Solving the brachistochrone and other variational problems with soap films

We show a method to solve the problem of the brachistochrone as well as other variational problems with the help of the soap films that are formed between two suitable surfaces. We also show the interesting connection between some variational problems of dynamics, statics, optics, and elasticity.Comment: 16 pages, 11 figures. This article, except for a small correction, has been submitted to the American Journal of Physic

THE INTRACELLULAR DISTRIBUTION OF GAMMA GLOBULIN IN A MOUSE PLASMA CELL TUMOR (X5563) AS REVEALED BY FLUORESCENCE AND ELECTRON MICROSCOPY

Ferritin- and fluorescein-conjugated antibody staining has been applied to a study of a mouse plasma cell tumor. The presence of myeloma globulin within cisternae of the endoplasmic reticulum was observed at a stage of the secretory process when the remainder of the cytoplasm was essentially free of labeled globulin. The distribution of ferritin suggested a functional heterogeneity among units of the endoplasmic reticulum. Apparently, progressive accumulation of globulin results in distension of the endoplasmic reticulum and, occasionally, in the appearance of considerable quantities of this secretory protein in the extracisternal cytoplasmic matrix. Participation of the Golgi apparatus in the packaging and release of small quantitites of globulin seems likely. In addition, however, fragmentation of the peripheral cytoplasm with rupture of distended ergastoplasmic vesicles appeared to be another pathway whereby globulin is secreted

Minimal surfaces bounded by elastic lines

In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in soapy water and then removing it; the shape of the spanning soap film is a solution to the Plateau problem. But what happens if a soap film spans a loop of inextensible but flexible wire? We consider this simple query that couples Plateau's problem to Euler's Elastica: a special class of twist-free curves of given length that minimize their total squared curvature energy. The natural marriage of two of the oldest geometrical problems linking physics and mathematics leads to a quest for the shape of a minimal surface bounded by an elastic line: the Euler-Plateau problem. We use a combination of simple physical experiments with soap films that span soft filaments, scaling concepts, exact and asymptotic analysis combined with numerical simulations to explore some of the richness of the shapes that result. Our study raises questions of intrinsic interest in geometry and its natural links to a range of disciplines including materials science, polymer physics, architecture and even art.Comment: 14 pages, 4 figures. Supplementary on-line material: http://www.seas.harvard.edu/softmat/Euler-Plateau-problem

Surfaces immersed in su(N+1) Lie algebras obtained from the CP^N sigma models

We study some geometrical aspects of two dimensional orientable surfaces arrising from the study of CP^N sigma models. To this aim we employ an identification of R^(N(N+2)) with the Lie algebra su(N+1) by means of which we construct a generalized Weierstrass formula for immersion of such surfaces. The structural elements of the surface like its moving frame, the Gauss-Weingarten and the Gauss-Codazzi-Ricci equations are expressed in terms of the solution of the CP^N model defining it. Further, the first and second fundamental forms, the Gaussian curvature, the mean curvature vector, the Willmore functional and the topological charge of surfaces are expressed in terms of this solution. We present detailed implementation of these results for surfaces immersed in su(2) and su(3) Lie algebras.Comment: 32 pages, 1 figure; changes: major revision of presentation, clarifications adde

On Uniqueness of Boundary Blow-up Solutions of a Class of Nonlinear Elliptic Equations

We study boundary blow-up solutions of semilinear elliptic equations $Lu=u_+^p$ with $p>1$, or $Lu=e^{au}$ with $a>0$, where $L$ is a second order elliptic operator with measurable coefficients. Several uniqueness theorems and an existence theorem are obtained.Comment: To appear in Comm. Partial Differential Equations; 10 page

Topology and Signature Changes in Braneworlds

It has been believed that topology and signature change of the universe can only happen accompanied by singularities, in classical, or instantons, in quantum, gravity. In this note, we point out however that in the braneworld context, such an event can be understood as a classical, smooth event. We supply some explicit examples of such cases, starting from the Dirac-Born-Infeld action. Topology change of the brane universe can be realised by allowing self-intersecting branes. Signature change in a braneworld is made possible in an everywhere Lorentzian bulk spacetime. In our examples, the boundary of the signature change is a curvature singularity from the brane point of view, but nevertheless that event can be described in a completely smooth manner from the bulk point of view.Comment: 26 pages, 8 figures, references and comments are added, minor revisions and a number of additional footnotes added, error corrected, minor corrections, to appear in Class. Quant. Gra

Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds

Let s be at least 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s,s) which are not locally homogeneous but whose curvature tensors never the less exhibit a number of important symmetry properties. They are curvature homogeneous; their curvature tensor is modeled on that of a local symmetric space. They are spacelike Jordan Osserman with a Jacobi operator which is nilpotent of order 3; they are not timelike Jordan Osserman. They are k-spacelike higher order Jordan Osserman for $2\le k\le s$; they are k-timelike higher order Jordan Osserman for $s+2\le k\le 2s$, and they are not k timelike higher order Jordan Osserman for $2\le s\le s+1$.Comment: Update bibliography, fix minor misprint

Late Onset Myasthenia Gravis Is Associated with HLA DRB1*15:01 in the Norwegian Population

BACKGROUND: Acquired myasthenia gravis (MG) is a rare antibody-mediated autoimmune disease caused by impaired neuromuscular transmission, leading to abnormal muscle fatigability. The aetiology is complex, including genetic risk factors of the human leukocyte antigen (HLA) complex and unknown environmental factors. Although associations between the HLA complex and MG are well established, not all involved components of the HLA predisposition to this heterogeneous disease have been revealed. Well-powered and comprehensive HLA analyses of subgroups in MG are warranted, especially in late onset MG. METHODOLOGY/PRINCIPAL FINDINGS: This case-control association study is of a large population-based Norwegian cohort of 369 MG patients and 651 healthy controls. We performed comprehensive genotyping of four classical HLA loci (HLA-A, -B, -C and -DRB1) and showed that the DRB1*15:01 allele conferred the strongest risk in late onset MG (LOMG; onset ≥ 60 years) (OR 2.38, p(c)7.4 × 10(-5)). DRB1*13:01 was found to be a protective allele for both early onset MG (EOMG) and LOMG (OR 0.31, p(c) 4.71 × 10(-4)), a finding not previously described. No significant association was found to the DRB1*07:01 allele (p(nc) = 0.18) in a subset of nonthymomatous anti-titin antibody positive LOMG as reported by others. HLA-B*08 was mapped to give the strongest contribution to EOMG, supporting previous studies. CONCLUSION: The results from this study provide important new information concerning the susceptibility of HLA alleles in Caucasian MG, with highlights on DRB1*15:01 as being a major risk allele in LOMG

Myasthenia gravis

Myasthenia gravis (MG) is a rare, autoimmune neuromuscular junction disorder. Contemporary prevalence rates approach 1/5,000. MG presents with painless, fluctuating, fatigable weakness involving specific muscle groups. Ocular weakness with asymmetric ptosis and binocular diplopia is the most typical initial presentation, while early or isolated oropharyngeal or limb weakness is less common. The course is variable, and most patients with initial ocular weakness develop bulbar or limb weakness within three years of initial symptom onset. MG results from antibody-mediated, T cell-dependent immunologic attack on the endplate region of the postsynaptic membrane. In patients with fatigable muscle weakness, the diagnosis of MG is supported by: 1. pharmacologic testing with edrophonium chloride that elicits unequivocal improvement in strength; 2. electrophysiologic testing with repetitive nerve stimulation (RNS) studies and/or single-fiber electromyography (SFEMG) that demonstrates a primary postsynaptic neuromuscular junctional disorder; and 3. serologic demonstration of acetylcholine receptor (AChR) or muscle-specific tyrosine kinase (MuSK) antibodies. Differential diagnosis includes congenital myasthenic syndromes, Lambert Eaton syndrome, botulism, organophosphate intoxication, mitochondrial disorders involving progressive external ophthalmoplegia, acute inflammatory demyelinating polyradiculoneuropathy (AIDP), motor neuron disease, and brainstem ischemia. Treatment must be individualized, and may include symptomatic treatment with cholinesterase inhibitors and immune modulation with corticosteroids, azathioprine, cyclosporine, and mycophenolate mofetil. Rapid, temporary improvement may be achieved for myasthenic crises and exacerbations with plasma exchange (PEX) or intravenous immunoglobulin (IVIg). Owing to improved diagnostic testing, immunotherapy, and intensive care, the contemporary prognosis is favorable with less than five percent mortality and nearly normal life expectancy