Helfrich-Canham bending energy as a constrained non-linear sigma model

The Helfrich-Canham bending energy is identified with a non-linear sigma model for a unit vector. The identification, however, is dependent on one additional constraint: that the unit vector be constrained to lie orthogonal to the surface. The presence of this constraint adds a source to the divergence of the stress tensor for this vector so that it is not conserved. The stress tensor which is conserved is identified and its conservation shown to reproduce the correct shape equation.Comment: 5 page

From the Mendeleev periodic table to particle physics and back to the periodic table

We briefly describe in this paper the passage from Mendeleev's chemistry (1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and particle physics (from 1953 to 2006). We show how the consideration of symmetries, largely used in physics since the end of the 1920's, gave rise to a new format of the periodic table in the 1970's. More specifically, this paper is concerned with the application of the group SO(4,2)xSU(2) to the periodic table of chemical elements. It is shown how the Madelung rule of the atomic shell model can be used for setting up a periodic table that can be further rationalized via the group SO(4,2)xSU(2) and some of its subgroups. Qualitative results are obtained from this nonstandard table.Comment: 15 pages; accepted for publication in Foundations of Chemistry (special issue to commemorate the one hundredth anniversary of the death of Mendeleev who died in 1907); version 2: 16 pages; some sentences added; acknowledgment and references added; misprints correcte

Membrane geometry with auxiliary variables and quadratic constraints

Consider a surface described by a Hamiltonian which depends only on the metric and extrinsic curvature induced on the surface. The metric and the curvature, along with the basis vectors which connect them to the embedding functions defining the surface, are introduced as auxiliary variables by adding appropriate constraints, all of them quadratic. The response of the Hamiltonian to a deformation in each of the variables is examined and the relationship between the multipliers implementing the constraints and the conserved stress tensor of the theory established.Comment: 8 page

Phase ordering and shape deformation of two-phase membranes

Within a coupled-field Ginzburg-Landau model we study analytically phase separation and accompanying shape deformation on a two-phase elastic membrane in simple geometries such as cylinders, spheres and tori. Using an exact periodic domain wall solution we solve for the shape and phase ordering field, and estimate the degree of deformation of the membrane. The results are pertinent to a preferential phase separation in regions of differing curvature on a variety of vesicles.Comment: 4 pages, submitted to PR

On CP1 and CP2 maps and Weierstrass representations for surfaces immersed into multi-dimensional Euclidean spaces

An extension of the classic Enneper-Weierstrass representation for conformally parametrised surfaces in multi-dimensional spaces is presented. This is based on low dimensional CP^1 and CP^2 sigma models which allow the study of the constant mean curvature (CMC) surfaces immersed into Euclidean 3- and 8-dimensional spaces, respectively. Relations of Weierstrass type systems to the equations of these sigma models are established. In particular, it is demonstrated that the generalised Weierstrass representation can admit different CMC-surfaces in R^3 which have globally the same Gauss map. A new procedure for constructing CMC-surfaces in R^n is presented and illustrated in some explicit examples.Comment: arxiv version is already officia

Silicon particles as trojan horses for potential cancer therapy

[EN] Background: Porous silicon particles (PSiPs) have been used extensively as drug delivery systems, loaded with chemical species for disease treatment. It is well known from silicon producers that silicon is characterized by a low reduction potential, which in the case of PSiPs promotes explosive oxidation reactions with energy yields exceeding that of trinitrotoluene (TNT). The functionalization of the silica layer with sugars prevents its solubilization, while further functionalization with an appropriate antibody enables increased bioaccumulation inside selected cells. Results: We present here an immunotherapy approach for potential cancer treatment. Our platform comprises the use of engineered silicon particles conjugated with a selective antibody. The conceptual advantage of our system is that after reaction, the particles are degraded into soluble and excretable biocomponents. Conclusions: In our study, we demonstrate in particular, specific targeting and destruction of cancer cells in vitro. The fact that the LD50 value of PSiPs-HER-2 for tumor cells was 15-fold lower than the LD50 value for control cells demonstrates very high in vitro specificity. This is the first important step on a long road towards the design and development of novel chemotherapeutic agents against cancer in general, and breast cancer in particular.The authors acknowledge financial support from the following projects FIS2009-07812, MAT2012-35040, PROMETEO/2010/043, CTQ2011-23167, CrossSERS, FP7 MC-IEF 329131, and HSFP (project RGP0052/2012) and Medcom Tech SA. Xiang Yu acknowledges support by the Chinese government (CSC, Nr. 2010691036).Fenollosa Esteve, R.; Garcia-Rico, E.; Alvarez, S.; Alvarez, R.; Yu, X.; Rodriguez, I.; Carregal-Romero, S.... (2014). Silicon particles as trojan horses for potential cancer therapy. 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The `Friction' of Vacuum, and other Fluctuation-Induced Forces

The static Casimir effect describes an attractive force between two conducting plates, due to quantum fluctuations of the electromagnetic (EM) field in the intervening space. {\it Thermal fluctuations} of correlated fluids (such as critical mixtures, super-fluids, liquid crystals, or electrolytes) are also modified by the boundaries, resulting in finite-size corrections at criticality, and additional forces that effect wetting and layering phenomena. Modified fluctuations of the EM field can also account for the `van der Waals' interaction between conducting spheres, and have analogs in the fluctuation--induced interactions between inclusions on a membrane. We employ a path integral formalism to study these phenomena for boundaries of arbitrary shape. This allows us to examine the many unexpected phenomena of the dynamic Casimir effect due to moving boundaries. With the inclusion of quantum fluctuations, the EM vacuum behaves essentially as a complex fluid, and modifies the motion of objects through it. In particular, from the mechanical response function of the EM vacuum, we extract a plethora of interesting results, the most notable being: (i) The effective mass of a plate depends on its shape, and becomes anisotropic. (ii) There is dissipation and damping of the motion, again dependent upon shape and direction of motion, due to emission of photons. (iii) There is a continuous spectrum of resonant cavity modes that can be excited by the motion of the (neutral) boundaries.Comment: RevTex, 2 ps figures included. The presentation is completely revised, and new sections are adde

SiOx/SiNy multilayers for photovoltaic and photonic applications

Microstructural, electrical, and optical properties of undoped and Nd3+-doped SiOx/SiNy multilayers fabricated by reactive radio frequency magnetron co-sputtering have been investigated with regard to thermal treatment. This letter demonstrates the advantages of using SiNy as the alternating sublayer instead of SiO2. A high density of silicon nanoclusters of the order 1019 nc/cm3 is achieved in the SiOx sublayers. Enhanced conductivity, emission, and absorption are attained at low thermal budget, which are promising for photovoltaic applications. Furthermore, the enhancement of Nd3+ emission in these multilayers in comparison with the SiOx/SiO2 counterparts offers promising future photonic applications

The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete