Search results for " Geometry."

Morphological Similarity of Channels: From Linear Erosional Features (Rill, Gully) to Alpine Rivers

2017

The geometric characteristics of incised features such as channels, rills, ephemeral gully, gully, represent the erosional transport regime and the fluvial dynamic equilibrium, and thus it is critical for the understanding of the long-term evolution of natural, agricultural, and anthropogenic landscapes. This paper examines the morphological similarity of channelized erosion in two different environments such as Alpine landscapes and cultivated hillslopes. The first dataset comprises six rivers in the Italian Alps, three in the Carnia region and three in the Dolomites, where erosion is mainly the effect of discharges with high sediment loads or landslides and debris flows. The agricultural …

Uniformization with infinitesimally metric measures

2019

We consider extensions of quasiconformal maps and the uniformization theorem to the setting of metric spaces $X$ homeomorphic to $\mathbb R^2$. Given a measure $\mu$ on such a space, we introduce $\mu$-quasiconformal maps $f:X \to \mathbb R^2$, whose definition involves deforming lengths of curves by $\mu$. We show that if $\mu$ is an infinitesimally metric measure, i.e., it satisfies an infinitesimal version of the metric doubling measure condition of David and Semmes, then such a $\mu$-quasiconformal map exists. We apply this result to give a characterization of the metric spaces admitting an infinitesimally quasisymmetric parametrization.

Ferrimagnetic Heisenberg chain; influence of a random exchange interaction

1985

We report on the magnetic behavior of ‘‘rigid’’ ferrimagnetic chains isolated in bimetallic complexes of the EDTA and ‘‘flexible’’ ones obtained in the amorphous variety. As shown by LAXS, the only noteworthy difference in the amorphous state is the random distribution of bond angles between nearest neighbors within chains. The ‘‘rigid’’ bimetallic chains in CoNi(EDTA)6H2O are described in terms of Heisenberg model with an exchange coupling J=−7.5 K. The behavior of the amorphous variety somewhat differs, following the law X=AT−0.8 typical of REHAC. A classical spin chain model involving a J distribution and alternating g factors allows to explain successfully the temperature dependence of …

A Rational Design for Imidazolate-Bridged Linear Trinuclear Compounds from Mononuclear Copper(II) Complexes with 2-[((Imidazol-2-ylmethylidene)amino)…

2001

Two mononuclear copper(II) complexes with the unsymmetrical tridentate ligand 2-[((imidazol-2-ylmethylidene)amino)ethyl]pyridine (HL), [Cu(HL)(H2O)](ClO4)2.2H2O (1) and [Cu(HL)Cl2] (2), have been prepared and characterized. The X-ray analysis of 2 revealed that the copper(II) ion assumes a pentacoordinated square pyramidal geometry with an N3Cl2 donor set. When 1 and 2 are treated with an equimolecular amount of potassium hydroxide, the deprotonation of the imidazole moiety promotes a self-assembled process, by coordination of the imidazolate nitrogen atom to a Cu(II) center of an adjacent unit, leading to the polynuclear complexes [[Cu(L)(H2O)](ClO4)]n (3) and [[Cu(L)Cl].2H2O]n (4). Variab…

On fermionic shadow wave functions for strongly correlated multi-reference systems based on a single Slater determinant

2015

We demonstrate that extending the Shadow Wave Function to fermionic systems facilitates to accurately calculate strongly-correlated multi-reference systems such as the stretched H2 molecule. This development considerably extends the scope of electronic structure calculations and enables to efficiently recover the static correlation energy using just a single Slater determinant.

Fourier transform nmr investigations of organotin compounds

1980

Abstract NMR spectra have been obtained for fiteen title compounds, mainly with R = Me. Tin chemical shifts were found to lie within the expected ranges, but to vary little with R or, apparently, with change in ring size. While the magnitute of 1 (SnSe) was as predicted, the of 1 (SnTe) was more than twice as large as that previously observed for (Me 3 Sn) 2 Te. In compounds Me 6 Sn( 3 X 3 , 2 J(SnMSn) varied systematically with variations in x, but within relatively narrow limits (195-250 Hz); a much more drastic variation was observed for Me 6 Sn 3 X 2 , possibly due to bond angle changes at Sn and X.

High-Resolution Spectroscopy and Structure of Osmium Tetroxide. A Benchmark Study on 192OsO4

2012

Osmium tetroxide (OsO(4)) is a heavy tetrahedral molecule that constitutes a benchmark for quantum chemistry calculations. Its favorable spin statistics (due to the zero nuclear spin of oxygen atoms) is such that only A(1) and A(2) (T(d) symmetry) rovibrational levels are allowed, leading to a dense but quite easily resolvable spectrum. We reinvestigate here the ν(1)/ν(3) stretching fundamental (940-980 cm(-1)) dyad region and perform new assignments and effective Hamiltonian parameter fits for the main isotopologue ((192)OsO(4)). We also investigate the ν(2)/ν(4) bending fundamental dyad (300-360 cm(-1)) for the first time and perform a preliminary analysis. New experimental data have been…

Analytic second derivatives for the spin-free exact two-component theory

2011

The formulation and implementation of the spin-free (SF) exact two-component (X2c) theory at the one-electron level (SFX2c-1e) is extended in the present work to the analytic evaluation of second derivatives of the energy. In the X2c-1e scheme, the four-component one-electron Dirac Hamiltonian is block diagonalized in its matrix representation and the resulting "electrons-only" two-component Hamiltonian is then used together with untransformed two-electron interactions. The derivatives of the two-component Hamiltonian can thus be obtained by means of simple manipulations of the parent four-component Hamiltonian integrals and derivative integrals. The SF version of X2c-1e can furthermore exp…

ChemInform Abstract: Dehydrotriphenylenes for the Generation of Bent Molecular Ribbons.

2010

Molecular association and dynamics in n-pentanol and 2-methyl-2-butanol

1985

Static dielectric constant, viscosity, density, ultrasonic and dielectric relaxation measurements are reported for two pentanol isomers (n-pentanol and 2-methyl-2-butanol) in a wide range of temperatures. The results show a different extent of H-bonds self-association in relation to the molecular geometry of the alcohol. The activation energies obtained from dielectric and ultrasonic studies are compared with those obtained from viscous flow. Such a comparison, together with the analysis of all the dielectric and ultrasonic relaxation data, show that in n-pentanol a correlation between viscosity and ultrasonic relaxation exists, while dielectric relaxation is not correlated with the other t…