Phase diagramA phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinct phases (such as solid, liquid or gaseous states) occur and coexist at equilibrium. Common components of a phase diagram are lines of equilibrium or phase boundaries, which refer to lines that mark conditions under which multiple phases can coexist at equilibrium. Phase transitions occur along lines of equilibrium.
Phase (matter)In the physical sciences, a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water. The glass of the jar is another separate phase. (See .) More precisely, a phase is a region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform.
Patterns in naturePatterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time.
Phase spaceIn dynamical systems theory and control theory, a phase space or state space is a space in which all possible "states" of a dynamical system or a control system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. It is the direct product of direct space and reciprocal space. The concept of phase space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré, and Josiah Willard Gibbs.
PolarizerA polarizer or polariser (see spelling differences) is an optical filter that lets light waves of a specific polarization pass through while blocking light waves of other polarizations. It can filter a beam of light of undefined or mixed polarization into a beam of well-defined polarization, that is polarized light. The common types of polarizers are linear polarizers and circular polarizers. Polarizers are used in many optical techniques and instruments, and polarizing filters find applications in photography and LCD technology.
Polarization (physics)Polarization (also polarisation) is a property of transverse waves which specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string (see image); for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string.
Phase transitionIn chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure.
Lyapunov stabilityVarious types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis).
Pattern formationThe science of pattern formation deals with the visible, (statistically) orderly outcomes of self-organization and the common principles behind similar patterns in nature. In developmental biology, pattern formation refers to the generation of complex organizations of cell fates in space and time. The role of genes in pattern formation is an aspect of morphogenesis, the creation of diverse anatomies from similar genes, now being explored in the science of evolutionary developmental biology or evo-devo.
Stability theoryIn mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.
Phase portraitIn mathematics, a phase portrait is a geometric representation of the trajectories of a dynamical system in the phase plane. Each set of initial conditions is represented by a different point or curve. Phase portraits are an invaluable tool in studying dynamical systems. They consist of a plot of typical trajectories in the phase space. This reveals information such as whether an attractor, a repellor or limit cycle is present for the chosen parameter value.
Linear polarizationIn electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation. The term linear polarization (French: polarisation rectiligne) was coined by Augustin-Jean Fresnel in 1822. See polarization and plane of polarization for more information. The orientation of a linearly polarized electromagnetic wave is defined by the direction of the electric field vector.
Dirac equationIn particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin- massive particles, called "Dirac particles", such as electrons and quarks for which parity is a symmetry. It is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics.
Circular polarizationIn electrodynamics, circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electromagnetic field of the wave has a constant magnitude and is rotating at a constant rate in a plane perpendicular to the direction of the wave. In electrodynamics, the strength and direction of an electric field is defined by its electric field vector. In the case of a circularly polarized wave, the tip of the electric field vector, at a given point in space, relates to the phase of the light as it travels through time and space.
Collective behaviorThe expression collective behavior was first used by Franklin Henry Giddings and employed later by Robert Park and Ernest Burgess, Herbert Blumer, Ralph H. Turner and Lewis Killian, and Neil Smelser to refer to social processes and events which do not reflect existing social structure (laws, conventions, and institutions), but which emerge in a "spontaneous" way. Use of the term has been expanded to include reference to cells, social animals like birds and fish, and insects including ants.
Elliptical polarizationIn electrodynamics, elliptical polarization is the polarization of electromagnetic radiation such that the tip of the electric field vector describes an ellipse in any fixed plane intersecting, and normal to, the direction of propagation. An elliptically polarized wave may be resolved into two linearly polarized waves in phase quadrature, with their polarization planes at right angles to each other. Since the electric field can rotate clockwise or counterclockwise as it propagates, elliptically polarized waves exhibit chirality.
Angular momentumIn physics, angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, flying discs, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum.
Phase ruleIn thermodynamics, the phase rule is a general principle governing "pVT" systems, whose thermodynamic states are completely described by the variables pressure (p), volume (V) and temperature (T), in thermodynamic equilibrium. If F is the number of degrees of freedom, C is the number of components and P is the number of phases, then It was derived by American physicist Josiah Willard Gibbs in his landmark paper titled On the Equilibrium of Heterogeneous Substances, published in parts between 1875 and 1878.
Sterile neutrinoSterile neutrinos (or inert neutrinos) are hypothetical particles (neutral leptons – neutrinos) that are believed to interact only via gravity and not via any of the other fundamental interactions of the Standard Model. The term sterile neutrino is used to distinguish them from the known, ordinary active neutrinos in the Standard Model, which carry an isospin charge of ± 1/ 2 and engage in the weak interaction. The term typically refers to neutrinos with right-handed chirality (see right-handed neutrino), which may be inserted into the Standard Model.
Fundamental interactionIn physics, the fundamental interactions or fundamental forces are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: gravity electromagnetism weak interaction strong interaction The gravitational and electromagnetic interactions produce long-range forces whose effects can be seen directly in everyday life. The strong and weak interactions produce forces at minuscule, subatomic distances and govern nuclear interactions inside atoms.
