Mathematical models for epidemiological simulations
The simulation of epidemic propagation is bringing valuable information about the main characteristics of the epidemic under study. Although the precise prediction of the spread have to be considered with care (e.g. due to stochastic elements) the qualitative study of the numerical results may help in proving the rightfulness of a given hypothesis concerning the underlying virus caracteristics.
the computations inab initio electronic structure have reached the point where interesting practical applications are in sight for biological-related molecures (proteines ...). On the other hand, in solid physics and in materials science one also sees the need for computations using a larger number of atoms and electrons. As the heart of these computations, the algorithms used to compute the energy and the electronic wavefunction are still source of interesting numerical analysis problems.
Dynamical discrimination of molecules
Similar molecules often may be characterized as sharing common chemical structures made up of the same atomic components. Such molecules are expected to have related Hamiltonians, and thus similar chemical and physical properties. Examples range from simple isotopic variants of diatomics (e.g., 79Br2, 81Br2) and isomers (e.g., cis- and trans-1,2-dichloroethylene) to highly complex molecules including those of biological relevance. A common need is to analyze or separate one molecular species in the presence of possibly many other similar agents. This problem often demands rapid, sensitive, and dependable identification or purification measures. Traditional approaches mainly focus on exploiting the subtle differences in the microscopic properties, or macroscopic properties; these methods have seen wide applications, but they may all be characterized as static or one-dimensional with their capabilities being pushed to the limit. To enhance the ability to distinguish molecules, a new paradigm is proposed aiming for optimal discrimination by actively amplifying the seemingly subtle differences between similar molecules. The proposed optimal dynamic discrimination (ODD) approach exploits the richness of quantum molecular dynamics. Although the dynamics of similar quantum systems are governed by related Hamiltonians, each species could evolve in a distinct fashion under the same properly tailored external control, e.g. a laser field. The wave packets of the similar molecules in the system are excited by a common laser pulse, which is tailored with the goal of inducing signals (possibly detected with another common laser pulse) from only one species, while suppressing signals from all the others. Optimal control techniques are potentially ideal tools for implementing ODD, as the underlying closed loop learning control process inherently operates based on achieving discrimination between one dynamical process versus another.
