Exact Casimir Interaction Between Semitransparent Spheres and Cylinders

A multiple scattering formulation is used to calculate the force, arising from fluctuating scalar fields, between distinct bodies described by $\delta$-function potentials, so-called semitransparent bodies. (In the limit of strong coupling, a semitransparent boundary becomes a Dirichlet one.) We obtain expressions for the Casimir energies between disjoint parallel semitransparent cylinders and between disjoint semitransparent spheres. In the limit of weak coupling, we derive power series expansions for the energy, which can be exactly summed, so that explicit, very simple, closed-form expressions are obtained in both cases. The proximity force theorem holds when the objects are almost touching, but is subject to large corrections as the bodies are moved further apart.Comment: 5 pages, 4 eps figures; expanded discussion of previous work and additional references added, minor typos correcte

Change of a Weibel-type to an Alfv\'enic shock in pair plasma by upstream waves

We examine with particle-in-cell (PIC) simulations how a parallel shock in pair plasma reacts to upstream waves, which are driven by escaping downstream particles. Initially, the shock is sustained in the two-dimensional simulation by a magnetic filamentation (beam-Weibel) instability. Escaping particles drive an electrostatic beam instability upstream. Modifications of the upstream plasma by these waves hardly affect the shock. In time, a decreasing density and increasing temperature of the escaping particles quench the beam instability. A larger thermal energy along than perpendicular to the magnetic field destabilizes the pair-Alfv\'en mode. In the rest frame of the upstream plasma, the group velocity of the growing pair-Alfv\'en waves is below that of the shock and the latter catches up with the waves. Accumulating pair-Alfv\'en waves gradually change the shock in the two-dimensional simulation from a Weibel-type shock into an Alfv\'enic shock with a Mach number that is about 6 for our initial conditions.Comment: 11 pages, 10 figures, accepted for publication in Physics of Plasma

Science and RE teachers' perspectives on the purpose of RE on the secondary school curriculum in England

Renewed interest in curriculum in English schooling over the past decade has emanated from a particular focus on the place and role of knowledge in the classroom. Significant changes in policy and examination specifications have led to changes in religious education (RE). However, little is known about teachers' perspectives on the purpose of RE. We asked teachers of science and RE what they understood as the purpose of RE on the school curriculum. Data from 10 focus groups and a survey with 276 secondary teachers demonstrated that many secondary teachers of science have a different understanding to RE teachers of the purpose of RE on the school curriculum. Findings also show a lack of consensus from RE teachers on the purpose of RE, suggesting the impact of the knowledge turn in RE is not as strong as the Ofsted Research Review implies. Findings are significant as little is known about how knowledge works across disciplinary boundaries in schools. If students are to come to a full understanding of how knowledge works, teachers need to have some understanding of how knowledge is being constructed and utilised in other curriculum subjects. Knowledge of the intended purpose of RE is important for respectful co-existence of subjects on the curriculum and essential when RE is declining as a subject in secondary schools

Shaping concepts of technology : what concepts and how to shape them?

Philosophy of technology is a discipline that has much to offer for technology education. Insights into the real nature of technology and its relationship with science and society can help technology educators to build a subject that helps pupils get a good concept of technology and to learn to understand and use concepts in technology. Here the way science educators have gained from the philosophy of science, for example in the idea of the way pupils learn concepts by reconstructing pre-concepts that they picked up from daily-life experiences. Research has shown that the learning of concepts and the learning of process skills have to be connected

Design and development of a low temperature, inductance based high frequency ac susceptometer

We report on the development of an induction based low temperature high frequency ac susceptometer capable of measuring at frequencies up to 3.5 MHz and at temperatures between 2 K and 300 K. Careful balancing of the detection coils and calibration have allowed a sample magnetic moment resolution of $5\times10^{-10} Am^2$ at 1 MHz. We will discuss the design and characterization of the susceptometer, and explain the calibration process. We also include some example measurements on the spin ice material CdEr$_2$S$_4$ and iron oxide based nanoparticles to illustrate functionality

Powers of Hamilton cycles in pseudorandom graphs

We study the appearance of powers of Hamilton cycles in pseudorandom graphs, using the following comparatively weak pseudorandomness notion. A graph $G$ is $(\varepsilon,p,k,\ell)$-pseudorandom if for all disjoint $X$ and $Y\subset V(G)$ with $|X|\ge\varepsilon p^kn$ and $|Y|\ge\varepsilon p^\ell n$ we have $e(X,Y)=(1\pm\varepsilon)p|X||Y|$. We prove that for all $\beta>0$ there is an $\varepsilon>0$ such that an $(\varepsilon,p,1,2)$-pseudorandom graph on $n$ vertices with minimum degree at least $\beta pn$ contains the square of a Hamilton cycle. In particular, this implies that $(n,d,\lambda)$-graphs with $\lambda\ll d^{5/2 }n^{-3/2}$ contain the square of a Hamilton cycle, and thus a triangle factor if $n$ is a multiple of $3$. This improves on a result of Krivelevich, Sudakov and Szab\'o [Triangle factors in sparse pseudo-random graphs, Combinatorica 24 (2004), no. 3, 403--426]. We also extend our result to higher powers of Hamilton cycles and establish corresponding counting versions.Comment: 30 pages, 1 figur

Normal Ordering for Deformed Boson Operators and Operator-valued Deformed Stirling Numbers

The normal ordering formulae for powers of the boson number operator $\hat{n}$ are extended to deformed bosons. It is found that for the `M-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = 1$, the extension involves a set of deformed Stirling numbers which replace the Stirling numbers occurring in the conventional case. On the other hand, the deformed Stirling numbers which have to be introduced in the case of the `P-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = q^{-\hat{n}}$, are found to depend on the operator $\hat{n}$. This distinction between the two types of deformed bosons is in harmony with earlier observations made in the context of a study of the extended Campbell-Baker-Hausdorff formula.Comment: 14 pages, Latex fil

Weak charge form factor and radius of 208Pb through parity violation in electron scattering

We use distorted wave electron scattering calculations to extract the weak charge form factor F_W(q), the weak charge radius R_W, and the point neutron radius R_n, of 208Pb from the PREX parity violating asymmetry measurement. The form factor is the Fourier transform of the weak charge density at the average momentum transfer q=0.475 fm$^{-1}$. We find F_W(q) =0.204 \pm 0.028 (exp) \pm 0.001 (model). We use the Helm model to infer the weak radius from F_W(q). We find R_W= 5.826 \pm 0.181 (exp) \pm 0.027 (model) fm. Here the exp error includes PREX statistical and systematic errors, while the model error describes the uncertainty in R_W from uncertainties in the surface thickness \sigma of the weak charge density. The weak radius is larger than the charge radius, implying a "weak charge skin" where the surface region is relatively enriched in weak charges compared to (electromagnetic) charges. We extract the point neutron radius R_n=5.751 \pm 0.175 (exp) \pm 0.026 (model) \pm 0.005 (strange) fm$, from R_W. Here there is only a very small error (strange) from possible strange quark contributions. We find R_n to be slightly smaller than R_W because of the nucleon's size. Finally, we find a neutron skin thickness of R_n-R_p=0.302\pm 0.175 (exp) \pm 0.026 (model) \pm 0.005 (strange) fm, where R_p is the point proton radius.Comment: 5 pages, 1 figure, published in Phys Rev. C. Only one change in this version: we have added one author, also to metadat

A Mentoring Guide for Female Faculty in Engineering

One widely accepted method for increasing the chances of success of female engineering and science students and faculty alike is to provide access to female role models and mentors. In this article we offer to new female faculty, and to those who would mentor them, an annotated list of text and electronic resources that address most of the most important challenges facing new female faculty in science and engineering

Statistical Properties of the Final State in One-dimensional Ballistic Aggregation

We investigate the long time behaviour of the one-dimensional ballistic aggregation model that represents a sticky gas of N particles with random initial positions and velocities, moving deterministically, and forming aggregates when they collide. We obtain a closed formula for the stationary measure of the system which allows us to analyze some remarkable features of the final `fan' state. In particular, we identify universal properties which are independent of the initial position and velocity distributions of the particles. We study cluster distributions and derive exact results for extreme value statistics (because of correlations these distributions do not belong to the Gumbel-Frechet-Weibull universality classes). We also derive the energy distribution in the final state. This model generates dynamically many different scales and can be viewed as one of the simplest exactly solvable model of N-body dissipative dynamics.Comment: 19 pages, 5 figures include