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Semi-log Plot
In science and engineering, a semi-log plot/graph or semi-logarithmic plot/graph has one axis on a logarithmic scale, the other on a linear scale. It is useful for data with exponential relationships, where one variable covers a large range of values.(1) (2) All equations of the form y=\lambda a^ form straight lines when plotted semi-logarithmically, since taking logs of both sides gives :\log_a y = \gamma x + \log_a \lambda. This is a line with slope \gamma and \log_a \lambda vertical intercept. The logarithmic scale is usually labeled in base 10; occasionally in base 2: :\log (y) = (\gamma \log (a)) x + \log (\lambda). A log–linear (sometimes log–lin) plot has the logarithmic scale on the ''y''-axis, and a linear scale on the ''x''-axis; a linear–log (sometimes lin–log) is the opposite. The naming is ''output–input'' (''y''–''x''), the opposite order from (''x'', ''y''). On a semi-log plot the spacing of the scale on the ''y''-axis (or ''x''-axis) is propo ...
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Phase Diagram Of Water
This page provides supplementary data to the article properties of water. Further comprehensive authoritative data can be found at the ''NIST Chemistry WebBook'' page on thermophysical properties of fluids. Structure and properties Thermodynamic properties Liquid physical properties Water/steam equilibrium properties Vapor pressure formula for steam in equilibrium with liquid water: : \log_ P = A - \frac, where ''P'' is equilibrium vapor pressure in k Pa, and ''T'' is temperature in kelvins. For ''T'' = 273 K to 333 K: ''A'' = 7.2326; ''B'' = 1750.286; ''C'' = 38.1. For ''T'' = 333 K to 423 K: ''A'' = 7.0917; ''B'' = 1668.21; ''C'' = 45.1. Data in the table above is given for water–steam equilibria at various temperatures over the entire temperature range at which liquid water can exist. Pressure of the equilibrium is given in the second column in k Pa. The third column is the heat content of each gram of the liquid phase relative to water at 0 °C. The ...
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Technical Drawing
Technical drawing, drafting or drawing, is the act and discipline of composing drawings that visually communicate how something functions or is constructed. Technical drawing is essential for communicating ideas in industry and engineering. To make the drawings easier to understand, people use familiar symbols, perspectives, units of measurement, notation systems, visual styles, and page layout. Together, such conventions constitute a visual language and help to ensure that the drawing is unambiguous and relatively easy to understand. Many of the symbols and principles of technical drawing are codified in an international standard called ISO 128. The need for precise communication in the preparation of a functional document distinguishes technical drawing from the expressive drawing of the visual arts. Artistic drawings are subjectively interpreted; their meanings are multiply determined. Technical drawings are understood to have one intended meaning. A draftsman is ...
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Charts
A chart (sometimes known as a graph) is a graphical representation for data visualization, in which "the data is represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart". A chart can represent tabular numeric data, functions or some kinds of quality structure and provides different info. The term "chart" as a graphical representation of data has multiple meanings: * A data chart is a type of diagram or graph, that organizes and represents a set of numerical or qualitative data. * Maps that are adorned with extra information ( map surround) for a specific purpose are often known as charts, such as a nautical chart or aeronautical chart, typically spread over several map sheets. * Other domain-specific constructs are sometimes called charts, such as the chord chart in music notation or a record chart for album popularity. Charts are often used to ease understanding of large quantities of data and the relationships between pa ...
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Log–log Plot
In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Exponentiation#Power_functions, Power functions – relationships of the form y=ax^k – appear as straight lines in a log–log graph, with the exponent corresponding to the slope, and the coefficient corresponding to the intercept. Thus these graphs are very useful for recognizing these relationships and estimating parameters. Any base can be used for the logarithm, though most commonly base 10 (common logs) are used. Relation with monomials Given a monomial equation y=ax^k, taking the logarithm of the equation (with any base) yields: \log y = k \log x + \log a. Setting X = \log x and Y = \log y, which corresponds to using a log–log graph, yields the equation Y = mX + b where ''m'' = ''k'' is the slope of the line (Grade (slope), gradient) and ''b'' = log ''a'' is the ...
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Nonlinear Regression
In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations (iterations). General In nonlinear regression, a statistical model of the form, \mathbf \sim f(\mathbf, \boldsymbol\beta) relates a vector of independent variables, \mathbf, and its associated observed dependent variables, \mathbf. The function f is nonlinear in the components of the vector of parameters \beta, but otherwise arbitrary. For example, the Michaelis–Menten model for enzyme kinetics has two parameters and one independent variable, related by f by: f(x,\boldsymbol\beta)= \frac This function, which is a rectangular hyperbola, is because it cannot be expressed as a linear combination of the two \betas. Systematic error may be present in the independent variables but its ...
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Nomograph
A nomogram (), also called a nomograph, alignment chart, or abac, is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a mathematical function. The field of nomography was invented in 1884 by the French engineer Philbert Maurice d'Ocagne (1862–1938) and used extensively for many years to provide engineers with fast graphical calculations of complicated formulas to a practical precision. Nomograms use a parallel coordinate system invented by d'Ocagne rather than standard Cartesian coordinates. A nomogram consists of a set of n scales, one for each variable in an equation. Knowing the values of n-1 variables, the value of the unknown variable can be found, or by fixing the values of some variables, the relationship between the unfixed ones can be studied. The result is obtained by laying a straightedge across the known values on the scales and reading the unknown value from where it crosses the scale for that v ...
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Bacterial Growth En
Bacteria (; : bacterium) are ubiquitous, mostly free-living organisms often consisting of one Cell (biology), biological cell. They constitute a large domain (biology), domain of Prokaryote, prokaryotic microorganisms. Typically a few micrometres in length, bacteria were among the first life forms to appear on Earth, and are present in most of its habitats. Bacteria inhabit the air, soil, water, Hot spring, acidic hot springs, radioactive waste, and the deep biosphere of Earth's crust. Bacteria play a vital role in many stages of the nutrient cycle by recycling nutrients and the nitrogen fixation, fixation of nitrogen from the Earth's atmosphere, atmosphere. The nutrient cycle includes the decomposition of cadaver, dead bodies; bacteria are responsible for the putrefaction stage in this process. In the biological communities surrounding hydrothermal vents and cold seeps, extremophile bacteria provide the nutrients needed to sustain life by converting dissolved compounds, suc ...
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Asexual Reproduction
Asexual reproduction is a type of reproduction that does not involve the fusion of gametes or change in the number of chromosomes. The offspring that arise by asexual reproduction from either unicellular or multicellular organisms inherit the full set of genes of their single parent and thus the newly created individual is genetically and physically similar to the parent or an exact clone of the parent. Asexual reproduction is the primary form of reproduction for single-celled organisms such as archaea and eubacteria, bacteria. Many Eukaryote, eukaryotic organisms including plants, animals, and Fungus, fungi can also reproduce asexually. In Vertebrate, vertebrates, the most common form of asexual reproduction is parthenogenesis, which is typically used as an alternative to sexual reproduction in times when reproductive opportunities are limited. Some Monitor lizard, monitor lizards, including Komodo dragons, can reproduce asexually. While all prokaryotes reproduce without the fo ...
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Microbes
A microorganism, or microbe, is an organism of microscopic size, which may exist in its single-celled form or as a colony of cells. The possible existence of unseen microbial life was suspected from antiquity, with an early attestation in Jain literature authored in 6th-century BC India. The scientific study of microorganisms began with their observation under the microscope in the 1670s by Anton van Leeuwenhoek. In the 1850s, Louis Pasteur found that microorganisms caused food spoilage, debunking the theory of spontaneous generation. In the 1880s, Robert Koch discovered that microorganisms caused the diseases tuberculosis, cholera, diphtheria, and anthrax. Microorganisms are extremely diverse, representing most unicellular organisms in all three domains of life: two of the three domains, Archaea and Bacteria, only contain microorganisms. The third domain, Eukaryota, includes all multicellular organisms as well as many unicellular protists and protozoans that ar ...
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Biological Engineering
Biological engineering or bioengineering is the application of principles of biology and the tools of engineering to create usable, tangible, economically viable products. Biological engineering employs knowledge and expertise from a number of pure and applied sciences, such as mass and heat transfer, kinetics, biocatalysts, biomechanics, bioinformatics, separation and purification processes, bioreactor design, surface science, fluid mechanics, thermodynamics, and polymer science. It is used in the design of medical devices, diagnostic equipment, biocompatible materials, renewable energy, ecological engineering, agricultural engineering, process engineering and catalysis, and other areas that improve the living standards of societies. Examples of bioengineering research include bacteria engineered to produce chemicals, new medical imaging technology, portable and rapid disease diagnostic devices, prosthetics, biopharmaceuticals, and tissue-engineered organs. Bio ...
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