Abstract:
Fission of metastable charged univalent metal clusters has been studied on example of Na_{10}^{2+} and Na_{18}^{2+} clusters by means of density functional theory methods. Energetics of the process, i.e. dissociation energies and fission barriers, as well as its dynamics, i.e. fission pathways, have been analyzed. The dissociation energies and fission barriers have been calculated for the full range of fission channels for the Na_{10}^{2+} cluster. The impact of cluster structure on the fission process has been elucidated. The calculations show that the geometry of the smaller fragment and geometry of its immediate neighborhood in the larger fragment play a leading role in defining the fission barrier height. The present study demonstrates importance of rearrangement of the cluster structure during fission. It may include forming a neck between the two fragments or fissioning via another isomer state of the parent cluster; examples of such processes are given. For several low-lying isomers of Na_{10}^{2+} cluster the potential barriers for transitions between these isomer states are calculated and compared with the corresponding fission barriers. These data suggest that there is a competition between "direct" fission and fission going via intermediate isomer states of the parent cluster. An impact of the cluster geometry on the change of the system's entropy due to fission is also discussed.

Abstract:
Fission of doubly charged metal clusters is studied using the open-shell two-center deformed jellium Hartree-Fock model and Local Density Approximation. Results of calculations of the electronic structure and fission barriers for the symmetric and asymmetric channels associated with the following processes Na_{10}^{2+} --> Na_{7}^{+} + Na_{3}^{+}, Na_{18}^{2+} --> Na_{15}^{+} + Na_{3}^{+} and Na_{18}^{2+} --> 2 Na_{9}^{+} are presented. The role of the exact exchange and many-body correlation effects in metal clusters fission is analysed. It is demonstrated that the influence of many-electron correlation effects on the height of the fission barrier is more profound if the barrier arises nearby or beyond the scission point. The importance of cluster deformation effects in the fission process is elucidated with the use of the overlapping-spheroids shape parametrization allowing one an independent variation of deformations in the parent and daughter clusters.

Abstract:
The rearrangement time \Deltat of the fission reaction can be extracted from the full-width at half maximum (f.w.h.m.) of the isotopic distributions of fission fragments if this width is attributed to an uncertainty \DeltaN in the neutron-number N of the fragment; then the energy-time uncertainty relation leads to \Deltat = 0.17 yoctosecond.

Abstract:
In this work we have performed for the first time a systematic analysis of the dissociation and fission pathways of neutral, singly and doubly charged alanine dipeptide ions with the aim to identify the fission mechanism and the most probable fragmentation channels of these type of molecules. We demonstrate the importance of rearrangement of the molecule structure during the fission process. This rearrangement may include transition to another isomer or a quasi-molecular state before actual separation of the daughter fragments begins.

Abstract:
Numerical simulations of Diffusion-Limited and Reaction-Limited Cluster-Cluster Aggregation processes of identical particles are performed in a two-dimensional box. It is shown that, for concentrations larger than a characteristic gel concentration, the morphology of the resulting spanning cluster at the gel time $t_g$ exhibits a crossover length $L_c$ between percolation ($l>L_c$) and aggregation ($lc_p$ the long-range correlations are similar to that of percolation, the vanishing links in the structure suggest that an homogeneous regime appears at small scales.

Abstract:
We investigate the steady states and dynamical instabilities resulting from ``particles'' depositing on (fusion) and pinching off (fission) a fluid membrane. These particles could be either small lipid vesicles or isolated proteins. In the stable case, such fusion/fission events suppress long wavelength fluctuations of the membrane. In the unstable case, the membrane shoots out long tubular structures reminiscent of endosomal compartments or folded structures as in internal membranes like the endoplasmic reticulum or Golgi. We argue that these fusion/fission events should be strongly affected by tension.

Abstract:
Jellium correction on the fissionability parameter is estimated within a Liquid Drop Model of the charged metallic cluster. This correction modifies the critical condition of fission and, it becomes relevant for small multicharged clusters.

Abstract:
The mechanism leading to the formation of the observed products of the collinear cluster tripartition is carried out within the framework of the model based on the dinuclear system concept. The yield of fission products is calculated using the statistical model based on the driving potentials for the fissionable system. The minima of potential energy of the decaying system correspond to the charge numbers of the products which are produced with large probabilities in the sequential fission (partial case of the collinear cluster tripartition) of the compound nucleus. The realization of this mechanism supposes the asymmetric fission channel as the first stage of sequential mechanism. It is shown that only the use of the driving potential calculated by the binding energies with the shell correction allows us to explain the yield of the true ternary fission products. The theoretical model is applied to research collinear cluster tripartition in the reaction $^{235}$U(n$_{\rm th}$,f). Calculations showed that in the first stage of this fission reaction, the isotopes $^{82}$Ge and $^{154}$Nd are formed with relatively large probabilities and in the second stage of sequential fission of the isotope Nd mainly Ni and Ge are formed. This is in agreement with the yield of the isotope $^{68}$Ni which is observed as the product of the collinear cluster tripartition in the experiment.

Abstract:
In this paper we prove scalar and sample path large deviation principles for a large class of Poisson cluster processes. As a consequence, we provide a large deviation principle for ergodic Hawkes point processes.

Abstract:
Calculations for fission and cluster decay of $^{76}Sr$ are presented for this nucleus to be in its ground-state or formed as an excited compound system in heavy-ion reactions. The predicted mass distribution, for the dynamical collective mass transfer process assumed for fission of $^{76}Sr$, is clearly asymmetric, favouring $\alpha $-nuclei. Cluster decay is studied within a preformed cluster model, both for ground-state to ground-state decays and from excited compound system to the ground-state(s) or excited states(s) of the fragments.