New duality relations for classical ground states.

Duality relations for the classical ground states of soft-matter systems

This work introduces novel duality relations that allow one to identify classical ground states of soft many-particle interactions using the ground states of the dual (Fourier-transformed) potentials. For potentials with the same functional form under Fourier transform, one can analytically relate the low-and high-density ground state energies and confi gurations. Bounded interactions are parti...

Ground states and formal duality relations in the Gaussian core model.

We study dimensional trends in ground states for soft-matter systems. Specifically, using a high-dimensional version of Parrinello-Rahman dynamics, we investigate the behavior of the Gaussian core model in up to eight dimensions. The results include unexpected geometric structures, with surprising anisotropy as well as formal duality relations. These duality relations suggest that the Gaussian ...

STONE DUALITY FOR R0-ALGEBRAS WITH INTERNAL STATES

$Rsb{0}$-algebras, which were proved to be equivalent to Esteva and Godo's NM-algebras modelled by Fodor's nilpotent minimum t-norm, are the equivalent algebraic semantics of the left-continuous t-norm based fuzzy logic firstly introduced by Guo-jun Wang in the mid 1990s.In this paper, we first establish a Stone duality for the category of MV-skeletons of $Rsb{0}$-algebras and the category of t...

A new class of function spaces on domains of R^d and its relations to classical function spaces

A Duality Theorem for Plastic Plates

Limit analysis studies the asymptotic behavior of elastic-plastic materials and structures. The asymptotic material properties exist for a class of ductile metals and are designed into optimal structural members such as I-beams and composite plates. The analysis automatically ignores the relatively small elastic deformations. Classical lower and upper bound theorems in the form of inequalities ...