In this work, we employed the concept of the first-passage time in stochastic processes to estimate node degrees and the degree distribution of a network. A statistical exploration of the coupling reveals the relation between the node degree and the coupling term. In practical terms, an effective way to reveal the statistical property is to investigate the differences between coupled oscillators in a network and uncoupled ones with the same initial states. We discovered a monotonically decreasing relation between the node degree and the mean first-passage time (MFPT) for the evolution of the coupled node deviating from the uncoupled one. Moreover, this relation can be understood as the competition of different relaxational time scales. The MFPT method is independent of both the dynamics of the nodes and the topological properties of the network. This might be advantageous in our efforts to build a bridge between the topological property and the dynamics of a network.

The delayed feedback control (DFC) methods are noninvasive, which means that the control signal vanishes if the delay time is adjusted to be equal to the period of a target unstable periodic orbit (UPO). If the delay time differs slightly from the UPO period, a nonvanishing periodic control signal is observed. We derive an analytical expression for this period for a general class of multiple-input multiple-output systems controlled by an extended DFC algorithm. Our approach is based on the phase-reduction theory adapted to systems with time delay. The analytical results are supported by numerical simulations of the controlled Rössler system.

In this paper, the physical behaviors of the interaction between a spark-generated bubble and a rubber beam are studied. Both numerical and experimental approaches are employed to investigate the bubble collapse near the rubber beam (which acts as a flexible boundary) and the corresponding large deformation of the beam. Good agreement between the numerical simulations and experimental observations is achieved. The analysis reveals that the ratio of the bubble-beam distance to the maximum bubble radius influences the bubble evolution (from expansion to collapse) and the beam deformation. The stiffness of the beam plays an important role in the elastic beam response to bubble expansion and collapse. The effect of the vapor pressure on both bubble collapses and beam deflections is also examined. The results from this paper may provide physical insight into the complex physics of the bubble-rubber interaction. The understanding is possibly applicable in biomedicine for drug delivery to tissue, which is a soft material. It is also probably useful in the marine industry where ultrasonic bubbles are generated for the defouling of ship surfaces, which has been coated with an elastic material. There is also potential interest in underwater explosions near elastic structures.

This study extends our previous work on droplet generation in microfluidic T-junction generators to include dynamic interfacial tension effects created by the presence of surfactants. In Paper I [T. Glawdel, C. Elbuken, and C. L. Ren, Phys. Rev. E 85, 016322 (2012)], we presented experimental findings regarding the formation process in the squeezing-to-transition regime, and in Paper II [T. Glawdel, C. Elbuken, and C. L. Ren, Phys. Rev. E 85, 016323 (2012)] we developed a theoretical model that describes the performance of T-junction generators without surfactants. Here we study dynamic interfacial tension effects for two surfactants, one with a small molecular weight that adsorbs quickly, and the other with a large molecular weight that adsorbs slowly. Using the force balance developed in Paper II we extract the dynamic interfacial tension from high speed videos obtained during experiments. We then develop a theoretical model to predict the dynamic interfacial tension in microfluidic T-junction generators as a function of the surfactant properties, flow conditions, and generator design. This model is then incorporated into the overall model for generator performance to effectively predict the size of droplets produced when surfactants are present.

We study the behavior of an algorithm derived from the cavity method for the prize-collecting steiner tree (PCST) problem on graphs. The algorithm is based on the zero temperature limit of the cavity equations and as such is formally simple (a fixed point equation resolved by iteration) and distributed (parallelizable). We provide a detailed comparison with state-of-the-art algorithms on a wide range of existing benchmarks, networks, and random graphs. Specifically, we consider an enhanced derivative of the Goemans-Williamson heuristics and the dhea solver, a branch and cut integer linear programming based approach. The comparison shows that the cavity algorithm outperforms the two algorithms in most large instances both in running time and quality of the solution. Finally we prove a few optimality properties of the solutions provided by our algorithm, including optimality under the two postprocessing procedures defined in the Goemans-Williamson derivative and global optimality in some limit cases.

We study the similarities and differences between different models concerning subdiffusion. More particularly, we calculate first passage time (FPT) distributions for subdiffusion, derived from Greens’ functions of nonlinear equations obtained from Sharma-Mittal's, Tsallis's, and Gauss's nonadditive entropies. Then we compare these with FPT distributions calculated from a fractional model using a subdiffusion equation with a fractional time derivative. All of Greens’ functions give us exactly the same standard relation $\langle {\left(\Delta x\right)}^2\rangle =2D_{\alpha }{t}^{\alpha }$ which characterizes subdiffusion ($0<\alpha <1$), but generally FPT distributions are not equivalent to one another. We will show here that the FPT distribution for the fractional model is asymptotically equal to the Sharma-Mittal model over the long time limit only if in the latter case one of the three parameters describing Sharma-Mittal entropy $r$ depends on $\alpha$, and satisfies the specific equation derived in this paper, whereas the other two models mentioned above give different FPT distributions with the fractional model. Greens’ functions obtained from the Sharma-Mittal and fractional models, for $r$ obtained from this particular equation, are very similar to each other. We will also discuss the interpretation of subdiffusion models based on nonadditive entropies and the possibilities of the experimental measurement of subdiffusion models’ parameters.

Equilibrium canonical distribution in statistical mechanics assumes weak system-bath coupling (SBC). In real physical situations this assumption can be invalid, and equilibrium quantum statistics of the system may be noncanonical. By exploiting both polaron transformation and perturbation theory in a spin-boson model, an analytical treatment is advocated to study noncanonical statistics of a two-level system at arbitrary temperature and for arbitrary SBC strength, yielding theoretical results in agreement with exact Monte Carlo simulations. In particular, the eigen-representation of system's reduced density matrix is used to quantify noncanonical statistics as well as the quantumness of the open system. For example, it is found that irrespective of SBC strength, noncanonical statistics enhances as temperature decreases but vanishes at high temperature.

A huge variety of natural phenomena, including prey-predator interaction, chemical reaction kinetics, foraging, and pharmacokinetics, are mathematically described as encounters between entities performing a random motion on an appropriate structure. On homogeneous structures, two random walkers meet with certainty if and only if the structure is recurrent, i.e., a single random walker returns to its starting point with probability 1. We prove here that this property does not hold on general inhomogeneous structures, and introduce the concept of two-particle transience, providing examples of realistic recurrent structures where two particles may never meet if they both move, while an encounter is certain if either stays put. We anticipate that our results will pave the way for the study of the effects of geometry in a wide array of natural phenomena involving interaction between randomly moving agents.

We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the walls, which implies that the density profile and the density-density correlation function depends explicitly on the distances to the walls. We discuss the residual symmetry properties in slab geometry and introduce a symmetry adapted complete set of two-point correlation functions. Since the currents naturally split into components parallel and perpendicular to the walls the mathematical structure of the theory differs from the established mode-coupling equations in bulk. We prove that the equations for the nonergodicity parameters still display a covariance property similar to bulk liquids.

Adsorption of surface coions and charge reversal are induced at the electrical double layer of a wall charged with positive and negative surface sites next to an electrolyte solution. While for the considered surface charge density these effects are found over a wide range of conditions, they are not observed for the typically employed surface models in equivalent conditions. Important consequences in electrophoresis experiments for different colloids with equal effective surface charge density are foreseen. This study is carried out by means of molecular dynamics simulations.

We explore the nematic ordering of the rodlike liquid crystals 5CB and 6CB, embedded into parallel-aligned nanochannels in mesoporous silicon and silica membranes as a function of mean channel radius ($4.7\le R\le 8.3$ nm), and, thus, geometrical confinement strength, by optical birefringence measurements in the infrared region. The orientational order inside the nanochannels results in an excess birefringence, which is proportional to the nematic order parameter. It evolves continuously on cooling with a precursor behavior, typical of a paranematic state at high temperatures. These observations are compared with the bulk behavior and analyzed within a phenomenological model. Such an approach indicates that the strength of the nematic ordering fields $\sigma$ is beyond a critical threshold ${\sigma }_c=$ 1/2 that separates discontinuous from continuous paranematic-to-nematic behavior. In agreement with the predictions of the phenomenological approach, a linear dependency of $\sigma$ on the inverse channel radius is found and we can infer therefrom the critical channel radii, $R_c$, separating continuous from discontinuous paranematic-to-isotropic behavior, for 5CB (12.1 nm) and 6CB (14.0 nm). Our analysis suggests that the tangential anchoring at the channel walls is of similar strength in mesoporous silicon and mesoporous silica membranes. A comparison with the bulk phase behavior reveals that the nematic order in nanoconfinement is significantly affected by channel wall roughness, leading to a reduction of the effective nematic ordering.

Mechanisms leading to initiation of crazing type failure in a glassy polymer are not clearly understood. This is mainly due to the difficulty in characterizing the stress state and polymer configuration sufficiently locally at the craze initiation site. Using molecular dynamics simulations, we have now been able to access this information and have shown that the local heterogeneous deformation leads to craze initiation in glassy polymers. We found that zones of high plastic activity are constrained by their neighborhood and become unstable, initiating crazing from these sites. Furthermore, based on the constant flow stresses observed in the unstable zones, we conclude that microcavitation is the essential local deformation mode to trigger crazing in glassy polymers. Our results demonstrate the basic difference in the local deformation mode as well as the conditions that lead to either shear-yielding or crazing type failures in glassy polymers. We anticipate our paper to help in devising a new criterion for craze initiation that not only considers the stress state, but also considers local deformation heterogeneities that form the necessary condition for crazing in glassy polymers.

Frette and Hemmer [Phys. Rev. E 85, 011130 (2012)] recently showed that for a simple model for the boarding of an airplane, the mean time to board scales as a power law with the number of passengers $N$ and the exponent is less than 1. They note that this scaling leads to the prediction that the “back-to-front” strategy, where passengers are divided into groups from contiguous ranges of rows and each group is allowed to board in turn from back to front once the previous group has found their seats, has a longer boarding time than would a single group. Here I extend their results to a larger number of passengers using a sampling approach and explore a scenario where the queue is presorted into groups from back to front, but allowed to enter the plane as soon as they can. I show that the power law dependence on passenger numbers is different for large $N$ and that there is a boarding time reduction for presorted groups, with a power law dependence on the number of presorted groups.

We study numerically the failure of an interface joining two elastic materials under load using a fiber bundle model connected to an elastic half space. We find that the breakdown process follows the equal load sharing fiber bundle model without any detectable spatial correlations between the positions of the failing fibers until localization sets in. Depending on the elastic constant describing the elastic half space, localization sets in before or after the critical load causing the interface to fail completely is reached. There is a crossover between failure due to localization and failure without spatial correlations when tuning the elastic constant, not a phase transition as has been proposed earlier. Also, contrary to earlier claims based on models different from ours, we find that a finite fraction of fibers must fail before the critical load is attained, even in the extreme localization regime, i.e., for very small elastic constant. We furthermore find that the critical load remains finite for all values of the elastic constant in the limit of an infinitely large system.

Many real networks are not isolated from each other but form networks of networks, often interrelated in nontrivial ways. Here, we analyze an epidemic spreading process taking place on top of two interconnected complex networks. We develop a heterogeneous mean-field approach that allows us to calculate the conditions for the emergence of an endemic state. Interestingly, a global endemic state may arise in the coupled system even though the epidemics is not able to propagate on each network separately and even when the number of coupling connections is small. Our analytic results are successfully confronted against large-scale numerical simulations.

The construction of the semiclassical trace formula for resonances with transverse electric polarization for two-dimensional dielectric cavities is discussed. Special attention is given to the derivation of the two first terms of Weyl's series for the average number of such resonances. The formulas obtained agree well with numerical calculations for dielectric cavities of different shapes.

In the time reverse process of a feedback manipulated stochastic system, we allow performing measurements without violating causality. As a result we come across an entropy production due to the measurement process. This entropy production, in addition to the usual system and medium entropy production, constitutes the total entropy production of the combined system of the reservoir, the system, and the feedback controller. We show that this total entropy production of “full” system satisfies an integrated fluctuation theorem as well as a detailed fluctuation theorem as expected. We illustrate and verify this idea through explicit calculation and direct simulation in two examples.

The cytoplasm of bacterial cells is filled with individual molecules and molecular complexes that rely on diffusion to bring them together for interaction. The mobility of molecules in the cytoplasm has been characterized by several techniques mainly using fluorescent probes and ensemble methods. In order to probe the microenvrionment inside the cytoplasm as viewed by an individual molecule, we have studied single green fluorescent proteins (GFPs) diffusing in the cytoplasm of Escherichia coli cells at observation at rates ranging from 60 to 1000 Hz. Over long times the diffusion shows confinement due to the geometry of the cells themselves. A simulation in model cells using the actual distribution of cell sizes found in the experiments describes accurately the experimental results as well as reveals a short time diffusion coefficient that agrees well with that determined by ensemble methods. Higher short time diffusion coefficients can be obtained by filling the simulated cell with small spheres modeling cytoplasmic molecules and, depending on the density of particles included in the modeled cytoplasm, can approach the diffusion coefficient of GFPs found in water. Thus, single-molecule tracking combined with analysis using simple simulation of Brownian motion is able to reveal the main contributors to the GFP mobility in the cytoplasm of E. coli.

A mesoscopic model which allows us to identify and quantify the strength of binding sites in DNA sequences is proposed. The model is based on the Peyrard-Bishop-Dauxois model for the DNA chain coupled to a Brownian particle which explores the sequence interacting more importantly with open base pairs of the DNA chain. We apply the model to promoter sequences of different organisms. The free energy landscape obtained for these promoters shows a complex structure that is strongly connected to their biological behavior. The analysis method used is able to quantify free energy differences of sites within genome sequences.