A computational study of nematic core structure and disclination interactions in elastically anisotropic nematics.

A singular potential method in the Q tensor order parameter representation of a nematic liquid crystal is used to study the equilibrium configuration of a disclination dipole. Unlike the well studied isotropic limit (the so called one constant approximation), we focus on the case of anisotropic Frank elasticity (bend/splay elastic constant contrast). Prior research has established that the singular potential method provides an accurate description of the tensor order parameter profile in the vicinity of a disclination core of a highly anisotropic lyotropic chromonic liquid crystal. This research is extended here to two interacting disclinations forming a dipole configuration. The director angle is shown to decay in the far field inversely with distance to the dipole as is the case in the isotropic limit, but with a different angular dependence. Therefore elastic constant anisotropy modifies the elastic screening between disclinations, with implications for the study of ensembles of defects as seen, for example, in active matter in the extended system limit.

Sublimation of isolated toric focal conic domains on micro-patterned surfaces.

Toric focal conic domains (TFCDs) in smectic liquid crystals exhibit distinct topological characteristics, featuring torus-shaped molecular alignment patterns with rotational symmetry around a central core. TFCDs have attracted much interest due to their unique topological structures and properties, enabling not only fundamental studies but also potential applications in liquid crystal (LC)-based devices. Here, we investigated the precise spatial control of the arrangement of TFCDs using micropatterns and sublimation of TFCDs to estimate the energy states of the torus-like structures. Through simulations, we observed that the arrangement of TFCDs strongly depends on the shape of the topographies of underlying substrates. To accurately estimate the energetic effects of non-zero eccentricity and evaluate their thermodynamic stability, we propose a geometric model. Our findings provide valuable insights into the behavior of smectic LCs, offering opportunities for developing novel LC-based devices with precise control over their topological properties.

Application Times, Placement Accuracy, and User Ratings of Commercially Available Manual and Battery-Powered Intraosseous Catheters in a High Bone Density Cadaveric Swine Model.

INTRODUCTION: Intraosseous (IO) infusion, the pressurized injection of fluids into bone through a catheter, is a life-preserving resuscitative technique for treating trauma patients with severe hemorrhage. However, little is known regarding the application times, placement accuracy, and end-user ratings of battery-powered and manual IO access devices. This study was specifically designed to fill these knowledge gaps on six FDA-approved IO access devices. MATERIALS AND METHODS: Three experienced U.S. Navy Emergency Medicine residents each placed commercially available 15-gauge IO catheters in cadaveric swine (Sus scrofa) proximal humeri and sternums in a randomized prospective experimental design. Devices included the battery-powered EZ-IO Rapid Infuser and the manual Jamshidi IO, PerSys NIO, SAM Manual IO, Tactical Advanced Lifesaving IO Needle (TALON), and PYNG First Access for Shock and Trauma 1 (30 trials per device, 10 per user, 210 total trials). Application times, placement accuracy in medullary (zone 1) and trabecular (zone 2) bone while avoiding cortical (zone 3) bone, and eight subjective user ratings were analyzed using ANOVA and nonparametric statistics at P < .05. RESULTS: The EZ-IO demonstrated the fastest application times, high rates in avoiding zone 3, and the highest user ratings (P < .0001). The TALON conferred intermediate placement times, highest rates of avoiding zone 3, and second-highest user ratings. The SAM Manual IO and Jamshidi performed poorly, with mixed results for the PerSys NIO and PYNG First Access for Shock and Trauma 1. CONCLUSIONS: The battery-powered EZ-IO performed best and remains the IO access device of choice. The present findings suggest that the TALON should be considered as a manual backup to the EZ-IO.

Equilibrium morphology of tactoids in elastically anisotropic nematics.

We study two dimensional tactoids in nematic liquid crystals by using a Q-tensor representation. A bulk free energy of the Maier-Saupe form with eigenvalue constraints on Q, plus elastic terms up to cubic order in Q are used to understand the effects of anisotropic anchoring and Frank-Oseen elasticity on the morphology of nematic-isotropic domains. Further, a volume constraint is introduced to stabilize tactoids of any size at coexistence. We find that anisotropic anchoring results in differences in interface thickness depending on the relative orientation of the director at the interface, and that interfaces become biaxial for tangential alignment when anisotropy is introduced. For negative tactoids, surface defects induced by boundary topology become sharper with increasing elastic anisotropy. On the other hand, by parametrically studying their energy landscape, we find that surface defects do not represent the minimum energy configuration in positive tactoids. Instead, the interplay between Frank-Oseen elasticity in the bulk, and anisotropic anchoring yields semi-bipolar director configurations with non-circular interface morphology. Finally, we find that for growing tactoids the evolution of the director configuration is highly sensitive to the anisotropic term included in the free energy, and that minimum energy configurations may not be representative of kinetically obtained tactoids at long times.

Singularity identification for the characterization of topology, geometry, and motion of nematic disclination lines.

We introduce a characterization of disclination lines in three dimensional nematic liquid crystals as a tensor quantity related to the so called rotation vector around the line. This quantity is expressed in terms of the nematic tensor order parameter Q, and shown to decompose as a dyad involving the tangent vector to the disclination line and the rotation vector. Further, we derive a kinematic law for the velocity of disclination lines by connecting this tensor to a topological charge density as in the Halperin-Mazenko description of defects in vector models. Using this framework, analytical predictions for the velocity of interacting line disclinations and of self-annihilating disclination loops are given and confirmed through numerical computation.

Phase-field model for a weakly compressible soft layered material: morphological transitions on smectic-isotropic interfaces.

A coupled phase-field and hydrodynamic model is introduced to describe a two-phase, weakly compressible smectic (layered phase) in contact with an isotropic fluid of different density. A non-conserved smectic order parameter is coupled to a conserved mass density in order to accommodate non-solenoidal flows near the smectic-isotropic boundary arising from density contrast between the two phases. The model aims to describe morphological transitions in smectic thin films under heat treatment, in which arrays of focal conic defects evolve into conical pyramids and concentric rings through curvature dependent evaporation of smectic layers. The model leads to an extended thermodynamic relation at a curved surface that includes its Gaussian curvature, non-classical stresses at the boundary and flows arising from density gradients. The temporal evolution given by the model conserves the overall mass of the liquid crystal while still allowing for the modulated smectic structure to grow or shrink. A numerical solution of the governing equations reveals that pyramidal domains are sculpted at the center of focal conics upon a temperature increase, which display tangential flows at their surface. Other cases investigated include the possible coalescence of two cylindrical stacks of smectic layers, formation of droplets, and the interactions between focal conic domains through flow.

Anisotropic disclination cores in nematic liquid crystals modeled by a self-consistent molecular field theory.

Disclination configurations of a nematic liquid crystal are studied within a self-consistent molecular field theory. The theory is based on a tensor order parameter, and can accommodate anisotropic elastic energies without the known divergences in the Landau-de Gennes formulation. Our results agree with the asymptotic results of Dzyaloshinskii for the Frank-Oseen energy far from the defect core, but reveal biaxial order at intermediate distances from the core, crossing over to uniaxial but axisymmetric configurations as the core is approached. The elastic terms considered in our energy allow for the separate control of surface tension, anchoring, and elasticity contrast, and are used to analyze recent results for lyotropic chromonic liquid crystals. The latter display unusually large defect cores (on the order of tens of microns) which can be used for a quantitative comparison with the theory. Both ±1/2 disclination configurations are well reproduced by our calculations. Elastic anisotropy is also shown to lead to qualitative changes in the disclination polarization, a quantity that is proportional to the active stress in models of active matter.

Computational molecular field theory for nematic liquid crystals.

Nematic liquid crystals exhibit configurations in which the underlying ordering changes markedly on macroscopic length scales. Such structures include topological defects in the nematic phase and tactoids within nematic-isotropic coexistence. We discuss a computational study of inhomogeneous configurations that is based on a field theory extension of the Maier-Saupe molecular model of a uniaxial, nematic liquid crystal. A tensor order parameter is defined as the second moment of an orientational probability distribution, leading to a free energy that is not convex within the isotropic-nematic coexistence region, and that goes to infinity if the eigenvalues of the order parameter become nonphysical. Computations of the spatial profile of the order parameter are presented for an isotropic-nematic interface in one dimension, a tactoid in two dimensions, and a nematic disclination in two dimensions. We compare our results to those given by the Landau-de Gennes free energy for the same configurations and discuss the advantages of such a model over the latter.

Erratum: Bifurcation threshold of the delayed van der Pol oscillator under stochastic modulation [Phys. Rev. E 85, 056214 (2012)].

This corrects the article DOI: 10.1103/PhysRevE.85.056214.

Role of Gaussian curvature on local equilibrium and dynamics of smectic-isotropic interfaces.

Recent research on interfacial instabilities of smectic films has shown unexpected morphologies that are not fully explained by classical local equilibrium thermodynamics. Annealing focal conic domains can lead to conical pyramids, changing the sign of the Gaussian curvature and exposing smectic layers at the interface. In order to explore the role of the Gaussian curvature on the stability and evolution of the film-vapor interface, we introduce a phase-field model of a smectic-isotropic system as a first step in the study. Through asymptotic analysis of the model, we generalize the classical condition of local equilibrium, the Gibbs-Thomson equation, to include contributions from surface bending and torsion and a dependence on the layer orientation at the interface. A full numerical solution of the phase-field model is then used to study the evolution of focal conic structures in smectic domains in contact with the isotropic phase via local evaporation and condensation of smectic layers. As in experiments, numerical solutions show that pyramidal structures emerge near the center of the focal conic owing to evaporation of adjacent smectic planes and to their orientation relative to the interface. Near the center of the focal conic domain, a correct description of the motion of the interface requires the additional curvature terms obtained in the asymptotic analysis, thus clarifying the limitations in modeling motion of hyperbolic surfaces solely driven by mean curvature.

Electrokinetic effects in nematic suspensions: Single-particle electro-osmosis and interparticle interactions.

Electrokinetic phenomena in a nematic suspension are considered when one or more dielectric particles are suspended in a liquid crystal matrix in its nematic phase. The long-range orientational order of the nematic constitutes a fluid with anisotropic properties. This anisotropy enables charge separation in the bulk under an applied electric field, and leads to streaming flows even when the applied field is oscillatory. In the cases considered, charge separation is seen to result from director field distortions in the matrix that are created by the suspended particles. We use a recently introduced electrokinetic model to study the motion of a single-particle hyperbolic hedgehog pair. We find this motion to be parallel to the defect-particle center axis, independent of field orientation. For a two-particle configuration, we find that the relative force of electrokinetic origin is attractive in the case of particles with perpendicular director anchoring, and repulsive for particles with tangential director anchoring. The study reveals large scale flow properties that are respectively derived from the topology of the configuration alone and from short scale hydrodynamics phenomena in the vicinity of the particle and defect.

A connection between living liquid crystals and electrokinetic phenomena in nematic fluids.

We develop a formal analogy between configurational stresses in physically distinct systems, and study the flows that they induce when the configurations of interest include topological defects. Our primary focus is on electrokinetic flows in a nematic fluid under an applied electrostatic field, which we compare with a class of systems in which internal stresses are generated due to configurational changes (e.g., active matter, liquid crystal elastomers). The mapping allows the extension, within certain limits, of existing results on transport in electrokinetic systems to active transport. We study motion induced by a pair of point defects in a dipole configuration, and steady rotating flows due to a swirling vortex nematic director pattern. The connection presented allows the design of electrokinetic experiments that correspond to particular active matter configurations that may be easier to conduct and control in the laboratory.

Separation of Elastic and Plastic Timescales in a Phase Field Crystal Model.

A consistent small-scale description of plasticity and dislocation motion in a crystalline solid is presented based on the phase field crystal description. By allowing for independent mass motion and lattice distortion, the crystal can maintain elastic equilibrium on the timescale of plastic motion. We show that the singular (incompatible) strains are determined by the phase field crystal density, while the smooth distortions are constrained to satisfy elastic equilibrium. A numerical implementation of the model is presented and used to study a benchmark problem: the motion of an edge dislocation dipole in a triangular lattice. The time dependence of the dipole separation agrees with continuum elasticity with no adjustable parameters.

Electrokinetic flows in liquid crystal thin films with fixed anchoring.

We study ionic and mass transport in a liquid crystalline fluid film in its nematic phase under an applied electrostatic field. Both analytic and numerical solutions are given for some prototypical configurations of interest in electrokinetics: thin films with spatially nonuniform nematic director that are either periodic or comprise a set of isolated disclinations. We present a quantitative description of the mechanisms inducing spatial charge separation in the nematic, and of the structure and magnitude of the resulting flows. The fundamental solutions for the charge distribution and flow velocities induced by disclinations of topological charge m = -1/2, 1/2 and 1 are given. These solutions allow the analysis of several designer flows, such as "pusher" flows created by three colinear disclinations, the flow induced by an immersed spherical particle (equivalent to an m = 1 defect) and its accompanying m = -1 hyperbolic hedgehog defect, and the mechanism behind nonlinear ionic mobilities when the imposed field is perpendicular to the line joining the defects.

Liquid crystals with patterned molecular orientation as an electrolytic active medium.

Transport of fluids and particles at the microscale is an important theme in both fundamental and applied science. One of the most successful approaches is to use an electric field, which requires the system to carry or induce electric charges. We describe a versatile approach to generate electrokinetic flows by using a liquid crystal (LC) with surface-patterned molecular orientation as an electrolyte. The surface patterning is produced by photoalignment. In the presence of an electric field, the spatially varying orientation induces space charges that trigger flows of the LC. The active patterned LC electrolyte converts the electric energy into the LC flows and transport of embedded particles of any type (fluid, solid, gaseous) along a predesigned trajectory, posing no limitation on the electric nature (charge, polarizability) of these particles and interfaces. The patterned LC electrolyte exhibits a quadratic field dependence of the flow velocities; it induces persistent vortices of controllable rotation speed and direction that are quintessential for micro- and nanoscale mixing applications.

Bifurcation threshold of the delayed van der Pol oscillator under stochastic modulation.

We obtain the location of the Hopf bifurcation threshold for a modified van der Pol oscillator, parametrically driven by a stochastic source and including delayed feedback in both position and velocity. We introduce a multiple scale expansion near threshold, and we solve the resulting Fokker-Planck equation associated with the evolution at the slowest time scale. The analytical results are compared with a direct numerical integration of the model equation. Delay modifies the Hopf frequency at threshold and leads to a stochastic bifurcation that is shifted relative to the deterministic limit by an amount that depends on the delay time, the amplitude of the feedback terms, and the intensity of the noise. Interestingly, stochasticity generally increases the region of stability of the limit cycle.

Correlation times in stochastic equations with delayed feedback and multiplicative noise.

We obtain the characteristic correlation time associated with a model stochastic differential equation that includes the normal form of a pitchfork bifurcation and delayed feedback. In particular, the validity of the common assumption of statistical independence between the state at time t and that at t-τ, where τ is the delay time, is examined. We find that the correlation time diverges at the model's bifurcation line, thus signaling a sharp bifurcation threshold, and the failure of statistical independence near threshold. We determine the correlation time both by numerical integration of the governing equation, and analytically in the limit of small τ. The correlation time T diverges as T~a(-1), where a is the control parameter so that a=0 is the bifurcation threshold. The small-τ expansion correctly predicts the location of the bifurcation threshold, but there are systematic deviations in the magnitude of the correlation time.

Analytical determination of the bifurcation thresholds in stochastic differential equations with delayed feedback.

Analytical expressions for pitchfork and Hopf bifurcation thresholds are given for a nonlinear stochastic differential delay equation with feedback. Our results assume that the delay time τ is small compared to other characteristic time scales, not a significant limitation close to the bifurcation line. A pitchfork bifurcation line is found, the location of which depends on the conditional average , where x(t) is the dynamical variable. This conditional probability incorporates the combined effect of fluctuation correlations and delayed feedback. We also find a Hopf bifurcation line which is obtained by a multiple scale expansion around the oscillatory solution near threshold. We solve the Fokker-Planck equation associated with the slowly varying amplitudes and use it to determine the threshold location. In both cases, the predicted bifurcation lines are in excellent agreement with a direct numerical integration of the governing equations. Contrary to the known case involving no delayed feedback, we show that the stochastic bifurcation lines are shifted relative to the deterministic limit and hence that the interaction between fluctuation correlations and delay affect the stability of the solutions of the model equation studied.

Collapse transition of a hydrophobic self-avoiding random walk in a coarse-grained model solvent.

In order to study solvation effects on protein folding, we analyze the collapse transition of a self-avoiding random walk composed of hydrophobic segments that is embedded in a lattice model of a solvent. As expected, hydrophobic interactions lead to an attractive potential of mean force among chain segments. As a consequence, the random walk in solvent undergoes a collapse transition at a higher temperature than in its absence. Chain collapse is accompanied by the formation of a region depleted of solvent around the chain. In our simulation, the depleted region at collapse is as large as our computational domain.

Pitchfork and Hopf bifurcation thresholds in stochastic equations with delayed feedback.

The bifurcation diagram of a model stochastic differential equation with delayed feedback is presented. We are motivated by recent research on stochastic effects in models of transcriptional gene regulation. We start from the normal form for a pitchfork bifurcation, and add multiplicative or parametric noise and linear delayed feedback. The latter is sufficient to originate a Hopf bifurcation in that region of parameters in which there is a sufficiently strong negative feedback. We find a sharp bifurcation in parameter space, and define the threshold as the point in which the stationary distribution function p(x) changes from a delta function at the trivial state x=0 to p(x) approximately x(alpha) at small x (with alpha=-1 exactly at threshold). We find that the bifurcation threshold is shifted by fluctuations relative to the deterministic limit by an amount that scales linearly with the noise intensity. Analytic calculations of the bifurcation threshold are also presented in the limit of small delay tau-->0 that compare quite favorably with the numerical solutions even for moderate values of tau .