Search results for "Abstract algebra"
showing 10 items of 452 documents
The transition state and cognate concepts
2019
Abstract This review aims firstly to clarify the meanings of key terms and concepts associated with the idea of the transition state, as developed by theoreticians and applied by experimentalist, and secondly to provide an update to the meaning and significance of the transition state in an era when computational simulation, in which complexity is being increasingly incorporated, is commonly employed as a means by which to bridge the realms of theory and experiment. The relationship between the transition state and the potential-energy surface for an elementary reaction is explored, with discussion of the following terms: saddle point, minimum-energy reaction path, reaction coordinate, acti…
On the ‘expanded local mode’ approach applied to the methane molecule: isotopic substitution CH2D2←CH4
2011
On the basis of a compilation of the ‘expanded local mode’ model and the general isotopic substitution theory, sets of simple analytical relations between different spectroscopic parameters (harmonic frequencies, ωλ, anharmonic coefficients, x λμ, ro-vibrational coefficients, , different kinds of Fermi- and Coriolis-type interaction parameters) of the CH2D2 molecule are derived. All of them are expressed as simple functions of a few initial spectroscopic parameters of the mother, CH4, molecule. Test calculations with the derived isotopic relations show that, in spite of a total absence of initial information about the CH2D2 species, the numerical results of the calculations have a very good…
Introducing Memory in Coarse-Grained Molecular Simulations
2021
[Image: see text] Preserving the correct dynamics at the coarse-grained (CG) level is a pressing problem in the development of systematic CG models in soft matter simulation. Starting from the seminal idea of simple time-scale mapping, there have been many efforts over the years toward establishing a meticulous connection between the CG and fine-grained (FG) dynamics based on fundamental statistical mechanics approaches. One of the most successful attempts in this context has been the development of CG models based on the Mori–Zwanzig (MZ) theory, where the resulting equation of motion has the form of a generalized Langevin equation (GLE) and closely preserves the underlying FG dynamics. In…
Elucidating the Influence of the Activation Energy on Reaction Rates by Simulations Based on a Simple Particle Model
2020
An application for visualizing the dynamic properties of an equimolar binary mixture of isotropic reactive particles is presented. By introducing a user selectable choice for the activation energy, the application is useful to demonstrate qualitatively that the reaction rate depends on the above choice and on temperature. The application is based on a 2D realistic dynamic model where atoms move because of their thermal energies and the trajectories are determined by solving numerically Newton’s laws according to a Molecular Dynamics (MD) scheme. Collisions are monitored as time progresses, and every time the collision energy is larger than the selected activation energy, a reactive event oc…
Efficient and simple synthesis of novel 1,2,3-triazolyl-linked benzimidazolone, molecular docking and evaluation of their antimicrobial activity
2020
In this study, a novel series of 1,2,3-triazolyl-benzimidazolone derivatives have been synthesized by click reaction of azides with benzimidazolones 2a–b. The latter compounds were prepared with excellent yields (85–97%), the structures of products were determined by spectral analysis. Then, the X-rays crystallographic analysis of compound 7a revealed the self-assembling properties. The new heterocycles were evaluated for their in vitro antimicrobial activities against Gram-positive and Gram-negative bacteria and against fungi strains. The most tested synthesized compounds showed potent antibacterial and antifungal activities against all tested strains. The compound 6c was found to be the m…
Developmental aspects of morphological disparity dynamics: a simple analytical exploration
2011
15 pages; International audience; We devised a simple model for assessing the role of development in shaping the evolution of morphological disparity. Disparity of a clade at any given time is expressed in terms of the developmental dynamics that lead to the variety of adult morphotypes observed. We use assumed phenotypic manifestations of developmental processes, as they could be detected from allometric characterizations, to distinguish a few, nonexclusive types of evolutionary changes in ontogeny. On the basis of this formalization, we describe the diversification of hypothetical clades, using the standard curve of adult morphological disparity, the curve of juvenile disparity, and the c…
A simple modelling of crop water balance for agrometeorological applications
1991
Abstract A simple agrometeorological model of crop water balance is presented. It aims at the best estimate possible of the water balance components with the simplest formulation and the minimum set of input data. The model works with a time step of one day and uses rainfall and the calculated evapotranspiration as the climatic inputs. Some soil and crop characteristics, such as the maximum available moisture and crop coefficients are required as input parameters. The model is tested using experimental data obtained on wheat and lucerne crops in the Paris region. The sensitivity of the model is discussed and some possible applications to rainfed crop management are presented.
Learning of Cooperative Behaviour in Robot Populations
2016
This paper addresses convergence and equilibrium properties of game theoretic learning algorithms in robot populations using simple and broadly applicable reward/cost models of cooperation between robotic agents. New models for robot cooperation are proposed by combining regret based learning methods and network evolution models. Results of mean-field game theory are employed in order to show the asymptotic second moment boundedness in the variation of cooperative behaviour. The behaviour of the proposed models are tested in simulation results, which are based on sample networks and a single lane traffic flow case study.
Secure and Privacy Preserving Pattern Matching in Distributed Cloud-based Data Storage
2019
Given two strings: pattern $p$ of length $m$ and text $t$ of length $n$ . The string matching problem is to find all (or some) occurrences of the pattern $p$ in the text $t$ . We introduce a new simple data structure, called index arrays, and design fast privacy-preserving matching algorithm for string matching. The motivation behind introducing index arrays is determined by the need for pattern matching on distributed cloud-based datasets with semi-trusted cloud providers. It is intended to use encrypted index arrays both to improve performance and protect confidentiality and privacy of user data.