Hierarchical Cont-Bouchaud model

We extend the well-known Cont-Bouchaud model to include a hierarchical topology of agent's interactions. The influence of hierarchy on system dynamics is investigated by two models. The first one is based on a multi-level, nested Erdos-Renyi random graph and individual decisions by agents according to Potts dynamics. This approach does not lead to a broad return distribution outside a parameter regime close to the original Cont-Bouchaud model. In the second model we introduce a limited hierarchical Erdos-Renyi graph, where merging of clusters at a level h+1 involves only clusters that have merged at the previous level h and we use the original Cont-Bouchaud agent dynamics on resulting clusters. The second model leads to a heavy-tail distribution of cluster sizes and relative price changes in a wide range of connection densities, not only close to the percolation threshold.Comment: 10 pages, 6 figure

Activation volume of selected liquid crystals in the density scaling regime

In this paper, we demonstrate and thoroughly analyze the activation volumetric properties of selected liquid crystals in the nematic and crystalline E phases in comparison with those reported for glass-forming liquids. In the analysis, we have employed and evaluated two entropic models (based on either total or configurational entropies) to describe the longitudinal relaxation times of the liquid crystals in the density scaling regime. In this study, we have also exploited two equations of state: volumetric and activation volumetric ones. As a result, we have established that the activation volumetric properties of the selected liquid crystals are quite opposite to such typical properties of glass-forming materials, i.e., the activation volume decreases and the isothermal bulk modulus increases when a liquid crystal is isothermally compressed. Using the model based on the configurational entropy, we suggest that the increasing pressure dependences of the activation volume in isothermal conditions and the negative curvature of the pressure dependences of isothermal longitudinal relaxation times can be related to the formation of antiparallel doublets in the examined liquid crystals. A similar pressure effect on relaxation dynamics may be also observed for other material groups in case of systems, the molecules of which form some supramolecular structures

The Enoch-Metatron tradition in the kabbalah of Nathan Neta Shapira of Krakow (1585-1633)

Nathan Neta ben Shlomo Shapira (1585-1633) is the most famous kabbalist stemming from the Jewish intellectual environment of Poland. His major treatise, Megaleh Amuqot, is among the most complex kabbalistic texts ever written. It combines variegated strata of older mystical traditions, to which the author applies diverse, often obscure modes of interpretation. For this reason, Nathan Shapira has remained one of the least studied figures in modern scholarship, despite the fact that he is generally acknowledged as the most important early-modern Ashkenazi kabbalist, whose influence on later Eastern-European mystical circles is well attested. Although there are some general accounts of Shapira’s religious activity in Kraków, and references have been made to his startling mathematical mind-set, scholarship still lacks a thorough examination of his literary legacy, and a detailed evaluation of his contribution to the development of Jewish mystical thought. My dissertation aims to integrate Nathan Shapira’s kabbalah within a broad panorama of Jewish mystical traditions of the early modern period. It challenges the notion of the dominance of Lurianic ideas in Shapira’s thought, arguing for a more pluralistic perspective of the historical development of the kabbalistic tradition. Recently, Yehuda Liebes and Moshe Idel have raised the possibility that Nathan Shapira’s kabbalah may have belonged to a tradition that sprang from a multifaceted cultural milieu of Ashkenazi mysticism, consisting of at least two distinct major strands. Following this notion, I propose to challenge the common view that the Ashkenazi mysticism was a homogenous entity, whose influences effectively ceased after 13th century. On the contrary, I claim that the medieval mystical Ashkenazi ideas underlie much of Nathan Shapira’s kabbalah. In considering medieval Ashkenazi mysticism as Shapira’s formative background, I focus on the ‘Enoch-Metatron’ cluster of traditions, which I claim was as central to Shapira’s thought as it was to his Ashkenazi predecessors