Stability of Cross-Feeding Polymorphisms in Microbial Communities

This is the final version of the article. Available from Public Library of Science via the DOI in this record.Cross-feeding, a relationship wherein one organism consumes metabolites excreted by another, is a ubiquitous feature of natural and clinically-relevant microbial communities and could be a key factor promoting diversity in extreme and/or nutrient-poor environments. However, it remains unclear how readily cross-feeding interactions form, and therefore our ability to predict their emergence is limited. In this paper we developed a mathematical model parameterized using data from the biochemistry and ecology of an E. coli cross-feeding laboratory system. The model accurately captures short-term dynamics of the two competitors that have been observed empirically and we use it to systematically explore the stability of cross-feeding interactions for a range of environmental conditions. We find that our simple system can display complex dynamics including multi-stable behavior separated by a critical point. Therefore whether cross-feeding interactions form depends on the complex interplay between density and frequency of the competitors as well as on the concentration of resources in the environment. Moreover, we find that subtly different environmental conditions can lead to dramatically different results regarding the establishment of cross-feeding, which could explain the apparently unpredictable between-population differences in experimental outcomes. We argue that mathematical models are essential tools for disentangling the complexities of cross-feeding interactions.IG was supported by a Natural Environment Research Council (NERC) Advanced Fellowship NE/E013007/3 and a European Research Council (ERC) Consolidator grant MathModExp 647292, MK was funded by a National Aeronautics and Space Administration (NASA) NPP Fellowship and NASA NNX12AD87G, IG and PR were funded by a Biotechnology and Biological Sciences Research Council (BBSRC) grant BB/J010340/1, KS was supported by National Human Genome Research Institute (NHGRI) 2R01HG003328 - 07A1 and FR was supported by NASA NNX12AD87G. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Numerical Study of the Lowest Energy Configurations for Global String-Antistring Pairs

We investigate the lowest energy configurations for string - antistring pairs at fixed separations by numerically minimizing the energy. We show that for separations smaller than a critical value, a region of false vacuum develops in the middle due to large gradient energy density. Consequently, well defined string - antistring pairs do not exist for such separations. We present an example of vortex - antivortex production by vacuum bubbles where this effect seems to play a dynamical role in the annihilation of the pair. We also study the dependence of the energy of an string-antistring pair on their separation and find deviations from a simple logarithmic dependence for small separations.Comment: 14 pages, in LATEX, 7 figures (not included

On the Theory of Relativistic Strong Plasma Waves

The influence of motion of ions and electron temperature on nonlinear one-dimensional plasma waves with velocity close to the speed of light in vacuum is investigated. It is shown that although the wavebreaking field weakly depends on mass of ions, the nonlinear relativistic wavelength essentially changes. The nonlinearity leads to the increase of the strong plasma wavelength, while the motion of ions leads to the decrease of the wavelength. Both hydrodynamic approach and kinetic one, based on Vlasov-Poisson equations, are used to investigate the relativistic strong plasma waves in a warm plasma. The existence of relativistic solitons in a thermal plasma is predicted.Comment: 13 pages, 8 figure

Stability of the Black Hole Horizon and the Landau Ghost

The stability of the black hole horizon is demanded by both cosmic censorship and the generalized second law of thermodynamics. We test the consistency of these principles by attempting to exceed the black hole extremality condition in various process in which a U(1) charge is added to a nearly extreme Reissner--Nordstr\"om black hole charged with a {\it different\/} type of U(1) charge. For an infalling spherical charged shell the attempt is foiled by the self--Coulomb repulsion of the shell. For an infalling classical charge it fails because the required classical charge radius exceeds the size of the black hole. For a quantum charge the horizon is saved because in order to avoid the Landau ghost, the effective coupling constant cannot be large enough to accomplish the removal.Comment: 12 pages, RevTe

Energy Loss of a High Charge Bunched Electron Beam in Plasma

There has been much interest in the blowout regime of plasma wakefield acceleration (PWFA), which features ultra-high fields and nonlinear plasma motion. Using an exact analysis, we examine here a fundamental limit of nonlinear PWFA excitation, by an infinitesimally short, relativistic electron beam. The beam energy loss in this case is shown to be linear in charge even for nonlinear plasma response, where a normalized, unitless charge exceeds unity. The physical basis for this effect is discussed, as are deviations from linear behavior observed in simulations with finite length beams.Comment: Submitted to Physical Review Letter

Novel Studies on the \eta' Effective Lagrangian

The effective Lagrangian for \eta' incorporating the effect of the QCD \theta-angle has been developed previously. We revisit this Lagrangian and carry out its canonical quantization with particular attention to the test function spaces of constraints and the topology of the \eta'-field. In this way, we discover a new chirally symmetric coupling of this field to chiral multiplets which involves in particular fermions. This coupling violates P and T symmetries. In a subsequent paper, we will evaluate its contribution to the electric dipole moment (EDM) of fermions. Our motivation is to test whether the use of mixed states restores P and T invariance, so that EDM vanishes. This calculation will be shown to have striking new physical consequences.Comment: 14 pages, 1 figure; V2: NEW TITLE; revised version to be published in JHEP; references adde