Chaotic dynamics of electric-field domains in periodically driven superlattices

Self-sustained time-dependent current oscillations under dc voltage bias have been observed in recent experiments on n-doped semiconductor superlattices with sequential resonant tunneling. The current oscillations are caused by the motion and recycling of the domain wall separating low- and high-electric-field regions of the superlattice, as the analysis of a discrete drift model shows and experimental evidence supports. Numerical simulation shows that different nonlinear dynamical regimes of the domain wall appear when an external microwave signal is superimposed on the dc bias and its driving frequency and driving amplitude vary. On the frequency-amplitude parameter plane, there are regions of entrainment and quasiperiodicity forming Arnold tongues. Chaos is demonstrated to appear at the boundaries of the tongues and in the regions where they overlap. Coexistence of up to four electric-field domains randomly nucleated in space is detected under ac+dc driving.

Self-similarities of periodic structures for a discrete model of a two-gene system

We report self-similar properties of periodic structures remarkably organized in the two-parameter space for a two-gene system, described by two-dimensional symmetric map. The map consists of difference equations derived from the chemical reactions for gene expression and regulation. We characterize the system by using Lyapunov exponents and isoperiodic diagrams identifying periodic windows, denominated Arnold tongues and shrimp-shaped structures. Period-adding sequences are observed for both periodic windows. We also identify Fibonacci-type series and Golden ratio for Arnold tongues, and period multiple-of-three windows for shrimps. (C) 2012 Elsevier B.V. All rights reserved.

Jean Baptiste Francois Pompallier, Thomas Arnold and Julian Edmund Tenison Woods and their contribution to the formation and development of Catholic schooling in Australasia

Histories of Catholic education have received little attention by Church historians and are usually written by members of the Catholic clergy, with a strong emphasis placed on the spiritual and building accomplishments of the bishops. This thesis examines the provision of Catholic Education in Australasia, with a focus on the contribution of three men, Jean Baptiste Francois Pompallier, Thomas Arnold and Julian Edmund Tenison Woods. These men received support from the female religious orders in the regions where they worked, frequently with little recognition or praise by Catholic Church authorities. The tenets of their faith gave Pompallier and Woods strength and reinforced their determination to succeed. Arnold, however, possessed a strong desire to change society. All three believed in the desirability of providing Catholic schooling for the poor, with the curriculum facilitating the acquisition of socially desirable values and traits, including obedience, honesty, moral respectability and a strong adherence to Catholic religious values. The beneficiaries included society, future employers, the Church, the children and their parents. With the exception of promoting distinctly Catholic religious values, Roman Catholic schools and National schools in Australasia shared identical objectives. Historians have neglected the contributions of these men.

Portrait of Yael Arnold Portraits Women

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Portrait of Rolf Arnold Portraits Men

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Sculptures by Ellen Bernkopf nee Catzenstein in the home of her daughter Yael Arnold; Waldstetten.

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Sculpture by Ellen Bernkopf nee Catzenstein in the home of her daughter Yael Arnold; Waldstetten Artworks

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Interior of the Konservenfabrik E. Arnold und Co. (Arnold and Co. canned goods factory); Fuerth, Bavaria Business Establishments; Factories

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Photographic reproduction of charcoal portrait of Arnold Gottlieb Portraits Men

Signed by artist bottom right

Portrait of Arnold Schoenberg Portraits Men

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Portrait of Yael Arnold Portraits Women

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Portrait of Rolf Arnold Portraits Men

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Sculptures by Ellen Bernkopf nee Catzenstein in the home of her daughter Yael Arnold; Waldstetten.

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