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Fourth Order (fourth + order)
Selected AbstractsA modest proposal: a testable differentiation between third- and fourth-order information complexityINTERNATIONAL JOURNAL OF APPLIED PSYCHOANALYTIC STUDIES, Issue 4 2006Kathryn Cason Abstract In Human Capability, Jaques and Cason (1994) described the importance of the Third and Fourth Orders of Information Complexity used by adults working to create and manage our commercial endeavors, govern our countries, and provide services such as healthcare and education to our populations. Today our knowledge of these two Orders is still in descriptive terms, therefore less subject to testing than meets the necessary scientific rigor. In order to pursue a better understanding of how to more effectively educate and employ this capability in the adult population it is necessary to have clarity about the boundaries of these apparently discontinuous innate human "processes." The authors here set out important aspects of their continued inquiry. Copyright © 2006 John Wiley & Sons, Ltd. [source] Retracted and replaced: A modelling study of hyporheic exchange pattern and the sequence, size, and spacing of stream bedforms in mountain stream networks, Oregon, USAHYDROLOGICAL PROCESSES, Issue 15 2005Michael N. Gooseff Abstract This article has been retracted and replaced. See Retraction and Replacement Notice DOI: 10.1002/hyp.6350 Studies of hyporheic exchange flows have identified physical features of channels that control exchange flow at the channel unit scale, namely slope breaks in the longitudinal profile of streams that generate subsurface head distributions. We recently completed a field study that suggested channel unit spacing in stream longitudinal profiles can be used to predict the spacing between zones of upwelling (flux of hyporheic water into the stream) and downwelling (flux of stream water into the hyporheic zone) in the beds of mountain streams. Here, we use two-dimensional groundwater flow and particle tracking models to simulate vertical and longitudinal hyporheic exchange along the longitudinal axis of stream flow in second-, third-, and fourth-order mountain stream reaches. Modelling allowed us to (1) represent visually the effect that the shape of the longitudinal profile has on the flow net beneath streambeds; (2) isolate channel unit sequence and spacing as individual factors controlling the depth that stream water penetrates the hyporheic zone and the length of upwelling and downwelling zones; (3) evaluate the degree to which the effects of regular patterns in bedform size and sequence are masked by irregularities in real streams. We simulated hyporheic exchange in two sets of idealized stream reaches and one set of observed stream reaches. Idealized profiles were constructed using regression equations relating channel form to basin area. The size and length of channel units (step size, pool length, etc.) increased with increasing stream order. Simulations of hyporheic exchange flows in these reaches suggested that upwelling lengths increased (from 2·7 m to 7·6 m), and downwelling lengths increased (from 2·9 m to 6·0 m) with increase in stream order from second to fourth order. Step spacing in the idealized reaches increased from 5·3 m to 13·7 m as stream size increased from second to fourth order. Simulated upwelling lengths increased from 4·3 m in second-order streams to 9·7 m in fourth-order streams with a POOL,RIFFLE,STEP channel unit sequence, and increased from 2·5 m to 6·1 m from second- to fourth-order streams with a POOL,STEP,RIFFLE channel unit sequence. Downwelling lengths also increased with stream order in these idealized channels. Our results suggest that channel unit spacing, size, and sequence are all important in determining hyporheic exchange patterns of upwelling and downwelling. Though irregularities in the size and spacing of bedforms caused flow nets to be much more complex in surveyed stream reaches than in idealized stream reaches, similar trends emerged relating the average geomorphic wavelength to the average hyporheic wavelength in both surveyed and idealized reaches. Copyright © 2005 John Wiley & Sons, Ltd. [source] Classical and advanced multilayered plate elements based upon PVD and RMVT.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2002Part 2: Numerical implementations Abstract This paper presents numerical evaluations related to the multilayered plate elements which were proposed in the companion paper (Part 1). Two-dimensional modellings with linear and higher-order (up to fourth order) expansion in the z -plate/layer thickness direction have been implemented for both displacements and transverse stresses. Layer-wise as well as equivalent single-layer modellings are considered on both frameworks of the principle of virtual displacements and Reissner mixed variational theorem. Such a variety has led to the implementation of 22 plate theories. As far as finite element approximation is concerned, three quadrilaters have been considered (four-, eight- and nine-noded plate elements). As a result, 22×3 different finite plate elements have been compared in the present analysis. The automatic procedure described in Part 1, which made extensive use of indicial notations, has herein been referred to in the considered computer implementations. An assessment has been made as far as convergence rates, numerical integrations and comparison to correspondent closed-form solutions are concerned. Extensive comparison to early and recently available results has been made for sample problems related to laminated and sandwich structures. Classical formulations, full mixed, hybrid, as well as three-dimensional solutions have been considered in such a comparison. Numerical substantiation of the importance of the fulfilment of zig-zag effects and interlaminar equilibria is given. The superiority of RMVT formulated finite elements over those related to PVD has been concluded. Two test cases are proposed as ,desk-beds' to establish the accuracy of the several theories. Results related to all the developed theories are presented for the first test case. The second test case, which is related to sandwich plates, restricts the comparison to the most significant implemented finite elements. It is proposed to refer to these test cases to establish the accuracy of existing or new higher-order, refined or improved finite elements for multilayered plate analyses. Copyright © 2002 John Wiley & Sons, Ltd. [source] Peculiarities of soliton motion in molecular systems with high dispersionPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 11 2004V. V. Krasilnikov Abstract In this work, features of propagating protons along molecular chain of hydrogen bonds are described from position of soliton dynamics with taking into account interaction of first and second neighbors of a proton sublattice. It is proposed extension of the model that is an endless chain of water molecules in which formation of hydrogen bonds is due to participating one proton of every water molecule, a second proton no participating in hydrogen bond and being confined by covalent bond of an oxygen atom. Nonlinearity is due to peculiar properties of proton sublattice potential. The model used to obtain continual equations which contain the spatial derivatives of the fourth order that is related with dispersion of longwave oscillations. The availability of such a dispersion changes essentially dynamics of the molecular chain, which allows of manifesting new peculiarities of propagating nonlinear excitations. It is shown there are two new sorts of charge density excitations transferred by solitons determined as exact analytic dependences in such a system. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||