Journal articles on the topic 'Euler principal axis'
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Iz, H., C. Shum, X. Ding, and C. Dai. "Orientation of the Geometrically Best fitting Triaxial Lunar Ellipsoid with Respect to the Mean Earth/Polar Axis Reference Frame." Journal of Geodetic Science 1, no. 1 (March 1, 2011): 52–58. http://dx.doi.org/10.2478/v10156-010-0007-2.
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Orientation of the Geometrically Best fitting Triaxial Lunar Ellipsoid with Respect to the Mean Earth/Polar Axis Reference FrameThis study provides new estimates for the orientation of a geometrically best fitting lunar triaxial ellipsoid with respect to the mean Earth/polar axis reference frame calculated from the footprint positions of the Chang'E-1 (CE-1), SELenological and ENgineering Explorer (SELENE) laser altimetry measurements and Unified Lunar Control Networks 2005, (ULCN 2005) station coordinates. The semi-principal axes of the triaxial ellipsoid and the coordinates of its geometric center are also calculated simultaneously. All the estimated parameters from all three data sets are found to be consistent. In particular, the RMS differences of the semi-principal axes of the triaxial ellipsoids and the locations of their geometric centers from solutions with and without modeling Euler angles (orientation of the triaxial ellipsoid) using uniformly distributed laser altimetry (LAL) footprints are 29 and 31 m respectively. The misclosures of all the solutions indicate a better fit for the triaxial ellipsoid to the footprint and station coordinates if the Euler angles are included in the models.
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Yin, Changchun. "Inherent nonuniqueness in magnetotelluric inversion for 1D anisotropic models." GEOPHYSICS 68, no. 1 (January 2003): 138–46. http://dx.doi.org/10.1190/1.1543201.
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This paper investigates the inherent nonuniqueness in the inversion of magnetotelluric (MT) measurements over an earth with a layered anisotropic resistivity distribution. This kind of nonuniqueness arises from the fact that even accurate and complete data contain insufficient information to uniquely resolve the earth parameters. For a very simple anisotropic case, where all layers in the earth have at least one horizontal principal axis in common coinciding with the x‐ or y‐axis of the Cartesian coordinate system, the resolvable parameters or parameter combinations from MT surface observations are identified by analyzing the structure of the conductivity tensor of the earth and the differential equations the electromagnetic (EM) fields satify. It is found that for a layered anisotropic earth model, several parameters can be uniquely resolved from the MT inversion while others are nonresolvable. However, particular combinations of the nonresolvable parameters can be uniquely resolved. These theoretical findings on the parameter resolvability of MT anisotropic inversion are further verified by a number of numerical experiments using synthetic data and a nonlinear parameter estimation technique. For this purpose, I parameterize the resistivity tensor assigned to each layer of the earth with three principal resistivities and three Euler angles, and then use the three Euler angles, the logarithms of three principal resistivities, and the logarithmic thickness as inverse parameters. This guarantees that the layer thickness is positive and the resistivity tensor is positive‐definite, while at the same time the inverse parameters may span the whole real axis. Numerical inversion results for different anisotropic models also reveal the fact that the resolvable parameters and parameter combinations are invariant with respect to the starting model. This means that for different starting models, the inversion results for some earth parameters might be individually quite different; however, particular combinations of these parameters remain unchanged.
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Li, Yan Bin, Ren Song Zou, and Tong Jiang. "Influence on Inertia the Moment of Inertia Matrix of Three Degrees of Freedom Air-Bearing Testbed." Advanced Materials Research 706-708 (June 2013): 1393–96. http://dx.doi.org/10.4028/www.scientific.net/amr.706-708.1393.
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To improve the accuracy of attitude determination and control stabilization when simulating attitude motion of satellites in the space, the finite element model of the platform of 3-DOF spacecraft attitude control simulator was founded. Gravity field of air bearing testbed and formula for platform’s moment of inertia on the action of gravity was induced The result shows platform’s attitude accuracy error exist because of main principal axis of inertia change of direction.on the action of gravity, The more large value it is, the more error is .Error of inertia main axis changes as sine curve with the change of two horizontal Euler angle.
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Sun, Xiaofeng, Liang Tao, Yuanzhe Zhao, Jingyu Qu, Di Yao, and Zijian Li. "Numerical Simulation of Hole Cleaning of a Horizontal Wellbore Model with Breakout Enlargement Section." Mathematics 11, no. 14 (July 12, 2023): 3070. http://dx.doi.org/10.3390/math11143070.
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Horizontal wells are more likely than vertical wells to have enlarged wellbore sections due to borehole instability. However, there is scarce research on borehole cleaning of horizontal wells with enlarged wellbore sections. In this paper, we establish a horizontal wellbore model with a breakout enlargement section using field borehole diameter data. We used the three-dimensional computational fluid dynamics (CFD) method and the Realizable k-ε turbulence model with the Euler–Euler approach to simulate the effects of the drilling fluid circulation return speed and the spinning speed of the drill pipe on the cutting movement of conventional horizontal wells and horizontal wells with a breakout enlargement section. The simulation results demonstrate that increasing the drilling fluid circulation return speed and the spinning speed of the drill pipe does not significantly improve the hole cleaning impact for horizontal wells with a breakout enlargement section. We analyzed the effects of the enlargement ratio, ellipticity, and principal axis orientation on the borehole cleaning effect of horizontal wells with a breakout enlargement section. The results show that the cleaning impact is better when the enlargement ratio is lower; moreover, the ellipticity is larger and the principal axis orientation is perpendicular to the gravity direction. This paper fills a gap in the existing theory of hole cleaning in horizontal wells and provides a theoretical basis for improving the hole cleaning effect in actual drilling processes.
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Wu, Jianwei, Fuyun Liu, Yong Deng, and Lin Gan. "Calculation of the principal moment of inertia and Euler angles of the centre inertia principal axis system: design and implementation of the algorithm." International Journal of Materials and Structural Integrity 9, no. 1/2/3 (2015): 180. http://dx.doi.org/10.1504/ijmsi.2015.071119.
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Nyaban, Christian Emile, Théophile Ndougsa-Mbarga, Marcelin Bikoro-Bi-Alou, Stella Amina Manekeng Tadjouteu, and Stephane Patrick Assembe. "Multi-scale analysis and modelling of aeromagnetic data over the Bétaré-Oya area in eastern Cameroon, for structural evidence investigations." Solid Earth 12, no. 4 (April 6, 2021): 785–800. http://dx.doi.org/10.5194/se-12-785-2021.
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Abstract. This study was carried out in the Lom series in Cameroon, at the border with Central African Republic, located between the latitudes 5∘30′–6∘ N and the longitudes 13∘30′–14∘45′ E. A multi-scale analysis of aeromagnetic data combining tilt derivative, Euler deconvolution, upward continuation, and 2.75D modelling was used. The following conclusions were drawn. (1) Several major families of faults were mapped. Their orientations are ENE–WSW, E–W, NW–SE, and N–S with a NE–SW prevalence. The latter are predominantly sub-vertical with NW and SW dips and appear to be prospective for future mining investigations. (2) The evidence of compression, folding, and shearing axis was concluded from superposition of null contours of the tilt derivative and Euler deconvolution. The principal evidence of the local tectonics was due to several deformation episodes (D1, D2, and D4) associated with NE–SW, E–W, and NW–SE events, respectively. (3) Depths of interpreted faults range from 1000 to 3400 m. (4) Several linear structures correlating with known mylonitic veins were identified. These are associated with the Lom faults and represent the contacts between the Lom series and the granito-gneissic rocks; we concluded the intense folding was caused by senestral and dextral NE–SW and NW–SE stumps. (5) We propose a structural model of the top of the crust (schists, gneisses, granites) that delineates principal intrusions (porphyroid granite, garnet gneiss, syenites, micaschists, graphite, and garnet gneiss) responsible for the observed anomalies. The 2.75D modelling revealed many faults with a depth greater than 1200 m and confirmed the observations from reduced-to-Equator total magnetic intensity (RTE-TMI), tilt derivative, and Euler deconvolution. (6) We developed a lithologic profile of the Bétaré-Oya basin.
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Ferretti, Roberta, and Silvana G. Dellepiane. "Multitemporal Volume Registration for the Analysis of Rheumatoid Arthritis Evolution in the Wrist." International Journal of Biomedical Imaging 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/7232751.
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This paper describes a method based on an automatic segmentation process to coregister carpal bones of the same patient imaged at different time points. A rigid registration was chosen to avoid artificial bone deformations and to allow finding eventual differences in the bone shape due to erosion, disease regression, or other eventual pathological signs. The actual registration step is performed on the basis of principal inertial axes of each carpal bone volume, as estimated from the inertia matrix. In contrast to already published approaches, the proposed method suggests splitting the 3D rotation into successive rotations about one axis at a time (the so-called basic or elemental rotations). In such a way, singularity and ambiguity drawbacks affecting other classical methods, for instance, the Euler angles method, are addressed. The proposed method was quantitatively evaluated using a set of real magnetic resonance imaging (MRI) sequences acquired at two different times from healthy wrists and by choosing a direct volumetric comparison as a cost function. Both the segmentation and registration steps are not based on a priori models, and they are therefore able to obtain good results even in pathological cases, as proven by the visual evaluation of actual pathological cases.
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Krasavin, V. V., and A. V. Krasavin. "Study of the elastic properties of hexagonal metal single crystals." Industrial laboratory. Diagnostics of materials 85, no. 9 (September 28, 2019): 29–35. http://dx.doi.org/10.26896/1028-6861-2019-85-9-29-35.
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Hexagonal metals (e.g., Be, Zr, Ti) are widely used in the nuclear industry, space and aircraft engineering (in manufacturing of the structural elements operating under extreme conditions). A promising way to improve the quality of products made of them is to improve the physical properties of materials using the natural anisotropy of metal single crystals. The results of studying anisotropy and a comparative analysis of the technical characteristics of the elastic properties of single crystals of hexagonal metals are presented. The equations of the elastic compliance matrix components are derived in the explicit form for arbitrary crystallographic direction proceeding from transformations of the elastic compliance tensor in the principal axes to a new arbitrary coordinate system with a subsequent use of Euler angles. Analytical expressions are presented for the technical characteristics of the elastic properties (shear and Young's moduli, Poisson's ratio) of the single crystals of 10 hep metals for an arbitrary crystallographic direction. The axial symmetry of the characteristics about the hexagonal axis is revealed. The sums of the elastic compliance coefficients which determine the shear moduli and the Poisson's ratios in two mutually perpendicular directions are constant in any crystallographic plane of the single crystal. A comparative analysis of the anisotropy of the elastic properties of single crystals of the studied group of metals revealed auxetic properties of Zn and Be single crystals and the region of crystallographic directions of uniaxia tension, leading to an auxetic effect The auxetic effect in Zn was observed under tension in the directions of the plane perpendicular to the hexagonal axis of the single crystal. The planes of the auxetic effect manifestation in Be single crystals are perpendicular to the directions making an angle of 45° with the hexagonal axis.
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Adiga, Samyuktha, Dominic Aebi, and David L. Bryce. "EFGShield — A program for parsing and summarizing the results of electric field gradient and nuclear magnetic shielding tensor calculations." Canadian Journal of Chemistry 85, no. 7-8 (July 1, 2007): 496–505. http://dx.doi.org/10.1139/v07-069.
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A computer program (EFGShield) is described that simplifies and summarizes the output from electric field gradient (EFG) and nuclear magnetic shielding tensor calculations performed independently using existing quantum chemical software. In addition to summarizing tensor magnitudes according to conventions commonly used by solid-state NMR spectroscopists, the program provides Euler angles relating the orientations of the EFG and shielding tensor principal axis systems (PAS). An atomic coordinate file is generated that also contains dummy atoms representing the orientations of the EFG and shielding tensor PASs in the molecular framework. We demonstrate the functionality of the program using calculations of the chlorine EFG and shielding tensors for strontium chloride dihydrate and calcium chloride dihydrate. Several models of the chloride environment in these compounds are tested, including those where point charges are used to represent the extended three-dimensional lattices within the self-consistent charge field perturbation approach. The results highlight both the shortcomings and successes of traditional localized orbital-based basis sets in the description of the NMR properties of extended systems. We anticipate that EFGShield will be a useful tool for spectroscopists using quantum chemical software to aid in the interpretation of experimental data.Key words: quantum chemical calculations, computer program, electric field gradient tensor, quadrupolar coupling constant, nuclear magnetic shielding tensor, Euler angles, alkaline earth chloride hydrates.
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Carretero, Paula, and Ildefonso Castro. "A New Approach to Rotational Weingarten Surfaces." Mathematics 10, no. 4 (February 12, 2022): 578. http://dx.doi.org/10.3390/math10040578.
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Weingarten surfaces are those whose principal curvatures satisfy a functional relation, whose set of solutions is called the curvature diagram or the W-diagram of the surface. Making use of the notion of geometric linear momentum of a plane curve, we propose a new approach to the study of rotational Weingarten surfaces in Euclidean 3-space. Our contribution consists of reducing any type of Weingarten condition on a rotational surface to a first-order differential equation on the momentum of the generatrix curve. In this line, we provide two new classification results involving a cubic and an hyperbola in the W-diagram of the surface characterizing, respectively, the non-degenerated quadric surfaces of revolution and the elasticoids, defined as the rotational surfaces generated by the rotation of the Euler elastic curves around their directrix line. As another application of our approach, we deal with the problem of prescribing mean or Gauss curvature on rotational surfaces in terms of arbitrary continuous functions depending on distance from the surface to the axis of revolution. As a consequence, we provide simple new proofs of some classical results concerning rotational surfaces, such as Euler’s theorem about minimal ones, Delaunay’s theorem on constant mean curvature ones, and Darboux’s theorem about constant Gauss curvature ones.
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Lidström, Per. "Frames of reference in multibody dynamics." Mathematics and Mechanics of Solids 24, no. 1 (November 7, 2017): 98–151. http://dx.doi.org/10.1177/1081286517731485.
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In this paper, a discussion is undertaken concerning the use of so-called floating frames of reference in the calculation of the kinetic and elastic energies of parts in a multibody system. The use of floating frames may simplify the calculation of the elastic energy, although sometimes at the expense of more elaborate expressions for the kinetic energy. These expressions may involve terms that couple the motion of the floating frame and the relative motion of the part. The choice of a floating frame may be arbitrary but in order to obtain as simple expressions as possible some care must be taken. When a (flexible) part is connected to a rigid part one may use a frame in which the rigid part is at rest. If so then one has, in general, to deal with coupling terms in the kinetic energy for the flexible part. There is one unique frame in which these coupling terms disappear. This frame is called the principal frame of reference. Relative to this frame the kinetic energy of the part is minimal compared to the kinetic energy relative to other frames. Two independent proofs of this property are presented. The principal frame is defined by the associated change of frame mapping. This mapping is given a full characterization. It may however be cumbersome to calculate the kinetic energy relative to the principal frame. A method for doing this is designated. A frame that has been given some attention in the literature is the principal axis frame of reference. In this paper, a full characterization of this frame and its relation to the principal frame is given. Two examples of an Euler–Bernoulli beam in rotational motion are presented and compared in the light of the theoretical findings of this paper. In conventional presentations of mechanics the Euclidean spaces associated with different frames of reference are taken to be identical. In this paper this assumption is abandoned and different frames of reference will correspond to different Euclidean spaces. From a conceptual point of view this is a natural step to take in order to increase clarity and generality. It automatically includes the dependence of the reference placement on the frame of reference. This approach has been analyzed in a previous paper by the present author. References to this paper will appear whenever needed for. Consequences of this approach are investigated in terms of transformation formulas for kinematical and dynamical quantities.
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Radzevich, Stephen. "Principal accomplishments in the scientific theory of gearing." MATEC Web of Conferences 287 (2019): 01001. http://dx.doi.org/10.1051/matecconf/201928701001.
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An in-depth analysis of the accomplishments in the theory of gearing has been undertaken by the author. The main results of the performed analysis are outlined in the paper in a chronological order. Two periods of time are proposed to be considered: pre-Eulerian and post-Eulerian time of the evolution of the gear art. No principal accomplishments in the theory of gearing were attained in the pre-Eulerian period of evolution of gearing. It is stated that scientific theory of gearing is originated from the publication by Leonhard Euler of two of his famous papers (1760). The main theorem of parallel-axes gearing, or, in other words, the “conjugate action law”, is loosely attributed to R. Willis (1841), which is not correct. Ch. Camus was the first (1733), who has carried out a research on this subject, however he failed to formulate this law of gearing correctly. In the final form the theorem was known to L. Euler and to F. Savaryr. Therefore, it is proposed to refer to the main theorem of parallel-axes gearing as to the “Camus-Euler-Savaryr theorem of gearing” (or just as to the “CES-theorem of gearing”, for simplicity). A huge mistake in the theory of gearing was committed by T. Olivier (1842). The effect of this mistake onto the evolution of the theory of gearing is discussed. Contributions by G. Grant (1887), and by V. Shishkovt (1948), that is, his well-known equation of contact, n·VΣ=0, are outlined. Introduced in around 2008, concept of the operating base pitch in a gear pair considered in detail. Latest accomplishments in the theory of gearing are summarized and briefly discussed in the paper. These accomplishments form the foundation of the self-consistent scientific theory of gearing (Radzevich, S.P., 2012, 2018). The scientific theory of gearing is not threatened with destruction, but only superstructure and development are extected (every scientific theory features this property).
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Courtillot, Vincent, Jean-Louis Le Mouël, Fernando Lopes, and Dominique Gibert. "On the Nature and Origin of Atmospheric Annual and Semi-Annual Oscillations." Atmosphere 13, no. 11 (November 15, 2022): 1907. http://dx.doi.org/10.3390/atmos13111907.
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This paper proposes a joint analysis of variations of global sea-level pressure (SLP) and of Earth’s rotation (RP), expressed as the coordinates of the rotation pole (m1, m2) and length of day (lod). We retain iterative singular spectrum analysis (iSSA) as the main tool to extract the trend, periods, and quasi periods in the data time series. SLP components are a weak trend, seven quasi-periodic or periodic components (∼130, 90, 50, 22, 15, 4, 1.8 years), an annual cycle, and its first three harmonics. These periods are characteristic of the space-time evolution of the Earth’s rotation axis and are present in many characteristic features of solar and terrestrial physics. The amplitudes of the annual SLP component and its three first harmonics decrease from 93 hPa for the annual to 21 hPa for the third harmonic. In contrast, the components with pseudo-periods longer than a year range between 0.2 and 0.5 hPa. We focus mainly on the annual and, to a lesser extent, the semi-annual components. The annual RP and SLP components have a phase lag of 152 days (half the Euler period). Maps of the first three components of SLP (that together comprise 85% of the data variance) reveal interesting symmetries. The trend is very stable and forms a triskeles structure that can be modeled as Taylor–Couette flow of mode 3. The annual component is characterized by a large negative anomaly extending over Eurasia in the NH summer (and the opposite in the NH winter) and three large positive anomalies over Australia and the southern tips of South America and South Africa in the SH spring (and the opposite in the SH autumn), forming a triskeles. The semi-annual component is characterized by three positive anomalies (an irregular triskeles) in the NH spring and autumn (and the opposite in the NH summer and winter), and in the SH spring and autumn by a strong stable pattern consisting of three large negative anomalies forming a clear triskeles within the 40–60∘ annulus formed by the southern oceans. A large positive anomaly centered over Antarctica, with its maximum displaced toward Australia, and a smaller one centered over Southern Africa, complement the pattern. Analysis of iSSA components of global sea level pressure shows a rather simple spatial distribution with the principal forcing factor being changes in parameters of the Earth’s rotation pole and velocity. The flow can probably best be modeled as a set of coaxial cylinders arranged in groups of three (triskeles) or four and controlled by Earth topography and continent/ocean boundaries. Flow patterns suggested by maps of the three main iSSA components of SLP (trend, annual, and semi-annual) are suggestive of Taylor–Couette flow. The envelopes of the annual components of SLP and RP are offset by four decades, and there are indications that causality is present in that changes in Earth rotation axis lead force pressure variations.
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Abdelrahman, Kamal, Reda Abdu Yousef El-Qassas, Mohammed S. Fnais, Peter Andráš, and Ahmed M. Eldosouky. "Geological Structures Controlling Au/Ba Mineralization from Aeromagnetic Data: Harrat ad Danun Area, Saudi Arabia." Minerals 13, no. 7 (June 26, 2023): 866. http://dx.doi.org/10.3390/min13070866.
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Positive and negative magnetic anomalies occupied the total aeromagnetic (TM) map of the Harrat ad Danun area, Saudi Arabia. Reduction to the pole (RTP) maps display the range of magnetic values (−312.4 to 209.4 nT) that vary in shape, size, and magnitude. These anomalies generally follow the NNW–SSE (Red Sea axis trend), NE–SW, and NNE–SSW trends. The NNW-SSE linear negative and positive magnetic anomalies could be brought on by buried faults, shear zones, or subsurface dikes. In the central part, the position of Au and Ba mineralization was connected to this trend. It is concluded that the principal structures are represented by the NNW–SSE, NE–SW, and NNE–SSW tendencies. Based on gridded RTP magnetic data, the 2-D power spectrum was computed and revealed the frequency of the near-surface and deep magnetic components. It is believed that the depths of the shallow and deep magnetic sources are typically 80 m and 570 m, respectively. Additional negative and positive magnetic anomalies with varied amplitudes and frequencies, trending in the NNW–SSE, ENE–WSW, and NE–SW directions, are seen when the high-pass and low-pass maps are closely examined. Many faults in various directions cut into these anomalies. The occurrence of negative linear magnetic anomalies (−36.6 nT to −137.3 nT) at this depth (80 m) is also confirmed by this map. The TDR filter and the Euler deconvolution method were used to identify the horizontal variations in magnetic susceptibility as well as the source position and depth of magnetic sources. The linear clustering rings are thought to be caused by contacts or faults with depths between 1 m to 474 m that are oriented WNW–ESE, NNE–SSW, and NNW–SSE. These faults or contacts are thought to be particularly prominent in the western, eastern, southern, northern, and central zones. The majority of felsic and mafic dikes are found to be connected to subsurface structures, showing that three structural trends—WNW–ESE, NNE–SSW, and NNW–SSE—affect the studied area. This demonstrates that important features and shear zones control the majority of Saudi Arabia’s gold deposits. A negative magnetic anomaly that is centered in the area, trending NNW–SSE and crossing the NNE–SSW fault, is connected to the plotted gold and barite mineralization in the study area. This may imply that these two tendencies are responsible for mineralization. This result raises the possibility of mineralization in the NNW negative magnetic feature located in the western part of the area. The occurrence of gold and barite was significantly impacted by the NNW–SSE and NNE–SSW structural lineaments.
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Giorgio, Ivan. "A discrete formulation of Kirchhoff rods in large-motion dynamics." Mathematics and Mechanics of Solids 25, no. 5 (February 3, 2020): 1081–100. http://dx.doi.org/10.1177/1081286519900902.
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A nonlinear model for the dynamics of a Kirchhoff rod in the three-dimensional space is developed in the framework of a discrete elastic theory. The formulation avoids the use of Euler angles for the orientation of the rod cross-sections to provide a computationally singularity-free parameterization of rotations along the motion trajectories. The material directions related to the principal axes of the cross-sections are specified using auxiliary points that must satisfy constraints enforced by the Lagrange multipliers method. A generalization of this approach is presented to take into account Poisson’s effect in an orthotropic rod. Numerical simulations are performed to test the presented formulation.
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Scott, J. A. "Miscellaneous triangle properties." Mathematical Gazette 94, no. 529 (March 2010): 103–11. http://dx.doi.org/10.1017/s0025557200007191.
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In this note we will discuss five topics from triangle geometry and occasionally encounter something new. Areal coordinates (presented as Appendix A in [1]) will be used throughout, with the exception of the final section where it is advantageous to employ Cartesians.The topics are:(1) examples of collinearities where the distance ratios for important points vary with triangle shape;(2) a pencil of lines which includes the Fermat, Napoleon and Vecten axes;(3) two more circles related to the Lester circle;(4) the family of rectangular hyperbolae which circumscribe the triangle of reference ABC and whose principal member is the Kiepert hyperbola [2];(5) Cartesian coordinates leading to a solution of the ‘Euler disc problem’ [3].
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Mokrova, S. M., R. P. Petrov, and V. N. Milich. "Algorithm for determining the orientation elements of an infrared image obtained from a drone using reference points." Geodesy and Cartography 958, no. 4 (May 20, 2020): 41–50. http://dx.doi.org/10.22389/0016-7126-2020-958-4-41-50.
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The article deals with the algorithm for determining the exterior and interior orientation elements of an infrared image obtained from an unmanned aerial vehicle using four reference points. The idea of the proposed algorithm is to determine the true position of the image by the defined three-dimensional spatial coordinates of the reference points in the image at the time of shooting. The image plane is built up on the defined points. The coordinates of the principal point of the image are calculated by making a perpendicular from the perspective center to the plane of the image. The focal length is equal to the length of this perpendicular. Euler angles characterizing the position of the camera at the time of shooting are calculated after determining the axes’ directions of the inclined image coordinate system. The proposed algorithm is effective even in the case when all the elements of the image orientation are unknown. Calculations of the image elements on model examples with different initial data show high accuracy. The possibility of obtaining the necessary accuracy for the orthotransformation procedure was confirmed on real images.
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ORLANDI, P. "Energy spectra power laws and structures." Journal of Fluid Mechanics 623 (March 6, 2009): 353–74. http://dx.doi.org/10.1017/s0022112008005016.
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Direct numerical simulations (DNS) of two inviscid flows, the Taylor–Green flow and two orthogonal interacting Lamb dipoles, together with the DNS of forced isotropic turbulence, were performed to generate data for a comparative study. The isotropic turbulent field was considered after the transient and, in particular, when the velocity derivative skewness oscillates around −0.5. At this time, Rλ ≈ 257 and a one decade wide k−5/3 range was present in the energy spectrum. For the inviscid flows the fields were considered when a wide k−3 range was achieved. This power law spectral decay corresponds to infinite enstrophy and is considered one of the requirements to demonstrate that the Euler equations lead to a finite time singularity (FTS). Flow visualizations and statistics of the strain rate tensor and vorticity components in the principal axes of the strain rate tensor (λ, λ) were used to classify structures. The key role of the intermediate component 2 is demonstrated by its good correlation with enstrophy production. Filtering of the fields shows that the slope of the power law is directly connected to self-similar structures, whose radius of curvature is smaller the steeper the spectrum.
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Karthikeyan, M. P., R. Venkatesan, V. Vijayakumar, Logesh Ravi, and V. Subramaniyaswamy. "White blood cell detection and classification using Euler’s Jenks optimized multinomial logistic neural networks." Journal of Intelligent & Fuzzy Systems 39, no. 6 (December 4, 2020): 8333–43. http://dx.doi.org/10.3233/jifs-189152.
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Due to the wide acceptance of White Blood Cells (WBCs) in disease diagnosis, detection and classification of WBC are hot topic. Existing methodologies have some drawbacks such as significant degree of error, higher accuracy, time bound and higher misclassification rate. A WBCs detection and classification called, Jenks Optimized Logistic Convolutional Neural Network (JO-LCNN) method has proposed. Initally, Eulers Principal Axis is used as a convolution model to obtain a rotation invariant form of image by differentiating the background and RBCs, then eliminating them which leaves only the WBCs. By eliminating the wanton features, inherent features are detected contributing to minimum misclassification rate. According to above, Jenks Optimization function is used as a pooling model to obtain feature map for lower resolution. Therefore JO-LCNN is used for removing tiny objects in image and complete nuclei. Finally, Multinomial Logistic classifier is used to classify five types of classes by means of loss function and updating weight according to the loss function, therefore classifying with higher accuracy rate. Using LISC database for WBCs with different parameters as classification accuracy, false positive rate and time complexity are performed. Result shows that JO-LCNN, efficiently improves accuracy with less time, misclassification rate than the state-of-art methods.
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Herrera-Sandate, P., D. Vega-Morales, A. L. De-Leon-Ibarra, P. Valdes-Torres, L. A. Chavez-Alvarez, I. D. J. Hernandez-Galarza, R. Pineda-Sic, and D. Á. Galarza-Delgado. "POS1446 ANTHROPOMETRIC MEASUREMENTS IN UPPER EXTREMITY REHABILITATION OF PATIENTS WITH RHEUMATIC DISEASES." Annals of the Rheumatic Diseases 80, Suppl 1 (May 19, 2021): 1007.1–1007. http://dx.doi.org/10.1136/annrheumdis-2021-eular.1301.
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Background:The chronic nature of rheumatic diseases has a negative impact in quality of life. Pain and loss of function in the upper extremity cause a progressive difficulty to perform daily activities, often requiring integral physical rehabilitation programs. Anthropometric measurements habitually take prolonged periods of time, given the extensive nature of physical examination in rheumatic patients. It is unknown which factors are most efficient to better reflect the functional status of the rheumatic patient.Objectives:Determine the most efficient anthropometric measurements in the upper extremity to assess the functional status of rheumatic patients in rehabilitation programs.Methods:Thirty-six patients were recruited from Rheumatology consultation of University Hospital “Dr. José Eleuterio González” in Monterrey, Mexico. Patients had a complete physical examination by a board-certified rheumatologist, which referred patients to Physical Rehabilitation consultation if necessary. A cross-sectional study was carried out in these patients with Disabilities of the Arm, Shoulder and Hand (DASH) questionnaire (1), measurement of ranges of motion (ROM) and hand strength with the Mathiowetz protocol (2). Analysis was performed through Principal Components Analysis including Total Variance Explained (TVE), Rotated Component Matrix (RCM) and dendrograms.Results:From the total of patients, 34 (94.4%) were women with a mean age of 34 years (SD 11.33). The most common diagnosis was rheumatoid arthritis (47.2%) followed by osteoarthritis (8.3%). The mean disability score in DASH was 29.3% (DE 23.36). The TVE analysis found that 3 elements explained 48.6% of the total variance, and 13 elements explained 89.4%. RCM correlations among hand strength parameters ranged from 0.51 to 0.93, whereas ROM correlation values were below 0.4. Graph 1 depicts data dispersion for ROM, grip strength and pinch gauge by dynamometer.Graph 1.Two main clusters are observed in the RCM plot of the data. In the center and superior to the x axis, a conglomeration corresponding to ROM is shown, consisting of radial and ulnar deviation; flexion, extension, abduction and adduction in carpal bones, metacarpophalangeal joints, and proximal and distal interphalangeal joints of the five fingers of both hands, accordingly. To the right and across the x axis, another cluster depicts the grip strength and tip, key, and lateral pinch gauge of the fingers according to the Mathiowetz protocol. Closeness of data points portray a higher similarity among variances in the second cluster.Conclusion:Hand strength is the most efficient parameter to assess the functional status of the upper extremity in rheumatic patients in rehabilitation programs.References:[1]Arreguín Reyes, R., López López, C. O., Alvarez Hernández, E., Medrano Ramírez, G., Montes Castillo, M., & Vázquez-Mellado, J. (2012). Evaluation of hand function in rheumatic disease. Validation and usefulness of the Spanish version AUSCAN, m-SACRAH and Cochin questionnaires. Reumatologia clinica, 8(5), 250–254. https://doi.org/10.1016/j.reuma.2012.03.005[2]Mathiowetz, V., Kashman, N., Volland, G., Weber, K., Dowe, M., & Rogers, S. (1985). Grip and pinch strength: normative data for adults. Archives of physical medicine and rehabilitation, 66(2), 69–74.Disclosure of Interests:None declared
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Kaan, E., T. Brunekreef, J. Drylewicz, L. Van den Hoogen, H. Leavis, J. M. Van Laar, M. Van der Vlist, H. Otten, and M. Limper. "AB0117 ASSOCIATION OF AUTOANTIBODIES WITH THE IFN SIGNATURE AND NETOSIS IN PATIENTS WITH SYSTEMIC LUPUS ERYTHEMATOSUS." Annals of the Rheumatic Diseases 82, Suppl 1 (May 30, 2023): 1237.2–1238. http://dx.doi.org/10.1136/annrheumdis-2023-eular.2799.
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BackgroundSystemic lupus erythematosus (SLE) is an autoimmune disease characterized by a variety of disease symptoms and an unpredictable clinical course. SLE can lead to premature death as the result of disease activity or because of treatment side effects. This underlines the urgency to identify patients at risk for a complicated disease course, and the need to tailor therapy. Stratification based on immunological manifestations such as autoantibodies, upregulation of type I interferon (IFN) regulated genes (IFN signature) and neutrophil extracellular trap (NET) formation via NETosis can help to improve treatment outcome in SLE.ObjectivesHere we study the association between SLE-related autoantibodies, the IFN signature and NET formation in patients with SLE, which could lead to improved tools for patient stratification and more targeted treatment options.MethodsWe studied the association between the IFN signature and plasma induced NET formation with 57 autoantibodies in 25 patients with SLE. The presence of an IFN signature was determined using the sum of standardized mRNA expression of IFI44L, IFITM1, SERPING1, and LY6E in monocytes from SLE patients. Plasma induced NET formation was studied with quantitative live imaging. The threshold for the presence of an IFN signature or NET formation were both set at 2 SD above the mean of a group of healthy controls. With principal component analysis (PCA) and hierarchical clustering we associated autoantibody concentrations with the IFN signature and NET formation. This study was a separate analysis from larger cohorts, of which results have been previously published.[1,2]ResultsWe observed two distinct clusters with the PCA: one cluster contained mostly patients with an IFN signature, and another cluster contained a mix of patients with (IFN) and without (noIFN) an IFN signature. Patients with (NET) and without (noNET) plasma induced NET formation were equally distributed between the clusters. PC1 explains 22.7% of total variability, and is mainly driven by antibodies against histones, RibP2, RibP0, EphB2, RibP1, PCNA, dsDNA, and nucleosome. Hierarchical cluster analysis confirmed the two clusters (Figure 1). In addition, we found a trend towards increased concentrations of autoantibodies against EphB2, RibP1, and RNP70 in patients with an IFN signature. We found a negative correlation of NET formation with anti-FcER and anti-PmScl100.ConclusionWe identified a subgroup of patients with an IFN signature who express increased concentrations of antibodies against DNA and RNA-associated proteins. We did not find positive associations between autoantibodies and plasma induced NET formation. Our study further strengthens the evidence of a correlation between RNA-binding autoantibodies and the IFN signature. As the IFN signature currently is not part of the standard follow-up for patients, partially due to its associated costs, a profile of DNA and RNA-binding autoantibodies might be used for patient stratification, especially related to anti-IFN treatment.References[1]Brunekreef, T., et al. (2021). “Microarray testing in patients with systemic lupus erythematosus identifies a high prevalence of CpG DNA-binding antibodies.” Lupus Sci Med 8(1).[2]van der Linden, M., et al. (2018). “Neutrophil extracellular trap release is associated with antinuclear antibodies in systemic lupus erythematosus and anti-phospholipid syndrome.” Rheumatology (Oxford) 57(7): 1228-1234.Figure 1.A distinct autoantibody pattern is present in a subgroup of patients with an IFN signature. Footnote: Heatmap of Z-scores for 57 autoantibodies in 25 SLE patients. Vertical axis shows clustering of patients based on IFN signature (blue) or NET formation (orange/brown). Horizontal axis represents clustering based on autoantibody profiles.Acknowledgements:NIL.Disclosure of InterestsNone Declared.
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Telegin, A. I. "Formalism of Writing Out of Manipulators Dynamic Equation." Bulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control & Radioelectronics 21, no. 4 (November 2021): 52–68. http://dx.doi.org/10.14529/ctcr210405.
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The problem of cumbersome equations of dynamics for manipulation systems of industrial robots (manipulators) with translational and rotational joints is solved. A new formalism for writing out the equations of dynamics of manipulators by using of guide cosines is proposed. Examples of writing out equations of dynamics of manipulators with guid cosines are given. The equations of dynamics in relative angles of rotation of bodies are obtained with the help of these guide cosines by applying their properties. These manipulators have from three to six degrees of freedom. In their equations of dynamics the geometric, kinematic, static and inertial parameters are explicit. The multipliers for accelerations and products of velocities are optimal in the sense of the minimum of arithmetic operations (additions and multiplications) that are needed for their calculations in the written out equations of dynamics. JS-code and method for verification of the equations of dynamics of manipulators written in analytical form are proposed. The problem is that when the equations are written out manually, errors and oversights in the intermediate entries and the final result are possible. Therefore it is necessary to check the results of writing out for absence of errors, i.e. to perform verification of formulas for calculation of constitutive equations of dynamics. To do this, we can use software designed to calculate the generalized driving forces of manipulators, i.e. to solve the first problem of dynamics. Such software is offered as a web-application, in which JS-function is used for verification of the equations of dynamics of manipulators. The method of verification of formulas to calculate the generalized forces of gravity and multipliers (coefficients) for generalized accelerations and products of generalized velocities in the equations of dynamics is developed. An example of verification of the equations of dynamics of the universal manipulator with six degrees of freedom in space is given. Aim. The aim of research is to develop a formalism for writing out the analytical form of the equations of the manipulators’ dynamics in the guide cosines of the principal axes of the coupled body coordinate systems, whose coefficients contain the minimum number of arithmetic operations. Research methods. The methods of research refer to vector and analytic mechanics of absolutely solid systems, to vector algebra, and to systems analysis and programming in scripting languages. Results. The results contain two proved statements, in which there are the formulas and the methodology that allow us to write manually the equations of dynamics of manipulators with three and six degrees of mobility both in guiding cosines and in generalized coordinates. In both cases it is impossible to simplify the obtained equations. Conclusion. The offered analytical types of the equations of dynamics occupy several lines. By the known classical formalisms (Lagrange, Appel, Nielsen, Newton-Euler, etc.) it is practically impossible to obtain similar results because of the large number of complex mathematical operations in their implementation and the cumbersomeness of the resulting formulas.
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Murakami, Hidenori, Oscar Rios, and Thomas Joseph Impelluso. "A Theoretical and Numerical Study of the Dzhanibekov and Tennis Racket Phenomena1." Journal of Applied Mechanics 83, no. 11 (September 8, 2016). http://dx.doi.org/10.1115/1.4034318.
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This paper presents a complete explanation of the Dzhanibekov and the tennis racket phenomena. These phenomena are described by Euler's equation for an unconstrained rigid body that has three distinct moment of inertia values. In the two phenomena, the rotations of a body about the principal axes that correspond to the largest and the smallest moments of inertia are stable. However, the rotation about the axis corresponding to the intermediate principal moment of inertia becomes unstable, leading to the unexpected rotations that are the basis of the phenomena. If this unexpected rotation is not explained from a complete perspective which accounts for the relevant physical and mathematical aspects, one might misconstrue the phenomena as a violation of the conservation of angular momenta. To address this, the phenomenon is investigated using more precise mathematical and graphical tools than those employed previously. The torque-free Euler equations are integrated using the fourth-order Runge–Kutta method. Then, a recovery equation is applied to obtain the rotation matrix for the body. By combining the geometrical solutions with numerical simulations, the unexpected rotations observed in the Dzhanibekov and the tennis racket experiments are shown to preserve the conservation of angular momentum.
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McGinnis, Ryan, N. C. Perkins, and Kevin King. "Reconstructing Free-Flight Angular Velocity from a Miniaturized Wireless Accelerometer." Journal of Applied Mechanics 79, no. 4 (May 11, 2012). http://dx.doi.org/10.1115/1.4006162.
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The theory governing the torque-free motion of a rigid body is well established, yet direct experimental measurement in the laboratory remains an obvious challenge. This paper addresses this challenge by presenting a novel miniature wireless inertial measurement unit (IMU) that directly measures the motion of a rigid body during free-flight. The IMU incorporates three-axis sensing of acceleration and three-axis sensing of angular velocity with a microcontroller and an RF transceiver for wireless data transmission to a host computer. Experiments consider a rigid body that is spun up by hand and then released into free-flight. The measured rotational dynamics from the IMU are carefully benchmarked against theoretical predictions. This benchmarking reveals that the angular velocity directly measured by the angular rate gyros lies within 6% of that predicted by the (Jacobi elliptic function) solutions to the Euler equations. Moreover, experimentally constructed polhodes elegantly illustrate the expected stable precession for rotations initiated close to the major or minor principal axes and the unstable precession for rotations initiated close to the intermediate axis. We then present a “gyro-free” design that employs a single, triaxial accelerometer to reconstruct the angular velocity during free-flight. A measurement theory is presented and validated experimentally. Results confirm that the angular velocity can be reconstructed with exceedingly small errors (less than 2%) when benchmarked against direct measurements using angular rate gyros. The simpler gyro-free design addresses restrictions imposed by rate gyro cost, size, and measurement range and may enable high-volume commercial applications of this technology in instrumented baseballs, basketballs, golf balls, footballs, soccer balls, softballs, and the like.
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Bağdatli, S. M., E. Özkaya, and H. R. Öz. "Dynamics of Axially Accelerating Beams With an Intermediate Support." Journal of Vibration and Acoustics 133, no. 3 (March 31, 2011). http://dx.doi.org/10.1115/1.4003205.
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The transverse vibrations of an axially accelerating Euler–Bernoulli beam resting on simple supports are investigated. The supports are at the ends, and there is a support in between. The axial velocity is a sinusoidal function of time varying about a constant mean speed. Since the supports are immovable, the beam neutral axis is stretched during the motion, and hence, nonlinear terms are introduced to the equations of motion. Approximate analytical solutions are obtained using the method of multiple scales. Natural frequencies are obtained for different locations of the support other than end supports. The effect of nonlinear terms on natural frequency is calculated for different parameters. Principal parametric resonance occurs when the velocity fluctuation frequency is equal to approximately twice of natural frequency. By performing stability analysis of solutions, approximate stable and unstable regions were identified. Effects of axial velocity and location of intermediate support on the stability regions have been investigated.
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Ismail, Abdelaziz I., Tarek S. Amer, and Wael S. Amer. "Advanced investigations of a restricted gyrostatic motion." Journal of Low Frequency Noise, Vibration and Active Control, February 28, 2023, 146134842311601. http://dx.doi.org/10.1177/14613484231160135.
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In this work, we present advanced investigations and treatments for the problem of a restricted vibrating motion of a connected gyrostat with a spring. It is supposed that the gyrostat spins slowly about the minor or major principal axis of the inertia ellipsoid. The gyrostat is acted upon by a gyrostatic couple vector besides the action of Newtonian and electromagnetic fields. The approach of the large parameter is applied to obtain the periodic solutions for the governing system of equations of motion of the gyrostat. A geometric illustration using the angles of Euler is given for such motion to evaluate and analyze the gyrostatic motion at any instant. The analysis of the obtained solutions is considered in terms of numerical data throughout computer programs. Characterized parametric data are assumed through one of the numerical methods for obtaining numerical solutions that prove the validity of the analytical obtained periodic solutions. The obtained solutions, besides the phase diagrams, have been drawn to describe these solutions’ periodicity and stability procedures. The novelty of this work comes from the imposition of a new initial condition that does not restrict movement around the dynamic symmetry axis. This assumption allows the use of a new technique for the solution called the large parameter. This technique gives solutions in a completely new domain that are different from the ones studied in previous works.
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Ma, Fengqun, Handong Tan, Wenxin Kong, and Depeng Zhu. "3D pole-pole responses of buried anisotropic targets and various anisotropic backgrounds in direct-current resistivity survey." Journal of Geophysics and Engineering, April 18, 2023. http://dx.doi.org/10.1093/jge/gxad030.
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Abstract Many rocks often have the electrical anisotropy property that produces quite different responses from the electrical isotropic rocks. We applied an advanced modeling method to calculate the apparent resistivity responses over an anisotropic target in a homogenous isotropic backgound and an isotropic target embedded in different anisotropic host rocks. We demonstrated comprehensive modeling experiments to characterize the responses of surface pole-pole surveys to the buried targets in different geological backgrounds, which vary in the principal resistivities and Euler angles of the targets or the host rocks. Our modeling results show that: (1) the location of current injection controls the apparent resistivity images in value and shape; (2) almost circle-contours or more or less elongated contours appear in the apparent resistivity images for the anisotropic targets; (3) the isotropic target embedded in the anisotropic host rock generates some radial patterns from the current injection point; (4) the anisotropy strike angles can be obtained from the symmetry axis of the apparent resistivity contours;.(5) multiple locations of current injections throughout the detection region are necessary for the surface pole-pole survey to avoid misleading data interpretation.
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Pak, Myong Chol, A. J. Giacomin, M. A. Kanso, and Hak Chol Pak. "Large-amplitude oscillatory shear flow from general rigid bead-rod theory." Physics of Fluids 35, no. 8 (August 1, 2023). http://dx.doi.org/10.1063/5.0165131.
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Oscillatory shear flow, performed at small-amplitude, interrogates polymeric liquids in their equilibrium states. The fluid responds in sinusoidal shear stress waves whose amplitude and phase lead depend on the dimensionless frequency (called the Deborah number). By contrast, this same flow field, performed at large-amplitude, probes departures from the equilibrium state, and the fluid responds with shear stress in the form of a Fourier series, whose component amplitudes and phase leads depend on both the dimensionless frequency (called the Deborah number) and the dimensionless shear rate amplitude (called the Weissenberg number). The physics of these departures from equilibrium in an oscillatory shear flow may be explained by (i) chain disentanglement or (ii) motion along the polymer chain axes (called reptation) or (iii) macromolecular orientation. Of these radically different and yet otherwise equally effective approaches, only (iii) allows the macromolecular structure to be varied arbitrary so that the effect of molecular architecture on the rheology can be explored. Though much has been written about a large-amplitude oscillatory shear flow, we understand little about the role of molecular structure on the measured behaviors, and this has limited its usefulness. In this work, we explain the higher harmonics of both the shear stress (first and third), the first normal stress differences (zeroth, second, and fourth), and the second normal stress differences (zeroth and second) arriving at analytical expressions for all three. These expressions, written in dimensionless form, express the dimensionless rheological responses in large-amplitude oscillatory shear flow in terms of the ratio of the two principal macromolecular moments of inertia. To get these expressions, we derive the first five terms of the orientation distribution function, by solving the general diffusion equation in Euler coordinates. We then integrate in phase space with this orientation result to arrive at our expression for the first seven terms of the polymer contribution to the extra stress tensor. From this tensor, we next write down the Fourier coefficients for the shear stress responses, and the normal stress difference responses, in large-amplitude oscillatory shear flow for a suspension of macromolecules sculpted from a rigid bead-rod structure of any arbitrary axisymmetric shape.