Performance Analysis of Two Quantum Reaction Dynamics Codes: Time-Dependent and Time-Independent Strategies

The computer simulation of reaction dynamics has nowadays reached a remarkable degree of accuracy. Triatomic elementary reactions are rigorously studied with great detail on a straightforward basis using a considerable variety of Quantum Dynamics computational tools available to the scientific community. In our contribution we compare the performance of two quantum scattering codes in the computation of reaction cross sections of a triatomic benchmark reaction such as the gas phase reaction Ne + H2+ %12. NeH++ H. The computational codes are selected as representative of time-dependent (Real Wave Packet [ ]) and time-independent (ABC [ ]) methodologies. The main conclusion to be drawn from our study is that both strategies are, to a great extent, not competing but rather complementary. While time-dependent calculations advantages with respect to the energy range that can be covered in a single simulation, time-independent approaches offer much more detailed information from each single energy calculation. Further details such as the calculation of reactivity at very low collision energies or the computational effort related to account for the Coriolis couplings are analyzed in this paper.

Monoidal functors, acyclic models and chain operads

We prove that for a topological operad $P$ the operad of oriented cubical singular chains, $C^{\ord}_\ast(P)$, and the operad of simplicial singular chains, $S_\ast(P)$, are weakly equivalent. As a consequence, $C^{\ord}_\ast(P\nsemi\mathbb{Q})$ is formal if and only if $S_\ast(P\nsemi\mathbb{Q})$ is formal, thus linking together some formality results which are spread out in the literature. The proof is based on an acyclic models theorem for monoidal functors. We give different variants of the acyclic models theorem and apply the contravariant case to study the cohomology theories for simplicial sets defined by $R$-simplicial differential graded algebras.

Dels jeroglífics egipcis a la compartició de secrets

En aquest article parlarem d'un jeroglífic inscrit als laterals de la llinda de Sant Andreu de la Barroca, una petita església perduda en un indret recòndit de la Vall del Llémena, a la Garrotxa. A propòsit d'aquest petit enigma ludolingüístic, plantejarem(i finalment resoldrem) un problema de naturalesa combinatòria que el lector interessat pot provar de resoldre com a exercici. També fem un breu repàs de la història del desxiframent '’escriptures de civilitzacions antigues. Aprofitem l'avinentesa per introduir els conceptes d'entropia i redundància del llenguatge, que ens ajudaran a entendre per què, tard o d'hora, qualsevolescriptura antiga finalment acaba essent desxifrada quan es té una conjectura raonable sobre quina és la llengua que transcriu. Finalment, definim el concepte d'esquema de compartició de secrets, un problema de criptografia moderna en el qual un conjunt de persones gestiona petits fragments d'informació compartida, i que es resol aplicant de manera brillant una idea que prové del món de l'àlgebra lineal més elemental

A Cartan-Eilenberg approach to Homotopical Algebra

In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects by an extension property analogous to the classical lifting property of projective modules. We define a Cartan-Eilenberg category as a category with strong and weak equivalences such that there is an equivalence of categories between its localisation with respect to weak equivalences and the relative localisation of the subcategory of cofibrant objects with respect to strong equivalences. This equivalence of categories allows us to extend the classical theory of derived additive functors to this non additive setting. The main examples include Quillen model categories and categories of functors defined on a category endowed with a cotriple (comonad) and taking values on a category of complexes of an abelian category. In the latter case there are examples in which the class of strong equivalences is not determined by a homotopy relation. Among other applications of our theory, we establish a very general acyclic models theorem.