Light-induced director orientation of polymeric liquid-crystalline systems was investigated. The materials under study were composed of a nematic liquid-crystalline polymer (NLCP) and a small amount (0.05–0.5 wt.%) of conformationally active (azobenzene) or stable (anthraquinone) dye impurity. Light action on the homogeneously aligned polymer films above glass transition temperature leads to the director reorientation and, consequently, to a change in the extraordinary refractive index. The effect is associated with the dye molecule excitation and related change of intermolecular forces. In the case of NLCP with conformationally active dye dopant, an extremely high orientational optical response was detected (nonlinear coefficient is $n_2\sim 0.1{\mathrm{cm}}^2/\mathrm{W}$). In contrast, the efficiency of orientational light action on NLCP with conformationally stable dye dopant is of the same order of magnitude as that of dye-doped low-molar-mass liquid crystals. At the normal light incidence on the NLCP doped with azo-dye, the threshold director orientation is observed which is similar to the Fréedericksz transition under the action of magnetic and electric fields. The obtained high-orientational optical response of NLCP caused by azo-dye dopant in combination with the possibility of the recording of deformed structure in the glassy state, typical for polymer compounds, reveals new opportunities in photonics applications.

We measured the Rapini-Papoular polar anchoring strength coefficient $W$ for $4^{\prime }$-pentyl-4-cyanobiphenyl (5CB) on alignment layers formed by the reactive mesogen photopolymers RM 257, RM 82, and RM 84 [4,$4^{\prime }$-bis(acryloyl)biphenyl] (by Merck). These materials are commonly used for the photostabilization of the liquid crystal (LC) director in the bulk as well as at the surface of the LC layer via the formation of a loose polymer network that captures the director orientation. We developed a method of fabrication of alignment layers from these polymers, and estimated $W$ from the measurements of the optical retardation as a function of applied voltage in uniformly aligned cells. We found that RM 257 yielded $W$ of about $6\times {10}^{-4}\mathrm{J}/{\mathrm{m}}^2$, whereas RM 82 and RM 84 provided anchoring strengths of about $2\times {10}^{-4}$ and $4\times {10}^{-4}\mathrm{J}/{\mathrm{m}}^2$, respectively. Subsequent heating of the sample either destroyed the alignment layer, or substantially decreased $W$ to about $1\times {10}^{-4}\mathrm{J}/{\mathrm{m}}^2$, which was comparable to the anchoring strength of weakly rubbed commercial polyimides.

We experimentally analyze the effect that particle size has on the mass flow rate of a quasi two-dimensional silo discharged by gravity. In a previous work, Janda et al. [Phys. Rev. Lett. 108, 248001 (2012)] introduced a new expression for the mass flow rate based on a detailed experimental analysis of the flow for 1-mm diameter beads. Here, we aim to extend these results by using particles of larger sizes and a variable that was not explicitly included in the proposed expression. We show that the velocity and density profiles at the outlet are self-similar and scale with the outlet size with the same functionalities as in the case of 1-mm particles. Nevertheless, some discrepancies are evidenced in the values of the fitting parameters. In particular, we observe that larger particles lead to higher velocities and lower packing fractions at the orifice. Intriguingly, both magnitudes seem to compensate giving rise to very similar flow rates. In order to shed light on the origin of this behavior we have computed fields of a solid fraction, velocity, and a kinetic-stress like variable in the region above the orifice.

We identify two orthogonal sources of structural entropy in rattler-free granular systems: affine, involving structural changes that only deform the contact network, and topological, corresponding to different topologies of the contact network. We show that a recently developed connectivity-based granular statistical mechanics separates the two naturally by identifying the structural degrees of freedom with spanning trees on the graph of the contact network. We extend the connectivity-based formalism to include constraints on, and correlations between, degrees of freedom as interactions between branches of the spanning tree. We then use the statistical mechanics formalism to calculate the partition function generally and the different entropies in the high-angoricity limit. We also calculate the degeneracy of the affine entropy and a number of expectation values. From the latter, we derive an equipartition principle and an equation of state relating the macroscopic volume and boundary stress to the analog of the temperature, the contactivity.

In this paper, we derive analytical expressions for the leading-order hydrodynamic mobility of a small solid particle undergoing motion tangential to a nearby large spherical capsule whose membrane possesses resistance toward shearing and bending. Together with the results obtained in the first part [Daddi-Moussa-Ider and Gekle, Phys. Rev. E 95, 013108 (2017)], where the axisymmetric motion perpendicular to the capsule membrane is considered, the solution of the general mobility problem is thus determined. We find that shearing resistance induces a low-frequency peak in the particle self-mobility, resulting from the membrane normal displacement in the same way, although less pronounced, to what has been observed for the axisymmetric motion. In the zero-frequency limit, the self-mobility correction near a hard sphere is recovered only if the membrane has a nonvanishing resistance toward shearing. We further compute the in-plane mean-square displacement of a nearby diffusing particle, finding that the membrane induces a long-lasting subdiffusive regime. Considering capsule motion, we find that the correction to the pair-mobility function is solely determined by membrane shearing properties. Our analytical calculations are compared and validated with fully resolved boundary integral simulations where a very good agreement is obtained.

Time evolution of the bound state of a molecular hydrogen cation in an intense, linearly polarized laser field is investigated by solving the full three-dimensional time-dependent Schrödinger equation. Our method is based on the Born-Oppenheimer and dipole approximations, and the wave function is expanded in finite series using B-spline functions and spherical harmonics in prolate spheroidal coordinates. After solving the stationary Schrödinger equation, the initial state is propagated under the influence of the laser field employing the Crank-Nicolson propagator. Using this method we calculate and present high-harmonic photon spectra and above-threshold ionization angle-resolved electron spectra.

Through experiments and numerical simulations we explore the behavior of rf SQUID (radio frequency superconducting quantum interference device) metamaterials, which show extreme tunability and nonlinearity. The emergent electromagnetic properties of this metamaterial are sensitive to the degree of coherent response of the driven interacting SQUIDs. Coherence suffers in the presence of disorder, which is experimentally found to be mainly due to a dc flux gradient. We demonstrate methods to recover the coherence, specifically by varying the coupling between the SQUID meta-atoms and increasing the temperature or the amplitude of the applied rf flux.

We establish a statistical relationship between the inverse energy cascade and the spatial correlations of clustered vortices in two-dimensional quantum turbulence. The Kolmogorov spectrum $k^{-5/3}$ on inertial scales $r$ corresponds to a pair correlation function between the vortices with different signs that decays as a power law with the pair distance given as $r^{-4/3}$. To test these scaling relations, we propose a forced and dissipative point vortex model that captures the turbulent dynamics of quantized vortices by the emergent clustering of same-sign vortices. The inverse energy cascade developing in a statistically neutral system originates from this vortex clustering that evolves with time.

We show that, at the critical temperature, there is a class of Lee-Yang zeros of the partition function in a general scalar field theory, which location scales with the size of the system with a characteristic exponent expressed in terms of the isothermal critical exponent $\delta$. In the thermodynamic limit the zeros belonging to this class condense to the critical point $\zeta =1$ on the real axis in the complex fugacity plane while the complementary set of zeros (with $\text{Re}\zeta <1)$ covers the unit circle. Although the aforementioned class degenerates to a single point for an infinite system, when the size is finite it contributes significantly to the partition function and reflects the self-similar structure (fractal geometry, scaling laws) of the critical system. This property opens up the perspective to formulate finite-size scaling theory in effective QCD, near the chiral critical point, in terms of the location of Lee-Yang zeros.

Square ice is a statistical mechanics model for two-dimensional ice, widely believed to have a conformally invariant scaling limit. We associate a Peano (space-filling) curve to a square ice configuration, and more generally to a so-called six-vertex model configuration, and argue that its scaling limit is a space-filling version of the random fractal curve ${SLE}_{\kappa }$, Schramm-Loewner evolution with parameter $\kappa$, where $4<\kappa \le 12+8\sqrt{2}$. For square ice, $\kappa =12$. At the “free-fermion point” of the six-vertex model, $\kappa =8+4\sqrt{3}$. These unusual values lie outside the classical interval $2\le \kappa \le 8$.

The continuous imaginary-time quantum Monte Carlo method with the worm update algorithm is applied to explore the ground-state properties of the spin-1/2 Heisenberg model with antiferromagnetic (AF) coupling $J>0$ and ferromagnetic (F) coupling $J^{\prime }<0$ along zigzag and armchair directions, respectively, on honeycomb lattice. It is found that by enhancing the F coupling $J^{\prime }$ between zigzag AF chains, the system is smoothly crossover from one-dimensional zigzag spin chains to a two-dimensional magnetic ordered state. In absence of an external field, the system is in a stripe-ordered phase. In the presence of uniform and staggered fields, the uniform and staggered out-of-plane magnetizations appear while the stripe order remains in the $xy$ plane, and a second-order quantum phase transition (QPT) at a critical staggered field is observed. The critical exponents of correlation length for QPTs induced by a staggered field for the cases with $J>0, J^{\prime }<0$ and $J<0, J^{\prime }>0$ are obtained to be $\nu =0.70046\left(1\right)$ and $0.7086\left(3\right)$, respectively, indicating that both cases belong to O(3) universality. The corresponding dynamic and susceptibility exponent z and $\gamma /\nu$ are fitted to be 1.006572(9), 1.9412(2) and 1.004615(8), 1.96121(9) for the two cases, respectively. The scaling behavior in a staggered field is analyzed, and the ground-state phase diagrams in the plane of coupling ratio and staggered field are presented for two cases. The temperature dependence of susceptibility and specific heat of both systems in external magnetic fields is also discussed. A Kosterlitz-Thouless phase transition is found for the present system in a uniform field.

The linear response is investigated in a long-range Hamiltonian system from the viewpoint of dynamics, which is described by the Vlasov equation in the large-population limit. Because of the existence of the Casimir invariants of the Vlasov dynamics, an external field does not drive the system to the forced thermal equilibrium in general, and the linear response is suppressed. With the aid of a linear response theory based on the Vlasov dynamics, we compute the suppressed linear response in a system having two order parameters, which introduce the conjugate two external fields and the susceptibility matrix of size 2 accordingly. Moreover, the two order parameters bring three phases and there are three types of second-order phase transitions between them. For each type of phase transition, all the critical exponents for elements of the susceptibility matrix are computed. The critical exponents reveal that some elements of the matrices do not diverge even at critical points, while the mean-field theory predicts divergences. The linear response theory also suggests the appearance of negative off-diagonal elements; in other words, an applied external field decreases the value of an order parameter. These theoretical predictions are confirmed by direct numerical simulations of the Vlasov equation.

We investigate adjacency matrices of bipartite graphs with a power-law degree distribution. Motivation for this study is twofold: first, vibrational states in granular matter and jammed sphere packings; second, graphs encoding social interaction, especially electronic commerce. We establish the position of the mobility edge and show that it strongly depends on the power in the degree distribution and on the ratio of the sizes of the two parts of the bipartite graph. At the jamming threshold, where the two parts have the same size, localization vanishes. We found that the multifractal spectrum is nontrivial in the delocalized phase, but still near the mobility edge. We also study an empirical bipartite graph, namely, the Amazon reviewer-item network. We found that in this specific graph the mobility edge disappears, and we draw a conclusion from this fact regarding earlier empirical studies of the Amazon network.

We consider the zero-temperature coarsening in the Ising model in two dimensions where the spins interact within the Moore neighborhood. The Hamiltonian is given by $H=-{\sum }_{〈i,j〉}{S}_i{S}_j-\kappa {\sum }_{〈i,j^{\prime }〉}{S}_i{S}_{j^{\prime }}$, where the two terms are for the first neighbors and second neighbors, respectively, and $\kappa \ge 0$. The freezing phenomenon, already noted in two dimensions for $\kappa =0$, is seen to be present for any $\kappa$. However, the frozen states show more complicated structure as $\kappa$ is increased; e.g., local antiferromagnetic motifs can exist for $\kappa >2$. Finite-sized systems also show the existence of an isoenergetic active phase for $\kappa >2$, which vanishes in the thermodynamic limit. The persistence probability shows universal behavior for $\kappa >0$; however, it is clearly different from the $\kappa =0$ results when a nonhomogeneous initial condition is considered. Exit probability shows universal behavior for all $\kappa \ge 0$. The results are compared with other models in two dimensions having interactions beyond the first neighbor.

We consider interacting electrons moving in a nonlinear Morse lattice. We set the initial conditions as follows: electrons were initially localized at the center of the chain and a solitonic deformation was produced by an impulse excitation on the center of the chain. By solving quantum and classical equations for this system numerically, we found that a fraction of electronic wave function was trapped by the solitonic excitation, and trapping specificities depend on the degree of interaction among electrons. Also, there is evidence that the effective electron velocity depends on Coulomb interaction and electron-phonon coupling in a nontrivial way. This association is explained in detail along this work. In addition, we briefly discuss the dependence of our results with the type of initial condition we choose for the electrons and lattice.

Pinning of vortices by obstacles plays an important role in various systems. In the heart, anatomical reentry is created when a vortex, also known as the spiral wave, is pinned to an anatomical obstacle, leading to a class of physiologically very important arrhythmias. Previous analyses of its dynamics and instability provide fine estimates in some special circumstances, such as large obstacles or weak excitabilities. Here, to expand theoretical analyses to all circumstances, we propose a general theory whose results quantitatively agree with direct numerical simulations. In particular, when obstacles are small and pinned spiral waves are destabilized, an accurate explanation of the instability in two-dimensional media is provided by the usage of a mapping rule and dimension reduction. The implications of our results are to better understand the mechanism of arrhythmia and thus improve its early prevention.

We study the effectiveness of locally controlling the impulse transmitted by parametric periodic excitations at inducing and suppressing chaos in starlike networks of driven damped pendula, leading to asynchronous chaotic states and equilibria, respectively. We found that the inducing (suppressor) effect of increasing (decreasing) the impulse transmitted by the parametric excitations acting on particular nodes depends strongly on their number and degree of connectivity as well as the coupling strength. Additionally, we provide a theoretical analysis explaining the basic physical mechanisms of the emergence and suppression of chaos as well as the main features of the chaos-control scenario. Our findings constitute proof of the impulse-induced control of chaos in a simple model of complex networks, thus opening the way to its application to real-world networks.

The determination of the microscopic dose-damage relationship for DNA in an aqueous environment is of a fundamental interest for dosimetry and applications in radiation therapy and protection. We combine geant4 particle-scattering simulations in water with calculations concerning the movement of biomolecules to obtain the energy deposit in the biologically relevant nanoscopic volume. We juxtaposition these results to the experimentally determined damage to obtain the dose-damage relationship at a molecular level. This approach is tested for an experimentally challenging system concerning the direct irradiation of plasmid DNA (pUC19) in water with electrons as primary particles. Here a microscopic target model for the plasmid DNA based on the relation of lineal energy and radiation quality is used to calculate the effective target volume. It was found that on average fewer than two ionizations within a 7.5-nm radius around the sugar-phosphate backbone are sufficient to cause a single strand break, with a corresponding median lethal energy deposit being $E_{1/2}=6\pm 4$ eV. The presented method is applicable for ionizing radiation (e.g., $\gamma$ rays, x rays, and electrons) and a variety of targets, such as DNA, proteins, or cells.

In this paper, we explore anisotropic interactions between particles with heterogeneous boundary conditions inside both nematic and cholesteric liquid crystals. The results show that when particles are put at different distances and angles with respect to each other, new types of defect structures are produced, depending on the relative distances and directions. In a cholesteric liquid crystal, the value of the pitch affects the defect structures and induced forces. Moreover, it was observed that it is energetically favorable for the particles to remain in a plane parallel to the far-field director in a nematic liquid crystal, while for particles immersed in a cholesteric there are multiple energy minima not all located in the same plane.

In this paper, we report the temperature behavior of an optimized disordered photonic system-based liquid crystal by means of heat capacity and refractive index measurements. The scattering system is formed by a porous borosilicate glass random matrix (about 60%) infiltrated with a smectogenic liquid crystal (about 16%) and a small amount of laser dye (0.1%). The rest of the scattering system is about 24% air, giving rise to a high refractive index contrast scattering system. Such a system has the functionality to change the refractive index contrast with temperature due to the liquid crystal temperature behavior. The system, optically pumped by the second harmonic of a $Q$-switched Nd:YAG pulsed laser working at 532 nm, exhibits random laser action, the threshold of which depends upon the liquid crystalline mesophase. Temperatures of existence of the smectic-$B$ phase correspond to the most optimized random laser. In such a mesophase, the transport mean free path has been determined as about 16 μm in a coherent backscattering experiment.