A Rigorous Derivation of Electromagnetic Self-force

During the past century, there has been considerable discussion and analysis of the motion of a point charge, taking into account "self-force" effects due to the particle's own electromagnetic field. We analyze the issue of "particle motion" in classical electromagnetism in a rigorous and systematic way by considering a one-parameter family of solutions to the coupled Maxwell and matter equations corresponding to having a body whose charge-current density $J^a(\lambda)$ and stress-energy tensor $T_{ab} (\lambda)$ scale to zero size in an asymptotically self-similar manner about a worldline $\gamma$ as $\lambda \to 0$. In this limit, the charge, $q$, and total mass, $m$, of the body go to zero, and $q/m$ goes to a well defined limit. The Maxwell field $F_{ab}(\lambda)$ is assumed to be the retarded solution associated with $J^a(\lambda)$ plus a homogeneous solution (the "external field") that varies smoothly with $\lambda$. We prove that the worldline $\gamma$ must be a solution to the Lorentz force equations of motion in the external field $F_{ab}(\lambda=0)$. We then obtain self-force, dipole forces, and spin force as first order perturbative corrections to the center of mass motion of the body. We believe that this is the first rigorous derivation of the complete first order correction to Lorentz force motion. We also address the issue of obtaining a self-consistent perturbative equation of motion associated with our perturbative result, and argue that the self-force equations of motion that have previously been written down in conjunction with the "reduction of order" procedure should provide accurate equations of motion for a sufficiently small charged body with negligible dipole moments and spin. There is no corresponding justification for the non-reduced-order equations.Comment: 52 pages, minor correction

The Pierre Auger Observatory: Results on Ultra-High Energy Cosmic Rays

The focus of this article is on recent results on ultra-high energy cosmic rays obtained with the Pierre Auger Observatory. The world's largest instrument of this type and its performance are described. The observations presented here include the energy spectrum, the primary particle composition, limits on the fluxes of photons and neutrinos and a discussion of the anisotropic distribution of the arrival directions of the most energetic particles. Finally, plans for the construction of a Northern Auger Observatory in Colorado, USA, are discussed.Comment: Proceedings of the International Workshop on Advances in Cosmic Ray Science, Waseda University, Shinjuku, Tokyo, Japan, March 2008; to be published in the Journal of the Physical Society of Japan (JPSJ) supplemen

An Index Theorem for Domain Walls in Supersymmetric Gauge Theories

The supersymmetric abelian Higgs model with N scalar fields admits multiple domain wall solutions. We perform a Callias-type index calculation to determine the number of zero modes of this soliton. We confirm that the most general domain wall has 2(N-1) zero modes, which can be interpreted as the positions and phases of (N-1) constituent domain walls. This implies the existence of moduli for a D-string interpolating between N D5-branes in IIB string theory.Comment: 9 pages, REVTeX4; v2: reference adde

Moderate temperature rechargeable sodium batteries

Cells utilizing the organic electrolyte, NaI in triglyme, operated at approx. 130 C with Na(+) - intercalating cathodes. However, their rate and stability were inadequate. NaAlCl4 was found to be a highly useful electrolyte for cell operation at 165-190 C. Na(+) intercalating chalcogenides reacted with NaAlCl4 during cycling to form stable phases. Thus, VS2 became essentially VS2Cl, with reversible capacity of approx 2.8 e(-)/V, and a mid-discharge voltage of approx 2.5V and 100 deep discharge cycles were readily achieved. A positive electrode consisting of VCl3 and S plus NaAlCl4 was subjected to deep-discharge cycles 300 times and it demonstrated identity with the in-situ-formed BSxCly cathode. NiS2 and NiS which are not Na(+)-intercalating structures formed highly reversible electrodes in NaAlCl4. The indicated discharge mechanism implies a theoretical capacity 4e(-)/Ni for NiS2 and 2e(-)/Ni for NiS. The mid-discharge potentials are, respectively, 2.4V and 2.1V. A Na/NiS2 cell cycling at a C/5 rate has exceeded 500 deep discharge cycles with 2.5e(-)/Ni average utilization. A 4 A-hr nominal capacity prototype Na/NiS2 cell was tested at 190 C. It was voluntarily terminated after 80 cycles. Further development, particularly of cathode structure and hardware should produce a battery capable of at least 50-W-hr/lb and more than 1000 cycles

Influence of Small Scale Businesses on Decision Making Capacity of Rural Women in Ethiopia: - The Case of Edget Bandinet Saving and Credit Cooperative in Muketuri

Ethiopia‘s poor have suffered from the global economic crisis, as the price of goods consumed increase. Rural women and girls bear the greatest burdens of this situation, since they have a role in livestock maintenance and management, crop production and marketing of agricultural produce (EMFA, 2010). Ethiopian women suffer from low literacy levels and poor access to public services, and most of them derive their income from small scale production. Lacks of investment make it difficult for women to earn a living from agriculture. Financially independence of women‘s doesn‘t always lead in decision making on issues related income utilization and choices of life. This research aimed to assess the influence of small scale business on women‘s decision making capacity. For the assessment the case of a credit and saving association in Muketure was taken. Using simple random sampling method 52 members were selected. 10 non-members were included as check. The tools of data collection were interview and questionnaires. Employment opportunities were extremely limited due to gender-based factors. As a result of tradition and a stereotyped gender division of labour between men and women, women and girls were placed in a subordinate position. The lack of access to and control over resources has forced females to bear the burden of poverty, be dependent on men and powerless to make decisions on family‘s incomes. Women were subjected to various types of gender based violence. The study showed that the flow of capital in women‘s hands has improved their decision making capacity on issues related with the family and community. Women were able to generate income from their business, buy materials for the family, and meet and bargain with people without the consent of their husbands. However, women‘s decision making capacity has depended on the family background. The study found out that small scale business has pragmatic and significant impact in improving women‘s decision making capacity within the family as well as in the community. Key words: small scale business; decision making capacity; saving and credit and povert

Casimir interactions in Ising strips with boundary fields: exact results

An exact statistical mechanical derivation is given of the critical Casimir forces for Ising strips with arbitrary surface fields applied to edges. Our results show that the strength as well as the sign of the force can be controled by varying the temperature or the fields. An interpretation of the results is given in terms of a linked cluster expansion. This suggests a systematic approach for deriving the critical Casimir force which can be used in more general models.Comment: 10 pages, 4 figure

New two-sided bound on the isotropic Lorentz-violating parameter of modified Maxwell theory

There is a unique Lorentz-violating modification of the Maxwell theory of photons, which maintains gauge invariance, CPT, and renormalizability. Restricting the modified-Maxwell theory to the isotropic sector and adding a standard spin-one-half Dirac particle p^\pm with minimal coupling to the nonstandard photon \widetilde{\gamma}, the resulting modified-quantum-electrodynamics model involves a single dimensionless "deformation parameter," \widetilde{\kappa}_{tr}. The exact tree-level decay rates for two processes have been calculated: vacuum Cherenkov radiation p^\pm \to p^\pm \widetilde{\gamma} for the case of positive \widetilde{\kappa}_{tr} and photon decay \widetilde{\gamma} \to p^+ p^- for the case of negative \widetilde{\kappa}_{tr}. From the inferred absence of these decays for a particular high-quality ultrahigh-energy-cosmic-ray event detected at the Pierre Auger Observatory and an excess of TeV gamma-ray events observed by the High Energy Stereoscopic System telescopes, a two-sided bound on \widetilde{\kappa}_{tr} is obtained, which improves by eight orders of magnitude upon the best direct laboratory bound. The implications of this result are briefly discussed.Comment: 18 pages, v5: published version in preprint styl

Polarizations and differential calculus in affine spaces

Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as linearity, iterability, Leibniz and chain rules, are shared -- at the finite level -- by the polarization operators. We give these results by means of explicit general formulae, which are valid at any order $n$, and are based on combinatorial identities. The infinitesimal limits of the $n$-th polarizations of a function will yield its $n$-th derivatives (without resorting to the usual recursive definition), and the above mentioned properties will be recovered directly in the limit. Polynomial functions will allow us to produce a coordinate free version of Taylor's formula