Kinetic Equations for Particle Clusters Differing in Shape and the H-theorem

The question of constructing models for the evolution of clusters that differ in shape based on the Boltzmann’s H-theorem is investigated. The first, simplest kinetic equations are proposed and their properties are studied: the conditions for fulfilling the H-theorem (the conditions for detailed and semidetailed balance). These equations are to generalize the classical coagulation–fragmentation type equations for cases when not only mass but also particle shape is taken into account. To construct correct (physically grounded) kinetic models, the fulfillment of the condition of detailed balance is shown to be necessary to monitor, since it is proved that for accepted frequency functions, the condition of detailed balance is fulfilled and the H-theorem is valid. It is shown that for particular and very important cases, the H-theorem holds: the fulfillment of the Arrhenius law and the additivity of the activation energy for interacting particles are found to be essential. In addition, based on the connection of the principle of detailed balance with the Boltzmann equation for the probability of state, the expressions for the reaction rate coefficients are obtained.

Asteroid cratering families: recognition and collisional interpretation

Aims. We continue our investigation of the bulk properties of asteroid dynamical families identified using only asteroid proper elements to provide plausible collisional interpretations. We focus on cratering families consisting of a substantial parent body and many small fragments. Methods. We propose a quantitative definition of cratering families based on the fraction in volume of the fragments with respect to the parent body; fragmentation families are above this empirical boundary. We assess the compositional homogeneity of the families and their shape in proper element space by computing the differences of the proper elements of the fragments with respect to the ones of the major body, looking for anomalous asymmetries produced either by post-formation dynamical evolution, or by multiple collisional/cratering events, or by a failure of the hierarchical clustering method (HCM) for family identification. Results. We identified a total of 25 dynamical families with more than 100 members ranging from moderate to heavy cratering. For three families (4, 15 and 283) we confirm the occurrence of two separate cratering events, while family (569) Misa is a mixed case, with one cratering event and one fragmentation event. The case of family 3 remains dubious, in that there could be either one or two collisions. For family 20, we propose a double collision origin, not previously identified. In four cases (31, 480, 163 and 179) we performed a dedicated search for dynamical resonant transport mechanisms that could have substantially changed the shape of the family. By using a new synthetic method for computation of secular frequencies, we found possible solutions for families 31, 480, and 163, but not for family 179, for which we propose a new interpretation, based on a secular resonance contaminating this family: the family of 179 should be split into two separate clusters, one containing (179) itself and the other, family (9506) Telramund, of fragmentation type, for which we have computed an age.

Anodic oxidation of bisamides from diaminoalkanes by constant current electrolysis

In general, bisamides derived from diamines and involving 3 and 4 methylene groups as spacers between the two amide functionalities behave similar to monoamides upon anodic oxidation in methanol/LiClO4 because both types undergo majorly mono- and dimethoxylations at the α-position to the N atom. However, in cases where the spacer contains two methylene groups only the anodic process leads mostly to CH2–CH2 bond cleavage to afford products of type RCONHCH2OCH3. Moreover, upon replacing LiClO4 with Et4NBF4 an additional fragmentation type of product was generated from the latter amides, namely RCONHCHO. Also, the anodic process was found to be more efficient with C felt as the anode, and in a mixture of 1:1 methanol/acetonitrile co-solvents.