Plasmon Resonances in Nanoparticles, Their Applications to Magnetics and Relation to the Riemann Hypothesis

The review of the mathematical treatment of plasmon resonances as an eigenvalue problem for specific boundary integral equations is presented and general properties of plasmon spectrum are outlined. Promising applications of plasmon resonances to magnetics are described. Interesting relation of eigenvalue treatment of plasmon resonances to the Riemann hypothesis is discussed.Comment: 10 pages; misprints corrected, some explanations added. Physica B (2011

Mathematical analysis of plasmonic nanoparticles: the scalar case

Localized surface plasmons are charge density oscillations confined to metallic nanoparticles. Excitation of localized surface plasmons by an electromagnetic field at an incident wavelength where resonance occurs results in a strong light scattering and an enhancement of the local electromagnetic fields. This paper is devoted to the mathematical modeling of plasmonic nanoparticles. Its aim is threefold: (i) to mathematically define the notion of plasmonic resonance and to analyze the shift and broadening of the plasmon resonance with changes in size and shape of the nanoparticles; (ii) to study the scattering and absorption enhancements by plasmon resonant nanoparticles and express them in terms of the polarization tensor of the nanoparticle. Optimal bounds on the enhancement factors are also derived; (iii) to show, by analyzing the imaginary part of the Green function, that one can achieve super-resolution and super-focusing using plasmonic nanoparticles. For simplicity, the Helmholtz equation is used to model electromagnetic wave propagation

Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions

We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodal-based finite elements may converge to the wrong solution due to a version of the Babuska paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms.Comment: 19 pages, 7 figure

Nondestructive monitoring of ageing of Alkali resistant Glass fiber reinforced cement (GRC)

Glass fiber reinforced cement (GRC) is a composite material made of portland cement mortar and alkali resistant (AR) fibers. AR fibers are added to portland cement to give the material additional flexural strength and toughness. However, ageing deteriorates the fibers and as a result the improvement in the mechanical properties resulted from the fiber addition disappears as the structure becomes old. The aim of this paper is monitoring GRC ageing by nondestructive evaluation (NDE) techniques. Two different NDE techniques (1) nonlinear impact resonant acoustic spectroscopy analysis and (2) propagating ultrasonic guided waves are used for this purpose. Both techniques revealed a reduction of the nonlinear behavior in the GRC material with ageing. Specimens are then loaded to failure to obtain their strength and stiffness. Compared to the un-aged specimens, the aged specimens are found to exhibit more linear behavior, have more stiffness but less toughness. Finally, undisturbed fragments on the fracture surface from mechanical tests are inspected under the electron microscope, to understand the fundamental mechanisms that cause the change in the GRC behavior with ageing.The authors want to acknowledge the financial support of the Ministerio de Ciencia e Innovacion MICINN, Spain, and FEDER funding (Ondacem Project: BIA 2010-19933) and BES-2011-044624. Also thanks to PAID-02-11 Program from Universitat Politecnica de Valencia.Eiras Fernández, JN.; Kundu, T.; Bonilla Salvador, MM.; Paya Bernabeu, JJ. (2013). Nondestructive monitoring of ageing of Alkali resistant Glass fiber reinforced cement (GRC). Journal of Nondestructive Evaluation - NDT and E International. 32:300-314. https://doi.org/10.1007/s10921-013-0183-yS30031432Bentur, A., Fibre, M.S.: Reinforced Cementitious Composites, 2nd edn. Taylor and Francis, New York (2007)Purnell, P., Short, N.R., Page, C.L.: A static fatigue model for the durability of glass fibre reinforced cement. J. 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Academic Press, New York (2003)Van Den Abeele, K.E.A., Carmeliet, J., Ten Cate, J.A., Johnson, P.A.: Nonlinear elastic wave spectroscopy (NEWS) techniques to discern material damage, part II: single-mode nonlinear resonance acoustic spectroscopy. Res. Nondestruct. Eval. 12(1), 31–42 (2000)Chen, J., Jayapalan, A.R., Kim, J.Y., Kurtis, K.E., Jacobs, L.J.: Rapid evaluation of alkali–silica reactivity of aggregates using a nonlinear resonance spectroscopy technique. Cem. Concr. Res. 40(6), 914–923 (2010)Leśnicki, K.J., Kim, J.Y., Kurtis, K.E., Jacobs, L.J.: Characterization of ASR damage in concrete using nonlinear impact resonance acoustic spectroscopy technique. Nondestruct. Test. Eval. Int. 44(8), 721–727 (2011)Bouchaala, F., Payan, C., Garnier, V., Balayssac, J.P.: Carbonation assessment in concrete by nonlinear ultrasound. Cem. Concr. 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[Mathematical models of hysteresis]

The research described in this proposal is currently being supported by the US Department of Energy under the contract Mathematical Models of Hysteresis''. Thus, before discussing the proposed research in detail, it is worthwhile to describe and summarize the main results achieved in the course of our work under the above contract. Our ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories''. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. Our research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. Our study has by and large been centered around the following topics: various generalizations and extensions of the classical Preisach model, finding of necessary and sufficient conditions for the representation of actual hysteretic nonlinearities by various Preisach type models, solution of identification problems for these models, numerical implementation and experimental testing of Preisach type models. Although the study of Preisach type models has constituted the main direction of the research, some effort has also been made to establish some interesting connections between these models and such topics as: the critical state model for superconducting hysteresis, the classical Stoner-Wohlfarth model of vector magnetic hysteresis, thermal activation type models for viscosity, magnetostrictive hysteresis and neural networks

Mathematical models of hysteresis

This report discusses the mathematical models of the hysteresis of magnet materials and superconducting materials. (LSP