By taking a cholesteric liquid crystal (CLC) as an example and treating it as a multilayer stack of birefringent plates, we use a transfer matrix method to analyze light propagation in a common chiral medium in consideration of interlayer reflection and transmission. Based on the transfer matrix, the electric field distribution can be expressed in the form of linearly as well as circularly polarized components, so as to discuss the change of the polarization state of light in the transmission process. The transfer matrix of the same medium with different chirality can be converted by only changing the rotation matrix in the calculation process. Electric field distributions, band structure, transmission, and reflection spectra are calculated when circularly polarized light is incident normally on CLCs or on composite periodic structures of left- and right-handed CLCs. The results obtained by using this transfer matrix method are in good agreement with those obtained by the method based on solving the eigenvalues of Maxwell's equations. Finally, the transfer matrix method is used to calculate the dynamic transmission properties of CLCs under external magnetic field, which is of great significance for the research of noncontact controllable optical devices. The presented computational method saves computing time and can be used for constructing new photonic microstructures with different chiral media.

We analyze the morphology and dynamic behavior of the interface separating a ferrofluid and a nonmagnetic fluid in a Hele-Shaw cell, when crossed radial and azimuthal magnetic fields are applied. In addition to inducing the formation of a variety of eye-catching, complex interfacial structures, the action of the crossed fields makes the deformed ferrofluid droplet to rotate. Numerical simulations and perturbative mode-coupling theory are employed to look into early linear, intermediate weakly nonlinear, and fully nonlinear dynamic regimes of the pattern-forming process. We investigate how the system responds to variations in the viscosity difference between the fluids, the magnetic susceptibility of the ferrofluid, the effects of surface tension, and in the relative strength between radial and azimuthal applied magnetic fields. The role played by random perturbations at the initial conditions in determining the ultimate shape and dynamic stability of the spinning ferrofluid patterns is also studied.

We demonstrate that size fluctuations close to polymers critical point originate the non-Gaussian diffusion of their center of mass. Static universal exponents $\gamma$ and $\nu$—depending on the polymer topology, on the dimension of the embedding space, and on equilibrium phase—concur to determine the potential divergency of a dynamic response, epitomized by the center-of-mass kurtosis. Prospects in experiments and stochastic modeling brought about by this result are briefly outlined.

The quenched Edwards-Wilkinson growth of the $1+1$ interface is considered in the background of the correlated random noise. We use random Coulomb potential as the background long-range correlated noise. A depinning transition is observed in a critical driving force ${\tilde{F}}_c\approx 0.037$ (in terms of disorder strength unit) in the vicinity of which the final velocity of the interface varies linearly with time. Our data collapse analysis for the velocity shows a crossover time $t^{*}$ at which the velocity is size independent. Based on a two-variable scaling analysis, we extract the exponents, which are different from all universality classes we are aware of. Especially noting that the dynamic and roughness exponents are $z_w=1.55\pm 0.05$, and ${\alpha }_w=1.05\pm 0.05$ at the criticality, we conclude that the system is different from both Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) universality classes. Our analysis shows therefore that making the noise long-range correlated, drives the system out of the EW universality class. The simulations on the tilted lattice show that the nonlinearity term ($\lambda$ term in the KPZ equations) goes to zero in the thermodynamic limit.

A variety of nonequilibrium systems display intermittent switching between semistable macroscopic behaviors. We identify a certain type of indeterminacy, with episodes of patterned behavior irregularly punctuated by transitions. It appears that the long-lived patterns are, not coincidentally, also low-fluctuation states. We describe these linked traits with a small set of examples.

This report is concerned with the relevance of the microscopic rules that implement individual neuronal activation, in determining the collective dynamics, under variations of the network topology. To fix ideas we study the dynamics of two cellular automaton models, commonly used, rather in-distinctively, as the building blocks of large-scale neuronal networks. One model, due to Greenberg and Hastings (GH), can be described by evolution equations mimicking an integrate-and-fire process, while the other model, due to Kinouchi and Copelli (KC), represents an abstract branching process, where a single active neuron activates a given number of postsynaptic neurons according to a prescribed “activity” branching ratio. Despite the apparent similarity between the local neuronal dynamics of the two models, it is shown that they exhibit very different collective dynamics as a function of the network topology. The GH model shows qualitatively different dynamical regimes as the network topology is varied, including transients to a ground (inactive) state, continuous and discontinuous dynamical phase transitions. In contrast, the KC model only exhibits a continuous phase transition, independently of the network topology. These results highlight the importance of paying attention to the microscopic rules chosen to model the interneuronal interactions in large-scale numerical simulations, in particular when the network topology is far from a mean-field description. One such case is the extensive work being done in the context of the Human Connectome, where a wide variety of types of models are being used to understand the brain collective dynamics.

Two approaches are outlined to characterize the fluctuation behavior of work applied to a system by a slow change of a parameter. One approach uses the adiabatic theorems of quantum and classical mechanics, and the other one is based on the behavior of the correlations of the generalized coordinate that is conjugate to the changed parameter. Criteria are obtained under which the work done on small thermally isolated as well as on open systems ceases to fluctuate in a quasistatic process.

The atmosphere is a thermo-hydrodynamical complex system and provides oxygen to most animal life at the Earth's surface. However, the detection of complexity for the atmosphere remains elusive and debated. Here we develop a percolation-based framework to explore its structure by using the global air temperature field. We find that the percolation threshold is much delayed compared with the prototypical percolation model and the giant cluster eventually emerges explosively. A finite-size-scaling analysis reveals that the observed transition in each atmosphere layer is genuine discontinuous. Furthermore, at the percolation threshold, we uncover that the boundary of the giant cluster is self-affine, with fractal dimension $d_f$, and can be utilized to quantify the atmospheric complexity. Specifically, our results indicate that the complexity of the atmosphere decreases superlinearly with height, i.e., the complexity is higher at the surface than at the top layer and vice versa, due to the atmospheric boundary forcings. The proposed methodology may evaluate and improve our understanding regarding the critical phenomena of the complex Earth system and can be used as a benchmark tool to test the performance of Earth system models.

We analytically and numerically discuss the dynamics of two pseudospin components Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in deep optical lattices. Rich localized phenomena, such as breathers, solitons, self-trapping, and diffusion, are revealed and strongly depend on the strength of the atomic interaction, SOC, Raman detuning, and the spin polarization (i.e., the initial population difference of atoms between the two pseudospin components of BECs). The critical conditions for the transition of localized states are derived analytically. Based on the critical conditions, the detailed dynamical phase diagram describing the different dynamical regimes is derived. When the Raman detuning satisfies a critical condition, localized states with a fixed initial spin polarization can be observed. When the critical condition is not satisfied, we use two quenching methods, i.e., suddenly and linearly quenching Raman detuning from the soliton or breather state, to discuss the spin dynamics, phase transition, and wave packet dynamics by numerical simulation. The sudden quenching results in a damped oscillation of spin polarization and transforms the system to a new polarized state. Interestingly, the linear quenching of Raman detuning induces a controllable phase transition from an unpolarized phase to an expected polarized phase, while the soliton or breather dynamics is maintained.

We investigate dynamical properties of a quantum generalization of classical reversible Boolean networks. The state of each node is encoded as a single qubit, and classical Boolean logic operations are supplemented by controlled bit-flip and Hadamard operations. We consider synchronous updating schemes in which each qubit is updated at each step based on stored values of the qubits from the previous step. We investigate the periodic or quasiperiodic behavior of quantum networks, and we analyze the propagation of single site perturbations through the quantum networks with input degree one. A nonclassical mechanism for perturbation propagation leads to substantially different evolution of the Hamming distance between the original and perturbed states.

Apoptosis is a mechanism of programmed cell death in which cells engage in a controlled demolition and prepare to be digested without damaging their environment. In normal conditions, apoptosis is repressed until it is irreversibly induced by an appropriate signal. In adult organisms, apoptosis is a natural way to dispose of damaged cells and its disruption or excess is associated with cancer and autoimmune diseases. Apoptosis is regulated by a complex signaling network controlled by caspases, specialized enzymes that digest essential cellular components and promote the degradation of genomic DNA. In this work, we propose an effective description of the signaling network focused on caspase-3 as a readout of cell fate. We integrate intermediate network interactions into a nonlinear feedback function acting on caspase-3 and introduce the effect of pro-apoptotic stimuli and regulatory elements as a saturating activation function. We show that activation dynamics in the theory is similar to previously reported experimental results. We compute bifurcation diagrams and obtain cell fate maps describing how stimulus intensity and feedback strength affect cell survival and death fates. These fates overlap within a bistable region that depends on total caspase concentration, regulatory elements, and feedback nonlinearity. We study a strongly nonlinear regime to obtain analytical expressions for bifurcation curves and fate map boundaries. For a broad range of parameters, strong stimuli can induce an irreversible switch to the death fate. We use the theory to explore dynamical stimulation conditions and determine how cell fate depends on stimulation temporal patterns. This analysis predicts a critical relation between transient stimuli intensity and duration to trigger irreversible apoptosis. We derive an analytical expression for this critical relation, valid for short stimuli. Our description provides distinct predictions and offers a framework to study how this signaling network processes different stimuli to make a cell fate decision.

Wide use of magnetic nanoparticles in modern technologies and biomedical applications requires reliable theoretical models capable of predicting physical properties. Solidification of a ferroparticle suspension under the action of permanent magnetic field allows us to obtain a ferrocomposite, characterized by some orientational texture of the nanoparticle easy magnetization axes. The static magnetic response of this ferrocomposite differs from that of the parent magnetic suspension due to “freezing” of nanoparticle translational and rotational degrees of freedom. Here the superparamagnetic fluctuations of the nanoparticle magnetic moments play a key role in the formation of the ferrocomposite magnetic response depending on the degree of orientational ordering, obtained during synthesis of a ferrocomposite. With the help of statistical mechanics we calculate the magnetization and the initial magnetic susceptibility of the textured ferrocomposite for various temperatures and magnetic field strengths. The easy axis texturing leads to a significant increase of the magnetic properties, and the effect intensifies with the growth of nanoparticle magnetocrystalline anisotropy. Theoretical predictions are supported by Monte Carlo simulations. The obtained results evidence that the texturing of a ferroparticle suspension and transforming it into a textured ferrocomposite are a real way to enhance the magnetic response of these magnetic soft materials.

An investigation of the two-dimensional Widom-Rowlinson lattice gas under an applied drive uncovered a remarkable nonequilibrium steady state in which uniform stripes (reminiscent of an equilibrium lamellar phase) form perpendicular to the drive direction [R. Dickman and R. K. P. Zia, Phys. Rev. E 97, 062126 (2018)]. Here we study this model at low particle densities in two and three dimensions, where we find a disordered phase with a characteristic length scale (a “microemulsion”) along the drive direction. We develop a continuum theory of this disordered phase to derive a coarse-grained field-theoretic action for the nonequilibrium dynamics. The action has the form of two coupled driven diffusive systems with different characteristic velocities, generated by an interplay between the particle repulsion and the drive. We then show how fluctuation corrections in the field theory may generate the characteristic features of the microemulsion phase, including a peak in the static structure factor corresponding to the characteristic length scale. This work lays the foundation for understanding the stripe phenomenon more generally.

Earth's climate can be understood as a dynamical system that changes due to external forcing and internal couplings. Essential climate variables, such as surface air temperature, describe this dynamics. Our current interglacial, the Holocene (11 700 yr ago to today), has been characterized by small variations in global mean temperature prior to anthropogenic warming. However, the mechanisms and spatiotemporal patterns of fluctuations around this mean, called temperature variability, are poorly understood despite their socioeconomic relevance for climate change mitigation and adaptation. Here we examine discrepancies between temperature variability from model simulations and paleoclimate reconstructions by categorizing the scaling behavior of local and global surface air temperature on the timescale of years to centuries. To this end, we contrast power spectral densities (PSD) and their power-law scaling using simulated and observation-based temperature series of the last 6000 yr. We further introduce the spectral gain to disentangle the externally forced and internally generated variability as a function of timescale. It is based on our estimate of the joint PSD of radiative forcing, which exhibits a scale break around the period of 7 yr. We find that local temperature series from paleoclimate reconstructions show a different scaling behavior than simulated ones, with a tendency towards stronger persistence (i.e., correlation between successive values within a time series) on periods of 10 to 200 yr. Conversely, the PSD and spectral gain of global mean temperature are consistent across data sets. Our results point to the limitation of climate models to fully represent local temperature statistics over decades to centuries. By highlighting the key characteristics of temperature variability, we pave a way to better constrain possible changes in temperature variability with global warming and assess future climate risks.

For nonequilibrium systems described by finite Markov processes, we consider the number of times that a system traverses a cyclic sequence of states (a cycle). The joint distribution of the number of forward and backward instances of any given cycle is described by universal formulas which depend on the cycle affinity, but are otherwise independent of system details. We discuss the similarities and differences of this result to fluctuation theorems, and generalize the result to families of cycles, relevant under coarse graining. Finally, we describe the application of large deviation theory to this cycle-counting problem.

Correlated disorder is at the heart of numerous challenging problematics in physics. In this work we focus on the propagation of acoustic coherent waves in two-dimensional dense disordered media exhibiting long- and short-range structural correlations. The media are obtained by inserting elastic cylinders randomly in a stealth hyperuniform medium itself made up of cylinders. The properties of the coherent wave is studied using an original numerical software. In order to understand and discuss the complex physical phenomena occurring in the different media, we also make use of effective media models derived from the quasicrystalline approximation and the theory of Fikioris and Waterman that provides an explicit expression of the effective wave numbers. Our study shows a very good agreement between numerical and homogenization models up to very high concentrations of scatterers. This study shows that media with both short- and long-range correlations are of strong interest to design materials with original properties.

In this work, we study the dynamics of a single active Brownian particle, as well as the collective behavior of interacting active Brownian particles, in a fluctuating heterogeneous environment. We employ a variant of the diffusing diffusivity model where the equation of motion of the active particle involves a time-dependent motility and diffusivities. Within our model, those fluctuations are coupled to each other. Using analytical methods, we obtain the probability distribution function of particle displacement and its moments for a single particle. We then investigate the impact of the environmental fluctuations on the collective behavior of the active Brownian particles by means of extensive numerical simulations. Our results show that the fluctuations hinder the motility-induced phase separation, accompanied by a significant change of the density dependence of particle velocities. These effects are interpreted using our analytical results for the dynamics of a single particle.

Analogous to other porous solids, pinned nanobubbles serve as a zero-dimensional stable nanoscale chamber with controllable thermodynamic parameters, whereas they can respond to state change of guest molecule. Here we analyzed peculiarities of phase transitions in pinned nanobubbles, which were experimentally proved to be superstable. By combining molecular dynamics simulation and thermodynamic analysis, we reveal that guest molecules encapsulated inside a nanobubble exhibit distinct state behaviors: a state in vapor phase, a reversible two-state oscillation, and a stable nanodroplet@nanobubble state, depending on the number of guest molecules and the external pressure. The free-energy landscape shows how state metastability gradually develops with external stimuli and leads to the specific bistable state of two-state oscillation. The existence of strong coupling between nanobubble breathing and two-state oscillation is identified. Our simulation results demonstrate that the flexibility of pinned nanobubbles plays at least the same important role as space confinement in determining the states of guest molecules. Our findings indicate that pinned nanobubbles, serving as soft porous media that possess high stability and reversible transformability, show a wealth of properties that are not found in bulk solutions and in porous solids.

Multiple emulsions are a class of soft fluid in which small drops are immersed within a larger one and stabilized over long periods of time by a surfactant. We recently showed that, if a monodisperse multiple emulsion is subject to a pressure-driven flow, a wide variety of nonequilibrium steady states emerges at late times, whose dynamics relies on a complex interplay between hydrodynamic interactions and multibody collisions among internal drops. In this work, we use lattice Boltzmann simulations to study the dynamics of polydisperse double emulsions driven by a Poiseuille flow within a microfluidic channel. Our results show that their behavior is critically affected by multiple factors, such as initial position, polydispersity index, and area fraction occupied within the emulsion. While at low area fraction inner drops may exhibit either a periodic rotational motion (at low polydispersity) or arrange into nonmotile configurations (at high polydispersity) located far from each other, at larger values of area fraction they remain in tight contact and move unidirectionally. This decisively conditions their close-range dynamics, quantitatively assessed through a time-efficiency-like factor. Simulations also unveil the key role played by the capsule, whose shape changes can favor the formation of a selected number of nonequilibrium states in which both motile and nonmotile configurations are found.