Third Harmonic Cavity Modal Analysis

Third harmonic cavities have been designed and fabricated by FNAL to be used at the FLASH/XFEL facility at DESY to minimise the energy spread along the bunches. Modes in these cavities are analysed and the sensitivity to frequency errors are assessed. A circuit model is employed to model the monopole bands. The monopole circuit model is enhanced to include successive cell coupling, in addition to the usual nearest neighbour coupling. A mode matching code is used to facilitate rapid simulations, incorporating fabrication errors. Curves surfaces are approximated by a series of abrupt transitions and the validity of this approach is examinedComment: Proceedings of 14th International Conference on RF Superconductivity (SRF 2009), 2009, Berlin, German

When does cyclic dominance lead to stable spiral waves?

Species diversity in ecosystems is often accompanied by characteristic spatio-temporal patterns. Here, we consider a generic two-dimensional population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species, mutation, pair-exchange and individual hopping. The dynamics is characterized by nonlinear mobility and a Hopf bifurcation around which the system's four-phase state diagram is inferred from a complex Ginzburg-Landau equation derived using a perturbative multiscale expansion. While the dynamics is generally characterized by spiraling patterns, we show that spiral waves are stable in only one of the four phases. Furthermore, we characterize a phase where nonlinearity leads to the annihilation of spirals and to the spatially uniform dominance of each species in turn. Away from the Hopf bifurcation, when the coexistence fixed point is unstable, the spiraling patterns are also affected by the nonlinear diffusion

Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level

We introduce the infinite-dimensional Lie superalgebra ${\mathcal A}$ and construct a family of mappings from certain category of ${\mathcal A}$-modules to the category of A_1^(1)-modules of critical level. Using this approach, we prove the irreducibility of a family of A_1^(1)-modules at the critical level. As a consequence, we present a new proof of irreducibility of certain Wakimoto modules. We also give a natural realizations of irreducible quotients of relaxed Verma modules and calculate characters of these representations.Comment: 21 pages, Late

Spirals and heteroclinic cycles in a spatially extended Rock-Paper-Scissors model of cyclic dominance

Spatially extended versions of the cyclic-dominance Rock-Paper-Scissors model have traveling wave (in one dimension) and spiral (in two dimensions) behaviour. The far field of the spirals behave like traveling waves, which themselves have profiles reminiscent of heteroclinic cycles. We compute numerically a nonlinear dispersion relation between the wavelength and wavespeed of the traveling waves, and, together with insight from heteroclinic bifurcation theory and further numerical results from 2D simulations, we are able to make predictions about the overall structure and stability of spiral waves in 2D cyclic dominance models

Production and characterization of recombinant protein preparations of Endonuclease G-homologs from yeast, C. elegans and humans

Nuc1p, CPS-6, EndoG and EXOG are evolutionary conserved mitochondrial nucleases from yeast, Caenorhabditis elegans and humans, respectively. These enzymes play an important role in programmed cell death as well as mitochondrial DNA-repair and recombination. Whereas a significant interest has been given to the cell biology of these proteins, in particular their recruitment during caspase-independent apoptosis, determination of their biochemical properties has lagged behind. In part, biochemical as well as structural analysis of mitochondrial nucleases has been hampered by the fact that upon cloning and overexpression in Escherichia coli these enzymes can exert considerable toxicity and tend to aggregate and form inclusion bodies. We have, therefore, established a uniform E. coli expression system allowing us to obtain these four evolutionary related nucleases in active form from the soluble as well as insoluble fractions of E. coli cell lysates. Using preparations of recombinant Nuc1p, CPS-6, EndoG and EXOG we have compared biochemical properties and the substrate specificities of these related nucleases on selected substrates in parallel. Whereas Nuc1p and EXOG in addition to their endonuclease activity exert 5'-3'- exonuclease activity, CPS-6 and EndoG predominantly are endonucleases. These findings allow speculating that the mechanisms of action of these related nucleases in cell death as well as DNA-repair and recombination differ according to their enzyme activities and substrate specificities. © 2010 Elsevier Inc. All rights reserved

Cyclotomic Gaudin models: construction and Bethe ansatz

This is a pre-copyedited author produced PDF of an article accepted for publication in Communications in Mathematical Physics, Benoit, V and Young, C, 'Cyclotomic Gaudin models: construction and Bethe ansatz', Commun. Math. Phys. (2016) 343:971, first published on line March 24, 2016. The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-016-2601-3 © Springer-Verlag Berlin Heidelberg 2016To any simple Lie algebra $\mathfrak g$ and automorphism $\sigma:\mathfrak g\to \mathfrak g$ we associate a cyclotomic Gaudin algebra. This is a large commutative subalgebra of $U(\mathfrak g)^{\otimes N}$ generated by a hierarchy of cyclotomic Gaudin Hamiltonians. It reduces to the Gaudin algebra in the special case $\sigma = \text{id}$. We go on to construct joint eigenvectors and their eigenvalues for this hierarchy of cyclotomic Gaudin Hamiltonians, in the case of a spin chain consisting of a tensor product of Verma modules. To do so we generalize an approach to the Bethe ansatz due to Feigin, Frenkel and Reshetikhin involving vertex algebras and the Wakimoto construction. As part of this construction, we make use of a theorem concerning cyclotomic coinvariants, which we prove in a companion paper. As a byproduct, we obtain a cyclotomic generalization of the Schechtman-Varchenko formula for the weight function.Peer reviewe

Gepner-like models and Landau-Ginzburg/sigma-model correspondence

The Gepner-like models of $k^{K}$-type is considered. When $k+2$ is multiple of $K$ the elliptic genus and the Euler characteristic is calculated. Using free-field representation we relate these models with $\sigma$-models on hypersurfaces in the total space of anticanonical bundle over the projective space $\mathbb{P}^{K-1}$

Effects of noise on convergent game learning dynamics

We study stochastic effects on the lagging anchor dynamics, a reinforcement learning algorithm used to learn successful strategies in iterated games, which is known to converge to Nash points in the absence of noise. The dynamics is stochastic when players only have limited information about their opponents' strategic propensities. The effects of this noise are studied analytically in the case where it is small but finite, and we show that the statistics and correlation properties of fluctuations can be computed to a high accuracy. We find that the system can exhibit quasicycles, driven by intrinsic noise. If players are asymmetric and use different parameters for their learning, a net payoff advantage can be achieved due to these stochastic oscillations around the deterministic equilibrium.Comment: 17 pages, 8 figure

Structure of the Head of the Bartonella Adhesin BadA

Trimeric autotransporter adhesins (TAAs) are a major class of proteins by which pathogenic proteobacteria adhere to their hosts. Prominent examples include Yersinia YadA, Haemophilus Hia and Hsf, Moraxella UspA1 and A2, and Neisseria NadA. TAAs also occur in symbiotic and environmental species and presumably represent a general solution to the problem of adhesion in proteobacteria. The general structure of TAAs follows a head-stalk-anchor architecture, where the heads are the primary mediators of attachment and autoagglutination. In the major adhesin of Bartonella henselae, BadA, the head consists of three domains, the N-terminal of which shows strong sequence similarity to the head of Yersinia YadA. The two other domains were not recognizably similar to any protein of known structure. We therefore determined their crystal structure to a resolution of 1.1 Å. Both domains are β-prisms, the N-terminal one formed by interleaved, five-stranded β-meanders parallel to the trimer axis and the C-terminal one by five-stranded β-meanders orthogonal to the axis. Despite the absence of statistically significant sequence similarity, the two domains are structurally similar to domains from Haemophilus Hia, albeit in permuted order. Thus, the BadA head appears to be a chimera of domains seen in two other TAAs, YadA and Hia, highlighting the combinatorial evolutionary strategy taken by pathogens