Impedance matching in an elastic actuator.

We optimize the performance of an elastic actuator consisting of an active core in a host which performs mechanical work on a load. The system, initially with localized elastic energy in the active component, relaxes and distributes energy to the rest of the system. Using the linearized Mooney-Rivlin hyperelastic model in a cylindrical geometry and assuming viscous relaxation, we show that the value of Young's modulus of the impedance matching host which maximizes the energy transfer from the active component to the load is the geometric mean of Young's moduli of the active component and the elastic load. This is similar to the classic results for impedance matching for maximizing the transmittance of light propagating through dielectric media.

Leaky cell model of hard spheres.

We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms of the accessible free volume, i.e., the volume of space that a sphere can explore without touching another sphere. We compute these free volumes using a leaky cell model, in which the accessible space accounts for the possibility that spheres may escape from the local cage of lattice neighbors. We describe how elementary geometry may be used to calculate the free volume exactly for this leaky cell model in two- and three-dimensional lattice packings and compare the results to the well-known Carnahan-Starling and Percus-Yevick liquid models. We provide formulas for the free volumes of various lattices and use the common tangent construction to identify several phase transitions between them in the leaky cell regime, indicating the possibility of coexistence in crystalline materials.

St. Petersburg Paradox and Failure Probability.

The St. Petersburg paradox provides a simple paradigm for systems that show sensitivity to rare events. Here, we demonstrate a physical realization of this paradox using tensile fracture, experimentally verifying for six decades of spatial and temporal data and two different materials that the fracture force depends logarithmically on the length of the fiber. The St. Petersburg model may be useful in a variety fields where failure and reliability are critical.

Small footprint cholesteric liquid crystal laser.

We demonstrate a small optical bench footprint laser assembly based on the small pulsed Nd:YAG laser head SSY-1 for pumping cholesteric liquid crystal (CLC) lasers and illustrate its performance using low molecular weight CLC samples doped with the fluorescent dye PM597. A low lasing threshold, narrow laser line, and far-field interference patterns of the CLC laser were observed using the SSY-1-based laser assembly as the pump. The emission characteristics of the CLC laser are similar to those observed with comparable CLC materials pumped by an order of magnitude physically larger and many orders of magnitude more expensive commercial Nd:YAG laser systems. The small footprint CLC laser demonstrated in this work provides an opportunity for significant size and cost reduction of CLC lasers and fostering their practical applications.

Electrically tunable laser based on oblique heliconical cholesteric liquid crystal.

A cholesteric liquid crystal (CLC) formed by chiral molecules represents a self-assembled one-dimensionally periodic helical structure with pitch [Formula: see text] in the submicrometer and micrometer range. Because of the spatial periodicity of the dielectric permittivity, a CLC doped with a fluorescent dye and pumped optically is capable of mirrorless lasing. An attractive feature of a CLC laser is that the pitch [Formula: see text] and thus the wavelength of lasing [Formula: see text] can be tuned, for example, by chemical composition. However, the most desired mode to tune the laser, by an electric field, has so far been elusive. Here we present the realization of an electrically tunable laser with [Formula: see text] spanning an extraordinarily broad range (>100 nm) of the visible spectrum. The effect is achieved by using an electric-field-induced oblique helicoidal (OH) state in which the molecules form an acute angle with the helicoidal axis rather than align perpendicularly to it as in a field-free CLC. The principal advantage of the electrically controlled CLCOH laser is that the electric field is applied parallel to the helical axis and thus changes the pitch but preserves the single-harmonic structure. The preserved single-harmonic structure ensures efficiency of lasing in the entire tunable range of emission. The broad tuning range of CLCOH lasers, coupled with their microscopic size and narrow line widths, may enable new applications in areas such as diagnostics, sensing, microscopy, displays, and holography.

In-fiber Fabry-Perot interferometer for strain and magnetic field sensing.

In this paper we discuss the results obtained with an in-fiber Fabry-Perot interferometer (FPI) used in strain and magnetic field (or force) sensing. The intrinsic FPI was constructed by splicing a small section of a capillary optical fiber between two pieces of standard telecommunication fiber. The sensor was built by attaching the FPI to a magnetostrictive alloy in one configuration and also by attaching the FPI to a small magnet in another. Our sensors were found to be over 4 times more sensitive to magnetic fields and around 10 times less sensitive to temperature when compared to sensors constructed with Fiber Bragg Grating (FBG).

Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra.

All hard, convex shapes are conjectured by Ulam to pack more densely than spheres, which have a maximum packing fraction of phi = pi/ radical18 approximately 0.7405. Simple lattice packings of many shapes easily surpass this packing fraction. For regular tetrahedra, this conjecture was shown to be true only very recently; an ordered arrangement was obtained via geometric construction with phi = 0.7786 (ref. 4), which was subsequently compressed numerically to phi = 0.7820 (ref. 5), while compressing with different initial conditions led to phi = 0.8230 (ref. 6). Here we show that tetrahedra pack even more densely, and in a completely unexpected way. Following a conceptually different approach, using thermodynamic computer simulations that allow the system to evolve naturally towards high-density states, we observe that a fluid of hard tetrahedra undergoes a first-order phase transition to a dodecagonal quasicrystal, which can be compressed to a packing fraction of phi = 0.8324. By compressing a crystalline approximant of the quasicrystal, the highest packing fraction we obtain is phi = 0.8503. If quasicrystal formation is suppressed, the system remains disordered, jams and compresses to phi = 0.7858. Jamming and crystallization are both preceded by an entropy-driven transition from a simple fluid of independent tetrahedra to a complex fluid characterized by tetrahedra arranged in densely packed local motifs of pentagonal dipyramids that form a percolating network at the transition. The quasicrystal that we report represents the first example of a quasicrystal formed from hard or non-spherical particles. Our results demonstrate that particle shape and entropy can produce highly complex, ordered structures.

Anticlinic order of long-range repulsive rodlike magnetic particles in two dimensions.

In the field of liquid crystals, it is well known that rodlike molecules interacting via long-range attractive interactions or short-range repulsive potentials can exhibit orientational order. In this work, we are interested in what would happen to systems of rodlike particles interacting via a long-range repulsive potential. In our model, each particle consists of a number of point dipoles uniformly distributed along the particle length, with all dipoles pointing along the z axis so that the rodlike particles repel each other when they lie in the x-y plane. Dipoles from different particles interact via an r^{-3} potential, where r is the distance between the dipoles. We have considered two model systems, each with N particles in a unit cell with periodic boundary conditions. In the first, particle centers are fixed on a square or triangular lattice but they are free to rotate. In the second, particles are free to translate as well as rotate in cells with variable shapes. Here they self-assemble to form configurations where the stress tensors are isotropic. Our numerical results show that, at low temperatures, the particles tend to form stripes with alternating orientations, resembling herringbone patterns or the anticlinic Sm-C_{A} liquid crystal phase.

Rogue ocean waves and the St. Petersburg paradox.

Powerful rogue ocean waves have been objects of fascination for centuries. Elusive and awe-inspiring, with the potential to inflict catastrophic damage, rogue waves remain unpredictable and imperfectly understood. To gain further insight into their behavior, we analyzed 3 441 188 683 ocean surface waves to determine the statistical height distribution of the largest waves. We found that the distribution of rare events which resolves the St. Petersburg paradox also describes the relative height distribution of the largest waves. This result is expected to contribute to the modeling of ocean surface dynamics and improve the accuracy of marine weather forecasts.

Performance of Composite Glass-Diarylethene Crystal Photomechanical Actuator Membranes.

Hybrid organic-inorganic composites based on organic photochromic crystals embedded in inorganic templates provide a new approach to photomechanical materials. Diarylethene (DAE) nanowire crystals grown in Al2O3 membranes have exhibited reversible photoinduced bending and lifting [Dong, X., Chem. Mater. 2019, 31, 1016-1022]. In this paper, the hybrid approach is extended to porous SiO2 membranes. Despite the different template material (SiO2 instead of Al2O3) and much larger channels (5 µm diameter instead of 0.2 µm diameter), similar photomechanical behavior is observed for this new class of organic-inorganic hybrid actuators. The ability to reuse individual glass templates across different DAE filling cycles allows us to show that the DAE filling step is crucial for determining the mechanical work done by the bending template. The bending curvature also depends quadratically on the template thickness, in good agreement with theory. The light-induced bending can be repeated for up to 150 cycles without loss of performance, suggesting good fatigue resistance. The results in this paper demonstrate that the hybrid organic-inorganic approach can be extended to other host materials and template geometries. They also suggest that optimizing the organic filling and template thickness could improve the work output by an order of magnitude.

Light-induced stress and work in photomechanical materials.

Increasingly important photomechanical materials produce stress and mechanical work when illuminated. We propose experimentally accessible performance metrics for photostress and photowork, enabling comparison of materials performance. We relate these metrics to material properties, providing a framework for the design and optimization of photomechanical materials.

Distance of closest approach of two arbitrary hard ellipsoids.

The distance of closest approach of particles with hard cores is a key parameter in statistical theories and computer simulations of liquid crystals and colloidal systems. In this Brief Report, we provide an algorithm to calculate the distance of closest approach of two ellipsoids of arbitrary shape and orientation. This algorithm is based on our previous analytic result for the distance of closest approach of two-dimensional ellipses. The method consists of determining the intersection of the ellipsoids with the plane containing the line joining their centers and rotating the plane. The distance of closest approach of the two ellipses formed by the intersection is a periodic function of the plane orientation, whose maximum corresponds to the distance of closest approach of the two ellipsoids.

Nonphotochemical laser-induced nucleation of nematic phase and alignment of nematic director from a supercooled thermotropic liquid crystal.

A nonphotochemical laser-induced phase transition was studied in a supercooled 4;{'}-n -pentyl-4-cyanobiphenyl (5CB, also referred to as PCB and K15) liquid crystal, using linearly polarized 45 ps light pulses at a wavelength of 532 nm. The laser induced nucleation from the metastable supercooled isotropic phase to the nematic phase during slow cooling (0.001 degrees C/min) and high light intensity (3.9 MW/cm{2}) . The resulting nematic director tended to be aligned along the direction of the plane of polarization of the light. At the intensities used, there is no observable laser-induced realignment of the director once the sample is in the nematic phase, nor any permanent laser-induced ordering when the sample is illuminated only in the stable isotropic phase during slow cooling. These experimental results are consistent with a mechanism based on optical Kerr alignment.

Director dynamics in liquid-crystal physical gels.

Nematic liquid-crystal (LC) elastomers and gels have a rubbery polymer network coupled to the nematic director. While LC elastomers show a single, non-hydrodynamic relaxation mode, dynamic light-scattering studies of self-assembled liquid-crystal gels reveal orientational fluctuations that relax over a broad time scale. At short times, the relaxation dynamics exhibit hydrodynamic behavior. In contrast, the relaxation dynamics at long times are non-hydrodynamic, highly anisotropic, and increase in amplitude at small scattering angles. We argue that the slower dynamics arise from coupling between the director and the physically associated network, which prevents director orientational fluctuations from decaying completely at short times. At long enough times the network restructures, allowing the orientational fluctuations to fully decay. Director dynamics in the self-assembled gels are thus quite distinct from those observed in LC elastomers in two respects: they display soft orientational fluctuations at short times, and they exhibit at least two qualitatively distinct relaxation processes.

Distance of closest approach of two arbitrary hard ellipses in two dimensions.

The distance of closest approach of hard particles is a key parameter of their interaction and plays an important role in the resulting phase behavior. For nonspherical particles, the distance of closest approach depends on orientation, and its calculation is surprisingly difficult. Although overlap criteria have been developed for use in computer simulations [Vieillard-Baron, J. Chem. Phys. 56, 4729 (1972); Perram and Wertheim, J. Comput. Phys. 58, 409 (1985)], no analytic solutions have been obtained for the distance of closest approach of ellipsoids in three dimensions, or, until now, for ellipses in two dimensions. We have derived an analytic expression for the distance of closest approach of the centers of two arbitrary hard ellipses as a function of their orientation relative to the line joining their centers. We describe our method for solving this problem, illustrate our result, and discuss its usefulness in modeling and simulating systems of anisometric particles such as liquid crystals.

Onsager's missing steps retraced.

Onsager's paper on phase transition and phase coexistence in anisotropic colloidal systems is a landmark in the theory of lyotropic liquid crystals. However, an uncompromising scrutiny of Onsager's original derivation reveals that it would be rigorously valid only for ludicrous values of the system's number density (of the order of the reciprocal of the number of particles). Based on Penrose's tree identity and an appropriate variant of the mean-field approach for purely repulsive, hard-core interactions, our theory shows that Onsager's theory is indeed valid for a reasonable range of densities.

Density functional theory for dense nematic liquid crystals with steric interactions.

The celebrated work of Onsager on hard particle systems, based on the truncated second order virial expansion, is valid at relatively low volume fractions for large aspect ratio particles. While it predicts the isotropic-nematic phase transition, it does not provide a realistic equation of state in that the pressure remains finite for arbitrarily high densities. In this work, we derive a mean field density functional form of the Helmholtz free energy for nematics with hard core repulsion. In addition to predicting the isotropic-nematic transition, the model provides a more realistic equation of state. The energy landscape is much richer, and the orientational probability distribution function in the nematic phase possesses a unique feature-it vanishes on a nonzero measure set in orientation space.

Curvature-driven foam coarsening on a sphere: A computer simulation.

The von Neumann-Mullins law for the area evolution of a cell in the plane describes how a dry foam coarsens in time. Recent theory and experiment suggest that the dynamics are different on the surface of a three-dimensional object such as a sphere. This work considers the dynamics of dry foams on the surface of a sphere. Starting from first principles, we use computer simulation to show that curvature-driven motion of the cell boundaries leads to exponential growth and decay of the areas of cells, in contrast to the planar case where the growth is linear. We describe the evolution and distribution of cells to the final stationary state.

Tunable lasing in cholesteric liquid crystal elastomers with accurate measurements of strain.

We report wide range and reversible tuning of the selective reflection band of a single crystal cholesteric liquid crystal elastomer (CLCE). The tuning is the result of mechanical shortening of the helical pitch achieved by imposing a uniform uniaxial strain along the helical axis. On doping the CLCE sample with a laser dye, we observe lasing from the CLCE in both glassy and rubbery states. By changing the cholesteric pitch, mechanical compression provides tuning of the laser emission from the dye doped CLCE over a significant part of the fluorescence band of the laser dye. In this work we demonstrate for the first time that both the CLCE pitch and the lasing wavelength are linearly dependent on the strain imposed on the CLCE film.