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X-wave
In physics, X-waves are localized solutions of the wave equation that travel at a constant velocity in a given direction. X-waves can be sound, electromagnetic, or gravitational waves. They are built as a non-monochromatic superposition of Bessel beams. Ideal X-waves carry infinite energy, but finite-energy realizations have been observed in various frameworks. Electromagnetic X-waves travel faster than the speed of light, and X-wave pulses can have superluminal phase and group velocity. In optics, X-waves solution have been reported within a quantum mechanical formulation.A. Ciattoni and C. ContiQuantum electromagnetic X-waves''arxiv.org'' 0704.0442v1. See also * Nonlinear X-wave * Droplet-shaped wave References * J. Lu and J. F. Greenleaf, "Nondiffracting X waves: exact solutions to free-space scalar wave equation and their infinite realizations", IEEE Trans. Ultrasonic Ferroelectric Frequency. ''Control Control may refer to: Basic meanings Economics and business * Con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear X-wave
In physics, a nonlinear X-wave (NLX) is a multi-dimensional wave that can travel without distortion. At variance with X-waves, a nonlinear X-wave does exist in the presence of nonlinearity, and in many cases it self-generates from a Gaussian (in any direction) wave packet. The distinctive feature of an NLX is its "biconical" shape, (see figure) which appears as an "X" in any section plane containing the wave peak and the direction of propagation. So far, nonlinear X-waves have been only observed in nonlinear optics experiments, and have been predicted to occur in a variety of nonlinear media including Bose–Einstein condensates. History * Preliminary experimental results were reported CLEO/QELS conference in 2001 * The first article was published in ''Physical Review Letters'' in 2003 and reported on the theoretical prediction of the existence of nonlinear X-waves. * The first experimental results also appeared in ''Physical Review Letters ''Physical Review Letters'' (''P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Droplet-shaped Wave
In physics, droplet-shaped waves are casual localized solutions of the wave equation closely related to the X-shaped waves, but, in contrast, possessing a finite support. A family of the droplet-shaped waves was obtained by extension of the "toy model" of X-wave generation by a superluminal point electric charge (tachyon) at infinite rectilinear motion to the case of a line source pulse started at time . The pulse front is supposed to propagate with a constant superluminal velocity (here is the speed of light, so ). In the cylindrical spacetime coordinate system , originated in the point of pulse generation and oriented along the (given) line of source propagation (direction ''z''), the general expression for such a source pulse takes the form : s(\tau ,\rho ,z) = \frac J(\tau ,z) H(\beta \tau -z) H(z), where and are, correspondingly, the Dirac delta and Heaviside step functions while is an arbitrary continuous function representing the pulse shape. Notably, for , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel Beam
A Bessel beam is a wave whose amplitude is described by a Bessel function of the first kind. Electromagnetic, acoustic, gravitational, and matter waves can all be in the form of Bessel beams. A true Bessel beam is non-diffractive. This means that as it propagates, it does not diffract and spread out; this is in contrast to the usual behavior of light (or sound), which spreads out after being focused down to a small spot. Bessel beams are also ''self-healing'', meaning that the beam can be partially obstructed at one point, but will re-form at a point further down the beam axis. As with a plane wave, a true Bessel beam cannot be created, as it is unbounded and would require an infinite amount of energy. Reasonably good approximations can be made, however, and these are important in many optical applications because they exhibit little or no diffraction over a limited distance. Approximations to Bessel beams are made in practice either by focusing a Gaussian beam with an axicon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J). Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object (for instance due to its position in a field), the elastic energy stored in a solid object, chemical energy associated with chemical reactions, the radiant energy carried by electromagnetic radiation, and the internal energy contained within a thermodynamic system. All living organisms constantly take in and release energy. Due to mass–energy equivalence, any object that has mass whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE
The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operations center in Piscataway, New Jersey. The mission of the IEEE is ''advancing technology for the benefit of humanity''. The IEEE was formed from the amalgamation of the American Institute of Electrical Engineers and the Institute of Radio Engineers in 1963. Due to its expansion of scope into so many related fields, it is simply referred to by the letters I-E-E-E (pronounced I-triple-E), except on legal business documents. , it is the world's largest association of technical professionals with more than 423,000 members in over 160 countries around the world. Its objectives are the educational and technical advancement of electrical and electronic engineering, telecommunications, computer engineering and similar disciplines. History Origin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scalar Wave
In mathematics and physics, a scalar field is a function associating a single number to every point in a space – possibly physical space. The scalar may either be a pure mathematical number (dimensionless) or a scalar physical quantity (with units). In a physical context, scalar fields are required to be independent of the choice of reference frame, meaning that any two observers using the same units will agree on the value of the scalar field at the same absolute point in space (or spacetime) regardless of their respective points of origin. Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, and spin-zero quantum fields, such as the Higgs field. These fields are the subject of scalar field theory. Definition Mathematically, a scalar field on a region ''U'' is a real or complex-valued function or distribution on ''U''. The region ''U'' may be a set in some Euclidean space, Minkowski space, or more generall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Velocity
The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the ''modulation'' or ''envelope'' of the wave—propagates through space. For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water, also known as a capillary wave. The expanding ring of waves is the wave group, within which one can discern individual waves that travel faster than the group as a whole. The amplitudes of the individual waves grow as they emerge from the trailing edge of the group and diminish as they approach the leading edge of the group. Definition and interpretation Definition The group velocity is defined by the equation: :v_ \ \equiv\ \frac\, where is the wave's angular frequency (usually expressed in radians per second), and is the angular wavenumber (usually expressed in radians per meter). The phase velocity is: . The function , which gi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Velocity
The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase velocity is given in terms of the wavelength (lambda) and time period as :v_\mathrm = \frac. Equivalently, in terms of the wave's angular frequency , which specifies angular change per unit of time, and wavenumber (or angular wave number) , which represent the angular change per unit of space, :v_\mathrm = \frac. To gain some basic intuition for this equation, we consider a propagating (cosine) wave . We want to see how fast a particular phase of the wave travels. For example, we can choose , the phase of the first crest. This implies , and so . Formally, we let the phase and see immediately that and . So, it immediately follows that : \frac = -\frac \frac = \frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Faster Than The Speed Of Light
Faster-than-light (also FTL, superluminal or supercausal) Superluminal motion, travel and Faster-than-light communication, communication are the conjectural propagation of matter or information faster than the speed of light (). The special theory of relativity implies that only particles with zero mass in special relativity, rest mass (i.e., photons) may travel ''at'' the speed of light, and that nothing may travel faster. Particles whose speed exceeds that of light (tachyons) have been hypothesized, but their existence would violate causality (physics), causality and would imply time travel. The scientific consensus is that they do not exist. "Apparent" or "effective" FTL, on the other hand, depends on the hypothesis that unusually distorted regions of spacetime might permit matter to reach distant locations in less time than light could in normal ("undistorted") spacetime. As of the 21st century, according to current scientific theories, matter is required to travel at slower- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinity
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Localized Solution
Local may refer to: Geography and transportation * Local (train), a train serving local traffic demand * Local, Missouri, a community in the United States * Local government, a form of public administration, usually the lowest tier of administration * Local news, coverage of events in a local context which would not normally be of interest to those of other localities * Local union, a locally based trade union organization which forms part of a larger union Arts, entertainment, and media * ''Local'' (comics), a limited series comic book by Brian Wood and Ryan Kelly * ''Local'' (novel), a 2001 novel by Jaideep Varma * Local TV LLC, an American television broadcasting company * Locast, a non-profit streaming service offering local, over-the-air television * ''The Local'' (film), a 2008 action-drama film * '' The Local'', English-language news websites in several European countries Computing * .local, a network address component * Local variable, a variable that is given loca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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