Effects of introduction of new resources and fragmentation of existing resources on limiting wealth distribution in asset exchange models

Pareto law, which states that wealth distribution in societies has a power-law tail, has been the subject of intensive investigations in the statistical physics community. Several models have been employed to explain this behavior. However, most of the agent based models assume the conservation of number of agents and wealth. Both these assumptions are unrealistic. In this paper, we study the limiting wealth distribution when one or both of these assumptions are not valid. Given the universality of the law, we have tried to study the wealth distribution from the asset exchange models point of view. We consider models in which (a) new agents enter the market at a constant rate (b) richer agents fragment with higher probability introducing newer agents in the system (c) both fragmentation and entry of new agents is taking place. While models (a) and (c) do not conserve total wealth or number of agents, model (b) conserves total wealth. All these models lead to a power-law tail in the wealth distribution pointing to the possibility that more generalized asset exchange models could help us to explain the emergence of a power-law tail in wealth distribution.     

Fragmentation associated with Lévy processes using snake

We consider the height process of a Lévy process with no negative jumps, and its associated continuous tree representation. Using Lévy snake tools developed by Le Gall-Le Jan and Duquesne-Le Gall, with an underlying Poisson process, we construct a fragmentation process, which in the stable case corresponds to the self-similar fragmentation described by Miermont. For the general fragmentation process we compute a family of dislocation measures as well as the law of the size of a tagged fragment. We also give a special Markov property for the snake which is of its own interest.      

Unprecedented dual reactivity of anhydrous potassium hydroxide in cascade cyclopropannelation/Haller-Bauer-scission/Grob-fragmentation reactions

We report an unprecedented type of reactivity of ‘anhydrous potassium hydroxide’ (‘APH’) in which it plays, over a large variety of related educts, sequentially the role of base and nucleophile. Some insight into the structure of reactive species as well as comparative reactivity of related reagents prepared by fusion of commercially available potassium hydroxide or by adding stoichiometric amount of water to potassium hydride is provided.     

Asymmetric synthesis of 2-alkyl-4-hydroxycyclohex-2-en-1-ones by scandium(III) triflate-catalyzed fragmentation of 2-alkyl-3-iodo-1-oxocyclohexan-2,4-carbolactones

Fragmentation of (2S,3S,4S)-2-allyl-3-iodo-1-oxocyclohexan-2,4-carbolactone to (4S)-2-allyl-4-hydroxycyclohex-2-en-1-one, a chiral building block of (−)-platensimycin, proceeded efficiently by using scandium(III) triflate in DMF-H₂O (1:3) at 100 °C.     

Kinetics of node splitting in evolving complex networks

We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of “splitting” nodes of degree k$k$ into k$k$ nodes of degree 1$1$. Four networks are considered, each evolves at each time step by either preferential attachment, with probability p$p$, or splitting with probability 1−p$1-p$. Two methods of attachment are considered; first, attachment of an edge between a newly created node and an existing node in the network, and secondly by attachment of an edge between two existing nodes. Splitting is also considered in two separate ways; first by selecting each node with equal probability and secondly, selecting the node with probability proportional to its degree. Exact solutions for the degree distributions are found and scale-free structure is exhibited in those networks where the candidates for splitting are chosen with uniform probability, those that are chosen preferentially are distributed with a power law with exponential cut-off.     

Momentum sum rules for fragmentation functions

Momentum sum rules for fragmentation functions are considered. In particular, we give a general proof of the Schäfer–Teryaev sum rule for the transverse momentum dependent Collins function. We also argue that corresponding sum rules for related fragmentation functions do not exist. Our model-independent analysis is supplemented by calculations in a simple field-theoretical model.     

Proof of factorization of fragmentation function in non-equilibrium QCD

In this paper, we prove factorization of fragmentation function in non-equilibrium QCD by using Schwinger-Keldysh closed-time path integral formalism. We use the background field method of QCD in a pure gauge in path integral approach to prove factorization of fragmentation function in non-equilibrium QCD. Our proof is valid in any arbitrary gauge fixing parameter α. This may be relevant to study hadron production from quark-gluon plasma at high energy heavy-ion colliders at RHIC and LHC.     

An open-and-shut strategy: preparation of benzo-fused indanes by ring-opening of a vinylogous acyl triflate and metal-catalyzed Asao-Yamamoto benzannulation

A two-step strategy for the synthesis of benzo-fused indanes is outlined herein. The strategy draws on two independent methodologies: the tandem addition/fragmentation of vinylogous acyl triflates (VATs) and the intramolecular benzannulation of o-alkynylphenyl ketones. Reduction of this strategy to practice involves the use of aryltriazenes as masked aryl iodides; a synthetic equivalent of 2-iodophenyllithium is featured. Benzo-fused indanes are prepared efficiently and in high yield.     

Fragmentation Processes with an Initial Mass Converging to Infinity

We consider a family of fragmentation processes where the rate at which a particle splits is proportional to a function of its mass. Let F ₁^(m)(t),F ₂^(m)(t),… denote the decreasing rearrangement of the masses present at time t in a such process, starting from an initial mass m. Let then m→∞. Under an assumption of regular variation type on the dynamics of the fragmentation, we prove that the sequence (F ₂^(m),F ₃^(m),…) converges in distribution, with respect to the Skorohod topology, to a fragmentation with immigration process. This holds jointly with the convergence of m−F ₁^(m) to a stable subordinator. A continuum random tree counterpart of this result is also given: the continuum random tree describing the genealogy of a self-similar fragmentation satisfying the required assumption and starting from a mass converging to ∞ will converge to a tree with a spine coding a fragmentation with immigration. Research supported in part by EPSRC GR/T26368.     

Synthesis of alkaloids from aminol derivatives by β-fragmentation of primary alkoxyl radicals

The fragmentation of primary alkoxyl radicals, often described as low yielding and plagued by side reactions, proceeded in good to excellent yields when aminol derivatives were used as substrates. Remarkably, no side reactions such as hydrogen abstraction or oxidation were observed. The fragmentation can be coupled with an alkylation reaction to give 2-substituted pyrrolidine and piperidine rings such as alkaloid analogues and functionalized, chiral nitrogen heterocycles.