Monte Carlo methodMonte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution.
State of matterIn physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Many intermediate states are known to exist, such as liquid crystal, and some states only exist under extreme conditions, such as Bose–Einstein condensates (in extreme cold), neutron-degenerate matter (in extreme density), and quark–gluon plasma (at extremely high energy). For a complete list of all exotic states of matter, see the list of states of matter.
MatterIn classical physics and general chemistry, matter is any substance with mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic particles, and in everyday as well as scientific usage, matter generally includes atoms and anything made up of them, and any particles (or combination of particles) that act as if they have both rest mass and volume. However it does not include massless particles such as photons, or other energy phenomena or waves such as light or heat.
Degenerate matterDegenerate matter occurs when the Pauli exclusion principle significantly alters a state of matter at low temperature. The term used in astrophysics to refer to dense stellar objects such as white dwarfs and neutron stars, where thermal pressure alone is not enough to avoid gravitational collapse. The term also applies to metals in the Fermi gas approximation. Degenerate matter is usually modelled as an ideal Fermi gas, an ensemble of non-interacting fermions.
Neutron starA neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses (), possibly more if the star was especially metal-rich. Except for black holes, neutron stars are the smallest and densest currently known class of stellar objects. Neutron stars have a radius on the order of and a mass of about . They result from the supernova explosion of a massive star, combined with gravitational collapse, that compresses the core past white dwarf star density to that of atomic nuclei.
Future of an expanding universeObservations suggest that the expansion of the universe will continue forever. The prevailing theory is that the universe will cool as it expands, eventually becoming too cold to sustain life. For this reason, this future scenario once popularly called "Heat Death" is now known as the "Big Chill" or "Big Freeze". If dark energy—represented by the cosmological constant, a constant energy density filling space homogeneously, or scalar fields, such as quintessence or moduli, dynamic quantities whose energy density can vary in time and space—accelerates the expansion of the universe, then the space between clusters of galaxies will grow at an increasing rate.
Dark matterDark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not absorb, reflect, or emit electromagnetic radiation and is, therefore, difficult to detect. Various astrophysical observations - including gravitational effects which cannot be explained by currently accepted theories of gravity unless more matter is present than can be seen - imply dark matter's presence.
Nuclear matterNuclear matter is an idealized system of interacting nucleons (protons and neutrons) that exists in several phases of exotic matter that, as of yet, are not fully established. It is not matter in an atomic nucleus, but a hypothetical substance consisting of a huge number of protons and neutrons held together by only nuclear forces and no Coulomb forces. Volume and the number of particles are infinite, but the ratio is finite. Infinite volume implies no surface effects and translational invariance (only differences in position matter, not absolute positions).
Markov chain Monte CarloIn statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain a sample of the desired distribution by recording states from the chain. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Various algorithms exist for constructing chains, including the Metropolis–Hastings algorithm.
Fuzzball (string theory)Fuzzball theory, which is derived from superstring theory, is advanced by its proponents as a description of black holes that harmonizes quantum mechanics and Albert Einstein's general theory of relativity, which have long been incompatible. Fuzzball theory dispenses with the singularity at the heart of a black hole by positing that the entire region within the black hole's event horizon is actually an extended object: a ball of strings, which are advanced as the ultimate building blocks of matter and light.