NUMERICAL SOLUTION OF TWO-DIMENSIONAL  PROBLEMS OF THERMOVISCOELASTICITY

This paper considers the numerical implementation of two-dimensional thermoviscoelastic waves. The elastic collision of an aluminum cylinder with a two-layer plate of aluminum and iron is considered. In work [1] the difference schemes and algorithm of their realization are given. The most complete reviews of the main methods of calculation of transients in deformable solids can be found in [2, 3, 4], which also indicates the need and importance of generalized studies on the comparative evaluation of different methods and identification of the areas of their most rational application. In the analysis and physical interpretation of numerical results in this work it is also useful to use a priori information about the qualitative behavior of the solution and all kinds of information about the physics of the phenomena under study. Here is the stage of evolution of contact resistance of collision – plate, stress profile.

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Smoothing error pitfalls

Atmospheric Measurement Techniques Discussions ◽

10.5194/amtd-7-3301-2014 ◽

2014 ◽

Vol 7 (4) ◽

pp. 3301-3319 ◽

Cited By ~ 1

Author(s):

T. von Clarmann

Keyword(s):

Covariance Matrix ◽

Error Propagation ◽

A Priori ◽

A Priori Information ◽

Atmospheric Variability ◽

True State ◽

Statistical Sense ◽

Atmospheric State ◽

The Difference ◽

Priori Information

Abstract. The difference due to the content of a priori information between a constrained retrieval and the true atmospheric state is usually represented by the so-called smoothing error. In this paper it is shown that the concept of the smoothing error is questionable because it is not compliant with Gaussian error propagation. The reason for this is that the smoothing error does not represent the expected deviation of the retrieval from the true state but the expected deviation of the retrieval from the atmospheric state sampled on an arbitrary grid, which is itself a smoothed representation of the true state. The idea of a sufficiently fine sampling of this reference atmospheric state is untenable because atmospheric variability occurs on all scales, implying that there is no limit beyond which the sampling is fine enough. Even the idealization of infinitesimally fine sampling of the reference state does not help because the smoothing error is applied to quantities which are only defined in a statistical sense, which implies that a finite volume of sufficient spatial extent is needed to meaningfully talk about temperature or concentration. Smoothing differences, however, which play a role when measurements are compared, are still a useful quantity if the involved a priori covariance matrix has been evaluated on the comparison grid rather than resulting from interpolation. This is, because the undefined component of the smoothing error, which is the effect of smoothing implied by the finite grid on which the measurements are compared, cancels out when the difference is calculated.

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Effects of <i>a priori</i> profile shape assumptions oncomparisons between satellite NO<sub>2</sub> columns and model simulations

10.5194/acp-2020-88 ◽

2020 ◽

Author(s):

Matthew J. Cooper ◽

Randall V. Martin ◽

Daven K. Henze ◽

Dylan B. A. Jones

Keyword(s):

Shape Factor ◽

A Priori ◽

Trace Gas ◽

A Posteriori ◽

A Priori Information ◽

Profile Shape ◽

Satellite Retrievals ◽

Mass Factor ◽

The Difference ◽

Priori Information

Abstract. A critical step in satellite retrievals of trace gas columns is the calculation of the air mass factor (AMF) used to convert observed slant columns to vertical columns. This calculation requires a priori information on the shape of the vertical profile. As a result, comparisons between satellite-retrieved and model-simulated column abundances are influenced by the a priori profile shape. We examine how differences between the shape of the simulated and a priori profile can impact the interpretation of satellite retrievals by performing an adjoint-based 4D-Var assimilation of synthetic NO2 observations for constraining NOx emissions. We use the GEOS-Chem Adjoint model to perform assimilations using a variety of AMFs to examine how a posteriori emission estimates are affected if the AMF is calculated using an a priori shape factor that is inconsistent with the simulated profile. In these tests, an inconsistent a priori shape factor increased errors in a posteriori emissions estimates by up to 80 % over polluted regions. As the difference between the simulated profile shape and the a priori profile shape increases, so do the corresponding assimilated emission errors. This reveals the importance of using simulated profile information for AMF calculations when comparing that simulated output to satellite retrieved columns.

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Simplified Two-Dimensional Partial Response Maximum Likelihood Detection Method Using a Priori Information for Holographic Data Storage Systems

Nonlinear Optics ◽

10.1364/isom_ods.2011.otud4 ◽

2011 ◽

Author(s):

Gyuyeol Kong ◽

Sooyong Choi

Keyword(s):

Data Storage ◽

Detection Method ◽

Storage Systems ◽

A Priori ◽

Holographic Data Storage ◽

Two Dimensional ◽

A Priori Information ◽

Maximum Likelihood Detection ◽

Priori Information ◽

Partial Response Maximum Likelihood

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AN APPROACH TO PROCESSING ELECTROTOMOGRAPHY DATA FOR ESTIMATING THE VOLUMES OF SUBSTANCES IN TAILINGS

Interexpo GEO-Siberia ◽

10.33764/2618-981x-2021-2-2-62-66 ◽

2021 ◽

Vol 2 (2) ◽

pp. 62-66

Author(s):

Yuri Grigorievich Karin ◽

Natalia Victorovna Yurkevich

Keyword(s):

A Priori ◽

Software Tools ◽

Two Dimensional ◽

A Priori Information ◽

Electrical Tomography ◽

One Dimensional ◽

Model Section ◽

Priori Information ◽

Tomography Data

Methodical recommendations for processing the data of electrotomography are given. Taking into account a priori information, in particular the results of the study of pits, can be carried out by carrying out a limited inversion of the ET data, while it is possible to limit either the resistance of some layers of the model or the position of the boundaries of some layers [1]. In the software used for processing electrical tomography data Res2dinv [2], it is possible to set the boundary of the assumed layer or to limit the resistance of the model section (to introduce local inhomogeneities with a given resistance). But it is difficult to fix the resistance of a particular layer with the available software tools. The proposed approach makes it possible to take into account the parameters of the model built from the pitting data using a preliminary one-dimensional inversion of the electrical tomography data in the Ip2win [1] program, followed by the export of the obtained assumed layer boundaries to the Res2dinv software for carrying out a limited two-dimensional inversion.

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