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Acoustic Metric
In mathematical physics, a metric describes the arrangement of relative distances within a surface or volume, usually measured by signals passing through the region – essentially describing the intrinsic geometry of the region. An acoustic metric will describe the signal-carrying properties characteristic of a given particulate medium in acoustics, or in fluid dynamics. Other descriptive names such as sonic metric are also sometimes used, interchangeably. A simple fluid example For simplicity, we will assume that the underlying background geometry is Euclidean, and that this space is filled with an isotropic inviscid fluid at zero temperature (e.g. a superfluid). This fluid is described by a density field ''ρ'' and a velocity field \vec. The speed of sound at any given point depends upon the compressibility which in turn depends upon the density at that point. It requires much work to compress anything more into an already compacted space. This can be specified by the "s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Physics
Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics (also known as physical mathematics). Scope There are several distinct branches of mathematical physics, and these roughly correspond to particular historical periods. Classical mechanics The rigorous, abstract and advanced reformulation of Newtonian mechanics adopting the Lagrangian mechanics and the Hamiltonian mechanics even in the presence of constraints. Both formulations are embodied in analytical mechanics and lead to understanding the deep interplay of the notions of symmetry (physics), symmetry and conservation law, con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric Tensor
In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows defining distances and angles there. More precisely, a metric tensor at a point of is a bilinear form defined on the tangent space at (that is, a bilinear function that maps pairs of tangent vectors to real numbers), and a metric tensor on consists of a metric tensor at each point of that varies smoothly with . A metric tensor is ''positive-definite'' if for every nonzero vector . A manifold equipped with a positive-definite metric tensor is known as a Riemannian manifold. Such a metric tensor can be thought of as specifying ''infinitesimal'' distance on the manifold. On a Riemannian manifold , the length of a smooth curve between two points and can be defined by integration, and the distance between and can be defined as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Gravity
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, such as neutron stars. Three of the four fundamental forces of physics are described within the framework of quantum mechanics and quantum field theory. The current understanding of the fourth force, gravity, is based on Albert Einstein's general theory of relativity, which is formulated within the entirely different framework of classical physics. However, that description is incomplete: describing the gravitational field of a black hole in the general theory of relativity leads physical quantities, such as the spacetime curvature, to diverge at the center of the black hole. This signals the breakdown of the general theory of relativity and the need for a theory that goes b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravastar
A gravastar is an object hypothesized in astrophysics by Pawel O. Mazur and Emil Mottola as an alternative to the black hole theory. It has usual black hole metric outside of the horizon, but de Sitter metric inside. On the horizon there is a thin shell of matter. The term "gravastar" is a portmanteau of the words "gravitational vacuum star".. This solution of Einstein equations is stable and has no singularities. Structure In the original formulation by Mazur and Mottola, gravastars contain a central region featuring a false vacuum or "dark energy", a thin shell of perfect fluid, and a true vacuum exterior. The dark energy-like behavior of the inner region prevents collapse to a singularity and the presence of the thin shell prevents the formation of an event horizon, avoiding the infinite blue shift. The inner region has thermodynamically no entropy and may be thought of as a gravitational Bose–Einstein condensate. Severe red-shifting of photons as they climb out of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analog Models Of Gravity
Analog models of gravity are attempts to model various phenomena of general relativity (e.g., black holes or cosmological geometries) using other physical systems such as acoustics in a moving fluid, superfluid helium, or Bose–Einstein condensate; gravity waves in water; and propagation of electromagnetic waves in a dielectric medium. These analogs (or analogies) serve to provide new ways of looking at problems, permit ideas from other realms of science to be applied, and may create opportunities for practical experiments within the analog that can be applied back to the source phenomena. History Analog models of gravity have been used in hundreds of published articles in the last decade. The use of these analogs can be traced back to the very start of scientific theories for gravity, with Newton and Einstein. Bose-Einstein condensates It has been shown that Bose-Einstein condensates (BEC) are a good platform to study analog gravity. Kerr (rotating) black holes have be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acoustics
Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an Acoustical engineering, acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries. Hearing (sense), Hearing is one of the most crucial means of survival in the animal world and speech is one of the most distinctive characteristics of human development and culture. Accordingly, the science of acoustics spreads across many facets of human society—music, medicine, architecture, industrial production, warfare and more. Likewise, animal species such as songbirds and frogs use sound and hearing as a key element of mating rituals or for marking territories. Art, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coupling (physics)
In physics, two objects are said to be coupled when they are interacting with each other. In classical mechanics, coupling is a connection between two oscillating systems, such as pendulums connected by a spring. The connection affects the oscillatory pattern of both objects. In particle physics, two particles are coupled if they are connected by one of the four fundamental forces. Wave mechanics Coupled harmonic oscillator If two waves are able to transmit energy to each other, then these waves are said to be "coupled." This normally occurs when the waves share a common component. An example of this is two pendulums connected by a spring. If the pendulums are identical, then their equations of motion are given by m\ddot = -mg\frac - k(x-y) m\ddot = -mg \frac + k(x-y) These equations represent the simple harmonic motion of the pendulum with an added coupling factor of the spring. This behavior is also seen in certain molecules (such as CO2 and H2O), wherein two of the atoms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Statistical mechanics arose out of the development of classical thermodynamics, a field for which it was successful in explaining macroscopic physical properties—such as temperature, pressure, and heat capacity—in terms of microscopic parameters that fluctuate about average values and are characterized by probability distributions. This established the fields of statistical thermodynamics and statistical physics. The founding of the field of statistical mechanics is generally credited to three physicists: *Ludwig Boltzmann, who developed the fundamental interpretation of entropy in terms of a collection of microstates *James Clerk Maxwell, who developed models of probability distr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hawking Radiation
Hawking radiation is theoretical black body radiation that is theorized to be released outside a black hole's event horizon because of relativistic quantum effects. It is named after the physicist Stephen Hawking, who developed a theoretical argument for its existence in 1974. Hawking radiation is a purely kinematic effect that is generic to Lorentzian geometries containing event horizons or local apparent horizons. Hawking radiation reduces the mass and rotational energy of black holes and is therefore also theorized to cause black hole evaporation. Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish. For all except the smallest black holes, this would happen extremely slowly. The radiation temperature is inversely proportional to the black hole's mass, so micro black holes are predicted to be larger emitters of radiation than larger black holes and should dissipate faster. Overview Black holes are astrophysica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weyl Rescaling
:''See also Wigner–Weyl transform, for another definition of the Weyl transform.'' In theoretical physics, the Weyl transformation, named after Hermann Weyl, is a local rescaling of the metric tensor: :g_\rightarrow e^g_ which produces another metric in the same conformal class. A theory or an expression invariant under this transformation is called conformally invariant, or is said to possess Weyl invariance or Weyl symmetry. The Weyl symmetry is an important symmetry in conformal field theory. It is, for example, a symmetry of the Polyakov action. When quantum mechanical effects break the conformal invariance of a theory, it is said to exhibit a conformal anomaly or Weyl anomaly. The ordinary Levi-Civita connection and associated spin connections are not invariant under Weyl transformations. An appropriately invariant notion is the Weyl connection, which is one way of specifying the structure of a conformal connection. Conformal weight A quantity \varphi has conformal weig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galilean Covariance
The Galilei-covariant tensor formulation is a method for treating non-relativistic physics using the extended Galilei group as the representation group of the theory. It is constructed in the light cone of a five dimensional manifold. Takahashi et al., in 1988, began a study of Galilean symmetry, where an explicitly covariant non-relativistic field theory could be developed. The theory is constructed in the light cone of a (4,1) Minkowski space. Previously, in 1985, Duval et al. constructed a similar tensor formulation in the context of Newton–Cartan theory. Some other authors also have developed a similar Galilean tensor formalism. Galilean manifold The Galilei transformations are : \begin \mathbf' &= R\mathbf - \mathbf t + \mathbf \\ t' &= t + \mathbf. \end where R stands for the three-dimensional Euclidean rotations, \mathbf is the relative velocity determining Galilean boosts, a stands for spatial translations and b, for time translations. Consider a free mas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric (mathematics)
In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane. A metric may correspond to a metaphorical, rather than physical, notion of distance: for example, the set of 100-character Unicode strings can be equipped with the Hamming distance, which measures the number of characters that need to be changed to get from one string to another. Since they are very general, metric spaces are a tool used in many different branches of mathematics. Many types of mathematical objects have a natural notion of distance and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
