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Natural History (Pliny)

The Natural History is a work by Pliny the Elder. It is one of the largest single works to have survived from the Roman Empire to the modern day and purports to cover all ancient knowledge; the work's subject area is thus not limited to. It is encyclopedic in scope, it is the only work by Pliny to have survived, the last that he published. He published the first 10 books in AD 77, but had not made a final revision of the remainder at the time of his death during the AD 79 eruption of Vesuvius; the rest was published posthumously by Pliny the Younger. The work is divided into 37 books, organised into ten volumes; these cover topics including astronomy, geography, anthropology, human physiology, botany, horticulture, mining, sculpture and precious stones. Pliny's Natural History became a model for encyclopedias and scholarly works as a result of its breadth of subject matter, its referencing of original authors, its index. Pliny's Natural History was written alongside other substantial works. Pliny combined his scholarly activities with a busy career as an imperial administrator for the emperor Vespasian.

Much of his writing was done at night. As for the nocturnal hours spent writing, these were seen not as a loss of sleep but as an addition to life, for as he states in the preface, Vita vigilia est, "to be alive is to be watchful", in a military metaphor of a sentry keeping watch in the night. Pliny claims to be the only Roman to have undertaken such a work, in his prayer for the blessing of the universal mother: Hail to thee, thou parent of all things! and do thou deign to show thy favour unto me, alone of all the citizens of Rome, have, in thy every department, thus made known thy praise. The Natural History is encyclopaedic in scope. However, it does have structure: Pliny uses Aristotle's division of nature to recreate the natural world in literary form. Rather than presenting compartmentalised, stand-alone entries arranged alphabetically, Pliny's ordered natural landscape is a coherent whole, offering the reader a guided tour: "a brief excursion under our direction among the whole of the works of nature..."

The work is unified but varied: "My subject is the world of nature... or in other words, life," he tells Titus. Nature for Pliny was divine, a pantheistic concept inspired by the Stoic philosophy which underlies much of his thought, but the deity in question was a goddess whose main purpose was to serve the human race: "nature, life" is human life in a natural landscape. After an initial survey of cosmology and geography, Pliny starts his treatment of animals with the human race, "for whose sake great Nature appears to have created all other things"; this teleological view of nature was common in antiquity and is crucial to the understanding of the Natural History. The components of nature are not just described in and for themselves, but with a view to their role in human life. Pliny devotes a number of the books to plants, with a focus on their medicinal value. Pliny's premise is distinct from modern ecological theories, reflecting the prevailing sentiment of his time. Pliny's work reflects Rome's imperial expansion which brought new and exciting things to the capital: exotic eastern spices, strange animals to be put on display or herded into the arena the alleged phoenix sent to the emperor Claudius in AD 47 – although, as Pliny admits, this was acknowledged to be a fake.

Pliny repeated Aristotle's maxim. Nature's variety and versatility were claimed to be infinite: "When I have observed nature she has always induced me to deem no statement about her incredible." This led Pliny to recount rumours of strange peoples on the edges of the world. These monstrous races – the Cynocephali or Dog-Heads, the Sciapodae, whose single foot could act as a sunshade, the mouthless Astomi, who lived on scents – were not new, they had been mentioned in the 5th century BC by the Greek historian Herodotus but Pliny made them better known."As full of variety as nature itself", stated Pliny's nephew, Pliny the Younger, this verdict explains the appeal of the Natural History since Pliny's death in the Eruption of Mount Vesuvius in 79. Pliny had gone to investigate the strange cloud – "shaped like an umbrella pine", according to his nephew – rising from the mountain; the Natural History was one of the first ancient European texts to be printed, in Venice in 1469. Philemon Holland's English translation of 1601 has influenced literature since.

The Natural History consists of 37 books. Pliny devised a summarium, or list of contents, at the beginning of the work, interpreted by modern printers as a table of contents; the table below is a summary based on modern names for topics. Pliny's purpose in writing the Natural History was to cover all learning and art so far as they are connected with nature or draw their materials from nature, he says:My subject is a barren one – the world of nature, or in other words life.

Colliding beam fusion

Colliding beam fusion, or colliding beam fusion reactor, is any member of a class of fusion energy concepts that are based on two or more intersecting beams of fusion fuel ions that are independently accelerated to fusion energies using a variety of particle accelerator designs or other means. One of the beams may be replaced by a static target, in which case the approach is known as accelerator based fusion or beam-target fusion, but the physics is the same as colliding beams. CBFR designs have parallels with the inertial electrostatic confinement, or IEC, which can be thought of a CBFR with an infinite number of beams. CBFR approaches contrast with the more common magnetic fusion energy concepts in that they do not attempt to heat the fuel to fusion energies in bulk, but provide the required energies one particle at a time; this process can be much more efficient than bulk heating. However, these designs all suffer from the problem that it is difficult to get the ions to hit each other. Particles that miss may be lost, taking their energy with them, whereas in magnetic systems the particles remain in the system for seconds or minutes, giving them ample opportunity to undergo a reaction.

A number of design concepts attempt to address this problem of leaking particles. One of the better-researched concepts was the Migma, which used a unique particle storage ring to capture any particles that did not collide and circulate them back into the reaction area so they would get multiple chances. A more modern version of this concept uses a field-reversed configuration to retain the particles, with TAE Technologies developing such a system as a commercial venture. In spite of no present CFBR approaching the energy levels seen in modern magnetic fusion machines, the colliding beam concept remains popular because it does not suffer from energy losses to the environment in the same way as magnetic machines; this makes it more suitable for aneutronic fusion fuels like p-B11, which lose energy at a much higher rate than the deuterium-tritium fuel used in most designs. Aneutronic fuels have the advantage that they do not give off high-energy neutrons, a problem in conventional designs. However, recent works cast doubt on the energy balance of such approaches and suggest that the loss mechanisms are higher in these systems than conventional designs.

Fusion takes place when atoms come into close proximity and the nuclear force pulls their nuclei together to form a single larger nucleus. Counteracting this process is the positive charge of the nuclei, which repel each other due to the electrostatic force. In order for fusion to occur, the nuclei must have enough energy to overcome this coulomb barrier; the barrier is lowered for atoms with those with the fewest protons. The nuclear force is increased with the total number of protons and neutrons; this means that a combination of deuterium and tritium has the lowest coulomb barrier, at about 100 keV. When the fuel is heated to high energies the electrons disassociate from the nuclei, which are left as individual ions and electrons mixed in a gas-like plasma. Particles in a gas are distributed across a wide range of energies in a spectrum known as the Maxwell–Boltzmann distribution. At any given temperature the majority of the particles are at lower energies, with a "long tail" containing smaller numbers of particles at much higher energies.

So while 100 keV represents a temperature of over one billion degrees, in order to produce fusion events the fuel does not have to be heated to this temperature as a whole. As the fusion reactions give off large amounts of energy, some of that energy will be deposited back in the fuel, these reactions heat the fuel. There is a critical temperature at which the rate of reactions, thus the energy deposited, balances losses to the environment. At this point the reaction becomes a point known as ignition. For D-T fuel, that temperature is between 100 million degrees; the overall rate of fusion and net energy release is dependent on the combination of temperature and confinement time, known as the fusion triple product. Two primary approaches have developed to attack the fusion energy problem. In the inertial confinement approach the fuel is squeezed to high densities, which increases the internal temperature through the adiabatic process. There is no attempt to maintain these conditions for any period of time, the fuel explodes outward as soon as the force is released.

The confinement time is on the order of microseconds, so the temperatures and density have to be high in order to any appreciable amount of the fuel to undergo fusion. This approach has been successful in producing fusion reactions, but to date, the devices that can provide the compression lasers, require much more energy than the reactions produce; the more studied approach is magnetic confinement. Since the plasma is electrically charged, it will follow magnetic lines of force and a suitable arrangement of fields can keep the fuel away from the container walls; the fuel is heated over an extended period until some of the fuel in the tail starts undergoing fusion. At the temperatures and densities that are possible using magnets the fusion process is slow, so this approach requires long confinement times on the order of tens of seconds, or minutes. Confining a gas at millions of degrees for this sort of time scale has proven difficult, although modern experimental machines are approaching the conditions needed for net power production, or "breakeven".

The energy levels needed to overcome the coulomb barrier, about 100 keV for D-T fuel, corresponds to m

Polynomial Wigner–Ville distribution

In signal processing, the polynomial Wigner–Ville distribution is a quasiprobability distribution that generalizes the Wigner distribution function. It was proposed by Boualem Boashash and Peter O'Shea in 1994. Many signals in nature and in engineering applications can be modeled as z = e j 2 π ϕ, where ϕ is a polynomial phase and j = − 1. For example, it is important to detect signals of an arbitrary high-order polynomial phase. However, the conventional Wigner–Ville distribution have the limitation being based on the second-order statistics. Hence, the polynomial Wigner–Ville distribution was proposed as a generalized form of the conventional Wigner–Ville distribution, able to deal with signals with nonlinear phase; the polynomial Wigner–Ville distribution W z g is defined as W z g = F τ → f where F τ → f denotes the Fourier transform with respect to τ, K z g is the polynomial kernel given by K z g = ∏ k = − q 2 q 2 b k where z is the input signal and q is an number. The above expression for the kernel may be rewritten in symmetric form as K z g = ∏ k = 0 q 2 b k − b − k The discrete-time version of the polynomial Wigner–Ville distribution is given by the discrete Fourier transform of K z g = ∏ k = 0 q 2 b k − b − k where n = t f s, m = τ f s, f s is the sampling frequency.

The conventional Wigner–Ville distribution is a special case of the polynomial Wigner–Ville distribution with q = 2, b − 1 = − 1, b 1 = 1, b 0 = 0, c − 1 = − 1 2, c 0 = 0, c 1 = 1 2 One of the simplest generalizations of the usual Wigner–Ville distribution kernel can be achieved by taking q = 4. The set of coefficients b k and c k must be found to specify the new kernel. For