The Torsional Rigidity of a Rectangular Prism

The Minkowski problem for the torsional rigidity

We prove the existence and uniqueness up to translations of the solution to a Minkowski type problem for the torsional rigidity in the class of open bounded convex subsets of R n. For the existence part we apply the variational method introduced by Jerison in: Adv. Math. 122 (1996), pp. 262–279. Uniqueness follows from the Brunn–Minkowski inequality for the torsional rigidity and corresponding ...

The demagnetizing field of a non-uniform rectangular prism

Torsional Rigidity of Submanifolds with Controlled Geometry

We prove explicit upper and lower bounds for the torsional rigidity of extrinsic domains of submanifolds P with controlled radial mean curvature in ambient Riemannian manifolds N with a pole p and with sectional curvatures bounded from above and from below, respectively. These bounds are given in terms of the torsional rigidities of corresponding Schwarz symmetrizations of the domains in warped...

Direct measurement of the torsional rigidity of single actin filaments.

Flexural and torsional rigidities of actin filaments are important factors in cell motility and muscle contraction, where actin filaments serve as mechanical elements. The flexural rigidity has already been determined by directly observing the bending of individual filaments under a microscope, but measurement of the torsional rigidity has been relatively scarce and indirect, because torsion of...

Enumeration of minimal 3D polyominoes inscribed in a rectangular prism

We consider the family of 3D minimal polyominoes inscribed in a rectanglar prism. These objects are polyominos and so they are connected sets of unitary cubic cells inscribed in a given rectangular prism of size b×k×h and of minimal volume equal to b + k + h − 2. They extend the concept of minimal 2D polyominoes inscribed in a rectangle studied in a previous work. Using their geometric structur...