Touchdown solutions in general MEMS models

A general infiltration model is derived using a systems approach. The models of Horton, Kostiakov, Overton, Green and Ampt, and Philip are some of the example models that are shown as special cases of the general model. An equivalence between the Green‐Ampt model and the Philip two‐term model is shown. The general model also provides a solution for the Holtan model expressing infiltration as a function of time. This solution of the Holtan model has not been reported in the literature. A first‐order analysis is performed to quantify the uncertainty involved with the generalized model. The general infiltration model contains five parameters. Two of the parameters are physically based and can therefore be estimated from the knowledge of soil properties, antecedent soil moisture conditions, and infiltration measurements; the remaining three can be determined using the least squares method. The model is verified using ten observed infiltration data sets. Agreement between observed and computed infiltration is quite good.

A global oceanic four-dimensional data assimilation system has been developed for use in initializing coupled ocean–atmosphere general circulation models and many other applications. The data assimilation system uses a high resolution global ocean model to extrapolate the information forward in time. The data inserted into the model currently consists only of conventional sea surface temperature observations and vertical temperature profiles. The data are inserted continuously into the model by updating the model's temperature solution every timestep. This update is created using a statistical interpolation routine applied to all data in a 30-day window centered on the present timestep. Large scale features in the sea surface temperature analyses are consistent with those from independent analyses. Subsurface fields created from the assimilation are much more realistic than those produced without the insertion of data. Furthermore, information contained in the assimilation field is shown to be retained in the model solution after the assimilation procedure is terminated. The results are encouraging but further improvements can be made.

Computationally efficient dynamic modelling and simulation of simulated moving bed chromatographic processes with linear isotherms

There are several main factors affect damping characteristics of a magnetorheological damper, the influence laws of some ones are eager to change with varying working conditions. Therefore, it is challengable to establish the relationship between the two: influence factors and damping characteristics of the magnetorheological damper. This paper proposed a new deep learning-based general inverse model to predict the required current value of a magnetorheological damper under changing complex working conditions. Specifically, a fully-connected multilayer perceptron was chosen to train the general forward model. The complex and time-varying relationships between the main factors and damping characteristics were accurately characterized on use of the high nonlinear mapping ability of the multilayer perceptron. Compared to most of general forward models, the proposed model was more excellent with an accuracy of 99.73% based on ensuring generality. Besides, the network inversion method was used in the inverse solution of the multilayer perceptron general forward model, which simplified the process of inverse solution without requiring a mass of training data. Furthermore, a genetic algorithm was used to replace the gradient descent method which was commonly used in network inversion, with the benefit of solving the problem of selecting the initial value and step size, as well as improving the accuracy. Simultaneously, the experiments were conducted on the proposed general inverse model, the experimental results, being consistent with the simulation results, demonstrated that the proposed model can accurately predict the control current value and track the required damping force in changing complex working conditions.

In the paper we consider a general fractional-order wave model with the general fractional-order derivative involving the Miller-Ross kernel for the first time. The analytical solution for the general fractional-order wave model is investigated in detail. The obtained result is given to explore the complex processes in the mining rock.

This paper concerns with the similarity analysis for a general discrete two-velocity model of the Boltzmann equation introduced by Illner [12]. We find the general groups of invariance and we get some exact solutions, recovering general results which contain either solutions extensively described in the literature or undiscovered ones.

J integral solutions for a general bending-tension model

Steady-state solution for a general Schnakenberg model

Smoothing inertial projection neural network for minimization [formula omitted] in sparse signal reconstruction

To find more deliberate f(R,T) cosmological solutions, we proceed our\nprevious paper further by studying some new aspects of the considered models\nvia investigation of some new cosmological parameters/quantities to attain the\nmost acceptable cosmological results. Our investigations are performed by\napplying the dynamical system approach. We obtain the cosmological\nparameters/quantities in terms of some defined dimensionless parameters that\nare used in constructing the dynamical equations of motion. The investigated\nparameters/quantities are the evolution of the Hubble parameter and its\ninverse, the "weight function", the ratio of the matter density to the dark\nenergy density and its time variation, the deceleration, the jerk and the snap\nparameters, and the equation-of-state parameter of the dark energy. We\nnumerically examine these quantities for two general models $R+\\alpha\nR^{-n}+\\sqrt{-T}$ and $R\\log{[\\alpha R]}^{q}+\\sqrt{-T}$. All considered models\nhave some inconsistent quantities (with respect to the available observational\ndata), except the model with n=-0.9 which has more consistent quantities than\nthe other ones. By considering the ratio of the matter density to the dark\nenergy density, we find that the coincidence problem does~not refer to a unique\ncosmological event, rather, this coincidence also occurred in the early\nuniverse. We also present the cosmological solutions for an interesting model\n$R+c_{1}\\sqrt{-T}$ in the non--flat FLRW metric. We show that this model has an\nattractor solution for the late times, though with $w^{(\\textrm{DE})}=-1/2$.\nThis model indicates that the spatial curvature density parameter gets\nnegligible values until the present era, in which it acquires the values of the\norder $10^{-4}$ or $10^{-3}$. As the second part of this work, we consider the\nweak-field [It continues ...]\n

3D ecosystem modelling in the North Atlantic: Relative impacts of physical and biological parameterizations

We describe an idealized primitive equation model for studying mesoscale turbulence and leverage a hierarchy of grid resolutions to make eddy-resolving calculations on the finest grids more affordable. The model has intermediate complexity, incorporating basin-scale geometry with idealized Atlantic and Southern oceans, and with non-uniform ocean depth to allow for mesoscale eddy interactions with topography. The model is perfectly adiabatic and spans the equator, and thus fills a gap between quasi-geostrophic models, which cannot span two hemispheres, and idealized general circulation models, which generally have diabatic processes and buoyancy forcing. We show that the model solution is approaching convergence in mean kinetic energy for the ocean mesoscale processes of interest, and has a rich range of dynamics with circulation features that emerge only due to resolving mesoscale turbulence.

Anomally models based on a spectral general circulation model (GCM) are formulated and applied to study of low-frequency atmospheric variability in the extratropics, and long-range forecasting research. A steady linear version of the anomaly model is treated by a matrix method. This model consists of nine vertical levels, 15 wave rhomboidal truncation, primitive equation system, and a fixed basic state, which is three-dimensionally variable. The matrix to be handled is extremely large, but can be solved using Krylov's technique. The solutions represent various teleconnection patterns known in the observed atmosphere. The sensitivity of the response of this anomaly model to zonally variability of the temporally fixed basic fields and to the geographical position of tropical heatings is investigated. The solutions of the steady linear anomaly model are compared with those of the original GCM, revealing that there are a few similarities among the solutions, but considerable discrepancies are also ev...

A general nonlinear model of illiquid markets with feedback effects is considered. This equation with 2 free functional parameters contains as partial cases the classical Black‐Scholes equation, Schönbucher‐Wilmott equation, and Sircar‐Papanicolaou equation of option pricing. We obtain here the complete group classification of the equation, and for every parameters specification we obtain the principal Lie algebra and its optimal system of 1‐dimensional subalgerbras. For every such subalgebra we calculate the invariant submodel and invariant solution, when it is possible. Thus, the series of invariant submodels and invariant solutions are derived for the considered nonlinear model.

Introduction Economical heavy oil production is possible by allowing formation sand to be produced along with fluid. Cold production has potential to increase subsequent enhanced oil recovery (EOR) efficiency, operating new technological possibilities for continuedeconomical oil production from these reservoirs. Heavy oil (10–15 ºAPI) in cohesionless sandstones (>30% porosity) can be exploited by permitting sand to enter the wellhole along with fluids. Information from Lloydminster and North Primrose areas is given in Table 1. To achieve sustained production, sand production must be encouraged through use of closely spaced high-energy perforations and through application or work over strategies that re-initiate sand production if it has stopped. Sand exclusion is disastrous; free sand flow is vital production mechanism, as yet incompletely understood(1). Blocking it by gravel packs or screens simply reduces the oil now below economical levels. Lowering Cold Production Costs To compete with offshore oil and absorb price differences between heavy and conventional oil production cost minimization is vital for the shallow (300 – 800 m) heavy oil reservoirs typical of Alberta and Saskatchewan Cretaceous deposit. Drilling costs can be lowered by using coiled tubing and smaller diameter drill hole; there is little evidence that a larger hole is better for cold production. Workover costs can be lowered by using better pumps that do not sand in, and by better workover methods to reduce service TABLE 1: Enhancement of oil rate through cold production. Table Available In Full Paper. rig time and re-establish sand production. Economic and environmentally acceptable sand disposal methods must be implemented(2). Finally, initial development must be planned with EOR production in mind to minimize additional redevelopment costs. Cold Production Mechanisms In these wells, conventional well theory predicts production rates of 0–2 m3/day, rather than the 5– 15 m3/day commonly obtained. Why does heavy oil flow more efficiently if 1–3% sand enters the wellbore with the fluids? A complete answer remains elusive, but the four major factors are likely enhanced drainage radius, grain movement, gas bubble expansion and continuous pore deblocking. Quantitative analyses have been developed for the first two(3, 4), and partly for the third mechanism(5). The fourth remains a qualitative concept. Enhanced drainage arises because thousands of cubic metres of reservoir are affected by large-scale sand production. Discrete cavities may exist, piping tubes may develop, and zones dilated from 30% to 36–40% porosity may all accompany massive sand production. Each of these will increase well flow capacity. Closed-form solutions for piping tube or general yield models show that a factor of 3 to 4 in sustained rate productivity can be expected (3). However, improvement factors of 4 to 10 and more are common in cold production. Grain mobility facilitates liquid movement, independent of permeability enhancement effects. A theoretical model of local fluid rate enhancement in mobile grain systems shows that increased flow rates up to a factor of two can be expected because of the reduction of drag forces(4). There is a variant of the gas bubble theory which may help explain improved production(5).