scholarly journals Analysis of a Parabolic Fin via Matrix Method

2021 ◽  
Vol 8 (3) ◽  
Author(s):  
Rohit Gupta ◽  
Inderdeep Singh
Keyword(s):  
Temperature Distribution ◽  
Cross Section ◽  
Cross Sections ◽  
Matrix Method ◽  
Science And Engineering ◽  
Engineering Problems ◽  
The Matrix

Heat is not lost equally by each element of the fin but is lost mostly near the base of the fin. Thus there would be wastage of the material if a uniform fin is used. Due to this reason fins of varying cross-sections like hyperbolic fins or parabolic fins are constructed. The parabolic fin of varying cross-section is usually analyzed by ordinary calculus approach. The paper analyses parabolic fin of varying cross-section to find the rate of conduction of heat through it via the application of matrix method. The matrix method has been applied successfully in science and engineering problems and also comes out to be very effective tool to find the temperature distribution and rate of conduction of heat through a parabolic fin.

The calculations of processes involving mesons by matrix methods

1940 ◽  
Vol 36 (3) ◽  
pp. 363-380 ◽  
Author(s):  
A. H. Wilson
Keyword(s):  
Electromagnetic Field ◽  
Cross Sections ◽  
Relativistic Theory ◽  
Matrix Method ◽  
Nuclear Interaction ◽  
New Method ◽  
Nuclear Scattering ◽  
Matrix Methods ◽  
Meson Theory ◽  
The Matrix

In a previous paper a new method, based on Kemmer's β-formalism, of calculating meson processes was given for the case in which the meson interacts with an electromagnetic field. This method is now extended to the nuclear interaction, so that the whole of the meson theory can be given either in tensor or in matrix form, the former being preferable when the wave aspect of the meson is important and the latter when the particle aspect is dominant.As examples of the matrix method, derivations are given of the cross-sections for the nuclear scattering of mesons and for the production of mesons from nuclei by photons. It is pointed out that the usual non-relativistic theory of the nuclear interaction is inadequate even for very small velocities.

ANN prediction of fire temperature in timber

2019 ◽  
Vol 10 (2) ◽  
pp. 233-244
Author(s):  
Paulo Cachim
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Design Methodology ◽  
Content Type ◽  
Construction Engineering ◽  
Standard Fire ◽  
Model Complex ◽  
Engineering Problems ◽  
The Cross ◽  
Fire Loading

Purpose Fire degradation is an extremely important risk that threatens timber structures. It is therefore normal that timber design codes include provisions for the design and verification of structures under fire loading. Eurocode 5 is no exception to this, but the simplified methods presented in the code show some inconsistencies, and the advanced method is not practical to use for design purposes. Artificial neural networks (ANNs) have the ability to model complex problems and have been used in a variety of construction engineering problems. They can learn from a subset of data, and then they can be used to predict the results for other input parameters. The purpose of this study is to present the possibility of the use of ANNs for the prediction of temperatures in rectangular timber cross sections, under fire exposure. Design/methodology/approach In this work, a multilayer feedforward ANN has been trained to predict the temperatures within a timber cross section, using as input the size of the cross section, the timber density, the time of exposure and the coordinates of the point within the cross section. Findings The results obtained clearly indicate that ANN can be used to predict the temperatures in a timber cross section subjected to fire. Originality/value ANNs have not been used for the prediction of temperatures in timber cross sections. The use of ANN makes the temperature prediction under a standard fire loading in a cross section extremely easy to implement in any code. These results can be used to calculate the strength of the elements after fire.

scholarly journals Torsional vibration of suspension bridge with a variable cross section

1981 ◽  
Vol 3 (2) ◽  
pp. 22-26
Author(s):  
Nguyen Van Tinh
Keyword(s):  
Computer Program ◽  
Transfer Matrix ◽  
Cross Section ◽  
Cross Sections ◽  
Torsional Vibration ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Suspension Bridge ◽  
Variable Cross Section ◽  
Variable Cross

The transfer matrix method to torsion’ al vibrations of a suspension bridge with variable cross sections is reported. The method described above is particularly suitable for implementing an efficient computer program. A numerical example is also givens.

Numerical and Experimental Evaluation of the Temperature Distribution Within Laminated Veneer Lumber (LVL) Exposed to Fire

2010 ◽  
Vol 1 (3) ◽  
pp. 145-159 ◽  
Author(s):  
Massimo Fragiacomo ◽  
Agnese Menis ◽  
Peter Moss ◽  
Andrew Buchanan ◽  
Isaia Clemente
Keyword(s):  
Temperature Distribution ◽  
Cross Section ◽  
Cross Sections ◽  
Structural Design ◽  
Experimental Tests ◽  
Radiata Pine ◽  
Complex Problem ◽  
Laminated Veneer Lumber ◽  
Timber Member ◽  
The University

The fire resistance evaluation of a timber member is an important and complex problem of structural design. In order to solve this problem, it is crucial to have reliable information on the temperature distribution within a timber cross-section exposed to fire, and to develop a numerical model for the prediction of such a quantity. The paper reports the experimental-numerical comparisons in terms of temperature distribution within a timber member made from radiata pine LVL (laminated veneer lumber) exposed to fire. The experimental tests were performed at the University of Canterbury and BRANZ (New Zealand) on 146×60, 300×105 and 360×133 mm LVL members. The temperature distribution was monitored using several thermocouples. The numerical results were obtained using the Abaqus FE code with different conductive models. The Eurocode 5 and Frangi's proposals led to similar results characterized by acceptable approximation close to the surface. Since the accuracy reduced for deeper fibres, a new proposal based on a different variation of the conductivity with the temperature was made. The proposal led to acceptable approximation throughout the tested cross-sections.

Electron Irradiation Effects in Polyoxymethylene Crystals Grown Inside Trioxane Crystals

1971 ◽  
Vol 29 ◽  
pp. 78-79
Author(s):  
J. P. Colson ◽  
D. H. Reneker
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Detailed Examination ◽  
The Other ◽  
Electron Micrograph ◽  
Irradiation Effects ◽  
Threefold Axis ◽  
Typical Sample ◽  
Polymer Crystals ◽  
Chain Axis

Polyoxymethylene (POM) crystals grow inside trioxane crystals which have been irradiated and heated to a temperature slightly below their melting point. Figure 1 shows a low magnification electron micrograph of a group of such POM crystals. Detailed examination at higher magnification showed that three distinct types of POM crystals grew in a typical sample. The three types of POM crystals were distinguished by the direction that the polymer chain axis in each crystal made with respect to the threefold axis of the trioxane crystal. These polyoxymethylene crystals were described previously.At low magnifications the three types of polymer crystals appeared as slender rods. One type had a hexagonal cross section and the other two types had rectangular cross sections, that is, they were ribbonlike.

A quantitative approach to inner shell losses

1978 ◽  
Vol 36 (1) ◽  
pp. 526-527 ◽  
Author(s):  
R.D. Leapman ◽  
P. Rez ◽  
D.F. Mayers
Keyword(s):  
Energy Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Background Intensity ◽  
Core Excitation ◽  
Quantitative Basis ◽  
Cross Section Differential ◽  
Bound Electrons

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

Oxygen K near edge structures studied with multiple scattering calculations

1988 ◽  
Vol 46 ◽  
pp. 504-505
Author(s):  
Xudong Weng ◽  
Peter Rez
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Partial Cross Section ◽  
Energy Window ◽  
Edge Structure ◽  
Fine Structures ◽  
Hydrogenic Model ◽  
Electron Energy Loss ◽  
Quantitative Chemical

In electron energy loss spectroscopy, quantitative chemical microanalysis is performed by comparison of the intensity under a specific inner shell edge with the corresponding partial cross section. There are two commonly used models for calculations of atomic partial cross sections, the hydrogenic model and the Hartree-Slater model. Partial cross sections could also be measured from standards of known compositions. These partial cross sections are complicated by variations in the edge shapes, such as the near edge structure (ELNES) and extended fine structures (ELEXFS). The role of these solid state effects in the partial cross sections, and the transferability of the partial cross sections from material to material, has yet to be fully explored. In this work, we consider the oxygen K edge in several oxides as oxygen is present in many materials. Since the energy window of interest is in the range of 20-100 eV, we limit ourselves to the near edge structures.

Absolute inner-shell cross section determination for EELS analysis

1988 ◽  
Vol 46 ◽  
pp. 534-535
Author(s):  
P.A. Crozier
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Absolute Cross Section ◽  
Specimen Thickness ◽  
Mass Thickness ◽  
Scattering Cross ◽  
Before And After ◽  
Estimated Error ◽  
Scattering Cross Sections ◽  
Electron Microscopist

Absolute inelastic scattering cross sections or mean free paths are often used in EELS analysis for determining elemental concentrations and specimen thickness. In most instances, theoretical values must be used because there have been few attempts to determine experimental scattering cross sections from solids under the conditions of interest to electron microscopist. In addition to providing data for spectral quantitation, absolute cross section measurements yields useful information on many of the approximations which are frequently involved in EELS analysis procedures. In this paper, experimental cross sections are presented for some inner-shell edges of Al, Cu, Ag and Au.Uniform thin films of the previously mentioned materials were prepared by vacuum evaporation onto microscope cover slips. The cover slips were weighed before and after evaporation to determine the mass thickness of the films. The estimated error in this method of determining mass thickness was ±7 x 107g/cm2. The films were floated off in water and mounted on Cu grids.

A technique for preparing semiconductor cross sections for both TEM and SEM analysis

1989 ◽  
Vol 47 ◽  
pp. 712-713
Author(s):  
Stanley J. Klepeis ◽  
J.P. Benedict ◽  
R.M Anderson
Keyword(s):  
Sample Preparation ◽  
Cross Section ◽  
Cross Sections ◽  
Sem Analysis ◽  
Preparation Technique ◽  
Ion Milling ◽  
Tem Analysis ◽  
Polished Cross Section ◽  
Area Of Interest ◽  
Polished Side

The ability to prepare a cross-section of a specific semiconductor structure for both SEM and TEM analysis is vital in characterizing the smaller, more complex devices that are now being designed and manufactured. In the past, a unique sample was prepared for either SEM or TEM analysis of a structure. In choosing to do SEM, valuable and unique information was lost to TEM analysis. An alternative, the SEM examination of thinned TEM samples, was frequently made difficult by topographical artifacts introduced by mechanical polishing and lengthy ion-milling. Thus, the need to produce a TEM sample from a unique,cross-sectioned SEM sample has produced this sample preparation technique.The technique is divided into an SEM and a TEM sample preparation phase. The first four steps in the SEM phase: bulk reduction, cleaning, gluing and trimming produces a reinforced sample with the area of interest in the center of the sample. This sample is then mounted on a special SEM stud. The stud is inserted into an L-shaped holder and this holder is attached to the Klepeis polisher (see figs. 1 and 2). An SEM cross-section of the sample is then prepared by mechanically polishing the sample to the area of interest using the Klepeis polisher. The polished cross-section is cleaned and the SEM stud with the attached sample, is removed from the L-shaped holder. The stud is then inserted into the ion-miller and the sample is briefly milled (less than 2 minutes) on the polished side. The sample on the stud may then be carbon coated and placed in the SEM for analysis.

Experimental Studies Of Multilayer Glass Structures On Compression, Compression With Bending And Simple Bending

2019 ◽  
pp. 22-30
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Applied Load ◽  
Experimental Studies ◽  
Strength Properties ◽  
Research Topic ◽  
Normative Values ◽  
Laminated Glass ◽  
The Cross ◽  
Experimental Values

The work of multilayer glass structures for central and eccentric compression and bending are considered. The substantiation of the chosen research topic is made. The description and features of laminated glass for the structures investigated, their characteristics are presented. The analysis of the results obtained when testing for compression, compression with bending, simple bending of models of columns, beams, samples of laminated glass was made. Overview of the types and nature of destruction of the models are presented, diagrams of material operation are constructed, average values of the resistance of the cross-sections of samples are obtained, the table of destructive loads is generated. The need for development of a set of rules and guidelines for the design of glass structures, including laminated glass, for bearing elements, as well as standards for testing, rules for assessing the strength, stiffness, crack resistance and methods for determining the strength of control samples is emphasized. It is established that the strength properties of glass depend on the type of applied load and vary widely, and significantly lower than the corresponding normative values of the strength of heat-strengthened glass. The effect of the connecting polymeric material and manufacturing technology of laminated glass on the strength of the structure is also shown. The experimental values of the elastic modulus are different in different directions of the cross section and in the direction perpendicular to the glass layers are two times less than along the glass layers.

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