Monte Carlo Simulation of the Heisenberg Antiferromagnet on a Triangular Lattice: Topological Excitations

We have simulated the classical Heisenberg antiferromagnet on a triangular lattice using a local Monte Carlo algorithm. The behavior of the correlation length $\xi$, the susceptibility at the ordering wavevector $\chi(\bf Q)$, and the spin stiffness $\rho$ clearly reflects the existence of two temperature regimes -- a high temperature regime $T > T_{th}$, in which the disordering effect of vortices is dominant, and a low temperature regime $T < T_{th}$, where correlations are controlled by small amplitude spin fluctuations. As has previously been shown, in the last regime, the behavior of the above quantities agrees well with the predictions of a renormalization group treatment of the appropriate nonlinear sigma model. For $T > T_{th}$, a satisfactory fit of the data is achieved, if the temperature dependence of $\xi$ and $\chi(\bf Q)$ is assumed to be of the form predicted by the Kosterlitz--Thouless theory. Surprisingly, the crossover between the two regimes appears to happen in a very narrow temperature interval around $T_{th} \simeq 0.28$.Comment: 13 pages, 8 Postscript figure

The Heisenberg antiferromagnet on a triangular lattice: topological excitations

We study the topological defects in the classical Heisenberg antiferromagnet in two dimensions on a triangular lattice (HAFT). While the topological analysis of the order parameter space indicates that the defects are of $Z_2$ type, consideration of the energy leads us to a description of the low--energy stationary points of the action in terms of $\pm$ vortices, as in the planar XY model. Starting with the continuum description of the HAFT, we show analytically that its partition function can be reduced to that of a 2--dimensional Coulomb gas with logarithmic interaction. Thus, at low temperatures, the correlation length is determined by the spinwaves, while at higher temperatures we expect a crossover to a Kosterlitz--Thouless type behaviour. The results of recent Monte Carlo calculations of the correlation length are consistent with such a crossover.Comment: 9 pages, revtex, preprint: ITP-UH 03/9

Nuclear Spin Relaxation for Higher Spin

We study the relaxation of a spin I that is weakly coupled to a quantum mechanical environment. Starting from the microscopic description, we derive a system of coupled relaxation equations within the adiabatic approximation. These are valid for arbitrary I and also for a general stationary non--equilibrium state of the environment. In the case of equilibrium, the stationary solution of the equations becomes the correct Boltzmannian equilibrium distribution for given spin I. The relaxation towards the stationary solution is characterized by a set of relaxation times, the longest of which can be shorter, by a factor of up to 2I, than the relaxation time in the corresponding Bloch equations calculated in the standard perturbative way.Comment: 4 pages, Latex, 2 figure

Constructive factorization of LPDO in two variables

We study conditions under which a partial differential operator of arbitrary order $n$ in two variables or ordinary linear differential operator admits a factorization with a first-order factor on the left. The factorization process consists of solving, recursively, systems of linear equations, subject to certain differential compatibility conditions. In the generic case of partial differential operators one does not have to solve a differential equation. In special degenerate cases, such as ordinary differential, the problem is finally reduced to the solution of some Riccati equation(s). The conditions of factorization are given explicitly for second- and, and an outline is given for the higher-order case.Comment: 16 pages, to be published in Journal "Theor. Math. Phys." (2005

Upper tropospheric ozone production from lightning NO_x-impacted convection: Smoke ingestion case study from the DC3 campaign

As part of the Deep Convective Cloud and Chemistry (DC3) experiment, the National Science Foundation/National Center for Atmospheric Research (NCAR) Gulfstream-V (GV) and NASA DC-8 research aircraft probed the chemical composition of the inflow and outflow of two convective storms (north storm, NS, south storm, SS) originating in the Colorado region on 22 June 2012, a time when the High Park wildfire was active in the area. A wide range of trace species were measured on board both aircraft including biomass burning (BB) tracers hydrogen cyanide (HCN) and acetonitrile (ACN). Acrolein, a much shorter lived tracer for BB, was also quantified on the GV. The data demonstrated that the NS had ingested fresh smoke from the High Park fire and as a consequence had a higher VOC OH reactivity than the SS. The SS lofted aged fire tracers along with other boundary layer ozone precursors and was more impacted by lightning NO_x (LNO_x) than the NS. The NCAR master mechanism box model was initialized with measurements made in the outflow of the two storms. The NS and SS were predicted to produce 11 and 14 ppbv of O_3, respectively, downwind of the storm over 2 days. Sensitivity tests revealed that the ozone production potential of the SS was highly dependent on LNO_x. Normalized excess mixing ratios, ΔX/ΔCO, for HCN and ACN were determined in both the fire plume and the storm outflow and found to be 7.0 ± 0.5 and 2.3 ± 0.5 pptv ppbv^(−1), respectively, and 1.4 ± 0.3 pptv ppbv^(−1) for acrolein in the outflow only

Quantum Hall Ferromagnets: Induced Topological term and electromagnetic interactions

The $\nu = 1$ quantum Hall ground state in materials like GaAs is well known to be ferromagnetic in nature. The exchange part of the Coulomb interaction provides the necessary attractive force to align the electron spins spontaneously. The gapless Goldstone modes are the angular deviations of the magnetisation vector from its fixed ground state orientation. Furthermore, the system is known to support electrically charged spin skyrmion configurations. It has been claimed in the literature that these skyrmions are fermionic owing to an induced topological Hopf term in the effective action governing the Goldstone modes. However, objections have been raised against the method by which this term has been obtained from the microscopics of the system. In this article, we use the technique of the derivative expansion to derive, in an unambiguous manner, the effective action of the angular degrees of freedom, including the Hopf term. Furthermore, we have coupled perturbative electromagnetic fields to the microscopic fermionic system in order to study their effect on the spin excitations. We have obtained an elegant expression for the electromagnetic coupling of the angular variables describing these spin excitations.Comment: 23 pages, Plain TeX, no figure

Metamorphic Domain-Specific Languages: A Journey Into the Shapes of a Language

External or internal domain-specific languages (DSLs) or (fluent) APIs? Whoever you are -- a developer or a user of a DSL -- you usually have to choose your side; you should not! What about metamorphic DSLs that change their shape according to your needs? We report on our 4-years journey of providing the "right" support (in the domain of feature modeling), leading us to develop an external DSL, different shapes of an internal API, and maintain all these languages. A key insight is that there is no one-size-fits-all solution or no clear superiority of a solution compared to another. On the contrary, we found that it does make sense to continue the maintenance of an external and internal DSL. The vision that we foresee for the future of software languages is their ability to be self-adaptable to the most appropriate shape (including the corresponding integrated development environment) according to a particular usage or task. We call metamorphic DSL such a language, able to change from one shape to another shape

Intersections of sequences of ideals generated by polynomials

AbstractWe present a method for determining the reduced Gröbner basis with respect to a given admissible term order of order type ω of the intersection ideal of an infinite sequence of polynomial ideals.As an application we discuss the Lagrange type interpolation on algebraic sets and the “approximation” of the ideal I of an algebraic set by zero dimensional ideals, whose affine Hilbert functions converge towards the affine Hilbert function of I