Applications of the dynamic mode decomposition

The decomposition of experimental data into dynamic modes using a data-based algorithm is applied to Schlieren snapshots of a helium jet and to time-resolved PIV-measurements of an unforced and harmonically forced jet. The algorithm relies on the reconstruction of a low-dimensional inter-snapshot map from the available flow field data. The spectral decomposition of this map results in an eigenvalue and eigenvector representation (referred to as dynamic modes) of the underlying fluid behavior contained in the processed flow fields. This dynamic mode decomposition allows the breakdown of a fluid process into dynamically revelant and coherent structures and thus aids in the characterization and quantification of physical mechanisms in fluid flow. © 2010 Springer-Verlag.

On the use of combined compact scheme for numerical solution of the two-layer oceanic shallow water equations

Many types of oceanic physical phenomena have a wide range in both space and time. In general, simplified models, such as shallow water model, are used to describe these oceanic motions. The shallow water equations are widely applied in various oceanic and atmospheric extents. By using the two-layer shallow water equations, the stratification effects can be considered too. In this research, the sixth-order combined compact method is investigated and numerically implemented as a high-order method to solve the two-layer shallow water equations. The second-order centered, fourth-order compact and sixth-order super compact finite difference methods are also used to spatial differencing of the equations. The first part of the present work is devoted to accuracy assessment of the sixth-order super compact finite difference method (SCFDM) and the sixth-order combined compact finite difference method (CCFDM) for spatial differencing of the linearized two-layer shallow water equations on the Arakawa's A-E and Randall's Z numerical grids. Two general discrete dispersion relations on different numerical grids, for inertia-gravity and Rossby waves, are derived. These general relations can be used for evaluation of the performance of any desired numerical scheme. For both inertia-gravity and Rossby waves, minimum error generally occurs on Z grid using either the sixth-order SCFDM or CCFDM methods. For the Randall's Z grid, the sixth-order CCFDM exhibits a substantial improvement , for the frequency of the barotropic and baroclinic modes of the linear inertia-gravity waves of the two layer shallow water model, over the sixth-order SCFDM. For the Rossby waves, the sixth-order SCFDM shows improvement, for the barotropic and baroclinic modes, over the sixth-order CCFDM method except on Arakawa's C grid. In the second part of the present work, the sixth-order CCFDM method is used to solve the one-layer and two-layer shallow water equations in their nonlinear form. In one-layer model with periodic boundaries, the performance of the methods for mass conservation is compared. The results show high accuracy of the sixth-order CCFDM method to simulate a complex flow field. Furthermore, to evaluate the performance of the method in a non-periodic domain the sixth-order CCFDM is applied to spatial differencing of vorticity-divergence-mass representation of one-layer shallow water equations to solve a wind-driven current problem with no-slip boundary conditions. The results show good agreement with published works. Finally, the performance of different schemes for spatial differencing of two-layer shallow water equations on Z grid with periodic boundaries is investigated. Results illustrate the high accuracy of combined compact method.

Physical and chemical characteristics of major aquatic ecosystems in the Victoria and Kyoga lake basins

The physical-chemical characteristics of any aquatic ecosystem include pH, conductivity, and temperature, water transparency, nutrient and the chlorophyll-a levels. Physical and chemical factors of any ecosystem determine the type and quality of flora present in it and these forms the basis on which the system operates. The elements required in largest amounts for plant productions are carbon, phosphorus, nitrogen, and silicon, which is important for diatoms as a major component of the cell wall. Nutrients may limit algal productivity in the tropics despite the high temperature there allowing rapid nutrient recycling. Nutrients most likely to be limiting African lakes are nitrogen (Talling & Talling 1965; Moss 1969; Lehman & Branstrator 1993, 1994) and phosphorus (Melack.et al l982; Kalff 1983) while silicon may limit diatom growth (Hecky & Kilham 1988). The objective of the study is to investigate the impact of physical-chemical characteristics on the distribution and abundance of organisms in the major aquatic ecosystems.

Perceptual thresholds for acoustical guitar models

Synthesised acoustic guitar sounds based on a detailed physical model are used to provide input for psychoacoustical testing. Thresholds of perception are found for changes in the main parameters of the model. Using a three-alternative forced-choice procedure, just-noticeable differences are presented for changes in frequency and damping of the modes of the guitar body, and also for changes in the tension, bending stiffness and damping parameters of the strings. These are compared with measured data on the range of variation of these parameters in a selection of guitars. © S. Hirzel Verlag © EAA.

The night purging of a two-storey atrium building

We examine the fluid mechanics of night purging in a two-storey naturally ventilated atrium building. We develop a mathematical model of a simplified atrium building and focus on the rate at which warm air purges from each storey and the atrium by displacement ventilation into a still cool night environment of a constant temperature. To develop a first insight into how the geometry of the building influences the rate at which warm air purges from each storey via the atrium we neglect heat exchange with the fabric (so there is no thermal buffering) and furthermore assume that the warm air layers in each storey and the atrium are of uniform temperature. The plumes of warm air that rise from the storeys into the atrium, causing the atrium to fill with warm air, have a very strong influence on the night purge. Modelling these as axisymmetric turbulent plumes, we identify three forms of purging behaviour. Each purge is characterised by five key times identified in the progression of the night purge and physical rationale for these differing behaviours is given. An interface velocity deficit and volumetric purge deficit are introduced as measures of the efficiency of a night purge. © 2010 Elsevier Ltd.

An example of the use of neural computing techniques in materials science - The modelling of fatigue thresholds in Ni-base superalloys

Two adaptive numerical modelling techniques have been applied to prediction of fatigue thresholds in Ni-base superalloys. A Bayesian neural network and a neurofuzzy network have been compared, both of which have the ability to automatically adjust the network's complexity to the current dataset. In both cases, despite inevitable data restrictions, threshold values have been modelled with some degree of success. However, it is argued in this paper that the neurofuzzy modelling approach offers real benefits over the use of a classical neural network as the mathematical complexity of the relationships can be restricted to allow for the paucity of data, and the linguistic fuzzy rules produced allow assessment of the model without extensive interrogation and examination using a hypothetical dataset. The additive neurofuzzy network structure means that redundant inputs can be excluded from the model and simple sub-networks produced which represent global output trends. Both of these aspects are important for final verification and validation of the information extracted from the numerical data. In some situations neurofuzzy networks may require less data to produce a stable solution, and may be easier to verify in the light of existing physical understanding because of the production of transparent linguistic rules. © 1999 Elsevier Science S.A.

A simplified mathematical approach for modelling stack ventilation in multi-compartment buildings

A simple mathematical model of stack ventilation flows in multi-compartment buildings is developed with a view to providing an intuitive understanding of the physical processes governing the movement of air and heat through naturally ventilated buildings. Rules of thumb for preliminary design can be ascertained from a qualitative examination of the governing equations of flow, which elucidate the relationships between 'core' variables - flow rates, air temperatures, heat inputs and building geometry. The model is applied to an example three-storey office building with an inlet plenum and atrium. An examination of the governing equations of flow is used to predict the behaviour of steady flows and to provide a number of preliminary design suggestions. It is shown that control of ventilation flows must be shared between all ventilation openings within the building in order to minimise the disparity in flow rates between storeys, and ensure adequate fresh air supply rates for all occupants. © 2013 Elsevier Ltd.

Raman and infrared properties and layer dependence of the phonon dispersions in multilayered graphene

The symmetry group analysis is applied to classify the phonon modes of N-stacked graphene layers (NSGLs) with AB and AA stacking, particularly their infrared and Raman properties. The dispersions of various phonon modes are calculated in a multilayer vibrational model, which is generalized from the lattice vibrational potentials of graphene to including the interlayer interactions in NSGLs. The experimentally reported redshift phenomena in the layer-number dependence of the intralayer optical C-C stretching mode frequencies are interpreted. An interesting low-frequency interlayer optical mode is revealed to be Raman or infrared active in even or odd NSGLs, respectively. Its frequency shift is sensitive to the layer number and saturated at about 10 layers.

Continuous weak measurement and feedback control of a solid-state charge qubit: A physical unravelling of non-Lindblad master equation

Conventional quantum trajectory theory developed in quantum optics is largely based on the physical unravelling of a Lindblad-type master equation, which constitutes the theoretical basis of continuous quantum measurement and feedback control. In this work, in the context of continuous quantum measurement and feedback control of a solid-state charge qubit, we present a physical unravelling scheme of a non-Lindblad-type master equation. Self-consistency and numerical efficiency are well demonstrated. In particular, the control effect is manifested in the detector noise spectrum, and the effect of measurement voltage is discussed.

High-frequency hydrogen-related infrared modes in silicon grown in a hydrogen atmosphere

High-frequency vibrational modes have been observed at liquid-helium temperature in silicon samples grown in a H-2 or D-2 atmosphere. The highest-frequency ones are due to the overtones and combination modes of SiH fundamentals. Others are CH modes due to (C,H) complexes, but the simultaneous presence of NH modes due to (N,H) complexes cannot be excluded. The present results seem to show also the existence of centers including both SiH and CH or NH bonds. One sharp mode at 4349 cm-l is related to a weak SiH fundamental at 2210 cm(-1). The related center is ascribed to a vacancy fully decorated with hydrogen with a nearest-neighbor C atom. [S0163-1829(99)00911-X].

Accurate determination of electronic transition energy of carbon nanotubes from the resonant behavior of radial breathing modes and their overtones

The resonant Raman behavior of the radial breathing modes are very useful to analyze the electronic property of carbon nanotubes. We investigated the resonant behaviors of Stokes and anti-Stokes radial breathing mode and its overtone of a metallic nanotube, and show how to accurately determine the electronic transition energy of carbon nanotubes from radial breathing modes and their overtones. Based on the present results, the previously reported resonant Raman behavior of the radial breathing modes of SWINT bundles can be interpreted very well.

空间电流体系地磁反演及理论研究

The space currents definitely take effects on electromagnetic environment and also are scientific highlight in the space research. Space currents as a momentum and energy provider to Geospace Storm, disturb the varied part of geomagnetic field, distort magnetospheric configuration and furthermore take control of the coupling between magnetosphere and ionosphere. Due to both academic and commercial objectives above, we carry on geomagnetic inverse and theoretical studies about the space currents by using geomagnetic data from INTERMAGNET. At first, we apply a method of Natural Orthogonal Components (NOC) to decomposition the solar daily variation, especially for (solar quiet variation). NOC is just one of eign mode analysis, the most advantage of this method is that the basic functions (BFs) were not previously designated, but naturally came from the original data so that there are several BFs usually corresponding to the process really happened and have more physical meaning than the traditional spectrum analysis with the fixed BFs like Fourier trigonometric functions. The first two eign modes are corresponding to the and daily variation and their amplitudes both have the seasonal and day-to-day trend, that will be useful for evaluating geomagnetic activity indices. Because of the too strict constraints of orthogonality, we try to extend orthogonal contraints to the non-orthogonal ones in order to give more suitable and appropriate decomposition of the real processes when the most components did not satisfy orthogonality. We introduce a mapping matrix which can transform the real physical space to a new mathematical space, after that process, the modified components which associated with the physical processes have satisfied the orthogonality in the new mathematical space, furthermore, we can continue to use the NOC decomposition in the new mathematical space, and then all the components inversely transform back to original physical space, so that we would have finished the non-orthogonal decomposition which more generally in the real world. Secondly, geomagnetic inverse of the ring current’s topology is conducted. Configurational changes of the ring current in the magnetosphere lead to different patterns of disturbed ground field, so that the global configuration of ring current can be inferred from its geomagnetic perturbations. We took advantages of worldwide geomagnetic observatories network to investigate the disturbed geomagnetic field which produced by ring current. It was found that the ring current was not always centered at geomagnetic equator, and significantly deviated off the equator during several intense magnetic storms. The deviation owing to the tilting and latitudinal shifting of the ring current with respect to the earth’s dipole can be estimated from global geomagnetic survey. Furthermore those two configurational factors which gave a quantitative description of the ring current configuration, will be helpful to improve the Dst calibration and understand the dependence of ring current’s configuration on the plasma sheet location relative to the equator when magnetotail field warped. Thirdly, the energization and physical acceleration process of ring current during magnetic storm has been proposed. When IMF Bz component increase, the enhanced convection electric field drive the plasma injection into the inner magnetosphere. During the transport process, a dynamic heating is happened which make the particles more ‘hot’ when the injection is more deeply inward. The energy gradient along the injection path is equivalent to a kind of force, which resist the plasma more earthward injection, as a diamagnetic effect of the magnetosphere anti and repellent action to the exotically injected plasma. The acceleration efficiency has a power law form. We use analytical way to quantitatively describe the dynamical process by introducing a physical parameter: energization index, which will be useful to understand how the particle is heated. At the end, we give a scheme of how to get the from storm time geomagnetic data. During intense magnetic storms, the lognormal trend of geomagnetic Dst decreases depend on the heating dynamic of magnetosphere controlling ring current. The descending pattern of main phase is governed by the magnetospheric configuration, which can be describled by the energization index. The amplitude of Dst correlated with convection electric field or south component of the solar wind. Finally, the Dst index is predicted by upstream solar wind parameter. As we known space weather have posed many chanllenges and impacts on techinal system, the geomagnetic index for evaluating the activity space weather. We review the most popular Dst prediction method and repeat the Dst forecasting model works. A concise and convnient Key Points model of the polar region is also introduced to space weather. In summary, this paper contains some new quantitative and physical description of the space currents with special focus on the ring current. Whatever we do is just to gain a better understanding of the natural world, particularly the space environment around Earth through analytical deduction, algorithm designing and physical analysis, to quantitative interpretation. Applications of theoretical physics in conjunction with data analysis help us to understand the basic physical process govering the universe.

油藏动态模型和剩余油分布模式

This paper belong to national "973" technological project undertaken by Shengli Oilfield. Work area is composed of turbidite reservoir of S212 and delta reservoir of S283 of Sheng2 unit in Shengtuo Oilfield that has a 36 years water injection development history. Change of the macroscopic, microscopic and filterational parameters and its mechanism have been studied in the 4 water-cut stages i.e. the primary, moderate, high and supper-high stage by using multi-disciplinary theories and approaches, computer techniques and physical simulation comprehensively. Dynamic reservoir models to different water-cut stages have been established. The study of forming mechanism and distribution of residual oil revealed the main types and spatial distribution of residual oil in different water-cut stages and the distribution mode has also been built up. Macroscopic, microscopic and filterational parameters selecting principle, optimizing and selecting standard, matching standard and laws and related database of various dynamic parameters in different water-cut stages have been established, which laid good basis for revealing reservoir macroscopic, microscopic and filterational parameters' dynamic change and residual oil distribution. The study indicated that in general, the macroscopic, microscopic and filterational parameters will slowly increase and become better in both shallow turbidite and delta reservoirs with the increasing of water cut, but different reservoirs have their own characteristics and change laws. Parameters of I~2 unit, whose petrophysical properties are better, increase more quickly than 8~3, whose petrophysical properties are more unfavorable. The changes was relatively quickly in high water-cut stage, while relatively slowly from primary to moderate and from high to supper-high water-cut stage. This paper firstly put forward that reservoir macroscopic, microscopic and filterational parameters are controlled by dynamic geological function of reservoir fluid, which is considered the major reason of reservoir parameters' dynamic changes and residual oil formation and distribution during reservoir development. Physical simulation of filterational parameters verified that forming mechanism and distribution of residual oil in different water-cut stages are also controlled by dynamic geological function of reservoir fluid. The idea of fluid geological function during reservoir development developed the theory of development geology, and has important practical values. This paper firstly constructed dynamic geological and mathematical models and five modes of residual oil distribution in Shengtuo Oilfield, and achieved four-dimensional forecast of residual oil distribution in different watercut stages. Dynamic changes and mechanism of macroscopic, microscopic and fliterational parameters of reservoir and their change process have been revealed. Forecast of residual oil distribution has been achieved by computers. This paper established the related theories, approaches and techniques for residual oil study, characterization and in different water-cut stages, and realized dynamic forecast of residual oil. It gained remarkable economic benefit and social effect in guiding field development. These theories and techniques had important meaningfulness for residual oil prediction in the terrestrial faulted basins not only in Shengli Oilfield but also in the east of China. Furthermore, this study has developed the theory of development geology.

Proceedings of the Fourth PHANTOM Users Group Workshop

This Report contains the proceedings of the Fourth Phantom Users Group Workshop contains 17 papers presented October 9-12, 1999 at MIT Endicott House in Dedham Massachusetts. The workshop included sessions on, Tools for Programmers, Dynamic Environments, Perception and Cognition, Haptic Connections, Collision Detection / Collision Response, Medical and Seismic Applications, and Haptics Going Mainstream. The proceedings include papers that cover a variety of subjects in computer haptics including rendering, contact determination, development libraries, and applications in medicine, path planning, data interaction and training.