In physics, the reciprocal lattice represents the Fourier transform of another lattice. In normal usage, this first lattice is a periodic spatial function in real-space and is known as the direct lattice. While the direct lattice exists in real-space and is what one would understand as a physical lattice, the reciprocal lattice exists in reciprocal space The reciprocal of a reciprocal lattice is the original direct lattice, since the two are Fourier transforms of each other; the reciprocal lattice plays a fundamental role in most analytic studies of periodic structures in the theory of diffraction. In neutron and X-ray diffraction, due to the Laue conditions, the momentum difference between incoming and diffracted X-rays of a crystal is a reciprocal lattice vector; the diffraction pattern of a crystal can be used to determine the reciprocal vectors of the lattice. Using this process, one can infer the atomic arrangement of a crystal; the Brillouin zone is a Wigner-Seitz cell of the reciprocal lattice.
Assuming a two-dimensional Bravais lattice R n = n 1 a 1 + n 2 a 2 where n 1, n 2 ∈ Z. Any quantity, e.g. the electronic density in an atomic crystal can be written as a periodic function f = f Due to the periodicity, it is useful to write f as a Fourier series f = ∑ m f m e i G m ⋅ r e i G m ⋅ R n Since f = f for any n, k ∈ Z 2 the last formula is true for the particular case R 0 = 0 ∑ m f m = ∑ m f m = ∑ m f m so must be true e i G m ⋅ R n = 1 that means G m ⋅ R n = 2 π N where N ∈ Z. Mathematically, we can describe the reciprocal lattice as the set of all vectors G m that satisfy the above identity for all lattice point position vectors R; this reciprocal lattice is itself a Bravais lattice, the reciprocal of the reciprocal lattice is the original lattice, which reveals the Pontryagin duality of their respective vector spaces. For an infinite two-dimensional lattice, defined by its primitive vectors, its reciprocal lattice can be determined by generating its two reciprocal primitive vectors, through the following formulae, G m = m 1 b 1 +
In navigation, the heading of a vessel or aircraft is the compass direction in which the craft's bow or nose is pointed. There are seven fundamental ways. Note that the heading may not be the direction that the vehicle travels, known as its course or track. Any difference between the heading and course is due to the motion of the underlying medium, the air or water, or other effects like skidding or slipping; the difference is known as the drift, can be determined by the wind triangle. Heading is based on compass directions, so 0° indicates a direction toward true North, 90° indicates a direction toward true East, 180° is true South, 270° is true West. Bearing Ship motions
A reciprocating engine often known as a piston engine, is a heat engine that uses one or more reciprocating pistons to convert pressure into a rotating motion. This article describes the common features of all types; the main types are: the internal combustion engine, used extensively in motor vehicles. Internal combustion engines are further classified in two ways: either a spark-ignition engine, where the spark plug initiates the combustion. There may be one or more pistons; each piston is inside a cylinder, into which a gas is introduced, either under pressure, or heated inside the cylinder either by ignition of a fuel air mixture or by contact with a hot heat exchanger in the cylinder. The hot gases expand; this position is known as the Bottom Dead Center, or where the piston forms the largest volume in the cylinder. The piston is returned to the cylinder top by a flywheel, the power from other pistons connected to the same shaft or by the same process acting on the other side of the piston.
This is. In most types the expanded or "exhausted" gases are removed from the cylinder by this stroke; the exception is the Stirling engine, which heats and cools the same sealed quantity of gas. The stroke is the distance between the TDC and the BDC, or the greatest distance that the piston can travel in one direction. In some designs the piston may be powered in both directions in the cylinder, in which case it is said to be double-acting. In most types, the linear movement of the piston is converted to a rotating movement via a connecting rod and a crankshaft or by a swashplate or other suitable mechanism. A flywheel is used to ensure smooth rotation or to store energy to carry the engine through an un-powered part of the cycle; the more cylinders a reciprocating engine has the more vibration-free it can operate. The power of a reciprocating engine is proportional to the volume of the combined pistons' displacement. A seal must be made between the sliding piston and the walls of the cylinder so that the high pressure gas above the piston does not leak past it and reduce the efficiency of the engine.
This seal is provided by one or more piston rings. These are rings made of a hard metal, are sprung into a circular groove in the piston head; the rings fit in the groove and press against the cylinder wall to form a seal, more when higher combustion pressure moves around to their inner surfaces. It is common to classify such engines by the number and alignment of cylinders and total volume of displacement of gas by the pistons moving in the cylinders measured in cubic centimetres or litres or. For example, for internal combustion engines and two-cylinder designs are common in smaller vehicles such as motorcycles, while automobiles have between four and eight, locomotives, ships may have a dozen cylinders or more. Cylinder capacities may range from 10 cm³ or less in model engines up to thousands of liters in ships' engines; the compression ratio affects the performance in most types of reciprocating engine. It is the ratio between the volume of the cylinder, when the piston is at the bottom of its stroke, the volume when the piston is at the top of its stroke.
The bore/stroke ratio is the ratio of the diameter of the piston, or "bore", to the length of travel within the cylinder, or "stroke". If this is around 1 the engine is said to be "square", if it is greater than 1, i.e. the bore is larger than the stroke, it is "oversquare". If it is less than 1, i.e. the stroke is larger than the bore, it is "undersquare". Cylinders may be aligned in line, in a V configuration, horizontally opposite each other, or radially around the crankshaft. Opposed-piston engines put two pistons working at opposite ends of the same cylinder and this has been extended into triangular arrangements such as the Napier Deltic; some designs have set the cylinders in motion around the shaft, such as the Rotary engine. In steam engines and internal combustion engines, valves are required to allow the entry and exit of gases at the correct times in the piston's cycle; these are worked by eccentrics or cranks driven by the shaft of the engine. Early designs used the D slide valve but this has been superseded by Piston valve or Poppet valve designs.
In steam engines the point in the piston cycle at which the steam inlet valve closes is called the cutoff and this can be controlled to adjust the torque supplied by the engine and improve efficiency. In some steam engines, the action of the valves can be replaced by an oscillating cylinder. Internal combustion engines operate through a sequence of strokes that admit and remove gases to and from the cylinder; these operations are repeated cyclically and an engine is said to be 2-stroke, 4-stroke or 6-stroke depending on the number of strokes it takes to complete a cycle. In some steam engines, the cylinders may be of varying size with the smallest bore cylinder working the highest pressure steam; this is fed through one or more larger bore cylinders successively, to extract power from the steam at lower pressures. These engines are called Compound engines. Aside from loo
In biology, a hybrid is the offspring resulting from combining the qualities of two organisms of different breeds, species or genera through sexual reproduction. Hybrids are not always intermediates between their parents, but can show hybrid vigour, sometimes growing larger or taller than either parent; the concept of a hybrid is interpreted differently in animal and plant breeding, where there is interest in the individual parentage. In genetics, attention is focused on the numbers of chromosomes. In taxonomy, a key question is how related the parent species are. Species are reproductively isolated by strong barriers to hybridisation, which include morphological differences, differing times of fertility, mating behaviors and cues, physiological rejection of sperm cells or the developing embryo; some act before fertilization and others after it. Similar barriers exist in plants, with differences in flowering times, pollen vectors, inhibition of pollen tube growth, somatoplastic sterility, cytoplasmic-genic male sterility and the structure of the chromosomes.
A few animal species and many plant species, are the result of hybrid speciation, including important crop plants such as wheat, where the number of chromosomes has been doubled. Human impact on the environment has resulted in an increase in the interbreeding between regional species, the proliferation of introduced species worldwide has resulted in an increase in hybridisation; this genetic mixing may threaten many species with extinction, while genetic erosion in crop plants may be damaging the gene pools of many species for future breeding. A form of intentional human-mediated hybridisation is the crossing of wild and domesticated species; this is common in modern agriculture. One such flower, Oenothera lamarckiana, was central to early genetics research into mutationism and polyploidy, it is more done in the livestock and pet trades. Human selective breeding of domesticated animals and plants has resulted is the development of distinct breeds. Hybrid humans existed in prehistory. For example and anatomically modern humans are thought to have interbred as as 40,000 years ago.
Mythological hybrids appear in human culture in forms as diverse as the Minotaur, blends of animals and mythical beasts such as centaurs and sphinxes, the Nephilim of the Biblical apocrypha described as the wicked sons of fallen angels and attractive women. The term hybrid is derived from Latin hybrida, used for crosses such as of a tame sow and a wild boar; the term came into popular use in English in the 19th century, though examples of its use have been found from the early 17th century. Conspicuous hybrids are popularly named with portmanteau words, starting in the 1920s with the breeding of tiger–lion hybrids. From the point of view of animal and plant breeders, there are several kinds of hybrid formed from crosses within a species, such as between different breeds. Single cross hybrids result from the cross between two true-breeding organisms which produces an F1 hybrid; the cross between two different homozygous lines produces an F1 hybrid, heterozygous. The F1 generation is phenotypically homogeneous, producing offspring that are all similar to each other.
Double cross hybrids result from the cross between two different F1 hybrids. Three-way cross hybrids result from the cross between an inbred line. Triple cross hybrids result from the crossing of two different three-way cross hybrids. Top cross hybrids result from the crossing of a top quality or pure-bred male and a lower quality female, intended to improve the quality of the offspring, on average. Population hybrids result from the crossing of plants or animals in one population with those of another population; these crosses between different breeds. In horticulture, the term stable hybrid is used to describe an annual plant that, if grown and bred in a small monoculture free of external pollen produces offspring that are "true to type" with respect to phenotype. Hybridisation can occur in the hybrid zones where the geographical ranges of species, subspecies, or distinct genetic lineages overlap. For example, the butterfly Limenitis arthemis has two major subspecies in North America, L. a. arthemis and L. a. astyanax.
The white admiral has a bright, white band on its wings, while the red-spotted purple has cooler blue-green shades. Hybridisation occurs between a narrow area across New England, southern Ontario, the Great Lakes, the "suture region", it is at these regions. Other hybrid zones have formed between described species of animals. From the point of view of genetics, several different kinds of hybrid can be distinguished. A genetic hybrid carries two different alleles of the same gene, where for instance one allele may code for a lighter coat colour than the other. A structural hybrid results from the fusion of gametes that have differing structure in at least one chromosome, as a result of structural abnormalities. A numerical hybrid results from the fusion of gamet