A unified analytical solution of the steady-state atmospheric diffusion equation

An alternative general solution of the steady-state heat diffusion equation

We consider the preconditioned Krylov subspace method for linear systems arising from the finite volume discretization method of steady-state variable-coefficient conservative space-fractional diffusion equations. We propose to use a scaled-circulant preconditioner to deal with such Toeplitz-like discretization matrices. We show that the difference between the scaled-circulant preconditioner and the coefficient matrix is equal to the sum of a small-norm matrix and a low-rank matrix. Numerical tests are conducted to show the effectiveness of the proposed method for one- and two-dimensional steady-state space-fractional diffusion equations and demonstrate that the preconditioned Krylov subspace method converges very quickly.

A potential and stream function analysis of two-dimensional steady-state convective diffusion equations involving Laplace fields

In this paper we describe, analyse and implement a parallel iterative method for the solution of the steady-state drift diffusion equations governing the behaviour of a semiconductor device in two space dimensions. The unknowns in our model are the electrostatic potential and the electron and hole quasi-Fermi potentials. Our discretisation consists of a finite element method with mass lumping for the electrostatic potential equation and a hybrid finite element with local current conservation properties for the continuity equations. A version of Gummel's decoupling algorithm which only requires the solution of positive definite symmetric linear systems is used to solve the resulting nonlinear equations. We show that this method has an overall rate of convergence which only degrades logarithmically as the mesh is refined. Indeed the (inner) nonlinear solves of the electrostatic potential equation converge quadratically, with a mesh independent asymptotic constant. We also describe an implementation on a MasPar MP-1 data parallel machine, where the required linear systems are solved by the preconditioned conjugate gradient method. Domain decomposition methods are used to parallelise the required matrix-vector multiplications and to build preconditioners for these very poorly-conditioned systems. Our preconditioned linear solves also have a rate of convergence which degrades logarithmically as the grid is refined relative to subdomain size, and their performance is resilient to the severe layers which arise in the coefficients of the underlying elliptic operators. Parallel experiments are given.

Often in reactor dynamics, higher eigenfunctions of the multigroup diffusion equation must be determined. An algorithm to calculate higher eigenfunctions (modes) of the [lambda]-eigenvalue problem corresponding to the steady-state two-group neutron diffusion equation is presented. The method is based on a special type of subspace iteration for large sparse nonsymmetric eigenvalue problems. Having been tested using an International Atomic Energy Agency benchmark problem and also applied to a VVER-1000 pressurized water reactor assembly, the algorithm was found to work very effectively and reliably. In its application, the algorithm presented is not restricted to the [lambda]-eigenvalue problem only but is also generally applicable to large sparse nonsymmetric eigenvalue problems even with multiple and complex eigenvalues.

Analysis of China’s Haze Days in the Winter Half-Year and the Climatic Background during 1961–2012

The state equations for orthotropic, doubly curved shells are established in an orthogonal curvilinear coordinate system. Simplifying hypotheses about displacement models or stress distribution that were assumed in early work are not introduced in this paper. The continuity conditions of stresses and displacements at the interfaces between the contacting layers are satisfied, and analytical solutions for statics and dynamics of the simply supported, doubly curved shells with ortho‐tropic layers are presented by means of the Cayley‐Hamilton theorem. For any number of layers considered, the problem reduces to solving a set of linear algebraic equations with three unknowns. A unified analytical solution is given for thin, moderately thick, and thick laminated shells. The solution satisfied all the equations of elasticity, and each of nine elastic constants is considered. Arbitrary precision of the desired order can be obtained. Numerical results are given to compare with solutions available in the literature.

The increase in the effectiveness of capital investments in the construction of hydropower, water-transport, oH-industry, and other hydraulic structures is in direct relation to the solution of the scientific problems of developing rationaltypes of structures and of methods of determining loads on them, resulting from the action of wind waves, ice, ships, and other floating objects. During recent years, Soviet scientists have carried out various investigations [3-7],t" from which the values of the above-mentioned loads have been substantially refined. Thus, in particular, at the level of a third approximation a theoretical solution for standing waves was worked out. Using data from experimental investigations, the procedure for analyzing the wave action on slopes protected with slabs was improved, and the field of rational application of run-of-quarry rock in the bodies of sloping structures was detemained. The coefficients of resistance for passage of waves around barriers of different shapes were analytically and experimentally studied, and a unified analytical solution, applicable to shallow and deep water, was developed fordetermining wave loads on barriers around which the water flows and on trussed structures in the foma of bar systems. Methods have been developed and tested for determining the elements of wind waves under deep and shallow-water conditions in open bodies of water, and many concepts concerning the analysis of elements of diffracted waves in protected bodies of water have been refined. Favorable results from this extensive work, carried out unintermptedly during several decades, have been achieved thanks to the unification of the efforts of the Wave Commission of the Institute of Water Problems of the Academy of Sciences, the Coordinating Commission on Water-Transport Hydraulic Structures of the VNHG Institute of the Ministry of Power and Electrification (Min~nergo) and the Section of Marine Wave Action of the Oceanographic Commission of the Academy of Sciences, all of the USSR. The thorough work on the problems serving as the basis of the draft of the new SNiP chapter has been accompanied by keen scientific discussions at All-Union Coordinating Conferences and Seminars on Hydraulic Engineering. held in Leningrad at the VNIIG Institute. The most important scientific investigations, used for preparing the draft of the norms, were published in the proceedings of the coordinaang conferences on hydraulic engineering [3-7]. The Draft Chapter SNiP II-57-75 was drawn up in accordance with a resolution of the Government Committee for Construction (Gosstroi) of the USSR for revision and unification of the following current All-Union construction norms: SN 92-60 [1], SN '/6-66 [9], SN 144-60 [2], and SN 288-64 [8]. One of the leading orgardzations in the preparation of the draft was the B. E. Vedeneev VNHG Institute of the Mmenergo of the USSR. The work was carried out with the cooperation of universities and of scientific and design insitutes of the nation, which expressed interest in this task; important contributions were made by the Soyuzmomiiproekt and the Chernomornliproekt institutes of the Ministry of Sea Transport, the Institute of Water Problems of the Academy of Sciences of the USS1L the State Oceanographic Institute and the State Hydrologic Institute of the Main Hydrometeorological Service, the V. V. Knibyshev Moscow Civil Engineering Institute, the Leningrad Hydrometeorologi eal Institute, the Leningrad Institute of Water Transport, the Gidrorechtrans and the Lengiprorechtrans of the Ministry of Inland Water Transport of the Russian Soviet Federated SR, the S. Ya. Zhuk Gidroproekt Institute of the Minenergo of the USSR, the Gipromomeft' Institute of the Ministry of the Oil Industry of the USSR. the TsNIIS and the Black-Sea

Closed-form solutions for the elastic–plastic buckling design of shell structures under external pressure

: Argus Island wind information was systematically recorded and processed over a three-year period. The recording, processing, and analysis procedures used are described. Monthly mean wind speeds with standard deviations are compared with monthly median wind speeds and quartiles. Monthly distributions of wind speed are given, as well as yearly distributions. Cumulative distribution plots compare wind-speed occurrences over the three-year period. A time plot of daily mean and maximum wind speeds is given, and diurnal variations are discussed. The distributions of wind direction for each month are also shown.

Wind power distributions: A review of their applications

This work presents an assessment of the wind potential and a design methodology for a 10 MW wind farm in the Arzew industrial region, located in northwest Algeria, to improve the quality of service of the electricity grid and increase Algeria's participation in the use of renewable energy. The hourly wind data of 10 years (2005-2015) that correspond to the wind potential of the site were analyzed, such as: dominant wind directions, probability distribution, Weibull parameters, mean wind speed and power potential. The site has a mean annual wind speed of 4.46 m/s at 10m height, and enough space to locate the wind turbines. A comparative study was carried out between four wind turbine technologies to improve the site's efficiency and select the appropriate technology: PowerWind 56/ 900 kW, Nordex N50/800 kW, Vestas V50/850 kW, NEG-Micon 44/750 kW. The estimate of the energy produced using WAsP software and the choice of the optimal architectural configuration for wind turbines installation was confirmed. A techno-economic and environmental study was carried out by HOMER software, to choose the model that produces the maximum annual net energy with a competitive cost in the global wind energy market, $ 0.068/kWh, and that provides clean energy with a reduced emission of polluting gases. Finally, this work provides a good indicator for the construction of a wind farm in Arzew.

The statistical prediction of local sea surface winds from large-scale, free-tropospheric fields is investigated at a number of locations over the global ocean using a statistical downscaling model based on multiple linear regression. The predictands (the mean and standard deviation of both vector wind components and wind speed) calculated from ocean buoy observations on daily, weekly, and monthly scales are regressed on upper-level predictor fields from reanalysis products. It is found that in general the mean vector wind components are more predictable than mean wind speed in the North Pacific and Atlantic, while in the tropical Pacific and Atlantic the difference in predictive skill between mean vector wind components and wind speed is not substantial. The predictability of wind speed relative to vector wind components is interpreted by an idealized model of the wind speed probability density function, which indicates that in the midlatitudes the mean wind speed is more sensitive to the vector wind standard deviations (which generally are not well predicted) than to the mean vector winds. In the tropics, the mean wind speed is found to be more sensitive to the mean vector winds. While the idealized probability model does a good job of characterizing month-to-month variations in the mean wind speed in terms of the vector wind statistics, month-to-month variations in the standard deviation of speed are not well modeled. A series of Monte Carlo experiments demonstrates that the inconsistency in the characterization of wind speed standard deviation is the result of differences of sampling variability between the vector wind and wind speed statistics.

Reliability analysis of a microwave tower for fluctuating mean wind with directional effect

Moored buoy observations began two to three decades ago. These datasets have value for calibration of remotely sensed data, validation of weather and ocean wave models, input to reanalysis models, and studies of climate trend and variability. Changes in buoy wind observation methods have the potential to introduce inhomogeneities into the time series. These include changes in anemometer height (typically between 5 and 10 m) with changes in platform type; the transition in the 1980s and 1990s from use of a vector‐mean to a scalar‐mean averaging method; and, in recent years, the introduction of ultrasonic anemometers in the buoy networks, as well as the continued use of mechanical propeller‐vane type of anemometers. This study examines differences in buoy wind measurements from RM Young propeller‐vane and Vaisala ultrasonic anemometers installed on the same buoy, and differences in vector‐averaged and scalar‐averaged wind speeds from the same RM Young anemometer. This study also considers the effect of waves on these differences. The comparisons are based on large multi‐year datasets from 6‐m buoys with boat‐shaped hulls (6N) and 3‐m buoys with round hulls (3D), deployed off the coasts of Canada in the northeast Pacific and northwest Atlantic Oceans. Results of the anemometer type comparison suggest that the Vaisala ultrasonic winds are 0.16 ms−1 + 1.6% of the RM Young winds. Results of the vector scalar comparison of Canadian buoy data show that scalar mean winds were 2.1% and 2.7% greater than RM Young vector mean winds from 6N and 3D buoys, respectively. Vector‐scalar differences increased with increasing wave height, more quickly with 3D than with 6N buoys. Results are used to adjust the winds from a long‐term buoy in the northeast Pacific. The height adjustment is shown to be more important than the adjustment for vector or scalar averaging of the sustained wind speed, in terms of the impact of monthly mean wind speeds. A homogeneity testing program finds other unexplained significant shifts in the time series of monthly mean wind speeds. Copyright © 2011 Royal Meteorological Society and Crown in the right of Canada.