Dynamical Systems Gradient method for solving nonlinear equations with monotone operators

A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new stopping rule. Numerical experiments show that the proposed stopping rule is efficient. Equations with monotone operators are of interest in many applications.Comment: 2 figure

A first approach to understanding and measuring naturalness in driver-car interaction

With technology changing the nature of the driving task, qualitative methods can help designers understand and measure driver-car interaction naturalness. Fifteen drivers were interviewed at length in their own parked cars using ethnographically-inspired questions probing issues of interaction salience, expectation, feelings, desires and meanings. Thematic analysis and content analysis found five distinct components relating to 'rich physical' aspects of natural feeling interaction typified by richer physical, analogue, tactile styles of interaction and control. Further components relate to humanlike, intelligent, assistive, socially-aware 'perceived behaviours' of the car. The advantages and challenges of a naturalness-based approach are discussed and ten cognitive component constructs of driver-car naturalness are proposed. These may eventually be applied as a checklist in automotive interaction design.This research was fully funded by a research grant from Jaguar Land Rover, and partially funded by project n.220050/F11 granted by Research Council of Norway

Trapped ions in optical lattices for probing oscillator chain models

We show that a chain of trapped ions embedded in microtraps generated by an optical lattice can be used to study oscillator models related to dry friction and energy transport. Numerical calculations with realistic experimental parameters demonstrate that both static and dynamic properties of the ion chain change significantly as the optical lattice power is varied. Finally, we lay out an experimental scheme to use the spin degree of freedom to probe the phase space structure and quantum critical behavior of the ion chain

Wave scattering by small bodies and creating materials with a desired refraction coefficient

Asymptotic solution to many-body wave scattering problem is given in the case of many small scatterers. The small scatterers can be particles whose physical properties are described by the boundary impedances, or they can be small inhomogeneities, whose physical properties are described by their refraction coefficients. Equations for the effective field in the limiting medium are derived. The limit is considered as the size $a$ of the particles or inhomogeneities tends to zero while their number $M(a)$ tends to infinity. These results are applied to the problem of creating materials with a desired refraction coefficient. For example, the refraction coefficient may have wave-focusing property, or it may have negative refraction, i.e., the group velocity may be directed opposite to the phase velocity. This paper is a review of the author's results presented in MR2442305 (2009g:78016), MR2354140 (2008g:82123), MR2317263 (2008a:35040), MR2362884 (2008j:78010), and contains new results.Comment: In this paper the author's invited plenary talk at the 7-th PACOM (PanAfrican Congress of Mathematicians), is presente

Resonance regimes of scattering by small bodies with impedance boundary conditions

The paper concerns scattering of plane waves by a bounded obstacle with complex valued impedance boundary conditions. We study the spectrum of the Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic behavior of the solutions of the scattering problem. The study includes the case when $k=0$ is an eigenvalue or a resonance. The transformation from the impedance to the Dirichlet boundary condition as impedance grows is described. A relation between poles and zeroes of the scattering matrix in the non-self adjoint case is established. The results are applied to a problem of scattering by an obstacle with a springy coating. The paper describes the dependence of the impedance on the properties of the material, that is on forces due to the deviation of the boundary of the obstacle from the equilibrium position

By hook or by crook? Morphometry, competition and cooperation in rodent sperm

Background Sperm design varies enormously across species and sperm competition is thought to be a major factor influencing this variation. However, the functional significance of many sperm traits is still poorly understood. The sperm of most murid rodents are characterised by an apical hook of the sperm head that varies markedly in extent across species. In the European woodmouse Apodemus sylvaticus (Muridae), the highly reflected apical hook of sperm is used to form sperm groups, or “trains,” which exhibited increased swimming velocity and thrusting force compared to individual sperm. Methodology/Principal Findings Here we use a comparative study of murine rodent sperm and demonstrate that the apical hook and sperm cooperation are likely to be general adaptations to sperm competition in rodents. We found that species with relatively larger testes, and therefore more intense sperm competition, have a longer, more reflected apical sperm hook. In addition, we show that sperm groups also occur in rodents other than the European woodmouse. Conclusions Our results suggest that in rodents sperm cooperation is more widespread than assumed so far and highlight the importance of diploid versus haploid selection in the evolution of sperm design and function

Timber gridshells: beyond the drawing board

In March 2011, a week-long workshop that invited participation from all architecture and architectural technology students at Sheffield Hallam University, UK was organised with the objective of enhancing students’ thinking and experience by construction thinking. It was aimed at creating a sense of realness to realise a design project collectively. Timber was set as the material of exploration. The students had to make use of bending to design and create a timber gridshell structure. This made use of a quality traditionally felt to be a structural weakness of the material. To do this, students form-found non-mathematically and non-digitally using paper gridmats. This paper describes the aims, activity and outcome of the timber gridshell workshop as a way of preparing architects and technologists of the future and introducing the challenges of architectural design in terms of economics and construction process, aesthetics, effective communication and structural intuition by working with a given material – all important aspects in achieving effective architecture