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Bohmian Quantum Gravity and Cosmology
Published in Xavier Oriols, Jordi Mompart, Applied Bohmian Mechanics, 2019
Nelson Pinto-Neto, Ward Struyve
The geometrical meaning of the lapse and shift is the following [16]. The unit vector field normal to the leaves is nµ = (1/N, − Ni/N). The lapse N(t, x) is the rate of change with respect to coordinate time t of the proper time of an observer with four-velocity nµ(t, x) at the point (t, x). The lapse function also determines the foliation. Lapse functions that differ only by a factor f(t) determine the same foliation. Lapse functions that differ by more than a factor f(t) determine different foliations. Ni(t, x) is the rate of change with respect to coordinate time t of the shift of the points with the same coordinates x when we go from one hypersurface to another. Different choices of Ni correspond to different choices of coordinates on the space-like hypersurfaces.
Fatigue of steel bridge infrastructure
Published in Hyun-Moo Koh, Dan M. Frangopol, Bridge Maintenance, Safety, Management, Health Monitoring and Informatics, 2008
Hyun-Moo Koh, Dan M. Frangopol
ABSTRACT: In this paper, we present a statistic model and preliminary analysis results of a prototype Structural Health Monitoring (SHM) system for the Nanpu Bridge in Shanghai, China. The proposed SHM system consists of two key components, i.e. data acquisition system and the statistic model that form basis elements of a damage identification and assessment system. In the prototype SHM system, the Real-Time Kinematic Global Positioning System (RTK GPS) was employed to acquire in-situ ambient dynamic responses of the civil structures and huge amount of raw data was obtained during field data acquisition. Three dimensional coordinate time series were obtained from these raw data and used in this paper for the creation of the statistic model and the analysis of the dynamics system of the civil structures. In a recent practice conducted in September 2006, 14 dual frequency GPS receivers were employed to acquire in-situ ambient dynamic responses of the Nanpu Bridge for four consecutive days. There are 12 monitoring points that were localized along the Nanpu Bridge and two other GPS receivers were installed on two well measured stationary locations as the reference stations. The data processing was carried out to obtain the coordinate time series of these 12 monitoring points.
Advanced Topic: A Moon-Based Imaging of Earth’s Surface
Published in Kun-Shan Chen, Radar Scattering and Imaging of Rough Surfaces, 2020
To define the Moon-based SAR’s imaging geometry as shown in Figure 10.1, it is critical to obtain the accurate position vectors of the ground target and SAR system under a spatial reference system in a specified time coordinate [12,13]. The Barycentric Dynamical Time (TBD) is used for providing the coordinate time scale [14,15]. Then, the Moon-based SAR and ground target are mapped to the same reference frame through a series of coordinate conversions.
Using Skeleton Correction to Improve Flash Lidar-based Gait Recognition
Published in Applied Artificial Intelligence, 2022
Nasrin Sadeghzadehyazdi, Tamal Batabyal, Alexander Glandon, Nibir Dhar, Babajide Familoni, Khan Iftekharuddin, Scott T. Acton
Let be a matrix of the size of , where each row represents the time sequence of one joint in one of the directions , and , extended over frames. Since each skeleton consists of joints, there are in total joint coordinate time sequences. To correct for missing joint location values and noisy outliers in a given video, we perform filtering of joint location on each row of the corresponding matrix. Let represent the th row of
Modeling of microparticle penetration through wire screen using a lattice Boltzmann method and Lagrangian tracking approach: Comparison with experiments
Published in Aerosol Science and Technology, 2022
Jia-Huan Li, Tsung-Hsien Yu, Kuang C. Lin
For fluid flow simulations, the 2-D incompressible lattice Boltzmann model (He and Luo 1997) is used to solve the pressure distribution function. Each dimensional variable is identified by a superscripted star and is non-dimensionalized in the LBM as follows: where and are velocity vectors, spatial coordinate, time, pressure, kinematic viscosity and gas density, respectively. Table 6 lists the unit conversion between the dimensional and LBM variables or parameters. The fluid equation of the LBM is detailed in our previous studies (Lin, Tao, and Lee 2014; Lin and Tsai 2018).
Modal Decomposition of the Flow in a Randomly Packed Pebble Bed with Direct Numerical Simulation
Published in Nuclear Technology, 2022
Mustafa Alper Yildiz, Elia Merzari, Thien Nguyen, Yassin A. Hassan
where = velocity field= Cartesian coordinate= time= density of the fluid= kinematic viscosity.