Technical note: application of ?-QSS to the numerical integration of kinetic equations in tropospheric chemistry

International audienceA major task in many applications of atmospheric chemistry transport problems is the numerical integration of stiff systems of Ordinary Differential Equations (ODEs) describing the chemical transformations. A faster solver that is easier to couple to the other physics in the problem is still needed. The integration method, ?-QSS, corresponding to the solver CHEMEQ2 aims at meeting the demands of a process-split, reacting-flow simulation (Mott 2000; Mott and Oran, 2001). However, this integrator has yet to be applied to the numerical integration of kinetic equations in tropospheric chemistry. A zero-dimensional (box) model is developed to test how well CHEMEQ2 works on the tropospheric chemistry equations. This paper presents the testing results. The reference chemical mechanisms herein used are Regional Atmospheric Chemistry Mechanism (RACM) (Stockwell et al., 1997) and its secondary lumped successor Regional Lumped Atmospheric Chemical Scheme (ReLACS) (Crassier et al., 2000). The box model is forced and initialized by the DRY scenarios of Protocol Ver. 2 developed by EUROTRAC (Poppe et al., 2001). The accuracy of CHEMEQ2 is evaluated by comparing the results to solutions obtained with VODE. This comparison is made with parameters of the error tolerance, relative difference with respect to VODE scheme, trade off between accuracy and efficiency, global time step for integration etc. The study based on the comparison concludes that the single-point ?-QSS approach is fast and moderately accurate as well as easy to couple to reacting flow simulation models, which makes CHEMEQ2 one of the best candidates for three-dimensional atmospheric Chemistry Transport Modelling (CTM) studies. In addition the RACM mechanism may be replaced by ReLACS mechanism for tropospheric chemistry transport modelling. The testing results also imply that the accuracy for chemistry numerical simulations is highly different from species to species. Therefore ozone is not the good choice for testing numerical ODE solvers or for evaluation of mechanisms because current tropospheric chemistry mechanisms are mainly designed for troposphere ozone prediction

Universal Distribution of Kondo Temperatures in Dirty Metals

Kondo screening of diluted magnetic impurities in a disordered host is studied analytically and numerically in one, two and three dimensions. It is shown that in the T_K \to 0 limit the distribution of Kondo temperatures has a universal form, P(T_K) \sim T_K^{-\alpha} that holds in the insulating phase and persists in the metallic phase close to the metal insulator transition. Moreover, the exponent \alpha depends only on the dimensionality. The most important consequence of this result is that the T-dependence of thermodynamic properties is smooth across the metal-insulator transition in three dimensional systems.Comment: 4 pages, 3 figures; added referenc

Correlation-induced metal insulator transition in a two-channel fermion-boson model

We investigate charge transport within some background medium by means of an effective lattice model with a novel form of fermion-boson coupling. The bosons describe fluctuations of a correlated background. By analyzing groundstate and spectral properties of this transport model, we show how a metal-insulator quantum phase transition can occur for the half-filled band case. We discuss the evolution of a mass-asymmetric band structure in the insulating phase and establish connections to the Mott and Peierls transition scenarios.Comment: 4 pages, 4 figures, 1 table, revised version accepted for publication in Phys. Rev. Let

Transport and Spectra in the Half-filled Hubbard Model: A Dynamical Mean Field Study

We study the issues of scaling and universality in spectral and transport properties of the infinite dimensional particle--hole symmetric (half-filled) Hubbard model within dynamical mean field theory. One of the simplest and extensively used impurity solvers, namely the iterated perturbation theory approach is reformulated to avoid problems such as analytic continuation of Matsubara frequency quantities or calculating multi-dimensional integrals, while taking full account of the very sharp structures in the Green's functions that arise close to the Mott transitions and in the Mott insulator regime. We demonstrate its viability for the half-filled Hubbard model. Previous known results are reproduced within the present approach. The universal behavior of the spectral functions in the Fermi liquid regime is emphasized, and adiabatic continuity to the non-interacting limit is demonstrated. The dc resistivity in the metallic regime is known to be a non-monotonic function of temperature with a `coherence peak'. This feature is shown to be a universal feature occurring at a temperature roughly equal to the low energy scale of the system. A comparison to pressure dependent dc resistivity experiments on Selenium doped NiS$_2$ yields qualitatively good agreement. Resistivity hysteresis across the Mott transition is shown to be described qualitatively within the present framework. A direct comparison of the thermal hysteresis observed in V$_2$O$_3$ with our theoretical results yields a value of the hopping integral, which we find to be in the range estimated through first-principle methods. Finally, a systematic study of optical conductivity is carried out and the changes in absorption as a result of varying interaction strength and temperature are identified.Comment: 19 pages, 12 figure

Optical conductivity of a metal-insulator transition for the Anderson-Hubbard model in 3 dimensions away from 1/2 filling

We have completed a numerical investigation of the Anderson-Hubbard model for three-dimensional simple cubic lattices using a real-space self-consistent Hartree-Fock decoupling approximation for the Hubbard interaction. In this formulation we treat the spatial disorder exactly, and therefore we account for effects arising from localization physics. We have examined the model for electronic densities well away 1/2 filling, thereby avoiding the physics of a Mott insulator. Several recent studies have made clear that the combined effects of electronic interactions and spatial disorder can give rise to a suppression of the electronic density of states, and a subsequent metal-insulator transition can occur. We augment such studies by calculating the ac conductivity for such systems. Our numerical results show that weak interactions enhance the density of states at the Fermi level and the low-frequency conductivity, there are no local magnetic moments, and the ac conductivity is Drude-like. However, with a large enough disorder strength and larger interactions the density of states at the Fermi level and the low-frequency conductivity are both suppressed, the conductivity becomes non-Drude-like, and these phenomena are accompanied by the presence of local magnetic moments. The low-frequency conductivity changes from a sigma-sigma_dc omega^{1/2} behaviour in the metallic phase, to a sigma omega^2 behaviour in the nonmetallic regime. Our numerical results show that the formation of magnetic moments is essential to the suppression of the density of states at the Fermi level, and therefore essential to the metal-insulator transition

Microarray-based ultra-high resolution discovery of genomic deletion mutations

BACKGROUND: Oligonucleotide microarray-based comparative genomic hybridization (CGH) offers an attractive possible route for the rapid and cost-effective genome-wide discovery of deletion mutations. CGH typically involves comparison of the hybridization intensities of genomic DNA samples with microarray chip representations of entire genomes, and has widespread potential application in experimental research and medical diagnostics. However, the power to detect small deletions is low. RESULTS: Here we use a graduated series of Arabidopsis thaliana genomic deletion mutations (of sizes ranging from 4 bp to ~5 kb) to optimize CGH-based genomic deletion detection. We show that the power to detect smaller deletions (4, 28 and 104 bp) depends upon oligonucleotide density (essentially the number of genome-representative oligonucleotides on the microarray chip), and determine the oligonucleotide spacings necessary to guarantee detection of deletions of specified size. CONCLUSIONS: Our findings will enhance a wide range of research and clinical applications, and in particular will aid in the discovery of genomic deletions in the absence of a priori knowledge of their existence

A new vibrational level of the H2+_2^+ molecular ion

A new state of the H$_2^+$ molecular ion with binding energy of 1.09$\times10^{-9}$ a.u. below the first dissociation limit is predicted, using highly accurate numerical nonrelativistic quantum calculations. It is the first L=0 excited state, antisymmetric with respect to the exchange of the two protons. It manifests itself as a huge p-H scattering length of $a=750\pm 5$ Bohr radii.Comment: 6 pages + 3 figure

Entanglement between static and flying qubits in quantum wires

A weakly bound electron in a semiconductor quantum wire is shown to become entangled with an itinerant electron via the coulomb interaction. The degree of entanglement and its variation with energy of the injected electron, may be tuned by choice of spin and initial momentum. Full entanglement is achieved close to energies where there are spin-dependent resonances. Possible realisations of related device structures are discussed

Search for Ferromagnetism in doped semiconductors in the absence of transition metal ions

In contrast to semiconductors doped with transition metal magnetic elements, which become ferromagnetic at temperatures below ~ 100K, semiconductors doped with non-magnetic ions (e.g. silicon doped with phosphorous) have not shown evidence of ferromagnetism down to millikelvin temperatures. This is despite the fact that for low densities the system is expected to be well modeled by the Hubbard model, which is predicted to have a ferromagnetic ground state at T=0 on 2- or 3-dimensional bipartite lattices in the limit of strong correlation near half-filling. We examine the impurity band formed by hydrogenic centers in semiconductors at low densities, and show that it is described by a generalized Hubbard model which has, in addition to strong electron-electron interaction and disorder, an intrinsic electron-hole asymmetry. With the help of mean field methods as well as exact diagonalization of clusters around half filling, we can establish the existence of a ferromagnetic ground state, at least on the nanoscale, which is more robust than that found in the standard Hubbard model. This ferromagnetism is most clearly seen in a regime inaccessible to bulk systems, but attainable in quantum dots and 2D heterostructures. We present extensive numerical results for small systems that demonstrate the occurrence of high-spin ground states in both periodic and positionally disordered 2D systems. We consider how properties of real doped semiconductors, such as positional disorder and electron-hole asymmetry, affect the ground state spin of small 2D systems. We also discuss the relationship between this work and diluted magnetic semiconductors, such as Ga_(1-x)Mn_(x)As, which though disordered, show ferromagnetism at relatively high temperatures.Comment: 47 page

Analytical calculation of the Green's function and Drude weight for a correlated fermion-boson system

In classical Drude theory the conductivity is determined by the mass of the propagating particles and the mean free path between two scattering events. For a quantum particle this simple picture of diffusive transport loses relevance if strong correlations dominate the particle motion. We study a situation where the propagation of a fermionic particle is possible only through creation and annihilation of local bosonic excitations. This correlated quantum transport process is outside the Drude picture, since one cannot distinguish between free propagation and intermittent scattering. The characterization of transport is possible using the Drude weight obtained from the f-sum rule, although its interpretation in terms of free mass and mean free path breaks down. For the situation studied we calculate the Green's function and Drude weight using a Green's functions expansion technique, and discuss their physical meaning.Comment: final version, minor correction