Nariai--Bertotti--Robinson spacetimes as a building material for one-way wormholes with horizons, but without singularity

We discuss the problem of wormholes from the viewpoint of gluing together two Reissner--Nordstr\"om-type universes while putting between them a segment of the Nariai-type world (in both cases there are also present electromagnetic fields as well as the cosmological constant). Such a toy wormhole represents an example of one-way topological communication free from causal paradoxes, though involving a travel to next spacetime sheet since one has to cross at least a pair of horizons through which the spacetimes' junction occurs. We also consider the use of thin shells in these constructions. Such a ``material'' for wormholes we choose taking into account specific properties of the Nariai--Bertotti--Robinson spacetimes.Comment: 5 pages, a talk delivered at the 11th Marcel Grossmann Meeting (2006

Magneto-Conductance Anisotropy and Interference Effects in Variable Range Hopping

We investigate the magneto-conductance (MC) anisotropy in the variable range hopping regime, caused by quantum interference effects in three dimensions. When no spin-orbit scattering is included, there is an increase in the localization length (as in two dimensions), producing a large positive MC. By contrast, with spin-orbit scattering present, there is no change in the localization length, and only a small increase in the overall tunneling amplitude. The numerical data for small magnetic fields $B$, and hopping lengths $t$, can be collapsed by using scaling variables $B_\perp t^{3/2}$, and $B_\parallel t$ in the perpendicular and parallel field orientations respectively. This is in agreement with the flux through a `cigar'--shaped region with a diffusive transverse dimension proportional to $\sqrt{t}$. If a single hop dominates the conductivity of the sample, this leads to a characteristic orientational `finger print' for the MC anisotropy. However, we estimate that many hops contribute to conductivity of typical samples, and thus averaging over critical hop orientations renders the bulk sample isotropic, as seen experimentally. Anisotropy appears for thin films, when the length of the hop is comparable to the thickness. The hops are then restricted to align with the sample plane, leading to different MC behaviors parallel and perpendicular to it, even after averaging over many hops. We predict the variations of such anisotropy with both the hop size and the magnetic field strength. An orientational bias produced by strong electric fields will also lead to MC anisotropy.Comment: 24 pages, RevTex, 9 postscript figures uuencoded Submitted to PR

Small oscillations and the Heisenberg Lie algebra

The Adler Kostant Symes [A-K-S] scheme is used to describe mechanical systems for quadratic Hamiltonians of $\mathbb R^{2n}$ on coadjoint orbits of the Heisenberg Lie group. The coadjoint orbits are realized in a solvable Lie algebra $\mathfrak g$ that admits an ad-invariant metric. Its quadratic induces the Hamiltonian on the orbits, whose Hamiltonian system is equivalent to that one on $\mathbb R^{2n}$. This system is a Lax pair equation whose solution can be computed with help of the Adjoint representation. For a certain class of functions, the Poisson commutativity on the coadjoint orbits in $\mathfrak g$ is related to the commutativity of a family of derivations of the 2n+1-dimensional Heisenberg Lie algebra $\mathfrak h_n$. Therefore the complete integrability is related to the existence of an n-dimensional abelian subalgebra of certain derivations in $\mathfrak h_n$. For instance, the motion of n-uncoupled harmonic oscillators near an equilibrium position can be described with this setting.Comment: 17 pages, it contains a theory about small oscillations in terms of the AKS schem

Stripe to spot transition in a plant root hair initiation model

A generalised Schnakenberg reaction-diffusion system with source and loss terms and a spatially dependent coefficient of the nonlinear term is studied both numerically and analytically in two spatial dimensions. The system has been proposed as a model of hair initiation in the epidermal cells of plant roots. Specifically the model captures the kinetics of a small G-protein ROP, which can occur in active and inactive forms, and whose activation is believed to be mediated by a gradient of the plant hormone auxin. Here the model is made more realistic with the inclusion of a transverse co-ordinate. Localised stripe-like solutions of active ROP occur for high enough total auxin concentration and lie on a complex bifurcation diagram of single and multi-pulse solutions. Transverse stability computations, confirmed by numerical simulation show that, apart from a boundary stripe, these 1D solutions typically undergo a transverse instability into spots. The spots so formed typically drift and undergo secondary instabilities such as spot replication. A novel 2D numerical continuation analysis is performed that shows the various stable hybrid spot-like states can coexist. The parameter values studied lead to a natural singularly perturbed, so-called semi-strong interaction regime. This scaling enables an analytical explanation of the initial instability, by describing the dispersion relation of a certain non-local eigenvalue problem. The analytical results are found to agree favourably with the numerics. Possible biological implications of the results are discussed.Comment: 28 pages, 44 figure

A review of research on the effects of drought and temperature stress and increased CO2 on Theobroma cacao L., and the role of genetic diversity to address climate change

The global status of research on the effects of drought, temperature and elevated carbon dioxide (CO2) levels on the cacao plant, and the role of genetic diversity in producing more resilient cacao, are presented in this report. With the aim to enhance what we know about the resilience of cacao to climate change, and generate a comprehensive understanding of the questions that remain, this report highlights significant advances in published and ongoing research on drought and temperature tolerance in cacao. Most of the information about ongoing or unpublished work was obtained from personal communications and surveys involving research institutes around the globe. Organizations were selected to participate in the survey based on their presence in the relevant literature, referrals from other organizations, or personal communications from individuals attesting to their involvement in research related to drought and temperature tolerance, or increased CO2 response, in cacao. A vast network of public and private sector partners including research institutes, producer organizations, and industry representatives around the world participated and were involved to collect additional information on unpublished and on-going research work in this area. Over a 100 scientists from 50 institutes across 29 countries participated. Additional information was gathered from personal communications, surveys carried out in collaboration with WCF and its USAID-supported Feed the Future Partnership for the Climate-Smart Cocoa Program, the Global Network for Cacao Genetic Resources (CacaoNet), the International Network for Cacao Genetic Improvement (INGENIC), the Regional Breeders Working Groups, and the research team on cacao and climate change at the University of Reading, UK. Fundamentally, the literature compiled in this report serves as a basis to understand the questions that still remain regarding cacao’s responses to abiotic stresses, highlight the resources that are available to answer them, and identify synergies and complementarities. The report also helps to identify key research questions and partners for the development of a proposal for an international/multi-institutional research programme, to be implemented over the next three to five years, as part of the Collaborative Framework for Cacao Evaluation (CFCE). Although future climatic predictions are worrisome, the genetic materials held within national and international collections offer much potential in the development of improved planting material. The objective of the report is to gather as much information as possible, so that we can aim to maximize the resilience of cacao through the discovery and use of improved planting material, in combination with improved management practices.  We express our gratitude to all of those who provided details of their research on cacao genetic resources and abiotic stress and we acknowledge financial support of WCF and its Feed the Future Partnership for Climate Smart Cocoa, through a grant to Bioversity International from USDA-FAS, the ECA/CAOBISCO/FCC Joint Working Group on Cocoa Quality and Productivity; and the CGIAR Research Program on Forests, Trees and Agroforestry (FTA)