Marginally stable systems exhibit rich critical mechanical behavior. Such isostatic assemblies can be actively driven, but it is unclear how their critical nature affects their nonequilibrium dynamics. Here, we study the influence of isostaticity on the nonequilibrium dynamics of active spring networks. In our model, heterogeneously distributed white or colored, motorlike noise drives the system into a nonequilibrium steady state. We quantify the nonequilibrium dynamics of pairs of network nodes by the characteristic cycling frequency $\omega$—an experimentally accessible measure of the circulation of the associated phase space currents. The distribution of these cycling frequencies exhibits critical scaling, which we approximately capture by a mean-field theory. Finally, we show that the scaling behavior of $\omega$ with distance is controlled by a diverging length scale. Overall, we provide a theoretical approach to elucidate the role of marginality in active disordered systems.

Wing flexibility is one of the important factors not only for lift and thrust generation and enhancement in flapping flight but also for development of micro-air vehicles with flapping wings. In this study, we construct a flexible wing with chordwise flexibility by connecting two rigid plates with a torsion spring, and investigate the effect of chordwise wing flexibility on the flapping flight of a simple butterfly model by using an immersed boundary-lattice Boltzmann method. First, we investigate the effects of the spring stiffness on the aerodynamic performance when the body of the model is fixed. We find that the time-averaged lift and thrust forces and the required power increase with the spring stiffness. In addition, we find an appropriate range of the spring stiffness where the time-averaged lift and thrust forces are larger than those of the rigid wings. The mechanism of the lift and thrust enhancements is as follows: in the downstroke the flexible wings can generate not only the lift force but also the thrust force due to the deformation of wings; in the upstroke the flexible wings can generate not only the thrust force but also the lift force due to the deformation of wings. Second, we simulate free flights when the body of the model can only move translationally. We find that the model with the flexible wings at an appropriate value of the spring stiffness can fly more effectively than the model with the rigid wings, which is consistent with the results when the body of the model is fixed. Finally, we simulate free flights with pitching rotation. We find that the model gets off balance for any value of the spring stiffness. Therefore, the passive control of the pitching motion by the chordwise wing flexibility cannot be expected for the present butterfly model.

Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the limiting factor for these calculations. Here we show that a partial diagonalization of the largest clusters in the expansion using the Lanczos algorithm can be as useful as full diagonalization for the method while mitigating some of the time and memory issues. As test cases, we consider the frustrated Heisenberg model on the checkerboard lattice and the Fermi-Hubbard model on the square lattice. We find that our approach can surpass state of the art in performance in a parallel environment.

The “edge of chaos” phase transition in artificial neural networks is of renewed interest in light of recent evidence for criticality in brain dynamics. Statistical mechanics traditionally studied this transition with connectivity $k$ as the control parameter and an exactly balanced excitation-inhibition ratio. While critical connectivity has been found to be low in these model systems, typically around $k=2$, which is unrealistic for natural neural systems, a recent study utilizing the excitation-inhibition ratio as the control parameter found a new, nearly degree independent, critical point when connectivity is large. However, the new phase transition is accompanied by an unnaturally high level of activity in the network. Here we study random neural networks with the additional properties of (i) a high clustering coefficient and (ii) neurons that are solely either excitatory or inhibitory, a prominent property of natural neurons. As a result, we observe an additional critical point for networks with large connectivity, regardless of degree distribution, which exhibits low activity levels that compare well with neuronal brain networks.

Dense Rydberg gases are out-of-equilibrium systems where strong density-density interactions give rise to effective kinetic constraints. They cause dynamic arrest associated with highly constrained many-body configurations, leading to slow relaxation and glassy behavior. Multicomponent Rydberg gases feature additional long-range interactions such as excitation exchange. These are analogous to particle swaps used to artificially accelerate relaxation in simulations of atomistic models of classical glass formers. In Rydberg gases, however, swaps are real physical processes, which provide dynamical shortcuts to relaxation. They permit the accelerated approach to stationarity in experiment and at the same time have an impact on the nonequilibrium stationary state. In particular, their interplay with radiative decay processes amplifies irreversibility of the dynamics, an effect which we quantify via the entropy production at stationarity. Our work highlights an intriguing analogy between real dynamical processes in Rydberg gases and artificial dynamics underlying advanced Monte Carlo methods. Moreover, it delivers a quantitative characterization of the dramatic effect swaps have on the structure and dynamics of their stationary state.

One of the vital roles of computing is to solve large-scale combinatorial optimization problems in a short time. In recent years, methods have been proposed that map optimization problems to ones of searching for the ground state of an Ising model by using a stochastic process. Simulated annealing (SA) is a representative algorithm. However, it is inherently difficult to perform a parallel search. Here we propose an algorithm called momentum annealing (MA), which, unlike SA, updates all spins of fully connected Ising models simultaneously and can be implemented on GPUs that are widely used for scientific computing. MA running in parallel on GPUs is 250 times faster than SA running on a modern CPU at solving problems involving 100 000 spin Ising models.

The structural, thermodynamic, and vapor-liquid equilibria properties of the double-Gaussian core model (DGM) potential are studied via molecular simulation. Results are presented for the pressure ($p$), potential energy (U), isochoric and isobaric heat capacities $\left(C_{V,p}\right)$, isothermal compressibility $\left({\beta }_T\right)$, isochoric thermal pressure coefficient $\left({\gamma }_V\right)$, thermal expansion coefficient $\left({\alpha }_p\right)$, speed of sound $\left({\omega }_0\right)$, and the Joule-Thomson coefficient $\left({\mu }_{\mathrm{JT}}\right)$, which are compared with simulations for the Gaussian core model (GCM) potential. A feature of the simulations is that both the GCM and DGM potentials reproduce many of the anomalous properties of water, such as a maximum density, ${\gamma }_V<0$, maximum values for both ${\alpha }_p$ and ${\beta }_T$, and minimum values in both $C_p$ and ${\omega }_0$. The presence of attractive interaction enhances the anomalies and also yields some additional features such as a more structured vapor phase and Joule-Thomson inversion.

The conformational states of a semiflexible polymer enclosed in a compact domain of typical size $a$ are studied as stochastic realizations of paths defined by the Frenet equations under the assumption that stochastic “curvature” satisfies a white noise fluctuation theorem. This approach allows us to derive the Hermans-Ullman equation, where we exploit a multipolar decomposition that allows us to show that the positional probability density function is well described by a telegrapher's equation whenever $2a/{\ell }_p>1$, where ${\ell }_p$ is the persistence length. We also develop a Monte Carlo algorithm for use in computer simulations in order to study the conformational states in a compact domain. In addition, the case of a semiflexible polymer enclosed in a square domain of side $a$ is presented as an explicit example of the formulated theory and algorithm. In this case, we show the existence of a polymer shape transition similar to the one found by Spakowitz and Wang [Phys. Rev. Lett. 91, 166102 (2003)] where in this case the critical persistence length is ${\ell }_p^{*}\simeq a/8$ such that the mean-square end-to-end distance exhibits an oscillating behavior for values ${\ell }_p>{\ell }_p^{*}$, whereas for ${\ell }_p<{\ell }_p^{*}$ it behaves monotonically increasing.

We study a dilute suspension of magnetic nanoparticles in a nematic-filled channel and how the spatial magnetization $\mathbf{M}$ can be tailored by the nematic anisotropy. We study the spatial configurations as stable critical points of a generalized phenomenological energy for a dilute ferronematic in the absence of external magnetic fields. We show how spatial inhomogeneities in the equilibrium nematic profile, induced by confinement and boundary effects, generate nonzero spatially inhomogeneous magnetization profiles in the system. Depending on the magnetonematic coupling energy, $\mathbf{M}$ can either follow the nematic profile for large coupling or exhibit distinct polydomain structures separated by defect lines for weak coupling and low temperatures. Some exact solutions for prototypical situations are also obtained.

We investigate the Marangoni instability in a thin layer of viscoelastic fluid, confined between its deformable free surface and a substrate of low thermal conductivity. Following a theoretical analysis, we study the stability of the present system for the case when the fluid layer is subjected to heating from below. Here, we use the Maxwell model to depict the rheology of the viscoelastic fluid. Linear stability analysis of the quiescent base state reveals that, in addition to the conventional short-wave mode, a long-wave instability can also emerge in this system. We demonstrate the appearance of both the long-wave monotonic and oscillatory instabilities in such a system. We study this long-wave mode analytically using the scaling $k\sim \sqrt{\mathrm{Bi}}$ ($k$ is the wave number and Bi is the Biot number), whereas the short-wave mode is examined numerically. The influential role of elasticity of the fluid and the other involved parameters on the stability of the system is aptly discussed, and their ranges are identified within which a particular instability mode gets critical.

We have revealed statistical physics of synchronized traffic flow that is governed by a spatiotemporal competition between $S\to F$ and $S\to J$ instabilities (where $F$, $S$, and $J$ denote, respectively, the free flow, synchronized flow, and wide moving jam traffic phases). A probabilistic analysis of synchronized flow based on simulations of a cellular automaton model in the framework of three-phase traffic theory is made. This probabilistic analysis shows that there is a finite range of the initial space gap between vehicles in synchronized flow within which during a chosen time for traffic observation either synchronized flow persists with probability $P_{\mathrm{S}}$, or an $S\to F$ transition occurs with probability $P_{SF}$, or else an $S\to J$ transition occurs with probability $P_{SJ}$. Space-gap dependencies of the probabilities $P_S$, $P_{SF}$, and $P_{SJ}$ have been found. It has been also found that (i) an initial $S\to F$ instability can lead to sequences of $S\to F\to S\to J$ transitions; (ii) an initial $S\to J$ instability can lead to sequences of $S\to J\to S\to F$ transitions. Each of the phase transitions in the sequences $S\to F\to S\to J$ transitions and $S\to J\to S\to F$ transitions exhibits the nucleation nature; these sequences of phase transitions determine spatiotemporal features of traffic patterns resulting from the competition between $S\to F$ and $S\to J$ instabilities. The statistical features of synchronized flow found for a homogeneous road remain qualitatively for a road with a bottleneck. However, rather than nuclei for $S\to F$ and $S\to J$ instabilities occurring at random road locations of the homogeneous road, due to a permanent nonhomogeneity introduced by the bottleneck, nuclei for initial $S\to F$ and $S\to J$ instabilities appear mostly at the bottleneck.

During mitosis, microtubules form a spindle, which is responsible for proper segregation of the genetic material. A common structural element in a mitotic spindle is a parallel bundle, consisting of two or more microtubules growing from the same origin and held together by cross-linking proteins. An interesting question is what are the physical principles underlying the formation and stability of such microtubule bundles. Here we show, by introducing the pivot-and-bond model, that random angular movement of microtubules around the spindle pole and forces exerted by cross-linking proteins can explain the formation of microtubule bundles as observed in our experiments. The model predicts that stable parallel bundles can form in the presence of either passive crosslinkers or plus-end directed motors, but not minus-end directed motors. In the cases where bundles form, the time needed for their formation depends mainly on the concentration of cross-linking proteins and the angular diffusion of the microtubule. In conclusion, the angular motion drives the alignment of microtubules, which in turn allows the cross-linking proteins to connect the microtubules into a stable bundle.

We investigate how chiral dopants affect the chiral symmetry breaking of lyotropic chromonic liquid crystals (LCLCs) focusing on the double-twist (DT) director configurations in a cylindrical capillary. LCLCs of unusual elastic properties tend to exhibit chiral director configurations under confinement despite the absence of intrinsic chirality. The DT director configuration in a cylindrical cavity with a degenerate planar anchoring, resulting from the large saddle-splay-to-twist elastic modulus ratio, is a representative example. Here we start by reexamining the DT configuration of nematic disodium cromoglycate in a cylindrical capillary and estimate the ratio of saddle splay to bend modulus $K_{24}/K_3=0.5\pm 0.1$. Additionally, we study the DT configurations of the chiral nematic LCLCs with chiral dopants. The DT configuration becomes homochiral when the dopant concentration surpasses the critical concentration. We characterize these chiral DT configurations and provide a theoretical model on their energetics. Finally, we observe how the enantiomeric excess of chiral dopants determines the director configuration when dopants of two different handednesses are mixed.

We investigate the finite-power performance of quantum heat engines working in the linear response regime where the temperature gradient is small. The engine cycles with working substances of ideal harmonic systems consist of two heat transfer and two adiabatic processes, such as the Carnot cycle, Otto cycle, and Brayton cycle. By analyzing the optimal protocol under maximum power we derive the explicitly analytic expression for the irreversible entropy production, which becomes the low dissipation form in the long duration limit. Assuming the engine to be endoreversible, we derive the universal expression for the efficiency at maximum power, which agrees well with that obtained from the phenomenological heat transfer laws holding in the classical thermodynamics. Through appropriate identification of the thermodynamic fluxes and forces that a linear relation connects, we find that the quantum engines under consideration are tightly coupled, and the universality of efficiency at maximum power is confirmed at the linear order in the temperature gradient.

A Lévy walk of order $\beta$ is studied on an interval of length $L$, driven out of equilibrium by different-density boundary baths. The anomalous current generated under these settings is nonlocally related to the density profile through an integral equation. While the asymptotic solution to this equation is known, its finite-$L$ corrections remain unstudied despite their importance in the study of anomalous transport. Here a perturbative method for computing such corrections is presented and explicitly demonstrated for the leading correction to the asymptotic transport of a Lévy walk of order $\beta =\frac{5}{3}$, which represents a broad universal class of anomalous transport models. Surprisingly, many other physical problems are described by similar integral equations, to which the method introduced here can be directly applied.

The brittle to quasibrittle transition has been studied for a compound of two different kinds of fibrous materials, having distinct difference in their breaking strengths under the framework of the fiber bundle model. A random fiber bundle model has been devised with a bimodal distribution of the breaking strengths of the individual fibers. The bimodal distribution is assumed to consist of two symmetrically placed rectangular probability distributions of strengths $p$ and $1-p$, each of width $d$, and separated by a gap $2s$. Different properties of the transition have been studied varying these three parameters and using the well-known equal load-sharing dynamics. Our study exhibits a brittle to quasibrittle transition at the critical width $d_c(s,p)=p(1/2-s)/(1+p)$ confirmed by our numerical results.

The big-jump principle is a well-established mathematical result for sums of independent and identically distributed random variables extracted from a fat-tailed distribution. It states that the tail of the distribution of the sum is the same as the distribution of the largest summand. In practice, it means that when in a stochastic process the relevant quantity is a sum of variables, the mechanism leading to rare events is peculiar: Instead of being caused by a set of many small deviations all in the same direction, one jump, the biggest of the lot, provides the main contribution to the rare large fluctuation. We reformulate and elevate the big-jump principle beyond its current status to allow it to deal with correlations, finite cutoffs, continuous paths, memory, and quenched disorder. Doing so we are able to predict rare events using the extended big-jump principle in Lévy walks, in a model of laser cooling, in a scattering process on a heterogeneous structure, and in a class of Lévy walks with memory. We argue that the generalized big-jump principle can serve as an excellent guideline for reliable estimates of risk and probabilities of rare events in many complex processes featuring heavy-tailed distributions, ranging from contamination spreading to active transport in the cell.

We suggest alternative quantum Otto engines, using heat bath algorithmic cooling with a partner pairing algorithm instead of isochoric cooling and using quantum swap operations instead of quantum adiabatic processes. Liquid state nuclear magnetic resonance systems in a single entropy sink are treated as working fluids. The extractable work and thermal efficiency are analyzed in detail for four-stroke and two-stroke types of alternative quantum Otto engines. The role of the heat bath algorithmic cooling in these cycles is to use a single entropy sink instead of two so that a single incoherent energy resource can be harvested and processed using an algorithmic quantum heat engine. Our results indicate a path to programmable quantum heat engines as analogs of quantum computers beyond traditional heat engine cycles. We find that for our NMR system example implementation of quantum algorithmic heat engine stages yields more power due to increased cycle speeds.

The flow of red blood cells within cylindrical vessels is complex and irregular, so long as the vessel diameter is somewhat larger than the nominal cell size. Long-time-series simulations, in which cells flow ${10}^5$ vessel diameters, are used to characterize the chaotic kinematics, particularly to inform reduced-order models. The simulation model used includes full coupling between the elastic red blood cell membranes and surrounding viscous fluid, providing a faithful representation of the cell-scale dynamics. Results show that the flow has neither classifiable recurrent features nor a dominant frequency. Instead, its kinematics are sensitive to the initial flow configuration in a way consistent with chaos and Lagrangian turbulence. Phase-space reconstructions show that a low-dimensional attractor does not exist, so the observed long-time dynamics are effectively stochastic. Based on this, a simple Markov chain model for the dynamics is introduced and shown to reproduce the statistics of the cell positions.

We study numerically the cubic-quintic-septic Swift-Hohenberg (SH357) equation on bounded one-dimensional domains. Under appropriate conditions stripes with wave number $k\approx 1$ bifurcate supercritically from the zero state and form S-shaped branches resulting in bistability between small and large amplitude stripes. Within this bistability range we find stationary heteroclinic connections or fronts between small and large amplitude stripes, and demonstrate that the associated spatially localized defectlike structures either snake or fall on isolas. In other parameter regimes we also find heteroclinic connections to spatially homogeneous states and a multitude of dynamically stable steady states consisting of patches of small and large amplitude stripes with different wave numbers or of spatially homogeneous patches. The SH357 equation is thus extremely rich in the types of patterns it exhibits. Some of the features of the bifurcation diagrams obtained by numerical continuation can be understood using a conserved quantity, the spatial Hamiltonian of the system.