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120-552: Insects all over the world begin to swarm for unknown reasons, with other animals and plants acting strangely as well. To investigate this, Takuya Kai is dispatched with an Earth Academia group. Investigating independently, Takuya encounters the insect elder Guru, who reveals that insects are preparing for battle against invaders from another dimension called the Jamahl. Offering their aid, the Earth Academia create suits of armor to combat

240-417: A carrion site, where decomposition likely increased soil nutrient levels and host plant quality. Midges, such as Tokunagayusurika akamusi , form swarms, dancing in the air. Swarming serves multiple purposes, including the facilitation of mating by attracting females to approach the swarm, a phenomenon known as lek mating . Such cloud-like swarms often form in early evening when the sun is getting low, at

360-405: A thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium. The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact,

480-503: A thermodynamic operation . In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties , other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings. In systems that are at

600-903: A "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10 years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium." Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." According to L. Tisza : "... in

720-415: A V-formation may conserve 12–20% of the energy they would need to fly alone. Red knots and dunlins were found in radar studies to fly 5 km per hour faster in flocks than when they were flying alone. The birds flying at the tips and at the front are rotated in a timely cyclical fashion to spread flight fatigue equally among the flock members. The formation also makes communication easier and allows

840-409: A common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on

960-476: A constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it to compensate for

1080-528: A deeper understanding of the behaviour. Early studies of swarm behaviour employed mathematical models to simulate and understand the behaviour. The simplest mathematical models of animal swarms generally represent individual animals as following three rules: The boids computer program, created by Craig Reynolds in 1986, simulates swarm behaviour following the above rules. Many subsequent and current models use variations on these rules, often implementing them by means of concentric "zones" around each animal. In

1200-507: A loss of alignment in the group appears to increase the randomness of its motion, until an aligned state is again achieved. This noise-induced alignment appears to be an intrinsic characteristic of collective coherent motion. Insect migration is the seasonal movement of insects , particularly those by species of dragonflies , beetles , butterflies , and moths . The distance can vary from species to species, but in most cases these movements involve large numbers of individuals. In some cases

1320-424: A natural thermodynamic process . It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It

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1440-488: A neighbour. The shape of these zones will necessarily be affected by the sensory capabilities of a given animal. For example, the visual field of a bird does not extend behind its body. Fish rely on both vision and on hydrodynamic perceptions relayed through their lateral lines , while Antarctic krill rely both on vision and hydrodynamic signals relayed through antennae . However recent studies of starling flocks have shown that each bird modifies its position, relative to

1560-558: A next action, by the same or a different agent. In that way, subsequent actions tend to reinforce and build on each other, leading to the spontaneous emergence of coherent, apparently systematic activity. Stigmergy is a form of self-organization. It produces complex, seemingly intelligent structures, without need for any planning, control, or even direct communication between the agents. As such it supports efficient collaboration between extremely simple agents, who lack any memory, intelligence or even awareness of each other. Swarm intelligence

1680-630: A non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface. Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse : "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium

1800-430: A number of aspects of flock behaviour. In order to gain insight into why animals evolve swarming behaviours, scientists have turned to evolutionary models that simulate populations of evolving animals. Typically these studies use a genetic algorithm to simulate evolution over many generations. These studies have investigated a number of hypotheses attempting to explain why animals evolve swarming behaviours, such as

1920-421: A particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential. A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for

2040-454: A queen leaving the nest along with some workers to found a colony at a new site, a process akin to swarming in honeybees . The concept of self-propelled particles (SPP) was introduced in 1995 by Tamás Vicsek et al. as a special case of the boids model introduced in 1986 by Reynolds. An SPP swarm is modelled by a collection of particles that move with a constant speed and respond to random perturbations by adopting at each time increment

2160-813: A set of tiny robots that appear to the roaches as other roaches and can thus alter the roaches' perception of critical mass . The robots were also specially scented so that they would be accepted by the real roaches. Locusts are the swarming phase of the short-horned grasshoppers of the family Acrididae . Some species can breed rapidly under suitable conditions and subsequently become gregarious and migratory. They form bands as nymphs and swarms as adults—both of which can travel great distances, rapidly stripping fields and greatly damaging crops . The largest swarms can cover hundreds of square miles and contain billions of locusts. A locust can eat its own weight (about 2 grams) in plants every day. That means one million locusts can eat more than one tonne of food each day, and

2280-485: A simple set of individual interactions. Cockroaches are mainly nocturnal and will run away when exposed to light. A study tested the hypothesis that cockroaches use just two pieces of information to decide where to go under those conditions: how dark it is and how many other cockroaches there are. The study conducted by José Halloy and colleagues at the Free University of Brussels and other European institutions created

2400-404: A single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous. This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes

2520-482: A source of fascination for children, naturalists and artists. Individual insects seem to do their own thing without any central control, yet the colony as a whole behaves in a highly coordinated manner. Researchers have found that cooperation at the colony level is largely self-organized . The group coordination that emerges is often just a consequence of the way individuals in the colony interact. These interactions can be remarkably simple, such as one ant merely following

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2640-574: A special term 'thermal equilibrium'. J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its " full thermodynamic equilibrium state". Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all

2760-586: A state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a "meta-stable equilibrium". Though not a widely named "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when an isolated body of material starts from an equilibrium state, in which portions of it are held at different states by more or less permeable or impermeable partitions, and

2880-418: A thermodynamic operation removes or makes the partitions more permeable, then it spontaneously reaches its own new state of internal thermodynamic equilibrium and this is accompanied by an increase in the sum of the entropies of the portions. Classical thermodynamics deals with states of dynamic equilibrium . The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential

3000-426: A thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example,

3120-653: A wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when

3240-434: A wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and

3360-400: Is also a scientific stream attempting to model the swarm systems themselves and understand their underlying mechanisms, and an engineering stream focused on applying the insights developed by the scientific stream to solve practical problems in other areas. Swarm algorithms follow a Lagrangian approach or an Eulerian approach. The Eulerian approach views the swarm as a field , working with

3480-410: Is also studied by active matter physicists as a phenomenon which is not in thermodynamic equilibrium , and as such requires the development of tools beyond those available from the statistical physics of systems in thermodynamic equilibrium. In this regard, swarming has been compared to the mathematics of superfluids , specifically in the context of starling flocks (murmuration). Swarm behaviour

3600-436: Is an axiomatic concept of thermodynamics . It is an internal state of a single thermodynamic system , or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls . In thermodynamic equilibrium, there are no net macroscopic flows of matter nor of energy within a system or between systems. In a system that is in its own state of internal thermodynamic equilibrium, not only

3720-537: Is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero. R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that

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3840-541: Is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory , and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example,

3960-418: Is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in

4080-483: Is essential for the strict meaning of thermodynamic equilibrium. A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium. " A monograph on classical thermodynamics by H.A. Buchdahl considers

4200-432: Is how a fish can choose to join a shoal of animals similar to themselves, given that it cannot know its own appearance. Experiments with zebrafish have shown that shoal preference is a learned ability, not innate. A zebrafish tends to associate with shoals that resemble shoals in which it was reared, a form of imprinting . Other open questions of shoaling behaviour include identifying which individuals are responsible for

4320-457: Is lost in the Eulerian approach. Ant colony optimization is a widely used algorithm which was inspired by the behaviours of ants, and has been effective solving discrete optimization problems related to swarming. The algorithm was initially proposed by Marco Dorigo in 1992, and has since been diversified to solve a wider class of numerical problems. Species that have multiple queens may have

4440-497: Is made by Poli. Researchers in Switzerland have developed an algorithm based on Hamilton's rule of kin selection. The algorithm shows how altruism in a swarm of entities can, over time, evolve and result in more effective swarm behaviour. The earliest evidence of swarm behaviour in animals dates back about 480 million years. Fossils of the trilobite Ampyx priscus have been recently described as clustered in lines along

4560-535: Is minimized (in the absence of an applied voltage), or for which the entropy ( S ) is maximized, for specified conditions. One such potential is the Helmholtz free energy ( A ), for a closed system at constant volume and temperature (controlled by a heat bath): Another potential, the Gibbs free energy ( G ), is minimized at thermodynamic equilibrium in a closed system at constant temperature and pressure, both controlled by

4680-433: Is no centralized control structure dictating how individual agents should behave, local, and to a certain degree random, interactions between such agents lead to the emergence of intelligent global behaviour, unknown to the individual agents. Swarm intelligence research is multidisciplinary. It can be divided into natural swarm research studying biological systems and artificial swarm research studying human artefacts. There

4800-412: Is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined. This local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles . In a radiating gas, the photons being emitted and absorbed by the gas do not need to be in a thermodynamic equilibrium with each other or with

4920-430: Is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium. Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other. For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in

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5040-501: Is the collective behaviour of decentralized , self-organized systems, natural or artificial. The concept is employed in work on artificial intelligence . The expression was introduced by Gerardo Beni and Jing Wang in 1989, in the context of cellular robotic systems. Swarm intelligence systems are typically made up of a population of simple agents such as boids interacting locally with one another and with their environment. The agents follow very simple rules, and although there

5160-410: Is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings. The various types of equilibriums are achieved as follows: Often the surroundings of

5280-443: Is there an absence of macroscopic change, but there is an “absence of any tendency toward change on a macroscopic scale.” Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal , mechanical , chemical , and radiative equilibria. Systems can be in one kind of mutual equilibrium, while not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by

5400-531: Is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within

5520-447: Is typically a kilometre or more from the original hive, though some species, e.g., Apis dorsata , may establish new colonies within as little as 500 meters from the natal nest. This collective decision-making process is remarkably successful in identifying the most suitable new nest site and keeping the swarm intact. A good hive site has to be large enough to accommodate the swarm (about 15 litres in volume), has to be well-protected from

5640-608: The Bosphorus at migration times. More common species, such as the European honey buzzard , can be counted in hundreds of thousands in autumn. Other barriers, such as mountain ranges, can also cause funnelling, particularly of large diurnal migrants. This is a notable factor in the Central American migratory bottleneck. This concentration of birds during migration can put species at risk. Some spectacular migrants have already gone extinct,

5760-488: The selfish herd theory the predator confusion effect, the dilution effect, and the many eyes theory. The concept of emergence—that the properties and functions found at a hierarchical level are not present and are irrelevant at the lower levels–is often a basic principle behind self-organizing systems . An example of self-organization in biology leading to emergence in the natural world occurs in ant colonies. The queen does not give direct orders and does not tell

5880-413: The "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium ." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely,

6000-481: The "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition , which apparently was suggested by Fowler .) Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by

6120-422: The "zone of repulsion", very close to the animal, the focal animal will seek to distance itself from its neighbours to avoid collision. Slightly further away, in the "zone of alignment", the focal animal will seek to align its direction of motion with its neighbours. In the outermost "zone of attraction", which extends as far away from the focal animal as it is able to sense, the focal animal will seek to move towards

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6240-520: The Earth Academia's brightest and infused with the life force of insects. The Beet Machines ( ビートマシン , Bīto Mashin ) are the mecha used by the B-Fighters to fight the Jamahl fighter jets , usually summoned by the command, "Beet Machines, launch!" They are housed within the Heavy Shell Base (重甲基地, Jukou Kichi ), a large hangar base located beneath the Earth Academia's parking lot; when summoned,

6360-546: The Synthetic Beast Army ( 合成獣軍団 , Gōseijū Gundan ) is composed of humanoid Chimeras created from Gigaro's blood. Led by Schwartz, the Combat-Mecha Army ( 戦闘メカ軍団 , Sentō Meka Gundan ) is composed of combat robots . Swarm Swarm behaviour , or swarming , is a collective behaviour exhibited by entities, particularly animals, of similar size which aggregate together, perhaps milling about

6480-404: The ability to solve geometric problems. For example, colonies routinely find the maximum distance from all colony entrances to dispose of dead bodies. A further key concept in the field of swarm intelligence is stigmergy . Stigmergy is a mechanism of indirect coordination between agents or actions. The principle is that the trace left in the environment by an action stimulates the performance of

6600-505: The ants what to do. Instead, each ant reacts to stimuli in the form of chemical scents from larvae, other ants, intruders, food and buildup of waste, and leaves behind a chemical trail, which, in turn, provides a stimulus to other ants. Here each ant is an autonomous unit that reacts depending only on its local environment and the genetically encoded rules for its variety. Despite the lack of centralized decision making, ant colonies exhibit complex behaviours and have even been able to demonstrate

6720-456: The average direction of motion of the other particles in their local neighbourhood. Simulations demonstrate that a suitable "nearest neighbour rule" eventually results in all the particles swarming together, or moving in the same direction. This emerges, even though there is no centralized coordination, and even though the neighbours for each particle constantly change over time. SPP models predict that swarming animals share certain properties at

6840-846: The base rises out of the ground, allowing the vehicles to exit (the Beetluder from the front, the Stagger Tank from the right side, and the Red Gyro from the top). The Jamahl ( ジャマール , Jamāru ) are beings from another dimension. Their base of operation, was the Jamahl Fortress ( ジャマール要塞 , Jamāru Yōsai ) , a claw-like dreadnaught. It had an opening where the palm would be, where the Jamar fighter jets emerged from and where Jamahl's new super-weapons were located. The Jamahl Kaijin ( ジャマール怪人 , Jamāru Kaijin ) come in different armies, each led by one of

6960-401: The best solutions. The solutions it finds are called particles . Each particle stores its position as well as the best solution it has achieved so far. The particle swarm optimizer tracks the best local value obtained so far by any particle in the local neighbourhood. The remaining particles then move through the problem space following the lead of the optimum particles. At each time iteration,

7080-447: The best, or closest, food source from several in the vicinity. Such collective decisions are achieved using positive feedback mechanisms. Selection of the best food source is achieved by ants following two simple rules. First, ants which find food return to the nest depositing a pheromone chemical. More pheromone is laid for higher quality food sources. Thus, if two equidistant food sources of different qualities are found simultaneously,

7200-459: The birds to maintain visual contact with each other. Other animals may use similar drafting techniques when migrating. Lobsters , for example, migrate in close single-file formation "lobster trains", sometimes for hundreds of miles. The Mediterranean and other seas present a major obstacle to soaring birds, which must cross at the narrowest points. Massive numbers of large raptors and storks pass through areas such as Gibraltar , Falsterbo , and

7320-477: The body remains sufficiently nearly in thermodynamic equilibrium during the process. A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium . This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium

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7440-404: The bottom wall, but the temperature is the same everywhere. A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within

7560-710: The chance of capture), enhanced foraging success, and higher success in finding a mate. It is also likely that fish benefit from shoal membership through increased hydrodynamic efficiency. Fish use many traits to choose shoalmates. Generally they prefer larger shoals, shoalmates of their own species, shoalmates similar in size and appearance to themselves, healthy fish, and kin (when recognised). The "oddity effect" posits that any shoal member that stands out in appearance will be preferentially targeted by predators. This may explain why fish prefer to shoal with individuals that resemble them. The oddity effect would thus tend to homogenise shoals. One puzzling aspect of shoal selection

7680-537: The cluster. If a scout finds a suitable location, she returns to the cluster and promotes it by dancing a version of the waggle dance . This dance conveys information about the quality, direction, and distance of the new site. The more excited she is about her findings, the more vigorously she dances. If she can convince others they may take off and check the site she found. If they approve they may promote it as well. In this decision-making process, scouts check several sites, often abandoning their own original site to promote

7800-411: The conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium". P.M. Morse writes that thermodynamics is concerned with " states of thermodynamic equilibrium ". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining

7920-413: The contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another. If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have

8040-416: The criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory! " J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems." Another author, cited by Callen as giving

8160-461: The density of the swarm and deriving mean field properties. It is a hydrodynamic approach, and can be useful for modelling the overall dynamics of large swarms. However, most models work with the Lagrangian approach, which is an agent-based model following the individual agents (points or particles) that make up the swarm. Individual particle models can follow information on heading and spacing that

8280-663: The direction of shoal movement. In the case of migratory movement, most members of a shoal seem to know where they are going. In the case of foraging behaviour, captive shoals of golden shiner (a kind of minnow ) are led by a small number of experienced individuals who knew when and where food was available. Radakov estimated herring schools in the North Atlantic can occupy up to 4.8 cubic kilometres (1.2 cu mi) with fish densities between 0.5 and 1.0 fish/cubic metre, totalling several billion fish in one school. Thermodynamic equilibrium Thermodynamic equilibrium

8400-540: The discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common." The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it

8520-697: The elements, receive an optimal amount of sunshine, be some height above the ground, have a small entrance and be capable of resisting ant infestation - that is why tree cavities are often selected. Unlike social insects, swarms of non-social insects that have been studied primarily seem to function in contexts such as mating, feeding, predator avoidance, and migration. Moths may exhibit synchronized mating, during which pheromones released by females initiate searching and swarming behavior in males. Males sense pheromones with sensitive antennae and may track females as far as several kilometers away. Swarm mating involves female choice and male competition. Only one male in

8640-401: The equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement

8760-429: The glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and

8880-422: The group level, regardless of the type of animals in the swarm. Swarming systems give rise to emergent behaviours which occur at many different scales, some of which are both universal and robust. It has become a challenge in theoretical physics to find minimal statistical models that capture these behaviours. Particle swarm optimization is another algorithm widely used to solve problems related to swarms. It

9000-447: The hind legs or, in some species, simply encountering other individuals causes an increase in levels of serotonin. The transformation of the locust to the swarming variety can be induced by several contacts per minute over a four-hour period. Notably, an innate predisposition to aggregate has been found in hatchlings of the desert locust, Schistocerca gregaria , independent of their parental phase. An individual locust's response to

9120-452: The individuals that migrate in one direction may not return and the next generation may instead migrate in the opposite direction. This is a significant difference from bird migration . Monarch butterflies are especially noted for their lengthy annual migration. In North America they make massive southward migrations starting in August until the first frost. A northward migration takes place in

9240-488: The intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field. J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with

9360-401: The largest swarms can consume over 100,000 tonnes each day. Swarming in locusts has been found to be associated with increased levels of serotonin which causes the locust to change colour, eat much more, become mutually attracted, and breed much more easily. Researchers propose that swarming behaviour is a response to overcrowding and studies have shown that increased tactile stimulation of

9480-423: The massive particles of the gas for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist. As an example, LTE will exist in a glass of water that contains a melting ice cube . The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of

9600-889: The melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous. Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated. For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice,

9720-445: The migration such as predation. Many birds migrate in flocks. For larger birds, it is assumed that flying in flocks reduces energy costs. The V formation is often supposed to boost the efficiency and range of flying birds, particularly over long migratory routes. All the birds except the first fly in the upwash from one of the wingtip vortices of the bird ahead. The upwash assists each bird in supporting its own weight in flight, in

9840-585: The molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature. Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have

9960-566: The most notable being the passenger pigeon . During migration the flocks were a mile (1.6 km) wide and 300 miles (500 km) long, taking several days to pass and containing up to a billion birds. The term "shoal" can be used to describe any group of fish, including mixed-species groups, while "school" is used for more closely knit groups of the same species swimming in a highly synchronised and polarised manner. Fish derive many benefits from shoaling behaviour including defence against predators (through better predator detection and by diluting

10080-779: The ocean floor. The animals were all mature adults, and were all facing the same direction as though they had formed a conga line or a peloton . It has been suggested they line up in this manner to migrate, much as spiny lobsters migrate in single-file queues; it has also been suggested that the formation is the precursor for mating, as with the fly Leptoconops torrens . The findings suggest animal collective behaviour has very early evolutionary origins. Examples of biological swarming are found in bird flocks , fish schools , insect swarms , bacteria swarms , molds, molecular motors , quadruped herds and people. The behaviour of social insects (insects that live in colonies , such as ants, bees, wasps and termites) has always been

10200-534: The particle swarm optimiser accelerates each particle toward its optimum locations according to simple mathematical rules . Particle swarm optimization has been applied in many areas. It has few parameters to adjust, and a version that works well for a specific applications can also work well with minor modifications across a range of related applications. A book by Kennedy and Eberhart describes some philosophical aspects of particle swarm optimization applications and swarm intelligence. An extensive survey of applications

10320-424: The pheromone trail to the better one will be stronger. Ants in the nest follow another simple rule, to favor stronger trails, on average. More ants then follow the stronger trail, so more ants arrive at the high quality food source, and a positive feedback cycle ensures, resulting in a collective decision for the best food source. If there are two paths from the ant nest to a food source, then the colony usually selects

10440-428: The pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work. A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when

10560-499: The respective intensive parameters of the system and surroundings are equal. This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state. M. Zemansky also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When

10680-606: The same basic behavioural and ecological syndrome, often referred to as "legionary behaviour", and may be an example of convergent evolution . The successful techniques used by ant colonies have been studied in computer science and robotics to produce distributed and fault-tolerant systems for solving problems. This area of biomimetics has led to studies of ant locomotion, search engines that make use of "foraging trails", fault-tolerant storage and networking algorithms . In temperate climates, honey bees usually form swarms in late spring. A swarm typically contains about half

10800-604: The same spot or perhaps moving en masse or migrating in some direction. It is a highly interdisciplinary topic. As a term, swarming is applied particularly to insects, but can also be applied to any other entity or animal that exhibits swarm behaviour. The term flocking or murmuration can refer specifically to swarm behaviour in birds, herding to refer to swarm behaviour in tetrapods , and shoaling or schooling to refer to swarm behaviour in fish. Phytoplankton also gather in huge swarms called blooms , although these organisms are algae and are not self-propelled

10920-437: The same way a glider can climb or maintain height indefinitely in rising air. Geese flying in a V formation save energy by flying in the updraft of the wingtip vortex generated by the previous animal in the formation. Thus, the birds flying behind do not need to work as hard to achieve lift. Studies show that birds in a V formation place themselves roughly at the optimum distance predicted by simple aerodynamic theory. Geese in

11040-468: The shorter path. This is because the ants that first return to the nest from the food source are more likely to be those that took the shorter path. More ants then retrace the shorter path, reinforcing the pheromone trail. Army ants , unlike most ant species, do not construct permanent nests; an army ant colony moves almost incessantly over the time it exists, remaining in an essentially perpetual state of swarming. Several lineages have independently evolved

11160-429: The six or seven animals directly surrounding it, no matter how close or how far away those animals are. Interactions between flocking starlings are thus based on a topological , rather than a metric, rule. It remains to be seen whether this applies to other animals. Another recent study, based on an analysis of high-speed camera footage of flocks above Rome and assuming minimal behavioural rules, has convincingly simulated

11280-571: The spring. How the species manages to return to the same overwintering spots over a gap of several generations is still a subject of research; the flight patterns appear to be inherited, based on a combination of the position of the sun in the sky and a time-compensated Sun compass that depends upon a circadian clock that is based in their antennae. Approximately 1800 of the world's 10,000 bird species are long-distance migrants. The primary motivation for migration appears to be food; for example, some hummingbirds choose not to migrate if fed through

11400-415: The spring. The monarch is the only butterfly that migrates both north and south as the birds do on a regular basis. But no single individual makes the entire round trip. Female monarchs deposit eggs for the next generation during these migrations. The length of these journeys exceeds the normal lifespan of most monarchs, which is less than two months for butterflies born in early summer. The last generation of

11520-533: The summer enters into a non-reproductive phase known as diapause and may live seven months or more. During diapause, butterflies fly to one of many overwintering sites. The generation that overwinters generally does not reproduce until it leaves the overwintering site sometime in February and March. It is the second, third and fourth generations that return to their northern locations in the United States and Canada in

11640-503: The superior site of another scout. Several different sites may be promoted by different scouts at first. After some hours and sometimes days, a preferred location eventually emerges from this decision-making process. When all scouts agree on the final location, the whole cluster takes off and swarms to it. Sometimes, if no decision is reached, the swarm will separate, some bees going in one direction; others, going in another. This usually results in failure, with both groups dying. A new location

11760-511: The surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to

11880-593: The surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables. It can be useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges . Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout

12000-406: The surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency ; a system in thermodynamic equilibrium is inanimate. Otherwise, a thermodynamic operation may directly affect a wall of the system. It is often convenient to suppose that some of

12120-405: The surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called

12240-468: The surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy. Another textbook author, J.R. Partington , writes: "(i) An equilibrium state is one which is independent of time ." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that

12360-633: The surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied. A thermodynamic system consisting of

12480-408: The surroundings: where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system. In other words, Δ G = 0 {\displaystyle \Delta G=0} is a necessary condition for chemical equilibrium under these conditions (in the absence of an applied voltage). Thermodynamic equilibrium

12600-518: The swarm—typically the first—will successfully copulate. Females maximize fitness benefits and minimize cost by governing the onset and magnitude of pheromone deployed. Too little pheromone will not attract a mate, too much allows less fit males to sense the signal. After copulation, females lay the eggs on a host plant. Quality of host plant may be a factor influencing the location of swarming and egg-laying. In one case, researchers observed pink-striped oakworm moths ( Anisota virginiensis ) swarming at

12720-421: The system must be isolated; Callen does not spell out what he means by the words "intrinsic factors". Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with

12840-410: The system was in equilibrium . In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium,

12960-454: The system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there

13080-419: The system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than

13200-540: The threat as the Jamahl arrive to Earth to enslave humans. Though they have trouble perfecting the Bio-Machinery, Guru arrives to infuse the armor with the life force of many insects. Once the suits become the B-Commanders, one suit chooses Takuya while the other two bond to Daisaku Katagiri and Rei Hayama. With their newfound power, the B-Fighters fight to drive back Jamahl's forces. The members use Bio-armor developed by

13320-621: The three Jamahl generals. During a fight with the B-Fighters, Gaohm would spirit all combatants into the Gaohm Zone ( ガオームゾーン , Gōmu Zōn ) , personalized super-dimensional battlefields where the Jamahl monsters can fight to their full potential. Led by Jera, the Mercenary Army ( 傭兵軍団 , Yōhei Gundan ) is composed of mercenary warriors from various dimensions who join Jamahl for various reasons. Some of these warriors are humans wearing armor while others are alien creatures. Led by Gigaro,

13440-960: The tip of a bush, on a hilltop, over a pool of water, or even sometimes above a person. The forming of such swarms is not out of instinct, but an adaptive behavior – a "consensus" – between the individuals within the swarms. It is also suggested that swarming is a ritual , because there is rarely any male midge by itself and not in a swarm. This could have formed due to the benefit of lowering inbreeding by having males of various genes gathering in one spot. The genus Culicoides , also known as biting midges, have displayed swarming behavior which are believed to cause confusion in predators. Cockroaches leave chemical trails in their feces as well as emitting airborne pheromones for mating. Other cockroaches will follow these trails to discover sources of food and water, and also discover where other cockroaches are hiding. Thus, groups of cockroaches can exhibit emergent behaviour , in which group or swarm behaviour emerges from

13560-619: The trail left by another ant. Yet put together, the cumulative effect of such behaviours can solve highly complex problems, such as locating the shortest route in a network of possible paths to a food source. The organised behaviour that emerges in this way is sometimes called swarm intelligence , a form of biological emergence . Individual ants do not exhibit complex behaviours, yet a colony of ants collectively achieves complex tasks such as constructing nests, taking care of their young, building bridges and foraging for food. A colony of ants can collectively select (i.e. send most workers towards)

13680-425: The two systems have the same temperature. The A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called

13800-522: The way animals are. By extension, the term "swarm" is applied also to inanimate entities which exhibit parallel behaviours, as in a robot swarm , an earthquake swarm , or a swarm of stars. From a more abstract point of view, swarm behaviour is the collective motion of a large number of self-propelled entities . From the perspective of the mathematical modeller, it is an emergent behaviour arising from simple rules that are followed by individuals and does not involve any central coordination. Swarm behaviour

13920-471: The whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point. If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and

14040-453: The winter. Also, the longer days of the northern summer provide extended time for breeding birds to feed their young. This helps diurnal birds to produce larger clutches than related non-migratory species that remain in the tropics. As the days shorten in autumn, the birds return to warmer regions where the available food supply varies little with the season. These advantages offset the high stress, physical exertion costs, and other risks of

14160-400: The workers together with the old queen, while the new queen stays back with the remaining workers in the original hive. When honey bees emerge from a hive to form a swarm, they may gather on a branch of a tree or on a bush only a few meters from the hive. The bees cluster about the queen and send out 20–50 scouts to find suitable new nest locations. The scouts are the most experienced foragers in

14280-412: Was developed in 1995 by Kennedy and Eberhart and was first aimed at simulating the social behaviour and choreography of bird flocks and fish schools. The algorithm was simplified and it was observed to be performing optimization. The system initially seeds a population with random solutions. It then searches in the problem space through successive generations using stochastic optimization to find

14400-416: Was first simulated on a computer in 1986 with the simulation program boids . This program simulates simple agents (boids) that are allowed to move according to a set of basic rules. The model was originally designed to mimic the flocking behaviour of birds, but it can be applied also to schooling fish and other swarming entities. In recent decades, scientists have turned to modeling swarm behaviour to gain

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