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Recently fractal theory has been used to model the observed paths of lightning discharges. This paper extends previous work by using a fractal approach to describe the effects of tortuosity and branching of the lightning channel. In particular, we use the model to make predictions of the probability of lightning strikes to practical structures. Some of the specific estimates include the probability of strikes as a function of interception angle, predictions of the strike points on structures, and the probability of ''side strikes'' to tall structures. Significant polarity and geometric effects are shown. The shielding effects of nearby taller structures, shielding failure or '' breakthrough'' probabilities of so-called protected objects, and the effects of ground topography are also examined. The results are discussed in terms of the implications for the protection of structures against lightning.

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Four new titanium catecholate complexes – [Ti2(Cat)2(CatH)2(OCH3)2(CH3OH)2] (1; Cat = C6H4O22–), [Ti2(4tBuCat)4(CH3OH)2]·2CH3OH (2·2CH3OH; 4tBuCat = [4‐t‐C4H9‐C6H3O2]2–), [Ti(Cat)2(dmf)2] (3; dmf = N,N‐dimethylformamide), and [Na(dme)Ti(Cat)3]2[Na(dme)CH3OH]2 (4; dme = 1,2‐dimethoxyethane) – have been obtained by treatment of Ti(OCH3)4 with catechols in methanol and structurally characterized. Complex 3 is the first example of a neutral mononuclear titanium catecholate containing more than one catechol molecule per titanium atom. Complexes 1 and 2 are neutral dimers in the solid state, each with a catechol/Ti ratio equal to 2 and featuring one of the catechol ligands bridging two titanium centres in a singly bridging chelate µ2‐(O,O′,O′) mode. The other catechol molecule is either a terminal bidentate chelating ligand (complex 2) or a Ti monodentate ligand (complex 1). Complex 4 is a heterometallic aryloxide complex with a tetrameric [{Na(dme)Ti(Cat)3)2]2– (Ti2Na2) core as an anionic moiety and Na ions, solvated by methanol and dme ligands – [{Na(dme)(CH3OH)}2]2+ – as a cationic counterpart. Each Ti centre in 4 is octahedrally coordinated by three catechol ligands, demonstrating three distinct types of bridging modality. It was shown that 1–4 effectively catalyze the selective homogeneous hydrogenation of acetylene to ethylene. Various kinetic relationships were determined and analyzed, enabling a reaction pathway for this catalytic reaction to be proposed.