We show in this paper that monolayers of the nonhydrophilic ${\text{F}}_8{\text{H}}_{18}$ semifluorinated $n$-alkane constitute when spread on the hydrophobic top of an alamethicin Langmuir monolayer, a very good experimental system in order to check the validity of Helmoltz equation. This system allows for a good agreement between measured and calculated surface potentials of unionized Langmuir monolayers. We show also that the relative dielectric constant of the ${\text{F}}_8{\text{H}}_{18}$ monolayer does not vary upon compression of the monolayer, the measured 2.9 value is in a very good agreement with literature data. We attribute this behavior to the self-aggregation of ${\text{F}}_8{\text{H}}_{18}$ molecules in nanosized circular domains whose size remains constant upon compression as shown by atomic force microscopy.

The phase behavior of the monodisperse $AB$ comb copolymer melt contained the macromolecules of special architecture is discussed. Each macromolecule is assumed to be composed of two comb blocks which differ in numbers of side chains and numbers of monomer units in these chains. It is shown (by analysis of the structure factor of the melt) that microphase separation at two different length scales in the melt is possible. The large and small length scales correspond to separation between comb blocks and separation between monomer units in repeating fragments of blocks, respectively. The classification diagrams indicated which length scale is favored for a given parameters of chemical structure of macromolecules are constructed.

Tethers are thin membrane tubes that can be formed when relatively small and localized forces are applied to cellular membranes and lipid bilayers. Tether pulling experiments have been used to better understand the fine membrane properties. These include the interaction between the plasma membrane and the underlying cytoskeleton, which is an important factor affecting membrane mechanics. We use a computational method aimed at the interpretation and design of tether pulling experiments in cells with a strong membrane-cytoskeleton attachment. In our model, we take into account the detailed information in the topology of bonds connecting the plasma membrane and the cytoskeleton. We compute the force-dependent piecewise membrane deflection and bending as well as modes of stored energy in three major regions of the system: body of the tether, membrane-cytoskeleton attachment zone, and the transition zone between the two. We apply our method to three cells: cochlear outer hair cells (OHCs), human embryonic kidney (HEK) cells, and Chinese hamster ovary (CHO) cells. OHCs have a special system of pillars connecting the membrane and the cytoskeleton, and HEK and CHO cells have the membrane-cytoskeleton adhesion arrangement via bonds (e.g., PIP2), which is common to many other cells. We also present a validation of our model by using experimental data on CHO and HEK cells. The proposed method can be an effective tool in the analyses of experiments to probe the properties of cellular membranes.

Protein amyloid fibrils are a form of linear protein aggregates that are implicated in many neurodegenerative diseases. Here, we study the dynamics of amyloid fibril elongation by performing Langevin dynamic simulations on a coarse-grained model of peptides. Our simulation results suggest that the elongation process is dominated by a series of local minimum due to frustration in monomer-fibril interactions. This rugged energy landscape picture indicates that the amount of recycling of monomers at the fibrils’ ends before being fibrilized is substantially reduced in comparison to the conventional two-step elongation model. This picture, along with other predictions discussed, can be tested with current experimental techniques.

Dispersal of species to find a more favorable habitat is important in population dynamics. Dispersal rates evolve in response to the relative success of different dispersal strategies. In a simplified deterministic treatment [J. Dockery, V. Hutson, K. Mischaikow, and M. Pernarowski, J. Math. Biol. 37, 61 (1998)] of two species which differ only in their dispersal rates the slow species always dominates. We demonstrate that fluctuations can change this conclusion and can lead to dominance by the fast species or to coexistence, depending on parameters. We discuss two different effects of fluctuations and show that our results are consistent with more complex treatments that find that selected dispersal rates are not monotonic with the cost of migration.

The hydrophobic effect is the major factor that drives a protein toward collapse and folding. As a consequence of the folding process a hydrophobic core is shielded by the solvent-accessible surface area of the protein. We analyze the solvent-accessible surface area of 1825 nonhomolog protein chains deposited in the Brookhaven Protein Data Bank. This solvent-accessible surface area presents an intrinsic self-similarity behavior. The comparison between the accessible surface area as function of the number of amino acids and the accessible surface area as function of gyration radius supplies a measure of the scaling exponent close to the one observed by volume as function of radius of gyration or by mass-size exponent. The present finding indicates that the fractal analysis describes the protein compactness as an object packing between random spheres in percolation threshold and crumpled wires.

The control of the light trajectories in a liquid crystal is studied through a theoretical model based in the variation of the molecular orientation of a ferronematic material. In this model, the director field is mapped into a Riemannian space where the light paths are obtained numerically through the calculation of the geodesics for the effective geometry perceived by light.

We present a network model of coupled oscillators to study how a weak signal is transmitted in complex networks. Through both theoretical analysis and numerical simulations, we find that the response of other nodes to the weak signal decays exponentially with their topological distance to the signal source and the coupling strength between two neighboring nodes can be figured out by the responses. This finding can be conveniently used to detect the topology of unknown network, such as the degree distribution, clustering coefficient and community structure, etc., by repeatedly choosing different nodes as the signal source. Through four typical networks, i.e., the regular one dimensional, small world, random, and scale-free networks, we show that the features of network can be approximately given by investigating many fewer nodes than the network size, thus our approach to detect the topology of unknown network may be efficient in practical situations with large network size.

Quantum tunneling in the presence of chaos is analyzed, focusing especially on the interplay between quantum tunneling and dynamical localization. We observed flooding of potentially existing tunneling amplitude by adding noise to the chaotic sea to attenuate the destructive interference generating dynamical localization. This phenomenon is related to the nature of complex orbits describing tunneling between torus and chaotic regions. The tunneling rate is found to obey a perturbative scaling with noise intensity when the noise intensity is sufficiently small and then saturate in a large noise intensity regime. A relation between the tunneling rate and the localization length of the chaotic states is also demonstrated. It is shown that due to the competition between dynamical tunneling and dynamical localization, the tunneling rate is not a monotonically increasing function of Planck’s constant. The above results are obtained for a system with a sharp border between torus and chaotic regions. The validity of the results for a system with a smoothed border is also explained.

A nonlinear car-following model is studied with driver reaction time delay by using state-of-the-art numerical continuations techniques. These allow us to unveil the detailed microscopic dynamics as well as to extract macroscopic properties of traffic flow. Parameter domains are determined where the uniform flow equilibrium is stable but sufficiently large excitations may trigger traffic jams. This behavior becomes more robust as the reaction time delay is increased.

The study of the linear stage of the incompressible Rayleigh-Taylor instability in elastic-plastic solids is performed by considering thick plates under a constant acceleration that is also uniform except for a small sinusoidal ripple in the horizontal plane. The analysis is carried out by using an analytical model based on the Newton second law and it is complemented with extensive two-dimensional numerical simulations. The conditions for marginal stability that determine the instability threshold are derived. Besides, the boundary for the transition from the elastic to the plastic regime is obtained and it is demonstrated that such a transition is not a sufficient condition for instability. The model yields complete analytical solutions for the perturbation amplitude evolution and reveals the main physical process that governs the instability. The theory is in general agreement with the numerical simulations and provides useful quantitative results. Implications for high-energy-density-physics experiments are also discussed.

On the basis of various direct numerical simulations (DNS) of turbulent channel flows the following picture is proposed. (i) At a distance $y$ from either wall, the Taylor microscale $\lambda$ is proportional to the average distance ${\ell }_s$ between stagnation points of the fluctuating velocity field, i.e., $\lambda \left(y\right)=B_1{\ell }_s\left(y\right)$ with $B_1$ constant, for ${\delta }_{\nu }⪡y\lesssim \delta$, where the wall unit ${\delta }_{\nu }$ is defined as the ratio of kinematic viscosity $\nu$ to skin friction velocity $u_{\tau }$ and $\delta$ is the channel’s half-width. (ii) The number density $n_s$ of stagnation points varies with height according to $n_s=\frac{C_s}{{\delta }_{\nu }^3}{y}_{+}^{-1}$ where $y_{+}\equiv y/{\delta }_{\nu }$ and $C_s$ is constant in the range ${\delta }_{\nu }⪡y\lesssim \delta$. (iii) In that same range, the kinetic energy dissipation rate per unit mass, $ϵ$, equals $\frac{2}{3}{E}_{+}\frac{u_{\tau }^3}{{\kappa }_{s}y}$ where $E_{+}$ is the total kinetic energy per unit mass normalized by $u_{\tau }^2$ and ${\kappa }_s=B_1^2/C_s$ is the stagnation point von Kármán coefficient. (iv) In the limit of exceedingly large Reynolds numbers ${\text{Re}}_{\tau }\equiv \delta /{\delta }_{\nu }$, large enough for the Reynolds stress $-⟨uv⟩$ to equal $u_{\tau }^2$ in the range ${\delta }_{\nu }⪡y⪡\delta$, and assuming that production of turbulent kinetic energy balances dissipation locally in that range and limit, the mean velocity $U_{+}$, normalized by $u_{\tau }$, obeys $\frac{d}{dy}{U}_{+}\simeq \frac{2}{3}\frac{E_{+}}{{\kappa }_{s}y}$ in that same range. (v) It follows that the von Kármán coefficient $\kappa$ is a meaningful and well-defined coefficient and the log law holds in turbulent channel/pipe flows only if $E_{+}$ is independent of $y_{+}$ and ${\text{Re}}_{\tau }$ in that range, in which case $\kappa \sim {\kappa }_s$. (vi) In support of $\frac{d}{dy}{U}_{+}\simeq \frac{2}{3}\frac{E_{+}}{{\kappa }_{s}y}$, DNS data of turbulent channel flows which include the highest currently available values of ${\text{Re}}_{\tau }$ are best fitted by $E_{+}\simeq \frac{2}{3}{B}_4{y}_{+}^{-2/15}$ and $\frac{d}{d{y}_{+}}{U}_{+}\simeq \frac{B_4}{{\kappa }_s}{y}_{+}^{-1-2/15}$ with $B_4$ independent of $y$ in ${\delta }_{\nu }⪡y⪡\delta$ if the significant departure from $-⟨uv⟩\simeq u_{\tau }^2$ at these ${\text{Re}}_{\tau }$ values is taken into account.

The momentum transfer to a scatterer from fluorescence photons was detected using an optical system that permits one to simultaneously measure the radiation force exerted on and fluorescence emission from the scatterer. The core of this technique is a partially metal covered dielectric bead optically trapped in a liquid with dye molecules. Fluorescence emission from the volume that includes the bead is measured simultaneously with the Brownian motion of the bead. The perturbed motion of the bead is a result of photon momentum transfer from the fluorescence of the dye to the trapped scatterer. The bead position fluctuations indicate the presence of the fluorescence and its bleaching nature. The results demonstrate the capability of the photonic force microscopy technique to be a complement to spectroscopy in the study of optical processes.

We study experimentally the dynamics of laser-induced cavitation bubbles created inside a narrow gap. The gap height, $h$, is varied from 15 to $400\mu \text{m}$ and the resulting bubble dynamics is compared to a semiunbounded fluid. The cavitation bubbles are created with pulsed laser light at constant laser energy and are imaged with a high-speed camera. The bubble lifetime increases with decreasing gap height by up to 50% whereas the maximum projected bubble radius remains constant. Comparing the radial dynamics to potential flow models, we find that with smaller gaps, the bubble-induced flow becomes essentially planar, thus slower flows with reduced shear. These findings might have important consequences for microfluidic applications where it is desirable to tune the strength and range of the interactions such as in the case of cell lysis and cell membrane poration.

Understanding the nature of dense particle packings is a subject of intense research in the physical, mathematical, and biological sciences. The preponderance of previous work has focused on spherical particles and very little is known about dense polyhedral packings. We formulate the problem of generating dense packings of nonoverlapping, nontiling polyhedra within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem, which we call the adaptive shrinking cell (ASC) scheme. This optimization problem is solved here (using a variety of multiparticle initial configurations) to find the dense packings of each of the Platonic solids in three-dimensional Euclidean space ${\mathbb{R}}^3$, except for the cube, which is the only Platonic solid that tiles space. We find the densest known packings of tetrahedra, icosahedra, dodecahedra, and octahedra with densities 0.823…, 0.836…, 0.904…, and 0.947…, respectively. It is noteworthy that the densest tetrahedral packing possesses no long-range order. Unlike the densest tetrahedral packing, which must not be a Bravais lattice packing, the densest packings of the other nontiling Platonic solids that we obtain are their previously known optimal (Bravais) lattice packings. We also derive a simple upper bound on the maximal density of packings of congruent nonspherical particles and apply it to Platonic solids, Archimedean solids, superballs, and ellipsoids. Provided that what we term the “asphericity” (ratio of the circumradius to inradius) is sufficiently small, the upper bounds are relatively tight and thus close to the corresponding densities of the optimal lattice packings of the centrally symmetric Platonic and Archimedean solids. Our simulation results, rigorous upper bounds, and other theoretical arguments lead us to the conjecture that the densest packings of Platonic and Archimedean solids with central symmetry are given by their corresponding densest lattice packings. This can be regarded to be the analog of Kepler’s sphere conjecture for these solids. The truncated tetrahedron is the only non-centrally symmetric Archimedean solid, the densest known packing of which is a non-lattice packing with density at least as high as $23/24=0.958333\dots$. We discuss the validity of our conjecture to packings of superballs, prisms, and antiprisms as well as to high-dimensional analogs of the Platonic solids. In addition, we conjecture that the optimal packing of any convex, congruent polyhedron without central symmetry generally is not a lattice packing. Finally, we discuss the possible applications and generalizations of the ASC scheme in predicting the crystal structures of polyhedral nanoparticles and the study of random packings of hard polyhedra.

The deterministic Nagel-Schreckenberg model with stochastic open boundary conditions is investigated in a mostly analytical way. By means of the Markov Chain, we model the working process of the stochastic open boundaries. First, the analytical expression of the free-flow density profiles is derived. Then, we discuss theoretically how the right boundary determines the traffic capacity, global density, and density profiles. For these features, the analytical and numerical results agree well. This paper implies that the deterministic Nagel-Schreckenberg model with stochastic open boundaries is almost totally analyzable.

During the generation and transmission of nerve impulses, the cytoplasm behaves like an excitable medium that self-regulates the shapes and magnitudes of the output excitation. In connection with this self-regulatory function, one can readily think of the plasma membrane as a nerve organ holding the key role in the mechanisms of generation and transmission of the transmembrane potential, namely, it is expected to provide the essential feedback that stabilizes the stimulus. Here, a simple and coherent picture of self-regulation of the nerve impulse is proposed in terms of one single feedback associated with the main excitable biological organ of the nervous system. In this purpose, an electrodynamic theory is developed within the framework of a cable model in which the membrane capacitor is regarded as a charge-management electrical component with a defined capacity-voltage characteristic. It is found that in both myelinated and myelin-free nerve fiber contexts, the transmembrane excitations are well-localized short impulses whose shape and stability are determined by the capacity-voltage characteristic assumed to govern the self-excitability properties of the nerve membrane.

We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (nonorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of weakly overlapping resonances, we apply the random matrix theory to the effective Hamiltonian formalism and derive analytically the probability distribution of the complexness parameter for two statistical ensembles describing the systems invariant under time reversal. For those with rigid spectra, we consider a Hamiltonian characterized by a picket-fence spectrum without spectral fluctuations. Then, in the more realistic case of a Hamiltonian described by the Gaussian orthogonal ensemble, we reveal and discuss the role of spectral fluctuations.

We study the statistical properties of return intervals $r$ between successive energy dissipation rates above a certain threshold $Q$ in three-dimensional fully developed turbulence. We find that the distribution function $P_Q\left(r\right)$ scales with the mean return interval $R_Q$ as $P_Q\left(r\right)=R_Q^{-1}f\left(r/R_Q\right)$ for $R_Q∊\left[50,500\right]$, where the scaling function $f\left(x\right)$ has two power-law regimes. The scaling behavior is statistically validated by the Cramér–von Mises criterion. The return intervals are short-term and long-term correlated and possess multifractal nature. The Hurst index of the return intervals decays exponentially against $R_Q$, predicting that rare extreme events with $R_Q\to \infty$ are also long-term correlated with the Hurst index $H_{\infty }=0.639$. These phenomenological findings have potential applications in risk assessment of extreme events at very large $R_Q$.

The power loss and electromagnetic energy density of a metamaterial consisting of arrays of wires and split-ring resonators are investigated. We show that a field energy density formula can be derived consistently from both the electrodynamic (ED) approach and the equivalent circuit (EC) approach. The derivations are based on the knowledge of the dynamical equations of the electric and magnetic dipoles in the medium and the correct form of the power loss. We discuss the role of power loss in determining the form of energy density and explain why the power loss should be identified first in the ED derivation. When the power loss is negligible and the field is harmonic, our energy density formula reduces to the result of Landau’s classical formula. For the general case with finite power loss, our investigation resolves the apparent contradiction between the previous results derived by the EC and ED approaches.