We investigate the optical properties of a metal-mirror microcavity containing a liquid-crystalline (LC) perylene tetracarboxylic bisimide (PTCBI) derivative. Measurements of the transmission's incidence angle dependence show that the peaks are split in a complex way and shift as the angle changes. Further, measurements of the photoluminescence spectrum's emission angle dependence show that the peak also shifts with the angle, as in the transmission experiment. We also carry out a theoretical analysis; the theoretical and experimental results are in very good agreement, and we estimate the vacuum Rabi splitting energies to be about 212, 180, and 240 meV. In addition, the peak photoluminescence energy coincides with the lower polariton branch obtained by transmission experiment. Finally, in a time-resolved photoluminescence experiment, we observe a fast relaxation component that is not seen in the bare LC PTCBI film. We believe this is due to cavity effects increasing the spontaneous emission transition rate, indicating that the emissions are due to cavity polaritons.

We employ Monte Carlo simulations to study the defects occurring in a nematic droplet formed by biaxial molecules. The simulations are carried out using a lattice model based on a dispersive orientational biaxial potential previously employed to establish the rich phase diagram of the system. The focus of the present investigation is on the molecular organization inside the droplet when bipolar and toroidal anchoring conditions at the surface are considered. In both cases, we describe how the defect structure arises in the system, and we analyze the behavior of the defect core region in connection with the elastic properties of the phase in a continuum theory perspective.

We consider a nanopatterned planar wall consisting of a periodic array of stripes of width $L$, which are completely wet by liquid (contact angle $\theta =0$), separated by regions of width $D$ which are completely dry (contact angle $\theta =\pi$). Using microscopic density functional theory, we show that, in the presence of long-ranged dispersion forces, the wall-gas interface undergoes a first-order wetting transition, at bulk coexistence as the separation $D$ is reduced to a value $D_w\propto lnL$, induced by the bridging between neighboring liquid droplets. Associated with this is a line of prewetting transitions occurring off coexistence. By varying the stripe width $L$, we show that the prewetting line shows universal scaling behavior and data collapse. This verifies predictions based on mesoscopic models for the scaling properties associated with finite-size effects at complete wetting including the logarithmic singular contribution to the surface free energy.

Metallic glasses with pronounced high-frequency β relaxation in their dynamic-mechanical response have been observed to exhibit large plasticity. Due to their disordered atomic structure, it is challenging to identify the microscopic mechanisms of their relaxation behavior. Quasistatic anelastic relaxation measurements have been performed over 10 orders of magnitude of time on $\mathrm{L}{\mathrm{a}}_{55}\mathrm{N}{\mathrm{i}}_{20}\mathrm{A}{\mathrm{l}}_{25}$ metallic glass, which exhibits a strong β relaxation. The corresponding time-constant spectra were computed from the data—they contain a series of peaks corresponding to an atomically quantized hierarchy of shear transformation zones (STZs), where both the α and β relaxations are consistent with the STZ model. Two different regimes of activation-volume increment between the peaks are observed, suggesting the involvement of different elements in STZs corresponding to α vs β relaxations. Room-temperature structural relaxation significantly affects the former but not the latter.

Deformation and breakup of droplets in confined shear flows have been attracting increasing attention from the research community over the past few years, as attributable to their implications in microfluidics and emulsion processing. Reported results in this regard have demonstrated that the primary effect of confinement happens to be the inception of complex oscillating transients, monotonic variation of droplet deformation, and droplet stabilization against breakup, as attributable to wall-induced distortion of the flow field. In sharp contrast to these reported findings, here, we show that a nonintuitive nonmonotonic droplet deformation may occur in a confined shear flow, under the influence of an external electric field. In addition, we demonstrate that the orientation angle of a droplet may either increase or decrease with the domain confinement under the influence of an electric field, whereas the same trivially decreases with the increase in degree of confinement in the absence of any electrical effects. Unlike the typical oscillatory transients observed in microconfined shear flows, we further bring out the possibility of an electrohydrodynamically induced dampening effect in the oscillation characteristics, as governed by a specific regime of the relevant dimensionless electrical parameters. Our results reveal that instead of arresting droplet deformation, the unique hydrodynamics of microconfined shear flow may augment the tendency of droplet breakup, and is likely to alter the droplet breakup mode from midpoint pinching to edge pinching at high electric field strength. These results may bear far reaching implications in a wide variety of applications ranging from the processing of emulsions to droplet based microfluidic technology.

Laser imprinting possesses a potential danger for low-adiabat and high-convergence implosions in direct-drive inertial confinement fusion (ICF). Within certain direct-drive ICF schemes, a laser picket (prepulse) is used to condition the target to increase the interaction efficiency with the main pulse. Whereas initially the target is in a solid state (of ablators such as polystyrene) with specific electronic and optical properties, the current state-of-the-art hydrocodes assume an initial plasma state, which ignores the detailed plasma formation process. To overcome this strong assumption, a model describing the solid-to-plasma transition, eventually aiming at being implemented in hydrocodes, is developed. It describes the evolution of main physical quantities of interest, including the free electron density, collision frequency, absorbed laser energy, temperatures, and pressure, during the first stage of the laser-matter interaction. The results show that a time about 100 ps is required for the matter to undergo the phase transition, the initial solid state thus having a notable impact on the subsequent plasma dynamics. The nonlinear absorption processes (associated to the solid state) are also shown to have an influence on the thermodynamic quantities after the phase transition, leading to target deformations depending on the initial solid state. The negative consequences for the ICF schemes consist in shearing of the ablator and possibly preliminary heating of the deuterium-tritium fuel.

Efficiently and accurately analyzing high-dimensional time series, such as the molecular dynamics (MD) trajectory of biomolecules, is a long-standing and intriguing task. Two different but related techniques, i.e., dimension reduction methods and clustering algorithms, have been developed and applied widely in this field. Here we show that the combination of these techniques enables further improvement of the analyses, especially with very complicated data. Specifically, we present an approach that combines the trajectory mapping (TM) method, which constructs slow collective variables of a time series, with density peak clustering (DPC) [A. Rodriguez and A. Laio, Science 344, 1492 (2014)], which identifies similar data points to form clusters in a static data set. We illustrate the application of the TMDPC approach with hundreds of microseconds of all-atomic MD trajectories of two proteins, the villin headpiece and protein G. The results show that TMDPC is a powerful tool for achieving the metastable states and slow dynamics of these high-dimensional time series due to the efficient consideration of the time successiveness and the geometric distances between data points.

The size of chemical compound space is too large to be probed exhaustively. This leads high-throughput protocols to drastically subsample and results in sparse and nonuniform datasets. Rather than arbitrarily selecting compounds, we systematically explore chemical space according to the target property of interest. We first perform importance sampling by introducing a Markov chain Monte Carlo scheme across compounds. We then train a machine learning (ML) model on the sampled data to expand the region of chemical space probed. Our boosting procedure enhances the number of compounds by a factor 2 to 10, enabled by the ML model's coarse-grained representation, which both simplifies the structure-property relationship and reduces the size of chemical space. The ML model correctly recovers linear relationships between transfer free energies. These linear relationships correspond to features that are global to the dataset, marking the region of chemical space up to which predictions are reliable; this is a more robust alternative to the predictive variance. Bridging coarse-grained simulations with ML gives rise to an unprecedented database of drug-membrane insertion free energies for 1.3 million compounds.

We study here one-dimensional model of aggregation and fragmentation of clusters of particles obeying the stochastic discrete-time kinetics of the generalized totally asymmetric simple exclusion process (gTASEP) on open chains. The gTASEP is essentially the ordinary TASEP with backward-ordered sequential update (BSU), however, equipped with two hopping probabilities: $p$ and $p_m$. The second modified probability $p_m$ models a special kinematic interaction between the particles of a cluster in addition to the simple hard-core exclusion interaction, existing in the ordinary TASEP. We focus on the nonequilibrium stationary properties of the gTASEP in the generic case of attraction between the particles of a cluster. In this case the particles of a cluster have higher chance to stay together than to split, thus producing higher throughput in the system. We explain how the topology of the phase diagram in the case of irreversible aggregation, occurring when the modified probability equals unity, changes sharply to the one, corresponding to the ordinary TASEP with BSU, as soon as the modified probability becomes less than unity and aggregation-fragmentation of clusters appears. We estimate various physical quantities in the system and determine the parameter-dependent injection and ejection critical values by extensive computer simulations. With the aid of random walk theory, supported by the Monte Carlo simulations, the properties of the phase transitions between the three stationary phases are assessed.

In this paper we study a chimera state in complex networks of bistable Hodgkin-Huxley neurons with excitatory coupling, which manifests as a termination of spiking activity of a part of interacting neurons. We provide a detailed investigation of this phenomenon in scale-free, small-world, and random networks and show that the chimera state is robust to the network topology. Nevertheless, network topological properties determine the stability of spatiotemporal states and therefore affect the excitability of the chimera state in the whole network. In particular, the scale-free network whose higher degree nodes are more stable to small perturbations is least exposed to chimera formation and exhibits an abrupt transition from a spiking to a silent regime. On the other hand, small-world and random networks are more likely to provide transitions to the chimera state.

Measurement noise may have an important impact on the collective motion. Here, we investigate the consensus problem of multiagent networks with multiplicative measurement noise. Based on the stability theory of stochastic differential equations and the algebra graph theory, we obtain sufficient conditions for the consensus and nonconsensus. Both of our analytical and numerical results show that the multiplicative measurement noise can facilitate the emergence of the consensus: the convergence rate increases with respect to the noise intensity if the topologies of the underlying networks satisfy some conditions. Our results provide a better understanding of the constructive role of noise. We also report that the convergence rate of multiagent networks is strongly affected by the network topology and the group size.

Spatial organization of physical form of an urban system, or city, both manifests and influences the way its social form functions. Mathematical quantification of the spatial pattern of a city is, therefore, important for understanding various aspects of the system. In this work, a framework to characterize the spatial pattern of urban locations based on the idea of entropy maximization is proposed. Three spatial length scales in the system with discerning interpretations in terms of the spatial arrangement of the locations are calculated. Using these length scales, two quantities are introduced to quantify the system's spatial pattern, namely, mass decoherence and space decoherence, whose combination enables the comparison of different cities in the world. The comparison reveals different types of urban morphology that could be attributed to the cities' geographical background and development status.

Using simulation and theory we study the dynamics of a colloidal suspension in two dimensions subject to a time-delayed repulsive feedback that depends on the positions of the colloidal particles. The colloidal particles experience an additional potential that is a superposition of repulsive potential energies centered around the positions of all the particles a delay time ago. Here we show that such a feedback leads to self-organization of the particles into traveling bands. The width of the bands and their propagation speed can be tuned by the delay time and the range of the imposed repulsive potential. The emerging traveling band behavior is observed in Brownian dynamics computer simulations as well as microscopic dynamic density functional theory. Traveling band formation also persists in systems of finite size leading to rotating traveling waves in the case of circularly confined systems.

Entropy growth and entropy production rate are analyzed in the stationary shock waves in a multitemperature model of a binary mixture of gases. The model is developed within the framework of extended thermodynamics. It is shown that the entropy density of the mixture increases monotonically through the shock profile, whereas the entropy densities of the constituents may not be monotonic. The analysis of entropy growth rate distinguished the contributions of momentum exchange (diffusion) and internal energy exchange between the constituents, and showed a substantially larger contribution of diffusion. At the same time, it is shown that the entropy production rates of the constituents may not be non-negative throughout the whole shock structure.

This work shows that dynamical features typical of full random matrices can be observed also in the simple finite one-dimensional (1D) noninteracting Anderson model with nearest-neighbor couplings. In the thermodynamic limit, all eigenstates of this model are exponentially localized in configuration space for any infinitesimal on-site disorder strength $W$. But this is not the case when the model is finite and the localization length is larger than the system size $L$, which is a picture that can be experimentally investigated. We analyze the degree of energy-level repulsion, the structure of the eigenstates, and the time evolution of the finite 1D Anderson model as a function of the parameter $\xi \propto {\left(W^{2}L\right)}^{-1}$. As $\xi$ increases, all energy-level statistics typical of random matrix theory are observed. The statistics are reflected in the corresponding eigenstates and also in the dynamics. We show that the probability in time to find a particle initially placed on the first site of an open chain decays as fast as in full random matrices and much faster than when the particle is initially placed far from the edges. We also see that at long times, the presence of energy-level repulsion manifests in the form of the correlation hole. In addition, our results demonstrate that the hole is not exclusive to random matrix statistics, but emerges also for $W=0$, when it is in fact deeper.

The ferromagnetic bidimensional Ising model with dipolar interactions has been proposed to model ultrathin films with strong out-of-plane anisotropy. The phase diagram presents a rich phenomenology that includes low-temperature phases characterized by stripes of width $n$ ($h_n$) and a high-temperature phase with domains of stripes with mutually perpendicular orientations, named tetragonal liquid (TL). The latter phase can be reached by two possible ways. One of them is the direct transition $h_n$ to TL, and the other one is through an intermediate phase with orientational order but short-range positional disorder, named nematic phase (NM). The regions of the phase diagram where these transitions occur, as well as their character, remain an open question and are the object of the present work. In order to clarify this topic, intensive Monte Carlo simulations were performed by employing short-time dynamics as the main tool for studying the phase transition behavior. The dynamic evolution of the orientational order parameter and its moments are measured for selected values of the ratio between the ferromagnetic exchange and dipolar constants, called $\delta$. The obtained results indicate that the intermediate NM phase is present for $\delta \ge 2$ in narrow ranges of temperatures. Also, the results suggest that both transitions, i.e., $h_n$-NM and NM-TL, have a Kosterlitz-Thouless character. This type of topological transition is observed in continuous bidimensional models and have been proposed for discrete ones, as in the case of the present work.

We present an analytical approach to study simple symmetric random walks on a crossing geometry consisting of a plane square lattice crossed by $n_l$ number of lines that all meet each other at a single point (the origin) on the plane. The probability density to find the walker at a given distance from the origin either in a line or in the plane geometry is exactly calculated as a function of time $t$. We find that the large-time asymptotic behavior of the walker for any arbitrary number $n_l$ of lines is eventually governed by the diffusion of the walker on the plane after a crossover time approximately given by $t_c\propto n_l^2$. We show that this competition can be changed in favor of the line geometry by switching on an arbitrarily small perturbation of a drift term in which even a weak biased walk is able to drain the whole probability density into the line at long-time limit. We also present the results of our extensive simulations of the model which perfectly support our analytical predictions. Our method can, however, be simply extended to other crossing geometries with a single common point.

Cancer cells have an altered metabolism that increases acid production driving to an extracellular $p\mathrm{H}$ significantly lower than normal. This leads to normal cell death, and extracellular matrix degradation allowing the formation of an interstitial gap between cancer and healthy cells. In this work, we present a mathematical model to study the interstitial gap formation and evolution considering a tissue with a non-uniform nutrient distribution. Our results indicate that the interstitial gap onsets at the region with highest nutrient consumption. Due to the gap formation, cancer cells near the interface have more nutrient and space availability. This induces cancer cell reproduction and migration toward the nutrient source. Our simulations suggest a strong correlation between gap size and the distance to the nutrient source. Although we do not find a correlation between tumor growth speed and gap size, our results indicate a high risk of metastasis for tumors that develop an interstitial gap, emphasizing the importance of gap detection as a hallmark for cancer invasion.

Hemodynamic modeling is used to explore the origin, predict, and analyze the power spectrum of the resting-state blood-oxygen-level-dependent (BOLD) signal measured by functional magnetic resonance imaging (fMRI), which has been reported to have a power-law form, i.e., $P\left(f\right)\propto f^{-s}$, where $P\left(f\right)$ is the power, $f$ is the frequency, and $s>0$ is the power-law exponent. However, current fMRI experimental paradigms have limited acquisition durations, affecting the spectral resolution of fMRI data at the low-frequency regime. Here, the claimed power-law spectrum is investigated by using a recent hemodynamic model to analytically derive the BOLD power spectrum, with parameters that are related to neurophysiology. The theoretical results show that, for all realistic parameter combinations, the BOLD power spectrum is flat at $f\lesssim 0.01\mathrm{Hz}$, has a weak resonance originating from intrinsic oscillations of vasodilatory response, and becomes a power law for high frequencies, all of which is in agreement with an empirical data set that describes the spectrum of one subject and brain region. However, the results are contrary to studies reporting a pure power-law spectrum at $f\lesssim 0.2\mathrm{Hz}$. The discrepancy is attributed largely to data averaging employed by current approaches that averages together important properties of the BOLD power spectrum, such as its resonance, that biases the spectrum to only show a power law. Data averaging also reduces the high-frequency power-law exponent relative to individual cases. Overall, this work demonstrates how the model can reproduce BOLD dynamics and further analyze its low-frequency behavior. Moreover, it also uses the model to explain the impact of procedures, such as data averaging, on the reported features of the BOLD power spectrum.