The non-Markovian effect on entropy production rate is an open question in quantum thermodynamics. By means of the change rate of the trace distance as the witness, we explore the non-Markovianities for their origin, i.e., from the initial correlation between the system and its heat reservoir and/or from the spectral density of the system-reservoir interaction. We show the possibility of positive entropy production rate regarding the initial correlation, which challenges the existing viewpoint of definitely negative entropy production rate under the non-Markovian condition. Our result is justified by an experimentally feasible model.

Aging is considered as the property of the elements of a system to be less prone to change states as they get older. We incorporate aging into the noisy voter model, a stochastic model in which the agents modify their binary state by means of noise and pairwise interactions. Interestingly, due to aging the system passes from a finite-size discontinuous transition between ordered (ferromagnetic) and disordered (paramagnetic) phases to a second order phase transition, well defined in the thermodynamic limit, belonging to the Ising universality class. We characterize it analytically by finding the stationary solution of an infinite set of mean field equations. The theoretical predictions are tested with extensive numerical simulations in low dimensional lattices and complex networks. We finally employ the aging properties to understand the symmetries broken in the phase transition.

We use a semiclassical approach to study out-of-equilibrium dynamics and transport in quantum systems with massive quasiparticle excitations having internal quantum numbers. In the universal limit of low-energy quasiparticles, the system is described in terms of a classical gas of colored hard-core particles. Starting from an inhomogeneous initial state, in this limit we give analytic expressions for the space- and time-dependent spin density and spin current profiles. Depending on the initial state, the spin transport is found to be ballistic or diffusive. In the ballistic case we identify a “second front” that moves more slowly than the maximal quasiparticle velocity. Our analytic results also capture the diffusive broadening of this ballistically propagating front. To go beyond the universal limit, we study the effect of nontrivial scattering processes in the $O\left(3\right)$ nonlinear sigma model by performing Monte Carlo simulations, and we observe local equilibration around the second front in terms of the densities of the particle species.

We engineer mechanical gain (loss) in a system formed by two optomechanical cavities (OMCs), that are mechanically coupled. The gain (loss) is controlled by driving the resonator with laser that is blue (red) detuned. We predict analytically the existence of multiple exceptional points (EPs), a form of degeneracy where the eigenvalues of the system coalesce. At each EP, phase transition occurs, and the system switches from weak to strong coupling regimes and vice versa. In the weak coupling regime, the system locks on an intermediate frequency, resulting from coalescence at the EP. In the strong coupling regime, however, two or several mechanical modes are excited depending on system parameters. The mechanical resonators exhibit Rabi oscillations when two mechanical modes are involved, otherwise the interaction triggers chaos in the strong coupling regime. This chaos is bounded by EPs, making it easily controllable by tuning these degeneracies. Moreover, this chaotic attractor shows up for low driving power, compared to what happens when the coupled OMCs are both driven in blue sidebands. This works opens up promising avenues to use EPs as a new tool to study collective phenomena (synchronization, locking effects) in nonlinear systems, and to control chaos.

Electrodynamic (ED) levitation of one or a few charged droplets using Paul traps offers opportunities to understand the Rayleigh instability as well as the role of various inter-particle forces on pattern formations. In this work, we develop a theory for two-dimensional patterns formed during levitation of two to a few droplets in an ED balance, based on an extension of the classical Dehmelt approximation to interacting particle systems. The theory presents closed-form solutions to the inter-particle separations, secular frequencies, orientation stabilities of two-drop systems, and collapse of droplets onto the XY plane. Based on symmetry considerations, the theory is extended to predict the sizes and shapes of closed structures formed for few-drop systems. The analysis specifically helps one to understand the charge independence of inter-particle separations for equal charge to mass ratio drops. This and several other results obtained in this analysis provide functional relationships for the various quantities examined in numerical simulations and experiments. The study thus significantly advances our understanding of many-body levitation in electrodynamic balance.

We describe a class of extreme events emerging in systems with discontinuous boundaries that exhibit stick-slip dynamics. This kind of systems is capable of generating extreme events when the system trajectory sticks to a sliding set and slides for a relatively large distance along the discontinuous boundary to one of the system's subspaces. We present two examples of such systems, a microelectromechanical cantilever and a driven class-B laser, where this type of extreme events appear. We show that their forecasting is possible by monitoring the sliding trajectory along the discontinuous boundary. In both cases, the probability distribution of recurrence times exhibits a power-law behavior, typical for extreme events. The results of this study can be of interest for engineering applications, for example, to predict extremely large-amplitude oscillations in cantilevers, systems with friction, lasers, and other systems with discontinuous boundaries.

We present and analyze a growth model of an avascular tumor that considers the basic biological principles of proliferation, motility, death, and genetic mutations of the cell. From an analysis of genomic data and considering the results of a regulatory network analysis we identify two sets of genes—a set of sixteen and six genes—that are believed to play an important role in the evolution of breast cancer. Considering that cancer cells shape the tissue microenvironment and niches to their competitive advantage, the model assumes that cancer and normal cells compete for essential nutrients and that the rate of mutations is affected by nutrients availability. To this end, we propose a coupling between the transport of nutrients and gene mutations dynamics. Gene mutation dynamics are modeled as a Yule-Furry Markovian process, while transport of nutrients is described with a system of reaction-diffusion equations. For each representative tumor we calculate its diversity, represented by the Shannon index, and its spatial heterogeneity, measured by its fractal dimension. These quantities are important in the clinical diagnosis of tumor malignancy. A tumor malignancy diagram, obtained by plotting diversity versus fractal dimension, is calculated for different values of a parameter $\beta$, that modulate proliferation rate. It is found that, when $\beta <1$, tumors show greater diversity and more spatial heterogeneity as compared with $\beta >1$. More importantly, it is found that the results and conclusions are similar when we use the six-gene set versus the sixteen-gene set.

The aim of this paper is to analyze the radial and longitudinal motion of the arterial wall in the context of pulsatile pressure and flow, and to understand their physiological implications for the cardiovascular system. A reexamination of the well-established one-dimensional governing equations for axial blood flow in the artery and the constitutive equation for the radial dilation of the arterial wall shows that two waves—a pulsatile pressure wave in the artery and a radial displacement wave in the arterial wall—propagate simultaneously along the arterial tree with the same propagation velocity, explaining why this velocity combines the physical properties and geometries of both the blood and the arterial wall. With consideration of their coupling, the governing equations for the radial motion and longitudinal motion of the arterial wall are derived separately. The driving force for the radial motion of the arterial wall arises from its longitudinal motion. The longitudinal motion of the arterial wall is the standard longitudinal elastic wave with two driving forces: one associated with the pulsatile flow rate and the other associated with the radial motion. These derived governing equations shed insights on some recent experimental findings in the literature, including the correlation of measured arterial wall stiffness (solely based on the radial motion) to its longitudinal motion, the decreasing trend of arterial wall distensibility from the aorta to the periphery, the underlying mechanism of the longitudinal motion pattern of the common carotid arterial wall, and the motion pattern variation in longitudinal motion with aging and diseases.

The plumage of birds often exhibits attractive color effects produced by the interaction of light with the photonic microstructure present in the feather barbs and barbules. This microstructure constitutes a natural photonic crystal that rejects radiation of wavelengths contained within the band gap, which significantly alters the observed coloration depending on the incidence conditions. In spite of the high degree of regularity exhibited by the barb's microstructure of many species, the disorder present in these natural photonic crystals might modify the reflected response. In this paper, we address the problem of modeling the electromagnetic response of a quasiordered photonic structure, using an electromagnetic method only suitable for strictly periodic structures. In particular, we simulate the reflected response of the plumage of the Swallow Tanager (Tersina viridis) by two different approaches. On the one hand, we compute the reflected response by averaging reflectance spectra calculated by the Korringa-Kohn-Rostoker method for different geometrical parameters. We also apply the inner extinction approximation, which represents imperfections in the structure by adding a small imaginary part to the dielectric constant of the inclusions. The agreement between the experimental and the simulated results evidences the potential of the proposed methods to reproduce the electromagnetic response of natural photonic structures.

We analyze the dewetting transition on a hydrophobic solid substrate of sinusoidal shape. For a given Young angle, this shape is compatible with air entrapment only for a sufficiently high amplitude (or, equivalently, for a sufficiently small period) of the shape. Entrapment may then take place in the form of either deep or shallow air pockets. Regardless of the amplitude, the interfacial energy associated with the formation of deep pockets is lower than that associated with the formation of shallow pockets. Compared with the nominal wetted state, the deep-pocket state is energetically beneficial only beyond a threshold amplitude, which is a strictly decreasing function of the contact angle. The apparent contact angle associated with that superhydrophobic state is obtained using the principle of virtual work.

In this study, we numerically investigate the interactions between pentagonal truncated pyramids in a nematic liquid crystal host. The colloidal arrangements are investigated by minimizing the Landau-de Gennes free energy in presence of homeotropic anchoring surface energy upon the particles. We further explain the interactions using symmetry breaking in the director field and particle-particle relative arrangements. In the case of long-range separations, interactions exhibit some deviations from those observed in the case of dipolar symmetry. We also exhibit that, in some cases, decreasing the bending elastic distortions between two adjacent lateral faces will cause a nonhorizontal side-to-side configuration. In many-body interactions, we evaluate the ability of the bent and branch configurations to form complex self-tiling assemblies pentagonal truncated pyramid blocks.

A study of large-scale motions from a direct numerical simulation database of the turbulent boundary layer up to ${\text{Re}}_{\theta }\sim 2500$ is presented. The statistics of large-scale streamwise structures have been investigated using two-dimensional and three-dimensional (3D) extraction procedures. The large-scale structures are abstracted using a robust skeletonization method usually applied to other research domains to simplify complex 3D objects. Different structure parameters such as the length, shape, or angle are investigated. The features of the detected structures are compared to their mean counterparts extracted from two-point correlations. Structures as large as ten boundary layer thicknesses are observed. The streamwise length of these structures follows a $-2$ power law distribution, similar to the experimental findings at higher Reynolds numbers.

The impulsively accelerated Richtmyer-Meshkov instability (RMI) of a fluid-solid interface is theoretically studied with a decomposition method, and the least stable mode is shown to oscillate but decay due to the combined effects of elasticity and viscosity. The dispersion relation of RMI in viscous fluids is obtained as well, and the predicted interface amplitude agrees with numerical simulations better than the previous linear and weakly nonlinear theories. As time tends to infinity, the asymptotic amplitude of the disturbed interface is found to be inversely proportional to the wave number in viscous fluids but to be independent of the wave number for the interface between elastic solids.

We ascertain the enhanced slip properties for a liquid flow over lubricant-infused unidirectional surfaces. This situation reflects many practical settings involving liquid flows past superhydrophobic grooves filled with gas, or past grooves infused with another, immiscible, liquid of smaller or equal viscosity, i.e., where the ratio of lubricant and liquid viscosities, $\mu \le 1$. To maximize the slippage, we consider deep grooves aligned with the flow. The (normalized by a texture period $L$) effective slip length, $b_{\mathrm{eff}}$, is found as an expansion to first order in protrusion angle $\theta$ about a solution for a flat liquid-lubricant interface. Our results show a significant increase in $b_{\mathrm{eff}}$ with the area fraction of lubricant, $\varphi$, and a strong decrease with $\mu$. By contrast, only little influence of $\theta$ on $b_{\mathrm{eff}}$ is observed. Convex meniscus slightly enhances and concave meniscus slightly reduces $b_{\mathrm{eff}}$ relative to the case of a flat liquid-lubricant interface. The largest correction for $\theta$ is found when $\mu =0$, it decreases with $\mu$, and disappears at $\mu =1$. Finally, we show that lubricant-infused surfaces of small $\theta$ can be modeled as flat with patterns of local slip boundary conditions, and that the (scaled with $L$) local slip length at the liquid-lubricant interface is a universal function of $\varphi$ and $\mu$ only.

A model of target charging in interaction with an intense short laser pulse is revised. It provides estimates of the current of energetic electrons escaping the target and the total accumulated electric charge as a function of the laser pulse characteristics and target thickness. Comparisons with experimental data show the model performance, in particular, in the case of targets thinner than the mean-free path of energetic electrons.

In this work, the phase-field-based lattice Boltzmann model is extended to simulate the multiphase ferrofluid flows. The hydrodynamical behavior of the ferrofluids is modeled by the incompressible Navier-Stokes equations with the nonlinear Langevin magnetization law. The phase interface is tracked by the conservative Allen-Cahn equation. A modified magnetic potential equation is used to describe the magnetic field. All governing equations are solved by the lattice Boltzmann method. Several typical problems, including a circular cylinder in a uniform applied magnetic field, deformation of a ferrofluid droplet under a uniform applied magnetic field, bubble merging in ferrofluid under a uniform applied magnetic field, and ferrofluid droplets moving and merging on a flat surface in the presence of a permanent magnet, are simulated to test the accuracy and numerical stability of the present model. The computations are performed in the range of density ratios from 1.975 to 850.7 and viscosity ratios from 20 to 279.3. Some basic phenomenological features of multiphase ferrofluid flows are captured.

We develop a finite difference scheme based on a grid staggered by flux points and solution points to solve Fokker-Planck equations with drift-admitting jumps. To satisfy the matching conditions at the jumps, i.e., the continuities of the propagator and the probability current, the jumps are set to be solution points and used to divide the solution domain into subdomains. While the values of the probability current at flux points are obtained within each subdomain, the values of its first derivative at solution points are evaluated by using stencils across the subdomains. Several benchmark problems are solved numerically to show the validity of the proposed scheme.

Frequency locking to an external forcing frequency is a well-known phenomenon. In the auditory system, it results in a localized traveling wave, the shape of which is essential for efficient discrimination between incoming frequencies. An amplitude equation approach is used to show that the shape of the localized traveling wave depends crucially on the relative strength of additive versus parametric forcing components; the stronger the parametric forcing, the more asymmetric is the response profile and the sharper is the traveling-wave front. The analysis qualitatively captures the empirically observed regions of linear and nonlinear responses and highlights the potential significance of parametric forcing mechanisms in shaping the resonant response in the inner ear.

Learning with an artificial neural network encodes the system behavior in a feed-forward function with a number of parameters optimized by data-driven training. An open question is whether one can minimize the network complexity without loss of performance to reveal how and why it works. Here we investigate the learning of the phase transition in the Ising model and find that having two hidden neurons can be enough for an accurate prediction of critical temperature. We show that the networks learn the scaling dimension of the order parameter while being trained as a phase classifier, demonstrating how the machine learning exploits the Ising universality to work for different lattices of the same criticality within a single set of trainings in one lattice geometry.