Neuromodulatory processes in the brain can critically change signal processing on a cellular level, leading to dramatic changes in network level reorganization. Here, we use coupled nonidentical Kuramoto oscillators to investigate how changes in the shape of phase response curves from Type 1 to Type 2, mediated by varying ACh levels, coupled with activity-dependent plasticity may alter network reorganization. We first show that, when plasticity is absent, the Type 1 networks with symmetric adjacency matrix, as expected, exhibit asynchronous dynamics with oscillators of the highest natural frequency robustly evolving faster in terms of their phase dynamics. However, interestingly, Type 1 networks with an asymmetric connectivity matrix can produce stable synchrony (so-called splay states) with complex phase relationships. At the same time, Type 2 networks synchronize independent of the symmetry of their connectivity matrix, with oscillators locked so that those with higher natural frequency have a constant phase lead as compared to those with lower natural frequency. This relationship establishes a robust mapping between the frequency and oscillators' phases in the network, leading to structure and frequency mapping when plasticity is present. Finally, we show that biologically realistic, phase-locking dependent, connection plasticity naturally produces splay states in Type 1 networks that do not display the structure-frequency reorganization observed in synchronized Type II networks. These results indicate that the formation of splay states in the brain could be a common phenomenon.

The inception of self-sustaining dc discharges is analyzed in terms of the bifurcation theory. The existence of a nonphysical solution with negative ion and electron densities must be taken into account in order to identify the bifurcation type. The bifurcation is transcritical for positive and negative corona discharges and, in more general terms, it is expected to be transcritical for all discharge configurations except for the parallel-plate discharge, where the bifurcation is pitchfork. General trends of the bifurcation theory suggest that the corona discharges should be stable immediately after the inception. This conclusion is tested numerically for negative coronas in atmospheric-pressure air in coaxial-cylinder geometry. Two independent approaches have been used: (1) study of linear stability against infinitesimal perturbations with the use of an eigenvalue solver, and (2) following the time development of finite perturbations with the use of a time-dependent solver. The numerical results agree with each other and with the theory. In particular, it is shown that the negative corona is stable, i.e., pulseless, immediately after the ignition. The loss of stability occurs through growth of harmonic perturbations, which subsequently evolve into Trichel pulses, and this happens on the ascending branch of the current-voltage characteristic, contrary to the popular concept of negative differential resistance. Results of the work are of theoretical interest and offer further insights into physics of negative corona discharges.

Onsager's variational principle provides us with a systematic way to derive dynamical equations for various soft matter and active matter. By reformulating the Onsager-Machlup variational principle (OMVP), which is a time-global principle, we propose a new method to incorporate thermal fluctuations. To demonstrate the utility of the statistical formulation of OMVP, we obtain the diffusion constant of a Brownian particle embedded in a viscous fluid by maximizing the modified Onsager-Machlup integral for the surrounding fluid. We also apply our formulation to a Brownian particle in a steady shear flow, which is a typical nonequilibrium system. Possible extensions of our formulation to internally driven active systems are also discussed.

For several decades now it has been known that systems with shearless invariant tori, nontwist Hamiltonian systems, possess barriers to chaotic transport. These barriers are resilient to breakage under perturbation and therefore regions where they occur are natural places to look for barriers to transport. Here we describe a kind of effective barrier that persists after the shearless torus is broken. Because phenomena are generic, for convenience we study the standard nontwist map (SNM), an area-preserving map that violates the twist condition locally in the phase space. The barrier occurs in nontwist systems when twin even period islands are present, which happens for a broad range of parameter values in the SNM. With a phase space composed of regular and irregular orbits, the movement of chaotic trajectories is hampered by the existence of shearless curves, total barriers, and a network of partial barriers formed by the stable and unstable manifolds of the hyperbolic points. Being a degenerate system, the SNM has twin islands and, consequently, twin hyperbolic points. We show that the structures formed by the manifolds intrinsically depend on period parity of the twin islands. For this even scenario the structure that we call a torus free barrier occurs because the manifolds of different hyperbolic points form an intricate chain atop a dipole configuration and the transport of chaotic trajectories through the chain becomes a rare event. This structure impacts the emergence of transport, the escape basin for chaotic trajectories, the transport mechanism, and the chaotic saddle. The case of odd periodic orbits is different: we find for this case the emergence of transport immediately after the breakup of the last invariant curve, and this leads to a scenario of higher transport, with intricate escape basin boundary and a chaotic saddle with nonuniformly distributed points.

We present probabilistic solutions to a pair of mutually coupled Van der Pol oscillators subjected to stochastic forcing. We consider three different types of coupling: reactive, dissipative, and nonlinear coupling. Using stochastic averaging, we derive the stationary Fokker-Planck equation for each oscillator, yielding a probability density function for the fluctuation amplitude. For each coupling type, we numerically validate the Fokker-Planck solutions for different noise levels and coupling strengths, with a focus on the stochastic and bifurcation characteristics. The validated analytical expressions derived in this study could serve to improve the prediction and control of a generic class of coupled oscillator systems operating near the Hopf point in the presence of noise.

An energy-based theory of autoresonance in driven dissipative chains of coupled generic oscillators is discussed on the basis of a variational principle concerning the energy functional. The theory is applied to chains of delayed Duffing-Ueda oscillators and the equations that together govern the autoresonance forces and solutions are derived and solved analytically for generic values of parameters and initial conditions, including the case of quenched time-delay disorder. Remarkably, the presence of retarded potentials with time-delayed feedback drastically modify the autoresonance scenario preventing the growth of the energy oscillation over specific regions of the parameter space. Additionally, effective harmonic forces with a slowly varying frequency are derived from the exact autoresonant excitations and the effectiveness of the theory is demonstrated at suppressing the chaos induced by homogeneous periodic excitations in such oscillator chains. Numerical experiments confirmed all the theoretical predictions.

We propose a stochastic model for the internalization of nanoparticles by cells formulating cellular uptake as a compound Poisson process with a random probability of success. This is an alternative approach to the one presented by Rees et al. [Nat. Commun. 10, 2341 (2019)] who explained overdispersion in nanoparticle uptake and associated negative binomial distribution by considering a Poisson distribution for particle arrival and a gamma-distributed cell area. In our stochastic model, the formation of new pits is represented by the Poisson process, whereas the capturing process and the population heterogeneity are described by a random Bernoulli process with a beta-distributed probability of success. The random probability of success generates ensemble-averaged conditional transition probabilities that increase with the number of newly formed pits (self-reinforcement). As a result, an ensemble-averaged nanoparticle uptake can be represented as a Polya process. We derive an explicit formula for the distribution of the random number of pits containing nanoparticles. In the limit of the fast nucleation and low probability of nanoparticle capture, we find the negative binomial distribution.

Stimulus-induced volumetric phase transition in gels may be potentially exploited for various bioengineering and mechanical engineering applications. Since the discovery of the phenomenon in the 1970s, extensive experimental research has helped understand the phase transition and related critical phenomena. However, little insight is available on the evolving microstructure. In this article, we aim at unravelling certain geometric aspects of the micromechanics underlying discontinuous phase transition in polyacrylamide gels. Towards this, we use geometric thermodynamics and a Landau-Ginzburg type free energy functional involving a squared gradient, in conjunction with Flory-Huggins theory. We specifically exploit Ruppeiner's approach of Riemannian geometry-enriched thermodynamic fluctuation theory, which was previously employed to investigate phase transitions in van der Waals fluids and black holes. The framework equips us with a scalar curvature that is typically indicative of certain aspects of the microstructure during phase transition. Since previous studies have indicated that curvature divergence relates to correlation length divergence, we infer that the gel possesses a heterogeneous microstructure during phase transition, i.e., at critical points. Curvature also provides an insight into the universality class of phase transition and the nature of polymer-polymer interactions.

We perform network analysis of a system described by the master equation to estimate the lower bound of the steady-state current noise, starting from the level 2.5 large deviation function and using the graph theory approach. When the transition rates are uniform, and the system is driven to a nonequilibrium steady state by unidirectional transitions, we derive a noise lower bound, which accounts for fluctuations of sojourn times at all states and is expressed using mesh currents. This bound is applied to the uncertainty in the signal-to-noise ratio of the fluctuating computation time of a schematic Brownian computation plus reset process described by a graph containing one cycle. Unlike the mixed and pseudo-entropy bounds that increase logarithmically with the length of the intended computation path, this bound depends on the number of extraneous predecessors and thus captures the logical irreversibility.

The spiral of silence is a classic theory originating from the age of mass media, which posits that individuals may suppress dissenting opinions to avoid social exclusion. In the digital era, despite the persistence of this phenomenon, the rise of social media has catalyzed the emergence of an antispiral of silence—a counterphenomenon fueled by growing self-awareness and online anonymity. In this paper, we focus on an interesting phenomenon: how these two spirals compete with each other to promote pluralism in social networks. To this end, we propose the spiral competition model (SCM) to quantify the two spirals and explore the impact of this phenomenon on the evolution of public opinion. In the SCM, agents can generate pseudo-opinions as well as antiopinions. In addition, we propose a time-varying network topology updating algorithm based on triangle closure, which simulates the fluid nature of social connections. Furthermore, we propose a community-based opinion initialization method with Gaussian distribution for enhancing simulation fidelity. Finally, we applied complex network theory to information dissemination, and the model was then simulated and analyzed in Erdős-Rényi random networks. And the rationality of SCM was verified using Sina Weibo data. The experimental results show that while the spiral of silence initially holds sway, the antispiral of silence can precipitate significant opinion divergence during critical junctures, challenging the status quo. And if the antispiral of silence fails to prevail, the trend of public opinion will be difficult to reverse. This research helps us recognize the influence that can be brought about by the awakening of individual consciousness, and provides an important reference for public opinion prediction.

Recently, nanofluidics experiments have been used to characterize the behavior of single DNA molecules confined to narrow slits etched with arrays of nanopits. Analysis of the experimental data relies on analytical estimates of the underlying free-energy landscape. In this study we use computer simulations to explicitly calculate the free energy and test the approximations employed in such analytical models. Specifically, Monte Carlo simulations were used to study a polymer confined to complex geometry consisting of a nanoslit with two square nanopits embedded in one of the surfaces. The two-dimensional weighted histogram analysis method is used to calculate the free energy, $F$, as a function of the sum $\left({\lambda }_1\right)$ and the difference $\left({\lambda }_2\right)$ of the length of the polymer contour contained in the two nanopits. We find the variation of the free-energy function with respect to confinement dimensions to be comparable to the analytical predictions that employ a simplistic theoretical model. However, there are some noteworthy quantitative discrepancies, particularly between the predicted and observed variation of $F$ with respect to ${\lambda }_1$. Our study provides a useful lesson on the limitations of using simplistic analytical expressions for polymer free-energy landscapes to interpret results for experiments of DNA confined to a complex geometry and points to the value of carrying out accurate numerical calculations of the free energy instead.

Capturing protracted binding kinetics of polymers onto the surface of nanoobjects is crucial for the rational design of multifunctional nanostructures, such as patchy nanoparticles and nanodrug carriers. Recently, we developed a method—integral of first-passage times (IFS)—to successfully predict nonequilibrium, kinetically stable superstructures fabricated by two star polymers. However, whether the protracted binding kinetics predicted by IFS corresponds to the actual polymer adsorption has only been incompletely explored. In this paper, we clarify this issue by using IFS to study polymer adsorption with binding ends onto a planar wall as an example. At low free-energy barriers, the IFS-predicted polymer binding kinetics is consistent with those extracted from direct simulations. At high free-energy barriers, the protracted polymer adsorption predicted by IFS coincides with those measured in experiments. Our findings demonstrate the feasibility of IFS to study long-lived formation kinetics of polymer nanostructures by spanning timescales from picoseconds to macroscopic minutes, which establishes a foundation to use IFS in different applications.

The generation of fluid flows by autophoretic microswimmers has been proposed as a mechanism to enhance mass transport and mixing at the micro- and nanoscale. Here, we experimentally investigate the ability of model 2D active baths of photocatalytic silica-titania Janus microspheres to enhance the diffusivity of tracer particles at different microswimmer densities below the onset of collective behavior. Inspired by the similarities between our experimental findings and previous results for biological microorganisms, we then model our Janus microswimmers using a general squirmer framework, specifically treating them as neutral squirmers. The numerical simulations faithfully capture our observations, offer an insight into the microscopic mechanism underpinning tracer transport, and allow us to expand the parameter space beyond our experimental system. We find strong evidence that near-field interactions dominate enhancements in tracer diffusivity in active Janus baths, leading to the identification of an operating window for enhanced tracer transport by chemical microswimmers based on scaling arguments. Based on this argumentation, we suggest that for many chemically active colloidal systems, hydrodynamics alone is likely to be insufficient to induce appreciable mixing of passive components with large diffusion coefficients.

We analyze a two-dimensional spring network model comprising breakable and unbreakable springs. Computer simulations showed this system to exhibit intermittent stress drops in a larger strain regime, and these stress drops resulted in ductilelike behavior. The scaling analysis reveals that the avalanche size distribution demonstrates a cutoff, depending on its internal structure. This study also investigates the relationship between cluster growth and stress drop, and we show that the amount of stress drop increases in terms of power law, corresponding to crack growth. The crack length distribution also demonstrates a cutoff depending on its internal structure. The results show that both the cluster growth-stress drop relationship and the crack size distribution are scaled by the quantity related to the internal structure, and the relevance of the exponent that scales the cluster growth-stress drop relationship to the exponent that scales crack size distribution is verified.

Increased speed is not only the goal of human sports but also the aim we seek to achieve for artificial microswimmers. Microswimmers driven by various power mechanisms have shown unrivaled advantages in drug delivery and cancer therapy. Attaining high mobility with limited power has been a never-ending motive for researchers. We show the speed of squirmer-type microswimmers can be noticeably enhanced as they are released to move along the surface of a pillar array, which is constructed of multiple pillars of equal sizes and spacing. An additional pressure force arising from the significant low pressure between the swimmers and the surface is likely behind this enhancement. According to their polarity strengths, the speed of the microswimmers can be double or triple (or even more) compared with that in an unbounded environment. In particular, for systems requiring microswimmers moving along a complex path, the transport rate, instead of being slowed down, may be increased owing to the curvatures of the path constructed by the pillar arrays. We reveal two types of motion for microswimmers after increasing the pillar gap: free and forced oscillating. Our study sheds light on the hydrodynamic interactions between squirmer-type microswimmers and a rough wall.

The onset of the Rayleigh-Bénard instability in a horizontal fluid layer is investigated by assuming the fluid as a binary mixture and the concentration buoyancy as the driving force. The focus of this study is on the anomalous diffusion phenomenology emerging when the mean squared displacement of molecules in the diffusive random walk is not proportional to time, as in the usual Fick's diffusion, but it is proportional to a power of time. The power-law model of anomalous diffusion identifies subdiffusion when the power-law index is smaller than unity, while it describes superdiffusion when the power-law index is larger than unity. This study reconsiders the stability analysis of the Rayleigh-Bénard problem by extending the governing equations to include the anomalous diffusion.

We investigate the onset of the inertial regime in the fluid flow at the pore level in three-dimensional, disordered, highly porous media. We analyze the flow structure in a wide range of Reynolds numbers starting from 0.01 up to 100. We focus on qualitative and quantitative changes that appear with increasing Reynolds number. To do that, we investigate the weakening of the channeling effect, defined as the existence of preferred flow paths in a system. We compute tortuosity, spatial kinetic energy localization, and the pore-space volume fraction containing negative streamwise velocity to assess accompanying changes quantitatively. Our results of tortuosity and participation number derivatives show that the onset of inertia is apparent for Reynolds number $\text{Re}\sim 0.1$, an order of magnitude lower than indicated by analyzing relations of friction factor with the Reynolds number. Moreover, we show that the vortex structures appear at Reynolds number two orders of magnitude higher than the onset of inertia.

Spontaneous symmetry breaking in phase transitions occurs when the system Hamiltonian is symmetric under a certain transformation, but the equilibrium states observed in nature are not. Here we build two noncommuting quantities from the order parameter of the transition and the symmetry operator that are constants of motion when such equilibrium states exist. Then, we derive a general equilibrium ensemble for the ordered phase and show that equilibrium states consisting of superpositions of different symmetry-breaking states, like positive and negative magnetized states, may exist. We propose an experimental realization of such equilibrium states with the state-of-the-art quantum technologies, and test it by means of numerical calculations. Finally, we show that a small symmetry-breaking perturbation in the Hamiltonian stabilizes the conservation of one of the two former quantities, implying that symmetry-breaking equilibrium states become stable even in small quantum systems.

We investigate the impact of confinement density (i.e., the number of individuals in a group per unit area of available space) on transitions from the polarized to milling state, using groups of rummy-nose tetra fish (Hemigrammus rhodostomus) under controlled experimental conditions. We demonstrate a continuous state transition controlled by confinement density in a group of live animals. During this transition, the school exhibits a bistable state, wherein both polarization and milling states coexist, with the group randomly alternating between them. A simple two-state Markov process describes the observed transition remarkably well. The confinement density influences the statistics of this bistability, shaping the distribution of transition times between states. Our findings suggest that confinement plays a crucial role in state transitions for moving animal groups. More generally, they provide an experimental benchmark for active matter models of macroscopic, self-propelled, confined agents.

We study the flow of grains under vibration passing through a small aperture in two dimensions using discrete element method simulations. Such systems are prone to clogging and strategies to ease the flow are desirable in multiple applications. We show that the addition of low-friction particles to the system can reduce clogging and lead to an enhancement of the net flux of the original species. Along with the role of the particle friction, we analyze the influence of both the size of the added particles and the mixing ratio. We consider systems with constant height of the granular column (using particle reinjection) as well as processes of fully emptying the containing hopper.