The quantum phase transition (QPT) describes a sudden qualitative change of the macroscopic properties mapped from the eigenspectrum of a quantum many-body system. It has been studied intensively in quantum systems with the spin-boson model, but it has barely been explored for systems in coupled spin-boson models. In this paper, we study the QPT with coupled spin-boson models consisting of coupled two-level atoms embedded in three-dimensional anisotropic photonic crystals. The dynamics of the system is derived exactly by means of the Laplace transform method, which has been proven to be equivalent to the dissipationless non-Markovian dynamics. Drawing on methods for analyzing the ground state, we obtain the phase diagrams through two exact critical equations and two QPTs are found: one QPT is that from the phase without one bound state to the phase with one bound state and another is that from one phase with the bound state having one eigenvalue to another phase where the bound state has two eigenvalues. Our analytical results also suggest a way of control to overcome the effect of decoherence by engineering the spectrum of the reservoirs to approach the non-Markovian regime and to form the bound state of the whole system for quantum devices and quantum statistics.

Natural and artificial honeycomb lattices are of great interest because the band structure of these lattices, if properly constructed, contains a Dirac point. Such lattices occur naturally in the form of graphene and carbon nanotubes. They have been created in the laboratory in the form of semiconductor 2DEGs, optical lattices, and photonic crystals. We show that, over a wide energy range, gases (of electrons, atoms, or photons) that propagate through these lattices are Lorentz gases and the corresponding classical dynamics is chaotic. Thus honeycomb lattices are also of interest for understanding eigenstate thermalization and the conductor-insulator transition due to dynamic Anderson localization.

The growth rate and carrying capacity of a cell population are key to the characterization of the population's viability and to the quantification of its responses to perturbations such as drug treatments. Accurate estimation of these parameters necessitates careful analysis. Here, we present a rigorous mathematical approach for the robust analysis of cell count data, in which all the experimental stages of the cell counting process are investigated in detail with the machinery of Bayesian probability theory. We advance a flexible theoretical framework that permits accurate estimates of the growth parameters of cell populations and of the logical correlations between them. Moreover, our approach naturally produces an objective metric of avoidable experimental error, which may be tracked over time in a laboratory to detect instrumentation failures or lapses in protocol. We apply our method to the analysis of cell count data in the context of a logistic growth model by means of a user-friendly computer program that automates this analysis, and present some samples of its output. Finally, we note that a traditional least squares fit can provide misleading estimates of parameter values, because it ignores available information with regard to the way in which the data have actually been collected.

Protein aggregation in cell membrane is vital for the majority of biological functions. Recent experimental results suggest that transmembrane domains of proteins such as $\alpha$-helices and $\beta$-sheets have different structural rigidities. We use molecular dynamics simulation of a coarse-grained model of protein-embedded lipid membranes to investigate the mechanisms of protein clustering. For a variety of protein concentrations, our simulations under thermal equilibrium conditions reveal that the structural rigidity of transmembrane domains dramatically affects interactions and changes the shape of the cluster. We have observed stable large aggregates even in the absence of hydrophobic mismatch, which has been previously proposed as the mechanism of protein aggregation. According to our results, semiflexible proteins aggregate to form two-dimensional clusters, while rigid proteins, by contrast, form one-dimensional string-like structures. By assuming two probable scenarios for the formation of a two-dimensional triangular structure, we calculate the lipid density around protein clusters and find that the difference in lipid distribution around rigid and semiflexible proteins determines the one- or two-dimensional nature of aggregates. It is found that lipids move faster around semiflexible proteins than rigid ones. The aggregation mechanism suggested in this paper can be tested by current state-of-the-art experimental facilities.

We present a detailed study of squared local roughness (SLRDs) and local extremal height distributions (LEHDs), calculated in windows of lateral size $l$, for interfaces in several universality classes, in substrate dimensions $d_s=1$ and 2. We show that their cumulants follow a Family-Vicsek-type scaling, and, at early times, when $\xi \ll l$ $(\xi$ is the correlation length), the rescaled SLRDs are given by log-normal distributions, with their $n\mathrm{th}$ cumulant scaling as ${(\xi /l)}^{(n-1)d_s}$. This gives rise to an interesting temporal scaling for such cumulants as ${〈w_n〉}_c\sim t^{{\gamma }_n}$, with ${\gamma }_n=2n\beta +(n-1)d_s/z=\left[2n+(n-1)d_s/\alpha \right]\beta$. This scaling is analytically proved for the Edwards-Wilkinson (EW) and random deposition interfaces and numerically confirmed for other classes. In general, it is featured by small corrections, and, thus, it yields exponents ${\gamma }_n$ (and, consequently, $\alpha ,\beta$ and $z)$ in good agreement with their respective universality class. Thus, it is a useful framework for numerical and experimental investigations, where it is usually hard to estimate the dynamic $z$ and mainly the (global) roughness $\alpha$ exponents. The stationary (for $\xi \gg l)$ SLRDs and LEHDs of the Kardar-Parisi-Zhang (KPZ) class are also investigated, and, for some models, strong finite-size corrections are found. However, we demonstrate that good evidence of their universality can be obtained through successive extrapolations of their cumulant ratios for long times and large $l$. We also show that SLRDs and LEHDs are the same for flat and curved KPZ interfaces.

A mechanism for the transport of microscale particles in viscous fluids is demonstrated. The mechanism exploits the trapping of such particles by rotational streaming cells established in the vicinity of an oscillating cylinder, recently analyzed in previous work. The present work explores a strategy of transporting particles between the trapping points established by multiple cylinders undergoing oscillations in sequential intervals. It is demonstrated that, by controlling the sequence of oscillation intervals, an inertial particle is effectively and predictably transported between the stable trapping points. Arrays of cylinders in various arrangements are investigated, revealing a technique for constructing arbitrary particle trajectories. It is found that the domain from which particles can be transported and trapped by an oscillator is extended, even to regions in which particles are shielded, by the presence of other stationary cylinders. The timescales for transport are examined, as are the mechanisms by which particles are drawn away from an obstacle toward the trapping point of an oscillator.

Direct production of electron-positron pairs in two-photon collisions, the Breit-Wheeler process, is one of the basic processes in the universe. However, it has never been directly observed in the laboratory because of the absence of the intense $\gamma$-ray sources. Laser-induced synchrotron sources emission may open a way to observe this process. The feasibility of an experimental setup using a MeV photon source is studied in this paper. We compare several $\gamma$-ray sources and estimate the expected number of electron-positron pairs and competing processes by using numerical simulations including quantum electrodynamic effects.

A theory is developed to explain the sub-Gaussian behavior of the Townsend-Perry constants $\left(A_p\right)$ recently measured for high-order fluctuation moments in turbulent boundary layers. It yields the generalized logarithmic law for high-order moments and $A_p/A_1={\left({\ell }^{*}\right)}^{{\zeta }_p/p-{\zeta }_1}{C}_p^{1/p}/C_1$, where ${\zeta }_p$ are the Kolmogorov-Obukhov-She-Leveque scaling characterizing intermittence effects; ${\ell }^{*}=1/225$ is the only free parameter describing a specific ratio between inertial and energy-containing eddy sizes; $C_p$ are raw moments of a Gaussian with unity mean and variance. The predicted $A_p/A_1$ are in good agreement with experimental data.

The evolution of many kinetic processes in 1+1 (space-time) dimensions results in $2\mathrm{D}$ directed percolative landscapes. The active phases of these models possess numerous hidden geometric orders characterized by various types of large-scale and/or coarse-grained percolative backbones that we define. For the patterns originated in the classical directed percolation (DP) and contact process we show from the Monte Carlo simulation data that these percolative backbones emerge at specific critical points as a result of continuous phase transitions. These geometric transitions belong to the DP universality class and their nonlocal order parameters are the capacities of corresponding backbones. The multitude of conceivable percolative backbones implies the existence of infinite cascades of such geometric transitions in the kinetic processes considered. We present simple arguments to support the conjecture that such cascades of transitions are a generic feature of percolation as well as of many other transitions with nonlocal order parameters.

We propose a general method for the construction and analysis of unweighted $\epsilon$-recurrence networks from chaotic time series. The selection of the critical threshold ${\epsilon }_c$ in our scheme is done empirically and we show that its value is closely linked to the embedding dimension $M$. In fact, we are able to identify a small critical range $\mathrm{\Delta }\epsilon$ numerically that is approximately the same for the random and several standard chaotic time series for a fixed $M$. This provides us a uniform framework for the nonsubjective comparison of the statistical measures of the recurrence networks constructed from various chaotic attractors. We explicitly show that the degree distribution of the recurrence network constructed by our scheme is characteristic to the structure of the attractor and display statistical scale invariance with respect to increase in the number of nodes $N$. We also present two practical applications of the scheme, detection of transition between two dynamical regimes in a time-delayed system and identification of the dimensionality of the underlying system from real-world data with a limited number of points through recurrence network measures. The merits, limitations, and the potential applications of the proposed method are also highlighted.

An energy shell structure depending on eccentricity is analyzed in a dielectric elliptic microcavity. Through the analysis, it is explicated that the energy shell structure is governed by classical constant actions of periodic orbits. For clarification, the relation between dominances of the periodic orbits and bifurcation behaviors are obtained and the length spectra based on eigenvalues computed by a numerical method are compared with the exact lengths of the periodic orbits obtained by analytic calculations. By matching effective wave numbers obtained from the periodic orbit lengths to exact wave numbers of stationary states in closed and open cavities, we find deviations provoked from the openness. We show that these deviations are caused by additional phase factors in the Einstein-Brillouin-Keller quantization.

Traditional mathematical models of epidemic disease had for decades conventionally considered static structure for contacts. Recently, an upsurge of theoretical inquiry has strived towards rendering the models more realistic by incorporating the temporal aspects of networks of contacts, societal and online, that are of interest in the study of epidemics (and other similar diffusion processes). However, temporal dynamics have predominantly focused on link fluctuations and nodal activities, and less attention has been paid to the growth of the underlying network. Many real networks grow: Online networks are evidently in constant growth, and societal networks can grow due to migration flux and reproduction. The effect of network growth on the epidemic properties of networks is hitherto unknown, mainly due to the predominant focus of the network growth literature on the so-called steady state. This paper takes a step towards alleviating this gap. We analytically study the degree dynamics of a given arbitrary network that is subject to growth. We use the theoretical findings to predict the epidemic properties of the network as a function of time. We observe that the introduction of new individuals into the network can enhance or diminish its resilience against endemic outbreaks and investigate how this regime shift depends upon the connectivity of newcomers and on how they establish connections to existing nodes. Throughout, theoretical findings are corroborated with Monte Carlo simulations over synthetic and real networks. The results shed light on the effects of network growth on the future epidemic properties of networks and offers insights for devising a priori immunization strategies.

We consider an equilibrium ensemble of large Erdős-Renyi topological random networks with fixed vertex degree and two types of vertices, black and white, prepared randomly with the bond connection probability $p$. The network energy is a sum of all unicolor triples (either black or white), weighted with chemical potential of triples $\mu$. Minimizing the system energy, we see for some positive $\mu$ the formation of two predominantly unicolor clusters, linked by a string of $N_{bw}$ black-white bonds. We have demonstrated that the system exhibits critical behavior manifested in the emergence of a wide plateau on the $N_{bw}\left(\mu \right)$ curve, which is relevant to a spinodal decomposition in first-order phase transitions. In terms of a string theory, the plateau formation can be interpreted as an entanglement between baby universes in two-dimensional gravity. We conjecture that the observed classical phenomenon can be considered as a toy model for the chiral condensate formation in quantum chromodynamics.

Recently, a phase transition has been discovered in the network community detection problem below which no algorithm can tell which nodes belong to which communities with success any better than a random guess. This result has, however, so far been limited to the case where the communities have the same size or the same average degree. Here we consider the case where the sizes or average degrees differ. This asymmetry allows us to assign nodes to communities with better-than-random success by examining their local neighborhoods. Using the cavity method, we show that this removes the detectability transition completely for networks with four groups or fewer, while for more than four groups the transition persists up to a critical amount of asymmetry but not beyond. The critical point in the latter case coincides with the point at which local information percolates, causing a global transition from a less-accurate solution to a more-accurate one.

We consider a set of identical mobile pointlike charges (counterions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are considered: a pair of parallel plates, the cylinder, and the sphere. The particle system in thermal equilibrium is assumed to be described by the nonlinear Poisson-Boltzmann theory. While the effectively one-dimensional plates and the two-dimensional cylinder have already been solved, the three-dimensional sphere problem is not integrable. It is shown that the contact density of particles at the charged surface is determined by a first-order Abel differential equation of the second kind which is a counterpart of Enig's equation in the critical theory of gravitation and combustion or explosion. This equation enables us to construct the exact series solutions of the contact density in the regions of small and large surface charge densities. The formalism provides, within the mean-field Poisson-Boltzmann framework, the complete thermodynamics of counterions inside a charged sphere (salt-free system).

We study the molecular reorientation induced by a textured external field in a nematic liquid crystal (nLC). In particular, we consider an infinitely wide cell with strong planar anchoring boundary conditions, subjected to a spatially periodic piecewise magnetic field. In the framework of the Frank's continuum theory, we use the perturbation analysis to study in detail the field-induced splay-bend Fréedericksz transition. A numerical approach, based on the finite differences method, is instead employed to solve the fully nonlinear equations. At high field strengths, an analytic approach allows us to draw the bulk profile of the director in terms of elliptic integrals. Finally, through the application of the Bruggeman texture hydrodynamics theory, we qualitatively discuss on the LCs piecewise director configuration under sliding interfaces, which can be adopted to actively regulate friction. Our study opens the pathway for the application of highly controlled nLC texturing for tribotronics.

The effect of oscillatory shear strain on nonaffine rearrangements of individual particles in a three-dimensional binary glass is investigated using molecular dynamics simulations. The amorphous material is represented by the Kob-Andersen mixture at the temperature well below the glass transition. We find that during periodic shear deformation of the material, some particles undergo reversible nonaffine displacements with amplitudes that are approximately power-law distributed. Our simulations show that particles with large amplitudes of nonaffine displacement exhibit a collective behavior; namely, they tend to aggregate into relatively compact clusters that become comparable with the system size near the yield strain. Along with reversible displacements there exist a number of irreversible ones. With increasing strain amplitude, the probability of irreversible displacements during one cycle increases, which leads to permanent structural relaxation of the material.

We investigate the critical transition from an inverse cascade of energy to a forward energy cascade in a two-dimensional magnetohydrodynamic flow as the ratio of magnetic to mechanical forcing amplitude is varied. It is found that the critical transition is the result of two competing processes. The first process is due to hydrodynamic interactions and cascades the energy to the large scales. The second process couples small-scale magnetic fields to large-scale flows, transferring the energy back to the small scales via a nonlocal mechanism. At marginality the two cascades are both present and cancel each other. The phase space diagram of the transition is sketched.

There is commonly no turbulence in microfluidics, and the flows are believed to be either laminar or chaotic, since Reynolds number (Re) in microflows is usually on the order of unity or lower. However, we recently demonstrated that it is possible to achieve turbulence with low Re (based on the measured flow velocity and the width of the channel entrance) when a pressure-driven flow is electrokinetically forced in a quasi T-microchannel. To be able to measure high frequency velocity fluctuations in microchannels, a velocimeter with submicrometer spatial resolution and microsecond temporal resolution, called a laser-induced fluorescence photobleaching anemometer, is developed. Here we characterize the microelectrokinetic turbulence and observe some typical and important features of high Re flows, such as Kolmogorov $-5/3$ spectrum of velocity fluctuation, which usually can be realized only at very high Re in macroturbulent flows.