Approximate Methods for Center of Pressure Prediction of Multi-Segment Wings

2003 ◽  
Author(s):  
Sarah Blackmar ◽  
Mark Miller ◽  
William Blake
Keyword(s):  
Center Of Pressure ◽  
Approximate Methods

Center of Pressure Variations in High-Heeled Shoes

2011 ◽  
Author(s):  
Thilina W. Weerasinghe ◽  
Ravindra S. Goonetilleke
Keyword(s):  
Center Of Pressure

Full Optical Rotation Tensor at CCSD Level in the Modified Velocity Gauge

2020 ◽  
Author(s):  
Kaihua Zhang ◽  
Ty Balduf ◽  
Marco Caricato
Keyword(s):  
Electric Dipole ◽  
Optical Rotation ◽  
Electric Quadrupole ◽  
Polarizability Tensor ◽  
Dipole Polarizability ◽  
Difficult Case ◽  
Computationally Efficient ◽  
Rotation Tensor ◽  
Approximate Methods ◽  
Velocity Gauge

<div> <div> <p> </p><div> <div> <div> <p>This work presents the first simulations of the full optical rotation (OR) tensor at coupled cluster with single and double excitations (CCSD) level in the modified velocity gauge (MVG) formalism. The CCSD-MVG OR tensor is origin independent, and each tensor element can in principle be related directly to experimental measurements on oriented systems. We compare the CCSD results with those from two density functionals, B3LYP and CAM-B3LYP, on a test set of 22 chiral molecules. The results show that the functionals consistently overestimate the CCSD results for the individual tensor components and for the trace (which is related to the isotropic OR), by 10-20% with CAM-B3LYP and 20-30% with B3LYP. The data show that the contribution of the electric dipole-magnetic dipole polarizability tensor to the OR tensor is on average twice as large as that of the electric dipole-electric quadrupole polarizability tensor. The difficult case of (1S,4S)-(–)-norbornenone also reveals that the evaluation of the former polarizability tensor is more sensitive than the latter. We attribute the better agreement of CAM-B3LYP with CCSD to the ability of this functional to better reproduce electron delocalization compared with B3LYP, consistently with previous reports on isotropic OR. The CCSD-MVG approach allows the computation of reference data of the full OR tensor, which may be used to test more computationally efficient approximate methods that can be employed to study realistic models of optically active materials. </p> </div> </div> </div> </div> </div>

Solution of heat and mass transfer problems with non-linear coefficients

2019 ◽  
Vol 5 (4) ◽  
pp. 10-20
Author(s):  
Boris G. Aksenov ◽  
Yuri E. Karyakin ◽  
Svetlana V. Karyakina
Keyword(s):  
Mass Transfer ◽  
Exact Solution ◽  
Numerical Methods ◽  
Heat And Mass Transfer ◽  
Unknown Function ◽  
Comparison Theorems ◽  
Upper And Lower Bounds ◽  
Maximum Deviation ◽  
Approximate Methods ◽  
Nonmonotonic Dependence

Equations, which have nonlinear nonmonotonic dependence of one of the coefficients on an unknown function, can describe processes of heat and mass transfer. As a rule, existing approximate methods do not provide solutions with acceptable accuracy. Numerical methods do not involve obtaining an analytical expression for the unknown function and require studying the convergence of the algorithm used. The value of absolute error is uncertain. The authors propose an approximate method for solving such problems based on Westphal comparison theorems. The comparison theorems allow finding upper and lower bounds of the unknown exact solution. A special procedure developed for the stepwise improvement of these bounds provide solutions with a given accuracy. There are only a few problems for equations with nonlinear nonmonotonic coefficients for which the exact solution has been obtained. One of such problems, presented in this article, shows the efficiency of the proposed method. The results prove that the proposed method for obtaining bounds of the solution of a nonlinear nonmonotonic equation of parabolic type can be considered as a new method of the approximate analytical solution having guaranteed accuracy. In addition, the proposed here method allows calculating the maximum deviation from the unknown exact solution of the results of other approximate and numerical methods.

Introduction to Relativistic Quantum Chemistry

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Dirac Equation ◽  
Quantum Chemistry ◽  
Relativistic Theory ◽  
Density Functional ◽  
Relativistic Quantum ◽  
Relativistic Effects ◽  
Basis Sets ◽  
Spin Orbit ◽  
Approximate Methods ◽  
Nonrelativistic Theory

This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a good background in nonrelativistic theory. In addition to explaining the necessary theory in detail, at a level that the non-expert and the student should readily be able to follow, the book discusses the implementation of the theory and practicalities of its use in calculations. After a brief introduction to classical relativity and electromagnetism, the Dirac equation is presented, and its symmetry, atomic solutions, and interpretation are explored. Four-component molecular methods are then developed: self-consistent field theory and the use of basis sets, double-group and time-reversal symmetry, correlation methods, molecular properties, and an overview of relativistic density functional theory. The emphases in this section are on the basics of relativistic theory and how relativistic theory differs from nonrelativistic theory. Approximate methods are treated next, starting with spin separation in the Dirac equation, and proceeding to the Foldy-Wouthuysen, Douglas-Kroll, and related transformations, Breit-Pauli and direct perturbation theory, regular approximations, matrix approximations, and pseudopotential and model potential methods. For each of these approximations, one-electron operators and many-electron methods are developed, spin-free and spin-orbit operators are presented, and the calculation of electric and magnetic properties is discussed. The treatment of spin-orbit effects with correlation rounds off the presentation of approximate methods. The book concludes with a discussion of the qualitative changes in the picture of structure and bonding that arise from the inclusion of relativity.

scholarly journals Minimal shoes improve stability and mobility in persons with a history of falls

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Tomasz Cudejko ◽  
James Gardiner ◽  
Asangaedem Akpan ◽  
Kristiaan D’Août
Keyword(s):  
Fall Prevention ◽  
Postural Stability ◽  
Center Of Pressure ◽  
Stability Margin ◽  
Timed Up And Go ◽  
Balance Test ◽  
Margin Of Stability ◽  
Eyes Open ◽  
History Of ◽  
Falls In Older Adults

AbstractPostural and walking instabilities contribute to falls in older adults. Given that shoes affect human locomotor stability and that visual, cognitive and somatosensory systems deteriorate during aging, we aimed to: (1) compare the effects of footwear type on stability and mobility in persons with a history of falls, and (2) determine whether the effect of footwear type on stability is altered by the absence of visual input or by an additional cognitive load. Thirty participants performed standing and walking trials in three footwear conditions, i.e. conventional shoes, minimal shoes, and barefoot. The outcomes were: (1) postural stability (movement of the center of pressure during eyes open/closed), (2) walking stability (Margin of Stability during normal/dual-task walking), (3) mobility (the Timed Up and Go test and the Star Excursion Balance test), and (4) perceptions of the shoes (Monitor Orthopaedic Shoes questionnaire). Participants were more stable during standing and walking in minimal shoes than in conventional shoes, independent of visual or walking condition. Minimal shoes were more beneficial for mobility than conventional shoes and barefoot. This study supports the need for longitudinal studies investigating whether minimal footwear is more beneficial for fall prevention in older people than conventional footwear.

scholarly journals Effects of white Gaussian noise on dynamic balance in healthy young adults

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ziyou Zhou ◽  
Can Wu ◽  
Zhen Hu ◽  
Yujuan Chai ◽  
Kai Chen ◽  
...  
Keyword(s):  
Young Adults ◽  
Gaussian Noise ◽  
Center Of Pressure ◽  
Dynamic Balance ◽  
White Gaussian Noise ◽  
Fluctuation Analysis ◽  
Balance Performance ◽  
Short Term ◽  
Crossover Point ◽  
Short Time

AbstractIt has been known that short-time auditory stimulation can contribute to the improvement of the balancing ability of the human body. The present study aims to explore the effects of white Gaussian noise (WGN) of different intensities and frequencies on dynamic balance performance in healthy young adults. A total of 20 healthy young participants were asked to stand at a dynamic balance force platform, which swung along the x-axis with an amplitude of ± 4° and frequency of 1 Hz. Their center of pressure (COP) trajectories were recorded when they were stimulated by WGN of different intensities (block 1) and different frequencies (block 2). A traditional method and detrended fluctuation analysis (DFA) were used for data preprocessing. The authors found that only with 75–85 dB WGN, the COP parameters improved. WGN frequency did not affect the dynamic balance performance of all the participants. The DFA results indicated stimulation with 75 dB WGN enhanced the short-term index and reduced the crossover point. Stimulation with 500 Hz and 2500 Hz WGN significantly enhanced the short-term index. These results suggest that 75 dB WGN and 500 Hz and 2500 Hz WGN improved the participants’ dynamic balance performance. The results of this study indicate that a certain intensity of WGN is indispensable to achieve a remarkable improvement in dynamic balance. The DFA results suggest that WGN only affected the short-term persistence, indicating the potential of WGN being considered as an adjuvant therapy in low-speed rehabilitation training.

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