Experiments of the recrystallization processes in two-dimensional complex plasmas are analyzed to rigorously test a recently developed scale-free phase transition theory. The “fractal-domain-structure” (FDS) theory is based on the kinetic theory of Frenkel. It assumes the formation of homogeneous domains, separated by defect lines, during crystallization and a fractal relationship between domain area and boundary length. For the defect number fraction and system energy a scale-free power-law relation is predicted. The long-range scaling behavior of the bond-order correlation function shows clearly that the complex plasma phase transitions are not of the Kosterlitz, Thouless, Halperin, Nelson, and Young type. Previous preliminary results obtained by counting the number of dislocations and applying a bond-order metric for structural analysis are reproduced. These findings are supplemented by extending the use of the bond-order metric to measure the defect number fraction and furthermore applying state-of-the-art analysis methods, allowing a systematic testing of the FDS theory with unprecedented scrutiny: A morphological analysis of lattice structure is performed via Minkowski tensor methods. Minkowski tensors form a complete family of additive, motion covariant and continuous morphological measures that are sensitive to nonlinear properties. The FDS theory is rigorously confirmed and predictions of the theory are reproduced extremely well. The predicted scale-free power-law relation between defect fraction number and system energy is verified for one more order of magnitude at high energies compared to the inherently discontinuous bond-order metric. It is found that the fractal relation between crystalline domain area and circumference is independent of the experiment, the particular Minkowski tensor method, and the particular choice of parameters. Thus, the fractal relationship seems to be inherent to two-dimensional phase transitions in complex plasmas. Minkowski tensor analysis turns out to be a powerful tool for investigations of crystallization processes. It is capable of revealing nonlinear local topological properties, however, still provides easily interpretable results founded on a solid mathematical framework.

Discrete-spin systems with maximally random nearest-neighbor interactions that can be symmetric or asymmetric, ferromagnetic or antiferromagnetic, including off-diagonal disorder, are studied, for the number of states $q=3,4$ in $d$ dimensions. We use renormalization-group theory that is exact for hierarchical lattices and approximate (Migdal-Kadanoff) for hypercubic lattices. For all $d>1$ and all noninfinite temperatures, the system eventually renormalizes to a random single state, thus signaling $q\times q$ degenerate ordering. Note that this is the maximally degenerate ordering. For high-temperature initial conditions, the system crosses over to this highly degenerate ordering only after spending many renormalization-group iterations near the disordered (infinite-temperature) fixed point. Thus, a temperature range of short-range disorder in the presence of long-range order is identified, as previously seen in underfrustrated Ising spin-glass systems. The entropy is calculated for all temperatures, behaves similarly for ferromagnetic and antiferromagnetic interactions, and shows a derivative maximum at the short-range disordering temperature. With a sharp immediate contrast of infinitesimally higher dimension $1+\epsilon$, the system is as expected disordered at all temperatures for $d=1$.

Graph theory constitutes a widely used and established field providing powerful tools for the characterization of complex networks. The intricate topology of networks can also be investigated by means of the collective dynamics observed in the interactions of self-sustained oscillations (synchronization patterns) or propagationlike processes such as random walks. However, networks are often inferred from real-data-forming dynamic systems, which are different from those employed to reveal their topological characteristics. This stresses the necessity for a theoretical framework dedicated to the mutual relationship between the structure and dynamics in complex networks, as the two sides of the same coin. Here we propose a rigorous framework based on the network response over time (i.e., Green function) to study interactions between nodes across time. For this purpose we define the flow that describes the interplay between the network connectivity and external inputs. This multivariate measure relates to the concepts of graph communicability and the map equation. We illustrate our theory using the multivariate Ornstein-Uhlenbeck process, which describes stable and non-conservative dynamics, but the formalism can be adapted to other local dynamics for which the Green function is known. We provide applications to classical network examples, such as small-world ring and hierarchical networks. Our theory defines a comprehensive framework that is canonically related to directed and weighted networks, thus paving a way to revise the standards for network analysis, from the pairwise interactions between nodes to the global properties of networks including community detection.

We experimentally characterize the impact response of concentrated suspensions consisting of cornstarch and water. We observe that the suspensions support a large normal stress—on the order of MPa—with a delay after the impactor hits the suspension surface. We show that neither the delay nor the magnitude of the stress can yet be explained by either standard rheological models of shear thickening in terms of steady-state viscosities, or impact models based on added mass or other inertial effects. The stress increase occurs when a dynamically jammed region of the suspension in front of the impactor propagates to the opposite boundary of the container, which can support large stresses when it spans between solid boundaries. We present a constitutive relation for impact rheology to relate the force on the impactor to its displacement. This can be described in terms of an effective modulus but only after the delay required for the dynamically jammed region to span between solid boundaries. Both the modulus and the delay are reported as a function of impact velocity, fluid height, and weight fraction. We report in a companion paper the structure of the dynamically jammed region when it spans between the impactor and the opposite boundary [Allen et al., Phys. Rev. E 97, 052603 (2018)]. In a direct follow-up paper, we show that this constitutive model can be used to quantitatively predict, for example, the trajectory and penetration depth of the foot of a person walking or running on cornstarch and water [Mukhopadhyay et al., Phys. Rev. E 97, 052604 (2018)].

We experimentally characterize the structure of concentrated suspensions of cornstarch and water in response to impact. Using surface imaging and particle tracking at the boundary opposite the impactor, we observed that a visible structure and particle flow at the boundary occur with a delay after impact. We show the delay time is about the same time as the strong stress response, confirming that the strong stress response results from deformation of the dynamically jammed structure once it spans between the impactor and a solid boundary. A characterization of this strong stress response is reported in a companion paper [Maharjan, Mukhopadhyay, Allen, Storz, and Brown, Phys. Rev. E 97, 052602 (2018)]. We observed particle flow in the outer part of the dynamically jammed region at the bottom boundary, with a net transverse displacement of up to about 5% of the impactor displacement, indicating shear at the boundary. Direct imaging of the surface of the outer part of the dynamically jammed region reveals a change in surface structure that appears the same as the result of dilation in other cornstarch suspensions. Imaging also reveals cracks, like a brittle solid. These observations suggest the dynamically jammed structure can temporarily support stress according to an effective modulus, like a soil or dense granular material, along a network of frictional contacts between the impactor and solid boundary.

The ability of a person to run on the surface of a suspension of cornstarch and water has fascinated scientists and the public alike. However, the constitutive relation obtained from traditional steady-state rheology of cornstarch and water suspensions has failed to explain this behavior. In another paper we presented an averaged constitutive relation for impact rheology consisting of an effective compressive modulus of a system-spanning dynamically jammed structure [R. Maharjan et al., this issue, Phys. Rev. E 97, 052602 (2018)]. Here we show that this constitutive model can be used to quantitatively predict, for example, the trajectory and penetration depth of the foot of a person walking or running on cornstarch and water. The ability of the constitutive relation to predict the material behavior in a case with different forcing conditions and flow geometry than it was obtained from suggests that the constitutive relation could be applied more generally. We also present a detailed calculation of the added mass effect to show that while it may be able to explain some cases of people running or walking on the surface of cornstarch and water for pool depths $H>1.2$ m and foot impact velocities $V_I>1.7$ m/s, it cannot explain observations of people walking or running on the surface of cornstarch and water for smaller $H$ or $V_I$.

Active colloids and liquid crystals are capable of locally converting the macroscopically supplied energy into directional motion and promise a host of new applications, ranging from drug delivery to cargo transport at the mesoscale. Here we uncover how topological solitons in liquid crystals can locally transform electric energy to translational motion and allow for the transport of cargo along directions dependent on frequency of the applied electric field. By combining polarized optical video microscopy and numerical modeling that reproduces both the equilibrium structures of solitons and their temporal evolution in applied fields, we uncover the physical underpinnings behind this reconfigurable motion and study how it depends on the structure and topology of solitons. We show that, unexpectedly, the directional motion of solitons with and without the cargo arises mainly from the asymmetry in rotational dynamics of molecular ordering in liquid crystal rather than from the asymmetry of fluid flows, as in conventional active soft matter systems.

We present a method and an implementation for smooth linear motion in a finite-difference-based micromagnetic simulation code, to be used in simulating magnetic friction and other phenomena involving moving microscale magnets. Our aim is to accurately simulate the magnetization dynamics and relative motion of magnets while retaining high computational speed. To this end, we combine techniques for fast scalar potential calculation and cubic b-spline interpolation, parallelizing them on a graphics processing unit (GPU). The implementation also includes the possibility of explicitly simulating eddy currents in the case of conducting magnets. We test our implementation by providing numerical examples of stick-slip motion of thin films pulled by a spring and the effect of eddy currents on the switching time of magnetic nanocubes.

The influence of natural convection on lamellar eutectic growth was determined by a comprehensive phase-field lattice-Boltzmann study for Al-Cu and $\mathrm{CB}{\mathrm{r}}_4\text{−}{\mathrm{C}}_2\mathrm{C}{\mathrm{l}}_6$ eutectic alloys. The mass differences resulting from concentration differences led to the fluid flow and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency. By means of carefully designed “numerical experiments”, the eutectic growth under natural convection was explored and a simple analytical model was proposed to predict the adjustment of the lamellar spacing. Furthermore, by alternating the solute expansion coefficient, initial lamellar spacing, and undercooling, the microstructure evolution was presented and compared with the classical eutectic growth theory. Results showed that both interfacial solute distribution and average curvature were affected by the natural convection, the effect of which could be further quantified by adding a constant into the growth rule proposed by Jackson and Hunt [Jackson and Hunt, Trans. Metall. Soc. AIME 236, 1129 (1966)].

Functional oscillator networks, such as neuronal networks in the brain, exhibit switching between metastable states involving many oscillators. We give exact results how such global dynamics can arise in paradigmatic phase oscillator networks: Higher-order network interactions give rise to metastable chimeras—localized frequency synchrony patterns—which are joined by heteroclinic connections. Moreover, we illuminate the mechanisms that underly the switching dynamics in these experimentally accessible networks.

Critical properties of the two-dimensional $XY$ model involving solely nematic-like terms of the second and third orders are investigated by spin-wave analysis and Monte Carlo simulation. It is found that, even though neither of the nematic-like terms alone can induce magnetic ordering, their coexistence and competition leads to an extended phase of the magnetic quasi-long-range-order phase, wedged between the two nematic-like phases induced by the respective couplings. Thus, except for the multicritical point, at which all the phases meet, for any finite value of the coupling parameters ratio there are two phase transition: one from the paramagnetic phase to one of the two nematic-like phases followed by another one at lower temperatures to the magnetic phase. The finite-size scaling analysis indicates that the phase transitions between the magnetic and nematic-like phases belong to the Ising and three-state Potts universality classes. Inside the competition-induced algebraic magnetic phase, the spin-pair correlation function is found to decay even much more slowly than in the standard $XY$ model with purely magnetic interactions. Such a magnetic phase is characterized by an extremely low vortex-antivortex pair density attaining a minimum close to the point at which the two couplings are of about equal strength.

This paper deals with the stabilization of a spatially uniform steady state in two coupled one-dimensional reaction-diffusion systems with Turing instability. This stabilization corresponds to amplitude death that occurs in a coupled system with Turing instability. Stability analysis of the steady state shows that stabilization does not occur if the two reaction-diffusion systems are identical. We derive a sufficient condition for the steady state to be stable for any length of system and any boundary conditions. Our analytical results are supported with numerical examples.

In the shear flow of liquid crystalline polymers (LCPs) the nematic director orientation can align with the flow direction for some materials but continuously tumble in others. The nematic dumbbell (ND) model was originally developed to describe the rheology of flow-aligning semiflexible LCPs, and flow-aligning LCPs are the focus in this paper. In the shear flow of monodomain LCPs, it is usually assumed that the spatial distribution of the velocity is uniform. This is in contrast to polymer solutions, where highly nonuniform spatial velocity profiles have been observed in experiments. We analyze the ND model, with an additional gradient term in the constitutive model, using a linear stability analysis. We investigate the separate cases of constant applied shear stress and constant applied shear rate. We find that the ND model has a transient flow instability to the formation of a spatially inhomogeneous flow velocity for certain starting orientations of the director. We calculate the spatially resolved flow profile in both constant applied stress and constant applied shear rate in start up from rest, using a model with one spatial dimension to illustrate the flow behavior of the fluid. For low shear rates flow reversal can be seen as the director realigns with the flow direction, whereas for high shear rates the director reorientation occurs simultaneously across the gap. Experimentally, this inhomogeneous flow is predicted to be observed in flow reversal experiments in LCPs.

Brine reaction and precipitation in porous media sometimes occur in the presence of a strong fluid flowing field, which induces the mobilization of the precipitated salts and distorts their spatial distribution. It is interesting to investigate how the distribution responds to such mobilization. We view these precipitates as random walkers in the complex inner space of the porous media, where they make stochastic jumps among locations and possibly wait between successive transitions. In consideration of related experimental results, the waiting time of the precipitates at a particular position is allowed to range widely from short sojourn to permanent residence. Through the model of a continuous-time random walk, a class of time-fractional equations for the precipitate's concentration profile is derived, including that in the Riemann-Liouville formalism and the Prabhakar formalism. The solutions to these equations show the general pattern of the precipitate's spatiotemporal evolution: a coupling of mass accumulation and mass transport. And the degree to which the mass is mobilized turns out to be monotonically correlated to the fractional exponent $\alpha$. Moreover, to keep the completeness of the model, we further discuss how the interaction among the precipitates influences the precipitation process. In doing so, a time-fractional non-linear Fokker-Planck equation with source term is introduced and solved. It is shown that the interaction among the precipitates slightly perturbs their spatial distribution. This distribution is largely dominated by the brine reaction itself and the interaction between the precipitates and the porous media.

We show that stability of planetary systems is intimately connected with their internal order. An arbitrary initial distribution of planets is susceptible to catastrophic events in which planets either collide or are ejected from the planetary system. These instabilities are a fundamental consequence of chaotic dynamics and of Arnold diffusion characteristic of many body gravitational interactions. To ensure stability over astronomical time scale of a realistic planetary system—in which planets have masses comparable to those of planets in the solar system—the motion must be quasiperiodic. A dynamical mechanism is proposed which naturally evolves a planetary system to a quasiperiodic state from an arbitrary initial condition. A planetary self-organization predicted by the theory is similar to the one found in our solar system.

Cooperation is central to the success of human societies as it is crucial for overcoming some of the most pressing social challenges of our time; still, how human cooperation is achieved and may persist is a main puzzle in the social and biological sciences. Recently, scholars have recognized the importance of social norms as solutions to major local and large-scale collective action problems, from the management of water resources to the reduction of smoking in public places to the change in fertility practices. Yet a well-founded model of the effect of social norms on human cooperation is still lacking. Using statistical-physics techniques and integrating findings from cognitive and behavioral sciences, we present an analytically tractable model in which individuals base their decisions to cooperate both on the economic rewards they obtain and on the degree to which their action complies with social norms. Results from this parsimonious model are in agreement with observations in recent large-scale experiments with humans. We also find the phase diagram of the model and show that the experimental human group is poised near a critical point, a regime where recent work suggests living systems respond to changing external conditions in an efficient and coordinated manner.

We investigate the application of artificial neural networks to stabilize proper orthogonal decomposition-based reduced order models for quasistationary geophysical turbulent flows. An extreme learning machine concept is introduced for computing an eddy-viscosity closure dynamically to incorporate the effects of the truncated modes. We consider a four-gyre wind-driven ocean circulation problem as our prototype setting to assess the performance of the proposed data-driven approach. Our framework provides a significant reduction in computational time and effectively retains the dynamics of the full-order model during the forward simulation period beyond the training data set. Furthermore, we show that the method is robust for larger choices of time steps and can be used as an efficient and reliable tool for long time integration of general circulation models.

Neural field theory is used to predict and analyze the phenomenon of perceptual echo in which random input stimuli at one location are correlated with electroencephalographic responses at other locations. It is shown that this echo correlation (EC) yields an estimate of the transfer function from the stimulated point to other locations. Modal analysis then explains the observed spatiotemporal structure of visually driven EC and the dominance of the alpha frequency; two eigenmodes of similar amplitude dominate the response, leading to temporal beating and a line of low correlation that runs from the crown of the head toward the ears. These effects result from mode splitting and symmetry breaking caused by interhemispheric coupling and cortical folding. It is shown how eigenmodes obtained from functional magnetic resonance imaging experiments can be combined with temporal dynamics from EC or other evoked responses to estimate the spatiotemporal transfer function between any two points and hence their effective connectivity.

We investigate the alternating current (ac) -driven electroconvection (EC) in one-dimensional cells (1DCs) under the in-plane switching mode. In 1DCs, defect-free EC can be realized. In the presence and absence of external multiplicative noise, the features of traveling waves (TWs), such as their Hopf frequency $f_{\mathrm{H}}$ and velocity, are examined in comparison with those of conventional two-dimensional cells (2DCs) accompanying defects of EC rolls. In particular, we show that the defects significantly contribute to the features of the TWs. Additionally, owing to the defect-free EC in the 1DCs, the effects of the ac and noise fields on the TW are clarified. The ac field linearly increases $f_{\mathrm{H}}$, independent of the ac frequency $f$. The noise increases $f_{\mathrm{H}}$ monotonically, but $f_{\mathrm{H}}$ does not vary below a characteristic noise intensity $V_{\mathrm{N}}^{*}$. In addition, soliton-like waves and unfamiliar oscillation of EC vortices in 1DCs are observed, in contrast to the localized EC (called worms) and the oscillation of EC rolls in 2DCs.

A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phase-field methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of interest to examine nucleation in the more recently proposed phase-field crystal (PFC) model, which attempts to bridge the atomic and mesoscale regimes in microstructure simulations. In this work, we numerically calculate homogeneous liquid-to-solid nucleation rates and incubation times in the simplest version of the PFC model, for various parameter choices. We show that the model naturally exhibits qualitative agreement with the predictions of classical nucleation theory (CNT) despite a lack of some explicit atomistic features presumed in CNT. We also examine the early appearance of lattice structure in nucleating grains, finding disagreement with some basic assumptions of CNT. We then argue that a quantitatively correct nucleation theory for the PFC model would require extending CNT to a multivariable theory.