We develop some theory of spinal decompositions of discrete and continuous fragmentation trees. Specifically, we consider a coarse and a fine spinal integer partition derived from spinal tree decompositions. We prove that for a two-parameter Poisson-Dirichlet family of continuous fragmentation trees, including the stable trees of Duquesne and Le Gall, the fine partition is obtained from the coa...

We develop some theory of spinal decompositions of discrete and continuous fragmentation trees. Specifically, we consider a coarse and a fine spinal integer partition derived from spinal tree decompositions. We prove that for a two-parameter Poisson–Dirichlet family of continuous fragmentation trees, including the stable trees of Duquesne and Le Gall, the fine partition is obtained from the coa...

We examine an infinite system of ordinary differential equations that models the coagulation and fragmentation of clusters. In contrast to previous investigations, we allow multiple fragmentation to occur and our analysis does not involve finite-dimensional truncations of the system. Instead, we treat the problem as an infinite-dimensional differential equation, posed in an appropriate Banach s...

We develop some theory of spinal decompositions of discrete and continuous fragmentation trees. Specifically, we consider a coarse and a fine spinal integer partition derived from spinal tree decompositions. We prove that for a two-parameter Poisson–Dirichlet family of continuous fragmentation trees, including the stable trees of Duquesne and Le Gall, the fine partition is obtained from the coa...

We present experiments on the dynamic buckling and fragmentation of slender rods axially impacted by a projectile. By combining the results of Saint-Venant and elastic beam theory, we derive a preferred wavelength lambda for the buckling instability, and experimentally verify the resulting scaling law for a range of materials including teflon, dry pasta, glass, and steel. For brittle materials,...

We compare recent experimental results for one-particle-inclusive processes in deeply inelastic scattering at HERA with theoretical predictions in nextto-leading-order QCD perturbation theory, and study the factorization scale dependence of cross sections and charged multiplicities. In the future, for the HERA machine running at design luminosity, scaling violations of fragmentation functions p...

The stability analysis of asynchronous sampled-data systems is studied. The approach is based on a recent result which allows to study, in an equivalent way, the quadratic stability of asynchronous sampled-data systems in a continuous-time framework via the use of peculiar functionals satisfying a necessary boundary condition. The method developed here is an extension of previous results using ...