AAcetylene

Simplest alkyne, CH. A colourless, flammable, explosive gas, it is used as a fuel in welding and cutting metals and as a raw material for many organic compounds and plastics. It is produced by reaction of water with calcium carbide, passage of a hydrocarbon through an electric arc, or partial combustion of methane. Decomposing it liberates heat; depending on degree of purity, it is also an explosive. An acetylene torch reaches about

6,000 °F (3,300 °C), hotter than combustion of any other known gas mixture.

Alcohols

Alcohol, any of a class of organic compounds characterized by one or more hydroxyl (−OH) groups attached to a carbon atom of an alkyl group (hydrocarbon chain). Alcohols may be considered as organic derivatives of water (H2O) in which one of

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the hydrogen atoms has been replaced by an alkyl group, typically represented by R in organic structures. For example, in ethanol (or ethyl alcohol) the alkyl group is the ethyl group, −CH2CH3.

Alcohols are among the most common organic compounds. They are used as sweeteners and in making perfumes, are valuable intermediates in the synthesis of other compounds, and are among the most abundantly produced organic chemicals in industry. Perhaps the two best-known alcohols are ethanol and methanol (or methyl alcohol). Ethanol is used in toiletries, pharmaceuticals, and fuels, and it is used to sterilize hospital instruments. It is, moreover, the alcohol in alcoholic beverages. The anesthetic ether is also made from ethanol. Methanol is used as a solvent, as a raw material for the manufacture of formaldehyde and special resins, in special fuels, in antifreeze, and for cleaning metals.

Amino Acid

Amino

acids are biologically important organic compounds composed of amine (-NH2) and carboxylic acid (-COOH) functional groups, along with a side-chain specific to each amino acid. The key elements of an amino acid are carbon,hydrogen, oxygen, and nitrogen, though other elements are found in the side-chains

of certain amino acids. About 500 amino acids are known and can be classified in many ways. They can be classified according to

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the core structural functional groups' locations as alpha- (α-), beta- (β-), gamma- (γ-) or delta- (δ-) amino acids; other

categories relate to polarity, pH level, and side-chain group type (aliphatic, acyclic, aromatic, containing hydroxyl

or sulfur, etc.). In the form of proteins, amino acids comprise the second-largest component (water is the largest) of

human muscles, cells and other tissues. Outside proteins, amino acids perform critical roles in processes such as neurotransmitter transport and biosynthesis.

Amino acids having both the amine and the carboxylic acid groups attached to the first (alpha-) carbon atom have particular importance in biochemistry. They are known as 2-, alpha-, or α-amino acids (genericformula H2NCHRCOOH in most caseswhere R is an organic substituent known as a "side-chain");often the term "amino acid" is used to refer specifically to these. They include the 22proteinogenic ("protein-building") amino acids, which combine into peptide chains ("polypeptides") to form the building-blocks of a vast array of proteins. These are all L-stereoisomers ("left-handed" isomers), although a few D-amino acids ("right-handed") occur in bacterial envelopes and some antibiotics. Twenty of the proteinogenic amino acids are encoded directly by triplet codons in the genetic code and are known as "standard" amino acids. The other two ("non-standard" or "non-canonical") are pyrrolysine (found inmethanogenic organisms and other eukaryotes) andselenocysteine (present in many noneukaryotes as well as most eukaryotes). For example, 25 human proteins include selenocysteine (Sec) in their primary structure, and the structurally characterized enzymes (selenoenzymes) employ Sec as the catalytic moiety in their active sites. Pyrrolysine and selenocysteine are encoded via variant codons; for example, selenocysteine is encoded by stop codon and SECIS element. Codon–tRNAcombinations not found in nature can also be used to"expand" the genetic code and create novel proteins known as alloproteins incorporating non-proteinogenic amino acids.

Many important proteinogenic and non-proteinogenic amino acids also play critical non-protein roles within the body. For example, in the human brain, glutamate (standard glutamic acid) and gamma-amino-butyric acid ("GABA", non-standard gamma-amino

acid) are, respectively, the main excitatory and inhibitory neurotransmitters; hydroxyproline (a major component of the connective tissue collagen) is synthesised from proline; the

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standard amino acid glycine is used to synthesise porphyrins used inred blood cells; and the non-standard carnitine is used in lipid transport.

Nine of the 20 standard amino acids are called "essential" for humans because they cannot be created from other compounds by the human body and, so, must be taken in as food. Others may be conditionally essential for certain ages or medical conditions. Essential amino acids may also differ between species.

Because of their biological significance, amino acids are important in nutrition and are commonly used in nutritional

supplements,fertilizers, and food technology. Industrial uses include the production of drugs, biodegradable plastics, and chiral catalysts.

Aromatic Hydrocarbon

An aromatic hydrocarbon or arene (or sometimes aryl hydrocarbon)is a hydrocarboncharacterized by general alternating double and single bonds between carbons. The term 'aromatic' was assigned before the physical mechanism determining aromaticity was discovered, and was derived from the fact that many of the compounds have a sweet scent. The configuration of six carbon atoms in aromatic compounds is known as a benzene ring, after the simplest possible such hydrocarbon,benzene. Aromatic hydrocarbons can be monocyclic(MAH) or polycyclic (PAH).

Some non-benzene-based compounds called heteroarenes, which follow Hückel's rule, are also aromatic compounds. In these compounds, at least one carbon atom is replaced by one of theheteroatoms oxygen, nitrogen, or sulfur. Examples of non-benzene compounds with aromatic properties are furan, a heterocyclic compound with a five-membered ring that includes an

oxygen atom, andpyridine, a heterocyclic compound with a six-membered ring containing one nitrogen atom

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Atoms

The atom is a basic unit of matter that consists of a dense central nucleussurrounded by a cloud of negatively charged electrons. The atomic nucleuscontains a mix of positively charged protons and electrically neutral neutrons(except in the case of hydrogen-1, which is the only stable nuclide with no neutrons).

The electrons of an atom are bound to the nucleus by theelectromagnetic force. Likewise, a group of atoms can remain bound to each other by chemical bonds based on the same force, forming a molecule. An atom containing an equal number of protons and electrons is electrically neutral, otherwise it is positively or negatively charged and is known as an ion. An atom is classified according to the number of protons and neutrons in its nucleus: the number of protons determines the chemical element, and thenumber of neutrons determines the isotope of the element.

Chemical atoms, which in science now carry the simple name of "atom," are minuscule objects with diameters of a few tenths of a nanometer and tiny masses proportional to the volume implied by these dimensions. Atoms can only be observed individually using special instruments such as the scanning tunneling microscope. Over 99.94% of an atom's mass is concentrated in the nucleus, with protons and neutrons having roughly equal mass. Each element has at least one isotope with an unstable nucleus that can undergoradioactive decay. This can result in a transmutation that changes the number of protons or neutrons in a nucleus. Electrons that are bound to atoms possess a set of stable energy levels, or orbitals, and can undergo transitions between them by absorbing or emitting photons that match the energy differences between the levels. The electrons determine the chemical properties of an element, and strongly influence an atom's magneticproperties. The principles of quantum

mechanics have been successfully used to model the observed properties of the atom.

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BBacteria

Bacteria (; singular: bacterium) constitute a large domain of prokaryotic microorganisms. Typically a few micrometers in length, bacteria have a number of shapes, ranging from spheres to rods and spirals. Bacteria were among the first life forms to appear on Earth, and are present in most of its habitats. Bacteria inhabit soil, water, acidic hot springs, radioactive waste, and the deep portions of Earth's crust. Bacteria also live in symbiotic and parasitic relationships with plants and animals. They are also known to have flourished in manned spacecraft.

There are typically 40 million bacterial cells in a gram of soil and a million bacterial cells in a milliliter of fresh water. There are approximately 5×1030 bacteria on Earth, forming a biomass which exceeds that of all plants and animals. Bacteria are vital in recycling nutrients, with many of the stages in nutrient cycles dependent on these organisms, such as the fixation of nitrogen from the atmosphere and putrefaction. In the biological communities surrounding hydrothermal vents and cold seeps, bacteria provide the nutrients needed to sustain life by converting dissolved compounds such as hydrogen sulphide and methane to energy. On 17 March 2013, researchers reported data that suggested bacterial life forms thrive in the Mariana Trench, the deepest spot on the Earth. Other researchers reported related studies that microbes thrive inside rocks up to 1900 feet below

the sea floor under 8500 feet of ocean off the coast of the northwestern United States. According to one of the researchers, “You can find microbes everywhere — they're extremely adaptable to conditions, and survive wherever they are."

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Most bacteria have not been characterized, and only about half of the phyla of bacteria have species that can be grown in the laboratory. The study of bacteria is known as bacteriology, a branch of microbiology.

There are approximately ten times as many bacterial cells in the human flora as there are human cells in the body, with the largest number of the human flora being in the gut flora, and a large number on the skin. The vast majority of the bacteria in the body are rendered harmless by the protective effects of the immune system, and some are beneficial. However, several species of bacteria are pathogenic and cause infectious diseases, including cholera, syphilis, anthrax, leprosy, and bubonic plague. The most common fatal bacterial diseases are respiratory infections, with tuberculosis alone killing about 2 million people a year, mostly in sub-Saharan Africa. In developed countries, antibiotics are used to treat bacterial infections and are also used in farming, making antibiotic resistance a growing problem. In industry, bacteria are important in sewage treatment and the breakdown of oil spills, the production of cheese and yogurt through fermentation, and the recovery of gold, palladium, copper and other metals in the mining sector, as well as in biotechnology, and the manufacture of antibiotics and other chemicals.

Once regarded as plants constituting the class Schizomycetes, bacteria are now classified as prokaryotes. Unlike cells of animals and other eukaryotes, bacterial cells do not contain a nucleus and rarely harbour membrane-bound organelles. Although the term bacteria traditionally included all prokaryotes, the scientific classification changed after the discovery in the 1990s that prokaryotes consist of two very different groups of organisms that evolved from an ancient common ancestor. These evolutionary domains are called Bacteria and Archaea.

Biodiversity 

Is the degree of variation of life. This can refer to genetic variation, species variation, or ecosystem variation within an area, biome, or planet. Terrestrial biodiversity tends to be highest at low latitudes near the equator, which seems to be the result of the warm climate and high primary productivity. Marine

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biodiversity tends to be highest along coasts in the Western Pacific, where sea surface temperature is highest and in mid-latitudinal band in all oceans. Biodiversity generally tends to cluster in hot spots and has been increasing through time but will be likely to slow in the future.

Rapid environmental changes typically cause mass extinctions. One estimate is that

<1%–3% of the species that have existed on Earth are extant.

The earliest evidences for life on Earth are graphite found to be biogenic in 3.7 billion-year-old metasedimentary rocks discovered in Western Greenland and microbial mat fossils found in 3.48 billion-year-old sandstone discovered in Western Australia. Since life began on Earth, five major mass extinctions and several minor events have led to large and sudden drops in biodiversity. The Phanerozoic eon (the last 540 million years) marked a rapid growth in biodiversity via the Cambrian explosion—a period during which the majority of multicellular phyla first appeared. The next 400 million years included repeated, massive biodiversity losses classified as mass extinction events. In the Carboniferous, rainforest collapse led to a great loss of plant and animal life. The Permian–Triassic extinction event, 251 million years ago, was the worst; vertebrate recovery took 30 million years.The most recent, the Cretaceous–Paleogene extinction event, occurred 65 million years ago and has often attracted more attention than others because it resulted in the extinction of the dinosaurs.

The period since the emergence of humans has displayed an ongoing biodiversity reduction and an accompanying loss of genetic diversity. Named the Holocene extinction, the reduction is caused

primarily by human impacts, particularly habitat destruction. Conversely, biodiversity impacts human health in a number of ways, both positively and negatively.

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Biomass Is biological material derived from living, or recently

living organisms. It most often refers to plants or plant-derived materials which are specifically called lignocellulosic biomass. As an energy source, biomass can either be used directly via combustion to produce heat, or indirectly after converting it to various forms of biofuel. Conversion of biomass to biofuel can be achieved by different methods which are broadly classified into: thermal, chemical, and biochemical methods.

Wood remains the largest biomass energy source today;examples include

forest residues (such as dead trees, branches and tree stumps), yard clippings, wood chips and even municipal solid waste. In the second sense, biomass includes plant or animal matter that can be converted into fibers or other industrial chemicals, including biofuels. Industrial biomass can be grown from numerous types of plants, including miscanthus, switchgrass, hemp, corn, poplar, willow, sorghum, sugarcane, bamboo and a variety of tree species, ranging from eucalyptus to oil palm (palm oil).

Plant energy is produced by crops specifically grown for use as fuel that offer high biomass output per hectare with low input energy. Some examples of these plants are wheat, which typically yield 7.5–8 tons (tonnes?) of grain per hectare, and straw, which typically yield 3.5–5 tons (tonnes?) per hectare in the UK.The grain can be used for liquid transportation fuels while the straw can be burned to produce heat or electricity. Plant biomass can also be degraded from cellulose to glucose through a series of chemical treatments, and the resulting sugar can then be used as a first generation biofuel.

Biomass can be converted to other usable forms of energy like methane gas or transportation fuels like ethanol and biodiesel.

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Rotting garbage, and agricultural and human waste, all release methane gas—also called "landfill gas" or "biogas." Crops, such as corn and sugar cane, can be fermented to produce the transportation fuel, ethanol. Biodiesel, another transportation fuel, can be produced from left-over food products like vegetable oils and animal fats.Also, biomass to liquids (BTLs) and cellulosic ethanol are still under research.

Biosynthesis  (Also called biogenesis or anabolism)

is a multi-step, enzyme-catalyzed process where substrates are converted into more complex products. In biosynthesis, simple compounds are modified, converted into other compounds, or joined together to form macromolecules. This process often consists of metabolic pathways. Some of these biosynthetic pathways are located within a single cellularorganelle, while others involve enzymes that are located within multiple cellular organelles. Examples of these biosynthetic pathways include the

production of lipid membrane components and nucleotides.

The prerequisite elements for biosynthesis include: precursor compounds, chemical energy (e.g. ATP), and catalytic enzymes which may require coenzymes (e.g.NADH, NADPH). These elements createmonomers, the building blocks for macromolecules. Some important biological macromolecules include: proteins, which are composed of amino acid monomers joined via peptide bonds, and DNA molecules, which are composed of nucleotides joined via phosphodiester bonds.

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Buoyancy

Is an upward force exerted by a fluid that opposes the weight of an immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the column than at the top. This difference in pressure results in a net force that tends to accelerate an object upwards. The magnitude of that force is proportional to the difference in the pressure between the top and the bottom of the column, and (as

explained by Archimedes' principle) is also equivalent to the weight of the fluid that would otherwise occupy the column, i.e. the displaced fluid. For this reason, an object whose density is greater than that of the fluid in which it is submerged tends to sink. If the object is either less dense than the liquid or is shaped appropriately (as in a boat), the force can keep the object afloat. This can occur only in a reference frame which either has a gravitational field or is accelerating due to a force other than gravity defining a "downward" direction (that is, a non-inertial reference frame). In a situation of fluid statics, the net upward buoyancy force is equal to the magnitude of the weight of fluid displaced by the body.

The center of buoyancy of an object is the centroid of the displaced volume of fluid.

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CCELL

Cell, in biology, the unit of structure and function of which all plants and animals are composed. The cell is the smallest

unit in the living organism that is capable of integrating the essential life processes. There are many unicellular organisms, e.g., bacteria and protozoans, in which the single cell performs all life functions. In higher organisms, a division of labor has evolved in which groups of cells have differentiated into specialized tissues, which in turn are grouped into organs and organ systems.

Cells can be separated into two major groups— prokaryotes, cells whose DNA is not segregated within a well-defined nucleus surrounded by a membranous nuclear envelope, and eukaryotes, those with a membrane-enveloped nucleus. The bacteria (kingdom Monera) are prokaryotes. They are smaller in size and simpler in internal structure than eukaryotes and are believed to have evolved much earlier. All organisms other than bacteria consists of one or more eukaryotic cells.

All cells share a number of common properties; they store information in genes made of DNA; they use proteins as their main structural material; they synthesize proteins in the cell's ribosomes using the information encoded in the DNA and mobilized

by means of RNA; they use adenosine triphosphate as the means of transferring energy for the cell's internal processes; and they

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are enclosed by a cell membrane, composed of proteins and a double layer of lipid molecules, that controls the flow of materials into and out of the cell.

CELLULOSE

Cellulose is an organic compound with the formula (C6H10O5)n, a polysaccharide consisting of a linear chain of several hundred to over ten thousand β(1→4) linked D-glucose units. Cellulose is an important structural component of the primary cell wall of green plants, many forms of algae and the oomycetes. Some species of bacteria secrete it to form biofilms.Cellulose is the most abundant organic polymer on Earth. The cellulose content of cotton

fiber is 90%, that of wood is 40–50% and that of dried hemp is approximately 45%.

Cellulose is mainly used to produce paperboard and paper. Smaller quantities are converted into a wide variety of derivative products such as cellophane and rayon. Conversion of cellulose from energy crops into biofuels such as cellulosic ethanol is under investigation as an alternative fuel source. Cellulose for industrial use is mainly obtained from wood pulp and cotton.

Some animals, particularly ruminants and termites, can digest cellulose with the help of symbiotic micro-organisms that live in their guts, such as Trichonympha. Humans can digest cellulose to some extent,however it mainly acts as a hydrophilic bulking agent for feces and is often referred to as a "dietary fiber".Cellulose was discovered in 1838 by the French chemist Anselme Payen, who isolated it from plant matter and determined its chemical formula.Cellulose was used to produce the first successful

thermoplastic polymer, celluloid, by Hyatt Manufacturing Company in 1870. Production to rayon ("artificial

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silk") from cellulose began in the 1890s and cellophane was invented in 1912. Hermann Staudinger determined the polymer structure of cellulose in 1920. The compound was first chemically synthesized (without the use of any biologically derived enzymes) in 1992, by Kobayashi and Shod.

CLEOPATRA

Cleopatra VII Philopator (Greek: Κλεοπάτρα Φιλοπάτωρ; Late 69 BC] – August 12, 30 BC), known to history as Cleopatra, was the last active pharaoh of Ancient Egypt, only shortly survived by her son, Caesarion as pharaoh. She was a member of the Ptolemaic dynasty, a family of Greek origin that ruled Ptolemaic Egypt after Alexander the Great's death during the Hellenistic period. The Ptolemies, throughout their dynasty, spoke Greek and refused to speak Egyptian, which is the reason that Greek as well as Egyptian languages were used on official court documents such as

the Rosetta Stone.By contrast, Cleopatra did learn to speak Egyptian and represented herself as the reincarnation of an Egyptian goddess, Isis.

Cleopatra originally ruled jointly with her father, Ptolemy XII Auletes, and later with her brothers, Ptolemy XIII and Ptolemy XIV, whom she married as per Egyptian custom, but eventually she became sole ruler. As pharaoh, she consummated a liaison with Julius Caesar that solidified her grip on the throne. She later elevated her son with Caesar, Caesarion, to co-ruler in name.

After Caesar's assassination in 44 BC, she aligned with Mark Antony in opposition to Caesar's legal heir, Gaius Julius Caesar

Octavianus(later known as Augustus. With Antony, she bore the twins Cleopatra Selene II and Alexander Helios, and another son,

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Ptolemy Philadelphus (her unions with her brothers had produced no children). After losing the Battle of Actium to Octavian's forces, Antony committed suicide. Cleopatra followed suit, according to tradition killing herself by means of an asp bite on August 12, 30 BC. She was briefly outlived by Caesarion, who was declared pharaoh by his supporters but soon killed on Octavian's orders. Egypt became the Roman province of Aegyptus.

To this day, Cleopatra remains a popular figure in Western culture. Her legacy survives in numerous works of art and the many dramatizations of her story in literature and other media, including William Shakespeare's tragedy Antony and Cleopatra, Jules Massenet's opera Cléopâtre and the 1963 film Cleopatra. In most depictions, Cleopatra is portrayed as a great beauty, and her successive conquests of the world's most powerful men are taken as proof of her aesthetic and sexual appeal.

CLIMATE

Climate is a measure of the average pattern of variation in temperature, humidity, atmospheric pressure, wind, precipitation, atmospheric particle count and other meteorological variables in a given region over long periods of time. Climate is different than weather, in that weather only describes the short-term conditions of these variables in a given region.

A region's climate is generated by the climate system, which has five components: atmosphere, hydrosphere, cryosphere, land surface, and biosphere

The climate of a location is affected by its latitude, terrain,

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and altitude, as well as nearby water bodies and their currents.

Climates can be classified according to the average and the typical ranges of different variables, most commonly temperature and precipitation. The most commonly used classification scheme was originally developed by Wladimir Köppen. The Thornthwaite system.in use since 1948, incorporates evapotranspiration along with temperature and precipitation information and is used in studying animal species diversity and potential effects of climate changes. The Bergeron and Spatial Synoptic Classification systems focus on the origin of air masses that define the climate of a region.

Paleoclimatology is the study of ancient climates. Since direct observations of climate are not available before the 19th century, paleoclimates are inferred from proxy variables that include non-biotic evidence such as sediments found in lake beds and ice cores, and biotic evidence such as tree rings and coral. Climate models are mathematical models of past, present and future climates. Climate change may occur over long and short timescales from a variety of factors; recent warming is discussed in global warming. Climate is commonly defined as the weather averaged over a long period.The standard averaging period is 30 years, but other periods may be used depending on the purpose. Climate also includes statistics other than the average, such as the magnitudes of day-to-day or year-to-year variations.

CRO-MAGNON

Cro-Magnon man (krō-măgˈnən, –mănˈyən) , an early Homo sapiens (the species to which modern humans belong) that lived about 40,000 years ago. Skeletal remains and

associated artifacts of the of the Aurignacian culture were first found in 1868 in Les Eyzies, Dordogne, France. Later discoveries were made in a number of caverns in

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the Dordogne valley, Solutré, and in Spain, Germany, and central Europe. Cro-Magnon man was anatomically identical to modern humans, but differed significantly from Neanderthals , who disappear in the fossil about 10,000 years after the appearance of Aurignacian and other upper Paleolithic populations (e.g. the Perigordian culture). The abrupt disappearance of Neanderthal populations and the associated Mousterian technologies, the sudden appearance of modern Homo sapiens (who had arisen earlier in Africa and migrated to Europe) and the associated upper Paleolithic technologies, and the absence of transitional anatomical or technological forms have led most researchers to conclude that Neanderthals were driven to extinction through competition with Cro-Magnon or related populations. Greater linguistic competence and cultural sophistication are often suggested as characteristics tilting the competitive balance in avour of upper Paleolithic groups. Finely crafted stone and bone tools, shell and ivory jewelry, and polychrome paintings found on cave walls all testify to the cultural advancement of Cro-Magnon man.

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DDensity

A graduated cylindercontaining various coloured liquids

with different densities.

The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ (the lower case Greek letter rho). Mathematically, density is defined as mass divided by volume:

Where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight.

For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser.

To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "specific gravity" or "relative density", i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a specific

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gravity less than one means that the substance floats in water.

The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance (with a few exceptions) decreases its density by increasing its volume. In most materials, heating the bottom of a fluid results in convection of the heat from the bottom to the top, due to the decrease in the density of the heated

fluid. This causes it to rise relative to more dense unheated material.

The reciprocal of the density of a substance

is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is an intensive property in that increasing the amount of a substance does not increase its density; rather it increases its mass.

Destructive interference

Once we have the condition for constructive interference, destructive interference is a straightforward extension. The basic requirement for destructive interference is that the two

waves are shifted by half a wavelength. This means that the path difference for the

Waves with the same frequency traveling in opposite directions.

two waves must be: R1 – R2 =  /2. But, since we can always shift a wave by one full wavelength, the full condition for destructive interference becomes:

R1 – R2 =  /2 + n .Now that we have mathematical statements for the requirements for constructive and destructive interference, we can apply them to a new situation and see what happens.To create two waves traveling in opposite directions, we can take

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our two speakers and point them at each other, as shown in the figure above. We again want to find the conditions for constructive and destructive interference. As we have seen, the simplest way to get constructive interference is for the distance from the observer to each source to be equal. Using our mathematical terminology, we want R1 – R2 = 0, or R1 = R2. Looking at the figure above, we see that the point where the two paths are equal is exactly midway between the two speakers (the point M in the figure). At this point, there will be constructive interference, and the sound will be strong.

It makes sense to use the midpoint as a reference, as we know that we have constructive interference. How far must we move our observer to get to destructive interference? If we move to the left by an amount x, the distance R1 increases by x and the distance R2 decreases by x. If R1 increases and R2 decreases, the difference between the two R1 – R2 increases by an amount 2x. So, at the point x, the path difference is R1 – R2 = 2x. Now comes the tricky part. If 2x happens to be equal to  /2, we have met the conditions for destructive interference. Therefore, if 2x =  /2, or x =  /4, we have destructive interference. To put it another way, in the situation above, if you move one quarter of a wavelength away from the midpoint, you will find destructive interference and the sound will sound very weak, or you might not hear anything at all.

What happens if we keep moving our observation point? If the path difference, 2x, equal one whole wavelength, we will have constructive interference, 2x =  . Solving for x, we have x =  /2. In other words, if we move by half a wavelength, we will again have constructive interference and the sound will be loud.

As we keep moving the observation point, we will find that we keep going through points of constructive and destructive interference. This is a bit more complicated than the first example, where we had either constructive or destructive interference regardless of where we listened. In this case, whether there is constructive or destructive interference depends on where we are listening. However, the fundamental conditions on the path difference are still the same.

What does this pattern of constructive and destructive interference look like? We can map it out by indicating where we have constructive (x) and destructive ( ) interference:

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What we see is a repeating pattern of constructive and destructive interference, and it takes a distance of  /4 to get from one to the other. Where have we seen this pattern before? At a point of constructive interference, the amplitude of the wave is large and this is just like an antinode. At a point of destructive interference, the amplitude is zero and this is like an node. So, if we think of the point above as antinodes and nodes, we see that we have exactly the same pattern of nodes and antinodes as in a standing wave. From this, we must conclude that two waves traveling in opposite directions create a standing wave with the same frequency! You can get a more intuitive understanding of this by looking at the Physlet entitled Superposition.

Translating the interference conditions into mathematical statements is an essential part of physics and can be quite difficult at first. Moreover, a rather subtle distinction was made that you might not have noticed. On the one hand, we have some physical situation or geometry. This refers to the placement of the speakers and the position of the observer. This really has nothing to do with waves and it simply depends on how the problem was set up. Given a particular setup, you can always figure out the path length from the observer to the two sources of the waves that are going to interference and hence you can also find the path difference R1 – R2.

On the other hand, completely independent of the geometry, there is a property of waves called superposition that can lead to constructive or destructive interference. We can express these conditions mathematically as:

R1 – R2 = 0 + n , for constructive interference, andR1 – R2 =  /2 + n for destructive interference.

Again, R1 – R2 was determined from the geometry of the problem. These two aspects must be understood separately: how to calculate the path difference and the conditions determining the type of interference.

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Diffraction

Diffraction pattern of red laser beam made on a plate after passing a small circular hole in another plate

Diffraction refers to various phenomena which occur when a wave encounters an obstacle. In classical physics, the diffraction phenomenon is described as the apparent bending of waves around small obstacles and the spreading out of waves past small openings. Similar effects occur when a light wave travels through a medium

with a varying refractive index, or a sound wave travels through one with varying acoustic impedance. Diffraction occurs with all waves, including sound waves, water waves, and electromagnetic waves such asvisible light, X-rays and radio waves. As physical objects have wave-like properties (at the atomic level), diffraction also occurs with matter and can be studied according to the principles of quantum mechanics. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1660.

Richard Feynman wrote:

No-one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a

question of usage, and there is no specific, important physical difference between them.

He suggested that when there are only a few sources, say two, we call it interference, as in Young's slits, but with a large number of sources, the process is labelled diffraction.

While diffraction occurs whenever propagating waves encounter such changes, its effects are generally most pronounced for waves whose wavelength is roughly similar to the dimensions of the diffracting objects. If the obstructing object provides multiple, closely spaced openings, a complex pattern of varying intensity can result. This is due to the superposition, or interference, of different parts of a wave that travels to

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the observer by different paths. The formalism of diffraction can also describe the way in which waves of finite extent propagate in free space. For example, the expanding profile of a laser beam, the beam shape of a radar antenna and the field of view of an ultrasonic transducer can all be analyzed using diffraction equations.

The effects of diffraction of light were first carefully observed and characterized by Francesco Maria Grimaldi, who also coined the term diffraction, from the Latin diffringere, 'to break into pieces', referring to light breaking up into different directions. The results of Grimaldi's observations were published posthumously in 1665. Isaac Newton studied these effects and attributed them to inflexion of light rays. James Gregory (1638–1675) observed the diffraction patterns caused by a bird feather, which was effectively the first diffraction grating to be discovered. Thomas Young performed a celebrated experiment in 1803 demonstrating interference from two closely spaced slits. Explaining his results by interference of the waves emanating from the two different slits, he deduced that light must propagate as waves. Augustin-Jean Fresnel did more definitive studies and calculations of diffraction, made public in 1815 and 1818, and thereby gave great support to the wave theory of light that had been advanced by Christiaan Huygens and reinvigorated by Young, against Newton's particle theory.

Distance

Also known as fairness, is a numerical description of how far

apart objects are. In physics or everyday usage, distance may refer to a physical length, or an estimation based on other criteria (e.g. "two counties over"). In mathematics, a distance function or metric is a generalization of the concept of physical distance. A metric is a function that behaves according to a specific set of rules, and is a concrete way of describing what it means for elements of some space to be "close

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to" or "far away from" each other. In most cases, "distance from A to B" is interchangeable with "distance between B and A".

In analytic geometry, the distance between two points of the xy-plane can be found using the distance formula. The distance between (x1, y1) and (x2, y2) is given by:

Similarly, given points (x1, y1, z1) and (x2, y2, z2) in three-space, the distance

between them is:

Illustration of distance

These formula are easily derived by constructing a right triangle with a leg on the hypotenuse of another (with the other leg orthogonal to the plane that contains the 1st triangle) and applying the Pythagorean theorem. In the study of complicated geometries,we call this (most common) type of distance Euclidean distance,as it is derived from the Pythagorean theorem,which does not hold in Non-Euclidean geometries.This distance formula can also be expanded into the arc-length formula.

Distance in Euclidean space

In the Euclidean space Rn, the distance between two points is usually given by the Euclidean distance (2-norm distance). Other distances, based on other norms, are sometimes used instead.

For a point (x1, x2, ...,xn) and a point (y1, y2, ...,yn), the Minkowski distance of order p (p-norm distance) is defined as:

1-norm distance

2-norm distance

p-norm distance

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infinity norm distance

p need not be an integer, but it cannot be less than 1, because otherwise the triangle inequality does not hold.

The 2-norm distance is the Euclidean distance, a generalization of the Pythagorean theorem to more than two coordinates. It is what would be obtained if the distance between two points were measured with a ruler: the "intuitive" idea of distance.

The 1-norm distance is more colourfully called the taxicab norm or Manhattan distance, because it is the distance a car would drive in a city laid out in square blocks (if there are no one-way streets).

The infinity norm distance is also called Chebyshev distance. In 2D, it is the minimum number of moves kings require to travel between two squares on a chessboard.

The p-norm is rarely used for values of p other than 1, 2, and infinity, but see super ellipse.

In physical space the Euclidean distance is in a way the most natural one, because in this case the length of a rigid body does not change with rotation.

Variational formulation of distance

The Euclidean distance between two points in space (

 and  ) may be written in a variational form where the distance is the minimum value of an integral:

Here   is the trajectory (path) between the two points. The value of the integral (D) represents the length of this trajectory. The distance is the minimal value of this integral and is obtained when   where   is the optimal trajectory. In the familiar Euclidean case (the above integral) this optimal

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Direct current Direct current (DC) is the unidirectional flow ofelectric charge. Direct current is produced by sources such as batteries, thermocouples, solar cells, and commutator-type electric machines of thedynamo type. Direct current may flow in a conductorsuch as a wire, but can also flow

throughsemiconductors, insulators, or even through avacuum as in electron or ion beams. The electric current flows in a constant direction, distinguishing it from alternating current (AC). A term formerly used for direct current was galvanic

current.

Direct current may be obtained from an alternating current supply by use of a current-switching arrangement called a rectifier, which contains electronic elements (usually) or electromechanical elements (historically) that allow current to flow only in one direction. Direct current may be made into alternating current with an inverter or a motor-generator set.

The first commercial electric power transmission (developed by Thomas Edison in the late nineteenth century) used direct current. Because of the significant advantages of alternating current over direct current in transforming and transmission, electric power distribution is nearly all alternating current today. In the mid-1950s, HVDC transmission was developed, and is now an option instead of long-distance high voltage alternating current systems. For long distance underseas cables (e.g. between countries, such as NorNed), this is the only technically feasible option. For applications requiring direct current, such as third rail power systems, alternating current is distributed to a substation, which utilizes a rectifier to convert the power to direct current. SeeWar of Currents.

Direct current is used to charge batteries, and in nearly all electronic systems, as the power supply. Very large quantities of direct-current power are used in production of aluminum and

otherelectrochemical processes. Direct current is used for some railway propulsion, especially in urban areas. High-voltage direct current is used to transmit large amounts of power from remote generation sites or to interconnect alternating current power grids.

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EEarthquake

An earthquake (also known as a quake, tremor or temblor) is the result of a sudden release of energy in the Earth's crust  that creates seismic waves. The seismicity, seismism or seismic activity of an area refers to the frequency, type and size of earthquakes experienced over a period of time.

Earthquakes are measured using observations from seismometers. The moment magnitude is the most common scale on which earthquakes larger than approximately 5 are reported for the entire globe. The more numerous earthquakes smaller than magnitude 5 reported by national seismological observatories are measured mostly on the local magnitude scale, also referred to as the Richter scale. These two scales are numerically similar over their range of validity. Magnitude 3 or lower earthquakes are mostly almost imperceptible or weak and magnitude 7 and over potentially cause serious damage over larger areas, depending on their depth. The largest earthquakes in historic times have been of magnitude slightly over 9, although there is no limit to the possible magnitude. The

most recent large earthquake of magnitude 9.0 or larger was a9.0

Faul types

magnitude earthquake in Japan in 2011 (as of October 2012), and it was the largest Japanese earthquake since records began. Intensity of shaking is measured on the modified Mercalli scale. The shallower an earthquake, the more damage to structures it causes, all else being equal.

At the Earth's surface, earthquakes manifest themselves by shaking and sometimes displacement of the ground. When

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the epicenter of a large earthquake is located offshore, the seabed may be displaced sufficiently to cause a tsunami. Earthquakes can also trigger landslides, and occasionally volcanic activity.

In its most general sense, the word earthquake is used to describe any seismic event — whether natural or caused by humans — that generates seismic waves. Earthquakes are caused mostly by rupture of geological faults, but also by other events such as volcanic activity, landslides, mine blasts, and nuclear tests. An earthquake's point of initial rupture is called its focus or hypocenter. The epicenter is the point at ground level directly above the hypocenter.

Electromagnetic radiation

Electromagnetic radiation (EM radiation or EMR) is a form of radiant energy, propagating through space via photon wave particles. In a vacuum, it propagates at a characteristic speed, the speed of light, normally in straight lines. EMR is emitted and absorbed by charged particles. As an electromagnetic wave, it has both electric and magnetic field components, which oscillate in a fixed relationship to one another, perpendicular to each other and perpendicular to the direction of energy and wave propagation.

EMR is characterized by the frequency or wavelength of its wave. The electromagnetic spectrum, in order of increasing frequency and decreasing wavelength, consists of radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays. The eyes of various organisms sense a somewhat variable but relatively small range of frequencies of EMR called the visible spectrum or light. Higher frequencies correspond to proportionately more energy carried by each photon; for instance, a single gamma ray photon carries far more energy than a single photon of visible light.

Electromagnetic radiation is associated with EM fields that are free to propagate themselves without the continuing influence of the moving charges that produced them, because they have achieved sufficient distance from those charges. Thus, EMR is sometimes referred to as the far field. In this language, the near field refers to EM fields near the charges and current that directly produced them, as for example with simple magnets

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and static electricity phenomena. In EMR, the magnetic and electric fields are each induced by changes in the other type of field, thus propagating itself as a wave. This close relationship assures that both types of fields in EMR stand in phase and in a fixed ratio of intensity to each other, with maxima and nodes in each found at the same places in space.

EMR carries energy—sometimes called radiant energy—through space continuously away from the source (this is not true of the near-field part of the EM field). EMR also carries both momentum and angular momentum. These properties may all be imparted to matter with which it interacts. EMR is produced from other types of energy when created, and it is converted to other types of energy when it is destroyed. Thephoton is the quantum of the electromagnetic interaction, and is the basic "unit" or constituent of all forms of EMR. The quantum nature of light becomes more apparent at high frequencies (thus high photon energy). Such photons behave more like particles than lower-frequency photons do.

In classical physics, EMR is considered to be produced when charged particles are accelerated by forces acting on them. Electrons are responsible for emission of most EMR because they have low mass, and therefore are easily accelerated by a variety of mechanisms. Rapidly moving electrons are most sharply accelerated when they encounter a region of force, so they are responsible for producing much of the highest frequency electromagnetic radiation observed in nature. Quantum processes can also produce EMR, such as when atomic nucleiundergo gamma decay, and processes such as neutral pion decay.

The effects of EMR upon biological systems (and also to many

This diagram shows a plane linearly polarized EMR wave propagating from left to right. The electric field is in a vertical plane and the magnetic field in a horizontal

plane. The two types of fields in EMR waves are always in phase with each other with a fixed ratio of electric to magnetic field intensity.

Other chemical systems, under standard conditions) depends both upon the radiation's power and frequency. For lower frequencies of EMR up to those of visible light (i.e., radio, microwave, infrared), the damage done to cells and also to many ordinary materials under such conditions is determined mainly by heating

29

effects, and thus by the radiation power. By contrast, for higher frequency radiations at ultraviolet frequencies and above (i.e., X-rays and gamma rays) the damage to chemical materials and living cells by EMR is far larger than that done by simple heating, due to the ability of single photons in such high frequency EMR to damage individual molecules chemically.

Electron transport chain

The electron transport chain consists of a spatially separated series of redox reactions in which electrons are transferred from a donor molecule to an acceptor molecule. The underlying force driving these reactions is the Gibbs free energy of the reactants and products. The Gibbs free energy is the energy available

("free") to do work. Any reaction that decreases the overall Gibbs free energy of a system is thermodynamically spontaneous.

The function of the electron transport chain is to produce a transmembrane proton electrochemical gradient as a result of the redox reactions.[1] If protons flow back through the membrane, they enable mechanical work, such as rotating bacterial flagella. ATP synthase, an enzyme

highly conserved among all domains of life, converts this mechanical work into chemical energy by producing ATP, which powers most cellular reactions. A small amount of ATP is available from substrate-level phosphorylation,

for example, in glycolysis. In most organisms the majority of ATP is generated in electron transport chains, while only some obtain ATP by fermentation.

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The electron transport chain in the mitochondrion is the site of oxidative phosphorylation in eukaryotes. The NADH and succinate generated in the citric acid cycle are oxidized, providing energy to power ATP synthase.

Equation

In mathematics, an equation is a formula of the form A = B, where A and B are expressions that may contain one or several variablescalled unknowns, and "=" denotes the equality binary relation. Although written in the form of proposition, an equation is not a statementthat is either true or false, but a problem consisting of finding the values, called solutions, that, when substituted for the unknowns, yield equal values of the expressions A and B. For example, 2 is the

Unique solution of the equation x + 2 = 4, in which the unknown is x.[1]Historically, equations arose from the mathematical discipline of algebra, but later become ubiquitous. "Equations" should not be confused with "identities", which are

presented with the same notation but have a different meaning: for example 2 + 2 = 4 andx + y = y + x are identities (which implies they are necessarily true) in arithmetic, and do not constitute a values-finding problem, even when variables are present as in the latter example.

The term "equation" may also refer to a relation between some variables that is presented as the equality of some expressions

Illustration of a simple equation; x, y, zare real numbers, analogous to weights.

written in terms of those variables' values. For example the equation of the unit circle is x2 + y2 = 1, which means that a point belongs to the circle if and only if its coordinates are related by this equation. Most physical lawsare expressed by equations. One of the most famous ones is Einstein's equation E = mc2.

The = symbol was invented by Robert Recorde (1510–1558), who

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considered that nothing could be more equal than parallel straight lines with the same length.

Extinction

A species is extinct when the last existing member dies. Extinction therefore becomes a certainty when there are no surviving individuals that can reproduce and create a new generation. A species may become functionally extinct when only a handful of individuals survive, which cannot reproduce due to poor health, age, sparse distribution over a large range, a lack of individuals of both sexes (in sexually reproducing species), or other reasons.

Pinpointing the extinction (or pseudoextinction) of a species requires a clear definition of that species. If it is to be declared extinct, the species in question must be uniquely distinguishable from any ancestor or daughter species, and from any other closely related species. Extinction of a species (or replacement by a daughter species) plays a key role in the punctuated equilibrium hypothesis of Stephen Jay Gould and Niles Eldredge.

In ecology, extinction is often used informally to refer to local extinction, in which a species ceases to exist in the chosen area of study, but may still exist elsewhere. This phenomenon is also known as extirpation. Local extinctions may be followed by a replacement of the species taken from other locations; wolf reintroduction is an example of this. Species which are not extinct are termed extant. Those that are extant but threatened by extinction are referred to as threatened or endangered species.

Currently an important aspect of extinction is human attempts to preserve critically endangered species. These are reflected by the

creation of the conservation status "Extinct in the Wild" (EW). Species listed under this status by the International Union for Conservation of Nature (IUCN) are not known to have any living specimens in the wild, and are

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maintained only in zoos or other artificial environments. Some of these species are functionally extinct, as they are no longer part of their natural habitat and it is unlikely the species will ever be restored to the wild. When possible, modern zoological institutions try to maintain a viable population for species preservation and possible future reintroduction to the wild, through use of carefully planned breeding programs. Extinct Species

The extinction of one species' wild population can have knock-on effects, causing further extinctions. These are also called "chains of extinction". This is especially common with extinction of keystone species.

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FFacula

A facula (plural: faculae), Latin for "little torch", is literally a "bright spot." The term has several common technical

uses. It is used in planetary nomenclature for naming certain surface features of planets and moons, and is also a type of surface phenomenon on the Sun. In addition, a bright region in the projected field of a light source is sometimes referred to as a facula, and photographers often use the term to describe bright, typically circular features in photographs that correspond to light sources or bright reflections in a defocused image.

Solar faculae are bright spots that form in the canyons between solar granules, short-lived convection cells several thousand kilometers across that constantly form and dissipate over timescales of several minutes. Faculae are produced by concentrations of magnetic field lines. Strong concentrations of faculae appear in solar activity, with or withoutsunspots. The faculae and the sunspots contribute noticeably to variations in the "solar constant". The chromospheric counterpart of a facular region is called a plage.

Facundity

Fecundity, derived from the word fecund, generally refers to the ability to reproduce. In demography, fecundity is the potential reproductive capacity of an individual orpopulation. In biology, the definition is more equivalent

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to fertility, or the actual reproductive rate of on an  organism or population, measured by the number

of gametes (eggs), seed set, or asexual propagules. This difference is because demography considers human fecundity which is often intentionally limited, while biology assumes that organisms do not limit fertility. Fecundity is under both genetic and environmental control, and is

the major measure of fitness. Fecundation is another term for fertilization. Superfecundity refers to an organism's ability to store another organism's sperm (after copulation) and fertilize its own eggs from that store after a period of time, essentially making it appear as though fertilization occurred without sperm (i.e. parthenogenesis).

Fecundity is important and well studied in the field of population ecology. Fecundity can increase or decrease in a population according to current conditions and certain regulating factors. For instance, in times of hardship for a population, such as a lack of food, juvenile and eventually adult fecundity has been shown to decrease.

Fecundity has also been shown to increase in ungulates with relation to warmer weather.

In sexual evolutionary biology, especially in sexual selection, fecundity is contrasted to reproductivity..

In obstetrics and gynecology, fecundability is the probability of being pregnant in a single menstrual cycle, and fecundity is the probability of achieving a live birth within a single cycle.

It is the ability of organism to breed

FahrenheitOn the Fahrenheit scale,the freezing point of water is 32

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32 degrees Fahrenheit (°F) and the boiling point 212 °F (atstandard atmospheric pressure). This puts the boiling and

freezing points of water exactly 180 degrees apart.[9]Therefore, a degree on the Fahrenheit scale is 1⁄180 of the interval between the freezing point and the boiling point. On the Celsius scale, the freezing and boiling points of water are 100 degrees apart.

A temperature interval of 1 °F is equal to an interval

of 5⁄9 degrees Celsius. The

Fahrenheit and Celsius scales intersect at −40° (−40 °F and −40 °C represent the same temperature).

Absolute zero is −273.15 °C or −459.67 °F. The Rankine temperature scale uses degree intervals of the same size as those of the Fahrenheit scale, except that absolute zero is 0 R – the same way that the Kelvin temperature scale matches the Celsius scale, except that absolute zero is 0 K.[9]

The Fahrenheit scale uses the symbol ° to denote a point on the temperature scale (as does Celsius) and the letter F to indicate the use of the Fahrenheit scale (e.g. "Gallium melts at 85.5763 °F"),[10] as well as to denote a difference between temperatures or an uncertainty in temperature (e.g. "The output of the heat exchanger experiences an increase of 72 °F" and "Our standard uncertainty is ±5 °F").

A rule of thumb for conversion between degrees Celsius and degrees Fahrenheit is as follows:

Fahrenheit to Celsius: Subtract 32 and halve the resulting number.

Celsius to Fahrenheit: Double the number and add 32.

Thermometer with Fahrenheit and Celsius units

This formula gives an answer correct to within 1 °C for 50 °F (10 °C). At 0 °F (-17.8 °C) and 100 °F (37.8 °C), it gives answers of -15 °C and 35 °C, respectively. Outside this range, the error is bigger. For an accurate conversion, consider that 1 Celsius is equal to 1.8 Fahrenheit: 32 F = 0 C, 50 F = 10 C, 68 F = 20 C, 86 F = 30 C, 104 F = 40 C, and so on.

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Free-electron laserA free-electron laser (FEL), is a type of laser that shares the same optical properties as conventional lasers such as emitting abeam consisting of coherent electromagnetic radiation that can reach high power, but that uses some very different operating principles to form the beam. Unlike gas-, liquid-, or solid-state lasers such as diode lasers, in which electrons are excited in bound atomic or molecular states, free-electron lasers use a relativistic electron beam that moves freely through a magnetic structure, hence the term free electron as the lasing medium. The free-electron laser has the widestfrequency range of any laser type, and can be widely tunable, currently ranging in wavelength from microwaves, throughterahertz radiation and infrared, to the visible spectrum, ultraviolet, and X-ray.

Free-electron lasers were invented by John Madey in 1976 at Stanford University. The work emanates from research done byHans Motz and his coworkers, who built an undulator at Stanford in 1953, using the wiggler magnetic configuration which is at the heart of a free electron laser. Madey used a 24 MeV electron beam and 5 m long wiggler to amplify a signal. Soon afterward, other laboratories with accelerators started developing such lasers. To create an FEL, a beam of electrons is accelerated to almost the speed of light. The beam passes through an undulator, a side to side magnetic field produced by a periodic arrangement of magnets with alternating poles across the beam path. The general direction of the beam is called the longitudinal direction, and the direction across the beam path is called transverse. This array of magnets is commonly known as an undulator in the light source community, or a wiggler in the FEL community,[citation needed] because it forces the electrons in the beam to wiggle transversely along a sinusoidal path about the axis of the undulator.

The transverse acceleration of the electrons across this path results in the release of photons (synchrotron radiation), which are monochromatic but still incoherent, because the electromagnetic waves from randomly distributed electrons interfere constructively and destructively in time, and the

resulting radiation power scales linearly with the number of electrons. If an external laser is provided or if the synchrotron radiation becomes sufficiently strong, the transverse electric field of the radiation beam interacts with the transverse electron current created by the sinusoidal wiggling motion, causing some electrons to gain and others to

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lose energy to the optical field.

This energy modulation evolves into electron density (current) modulations with a period of one optical wavelength. The electrons are thus bunched into little clumps, called microbunches, separated by one optical wavelength along the axis. Whereas conventional undulators would cause the electrons to radiate independently, the radiation emitted by the microbunched electrons are in phase, and the fields add together coherently.

The FEL radiation intensity grows, causing additional microbunching of the electrons, which continue to radiate in phase with each other. This process continues until the electrons are completely microbunched and the radiation reaches a saturated power several orders of magnitude higher than that of the

undulator radiation.

The wavelength of the radiation emitted can be readily tuned by adjusting the energy of the electron beam or the magnetic field strength of the undulators.

FELs are relativistic machines. The wavelength of the emitted radiation,  , is given by 

 ,

or when the wiggler strength parameter K, discussed below, is small

 ,

where   is the undulator wavelength (the spatial period of the magnetic field),   is the relativistic Lorentz factor and the proportionality constant depends on the undulator geometry and is of the order of 1.

The free-electron laser FELIX at the FOM Institute for Plasma Physics

This formula can be understood as a combination of two relativistic effects. Imagine you are sitting on an electron passing through the undulator. Due to Lorentz contraction the undulator is shortened by a   factor and the electron

experiences much shorter undulator wavelength  . However, the radiation emitted at this

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wavelength is observed in the laboratory frame of reference and the relativistic Doppler effect brings the second   factor to the above formula. Rigorous derivation from Maxwell's equations gives the divisor of 2 and the proportionality constant. In an x-ray FEL the typical undulator wavelength of 1 cm is transformed to x-ray wavelengths on the order of 1 nm by   ≈ 2000, i.e. the electrons have to travel with the speed of 0.9999998c.

Friction

The classic rules of sliding friction were discovered by Leonardo da Vinci (1452–1519), but remained unpublished in his notebooks. They were rediscovered by Guillaume Amontons (1699). Amontons presented the nature of friction in terms of surface irregularities and the force required to raise the weight pressing the surfaces together. This view was further elaborated

by Belidor (representation of rough surfaces with spherical asperities, 1737) and Leonhard Euler (1750), who derived the angle of repose of a weight on an inclined plane and first distinguished between static and kinetic friction. A different explanation was provided by Desaguliers (1725), who demonstrated the strong cohesion forces between lead spheres of which a small cap is cut off and which were then brought into contact with each other.

The understanding of friction was further developed by Charles-Augustin de Coulomb (1785). Coulomb investigated the influence of four main factors on friction:

Block on a ramp (top) and corresponding free body diagramof just the block (bottom). For equilibrium, the line of action of the three force arrows must intersect at a common point.

the nature of the materials in contact and their surface coatings; the extent of the surface area; the normal pressure (or load); and the length of time that the surfaces remained in contact (time of repose). Coulomb further considered the

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influence of sliding velocity, temperature and humidity, in order to decide between the different explanations on the nature of friction that had been proposed. The

distinction between static and dynamic friction is made in Coulomb's friction law (see below), although this distinction was already drawn by Johann Andreas von Segner in 1758. The effect of the time of repose was explained by Musschenbroek (1762) by considering the surfaces of fibrous materials, with fibers meshing together, which takes a finite time in which the friction increases.

John Leslie (1766–1832) noted a weakness in the views of Amontons and Coulomb. If friction arises from a weight being drawn up the inclined plane of successive asperities, why isn't it balanced then through descending the opposite slope? Leslie was equally skeptical about the role of adhesion proposed by Desaguliers, which should on the whole have the same tendency to accelerate as to retard the motion.

In his view friction should be seen as a time-dependent process of flattening, pressing down asperities, which creates new obstacles in what were cavities before.

Arthur Morrin (1833) developed the concept of sliding versus rolling friction. Osborne Reynolds (1866) derived the equation of viscous flow. This completed the classic empirical model of friction (static, kinetic, and fluid) commonly used today in engineering.

The focus of research during the last century has been to understand the physical mechanisms behind friction. F. Phillip Bowden and David Tabor (1950) showed that at a microscopic level, the actual area of contact between surfaces is a very small fraction of the apparent area. This actual area of contact, caused by "asperities" (roughness) increases with pressure, explaining the proportionality between normal force and frictional force. The development of the atomic force microscope (1986) has recently enabled scientists to study friction at the atomic scale

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INDEXA

Acetylene, p.1

Alcohols, pp.1-2

Amino acid, pp.2-3

Aromatic hydrocarbon, p.4

Atoms, p.5

B

Bacteria, pp.6-7

Biochemistry, pp.7-8

Biomass, pp.9-10

Biosynthesis, p.10

Buoyancy, p.11

C

Cell, pp.12-13

Cellulose, pp.13-14

Cleopatra, pp.14-15

Climate, pp.15-16

Cro-magnon, pp.16-17

D

Density, pp.18-19

Destructive interference, pp.19-21

Diffraction, pp.22-23

Direct current, p.26

Distance, pp.23-25

E

Earthquake, pp.27-28

Electromagnetic radiation, pp.28-30

Electron transport chain, pp.30-31

Equation, pp.31-32

Extinction, pp.32-33

F

Facula, p.34

Fecundity, pp.34-35

Fahrenheit, pp.35-36

Free electron loser, pp.37-39

Friction, pp.39-40