Search results for "Intersection"
showing 10 items of 213 documents
Quantum dynamics of the photostability of pyrazine
2015
We investigate the radiationless decay of photoexcited pyrazine to its ground electronic state using multireference electronic structure and quantum dynamics calculations. We construct a quadratic vibronic coupling Hamiltonian, including the four lowest electronic states and ten vibrational modes, by fitting to more than 5000 ab initio points. We then use this model to simulate the non-adiabatic excited state dynamics of the molecule using the multi-configuration time-dependent Hartree method. On the basis of these calculations, we propose a new mechanism for this decay process involving a conical intersection between the Au(nπ*) state and the ground state. After excitation to the B2u(ππ*) …
Basic Concepts and Methodology
2016
In this chapter, the main concepts relevant for the theoretical study of elementary photochemical processes are briefly reviewed. The notions of vibronic coupling and conical intersection are first introduced. The main basic tools from the molecular electronic structure theory and their use for the exploration of potential energy surfaces are then presented.
Real-time Sub-pixel Cross Bar Position Metrology
2002
Many measurement application fields need to calculate cross bar intersection locations of horizontal and vertical bars. The system we developed and that we present in this paper is an embedded system that measures cross bar positions with sub-pixel accuracy on 1024×1024 pixel images delivered by a camera at a 50 MHz data rate in real time. This is done using an algorithm that looks for intersection areas and then locally calculates two lines representing horizontal and vertical bars. The two line intersection is considered to be the bar intersection. To achieve real time, we developed a hybrid architecture in which low level processes are implemented into FPGAs and others into DSPs. As a re…
Signalling Three-Way Intersections: Is Redundancy Better Than Only Mandatory or Prohibitory Signs?
2021
This work was supported by the Spanish Government, Ministry of Economy and Competitiveness (PGC2018-095868-B-I00).
Short hydrogen bonds enhance non-aromatic protein-related fluorescence
2020
AbstractFluorescence in biological systems is usually associated with the presence of aromatic groups. Here, we show that specific hydrogen bonding networks can significantly affect fluorescence employing a combined experimental and computational approach. In particular, we reveal that the single amino acid L-glutamine, by undergoing a chemical transformation leading to the formation of a short hydrogen bond, displays optical properties that are significantly enhanced compared to L-glutamine itself. Ab initio molecular dynamics simulations highlight that these short hydrogen bonds prevent the appearance of a conical intersection between the excited and the ground states and thereby signific…
Expecting the unexpected: Quantifying the persistence of unexpected hypersurfaces
2021
If $X \subset \mathbb P^n$ is a reduced subscheme, we say that $X$ admits an unexpected hypersurface of degree $t$ for multiplicity $m$ if the imposition of having multiplicity $m$ at a general point $P$ fails to impose the expected number of conditions on the linear system of hypersurfaces of degree $t$ containing $X$. Conditions which either guarantee the occurrence of unexpected hypersurfaces, or which ensure that they cannot occur, are not well understand. We introduce new methods for studying unexpectedness, such as the use of generic initial ideals and partial elimination ideals to clarify when it can and when it cannot occur. We also exhibit algebraic and geometric properties of $X$ …
Hodge Theory and Algebraic Cycles
2006
Algebraic cycles and Hodge theory, in particular Chow groups, Deligne cohomology and the study of cycle class maps were some of the themes of the Schwerpunkt ”Globale Methoden in der Komplexen Geometrie”. In this survey we report about several projects around the structure of (higher) Chow groups CH(X,n) [3] which the author has studied with his coauthors during this time by using different methods. In my opinion there are two interesting view points: first the internal structure of higher Chow groups, i.e., the existence of interesting elements and nontriviality of parts of their Bloch-Beilinson filtrations. This case has arithmetic and geometric features, and the groups in question show d…
Families of ICIS with constant total Milnor number
2021
We show that a family of isolated complete intersection singularities (ICIS) with constant total Milnor number has no coalescence of singularities. This extends a well-known result of Gabriélov, Lazzeri and Lê for hypersurfaces. We use A’Campo’s theorem to see that the Lefschetz number of the generic monodromy of the ICIS is zero when the ICIS is singular. We give a pair applications for families of functions on ICIS which extend also some known results for functions on a smooth variety.
Logarithmic Vector Fields and the Severi Strata in the Discriminant
2017
The discriminant, D, in the base of a miniversal deformation of an irreducible plane curve singularity, is partitioned according to the genus of the (singular) fibre, or, equivalently, by the sum of the delta invariants of the singular points of the fibre. The members of the partition are known as the Severi strata. The smallest is the δ-constant stratum, D(δ), where the genus of the fibre is 0. It is well known, by work of Givental’ and Varchenko, to be Lagrangian with respect to the symplectic form Ω obtained by pulling back the intersection form on the cohomology of the fibre via the period mapping. We show that the remaining Severi strata are also co-isotropic with respect to Ω, and mor…
P-spaces and the Volterra property
2012
We study the relationship between generalizations of $P$-spaces and Volterra (weakly Volterra) spaces, that is, spaces where every two dense $G_\delta$ have dense (non-empty) intersection. In particular, we prove that every dense and every open, but not every closed subspace of an almost $P$-space is Volterra and that there are Tychonoff non-weakly Volterra weak $P$-spaces. These results should be compared with the fact that every $P$-space is hereditarily Volterra. As a byproduct we obtain an example of a hereditarily Volterra space and a hereditarily Baire space whose product is not weakly Volterra. We also show an example of a Hausdorff space which contains a non-weakly Volterra subspace…