The Power of Poincar\'e: Elucidating the Hidden Symmetries in Focal Conic Domains

Focal conic domains are typically the "smoking gun" by which smectic liquid crystalline phases are identified. The geometry of the equally-spaced smectic layers is highly generic but, at the same time, difficult to work with. In this Letter we develop an approach to the study of focal sets in smectics which exploits a hidden Poincar\'e symmetry revealed only by viewing the smectic layers as projections from one-higher dimension. We use this perspective to shed light upon several classic focal conic textures, including the concentric cyclides of Dupin, polygonal textures and tilt-grain boundaries.Comment: 4 pages, 3 included figure

Topological mechanics of origami and kirigami

Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major obstacle to exploiting this property is the scarcity of tools to identify and program the flexibility of fold patterns. We exploit a recent connection between spring networks and quantum topological states to design origami with localized folding motions at boundaries and study them both experimentally and theoretically. These folding motions exist due to an underlying topological invariant rather than a local imbalance between constraints and degrees of freedom. We give a simple example of a quasi-1D folding pattern that realizes such topological states. We also demonstrate how to generalize these topological design principles to two dimensions. A striking consequence is that a domain wall between two topologically distinct, mechanically rigid structures is deformable even when constraints locally match the degrees of freedom.Comment: 5 pages, 3 figures + ~5 pages S

Colloquium : disclination loops, point defects, and all that in nematic liquid crystals

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress was made in controlling and measuring colloidal inclusions in liquid crystalline phases. The topological structure of these systems is quite rich but, at the same time, subtle. Motivated by experiment and the power of topological reasoning, the classification of defects in uniaxial nematic liquid crystals was reviewed and expounded upon. Particular attention was paid to the ambiguities that arise in these systems, which have no counterpart in the much-storied XY model or the Heisenberg ferromagnet

Response to pulmonary arterial hypertension drug therapies in patients with pulmonary arterial hypertension and cardiovascular risk factors.

The age at diagnosis of pulmonary arterial hypertension (PAH) and the prevalence of cardiovascular (CV) risk factors are increasing. We sought to determine whether the response to drug therapy was influenced by CV risk factors in PAH patients. We studied consecutive incident PAH patients (n = 146) between January 1, 2008, and July 15, 2011. Patients were divided into two groups: the PAH-No CV group included patients with no CV risk factors (obesity, systemic hypertension, type 2 diabetes mellitus, permanent atrial fibrillation, mitral and/or aortic valve disease, and coronary artery disease), and the PAH-CV group included patients with at least one. The response to PAH treatment was analyzed in all the patients who received PAH drug therapy. The PAH-No CV group included 43 patients, and the PAH-CV group included 69 patients. Patients in the PAH-No CV group were younger than those in the PAH-CV group (P < 0.0001). In the PAH-No CV group, 16 patients (37%) improved on treatment and 27 (63%) did not improve, compared with 11 (16%) and 58 (84%) in the PAH-CV group, respectively (P = 0.027 after adjustment for age). There was no difference in survival at 30 months (P = 0.218). In conclusion, in addition to older age, CV risk factors may predict a reduced response to PAH drug therapy in patients with PAH

The design and analysis of a large angular range, two-axis flexure assembly

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1988.Bibliography: leaf 97.by Barry A. Gin.M.S

Intermediate Wakimoto modules for Affine sl(n+1)

We construct certain boson type realizations of affine sl(n+1) that depend on a parameter r. When r=0 we get a Fock space realization of Imaginary Verma modules appearing in the work of the first author and when r=n they are the Wakimoto modules described in the work of Feigin and Frenkel

Optimum structure for a uniform load over multiple spans

This paper presents a new half-plane Michell structure that transmits a uniformly distributed load of infinite horizontal extent to a series of equally-spaced pinned supports. Full kinematic description of the structure is obtained for the case when the maximum allowable tensile stress is greater than or equal to the allowable compressive stress. Although formal proof of optimality of the solution presented is not yet available, the proposed analytical solution is supported by substantial numerical evidence, involving the solution of problems with in excess of 10 billion potential members. Furthermore, numerical solutions for various combinations of unequal allowable stresses suggest the existence of a family of related, simple, and practically relevant structures, which range in form from a Hemp-type arch with vertical hangers to a structure which strongly resembles a cable-stayed bridge