The static director distribution in thin nematic liquid crystal cells, subject to both electric and magnetic fields, has been investigated using a combination of deuterium nuclear magnetic resonance (NMR) spectroscopy and continuum theory in terms of the director distribution function, which gives the probability density for finding the director at a given orientation. A series of deuterium NMR spectra for the nematic liquid crystal, 4-pentyl-$d_2$-4′-cyanobiphenyl deuteriated in the α position of the pentyl chain were acquired as a function of the applied electric field. This powerful experimental technique allowed us to observe uniform and nonuniform director alignment depending on the angle between the two fields and their relative strength. On the basis of the detailed experimental results, we have explored the factors that influence the nature of both the uniform and the nonuniform director distributions. We have discussed the questions that are raised by our attempt to understand the static director distribution as a function of the angle between the two fields. We have discovered that the alignment of the director at the surface of the Teflon spacers is essential in addition to the random variation in the cell thickness in order to account for the static director distribution determined from the NMR spectra.

The chiral antiferroelectric structure of an achiral bent-core liquid crystal is characterized by resonant x-ray scattering at chlorine $K$ edge. The “forbidden” reflections resulting from the glide or screw symmetry elements are restored by the anisotropy of the tensor structure factor, which we calculate for two possible structural models. A careful analysis of the polarization states of the restored “forbidden” reflections enables an unambiguous identification of a chiral structure (i.e., the so-called anticlinic, antiferroelectric smectic-$C$ or Sm-$C_A$$P_A$) coexisting with the achiral synclinic antiferroelectric smectic-$C$ or Sm-$C_S$$P_A$. The method proves to be quite powerful as it identifies the chiral structure within coexisting phases despite an imperfect orientation of the sample. The volume fraction of the chiral phase and the distribution of alignment are extracted from the data.

The statistical mechanics of a linear noninteracting polymer chain with a large number of monomers is considered with fixed angular momentum. The radius of gyration for a linear polymer is derived exactly by functional integration. This result is then compared to simulations done with a large number of noninteracting rigid links at fixed angular momentum. The simulation agrees with the theory up to finite-size corrections. The simulations are also used to investigate the anisotropic nature of a spinning polymer. We find universal scaling of the polymer size along the direction of the angular momentum, as a function of rescaled angular momentum.

We study how self-propelled organisms administer their energetic resources in order to optimize space exploration. Noting the existence of two very different time scales, we use a quasistatic approximation to analyze the relation between bacterial dynamics and changes in the energy stored by a bacterium. We then find both steady-state and time-dependent solutions for the bacterial speed and stored energy. The model also predicts the volume of the region that a bacterium may visit in a resource-depleted medium.

Transitional pipe flow is modeled as a one-dimensional excitable and bistable medium. Models are presented in two variables, turbulence intensity and mean shear, that evolve according to established properties of transitional turbulence. A continuous model captures the essence of the puff-slug transition as a change from excitability to bistability. A discrete model, which additionally incorporates turbulence locally as a chaotic repeller, reproduces almost all large-scale features of transitional pipe flow. In particular, it captures metastable localized puffs, puff splitting, slugs, localized edge states, a continuous transition to sustained turbulence via spatiotemporal intermittency (directed percolation), and a subsequent increase in turbulence fraction toward uniform, featureless turbulence.

We report structural results that evidence the polarization distribution of the blocks in the columnar phase of an achiral bent-core liquid crystal. The study was performed using resonant x-ray diffraction at the sulfur $K$ edge on oriented samples aligned on substrates. The extra periodicity is revealed through the violation of the systematic extinction rule of the structural symmetry group along the experimentally accessible diffraction direction. Further data obtained from the polarization analysis of a resonant reflection give information concerning the transition mechanism between $B_1$ and $B_2$ phases.

The van der Waals interaction free energy $A_{\mathrm{int}}$ between two spherical bodies of Stockmayer fluid across a vacuum is calculated using molecular simulations and classical perturbation theory. The results are decomposed into their electrostatic and Lennard-Jones parts, and the former is shown to agree excellently with predictions from dielectric continuum theory. $A_{\mathrm{int}}$ is decomposed into its energetic and entropic contributions and the results are compared with analytical predictions. Finally, we expand the electrostatic part of $A_{\mathrm{int}}$ in a multipole expansion, and show that the surprisingly good agreement between the molecular and continuum descriptions is likely due to a cancellation of errors coming from the neglect of the discrete nature of the fluid within the dielectric description.

Diffusion of pointlike noninteracting particles in a two-dimensional channel of varying cross section is considered. The particles are biased by a constant force in the transverse direction. A recurrence mapping procedure is applied, which enables the derivation of an effective one-dimensional (1D) evolution equation that governs the 1D density of the particles in the channel. In the limit of stationary flow, an extended Fick-Jacobs equation is reached, which is corrected by an effective diffusion coefficient $D\left(x\right)$ that depends on the longitudinal coordinate $x$. The result is an approximate formula for $D\left(x\right)$ that also involves the influence of the transverse force. The calculations are verified by the stationary diffusion in a linear cone, which is exactly solvable.

The phase behavior of an inverse microemulsion composed of 4-cyano-4-$n$-pentylbiphenyl (5CB), didodecyl dimethyl ammonium bromide, and water was intensively studied recently, but controversy still remains on the existence of a “transparent nematic” (TN) phase. Previously, we studied the temperature-dependent dielectric behavior of this microemulsion [Z. Chen and R. Nozaki, J. Chem. Phys. 134, 034505 (2011)]. The results suggested that a superstructure composed of water droplets and confined 5CB molecules exists in the coexistence phase region, which may correspond to the notion of a TN phase. In this study, the time-dependent dielectric behaviors of this microemulsion in the isotropic, coexistence, and supercooled phase regions were investigated. In the coexistence and supercooled phase regions, the dielectric behaviors showed strong dependence on time, due to the hysteresis of phase transition and the upward diffusion of the water-droplet-rich isotropic phase. After the isotropic phase has been totally excluded out of the effective measurement area, the slow process was still observed in these two phase regions, which suggests that water droplets can stably exist in the liquid crystalline phase. A local microscopic phase evolution was observed in the coexistence phase region, which is similar to the temperature-induced phase evolution previously proposed by us. The dielectric behavior of the slow process during the phase evolution also suggests the existence of the superstructure. In addition, the mechanism of the slow process in different phase regions proposed in our previous study is also confirmed.

Molecular dynamics (MD) simulations have been carried out on the crystallization of single-chain polyethylene (PE) which was adsorbed on a graphite (001) surface on one side and exposed to vacuum on the other at different temperatures. The MD simulation data have been analyzed to provide information about the crystallization process of polymer adsorbed on the solid substrate. The isothermal crystallization of PE proceeds in two steps: (1) adsorption and (2) orientation. The results detail the radial density distribution function, ordered parameters, local bond-orientational order parameters, and the local properties displayed in layers of the polymer parallel to the graphite and vacuum interfaces. It was also shown that the film thickness affected the critical crystallization temperature of the adsorbed polymer on the substrate surface. Furthermore, the influence of the graphite surface area on the crystallization of PE is discussed by comparing the crystallinity evolution of PE on graphite with different coverage.

Atomic displacements of hydrated proteins are dominated by phonon vibrations at low temperatures and by dissipative large-amplitude motions at high temperatures. A crossover between the two regimes is known as a dynamical transition. Recent experiments indicate a connection between the dynamical transition and the dielectric response of the hydrated protein. We analyze two mechanisms of the coupling between the protein atomic motions and the protein-water interface. The first mechanism considers viscoelastic changes in the global shape of the protein plasticized by its coupling to the hydration shell. The second mechanism involves modulations of the local motions of partial charges inside the protein by electrostatic fluctuations. The model is used to analyze mean-square displacements of iron of metmyoglobin reported by Mössbauer spectroscopy. We show that high displacement of heme iron at physiological temperatures is dominated by electrostatic fluctuations. Two onsets, one arising from the viscoelastic response and the second from electrostatic fluctuations, are seen in the temperature dependence of the mean-square displacements when the corresponding relaxation times enter the instrumental resolution window.

$\Phi$-value analysis has proved to be a powerful technique in protein folding studies. It has been used to study the transition state structures, to infer microscopic folding pathways, and to identify key residues in the protein folding process. However, its effectiveness in protein binding reaction has not been tested, especially when a fly-casting mechanism is involved. In this article we attempt to answer this question through a coarse-grained study of the binding reaction of Arc repressor dimer. Our simulations show that its binding process proceeds through a fly-casting mechanism, consistent with previous results. We then estimate the importance of the residues for the fly-casting binding by computationally mutating each of them into glycine and calculating their respective effects on the capture radius. It is found that (1) the residues with high $\Phi$ values may not be responsible for the large capture radius in the fly-casting binding; (2) mutation of residues with low $\Phi$ values may destabilize the denatured states and then increase the capture radius, presumably further increasing the binding rate. Based on our simulations, we conclude that $\Phi$ values do not reflect well the importance of residues in the fly-casting binding reaction and need to be combined with other techniques to provide a complete picture.

Many microorganisms propel themselves through their fluid environment by means of multiple rotating flagella that self-organize to form bundles, a process that is complex and poorly understood. In the present work, the bundling behavior of a pair of flexible flagella, each driven by a constant torque motor, is investigated, using a mathematical model incorporating the fluid motion generated by each flagellum as well as the finite flexibility of the flagella. The initial stage of bundling is driven purely by hydrodynamics but the final state of the bundle is determined by a nontrivial balance between hydrodynamics and elasticity. As the flexibility of the flagella increases a regime is found where, depending on initial conditions, one finds bundles that are either tight, with the flagella in mechanical contact, or loose, with the flagella intertwined but not touching. That is, multiple coexisting states of bundling are found. The parameter regime (in terms of flexibility and distance between motors) at which this multiplicity occurs is comparable to the parameters for a number of bacteria.

Low-temperature structures of Yukawa particles in systems with cylindrical symmetry are analyzed by numerical simulations. Particles are organized into well-defined thin concentric shells forming triangular lattices with defects on each shell and structural parameters are expressed by simple interpolation formulas including the limiting case of Coulomb particles. In outer shells, the local structure can be regarded as three-dimensional closest packing as in the case of the background of uniform spheres. These formulas can be directly compared with fine particle experiments in long cylindrical chambers under microgravity or colloidal suspensions in cylinders and may be useful as a basis of structural analyses in cylindrical systems.

In this paper we present an extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first show numerically that due to a nonlinear distortion, traditional methods require high-order harmonic components to represent nonlinear processes, except for the Hilbert-based method. This will lead to an artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus the power law, if it exists, is contaminated. We then compare the Hilbert method with structure functions (SF), detrended fluctuation analysis (DFA), and wavelet leader (WL) by analyzing fractional Brownian motion and synthesized multifractal time series. For the former simulation, we find that all methods provide comparable results. For the latter simulation, we perform simulations with an intermittent parameter $\mu =0.15$. We find that the SF underestimates scaling exponent when $q>3$. The Hilbert method provides a slight underestimation when $q>5$. However, both DFA and WL overestimate the scaling exponents when $q>5$. It seems that Hilbert and DFA methods provide better singularity spectra than SF and WL. We finally apply all methods to a passive scalar (temperature) data obtained from a jet experiment with a Taylor’s microscale Reynolds number Re${}_{\lambda }\simeq 250$. Due to the presence of strong ramp-cliff structures, the SF fails to detect the power law behavior. For the traditional method, the ramp-cliff structure causes a serious artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus DFA and WL underestimate the scaling exponents. However, the Hilbert method provides scaling exponents ${\xi }_{\theta }\left(q\right)$ quite close to the one for longitudinal velocity, indicating a less intermittent passive scalar field than what was believed before.

The parametrization of small-scale turbulent fluctuations in convective systems and in the presence of strong stratification is a key issue for many applied problems in oceanography, atmospheric science, and planetology. In the presence of stratification, one needs to cope with bulk turbulent fluctuations and with inversion regions, where temperature, density, or both develop highly nonlinear mean profiles due to the interactions between the turbulent boundary layer and the unmixed—stable—flow above or below it. We present a second-order closure able to cope simultaneously with both bulk and boundary layer regions, and we test it against high-resolution state-of-the-art two-dimensional numerical simulations in a convective and stratified belt for values of the Rayleigh number up to $\mathrm{Ra}\sim {10}^{10}$. Data are taken from a Rayleigh-Taylor system confined by the existence of an adiabatic gradient.

The influence of the horizontal component of the temperature gradient on nonlinear regimes of oscillatory convection developed under the joint action of buoyant and thermocapillary effects in a multilayer system is investigated. Two-dimensional convective regimes are studied by the finite difference method. Rigid heat-insulated lateral walls are considered. It is found that the region of nonlinear asymmetric oscillations is restricted by the Grashof number values, both from below and from above, by the steady states.

This paper deals with the mathematical modeling of traveling-wave ac electro-osmotic micropumps with a zig-zag arrangement of microelectrodes. A mathematical model based on the Poisson-Nernst-Planck-Navier-Stokes description is used in this study within the physically relevant ranges of the model parameters. We present an extensive set of parametrical studies concerning the dependence of the net velocity on a variety of parameters. We also demonstrate limits of the validity of the commonly used Capacitor-Resistor-Capacitor model. In order to achieve high net velocities, we found that there are the optimal values of the electrode length, the shift between the top and bottom electrode arrays, and the signal frequency. Performance of the zig-zag micropumps is evaluated by the means of back-pressure loads. The suggested zig-zag design brings two main benefits: (i) it allows an easier construction of four-phase traveling-wave micropumps without the need of spatially complicated electrode connections, and (ii) the zig-zag pumps can provide higher flow rates than those with single-sided coplanar arrangements. Another robust feature of the proposed zig-zag system is that a single flow reversal is observed at the ac frequency approximately six times higher than the reciprocal resistor-capacitor time even in low-amplitude regimes.