On the differential geometry of curves in Minkowski space

We discuss some aspects of the differential geometry of curves in Minkowski space. We establish the Serret-Frenet equations in Minkowski space and use them to give a very simple proof of the fundamental theorem of curves in Minkowski space. We also state and prove two other theorems which represent Minkowskian versions of a very known theorem of the differential geometry of curves in tridimensional Euclidean space. We discuss the general solution for torsionless paths in Minkowki space. We then apply the four-dimensional Serret-Frenet equations to describe the motion of a charged test particle in a constant and uniform electromagnetic field and show how the curvature and the torsions of the four-dimensional path of the particle contain information on the electromagnetic field acting on the particle.Comment: 10 pages. Typeset using REVTE

Programmed buckling by controlled lateral swelling in a thin elastic sheet

Recent experiments have imposed controlled swelling patterns on thin polymer films, which subsequently buckle into three-dimensional shapes. We develop a solution to the design problem suggested by such systems, namely, if and how one can generate particular three-dimensional shapes from thin elastic sheets by mere imposition of a two-dimensional pattern of locally isotropic growth. Not every shape is possible. Several types of obstruction can arise, some of which depend on the sheet thickness. We provide some examples using the axisymmetric form of the problem, which is analytically tractable.Comment: 11 pages, 9 figure

Suscetibilidade dos estágios imaturos de Trichogramma pretiosum a óleos inseticidas.

O objetivo desse trabalho foi avaliar a suscetibilidade das fases imaturas do parasitoide Trichogramma pretiosum a óleos vegetais e sintéticos utilizados no controle fitossanitário de pragas.Resumo

Soliton surfaces associated with symmetries of ODEs written in Lax representation

The main aim of this paper is to discuss recent results on the adaptation of the Fokas-Gel'fand procedure for constructing soliton surfaces in Lie algebras, which was originally derived for PDEs [Grundland, Post 2011], to the case of integrable ODEs admitting Lax representations. We give explicit forms of the \g-valued immersion functions based on conformal symmetries involving the spectral parameter, a gauge transformation of the wave function and generalized symmetries of the linear spectral problem. The procedure is applied to a symmetry reduction of the static $\phi^4$-field equations leading to the Jacobian elliptic equation. As examples, we obtain diverse types of surfaces for different choices of Jacobian elliptic functions for a range of values of parameters.Comment: 14 Pages, 2 figures Conference Proceedings for QST7 Pragu

Aharonov-Bohm-like effect for light propagating in nematics with disclinations

Using a geometric approach for the propagation of light in anisotropic media, we investigate what effect the director field of disclinations may have on the polarization state of light. Parallel transport around the defect, of the spinor describing the polarization, indicates the acquisition of a topological phase, in analogy with the Aharonov-Bohm effect.Comment: 6 pages, to appear in Europhysics Letter

Primary and secondary scintillation measurements in a xenon Gas Proportional Scintillation Counter

NEXT is a new experiment to search for neutrinoless double beta decay using a 100 kg radio-pure high-pressure gaseous xenon TPC. The detector requires excellent energy resolution, which can be achieved in a Xe TPC with electroluminescence readout. Hamamatsu R8520-06SEL photomultipliers are good candidates for the scintillation readout. The performance of this photomultiplier, used as VUV photosensor in a gas proportional scintillation counter, was investigated. Initial results for the detection of primary and secondary scintillation produced as a result of the interaction of 5.9 keV X-rays in gaseous xenon, at room temperature and at pressures up to 3 bar, are presented. An energy resolution of 8.0% was obtained for secondary scintillation produced by 5.9 keV X-rays. No significant variation of the primary scintillation was observed for different pressures (1, 2 and 3 bar) and for electric fields up to 0.8 V cm-1 torr-1 in the drift region, demonstrating negligible recombination luminescence. A primary scintillation yield of 81 \pm 7 photons was obtained for 5.9 keV X-rays, corresponding to a mean energy of 72 \pm 6 eV to produce a primary scintillation photon in xenon.Comment: 16 pages, 10 figures, accepted for publication in JINS

Interface mediated interactions between particles -- a geometrical approach

Particles bound to an interface interact because they deform its shape. The stresses that result are fully encoded in the geometry and described by a divergence-free surface stress tensor. This stress tensor can be used to express the force on a particle as a line integral along any conveniently chosen closed contour that surrounds the particle. The resulting expression is exact (i.e., free of any "smallness" assumptions) and independent of the chosen surface parametrization. Additional surface degrees of freedom, such as vector fields describing lipid tilt, are readily included in this formalism. As an illustration, we derive the exact force for several important surface Hamiltonians in various symmetric two-particle configurations in terms of the midplane geometry; its sign is evident in certain interesting limits. Specializing to the linear regime, where the shape can be analytically determined, these general expressions yield force-distance relations, several of which have originally been derived by using an energy based approach.Comment: 18 pages, 7 figures, REVTeX4 style; final version, as appeared in Phys. Rev. E. Compared to v2 several minor mistakes, as well as one important minus sign in Eqn. (18a) have been cured. Compared to v1, this version is significantly extended: Lipid tilt degrees of freedom for membranes are included in the stress framework, more technical details are given, estimates for the magnitude of forces are mad

Perturbation theory for plasmonic eigenvalues

We develop a perturbative approach for calculating, within the quasistatic approximation, the shift of surface resonances in response to a deformation of a dielectric volume. Our strategy is based on the conversion of the homogeneous system for the potential which determines the plasmonic eigenvalues into an inhomogeneous system for the potential's derivative with respect to the deformation strength, and on the exploitation of the corresponding compatibility condition. The resulting general expression for the first-order shift is verified for two explicitly solvable cases, and for a realistic example of a deformed nanosphere. It can be used for scanning the huge parameter space of possible shape fluctuations with only quite small computational effort