Spline-approximation as the basis  of computer technology design of linear structures routes

This article is a continuation of the article published in Journal of Applied Informatics nо.1 in 2019 [1]. In it, the problems of computer design of routes of various linear structures (new and reconstructed railways and highways, pipelines for various purposes, canals, etc.) are considered from a unified standpoint, as problems of approximating a sequence of points on plane of a smooth curve consisting of elements of a given type, i.e. spline. The fundamental difference from other approximation problems considered in the theory of splines and its applications is that the boundaries of the elements of the spline and even their number are unknown. Therefore, a two-stage scheme for finding a solution has been proposed. At the first stage, the number of spline elements and their parameters are determined using dynamic programming. For some tasks, this stage is the only one. In more complex cases, the result of the first stage is used as an initial approximation to optimize the spline parameters using nonlinear programming. Another complicating factor is the presence of numerous restrictions on the spline parameters, which take into account design standards and conditions for the construction and subsequent operation of the structure. The article discusses the features of mathematical models of the corresponding design problems. For a spline consisting of arcs of circles, mated by line segments, used in the design of the longitudinal profile of both new and reconstructed railways and highways and pipelines, a mathematical model is built and a new algorithm for solving a nonlinear programming problem is proposed, taking into account the structural features of the constraint system. In contrast to standard nonlinear programming algorithms, a basis is constructed in the zero-space of the matrix of active constraints and its modification is used when the set of active constraints changes. At the same time, to find the direction of descent at each iteration, no solution of auxiliary systems of equations is required at all. Two options for organizing the iterative optimization process are considered: descent through groups of variables in the presence of sections for independent construction of the descent direction and the traditional change of all variables in one iteration. Experimentally, no significant advantage of one of these options has been revealed.

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Two-stage spline-approximation in linear structure routing

Российский технологический журнал ◽

10.32362/2500-316x-2021-9-5-45-56 ◽

2021 ◽

Vol 9 (5) ◽

pp. 45-56

Author(s):

D. A. Karpov ◽

V. I. Struchenkov

Keyword(s):

Nonlinear Programming ◽

Spline Approximation ◽

Linear Structure ◽

Approximation Problem ◽

Sum Of Squares ◽

Normal Operation ◽

Difficult Case ◽

Linear Structures ◽

Two Stage ◽

Constraint Matrix

In the article, computer design of routes of linear structures is considered as a spline approximation problem. A fundamental feature of the corresponding design tasks is that the plan and longitudinal profile of the route consist of elements of a given type. Depending on the type of linear structure, line segments, arcs of circles, parabolas of the second degree, clothoids, etc. are used. In any case, the design result is a curve consisting of the required sequence of elements of a given type. At the points of conjugation, the elements have a common tangent, and in the most difficult case, a common curvature. Such curves are usually called splines. In contrast to other applications of splines in the design of routes of linear structures, it is necessary to take into account numerous restrictions on the parameters of spline elements arising from the need to comply with technical standards in order to ensure the normal operation of the future structure. Technical constraints are formalized as a system of inequalities. The main distinguishing feature of the considered design problems is that the number of elements of the required spline is usually unknown and must be determined in the process of solving the problem. This circumstance fundamentally complicates the problem and does not allow using mathematical models and nonlinear programming algorithms to solve it, since the dimension of the problem is unknown. The article proposes a two-stage scheme for spline approximation of a plane curve. The curve is given by a sequence of points, and the number of spline elements is unknown. At the first stage, the number of spline elements and an approximate solution to the approximation problem are determined. The method of dynamic programming with minimization of the sum of squares of deviations at the initial points is used. At the second stage, the parameters of the spline element are optimized. The algorithms of nonlinear programming are used. They were developed taking into account the peculiarities of the system of constraints. Moreover, at each iteration of the optimization process for the corresponding set of active constraints, a basis is constructed in the null space of the constraint matrix and in the subspace – its complement. This makes it possible to find the direction of descent and solve the problem of excluding constraints from the active set without solving systems of linear equations. As an objective function, along with the traditionally used sum of squares of the deviations of the initial points from the spline, the article proposes other functions taking into account the specificity of a particular project task.

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Electron microscopy and diffraction studies of polyimides

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100074069 ◽

1983 ◽

Vol 41 ◽

pp. 28-29

Author(s):

O.C. de Hodgins ◽

K. R. Lawless ◽

R. Anderson

Keyword(s):

Electron Microscopy ◽

Electron Microscope ◽

Structural Features ◽

Inert Atmosphere ◽

Polyimide Films ◽

Resolution Electron ◽

The Matrix ◽

High Resolution Electron Microscope ◽

Diffraction Patterns ◽

Polymeric Samples

Commercial polyimide films have shown to be homogeneous on a scale of 5 to 200 nm. The observation of Skybond (SKB) 705 and PI5878 was carried out by using a Philips 400, 120 KeV STEM. The objective was to elucidate the structural features of the polymeric samples. The specimens were spun and cured at stepped temperatures in an inert atmosphere and cooled slowly for eight hours. TEM micrographs showed heterogeneities (or nodular structures) generally on a scale of 100 nm for PI5878 and approximately 40 nm for SKB 705, present in large volume fractions of both specimens. See Figures 1 and 2. It is possible that the nodulus observed may be associated with surface effects and the structure of the polymers be regarded as random amorphous arrays. Diffraction patterns of the matrix and the nodular areas showed different amorphous ring patterns in both materials. The specimens were viewed in both bright and dark fields using a high resolution electron microscope which provided magnifications of 100,000X or more on the photographic plates if desired.

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Calculation features of wall panels with monolithic cement bond of layers in the stages of installation, transportation and maintenance

Vestnik MGSU ◽

10.22227/1997-0935.2019.3.367-375 ◽

2019 ◽

pp. 367-375 ◽

Cited By ~ 1

Author(s):

Elena A. Korol’ ◽

Marina N. Berlinova

Keyword(s):

Middle Layer ◽

Structural Features ◽

Design Parameters ◽

Competitive Advantages ◽

Design Standards ◽

Wall Panels ◽

Multilayer Wall ◽

Current Design ◽

Infinite Variety ◽

Construction Practice

Introduction. When building residential, public and administrative buildings of various spatial structural designs (monolithic, precast-monolithic, precast, etc.), it is common practice to design self-sustaining (non-structural) outer walls within a storey. Developing and using new design and fabrication solutions of multilayer industrial-made wall panels in modern construction practice makes actual the issue of improving methods of their calculation in different stages of maintenance and under various sorts and combinations of loads and effects. However, there is an infinite variety of possible loading levels in practice and, therefore, the same variety of design approaches would be required. This is obviously unacceptable for engineering calculations, hence it is necessary to provide a monolithic matrix bond of layers, both technologically and structurally, which can provide a generalized approach to the calculation of multilayer enclosing structures in accordance with current design standards. Materials and methods. The article describes structural features of a multilayer wall panel made of structural concrete with the middle layer of concrete with low thermal conductivity and monolithic bond of layers. These features have an influence on creation of a design model and a calculation procedure in the stages of transportation, installation and maintenance. Results. The article has examined the structures described above in the sense of design parameters that provide their competitive advantages in strength and maintenance as compared with conventional mass-built enclosures. Conclusions. The studies demonstrate that when combining loads of force and non-force character, stresses in the considered structure do not exceed allowable values in all the stages what proves the prospects of using the multilayer panels with monolithic bond of layers for erection of various-purpose frame-panel buildings.

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Levels of Reality

Languages ◽

10.3390/languages4020022 ◽

2019 ◽

Vol 4 (2) ◽

pp. 22 ◽

Cited By ~ 1

Author(s):

Ronald W. Langacker

Keyword(s):

Structural Features ◽

Epistemic Status ◽

Clause Structure ◽

Matrix Clause ◽

Linguistic Structure ◽

The Matrix ◽

The Status ◽

History Of ◽

Levels Of Reality

Two fundamental aspects of conceptual and linguistic structure are examined in relation to one another: organization into strata, each a baseline giving rise to the next by elaboration; and the conceptions of reality implicated at successive levels of English clause structure. A clause profiles an occurrence (event or state) and grounds it by assessing its epistemic status (location vis-à-vis reality). Three levels are distinguished in which different notions of reality correlate with particular structural features. In baseline clauses, grounded by “tense,” the profiled occurrence belongs to baseline reality (the established history of occurrences). Basic clauses incorporate perspective (passive, progressive, and perfect), and since grounding includes the grammaticized modals, as well as negation, basic reality is more elaborate. A basic clause expresses a proposition, comprising the grounded structure and the epistemic status specified by basic grounding. At higher strata, propositions are themselves subject to epistemic assessment, in which conceptualizers negotiate their validity; propositions accepted as valid constitute propositional reality. Propositions are assessed through interactive grounding, in the form of questioning and polarity focusing, and by complementation, in which the matrix clause indicates the status of the complement.

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Proteins Encapsulated in Porous Sol-Gels: Biomolecules as Pore Structure Templates

MRS Proceedings ◽

10.1557/proc-431-285 ◽

1996 ◽

Vol 431 ◽

Cited By ~ 7

Author(s):

B. C. Dave ◽

B. Dunn ◽

J. S. Valentine ◽

J. I. Zink

Keyword(s):

Pore Structure ◽

Pore Formation ◽

Noncovalent Interactions ◽

Sol Gel ◽

Structural Features ◽

Specific Model ◽

The Matrix ◽

Model Protein ◽

Cyt C ◽

Physical And Chemical

AbstractPorous inorganic SiO2 glasses obtained by the sol-gel route represent a unique matrix for encapsulation of biomolecules wherein the pores act as enclosures for high molecular weight proteins. These hybrid materials are characterized by a pore-biomolecule interface between the pore walls and the protein surface. As a specific model protein, cytochrome c (cyt c) is used to elucidate the nature of physical and chemical interactions between the pores of the matrix and the protein. Evidence from optical absorption, and resonance Raman (RR) spectroscopy methods indicates that the dopant protein alters the structural features of the pore walls. The optical and vibrational measurements strongly suggest that the pores that contain the trapped protein undergo little or no structural change during aging and drying as compared to protein-free pores. Vibrational RR analysis of the trapped cyt c also suggests that the protein resides in a pore where the pore dimensions conform to the shape of the protein. The results indicate that noncovalent interactions between the surface of the protein and the pore walls govern the dynamics of pore formation during gelation and individual biomolecules act as structural templates to design local pore structure.

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The plant remains

Proceedings of the Prehistoric Society ◽

10.1017/s0079497x00078725 ◽

1987 ◽

Vol 53 (S2) ◽

pp. 33-36

Author(s):

Marijke van der Veen

Keyword(s):

Structural Features ◽

Species Level ◽

Systematic Sampling ◽

Grass Seed ◽

Cereal Grain ◽

Plant Remains ◽

Two Samples ◽

The Matrix ◽

Sampling Programme ◽

Mesh Sieve

The absence of earth-filled structural features or easily identifiable graves precluded any systematic sampling programme for environmental evidence. However, two samples for the analysis of carbonised plant remains were collected from each of the two insitu inhumations (SF55 and SF73). The samples consisted of the sediment associated with the burials which included the matrix of the overlying cairn (context 002), and were processed using manual flotation into an 0.5 mm mesh sieve. The sample sizes and results are given in Table 1.The evidence was minimal: only three fragments were found, none of which could be adequately identified. In sample 1, one grass seed was found, but it was badly preserved and could not be identified to genus. In sample 2, one cereal grain was found, again too badly preserved to distinguish it as either wheat or barley. The Polygonumsp. seed from sample 4 again is too fragmented to allow an identification to species level.

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Structural characterization of fibrous synthetic hydrogels using fluorescence microscopy

Soft Matter ◽

10.1039/c9sm01828j ◽

2020 ◽

Vol 16 (17) ◽

pp. 4210-4219 ◽

Cited By ~ 2

Author(s):

Johannes Vandaele ◽

Boris Louis ◽

Kaizheng Liu ◽

Rafael Camacho ◽

Paul H. J. Kouwer ◽

...

Keyword(s):

Fluorescence Microscopy ◽

Structural Characterization ◽

Crucial Role ◽

Structural Features ◽

The Matrix ◽

Synthetic Hydrogels

The structural features of the matrix surrounding the cells play a crucial role in regulating their behavior.

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Tribological Properties of MWCNTs Strengthened Aluminum Composite Fabricated by Induction Melting

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1101.62 ◽

2015 ◽

Vol 1101 ◽

pp. 62-65 ◽

Cited By ~ 1

Author(s):

Muhammad Mansoor ◽

Muhammad Shahid

Keyword(s):

Tribological Properties ◽

Molten Aluminum ◽

Structural Features ◽

Induction Melting ◽

Multiwalled Carbon ◽

Aluminum Composite ◽

Metallographic Examination ◽

Melting Technique ◽

The Matrix ◽

Wear Condition

Aluminum-Multiwalled carbon nanotubes (Al-CNTs) composite was fabricated using air induction melting technique. The nanotubes were dispersed in molten aluminum using innate string action of induction heating at 760 °C. A heavy fluxing condition was used to avoid oxidation of the nanotubes and molten aluminum. The nanotubes were satisfactorily dispersed in the matrix as observed during metallographic examination using scanning electron microscope. The tribological properties (i.e. coefficient of friction and wear rate) of the Al-CNTs composite were investigated using ball-on-disk machine under dry wear condition at 2 cm/sec speed and 3N load. It was observed that both of the tribological parameters exhibited decreasing trends with increasing contents of the nanotubes, which was due to the self lubricating and structural features of the nanotubes. Improved tribology of the composite was the attribute of appreciable dispersion of the nanotubes in the matrix besides their exceptional mechanical properties and reinforcement.

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Nanocomposite Bi(Sb)Te(Se) Materials by Cryogenic Mechanical Alloying and Optimized High Pressure Hot-pressing

MRS Proceedings ◽

10.1557/opl.2012.1369 ◽

2012 ◽

Vol 1456 ◽

Author(s):

Tsung-ta E. Chan ◽

Rama Venkatasubramanian ◽

James M. LeBeau ◽

Peter Thomas ◽

Judy Stuart ◽

...

Keyword(s):

Mechanical Alloying ◽

Hot Pressing ◽

High Energy ◽

Structural Features ◽

Milling Process ◽

Nanocrystalline Powders ◽

Full Density ◽

Seebeck Coefficients ◽

The Matrix ◽

Cryogenic Process

ABSTRACTNanocomposite Bi2Te3 based alloys are attractive for their potentially high thermoelectric figure-of-merit (ZT) around room temperature. The nano-scale structural features embedded in the matrix provide more scattering of phonons and can thus reduce the lattice thermal conductivity. To further take advantage of such nanocomposite structures, we focus on the development of nanocrystalline Bi(Sb)Te(Se) powders by high energy cryogenic mechanical alloying followed by an optimized hot pressing process. This approach is shown to successfully produce Bi(Sb)Te(Se) alloy powders with grain size averaging about 9 nm for n-type BiTe(Se) and about 16 nm for p-type Bi(Sb)Te respectively. This cryogenic process offers much less milling time and prevents thermally activated contamination or imperfections from being introduced during the milling process. The nanocrystalline powders are then compacted at optimized pressures and temperatures to achieve full density compactions and preserve the grain sizes effectively. The resulting nano-bulk materials have optimal Seebeck coefficients and are expected to have improved ZT. Thermoelectric properties and microstructure studies by X-ray diffraction and transmission electron microscopy will also be presented and discussed.

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Nano- and Microcrystal Investigations of Precipitates, Interfaces and Strain Fields in Ni-Ti-Nb by Various TEM Techniques

Materials Science Forum ◽

10.4028/www.scientific.net/msf.738-739.65 ◽

2013 ◽

Vol 738-739 ◽

pp. 65-71 ◽

Cited By ~ 2

Author(s):

Dominique Schryvers ◽

Hui Shi ◽

Gerardo T. Martinez ◽

Sandra Van Aert ◽

Jan Frenzel ◽

...

Keyword(s):

Electron Microscopy ◽

Martensite Plate ◽

Structural Features ◽

Present Contribution ◽

Cast Material ◽

Strain Fields ◽

Transformation Temperatures ◽

The Matrix ◽

Concentration Changes ◽

Microscopy Techniques

In the present contribution several advanced electron microscopy techniques are employed in order to describe chemical and structural features of the nano- and microstructure of a Ni45.5Ti45.5Nb9 alloy. A line-up of Nb-rich nano-precipitates is found in the Ni-Ti-rich austenite of as-cast material. Concentration changes of the matrix after annealing are correlated with changes in the transformation temperatures. The formation of rows and plates of larger Nb-rich precipitates and particles is described. The interaction of a twinned martensite plate with a Nb-rich nano-precipitate is discussed and the substitution of Nb atoms on the Ti-sublattice in the matrix is confirmed.

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