Hamiltonian Frenet-Serret dynamics

The Hamiltonian formulation of the dynamics of a relativistic particle described by a higher-derivative action that depends both on the first and the second Frenet-Serret curvatures is considered from a geometrical perspective. We demonstrate how reparametrization covariant dynamical variables and their projections onto the Frenet-Serret frame can be exploited to provide not only a significant simplification of but also novel insights into the canonical analysis. The constraint algebra and the Hamiltonian equations of motion are written down and a geometrical interpretation is provided for the canonical variables.Comment: Latex file, 14 pages, no figures. Revised version to appear in Class. Quant. Gra

Covariant perturbations of domain walls in curved spacetime

A manifestly covariant equation is derived to describe the perturbations in a domain wall on a given background spacetime. This generalizes recent work on domain walls in Minkowski space and introduces a framework for examining the stability of relativistic bubbles in curved spacetimes.Comment: 15 pages,ICN-UNAM-93-0

Guided and magnetic self-assembly of tunable magnetoceptive gels

Self-assembly of components into complex functional patterns at microscale is common in nature, and used increasingly in numerous disciplines such as optoelectronics, microfabrication, sensors, tissue engineering and computation. Here, we describe the use of stable radicals to guide the self-assembly of magnetically tunable gels, which we call ‘magnetoceptive’ materials at the scale of hundreds of microns to a millimeter, each can be programmed by shape and composition, into heterogeneous complex structures. Using paramagnetism of free radicals as a driving mechanism, complex heterogeneous structures are built in the magnetic field generated by permanent magnets. The overall magnetic signature of final structure is erased via an antioxidant vitamin E, subsequent to guided self-assembly. We demonstrate unique capabilities of radicals and antioxidants in fabrication of soft systems with heterogeneity in material properties, such as porosity, elastic modulus and mass density; then in bottom-up tissue engineering and finally, levitational and selective assembly of microcomponents

Impact of maximum back-EMF limits on the performance characteristics of interior permanent magnet synchronous machines

Interior permanent magnet (IPM) synchronous machines are vulnerable to uncontrolled generator (UCG) faults at high speed that can damage the inverter. One approach to reducing this risk is to impose limits on the maximum machine back-EMF voltage at top speed. This paper presents the results of a comparative design study that clarifies the nature and extent of the penalties imposed on the IPM machine metrics and performance characteristics as a result of imposing progressively tighter values of back-EMF voltage limits. As an alternative to limiting back-EMF and penalizing machine designs, this paper also investigates the effectiveness of the system-side protection approach to the same UCG fault problem.Seok-hee Han, Thomas M. Jahns, Metin Aydin, Mustafa K. Guven, Wen L. Soon

Recapitulating cranial osteogenesis with neural crest cells in 3-D microenvironments

The experimental systems that recapitulate the complexity of native tissues and enable precise control over the microenvironment are becoming essential for the pre-clinical tests of therapeutics and tissue engineering. Here, we described a strategy to develop an in vitro platform to study the developmental biology of craniofacial osteogenesis. In this study, we directly osteo-differentiated cranial neural crest cells (CNCCs) in a 3-D in vitro bioengineered microenvironment. Cells were encapsulated in the gelatin-based photo-crosslinkable hydrogel and cultured up to three weeks. We demonstrated that this platform allows efficient differentiation of p75 positive CNCCs to cells expressing osteogenic markers corresponding to the sequential developmental phases of intramembranous ossification. During the course of culture, we observed a decrease in the expression of early osteogenic marker Runx2, while the other mature osteoblast and osteocyte markers such as Osterix, Osteocalcin, Osteopontin and Bone sialoprotein increased. We analyzed the ossification of the secreted matrix with alkaline phosphatase and quantified the newly secreted hydroxyapatite. The Field Emission Scanning Electron Microscope (FESEM) images of the bioengineered hydrogel constructs revealed the native-like osteocytes, mature osteoblasts, and cranial bone tissue morphologies with canaliculus-like intercellular connections. This platform provides a broadly applicable model system to potentially study diseases involving primarily embryonic craniofacial bone disorders, where direct diagnosis and adequate animal disease models are limited

The Jang equation, apparent horizons, and the Penrose inequality

The Jang equation in the spherically symmetric case reduces to a first order equation. This permits an easy analysis of the role apparent horizons play in the (non)existence of solutions. We demonstrate that the proposed derivation of the Penrose inequality based on the Jang equation cannot work in the spherically symmetric case. Thus it is fruitless to apply this method, as it stands, to the general case. We show also that those analytic criteria for the formation of horizons that are based on the use of the Jang equation are of limited validity for the proof of the trapped surface conjecture.Comment: minor misprints correcte

The isolation of gravitational instantons: Flat tori V flat R^4

The role of topology in the perturbative solution of the Euclidean Einstein equations about flat instantons is examined.Comment: 15 pages, ICN-UNAM 94-1

Untethered micro-robotic coding of three-dimensional material composition

Complex functional materials with three-dimensional micro- or nano-scale dynamic compositional features are prevalent in nature. However, the generation of three-dimensional functional materials composed of both soft and rigid microstructures, each programmed by shape and composition, is still an unsolved challenge. Herein, we describe a method to code complex materials in three-dimensions with tunable structural, morphological, and chemical features using an untethered magnetic micro-robot remotely controlled by magnetic fields. This strategy allows the micro-robot to be introduced to arbitrary microfluidic environments for remote two- and three-dimensional manipulation. We demonstrate the coding of soft hydrogels, rigid copper bars, polystyrene beads, and silicon chiplets into three-dimensional heterogeneous structures. We also use coded microstructures for bottom-up tissue engineering by generating cell-encapsulating constructs

Axially symmetric membranes with polar tethers

Axially symmetric equilibrium configurations of the conformally invariant Willmore energy are shown to satisfy an equation that is two orders lower in derivatives of the embedding functions than the equilibrium shape equation, not one as would be expected on the basis of axial symmetry. Modulo a translation along the axis, this equation involves a single free parameter c.If c\ne 0, a geometry with spherical topology will possess curvature singularities at its poles. The physical origin of the singularity is identified by examining the Noether charge associated with the translational invariance of the energy; it is consistent with an external axial force acting at the poles. A one-parameter family of exact solutions displaying a discocyte to stomatocyte transition is described.Comment: 13 pages, extended and revised version of Non-local sine-Gordon equation for the shape of axi-symmetric membrane

Hamilton's equations for a fluid membrane: axial symmetry

Consider a homogenous fluid membrane, or vesicle, described by the Helfrich-Canham energy, quadratic in the mean curvature. When the membrane is axially symmetric, this energy can be viewed as an `action' describing the motion of a particle; the contours of equilibrium geometries are identified with particle trajectories. A novel Hamiltonian formulation of the problem is presented which exhibits the following two features: {\it (i)} the second derivatives appearing in the action through the mean curvature are accommodated in a natural phase space; {\it (ii)} the intrinsic freedom associated with the choice of evolution parameter along the contour is preserved. As a result, the phase space involves momenta conjugate not only to the particle position but also to its velocity, and there are constraints on the phase space variables. This formulation provides the groundwork for a field theoretical generalization to arbitrary configurations, with the particle replaced by a loop in space.Comment: 11 page