Artykuły w czasopismach na temat „Logarithmic grids”
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Ha, Wansoo, i Changsoo Shin. "Efficient Laplace-domain modeling and inversion using an axis transformation technique". GEOPHYSICS 77, nr 4 (1.07.2012): R141—R148. http://dx.doi.org/10.1190/geo2011-0424.1.
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We tested an axis-transformation technique for modeling wave propagation in the Laplace domain using a finite-difference method. This technique enables us to use small grids near the surface and large grids at depth. Accordingly, we can reduce the number of grids and attain computational efficiency in modeling and inversion in the Laplace domain. We used a dispersion analysis and comparisons between modeled wavefields obtained on the regular and transformed axes. We demonstrated in a synthetic Laplace-domain inversion technique shows that this method is efficient and yields a result comparable to that of a Laplace-domain inversion using a regular grid. In a synthetic inversion example, the memory usage reduced to less than 33%, and the computation time reduced to 39% of those required for the regular grid case using a logarithmic transformation function.
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Nguyen, Philipp T. L., Juan C. Uribe, Imran Afgan i Dominique R. Laurence. "A Dual-Grid Hybrid RANS/LES Model for Under-Resolved Near-Wall Regions and its Application to Heated and Separating Flows". Flow, Turbulence and Combustion 104, nr 4 (23.10.2019): 835–59. http://dx.doi.org/10.1007/s10494-019-00070-8.
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Abstract A hybrid RANS/LES model for high Reynolds number wall-bounded flows is presented, in which individual Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulations (LES) are computed in parallel on two fully overlapping grids. The instantaneous, fluctuating subgrid-scale stresses are blended with a statistical eddy viscosity model in regions where the LES grid is too coarse. In the present case, the hybrid model acts as a near-wall correction to the LES, while it retains the fluctuating nature of the flow field. The dual computation enables the LES to be run on isotropic grids with very low wall-normal and wall-parallel resolution, while the auxiliary RANS simulation is conducted on a wall-refined high-aspect ratio grid. Running distinct, progressively corrected simulations allows a clearer separation of the mean and instantaneous flow fields, compliant with the fundamentally dissimilar nature of RANS and LES. Even with the wall-nearest grid point lying far in the logarithmic layer, velocity and temperature predictions of a heated plane channel flow are corrected. For a periodic hill flow, the dual-grid system improves the boundary layer separation and velocity field prediction both for a constant-spaced and a wall-refined LES grid.
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Pianko-Oprych, Paulina. "Modelling of heat transfer in a packed bed column". Polish Journal of Chemical Technology 13, nr 4 (1.01.2011): 34–41. http://dx.doi.org/10.2478/v10026-011-0046-1.
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Modelling of heat transfer in a packed bed column The CFD modelling of heat transfer in the packed bed column in the laminar and turbulent flow regimes has been presented. Three numerical grids with different densities were generated for the packed bed column. The modelling was performed with the use of the Porous Media Model for treating the flow inside a porous structure. The standard k-ε model along with the logarithmic wall functions for the turbulent flow range was used. The influence of the mesh size on the accuracy of the fluid flow was studied. Both radial and axial direction temperature distributions have been compared with the experimental data1 and the values calculated from a 2DADPF model. A good agreement between the experimental and the predicted values of the pressure drop, temperature distributions and heat transfer coefficient was obtained.
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ALLEY, KAREN E., TED A. SCAMBOS, ROBERT S. ANDERSON, HARIHAR RAJARAM, ALLEN POPE i TERRY M. HARAN. "Continent-wide estimates of Antarctic strain rates from Landsat 8-derived velocity grids". Journal of Glaciology 64, nr 244 (19.03.2018): 321–32. http://dx.doi.org/10.1017/jog.2018.23.
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ABSTRACTStrain rates are fundamental measures of ice flow and are used in a wide variety of glaciological applications including investigations of bed properties, calculations of basal mass balance on ice shelves, and constraints on ice rheological models. However, despite their extensive application, strain rates are calculated using a variety of methods and length scales and the details are often not specified. In this study, we compare the results of nominal and logarithmic strain-rate calculations based on a satellite-derived velocity field of the Antarctic ice sheet generated from Landsat 8 satellite data. Our comparison highlights the differences between the two common approaches in the glaciological literature. We evaluate the errors introduced by each approach and their impacts on the results. We also demonstrate the importance of choosing and specifying a length scale over which strain-rate calculations are made, which can strongly influence other derived quantities such as basal mass balance on ice shelves. Finally, we present strain-rate data products calculated using an approximate viscous length-scale with satellite observations of ice velocity for the Antarctic continent.
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Masood, Muhammad Yasir, Sana Aurangzeb, Muhammad Aleem, Ameen Chilwan i Muhammad Awais. "Demand-side load forecasting in smart grids using machine learning techniques". PeerJ Computer Science 10 (29.04.2024): e1987. http://dx.doi.org/10.7717/peerj-cs.1987.
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Electrical load forecasting remains an ongoing challenge due to various factors, such as temperature and weather, which change day by day. In this age of Big Data, efficient handling of data and obtaining valuable information from raw data is crucial. Through the use of IoT devices and smart meters, we can capture data efficiently, whereas traditional methods may struggle with data management. The proposed solution consists of two levels for forecasting. The selected subsets of data are first fed into the “Daily Consumption Electrical Networks” (DCEN) network, which provides valid input to the “Intra Load Forecasting Networks” (ILFN) network. To address overfitting issues, we use classic or conventional neural networks. This research employs a three-tier architecture, which includes the cloud layer, fog layer, and edge servers. The classical state-of-the-art prediction schemes usually employ a two-tier architecture with classical models, which can result in low learning precision and overfitting issues. The proposed approach uses more weather features that were not previously utilized to predict the load. In this study, numerous experiments were conducted and found that support vector regression outperformed other methods. The results obtained were 5.055 for mean absolute percentage error (MAPE), 0.69 for root mean square error (RMSE), 0.37 for normalized mean square error (NRMSE), 0.0072 for mean squared logarithmic error (MSLE), and 0.86 for R2 score values. The experimental findings demonstrate the effectiveness of the proposed method.
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Daniels, Megan H., Katherine A. Lundquist, Jeffrey D. Mirocha, David J. Wiersema i Fotini K. Chow. "A New Vertical Grid Nesting Capability in the Weather Research and Forecasting (WRF) Model". Monthly Weather Review 144, nr 10 (październik 2016): 3725–47. http://dx.doi.org/10.1175/mwr-d-16-0049.1.
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Mesoscale atmospheric models are increasingly used for high-resolution (<3 km) simulations to better resolve smaller-scale flow details. Increased resolution is achieved using mesh refinement via grid nesting, a procedure where multiple computational domains are integrated either concurrently or in series. A constraint in the concurrent nesting framework offered by the Weather Research and Forecasting (WRF) Model is that mesh refinement is restricted to the horizontal dimensions. This limitation prevents control of the grid aspect ratio, leading to numerical errors due to poor grid quality and preventing grid optimization. Herein, a procedure permitting vertical nesting for one-way concurrent simulation is developed and validated through idealized cases. The benefits of vertical nesting are demonstrated using both mesoscale and large-eddy simulations (LES). Mesoscale simulations of the Terrain-Induced Rotor Experiment (T-REX) show that vertical grid nesting can alleviate numerical errors due to large aspect ratios on coarse grids, while allowing for higher vertical resolution on fine grids. Furthermore, the coarsening of the parent domain does not result in a significant loss of accuracy on the nested domain. LES of neutral boundary layer flow shows that, by permitting optimal grid aspect ratios on both parent and nested domains, use of vertical nesting yields improved agreement with the theoretical logarithmic velocity profile on both domains. Vertical grid nesting in WRF opens the path forward for multiscale simulations, allowing more accurate simulations spanning a wider range of scales than previously possible.
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Goldberg, J. J., i T. E. Jensen. "Quantitative Analysis of Metal Sequestering in Different Cell Components of Gloeocapsa alpicola in the Overplus Phase". Microscopy and Microanalysis 6, S2 (sierpień 2000): 908–9. http://dx.doi.org/10.1017/s143192760003703x.
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The elemental composition of polyphosphate bodies (PPB's) and other components of the cell have previously been determined by using energy dispersive X-ray spectrometers(EDX). In this present study we perform a quantitative analysis of normally grown cells and cells that were grown in the overplus phenomenon.Cells of Gloeocapsa alpicola were grown in modified Fitzgerald's media and harvested after a logarithmic growth phase of 14 days. The overplus cells were grown, as has been previously described. The cells were exposed to 20ppm of Al, Cd, Cu, Mn, Ni, Pb, and Zn, as well as a control, for one hour. The cells were then air dried on formvar coated grids or fixed and embedded in EPON according to Luft's procedure.For Xn-ay analysis cells were first located using the TEM mode, and then the microscope was switched to the STEM mode. Analyses of cell components were carried out using the spot mode (75Kv).
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Xu, Xiaorui, i Yu-Xin Ren. "Resolving turbulent boundary layer on coarse grid using function enrichment based on variational reconstructions". Physics of Fluids 34, nr 12 (grudzień 2022): 125106. http://dx.doi.org/10.1063/5.0124478.
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An improved finite volume scheme based on variational reconstruction and function enrichment has been proposed in this paper. By incorporating the law-of-the-wall into the variational reconstruction, the proposed method can resolve turbulent flow accurately on grids much coarser than those needed by traditional methods. The usual reconstruction in a finite volume scheme assumes that the solution is belonging to a polynomial function space, which is inaccurate to resolve the velocity profile within the turbulent boundary layer unless the grid in wall-normal direction is fine enough. In the present paper, this function space is “enriched” by adding a basis function that is derived from the logarithmic law of the turbulent boundary layer. Then variational reconstruction procedure is applied to find the “best” solution belonging to the expanded function space. The advantage of the present method over the traditional wall function model is that the turbulent flow within the boundary layer is resolved rather than modeled. The algorithms and the implementations are discussed in detail. The proposed method is applied to the turbulent flow over a flat plate at a Reynolds number of [Formula: see text] and the turbulent flow over a plate with a bump at a Reynolds number of [Formula: see text]. The results of second- and third-order schemes are presented for the turbulent velocity profile and the skin friction coefficients. The numerical results suggest that this approach not only resolves the near wall turbulent accurately on very coarse grids but also reduces the computational time significantly.
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Yang, Zon-Yee, i Jian-Liang Juo. "Interpretation of sieve analysis data using the box-counting method for gravelly cobbles". Canadian Geotechnical Journal 38, nr 6 (1.12.2001): 1201–12. http://dx.doi.org/10.1139/t01-052.
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In fractal theory, the fractal dimension (D) is a measure of the complexity of particle distribution in nature. It can provide a description of how much space a particle set fills. The box-counting method uses squared grids of various sizes to cover the particles to obtain a box dimension. This sequential counting concept is analogous to the sieve analysis test using stacked sieves. In this paper the box-counting method is applied to describe the particle-size distribution of gravelly cobbles. Three approaches to obtain the fractal dimension are presented. In the first approach the data obtained from a classic laboratory sieve analysis are rearranged into a double-logarithmic plot, according to a fractal model, to obtain the fractal dimension of the particle collection. In addition, an equivalent number of covered grids on each sieve during the sieve analysis are counted to produce the box dimension. According to the box-counting method concept, a photo-sieving technique used in scanning electron microscope microstructure analysis is adopted for use on gravelly cobbles in the field. The box-counting method concept is capable of explaining the sieve analysis data to clarify the information on the particle-size distribution. Using photo-sieving to produce the fractal dimension from field photographs can provide another approach for understanding the particle-size distribution. However, the representative cross-profile should be chosen carefully. The composition of the particle-size distribution for gravelly cobbles with higher D values is more complicated than those at sites with smaller D values.Key words: sieve analysis, box-counting method, fractal dimension, particle-size distribution, gravelly cobbles.
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Igel, Jonas K. H., Laura A. Ermert i Andreas Fichtner. "Rapid finite-frequency microseismic noise source inversion at regional to global scales". Geophysical Journal International 227, nr 1 (28.05.2021): 169–83. http://dx.doi.org/10.1093/gji/ggab210.
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SUMMARY Ambient noise cross-correlations can be used as self-consistent observables, opening novel possibilities for investigating ambient noise sources. To optimize the forward-modelling of global ambient noise cross-correlations for any given distribution of noise sources in the microseismic frequency range up to 0.2 Hz, we implement (i) pre-computed wavefields and (ii) spatially variable grids. This enables rapid inversions for microseismic noise sources based on finite-frequency source sensitivity kernels. We use this advancement to perform regional and global gradient-based iterative inversions of the logarithmic energy ratio in the causal and acausal branches of microseismic noise cross-correlations. Synthetic inversions show promising results, with good recovery of the main dominant noise sources of the target model. Data inversions for several consecutive days at the beginning of October 2019 demonstrate the capability of inverting for the spatio-temporal variations of the sources of secondary microseisms in the ocean. This paves the way for daily ambient noise source inversions which could help improve full-waveform ambient noise tomography and subsurface monitoring methods.
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Idrissi, Mohamed Salah, Nabil Ben Salah i Mouldi Chrigui. "Numerical Modelling of Air Pollutant Dispersion in Complex Urban Areas: Investigation of City Parts from Downtowns Hanover and Frankfurt". Fluids 4, nr 3 (18.07.2019): 137. http://dx.doi.org/10.3390/fluids4030137.
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Hazardous gas dispersion within a complex urban environment in 1:1 scaled geometry of German cities, Hanover and Frankfurt, is predicted using an advanced turbulence model. The investigation involves a large group of real buildings with a high level of details. For this purpose, Computer Aided Design (CAD) of two configurations are cleaned, then fine grids meshed in. Weather conditions are introduced using power law velocity profiles at inlets boundary. The investigation focused on the effects of release locations and material properties of the contaminants (e.g., densities) on the convection/diffusion of pollutants within complex urban area. Two geometries demonstrating different topologies and boundaries conditions are investigated. Pollutants are introduced into the computational domain through chimney and/or pipe leakages in various locations. Simulations are carried out using Large Eddy Simulation (LES) turbulence model and species transport for the pollutants. The weather conditions are accounted for using a logarithmic velocity profile at inlets. CH4 and CO2 distributions, as well as turbulence quantities and velocity profiles, show important influences on the dispersion behavior of the hazardous gas.
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Werthmüller, Dieter, Wim A. Mulder i Evert C. Slob. "Fast Fourier transform of electromagnetic data for computationally expensive kernels". Geophysical Journal International 226, nr 2 (26.04.2021): 1336–47. http://dx.doi.org/10.1093/gji/ggab171.
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SUMMARY 3-D controlled-source electromagnetic data are often computed directly in the domain of interest, either in the frequency domain or in the time domain. Computing it in one domain and transforming it via a Fourier transform to the other domain is a viable alternative. It requires the evaluation of many responses in the computational domain if standard Fourier transforms are used. This can make it prohibitively expensive if the kernel is time-consuming as is the case in 3-D electromagnetic modelling. The speed of modelling obtained through such a transform is defined by three key points: solver, method and implementation of the Fourier transform, and gridding. The faster the solver, the faster modelling will be. It is important that the solver is robust over a wide range of values (frequencies or times). The method should require as few kernel evaluations as possible while remaining robust. As the frequency and time ranges span many orders of magnitude, the required values are ideally equally spaced on a logarithmic scale. The proposed fast method uses either the digital linear filter method or the logarithmic fast Fourier transform together with a careful selection of evaluation points and interpolation. In frequency-to-time domain tests this methodology requires typically 15–20 frequencies to cover a wide range of offsets. The gridding should be frequency- or time-dependent, which is accomplished by making it a function of skin depth. Optimizing for the least number of required cells should be combined with optimizing for computational speed. Looking carefully at these points resulted in much smaller computation times with speedup factors of ten or more over previous methods. A computation in one domain followed by transformation can therefore be an alternative to computation in the other domain domain if the required evaluation points and the corresponding grids are carefully chosen.
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Ho, Je Ee, i Hong Tsu Young. "The Analysis on Penetrating Efficiency in High-Energy Beam Drilling". Key Engineering Materials 364-366 (grudzień 2007): 308–14. http://dx.doi.org/10.4028/www.scientific.net/kem.364-366.308.
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In Laser Beam (L.B.) and Electron Beam (E.B.) drilling, the energy distribution significantly affects both the penetrating efficiency and working performance, both of which are usually estimated by numerical skill or experimental measure. Through the application of a stimulation model, an unstable solution with the finite difference method will result near the solidliquid interface unless much finer grid sizes are set up. To improve on the above defect, nonuniform grids are therefore utilized; this will complicate the built-up of the program and also easily causes the simulated energy distribution to be divergent in the iteration process. In this study, an estimated small Peclet number and observed narrow-deep cavity made the convective and radial diffusion terms small enough to be neglected in the governing equation. From these assumptions, the model was then used to investigate the drilling efficiency where two-phase flow convection could be simplified further into one dimension and thus the analytical solution becomes possible by transferring the penetration velocity into the logarithmic form. When compared with the experiment made by Allmen [1] , the present model shows good agreement in higher energy density and relative errors are no more than 10%.
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Chen, Jianfeng, Junsong Jia, Lin Wang, Chenglin Zhong i Bo Wu. "Carbon Reduction Countermeasure from a System Perspective for the Electricity Sector of Yangtze River Delta (China) by an Extended Logarithmic Mean Divisia Index (LMDI)". Systems 11, nr 3 (23.02.2023): 117. http://dx.doi.org/10.3390/systems11030117.
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The electricity sector is a complex system, especially in the Yangtze River Delta (YRD) of China. Thus, the carbon dioxide (CO2) emission of YRD’s electricity sector during 2000–2020 was first calculated and then evaluated from two systematical dimensions of cross-region and the whole process (production, trade, transmission, and consumption) by an extended logarithmic mean Divisia index (LMDI). (1) During 2000–2020, the CO2 emission of YRD’s electricity sector increased from 228.12 Mt to 807.55 Mt, with an average annual growth rate of 6.52%. Compared to other regions, the YRD’s electricity mix effect had the strongest mitigation impact on CO2 growth. Therefore, it is important for YRD to build a low-carbon electricity system itself, including the de-carbonization of electricity production and the carbon reduction of the electricity-use process. (2) Nationally, electricity trade had an overall mitigating impact on emission growth during 2000–2020. This result means that cross-regional cooperation or trade in the electricity sector is beneficial to emission reduction. So, it is important to improve the national power grids to promote trade. (3) Jiangsu had the largest CO2 emissions, while Anhui had the fastest average annual growth rate (9.71%). Moreover, the economic activity effect was the most significant driver in all provinces, especially in Jiangsu and Anhui. Thus, Jiangsu and Anhui should strive to improve the quality of economic growth while vigorously cutting carbon emissions. (4) Electricity transmission loss had an overall driving impact on emission growth in each YRD province, especially in Zhejiang and Anhui. Meanwhile, electricity structure, electricity trade, and electricity intensity were the inhibiting factors. Particularly, the inhibiting effect of Shanghai’s electricity structure was notably weak (−2.17 Mt). So, Shanghai should try hard to increase the proportion of renewable energy, while Zhejiang and Anhui should upgrade their electricity transmission equipment.
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Fernández, V., R. Amorín, E. Pérez-Montero, P. Papaderos, C. Kehrig i J. M. Vílchez. "New insights on the nebular emission, ionizing radiation, and low metallicity of Green Peas from advanced modelling". Monthly Notices of the Royal Astronomical Society 511, nr 2 (1.11.2021): 2515–34. http://dx.doi.org/10.1093/mnras/stab3150.
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ABSTRACT Low-metallicity, compact starburst galaxies referred to as Green Peas (GPs) provide a unique window to study galactic evolution across cosmic epochs. In this work, we present new deep optical spectra for three GPs from OSIRIS at the 10-m Gran Telescopio Canarias, which are studied using a state-of-the-art methodology. A stellar population synthesis is conducted with 1098 spectral templates. The methodology succeeds at characterizing stellar populations from 0.5 Myr to 10 Gyr. The light distribution shows a large red excess from a single population with ${log}\left({age}\right) \gt 8.5\, \mathrm{yr}$ in the GP sample analysed. This points towards an incomplete characterization of the gas luminosity, whose continuum already accounts between 7.4 and $27.6{{\ \rm per\ cent}}$ in the galaxy sample. The emission spectra are fitted with the largest Bayesian chemical model consisting of an electron temperature, an electron density, the logarithmic extinction coefficient and eleven ionic species under the direct method paradigm. Additionally, building on previous work, we propose a neural networks sampler to constrain the effective temperature and ionization parameter of each source from photoionization model grids. Finally, we combine both methodologies into a 16-dimensional model, which for the first time, simultaneously explores the direct method and photoionization parameter spaces. Both techniques consistently indicate a low-metallicity gas, $7.76\lt 12+{\rm log}\left(O/H \right)\lt 8.04$, ionized by strong radiation fields, in agreement with previous works.
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Fang, Fang, i Klee Irwin. "From the Fibonacci Icosagrid to E8 (Part I): The Fibonacci Icosagrid, an H3 Quasicrystal". Crystals 14, nr 2 (31.01.2024): 152. http://dx.doi.org/10.3390/cryst14020152.
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This paper introduces a new kind of quasicrystal by Fibonacci-spacing a multigrid of a certain symmetry, like H2, H3, T3, etc. Multigrids of a certain symmetry can be used to generate quasicrystals, but multigrid vertices are not a quasicrystal due to arbitrary closeness. By Fibonacci-spacing the grids, the structure transit into an aperiodic order becomes a quasicrystal itself. Unlike the quasicrystal generated by the dual-grid method, this kind of quasicrystal does not live in the dual space of the grid space. It is the grid space itself and possesses quasicrystal properties, except that its total number of vertex types are not finite and fixed for the infinite size of the quasicrystal but bounded by a slowly logarithmic growing number. A 2D example, the Fibonacci pentagrid, is given. A 3D example, the Fibonacci icosagrid (FIG), is also introduced, as well as its subsets, the Fibonacci tetragrid (FTG). The FIG can be thought of as a golden composition of five sets of FTGs. The golden composition procedure is another way to transit a random structure into aperiodic order, and the associated rotational angle is the same as the angle that resolves the geometric frustration for the H3 tetrahedral clusters. The FIG resembles another quasicrystal that is the same golden composition of five quasicrystals that are cut and projected and sliced from the E8 lattice. This leads to further exploration in mapping the FIG to the E8 lattice, and the results will be published following this paper.
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Ding, Yu, Gerard Renard i Luce Weill. "Representation of Wells in Numerical Reservoir Simulation". SPE Reservoir Evaluation & Engineering 1, nr 01 (1.02.1998): 18–23. http://dx.doi.org/10.2118/29123-pa.
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Summary In reservoir simulation, linear approximations generally are used for well modeling. However, these types of approximations can be inaccurate for fluid-flow calculation in the vicinity of wells, leading to incorrect well-performance predictions. To overcome such problems, a new well representation1 has been proposed that uses a "logarithmic" type of approximation for vertical wells. In this paper, we show how the new well model can be implemented easily in existing simulators through the conventional productivity index (PI). We discuss the relationship between wellbore pressure, wellblock pressure, and flow rate in more detail, especially for the definition of wellblock pressure. We present an extension of the new approach to off-center wells and to flexible grids. Through this extension, the equivalence of various gridding techniques for the well model is emphasized. The key element is the accurate calculation of flow components in the vicinity of wells. Introduction The well model plays an important role in reservoir simulation because the precision of calculation in well-production rate or bottomhole pressure is directly related to this well model. The main difficulty of well modeling is the problem of singularity because of the difference in scale between the small wellbore diameter (less than 0.3 m) and the large wellblock grid dimensions used in the simulation (from tens to hundreds of meters), and to the radial nature of the flow around the well (i.e., nonlinear but logarithmic variation of the pressure away from the well). Thus, the wellblock pressure calculated by standard finite-difference methods is not the wellbore pressure. Peaceman2,3 first demonstrated that wellblock pressure calculated by finite difference in a uniform grid corresponds to the pressure at an equivalent wellblock radius, r0, related to gridblock dimensions. Assuming a radial flow around the well, he demons-trated that this radius could be used to relate the wellblock pressure to the wellbore pressure. However, there are problems with this approach in many practical reservoir simulation studies:For routinely used nonuniform Cartesian grids,4 there is no easy means to determine an r0 value.In three-dimensional (3D) cases with non-fully-penetrating wells, the basic radial flow assumption does not apply,5 whereas vertical flow effects must be included.6Off-center wells are not correctly treated.7,8Treatment of the well model is much more complicated with non Cartesian or flexible grids.9–11 The aim of this paper is to show that the new well representation1 proposed in a previous paper can handle these problems accurately. Wellblock Pressure Calculation A previous paper1 presented a new approach particularly well-suited to nonuniform grids for the modeling of vertical wells in numerical simulation. The principle of this new approach, which is based on a finite-volume method, is to calculate new interblock distances that improve the modeling of flow in the vicinity of wells. Because the new approach was originally presented for two-dimensional (2D)-XY problems, it was shown that for such problems the wellbore pressure could be calculated without both the intermediate computation of the wellblock pressure and introduction of an equivalent wellblock radius. However, for at least two reasons, it is convenient to keep this standard method commonly used in numerical models, which consists of relating the wellbore pressure and wellblock pressure through the use of a numerical PI and equivalent wellblock radius. One reason is practical. To implement the new approach more easily into standard numerical models, it is better to keep their internal structure unchanged. The other reason is dictated by the necessity of having a wellblock pressure in particular 3D simulation studies. When a well partially penetrates the reservoir or when there is communication between different layers, there is a vertical flow component in the vicinity of the well that necessitates that the wellblock pressure be calculated. How should the new approach be implemented in standard reservoir simulators- In these simulators, a numerical PI is used in the well model to relate the wellbore pressure, pw, to the wellblock pressure, p0. Usually, this PI is written as where r0 is the equivalent wellblock radius at which the pressure is equal to p0. Within the new well representation,1 to obtain a pressure p0 corresponding to a radius r0, it is sufficient to use equivalent wellblock transmissibilities relating p0 to the pressures of adjacent blocks through equivalent interblock distances, Leq, i (Fig. 1: where ?x0, ?y0 are the wellblock dimensions. For instance, in the x+ direction, Leq,1 is written where ?1+2 arctg (?y0 /?x0) is the angle formed by the right wellblock interface seen from the well. Because wellblock transmissibilities in standard models are conventionally expressed by the new approach can be implemented easily in standard models multiplying the conventional wellblock transmissibilities by constant factors. For instance, in the x+ direction, this factor is By use of equivalent transmissibilities, the calculated wellblock pressure, p0, should correspond to the equivalent wellblock radius, r0, which is involved in transmissibility calculations (Eq. 3). Then, the wellblock pressure can be related to the wellbore pressure with the conventional PI (Eq. 1).
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Ly, S., C. Charles i A. Degré. "Spatial interpolation of daily rainfall at catchment scale: a case study of the Ourthe and Ambleve catchments, Belgium". Hydrology and Earth System Sciences Discussions 7, nr 5 (27.09.2010): 7383–416. http://dx.doi.org/10.5194/hessd-7-7383-2010.
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Abstract. Spatial interpolation of precipitation data is of great importance for hydrological modelling. Geostatistical methods (krigings) are widely used in spatial interpolation from point measurement to continuous surfaces. However, the majority of existing geostatistical algorithms are available only for single-moment data. The first step in kriging computation is the semi-variogram modelling which usually uses only one variogram model for all-moment data. The objective of this paper was to develop different algorithms of spatial interpolation for daily rainfall on 1 km2 regular grids in the catchment area and to compare the results of geostatistical and deterministic approaches. In this study, we used daily rainfall data from 70 raingages in the hilly landscape of the Ourthe and Ambleve catchments in Belgium (2908 km2). This area lies between 35 and 693 m in elevation and consists of river networks, which are tributaries of the Meuse River. For geostatistical algorithms, Cressie's Approximate Weighted Least Squares method was used to fit seven semi-variogram models (logarithmic, power, exponential, Gaussian, rational quadratic, spherical and penta-spherical) to daily sample semi-variogram on a daily basis. Seven selected raingages were used to compare the interpolation performance of these algorithms applied to many degenerated-raingage cases. Spatial interpolation with the geostatistical and Inverse Distance Weighting (IDW) algorithms outperformed considerably interpolation with the Thiessen polygon that is commonly used in various hydrological models. Kriging with an External Drift (KED) and Ordinary Cokriging (OCK) presented the highest Root Mean Square Error (RMSE) between the geostatistical and IDW methods. Ordinary Kriging (ORK) and IDW were considered to be the best methods, as they provided smallest RMSE value for nearly all cases.
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Li, Yanfeng, Yongping Li, Guohe Huang i Rubing Zheng. "Inter-Provincial Electricity Trading and Its Effects on Carbon Emissions from the Power Industry". Energies 15, nr 10 (14.05.2022): 3601. http://dx.doi.org/10.3390/en15103601.
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Electricity trading is an effective measure to minimize carbon emissions and alleviate the imbalance between reverse distribution of regional energy resources and power load. However, the effects of China’s electricity trading on carbon emissions have not been fully explored due to lack of complete and balanced inter-provincial power transmission data. Therefore, the electricity generation–consumption downscaling model, logarithmic mean Divisia index (LMDI) model, and random forest clustering algorithm within a general framework were used in the present study to explore the effect of electricity trading on level of carbon emissions. Comprehensive inter-provincial electricity transmission data were generated, driving factors including electricity imports and exports were decomposed at the national and provincial scales, and clustered provincial policy implications were evaluated. The results revealed that: (i) although economic activities were the main driving factor for increase in carbon emissions at the national level, 382.95 million tons carbon emissions were offset from 2005 to 2019 due to inter-provincial electricity importation, whereas electricity export increased carbon emission by 230.30 million tons; (ii) analysis at the provincial level showed that electricity exports from Sichuan and Yunnan provinces accounted for more than 20% of the nation’s total electricity flow. Notably, this high level of exports did not significantly increase carbon emissions in these provinces owing to the abundant hydropower resources; (iii) emission reductions were only observed at the national level if the carbon intensity of the exporting provinces was lower compared with that of importing provinces, or if the electricity trading was generated from renewable sources; (iv) the effect of electricity import on emissions reduction was markedly higher relative to the effect of electricity export in most provinces, which reflected the actual situation of sustaining optimization of electricity generation structure in provincial grids of China. These findings provide a basis for decision makers to understand the contributions of electricity trading to the changes in carbon emissions from electricity generation, as well as form a foundation to explore practicable carbon emission mitigation strategies in the power industry.
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Gao, Dapeng, Yuewu Liu, Daigang Wang i Guofeng Han. "Numerical Analysis of Transient Pressure Behaviors with Shale Gas MFHWs Interference". Energies 12, nr 2 (15.01.2019): 262. http://dx.doi.org/10.3390/en12020262.
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After the large-scale horizontal well pattern development in shale gas fields, the problem of fast pressure drop and gas well abandonment caused by well interference becomes more serious. It is urgent to understand the downhole transient pressure and flow characteristics of multi-stage fracturing horizontal well (MFHW) with interference. Therefore, the reservoir around the MFHW is divided into three regions: fracturing fracture, Stimulated reservoir volume (SRV), and unmodified matrix. Then, multi-region coupled flow model is established according to reservoir physical property and flow mechanism of each part. The model is numerically solved using the perpendicular bisection (PEBI) grids and the finite volume method. The accuracy of the model is verified by analyzing the measured pressure recovery data of one practical shale gas well and fitting the monitoring data of the later production pressure. Finally, this model is used to analyze the effects of factors, such as hydraulic fractures’ connectivity, well distance, the number of neighboring wells and well pattern arrangement, on the transient pressure and seepage characteristics of the well. The study shows that the pressure recovery double logarithmic curves fall in later part when the well is disturbed by a neighboring production well. The earlier and more severe the interference, the sooner the curve falls off and the larger the amplitude shows. If the well distance is closer, and if there are more neighboring wells and interconnected corresponding fracturing segments, the more severe interference appears among the wells. Moreover, the well interference may still exist even without interlinked fractures or SRV. Especially, severe interference will affect production when the hydraulic fractures are connected directly, and the interference is weaker when only SRV induced fracture network combined between wells, which is beneficial to production sometimes. When severe well interference occurs, periodic well shut-in is needed to help restore the reservoir pressure and output capacity. In the meanwhile, the daily output should be controlled reasonably to prolong the stable production time. This research will help to understand the impact of well interference to gas production, and to optimize the well spacing and achieve satisfied performance.
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ZUBAIR, FAZLUL R., i HARIS J. CATRAKIS. "On separated shear layers and the fractal geometry of turbulent scalar interfaces at large Reynolds numbers". Journal of Fluid Mechanics 624 (10.04.2009): 389–411. http://dx.doi.org/10.1017/s0022112008005612.
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This work explores fractal geometrical properties of scalar turbulent interfaces derived from experimental two-dimensional spatial images of the scalar field in separated shear layers at large Reynolds numbers. The resolution of the data captures the upper three decades of scales enabling examination of multiscale geometrical properties ranging from the largest energy-containing scales to inertial scales. The data show a −5/3 spectral exponent over a wide range of scales corresponding to the inertial range in fully developed turbulent flows. For the fractal aspects, we utilize two methods as it is known that different methods may lead to different fractal aspects. We use the recently developed method for fractal analysis known as the Multiscale-Minima Meshless (M3) method because it does not require the use of grids. We also use the conventional box-counting approach as it has been frequently employed in various past studies. The outer scalar interfaces are identified on the basis of the probability density function (p.d.f.) of the scalar field. For the outer interfaces, the M3 method shows strong scale dependence of the generalized fractal dimension with approximately linear variation of the dimension as a function of logarithmic scale, for interface-fitting reference areas, but there is evidence of a plateau near a dimension D ~ 1.3 for larger reference areas. The conventional box-counting approach shows evidence of a plateau with a constant dimension also of D ~ 1.3, for the same reference areas. In both methods, the observed plateau dimension value agrees with other studies in different flow geometries. Scalar threshold effects are also examined and show that the internal scalar interfaces exhibit qualitatively similar behaviour to the outer interfaces. The overall range of box-counting fractal dimension values exhibited by outer and internal interfaces is D ~ 1.2–1.4. The present findings show that the fractal aspects of scalar interfaces in separated shear layers at large Reynolds number with −5/3 spectral behaviour can depend on the method used for evaluating the dimension and on the reference area. These findings as well as the utilities and distinctions of these two different definitions of the dimension are discussed in the context of multiscale modelling of mixing and the interfacial geometry.
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Ly, S., C. Charles i A. Degré. "Geostatistical interpolation of daily rainfall at catchment scale: the use of several variogram models in the Ourthe and Ambleve catchments, Belgium". Hydrology and Earth System Sciences 15, nr 7 (18.07.2011): 2259–74. http://dx.doi.org/10.5194/hess-15-2259-2011.
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Abstract. Spatial interpolation of precipitation data is of great importance for hydrological modelling. Geostatistical methods (kriging) are widely applied in spatial interpolation from point measurement to continuous surfaces. The first step in kriging computation is the semi-variogram modelling which usually used only one variogram model for all-moment data. The objective of this paper was to develop different algorithms of spatial interpolation for daily rainfall on 1 km2 regular grids in the catchment area and to compare the results of geostatistical and deterministic approaches. This study leaned on 30-yr daily rainfall data of 70 raingages in the hilly landscape of the Ourthe and Ambleve catchments in Belgium (2908 km2). This area lies between 35 and 693 m in elevation and consists of river networks, which are tributaries of the Meuse River. For geostatistical algorithms, seven semi-variogram models (logarithmic, power, exponential, Gaussian, rational quadratic, spherical and penta-spherical) were fitted to daily sample semi-variogram on a daily basis. These seven variogram models were also adopted to avoid negative interpolated rainfall. The elevation, extracted from a digital elevation model, was incorporated into multivariate geostatistics. Seven validation raingages and cross validation were used to compare the interpolation performance of these algorithms applied to different densities of raingages. We found that between the seven variogram models used, the Gaussian model was the most frequently best fit. Using seven variogram models can avoid negative daily rainfall in ordinary kriging. The negative estimates of kriging were observed for convective more than stratiform rain. The performance of the different methods varied slightly according to the density of raingages, particularly between 8 and 70 raingages but it was much different for interpolation using 4 raingages. Spatial interpolation with the geostatistical and Inverse Distance Weighting (IDW) algorithms outperformed considerably the interpolation with the Thiessen polygon, commonly used in various hydrological models. Integrating elevation into Kriging with an External Drift (KED) and Ordinary Cokriging (OCK) did not improve the interpolation accuracy for daily rainfall. Ordinary Kriging (ORK) and IDW were considered to be the best methods, as they provided smallest RMSE value for nearly all cases. Care should be taken in applying UNK and KED when interpolating daily rainfall with very few neighbourhood sample points. These recommendations complement the results reported in the literature. ORK, UNK and KED using only spherical model offered a slightly better result whereas OCK using seven variogram models achieved better result.
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Mayers, D. F., i D. M. Turner. "Relativistic inelastic scattering using a logarithmic grid". Journal of Computational Physics 62, nr 2 (luty 1986): 331–39. http://dx.doi.org/10.1016/0021-9991(86)90131-2.
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Liu, Zhenxin, Yuanhao Chen, Yuhang Wang, Cheng Liu, Shuhua Liu i Hong Liao. "The development and validation of the Inhomogeneous Wind Scheme for Urban Street (IWSUS-v1)". Geoscientific Model Development 16, nr 15 (1.08.2023): 4385–403. http://dx.doi.org/10.5194/gmd-16-4385-2023.
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Abstract. The layout of urban buildings shows significant heterogeneity, which leads to the significant spatial inhomogeneity of the wind field in and over the canopy of urban street canyons. However, most of the current urban canopy models do not fully consider the heterogeneity of the urban canopy. Large discrepancies thus exist between the wind speeds simulated by the current urban canopy models and those observed in the street canyon. In this study, a parameterization scheme for wind fields, Inhomogeneous Wind Scheme for Urban Street (IWSUS), is developed to better characterize the heterogeneity of the urban canopy. We use a computational fluid dynamics method to generate the IWSUS scheme and compare it with observations of the wind profile and turbulent flux in and over the street canyon for validation. In IWSUS, the wind speed vertical profiles at six representative positions located in a typical street canyon (i.e., the windward or leeward side of a long straight street or the inflow or outflow end) are parameterized separately. The wind profile by IWSUS thus can better describe the horizontal heterogeneity of the urban near-surface wind field, e.g., the dynamic drag effect of buildings in the lower atmospheric layer over the urbanized land use. The validation based on observations shows that the performance of simulation results by IWSUS is better than that by the exponential–logarithmic (exp-log) law widely used in the current urban schemes. We consider typical building arrangement and specific street orientations in IWSUS for wind field simulations, which can better match the distribution characteristics of street canyons around the observation point in the street canyon. The averaged wind profiles and turbulence energy fluxes in the model grids of urban areas by IWSUS are also nearer to the observations than those by the exp-log law. The normalized mean errors (NMEs) between the simulated and the observed vertical average wind speed are 49.0 % for IWSUS and 56.1 % for exp-log law in the range from the ground to 4 times the average height of the buildings and 70 % for IWSUS and 285.8 % for exp-log law in the street canyon (range from the ground to building top). This study proves that the accuracy of simulations of land surface processes and near-ground meteorological processes over the urban canopy can be improved by fully considering the heterogeneity of the urban canopy layout structures and the inhomogeneity of wind field distributions in and over the street canyon. IWSUS is expected to be coupled with mesoscale atmospheric models to improve the accuracy of the wind field, land surface energy budget, meteorological and atmospheric chemistry simulations.
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Montazer, M. Ali, i John G. Thomas. "Grip Strength as a Function of 200 Repetitive Trials". Perceptual and Motor Skills 75, nr 3_suppl (grudzień 1992): 1320–22. http://dx.doi.org/10.2466/pms.1992.75.3f.1320.
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A study was done to see how grip strength deteriorates after an extended number of grips. Eight male subjects, all right-handed and 23 to 35 years old, participated. Each subject made 200 grips on a dynamometer at his maximum strength. There were 15-sec. rests between trials. Performance dropped significantly after two trials. There were drops of about 40% and 50% at Trials 100 and 200, respectively. The grip strength/trial relationship is logarithmic as noted by Montazer and Thomas in 1991.
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Hong, Bo-Ram, Ho-Seuk Bae, Wan-Soo Ha i Woo-Keen Chung. "Improved efficiency of numerical modeling using the expanding domain method with a logarithmic grid". Journal of the Korean Society of Marine Engineering 40, nr 1 (31.01.2016): 75–80. http://dx.doi.org/10.5916/jkosme.2016.40.1.75.
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ROSAS-CASALS, MARTÍ, SERGI VALVERDE i RICARD V. SOLÉ. "TOPOLOGICAL VULNERABILITY OF THE EUROPEAN POWER GRID UNDER ERRORS AND ATTACKS". International Journal of Bifurcation and Chaos 17, nr 07 (lipiec 2007): 2465–75. http://dx.doi.org/10.1142/s0218127407018531.
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We present an analysis of the topological structure and static tolerance to errors and attacks of the September 2003 actualization of the Union for the Coordination of Transport of Electricity (UCTE) power grid, involving thirty-three different networks. Though every power grid studied has exponential degree distribution and most of them lack typical small-world topology, they display patterns of reaction to node loss similar to those observed in scale-free networks. We have found that the node removal behavior can be logarithmically related to the power grid size. This logarithmic behavior would suggest that, though size favors fragility, growth can reduce it. We conclude that, with the ever-growing demand for power and reliability, actual planning strategies to increase transmission systems would have to take into account this relative increase in vulnerability with size, in order to facilitate and improve the power grid design and functioning.
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Bobachev, A. A., A. V. Deshcherevskii i A. Ya Sidorin. "The effect of spacing grid in the precision solution of the inverse vertical electric sounding problem". Vestnik MGTU 27, nr 1 (3.04.2024): 5–23. http://dx.doi.org/10.21443/1560-9278-2024-27-1-5-23.
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Electrical methods for monitoring the stress-strain state of the Earth's crust involve measuring apparent resistivity, but changes in resistivity are of physical interest. During daily (for 12 years) measurements of the apparent resistivity of the Earth's crust using a stationary 32-electrode vertical electrical sounding installation in a highly seismic region of Tajikistan and precision equipment, a vertical electrical sounding profile of a special type was obtained for which the sounding date changes from picket to picket. To invert field data, a special version of the IPI program was developed taking into account the features of the measuring setup. Initially, the direct and inverse problems of vertical electrical sounding were solved on a standard logarithmic spacing grid which significantly increased the speed of calculations. The actual data were interpolated to this grid. However, testing the algorithm on synthetic data showed that in this case the maximum achievable accuracy is limited by a special type of equivalence – the effect of resistance buildup. The precision version of the IPI program implements several algorithmic techniques aimed at reducing the error in solving the inverse problem. When describing the effects that depend on the choice of one or another spacing grid, the results of solving the inverse problem for synthetic profiles in two versions of the IPI program were compared and the beneficial effect of switching to the actual spacing grid was determined. When comparing the results of inversion of the experimental vertical electrical sounding profile obtained as a result of long-term observations, the amplitude of errors arising when using a logarithmic spacing grid was assessed using indirect evidence.
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Zhu, Zhiping, Chun Shi, Yu Zhang i Zhifeng Liu. "The effects of Cl− and direct stray current on soil corrosion of three grounding grid materials". Anti-Corrosion Methods and Materials 67, nr 1 (6.01.2020): 73–82. http://dx.doi.org/10.1108/acmm-06-2019-2136.
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Purpose The purpose of this paper is to study the effects of Cl− and direct stray current on the soil corrosion of three grounding grid materials. Design/methodology/approach The electrochemical corrosion properties of three grounding grid materials, which include the Q235 steel, Q235 galvanized flat steel and copper, were measured by means of the weak polarization curve method and electrochemical impedance spectroscopy; the corrosion rate of specimens was calculated using the weight loss method; and the specimen surfaces were characterized using the scanning electron microscopy, energy-dispersive spectroscopy and X-ray diffraction analysis. Findings Results showed that both factors, Cl− and direct stray current, can accelerate the corrosion rate of grounding grid materials. The magnitude of DC stray current density affected the mass transfer type and response frequency of the anode and cathode reaction of grounding materials, while the Cl− contents of the soil only affect the mass transfer rate of the electrode material from the electrochemical impedance spectroscopy diagrams. The electric field generated by the DC stray current caused Cl− directed migration. The larger the DC stray current density, the greater the diffusion process and the greater the weight loss rate of the grounding grid materials that would have a logarithmic relationship with the Cl− content at the same DC stray current density. The corrosion resistance of the three materials is copper > Q235 galvanized flat steel > Q235 flat steel. Originality/value The paper provides information regarding the relationship among Cl−, direct stray current and corrosion of three grounding grid materials by means of electrochemical impedance spectroscopy. Meanwhile the weight loss rate is the logarithmic relationship with the Cl− content, which is useful for understanding the corrosion mechanism of Q235 steel, Q235 galvanized flat steel and copper under the condition of Cl− and direct stray current in soil.
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Kamil, Ismaila Adeniyi, i Sunday Oyinlola Ogundoyin. "A Privacy-Aware Data Aggregation Scheme for Smart Grid Based on Elliptic Curve Cryptography With Provable Security Against Internal Attacks". International Journal of Information Security and Privacy 13, nr 4 (październik 2019): 109–38. http://dx.doi.org/10.4018/ijisp.2019100107.
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In smart grids (SGs), smart meters (SMs) are usually deployed to collect and transmit customers' electricity consumption data in real-time to the control center. Due to the open nature of the SG communication, several privacy-preserving data aggregation schemes have been proposed to protect the privacy of customers. However, most of these schemes cannot protect against internal attackers and they are not efficient, since SMs are constrained in processing, memory, and computing capabilities. To address these problems, the authors propose a privacy-aware lightweight data aggregation scheme against internal attackers based on Elliptic Curve Cryptography (ECC). The scheme satisfies all the security requirements of SG, and supports conditional traceability, strong anonymity and autonomy. The authors demonstrate that the proposed scheme provides confidentiality based on the Computational Diffie-Hellman (CDH) assumption and unforgeability in the security model based on the intractability of the Discrete Logarithm (DL) problem. Extensive performance analysis shows that the proposed scheme is very efficient.
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Abdullah, A. "Formulation of Low Peclet Number Based Grid Expansion Factor for the Solution of the Convection Diffusion Equation". Engineering, Technology & Applied Science Research 8, nr 2 (19.04.2018): 2680–84. http://dx.doi.org/10.48084/etasr.1858.
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Convection-diffusion problems, due to its fundamental nature, are found in various science and engineering applications. In this research, the importance of the relationship between grid structure and flow parameters in such problems is emphasized. In particular, we propose a systematic technique in the selection of the grid expansion factor based on its logarithmic relationship with low Peclet number. Such linear mathematical connection between the two non-dimensional parameters serves as a guideline for more structured decision-making and improves the heuristic process in the determination of the computational domain grid for the numerical solution of convection-diffusion equations especially in the prediction of the concentration of the scalar. Results confirm the effectiveness of the new approach.
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Acurio, Liliana, Diego Salazar, Purificación García-Segovia, Javier Martínez-Monzó i Marta Igual. "Third-Generation Snacks Manufactured from Andean Tubers and Tuberous Root Flours: Microwave Expansion Kinetics and Characterization". Foods 12, nr 11 (27.05.2023): 2168. http://dx.doi.org/10.3390/foods12112168.
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Andean tubers and tuberous roots have nutritional and medicinal properties transferred through ancestral generations. In this study, we aim to promote cultivation and consumption by developing a snack based on these crops. Corn grits were thoroughly mixed with sweet potato, mashua, and three varieties of oca flour (white, yellow, and red) in an 80:20 ratio, and a single-screw laboratory extruder was utilized to produce third-generation (3G) dried pellets. Microwave expansion was studied, and the dried 3G pellets and expanded snacks were characterized. The microwave expansion curves of the dried 3G pellets were adjusted to the Page, logarithmic, and Midilli–Kucuk models. During the characterization, the influence of the raw material composition was observed in sectional expansion, water content, water activity, water absorption, water solubility, swelling, optical and textural properties, and bioactive compounds. According to global color variation (mixture vs. expanded and dried vs. expanded) and bioactive compound analysis, the mashua suffered little chemical change or nutritional loss during the process. The extrusion process was shown to be an ideal method for manufacturing snacks from Andean tuber flours.
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Xu, Zhihong, Liangyu Guo, Yan Gao, Muhammad Hussain i Panhong Cheng. "Real-Time Pricing of Smart Grid Based on Piece-Wise Linear Functions". Journal of Systems Science and Information 7, nr 4 (25.09.2019): 295–316. http://dx.doi.org/10.21078/jssi-2019-295-22.
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Abstract In a power grid system, utility is a measure of the satisfaction of users’ electricity consumption; cost is a monetary value of electricity generated by the supplier. The utility and cost functions represent the satisfaction of different users and the supplier. Quadratic utility, logarithmic utility, and quadratic cost functions are widely used in social welfare maximization models of real-time pricing. These functions are not universal; they have to be discussed in detail for individual models. To overcome this problem, a piece-wise linear utility function and a piece-wise linear cost function with general properties are proposed in this paper. By smoothing the piece-wise linear utility and cost functions, a social welfare maximization model can be transformed into a differentiable convex optimization problem. A dual optimization method is used to solve the smoothed model. Through mathematical deduction and numerical simulations, the rationality of the model and the validity of the algorithm are verified as long as the elastic and cost coefficients take appropriate values. Thus, different user types and the supplier can be determined by selecting different elastic and cost coefficients.
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Kumar, Nishant, Bhim Singh, Bijaya Ketan Panigrahi i Lie Xu. "Leaky-Least-Logarithmic-Absolute-Difference-Based Control Algorithm and Learning-Based InC MPPT Technique for Grid-Integrated PV System". IEEE Transactions on Industrial Electronics 66, nr 11 (listopad 2019): 9003–12. http://dx.doi.org/10.1109/tie.2018.2890497.
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Mehta, Ridhima. "Optimal assessment of smart grid based photovoltaic cell operational parameters using simulated annealing". International Journal of Applied Power Engineering (IJAPE) 11, nr 4 (1.12.2022): 333. http://dx.doi.org/10.11591/ijape.v11.i4.pp333-344.
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With the ever-increasing load demand throughout the globe, natural renewable resources integrated into the existing network architecture for sustainable energy production are gaining considerable significance. Photovoltaic (PV) generation systems is one such technique to deal with the worldwide challenge for achieving green energy and low carbon footprint while simultaneously providing emission free electrical power from solar radiations. In this paper, we consider smart grid architecture connecting the end-users and the utility power plant with solar energy sources through an effective power optimization system. Multiple performance criteria associated with solar cell operation are evaluated and analyzed using the simulated annealing algorithm. These objectives considered for optimization include the cell saturation current, photo-generated current, material band gap, cell temperature, annualized life cycle cost, fill factor and cell efficiency. The formulated optimization conditions are specified in terms of two independent variables of cell ambient temperature and cell illumination. Moreover, the adaption of distinct values of short circuit current coefficients on the light originated current is measured. Through extensive simulation experiments, two disparate annealing procedures of fast annealing and Boltzmann annealing are applied coupled with three categories of temperature update schemes, viz. exponential, logarithmic and linear.
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Busto, Saray, Michael Dumbser i Laura Río-Martín. "Staggered Semi-Implicit Hybrid Finite Volume/Finite Element Schemes for Turbulent and Non-Newtonian Flows". Mathematics 9, nr 22 (21.11.2021): 2972. http://dx.doi.org/10.3390/math9222972.
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This paper presents a new family of semi-implicit hybrid finite volume/finite element schemes on edge-based staggered meshes for the numerical solution of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations in combination with the k−ε turbulence model. The rheology for calculating the laminar viscosity coefficient under consideration in this work is the one of a non-Newtonian Herschel–Bulkley (power-law) fluid with yield stress, which includes the Bingham fluid and classical Newtonian fluids as special cases. For the spatial discretization, we use edge-based staggered unstructured simplex meshes, as well as staggered non-uniform Cartesian grids. In order to get a simple and computationally efficient algorithm, we apply an operator splitting technique, where the hyperbolic convective terms of the RANS equations are discretized explicitly at the aid of a Godunov-type finite volume scheme, while the viscous parabolic terms, the elliptic pressure terms and the stiff algebraic source terms of the k−ε model are discretized implicitly. For the discretization of the elliptic pressure Poisson equation, we use classical conforming P1 and Q1 finite elements on triangles and rectangles, respectively. The implicit discretization of the viscous terms is mandatory for non-Newtonian fluids, since the apparent viscosity can tend to infinity for fluids with yield stress and certain power-law fluids. It is carried out with P1 finite elements on triangular simplex meshes and with finite volumes on rectangles. For Cartesian grids and more general orthogonal unstructured meshes, we can prove that our new scheme can preserve the positivity of k and ε. This is achieved via a special implicit discretization of the stiff algebraic relaxation source terms, using a suitable combination of the discrete evolution equations for the logarithms of k and ε. The method is applied to some classical academic benchmark problems for non-Newtonian and turbulent flows in two space dimensions, comparing the obtained numerical results with available exact or numerical reference solutions. In all cases, an excellent agreement is observed.
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Alidaee, Bahram, Haibo Wang, Jun Huang i Lutfu S. Sua. "Integrating Statistical Simulation and Optimization for Redundancy Allocation in Smart Grid Infrastructure". Energies 17, nr 1 (31.12.2023): 225. http://dx.doi.org/10.3390/en17010225.
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It is a critical issue to allocate redundancy to critical smart grid infrastructure for disaster recovery planning. In this study, a framework to combine statistical prediction methods and optimization models for the optimal redundancy allocation problem is presented. First, statistical simulation methods to identify critical nodes of very large-scale smart grid infrastructure based on the topological features of embedding networks are developed, and then a linear integer programming model based on generalized assignment problem (GAP) for the redundancy allocation of critical nodes in smart grid infrastructure is presented. This paper aims to contribute to the field by employing a general redundancy allocation problem (GRAP) model from high-order nonlinear to linear model transformation. The model is specifically implemented in the context of smart grid infrastructure. The innovative linear integer programming model proposed in this paper capitalizes on the logarithmic multiplication property to reframe the inherently nonlinear resource allocation problem (RAP) into a linearly separable function. This reformulation markedly streamlines the problem, enhancing its suitability for efficient and effective solutions. The findings demonstrate that the combined approach of statistical simulation and optimization effectively addresses the size limitations inherent in a sole optimization approach. Notably, the optimal solutions for redundancy allocation in large grid systems highlight that the cost of redundancy is only a fraction of the economic losses incurred due to weather-related outages.
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Karthik, Markala, N. Venkata Ramana Naik, Anup Kumar Panda i Sameer Kumar Behera. "A robust variable-λ least logarithmic hyperbolic cosine function adaptive filtering-based control algorithm for grid-connected solar PV system". Electric Power Systems Research 227 (luty 2024): 109955. http://dx.doi.org/10.1016/j.epsr.2023.109955.
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Young, C. D., J. C. Han, Y. Huang i R. B. Rivir. "Influence of Jet-Grid Turbulence on Flat Plate Turbulent Boundary Layer Flow and Heat Transfer". Journal of Heat Transfer 114, nr 1 (1.02.1992): 65–72. http://dx.doi.org/10.1115/1.2911269.
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The influence of high mainstream turbulence on turbulent boundary layer flow and heat transfer is experimentally investigated for length Reynolds numbers between 4 × 104 and 1.5 × 106. The high mainstream turbulence is produced by a round tube grid with uniform jet injection. Injected air is blown in either an upwind or downwind direction at a controllable flow rate. A flat plate test section instrumented with foil thermocouples is located downstream from the jet grid. The turbulence intensity decay and length scale growth along the test plate, the mean velocity and temperature profiles across the boundary layer, and surface heat transfer distribution are measured. The results show that the grid with downwind injection produces a slightly higher turbulence intensity and a smaller length scale than the grid with upwind injection. A higher turbulence intensity and a smaller length scale further enhance the surface heat transfer coefficient. The jet-induced high turbulence does not alter the downstream velocity and temperature profiles in their logarithmic regions, but the wake regions are lower than the zero turbulence profiles. The Reynolds analogy factor, the augmented friction factor, and the augmented Stanton number are higher than those from existing correlations when the jet grid turbulence intensity is greater than 6 percent.
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Zhang, Weijian, Zhimin Guo, Nuannuan Li, Mingyan Li, Qing Fan i Min Luo. "A Blind Signature-Aided Privacy-Preserving Power Request Scheme for Smart Grid". Wireless Communications and Mobile Computing 2021 (29.06.2021): 1–10. http://dx.doi.org/10.1155/2021/9988170.
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Smart grid is an emerging power system capable of providing appropriate electricity generation and distribution adjustments in the two-way communication mode. However, privacy preservation is a critical issue in the power request system since malicious adversaries could obtain users’ daily schedule through power transmission channel. Blind signature is an effective method of hiding users’ private information. In this paper, we propose an untraceable blind signature scheme under the reputable modification digital signature algorithm (MDSA). Moreover, we put forward an improved credential-based power request system architecture integrated with the proposed blind signature. In addition, we prove our blind signature’s blindness and unforgeability under the assumption of Elliptic Curve Discrete Logarithm Problem (ECDLP). Meanwhile, we analyze privacy preservation, unforgeability, untraceability, and verifiability of the proposed scheme. Computational cost analysis demonstrates that our scheme has better efficiency compared with other two blind signatures.
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Jia, Hongen, Yang Li, Guorui Feng i Kaitai Li. "An efficient two-grid method for the Cahn–Hilliard equation with the concentration-dependent mobility and the logarithmic Flory-Huggins bulk potential". Applied Mathematics and Computation 387 (grudzień 2020): 124548. http://dx.doi.org/10.1016/j.amc.2019.06.062.
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Kumbár, Vojtěch, i Jiří Votava. "Influence of Storage Temperature on the Viscous Behaviour of Partially Fermented Wine Must (Pinot Gris)". Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 63, nr 3 (2015): 781–85. http://dx.doi.org/10.11118/actaun201563030781.
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The main goal of this article deals with effect of storage temperature on the partially fermented wine must viscosity. Four samples of partially femrented wine must (Pinot Gris) wre observed. Two samples were stored in cold temperature 5 °C and another two samples were stored at the room temperature ~20 °C. The kinematic viscosity has measured for 132 hours from start of stormy fermetation (in the interval about 16 hours). Rotary viscometer with standard spinde and low-volume adapter was used to experimental measured. Results of kinematic viscosity process were mathematically modelled using logarithms function. Created mathematical models were precision because correlation coefficients and values of significance achieved very high values. Results and trends form this article can be used to the partially fermented wine must viscosity process prediction.
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Smets, Vincent, Boud Verbeiren, Martin Hermy i Ben Somers. "Urban Spatial Configuration and Functional Runoff Connectivity: Influence of Drainage Grid Density and Landscape Metrics". Water 11, nr 12 (17.12.2019): 2661. http://dx.doi.org/10.3390/w11122661.
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Due to changing precipitation patterns induced by climate change, urban planners are confronted with new challenges to effectively mitigate rainfall runoff. An important knowledge gap that needs to be addressed before tackling these challenges is how and to which extent street/drainage grid density and spatial land use configuration influence the amount of runoff. Therefore, a virtual experiment was conducted to assess the influence of grid density and spatial land use configuration on the functional runoff connectivity (Fc), which is a measure of the easiness by which water flows through the landscape. Through the use of a design of experiments approach in combination with the SCS—Curve Number runoff model, a wide variety of neutral landscape models with a fixed percentage of pervious- and impervious cover were generated that maximized the variance of Fc. Correlations between landscape metrics and neutral landscape models were calculated. Our results indicated that, out of the 17 landscape metrics tested, the average impervious cluster area, the number of impervious clusters, the standard deviation of the cluster size, two proximity indexes and the effective impervious area were strongly correlated with Fc throughout all grid scenarios. The relationship between Fc on the one hand and the average impervious cluster area and the effective impervious area on the other hand, was modelled. The average impervious cluster area models showed a relationship with Fc that closely approximated a logarithmic function (R2: 0.49–0.73), while the effective impervious area models were found to have a linear relationship with Fc (R2: 0.63–0.99). A dense grid was shown to cause a strong increase in Fc, demonstrating the effectiveness of an urban grid in channeling and removing runoff. Our results further indicate that fine-grained landscapes with a lot of small impervious clusters are preferred over course-grained landscapes when the goal is to reduce Fc. In highly urbanized landscapes, where the percentage of impervious area is high, small changes in landscape pattern could significantly reduce Fc. By using a downward hydrological modeling approach this research aims to bring more clarity to the underlying variables influencing Fc, rather than trying to generate realistic prediction values.
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Osaloni, Oluwafunso Oluwole, Ayodeji Stephen Akinyemi, Abayomi Aduragba Adebiyi i Ayodeji Olalekan Salau. "An Effective Control Technique to Implement an IUPQC Design for Sensitive Loads in a Hybrid Solar PV-Grid Connection". WSEAS TRANSACTIONS ON POWER SYSTEMS 18 (17.03.2023): 26–38. http://dx.doi.org/10.37394/232016.2023.18.4.
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The recent innovation in power electronic application in the electrical power system (EPS) has given birth to an Improved Unified Power Quality Conditioner (IUPQC) that positively impacts the electrical power system (EPS). The previously available mitigation approaches with the application IUPQC are monotonous and are major designs for a particular power quality (PQ) issue which does not take care of the degree of impart. This paper presents an effective control architecture of an IUPQC design for sensitive loads in hybrid Photovoltaic Solar (PV) connected grid, concentrating on the voltage demand of loads that respond to slight changes. The objective of this work is to design a flexible controller that can respond to the different degrees of PQ challenges concerning voltage, variable load, and solar irradiation. It has combined the merits of an IUPQC and grid-integrated PV source. Effective controllers for Voltage Source Inverter (VSI) connected in series and Current Source Inverter (CSI) connected in shunt compensators of the UPQC are implemented to increase device strength for different voltage and current distortions. The series compensator was controlled using an enhanced Synchronous Reference Frame (SRF) technique based on adaptive notch filters. An Adaptive Logarithmic Absolute Algorithm (ALAL) was deployed for the parallel section of the proposed approach. The Mean Turning Filter (MTF) was used as a replacement for a low pass filter (LPF) for direct current node voltage management, leaving high and low-frequency ripples unaffected. To maintain a constant current on the grid side during grid disturbances, a feed-forward element has been introduced to the shunt CSI controller. Under various network situations, such as under-voltage, over-voltage, voltage distortion, harmonics, rapid load changes, and fluctuation in solar power, the control system performance is better as confirmed by experimental validation. Finally, it is observed that the voltage profile of 0.984 p.u. due to application control falling within the permissible limits. The proposed controllers are tested in the MATLAB Simulink on a developed distribution system model and validated experimental prototype.
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Susanti, Indah, Lilik Slamet S i Waluyo Eko Cahyono. "KARAKTERISTIK KONSENTRASI CH4 (METANA) DI BEBERAPA KOTA BESAR DAN KOTA KECIL DI INDONESIA". MAJALAH ILMIAH GLOBE 19, nr 2 (31.10.2017): 167. http://dx.doi.org/10.24895/mig.2017.19-2.619.
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<p class="JudulABSInd"><strong>ABSTRAK</strong></p><p class="abstrakindo">Keberadaan konsentrasi CH<sub>4</sub> di atmosfer berasal dari sumber emisi CH<sub>4</sub> di permukaan bumi baik asal antropogenik maupun alami. Bobot molekul CH<sub>4</sub> yang ringan mengakibatkan CH<sub>4</sub> dapat bergerak vertikal sampai ke stratosfer. Konsentrasi CH<sub>4</sub> yang tak terkendali berakibat pada pemanasan global dan perubahan iklim, sehingga perlu dipahami karakteristik CH<sub>4</sub> terutama di beberapa kota besar (Jakarta, Medan, Makassar) dan kota kecil (Ambon, Biak Numfor, Pangkal Pinang) di Indonesia. Dengan menggunakan data <em>Atmospheric Infra Red Soundings</em><em> </em>(AIRS) level 3 yang memiliki resolusi spasial satu derajat dan resolusi temporal bulanan, untuk periode waktu 2003-2015, dikaji kecenderungan konsentrasi CH<sub>4</sub> di enam kota dan anomalinya pada beberapa ketinggian atmosfer serta analisis pengaruh kategori kota (kota besar dan kota kecil berdasarkan jumlah penduduk) terhadap konsentrasi CH<sub>4</sub>. Metode yang digunakan pada penelitian ini adalah analisis spasial horizontal dan vertical dengan bantuan <em>Software Grads</em> untuk mengetahui daerah mana dan pada level ketinggian mana terjadi perubahan konsentrasi CH<sub>4</sub>, serta ditunjang oleh analisis statistik regresi dan uji Friedman serta uji Tukey untuk mengetahui apakah ada pengaruh kategori kota terhadap konsentrasi CH<sub>4</sub> di atmosfer. Hasilnya menunjukkan adanya penurunan konsentrasi CH<sub>4 </sub>terhadap ketinggian atmosfer dengan pola logaritmik (eksponensial) yang sebagian besar berasal dari kegiatan di permukaan bumi. Fluktuasi konsentrasi CH<sub>4</sub> di atmosfer disebabkan salah satunya oleh <em>El Nino Southern Oscilation</em> (ENSO). Kondisi ini tampak dari kesamaan pola nilai indeks ENSO dan konsentrasi CH<sub>4</sub>. Berdasarkan penelitian dengan menggunakan uji Friedman dan uji Tukey dihasilkan bahwa klasifikasi kota menjadi kota besar dan kota kecil tidak berpengaruh pada konsentrasi CH<sub>4</sub>.</p><p><strong>Kata kunci</strong>: profil, metana, AIRS, statistik, klasifikasi, kota</p><p class="judulABS"><strong>ABSTRACT</strong></p><p><em>C</em><em>oncentration of CH<sub>4</sub> in the atmosphere comes from the source of CH<sub>4</sub> emissions on the earth's surface either natural or anthropogenic activities. </em><em>The light m</em><em>olecular weight resulting CH<sub>4</sub> can move vertically up into the stratosphere. Unbridled CH<sub>4</sub> concentration resulted in global warming and climate change</em><em>. So, it’s</em><em> important to understand CH4 characteristics, especially in large cities (Jakarta, Medan, Makassar) and small towns (Ambon, Biak Noemfoor, Pangkal Pinang) in Indonesia. Using data Atmospheric Infra Red Soundings (</em><em>AIRS</em><em>) level 3 which has a spatial resolution of one degree and monthly temporal resolution, for time period from 2003 to 2015, we analyzed the tendency of concentration of CH<sub>4</sub> in 6 cities and its anomalies in some altitude atmosphere as well as analysis of the influence of the city category (cities and towns based on population) </em><em>towards</em><em> the CH<sub>4 </sub>concentration. The method used in this research is the analysis of spatial horizontal and vertical </em><em>using</em><em> Grads to know </em><em>region</em><em> and altitude levels which </em><em>have </em><em>change the concentration of CH<sub>4</sub>. In additon, supported by statistical regression analysis and Friedman test and Tukey test to determine whether there is any relation between city category against concentration of CH<sub>4</sub> in the atmosphere. The results indicate a decrease in the height of atmospheric CH<sub>4</sub> concentrations with the pattern of logarithmic (exponential) is mostly derived from activities in the Earth's surface. Fluctuations in the concentration of CH<sub>4</sub> in the atmosphere caused among other is by </em><em>El Nino Southern Oscilation</em> (<em>ENSO</em><em>)</em><em>. This condition appears on the similarities of the ENSO index values and CH<sub>4</sub> concentrations. Based on research by using the Friedman test and Tukey's test result that classification of cities and towns has no effect on the concentration of CH<sub>4</sub>.</em></p><p><strong><em>Keywords:</em></strong><em> profile, </em><em>CH<sub>4</sub>, AIRS, statistic, classification, city </em></p>
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Maltoni, Fabio, Giovanni Ridolfi, Maria Ubiali i Marco Zaro. "Resummation effects in the bottom-quark fragmentation function". Journal of High Energy Physics 2022, nr 10 (5.10.2022). http://dx.doi.org/10.1007/jhep10(2022)027.
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Abstract We compute the perturbative component of the fragmentation function of the b quark to the best of the present theoretical knowledge. The fixed-order calculation to order $$ {\alpha}_s^2 $$ α s 2 of the fragmentation function at the initial scale is matched with soft-emission logarithm resummation to next-to-next-to-leading logarithmic accuracy, so that order-$$ {\alpha}_s^2 $$ α s 2 corrections are accounted for exactly, and logarithmically enhanced contributions from loops of b quarks are included. This requires the calculation of the Mellin transform of the order-$$ {\alpha}_s^2 $$ α s 2 result in the whole complex plane for the Mellin variable, which we provide for the first time for all the fragmenting partons. Evolution is performed to next-to-next-to-leading log accuracy, and mixing with the gluon fragmentation function is taken into account. The perturbative fragmentation functions are made available via LHAPDF grids.
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Bonnans, Frédéric, Guillaume Bonnet i Jean-Marie Mirebeau. "A linear finite-difference scheme for approximating Randers distances on Cartesian grids". ESAIM: Control, Optimisation and Calculus of Variations, 2.06.2022. http://dx.doi.org/10.1051/cocv/2022043.
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Randers distances are an asymmetric generalization of Riemannian distances, and arise in optimal control problems subject to a drift term, among other applications. We show that Randers eikonal equation can be approximated by a logarithmic transformation of an anisotropic second order linear equation, generalizing Varadhan's formula for Riemannian manifolds. Based on this observation, we establish the convergence of a numerical method for computing Randers distances, from point sources or from a domain's boundary, on Cartesian grids of dimension two and three, which is consistent at order two thirds, and uses tools from low-dimensional algorithmic geometry for best efficiency. We also propose a numerical method for optimal transport problems whose cost is a Randers distance, exploiting the linear structure of our discretization and generalizing previous works in the Riemannian case. Numerical experiments illustrate our results.
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Zeiser, Andreas. "Sparse grid time-discontinuous Galerkin method with streamline diffusion for transport equations". Partial Differential Equations and Applications 4, nr 4 (sierpień 2023). http://dx.doi.org/10.1007/s42985-023-00250-2.
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AbstractHigh-dimensional transport equations frequently occur in science and engineering. Computing their numerical solution, however, is challenging due to its high dimensionality. In this work we develop an algorithm to efficiently solve the transport equation in moderately complex geometrical domains using a Galerkin method stabilized by streamline diffusion. The ansatz spaces are a tensor product of a sparse grid in space and discontinuous piecewise polynomials in time. Here, the sparse grid is constructed upon nested multilevel finite element spaces to provide geometric flexibility. This results in an implicit time-stepping scheme which we prove to be stable and convergent. If the solution has additional mixed regularity, the convergence of a 2d-dimensional problem equals that of a d-dimensional one up to logarithmic factors. For the implementation, we rely on the representation of sparse grids as a sum of anisotropic full grid spaces. This enables us to store the functions and to carry out the computations on a sequence regular full grids exploiting the tensor product structure of the ansatz spaces. In this way existing finite element libraries and GPU acceleration can be used. The combination technique is used as a preconditioner for an iterative scheme to solve the transport equation on the sequence of time strips. Numerical tests show that the method works well for problems in up to six dimensions. Finally, the method is also used as a building block to solve nonlinear Vlasov-Poisson equations.
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Abreu, Samuel, Jonathan R. Gaunt, Pier Francesco Monni, Luca Rottoli i Robert Szafron. "Quark and gluon two-loop beam functions for leading-jet pT and slicing at NNLO". Journal of High Energy Physics 2023, nr 4 (26.04.2023). http://dx.doi.org/10.1007/jhep04(2023)127.
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Abstract We compute the complete set of two-loop beam functions for the transverse momentum distribution of the leading jet produced in association with an arbitrary colour-singlet system. Our results constitute the last missing ingredient for the calculation of the jet-vetoed cross section at small veto scales at the next-to-next-to-leading order, as well as an important ingredient for its resummation to next-to-next-to-next-to-leading logarithmic order. Our calculation is performed in the soft-collinear effective theory framework with a suitable regularisation of the rapidity divergences occurring in the phase-space integrals. We discuss the occurrence of soft-collinear mixing terms that might violate the factorisation theorem, and demonstrate that they are naturally absorbed into the beam functions at two loops in the exponential rapidity regularisation scheme when performing a multipole expansion of the measurement function. As in our recent computation of the two-loop soft function, we present the results as a Laurent expansion in the jet radius R. We provide analytic expressions for all flavour channels in x space with the exception of a set of R-independent non-logarithmic terms that are given as numerical grids. We also perform a fully numerical calculation with exact R dependence, and find that it agrees with our analytic expansion at the permyriad level or better. Our calculation allows us to define a next-to-next-to-leading order slicing method using the leading-jet pT as a slicing variable. As a check of our results, we carry out a calculation of the Higgs and Z boson total production cross sections at the next-to-next-to-leading order in QCD.
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Chassagneux, Jean-François, Junchao Chen, Noufel Frikha i Chao Zhou. "A learning scheme by sparse grids and Picard approximations for semilinear parabolic PDEs". IMA Journal of Numerical Analysis, 9.11.2022. http://dx.doi.org/10.1093/imanum/drac066.
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Abstract Relying on the classical connection between backward stochastic differential equations and nonlinear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional semilinear parabolic PDEs. This scheme is inspired by the approach coming from machine learning and developed using deep neural networks in Han et al. (2018, Solving high-dimensional partial differential equations using deep learning. Proc. Natl. Acad. Sci., 115, 8505–8510. Our algorithm is based on a Picard iteration scheme in which a sequence of linear-quadratic optimization problem is solved by means of stochastic gradient descent algorithm. In the framework of a linear specification of the approximation space, we manage to prove a convergence result for our scheme, under some smallness condition. In practice, in order to be able to treat high-dimensional examples, we employ sparse-grid approximation spaces. In the case of periodic coefficients and using pre-wavelet basis functions, we obtain an upper bound on the global complexity of our method. It shows, in particular, that the curse of dimensionality is tamed in the sense that in order to achieve a root mean squared error of order $\varepsilon $, for a prescribed precision $\varepsilon $, the complexity of the Picard algorithm grows polynomially in $\varepsilon ^{-1}$ up to some logarithmic factor $|\!\log (\varepsilon )|$, whose exponent grows linearly with respect to the PDE dimension. Various numerical results are presented to validate the performance of our method, and to compare them with some recent machine learning schemes proposed in E et al. (2017, Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Commun. Math. Stat., 5, 349–380) and Huré et al. (2020, Deep backward schemes for high-dimensional nonlinear PDEs. Math. Comput., 89, 1547–1579).