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Flow structures, nonlinear inertial waves and energy transfer in rotating spheres

Tianyi Li, Minping Wan, Shiyi Chen

Accepted Manuscript

[Abstract] (0) [FullText HTML] (0) [PDF 3845KB] (0)

Abstract:
We investigate flow structures, nonlinear inertial waves and energy transfer in a rotating fluid sphere, using a Galerkin spectral method based on helical-wave decomposition (HWD). Numerical simulations of flows in a sphere are performed with different system rotation rates, where a large-scale forcing is employed. For the case without system rotation, the intense vortex structures are tube-like. When a weak rotation is introduced, small-scale structures are reduced and vortex tubes tend to align with the rotation axis. As the rotation rate increases, a large-scale anticyclonic vortex structure is formed near the rotation axis. The structure is shown to be led by certain geostrophic modes. When the rotation rate further increases, a cyclone and an anticyclone emerge from the top and bottom of the boundary, respectively, where two quasi-geostrophic equatorially symmetric inertial waves dominate the flow. Based on HWD, effects of spherical confinement on rotating turbulence are systematically studied. It is found that the forward cascade becomes weaker as the rotation increases. When the rotation rate becomes larger than some critical value, dual energy cascades emerge, with an inverse cascade at large scales and a forward cascade at small scales. Finally, the flow behavior near the boundary is studied, where the average boundary layer thickness gets smaller when system rotation increases. The flow behavior in the boundary layer is closely related to the interior flow structures, which create significant mass flux between the boundary layer and the interior fluid through Ekman pumping.

Capturing the Baroclinic Effect in non-Boussinesq Gravity Currents

Shengqi Zhang, Zhenhua Xia

Accepted Manuscript

[Abstract] (2) [FullText HTML] (2) [PDF 0KB] (0)

Abstract:
Direct numerical simulations of two-dimensional gravity currents with small and medium density variations are performed using different non-Boussinesq buoyancy approximations. Taking the full low-Mach-number approximation as the reference, the accuracy of several buoyancy terms are examined. It is found that all considered buoyancy terms performed well in the cases with small density variation. In the cases with medium density variation, the classical gravitational Boussinesq's buoyancy term showed the lack of accuracy, and a simple correction did not make any improvement. In contrast, the recently introduced second-order buoyancy term showed a significantly higher accuracy. The present results and our previous derivations indicate that simple algebraic buoyancy approximations extended from the Boussinesq's gravitational buoyancy are unlikely to achieve an accuracy beyond first order. Instead, it seems necessary to solve at least one extra Poisson equation for buoyancy terms to capture the higher-order baroclinic effect. An approximate analysis is also provided to show the leading term of the non-Boussinesq effect corresponding to gravity.

A universal bifurcation mechanism arising from progressive hydroelastic waves

Zhan Wang

Accepted Manuscript

[Abstract] (13) [FullText HTML] (2) [PDF 0KB] (2)

Abstract:
A unidirectional, weakly dispersive nonlinear model is proposed to describe the supercritical bifurcation arising from hydroelastic waves in deep water. This model equation, including quadratic, cubic, and quartic nonlinearities, is an extension of the famous Whitham equation. The coefficients of the nonlinear terms are chosen to match with the key properties of the full Euler equations, precisely, the associated cubic nonlinear Schrödinger equation and the amplitude of the solitary wave at the bifurcation point. It is shown that the supercritical bifurcation, rich with Stokes, solitary, generalized solitary, and dark solitary waves in the vicinity of the phase speed minimum, is a universal bifurcation mechanism. The newly developed model can capture the essential features near the bifurcation point and easily be generalized to other nonlinear wave problems in hydrodynamics.

Effect of a rigid structure on the dynamics of a bubble beneath the free surface

Shi-Min Li, A-Man Zhang, Nian-Nian Liu

Accepted Manuscript

[Abstract] (22) [FullText HTML] (22) [PDF 0KB] (0)

Abstract:
The coupling effect between a pulsating bubble and a free surface near a rigid structure is a complicated physical process. In this study, the evolution of an underwater explosion bubble and the free surface near a rigid structure is modelled by the boundary integral method. An approach of 'double-node method' is used to maintain the stability of fluid-structure junction in the simulations, and meshes on the free surface and the structure are transformed to an open domain to ensure the calculation accuracy and efficiency. Validations are conducted against an underwater explosion experiment near a rigid structure. As a result, the simulations trace the jetting behaviour of the bubble and the rise of the free surface. Finally, the bubble migration and the height of the free surface for different structure draughts are analyzed.

A three-dimensional robust volume-of-fluid solver based on the adaptive mesh refinement

Xin Zhao

Accepted Manuscript

[Abstract] (26) [FullText HTML] (23) [PDF 0KB] (1)

Abstract:
The present study provides a three-dimensional volume-of-fluid method based on the adaptive mesh refinement technique. The projection method on the adaptive mesh is introduced for solving the incompressible Navier-Stokes equations. The octree structure mesh is employed to solve the flow velocities and the pressure. The developed solver is applied to simulate the deformation of the cubic droplet driven by the surface tension without the effect of the gravity. The numerical results well predict the shape evolution of the droplet.

A new strategy to strength-toughen metals: Tailoring disorder

Minqiang Jiang, Lanhong Dai

Accepted Manuscript

[Abstract] (28) [FullText HTML] (19) [PDF 0KB] (0)

Abstract:
Metals have been mankind’s most essential materials for thousands of years. In recent years, however, innovation-driven development of major national security strategy and core areas of the national economy is highly impeded by a shortage of advanced higher-strength-toughness metals. One of the main reasons is that metals inherently exhibit the inverted-relationship of strength-toughness. The emergence of two types of disordered metals: amorphous alloys and high entropy alloys, provides a fully-fresh strategy for strength-toughening by tailoring the topological and/or chemical disorder. In this paper, we first briefly review the history of strength-toughening of metals, and summarize the development route-map. We then introduce amorphous alloys and high entropy alloys, as well as some case studies in tailoring disorder to successfully achieve coexisting high strength and high ductility/toughness. Relevant challenges that await further research are summarized in concluding remarks.

Switchable dry adhesive based on shape memory polymer with hemispherical indenters for transfer printing

Hongyu Luo, Chenglong Li, Chuanqian Shi, Shuang Nie, Jizhou Song

Accepted Manuscript

[Abstract] (30) [FullText HTML] (27) [PDF 0KB] (0)

Abstract:
Transfer printing based on switchable adhesive is essential for developing unconventional systems, including flexible electronics, stretchable electronics, and micro light-emitting diode (LED) displays. Here we report a design of switchable dry adhesive based on shape memory polymer (SMP) with hemispherical indenters, which offers a continuously tunable and reversible adhesion through the combination of the preloading effect and the thermal actuation of SMP. Experimental and numerical studies reveal the fundamental aspects of design, fabrication, and operation of the switchable dry adhesive. Demonstrations of this adhesive concept in transfer printing of flat objects (e.g., silicon wafers), three-dimensional (3D) objects (e.g., stainless steel balls), and rough objects (e.g., frosted glasses) in two-dimensional (2D) or 3D layouts illustrate its unusual manipulation capabilities in heterogeneous material integration applications.

Multiscale mechanics of noncovalent interface in graphene oxide layered nanocomposites

ZeZhou He, YinBo Zhu, HengAn Wu

Accepted Manuscript

[Abstract] (38) [FullText HTML] (25) [PDF 0KB] (1)

Abstract:
Noncovalent interfaces play a vital role in inelastic deformation and toughening mechanisms in layered nanocomposites due to their dynamical recoverability. When interfacial engineering is applied to design layered nanocomposites, shear-lag analysis is usually implemented to evaluate the capability of interfacial loading transfer. Here, we introduce a multiscale shear-lag model that correlates macroscale mechanical properties with the molecular mechanisms to quantify the effects of interfacial configuration in graphene oxide (GO) layered nanocomposites. By investigating the mechanical responses of commensurate and incommensurate interfaces, we identify that the commensurate interface exhibits a pronounced size effect due to the nucleation and propagation of interfacial defects, whereas the incommensurate interface displays uniform deformation. Our predictions are further validated through large-scale molecular dynamics simulations for GO layered nanocomposites. This work demonstrates how size effects and interfacial configurations can be exploited to fabricate layered nanocomposites with superior mechanical properties despite relying on weak noncovalent interfaces.

Characteristics of Air-Water Flow in An Emptying Tank Under Different Conditions

Jialing Liang, Yiyi Ma, Yi Zheng

Accepted Manuscript

[Abstract] (54) [FullText HTML] (41) [PDF 0KB] (7)

Abstract:
This paper experimentally studied the features of air-water flow during the emptying of a water-filled prismatic tank with a bottom orifice under different conditions. The experiments were conducted with both circular and elliptical orifices, with and without ventilation. The evolution of bubbles, water pressure variation, and water level change with time were recorded in the experiments and analyzed. Based on the results, the evolution of bubbles could be mainly divided into three stages of formation, deformation, and decomposition. Ventilation was found important to the emptying process, with which the drainage efficiency was much higher than that under the unventilated condition. Additionally, under the unventilated condition, the drainage efficiency with the circular orifice was slightly higher than that with the elliptical orifice.

Validation of Actuator Disc Circulation Distribution for Unsteady Virtual Blades model

A N Kusyumov, S A Kusyumov, S A Mikhailov, G N Barakos

Accepted Manuscript

[Abstract] (68) [FullText HTML] (44) [PDF 0KB] (3)

Abstract:
The actuator disc method is an engineering approach to reduce computer resources in Computational Fluid Dynamics (CFD) simulations of helicopter rotors or aeroplane propellers. Implementation of an actuator disc based on rotor circulation distribution allows for approximations to be made while reproducing the blade tip vortices. Radial circulation distributions can be formulated according to the nonuniform Heyson-Katzoff “typical load” in hover. In forward flight, the nonuniform disk models include “azimuthal” sin and cos terms to reproduce the blade cyclic motion. The azimuthal circulation distribution for a forward flight mode corresponds to trimmed conditions for the disk rolling and pitching moments. The amplitude of the cos harmonic is analysed and compared here with presented in references data and CFD simulations results.

Noether symmetry method for Birkhoffian systems in terms of generalized fractional operators

Chuan-Jing Song, Shi-Lei Shen

Accepted Manuscript

[Abstract] (81) [FullText HTML] (46) [PDF 0KB] (1)

Abstract:
Compared with the Hamiltonian mechanics and the Lagrangian mechanics, the Birkhoffian mechanics is more general. The Birkhoffian mechanics is discussed on the basis of the generalized fractional operators, which are proposed recently. Therefore, differential equations of motion within generalized fractional operators are established. Then, in order to find the solutions to the differential equations, Noether symmetry, conserved quantity, perturbation to Noether symmetry and adiabatic invariant are investigated. In the end, two applications are given to illustrate the methods and results.

Detection of Mechanical Stress in the Steel Structure of a Bridge Crane

Leopold Hrabovský, Daniel Čepica, Karel Frydrýšek

Accepted Manuscript

[Abstract] (73) [FullText HTML] (51) [PDF 0KB] (1)

Abstract:
A significant negative aspect in the operation of bridge-type cranes are the technical problems associated with wear of the wheels and the crane track, which causes crane skewing. The main causes of crane skewing include unevenness of the crane track, unequal loading of the traction drives depending on the position of the crane trolley, slips and different sizes of travel wheels and combinations of these causes. The paper presents a design solution that can be used to detect the magnitude of mechanical stress and deformation of the steel structure of the crane, caused by the effects of skewing. The mechanical stress generated by the transverse forces of the deformed geometric shape of the crane bridge structure is recorded by mechanical stress detectors installed in the inner corners of the crane bridge. The resulting electrical signal from element mechanical voltage detectors, loaded by axial forces, can be used for feedback control of separate crane travel drives controlled by frequency converters. The paper presents the calculation of the lateral transverse forces according to CSN 27 0103 and the determination of the values of mechanical stresses of the deformed steel structure of the crane bridge of a two-girder bridge crane using the finite element method in the program MSC.MARC 2019. The paper presents the structural and strength design of mechanical stress detectors and the conclusions of laboratory tests of axial force loading of mechanical stress detectors on the test equipment. At the same time, it presents records of the measured axial forces acting in the mechanical stress detectors, arising from the deformation and warping of the crane bridge by the known magnitude of the axial force acting on the crossbeam and from the deformation of the crane bridge caused by the crane operating modes.

Optimization of the forearm angle for arm wrestling using multi-camera stereo digital image correlation: a preliminary study

Zixiang Tong, Xinxing Shao, Zhenning Chen, Xiaoyuan He

Corrected proof , doi: 10.1016/j.taml.2021.100287

[Abstract] (125) [FullText HTML] (100) [PDF 0KB] (1)

Abstract:
This study analyzes the function of different muscles during arm wrestling and proposes a method to analyze the optimal forearm angle for professional arm wrestlers. We built a professional arm-wrestling platform to measure the shape and deformation of the skin at the biceps brachii of a volunteer in vivo during arm wrestling. We observed the banding phenomenon of arm skin strain during muscle contraction and developed a model to evaluate the moment provided by the biceps brachii. According to this model, the strain field of the area of interest on the skin was measured, and the forearm angles most favorable and unfavorable to the work of the biceps brachii were analyzed. This study demonstrates the considerable potential of applying DIC and its extension method to the in vivo measurement of human skin and facilitates the use of the in vivo measurement of skin deformation in various sports in the future.

Displacement reconstruction and strain refinement of clustering-based homogenization

Lei Zhang, Shaoqiang Tang

Corrected proof

[Abstract] (150) [FullText HTML] (130) [PDF 0KB] (5)

Abstract:
Recently proposed clustering-based methods provide an efficient way for homogenizing heterogeneous materials, yet without concerning the detailed distribution of the mechanical responses. With coarse fields of the clustering-based methods as an initial guess, we develop an iteration strategy to fastly and accurately resolve the displacement, strain and stress based on the Lippmann-Schwinger equation, thereby benefiting the local mechanical analysis such as the detection of the stress concentration. From a simple elastic case, we explore the convergence of the method and give an instruction for the selection of the reference material. Numerical tests show the efficiency and fast convergence of the reconstruction method in both elastic and hyper-elastic materials.

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Letter

Editorial: Fluid mechanics problems in wind energy

Theoretical and Applied Mechanics Letters 11 (2021) 100303. doi: 10.1016/j.taml.2021.100303

[Abstract] (79) [FullText HTML] (63) [PDF 3123KB] (9)

Abstract:

Coherent vorticity dynamics and dissipation in a utility-scale wind turbine wake with uniform inflow

Daniel Foti

Theoretical and Applied Mechanics Letters 11 (2021) 100292. doi: 10.1016/j.taml.2021.100292

[Abstract] (135) [FullText HTML] (109) [PDF 1911KB] (2)

Abstract:
The vorticity dynamics and its relationship to dissipation in the wake of a utility-scale wind turbine are investigated through large-eddy simulation. The vorticity dynamics is assessed through the enstrophy, which is related to the turbulent dissipation. The averaged enstrophy and turbulent dissipation are shown to be quantitatively similar in the wake. Using temporal phase averaging, the vorticity fluctuations are decomposed into coherent and random fluctuations with respect to the frequency of the tip vortices. The enstrophy in the tip vortices is dominated by coherent fluctuations, while the coherent fluctuations of root vortices are immediately saturated by the random vorticity fluctuations of the unstable hub vortex. The coherent strain rate has significant differences compared to the coherent enstrophy within one diameter downwind of blade tip, but the random enstrophy and strain rate are relatively similar. Differences in coherent enstrophy and strain rate decrease further from the rotor.

A quasi-coupled wind wave experimental framework for testing offshore wind turbine floating systems

C. Feist, F. Sotiropoulos, M. Guala

Theoretical and Applied Mechanics Letters 11 (2021) 100294. doi: 10.1016/j.taml.2021.100294

[Abstract] (183) [FullText HTML] (77) [PDF 2484KB] (6)

Abstract:
Two sets of experiments in the St. Anthony Falls Laboratory (SAFL) wave tank facility and atmospheric wind tunnel are integrated to provide a scaled representation of a floating wind turbine under heave and pitch motions due to ocean waves. The quasi-coupling is established by controlling the turbine rotor speed to generate a thrust force mimicking steady or fluctuating wind gusts in the wave tank, and by using two actuators to oscillate a miniature turbine in the wind tunnel. Measured pitch and heave motions under varying waves are scaled down using rotor geometry and the wake meandering frequency to study the effect of the floating platform kinematics on the evolution and characteristics of the oscillating turbine wake. For a limited case of experimental conditions results provide a phenomenological and quantitative description of the floating-turbine system under variable waves and simulated wind gusts. Specifically, we demonstrate that wind gusts contribute to increase the platform pitch range, and that periodic large scale flow patches of high and low momentum flow are generated by the oscillating rotor in the turbulent boundary layer and are coherently convected through the wake. Both mechanisms could amplify the pitch response of downwind floating turbine units within the offshore power plant, in particular if the wave and/or wind forcing frequencies happen to approach the pitch natural frequency of the floating system.

Platform motion minimization using model predictive control of a floating offshore wind turbine

Kamran Ali Shah, Ye Li, Ryozo Nagamune, Yarong Zhou, Waheed Ur Rehman

Theoretical and Applied Mechanics Letters 11 (2021) 100295. doi: 10.1016/j.taml.2021.100295

[Abstract] (98) [FullText HTML] (96) [PDF 1570KB] (4)

Abstract:
Wind turbines are installed offshore with the assistance of a floating platform to help meet the world's increasing energy needs. However, the incident wind and extra incident wave disturbances have an impact on the performance and operation of the floating offshore wind turbine (FOWT) in comparison to bottom-fixed wind turbines. In this paper, model predictive control (MPC) is utilized to overcome the limitation caused by platform motion. Due to the ease of control synthesis, the MPC is developed using a simplified model instead of high fidelity simulation models. The performance of the controller is verified in the presence of realistic wind and wave disturbances. The study demonstrates the effectiveness of MPC in reducing platform motions and power regulation of FOWTs.

Effects of a Rooftop Wind Turbine on the Dispersion of Air Pollutant behind a cube-shaped building

Shuaibin Zhang, Haoze Yang, Bowen Du, Mingwei Ge

Theoretical and Applied Mechanics Letters 11 (2021) 100296. doi: 10.1016/j.taml.2021.100296

[Abstract] (97) [FullText HTML] (73) [PDF 2427KB] (6)

Abstract:
The concentration distribution of urban air pollutants is closely related to people's health. As an important utilization form of urban wind power, rooftop wind turbines have been widely used in cities. The wake effect of the rooftop wind turbines will change the flow behind buildings and then affect the pollutant dispersion. To this end, the pollutant dispersion behind the building is studied via the computational fluid dynamics method. The actuator disk model and idealized cube are adopted to model the wind turbine and the building, respectively. The study shows that the rooftop wind turbine can reduce the pollutant mass fraction near the ground and the pedestrian level. Due to the wake effect of the rooftop wind turbine, the turbulent fluctuation behind the building is weakened, and the spanwise pollutant dispersion is suppressed. Besides, the rooftop wind turbine weakens the downwash movement of the building, which enhances the vertical pollutant dispersion.

Local topography-induced pressure gradient effects on the wake and power output of a model wind turbine

Tengfei Cai, Shyuan Cheng, Antonio Segalini, Leonardo P. Chamorro

Theoretical and Applied Mechanics Letters 11 (2021) 100297. doi: 10.1016/j.taml.2021.100297

[Abstract] (83) [FullText HTML] (73) [PDF 2639KB] (3)

Abstract:
Wind-tunnel experiments were performed to study the effect of favorable and adverse constant pressure gradients (PG) from local changes in the topography right downwind of a model wind turbine. Particle image velocimetry was used to characterize the near and intermediate wake regions. We explored five scenarios, two favorable, two adverse PG, and a case with negligible PG. Results show that the PGs induce a wake deflection and modulate the wake. They imposed a relatively small impact on the turbulence kinetic energy and kinematic shear stress but a comparatively dominant effect on the bulk flow on the flow recovery. Based on this, a simple formulation is used to describe the impact of PG on the wake. We modeled the base flow through a linearized perturbation method; the wake is obtained by solving a simplified, integrated streamwise momentum equation. This approach reasonably estimated the flow profile and PG-induced power output variations.

Closed-Form Solution for Shock Wave Propagation in Density-Graded Cellular Material Under Impact

Vijendra Gupta, Addis Kidane, Michael Sutton

Theoretical and Applied Mechanics Letters 11 (2021) 100288. doi: 10.1016/j.taml.2021.100288

[Abstract] (144) [FullText HTML] (103) [PDF 1517KB] (6)

Abstract:
Density-graded cellular materials have tremendous potential in structural applications where impact resistance is required. Cellular materials subjected to high impact loading result in a compaction type deformation, usually modeled using continuum-based shock theory. The resulting governing differential equation of the shock model is nonlinear, and density gradation further complicates the problem. Earlier studies have employed numerical methods to obtain the solution. In this study, an analytical closed-form solution is proposed to predict the response of density-graded cellular materials subjected to a rigid body impact. Solutions for the velocity of the impinging rigid body mass, the energy absorption capacity of the cellular material, and the incident stress are obtained for a single shock propagation. The results obtained are in excellent agreement with the existing numerical solutions found in the literature. The proposed analytical solution can be potentially used for parametric studies and for effectively designing graded structures to mitigate impact.

Alternating minimization for data-driven computational elasticity from experimental data: kernel method for learning constitutive manifold

Yoshihiro Kanno

Theoretical and Applied Mechanics Letters 11 (2021) 100289. doi: 10.1016/j.taml.2021.100289

[Abstract] (126) [FullText HTML] (117) [PDF 932KB] (0)

Abstract:
Data-driven computing in elasticity attempts to directly use experimental data on material, without constructing an empirical model of the constitutive relation, to predict an equilibrium state of a structure subjected to a specified external load. Provided that a data set comprising stress–strain pairs of material is available, a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie (Kanno 2021, Jpn. J. Ind. Appl. Math.). From the perspective of physical experiments, stress field cannot be directly measured, while displacement and force fields are measurable. In this study, we extend the previous kernel method to the situation that pairs of displacement and force, instead of pairs of stress and strain, are available as an input data set. A new regularized least-squares problem is formulated in this problem setting, and an alternating minimization algorithm is proposed to solve the problem.

On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge

Dian Xu, Zhuofan Ni, Yihao Li, Zhaoyang Hu, Yu Tian, Bo Wang, Rui Li

Theoretical and Applied Mechanics Letters 11 (2021) 100293. doi: 10.1016/j.taml.2021.100293

[Abstract] (99) [FullText HTML] (75) [PDF 1022KB] (2)

Abstract:
A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years. The method has yielded many new analytic solutions due to its rigorousness. In this study, the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge. The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied. The solution procedure incorporates separation of variables, symplectic eigen solution and superposition. The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems. The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use. The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.

Mei's symmetry theorem for time scales nonshifted mechanical systems

Yi Zhang

Theoretical and Applied Mechanics Letters 11 (2021) 100286. doi: 10.1016/j.taml.2021.100286

[Abstract] (175) [FullText HTML] (123) [PDF 398KB] (7)

Abstract:
We focus on Mei symmetry for time scales nonshifted mechanical systems within Lagrangian framework and its resulting new conserved quantities. Firstly, the dynamic equations of time scales nonshifted holonomic systems and time scales nonshifted nonholonomic systems are derived from the generalized Hamilton's principle. Secondly, the definitions of Mei symmetry on time scales are given and its criterions are deduced. Finally, Mei's symmetry theorems for time scales nonshifted holonomic conservative systems, time scales nonshifted holonomic nonconservative systems and time scales nonshifted nonholonomic systems are established and proved, and new conserved quantities of above systems are obtained. Results are illustrated with two examples.

Crack propagation simulation in brittle elastic materials by a phase field method

Xingxue Lu, Cheng Li, Ying Tie, Yuliang Hou, Chuanzeng Zhang

2019, 9(6): 339-352 doi: 10.1016/j.taml.2019.06.001

[Abstract](1164) [FullText HTML](663) [PDF 3845KB](81)

On the Weissenberg effect of turbulence

Yu-Ning Huang, Wei-Dong Su, Cun-Biao Lee

2019, 9(4): 236-245 doi: 10.1016/j.taml.2019.03.004

[Abstract](711) [FullText HTML](394) [PDF 2579KB](75)

Mechanistic Machine Learning: Theory, Methods, and Applications

2020, 10(3): 141-142 doi: 10.1016/j.taml.2020.01.041

[Abstract](6276) [FullText HTML](575) [PDF 3081KB](72)

Frame-indifference of cross products, rotations, and the permutation tensor