Space-time discontinuous Galerkin method for the solution of fluid-structure interaction

The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic structure. The domain occupied by the fluid depends on time. It is taken into account in the Navier-Stokes equations rewritten with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The resulting coupled system is discretized by the STDGM using piecewise polynomial approximations of the sought solution both in space and time. The developed method can be applied to the solution of the compressible flow for a wide range of Mach numbers and Reynolds numbers. For the simulation of elastic deformations two models are used: the linear elasticity model and the nonlinear neo-Hookean model. The main goal is to show the robustness and applicability of the method to the simulation of the air flow in a simplified model of human vocal tract and the flow induced vocal folds vibrations. It will also be shown that in this case the linear elasticity model is not adequate and it is necessary to apply the nonlinear model.     

On Weierstrass semigroups and sets: a review with new results

In this work we present a survey of the main results in the theory of Weierstrass semigroups at several points, with special attention to the determination of bounds for the cardinality of its set of gaps. We also review results on applications to the theory of error correcting codes. We then recall a generalization of the concept of Weierstrass semigroup, which is the Weierstrass set associated to a linear system and several points. We finish by presenting new results on this Weierstrass set, including some on the cardinality of its set of gaps.      

A Study of the Intrinsic Autofluorescence of Poly (ethylene glycol)-co-(<Subscript><Emphasis Type="Italic">L</Emphasis></Subscript>-Lactic acid) Diacrylate

Poly (ethylene glycol)-co-( _L -Lactic acid) diacrylate (PEG-PLLA-DA) copolymers have been extensively investigated for a number of applications in medicine. PEG-PLLA-DA is biodegradable and the human body can process its degradation products. In this study, we describe the autofluorescence of PEG-PLLA-DA copolymers and compared it to the fluorescence of poly(ethylene glycol) diacrylate (PEG-DA) and the precursor molecules used for their synthesis. In addition, we examined the influence of pH on the fluorescence spectra. We found that PEG-PLLA-DA exhibits higher fluorescence than PEG-DA and all reagents involved in the synthesis of PEG-PLLA-DA. The fluorescence of PEG-PLLA-DA was affected by pH with fluorescence decreasing at high pH values. At high pH, PEG-PLLA-DA could not polymerize into hydrogels and exhibited a dramatic decrease in autofluorescence, suggesting that hydrolysis of the ester bond affected its autofluorescence. At low pH, PEG-PLLA-DA exhibited higher fluorescence and it was able to form crosslinked hydrogels. The autofluorescence of PEG-PLLA-DA could be exploited to monitor polymer degradation and material structure without the need to introduce exogenous fluorescent probes. The origin of fluorescence is not clear at this point in time but it appears to result from a synergetic effect of both lactate units and diacrylate groups in the PEG-PLLA-DA backbone. The observed autofluorescence of PEG-PLLA-DA persists after reaction of the acrylate groups in the polymerization reaction. This autofluorescence is advantageous because it could assist in the study of polymers used for drug delivery and tissue engineering applications.     

Heuristic solution approaches for the maximum minsum dispersion problem

The Maximum Minsum Dispersion Problem (Max-Minsum DP) is a strongly NP-Hard problem that belongs to the family of equitable dispersion problems. When dealing with dispersion, the operations research literature has focused on optimizing efficiency-based objectives while neglecting, for the most part, measures of equity. The most common efficiency-based functions are the sum of the inter-element distances or the minimum inter-element distance. Equitable dispersion problems, on the other hand, attempt to address the balance between efficiency and equity when selecting a subset of elements from a larger set. The objective of the Max-Minsum DP is to maximize the minimum aggregate dispersion among the chosen elements. We develop tabu search and GRASP solution procedures for this problem and compare them against the best in the literature. We also apply LocalSolver, a commercially available black-box optimizer, to compare our results. Our computational experiments show that we are able to establish new benchmarks in the solution of the Max-Minsum DP.     

Existence and fractional regularity of solutions for a doubly nonlinear differential inclusion

This article considers the issues of existence and regularity of solutions to the following doubly nonlinear differential inclusion $$\omega_t+\alpha (\omega_t)-\Delta \omega-\Delta_p{\omega} \ni f$$ where α is a maximal monotone operator in ${\mathbb{R}^2}$ and Δ _p denotes the p-Laplacian with p > 2. The investigation on fractional regularity is based on the Galerkin method combined with a suitable basis for W ^1,p , which we exhibit as a preliminary result. This approach also allows the obtaining of estimates in the so-called Nikolskii spaces, since it balances the interplay between the maximal monotone operator with the appearing higher order nonlinear terms.     

Upper bound for the magnetic force gradient in graphite

In this work we investigate possible ferromagnetic order on the graphite surface by using magnetic force microscopy (MFM). Our data show that the tip-sample interaction along the steps is independent of an external magnetic field. Moreover, by combining kelvin probe force microscopy and MFM, we are able to separate the electrostatic and magnetic interactions along the steps obtaining an upper bound for the magnetic force gradient of 16 μN/m. Our experiments suggest the absence of ferromagnetic signal in graphite at room temperature.     

Relation between asymmetrical orbital angular momentum and irradiance-profile rotation for partially coherent beams

On the basis of the irradiance-moment formalism for describing general partially coherent beams, we investigate the relation between the spatial orientation of the transverse beam profile upon propagation and the asymmetrical part of its orbital angular momentum (OAM). More specifically, a necessary and sufficient condition (one-to-one correspondence) is shown between freely propagating non-rotating beams and vanishing asymmetrical OAM. As a corollary, it is obtained that any beam emerging from optical systems that transform a rotating field into a non-rotating beam exhibits vortex OAM only.     

Analytic wave functions and energies for two-dimensional \mathcal{P}\mathcal{T} -symmetric quartic potentials

Analytic wave functions and the corresponding energies for a class of the $ \mathcal{P}\mathcal{T} $ -symmetric two-dimensional quartic potentials are found. The general form of the solutions is discussed.     

Design and validation of a single sphere multi-detector neutron spectrometer based on LiF: Mg,Cu,P thermoluminescent dosemeters

This communication describes a new neutron spectrometer consisting of pairs of ⁷Li and ⁶Li based thermoluminescent dosemeters (MCP-6, MCP-7) located at selected positions within a single moderating polyethylene sphere. The spatial arrangement of the dosemeters has been designed using the MCNPX Monte Carlo code to calculate the response matrix in order to obtain a nearly isotropic response for neutrons in the energy range up to 20 MeV. A partial validation of the calculated response matrix has been performed with the calibrated ²⁴¹Am–Be neutron source at the INFN–LNF Laboratory, using the shadow cone technique.