In geometry, a figure is chiral if it is not identical to its mirror image, or, more if it cannot be mapped to its mirror image by rotations and translations alone. An object, not chiral is said to be achiral. In 3 dimensions, not all achiral objects have a mirror plane. For example, a 3-dimensional object with inversion centre as its only nontrivial symmetry operation is achiral but has no mirror plane. A chiral object and its mirror image are said to be enantiomorphs; the word chirality is derived from the hand, the most familiar chiral object. A non-chiral figure is called amphichiral; some chiral three-dimensional objects, such as the helix, can be assigned a right or left handedness, according to the right-hand rule. Many other familiar objects exhibit the same chiral symmetry of the human body, such as gloves and shoes. Right shoes differ from left shoes only by being mirror images of each other. In contrast thin gloves may not be considered chiral; the J, L, S and Z-shaped tetrominoes of the popular video game Tetris exhibit chirality, but only in a two-dimensional space.
Individually they contain no mirror symmetry in the plane. A figure is achiral if and only if its symmetry group contains at least one orientation-reversing isometry. See for a full mathematical definition of chirality. In three dimensions, every figure that possesses a mirror plane of symmetry S1, an inversion center of symmetry S2, or a higher improper rotation Sn axis of symmetry is achiral. Note, that there are achiral figures lacking both plane and center of symmetry. An example is the figure F 0 =, invariant under the orientation reversing isometry ↦ and thus achiral, but it has neither plane nor center of symmetry; the figure F 1 = is achiral as the origin is a center of symmetry, but it lacks a plane of symmetry. Note that achiral figures can have a center axis. In two dimensions, every figure which possesses an axis of symmetry is achiral
The term chiral describes an object a molecule, which has or produces a non-superposable mirror image of itself. In chemistry, such a molecule is called an enantiomer or is said to exhibit chirality or enantiomerism; the term "chiral" comes from the Greek word for the human hand, which itself exhibits such non-superimposeability of the left hand over the right. Due to the opposition of the fingers and thumbs, no matter how the two hands are oriented, it is impossible for both hands to coincide. Helices, chiral characteristics, chiral media and symmetry all relate to the concept of left- and right-handedness. Electromagnetic wave propagation as handedness is wave polarization and described in terms of helicity. Polarization of an electromagnetic wave is the property that describes the orientation, i.e. the time-varying and amplitude of the electric field vector. For a depiction, see the adjacent image. In the image, it can be seen that polarizations are described in terms of the figures traced as a function of time all along the electric field vector.
A representation of the electric field, as a vector, is placed onto a fixed plane in space. The plane is perpendicular to the direction of propagation. In general, polarization is elliptical and is traced in a clockwise or counterclockwise sense, as viewed in the direction of propagation. If, the major and minor axes of the ellipse are equal the polarization is said to be circular. If the minor axis of the ellipse is zero, the polarization is said to be linear. Rotation of the electric vector in a clockwise sense is designated right-hand polarization, rotation in a counterclockwise sense is designated left-hand polarization Mathematically, an elliptically polarized wave may be described as the vector sum of two waves of equal wavelength but unequal amplitude, in quadrature. Circular polarization, regarding electromagnetic wave propagation, is polarization such that the tip of the electric field vector describes a helix; the magnitude of the electric field vector is constant. The projection of the tip of the electric field vector upon any fixed plane intersecting, normal to, the direction of propagation, describes a circle.
A circularly polarized wave may be resolved into two linearly polarized waves in phase quadrature with their planes of polarization at right angles to each other. Circular polarization may be referred to as "right-hand" or "left-hand," depending on whether the helix describes the thread of a right-hand or left-hand screw This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C". in support of the series on U. S. military standards relating to telecommunications, MIL-STD-188 Chiral material presents optical activity. Optical activity is very weak in the chiral material found in nature, but it can be enhanced in an artificial chiral material, i.e. chiral metamaterial. In a chiral metamaterial, aligned electric- and magnetic-dipole pairs are induced; the strong coupling between electric and magnetic dipoles results in large optical activity so that the chiral metamaterial can be used for circular polarizer design. Handedness is intrinsic to chiral materials.
Handedness is manifest in the microstructure of homogeneous/homogenizable chiral materials. For example, an isotropic chiral material comprises a random dispersion of handed molecules or inclusions. In contrast, handedness is manifest at the macroscopic level in structurally chiral materials. For example, the molecules of cholesteric liquid crystals are randomly positioned but macroscopically they exhibit a helicoidal orientational order. Other examples of structurally chiral materials can be fabricated either as stacks of uniaxial laminas or using sculptured thin films. Remarkably, artificial examples of both types of chiral materials were produced by J. C. Bose more than 11 decades ago. Parenthetically, a third type of chiral material has entered scientific literature; such a material is made by depositing spirals on some flat surface. Spirals, being two-dimensional objects, cannot be chiral, planar chirality is an infelicitous term that ought to be replaced by a meaningful term. Casimir forces observed experimentally in nature have always been attractive and have rendered nanoscale and microscale machines inoperable by causing their moving parts to permanently stick together.
This has been a long-standing problem. Nanoscale machines expected to have wide application in industry, energy and other fields may someday operate far more efficiently thanks to important theoretical discoveries concerning the manipulation of famous Casimir forces that took place at the U. S. Department of Energy's Ames Laboratory; the ground breaking research, conducted through mathematical simulations, revealed the possibility of a new class of materials able to exert a repulsive force when they are placed in close proximity to each other. The repulsive force, which harnesses a quantum phenomenon known as the Casimir effect, may someday allow nanoscale machines to overcome mechanical friction. Though the frictional forces in nanoscale environments are small, they inhibit the function of the tiny devices designed to operate in that realm, explained Costas Soukoulis, a senior physicist at the Ames Lab and Distinguished Professor of physics at Iowa State University, who led the research effort.
Soukoulis and his teammates, including Ames Laboratory assistant scientist Thomas Koschny, were the first to study the use of exotic materials known as chiral metamaterial
Chirality is a 4-volume yuri manga series written and illustrated by author Satoshi Urushihara. The manga was serialized in Comic NORA in 1995, published in three bound volumes, re-released into two bound volumes in 2003. In 1997 Chirality was licensed for released in North America by Central Park Media, it was published as 18 issues between March 1997 and August 1998, as well as being released into four bound volumes from 1997 to 2000. The art was flipped so that it would read left to right, not an uncommon practice for manga released in Western Hemisphere at the time; the story is set in a not too distant future, in which Earth has been overrun by a horrifying technovirus. Mechanical parasites, mistakenly created in an attempt to advance technology, attach themselves to human spinal cords and turn their hosts into cyborgs, called GM; the Original GM were created by a program designed by humans to regulate nature. Gaia malfunctioned and started creating their own GM. Gaia is repairing parts of it that were damaged, once this is done, it will attempt to destroy the Earth.
Desperate to rid themselves of this technological terror, the remaining human survivors try to band together and learn to defend themselves against these android enemies. Carol is an artificial being, created to save mankind. In her youth she suffered at the hands of the humans she sought to save, lost sight of her mission. Only through the kindness of one human girl named Shiori was Carol able to find her focus and a reason to save the world; the two reunite years as Carol saves Shiori from her friend Elena, tragically infected with the parasitic virus. Although Shiori doesn't remember Carol at first, Carol remembers Shiori and stops at nothing to protect her and express her love for her. Though Shiori is uncomfortable and embarrassed with Carol at first, she grows to return her feelings. However, the two soon find out that their deep love isn't just a small matter between the two of them. Carol An artificial being, created to save mankind. In her youth, she suffered at the hands of the humans she sought to save and lost sight of her mission.
Due to the kindness of Shiori, a human girl, she now stops at nothing to protect her and express her love for her. Author notes say, her abilities include immunity to GM infestation, assuming a male form -which provides her with additional strength during battle-, creating animals from her own body. She was implanted with many kinds of animal DNA, meant to restore the animal population. Since Carol is able to absorb DNA through physical contact, she has been able to donate organs to injured humans with no chance of rejection, since they are their organs. Shiori A human girl who showed kindness towards Carol, becomes the one thing that Carol strives to protect, she is brave and compassionate close to her family and friends, wholeheartedly wishes to end the GM threat with Carol and her family. While not trained in combat, she doesn't panic in the middle of a battle, has some skill with firearms. Big Carol's robot companion and auxiliary weapon against the GM. Maintains a sort of telepathic contact with her, which proves decisive in their mission to take down Gaia.
Big has a veritable arsenal of weapons hidden in his body. Adam An with male genes, he was intended to protect Carol. Being left incomplete, he was revived by Gaia, therefore making his mission from protecting Carol to having to kill her. Patty A medic who accompanies the Gaia expedition and knows of Shiori and Carol's relationship. Shizuma Shiori's older brother who's oblivious to Carol's relationship. CPM Press Chirality at the Wayback Machine Chirality at Anime News Network's encyclopedia
Chirality is a property of asymmetry important in several branches of science. The word chirality is derived from "hand," a familiar chiral object. An object or a system is chiral. Conversely, a mirror image of an achiral object, such as a sphere, cannot be distinguished from the object. A chiral object and its mirror image are called enantiomorphs or, when referring to molecules, enantiomers. A non-chiral object can be superposed on its mirror image. If the object is non-chiral and is imagined as being colored blue and its mirror image is imagined as colored yellow by a series of rotations and translations the two can be superposed, producing green, with none of the original colors remaining; the term was first used by Lord Kelvin in 1893 in the second Robert Boyle Lecture at the Oxford University Junior Scientific Club, published in 1894: I call any geometrical figure, or group of points,'chiral', say that it has chirality if its image in a plane mirror, ideally realized, cannot be brought to coincide with itself.
Human hands are the most universally recognized example of chirality. The left hand is a non-superimposable mirror image of the right hand; this difference in symmetry becomes obvious if someone attempts to shake the right hand of a person using their left hand, or if a left-handed glove is placed on a right hand. In mathematics, chirality is the property of a figure, not identical to its mirror image. In mathematics, a figure is chiral if it cannot be mapped to its mirror image by rotations and translations alone. For example, a right shoe is different from a left shoe, clockwise is different from anticlockwise. See for a full mathematical definition. A chiral object and its mirror image are said to be enantiomorphs; the word enantiomorph stems from the Greek ἐναντίος'opposite' + μορφή'form'. A non-chiral figure is called amphichiral; the helix and Möbius strip are chiral two-dimensional objects in three-dimensional ambient space. The J, L, S and Z-shaped tetrominoes of the popular video game Tetris exhibit chirality, but only in a two-dimensional space.
Many other familiar objects exhibit the same chiral symmetry of the human body, such as gloves and shoes. A similar notion of chirality is considered in knot theory; some chiral three-dimensional objects, such as the helix, can be assigned a right or left handedness, according to the right-hand rule. In geometry a figure is achiral if and only if its symmetry group contains at least one orientation-reversing isometry. In two dimensions, every figure that possesses an axis of symmetry is achiral, it can be shown that every bounded achiral figure must have an axis of symmetry. In three dimensions, every figure that possesses a plane of symmetry or a center of symmetry is achiral. There are, achiral figures lacking both plane and center of symmetry. In terms of point groups, all chiral figures lack an improper axis of rotation; this means that they can not contain a center of a mirror plane. Only figures with a point group designation of C1, Cn, Dn, T, O, or I can be chiral. A knot is called achiral if it can be continuously deformed into its mirror image, otherwise it is called chiral.
For example, the unknot and the figure-eight knot are achiral. In physics, chirality may be found in the spin of a particle, where the handedness of the object is determined by the direction in which the particle spins. Not to be confused with helicity, the projection of the spin along the linear momentum of a subatomic particle, chirality is a purely quantum mechanical phenomenon like spin. Although both can have left-handed or right-handed properties, only in the massless case do they have a simple relation. In particular for a massless particle the helicity is the same as the chirality while for an antiparticle they have opposite sign; the handedness in both chirality and helicity relate to the rotation of a particle while it proceeds in linear motion with reference to the human hands. The thumb of the hand points towards the direction of linear motion whilst the fingers curl into the palm, representing the direction of rotation of the particle. Depending on the linear and rotational motion, the particle can either be defined by left-handedness or right-handedness.
A symmetry transformation between the two is called parity. Invariance under parity by a Dirac fermion is called chiral symmetry. Electromagnetic wave propagation as handedness is wave polarization and described in terms of helicity. Polarization of an electromagnetic wave is the property that describes the orientation, i.e. the time-varying and amplitude of the electric field vector. For a depiction, see the adjacent image. A chiral molecule is a type of molecule; the feature, most the cause of chirality in molecules is the presence of an asymmetric carbon atom. The term "chiral" in general is used to describe the object, non-superposable on its mirror image. In chemistry, chirality refers to molecules. Two mirror images of a chiral molecule are called enantiomers or optical isomers
The gastropod shell is part of the body of a gastropod or snail, a kind of mollusc. The shell is an exoskeleton, which protects from predators, mechanical damage, dehydration, but serves for muscle attachment and calcium storage; some gastropods appear shell-less but may have a remnant within the mantle, or the shell is reduced such that the body cannot be retracted within. Some snails possess an operculum that seals the opening of the shell, known as the aperture, which provides further protection; the study of mollusc shells is known as conchology. The biological study of gastropods, other molluscs in general, is malacology. Shell morphology terms vary by species group. An excellent source for terminology of the gastropod shell is "How to Know the Eastern Land Snails" by John B. Burch now available at the Hathi Trust Digital Library; the gastropod shell has three major layers secreted by the mantle. The calcareous central layer, tracum, is made of calcium carbonate precipitated into an organic matrix known as conchiolin.
The outermost layer is the periostracum, resistant to abrasion and provides most shell coloration. The body of the snail contacts the innermost smooth layer that may be composed of mother-of-pearl or shell nacre, a dense horizontally packed form of conchiolin, layered upon the periostracum as the snail grows. Gastropod shell morphology is quite constant among individuals of a species. Controlling variables are: The rate of growth per revolution around the coiling axis. High rates give wide-mouthed forms such as the abalone, low rates give coiled forms such as Turritella or some of the Planorbidae; the shape of the generating curve equivalent to the shape of the aperture. It may be round, for instance in the turban shell, elongate as in the cone shell or have an irregular shape with a siphonal canal extension, as in the Murex; the rate of translation of the generating curve along the axis of coiling, controlling how high-spired the resulting shell becomes. This may range from a flat planispiral shell, to nearly the diameter of the aperture.
Irregularities or "sculpturing" such as ribs, spines and varices made by the snail changing the shape of the generating curve during the course of growth, for instance in the many species of Murex. Ontologic growth changes as the animal reaches adulthood. Good examples are the inward-coiled lip of the cowry; some of these factors can be modelled mathematically and programs exist to generate realistic images. Early work by David Raup on the analog computer revealed many possible combinations that were never adopted by any actual gastropod; some shell shapes are found more in certain environments, though there are many exceptions. Wave-washed high-energy environments, such as the rocky intertidal zone, are inhabited by snails whose shells have a wide aperture, a low surface area, a high growth rate per revolution. High-spired and sculptured forms become more common in quiet water environments; the shell of burrowing forms, such as the olive and Terebra, are smooth and lack elaborate sculpture, in order to decrease resistance when moving through sand.
On land, high-spired forms are associated with vertical surfaces, whereas flat-shelled snails tend to live on the ground. A few gastropods, for instance the Vermetidae, cement the shell to, grow along, solid surfaces such as rocks, or other shells. Most gastropod shells are spirally coiled; the majority of gastropod species have dextral shells, but a small minority of species and genera are always sinistral, a few species show a mixture of dextral and sinistral individuals. There occur aberrantly sinistral forms of dextral species and some of these are sought by shell collectors. If a coiled gastropod shell is held with the spire pointing upwards and the aperture more or less facing the observer, a dextral shell will have the aperture on the right-hand side, a sinistral shell will have the aperture on the left-hand side; this chirality of gastropods is sometimes overlooked when photographs of coiled gastropods are "flipped" by a non-expert prior to being used in a publication. This image "flipping" results in a normal dextral gastropod appearing to be a rare or abnormal sinistral one.
Sinistrality arose independently 19 times among marine gastropods since the start of the Cenozoic. This left-handedness seems to be more common in land pulmonates, but still the dextral living species in gastropods seem to account for 99% of the total number. The chirality in gastropods appears in the gene NODAL is involved. A more recent study correlates the asymmetric coiling of the shell by the left-right asymmetric expression of the decapentaplegic gene in the mantle. In a few cases, both left- and right-handed coiling are found in the same population. Sinistral mutants of dextral species and dextral mutants of sinistral species are rare but well documented occurrences among land snails in general. Populations or species with mixed coiling are much rarer, and, so far as is known, are confined, with one exception, to a few genera of arboreal tropical snails. Besides Amphidromus, the Cuban Liguus vittatus, Haitian Liguus virgineus, some Hawaiian Partulina and many Hawaiian Achatinella, as well as several species of Pacific islands Partula, are known to have mixed dextral-sinistral populations.
A possible exception may concern some of the European clausiliids of the subfamily Alopiinae. They are ob