Global Existence Results and Uniqueness for Dislocation Equations

We are interested in nonlocal Eikonal Equations arising in the study of the dynamics of dislocations lines in crystals. For these nonlocal but also non monotone equations, only the existence and uniqueness of Lipschitz and local-in-time solutions were available in some particular cases. In this paper, we propose a definition of weak solutions for which we are able to prove the existence for all time. Then we discuss the uniqueness of such solutions in several situations, both in the monotone and non monotone case

Quantum-state input-output relations for absorbing cavities

The quantized electromagnetic field inside and outside an absorbing high-$Q$ cavity is studied, with special emphasis on the absorption losses in the coupling mirror and their influence on the outgoing field. Generalized operator input-output relations are derived, which are used to calculate the Wigner function of the outgoing field. To illustrate the theory, the preparation of the outgoing field in a Schr\"{o}dinger cat-like state is discussed.Comment: 12 pages, 5 eps figure

Competitiveness and sustainability: can ‘smart city regionalism’ square the circle?

Increasingly, the widely established, globalisation-driven agenda of economic competitiveness meets a growing concern with sustainability. Yet, the practical and conceptual co-existence—or fusion—of these two agendas is not always easy. This includes finding and operationalising the ‘right’ scale of governance, an important question for the pursuit of the distinctly transscalar nature of these two policy fields. ‘New regionalism’ has increasingly been discussed as a pragmatic way of tackling the variable spatialities associated with these policy fields and their changing articulation. This paper introduces ‘smart (new) city-regionalism’, derived from the principles of smart growth and new regionalism, as a policy-shaping mechanism and analytical framework. It brings together the rationales, agreed principles and legitimacies of publicly negotiated polity with collaborative, network-based and policy-driven spatiality. The notion of ‘smartness’, as suggested here as central feature, goes beyond the implicit meaning of ‘smart’ as in ‘smart growth’. When introduced in the later 1990s the term embraced a focus on planning and transport. Since then, the adjective ‘smart’ has become used ever more widely, advocating innovativeness, participation, collaboration and co-ordination. The resulting ‘smart city regionalism’ is circumscribed by the interface between the sectorality and territoriality of policy-making processes. Using the examples of Vancouver and Seattle, the paper looks at the effects of the resulting specific local conditions on adopting ‘smartness’ in the scalar positioning of policy-making

The reaction 2H(p,pp)n in three kinematical configurations at E_p = 16 MeV

We measured the cross sections of the $^2$H(p,pp)n breakup reaction at E$_p$=16 MeV in three kinematical configurations: the np final-state interaction (FSI), the co-planar star (CST), and an intermediate-star (IST) geometry. The cross sections are compared with theoretical predictions based on the CD Bonn potential alone and combined with the updated 2$\pi$-exchange Tucson-Melbourne three-nucleon force (TM99'), calculated without inclusion of the Coulomb interaction. The resulting excellent agreement between data and pure CD Bonn predictions in the FSI testifies to the smallness of three-nucleon force (3NF) effects as well as the insignificance of the Coulomb force for this particular configuration and energy. The CST also agrees well whereas the IST results show small deviations between measurements and theory seen before in the pd breakup space-star geometries which point to possible Coulomb effects. An additional comparison with EFT predictions (without 3NF) up to order N$^3$LO shows excellent agreement in the FSI case and a rather similar agreement as for CD Bonn in the CST and IST situations.Comment: 20 pages, 11 figure

Detecting the direction of a signal on high-dimensional spheres: Non-null and Le Cam optimality results

We consider one of the most important problems in directional statistics, namely the problem of testing the null hypothesis that the spike direction $\theta$ of a Fisher-von Mises-Langevin distribution on the $p$-dimensional unit hypersphere is equal to a given direction $\theta_0$. After a reduction through invariance arguments, we derive local asymptotic normality (LAN) results in a general high-dimensional framework where the dimension $p_n$ goes to infinity at an arbitrary rate with the sample size $n$, and where the concentration $\kappa_n$ behaves in a completely free way with $n$, which offers a spectrum of problems ranging from arbitrarily easy to arbitrarily challenging ones. We identify various asymptotic regimes, depending on the convergence/divergence properties of $(\kappa_n)$, that yield different contiguity rates and different limiting experiments. In each regime, we derive Le Cam optimal tests under specified $\kappa_n$ and we compute, from the Le Cam third lemma, asymptotic powers of the classical Watson test under contiguous alternatives. We further establish LAN results with respect to both spike direction and concentration, which allows us to discuss optimality also under unspecified $\kappa_n$. To investigate the non-null behavior of the Watson test outside the parametric framework above, we derive its local asymptotic powers through martingale CLTs in the broader, semiparametric, model of rotationally symmetric distributions. A Monte Carlo study shows that the finite-sample behaviors of the various tests remarkably agree with our asymptotic results.Comment: 47 pages, 4 figure

Positronium Hyperfine Splitting in Non-commutative Space at the Order α6\alpha^6

We obtain positronium Hyperfine Splitting owing to the non-commutativity of space and show that, in the leading order, it is proportional to $\theta \alpha^6$ where, $\theta$ is the parameter of non-commutativity. It is also shown that spatial non-commutativity splits the spacing between $n=2$ triplet excited levels $E(2^3S_1)\to E(2^3P_2)$ which provides an experimental test on the non-commutativity of space.Comment: 7 pages, 2 figures, to appear in Phys. Rev.

Full capacitance-matrix effects in driven Josephson-junction arrays

We study the dynamic response to external currents of periodic arrays of Josephson junctions, in a resistively capacitively shunted junction (RCSJ) model, including full capacitance-matrix effects}. We define and study three different models of the capacitance matrix $C_{\vec{r},\vec{r}'}$: Model A includes only mutual capacitances; Model B includes mutual and self capacitances, leading to exponential screening of the electrostatic fields; Model C includes a dense matrix $C_{\vec{r},\vec{r}'}$ that is constructed approximately from superposition of an exact analytic solution for the capacitance between two disks of finite radius and thickness. In the latter case the electrostatic fields decay algebraically. For comparison, we have also evaluated the full capacitance matrix using the MIT fastcap algorithm, good for small lattices, as well as a corresponding continuum effective-medium analytic evaluation of a finite voltage disk inside a zero-potential plane. In all cases the effective $C_{\vec{r},\vec{r}'}$ decays algebraically with distance, with different powers. We have then calculated current voltage characteristics for DC+AC currents for all models. We find that there are novel giant capacitive fractional steps in the I-V's for Models B and C, strongly dependent on the amount of screening involved. We find that these fractional steps are quantized in units inversely proportional to the lattice sizes and depend on the properties of $C_{\vec{r},\vec{r}'}$. We also show that the capacitive steps are not related to vortex oscillations but to localized screened phase-locking of a few rows in the lattice. The possible experimental relevance of these results is also discussed.Comment: 12 pages 18 Postscript figures, REVTEX style. Paper to appear in July 1, Vol. 58, Phys. Rev. B 1998 All PS figures include

Regulation of surface architecture by symbiotic bacteria mediates host colonization

Microbes occupy countless ecological niches in nature. Sometimes these environments may be on or within another organism, as is the case in both microbial infections and symbiosis of mammals. Unlike pathogens that establish opportunistic infections, hundreds of human commensal bacterial species establish a lifelong cohabitation with their hosts. Although many virulence factors of infectious bacteria have been described, the molecular mechanisms used during beneficial host–symbiont colonization remain almost entirely unknown. The novel identification of multiple surface polysaccharides in the important human symbiont Bacteroides fragilis raised the critical question of how these molecules contribute to commensalism. To understand the function of the bacterial capsule during symbiotic colonization of mammals, we generated B. fragilis strains deleted in the global regulator of polysaccharide expression and isolated mutants with defects in capsule expression. Surprisingly, attempts to completely eliminate capsule production are not tolerated by the microorganism, which displays growth deficits and subsequent reversion to express capsular polysaccharides. We identify an alternative pathway by which B. fragilis is able to reestablish capsule production and modulate expression of surface structures. Most importantly, mutants expressing single, defined surface polysaccharides are defective for intestinal colonization compared with bacteria expressing a complete polysaccharide repertoire. Restoring the expression of multiple capsular polysaccharides rescues the inability of mutants to compete for commensalism. These findings suggest a model whereby display of multiple capsular polysaccharides provides essential functions for bacterial colonization during host–symbiont mutualism

Please mind the gap: students’ perspectives of the transition in academic skills between A-level and degree level geography

This paper explores first-year undergraduates’ perceptions of the transition from studying geography at pre-university level to studying for a degree. This move is the largest step students make in their education, and the debate about it in the UK has been reignited due to the government’s planned changes to A-level geography. However, missing from most of this debate is an appreciation of the way in which geography students themselves perceive their transition to university. This paper begins to rectify this absence. Using student insights, we show that their main concern is acquiring the higher level skills required for university learning