Transition state theory and the dynamics of hard disks

The dynamics of two and five disk systems confined in a square has been studied using molecular dynamics simulations and compared with the predictions of transition state theory. We determine the partition functions Z and Z^\ddagger of transition state theory using a procedure first used by Salsburg and Wood for the pressure. Our simulations show this procedure and transition state theory are in excellent agreement with the simulations. A generalization of the transition state theory to the case of a large number of disks N is made and shown to be in full agreement with simulations of disks moving in a narrow channel. The same procedure for hard spheres in three dimensions leads to the Vogel-Fulcher-Tammann formula for their alpha relaxation time.Comment: 1 new author, new simulations and figures, less speculation. Now 6 pages, 6 figures, 1 animation. Animation may be viewed at http://www.theory.physics.manchester.ac.uk/~godfrey/supplement/activated_dynamics2.htm

A Search for Biomolecules in Sagittarius B2 (LMH) with the ATCA

We have used the Australia Telescope Compact Array to conduct a search for the simplest amino acid, glycine (conformers I and II), and the simple chiral molecule propylene oxide at 3-mm in the Sgr B2 LMH. We searched 15 portions of spectrum between 85 and 91 GHz, each of 64 MHz bandwidth, and detected 58 emission features and 21 absorption features, giving a line density of 75 emission lines and 25 absorption lines per GHz stronger than the 5 sigma level of 110 mJy. Of these, 19 are transitions previously detected in the interstellar medium, and we have made tentative assignments of a further 23 features to molecular transitions. However, as many of these involve molecules not previously detected in the ISM, these assignments cannot be regarded with confidence. Given the median line width of 6.5 km/s in Sgr B2 LMH, we find that the spectra have reached a level where there is line confusion, with about 1/5 of the band being covered with lines. Although we did not confidently detect either glycine or propylene oxide, we can set 3 sigma upper limits for most transitions searched. We also show that if glycine is present in the Sgr B2 LMH at the level of N = 4 x 10^{14} cm^{-2} found by Kuan et al. (2003) in their reported detection of glycine, it should have been easily detected with the ATCA synthesized beam size of 17.0 x 3.4 arcsec^{2}, if it were confined to the scale of the LMH continuum source (< 5 arcsec). This thus puts a strong upper limit on any small-scale glycine emission in Sgr B2, for both of conformers I and II.Comment: 12 pages, 2 figures, 5 tables, accepted by MNRA

Finite size scaling of the correlation length above the upper critical dimension

We show numerically that correlation length at the critical point in the five-dimensional Ising model varies with system size L as L^{5/4}, rather than proportional to L as in standard finite size scaling (FSS) theory. Our results confirm a hypothesis that FSS expressions in dimension d greater than the upper critical dimension of 4 should have L replaced by L^{d/4} for cubic samples with periodic boundary conditions. We also investigate numerically the logarithmic corrections to FSS in d = 4.Comment: 5 pages, 6 postscript figure

A Nearly Scale Invariant Spectrum of Gravitational Radiation from Global Phase Transitions

Using a large N sigma model approximation we explicitly calculate the power spectrum of gravitational waves arising from a global phase transition in the early universe and we confirm that it is scale invariant, implying an observation of such a spectrum may not be a unique feature of inflation. Moreover, the predicted amplitude can be over 3 orders of magnitude larger than the naive dimensional estimate, implying that even a transition that occurs after inflation may dominate in Cosmic Microwave Background polarization or other gravity wave signals.Comment: 4 pages, PRL published versio

Mopra CO Observations of the Bubble HII Region RCW120

We use the Mopra radio telescope to test for expansion of the molecular gas associated with the bubble HII region RCW120. A ring, or bubble, morphology is common for Galactic HII regions, but the three-dimensional geometry of such objects is still unclear. Detected near- and far-side expansion of the associated molecular material would be consistent with a three-dimensional spherical object. We map the $J = 1\rightarrow 0$ transitions of $^{12}$CO, $^{13}$CO, C$^{18}$O, and C$^{17}$O, and detect emission from all isotopologues. We do not detect the $0_0\rightarrow 1_{-1} E$ masing lines of CH$_3$OH at 108.8939 GHz. The strongest CO emission is from the photodissociation region (PDR), and there is a deficit of emission toward the bubble interior. We find no evidence for expansion of the molecular material associated with RCW120 and therefore can make no claims about its geometry. The lack of detected expansion is roughly in agreement with models for the time-evolution of an HII region like RCW120, and is consistent with an expansion speed of $< 1.5\, {\rm km\, s^{-1}}$. Single-position CO spectra show signatures of expansion, which underscores the importance of mapped spectra for such work. Dust temperature enhancements outside the PDR of RCW120 coincide with a deficit of emission in CO, confirming that these temperature enhancements are due to holes in the RCW120 PDR. H$\alpha$ emission shows that RCW120 is leaking $\sim5\%$ of the ionizing photons into the interstellar medium (ISM) through PDR holes at the locations of the temperature enhancements. H-alpha emission also shows a diffuse "halo" from leaked photons not associated with discrete holes in the PDR. Overall $25\pm10\%$ of all ionizing photons are leaking into the nearby ISM.Comment: 35 pages, 14 figures. Accepted to Ap

Turning the Quantum Group Invariant XXZ Spin-Chain Hermitian: A Conjecture on the Invariant Product

This is a continuation of a previous joint work with Robert Weston on the quantum group invariant XXZ spin-chain (math-ph/0703085). The previous results on quasi-Hermiticity of this integrable model are briefly reviewed and then connected with a new construction of an inner product with respect to which the Hamiltonian and the representation of the Temperley-Lieb algebra become Hermitian. The approach is purely algebraic, one starts with the definition of a positive functional over the Temperley-Lieb algebra whose values can be computed graphically. Employing the Gel'fand-Naimark-Segal (GNS) construction for C*-algebras a self-adjoint representation of the Temperley-Lieb algebra is constructed when the deformation parameter q lies in a special section of the unit circle. The main conjecture of the paper is the unitary equivalence of this GNS representation with the representation obtained in the previous paper employing the ideas of PT-symmetry and quasi-Hermiticity. An explicit example is presented.Comment: 12 page

A view of Large Magellanic Cloud HII regions N159, N132, and N166 through the 345 GHz window

We present results obtained towards the HII regions N159, N166, and N132 from the emission of several molecular lines in the 345 GHz window. Using ASTE we mapped a 2.4' $\times$ 2.4' region towards the molecular cloud N159-W in the $^{13}$CO J=3-2 line and observed several molecular lines at an IR peak very close to a massive young stellar object. $^{12}$CO and $^{13}$CO J=3-2 were observed towards two positions in N166 and one position in N132. The $^{13}$CO J=3-2 map of the N159-W cloud shows that the molecular peak is shifted southwest compared to the peak of the IR emission. Towards the IR peak we detected emission from HCN, HNC, HCO$^{+}$, C$_{2}$H J=4-3, CS J=7-6, and tentatively C$^{18}$O J=3-2. This is the first reported detection of these molecular lines in N159-W. The analysis of the C$_{2}$H line yields more evidence supporting that the chemistry involving this molecular species in compact and/or UCHII regions in the LMC should be similar to that in Galactic ones. A non-LTE study of the CO emission suggests the presence of both cool and warm gas in the analysed region. The same analysis for the CS, HCO$^{+}$, HCN, and HNC shows that it is very likely that their emissions arise mainly from warm gas with a density between $5 \times 10^5$ to some $10^6$ cm$^{-3}$. The obtained HCN/HNC abundance ratio greater than 1 is compatible with warm gas and with an star-forming scenario. From the analysis of the molecular lines observed towards N132 and N166 we propose that both regions should have similar physical conditions, with densities of about 10$^3$ cm$^{-3}$.Comment: accepted in MNRAS (October 5, 2015

Modulation of endoglin expression in islets of langerhans by VEGF reveals a novel regulator of islet endothelial cell function

BACKGROUND: Endoglin/CD105 is an auxiliary receptor for transforming growth factor-β with established roles in vascular remodelling. It has recently been shown that heterozygous endoglin deficiency in mice decreases insulin secretion in an animal model of obesity, highlighting a potential role for endoglin in the regulation of islet function. We have previously identified two different populations of endoglin expressing cells in human and mouse islets which are: (i) endothelial cells (ECs) and (ii) islet mesenchymal stromal cells. The contribution of islet EC endoglin expression to islet development and sensitivity to VEGF is unknown and is the focus of this study. RESULTS: In vitro culture of mouse islets with VEGF164 for 48 h increased endoglin mRNA levels above untreated controls but VEGF did not modulate VEGFR2, CD31 or CD34 mRNA expression or islet viability. Removal of EC-endoglin expression in vivo reduced islet EC area but had no apparent effect on islet size or architecture. CONCLUSION: EC-specific endoglin expression in islets is sensitive to VEGF and plays partial roles in driving islet vascular development, however such regulation appears to be distinct to mechanisms required to modulate islet viability and size