Search results for "Computational Mathematic"
showing 10 items of 987 documents
New insights in chemical reactivity from quantum chemical topology.
2021
International audience; Based on the quantum chemical topology of the modified electron localization function ELFx, an efficient and robust mechanistic methodology designed to identify the favorable reaction pathway between two reactants is proposed. We first recall and reshape how the supermolecular interaction energy can be evaluated from only three distinct terms, namely the intermolecular coulomb energy, the intermolecular exchange‐correlation energy and the intramolecular energies of reactants. Thereafter, we show that the reactivity between the reactants is driven by the first‐order variation in the coulomb intermolecular energy defined in terms of the response to changes in the numbe…
Weakly nonlinear analysis of Turing patterns in a morphochemical model for metal growth
2015
We focus on the morphochemical reaction–diffusion model introduced in Bozzini et al. (2013) and carry out a nonlinear bifurcation analysis with the aim to characterize the shape and the amplitude of the patterns arising as the result of Turing instability of the physically relevant equilibrium. We perform a weakly nonlinear multiple scales analysis, and derive the normal form equations governing the amplitude of the patterns. These amplitude equations allow us to construct relevant solutions of the model equations and reveal the presence of multiple branches of stable solutions arising as the result of subcritical bifurcations. Hysteretic type phenomena are highlighted also through numerica…
Optical phase retrieval using four rotated versions of a single binary mask – simulation results
2018
In signal processing one often faces the phase problem, i.e., when an image is formed information about the phase is lost so that only information about intensity is available. This is often an issue in astronomy, biology, crystallography, speckle imaging, diffractive imaging where the phase of the object must be known. While there have been many approaches how to find a solution to the phase problem, numerical algorithms recovering the phase from intensity measurements become more and more popular. One of such algorithms called PhaseLift has been recently proposed. In this study, we show that even 4 masks may be sufficient for reasonable recovery of the phase. The original wavefront and th…
Rotationally symmetric 1-harmonic flows from D2 TO S 2: Local well-posedness and finite time blowup
2010
The 1-harmonic flow from the disk to the sphere with constant Dirichlet boundary conditions is analyzed in the case of rotational symmetry. Sufficient conditions on the initial datum are given, such that a unique classical solution exists for short times. Also, a sharp criterion on the boundary condition is identified, such that any classical solution will blow up in finite time. Finally, nongeneric examples of finite time blowup are exhibited for any boundary condition.
Towards Stable Radial Basis Function Methods for Linear Advection Problems
2021
In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced strongly in RBF methods. By now it is well-known that this can lead to stability problems, however. Here, we follow a different path and propose two novel RBF approaches which are based on a weak enforcement of BCs. By using the concept of flux reconstruction and simultaneous approximation terms (SATs), respectively, we are able to prove that both new RBF schemes are strongly (energy) stable. Numerical results in one and two spatial dimensions for both scalar equations and systems are presented, supporting our theoret…
On the a posteriori error analysis for linear Fokker-Planck models in convection-dominated diffusion problems
2018
This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain computable error bounds of the functional type for the static and time-dependent case and for different boundary conditions (mixed and pure Neumann boundary conditions). Finally, we present a set of various numerical examples including discussions on mesh adaptivity and space-time discretisation. The numerical results confirm the reliability and efficiency of the error estimates derived.
Theoretical study on hydrogen storage capacity of expanded h-BN systems
2017
In this work, the hydrogen storage capacity of the expanded hexagonal Boron Nitride (eh-BN) systems has been presented. We have employed a new equation of state (EOS) for hydrogen gas to figure out the hydrogen density distribution profiles in the eh-BN systems. In this regard, the environmental conditions (i.e., temperature and pressure) are considered in the prediction procedure using DFT single point calculations. The eh-BN systems with different layer spacings are studied by PBE method with consideration of the long range dispersion corrections. On account of the in-plane polar bonds, a series of adsorption positions are considered. Additionally, the adsorption energy and hydrogen densi…
A study of Wigner functions for discrete-time quantum walks
2013
We perform a systematic study of the discrete time Quantum Walk on one dimension using Wigner functions, which are generalized to include the chirality (or coin) degree of freedom. In particular, we analyze the evolution of the negative volume in phase space, as a function of time, for different initial states. This negativity can be used to quantify the degree of departure of the system from a classical state. We also relate this quantity to the entanglement between the coin and walker subspaces.
Estimating the temperature evolution of foodstuffs during freezing with a 3D meshless numerical method
2015
Abstract Freezing processes are characterised by sharp changes in specific heat capacity and thermal conductivity for temperatures close to the freezing point. This leads to strong nonlinearities in the governing PDE that may be difficult to resolve using traditional numerical methods. In this work we present a meshless numerical method, based on a local Hermite radial basis function collocation approach in finite differencing mode, to allow the solution of freezing problems. By introducing a Kirchhoff transformation and solving the governing equations in Kirchhoff space, the strength of nonlinearity is reduced while preserving the structure of the heat equation. In combination with the hig…
A thread through challenging questions
2015
In the pages which follow I shall try to present a network relating some challenging different problems and questions; questions and problems which in different forms have been discussed with Enric along the years. The thread, of course, is constructed by me and now, and is based on my memory, choices and preferences. For these reasons I am not sure that Enric will totally agree with the particular way in which I have intertwined the different elements composing the thread as well as the pieces it connects. However I presume that this thread - also in the specific subjective form as it appears - will show, anyway, some elements of Enric’s activity and the way in which we have interacted alo…