Folded structures are often idealized as a series of rigid faces connected by creases acting as revolute hinges. However, real folded structures can deform between creases. An example of particular interest is a disk decorated by multiple radial creases. Such disks are bistable, snapping between a “natural” and “inverted” shape. We investigate the mechanical behavior of these creased disks and propose a new analytical approach to describe their mechanics. Detailed experiments are performed which show that, when indented at the center, a localized dimple forms, precluding the conical shape assumed in previous studies. As the indentation depth increases this dimple expands radially until reaching the disk edge when it snaps to the inverted shape, which has a conical form. We develop an analytical model which approximates each face as a series of rigid facets connected by hinges that can both rotate and stretch. Energy expressions are derived relating hinge rotation and stretching to compatible shell deformations of the facets and equilibrium enforced by minimizing the total strain energy. By increasing the number of facets, the mechanics of the continuum shell is approached asymptotically. The analysis shows that membrane stretching of the faces is required when a conical form of deformation is enforced. However, in the limit of zero thickness, the forming and propagation of a localized dimple is inextensional. This new approach relates the kinematic analysis of rigid origami to the mechanics of thin shells, offering an efficient method to predict the behavior of folded structures.

In a magnetized uniform plasma, firehose instability may arise as a result of pressure anisotropy of $P_{\left|\right|}>P_{\perp }$, where $P_{\left|\right|}$ and $P_{\perp }$ are the thermal pressure parallel and perpendicular to the magnetic field, respectively. In this paper, we examine the parallel firehose instability in electron-positron plasmas based on the particle simulations along with the linear fluid theory, which may give rise to the dispersion relation, instability criteria, and growth rate, etc., for comparisons with those calculated from the kinetic simulations. As for the firehose instability in electron-proton plasmas, the magnetic field grows rapidly and then decreases with oscillations. The nonlinear saturated state complies with the linear stability criterion, $\alpha ={\mu }_0\left(P_{\left|\right|}-P_{\perp }\right)/B^2=1$, derived from the fluid theory only for relatively smaller values of initial α or ${\omega }_p/{\omega }_c$, where ${\omega }_p$ and ${\omega }_c$ are the plasma and cyclotron frequencies, respectively. For relatively larger values of initial α and ${\omega }_p/{\omega }_c$, the saturated α values are smaller than 1 as a result of kinetic resonant effects. The dominant wave numbers are $kc/{\omega }_p<0.5$ and the growth rates are in the range of $0.1–0.3{\omega }_c$, which are approximately consistent with the linear fluid theory for the same wavelengths. Both electrostatic and electromagnetic modes predicted by the linear fluid theory are identified in the kinetic simulations.

Theoretical analysis and a large number of experiments have proved that plasma components do not satisfy Boltzmann-Gibbs statistics and can be well described by nonextensive statistical mechanics, while new plasma parameters, electron nonextensive parameters, which are introduced to describe the nonextensive properties of plasma, cannot be diagnosed yet. Here we show measurement of electron nonextensive parameters of plasma with a nonextensive single electric probe. Our results show that nonextensive electric probe may play a role in plasma diagnosis, measuring nonextensivity of plasma and improving diagnostic accuracy of other plasma parameters. We expect the proposed nonextensive single electric probe can be starting point of more complex nonextensive electric probe. In addition, nonextensive electric probe is an important means to study various plasma waves and instability, turbulence, and anomalous transport, and a definite and quantitative test of the theory of nonextensive geodetic acoustic models will be relevant to such development.

We investigate steady states of macroscopic quantum systems under dissipation not obeying the detailed balance condition. We argue that the Gibbs state at an effective temperature gives a good description of the steady state provided that the system Hamiltonian obeys the eigenstate thermalization hypothesis (ETH) and the perturbation theory in the weak system-environment coupling is valid in the thermodynamic limit. We derive a criterion to guarantee the validity of the perturbation theory, which is satisfied in the thermodynamic limit for sufficiently weak dissipation when the Liouvillian is gapped for bulk-dissipated systems, while the perturbation theory breaks down in boundary-dissipated chaotic systems due to the presence of diffusive transports. We numerically confirm these theoretical predictions. This paper suggests a connection between steady states of macroscopic open quantum systems and the ETH.

In statistical mechanics, a small system exchanges conserved quantities—heat, particles, electric charge, etc.—with a bath. The small system thermalizes to the canonical ensemble or the grand canonical ensemble, etc., depending on the quantities. The conserved quantities are represented by operators usually assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed “the non-Abelian thermal state (NATS).” We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which forms the system of interest. The conserved quantities manifest as spin components. Heisenberg interactions push the conserved quantities between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to near the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.

To investigate the evolution of cooperation in spatial public goods games, this paper establishes a birandom geometric graph, in which two types of nodes, representing players and public goods respectively, are placed at random locations in the unit square. Each public good has a limit influence range and the individuals that fall into the same range engage in a public good game. In contrast to the classical network models consisting of only one type of nodes, the birandom geometric graph provides a natural way to describe the scenarios where individuals and public resources are independent of each other. Numerical simulations reveal that cooperation can be significantly promoted when the group size and the average number of groups that each player participates in are relatively small, which is at odds with the results on the square lattice, but is consistent with a body of empirical evidence reported by Ostrom and Olson et al. Analysis of the evolutionary process suggests that the facilitation of cooperation is due primarily to the formation of the cooperative clusters, which can effectively resist the invasion of the defectors.

A dynamic mitigation is presented for sausage and kink instability growths of a $z$-current-driven magnetized plasma column. In this Rapid Communication we found that a wobbling motion of the $z$-current electron axis induces a phase-controlled perturbation, so that the growths of the sausage and kink instabilities are successfully and remarkably mitigated. In general, plasma instabilities emerge from perturbations, and the perturbation phase is normally unknown. However, if the perturbation phase is known or actively imposed by, for example, a designed driver wobbling behavior, the instability growth would be controlled and mitigated by a superimposition of the perturbations imposed. The results in this Rapid Communication demonstrate that the wobbling $z$-current electron beam would provide an improvement in the plasma column stability and uniformity.

We compute the critical exponents $\nu$, $\eta$ and $\omega$ of $\text{O}\left(N\right)$ models for various values of $N$ by implementing the derivative expansion of the nonperturbative renormalization group up to next-to-next-to-leading order [usually denoted $O\left({\partial }^4\right)$]. We analyze the behavior of this approximation scheme at successive orders and observe an apparent convergence with a small parameter, typically between $\frac{1}{9}$ and $\frac{1}{4}$, compatible with previous studies in the Ising case. This allows us to give well-grounded error bars. We obtain a determination of critical exponents with a precision which is similar or better than those obtained by most field-theoretical techniques. We also reach a better precision than Monte Carlo simulations in some physically relevant situations. In the $\text{O}\left(2\right)$ case, where there is a long-standing controversy between Monte Carlo estimates and experiments for the specific heat exponent $\alpha$, our results are compatible with those of Monte Carlo but clearly exclude experimental values.

The de Almeida–Thouless (AT) line is the phase boundary in the temperature–magnetic field plane of an Ising spin glass at which a continuous (i.e., second-order) transition from a paramagnet to a replica-symmetry-breaking (RSB) phase occurs, according to mean-field theory. Here, using field-theoretic perturbative renormalization group methods on the Bray-Roberts reduced Landau-Ginzburg-type theory for a short-range Ising spin glass in space of dimension $d$, we show that at nonzero magnetic field the nature of the corresponding transition is modified as follows: (a) For $d-6$ small and positive, with increasing field on the AT line, first, the ordered phase just below the transition becomes the so-called one-step RSB, instead of the full RSB that occurs in mean-field theory; the transition on the AT line remains continuous with a diverging correlation length. Then at a higher field, a tricritical point separates the latter transition from a quasi-first-order one, that is one at which the correlation length does not diverge, and there is a jump in part of the order parameter, but no latent heat. The location of the tricritical point tends to zero as $d\to 6^{+}$. (b) For $d\le 6$, we argue that the quasi-first-order transition could persist down to arbitrarily small nonzero fields, with a transition to full RSB still expected at lower temperature. Whenever the quasi-first-order transition occurs, it is at a higher temperature than the AT transition would be for the same field, preempting it as the temperature is lowered. These results may explain the reported absence of a diverging correlation length in the presence of a magnetic field in low-dimensional spin glasses in some simulations and in high-temperature series expansions. We also draw attention to the similarity of the “dynamically frozen” state, which occurs at temperatures just above the quasi-first-order transition, and the “metastate-average state” of the one-step RSB phase, and discuss the issue of the number of pure states in either.

Managing thermal transport in nanostructured materials possesses both theoretical and application value in thermoelectric and microelectronics design. Though a suppressed thermal conductivity could be easily achieved through disorder-induced phonon scattering in a superlattice, it is challenging to enhance thermal transport in a periodically designed lattice. In this paper, we show the possibility of mediating thermal conductivity from a suppressed to an enhanced value in a Fermi-Pasta-Ulam $\beta$ superlattice with periodic cells of arithmetically increased nonlinearity. When the cell length is increased, thermal conductivity in the superlattice crosses over a suppressed region into an enhanced one and it is even higher than in a homogeneous lattice with the same nonlinearity strength. The mediation originates from the long-lived nonlinear wave packets as solitons across the disorder-induced interface between cells of the superlattice, while at the same time the normal vibrational modes as phonons are suppressed. Our result shows a promising strategy to manipulate thermal transport over a wide range in a superlattice with strong nonlinearity.

This paper generalizes and extends previous work on using neural field theory to quantitatively analyze the two-dimensional (2D) spatiotemporal correlation properties of gamma-band (30–70 Hz) oscillations evoked by stimuli arriving at the primary visual cortex, and modulated by patchy connectivities that depend on orientation preference (OP). Correlation functions are derived analytically for general stimulus and measurement conditions. The theoretical results reproduce a range of published experimental results. These include (i) the existence of two-point oscillatory temporal cross correlations with zero time lag between neurons with similar OP; (ii) the influence of spatial separation of neurons on the strength of the correlations; and (iii) the effects of differing stimulus orientations. They go beyond prior work by incorporating experimentally observed patchy projection patterns to predict the 2D correlation structure including both OP and ocular dominance effects, thereby relaxing assumptions of translational invariance implicit in prior one-dimensional analysis.

Herein we numerically study the rheology of a two-dimensional frictional granular system confined by constant pressure under oscillatory shear. Several scaling laws for the storage and loss moduli against the scaled strain amplitude have been found. The scaling laws in plastic regime for large strain amplitude can be understood by the angular distributions of the contact force. The scaling exponents are estimated by considering the physical mechanism.

We investigate the collective dynamics of self-propelled droplets, confined in a one-dimensional microfluidic channel. On the one hand, neighboring droplets align and form large trains of droplets moving in the same direction. On the other hand, the droplets condensate, leaving large regions with very low density. A careful examination of the interactions between two “colliding” droplets demonstrates that local alignment takes place as a result of the interplay between the dispersion of their speeds and the absence of Galilean invariance. Inspired by these observations, we propose a minimalistic 1D model of active particles reproducing such dynamical rules and, combining analytical arguments and numerical evidences, we show that the model exhibits a transition to collective motion in 1D for a large range of values of the control parameters. Condensation takes place as a transient phenomena, which tremendously slows down the dynamics, before the system eventually settles into a homogeneous aligned phase.

We discuss a thermodynamic process with information and justify a general form of fluctuation relation. It shows that the fluctuation relation is valid whatever it is the temperature or Hamiltonian that drives the system out of equilibrium state. Based on the stochastic equation we obtain a nonequilibrium equality that involves both information and time-varying temperature. Through the processing of a harmonic system we demonstrate the validity of the equality by converting information into work. We also discuss the general second law of thermodynamics with time-varying temperature and verify its validity in an example by using information to reduce the total entropy.

We study a variation of the trapping reaction, $A+B\to A$, in which both the traps ($A$) and the particles ($B$) undergo diffusion, and the traps upon meeting react according to $A+A\to 0$ or $A$. This two-species reaction-diffusion system is known to exhibit a nontrivial decay exponent for the $B$ particles, and recently renormalization group methods have predicted an anomalous dimension in the $BB$ correlation function. To test these predictions, we develop a computer simulation method, motivated by the technique of Mehra and Grassberger [Phys. Rev. E 65, 050101(R) (2002)], that determines the complete probability distribution of the $B$ particles for a given realization of the $A$-particle dynamics, thus providing a significant increase in the quality of statistics. Our numerical results indeed reveal the anomalous dimension predicted by the renormalization group, and compare well quantitatively to precisely known values in cases where the problem can be related to a four-walker problem.

The reliability of logical operations is indispensable for the reliable operation of computational systems. Since the downsizing of microfabrication generates nonnegligible noise in these systems, a new approach for designing noise-immune gates is required. In this paper, we demonstrate that noise-immune gates can be designed by combining Bayesian inference theory with the idea of computation over noisy channels. To reveal their practical advantages, the performance of these gates is evaluated in comparison with a stochastic resonance-based gate proposed previously. We also demonstrate that, in a high noise-level situation, this approach for computation can be better than a conventional one that conducts information transmission and computation separately.

Origami-based mechanical metamaterials and metastructure have been demonstrated to exhibit unique properties originating from their intricate geometries of folding. This research aims to extend the current investigation level from quasistatics to dynamics. In detail, this research focuses on the wave dynamics of a metastructure composed of stacked Miura-origami (SMO) units. The SMO unit could possess two stable configurations, endowing the metastructure with rich possibilities in the layout of its periodic repeating cell. Through linear dispersion analyses and numerical studies, we show that the long-desired stopband tunability and programmability of the metastructure along the three principal directions can be acquired by strategically programming the layout of the periodic cell. Based upon that, we further discover that energy supratransmission through the metastructure is possible within the stopband by increasing the driving amplitude. Through numerical means, the amplitude threshold of supratransmission is obtained. We demonstrate that the fundamental mechanism that triggers the supratransmission phenomenon is the transition of the responses from the low-energy intrawell oscillations to the high-energy interwell oscillations. Numerical studies also indicate that the supratransmission threshold can be effectively tailored by adjusting the periodic cell layout. The results of this research provide a wealth of fundamental insights into the origami wave dynamics and offer useful guidelines for developing origami metastructures with tunable and programmable dynamic characteristics.

We study experimentally the properties of the flow of mechanical vibration-driven vehicles confined in two chambers connected through a narrow opening. We report that the density of particles around the opening presents critical behavior and scaling properties. By mapping this density to the financial market price, we document that the main stylized facts observed in financial systems have their counterparts in the mechanical system. The experimental model accurately reproduces financial properties such as scaling of the price fluctuation, volatility clustering, and multiscaling.

Growing rod-shaped bacterial cells need to modulate the production rates of different surface and bulk components. Population data show that the balance between these rates is central for cell physiology and affects cell shape, but we still know little about these processes in single cells. We study a minimal stochastic model where single cells grow by two fluctuating volume-specific surface and volume growth rates, solving for the steady-state distributions and the correlation functions of the main geometric features. Our predictions allow us to address the detectability of different scenarios for the intrinsic coupling between the allocation of resources to surface and bulk growth.