We show that the optical structure of the helical phase of a chiral nematic is naturally associated with the Bianchi VII${}_0$ group manifold, of which we give a full account. The Joets-Ribotta metric governing propagation of the extraordinary rays is invariant under the simply transitive action of the universal cover $\tilde{E}\left(2\right)$ of the three-dimensional Euclidean group of two dimensions. Thus extraordinary light rays are geodesics of a left-invariant metric on this Bianchi type VII${}_0$ group. We are able to solve, by separation of variables, both the wave equation and the Hamilton-Jacobi equation for this metric. The former reduces to Mathieu’s equation, and the latter to the quadrantal pendulum equation. We discuss Maxwell’s equations for uniaxial optical materials where the configuration is invariant under a group action and develop a formalism to take advantage of these symmetries. The material is not assumed to be impedance matched, thus going beyond the usual scope of transformation optics. We show that for a chiral nematic in its helical phase Maxwell’s equations reduce to a generalized Mathieu equation. Our results may also be relevant to helical phases of some magnetic materials and to light propagation in certain cosmological models.

Many biological networks are characterized by directed edges that represent either activating (positive) or inhibiting (negative) regulation. Most graph-theoretical methods used to study biological networks either disregard this important feature, or study the role of edge sign only in the context of small subgraphs called motifs. Here, we develop path-based measures which capture, on continuous scales spanning negative and positive values, both the long- and short-range regulatory relationships among node pairs. These measures also allow the quantification of each node's overall influence on the whole network and its susceptibility to regulation by the rest of the network. We apply the measures to a network representation of the mammalian immune response to simultaneous attack by allergen and respiratory bacteria. Although allergen and bacteria elicit different immune pathways, there is significant overlap (cross-talk) and feedback between these pathways. We identify key immune components in this cross-talk; particularly revealing the importance of natural killer cells as a key regulatory target in the cross-talk.

We generalize the pruned-enriched method to simulate the probability distribution of the continuous-time random walk. The small probabilities that the pruned-enriched method can simulate could be many orders of magnitude smaller than the minimum probability obtained from the particle-tracking method when the computational costs of the two methods are the same. In addition, we propose a new criterion for pruning enrichment to improve the efficiency of the pruned-enriched method.

We study the effect of local wettability reversal on remobilizing immobile fluid clusters in steady-state two-phase flow in porous media. We consider a two-dimensional network model for a porous medium and introduce a wettability alteration mechanism. A qualitative change in the steady-state flow patterns, destabilizing the percolating and trapped clusters, is observed as the system wettability is varied. When capillary forces are strong, a finite wettability alteration is necessary to move the system from a single-phase to a two-phase flow regime. When both phases are mobile, we find a linear relationship between fractional flow and wettability alteration.

The average number of constraints per particle $\langle C_{\text{total}}\rangle$ in mechanically stable amorphous systems of Platonic solids approaches the isostatic limit at the jamming point ($\langle C_{\text{total}}\rangle \to 12$), though average number of contacts are hypostatic. By introducing angular alignment metrics to classify the degree of constraint imposed by each contact, constraints are shown to arise as a direct result of local orientational order reflected in edge-face and face-face alignment angle distributions. With approximately one face-face contact per particle at jamming, chainlike face-face clusters form with finite extent—a signature of amorphous jammed systems.

We consider a time-reversal invariant dynamical model of a binary ideal gas of $N$ molecules in one spatial dimension. By making time-asymmetric assumptions about the behavior of the gas, we derive Boltzmann and anti-Boltzmann equations that describe the evolution of the single-molecule velocity distribution functions for an ensemble of such systems. We show that for a special class of initial states of the ensemble one can obtain an exact expression for the $N$-molecule velocity distribution function, and we use this expression to rigorously prove that the time-asymmetric assumptions needed to derive the Boltzmann and anti-Boltzmann equations hold in the limit of large $N$. Our results clarify some subtle issues regarding the origin of the time asymmetry of Boltzmann’s $H$ theorem.

Equilibrium properties of long-range interacting systems on lattices are investigated. There was a conjecture by Cannas et al. [Phys. Rev. B 61, 11521 (2000)] that the mean-field theory is exact for spin systems with nonadditive long-range interactions. This is called “exactness of the mean-field theory.” We show that the exactness of the mean-field theory holds for systems on a lattice with nonadditive two-body long-range interactions in the canonical ensemble with unfixed order parameters. We also show that in a canonical ensemble with fixed order parameters, exactness of the mean-field theory does not hold in one parameter region, which we call the “non-mean-field region.” In the non-mean-field region, an inhomogeneous configuration appears, in contrast to the uniform configuration in the region where the mean-field theory holds. This inhomogeneous configuration is not the one given by the standard phase separation. Therefore, the mean-field picture is not adequate to describe these states. We discuss phase transitions between the mean-field region and the non-mean-field region. Exactness of the mean-field theory in spin glasses is also discussed.

Tailoring rheological properties of colloidal suspensions with the adsorption of polyelectrolyte multilayers (PEMs) is based on the idea of controlling macroscopic mechanical properties by modifying the particle surface in a reproducible and well-understood manner. With layer-by-layer self-assembly, monodisperse polystyrene particles are coated with up to ten layers of the oppositely charged strong polyelectrolytes: poly(diallyl dimethyl ammonium chloride) and poly(styrene sulfonate). The conformation of the adsorbed polyelectrolyte is controlled by the ionic strength of the used aqueous polyelectrolyte solution. For 1M NaCl solution, a brushlike adsorption of the polyelectrolyte is expected. The ability of PEMs to serve on a nanoscale level as surface modifiers and influence macroscopic rheological properties like viscoelasticity, yield stress, and shear banding is discussed. The mechanical behavior of these suspensions is qualitatively described by the theory of Derjaguin-Landau-Verwey-Overbeek with short-range repulsion and long-range attraction. A scaling rule is proposed which distinguishes between the precusor and the multilayer regime.

A large flexoelectric polarization might be expected for a bent-core nematic liquid crystal, due to the combination of molecular shape and transverse dipole component. In this study a bent-core nematic compound is doped to be highly chiral, and measurements of the difference in flexoelectric coefficients $(e_1-e_3)$ are carried out by exploiting the chiral flexoelectro-optic effect. The measured flexoelectric coefficients are greater than those for many conventional calamitic nematics, but several orders of magnitude lower than recent reports on other bent-core compounds. The influence of the bent molecular shape on the nematic phase is evident from measurements of the elastic constants, where an unusually low ratio of $k_3$ to $k_1$ indicates that bend distortions of the director are relatively lower in energy compared to those involving splay.

We study the evolution of a population of sequences, where each sequence is divided into a reproduction-rate (fitness) encoding part and a mutation-rate regulating part. Evolutionary selection acts on the sequence both by a direct fitness landscape and by indirect selection on a mutation landscape through which the sequence's mutation rate is determined, thereby providing a model of a mutation-rate-regulating gene. Coupling of the fitness landscape and mutation landscape leads to adaptive evolution of the sequence. We investigate the effects of robustness in the mutation landscape and fitness landscapes on selection of the sequence. We find that the effects of robustness in both the mutation and the fitness landscape can be described by an effective sequence length, defined as the mutational load divided by the per-base mutation rate, and we give expressions for the effective sequence length for various fitness and mutation landscapes. The probability that the sequence with a reduced mutation rate evolves is increased by increasing the robustness of the mutation landscape, and decreased by increasing the robustness of the fitness landscape. However, in the case of the mutation-rate-regulating part making up only a very small part of the total sequence length, we show that selection for a more robust sequence with less-reduced mutation rate is very weak, and therefore we conjecture that robust sequences play little role in selection of error-reducing mechanisms in real populations.

Several numerical methods for measuring the bending rigidity and the spontaneous curvature of fluid membranes are studied using two types of meshless membrane models. The bending rigidity is estimated from the thermal undulations of planar and tubular membranes and the axial force of tubular membranes. We found a large dependence of its estimate value from the thermal undulation analysis on the upper-cutoff frequency $q_{\mathrm{cut}}$ of the least-squares fit. The inverse power-spectrum fit with an extrapolation to $q_{\mathrm{cut}}\to 0$ yields the smallest estimation error among the investigated methods. The spontaneous curvature is estimated from the axial force of tubular membranes and the average curvature of bent membrane strips. The results of these methods show good agreement with each other.

Self-propelled particles are used to simulate cell aggregates in a model considering homogeneous adhesion forces between cells and using only motility differences as segregation drivers. The tendency of cells to follow their neighbors is also included in the formulation. Three model variants are explored, and the conditions on which motility differences may produce segregation are mapped in parameter diagrams. The evolution of the order parameter measuring cell segregation is similar to those found by models based on differential adhesion. It is also found that, considering only velocity differences, the faster cells envelope the slower ones, which is opposite to the ordering observed in early experiments by Jones and co-workers [Jones, Evans, and Lee, Exp. Cell. Res. 180, 287 (1989)].

Base pair opening in an inhomogeneous, DNA double helical molecular chain with flexible strands is investigated by studying its internal dynamics. For the study, a generalized model which takes into account the energies involved in stacking and hydrogen bonds along with inhomogeneity, helicity, and phonons coupled to the stacking and hydrogen bonds is proposed. The internal dynamics of the proposed DNA model is governed by a perturbed nonlinear Schrödinger equation. The unperturbed, completely integrable nonlinear Schrödinger equation which admits soliton solutions and forming a bubble corresponds to DNA dynamics with homogeneous and rigid strands. The results of the soliton perturbation analysis show that the inhomogeneity in stacking and hydrogen bonds in localized and periodic forms and the helicity do not alter the amplitude under perturbation. However, the flexibility of the strands diminishes the perturbed amplitude. On the other hand, the velocity of the soliton and bubble are unaltered due to all the above effects. However, the position and phase of the soliton and the bubble vary linearly in time. While the position of the soliton depends on the initial velocity, the phase depends on both the initial velocity and the initial amplitude of the soliton. The above effects introduce small fluctuation in the tail of the soliton, without affecting the robust nature of the soliton and the bubble during propagation. The soliton and the bubble obtained as solutions of the internal dynamics of the DNA molecule represent an opening of the base pairs which is essential for the transcription process.

We study the morphology of watersheds in two and three dimensional systems subjected to different degrees of spatial correlations. The response of these objects to small, local perturbations is also investigated with extensive numerical simulations. We find the fractal dimension of the watersheds to generally decrease with the Hurst exponent, which quantifies the degree of spatial correlations. Moreover, in two dimensions, our results match the range of fractal dimensions $1.10\le d_f\le 1.15$ observed for natural landscapes. We report that the watershed is strongly affected by local perturbations. For perturbed two and three dimensional systems, we observe a power-law scaling behavior for the distribution of areas (volumes) enclosed by the original and the displaced watershed and for the distribution of distances between outlets. Finite-size effects are analyzed and the resulting scaling exponents are shown to depend significantly on the Hurst exponent. The intrinsic relation between watershed and invasion percolation, as well as relations between exponents conjectured in previous studies with two dimensional systems, are now confirmed by our results in three dimensions.

Cluster identification tasks occur in a multitude of contexts in physics and engineering such as, for instance, cluster algorithms for simulating spin models, percolation simulations, segmentation problems in image processing, or network analysis. While it has been shown that graphics processing units (GPUs) can result in speedups of two to three orders of magnitude as compared to serial codes on CPUs for the case of local and thus naturally parallelized problems such as single-spin flip update simulations of spin models, the situation is considerably more complicated for the nonlocal problem of cluster or connected component identification. I discuss the suitability of different approaches of parallelization of cluster labeling and cluster update algorithms for calculations on GPU and compare to the performance of serial implementations.

We study finite-size effects on properties of stationary state and also transient process of a bistable system with long range interaction. We adopt an Ising-like model with infinite range interaction (Husimi-Temperlay model). In particular, we formulate this problem in light of the Langevin equation and investigate study the effects of various types of noises. We study characteristics of the probability of stationary state of a finite system and find that there exist two types of regions in the ordered state: the saturated region in which the maximum of the distribution locates at the maximum value of the Ising variable ($\pm 1$) and the transient region in which the maximum of the distribution locates at a nonsaturated value. We introduce an additional type of noise that represents fluctuation due to direct coupling to the thermal bath. Finally we also study the finite-size effects on the dynamical aspect by studying the mean first-passage times.

We present experimental data corresponding to a two-dimensional dense granular flow, namely, the gravity-driven discharge of grains from a small opening in a silo. We study the local velocity field at the scale of single grains at different places with the help of particle-tracking techniques. From these data, the velocity profiles can be obtained and the validity of some long-standing approaches can be assessed. Moreover, the fluctuations of the velocities are taken into consideration to characterize the features of the advective motion (due to the gravity force) and the diffusive motion, which shows nontrivial behavior.

Real-time monitoring of the whole growth process of evaporation-induced colloidal self-assembly has been conducted using an optical microspectroscopy setup. Our observations suggest that the assembly process can be divided into three different growth stages as evidenced by the variations detected in the reflectance spectra. The thickness variation of the growing colloidal crystal was monitored by examining the Fabry-Perot fringes in the reflectance spectra. Furthermore, the scalar wave approximation was utilized to analyze the evolution of optical properties with growth. More detailed information, including the time dependence of number of layers and volume fraction of water, has been revealed by comparing the experimental and calculated reflectance spectra. The present work demonstrates that in situ real-time microspectroscopy is a promising technique for monitoring and investigating the dynamic process of colloidal self-assembly.