Models of Microbial Dormancy in Biofilms and Planktonic Cultures

We present models of dormancy in a planktonic culture and in biofilm, and examine the relative advantage of short dormancy versus long dormancy times in each case. Simulations and analyses indicate that in planktonic batch cultures and in chemostats, live biomass is maximized by the fastest possible exit from dormancy. The lower limit of time to reawakening is thus perhaps governed by physiological, biochemical or other constraints within the cells. In biofilm we see that the slower waker has a defensive advantage over the fast waker due to a larger amount of dormant biomass, without an appreciable difference in total live biomass. Thus it would seem that typical laboratory culture conditions can be unrepresentative of the natural state. We discuss the computational methods developed for this work

Research into advanced concepts of microwave power amplification and generation utilizing linear beam devices Semiannual status report

Coupled mode theory for interaction of spiraling filamentary electron beam and modes of square waveguid

Fatigue crack growth rates for offshore wind monopile weldments in air and seawater: SLIC inter-laboratory test results

The majority of fatigue crack growth (FCG) data sets available on steels in air and seawater environments are several decades old and may not be appropriate for structural integrity assessment of offshore wind turbine foundations, which are fabricated using contemporary materials and welding technologies. Therefore, the SLIC joint industry project was formed to investigate the fatigue crack initiation and growth behaviour in offshore wind welded steel foundations. The FCG test data from the SLIC inter-laboratory (round robin) test programme have been analysed using a new proposed shape function solution and the results are presented and discussed. The obtained FCG trends in air and seawater environments have been compared with the recommended trends available in standards. The Paris-law constants and ΔKth values obtained from this programme can be used for defect assessment and remaining life prediction of offshore monopile weldments in air and seawater environments. The results from the SLIC project show that for a given value of ΔK the fatigue crack growth rate, da/dN, is on average around 2 times higher in seawater compared to air for the base metal and weldments. This factor of 2 in the seawater environment is almost half of the crack acceleration factor recommended by standards

Z2×Z2 \mathbb{Z}_2 \times \mathbb{Z}_2 generalizations of N=1{\cal N} = 1 superconformal Galilei algebras and their representations

We introduce two classes of novel color superalgebras of $\mathbb{Z}_2 \times \mathbb{Z}_2$ grading. This is done by realizing members of each in the universal enveloping algebra of the ${\cal N}=1$ supersymmetric extension of the conformal Galilei algebra. This allows us to upgrade any representation of the super conformal Galilei algebras to a representation of the $\mathbb{Z}_2 \times \mathbb{Z}_2$ graded algebra. As an example, boson-fermion Fock space representation of one class is given. We also provide a vector field realization of members of the other class by using a generalization of the Grassmann calculus to $\mathbb{Z}_2 \times \mathbb{Z}_2$ graded setting.Comment: 17 pages, no figur

A Multiscale Model of Biofilm as a Senescence-Structured Fluid

We derive a physiologically structured multiscale model for biofilm development. The model has components on two spatial scales, which induce different time scales into the problem. The macroscopic behavior of the system is modeled using growth-induced flow in a domain with a moving boundary. Cell-level processes are incorporated into the model using a so-called physiologically structured variable to represent cell senescence, which in turn affects cell division and mortality. We present computational results for our models which shed light on modeling the combined role senescence and the biofilm state play in the defense strategy of bacteria

Representations of the quantum doubles of finite group algebras and solutions of the Yang--Baxter equation

Quantum doubles of finite group algebras form a class of quasi-triangular Hopf algebras which algebraically solve the Yang--Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang--Baxter equation. Such solutions do not depend on a spectral parameter, and to date there has been little investigation into extending these solutions such that they do depend on a spectral parameter. Here we first explicitly construct the matrix elements of the generators for all irreducible representations of quantum doubles of the dihedral groups $D_n$. These results may be used to determine constant solutions of the Yang--Baxter equation. We then discuss Baxterisation ans\"atze to obtain solutions of the Yang--Baxter equation with spectral parameter and give several examples, including a new 21-vertex model. We also describe this approach in terms of minimal-dimensional representations of the quantum doubles of the alternating group $A_4$ and the symmetric group $S_4$.Comment: 19 pages, no figures, changed introduction, added reference

Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras

The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are viewed as descendants of the six-vertex model case, are then obtained using tensor product graph methods which were originally formulated for quantum algebras. Connections with the Fateev-Zamolodchikov model are discussed.Comment: 34 pages, 2 figure