Optical investigations and calculation of structures were performed on films of liquid crystal with the sequence of phase transitions in the bulk sample $\mathrm{Sm}{C}_A^{*}-\mathrm{Sm}{C}_{d3}^{*}-\mathrm{Sm}{C}_{d4}^{*}-\mathrm{Sm}{C}^{*}-\mathrm{Sm}{C}_{\alpha }^{*}-\mathrm{Sm}A-I$. We investigated freestanding nanofilms with number of smectic layers from 2 to 6 with thickness commensurate, smaller, or greater than the period of $\mathrm{Sm}{C}_{d3}^{*}$ and $\mathrm{Sm}{C}_{d4}^{*}$ phases of the bulk sample. The number of phase transitions increases as the film thickness increases. Under temperature change the transitions occur with conservation as well as with change of the direction of film polarization with respect to the molecular tilt plane. In thick films at high temperature the film can be switched by electric field from the state with longitudinal (parallel to the molecular tilt plane) into a state with transverse (perpendicular to the molecular tilt plane) electric polarization. In the framework of Landau theory of phase transitions, structures and phase transitions in the bulk sample and in nanofilms were calculated; values of interlayer interactions were estimated. The molecular structure was assumed to be planar with different sequences of synclinic and anticlinic orderings in nearest layers. The results of calculations are in good agreement with experiment.

The response of granular materials to plate drag is numerically studied using a large-scale discrete element method (DEM) simulation. The effect of the initial volume fraction of the materials on the drag force acting on the plate is examined. The results show that a volume-fraction-dependent bifurcation occurs in the force; in an initially loose granular bed, the force reaches an approximately constant value as the plate advances, while in an initially dense bed, the force oscillates with a large amplitude. The force oscillation is attributed to the periodic evolution of a shear band formed only in the dense bed. The behaviors of the drag force and shear band, which depend on the initial volume fraction in the DEM simulation, are in close agreement with those obtained experimentally in previous studies [N. Gravish et al., Phys. Rev. Lett. 105, 128301 (2010); Phys. Rev. E 89, 042202 (2014)]. Further analysis using the DEM simulation shows that the formation of the shear band is explained by the local dilation and compaction of the granular materials induced by the plate drag. Independent of the volume fraction, materials dilate in a wedge-shaped flow region that formed in front of the plate. In the loose bed, a compacted front builds up ahead of the flow region. Because the compacted front advances into a weaker undisturbed region, the flow region behind the front can constantly advance. On the other hand, in the dense bed, the materials largely dilate in a disturbed flow region formed in front of the plate. Because a denser undisturbed region is more stable compared to the flow region, the flow region is strongly confined. As a result, the shear strain is localized along a flow boundary between these regions, and the shear band develops.

We propose a data-driven procedure for diagnosing the results of compressed sensing as success or failure. Compressed sensing is an efficient data-acquisition method widely used in experimental physics. Many previous studies demonstrated that compressed sensing works well if sparse modeling can be applied; that is, physical phenomena of interest are assumed to be described by only a few explanatory factors. However, it is difficult to confirm the assumption of sparse modeling for respective instances in advance because we do not know the true representation or its sparseness of the instance being investigated. To overcome this difficulty, we examined a statistical tool called cross validation, in which all available data are randomly divided into two subsets and the accuracy of describing data in one subset by a sparse representation estimated from only data in the other subset is evaluated as an error. In particular, we focused on the dependence of the cross-validation error on the size ratio of the two subsets. Our analysis, inspired by statistical mechanics, showed that the cross-validation error asymptotically follows a power law of the size ratio when the total amount of available data is exactly at the critical point between success and failure. Hence, compressed-sensing results can be diagnosed in a data-driven manner by comparing the behavior of the cross-validation error with the power law.

The percolation problem of irreversibly deposited dimers on honeycomb and triangular lattices is studied. A dimer is composed of two segments, and occupies two adjacent adsorption sites. Each segment can be either a conductive segment (segment type $A$) or a nonconductive segment (segment type $B$). Three types of dimers are considered: $AA$, $BB$, and $AB$. The connectivity analysis is carried out by accounting only for the conductive segments (segments type $A$), whereas the $B$ segments occupy a site in the lattice but are not taken into account in the percolation study. Different cases were investigated, according to the types of dimers involved in the process. By means of numerical simulations and finite-size scaling techniques, the complete phase diagram separating the percolating from the nonpercolating regions was determined for each considered lattice. The present results are compared with the previous study of deposition of defective dimers on square lattices.

Dynamical transitions, such as a change from bound to unbound motion, often occur as post-adiabatic crossings of a time-dependent separatrix. Whether or not any given orbit will include such a crossing transition typically depends sensitively on initial conditions, but a simple estimate for the fraction of orbits which will cross the separatrix, based on Liouville's theorem, has appeared several times in the literature. Post-adiabatic dynamical transitions have more recently been reconsidered as a control problem rather than an initial value problem: What forms of time-dependent Hamiltonian can most efficiently induce desired transitions, or prevent unwanted ones? We therefore apply the Liouvillian estimate for the transition fraction to show how engineering separatrix volumes in phase space can be a control technique for dynamical transitions.

We consider effectively one-dimensional planar and radial kinks in two-dimensional nonlinear Klein-Gordon models and focus on the sine-Gordon model and the ${\varphi }^4$ variants thereof. We adapt an adiabatic invariant formulation recently developed for nonlinear Schrödinger equations, and we study the transverse stability of these kinks. This enables us to characterize one-dimensional planar kinks as solitonic filaments, whose stationary states and corresponding spectral stability can be characterized not only in the homogeneous case, but also in the presence of external potentials. Beyond that, the full nonlinear (transverse) dynamics of such filaments are described using the reduced, one-dimensional, adiabatic invariant formulation. For radial kinks, this approach confirms their azimuthal stability. It also predicts the possibility of creating stationary and stable ringlike kinks. In all cases, we corroborate the results of our methodology with full numerics on the original sine-Gordon and ${\varphi }^4$ models.

The interplay between time delay and phase shifts plays an important role for the regulation of synchronization and gives rise to interesting collective dynamical phenomena. Here we derive a stability criterion for the synchronous state in a system of identical oscillators in the presence of inertia, time delay, and a phase shift. We investigate how the combination of these factors influences the synchronization rates of the system approaching steady states after small perturbations. In particular, we prove that the global synchronization rate is twice the smallest local synchronization rate. We also find that the fastest synchronization rate increases with inertia but occurs at smaller values of critical delay.

We consider the dynamics of electrons in combined strong laser and Coulomb fields. Under a timescale separation condition, we reduce this dynamics to a guiding-center framework. More precisely, we derive a hierarchy of models for the guiding-center dynamics based on averaging over the fast motion of the electron using Lie transforms. The reduced models we obtain describe well the different ionization channels, in particular, the conditions under which an electron is rescattered by the ionic core or is directly ionized. The comparison between these models highlights the models which are best suited for qualitative and quantitative agreement with the parent dynamics.

We consider an anisotropic opinion formation process where the set of rules $B$, that dictates what is the socially acceptable position, changes following the average voters' opinion. As in the case of a constant $B$, conservative (agreement with $B$) and liberal (agreement with neighbors) voters' attitudes are still represented by stable fixed points in the phase space of the system but with the difference that the conservative fixed point is stable for all possible values of the intervoter interaction. It has been also observed that, when the model is applied to sufficiently large populations, the time needed to consolidate a position in agreement with $B$ is finite. We observed that there is also a range of values of the interaction where the two stable points coexist, opening the door for the modeling of bistability related phenomena, such as stochastic resonance and hysteresis.

Multiflagellated bacteria such as E. coli exploit the polymorphic transformations of helical flagella to explore their fluid environment. In these bacteria, a sequence of polymorphic helical forms appears consecutively as the cell “runs” and “tumbles.” During a run, the molecular motors that drive the twirling flagella spin counterclockwise, and the flagella form a normal flagellar bundle. Reversing one or more of these motors, from counterclockwise to clockwise, initiates a tumble by inducing shape transformations of the associated filaments, from normal to semicoiled and then to curly 1 forms. The next run begins when the motors switch back to counterclockwise rotations. This causes the flagella to revert from curly 1 back to normal forms. This paper investigates the dynamics of elastic flagella when one or two flagella undergo a full cycle of polymorphic transformations using a computational method in which the flagellar motors are tethered in space and connected via flexible hooks to the filaments. We describe the flagellar filaments and their hooks as elastic rods adopting Kirchhoff rod theory and their hydrodynamic interaction using a generalization of the method of regularized Stokeslets. We also investigate the role of a compliant hook in flagellar bundling.

We analyze the movement of a starving forager on a one-dimensional periodic lattice, where each location contains one unit of food. As the forager lands on sites with food, it consumes the food, leaving the sites empty. If the forager lands consecutively on $s$ empty sites, then it will starve. The forager has two modes of movement: it can either diffuse, by moving with equal probability to adjacent sites on the lattice, or it can jump to a uniformly randomly chosen site on the lattice. We show that the lifetime $T$ of the forager in either paradigm can be approximated by the sum of the cover time ${\tau }_{\mathrm{cover}}$ and the starvation time $s$, when $s$ far exceeds the number $n$ of lattice sites. Our main findings focus on the hybrid model, where the forager has a probability of either jumping or diffusing. The lifetime of the forager varies nonmonotonically according to $p_j$, the probability of jumping. By examining a small system, analyzing a heuristic model, and using direct numerical simulation, we explore the tradeoff between jumps and diffusion, and show that the strategy that maximizes the forager lifetime is a mixture of both modes of movement. However, when extending the model to include time penalties for long-range movement, the forager's lifetime is no longer typically nonmonotonic in $p_j$. Pure jumping is typically optimal when there is an upper bound on the time penalty, but pure diffusion is optimal when jumping becomes too perilous. A mixed jump-diffusion strategy is recovered if a forager is allowed to avoid jumping if they will die midjump.

Particle systems interacting with a soft repulsion, at thermal equilibrium and under some circumstances, are known to form cluster crystals, i.e., periodic arrangements of particle aggregates. We study here how these states are modified by the presence of an additional hard-core repulsion, accounting for particle size. To this end we consider a two-dimensional system of Brownian particles interacting through a potential which includes hard-core and soft-core (of the GEM-$\alpha$ type) repulsive terms. The system shows different phases, and we focus in the regime where cluster crystals form. We consider two situations: the low-temperature one in which particles inside the clusters also show an ordered structure (crystal cluster-crystal phase), and the one occurring at higher temperature in which particles within the clusters are spatially disordered (fluid cluster crystal). An explicit expression for the energy in terms of the typical distance between clusters and the typical distance of the particles within the clusters is obtained for vanishing temperature, from which mean mean inter- and intracluster distances are obtained. Finite-temperature corrections are also discussed, considering explicitly the role of entropy.

We study electrohydrodynamic convection (EHC) patterns in twisted nematic liquid crystal (TNCL) cells with an initial homeotropic alignment. In addition, we demonstrate switching characteristics due to the transition between the 90° and $-{90}^{\circ }$ twisted states. The pattern formations are similar to those obtained in a parallel-aligned nontwisted liquid crystal cell. Calculations of the free energy in an initially, homeotropically aligned TNLC in an electric field demonstrate that the energy barrier between the two states decreases with the increase of the electric field. The mutual transition is caused by the fluctuating flow at the dynamic scattering mode 2, where the energy barrier between the two states is reduced by applying a strong electric field. These properties may be employed for the development of a redirectable dynamic lenticular lens, as an extended version of the dynamic lenticular lens using EHC. The transition between the two states caused by EHC is reversible, and the convection roll pattern of the Williams domain rotates by 90° at each transition.

The liquid slippage behavior due to molecular interactions at fluid-solid (F-S) interfaces is of great importance to the transport of shale oil and clay water. A mesoscopic single-phase lattice Boltzmann method (LBM), based on a continuous and exponentially decaying F-S interaction force and a midgrid bounce-back boundary condition, is proposed to be responsible for the apparent liquid slippage. The F-S interaction force is established at the particle level and thus can be readily extended to porous media. When it is repulsive (attractive), the phenomena of positive (negative) slip lengths and fluid slip (damping) are successfully recovered. This model is validated by the velocity profiles on hydrophobic and hydrophilic surfaces in a benchmark microchannel flow experiment. The slip length is found to be independent of shear rate (its constituents including body force, pore diameter, and kinematic viscosity), but dependent on pore geometry (smaller in porous media than in capillary tubes). Both slip length and permeability ratio follow a power law relationship with interaction parameters (strength and decay length) in capillary tubes and porous media. The permeability ratio estimated analytically with the slip length considered agrees well with that calculated from the LBM simulations, except for the fluid slip in porous media with a significant overestimation. The estimated permeability ratio indicates that it increases (decreases) nonlinearly as the pore diameter decreases, suggesting the great importance of the F-S interaction particularly for thin capillary tubes and microporous media.

Shearing wet granular systems causes a redistribution of the interstitial liquid, which can affect the material's bulk behavior. Using the discrete-element method, we study the early rapid transients, the intermediate states, and the slow long-term evolution of liquid redistribution for various material parameters and different initial wetting conditions in an inhomogeneous split-bottom ring-shear cell featuring a wide shear band away from the system walls. In our model, liquid exists in two states, either in liquid bridges between particles or in liquid films on the particle surfaces. Under deformations like shear, the liquid is redistributed due to the rupture of existing and formation of new liquid bridges. Since we assume the immediate redistribution limit as a new model parameter, a liquid bridge limit volume is imposed to avoid extensive clustering of liquid. Studying the effect of the local shear rate on the liquid redistribution, two distinct effects are observed: For small amounts of shear, i.e., small strain amplitude, the interstitial liquid is randomly redistributed locally, and for larger amounts of shear, liquid is transported away from the shear zone. The local redistribution quickly results in a characteristic probability distribution of liquid bridge volumes, independent of the initial wetting conditions, but the mean and the shape of the distribution are dependent on the limit volume. Although the shear-driven diffusion-like liquid transport is active from the beginning, it dominates the transport in the long term, when the liquid moves out of the shear band, making the shear band dry. Ongoing theoretical analysis suggests a competition of drift and diffusive mechanisms in a different set of coordinates that can explain all our observations by defining a local Péclet number that quantifies the relative strength of the two transport mechanisms.

We investigate cross-beam energy transfer (CBET), where power is transferred from one laser beam to another via a shared ion acoustic wave in hohlraums with low-gas-fill density as a tool for late-time symmetry control for long-pulse (greater than $10\mathrm{ns}$) inertial confinement fusion (ICF) and laboratory astrophysics experiments. We show that the radiation drive symmetry can be controlled and accurately predicted during the foot of the pulse (until the rise to peak power), which is important for mitigating areal density variations in the compressed fuel in ICF implosions. We also show that the effective inner-beam drive after CBET is much greater than observed in previous high-gas-filled-hohlraum experiments, which is thought to be a result of less inverse bremsstrahlung absorption of the incident laser light and reduced (by more than 10 times) stimulated Raman scattering (and Langmuir wave heating). With the inferred level of inner-beam drive after transfer, we estimate that more than $1.25$ times larger plastic capsules could be fielded in this platform with sufficient laser-beam propagation to the waist of the hohlraum. We also estimate that a full-scale plastic capsule, $1100\mu \mathrm{m}$ in capsule radius, would require $\sim 1–2\AA$ of $1\omega$ wavelength separation between the outer and inner beams to achieve a symmetric implosion in this platform.

Omnidirectional light propagation in two-dimensional (2D) photonic crystals (PCs) has been investigated by extending the formerly developed 2D finite element analysis (FEA) of in-plane light propagation in which the corresponding band structure (BS) and photon density of states (PDOS) of 2D PCs with complex geometry configurations had been calculated more accurately by using an adaptive FEA in real space for both the transverse electric (TE) and transverse magnetic (TM) modes. In this work, by adopting a wave-guiding theory under the consideration of translational symmetry, the omnidirectional PDOS corresponding to both the radiative and evanescent waves can be calculated efficiently based on the in-plane dispersion relations of both TE and TM modes within the irreducible Brillouin zone. We demonstrate that the complete band gaps shown by previous work considering only the radiative modes will be closed by including the contributions of the evanescent modes. These results are of general importance and relevance to the spontaneous emission by an atom or to dipole radiation in 2D periodic structures. In addition, it may serve as an efficient approach to identifying the existence of a complete photonic band gap in a 2D PC instead of using time-consuming three-dimensional BS calculations.

A Brownian information engine can induce directed motion of a Brownian particle in a single heat bath at constant temperature by extracting work from the information about the microscopic state of the particle, and serves as a model for artificial and biological submicron scale engines. Much of the experimental studies to date are limited to the realization of an information engine where the initial state of the system is in thermal equilibrium; however, most of the biological and artificial motors operate far from equilibrium. Here, we realize a cyclic information engine operating in a nonequilibrium steady state consisting of a Brownian particle in an optical trap and investigate the optimal operating conditions for maximum work, power, and efficiency. The performance of our information engine depends on the cycle period $\tau$ and the distance $x_f$ that the trap center is shifted with respect to the reference distance $x_m$. We found that the extracted work increases with increasing $\tau$ and is maximum when $\tau$ reaches infinity and $x_f=2x_m$, while the extracted power is maximum at finite $\tau$ for $x_f\ge x_m$ and when $\tau$ approaches zero for $x_f<x_m$. By measuring the steady-state information, we have also measured the efficiency at maximum power.