A family of interatomic potentials is constructed for which the intrinsic ductility can be tuned systematically. Specifically, the elastic constants and critical energy release rate for Griffith cleavage, GIc, are held constant, while the critical energy release rate for dislocation emission, GIe, can be varied. This behavior is achieved by modifying a standard near-neighbor pair potential; the...

Potential-density pair basis sets can be used for highly efficient N-body simulation codes, but they suffer from a lack of versatility, i.e. a basis set has to be constructed for each different class of stellar system. We present numerical techniques for generating a biorthonormal potential-density pair basis set which has a general specified pair as its lowest order member. We go on to demonst...

v CHAPTER 1. GENERAL INTRODUCTION 1 Research Motivation 1 Thesis Organization 2 CHAPTER 2. GENERAL METHODS 3 General Methods 3 CHAPTER 3. LENNARD-JONES SYSTEM 7 Overall Introduction 7 Method on BCC Solid Reference Free Energy 8 Method on BCC Solid Perturbation Free Energy 11 Results of BCC Solid Free Energy of LJ System 12 Method on Liquid Hard Sphere Free Energy 13 Method on Liquid Perturbatio...

Simulations of charged colloidal dispersions are technically challenging. One possible workaround consists in reducing the system to the colloids only, whose interactions are described through an effective pair potential, wf. Still, the determination of wf is difficult mainly because it depends on the colloidal density, ϕ. Here we propose to calculate wf from simulations of a pair of colloids p...

In this article, we consider pair frames in Banach spaces and   introduce Banach pair frames. Some various concepts in the frame theory such as frames, Schauder frames, Banach frames and atomic decompositions are considered as   special kinds of (Banach) pair frames.  Some frame-like inequalities  for (Banach)  pair frames are presented. The elements that participant  in the construction of (Ba...

We discuss inverse spectral theory for singular differential operators on arbitrary intervals (a, b) ⊆ R associated with rather general differential expressions of the type τf = 1 r ( − ( p[f ′ + sf ] )′ + sp[f ′ + sf ] + qf ) , where the coefficients p, q, r, s are Lebesgue measurable on (a, b) with p−1, q, r, s ∈ Lloc((a, b); dx) and real-valued with p 6= 0 and r > 0 almost everywhere on (a, ...