OZM Ball Drop Impact Tester (BIT‐132) vs. BAM Standard Method – a Comparative Investigation

Safety, performance, cost efficient synthesis and toxicity are the most important aspects of modern explosives. Sensitivity measurements are performed in accordance with different protocols all around the world. Sometimes the BAM drop hammer does not accurately reflect the sensitivity of an energetic material, in particular the sensitivity of primary explosives. Therefore, we present here preliminary results obtained using the novel ball drop tester (BIT‐132), manufactured by OZM research, following MIL‐STD‐1751 A (method 1016). The ball drop impact sensitivity tester is a device in which a free‐falling steel ball is dropped onto an unconfined sample, and is expected to produce more realistic results than the currently commonly used BAM method. The results obtained using the probit analysis were compared to those from the BAM drop hammer and friction tester. The following sensitive explosives were investigated: HMTD, TATP, TAT, Tetrazene, MTX‐1, KDNBF, KDNP, K2DNABT, Lead Styphnate Monohydrate, DBX‐1, Nickel(II) Hydrazine Nitrate, Silver Acetylide, AgN3, Pb(N3)2 RD‐1333, AgCNO, and Hg(CNO)2

Bifurcations in the Space of Exponential Maps

This article investigates the parameter space of the exponential family $z\mapsto \exp(z)+\kappa$. We prove that the boundary (in \C) of every hyperbolic component is a Jordan arc, as conjectured by Eremenko and Lyubich as well as Baker and Rippon. In fact, we prove the stronger statement that the exponential bifurcation locus is connected in \C, which is an analog of Douady and Hubbard's celebrated theorem that the Mandelbrot set is connected. We show furthermore that $\infty$ is not accessible through any nonhyperbolic ("queer") stable component. The main part of the argument consists of demonstrating a general "Squeezing Lemma", which controls the structure of parameter space near infinity. We also prove a second conjecture of Eremenko and Lyubich concerning bifurcation trees of hyperbolic components.Comment: 29 pages, 3 figures. The main change in the new version is the introduction of Theorem 1.1 on the connectivity of the bifurcation locus, which follows from the results of the original version but was not explicitly stated. Also, some small revisions have been made and references update

Higher-dimensional multifractal value sets for conformal infinite graph directed Markov systems

We give a description of the level sets in the higher dimensional multifractal formalism for infinite conformal graph directed Markov systems. If these systems possess a certain degree of regularity this description is complete in the sense that we identify all values with non-empty level sets and determine their Hausdorff dimension. This result is also partially new for the finite alphabet case.Comment: 20 pages, 1 figur

Complex maps without invariant densities

We consider complex polynomials $f(z) = z^\ell+c_1$ for $\ell \in 2\N$ and $c_1 \in \R$, and find some combinatorial types and values of $\ell$ such that there is no invariant probability measure equivalent to conformal measure on the Julia set. This holds for particular Fibonacci-like and Feigenbaum combinatorial types when $\ell$ sufficiently large and also for a class of `long-branched' maps of any critical order.Comment: Typos corrected, minor changes, principally to Section

Schmidt games and Markov partitions

Let T be a C^2-expanding self-map of a compact, connected, smooth, Riemannian manifold M. We correct a minor gap in the proof of a theorem from the literature: the set of points whose forward orbits are nondense has full Hausdorff dimension. Our correction allows us to strengthen the theorem. Combining the correction with Schmidt games, we generalize the theorem in dimension one: given a point x in M, the set of points whose forward orbit closures miss x is a winning set.Comment: 32 page