Wiggly strain localizations in peridynamic bars with non-convex potential

Triangulating a convex polygon with fewer number of non-standard bars

For a given convex polygon with inner angle no less than 3π and boundary edge bounded by [l, αl] for 1 ≤ α ≤ 1.4, where l is a given standard bar’s length, we investigate the problem of triangulating the polygon using some Steiner points such that (i) the length of each edge in triangulation is bounded by [βl, 2l], where β is a given constant and meets 0 < β ≤ 1 2 , and (ii) the number of non-s...

Triangulating a Convex Polygon with Small Number of Non-standard Bars

For a given convex polygon with inner angle no less than 2 3 π and boundary edge bounded by [l, αl] for 1 ≤ α ≤ 1.4, where l is a given standard bar’s length, we investigate the problem of triangulating the polygon using some Steiner points such that (i) the length of each edge in triangulation is bounded by [βl, 2l], where β is a given constant and meets 0 < β < 1 2 , and (ii) the number of no...

Bulk Universality of General β-Ensembles with Non-convex Potential

We prove the bulk universality of the β-ensembles with non-convex regular analytic potentials for any β > 0. This removes the convexity assumption appeared in the earlier work [6]. The convexity condition enabled us to use the logarithmic Sobolev inequality to estimate events with small probability. The new idea is to introduce a “convexified measure” so that the local statistics are preserved ...

Non convex technologies and economic efficiency measure with imprecise data

Wiggly relativistic strings.

We derive the equations of motion for general strings, i.e. strings with arbitrary relation between tension τ and energy per unit length ǫ. The renormalization of τ and ǫ that results from averaging out small scale wiggles on the string is obtained in the general case to lowest order in the amount of wiggliness. For Nambu-Goto strings we find deviations from the equation of state ǫτ = constant ...