Past, present, and future distribution of Afromontane rodents (Muridae: Otomys) reflect climate-change predicted biome changes

Climate change constitutes a potential threat to montane biodiversity, particularly in low-altitude, tropical mountains; however, few data exist for the Afromontane taxa. In South Africa, the temperate grassland and fynbos biomes are mostly associated with the Great Escarpment and the high-lying central plateau. Varying contractions of the grassland and fynbos biomes are predicted under different climate scenarios by 2050. Animal taxa adapted to these biomes should suffer similar range declines and can be used to independently test the vegetation models. We constructed MaxEnt models from 271 unique locality records for three species of montane and submontane vlei rats that are closely associated with grassland (Otomys auratus, Wroughton 1906), mesic savanna (Otomys angoniensis, Wroughton 1906), and fynbos (Otomys irroratus, Brants 1827) biomes in South Africa. Projected range shifts under the A2 emission scenario of the Intergovernmental Panel on Climate Change showed increases (O. angoniensis) and decreases (O. auratus) that closely mirrored those expected for the savanna and grassland biomes, respectively. Comparison of historical (from 90 years ago) and current occurrence data from a zone of sympatry in the tropical Soutpansberg Mountains (at 1250 m asl) showed complete replacement of the grassland-adapted rodent species (O. auratus) by the savanna-adapted species (O. angoniensis) due to historically documented changes from a grassland-dominated to thicket-dominated landscape

The Uq(sl^(2/1))1U_q(\hat{sl}(2/1))_1-module V(Λ2)V(\Lambda_2) and a Corner Transfer Matrix at q=0

The north-west corner transfer matrix of an inhomogeneous integrable vertex model constructed from the vector representation of $U_q\bigl(sl(2/1)\bigr)$ and its dual is investigated. In the limit $q\to0$, the spectrum can be obtained. Based on an analysis of the half-infinite tensor products related to all CTM-eigenvalues $\geq -4$, it is argued that the eigenvectors of the corner transfer matrix are in one-to-one correspondance with the weight states of the $U_q\bigl((\hat{sl}(2/1)\bigr)_1-$module $V(\Lambda_2)$ at level one. This is supported by a comparison of the comlete set of eigenvectors with a nondegenerate triple of eigenvalues of the CTM-Hamiltonian and the generators of the Cartan-subalgebra of $U_q\bigl(sl(2|1)\bigr)$ to the weight states of $V(\Lambda_2)$ with multiplicity one.Comment: 28 pages, revtex accepted for publication in Nuclear Physics

Thermodynamic Bethe Ansatz for the subleading magnetic perturbation of the tricritical Ising model

We give further support to Smirnov's conjecture on the exact kink S-matrix for the massive Quantum Field Theory describing the integrable perturbation of the c=0.7 minimal Conformal Field theory (known to describe the tri-critical Ising model) by the operator $\phi_{2,1}$. This operator has conformal dimensions $(7/16,7/16)$ and is identified with the subleading magnetic operator of the tri-critical Ising model. In this paper we apply the Thermodynamic Bethe Ansatz (TBA) approach to the kink scattering theory by explicitly utilising its relationship with the solvable lattice hard hexagon model. Analytically examining the ultraviolet scaling limit we recover the expected central charge c=0.7 of the tri-critical Ising model. We also compare numerical values for the ground state energy of the finite size system obtained from the TBA equations with the results obtained by the Truncated Conformal Space Approach and Conformal Perturbation Theory.Comment: 22 pages, minor changes, references added. LaTeX file and postscript figur

Computation of the Heavy-Light Decay Constant using Non-relativistic Lattice QCD

We report results on a lattice calculation of the heavy-light meson decay constant employing the non-relativistic QCD approach for heavy quark and Wilson action for light quark. Simulations are carried out at $\beta=6.0$ on a $16^3\times 48$ lattice. Signal to noise ratio for the ground state is significantly improved compared to simulations in the static approximation, enabling us to extract the decay constant reliably. We compute the heavy-light decay constant for several values of heavy quark mass and estimate the magnitude of the deviation from the heavy mass scaling law $f_{P} \sqrt{m_{P}} = const$. For the $B$ meson we find $f_{B} = 171\pm 22^{+19}_{-45}$ MeV, while an extrapolation to the static limit yields $f_{B}^{static}$ = $297\pm 36^{+15}_{-30}$ MeV.Comment: 34 pages in LaTeX including 10 figures using epsf.sty, uuencoded-gziped-shar format, HUPD-940

Granular discharge and clogging for tilted hoppers

We measure the flux of spherical glass beads through a hole as a systematic function of both tilt angle and hole diameter, for two different size beads. The discharge increases with hole diameter in accord with the Beverloo relation for both horizontal and vertical holes, but in the latter case with a larger small-hole cutoff. For large holes the flux decreases linearly in cosine of the tilt angle, vanishing smoothly somewhat below the angle of repose. For small holes it vanishes abruptly at a smaller angle. The conditions for zero flux are discussed in the context of a {\it clogging phase diagram} of flow state vs tilt angle and ratio of hole to grain size

Excited State TBA for the ϕ2,1\phi_{2,1} perturbed M3,5M_{3,5} model

We examine some excited state energies in the non-unitary integrable quantum field theory obtained from the perturbation of the minimal conformal field theory model $M_{3,5}$ by its operator $\phi_{2,1}$. Using the correspondence of this IQFT to the scaling limit of the dilute $A_2$ lattice model (in a particular regime) we derive the functional equations for the QFT commuting transfer matrices. These functional equations can be transformed to a closed set of TBA-like integral equations which determine the excited state energies in the finite-size system. In particular, we explicitly construct these equations for the ground state and two lowest excited states. Numerical results for the associated energy gaps are compared with those obtained by the truncated conformal space approach (TCSA).Comment: LaTeX, 32 pages, 6 figure

Ratios of BB and DD Meson Decay Constants in Relativistic Quark Model

We calculate the ratios of $B$ and $D$ meson decay constants by applying the variational method to the relativistic hamiltonian of the heavy meson. We adopt the Gaussian and hydrogen-type trial wave functions, and use six different potentials of the potential model. We obtain reliable results for the ratios, which are similar for different trial wave functions and different potentials. The obtained ratios show the deviation from the nonrelativistic scaling law, and they are in a pretty good agreement with the results of the Lattice calculations.Comment: 13 pages, 1 Postscript figur

Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz

We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as ``${\bf T}$-operators'', act in highest weight Virasoro modules. The ${\bf T}$-operators depend on the spectral parameter $\lambda$ and their expansion around $\lambda = \infty$ generates an infinite set of commuting Hamiltonians of the quantum KdV system. The ${\bf T}$-operators can be viewed as the continuous field theory versions of the commuting transfer-matrices of integrable lattice theory. In particular, we show that for the values $c=1-3{{(2n+1)^2}\over {2n+3}} , n=1,2,3,...$of the Virasoro central charge the eigenvalues of the ${\bf T}$-operators satisfy a closed system of functional equations sufficient for determining the spectrum. For the ground-state eigenvalue these functional equations are equivalent to those of massless Thermodynamic Bethe Ansatz for the minimal conformal field theory ${\cal M}_{2,2n+3}$; in general they provide a way to generalize the technique of Thermodynamic Bethe Ansatz to the excited states. We discuss a generalization of our approach to the cases of massive field theories obtained by perturbing these Conformal Field Theories with the operator $\Phi_{1,3}$. The relation of these ${\bf T}$-operators to the boundary states is also briefly described.Comment: 24 page

Time-ordering and a generalized Magnus expansion

Both the classical time-ordering and the Magnus expansion are well-known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering and time derivation, and related problems raised recently in statistical physics, we introduce a generalization of the Magnus expansion. Whereas the classical expansion computes the logarithm of the evolution operator of a linear differential equation, our generalization addresses the same problem, including however directly a non-trivial initial condition. As a by-product we recover a variant of the time ordering operation, known as T*-ordering. Eventually, placing our results in the general context of Rota-Baxter algebras permits us to present them in a more natural algebraic setting. It encompasses, for example, the case where one considers linear difference equations instead of linear differential equations

Adsorption of Reactive Particles on a Random Catalytic Chain: An Exact Solution

We study equilibrium properties of a catalytically-activated annihilation $A + A \to 0$ reaction taking place on a one-dimensional chain of length $N$ ($N \to \infty$) in which some segments (placed at random, with mean concentration $p$) possess special, catalytic properties. Annihilation reaction takes place, as soon as any two $A$ particles land onto two vacant sites at the extremities of the catalytic segment, or when any $A$ particle lands onto a vacant site on a catalytic segment while the site at the other extremity of this segment is already occupied by another $A$ particle. Non-catalytic segments are inert with respect to reaction and here two adsorbed $A$ particles harmlessly coexist. For both "annealed" and "quenched" disorder in placement of the catalytic segments, we calculate exactly the disorder-average pressure per site. Explicit asymptotic formulae for the particle mean density and the compressibility are also presented.Comment: AMSTeX, 27 pages + 4 figure