|
Lord Rayleigh
John William Strutt, 3rd Baron Rayleigh, (; 12 November 1842 – 30 June 1919) was an English mathematician and physicist who made extensive contributions to science. He spent all of his academic career at the University of Cambridge. Among many honors, he received the 1904 Nobel Prize in Physics "for his investigations of the densities of the most important gases and for his discovery of argon in connection with these studies." He served as president of the Royal Society from 1905 to 1908 and as chancellor of the University of Cambridge from 1908 to 1919. Rayleigh provided the first theoretical treatment of the elastic scattering of light by particles much smaller than the light's wavelength, a phenomenon now known as "Rayleigh scattering", which notably explains why the sky is blue. He studied and described transverse surface waves in solids, now known as "Rayleigh waves". He contributed extensively to fluid dynamics, with concepts such as the Rayleigh number (a d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maldon, Essex
Maldon (, locally ) is a town and civil parish on the Blackwater estuary in Essex, England. It is the seat of the Maldon District and starting point of the Chelmer and Blackwater Navigation. It is known for Maldon Sea Salt which is produced in the area. History Early and medieval history The place-name ''Maldon'' is first attested in 913 in the '' Anglo-Saxon Chronicle'', where it appears as ''Maeldun''. Maldon's name comes from ''mǣl'' meaning 'monument or cross' and ''dūn'' meaning 'hill', so translates as 'monument hill'. East Saxons settled the area in the 5th century and the area to the south is still known as the Dengie Peninsula after the Dæningas. It became a significant Saxon port with a hythe or quayside and artisan quarters. Evidence of imported pottery from this period has been found in archaeological digs. From 958 there was a royal mint issuing coins for the late Anglo-Saxon and early Norman kings. It was one of the only two towns in Essex (Colchest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rayleigh–Faber–Krahn Inequality
In spectral geometry, the Rayleigh–Faber–Krahn inequality, named after its conjecturer, Lord Rayleigh, and two individuals who independently proved the conjecture, G. Faber and Edgar Krahn, is an inequality concerning the lowest Dirichlet eigenvalue of the Laplace operator on a bounded domain in \mathbb^n, n \ge 2. It states that the first Dirichlet eigenvalue is no less than the corresponding Dirichlet eigenvalue of a Euclidean ball having the same volume. Furthermore, the inequality is rigid in the sense that if the first Dirichlet eigenvalue is equal to that of the corresponding ball, then the domain must actually be a ball. In the case of n=2, the inequality essentially states that among all drums of equal area, the circular drum (uniquely) has the lowest voice. More generally, the Faber–Krahn inequality holds in any Riemannian manifold in which the isoperimetric inequality holds. In particular, according to Cartan–Hadamard conjecture, it should hold in all simp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rayleigh Flow
Rayleigh flow refers to frictionless, non- adiabatic flow through a constant area duct where the effect of heat addition or rejection is considered. Compressibility effects often come into consideration, although the Rayleigh flow model certainly also applies to incompressible flow. For this model, the duct area remains constant and no mass is added within the duct. Therefore, unlike Fanno flow, the stagnation temperature is a variable. The heat addition causes a decrease in stagnation pressure, which is known as the Rayleigh effect and is critical in the design of combustion systems. Heat addition will cause both supersonic and subsonic Mach numbers to approach Mach 1, resulting in choked flow. Conversely, heat rejection decreases a subsonic Mach number and increases a supersonic Mach number along the duct. It can be shown that for calorically perfect flows the maximum entropy occurs at M = 1. Rayleigh flow is named after John Strutt, 3rd Baron Rayleigh. Theory The Ray ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rayleigh Fading
Rayleigh fading is a statistical model for the effect of a propagation environment on a radio signal, such as that used by wireless devices. Rayleigh fading models assume that the magnitude of a signal that has passed through such a transmission medium (also called a communication channel) will vary randomly, or fade, according to a Rayleigh distribution — the radial component of the sum of two uncorrelated Gaussian random variables. Rayleigh fading is viewed as a reasonable model for tropospheric and ionospheric signal propagation as well as the effect of heavily built-up urban environments on radio signals. Rayleigh fading is most applicable when there is no dominant propagation along a line of sight between the transmitter and receiver. If there is a dominant line of sight, Rician fading may be more applicable. Rayleigh fading is a special case of two-wave with diffuse power (TWDP) fading. The model Rayleigh fading is a reasonable model when there are many objects in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rayleigh Dissipation Function
In physics, the Rayleigh dissipation function, named after Lord Rayleigh, is a function used to handle the effects of velocity-proportional frictional forces in Lagrangian mechanics In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph- .... If the frictional force on a particle with velocity \vec can be written as \vec_f = -\vec\cdot\vec, the Rayleigh dissipation function can be defined for a system of N particles as :G(v) = \frac \sum_^N ( k_x v_^2 + k_y v_^2 + k_z v_^2 ). The force of friction is negative the velocity gradient of the dissipation function, \vec_f = -\nabla_v G(v). The function is half the rate at which energy is being dissipated by the system through friction. As friction is not conservative, it is included in the ''Qj'' term of Lagrange's equations. References * Funct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rayleigh–Gans Approximation
Rayleigh–Gans approximation, also known as Rayleigh–Gans–Debye approximation and Rayleigh–Gans–Born approximation, is an approximate solution to light scattering by optically soft particles. Optical softness implies that the relative refractive index of particle is close to that of the surrounding medium. The approximation holds for particles of arbitrary shape that are relatively small but can be larger than Rayleigh scattering limits. The theory was derived by Lord Rayleigh in 1881 and was applied to homogeneous spheres, spherical shells, radially inhomogeneous spheres and infinite cylinders. Peter Debye has contributed to the theory in 1881. The theory for homogeneous sphere was rederived by Richard Gans in 1925. The approximation is analogous to Born approximation in quantum mechanics. Theory The validity conditions for the approximation can be denoted as: :, n-1, \ll 1 :kd, n-1, \ll 1 k is the wavevector of the light (k=\frac), whereas d refers to the linear dimen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rayleigh–Lorentz Pendulum
Rayleigh–Lorentz pendulum (or Lorentz pendulum) is a simple pendulum, but subjected to a slowly varying frequency due to an external action (frequency is varied by varying the pendulum length), named after Lord Rayleigh and Hendrik Lorentz. This problem formed the basis for the concept of adiabatic invariants in mechanics. On account of the slow variation of frequency, it is shown that the ratio of average energy to frequency is constant. History The pendulum problem was first formulated by Lord Rayleigh in 1902, although some mathematical aspects have been discussed before by Léon Lecornu in 1895. Unaware of Rayleigh's work, at the first Solvay conference in 1911, Hendrik Lorentz proposed a question, ''How does a simple pendulum behave when the length of the suspending thread is gradually shortened?'', in order to clarify the quantum theory at that time. To that Albert Einstein responded the next day by saying that both energy and frequency of the quantum pendulum changes suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rayleigh Quotient
In mathematics, the Rayleigh quotient () for a given complex Hermitian matrix ''M'' and nonzero vector ''x'' is defined as: R(M,x) = . For real matrices and vectors, the condition of being Hermitian reduces to that of being symmetric, and the conjugate transpose x^ to the usual transpose x'. Note that R(M, c x) = R(M,x) for any non-zero scalar ''c''. Recall that a Hermitian (or real symmetric) matrix is diagonalizable with only real eigenvalues. It can be shown that, for a given matrix, the Rayleigh quotient reaches its minimum value \lambda_\min (the smallest eigenvalue of ''M'') when ''x'' is v_\min (the corresponding eigenvector). Similarly, R(M, x) \leq \lambda_\max and R(M, v_\max) = \lambda_\max. The Rayleigh quotient is used in the min-max theorem to get exact values of all eigenvalues. It is also used in eigenvalue algorithms (such as Rayleigh quotient iteration) to obtain an eigenvalue approximation from an eigenvector approximation. The range of the Rayleigh quotien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rayleigh–Ritz Method
The Rayleigh–Ritz method is a direct numerical method of approximating eigenvalues, originated in the context of solving physical boundary value problems and named after Lord Rayleigh and Walther Ritz. The name Rayleigh–Ritz is being debated vs. the Ritz method after Walther Ritz, since the numerical procedure has been published by Walther Ritz in 1908-1909. According to, Lord Rayleigh wrote a paper congratulating Ritz on his work in 1911, but stating that he himself had used Ritz's method in many places in his book and in another publication. This statement, although later disputed, and the fact that the method in the trivial case of a single vector results in the Rayleigh quotient make the arguable misnomer persist. According to, citing Richard Courant, both Lord Rayleigh and Walther Ritz independently conceived the idea of utilizing the equivalence between boundary value problems of partial differential equations on the one hand and problems of the calculus of variations on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rayleigh's Method Of Dimensional Analysis
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as miles vs. kilometres, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. The conversion of units from one dimensional unit to another is often easier within the metric or the SI than in others, due to the regular 10-base in all units. ''Commensurable'' physical quantities are of the same kind and have the same dimension, and can be directly compared to each other, even if they are expressed in differing units of measure, e.g. yards and metres, pounds (mass) and kilograms, seconds and years. ''Incommensurable'' physical quantities are of different kinds and have different dimensions, and can not be directly compared to each other, no matter what units they are expressed in, e.g. metres an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rayleigh Interferometer
In optics, a Rayleigh interferometer is a type of interferometer which employs two beams of light from a single source. The two beams are recombined after traversing two optical paths, and the interference pattern after recombination allows the determination of the difference in path lengths. Principle of Operation Light from a source (left) is collimated by a lens and split into two beams using slits. The beams are sent through two different paths and pass through compensating plates. They are brought to a focus by a second lens (bottom) where an interference pattern is observed to determine the optical path difference in terms of wavelengths of the light. Advantages and disadvantages The advantage of the Rayleigh interferometer is its simple construction. Its drawbacks are (i) it requires a point or line source of light for good fringe visibility, and (ii) the fringes must be viewed with high magnification. See also *List of types of interferometers An interferometer is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
