Search results for "Conical surface"
showing 10 items of 56 documents
Computation of conical intersections by using perturbation techniques
2005
Multiconfigurational second-order perturbation theory, both in its single-state multiconfigurational second-order perturbation theory (CASPT2) and multistate (MS-CASPT2) formulations, is used to search for minima on the crossing seams between different potential energy hypersurfaces of electronic states in several molecular systems. The performance of the procedures is tested and discussed, focusing on the problem of the nonorthogonality of the single-state perturbative solutions. In different cases the obtained structures and energy differences are compared with available complete active space self-consistent field and multireference configuration interaction solutions. Calculations on dif…
Tangential behavior of functions and conical densities of Hausdorff measures.
2005
We construct a $C^1$-function $f\colon [0,1]\to \mathbb{R}$ such that for almost all $x\in(0,1)$, there is $r>0$ for which $f(y)>f(x)+f'(x)(y-x)$ when $y\in(x,x+r)$ and $f(y)< f(x)+f'(x)(y-x)$ when $y\in(x-r,x)$. The existence of such functions is related to a problem concerning conical density properties of Hausdorff measures on $\mathbb{R}^n$. We also discuss the tangential behavior of typical $C^1$-functions, using an improvement of Jarnik's theorem on essential derived numbers
Dynamics of the scenery flow and geometry of measures
2015
We employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely linked to rectifiability. Moreover, we show that the dimension theory of measure-theoretical porosity can be reduced back to its set-theoretic version, that Hausdorff and packing dimensions yield the same maximal dimension for porous and even mean porous measures, and that extremal measures exist and can be chosen to satisfy a generalized notion of self-similarity. These are sharp general formulations of phenomena that had been earlier found to hold in a n…
Pore structure and function of synthetic nanopores with fixed charges: tip shape and rectification properties
2011
We present a complete theoretical study of the relationship between the structure (tip shape and dimensions) and function (selectivity and rectification) of asymmetric nanopores on the basis of previous experimental studies. The theoretical model uses a continuum approach based on the Nernst-Planck equations. According to our results, the nanopore transport properties, such as current-voltage (I-V) characteristics, conductance, rectification ratio, and selectivity, are dictated mainly by the shape of the pore tip (we have distinguished bullet-like, conical, trumpet-like, and hybrid shapes) and the concentration of pore surface charges. As a consequence, the nanopore performance in practical…
Fluoride-Induced Negative Differential Resistance in Nanopores: Experimental and Theoretical Characterization
2021
We describe experimentally and theoretically the fluoride-induced negative differential resistance (NDR) phenomena observed in conical nanopores operating in aqueous electrolyte solutions. The threshold voltage switching occurs around 1 V and leads to sharp current drops in the nA range with a peak-to-valley ratio close to 10. The experimental characterization of the NDR effect with single pore and multipore samples concern different pore radii, charge concentrations, scan rates, salt concentrations, solvents, and cations. The experimental fact that the effective radius of the pore tip zone is of the same order of magnitude as the Debye length for the low salt concentrations used here is su…
Nonsymmetric conical upper density and $k$-porosity
2017
We study how the Hausdorff measure is distributed in nonsymmetric narrow cones in R n \mathbb {R}^n . As an application, we find an upper bound close to n − k n-k for the Hausdorff dimension of sets with large k k -porosity. With k k -porous sets we mean sets which have holes in k k different directions on every small scale.
Testing jet geometries and disc-jet coupling in the neutron star LMXB 4U 0614 + 091 with the internal shocks model
2020
Multi-wavelength spectral energy distributions of Low Mass X-ray Binaries in the hard state are determined by the emission from a jet, for frequencies up to mid-infrared, and emission from the accretion flow in the optical to X-ray range. In the last years, the flat radio-to-mid-IR spectra of Black Hole (BH) X-ray binaries was described using the internal shocks model, which assumes that the fluctuations in the velocity of the ejecta along the jet are driven by the fluctuations in the accretion flow, described by the X-ray Power Density Spectrum (PDS). In this work we attempt to apply this model for the first time to a Neutron Star (NS) LMXB, i.e. 4U 0614+091. We used the multi-wavelength d…
Ultrafast ring-opening/closing and deactivation channels for a model spiropyran-merocyanine system.
2011
The photochemistry of a model merocyanine-spiropyran system was analyzed theoretically at the MS-CASPT2//SA-CASSCF(14,12) level. Several excited singlet states were studied in both the closed spiropyran and open merocyanine forms, and the paths to the different S(1)/S(0) conical intersections found were analyzed. After absorption of UV light from the spiropyran form, there are two possible ultrafast routes to efficient conversion to the ground state; one involves the rupture of the C(spiro)-O bond leading to the open form and the other involves the lengthening of the C(spiro)-N bond with no photoreaction. From the merocyanine side the excited state can reach a very broad S(1)/S(0) conical i…
On the use of reduced active space in CASSCF calculations
2014
Abstract The complete active space self-consistent field (CASSCF) method is one of the most used approaches to explore theoretically non-adiabatic photochemical processes in medium-size molecular systems. It is also frequently utilized in direct dynamics studies because this method offers a reliable description of the electronic state mixing in the regions of surface crossings (conical intersections). In this context, however, the large computational demand required to perform such on-the-fly molecular dynamics simulations using CASSCF as the electronic structure method means that only relatively small active space can be handled (typically not more than 10 electrons distributed in 10 orbit…
Polymer Brushes on Flat and Curved Substrates: Scaling Concepts and Computer Simulations
2007
The scaling concepts for isolated flexible macromolecules in good solvent grafted with one chain end to a flat surface (polymer mushrooms) as well as for layers of many overlapping end-grafted chain molecules (polymer brushes) are introduced. Monte Carlo attempts to test these concepts are briefly reviewed. Then the extension of these concepts to polymer brushes grafted to the interior of a cylinder surface is discussed. Molecular Dynamics results on chain average linear dimensions in the direction normal to the grafting surface and in axial direction are described, as well as distribution functions for the density of end monomers and of all monomers of the chains. It is argued that under t…