Large N lattice QCD and its extended strong-weak connection to the hypersphere

We calculate an effective Polyakov line action of QCD at large Nc and large Nf from a combined lattice strong coupling and hopping expansion working to second order in both, where the order is defined by the number of windings in the Polyakov line. We compare with the action, truncated at the same order, of continuum QCD on S^1 x S^d at weak coupling from one loop perturbation theory, and find that a large Nc correspondence of equations of motion found in \cite{Hollowood:2012nr} at leading order, can be extended to the next order. Throughout the paper, we review the background necessary for computing higher order corrections to the lattice effective action, in order to make higher order comparisons more straightforward.Comment: 33 pages, 7 figure

Calculating the chiral condensate diagrammatically at strong coupling

We calculate the chiral condensate of QCD at infinite coupling as a function of the number of fundamental fermion flavours using a lattice diagrammatic approach inspired by recent work of Tomboulis, and other work from the 80's. We outline the approach where the diagrams are formed by combining a truncated number of sub-diagram types in all possible ways. Our results show evidence of convergence and agreement with simulation results at small Nf. However, contrary to recent simulation results, we do not observe a transition at a critical value of Nf. We further present preliminary results for the chiral condensate of QCD with symmetric or adjoint representation fermions at infinite coupling as a function of Nf for Nc = 3. In general, there are sources of error in this approach associated with miscounting of overlapping diagrams, and over-counting of diagrams due to symmetries. These are further elaborated upon in a longer paper.Comment: presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, New York, NY, US

Experimental and numerical study of error fields in the CNT stellarator

Sources of error fields were indirectly inferred in a stellarator by reconciling computed and numerical flux surfaces. Sources considered so far include the displacements and tilts (but not the deformations, yet) of the four circular coils featured in the simple CNT stellarator. The flux surfaces were measured by means of an electron beam and phosphor rod, and were computed by means of a Biot-Savart field-line tracing code. If the ideal coil locations and orientations are used in the computation, agreement with measurements is poor. Discrepancies are ascribed to errors in the positioning and orientation of the in-vessel interlocked coils. To that end, an iterative numerical method was developed. A Newton-Raphson algorithm searches for the coils' displacements and tilts that minimize the discrepancy between the measured and computed flux surfaces. This method was verified by misplacing and tilting the coils in a numerical model of CNT, calculating the flux surfaces that they generated, and testing the algorithm's ability to deduce the coils' displacements and tilts. Subsequently, the numerical method was applied to the experimental data, arriving at a set of coil displacements whose resulting field errors exhibited significantly improved quantitative and qualitative agreement with experimental results.Comment: Special Issue on the 20th International Stellarator-Heliotron Worksho

Tur\'an Graphs, Stability Number, and Fibonacci Index

The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Tur\'an graphs frequently appear in extremal graph theory. We show that Tur\'an graphs and a connected variant of them are also extremal for these particular problems.Comment: 11 pages, 3 figure

Thermodynamics of Heat Shock Response

Production of heat shock proteins are induced when a living cell is exposed to a rise in temperature. The heat shock response of protein DnaK synthesis in E.coli for temperature shifts from temperature T to T plus 7 degrees, respectively to T minus 7 degrees is measured as function of the initial temperature T. We observe a reversed heat shock at low T. The magnitude of the shock increases when one increase the distance to the temperature $T_0 \approx 23^o$, thereby mimicking the non monotous stability of proteins at low temperature. Further we found that the variation of the heat shock with T quantitatively follows the thermodynamic stability of proteins with temperature. This suggest that stability related to hot as well as cold unfolding of proteins is directly implemented in the biological control of protein folding. We demonstrate that such an implementation is possible in a minimalistic chemical network.Comment: To be published in Physical Review Letter

Clar Sextet Analysis of Triangular, Rectangular and Honeycomb Graphene Antidot Lattices

Pristine graphene is a semimetal and thus does not have a band gap. By making a nanometer scale periodic array of holes in the graphene sheet a band gap may form; the size of the gap is controllable by adjusting the parameters of the lattice. The hole diameter, hole geometry, lattice geometry and the separation of the holes are parameters that all play an important role in determining the size of the band gap, which, for technological applications, should be at least of the order of tenths of an eV. We investigate four different hole configurations: the rectangular, the triangular, the rotated triangular and the honeycomb lattice. It is found that the lattice geometry plays a crucial role for size of the band gap: the triangular arrangement displays always a sizable gap, while for the other types only particular hole separations lead to a large gap. This observation is explained using Clar sextet theory, and we find that a sufficient condition for a large gap is that the number of sextets exceeds one third of the total number of hexagons in the unit cell. Furthermore, we investigate non-isosceles triangular structures to probe the sensitivity of the gap in triangular lattices to small changes in geometry