Lojasiewicz exponent of families of ideals, Rees mixed multiplicities and Newton filtrations

We give an expression for the {\L}ojasiewicz exponent of a wide class of n-tuples of ideals $(I_1,..., I_n)$ in \O_n using the information given by a fixed Newton filtration. In order to obtain this expression we consider a reformulation of {\L}ojasiewicz exponents in terms of Rees mixed multiplicities. As a consequence, we obtain a wide class of semi-weighted homogeneous functions $(\mathbb{C}^n,0)\to (\mathbb{C},0)$ for which the {\L}ojasiewicz of its gradient map $\nabla f$ attains the maximum possible value.Comment: 25 pages. Updated with minor change

Rank one discrete valuations of power series fields

In this paper we study the rank one discrete valuations of the field $k((X_1,..., X_n))$ whose center in k\lcor\X\rcor is the maximal ideal. In sections 2 to 6 we give a construction of a system of parametric equations describing such valuations. This amounts to finding a parameter and a field of coefficients. We devote section 2 to finding an element of value 1, that is, a parameter. The field of coefficients is the residue field of the valuation, and it is given in section 5. The constructions given in these sections are not effective in the general case, because we need either to use the Zorn's lemma or to know explicitly a section $\sigma$ of the natural homomorphism R_v\to\d between the ring and the residue field of the valuation $v$. However, as a consequence of this construction, in section 7, we prove that k((\X)) can be embedded into a field L((\Y)), where $L$ is an algebraic extension of $k$ and the {\em ``extended valuation'' is as close as possible to the usual order function}

Acoustic Phonon-Assisted Resonant Tunneling via Single Impurities

We perform the investigations of the resonant tunneling via impurities embedded in the AlAs barrier of a single GaAs/AlGaAs heterostructure. In the $I(V)$ characteristics measured at 30mK, the contribution of individual donors is resolved and the fingerprints of phonon assistance in the tunneling process are seen. The latter is confirmed by detailed analysis of the tunneling rates and the modeling of the resonant tunneling contribution to the current. Moreover, fluctuations of the local structure of the DOS (LDOS) and Fermi edge singularities are observed.Comment: accepted in Phys. Rev.

The effect of inelastic processes on tunneling

We study an electron that interacts with phonons or other linear or nonlinear excitations as it resonantly tunnels. The method we use is based on mapping a many-body problem in a large variational space exactly onto a one-body problem. The method is conceptually simpler than previous Green's function approaches, and allows the essentially exact numerical solution of much more general problems. We solve tunneling problems with transverse channels, multiple sites coupled to phonons, and multiple phonon degrees of freedom and excitations.Comment: 12 pages, REVTex, 4 figures in compressed tar .ps forma

Singularities and Topology of Meromorphic Functions

We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of polynomial functions.Comment: 21 pages, 1 figur

Strong Discontinuities in the Complex Photonic Band Structure of Transmission Metallic Gratings

Complex photonic band structures (CPBS) of transmission metallic gratings with rectangular slits are shown to exhibit strong discontinuities that are not evidenced in the usual energetic band structures. These discontinuities are located on Wood's anomalies and reveal unambiguously two different types of resonances, which are identified as horizontal and vertical surface-plasmon resonances. Spectral position and width of peaks in the transmission spectrum can be directly extracted from CPBS for both kinds of resonances.Comment: 4 pages, 4 figures, REVTeX version

Role of the hyporheic heterotrophic biofilm on transformation and toxicity of pesticides

The role of heterotrophic biofilm of water–sediment interface in detoxification processes was tested in abiotic and biotic conditions under laboratory conditions. Three toxicants, a herbicide (Diuron), a fungicide (Dimethomorph) and an insecticide (Chlorpyrifos-ethyl) have been tested in water percolating into columns reproducing hyporheic sediment. The detoxification processes were tested by comparing the water quality after 18 days of percolation with and without heterotrophic biofilm. Tested concentrations were 30 mg.Lx1 of Diuron diluted in 0.1% dimethyl sulfoxide (DMSO), 2 mg.Lx1 of Dimethomorph and 0.1 mg.Lx1 of Chlorpyrifos-ethyl. To characterise the detoxification efficiency of the system, we performed genotoxicity bioassays in amphibian larvae and rotifers and measured the respiration and denitrification of sediments. Although the presence of biofilm increased the production of N-(3,4 dichlorophenyl)-N-(methyl)-urea, a metabolite of diuron, the toxicity did not decrease irrespective of the bioassay. In the presence of biofilm, Dimethomorph concentrations decreased compared with abiotic conditions, from 2 mg.Lx1 to 0.4 mg.Lx1 after 18 days of percolation. For both Dimethomorph and Chlorpyrifos-ethyl additions, assessment of detoxification level by the biofilm depended on the test used: detoxification effect was found with amphibian larvae bioassay and no detoxification was observed with the rotifer test. Heterotrophic biofilm exerts a major influence in the biochemical transformation of contaminants such as pesticides, suggesting that the interface between running water and sediment plays a role in self-purification of stream reaches

Elastic strains at interfaces in InAs/AlSb multilayer structures for quantum cascade lasers

InAs/AlSb multilayers similar to those used in quantum cascade lasers have been grown by molecular beam epitaxy on (001) InAs substrates. Elastic strain is investigated by high resolution transmission electron microscopy. Thin interfacial regions with lattice distortions significantly different from the strain of the AlSb layers themselves are revealed from the geometrical phase analysis. Strain profiles are qualitatively compared to the chemical contrast of high angle annular dark field images obtained by scanning transmission electron microscopy. The strain and chemical profiles are correlated with the growth sequences used to form the interfaces. Tensile strained AlAs-like interfaces tend to form predominantly due to the high thermal stability of AlAs. Strongly asymmetric interfaces, AlAs-rich and (Al, In)Sb, respectively, can also be achieved by using appropriate growth sequences