The deformation problem of elasticity theory with regard to nonlinear deformations is examined. The expressions of deformations through displacements in the orthogonal curvilinear coordinate system ...are recorded. The relations for finite deformations in cylindrical and polar coordinate systems are derived. Physical relations for finite deformations and corresponding generalized stresses are recorded.
•Bicubic interpolation over sun path in equatorial coordinates.•Approximation of the efficiency using multi-dimensional approximation methods.•Lagrange interpolation over sun path in equatorial ...coordinates.•Calculation of the annual energy production by interpolating the power plant efficiency.•Accuracy of 99.9% while using around 40 simulation points.
Heliostat field layout optimization bases on simulations of the annual energy production. To reduce the computation time of the optimization process, one can try to reduce the number of simulation points of the annual domain, while keeping similar accuracy. For the temporal domain, there exist already different approaches as aggregation of days. To further reduce the number of needed simulation points, in this paper we decouple the power computation from the irradiation, such that we just regard the computation of the power plant efficiency. This time-dependent parameter is transformed into a celestial coordinate system where the solar angle-dependent efficiency will be approximated using suitable multi-dimensional interpolation methods.
We distinguish between an accurate approximation of the received annual optical energy and the electrical energy of each moment of a year. These methods are demonstrated for the existing heliostat field layouts PS10 and Gemasolar in Seville, while using realistic weather conditions. With this new approach just around 40 simulation points suffice to reach an accuracy of 99.9% for the received power for smaller power plants as PS10, and for larger plants as Gemasolar. Compared to a state-of-the-art method, this investigation helps to accelerate the simulation by factor three.
Abstract
Recently, Rozelot & Eren pointed out that the first solar gravitational moment (
J
2
) might exhibit a temporal variation. The suggested explanation is through the temporal variation of the ...solar rotation with latitude. This issue is deeper developed due to an accurate knowledge of the long-term variations in solar differential rotation regarding solar activity. Here we analyze solar cycles 12–24, investigating the long-term temporal variations in solar differential rotation. It is shown that
J
2
exhibits a net modulation over the 13 studied cycles of ≈(89.6 ± 0.1) yr, with a peak-to-peak amplitude of ≈0.1 × 10
−7
for a reference value of 2.07 × 10
−7
). Moreover,
J
2
exhibits a positive linear trend in the period of minima solar activity (sunspot number up to around 40) and a marked declining trend in the period of maxima (sunspot number above 50). In absolute magnitude, the mean value of
J
2
is more significant during periods of minimum than in periods of maximum. These findings are based on observational results that are not free of errors and can be refined further by considering torsional oscillations for example. They are comforted by identifying a periodic variation of the
J
2
term evidenced through the analysis of the perihelion precession of planetary orbits either deduced from ephemerides or computed in the solar equatorial coordinate system instead of the ecliptic coordinate one usually used.
An LMN coordinate system for magnetic reconnection events is sometimes determined by defining N as the direction of the gradient across the current sheet and L as the direction of maximum variance of ...the magnetic field. The third direction, M, is often assumed to be the direction of zero gradient, and thus the orientation of the X line. But when there is a guide field, the X line direction may have a significant component in the L direction defined in this way. For a 2D description, a coordinate system describing such an event would preferably be defined using a different coordinate direction M′ oriented along the X line. Here we use a 3D particle‐in‐cell simulation to show that the X line is oriented approximately along the direction bisecting the asymptotic magnetic field directions on the two sides of the current sheet. We describe two possible ways to determine the orientation of the X line from spacecraft data, one using the minimum gradient direction from Minimum Directional Derivative analysis at distances of the order of the current sheet thickness from the X line, and another using the bisection direction based on the asymptotic magnetic fields outside the current sheet. We discuss conditions for validity of these estimates, and we illustrate these conditions using several Magnetospheric Multiscale (MMS) events. We also show that intersection of a flux rope due to secondary reconnection with the primary X line can destroy invariance along the X line and negate the validity of a two‐dimensional description.
Plain Language Summary
At an interface between two regions with magnetic field pointing in different directions, the magnetic fields can reconnect across the interface. While real magnetic reconnection events are three‐dimensional, there can sometimes be a direction of approximate invariance, so that a two‐dimensional description can be valid. In such cases, it can be beneficial to define a coordinate system with one coordinate along the direction of the smallest gradient in the magnetic field. Using a simulation of magnetic reconnection, we show how the direction of smallest gradient, eM′, is determined, and also discuss how spacecraft observations could be used to find that direction. We also illustrate how the invariant direction can be determined using several events observed by the Magnetospheric Multiscale (MMS) spacecraft.
Key Points
When there is a guide field, the orientation of the X line may be tilted toward the direction of maximum magnetic field variance
Under certain circumstances Minimum Directional Derivative analysis can be used to determine the orientation of the X line
Intersection of a flux rope with the primary X line due to secondary reconnection can destroy two dimensionality
As a concept put forward by Prof Zadeh, Z-numbers have become a research hotspot in fuzzy theory. Different from the previous fuzzy sets, Z-numbers possess a stronger ability in expressing ...uncertainty because of the unique structure. The chief purpose of this paper is to research linguistic uncertain Z-numbers with a rectangular coordinate system. Taking into account the shortcomings of previous studies, the rectangular coordinate system is firstly adopted to address linguistic Z-numbers. Based on the new expression, arithmetic operations are defined. After summarizing the drawbacks of the previous aggregation operators, a novel approach named linguistic uncertain Z-numbers weighted averaging aggregation operator based on the rectangular coordinate system (LUZWAAORCS) is defined. Subsequently, the Minkowski distance measure of linguistic uncertain Z-numbers is proposed and the rationality is proven by a theorem. Follow that, a score function considering the Minkowski distance measure and technique for order preference by similarity to an ideal solution (TOPSIS) is suggested to quantify the information in different Z-numbers. Besides, an innovative Cosine similarity is defined to measure the similarity. Simultaneously, several examples are used to describe the proposed innovations. As far as our latest knowledge is concerned, Z-numbers have never been researched with a rectangular coordinate system, so this may be another door to process Z-number-based information.
Large-Scale Gradients in Human Cortical Organization Huntenburg, Julia M.; Bazin, Pierre-Louis; Margulies, Daniel S.
Trends in cognitive sciences,
January 2018, 2018-01-00, 20180101, 2018-01, Volume:
22, Issue:
1
Journal Article
Peer reviewed
Open access
Recent advances in mapping cortical areas in the human brain provide a basis for investigating the significance of their spatial arrangement. Here we describe a dominant gradient in cortical features ...that spans between sensorimotor and transmodal areas. We propose that this gradient constitutes a core organizing axis of the human cerebral cortex, and describe an intrinsic coordinate system on its basis. Studying the cortex with respect to these intrinsic dimensions can inform our understanding of how the spectrum of cortical function emerges from structural constraints.
Advances in neuroimaging technologies and analytics have enabled the discovery of gradients in microstructure, connectivity, gene expression, and function in the human cerebral cortex.
The notion that functional processing hierarchies are confined to sensorimotor systems is challenged by recent descriptions of global hierarchies, extending throughout transmodal association areas.
An innovative line of research has uncovered a cortical hierarchy in the temporal domain that accounts for spatially distributed functional specialization.
We discuss methods to determine L‐M‐N coordinate systems for current sheet crossings observed by the Magnetospheric Multiscale (MMS) spacecraft mission during ongoing reconnection, where eL is the ...direction of the reconnecting component of the magnetic field, B, and eN is normal to the magnetopause. We present and test a new hybrid method, with eL estimated as the maximum variance direction of B (MVAB) and eN as the direction of maximum directional derivative of B, and then adjust these directions to be perpendicular. In the best case, only small adjustment is needed. Results from this method, applied to an MMS crossing of the dayside magnetopause at 1305:45 UT on 16 October 2015, are discussed and compared with those from other methods for which eN is obtained by other means. Each of the other evaluations can be combined with eL from MVAB in a generalized hybrid approach to provide an L‐M‐N system. The quality of the results is judged by eigenvalue ratios, constancy of directions using different data segments and methods, and expected sign and magnitude of the normal component of B. For this event, the hybrid method appears to produce eN accurate to within less than 10°. We discuss variance analysis using the electric current density, J, or the J × B force, which yield promising results, and minimum Faraday residue analysis and MVAB alone, which can be useful for other events. We also briefly discuss results from our hybrid method and MVAB alone for a few other MMS reconnection events.
Plain Language Summary
We discuss methods for determining coordinate systems in order to study magnetic reconnection events at the magnetopause, the boundary between the ionized gas in the region of space dominated by the Earth's magnetic field and the ionized gas coming from the solar wind. We introduce a new method that combines results from multiple methods in order to determine the three coordinate directions in space. We demonstrate this method by applying it to an event observed by the Magnetospheric Multiscale spacecraft on 16 October 2015 and at other times.
Key Points
Methods to determine L‐M‐N current sheet coordinates are described and tested
Quality of results is judged by eigenvalue ratios and consistency using different data intervals and methods and with the geophysical context
For the interval examined here, the uncertainty of the normal direction was at least several degrees but probably less than 10°
Art and design professional education can not keep up with the development speed of the industry, and there is no reference to the market demand data, failing to keep pace with the times, which ...brings many negative impacts on the employment of students. This paper suggests an art design professional education model that incorporates VR interactive scene technology for this reason. Through the double camera, we simulate the visual principle of the human eye, collect three-dimensional data from VR interactive scenes, and use the image coordinate system and pixel coordinate system conversion operations to pre-process the collected data. The optimal layout solution is sought by adjusting the layout to generate a realistic 3D model of the teaching scene and to realize the construction of the VR interactive scene. The principle and implementation process of the art professional education model supported by the VR interactive scene is elaborated, and the experimental comparison method is used to empirically analyze the art and design professional education model integrating VR technology. The results show that there is a significant difference between the experimental group and the control group in the dimensions of adaptability (0.004) and uniqueness (0.044) of design thinking and the cultivation of design thinking ability (0.016) (P<0.05), which indicates that the art and design professional education model integrating the VR scene interaction technology constructed in this paper has a significant effect on the enhancement of design thinking ability of college students.
The position and attitude information obtained by the position and orientation system (POS) are defined by using the navigation coordinate system, but the actual production application is generally ...carried out under the map projection frame. Therefore, it is necessary to transform POS data into the map projection frame before it is applied in practice. Considering the complexity of the existing algorithms, and the geocentric coordinate systems that are currently widely used, such as WGS84 and CGCS2000, this letter proposes a simplified transformation method (ST-method) for the POS attitude transformation. It is obviously different from the classical Legat's method which is widely used at present. The algorithm in this letter can be called one-step transformation method, in which the geocentric coordinate system and the local tangent plane coordinate system are not involved. The conversion process has been deeply analyzed and the conversion formula is deduced, directly from navigation coordinate system to projection coordinate system. Compared with the classical methods, the most important contribution of this letter is to simplify the conversion process, and the experimental results show that the proposed method can achieve the same effect as the existing methods with no loss of accuracy.
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