniques based on electrokinetic phenomena constitute an important set of tools for the electrical characterization of colloids because of their sensitivity to the properties of particle-solution interfaces. Their rigorous description may require inclusion of the effects of finite size of chemical species in the theoretical models, and, particularly in the case of salt-free (no external salt added) aqueous colloids, also consideration of water dissociation and possible carbon dioxide contamination in the aqueous solution. A new ac electrokinetic model is presented for concentrated salt-free spherical colloids for arbitrary characteristics of the particles and aqueous solution, including finite-size effects of chemical species by appropriate modifications of the chemical reaction equations to include such non-ideal aspects. The numerical solution of the electrokinetic equations in an alternating electric field has also been carried out by using a realistic non-equilibrium scenario accounting for association-dissociation processes in the chemical reactions. The results demonstrate the importance of including finite-size effects in the electrokinetic response of the colloid, mainly at high frequencies of the electric field, and for highly charged colloids. Findings of previous models for pointlike ions or for ideal salt-free colloids including finite ion size effects are recovered with the present model, for the appropriate limiting conditions.