Sensory mechanisms in biology, from cells to humans, have the property of adaptivity, whereby the response produced by the sensor is adapted to the overall amplitude of the signal, reducing the sensitivity in the presence of strong stimulus, while increasing it when it is weak. This property is inherently energy consuming and a manifestation of the nonequilibrium nature of living organisms. We explore here how adaptivity affects the effective forces that organisms feel due to others in the context of a uniform swarm, in both two and three dimensions. The interactions between the individuals are taken to be attractive and long-range and of power-law form. We find that the effects of adaptivity inside the swarm are dramatic, where the effective forces decrease (or remain constant) with increasing swarm density. Linear stability analysis demonstrates how this property prevents collapse (Jeans instability), when the forces are adaptive. Adaptivity therefore endows swarms with a natural mechanism for self-stabilization.

We demonstrate a fast-switching liquid-crystal mode with polymer-sustained twisted vertical alignment. By optimizing the polymerization condition, a polymer microstructure with controlled orientation is produced. The polymer microstructure not only synergistically suppresses the optical bounce during field-induced homeotropic-twist transition but also shortens the response time significantly. Theoretical analyses validate that the ground state free energy density is modified by the aligning field of the polymer microstructure, which affects the driving voltage of the device. The outcomes of this paper will enable the development of fast-switching and achromatic electro-optical and photonic devices.

The phase behavior of the monodisperse melt of V-shaped molecules composed of two rigid segments of different lengths joined at their ends at an external angle $\alpha$ has been examined within the Landau–de Gennes approach. Each rigid segment consists of a sequence of monomer units; the anisotropic interactions in the system are assumed to be of the Maier-Saupe form. The coefficients of the Landau–de Gennes free-energy expansion have been found from a microscopic model of V-shaped molecule. A single Landau point at which the system undergoes direct continuous transition from isotropic to biaxial nematic phase is found for asymmetry parameter $\varphi =1/3$ or $\varphi =2/3$, where $\varphi$ is the number fraction of monomer units in one of the segments. Two Landau points are found in a range $1/3<\varphi <2/3$. Only isotropic and nematic states are found to be stable for $0\le \varphi <1/3$ and $2/3<\varphi \le 1$. Regions of stability of isotropic, prolate uniaxial, and biaxial nematic phases are found for $\varphi =1/3$ and $\varphi =2/3$. In addition, a stable oblate uniaxial phase is revealed if asymmetry parameter falls in the range $1/3<\varphi <2/3$. The region of stability of the biaxial nematic phase becomes smaller as parameter $\varphi$ increases from $1/3$ to $1/2$ (or decreases from $2/3$ to $1/2$). Coefficients of the gradient terms have been found; for certain values of asymmetry parameter these coefficients can become negative in some ranges of angles.

The critical radius of a core-shell-type nucleus grown by diffusion in a phase-separated solution is studied. A kinetic critical radius rather than the thermodynamic critical radius of standard classical nucleation theory can be defined from the diffusional growth equations. It is shown that there exist two kinetic critical radii for the core-shell-type nucleus, for which both the inner-core radius and the outer-shell radius will be stationary. Therefore, these two critical radii correspond to a single critical point of the nucleation path with a single energy barrier even though the nucleation looks like a two-step process. The two radii are given by formulas similar to that of classical nucleation theory if the Ostwald-Freundlich boundary condition is imposed at the surface of the inner nucleus and that of the outer shell. The subsequent growth of a core-shell-type postcritical nucleus follows the classical picture of Ostwald's step rule. Our result is consistent with some of the experimental and numerical results which suggest the core-shell-type critical nucleus.

A one-dimensional fluid model for ions in weakly ionized plasma is proposed. The model differs from the existing ones in two aspects. First, a more accurate approximation of the collision terms in the fluid equations is suggested. For this purpose, the results obtained using the Monte Carlo kinetic model of the ion swarm experiments are considered. Second, the ion energy equation is taken into account. The fluid equations are closed using a simple model of the ion velocity distribution function. The accuracy of the fluid model is examined by comparing with the results of particle-in-cell Monte Carlo simulations. In particular, several test problems are considered using a parallel plate model of the capacitively coupled radio-frequency discharge. It is shown that the results obtained using the proposed fluid model are in good agreement with those obtained from the simulations over a wide range of discharge conditions. An approximation of the ion velocity distribution function for the problem under consideration is also discussed.

The chiral clock spin-glass model with $q=5$ states, with both competing ferromagnetic-antiferromagnetic and left-right chiral frustrations, is studied in $d=3$ spatial dimensions by renormalization-group theory. The global phase diagram is calculated in temperature, antiferromagnetic bond concentration $p$, random chirality strength, and right-chirality concentration $c$. The system has a ferromagnetic phase, a multitude of different chiral phases, a chiral spin-glass phase, and a critical (algebraically) ordered phase. The ferromagnetic and chiral phases accumulate at the disordered phase boundary and form a spectrum of devil's staircases, where different ordered phases characteristically intercede at all scales of phase-diagram space. Shallow and deep reentrances of the disordered phase, bordered by fragments of regular and temperature-inverted devil's staircases, are seen. The extremely rich phase diagrams are presented as continuously and qualitatively changing videos.

Ordered chains (such as chains of amino acids) are ubiquitous in biological cells, and these chains perform specific functions contingent on the sequence of their components. Using the existence and general properties of such sequences as a theoretical motivation, we study the statistical physics of systems whose state space is defined by the possible permutations of an ordered list, i.e., the symmetric group, and whose energy is a function of how certain permutations deviate from some chosen correct ordering. Such a nonfactorizable state space is quite different from the state spaces typically considered in statistical physics systems and consequently has novel behavior in systems with interacting and even noninteracting Hamiltonians. Various parameter choices of a mean-field model reveal the system to contain five different physical regimes defined by two transition temperatures, a triple point, and a quadruple point. Finally, we conclude by discussing how the general analysis can be extended to state spaces with more complex combinatorial properties and to other standard questions of statistical mechanics models.

The Kubo formula expresses a linear response of the quantum system to weak classical fields. Previous studies showed that the environment degrades the quantum Hall conductance. By studying the dynamics of dissipative two-band systems, in this paper we find that the formation of system-environment bound states is responsible for the Hall conductance immune to the effect of the environment. The bound states can form only when the system-environment couplings are below a threshold. Our results may be of both theoretical and experimental interest in exploring dissipative topological insulators in realistic situations, and may open new perspectives for designing active quantum Hall devices working in realistic environments.

We investigate numerically the interaction between two finite Airy-Gaussian (AiG) beams in different media with the defected photonic lattices in one transverse dimension. We discuss that the beams with different intensities and phases launch into the different lattice structures but accelerate in opposite directions. During interactions, the interference fringe, breathers, and soliton pairs are observed. In the linear media, the initial deflection direction of the accelerated beams is changed by adjusting the phase shift and the beam interval. For a certain lattice period, the periodic interference fringe can form. A constructive or destructive interference can vary with the defect depth and phase shift. While the nonlinearity is introduced, the breathers is generated. Especially in the self-defocusing media, the appropriate AiG beam amplitude and lattice depth may lead to the formation of soliton pairs, On the contrary, the interaction of two Gaussian beams is diffraction.

We report on numerical studies of avalanches of an autocatalytic reaction front in a porous medium. The front propagation is controlled by an adverse flow resulting in upstream, static, or downstream regimes. In an earlier study focusing on front shape, we identified three different universality classes associated with this system by following the front dynamics experimentally and numerically. Here, using numerical simulations in the vicinity of the second-order transition, we identify an avalanche dynamics characterized by power-law distributions of avalanche sizes, durations, and lateral extensions. The related exponents agree well with the quenched-Kardar-Parisi-Zhang theory, which describes the front dynamics. However, the geometry of the propagating front differs slightly from that of the theoretical one. We show that this discrepancy can be understood in terms of the nonquasistatic correction induced by the finite front velocity.

The problem of community detection in networks has received wide attention and proves to be computationally challenging. In recent years, with the surge of signed networks with positive links and negative links, to find community structure in such signed networks has become a research focus in the area of network science. Although many methods have been proposed to address the problem, their performance seriously depends on the predefined optimization objectives or heuristics which are usually difficult to accurately describe the intrinsic structure of community. In this study, we present a statistical inference method for community detection in signed networks, in which a probabilistic model is proposed to model signed networks and the expectation-maximization–based parameter estimation method is deduced to find communities in signed networks. In addition, to efficiently analyze signed networks without any a priori information, a model selection criterion is also proposed to automatically determine the number of communities. In our experiments, the proposed method is tested in the synthetic and real-word signed networks and compared with current methods. The experimental results show the proposed method can more efficiently and accurately find the communities in signed networks than current methods. Notably, the proposed method is a mathematically principled method.

One's reputation in human society depends on what and how one did in the past. If the reputation of a counterpart is too bad, we often avoid interacting with the individual. We introduce a selective cooperator called the goodie, who participates in the prisoner's dilemma game dependent on the opponent's reputation, and study its role in forming a cooperative society. We observe enhanced cooperation when goodies have a small but nonzero probability of playing the game with an individual who defected in previous rounds. Our finding implies that even this small generosity of goodies can provide defectors chances of encountering the better world of cooperation, encouraging them to escape from their isolated world of selfishness.

The limiting similarity of competitive species and its relationship with the competitive exclusion principle is still one of the most important concepts in ecology. In the 1970s, May [R. M. May, Stability and Complexity in Model Ecosystems (Princeton University, Princeton, NJ, 1973)] developed a concise theoretical framework to investigate the limiting similarity of competitive species. His theoretical results show that no limiting similarity threshold of competitive species can be identified in the deterministic model system whereby species more similar than this threshold never coexist. Theoretically, for competitive species coexisting in an unvarying environment, deterministic interspecific interactions and demographic stochasticity can be considered two sides of a coin. To investigate how the “tension” between these two forces affects the coexistence of competing species, a simple two-species competitive system based only on May's model system is transformed into an equivalent replicator equation. The effect of demographic stochasticity on the system stability is measured by the expected drift of the Lyapunov function. Our main results show that the limiting similarity of competitive species should not be considered to be an absolute measure. Specifically, very similar competitive species should be able to coexist in an environment with a high productivity level but big differences between competitive species should be necessary in an ecosystem with a low productivity level.

A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous “sweeping effect,” a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of “Reynolds numbers” and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.

We have studied the slip length of confined liquid with small roughness of solid-liquid interfaces. Dyadic Green function and perturbation expansion have been applied to get the slip length quantitatively. In the slip length, both the effects of the roughness of the interfaces and the chemical interaction between the liquid and the solid surface are involved. For the numerical calculation, Monte Carlo method has been used to simulate the rough interfaces and the physical quantities are obtained statistically over the interfaces. Results show that the total slip length of the system is linearly proportional to the slip length contributed from the chemical interaction. And the roughness of the interfaces plays its role as the proportionality factor. For the roughness, the variance of the roughness decreases the total slip length while the correlation length of the roughness can enhance the slip length dramatically to a saturation value.

The hosing processes of a relativistic laser pulse, electron acceleration, and betatron radiation in a parabolic plasma channel are investigated in the direct laser acceleration regime. It is shown that the laser hosing instability would result in the generation of a randomly directed off-axis electron beam and radiation source with a large divergence angle. While employing a preformed parabolic plasma channel, the restoring force provided by the plasma channel would correct the perturbed laser wave front and thus suppress the hosing instability. As a result, the accelerated electron beam and the emitted photons are well guided and concentrated along the channel axis. The employment of a proper plasma density channel can stably guide the relativistically intense laser pulse and greatly improve the properties of the electron beam and radiation source. This scheme is of great interest for the generation of high quality electron beams and radiation sources.

Proton radiography is a technique extensively used to resolve magnetic field structures in high-energy-density plasmas, revealing a whole variety of interesting phenomena such as magnetic reconnection and collisionless shocks found in astrophysical systems. Existing methods of analyzing proton radiographs give mostly qualitative results or specific quantitative parameters, such as magnetic field strength, and recent work showed that the line-integrated transverse magnetic field can be reconstructed in specific regimes where many simplifying assumptions were needed. Using artificial neural networks, we demonstrate for the first time 3D reconstruction of magnetic fields in the nonlinear regime, an improvement over existing methods, which reconstruct only in 2D and in the linear regime. A proof of concept is presented here, with mean reconstruction errors of less than 5% even after introducing noise. We demonstrate that over the long term, this approach is more computationally efficient compared to other techniques. We also highlight the need for proton tomography because (i) certain field structures cannot be reconstructed from a single radiograph and (ii) errors can be further reduced when reconstruction is performed on radiographs generated by proton beams fired in different directions.

We investigate the statistics of heat exchange between a finite system coupled to reservoir(s). We have obtained analytical results for heat fluctuation theorems in the transient regime considering the Hamiltonian dynamics of the composite system consisting of the system of interest and the heat bath(s). The system of interest is driven by an external protocol. We first derive it in the context of a single heat bath. The result is in exact agreement with known result. We then generalize the treatment to two heat baths. We further extend the study to quantum systems and show that relations similar to the classical case hold in the quantum regime. For our study we invoke von Neumann two-point projective measurement in quantum mechanics in the transient regime. The study of quantum systems follows the same lines of argument as that of the classical system, and as a result the treatment used in the latter complements that used in the former. Our result is a generalization of Jarzynski-Wòjcik heat fluctuation theorem.