Alignment Order Parameters Research Articles

Migration of active filaments under Poiseuille flow in a microcapillary tube.

We present a comprehensive study of active filaments confined in a cylindrical channel under Poiseuille flow. The activity drives the filament towards the channel boundary, whereas external fluid flow migrates the filament away from the boundary. This migration further shifts towards the centre for higher flow strength. The migration behaviour of the filaments is presented in terms of the alignment order parameter that shows the alignment grows with shear and activity. Further, we have also addressed the role of length of filament on the migration behaviour, which suggests higher migration for larger filaments. Moreover, we discuss the polar ordering of filaments as a function of distance from the centre of channel that displays upstream motion near the boundary and downstream motion at the centre of the tube.

Optimal collision avoidance in swarms of active Brownian particles

The effectiveness of collective navigation of biological or artificial agents requires to accommodate for contrasting requirements, such as staying in a group while avoiding close encounters and at the same time limiting the energy expenditure for maneuvering. Here, we address this problem by considering a system of active Brownian particles in a finite two-dimensional domain and ask what is the control that realizes the optimal tradeoff between collision avoidance and control expenditure. We couch this problem in the language of optimal stochastic control theory and by means of a mean-field game approach we derive an analytic mean-field solution, characterized by a second-order phase transition in the alignment order parameter. We find that a mean-field version of a classical model for collective motion based on alignment interactions (Vicsek model) performs remarkably close to the optimal control. Our results substantiate the view that observed group behaviors may be explained as the result of optimizing multiple objectives and offer a theoretical ground for biomimetic algorithms used for artificial agents.

Polarization resolved radiation angular patterns of orientationally ordered nanorods

We combine the transfer matrix based algebraic approach with the Green’s function method to theoretically study polarization resolved far-field angular distributions of photoluminescence from quantum nanorods (NRs) embedded in an optically anisotropic film. The emission and excitation properties of NRs are described by the emission and excitation anisotropy tensors. These tensors and the solution of the emission problem expressed in terms of the evolution operators are used to derive the orientationally averaged coherency matrix of the emitted wavefield. For the case of in-plane alignment and unpolarized excitation, we estimate the emission anisotropy parameter and compute the angular profiles for the photoluminescence polarization parameters such as the degree of linear polarization, the Stokes parameter s1, the ellipticity and the polarization azimuth. We show that the alignment order parameter has a profound effect on the angular profiles.

Extracting cellular automaton rules from physical Langevin equation models for single and collective cell migration

Cellular automata (CA) are discrete time, space, and state models which are extensively used for modeling biological phenomena. CA are "on-lattice" models with low computational demands. In particular, lattice-gas cellular automata (LGCA) have been introduced as models of single and collective cell migration. The interaction rule dictates the behavior of a cellular automaton model and is critical to the model's biological relevance. The LGCA model's interaction rule has been typically chosen phenomenologically. In this paper, we introduce a method to obtain lattice-gas cellular automaton interaction rules from physically-motivated "off-lattice" Langevin equation models for migrating cells. In particular, we consider Langevin equations related to single cell movement (movement of cells independent of each other) and collective cell migration (movement influenced by cell-cell interactions). As examples of collective cell migration, two different alignment mechanisms are studied: polar and nematic alignment. Both kinds of alignment have been observed in biological systems such as swarms of amoebae and myxobacteria. Polar alignment causes cells to align their velocities parallel to each other, whereas nematic alignment drives cells to align either parallel or antiparallel to each other. Under appropriate assumptions, we have derived the LGCA transition probability rule from the steady-state distribution of the off-lattice Fokker-Planck equation. Comparing alignment order parameters between the original Langevin model and the derived LGCA for both mechanisms, we found different areas of agreement in the parameter space. Finally, we discuss potential reasons for model disagreement and propose extensions to the CA rule derivation methodology.

Effect of orientation on the piezoresistivity of mechanically drawn single walled carbon nanotube (SWCNT) thin films

Mechanically drawn SWCNT thin films were prepared and systematically investigated for understanding the effect of SWCNT orientation on the piezoresistive response of SWCNT thin film based piezoresistive sensors. Through polarized Raman spectroscopy analysis and coupled electrical–mechanical test, a quantitative relationship between the piezoresistive sensitivity and SWCNT alignment order parameter was established. This along with the morphological characterization, film area and sheet resistance measurement allow identifying the critical roles of SWCNT orientation, packing density, and micro-crack formation in dictating the piezoresistivity of mechanically drawn SWCNT thin film strain sensors. As compared to the randomly oriented SWCNT thin film sensor, the one with draw ratio of 3.2 exhibited 6times increase on the gauge factor.

Nanoparticle‐Driven Orientation Transition and Soft‐Shear Alignment in Diblock Copolymer Films via Dynamic Thermal Gradient Field

Sharp dynamic thermal gradient (∇T ≈ 45 °C mm(-1)) field-driven assembly of cylinder-forming block copolymer (c-BCP) films filled with PS-coated gold nanoparticles (AuNPs; dNP ≈ 3.6 nm, φNP ≈ 0-0.1) is studied. The influence of increasing AuNP loading fraction on dispersion and assembly of AuNPs within c-BCP (PS-PMMA) films is investigated via both static and dynamic thermal gradient fields. With φNP increasing, a sharp transition from vertical to random in-plane horizontal cylinder orientation is observed due to enrichment of AuNPs at the substrate side and favorable interaction of PMMA chains with gold cores. Furthermore, a detachable capping elastomer layer can self-align these random oriented PMMA microdomains into unidirectional hybrid AuNP/c-BCP nanolines, quantified with an alignment order parameter, S.

Synthesis and optical properties of a carbazole-containing novel oligomer

We report on the synthesis and optical properties of a novel oligomer (oligo(2-{2-but-1-enyl-6-[2-(9-decyl-6-formyl-9 H-carbazol-3-yl)-vinyl]-pyran-4-ylidene}-malononitrile)) (Olg(Cz–Pyr–CN)) with an average degree of polymerization three. The molecule was designed to have push–pull structure and was synthesized by Knovenagel condensation reaction. The resulting Olg(Cz–Pyr–CN) was characterized by means of 1H NMR spectroscopy and IR spectroscopy. The initial decomposition temperature ( T id) of Olg(Cz–Pyr–CN) appeared at 372 °C. The alignment order parameter of the poled Olg(Cz–Pyr–CN) film was 0.31. The electro-optic (EO) coefficients ( r 33) and their NLO properties were evaluated by simple reflection and the Maker fringe method. The EO coefficients of Olg(Cz–Pyr–CN) was found to be 28.7 pm/V at 632.8 nm.

Top-down approach in protein RDC data analysis: de novo estimation of the alignment tensor

In solution NMR spectroscopy the residual dipolar coupling (RDC) is invaluable in improving both the precision and accuracy of NMR structures during their structural refinement. The RDC also provides a potential to determine protein structure de novo. These procedures are only effective when an accurate estimate of the alignment tensor has already been made. Here we present a top-down approach, starting from the secondary structure elements and finishing at the residue level, for RDC data analysis in order to obtain a better estimate of the alignment tensor. Using only the RDCs from N-H bonds of residues in alpha-helices and CA-CO bonds in beta-strands, we are able to determine the offset and the approximate amplitude of the RDC modulation-curve for each secondary structure element, which are subsequently used as targets for global minimization. The alignment order parameters and the orientation of the major principal axis of individual helix or strand, with respect to the alignment frame, can be determined in each of the eight quadrants of a sphere. The following minimization against RDC of all residues within the helix or strand segment can be carried out with fixed alignment order parameters to improve the accuracy of the orientation. For a helical protein Bax, the three components A(xx), A(yy) and A(zz), of the alignment order can be determined with this method in average to within 2.3% deviation from the values calculated with the available atomic coordinates. Similarly for beta-sheet protein Ubiquitin they agree in average to within 8.5%. The larger discrepancy in beta-strand parameters comes from both the diversity of the beta-sheet structure and the lower precision of CA-CO RDCs. This top-down approach is a robust method for alignment tensor estimation and also holds a promise for providing a protein topological fold using limited sets of RDCs.

低屈折率異方性のツイスト配向ゲストホスト液晶を用いた反射型表示素子

We fabricated reflective display devices using twisted-alignment guest-host liquid crystal with low refractive index anisotropy and evaluated their electro-optic properties. The dark state reflectance of the devices was reduced to 1/3 by using the liquid crystal (containing dichroic dye) with low refractive index anisotropy. The bright state reflectance could keep more than 50% by using liquid crystal with a high alignment order parameter. These results indicated that high-contrast reflective display devices can be made using a liquid crystal material with low refractive index anisotropy and a high order parameter.

Viscosities of Nematic and Discotic Nematic Liquid Crystals According to the Affine Transformation Model

An affine transformation model is used to calculate the macroscopic stress tensor for uniaxial liquid crystals. In the special case of constant degrees of alignment, it is shown to be of the form occurring in the Ericksen-Leslie director theory for nematic liquid crystals, resolving an apparent discrepancy on the form of the stress tensor. The corresponding Leslie and Miesowicz viscosities are calculated in terms of the alignment order parameters and those of the affine model. These results improve the approximate calculations of Ehrentraut and Hess [Phys. Reo. E 51, 2203 (1995)] based on a hindered rotation assumption. It is further shown that the calculated orientation-dependence of the viscosities based on the affine model is the same as that resulting from calculations based on an alternative Fokker-Planck equation for the one particle orientational distribution function.

On the Signs of the Leslie Viscosities α2 and α3 for Nematics and Discotic Nematics

The signs of the Leslie viscosities α2 and α3 for rod-like and disc-like molecules in the uniaxial nematic phase are discussed using a dynamic molecular mean field theory based upon a Fokker-Planck equation. The viscosities are shown to depend on the particle geometry and alignment order parameters. In particular, for positive degree of alignment S 2, the calculations tend to confirm Carlsson's conjecture relating the signs of the two viscosities to the particle geometry. Furthermore, a transition in the signs of α2 for discotics and α3 for nematics is predicted with increasing order parameter S 2 in accord with recent experiments. For small degree of alignment S 2, the results reproduce previous calculations obtained by Hess in a truncation approximation. The qualitative flow behaviour depends upon the signs of these viscosities.

On the Unified Theory for Non-Equilibrium Phenomena in the Isotropic and Nematic Phases of a Liquid Crystal; Spatially Inhomogeneous Alignment

Abstract A nonlinear equation is derived which describes the relaxation of the alignment and the flow alignment in the isotropic and nematic phases of a liquid crystal. In addition to the previously treated case, contributions associated with spatial derivatives of the alignment are taken into account which stem from gradient terms occuring in the free energy (elastic energy) and from the flux of the alignment. Some applications are discussed. In particular, the Leslie and Frank coefficients of the nematic phase are expressed in terms of the equilibrium alignment order parameter and coefficients which are meaningful in both phases