Black hole boundaries

Classical black holes and event horizons are highly non-local objects, defined in relation to the causal past of future null infinity. Alternative, quasilocal characterizations of black holes are often used in mathematical, quantum, and numerical relativity. These include apparent, killing, trapping, isolated, dynamical, and slowly evolving horizons. All of these are closely associated with two-surfaces of zero outward null expansion. This paper reviews the traditional definition of black holes and provides an overview of some of the more recent work on alternative horizons.Comment: 27 pages, 8 figures, invited Einstein Centennial Review Article for CJP, final version to appear in journal - glossary of terms added, typos correcte

Is entanglement entropy proportional to area?

It is known that the entanglement entropy of a scalar field, found by tracing over its degrees of freedom inside a sphere of radius ${\cal R}$, is proportional to the area of the sphere (and not its volume). This suggests that the origin of black hole entropy, also proportional to its horizon area, may lie in the entanglement between the degrees of freedom inside and outside the horizon. We examine this proposal carefully by including excited states, to check probable deviations from the area law.Comment: 6 pages. Based on talk by S. Das at Theory Canada 1, Vancouver, 3 June, 2005. To be published in a special edition of the Canadian Journal of Physics. Minor changes to match published versio

Design of Multi-Dimensional Recursive Systems through Pad'e Type Rational Approximation

The results obtained in classical 1-D rational approximation are extended in this paper to rational approximation of M-D functions. A full analog of classical Montessus de Ballore theorem for the convergence of the rows of Pad´e’s tables is obtained. It is shown that the appropriate theorem for uniform convergence in C2 will really take place only in the case of choosing the necessary determinative (interpolation) sets Ij(n,m), j = 1, 2. This theorem allows us to handle the problem of deriving the transfer function of a M-D digital system, that is described by its state-space representation1. The results of computer modelling by using MATLAB software are presented. Both the convergence theorem and results of modelling show that from theoretical and practical points of view the proposed approach is promising

Compactons and topological solitons of the Drinfel'd–Sokolov system

This paper presents the Drinfel’d–Sokolov system (shortly D(m, n)) in a detailed fashion. The Jacobi’s elliptic function method is employed to extract the cnoidal and snoidal wave solutions. The compacton and solitary pattern solutions are also retrieved. The ansatz method is applied to extract the topological 1-soliton solutions of the D(m, n) with generalized evolution. There are a couple of constraint conditions that will fall out in order to exist the topological soliton solutions

The D to K and D to pi semileptonic decay form factors from Lattice QCD

We present a new and very high statistics study of D and D_s semileptonic decay form factors on the lattice. We work with MILC N_f=2+1 lattices and use the Highly Improved Staggered Action (HISQ) for both the charm and the light valence quarks. We use both scalar and vector currents to determine the form factors f_0(q^2) and f_+(q^2) for a range of D and D_s form factors including those for D to pi and D to K semileptonic decays. By using a phased boundary condition we are able to tune accurately to q^2=0. We also compare the shape in q^2 to that from experiment. We show that the form factors are very insensitive to the spectator quark: D to K and D_s to eta_s form factors are essentially the same, and the same is true for D to pi and D_s to K. This has important implications when considering the corresponding B/B_s processes.Comment: 7 pages, 9 figures, talk given at the XXIX International Symposium on Lattice Field Theory, July 10-16, 2011, Squaw Valley, Lake Tahoe, C

Design for sustainable behaviour: Investigating design methods for influencing user behaviour

This research aims to develop a design tool for product and service innovation which influences users towards more sustainable behaviour, reducing resource use and leading to a lower carbon footprint for everyday activities. The paper briefly explains the reasoning behind the tool and its structure, and presents an example application to water conservation with concept ideas generated by design students

Concept generation for persuasive design

Designing ‘persuasive’ products and services for social benefit often involves adopting and adapting principles and patterns from other disciplines and contexts where behaviour change is a goal. This poster briefly reports on a series of controlled trials of an idea generation toolkit which aims to make this transposition of patterns easier, with designers and students applying the toolkit to four ‘design for sustainable behaviour’ briefs to generate new concepts for influencing user behaviour. While only a small sample, results show that using the toolkit does lead to an increase in the number of concepts generated for a majority of participants, compared with the control condition

Upaya Meningkatkan Hasil Belajar Siswa Dalam Penguasaan Materi Pelajaran Narrative Text Pada Pelajaran Bahasa Inggris Melalui Penerapan Model Pembelajaran Kooperatif Tipe Jigsaw Di Kelas Viii-d SMP Negeri 3 Medan

 Penelitian ini dilatarbelakangi permasalahan yang muncul di SMP Negeri 3 Medan yaitu setelah guru melaksanakan pembelajaran Bahasa Inggris pada materi Narrative text guru mengetahui bahwa hasil belajar masih rendah. Hal ini tercermin dari perolehan tes hasil belajar yaitu bahwa tidak ada siswa yang mencapai ketuntasan individual. Ini juga menunjukkan bahwa belum tercapai standar ketuntasan klasikal karena prosentase ketuntasan adalah sebesar 0%. Dalam proses pembelajaran keaktifan siswalah yang seharusnya ditingkatkan karena proses belajar bukanlah menyampaikan materi tapi bagaimana siswa dapat memperoleh informasi dengan cara-cara mereka sendiri maupun bimbingan guru. Selain itu dalam pembelajaran, ketertarikan siswa atau respon siswa juga sangat mempengaruhi perolehan hasil belajar. Dengan menyadari berbagai Kenyataan diatas maka sebagai seorang guru professional merasa perlu untuk memperbaiki pembelajaran yaitu dengan mengadakan penelitian. Penelitian ini merupakan penelitian tindakan kelas dengan meningkatkan pembelajaran Bahasa Inggris untuk meningkatkan hasil belajar siswa Kelas VIII-D SMP Negeri 3 Medan. Penelitian ini merupakan penelitian tindakan kelas yang dilakukan sebanyak dua siklus. Berdasarkan analisis data dalam penelitian ini bahwa penerapan metode Jigsawdapat meningkatkan kemampuan individual siswa dan ketuntasan klasikal siswa. Penerapan Model Pembelajaran Jigsaw juga dapat membuat siswa lebih aktif. Siswa merespon positif terhadap pembelajaran dengan menerapkan Model Pembelajaran Jigsaw. Model Pembelajaran Jigsawdapat meningkatkan Hasil Belajar Narrative text  siswa Kelas VIII-DSMP Negeri 3 Medan, yaitu nilai rata-rata kelas pada saat pre test 47,537,44; siklus 1: 70,26; siklus 2: 81,79. Model pembelajaran kooperatif tipe Jigsaw dapat menciptakan suasana pembelajaran yang efektif, dan siswa aktif bekerja sama, hal ini ditunjukkan pada nilai sikap siswa pada siklus 1: 45,95; meningkat pada siklus 2: 80,62