Relevant bibliographies by topics / Second order difference array

Academic literature on the topic 'Second order difference array'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Second order difference array"

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Raza, Ahsan, Wei Liu, and Qing Shen. "Thinned Coprime Array for Second-Order Difference Co-Array Generation With Reduced Mutual Coupling." IEEE Transactions on Signal Processing 67, no. 8 (April 15, 2019): 2052–65. http://dx.doi.org/10.1109/tsp.2019.2901380.

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Zhang, Lei, Shiwei Ren, Xiangnan Li, Guishan Ren, and Xiaohua Wang. "Generalized L-Shaped Nested Array Concept Based on the Fourth-Order Difference Co-Array." Sensors 18, no. 8 (August 1, 2018): 2482. http://dx.doi.org/10.3390/s18082482.

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In this paper, a generalized L-shaped nested array based on the fourth-order difference co-array is proposed for two-dimensional (2D) directions’ estimation. The new structure framework makes full use of the physical sensor locations to form a virtual uniform rectangular array (URA) as large as possible. As it utilizes the fourth-order difference instead of the traditional second-order difference result, this structure framework can acquire a much higher degree-of-freedom (DOF) than the existing 2D sparse arrays. The proposed structures have two advantages. One is that the subarrays can be chosen as any nested-class arrays, which makes the sparse array design more flexible. We can choose arbitrary subarray structures for DOF enhancement purposes. Another advantage is that the relative position of two subarrays can be set as any integral multiple of half wavelength. This means that two subarrays can be located as far as possible so that the relative influence between two physical subarrays can be ignored. The DOFs of several typical generalized L-shaped nested arrays (GLNAs) are compared in this paper. By setting the subarrays as different types and the relative position as a special value, a special GLNA is presented. Simulations show that GLNAs have obvious superiority in 2D direction-of-arrival estimation.
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Halim, Yacine, and Julius Fergy T. Rabago. "On the solutions of a second-order difference equation in terms of generalized Padovan sequences." Mathematica Slovaca 68, no. 3 (June 26, 2018): 625–38. http://dx.doi.org/10.1515/ms-2017-0130.

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AbstractThis paper deals with the solution, stability character and asymptotic behavior of the rational difference equation$$\begin{array}{} \displaystyle x_{n+1}=\frac{\alpha x_{n-1}+\beta}{ \gamma x_{n}x_{n-1}},\qquad n \in \mathbb{N}_{0}, \end{array}$$where ℕ0= ℕ ∪ {0},α,β,γ∈ ℝ+, and the initial conditionsx–1andx0are non zero real numbers such that their solutions are associated to generalized Padovan numbers. Also, we investigate the two-dimensional case of the this equation given by$$\begin{array}{} \displaystyle x_{n+1} = \frac{\alpha x_{n-1} + \beta}{\gamma y_n x_{n-1}}, \qquad y_{n+1} = \frac{\alpha y_{n-1} +\beta}{\gamma x_n y_{n-1}} ,\qquad n\in \mathbb{N}_0. \end{array}$$
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Vazquez, J. H., and A. N. Williams. "Second-Order Diffraction Forces on an Array of Vertical Cylinders in Bichromatic Bidirectional Waves." Journal of Offshore Mechanics and Arctic Engineering 117, no. 1 (February 1, 1995): 12–18. http://dx.doi.org/10.1115/1.2826984.

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A complete second-order solution is presented for the hydrodynamic forces due to the action of bichromatic, bidirectional waves on an array of bottom-mounted, surface-piercing cylinders of arbitrary cross section in water of uniform finite depth. Based on the constant structural cross section, the first-order problem is solved utilizing a two-dimensional Green function approach, while an assisting radiation potential approach is used to obtain the hydrodynamic loads due to the second-order potential. Results are presented which illustrate the influence of wave directionality on the second-order sum and difference frequency hydrodynamic forces on a two-cylinder array. It is found that wave directionality may have a significant influence on the second-order hydrodynamic forces on these arrays and that the assumption of unidirectional waves does not always lead to conservative estimates of the second-order loading.
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Ashyralyev, Allaberen, and Betul Hicdurmaz. "Bounded solutions of second order of accuracy difference schemes for semilinear fractional schrödinger equations." Fractional Calculus and Applied Analysis 23, no. 6 (December 16, 2020): 1723–61. http://dx.doi.org/10.1515/fca-2020-0086.

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AbstractThe present paper deals with initial value problem (IVP) for semilinear fractional Schrödinger integro-differential equation$$\begin{array}{} \displaystyle i\!\frac{du}{dt}+Au = \int\limits_{0}^{t}f\left( s,D_{s}^{\alpha }u(s)\right) ds,\, \, \, 0 \lt t \lt T,\, u\left( 0\right) = 0 \end{array} $$in a Hilbert space H with a self-adjoint positive definite (SAPD) operator A. Stable difference schemes (DSs) have significant interest in investigations of fractional partial differential equations. The main theorem concerns the existence and uniqueness of the uniformly bounded solutions (UBSs) with respect to step time of second order of accuracy DSs for this semilinear fractional Schrödinger differential problem. In practice, existence and uniqueness theorems for a UBS of the one-dimensional initial boundary value problem (BVP) with nonlocal condition and multi-dimensional problem with local condition on the boundary are proved. Numerical results and explanatory illustrations are presented to show the validation of the theoretical results.
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Thomson, Antonio, Atef Elsherbeni, and Mohammed Hadi. "A Practical Fourth Order Finite-Difference Time-Domain Algorithm for the Solution of Maxwell’s Equations." Applied Computational Electromagnetics Society 35, no. 11 (February 5, 2021): 1422–23. http://dx.doi.org/10.47037/2020.aces.j.351180.

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Implementing a practical fourth order accurate in time and second order accurate in space finite difference time domain simulation using MATLAB is the goal of this paper. The formulation presented for the fourth order approximation is simple to integrate into an existing second order accurate in time and second order accurate in space formulation and well-established code. The fourth order formulation has been verified and simulation accuracy is confirmed through the application of radiation from a single and an array of dipole antennas.
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Liu, Mingxin, Lin Zou, Haohao Ren, Xuelian Yu, Yun Zhou, and Xuegang Wang. "A Novel MIMO Array with Reduced Mutual Coupling and Increased Degrees of Freedom." Mathematical Problems in Engineering 2021 (February 15, 2021): 1–6. http://dx.doi.org/10.1155/2021/3703657.

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In this paper, we consider the problem of array design for Multiple-Input Multiple-Output (MIMO) array under the condition of fixed number of physical sensors and mutual coupling. A novel MIMO array based on the second-order super nested transmit and receive arrays is proposed by using the difference coarray. It can obtain the closed form expressions for the physical sensor locations and the degrees of freedom (DOF) from any given number physical sensors. The proposed array structure can significantly enhance DOF and effectively decrease unknown mutual coupling effect. The effectiveness and superiority of the proposed MIMO array structure are verified from the number of DOF and MUSIC spectra by numerical simulations.
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Ye, Changbo, Luo Chen, and Beizuo Zhu. "Sparse Array Design for DOA Estimation of Non-Gaussian Signals: From Global Postage-Stamp Problem Perspective." Wireless Communications and Mobile Computing 2021 (February 23, 2021): 1–11. http://dx.doi.org/10.1155/2021/6616112.

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In this paper, a sparse array design problem for non-Gaussian signal direction of arrival (DOA) estimation is investigated. Compared with conventional second-order cumulant- (SOC-) based methods, fourth-order cumulant- (FOC-) based methods achieve improved DOA estimation performance by utilizing all information from received non-Gaussian sources. Considering the virtual sensor location of vectorized FOC-based methods can be calculated from the second order difference coarray of sum coarray (2-DCSC) of physical sensors, it is important to devise a sparse array design principle to obtain extended degree of freedom (DOF). Based on the properties of unfolded coprime linear array (UCLA), we formulate the sparse array design problem as a global postage-stamp problem (GPSP) and then present an array design method from GPSP perspective. Specifically, for vectorized FOC-based methods, we divide the process of obtaining physical sensor location into two steps; the first step is to obtain the two consecutive second order sum coarrays (2-SC), which can be modeled as GPSP, and the solutions to GPSP can also be utilized to determine the physical sensor location sets without interelement spacing coefficients. The second step is to adjust the physical sensor sets by multiplying the appropriate coprime coefficients, which is determined by the structure of UCLA. In addition, the 2-DCSC can be calculated from physical sensors directly, and the properties of UCLA are given to confirm the degree of freedom (DOF) of the proposed geometry. Simulation results validate the effectiveness and superiority of the proposed array geometry.
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Rosas Almeida, David I., and Laura O. Orea Leon. "Robust-Output-Controlled Synchronization Strategy for Arrays of Pancreatic β-Cells." Complexity 2018 (November 5, 2018): 1–10. http://dx.doi.org/10.1155/2018/5174981.

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This paper presents a synchronization strategy based on second-order sliding mode control, to obtain robust controlled synchronization in an array of uncertain pancreatic β-cells. This strategy considers a synchronization scheme with a reference cell, which incorporates the desired dynamics, and an array of cells, which does not demonstrate adequate synchronization. The array may be formed by active and inactive cells having different strengths in gap junctions. For an array with three cells, we design the coupling signal considering that only the output of an active cell of the array is available. The coupling signal is the signum of the difference between the output of the reference cell and the output of an active cell in the array; this ensures exact synchronization in finite time between both cells. Then, this coupling signal is applied to the other cells in the array, and we establish the conditions required to be satisfied to obtain approximate synchronization between the reference cell and all other cells in the array. The performance of this technique is demonstrated by the results of numerical simulations performed for several cases of connections for an array with three cells and the reference cell. Finally, we show through a numerical simulation that this technique can be applied to arrays with many β-cells.
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Zhao, Meiling, Jiahui He, and Na Zhu. "Fast High-Order Algorithms for Electromagnetic Scattering Problem from Finite Array of Cavities in TE Case with High Wave Numbers." Mathematics 10, no. 16 (August 15, 2022): 2937. http://dx.doi.org/10.3390/math10162937.

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In this paper, fast high-order finite difference algorithms for solving the electromagnetic scattering from the finite array of two-dimensional rectangular cavities are proposed in TE polarization. The scattering problem from the cavity array is described as coupled Helmholtz equations with transparent boundary conditions on open apertures. Second-order and fourth-order schemes for solving the coupled systems are developed in TE polarization respectively. A special technique is applied to construct a fourth-order scheme for transparent boundary conditions. Further, we propose fast algorithms which can simplify the larger global system to a small linear interface system on the apertures of cavities. Numerical experiments show the validity and efficiency of the proposed fast algorithms for solving the scattering problem with high wave numbers.
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Dissertations / Theses on the topic "Second order difference array"

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Cotterell, Philip S. "On the theory of second-order soundfield microphone." Thesis, University of Reading, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.250639.

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Pellegrini, Joseph Charles. "Neural network emulation of temporal second order linear difference equations." Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/42505.

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Basu, Sukanya. "Global behavior of solutions to a class of second-order rational difference equations /." View online ; access limited to URI, 2009. http://0-digitalcommons.uri.edu.helin.uri.edu/dissertations/AAI3367987.

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Pefferly, Robert J. "Finite difference approximations of second order quasi-linear elliptic and hyperbolic stochastic partial differential equations." Thesis, University of Edinburgh, 2001. http://hdl.handle.net/1842/11244.

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This thesis covers topics such as finite difference schemes, mean-square convergence, modelling, and numerical approximations of second order quasi-linear stochastic partial differential equations (SPDE) driven by white noise in less than three space dimensions. The motivation for discussing and expanding these topics lies in their implications in such physical phenomena as signal and information flow, gravitational and electromagnetic fields, large scale weather systems, and macro-computer networks. Chapter 2 delves into the hyperbolic SPDE in one space and one time dimension. This is an important equation to such fields as signal processing, communications, and information theory where singularities propagate throughout space as a function of time. Chapter 3 discusses some concepts and implications of elliptic SPDE's driven by additive noise. These systems are key for understanding steady state phenomena. Chapter 4 presents some numerical work regarding elliptic SPDE's driven by multiplicative and general noise. These SPDE's are open topics in the theoretical literature, hence numerical work provides significant insight into the nature of the process. Chapter 5 presents some numerical work regarding quasi-geostrophic geophysical fluid dynamics involving stochastic noise and demonstrates how these systems can be represented as a combination of elliptic and hyperbolic components.
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Top, Can Baris. "Design Of A Slotted Waveguide Array Antenna And Its Feed System." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/3/12607642/index.pdf.

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Slotted waveguide array (SWGA) antennas find application in systems which require planarity, low profile, high power handling capabilities such as radars. In this thesis, a planar, low sidelobe, phased array antenna, capable of electronically beam scanning in E-plane is designed, manufactured and measured. In the design, slot characterization is done with HFSS and by measurements, and mutual coupling between slots are calculated analytically. A MATLAB code is developed for the synthesis of the SWGA antenna. Grating lobe problem in the scanning array, which is caused by the slot positions, is solved using baffles on the array. A high power feeding section for the planar array, having an amplitude tapering to get low sidelobes is also designed using a corrugated E-plane sectoral horn. The power divider is designed analytically, and simulated and optimized with HFSS.
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Bellew, Sarah Louise. "Investigation of the response of groups of wave energy devices." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/investigation-of-the-response-of-groups-of-wave-energy-devices(3db5db0d-a6af-4715-9f0b-19d53cf6dcf4).html.

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Placing wave energy devices within close proximity to each other can be beneficial as the costs of deployment, maintenance and infrastructure are reduced significantly compared to if the devices are deployed in isolation. A mathematical model is presented in this thesis which combines linear wave theory with a series of linear driven harmonic oscillators to model an array (group) of floating wave energy devices which move predominantly in heave (vertically) in a train of incident regular waves. Whilst similar mathematical models have been used previously to investigate interactions between fluids and groups of structures, much of the published work does not address array configurations or device constraints that are relevant to designers of structure-supported array devices. The suitability of linear theory for application to closely spaced arrays is assessed in this thesis through comparison to small-scale experimental data and by evaluation of the magnitude of second-order hydrodynamic forces. Values of mechanical damping and mass are determined for each element of an array in order to achieve the maximum power from an array of floats without requiring the knowledge of the motion of every float within the array in order to apply the forces to any one float. Further to this, the analysis of floats of varying geometry is performed in order to assess the possibility of array optimisation through the variation of float geometries within a closely spaced array.It is shown in this thesis that linear theory provides a reasonable prediction of the response of floats that are sufficiently close together to interact for most wave frequencies to which the arrays are likely to be subjected. Under the assumption of easily implementable mechanical damping, it is determined that the power output from an array of floats of equal geometry can be increased by specifying different magnitudes of mechanical damping on each float independently of the radiation damping. Variations in submerged float geometries for the purpose of manipulating array characteristics according to the incident wave frequency are best applied through the variation in draft of a single geometry. Variations in submerged float geometry which occur close to the free surface are found to be of the greatest significance. Where the float is uniform in cross-section, the most appropriate method to select float drafts within an array is found to be based on the evaluation of the total damping on each float.
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Revoredo, Igor Feliciano Simplicio. "Solução Numérica de escoamentos viscoelásticos tridimensionais com superfícies livres: fluidos de segunda ordem." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-18052010-161846/.

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Este trabalho apresenta uma técnica de diferenças finitas para resolver a equação constitutiva Fluido de Segunda Ordem para escoamentos tridimensionais com superfície livre. As equações governantes são resolvidas pelo método de diferenças finitas em uma malha deslocada 3D. A superfície livre é modelada por células marcadoras (Marker-and-Cell) e as condições de contorno a superfície livre são empregadas. O método numérico apresentado neste trabalho foi validado pela comparação entre as soluções numéricas obtidas para o escoamento em um tubo com a solução analítica correspondente para Fluidos de Segunda Ordem. Ao fazer refinamento de malha, a convergência do método numérico foi verificada. Resultados numéricos da simulação do problema do inchamento do extrudado para números de Deborah De \'< OU =\' 0:3 são apresentados
This work presents a finite difference method to simulate three-dimensional viscoelastic flow with free surfaces governed by the constitutive equation Second Order Fluid. The governing equations are solved by the finite difference method in a three-dimensional shifted mesh. The free surface of fluid is modeled by the Marker-and-Cell method which allows for the visualization and the location of the free surface of fluid. The full free surface stress conditions are employed. The numerical method developed in this work is validated by comparing the numerical and analytic solutions for the steady state flow of a Second Order Fluid in a pipe. By using mesh refinement convergence results are given. Numerical results of the simulation of the transient extrudate swell of a Second Order Fluid of the Deborah number De \'< OR =\' 0:3 are presented
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Souza, Grazione de. "Modelagem computacional de escoamentos com duas e três fases em reservatórios petrolíferos heterogêneos." Universidade do Estado do Rio de Janeiro, 2008. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=711.

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Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro
Considera-se neste trabalho um modelo matemático para escoamentos com duas e três fases em reservatórios petrolíferos e a modelagem computacional do sistema de equações governantes para a sua solução numérica. Os fluidos são imiscíveis e incompressíveis e as heterogeneidades da rocha reservatório são modeladas estocasticamente. Além disso, é modelado o fenômeno de histerese para a fase óleo via funções de permeabilidades relativas. No caso de escoamentos trifásicos água-óleo-gás a escolha de expressões gerais para as funções de permeabilidades relativas pode levar à perda de hiperbolicidade estrita e, desta maneira, à existência de uma região elíptica ou de pontos umbílicos para o sistema não linear de leis de conservação hiperbólicas que descreve o transporte convectivo das fases fluidas. Como conseqüência, a perda de hiperbolicidade estrita pode levar à existência de choques não clássicos (também chamados de choques transicionais ou choques subcompressivos) nas soluções de escoamentos trifásicos, de difícil simulação numérica. Indica-se um método numérico com passo de tempo fracionário, baseado em uma técnica de decomposição de operadores, para a solução numérica do sistema governante de equações diferenciais parciais que modela o escoamento bifásico água-óleo imiscível em reservatórios de petróleo heterogêneos. Um simulador numérico bifásico água-óleo eficiente desenvolvido pelo grupo de pesquisa no qual o autor está inserido foi modificado com sucesso para incorporar a histerese sob as hipóteses consideradas. Os resultados numéricos obtidos para este caso indicam fortes evidências que o método proposto pode ser estendido para o caso trifásico água-óleo-gás. A técnica de decomposição de operadores em dois níveis permite o uso de passos de tempo distintos para os quatro problemas definidos pelo procedimento de decomposição: convecção, difusão, pressão-velocidade e relaxação para histerese. O problema de transporte convectivo (hiperbólico) das fases fluidas é aproximado por um esquema central de diferenças finitas explícito, conservativo, não oscilatório e de segunda ordem. Este esquema é combinado com elementos finitos mistos, localmente conservativos, para a aproximação dos problemas de transporte difusivo (parabólico) e de pressão-velocidade (elíptico). O operador temporal associado ao problema parabólico de difusão é resolvido fazendo-se uso de uma estratégia implícita de solução (Backward Euler). Uma equação diferencial ordinária é resolvida (analiticamente) para a relaxação relacionada à histerese. Resultados numéricos para o problema bifásico água-óleo em uma dimensão espacial em concordância com resultados semi-analíticos disponíveis na literatura foram reproduzidos e novos resultados em meios heterogêneos, em duas dimensões espaciais, são apresentados e a extensão desta técnica para o caso de problemas trifásicos água-óleo-gás é proposta.
We consider in this work a mathematical model for two- and three-phase flow problems in petroleum reservoirs and the computational modeling of the governing equations for its numerical solution. We consider two- (water-oil) and three-phase (water-gas-oil) incompressible, immiscible flow problems and the reservoir rock is considered to be heterogeneous. In our model, we also take into account the hysteresis effects in the oil relative permeability functions. In the case of three-phase flow, the choice of general expressions for the relative permeability functions may lead to the loss of strict hyperbolicity and, therefore, to the existence of an elliptic region or umbilic points for the system of nonlinear hyperbolic conservation laws describing the convective transport of the fluid phases. As a consequence, the loss of hyperbolicity may lead to the existence of nonclassical shocks (also called transitional shocks or undercompressive shocks) in three-phase flow solutions. We present a new, accurate fractional time-step method based on an operator splitting technique for the numerical solution of a system of partial differential equations modeling two-phase, immiscible water-oil flow problems in heterogeneous petroleum reservoirs. An efficient two-phase water-oil numerical simulator developed by our research group was sucessfuly extended to take into account hysteresis effects under the hypotesis previously annouced. The numerical results obtained by the procedure proposed indicate numerical evidence the method at hand can be extended for the case of related three-phase water-gas-oil flow problems. A two-level operator splitting technique allows for the use of distinct time steps for the four problems defined by the splitting procedure: convection, diffusion, pressure-velocity and relaxation for hysteresis. The convective transport (hyperbolic) of the fluid phases is approximated by a high resolution, nonoscillatory, second-order, conservative central difference scheme in the convection step. This scheme is combined with locally conservative mixed finite elements for the numerical solution of the diffusive transport (parabolic) and the pressure-velocity (elliptic) problems. The time discretization of the parabolic problem is performed by means of the implicit Backward Euler method. An ordinary diferential equation is solved (analytically) for the relaxation related to hysteresis. Two-phase water-oil numerical results in one space dimensional, in which are in a very good agreement with semi-analitycal results available in the literature, were computationaly reproduced and new numerical results in two dimensional heterogeneous media are also presented and the extension of this technique to the case of three-phase water-oil-gas flows problems is proposed.
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Ly, Peter Quoc Cuong. "Fast and unambiguous direction finding for digital radar intercept receivers." Thesis, 2013. http://hdl.handle.net/2440/90332.

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This thesis considers the problem of angle-of-arrival (AOA) estimation in the context of its application to electronic surveillance systems. Due to the operational requirements of such systems, the AOA estimation algorithm must be computationally fast, accurate and will need to be implemented using sparse, large aperture arrays. Interferometry is proposed as a suitable algorithm that meets the operational requirements of electronic surveillance systems. However, for sparse array geometries, phase wrapping effects introduce ambiguities to the phase measurements and so unambiguous AOA estimation requires the use of computationally intensive ambiguity resolution algorithms using three or more antennas. Beamforming and array processing techniques are another class of AOA estimation algorithms that can unambiguously estimate the AOA using sparse, large aperture arrays. While these techniques generally offer better AOA estimation performance than interferometric techniques, they are also comparatively more computationally intensive algorithms. Furthermore, by virtue of using very sparse arrays, high sidelobes in the array beampattern may cause incorrect AOA estimation. This thesis will introduce the concept of using second-order difference array (SODA) geometries which allow unambiguous AOA estimation to be performed in a computationally effcient manner. In the context of interferometry, the so-called “SODA interferometer" will be shown to synthesise the equivalent output of a smaller virtual aperture to allow unambiguous AOA estimation to be performed at the expense of a coarser estimation performance compared to the physical aperture of the array. It will also be shown that the coarse SODA AOA estimate can be used to cue the conventional ambiguity resolution algorithms to provide higher accuracy in a computationally efficient manner. This thesis will also show that the creation of virtual arrays from SODA geometries can be generalised to a larger number of antennas to allow conventional array processing techniques to perform unambiguous AOA estimation in a computationally fast manner. The AOA estimation performance of each algorithm is compared through simulations and also verified using experimental data. This thesis will show that the SODA interferometer, SODA-cued ambiguity resolution algorithms and so-called “second-order array processors" can be used to obtain high accuracy AOA estimates in a more computationally efficient manner than the conventional algorithms.
Thesis (Ph.D.) -- University of Adelaide, School of Electrical and Electronic Engineering, 2013
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Li, Henian. "Asymptotic solutions of second order difference equations." 1991. http://hdl.handle.net/1993/18264.

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Books on the topic "Second order difference array"

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Jirari, Alouf. Second-order Sturm-Liouville difference equations and orthogonal polynomials. Providence, R.I: American Mathematical Society, 1995.

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E, Ladas G., ed. Dynamics of second order rational difference equations: With open problems and conjectures. Boca Raton, FL: Chapman & Hall/CRC, 2002.

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Heinrich, Bernd. Finite difference methods on irregular networks: A generalized approach to second order elliptic problems. Berlin: Akademie-Verlag, 1987.

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Heinrich, Bernd. Finite difference methods on irregular networks: A generalized approach to second order elliptic problems. Basel: Birkhäuser Verlag, 1987.

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Sequeira, A., H. Beirão da Veiga, and V. A. Solonnikov. Recent advances in partial differential equations and applications: International conference in honor of Hugo Beirao de Veiga's 70th birthday, February 17-214, 2014, Levico Terme (Trento), Italy. Edited by Rădulescu, Vicenţiu D., 1958- editor. Providence, Rhode Island: American Mathematical Society, 2016.

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Habib, Ammari, Capdeboscq Yves 1971-, and Kang Hyeonbae, eds. Multi-scale and high-contrast PDE: From modelling, to mathematical analysis, to inversion : Conference on Multi-scale and High-contrast PDE:from Modelling, to Mathematical Analysis, to Inversion, June 28-July 1, 2011, University of Oxford, United Kingdom. Providence, R.I: American Mathematical Society, 2010.

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Stanghellini, Giovanni. Second-order empathy. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780198792062.003.0035.

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This chapter reports a case study of ‘manipulation’. It argues that the case study of manipulation confirms that the supposition that the Other lives in a world just like my own is often the cause of serious misunderstandings—the source of negative emotions and of misleading value judgements and stigmatization that interfere with one’s capacity to care for other persons and to make sense of their behaviour. In order to empathize with these persons and make sense of their behaviour we need to acknowledge the existential difference, the particular autonomy, which separates us from their way of being in the world. Any forgetting of this difference—for instance between my own world and that of a person who ‘manipulates’ the others—will be an obstacle to empathic understanding, since these people live in a life-world of which the structure is (at least in part) different from my own.
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Ladas, G. E. Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures. Chapman & Hall/CRC, 2001.

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Ladas, G. E. Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures. Taylor & Francis Group, 2001.

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Ladas, G. E. Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures. Taylor & Francis Group, 2002.

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Book chapters on the topic "Second order difference array"

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Gandolfo, Giancarlo. "Second-order Difference Equations." In Economic Dynamics, 53–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-06822-9_5.

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Gandolfo, Giancarlo. "Second-order Difference Equations." In Economic Dynamics, 55–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03871-6_5.

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Djafari-Rouhani, Behzad, and Hadi Khatibzadeh. "Second Order Difference Equations." In Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces, 145–206. Boca Raton, FL: CRC Press, 2019. | “A science publishers book.”: CRC Press, 2019. http://dx.doi.org/10.1201/9780429156908-8.

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Ahlbrandt, Calvin D., and Allan C. Peterson. "Second Order Scalar Difference Equations." In Discrete Hamiltonian Systems, 1–44. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4757-2467-7_1.

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Agarwal, Ravi P., Claudio Cuevas, and Carlos Lizama. "Second-Order Linear Difference Equations." In Regularity of Difference Equations on Banach Spaces, 71–97. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06447-5_5.

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Agarwal, Ravi P., Claudio Cuevas, and Carlos Lizama. "Second-Order Semilinear Difference Equations." In Regularity of Difference Equations on Banach Spaces, 99–118. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06447-5_6.

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Maximon, Leonard C. "Second Order Homogeneous and Inhomogeneous Equations." In Differential and Difference Equations, 27–34. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29736-1_4.

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Djafari-Rouhani, Behzad, and Hadi Khatibzadeh. "Second Order Evolution Equations." In Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces, 71–120. Boca Raton, FL: CRC Press, 2019. | “A science publishers book.”: CRC Press, 2019. http://dx.doi.org/10.1201/9780429156908-5.

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Agarwal, Ravi P., Donal O’Regan, and Patricia J. Y. Wong. "Second Order Initial Value Problems." In Positive Solutions of Differential, Difference and Integral Equations, 11–18. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-015-9171-3_2.

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Agarwal, Ravi P., and Patricia J. Y. Wong. "Periodic Boundary Value Problems: Second Order Systems." In Advanced Topics in Difference Equations, 33–40. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8899-7_4.

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Conference papers on the topic "Second order difference array"

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Nagem, Raymond J., Xun Lei, and Leopold B. Felsen. "Finite Difference Time Domain Simulation of Scattering From Submerged Elastic Bodies." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-1029.

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Abstract A two-dimensional finite difference time domain (FDTD) algorithm is implemented to simulate wave propagation and scattering in a heterogeneous fluid-elastic environment. The FDTD algorithm is fourth-order accurate in space and second-order accurate in time. The perfectly matched layer (PML) absorbing boundary condition is adapted to eliminate artificial reflections caused by the boundaries of the finite computational domain. Computational accuracy is verified by considering radiation from a periodic array of pulsed line sources and from a fluid line source near a submerged elastic layer. The finite difference results are in excellent agreement with the numerically evaluated spectral integrals which can be derived for these problems. The finite difference algorithm is then applied to scattering from a rough fluid-solid interface, and to scattering from an elastic cylinder above or buried beneath a rough fluid-solid interface. Scattered signals are processed with the Gaussian windowed transform, which provides an initial image representation for signature identification and classification algorithms.
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Zhang, Conan, and Carlos H. Hidrovo. "Investigation of Nanopillar Wicking Capabilities for Heat Pipes Applications." In ASME 2009 Second International Conference on Micro/Nanoscale Heat and Mass Transfer. ASMEDC, 2009. http://dx.doi.org/10.1115/mnhmt2009-18484.

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Since Moore’s prediction in 1965, transistor count density on computer chips has grown exponentially and roadmaps for future industry growth still project exponential development for the next decade. With higher transistor densities, greater heat flux dissipation is required in order for performance to keep par with chip development. However, it is theorized that current cooling systems would not be able to cope with heat fluxes of future computer chips. Microchip heat management systems can be either active or passive. Active systems require an external driving component that increases the system’s complexity and ultimately power consumption. Heat pipes are passive fluidic systems, which are more robust and easier to implement than their active counterparts. Recirculation of the coolant in a heat pipe is done passively by means of a wicking structure that induces capillary flow from the condenser to the evaporator. However, there are many limiting factors associated with heat pipes based on the wick dimensions, fluid selection and orientation. At CPU chip operating temperatures the most significant limitation is the capillary limit. This limitation must be addressed in order to meet future computer chip heat dissipation requirements. In order to find an optimal geometry that would maximize the capillary flow, a theoretical model was developed using a rectangular pillar array. Surface tension forces induce a capillary flow that is opposed by viscous stresses from the pillars. Due to the regular and well-defined geometry of the pillar array, an ab initio approach can be used to model this flow, rather than resorting to Darcy’s flow and empirical permeability correlations. Predicted values of maximum flow rate were obtained from this theoretical model. This model and its results are directly applicable to carbon nanotube (CNT) and nanowire (NW) based wick structures. To validate the merit of nanostructure wicks for use in heat pipes, experimental data was collected to show the capillary limits of various nanowicks. The capillary limit of a wick was associated with the heat flux at which the wick cannot sustain the fluid flow necessary for heat removal and burnout occurs. When a baseline wick was experimentally compared to a nanowick, it was found that due to the difference in thickness of the wicks, the baseline wick provided higher flow rates. However, when the data were normalized to produce velocity values, the nanowick was found to have a higher velocity than the baseline wicks.
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Jing, Changxing, Dongping Zhang, Peiqing Ni, Kun Zhang, and Li Yang. "Difference networks and second-order difference networks." In 2017 4th International Conference on Systems and Informatics (ICSAI). IEEE, 2017. http://dx.doi.org/10.1109/icsai.2017.8248500.

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Sharma, Chirdeep, and Sumanta Acharya. "Direct Numerical Simulation of a Coolant Jet in a Periodic Crossflow." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-0671.

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Abstract A Direct Numerical Simulation of a coolant jet injected normally into a periodic crossflow is presented. The physical situation simulated represents a periodic module in a coolant hole array with a heated crossflow. A collocated finite difference scheme is used which is fifth-order accurate spatially and second-order accurate temporally. The scheme is based on a fractional step approach and requires the solution of a pressure-Poisson equation. The simulations are obtained for a blowing ratio of 0.25 and a channel Reynolds number of 5600. The simulations reveal the dynamics of several large scale structures including the Counter-rotating Vortex Pair (CVP), the horse-shoe vortex, the shear layer vortex, the wall vortex and the wake vortex. The origins and the interactions of these vortical structures are identified and explored. Also presented are the turbulence statistics and how they relate to the flow structures.
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Wojcik, Gregory L., John C. Mould, and Laura M. Carcione. "Combined Transducer and Nonlinear Tissue Propagation Simulations." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0216.

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Abstract Ultrasonic imaging system evaluation is often based on models of the transducer as a distribution of baffled piston sources, and of the tissue as a homogeneous, linear acoustic medium, e.g., Jensen’s Field code. In reality, these are fairly gross idealizations, since the transducer exhibits more complicated response modes and real tissue is inhomogeneous and nonlinear. Greater model fidelity would be useful, especially in the context of transducer design qualification, second harmonic imaging, and acoustic power indices. To this end we combine 2D finite element models of transducer dynamics with highly accurate 2D finite difference propagation models in the large-scale inhomogeneous tissue cross-sections. Transducer models employ the time-domain code, PZFlex, and tissue models utilize a new pseudospectral solver to be included in PZFlex. The pseudospectral algorithm solves the inhomogeneous acoustic wave equation using FFTs for high order approximation of the spatial differential operator and a fourth-order, explicit time integrator. Second-order (B/A) nonlinearity and frequency-accurate, causal absorption are included. We describe the algorithmic and modeling issues, and present a suite of simulations in lossy, nonlinear abdominal cross sections and tissue showing coupling of the 1D medical array to the tissue model and scattering from deeper inhomogeneities and back to the transducer. In contrast to paraxial schemes, like the KZK method, details of the field transmitted from the transducer and all backscatter within the model are included. However, models are currently limited to 2D (plane or axisymmetric) on readily available hardware.
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Fouques, Sébastien, Sébastien Laflèche, Andreas Akselsen, and Thomas Sauder. "An Experimental Investigation of Nonlinear Wave Generation by Flap Wavemakers." In ASME 2021 40th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/omae2021-63120.

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Abstract It is well known that flap wavemakers behave in a nonlinear way when either the flap angle or the flap velocity becomes large. Moreover, the hinge depth should be adapted to the period of the generated waves in order to minimize linear evanescent modes, which may contribute to the formation of nonlinear spurious waves. For example, imposing a sinusoidal motion with a relatively long period and a large amplitude to a short flap will result in a surface elevation composed of a regular wave with the same period as the flap motion, but also of a variety of harmonics with higher frequencies. Second-order harmonics can be predicted theoretically for regular and irregular waves, and they can be corrected by modifying the control signal of the wavemaker. However, there is no theory that can describe nor mitigate effects of orders higher than two. The design of the wavemaker is then essential to generate extreme sea states with good quality and predictability in a laboratory. In this paper, the nonlinearities of flap wavemakers are investigated experimentally for regular and irregular waves generated in SINTEF Ocean’s laboratories. Nonlinearities of order two and three are estimated from times series of the surface elevation measured at different locations by an array of wave probes. Particular focus is put on identifying the effects of the classical second-order correction on the second- and third-order harmonics.
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Selvam, A. George Maria, and R. Janagaraj. "Oscillation theorems for damped fractional order difference equations." In SECOND INTERNATIONAL CONFERENCE OF MATHEMATICS (SICME2019). Author(s), 2019. http://dx.doi.org/10.1063/1.5097518.

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Berinde, Vasile. "A Method For Solving Second Order Difference Equations." In Proceedings of the Third International Conference on Difference Equations. Taylor & Francis Group, 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742: CRC Press, 2017. http://dx.doi.org/10.4324/9780203745854-6.

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Zhao, Dongming, Qingbin Wang, Huan Bao, and Zhan Gao. "The second order Central Divided-difference Kalman Filter." In 2011 Eighth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2011). IEEE, 2011. http://dx.doi.org/10.1109/fskd.2011.6020008.

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Elko, Gary W., and Jens Meyer. "Second-order differential adaptive microphone array." In ICASSP 2009 - 2009 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2009. http://dx.doi.org/10.1109/icassp.2009.4959523.

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Reports on the topic "Second order difference array"

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Petersson, N., and B. Sjogreen. Serpentine: Finite Difference Methods for Wave Propagation in Second Order Formulation. Office of Scientific and Technical Information (OSTI), March 2012. http://dx.doi.org/10.2172/1046802.

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Kuznetsov, Victor, Vladislav Litvinenko, Egor Bykov, and Vadim Lukin. A program for determining the area of the object entering the IR sensor grid, as well as determining the dynamic characteristics. Science and Innovation Center Publishing House, April 2021. http://dx.doi.org/10.12731/bykov.0415.15042021.

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Currently, to evaluate the dynamic characteristics of objects, quite a large number of devices are used in the form of chronographs, which consist of various optical, thermal and laser sensors. Among the problems of these devices, the following can be distinguished: the lack of recording of the received data; the inaccessibility of taking into account the trajectory of the object flying in the sensor area, as well as taking into consideration the trajectory of the object during the approach to the device frame. The signal received from the infrared sensors is recorded in a separate document in txt format, in the form of a table. When you turn to the document, data is read from the current position of the input data stream in the specified list by an argument in accordance with the given condition. As a result of reading the data, it forms an array that includes N number of columns. The array is constructed in a such way that the first column includes time values, and columns 2...N- the value of voltage . The algorithm uses cycles that perform the function of deleting array rows where there is a fact of exceeding the threshold value in more than two columns, as well as rows where the threshold level was not exceeded. The modified array is converted into two new arrays, each of which includes data from different sensor frames. An array with the coordinates of the centers of the sensor operation zones was created to apply the Pythagorean theorem in three-dimensional space, which is necessary for calculating the exact distance between the zones. The time is determined by the difference in the response of the first and second sensor frames. Knowing the path and time, we are able to calculate the exact speed of the object. For visualization, the oscillograms of each sensor channel were displayed, and a chronograph model was created. The chronograph model highlights in purple the area where the threshold has been exceeded.
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Riveros, Guillermo, Felipe Acosta, Reena Patel, and Wayne Hodo. Computational mechanics of the paddlefish rostrum. Engineer Research and Development Center (U.S.), September 2021. http://dx.doi.org/10.21079/11681/41860.

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Purpose – The rostrum of a paddlefish provides hydrodynamic stability during feeding process in addition to detect the food using receptors that are randomly distributed in the rostrum. The exterior tissue of the rostrum covers the cartilage that surrounds the bones forming interlocking star shaped bones. Design/methodology/approach – The aim of this work is to assess the mechanical behavior of four finite element models varying the type of formulation as follows: linear-reduced integration, linear-full integration, quadratic-reduced integration and quadratic-full integration. Also presented is the load transfer mechanisms of the bone structure of the rostrum. Findings – Conclusions are based on comparison among the four models. There is no significant difference between integration orders for similar type of elements. Quadratic-reduced integration formulation resulted in lower structural stiffness compared with linear formulation as seen by higher displacements and stresses than using linearly formulated elements. It is concluded that second-order elements with reduced integration and can model accurately stress concentrations and distributions without over stiffening their general response. Originality/value – The use of advanced computational mechanics techniques to analyze the complex geometry and components of the paddlefish rostrum provides a viable avenue to gain fundamental understanding of the proper finite element formulation needed to successfully obtain the system behavior and hot spot locations.
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Or, Etti, David Galbraith, and Anne Fennell. Exploring mechanisms involved in grape bud dormancy: Large-scale analysis of expression reprogramming following controlled dormancy induction and dormancy release. United States Department of Agriculture, December 2002. http://dx.doi.org/10.32747/2002.7587232.bard.

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The timing of dormancy induction and release is very important to the economic production of table grape. Advances in manipulation of dormancy induction and dormancy release are dependent on the establishment of a comprehensive understanding of biological mechanisms involved in bud dormancy. To gain insight into these mechanisms we initiated the research that had two main objectives: A. Analyzing the expression profiles of large subsets of genes, following controlled dormancy induction and dormancy release, and assessing the role of known metabolic pathways, known regulatory genes and novel sequences involved in these processes B. Comparing expression profiles following the perception of various artificial as well as natural signals known to induce dormancy release, and searching for gene showing similar expression patterns, as candidates for further study of pathways having potential to play a central role in dormancy release. We first created targeted EST collections from V. vinifera and V. riparia mature buds. Clones were randomly selected from cDNA libraries prepared following controlled dormancy release and controlled dormancy induction and from respective controls. The entire collection (7920 vinifera and 1194 riparia clones) was sequenced and subjected to bioinformatics analysis, including clustering, annotations and GO classifications. PCR products from the entire collection were used for printing of cDNA microarrays. Bud tissue in general, and the dormant bud in particular, are under-represented within the grape EST database. Accordingly, 59% of the our vinifera EST collection, composed of 5516 unigenes, are not included within the current Vitis TIGR collection and about 22% of these transcripts bear no resemblance to any known plant transcript, corroborating the current need for our targeted EST collection and the bud specific cDNA array. Analysis of the V. riparia sequences yielded 814 unigenes, of which 140 are unique (keilin et al., manuscript, Appendix B). Results from computational expression profiling of the vinifera collection suggest that oxidative stress, calcium signaling, intracellular vesicle trafficking and anaerobic mode of carbohydrate metabolism play a role in the regulation and execution of grape-bud dormancy release. A comprehensive analysis confirmed the induction of transcription from several calcium–signaling related genes following HC treatment, and detected an inhibiting effect of calcium channel blocker and calcium chelator on HC-induced and chilling-induced bud break. It also detected the existence of HC-induced and calcium dependent protein phosphorylation activity. These data suggest, for the first time, that calcium signaling is involved in the mechanism of dormancy release (Pang et al., in preparation). We compared the effects of heat shock (HS) to those detected in buds following HC application and found that HS lead to earlier and higher bud break. We also demonstrated similar temporary reduction in catalase expression and temporary induction of ascorbate peroxidase, glutathione reductase, thioredoxin and glutathione S transferase expression following both treatments. These findings further support the assumption that temporary oxidative stress is part of the mechanism leading to bud break. The temporary induction of sucrose syntase, pyruvate decarboxylase and alcohol dehydrogenase indicate that temporary respiratory stress is developed and suggest that mitochondrial function may be of central importance for that mechanism. These finding, suggesting triggering of identical mechanisms by HS and HC, justified the comparison of expression profiles of HC and HS treated buds, as a tool for the identification of pathways with a central role in dormancy release (Halaly et al., in preparation). RNA samples from buds treated with HS, HC and water were hybridized with the cDNA arrays in an interconnected loop design. Differentially expressed genes from the were selected using R-language package from Bioconductor project called LIMMA and clones showing a significant change following both HS and HC treatments, compared to control, were selected for further analysis. A total of 1541 clones show significant induction, of which 37% have no hit or unknown function and the rest represent 661 genes with identified function. Similarly, out of 1452 clones showing significant reduction, only 53% of the clones have identified function and they represent 573 genes. The 661 induced genes are involved in 445 different molecular functions. About 90% of those functions were classified to 20 categories based on careful survey of the literature. Among other things, it appears that carbohydrate metabolism and mitochondrial function may be of central importance in the mechanism of dormancy release and studies in this direction are ongoing. Analysis of the reduced function is ongoing (Appendix A). A second set of hybridizations was carried out with RNA samples from buds exposed to short photoperiod, leading to induction of bud dormancy, and long photoperiod treatment, as control. Analysis indicated that 42 genes were significant difference between LD and SD and 11 of these were unique.
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