scholarly journals Explicit representation for the SO(3) rotation tensor of deformable bodies

2021 ◽  
Vol 111 ◽  
pp. 106606
Author(s):  
Bo-Hua Sun
Keyword(s):  
Explicit Representation ◽  
Rotation Tensor ◽  
Deformable Bodies

scholarly journals Explicit Representation of SO(3) Rotation Tensor for Deformable Bodies

2020 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Shear Deformation ◽  
Explicit Expression ◽  
Simple Shear ◽  
Deformation Gradient ◽  
Explicit Representation ◽  
Exponential Mapping ◽  
Rotation Tensor ◽  
Deformable Bodies ◽  
Simple Shear Deformation

Computing the rotation tensor is vital in the analysis of deformable bodies. This paper describes an explicit expression for the SO(3) rotation tensor R of the deformation gradient F, and successfully establishes an intrinsic relation between the exponential mapping Q = exp A and the deformation F. As an application, Truesdell's simple shear deformation is revisited.

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>

scholarly journals On the explicit representation of the trace space $$H^{\frac{3}{2}}$$ and of the solutions to biharmonic Dirichlet problems on Lipschitz domains via multi-parameter Steklov problems

2021 ◽  
Author(s):  
Pier Domenico Lamberti ◽  
Luigi Provenzano
Keyword(s):  
Fourier Series ◽  
Dirichlet Problem ◽  
Lipschitz Domain ◽  
Spectral Properties ◽  
Explicit Representation ◽  
Lipschitz Domains ◽  
Dirichlet Problems ◽  
Trace Space ◽  
In Series ◽  
Definition Of

AbstractWe consider the problem of describing the traces of functions in $$H^2(\Omega )$$ H 2 ( Ω ) on the boundary of a Lipschitz domain $$\Omega $$ Ω of $$\mathbb R^N$$ R N , $$N\ge 2$$ N ≥ 2 . We provide a definition of those spaces, in particular of $$H^{\frac{3}{2}}(\partial \Omega )$$ H 3 2 ( ∂ Ω ) , by means of Fourier series associated with the eigenfunctions of new multi-parameter biharmonic Steklov problems which we introduce with this specific purpose. These definitions coincide with the classical ones when the domain is smooth. Our spaces allow to represent in series the solutions to the biharmonic Dirichlet problem. Moreover, a few spectral properties of the multi-parameter biharmonic Steklov problems are considered, as well as explicit examples. Our approach is similar to that developed by G. Auchmuty for the space $$H^1(\Omega )$$ H 1 ( Ω ) , based on the classical second order Steklov problem.

scholarly journals Secondary Science Teachers’ Views on Environmental Citizenship in The Netherlands

2021 ◽  
Vol 13 (14) ◽  
pp. 7963
Author(s):  
Michiel van Harskamp ◽  
Marie-Christine P. J. Knippels ◽  
Wouter R. van Joolingen
Keyword(s):  
Science Teachers ◽  
Citizenship Education ◽  
Renewable Energy Sources ◽  
Explicit Representation ◽  
Secondary Science ◽  
Added Value ◽  
Face To Face ◽  
Secondary Science Teachers ◽  
Environmental Citizenship ◽  
Teacher Professional

Environmental Citizenship (EC) is a promising aim for science education. EC enables people not only to responsibly make decisions on sustainability issues—such as use of renewable energy sources—but also to take action individually and collectively. However, studies show that education for EC is challenging. Because our understanding of EC practice remains limited, an in-depth, qualitative view would help us better understand how to support science teachers during EC education. This study aims to describe current EC education practices. What do secondary science teachers think sustainability and citizenship entail? What are their experiences (both positive and negative) with education for EC? A total of 41 Dutch science teachers were interviewed in an individual, face-to-face setting. Analysis of the coded transcripts shows that most teachers see the added value of EC but struggle to fully implement it in their teaching. They think the curriculum is unsuitable to reach EC, and they see activities such as guiding discussions and opinion forming as challenging. Furthermore, science teachers’ interpretation of citizenship education remains narrow, thus making it unlikely that their lessons are successful in fostering EC. Improving EC education therefore may be supported by explicit representation in the curriculum and teacher professional development directed at its implementation.

scholarly journals Pattern discovery and disentanglement on relational datasets

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Andrew K. C. Wong ◽  
Pei-Yuan Zhou ◽  
Zahid A. Butt
Keyword(s):  
Machine Learning ◽  
Knowledge Base ◽  
Case Studies ◽  
Prediction Accuracy ◽  
Pattern Discovery ◽  
Explicit Representation ◽  
Human Cognition ◽  
Source Level ◽  
Low Volume

AbstractMachine Learning has made impressive advances in many applications akin to human cognition for discernment. However, success has been limited in the areas of relational datasets, particularly for data with low volume, imbalanced groups, and mislabeled cases, with outputs that typically lack transparency and interpretability. The difficulties arise from the subtle overlapping and entanglement of functional and statistical relations at the source level. Hence, we have developed Pattern Discovery and Disentanglement System (PDD), which is able to discover explicit patterns from the data with various sizes, imbalanced groups, and screen out anomalies. We present herein four case studies on biomedical datasets to substantiate the efficacy of PDD. It improves prediction accuracy and facilitates transparent interpretation of discovered knowledge in an explicit representation framework PDD Knowledge Base that links the sources, the patterns, and individual patients. Hence, PDD promises broad and ground-breaking applications in genomic and biomedical machine learning.

Note on the swimming of slender fish

1960 ◽  
Vol 9 (2) ◽  
pp. 305-317 ◽  
Author(s):  
M. J. Lighthill
Keyword(s):  
Swimming Speed ◽  
Critical Value ◽  
Slender Body ◽  
Vortex Wake ◽  
Frictional Drag ◽  
Slender Body Theory ◽  
Propulsive Efficiency ◽  
Deformable Bodies ◽  
Work Done ◽  
Body Theory

The paper seeks to determine what transverse oscillatory movements a slender fish can make which will give it a high Froude propulsive efficiency, $\frac{\hbox{(forward velocity)} \times \hbox{(thrust available to overcome frictional drag)}} {\hbox {(work done to produce both thrust and vortex wake)}}.$ The recommended procedure is for the fish to pass a wave down its body at a speed of around $\frac {5} {4}$ of the desired swimming speed, the amplitude increasing from zero over the front portion to a maximum at the tail, whose span should exceed a certain critical value, and the waveform including both a positive and a negative phase so that angular recoil is minimized. The Appendix gives a review of slender-body theory for deformable bodies.

THE APPLICATION OF PETRI NETS TO WORKFLOW MANAGEMENT

1998 ◽  
Vol 08 (01) ◽  
pp. 21-66 ◽  
Author(s):  
W. M. P. VAN DER AALST
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Business Processes ◽  
State Of The Art ◽  
Workflow Management ◽  
Explicit Representation ◽  
The Other ◽  
Application Domain ◽  
Analysis Techniques ◽  
The One

Workflow management promises a new solution to an age-old problem: controlling, monitoring, optimizing and supporting business processes. What is new about workflow management is the explicit representation of the business process logic which allows for computerized support. This paper discusses the use of Petri nets in the context of workflow management. Petri nets are an established tool for modeling and analyzing processes. On the one hand, Petri nets can be used as a design language for the specification of complex workflows. On the other hand, Petri net theory provides for powerful analysis techniques which can be used to verify the correctness of workflow procedures. This paper introduces workflow management as an application domain for Petri nets, presents state-of-the-art results with respect to the verification of workflows, and highlights some Petri-net-based workflow tools.

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