This paper is intended to serve as a model for the first few chapters of future textbooks on continuum mechanics and continuum thermomechanics. It may be considered an update of the paper Lectures on the Foundations of Continuum Mechanics and Thermodynamics [N2] by one of us (W.N.), published in 1973, and an elaboration of topics treated in Part 3, entitled Updating the Non-Linear Field Theorie...

A literature review of electrochemical impedance spectroscopy (EIS) analysis of proton exchange membrane fuel cells (PEMFCs) is presented. Emphasis is placed on the papers that analyse the impedance response of the cathode and anode half-cells of the PEMFCs based on a continuum-mechanics approach. The other type of analysis, which is based on the equivalent-circuits approach, is addressed for c...

Molecular dynamics (MD) is a computer simulation technique where the time evolution of a set of interacting atoms is approximated by integrating their equations of motion. Our goal is to explain the mathematical background of MD for practitioners and researchers in numerical analysis and computational mechanics. The vast majority of these practitioners and researchers work with continuum mechan...

The partial phase behavior of a continuum molecular model for self-assembling semiflexible equilibrium polymers is studied via Monte Carlo and molecular dynamics simulation. We investigate the transfer from ordinary gas-liquid coexistence to the appearance of liquid crystallinity driven by excluded volume interaction between rodlike aggregates. The transfer between the two types of phase behavi...

We study the shapes of human red blood cells using continuum mechanics. In particular, we model the crenated, echinocytic shapes and show how they may arise from a competition between the bending energy of the plasma membrane and the stretching/shear elastic energies of the membrane skeleton. In contrast to earlier work, we calculate spicule shapes exactly by solving the equations of continuum ...

We discuss a dispersion relation in the photon mass and show how (in principle) model-independent constraints on the parton distribution functions of the photon, notably a momentum sumrule, can be obtained. We present two sets of parametrizations, SaS 1 and 2, corresponding to two rather extreme realizations of the non-perturbative part. Inclusive electron scattering off a real photon is found ...

We evolve virtual photon parton densities up to the SUSY threshold and higher using coupled inhomogeneous DGLAP differential equations. Reliable input parameterizations were available from the c-quark threshold. Limited P 2 ( target photon virtuality ) dependence is observed. The difference to the photon structure function is shown to be significant with the introduction of SUSY dependent split...

Mimetic discretization methods for the numerical solution of continuum mechanics problems rely on analogs of vector calculus and differential forms identities in their derivation and analysis. Fully mimetic discretizations satisfy discrete analogs of the continuum theory results used to derive energy inequalities. Consequently, continuum arguments carry over and can be used to show that discret...

Abstract. The correlator of vector heavy-quark currents at small q is considered in the large-β0 limit. The leading IR renormalon ambiguity of the sum of the perturbative series is canceled by the UV renormalon ambiguity of the gluon condensate. Asymptotic behaviour of the perturbative series is obtained in a modelindependent way, up to a single unknown normalization factor. Gluon-virtuality di...

We describe a model based in continuum mechanics that reduces the study of a significant class of problems of discrete dislocation dynamics to questions of the modern theory of continuum plasticity. As applications, we explore the questions of the existence of a Peierls stress in a continuum theory, dislocation annihilation, dislocation dissociation, finite-speed-of-propagation effects of elast...