We seldom measure H from the center of earth. Therefore what we can easily measure is the change of the potential energy ∆W = (mg)(H −Ho) (8.2) The energy is always positive. It can e zero but it cannot be negative. The gravity force F = mg is directed towards the center of earth. Therefore there is a need for the negative sign in Eq. (8.2)). In the coordinate system of Fig. (8.1), the gravity ...

INTRODUCTION The determination of energy expenditure, considering the physical activity level and health status, is very important to adjust the individuals' nutritional supply. Energy expenditure can be determined by using indirect calorimetry, bioelectrical impedance, doubly labeled water, predictive equations, among others. All these methods have been used in clinical and research areas. How...

We shall study multigrid methods from energy minimizations and approximations. Through the analysis of an multigrid method in 1D, we introduce the concepts of stability and the approximation property in the classical theory. Based on them, we derive an energy-minimizing interpolation and present a two level analysis for it. Issues on coarsening are also addressed. Finally, we demonstrate the ee...

We investigate linear energy preserving methods for the Volterra lattice equation as non-canonical Hamiltonian system. The averaged vector field method was applied to the Volterra lattice equation in bi-Hamiltonian form with quadratic and cubic Poisson brackets. Numerical results confirm the excellent long time preservation of the Hamiltonians and the polynomial integrals.

We investigate the use of stochastic methods for zero energy quantum scattering based on a path integral approach. With the application to the scattering of a projectile from a nuclear many body target in mind, we use the potential scattering of a particle as a test for the accuracy and efficiency of several methods. To be able to deal with complex potentials, we introduce a path sampling actio...

A simple, efficient, and accurate method is proposed to map multidimensional free energy landscapes. The method combines the temperature-accelerated molecular dynamics (TAMD) proposed in [L. Maragliano and E. Vanden-Eijnden, Chem. Phys. Lett. 426, 168 (2006)] with a variational reconstruction method using radial-basis functions for the representation of the free energy. TAMD is used to rapidly ...

We propose a modification of collocation methods extending the ‘averaged vector field method’ to high order. These new integrators exactly preserve energy for Hamiltonian systems, are of arbitrarily high order, and fall into the class of B-series integrators. We discuss their symmetry and conjugate-symplecticity, and we compare them to energypreserving composition methods. c © 2010 European Soc...