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Epilogue: Towards “big data”
Published in Benjamin S. Baumer, Daniel T. Kaplan, Nicholas J. Horton, Modern Data Science with R, 2021
Benjamin S. Baumer, Daniel T. Kaplan, Nicholas J. Horton
For us, the relative definition becomes more meaningful. A big data problem occurs when the workflow that you have been using to solve problems becomes infeasible due to the expansion in the size of your data. It is useful in this context to think about orders of magnitude of data. The evolution of baseball data illustrates how “big data problems” have arisen as the volume and variety of the data has increased over time.
Metal Crystals—III Energies and Processes
Published in Alan Cottrell, An Introduction to Metallurgy, 2019
Surface energy is also important in the fracture of solids, since fracture is a process in which new surfaces are created. In an ideally simple process of tensile fracture we uniformly stretch all the interatomic bonds between two adjoining cleavage planes, by an increasing tensile stress, until they all simultaneously break. If Hooke’s law were obeyed right up to the fracture stress σt, we could equate the elastic energy, aσt2/2E per unit area, where a is the initial spacing of the planes, to the energy 2γ of the two surfaces so created, i.e. σt=4Eγ/a. However, this overlooks the softening of the law of force at large strains. Much of the contribution to the surface energy in fact occurs after the maximum in the force-displacement curve has been passed. The estimate of this effect depends on the detailed law of force between the atoms. Most calculations lead to the order-of-magnitude value σt≃Eγa
Fundamental concepts
Published in Bernard S. Massey, John Ward-Smith, Mechanics of Fluids, 2018
Bernard S. Massey, John Ward-Smith
There are circumstances where great precision is not required and just a general indication of magnitude is sufficient. In such cases we refer to the order of magnitude of a quantity. To give meaning to the term, consider the following statements concerning examples taken from everyday life: the thickness of the human hair is of the order 10−4 m; the length of the human thumb nail is of order 10−2 m; the height of a human is of order 1 m; the height of a typical two-storey house is of order 10 m; the cruise altitude of a subsonic civil aircraft is of order 104 m. These examples cover a range of 8 orders of magnitude. The height of a human is typically 4 orders of magnitude larger than the thickness of the human hair. The cruise altitude of an airliner exceeds the height of a human by 4 orders of magnitude. In this context, it is unimportant that the height of most humans is nearer 2 m, rather than 1 m. Here we are simply saying that the height of a human is closer to 1 m rather than 10 m, the next nearest order of magnitude.
A novel deep U-Net-LSTM framework for time-sequenced hydrodynamics prediction of the SUBOFF AFF-8
Published in Engineering Applications of Computational Fluid Mechanics, 2022
Yuqing Hou, Hui Li, Hong Chen, Wei Wei, Jiayue Wang, Yicang Huang
The convergence history of the traditional CNN-LSTM framework and the proposed deep U-Net-LSTM framework is shown in Figure 9. Both the MSE and MAE decrease as the epoch increases. When the convergence curve is stable, both the MSE and MAE are reduced by at least one order of magnitude and two orders of magnitude, respectively. In addition, the performance comparison of the predicted results at three different timesteps between the traditional CNN-LSTM and proposed deep U-Net-LSTM frameworks are summarized in Table 3. The training time and predicted time of each result are also slightly reduced. The proposed deep U-Net-LSTM framework has an MSE of 2.0 × 10−4 at the last timestep of the pressure validation set. This is still an order of magnitude lower than that of the traditional CNN-LSTM framework at the first validation timestep. A prediction framework with a smaller MSE ensures more accurate hydrodynamic prediction results.
Aeration strategies and temperature effects on the partial nitritation/anammox process for nitrogen removal: performance and bacterial community assessment
Published in Environmental Technology, 2022
Brenda Gonçalves Piteira Carvalho, Francis Anthony Cristófaro Warrener, Helena Maria Campos Castro, Alyne Duarte Pereira, Cíntia Dutra Leal, Juliana Calábria de Araújo
AOB abundance was in the same order of magnitude in relation to anammox bacteria abundance, but two orders of magnitude lower than the denitrifiers abundance (Figure 3). Denitrifiers survival was favoured by the formation of -N and the presence of biodegradable organic matter in food waste digestate, even in low concentrations. In addition, we used inoculum sludge from the recirculation line of an activated sludge system, which contains denitrifiers. This group is commonly found in anammox reactors inoculated with activated sludge, even in systems without air supply [18,20,22]. These authors reported heterotrophic denitrification occurrence and denitrifiers abundance at the same order of magnitude as observed in the present study (109nosZ gene copies.gsludge−1).
High-order contact transformations of molecular Hamiltonians: general approach, fast computational algorithm and convergence of ro-vibrational polyad models
Published in Molecular Physics, 2022
Vladimir Tyuterev, Sergey Tashkun, Michael Rey, Andrei Nikitin
We shall use the standard ket notations for the zero-order eigen vectors , where is the set of vibration quantum numbers . According to Amat-Nielsen ordering scheme, the order of magnitude of operators is assessed via the orders of magnitude of their matrix elements in the zero-order wavefunctions. For relatively small vibrational quantum numbers, this implies . The Coriolis constants are assumed to be of the order of 1 in average, and therefore . The n-th order term of the Hamiltonian expansion for n > 0 reads The second and the third terms in (59) appear for . An alternative description of this procedure is to say that elementary operators {p … pq … q, q … qp … p} form a basis set for H expansion in the algebra introduced in Sections 2.2–2.4 because operators are expressed in terms of qp products. However, this -basis in not the most convenient one for the high-order CT calculations.