Algebras in Higher Dimensional Statistical Mechanics - the Exceptional Partition (MEAN Field) Algebras

We determine the structure of the partition algebra $P_n(Q)$ (a generalized Temperley-Lieb algebra) for specific values of Q \in \C, focusing on the quotient which gives rise to the partition function of $n$ site $Q$-state Potts models (in the continuous $Q$ formulation) in arbitrarily high lattice dimensions (the mean field case). The algebra is non-semi-simple iff $Q$ is a non-negative integer less than $n$. We determine the dimension of the key irreducible representation in every specialization.Comment: 4 page

Optical and Infrared Analysis of Type II SN 2006BC

We present nebular phase optical imaging and spectroscopy and near/mid-IR imaging of the Type II SN 2006bc. Observations reveal the central wavelength of the symmetric H$\alpha$ line profile to be red-shifted with respect to the host galaxy H$\alpha$ emission by day 325. Such an phenomenon has been argued to result from an asymmetric explosion in the iron-peak elements resulting in a larger mass of $^{56}$Ni and higher excitation of hydrogen on the far side of the SN explosion. We also observe a gradual blue-shifting of this H$\alpha$ peak which is indicative of dust formation in the ejecta. Although showing a normal peak brightness, V $\sim$ -17.2, for a core-collapse SN, 2006bc fades by $\sim$6 mag during the first 400 days suggesting either a relatively low $^{56}$Ni yield, an increase in extinction due to new dust, or both. A short duration flattening of the light curve is observed from day 416 to day 541 suggesting an optical light echo. Based on the narrow time window of this echo, we discuss implications on the location and geometry of the reflecting ISM. With our radiative transfer models, we find an upper limit of 2 x 10$^{-3}$ M$_{\odot}$ of dust around SN 2006bc. In the event that all of this dust were formed during the SN explosion, this quantity of dust is still several orders of magnitude lower than that needed to explain the large quantities of dust observed in the early universe.Comment: 6 pages, 10 figures, accepted for publication in Ap

Exact S-matrices for supersymmetric sigma models and the Potts model

We study the algebraic formulation of exact factorizable S-matrices for integrable two-dimensional field theories. We show that different formulations of the S-matrices for the Potts field theory are essentially equivalent, in the sense that they can be expressed in the same way as elements of the Temperley-Lieb algebra, in various representations. This enables us to construct the S-matrices for certain nonlinear sigma models that are invariant under the Lie ``supersymmetry'' algebras sl(m+n|n) (m=1,2; n>0), both for the bulk and for the boundary, simply by using another representation of the same algebra. These S-matrices represent the perturbation of the conformal theory at theta=pi by a small change in the topological angle theta. The m=1, n=1 theory has applications to the spin quantum Hall transition in disordered fermion systems. We also find S-matrices describing the flow from weak to strong coupling, both for theta=0 and theta=pi, in certain other supersymmetric sigma models.Comment: 32 pages, 8 figure

Sensitivity of historical climate simulations to uncertain aerosol forcing

The relative importance of anthropogenic aerosol in decadal variations of historical climate is uncertain, largely due to uncertainty in aerosol radiative forcing. We analyse a novel large ensemble of simulations with HadGEM3-GC3.1 for 1850-2014, where anthropogenic aerosol and precursor emissions are scaled to sample a wide range of historical aerosol radiative forcing with present-day values ranging from -0.38 to -1.50 Wm-2. Five ensemble members are run for each of five aerosol scaling factors. Decadal variations in surface temperatures are strongly sensitive to aerosol forcing, particularly between 1950 and 1980. Post-1980, trends are dominated by greenhouse-gas forcing, with much lower sensitivity to aerosol emission differences. Most realisations with aerosol forcing more negative than about -1 Wm-2 simulate stronger cooling trends in the mid-twentieth century compared to observations, while the simulated warming post-1980 always exceeds observed warming, likely due to a warm bias in the Transient Climate Response in HadGEM3-GC3.1

Hydrodynamic excitations of Bose condensates in anisotropic traps

The collective excitations of Bose condensates in anisotropic axially symmetric harmonic traps are investigated in the hydrodynamic and Thomas-Fermi limit. We identify an additional conserved quantity, besides the axial angular momentum and the total energy, and separate the wave equation in elliptic coordinates. The solution is reduced to the algebraic problem of diagonalizing finite dimensional matrices. The classical quasi-particle dynamics in the local density approximation for energies of the order of the chemical potential is shown to be chaotic.Comment: 4 pages revtex including 1 table, and 1 figure in postscrip

Turbulent Linewidths as a Diagnostic of Self-Gravity in Protostellar Discs

We use smoothed particle hydrodynamics simulations of massive protostellar discs to investigate the predicted broadening of molecular lines from discs in which self-gravity is the dominant source of angular momentum transport. The simulations include radiative transfer, and span a range of disc-to-star mass ratios between 0.25 and 1.5. Subtracting off the mean azimuthal flow velocity, we compute the distribution of the in-plane and perpendicular peculiar velocity due to large scale structure and turbulence induced by self-gravity. For the lower mass discs, we show that the characteristic peculiar velocities scale with the square root of the effective turbulent viscosity parameter, as expected from local turbulent-disc theory. The derived velocities are anisotropic, with substantially larger in-plane than perpendicular values. As the disc mass is increased, the validity of the locally determined turbulence approximation breaks down, and this is accompanied by anomalously large in-plane broadening. There is also a high variance due to the importance of low-m spiral modes. For low-mass discs, the magnitude of in-plane broadening is, to leading order, equal to the predictions from local disc theory and cannot constrain the source of turbulence. However, combining our results with prior evaluations of turbulent broadening expected in discs where the magnetorotational instability (MRI) is active, we argue that self-gravity may be distinguishable from the MRI in these systems if it is possible to measure the anisotropy of the peculiar velocity field with disc inclination. Furthermore, for large mass discs, the dominant contribution of large-scale modes is a distinguishing characteristic of self-gravitating turbulence versus MRI driven turbulence.Comment: 8 pages, 13 figures, accepted for publication in MNRA

Numerical Estimation of the Asymptotic Behaviour of Solid Partitions of an Integer

The number of solid partitions of a positive integer is an unsolved problem in combinatorial number theory. In this paper, solid partitions are studied numerically by the method of exact enumeration for integers up to 50 and by Monte Carlo simulations using Wang-Landau sampling method for integers up to 8000. It is shown that, for large n, ln[p(n)]/n^(3/4) = 1.79 \pm 0.01, where p(n) is the number of solid partitions of the integer n. This result strongly suggests that the MacMahon conjecture for solid partitions, though not exact, could still give the correct leading asymptotic behaviour.Comment: 6 pages, 4 figures, revtex

Adiabatic Output Coupling of a Bose Gas at Finite Temperatures

We develop a general theory of adiabatic output coupling from trapped atomic Bose-Einstein Condensates at finite temperatures. For weak coupling, the output rate from the condensate, and the excited levels in the trap, settles in a time proportional to the inverse of the spectral width of the coupling to the output modes. We discuss the properties of the output atoms in the quasi-steady-state where the population in the trap is not appreciably depleted. We show how the composition of the output beam, containing condensate and thermal component, may be controlled by changing the frequency of the output coupler. This composition determines the first and second order coherence of the output beam. We discuss the changes in the composition of the bose gas left in the trap and show how nonresonant output coupling can stimulate either the evaporation of thermal excitations in the trap or the growth of non-thermal excitations, when pairs of correlated atoms leave the condensate.Comment: 22 pages, 6 Figs. To appear in Physical Review A All the typos from the previous submission have been fixe

Feedback control architecture and the bacterial chemotaxis network.

PMCID: PMC3088647This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Bacteria move towards favourable and away from toxic environments by changing their swimming pattern. This response is regulated by the chemotaxis signalling pathway, which has an important feature: it uses feedback to 'reset' (adapt) the bacterial sensing ability, which allows the bacteria to sense a range of background environmental changes. The role of this feedback has been studied extensively in the simple chemotaxis pathway of Escherichia coli. However it has been recently found that the majority of bacteria have multiple chemotaxis homologues of the E. coli proteins, resulting in more complex pathways. In this paper we investigate the configuration and role of feedback in Rhodobacter sphaeroides, a bacterium containing multiple homologues of the chemotaxis proteins found in E. coli. Multiple proteins could produce different possible feedback configurations, each having different chemotactic performance qualities and levels of robustness to variations and uncertainties in biological parameters and to intracellular noise. We develop four models corresponding to different feedback configurations. Using a series of carefully designed experiments we discriminate between these models and invalidate three of them. When these models are examined in terms of robustness to noise and parametric uncertainties, we find that the non-invalidated model is superior to the others. Moreover, it has a 'cascade control' feedback architecture which is used extensively in engineering to improve system performance, including robustness. Given that the majority of bacteria are known to have multiple chemotaxis pathways, in this paper we show that some feedback architectures allow them to have better performance than others. In particular, cascade control may be an important feature in achieving robust functionality in more complex signalling pathways and in improving their performance