The most familiar approaches used to describe the dynamical structure factor from adiabatic density fluctuations in liquids are based on generalized hydrodynamics and on the memory function, respectively. We show that, contrary to the common belief, the two approaches are not fully equivalent. In particular, models based on the memory function of a normalized damped oscillator fail in reproducing the correct experimental spectral profiles of systems close to the relaxation process. The discrepancy is due to misleading interpretation of the theoretical memory-function expressions, producing an unavoidable mixing of spectral contribution at different wave vectors when the theory is forced beyond its limits of validity.

We study the expansion of biomolecular networks from the view point of first evolutionary principles based on the duplication and divergence of ancestral genes. The expansion of gene families and subnetworks is analyzed in terms of logistic map compositions, which capture the varying functional constraints of individual genes in the course of evolution. Using a mean-field approach, we then demonstrate the existence of spontaneous growth-rate variations between gene families and discuss the relevance of such heterogeneous expansions for the emergent properties of actual biomolecular networks.

The diffusion coefficient is calculated for a charge propagating along a double-stranded DNA, while it interacts with the nonlinear fluctuational openings of base pairs. The latter structural dynamics of DNA is described by the Peyrard-Bishop-Dauxois model [T. Dauxois, M. Peyrard, and A. R. Bishop, Phys Rev. E 47 R44 (1993)], which represents essential anharmonicities of base-pair stretchings. The dependence of the diffusion coefficient on the temperature and the electron-phonon coupling constant is presented. The diffusion coefficient decreases when either the temperature or the electron-phonon coupling increases. Analytical expressions are provided that describe the temperature dependence of the diffusion coefficient. The variation of the parameters of these expressions with the electron-phonon coupling constant is also discussed. These results quantitatively demonstrate how DNA structural nonlinear dynamics affects macroscopic charge transport properties.

Blebs are balloon-shaped membrane protrusions that form during many physiological processes. Using computer simulation of a particle-based model for self-assembled lipid bilayers coupled to an elastic meshwork, we investigated the phase behavior and kinetics of blebbing. We found that blebs form for large values of the ratio between the areas of the bilayer and the cytoskeleton. We also found that blebbing can be induced when the cytoskeleton is subject to a localized ablation or a uniform compression. The results obtained are qualitatively in agreement with the experimental evidence and the model opens up the possibility to study the kinetics of bleb formation in detail.

Adhesion bonds between membranes and surfaces are attracted to each other via effective interactions whose origin is the entropy loss due to the reduction in the amplitude of the membrane thermal fluctuations in the vicinity of the adhesion bonds. These fluctuation-induced interactions are also expected to drive the adhesion bonds toward the rim of the cell as well as toward the surfaces of membrane inclusions. In this paper we analyze the attraction of adhesion bonds to the cell inner and outer boundaries. Our analysis shows that the probability distribution function of a single (diffusing) adhesion bond decays algebraically with the distance from the boundaries. Upon increasing the concentration of the adhesion bonds, the attraction to the boundaries becomes strongly self-screened.

In this paper investigations of the voltage required to break down water vapor are reported for the region around the Paschen minimum and to the left of it. In spite of numerous applications of discharges in biomedicine, and recent studies of discharges in water and vapor bubbles and discharges with liquid water electrodes, studies of the basic parameters of breakdown are lacking. Paschen curves have been measured by recording voltages and currents in the low-current Townsend regime and extrapolating them to zero current. The minimum electrical breakdown voltage for water vapor was found to be 480 V at a pressure times electrode distance ($pd$) value of around 0.6 Torr cm (∼0.8 Pa m). The present measurements are also interpreted using (and add additional insight into) the developing understanding of relevant atomic and particularly surface processes associated with electrical breakdown.

In seasonally ice-covered seas and along the margins of perennial ice pack, i.e., in regions with medium ice concentrations, the ice cover typically consists of separate floes interacting with each other by inelastic collisions. In this paper, hitherto unexplored analogies between this type of ice cover and two-dimensional granular gases are used to formulate a model of ice dynamics at the floe level. The model consists of (i) momentum equations for floe motion between collisions, formulated in the form of a Stokes-flow problem, with floe-size-dependent time constant and equilibrium velocity, and (ii) a hard-disk collision model. The numerical algorithm developed is suitable for simulating particle-laden flow of $N$ disk-shaped floes with arbitrary size distributions. The model is applied to study clustering phenomena in sea ice with power-law floe-size distribution. In particular, the influence of the average ice concentration $\overline{A}$ on the formation and characteristics of clusters is analyzed in detail. The results show the existence of two regimes, at low and high ice concentrations, differing in terms of the exponents of the cluster-size distribution and of the size of the largest cluster.

In this paper, we analyze the sudden change from chaos to oscillation death generated by the Bonhoeffer–van der Pol (BVP) oscillator under weak periodic perturbation. The parameter values of the BVP oscillator are chosen such that a stable focus and a stable relaxation oscillation coexist if no perturbation is applied. In such a system, complicated bifurcation structure is expected to emerge when weak periodic perturbation is applied because the stable focus and the stable relaxation oscillation coexist in close proximity in the phase plane. We draw a bifurcation diagram of the fundamental harmonic entrainment. The bifurcation structure is complex because there coexist two bifurcation sets. One is the bifurcation set generated in the vicinity of the stable focus, and the other is that generated in the vicinity of the stable relaxation oscillation. By analyzing the bifurcation diagram in detail, we can explain the sudden change from chaos with complicated waveforms to oscillation death. We make it clear that this phenomenon is caused by a saddle-node bifurcation.

Scroll waves are prominent patterns formed in three-dimensional excitable media, and they are frequently considered highly relevant for some types of cardiac arrhythmias. Experimentally, scroll wave dynamics is often studied by optical tomography in the Belousov-Zhabotinsky reaction, which produces CO${}_2$ as an undesired product. Addition of small concentrations of a surfactant to the reaction medium is a popular method to suppress or retard CO${}_2$ bubble formation. We show that in closed reactors even these low concentrations of surfactants are sufficient to generate vertical gradients of excitability which are due to gradients in CO${}_2$ concentration. In reactors open to the atmosphere such gradients can be avoided. The gradients induce a twist on vertically oriented scroll waves, while a twist is absent in scroll waves in a gradient-free medium. The effects of the CO${}_2$ gradients are reproduced by a numerical study, where we extend the Oregonator model to account for the production of CO${}_2$ and for its advection against the direction of gravity. The numerical simulations confirm the role of solubilized CO${}_2$ as the source of the vertical gradient of excitability in reactors closed to the atmosphere.

In the Martian atmosphere dust is abundant and is continuously replenished by the entrainment of materials and sediments from the surface of the planet. The sediment concentrations are particularly high and noticeable in whirlwinds, also known as dust devils. Assuming the thermophoresis force as the main driver of dust particles lifting from the surface, the dust process of the Martian atmosphere and its naturally formed dust devils are investigated for the northern polar region of the planet. Our simulated convective boundary layer shows that it may be unlikely that visible dust devils are formed only due to thermophoresis effects and some other lifting mechanisms are required.

Spatiotemporal patterns in nature, such as ripples or dunes, formed by a fluid streaming over a sandy surface show complex behavior despite their simple forms. Below the surface, the granular structure of the sand particles is subject to self-organization processes, exhibiting such phenomena as reverse grading when larger particles are found on top of smaller ones. Here we report results of an experimental investigation with downscaled model dunes revealing that, if the particles differ not in size but in density, the heavier particles, surprisingly, accumulate in the central core close to the top of the dune. This finding contributes to the understanding of sedimentary structures found in nature and might be helpful to improve existing dating methods for desert dunes.

We studied the self-similar properties of the phase spaces of two frustrated spin models and two lattice gas models. The two frustrated spin models were (1) the antiferromagnetic Ising model on a two-dimensional triangular lattice (1a) at the ground states and (1b) above the ground states and (2) the six-vertex model. The two lattice gas models were (3) the one-dimensional lattice gas model and (4) the two-dimensional lattice gas model. Their phase spaces were mapped to networks so that the fractal analysis of complex networks can be applied. These phase spaces, in turn, establish new classes of networks with unique self-similar properties. Models 1a, 2, and 3 with long-range power-law correlations in real space exhibit fractal phase spaces, while models 1b and 4 with short-range exponential correlations in real space exhibit nonfractal phase spaces. This behavior agrees with one of the untested assumptions in Tsallis nonextensive statistics. All the phase spaces have power-law “mass” -radius relations that reflect the local self-similar structures.

The $q$ model is a random walk model used to describe the flow of stress in a stationary granular medium. Here we derive the exact horizontal and vertical correlation functions for the $q$ model in two dimensions. We show that close to a critical point identified in earlier work these correlation functions have a universal scaling form reminiscent of thermodynamic critical phenomena. We determine the form of the universal scaling function and the associated critical exponents $\nu$ and $z$.

Two modified mean-field $J_1-J_2$ models are studied to explain the surface reduction of twisting power in the helical smectic-$C_{\alpha }^{*}$ phase in free-standing liquid crystal films. Profiles of the surface interlayer interaction are calculated from the experimental results. The calculations reveal the existence of a strong surface field and indicate that the surface field is the reason for the observed reduced twisting power near the surface region. Our results provide a quantitative study of the interlayer interactions through surface effects in smectic liquid crystals.

Cylindrical structures in a group are frequently seen on land and in the ocean. Mutual flow interaction between the structures makes the wake very excited or tranquil depending on the spacing between the structures. The excited wake-enhancing forces in some cases cause a catastrophic failure of the structures. This paper presents results of an experimental investigation of Strouhal number (St), time-mean, and fluctuating forces on, and flow structures around, two identical circular cylinders at stagger angle α = 0 °–180 ° and gap-spacing ratio $T/D=0.1$–5, where $T$ is the gap width between the cylinders, and $D$ is the diameter of a cylinder. While forces were measured using a load cell, St was from spectral analysis of fluctuating pressures measured on the side surfaces of the cylinders. A flow visualization test was conducted to observe flow structures around the cylinders. Based on forces, St, and flow structures, 19 distinct flow categories in the ranges of α and $T/D$ investigated are observed, including one quadristable flow, three kinds of tristable flows, and four kinds of bistable flows. The quadristable, tristable, and bistable flows ensue from instabilities of the gap flow, shear layers, vortices, separation bubbles, and wakes, engendering a strong jump or drop in forces and St of the cylinders. The two cylinders interact with each other in six different mechanisms, namely interaction between boundary layer and cylinder, shear layer or wake and cylinder, shear layer and shear layer, vortex and cylinder, vortex and shear layer, and vortex and vortex. While the interaction between vortex and cylinder results in a very high fluctuating drag, that between vortex and shear layer results in a high fluctuating lift. On the other hand, the interaction between shear layer or wake and cylinder weakens mean and fluctuating forces and flow unsteadiness. A mutual discussion of forces, St, and flow structures is presented in this paper.

We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements, without restricting to variational ansatzes. The lattice of size $N$ is partitioned into two subclusters. At each iteration the Lanczos vector is projected into two sets of $n_{\mathrm{svd}}$ smaller subcluster vectors using singular value decomposition. For low entanglement entropy $S_{\mathrm{ee}}$, (satisfied by short-range Hamiltonians), the truncation error is expected to vanish as $\exp (-n_{\mathrm{svd}}^{1/S_{\mathrm{ee}}})$. Convergence is tested for the Heisenberg model on Kagomé clusters of 24, 30, and 36 sites, with no lattice symmetries exploited, using less than 15 GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given.

In a recent paper, Zhan, Zhang, Guan, and Zhou $[$Phys. Rev. E 83, 066120 (2011)$]$ presented a modified adaptive genetic algorithm (MAGA) tailored to the discovery of maximum modularity partitions of the node set into communities in unipartite, bipartite, and directed networks. The authors claim that “detection of communities in unipartite networks or in directed networks can be transformed into the same task in bipartite networks.” Actually, some tests show that it is not the case for the proposed transformations, and why. Experimental results of MAGA for modularity maximization of untransformed unipartite or bipartite networks are also discussed.

We develop a microscopic theory to analyze the phase behavior and compute correlation functions of dense assemblies of soft repulsive particles both at finite temperature, as in colloidal materials, and at vanishing temperature, a situation relevant for granular materials and emulsions. We use a mean-field statistical mechanical approach which combines elements of liquid state theory to replica calculations to obtain quantitative predictions for the location of phase boundaries, macroscopic thermodynamic properties, and microstructure of the system. We focus, in particular, on the derivation of scaling properties emerging in the vicinity of the jamming transition occurring at large density and zero temperature. The new predictions we obtain for pair correlation functions near contact are tested using computer simulations. Our work also clarifies the conceptual nature of the jamming transition and its relation to the phenomenon of the glass transition observed in atomic liquids.

We consider ideal chains in a hypercubic lattice ${\mathbb{Z}}^d$, $d\ge 3$, with a fixed ratio $m$ of self-intersection per monomer. Despite the simplicity of the geometrical constraint, this model shows some interesting properties, such as a collapse transition for a critical value $m_c$. Numerical simulations show a self-avoiding-walk-like behavior for $m<m_c$, and a compact cluster configuration for $m>m_c$. The collapse seems to show the same characteristics as the canonical thermodynamical models for the coil-globule transition.

The disclination loops entangling colloidal structures in nematics are geometrically stabilized and restricted according to topological rules. We focus on colloidal dimers and show how the writhe and twist, which are constrained to sum to a constant value, are affected by changing the intercolloidal spacing, the twist angle of the cell, and the cholesteric pitch. We analyze the geometric properties of disclination loops using finite difference numerical simulations of colloidal dimers. The observed trends are explained and correlated to the symmetry properties and effects of liquid crystal elasticity.