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Relevant bibliographies by topics / Real singularity theory

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Journal articles

Academic literature on the topic 'Real singularity theory'

Author: Grafiati

Published: 1 September 2023

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Journal articles on the topic "Real singularity theory"

1

Xiong, Gang, Wenxian Yu, and Shuning Zhang. "Dynamic Singularity Spectrum Distribution of Sea Clutter." Fluctuation and Noise Letters 14, no. 01 (2014): 1550004. http://dx.doi.org/10.1142/s0219477515500042.

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The fractal and multifractal theory have provided new approaches for radar signal processing and target-detecting under the background of ocean. However, the related research mainly focuses on fractal dimension or multifractal spectrum (MFS) of sea clutter. In this paper, a new dynamic singularity analysis method of sea clutter using MFS distribution is developed, based on moving detrending analysis (DMA-MFSD). Theoretically, we introduce the time information by using cyclic auto-correlation of sea clutter. For transient correlation series, the instantaneous singularity spectrum based on multi

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2

Baker, Gregory, Russel E. Caflisch, and Michael Siegel. "Singularity formation during Rayleigh–Taylor instability." Journal of Fluid Mechanics 252 (July 1993): 51–78. http://dx.doi.org/10.1017/s0022112093003660.

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During the motion of a fluid interface undergoing Rayleigh-Taylor instability, vorticity is generated on the interface baronclinically. This vorticity is then subject to Kelvin-Helmholtz instability. For the related problem of evolution of a nearly flat vortex sheet without density stratification (and with viscosity and surface tension neglected), Kelvin-Helmholtz instability has been shown to lead to development of curvature singularities in the sheet. In this paper, a simple approximate theory is developed for Rayleigh-Taylor instability as a generalization of Moore's approximation for vorte

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3

Dubrulle, Bérengère. "Multi-Fractality, Universality and Singularity in Turbulence." Fractal and Fractional 6, no. 10 (2022): 613. http://dx.doi.org/10.3390/fractalfract6100613.

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In most geophysical flows, vortices (or eddies) of all sizes are observed. In 1941, Kolmogorov devised a theory to describe the hierarchical organization of such vortices via a homogeneous self-similar process. This theory correctly explains the universal power-law energy spectrum observed in all turbulent flows. Finer observations however prove that this picture is too simplistic, owing to intermittency of energy dissipation and high velocity derivatives. In this review, we discuss how such intermittency can be explained and fitted into a new picture of turbulence. We first discuss how the co

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4

Kaneko, Akira. "On the analyticity of the locus of singularity of real analytic solutions with minimal dimension." Nagoya Mathematical Journal 104 (December 1986): 63–84. http://dx.doi.org/10.1017/s0027763000022686.

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Let P(x, D) be a linear partial differential operator with real analytic coefficients and let C ⊂ Rn be a germ of closed subset, say at the origin. We say that C is (the locus of) an irremovable singularity of a real analytic solution u of P(x, D)u = 0 if u is defined outside C on a neighborhood Ω of 0 but cannot be extended to the whole neighborhood Ω even as a hyperfunction solution of P(x, D)u = 0. This usage of the word “singularity” is the same as the one for the analytic functions in complex analysis, and is different of the usual usage of “singularities of solutions” in the theory of pa

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5

Yau, Stephen T., and Letian Zhang. "An upper estimate of integral points in real simplices with an application to singularity theory." Mathematical Research Letters 13, no. 6 (2006): 911–21. http://dx.doi.org/10.4310/mrl.2006.v13.n6.a6.

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6

Klehn, Oliver. "Real and complex indices of vector fields on complete intersection curves with isolated singularity." Compositio Mathematica 141, no. 02 (2005): 525–40. http://dx.doi.org/10.1112/s0010437x04000958.

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7

Shalaby, Abouzeid M. "Effective action study of the 𝒫𝒯-symmetric (iϕ3)6−𝜖 theory and the Yang–Lee edge singularity". International Journal of Modern Physics A 34, № 17 (2019): 1950090. http://dx.doi.org/10.1142/s0217751x19500908.

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We use the effective potential method to study the [Formula: see text]-symmetric [Formula: see text] field theory in [Formula: see text] space–time dimensions. For [Formula: see text], we obtained the first two energy levels which are real as well as reflecting the stability of the spectrum. [Formula: see text]-symmetry breaking occurs at [Formula: see text] where the two levels merge and beyond this critical point they have complex values. Since there exist no results in the literature to compare with, we extracted the critical exponents of the theory to test the accuracy of our calculations

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8

Zhai, Liang-Jun, Huai-Yu Wang, and Guang-Yao Huang. "Scaling of the Berry Phase in the Yang-Lee Edge Singularity." Entropy 21, no. 9 (2019): 836. http://dx.doi.org/10.3390/e21090836.

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We study the scaling behavior of the Berry phase in the Yang-Lee edge singularity (YLES) of the non-Hermitian quantum system. A representative model, the one-dimensional quantum Ising model in an imaginary longitudinal field, is selected. For this model, the dissipative phase transition (DPT), accompanying a parity-time (PT) symmetry-breaking phase transition, occurs when the imaginary field changes through the YLES. We find that the real and imaginary parts of the complex Berry phase show anomalies around the critical points of YLES. In the overlapping critical regions constituted by the (0 +

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9

Loudon, Rodney. "One-dimensional hydrogen atom." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2185 (2016): 20150534. http://dx.doi.org/10.1098/rspa.2015.0534.

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The theory of the one-dimensional (1D) hydrogen atom was initiated by a 1952 paper but, after more than 60 years, it remains a topic of debate and controversy. The aim here is a critique of the current status of the theory and its relation to relevant experiments. A 1959 solution of the Schrödinger equation by the use of a cut-off at x = a to remove the singularity at the origin in the 1/| x | form of the potential is clarified and a mistaken approximation is identified. The singular atom is not found in the real world but the theory with cut-off has been applied successfully to a range of fou

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10

Sinclair, GB. "Stress singularities in classical elasticity—II: Asymptotic identification." Applied Mechanics Reviews 57, no. 5 (2004): 385–439. http://dx.doi.org/10.1115/1.1767846.

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This review article (Part II) is a sequel to an earlier one (Part I) that dealt with means of removal and interpretation of stress singularities in elasticity, as well as their asymptotic and numerical analysis. It reviews contributions to the literature that have actually effected asymptotic identifications of possible stress singularities for specific configurations. For the most part, attention is focused on 2D elastostatic configurations with constituent materials being homogeneous and isotropic. For such configurations, the following types of stress singularity are identified: power singu

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