Edge dynamics is relevant to various real-world systems with complex network topological features. An edge dynamical system is controllable if it can be driven from any initial state to any desired state in finite time with appropriate control inputs. Here a framework is proposed to study the impact of correlation between in- and out-degrees on controlling the edge dynamics in complex networks. We use the maximum matching and direct acquisition methods to determine the controllability limit, i.e., the limit of acceptable change of the edge controllability by adjusting the degree correlation only. Applying the framework to plenty complex networks, we find that the controllability limits are ubiquitous in model and real networks. Arbitrary edge controllability in between the limits can be achieved by properly adjusting the degree correlation. Moreover, a nonsmooth phenomenon occurs in the upper limits, and exponential and power-law scaling behaviors are widespread in the approach or separation speed between the upper and lower limits.

Bent-core (BC) molecules usually exhibit polar packing in smectic layers in which the long or bow axes tilt with respect to the layer normal. In many compounds, the tilt angle goes to zero, and typically the polarization (P) of neighboring layers has an antiferroelectric order ($\mathrm{Sm}A{P}_{\mathrm{AF}}$). A careful molecular engineering has led to the discovery of the ferroelectric $\mathrm{Sm}A{P}_{\mathrm{F}}$ phase in a few BC compounds. Detailed experimental studies [Zhu et al., J. Am. Chem. Soc. 134, 9681 (2012)] have shown that one of the compounds undergoes a weak first order transition to a striped phase $\left(\mathrm{Sm}A{P}_{\mathrm{Fmod}}\right)$, in which the repolarization switching occurs at a threshold electric field, the latter increasing with temperature. The main optical birefringence of the $\mathrm{Sm}A{P}_{\mathrm{Fmod}}$ phase increases rapidly with the field at lower temperatures of its range. A small $(<10\%)$ fraction of the BC molecules can be expected to have less bent conformations in excited states (ESs), and we argue that the ES conformers rotate freely about the bow axes, and aggregate to form regions without any polar order to gain rotational entropy. In turn, a favorable divP term leads to the formation of stripes in the polarized regions made of ground state conformers. Based on this physical picture, we develop a simple phenomenological model to reproduce all the experimental trends qualitatively. In sample cells with insulating layers neighboring stripes prefer to have an antiparallel orientation of the mean P direction. The dielectric constant of the stripe phase increases with a dc bias electric field, a trend which is opposite to that in other ferroelectric liquid crystals.

Bulk-boundary correspondence is the emergence of features at the boundary of a material that are dependent on and yet distinct from the properties of the bulk of the material. The diverse applications of this idea in topological insulators as well as high energy physics prove its universality. However, whether a form of bulk-boundary correspondence holds also in soft matter such as gels, polymers, lipids, and other biomaterials is thus far unknown. Aerosil-dispersed liquid crystal gels provide a good testing ground to explore the relation between the controlled variations of the aerosil density within the liquid crystal bulk and the surface topography of the sample. Here we report on a direct observation of such a correspondence where the controlled strength of random disorder created by aerosil dispersion in the bulk liquid crystal is correlated with the fractal dimension of the surface. We obtained the surface topography of our gel samples with different quenched random disorder strengths by using atomic force microscope techniques, and computed the fractal dimension for each sample. We found that an increase of the aerosil gel density in the bulk corresponds to an increase in the fractal dimension at the surface. From our results emerges a method to acquire the bulk properties of soft matter such as density, randomness, and phase merely from the fractal dimension of the surface.

We propose here an alternative way to understand the characteristic pattern formation found in the so-called viscoelastic phase separations. Since the viscoelastic phase separations have been observed in systems with strong viscoelastic nature such as polymer solutions, numerical modelings for them have been conducted so far by introducing dynamic properties such as concentration-dependent mobility or elastic relaxation moduli to a usual scheme of phase separations. In contrast to these approaches, we propose the introduction of a small change, a bump, in the local free-energy function, keeping a parameter representing dynamic properties constant. We show that the bump in the local free-energy function successfully induces desired pattern formations in a controlled way, while it does not change equilibrium states. The mechanisms by which this free-energy approach reproduces experimentally observed pattern formations are discussed.

We show that the critical manifold of a statistical mechanical system in the vicinity of a critical point is locally accessible through correlation functions at that point. A practical numerical method is presented to determine the tangent space and the curvature to the critical manifold with variational Monte Carlo renormalization group. Because of the use of a variational bias potential of the coarse-grained variables, critical slowing down is greatly alleviated in the Monte Carlo simulation. In addition, this method is free of truncation error. We study the isotropic Ising model on square and cubic lattices, the anisotropic Ising model, and the tricritical Ising model on square lattices to illustrate the method.

In this paper, we study a finite direct electrical transmission line when we distribute resistors $R_n$ according to a parity-time ($\mathcal{PT}$) distribution composed of a gain ($-R$) and loss ($+R$) sequence. Considering zero boundary conditions, we find analytical results for the frequency spectrum $\omega (R,k_d)$ as a function of resistance $R$ and the wave number $k_d$. A frequency spectrum analysis shows a phase transition from real to complex eigenvalues as a function $R$ for fixed $k_{d=N}$, where $2N$ is the size of the transmission line. Numerically, we study localization properties through the normalized localization length $\mathrm{\Lambda }(R,k_d)$. This measure shows good agreement with the analytical results and gives an account of the $\mathcal{PT}$-phase transition. Our results pave a solid way toward studying the interplay between parity-time symmetry concepts and one-dimensional electrical transmission lines, aiming to find another generation of electronic devices capable of controlling the flow of energy.

Although non-Markovian processes are considerably more complicated to analyze, real-world epidemics are likely non-Markovian, because the infection time is not always exponentially distributed. Here, we present analytic expressions of the epidemic threshold in a Weibull and a Gamma SIS epidemic on any network, where the infection time is Weibull, respectively, Gamma, but the recovery time is exponential. The theory is compared with precise simulations. The mean-field non-Markovian epidemic thresholds, both for a Weibull and Gamma infection time, are physically similar and interpreted via the occurrence time of an infection during a healthy period of each node in the graph. Our theory couples the type of a viral item, specified by a shape parameter of the Weibull or Gamma distribution, to its corresponding network-wide endemic spreading power, which is specified by the mean-field non-Markovian epidemic threshold in any network.

Near a bifurcation point, the response time of a system is expected to diverge due to the phenomenon of critical slowing down. We investigate critical slowing down in well-mixed stochastic models of biochemical feedback by exploiting a mapping to the mean-field Ising universality class. We analyze the responses to a sudden quench and to continuous driving in the model parameters. In the latter case, we demonstrate that our class of models exhibits the Kibble-Zurek collapse, which predicts the scaling of hysteresis in cellular responses to gradual perturbations. We discuss the implications of our results in terms of the tradeoff between a precise and a fast response. Finally, we use our mapping to quantify critical slowing down in T cells, where the addition of a drug is equivalent to a sudden quench in parameter space.

We explain theoretical peculiarities of the smectic-$A$–hexatic-$B$ equilibrium phase coexistence in a finite-temperature range recently observed experimentally in free-standing smectic films [I. A. Zaluzhnyy et al., Phys. Rev. E 98, 052703 (2018)]. We quantitatively describe this unexpected phenomenon within Landau phase transitions theory assuming that the film state is close to a tricritical point. We found that the surface hexatic order diminishes the phase coexistence range as the film thickness decreases, shrinking it to zero at some minimal film thickness $L_c$, of the order of a few hexatic correlation length. We established universal laws for the temperature width of the phase coexistence range in terms of the reduced variables. Our theory is in agreement with the existing experimental data.

In a recent article, we described how the microscopic structure of density-density correlations in the fluid interfacial region, for systems with short-ranged forces, can be understood by considering the resonances of the local structure factor occurring at specific parallel wave vectors $q$ [Nat. Phys. 15, 287 (2019)]. Here we investigate this further by comparing approximations for the local structure factor and pair correlation function against three new examples of analytically solvable models within square-gradient theory. Our analysis further demonstrates that these approximations describe the pair correlation function and structure factor across the whole spectrum of wave vectors, encapsulating the crossover from the Goldstone mode divergence (at small $q$) to bulklike behavior (at larger $q$). As shown, these approximations are exact for some square-gradient model potentials and never more than a few percent inaccurate for the others. Additionally, we show that they describe very accurately the correlation function structure for a model describing an interface near a tricritical point. In this case, there are no analytical solutions for the correlation functions, but the approximations are nearly indistinguishable from the numerical solutions of the Ornstein-Zernike equation.

We studied the wetting behavior of silver and copper thin films versus their kinetic roughening upon deposition at room temperature on glass substrates. Time-dependent height-height correlation functions were extracted from atomic force microscopy images, and they demonstrated a nonstationary growth front of the film roughness associated with a temporal evolution of the local surface slope. As a result, we tried to correlate the roughness statistical properties such as the root-mean-square (rms) roughness $\sigma$, the correlation length $\xi$, and the local surface slope $\left(\rho \approx \sigma /\xi \right)$ with the wetting behavior of the films’ surfaces. The contact angle behavior was also studied by analyzing the variation of the energy of the system with water penetrating into the surface cavities, and the associated Laplace pressure induced by the local surface curvature. Hence, it was demonstrated that the wetting transition from a metastable Cassie-Baxter state to a Wenzel state as well as the penetration of a droplet into the surface crevices occur at the smaller local surface slopes for the higher surface energy material.

Superballs represent a class of particles whose shapes are defined by the domain ${\left|x\right|}^{2p}+{\left|y\right|}^{2p}+{\left|z\right|}^{2p}\le R^{2p}$, with $p\in (0,\infty )$ being the deformation parameter. $0<p<0.5$ represents a family of hexapodlike (concave octahedral-like) particles, $0.5\le p<1$ and $p>1$ represent, respectively, families of convex octahedral-like and cubelike particles, with $p=1,0.5$, and $\infty$ representing spheres, octahedra, and cubes. Colloidal zeolite suspensions, catalysis, and adsorption, as well as biomedical magnetic nanoparticles are but a few of the applications of packing of superballs. We introduce a universal method for simulating random sequential adsorption of superballs, which we refer to as the low-entropy algorithm, which is about two orders of magnitude faster than the conventional algorithms that represent high-entropy methods. The two algorithms yield, respectively, precise estimates of the jamming fraction ${\varphi }_{\infty }\left(p\right)$ and $\nu \left(p\right)$, the exponent that characterizes the kinetics of adsorption at long times $t$, ${\varphi }_{\infty }\left(p\right)-\varphi (p,t)\sim t^{-\nu \left(p\right)}$. Precise estimates of ${\varphi }_{\infty }\left(p\right)$ and $\nu \left(p\right)$ are obtained and shown to be in agreement with the existing analytical and numerical results for certain types of superballs.

Heterogeneous materials are often organized in a hierarchical manner, where a basic unit is repeated over multiple scales. The structure then acquires a self-similar pattern. Examples of such structure are found in various biological and synthetic materials. The hierarchical structure can have significant consequences for the failure strength and the mechanical response of such systems. Here we consider a fiber bundle model with hierarchical structure and study the avalanche dynamics exhibited by the model during the approach to failure. We show that the failure strength of the model generally decreases in a hierarchical structure, as opposed to the situation where no such hierarchy exists. However, we also report a special arrangement of the hierarchy for which the failure threshold could be substantially above that of a nonhierarchical reference structure.

We consider the inference of the drift velocity and the diffusion coefficient of a particle undergoing a directed random walk in the presence of static localization error. A weighted least-squares fit to mean-square displacement (MSD) data is used to infer the parameters of the assumed drift-diffusion model. For experiments which cannot be repeated we show that the quality of the inferred parameters depends on the number of MSD points used in the fitting. An optimal number of fitting points $p_{\mathrm{opt}}$ is shown to exist which depends on the time interval between frames $\mathrm{\Delta }t$ and the unknown parameters. We therefore also present a simple iterative algorithm which converges rapidly toward $p_{\mathrm{opt}}$. For repeatable experiments the quality depends crucially on the measurement time interval over which measurements are made, reflecting the different timescales associated with drift and diffusion. An optimal measurement time interval $T_{\mathrm{opt}}$ exists, which depends on the number of measurement points and the unknown parameters, and so again we present an iterative algorithm which converges quickly toward $T_{\mathrm{opt}}$ and is shown to be robust to initial parameter guesses.

We extend the theory of stochastic thermodynamics in three directions: (i) instead of a continuously monitored system we consider measurements only at an arbitrary set of discrete times, (ii) we allow for imperfect measurements and incomplete information in the description, and (iii) we treat arbitrary manipulations (e.g., feedback control operations) which are allowed to depend on the entire measurement record. For this purpose we define for a driven system in contact with a single heat bath the four key thermodynamic quantities—internal energy, heat, work, and entropy—along a single “trajectory” for a causal model. The first law at the trajectory level and the second law on average is verified. We highlight the special case of Bayesian or “bare” measurements (incomplete information, but no average disturbance) which allows us to compare our theory with the literature and to derive a general inequality for the estimated free energy difference in Jarzynski-type experiments. An analysis of a recent Maxwell demon experiment using real-time feedback control is also given. As a mathematical tool, we prove a classical version of Stinespring's dilation theorem, which might be of independent interest.

Jamming and percolation of three-dimensional (3D) $k\times k\times k$ cubic objects ($k^3$-mers) deposited on simple cubic lattices have been studied by numerical simulations complemented with finite-size scaling theory. The $k^3$-mers were irreversibly deposited into the lattice. Jamming coverage ${\theta }_{j,k}$ was determined for a wide range of $k$ ($2\le k\le 40$). ${\theta }_{j,k}$ exhibits a decreasing behavior with increasing $k$, being ${\theta }_{j,k=\infty }=0.4204\left(9\right)$ the limit value for large $k^3$-mer sizes. In addition, a finite-size scaling analysis of the jamming transition was carried out, and the corresponding spatial correlation length critical exponent ${\nu }_j$ was measured, being ${\nu }_j\approx 3/2$. However, the obtained results for the percolation threshold ${\theta }_{p,k}$ showed that ${\theta }_{p,k}$ is an increasing function of $k$ in the range $2\le k\le 16$. For $k\ge 17$, all jammed configurations are nonpercolating states, and consequently, the percolation phase transition disappears. The interplay between the percolation and the jamming effects is responsible for the existence of a maximum value of $k$ (in this case, $k=16$) from which the percolation phase transition no longer occurs. Finally, a complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system has the same universality class as the 3D random percolation, regardless of the size $k$ considered.

Real-world systems, ranging from social and biological to infrastructural, can be modeled by multilayer networks. Promoting spreading dynamics in multilayer networks may significantly facilitate electronic advertising and predicting popular scientific publications. In this study, we propose a strategy for promoting the spreading dynamics of the susceptible-infected-susceptible model by adding one interconnecting edge between two isolated networks. By applying a perturbation method to the discrete Markovian chain approach, we derive an index that estimates the spreading prevalence in the interconnected network. The index can be interpreted as a variant of Katz centrality, where the adjacency matrix is replaced by a weighted matrix with weights depending on the dynamical information of the spreading process. Edges that are less infected at one end and its neighborhood but highly infected at the other will have larger weights. We verify the effectiveness of the proposed strategy on small networks by exhaustively examining all latent edges and demonstrate that performance is optimal or near-optimal. For large synthetic and real-world networks, the proposed method always outperforms other static strategies such as connecting nodes with the highest degree or eigenvector centrality.

Many small organisms such as bacteria can attract each other by depositing chemical attractants. At the same time, they exert repulsive force on each other when crowded, which can be modeled by effective pressure as an increasing function of the organisms' density. As the chemical attraction becomes strong compared to the effective pressure, the system will undergo a phase transition from homogeneous distribution to aggregation. In this work, we describe the interplay of organisms and chemicals on a two-dimensional disk with a set of partial differential equations of the Patlak-Keller-Segel type. By analyzing its Lyapunov functional, we show that the aggregation transition occurs discontinuously, forming an aggregate near the boundary of the disk. The result can be interpreted within a thermodynamic framework by identifying the Lyapunov functional with free energy.