Results of large scale nonequilibrium molecular dynamics simulations are presented for nanoparticles in an explicit solvent. The nanoparticles are modeled as a uniform distribution of Lennard-Jones particles, while the solvent is represented by standard Lennard-Jones particles. We present results for the shear rheology of spherical nanoparticles of diameter 10 times that of the solvent for a range of nanoparticle volume fractions. By varying the strength of the interactions between nanoparticles and with the solvent, this system can be used to model colloidal gels and glasses as well as hard spherelike nanoparticles. Effect of including the solvent explictly is demonstrated by comparing the pair correlation function of nanoparticles to that in an implicit solvent. The shear rheology for dumbbell nanoparticles made of two fused spheres is similar to that of single nanoparticle.

A nonphotochemical laser-induced phase transition was studied in a supercooled $4^{\prime }\text{‐}n$-pentyl-4-cyanobiphenyl (5CB, also referred to as PCB and K15) liquid crystal, using linearly polarized $45\mathrm{ps}$ light pulses at a wavelength of $532\mathrm{nm}$. The laser induced nucleation from the metastable supercooled isotropic phase to the nematic phase during slow cooling $(0.001°\mathrm{C}∕\min )$ and high light intensity $(3.9\mathrm{MW}∕{\mathrm{cm}}^2)$. The resulting nematic director tended to be aligned along the direction of the plane of polarization of the light. At the intensities used, there is no observable laser-induced realignment of the director once the sample is in the nematic phase, nor any permanent laser-induced ordering when the sample is illuminated only in the stable isotropic phase during slow cooling. These experimental results are consistent with a mechanism based on optical Kerr alignment.

In this work, we report an alternative microfluidic approach to studying the motion of single DNA molecules in an electric field. Making use of a closely fitting droplet in a microchannel, DNA molecules can be confined within the submicrometer film beneath the droplet. Several dynamic events at the single-molecule level and self-assembly phenomena at mesoscales are observed. We find that DNA can be trapped and stretched at the entrance to the film due to entropic effects. After escaping the trap, DNA can exhibit cyclic stick-slip motion with a field-dependent mobility owing to interim anchoring to surface surfactants. We also observe that, by incorporation of surface modification effects with plasma oxidation, DNA can be combed onto the channel surface at sufficiently high fields. In this case, upon removing the field, as-stretched DNA molecules can aggregate into larger clusters or self-organize into mesoscale bundles aligned in the direction of the previously applied field. The physics underlying these phenomena is discussed in detail.

Problems with artificial neural networks originate from their deterministic nature and inevitable prior learnings, resulting in inadequate adaptability against unpredictable, abrupt environmental change. Here we show that a stochastically excitable threshold unit can be utilized by these systems to partially overcome the environmental change. Using an excitable threshold system, attractors were created that represent quasiequilibrium states into which a system settles until disrupted by environmental change. Furthermore, noise-driven attractor stabilization and switching were embodied by inhibitory connections. Noise works as a power source to stabilize and switch attractors, and endows the system with hysteresis behavior that resembles that of stereopsis and binocular rivalry in the human visual cortex. A canonical model of the ring network with inhibitory connections composed of class 1 neurons also shows properties that are similar to the simple threshold system.

Nematic cells with surface anchoring fields exhibiting quasicrystalline symmetry can be fabricated using linear photopolymerizable polymers and suitable optics. Using the Lebwohl-Lasher model we carry out Monte Carlo simulations of a nematic cell where the top and bottom surfaces have an anchoring field with the symmetry of a periodic approximant to a Penrose lattice. We show that the anchoring field has point topological defects, nearly all with topological charge $\pm 1$. Our simulations, which assume infinitely strong anchoring of the nematic to the anchoring field, show that half-integer disclination lines emerge from the point defects and either traverse the thickness of the cell for small cell thicknesses, hug the patterned surfaces for large thicknesses, or combine these behaviors for intermediate thicknesses. We show that estimates of the values of the thicknesses separating these three behaviors can be obtained using the properties of Penrose tilings.

Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches. The first approach, generally known as compartmental modeling, addresses the time evolution of disease propagation at the expense of simplifying the pattern of transmission. The second approach uses network theory to incorporate detailed information pertaining to the underlying contact structure among individuals while disregarding the progression of time during outbreaks. So far, the only alternative that enables the integration of both aspects of disease propagation simultaneously while preserving the variety of outcomes has been to abandon the analytical approach and rely on computer simulations. We offer an analytical framework, that incorporates both the complexity of contact network structure and the time progression of disease spread. Furthermore, we demonstrate that this framework is equally effective on finite- and “infinite”-size networks. This formalism can be equally applied to similar percolation phenomena on networks in other areas of science and technology.

Two natural and widely used representations for the community structure of networks are clusterings, which partition the vertex set into disjoint subsets, and layouts, which assign the vertices to positions in a metric space. This paper unifies prominent characterizations of layout quality and clustering quality, by showing that energy models of pairwise attraction and repulsion subsume Newman and Girvan’s modularity measure. Layouts with optimal energy are relaxations of, and are thus consistent with, clusterings with optimal modularity, which is of practical relevance because the two representations are complementary and often used together.

We evaluate information-theoretic quantities that quantify complexity in terms of $k\text{th}$-order statistical dependences that cannot be reduced to interactions among $k-1$ random variables. Using symbolic dynamics of coupled maps and cellular automata as model systems, we demonstrate that these measures are able to identify complex dynamical regimes.

We report a comparative study on pattern formation between the methods of cellular automata (CA) and reaction-diffusion equations (RD) applying to a morphology of bacterial colony formation. To do so, we began the study with setting an extremely simple model, which was designed to realize autocatalytic proliferation of bacteria (denoted as $X$) fed with nutrition $\left(N\right)$ and their inactive state (prespore state) $P_1$ due to starvation: $X+N\to 2X$ and $X\to P_1$, respectively. It was found numerically that while the CA could successfully generate rich patterns ranging from the circular fat structure to the viscous-finger-like complicated one, the naive RD reproduced only the circular pattern but failed to give a finger structure. Augmenting the RD equations by adding two physical factors, (i) a threshold effect in the dynamics of $X+N\to 2X$ (breaking the continuity limit of RD) and (ii) internal noise with onset threshold (breaking the inherent symmetry of RD), we have found that the viscous-finger-like realistic patterns are indeed recovered by thus modified RD. This highlights the important difference between CA and RD, and at the same time, clarifies the necessary factors for the complicated patterns to emerge in such a surprisingly simple model system.

Boundary walls in microfluidic devices have a strong influence on the fluid flow and drag forces on moving objects. The Stokes drag force acting on a sphere translating in the fluid is increased by the presence of a neighboring wall by a factor given by Faxén’s correction. A similar increase in the rotational drag is expected when spinning close to a wall. We use optical tweezers to confirm the translational drag correction and report the hitherto unmeasured rotational equivalent. We find that the corrections for the rotational motion is only required for particle-wall separations an order of magnitude shorter than that for the translational cases. These results are particularly significant in the use of optical tweezers for measuring viscosity on a picolitre scale.

In this paper, the electromagnetic (EM) tunneling phenomenon in a sandwich structure consisting of an mu-negative (MNG) medium, air, and an epsilon-negative (ENG) medium is investigated by means of the transfer-matrix method and microwave experiments. Both results demonstrate that by properly choosing parameters, EM waves can efficiently tunnel through a long distance over several hundreds times the length of the device. Unlike in the ENG-MNG slabs, the electric and the magnetic field of the tunneling mode is interestingly separated and localized at the interface of MNG-air and ENG-air, respectively. Therefore, this structure may be important for potential applications in wireless information and energy transmission, for its high efficiency, security, and health.

Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various such distribution functions in the limits where certain scaling variables become small or large. Our study includes the pair-connection probability, the distributions of the fractal masses of the backbone, the red bonds, and the shortest, the longest, and the average self-avoiding walk between any two points on a cluster, as well as the distribution of the total resistance in the random resistor network. Our analysis draws solely on general, structural features of the underlying diagrammatic perturbation theory, and hence our main results are valid to arbitrary loop order.

Large scale, discrete element simulations are performed to study the dynamics of a rotating drum partially filled with cohesive granular particles. The continuous avalanche regime is explored using a simple model for interparticle cohesion in order to simulate the effects of granular media in the presence of a wetting fluid. The shape of the free surface for cohesionless particles ranges from flat to a concave S shape depending on the rotation rate and frictional properties between the grains and the drum side walls. The presence of interparticle cohesion reduces the concavity of the free surface and pushes the free surface towards a flat or even slightly convex shape. From contour plots of the velocity, we show how the position of the vortex core (the stationary spot in the laboratory frame) depends on the rotation speed and interparticle cohesion strength and how this relationship can be understood from considerations of the incompressibility condition on the mass flow.

We show that the relative stability of the nematic tetratic phase with respect to the usual uniaxial nematic phase can be greatly enhanced by clustering effects. Two-dimensional rectangles of aspect ratio $\kappa$ interacting via hard interactions are considered, and the stability of the two nematic phases (uniaxial and tetratic) is examined using an extended scaled-particle theory applied to a polydispersed fluid mixture of $n$ species. Here the $i\text{th}$ species is associated with clusters of $i$ rectangles, with clusters defined as stacks of rectangles containing approximately parallel rectangles, with frozen internal degrees of freedom. The theory assumes an exponential cluster size distribution (an assumption fully supported by Monte Carlo simulations and by a simple chemical-reaction model), with fixed value of the second moment. The corresponding area distribution presents a shoulder, and sometimes even a well-defined peak, at cluster sizes approximately corresponding to square shape (i.e., $i\simeq \kappa$), meaning that square clusters have a dominant contribution to the free energy of the hard-rectangle fluid. The theory predicts an enhanced region of stability of the tetratic phase with respect to the standard scaled-particle theory, much closer to simulation and to experimental results, demonstrating the importance of clustering in this fluid.

By means of a molecular model, we examine hybrid nematic films with antagonistic anchoring angles where one of the surfaces is in the strong anchoring regime. If anchoring at the other surface is weak, and in the absence of wetting by the isotropic phase, the anchoring transition may interact with the capillary isotropic-nematic transition. For general anchoring conditions on this surface we confirm the existence of the steplike biaxial phase and the associated transition to the linear constant-tilt-rotation, configuration. The steplike phase is connected with the bulk isotropic phase for increasing film thickness so that the latter transition is to be interpreted as the capillary isotropic-nematic transition in a hybrid film.

We develop an analytical method for studying the properties of a noninteracting wormlike chain (WLC) in confined geometries. The mean-field-like theory replaces the rigid constraints of confinement with average constraints, thus allowing us to develop a tractable method for treating a WLC wrapped on the surface of a sphere, and fully encapsulated within it. The efficacy of the theory is established by reproducing the exact correlation functions for a WLC confined to the surface of a sphere. In addition, the coefficients in the free energy are exactly calculated. We also describe the behavior of a surface-confined chain under external tension that is relevant for single molecule experiments on histone-DNA complexes. The force-extension curves display spatial oscillations, and the extension of the chain, whose maximum value is bounded by the sphere diameter, scales as $f^{-1}$ at large forces, in contrast to the unconfined chain that approaches the contour length as $f^{-1∕2}$. A WLC encapsulated in a sphere, that is relevant for the study of the viral encapsulation of DNA, can also be treated using the mean-field approach. The predictions of the theory for various correlation functions are in excellent agreement with Langevin simulations. We find that strongly confined chains are highly structured by examining the correlations using a local winding axis. The predicted pressure of the system is in excellent agreement with simulations but, as is known, is significantly lower than the pressures seen for DNA packaged in viral capsids.

We study the propagation of information in social networks. To do so, we focus on a cascade model where nodes are infected with probability $p_1$ after their first contact with the information and with probability $p_2$ at all subsequent contacts. The diffusion starts from one random node and leads to a cascade of infection. It is shown that first and subsequent trials play different roles in the propagation and that the size of the cascade depends in a nontrivial way on $p_1$, $p_2$, and on the network structure. Second trials are shown to amplify the propagation in dense parts of the network while first trials are dominant for the exploration of new parts of the network and launching new seeds of infection.

Superlinear scaling in cities, which appears in sociological quantities such as economic productivity and creative output relative to urban population size, has been observed, but not been given a satisfactory theoretical explanation. Here we provide a network model for the superlinear relationship between population size and innovation found in cities, with a reasonable range for the exponent.

It is believed that water anomalies are related to the hydrogen bonds between water molecules, but the relationship still remains a challenge. Here, by introducing two types of hydrogen bond—strong and weak, we successfully reproduce many liquid water anomalies, particularly the thermodynamic anomalies at supercooled temperature. We find that the exchange of strong and weak H bonds, which enhance the competition between the open and collapsed structures of liquid water, might be the key to those anomalies of supercooled liquid water. Our study is helpful in understanding the hydrogen bond structure in liquid water.

We investigate how a catastrophic event (modeled as a temporary fall of the reproduction rate) increases the extinction probability of an isolated self-regulated stochastic population. Using a variant of the Verhulst logistic model as an example, we combine the probability generating function technique with an eikonal approximation to evaluate the exponentially large increase in the extinction probability caused by the catastrophe. This quantity is given by the eikonal action computed over “the optimal path” (instanton) of an effective classical Hamiltonian system with a time-dependent Hamiltonian. For a general catastrophe the eikonal equations can be solved numerically. For simple models of catastrophic events analytic solutions can be obtained. One such solution becomes quite simple close to the bifurcation point of the Verhulst model. The eikonal results for the increase in the extinction probability caused by a catastrophe agree well with numerical solutions of the master equation.