1N2 corrections in two-dimensional lattice gauge system with mixed action

A form of the $\text{1}\text{N}{}^2$ correction for a two-dimensional system described by the mixed fundamental-adjoint action is discussed. An exact result for the U(N) gauge group is derived. The form of correction in SU(N) is also discussed and the difference between the two groups is pointed out. The form of correction in two dimensions can be generalized for any number of dimensions if corrections to the plaquette free energy are to be calculated.     

Asymptotic freedom scales for any single plaquette action

We analyze with the background field method the ratio of the renormalization group scales in the continuum, Λ_cont, and on the lattice, Λ_L. We find, in contrast to an earlier background field calculation, good agreement with conventional calculations, extend the result in analytic form to any acceptable lattice action and find actions where the ratio can take any value. Comparison with available computer data is made. Qualitative agreement is found.     

Unusual patterns in 15N blood values after a diet switch in red knot shorebirds

When a diet switch results in a change in dietary isotopic values, isotope ratios of the consumer's tissues will change until a new equilibrium is reached. This change is generally best described by an exponential decay curve. Indeed, after a diet switch in captive red knot shorebirds (Calidris canutus islandica), the depletion of ¹³C in both blood cells and plasma followed an exponential decay curve. Surprisingly, the diet switch with a dietary ¹⁵N/¹⁴N ratio (δ¹⁵N) change from 11.4 to 8.8 ‰ had little effect on δ¹⁵N in the same tissues. The diet-plasma and diet-cellular discrimination factors of ¹⁵N with the initial diet were very low (0.5 and 0.2 ‰, respectively). δ¹⁵N in blood cells and plasma decreased linearly with increasing body mass, explaining about 40 % of the variation in δ¹⁵N. δ¹⁵N in plasma also decreased with increasing body-mass change (r ²=.07). This suggests that the unusual variation in δ¹⁵N with time after the diet switch was due to interferences with simultaneous changes in body-protein turnover.     

More efficient Brownian dynamics algorithms

We examine the relative efficiencies of three- algorithms for performing Brownian Dynamics simulations without many-body hydrodynamics. We compare the conventional Brownian Dynamics algorithm of Ermak (CBD), Smart Monte Carlo (SMC) which incorporates Boltzmann sampling into essentially a CBD procedure, and the Stochastic Runge Kutta (SRK) method. We show, using the repulsive potential φ(r) = ε(σ/r) ⁿ , where n = 36 and 72, that the SRK algorithm gives the most accurate short-time dynamics for the mean-square displacements. The SRK algorithm static and dynamical properties converge better with a reducing time step to the exact values, than those generated by the CBD algorithm; giving efficiency gains typically of a factor of 3–4. Both CBD and SMC have the incorrect sign for the first correction term to the mean square displacement in a time step, whereas the SRK algorithm gives essentially the exact solution to order Δt ², where Δt is the simulation time step. In fact, these correction terms are almost equal and opposite in sign. Expressions for these terms were derived in terms of the average interaction energy per particle. The force, shear and bulk stress autocorrelation functions were calculated. The average energy per particle and time correlation functions at short time have values in excess of the exact values, while the corresponding quantities for SRK are below this. This difference in behaviour can be traced back to the extent of compliance of the particle trajectories with the exact expansion of the Smoluchowski equation. The accuracy, at a given value of the time step, of the stochastic algorithms can significantly depend on the form of the interaction potential between particles. It is also demonstrated that the long time limits of various correlation functions are fairly insensitive to a particular scheme (SRK or CBD) used in the simulations. All the correlation functions have a stretched exponential region at intermediate to long times, and the values of the exponents on density and force law steepness have been determined.     

Large-N universality of variant actions

Corrections to large-N universality in mixed action lattice gauge theories imply constraints on the cut-off dependence. We state the form of these constraints and show that they are satisfied up to and including two loops (weak coupling). This implies that the second coefficient of the β function on the lattice is indeed universal as expected. We then evaluate the complete form of the corrections to large-N universality up to and including two loops. They give a sizeable contribution and determine qualitative aspects of equal string tension data like the bending seen for SU(2).     

Inequalities for order and disorder parameters in SU(N) gauge theories

We discuss inequalities of the Mack-Fröhlich type in SU(N) gauge theories and their possible implications for the various phases of those theories.     

Catalytic cyclopropanation of polybutadienes

Catalytic cyclopropanation of commercial 1,2‐ or 1,4‐cis‐polybutadiene, respectively, with ethyl diazoacetate catalyzed by [Tp^Br3Cu(NCMe)] (Tp^Br3 = hydrotris(3,4,5‐tribromo‐1‐pyrazolyl)borate) at room temperature afforded high molecular weight (M_n > 10⁵ mol^?1) side‐chain or main‐chain, respectively, carboxyethyl cyclopropyl‐substituted polymers with variable and controlled degrees of functionalization. Complete functionalization of 1,4‐cis‐polybutadiene afforded poly[ethylene‐alt‐(3‐ethoxycarbonyl‐cyclopropene)]. Catalytic hydrogenation of residual double bonds of partially cyclopropanated polybutadienes provided access to the corresponding saturated polyolefins. Thermal properties are reported. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Simultaneous synthesis of both rings of chromenes via a benzannulation/o-quinone methide formation/electrocyclization cascade

A new route to the chromene ring system has been developed which involves the reaction of an α,β-unsaturated Fischer carbene complex of chromium with a propargyl ether bearing an alkenyl group on the propargylic carbon. This transformation involves a cascade of reactions that begins with a benzannulation reaction and is followed by the formation of an o-quinone methide, and finally results in the emergence of a chromene upon an electrocyclization. This reaction was extended to provide access by employing an aryl carbene complex. This constitutes the first synthesis of chromenes in which both rings of the chromene system are generated in a single step and is highlighted in the synthesis of lapachenole and vitamin E.