On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and Stability

In this paper we investigate the role of Parodi's relation in the well-posedness and stability of the general Ericksen-Leslie system modeling nematic liquid crystal flows. First, we give a formal physical derivation of the Ericksen-Leslie system through an appropriate energy variational approach under Parodi's relation, in which we can distinguish the conservative/dissipative parts of the induced elastic stress. Next, we prove global well-posedness and long-time behavior of the Ericksen-Leslie system under the assumption that the viscosity $\mu_4$ is sufficiently large. Finally, under Parodi's relation, we show the global well-posedness and Lyapunov stability for the Ericksen-Leslie system near local energy minimizers. The connection between Parodi's relation and linear stability of the Ericksen-Leslie system is also discussed

Trajectory attractors for the Sun-Liu model for nematic liquid crystals in 3D

In this paper we prove the existence of a trajectory attractor (in the sense of V.V. Chepyzhov and M.I. Vishik) for a nonlinear PDE system coming from a 3D liquid crystal model accounting for stretching effects. The system couples a nonlinear evolution equation for the director d (introduced in order to describe the preferred orientation of the molecules) with an incompressible Navier-Stokes equation for the evolution of the velocity field u. The technique is based on the introduction of a suitable trajectory space and of a metric accounting for the double-well type nonlinearity contained in the director equation. Finally, a dissipative estimate is obtained by using a proper integrated energy inequality. Both the cases of (homogeneous) Neumann and (non-homogeneous) Dirichlet boundary conditions for d are considered.Comment: 32 page

Flow-Induced Twist-Compression in a Twisted Nematic Cell

Lizhen Ruan and J. Roy Sambles, Physical Review Letters, Vol. 90, article 168701 (2003). "Copyright © 2003 by the American Physical Society."An optical convergent-beam guided-wave technique is used to explore in detail the dynamic flow effects in a twisted nematic cell. During switch-on it is found that the dynamic flow compresses the director twist to regions close to the cell walls. For high fields this twist compression takes the cell far beyond the Mauguin limit and it no longer effectively guides the polarization of the light through the cell. This results in a very fast switch to a transient dark state

Improving food production from livestock

This chapter is made accessible with permission from the Worldwatch Institute. Purchase the full report online at: http://www.nourishingtheplanet.or

A Preliminary Study on the Potential of Manuka Honey and Platelet-Rich Plasma in Wound Healing

Aim. The purpose of this study was to determine the in vitro response of cells critical to the wound healing process in culture media supplemented with a lyophilized preparation rich in growth factors (PRGF) and Manuka honey. Materials and Methods. This study utilized cell culture media supplemented with PRGF, as well as whole Manuka honey and the medical-grade Medihoney (MH), a Manuka honey product. The response of human fibroblasts (hDF), macrophages, and endothelial cells (hPMEC) was evaluated, with respect to cell proliferation, chemotaxis, collagen matrix production, and angiogenic potential, when subjected to culture with media containing PRGF, MH, Manuka honey, and a combination of PRGF and MH. Results. All three cell types demonstrated increases in cellular activity in the presence of PRGF, with further increases in activity seen in the presence of PRGF+MH. hDFs proved to be the most positively responsive cells, as they experienced enhanced proliferation, collagen matrix production, and migration into an in vitro wound healing model with the PRGF+MH-supplemented media. Conclusion. This preliminary in vitro study is the first to evaluate the combination of PRGF and Manuka honey, two products with the potential to increase regeneration individually, as a combined product to enhance dermal regeneration

Poisson-Bracket Approach to the Dynamics of Nematic Liquid Crystals. The Role of Spin Angular Momentum

Nematic liquid crystals are well modeled as a fluid of rigid rods. Starting from this model, we use a Poisson-bracket formalism to derive the equations governing the dynamics of nematic liquid crystals. We treat the spin angular momentum density arising from the rotation of constituent molecules about their centers of mass as an independent field and derive equations for it, the mass density, the momentum density, and the nematic director. Our equations reduce to the original Leslie-Ericksen equations, including the inertial director term that is neglected in the hydrodynamic limit, only when the moment of inertia for angular momentum parallel to the director vanishes and when a dissipative coefficient favoring locking of the angular frequencies of director rotation and spin angular momentum diverges. Our equations reduce to the equations of nematohydrodynamics in the hydrodynamic limit but with dissipative coefficients that depend on the coefficient that must diverge to produce the Leslie-Ericksen equations.Comment: 10 pages, to be published in Phys. Rev. E 72(5

A Preliminary Study on the Potential of Manuka Honey and Platelet-Rich Plasma in Wound Healing

Aim. The purpose of this study was to determine the in vitro response of cells critical to the wound healing process in culture media supplemented with a lyophilized preparation rich in growth factors (PRGF) and Manuka honey. Materials and Methods. This study utilized cell culture media supplemented with PRGF, as well as whole Manuka honey and the medical-grade Medihoney (MH), a Manuka honey product. The response of human fibroblasts (hDF), macrophages, and endothelial cells (hPMEC) was evaluated, with respect to cell proliferation, chemotaxis, collagen matrix production, and angiogenic potential, when subjected to culture with media containing PRGF, MH, Manuka honey, and a combination of PRGF and MH. Results. All three cell types demonstrated increases in cellular activity in the presence of PRGF, with further increases in activity seen in the presence of PRGF+MH. hDFs proved to be the most positively responsive cells, as they experienced enhanced proliferation, collagen matrix production, and migration into an in vitro wound healing model with the PRGF+MH-supplemented media. Conclusion. This preliminary in vitro study is the first to evaluate the combination of PRGF and Manuka honey, two products with the potential to increase regeneration individually, as a combined product to enhance dermal regeneration