For an owner or operator of a building, benchmarking can be a useful guide for finding out how energy efficient the building is and identifying what to improve. For successful evaluation of the building energy efficiency, the categorization as well as the parameter identification has decisive importance. That selection can be based on mathematical modeling such as linear regression accompanied ...

ENERGY METHODS FOR REACTION-DIFFUSION PROBLEMS by Xing Zhong Nonlinear reaction-diffusion equations arise in many areas of applied sciences such as combustion modeling, population dynamics, chemical kinetics, etc. A fundamental problem in the studies of these equations is to understand the long time behavior of solutions of the associated Cauchy problem. These kinds of questions were originally...

This compact set of notes present some basic, abstract results with two examples of boundary-value problems on weak convergence methods for the study of existence of minimizers of essentially convex functionals. The method described here is called the direct method in the calculus of variations. The main results are stated in their simplest possible setting. But, they have many variations that ...

We present and analyze energy-conserving methods for the numerical inte-gration of IVPs of Poisson type systems that are able to preserve some Casimirs.Their derivation and analysis is done within the framework following the ideasof Hamiltonian BVMs (HBVMs) (see [1] and references therein). The pro-posed methods turn out to be equivalent to those recently derived in [2], giv...

An overview is given of methods for calculating free energies by molecular simulation. Techniques may be categorized as density-of-states methods and work-based methods. Emphasis is given to the latter, with particular focus on issues of performance and accuracy. Two points of view are provided for understanding these issues. One is based on the distribution of work values observed in the calcu...