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Using a grounded theory approach, the authors investigate the nature and consequences of brand love. Arguing that research on brand love needs to be built on an understanding of how consumers actually experience this phenomenon, they conduct two qualitative studies to uncover the different elements (\"features\") of the consumer prototype of brand love. Then, they use structural equations modeling on survey data to explore how these elements can be modeled as both first-order and higher-order structural models. A higher-order model yields seven core elements: self-brand integration, passion-driven behaviors, positive emotional connection, long-term relationship, positive overall attitude valence, attitude certainty and confidence (strength), and anticipated separation distress. In addition to these seven core elements of brand love itself, the prototype includes quality beliefs as an antecedent of brand love and brand loyalty, word of mouth, and resistance to negative information as outcomes. Both the firstorder and higher-order brand love models predict loyalty, word of mouth, and resistance better, and provide a greater understanding, than an overall summary measure of brand love. The authors conclude by presenting theoretical and managerial implications.

The interaction of ocean surface waves produces pressure fluctuations at the seafloor capable of generating seismic waves in the solid Earth. The accepted mechanism satisfactorily explains secondary microseisms of the Rayleigh type, but it does not justify the presence of transversely polarized Love waves, nevertheless widely observed. An explanation for two-thirds of the worldwide ambient wave field has been wanting for over a century. Using numerical simulations of global-scale seismic wave propagation at unprecedented high frequency, here we explain the origin of secondary microseism Love waves. A small fraction of those is generated by boundary force-splitting at bathymetric inclines, but the majority is generated by the interaction of the seismic wave field with three-dimensional heterogeneity within the Earth.We present evidence for an ergodic model that explains observed seismic wave partitioning, a requirement for full-wave field ambient-noise tomography to account for realistic source distributions.

This paper presents a new triangular nonlinear shell finite element with a novel kinematic model suitable for simulation with large displacements and rotations, herein introduced as “T6-3iKL”. This element has 6 nodes, a quadratic displacement field, and a linear rotation field based on Rodrigues incremental rotation parameters, giving in total 21 degrees of freedom. The novelty of this shell element concerns a new kinematic model with properties from Kirchhoff-Love shell theory, making it possible to eliminate the drilling DOF in the rotation field (compared to Mindlin-Reissner models), approximating the rotation continuity between adjacent elements by a single scalar and allowing multiple branch connections in the mesh, making this element very simple and interesting, with no artificial parameters imputed by the code (such as penalties or Lagrange multipliers). The element permits the implementation of different material constitutive equations, including elastic anisotropic models, and the thickness of the shell is optionally allowed to change through the simulation. The model developed in this article is numerically implemented and the results compared to different references in multiple examples, showing the consistency and reliability of the new formulation. It is believed that this new versatile triangular shell element, with no necessity of artificial penalty calibration, simple kinematics, a relatively small number of DOFs, geometric exactness, the possibility to use 3D material constitutive models, and easy connection with multiple branched shells and beams, implemented together with reliable mesh generation, may be an effective option for shell simulation in many engineering applications.

We describe novel numerical methods for solving a class of high-order time-dependent PDEs on general geometries, which involve second-order derivatives in time and up-to fourth-order derivatives in space. This type of PDEs are widely used in applications such as the Boussinesq equation and in modeling thin-walled elastic structures such as beams, plates and shells, etc. High-order spatial derivatives together with general geometries bring a number of challenges for many numerical methods. In this paper, we resolve these challenges by discretizing the spatial derivatives in domains with general geometries using the composite overlapping grid method. The discretization on overlapping grids requires numerical interpolations to couple solutions on different component grids. However, the presence of interpolation equations breaks the symmetry of the overall spatial discretization, causing numerical instability in time-stepping schemes. To address this, a fourth-order hyper-dissipation term is included for stabilization. Investigation of incorporating the hyper-dissipation term into several time-stepping schemes for solving the semi-discrete system leads to the development of a series of algorithms. Accurate and stable numerical boundary conditions for Dirichlet and Neumann type boundaries are also developed for general geometries. Quadratic eigenvalue problems for a simplified model problem on 1D overlapping grids are considered to reveal the weak instability caused by interpolation between component grids. This model problem is also investigated for the stabilization effects of the proposed algorithms. Carefully designed numerical experiments and two benchmark problems concerning the Kirchhoff–Love plate model are presented to demonstrate the accuracy and efficiency of our approaches. This work shows that finite difference methods on overlapping grids are well-suited for solving high-order PDEs in complex domains for realistic applications.

PurposeThis study aims to perform dynamic response analysis of damaged rigid-frame bridges under multiple moving loads using analytical based transfer matrix method (TMM). The effects of crack depth, moving load velocity and damping on the dynamic response of the model are discussed. The dynamic amplifications are investigated for various damage scenarios in addition to displacement time-histories.Design/methodology/approachTimoshenko beam theory (TBT) and Rayleigh-Love bar theory (RLBT) are used for bending and axial vibrations, respectively. The cracks are modeled using rotational and extensional springs. The structure is simplified into an equivalent single degree of freedom (SDOF) system using exact mode shapes to perform forced vibration analysis according to moving load convoy.FindingsThe results are compared to experimental data from literature for different damaged beam under moving load scenarios where a good agreement is observed. The proposed approach is also verified using the results from previous studies for free vibration analysis of cracked frames as well as dynamic response of cracked beams subjected to moving load. The importance of using TBT and RLBT instead of Euler–Bernoulli beam theory (EBT) and classical bar theory (CBT) is revealed. The results show that peak dynamic response at mid-span of the beam is more sensitive to crack length when compared to moving load velocity and damping properties.Originality/valueThe combination of TMM and modal superposition is presented for dynamic response analysis of damaged rigid-frame bridges subjected to moving convoy loading. The effectiveness of transfer matrix formulations for the free vibration analysis of this model shows that proposed approach may be extended to free and forced vibration analysis of more complicated structures such as rigid-frame bridges supported by piles and having multiple cracks.

Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio. In this paper, a full-scale isogeometric topology optimization (ITO) method based on Kirchhoff–Love shells for designing cellular tshin-shell structures with excellent damage tolerance ability is proposed. This method utilizes high-order continuous nonuniform rational B-splines (NURBS) as basis functions for Kirchhoff–Love shell elements. The geometric and analysis models of thin shells are unified by isogeometric analysis (IGA) to avoid geometric approximation error and improve computational accuracy. The topological configurations of thin-shell structures are described by constructing the effective density field on the control mesh. Local volume constraints are imposed in the proximity of each control point to obtain bone-like cellular structures. To facilitate numerical implementation, the p-norm function is used to aggregate local volume constraints into an equivalent global constraint. Several numerical examples are provided to demonstrate the effectiveness of the proposed method. After simulation and comparative analysis, the results indicate that the cellular thin-shell structures optimized by the proposed method exhibit great load-carrying behavior and high damage robustness.

Using body wave arrival times from 31 seismic events recorded on Mars by the InSight mission, combined with topography and gravity field modeling, we constrained lateral variations of crustal thickness through a Bayesian inversion approach. The parameterization of the seismic structure relies on quantities that influence the thermochemical evolution of Mars, enabling the seismic velocities and densities in the different planetary envelopes to be consistently linked through common physical assumptions. Compared to a 1D structure, models with lateral variations of crustal thickness show two possible interpretations of the thermal evolution of Mars, with either a hot or cold scenario at the present‐day. We found the hot scenario to be more compatible with InSight's radiotracking data and the tidal Love number. We relocated the marsquakes and derived maps of seismicity recorded by InSight, which is mostly located along or North of the boundary between the Northern lowlands and the Southern highlands. Plain Language Summary Thanks to the seismometer of the InSight mission, which recorded ground vibration measurements emanating from marsquakes and meteorite impacts during almost 4 years, the 1D interior structure of the crust, mantle, and core have been revealed. These models are mainly based on the assumption that the crustal thickness is similar everywhere on Mars. However, both the InSight lander and the most of the seismic events are located between the Northern lowlands and the Southern highlands where the crustal thickness varies widely, which can bias the interpretation of a 1D crustal model. In this study, combining the InSight seismic data with other independent geophysical measurements (topography and gravimetry data), we investigated to what extent the interior structure models are modified if lateral variations of crustal thickness are considered. Our results show that two different interpretations of Mars' thermal history can be considered, with either a hot or a cold scenario. We assessed the compatibility of our results with independent observations of oscillation of Mars' rotational axis, and found that the hot scenario is most likely. Key Points We infer lateral variation of Martian crustal thickness using InSight seismic data combined with topography and gravity field modeling Marsquakes are relocated and maps of the seismicity recorded by InSight are proposed Two families of models are found, leading to different interpretations of Mars' thermochemical evolution, with hot and cold scenarios

Love numbers h , k , and l are convenient parameters to assess the deformation of the Earth or other planet due to external perturbing forces. While the elastic Love numbers are used for tidal deformation, the correct amount of permanent tidal deformation can be assessed using the fluid Love numbers. Accurate values of the elastic Love numbers of Earth have been repeatedly attained for several Earth models, and also the fluid Love numbers h f and k f of the Earth were recently reported. In this short note, new evaluation of the Earth’s fluid Love number as well as secular Love number, both originally defined by Munk and MacDonald, is presented using updated values of the Earth’s physical property model and with minute enhancement in the formulation; ( h s , k s ) = ( 1.9437 , 0.9437 ) by their 1st approach and ( h f , k f ) = ( 1.9337 , 0.9337 ) by their 2nd approach. Through numerical calculations with gradual stepwise reduction in rigidity, the three fluid Love numbers of the Earth were determined as: ( h f , k f , l f ) = (1.935, 0.935, 1.07) for PREM and ( h f , k f , l f ) = (1.937, 0.937, 1.07) for ak135-F Earth models. In addition, the fluid Love numbers of other spherical harmonic degrees 0, 3, 4, and 5 were estimated. The permanent tide of the Earth ellipsoid due to the Moon and the Sun has been re-calculated: the vertical displacement of the permanent tide is 0.1924 m at the equator and - 0.3801 m at the pole, while the horizontal displacement of the permanent tide is found to be 0.317 m at mid-latitude.

Within the framework of Kirchhoff–Love plate theory, we analyze a variational model for elastic plates with rigid inclusions and interfacial cracks. The main feature of the model is a fully coupled nonpenetration condition that involves both the normal component of the longitudinal displacements and the normal derivative of the transverse deflection of the crack faces. Without making any artificial assumptions on the crack geometry and shape variation, we prove that the first-order shape derivative of the potential deformation energy is well defined and provide an explicit representation for it. The result is applied to derive the Griffith formula for the energy release rate associated with crack extension.