The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
Shijun Liao - One of the best experts on this subject based on the ideXlab platform.
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an explicit Analytic Solution to the thomas fermi equation
Applied Mathematics and Computation, 2003Co-Authors: Shijun LiaoAbstract:A new kind of Analytic technique, namely the homotopy analysis method, is employed to give an explicit Analytic Solution of the Thomas-Fermi equation and the related recurrence formulae of constant coefficients. This Solution can be regarded as the definition of the exact Solution of the Thomas-Fermi equation.
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A uniformly valid Analytic Solution of two-dimensional viscous flow over a semi-infinite flat plate
Journal of Fluid Mechanics, 1999Co-Authors: Shijun LiaoAbstract:We apply a new kind of Analytic technique, namely the homotopy analysis method (HAM), to give an explicit, totally Analytic, uniformly valid Solution of the two-dimensional laminar viscous flow over a semi-infinite flat plate governed by f ‴(η)+α f (η) f ″(η)+β[1− f ′ 2 (η)]=0 under the boundary conditions f (0)= f ′(0)=0, f ′(+∞)=1. This Analytic Solution is uniformly valid in the whole region 0[les ]η
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a uniformly valid Analytic Solution of two dimensional viscous flow over a semi infinite flat plate
Journal of Fluid Mechanics, 1999Co-Authors: Shijun LiaoAbstract:We apply a new kind of Analytic technique, namely the homotopy analysis method (HAM), to give an explicit, totally Analytic, uniformly valid Solution of the two-dimensional laminar viscous flow over a semi-infinite flat plate governed by f ‴(η)+α f (η) f ″(η)+β[1− f ′ 2 (η)]=0 under the boundary conditions f (0)= f ′(0)=0, f ′(+∞)=1. This Analytic Solution is uniformly valid in the whole region 0[les ]η<+∞. For Blasius' (1908) flow (α=1/2, β=0), this Solution converges to Howarth's (1938) numerical result and gives a purely Analytic value f ″(0)=0.332057. For the Falkner–Skan (1931) flow (α=1), it gives the same family of Solutions as Hartree's (1937) numerical results and a related Analytic formula for f ″(0) when 2[ges ]β[ges ]0. Also, this Analytic Solution proves that when −0.1988[les ]β0 Hartree's (1937) family of Solutions indeed possess the property that f ′→1 exponentially as η→+∞. This verifies the validity of the homotopy analysis method and shows the potential possibility of applying it to some unsolved viscous flow problems in fluid mechanics.
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an explicit totally Analytic Solution of laminar viscous flow over a semi infinite flat plate
Communications in Nonlinear Science and Numerical Simulation, 1998Co-Authors: Shijun LiaoAbstract:Abstract In this paper, a new kind of Analytic technique for nonlinear problems, namely the Homotopy Analysis Method, is applied to give an explicit, totally Analytic Solution of the Blasius' flow, i.e. the two dimensional (2D) laminar viscous flow over a semi-infinite flat plate. This Analytic Solution is valid in the whole region having physical meanings. To our knowledge, it is the first time in history that such a kind of explicit, totally Analytic Solution is given. This fact well verifies the great potential and validity of the Homotopy Analysis Method as a kind of powerful Analytic tool for nonlinear problems in science and engineering.
Theodore Erler - One of the best experts on this subject based on the ideXlab platform.
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Analytic Solution for tachyon condensation in berkovits open superstring field theory
Journal of High Energy Physics, 2013Co-Authors: Theodore ErlerAbstract:We present an Analytic Solution for tachyon condensation on a non-BPS D-brane in Berkovits’ open superstring field theory. The Solution is presented as a product of 2 × 2 matrices in two distinct GL 2 subgroups of the open string star algebra. All string fields needed for computation of the nonpolynomial action can be derived in closed form, and the action produces the expected non-BPS D-brane tension in accordance with Sen’s conjecture. We also comment on how D-brane charges may be encoded in the topology of the tachyon vacuum gauge orbit.
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Analytic Solution for tachyon condensation in berkovits open superstring field theory
arXiv: High Energy Physics - Theory, 2013Co-Authors: Theodore ErlerAbstract:We present an Analytic Solution for tachyon condensation on a non-BPS D-brane in Berkovits' open superstring field theory. The Solution is presented as a product of $2\times 2$ matrices in two distinct $GL_2$ subgroups of the open string star algebra. All string fields needed for computation of the nonpolynomial action can be derived in closed form, and the action produces the expected non-BPS D-brane tension in accordance with Sen's conjecture. We also comment on how D-brane charges may be encoded in the topology of the tachyon vacuum gauge orbit.
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A Simple Analytic Solution for Tachyon Condensation
Journal of High Energy Physics, 2009Co-Authors: Theodore Erler, Martin SchnablAbstract:In this paper we present a new and simple Analytic Solution for tachyon condensation in open bosonic string field theory. Unlike the 0 gauge Solution, which requires a carefully regulated discrete sum of wedge states subtracted against a mysterious ``phantom'' counter term, this new Solution involves a continuous integral of wedge states, and no regularization or phantom term is necessary. Moreover, we can evaluate the action and prove Sen's conjecture in a mere few lines of calculation.
Martin Schnabl - One of the best experts on this subject based on the ideXlab platform.
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A Simple Analytic Solution for Tachyon Condensation
Journal of High Energy Physics, 2009Co-Authors: Theodore Erler, Martin SchnablAbstract:In this paper we present a new and simple Analytic Solution for tachyon condensation in open bosonic string field theory. Unlike the 0 gauge Solution, which requires a carefully regulated discrete sum of wedge states subtracted against a mysterious ``phantom'' counter term, this new Solution involves a continuous integral of wedge states, and no regularization or phantom term is necessary. Moreover, we can evaluate the action and prove Sen's conjecture in a mere few lines of calculation.
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Analytic Solution for tachyon condensation in open string field theory
arXiv: High Energy Physics - Theory, 2005Co-Authors: Martin SchnablAbstract:We propose a new basis in Witten's open string field theory, in which the star product simplifies considerably. For a convenient choice of gauge the classical string field equation of motion yields straightforwardly an exact Analytic Solution that represents the nonperturbative tachyon vacuum. The Solution is given in terms of Bernoulli numbers and the equation of motion can be viewed as novel Euler--Ramanujan-type identity. It turns out that the Solution is the Euler--Maclaurin asymptotic expansion of a sum over wedge states with certain insertions. This new form is fully regular from the point of view of level truncation. By computing the energy difference between the perturbative and nonperturbative vacua, we prove Analytically Sen's first conjecture.
Axel Brandenburg - One of the best experts on this subject based on the ideXlab platform.
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Analytic Solution of an oscillatory migratory α2 stellar dynamo
Astronomy and Astrophysics, 2017Co-Authors: Axel BrandenburgAbstract:Context. Analytic Solutions of the mean-field induction equation predict a nonoscillatory dynamo for homogeneous helical turbulence or constant α effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant α . Aims. We present an Analytic Solution for a one-dimensional bounded domain resulting in oscillatory Solutions for constant α , but different (Dirichlet and von Neumann or perfect conductor and vacuum) boundary conditions on the two boundaries. Methods. We solve a second order complex equation and superimpose two independent Solutions to obey both boundary conditions. Results. The Solution has time-independent energy density. On one end where the function value vanishes, the second derivative is finite, which would not be correctly reproduced with sine-like expansion functions where a node coincides with an inflection point. The field always migrates away from the perfect conductor boundary toward the vacuum boundary, independently of the sign of α . Conclusions. The obtained Solution may serve as a benchmark for numerical dynamo experiments and as a pedagogical illustration that oscillatory migratory dynamos are possible with constant α .
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Analytic Solution of an oscillatory migratory alpha 2 stellar dynamo
arXiv: Solar and Stellar Astrophysics, 2016Co-Authors: Axel BrandenburgAbstract:Analytic Solutions of the mean-field induction equation predict a nonoscillatory dynamo for uniform helical turbulence or constant alpha effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant alpha. We present an Analytic Solution for a one-dimensional bounded domain resulting in oscillatory Solutions for constant alpha, but different (Dirichlet and von Neumann or perfect conductor and vacuum) boundary conditions on the two ends. We solve a second order complex equation and superimpose two independent Solutions to obey both boundary conditions. The Solution has time-independent energy density. On one end where the function value vanishes, the second derivative is finite, which would not be correctly reproduced with sine-like expansion functions where a node coincides with an inflection point. The obtained Solution may serve as a benchmark for numerical dynamo experiments and as a pedagogical illustration that oscillatory dynamos are possible for dynamos with constant alpha.
Arjun G. Yodh - One of the best experts on this subject based on the ideXlab platform.
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scattering of diffuse photon density waves by spherical inhomogeneities within turbid media Analytic Solution and applications
Proceedings of the National Academy of Sciences of the United States of America, 1994Co-Authors: David A. Boas, Britton Chance, M A Oleary, Arjun G. YodhAbstract:Abstract We present an Analytic Solution for the scattering of diffuse photon density waves by spherical inhomogeneities within turbid media. The Analytic result is compared to experimental measurements. Close agreement between theory and experiment permits the use of the theory to determine the properties of unknown sphere-like objects embedded in turbid media. The Analytic Solution is extended to encompass several problems of practical interest in imaging, including the influence of multiple sources, multiple objects, and boundaries on the characterization of spherical inhomogeneities. We also extend the Solution to encompass time-domain measurements.