Mesh ratios for best-packing and limits of minimal energy configurations

MINIMAL RIESZ ENERGY POINT CONFIGURATIONS FOR RECTIFIABLE d-DIMENSIONAL MANIFOLDS

We investigate the energy of arrangements of N points on a rectifiable d-dimensional manifold A ⊂ Rd′ that interact through the power law (Riesz) potential V = 1/r, where s > 0 and r is Euclidean distance in R ′ . With Es(A, N) denoting the minimal energy for such N -point configurations, we determine the asymptotic behavior (as N → ∞) of Es(A, N) for each fixed s ≥ d. Moreover, if A has positi...

Ideal, best packing, and energy minimizing double helices

We study optimal double helices with straight axes (or the fattest tubes around them) computationally using three kinds of functionals; ideal ones using ropelength, best volume packing ones, and energy minimizers using two one-parameter families of interaction energies between two strands of types r−α and 1 r exp(−kr). We compare the numerical results with experimental data of DNA.

Minimal Energy Configurations of Gravitationally Interacting Rigid Bodies

Consider a collection of n rigid, massive bodies interacting according to their mutual gravitational attraction. A relative equilibrium motion is one where the entire configuration rotates rigidly and uniformly about a fixed axis in R. Such a motion is possible only for special positions and orientations of the bodies. A minimal energy motion is one which has the minimum possible energy in its ...

Maximum packing for perfect four-triple configurations

für Mathematik in den Naturwissenschaften Leipzig Minimal energy configurations

We derive an effective plate theory for internally stressed thin elastic layers as are used e.g. in the fabrication of nanoand microscrolls. The shape of the energy minimizers of the effective energy functional is investigated without a priori assumptions on the geometry. For configurations in two dimensions (corresponding to Euler-Bernoulli theory) we also take into account a non-interpenetrat...