Numerical simulation of the light field in the atmosphere–ocean system using the matrix-operator method

It is well known that the orbital angular momentum (OAM) of a light field is conserved on propagation. In this work, in contrast to the OAM, we analytically study conservation of the topological charge (TC), which is often confused with OAM, but has quite different physical meaning. To this end, we propose a huge-ring approximation of the Huygens–Fresnel principle, when the observation point is located on an infinite-radius ring. Based on this approximation, our proof of TC conservation reveals that there exist other quantities that are also propagation-invariant, and the number of these invariants is theoretically infinite. Numerical simulation confirms the conservation of two such invariants for two light fields. The results of this work can find applications in optical data transmission to identify optical signals.

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Numerical Simulation on Nanoparticles Integrated Laser Shock Peening of Aluminum Alloy

ASME 2009 International Manufacturing Science and Engineering Conference, Volume 1 ◽

10.1115/msec2009-84088 ◽

2009 ◽

Author(s):

Chang Ye ◽

Gary J. Cheng

Keyword(s):

Numerical Simulation ◽

Particle Size ◽

Laser Shock Peening ◽

Particle Orientation ◽

Stress Wave Propagation ◽

Stress And Strain ◽

Laser Shock ◽

The Matrix ◽

Final Stress ◽

Shock Peening

In this paper, numerical simulation of nanoparticle integrated laser shock peening of aluminum alloys was carried out. A “tied constraint” was used to connect the matrix and nanoparticle assembly in ABAQUS package. Different particle size and particle volumes fraction (PVF) were studied. It was found that there is significant stress concentration around the nanoparticles. The existence of nanoparticle will influence the stress wave propagation and thus the final stress and strain state of the material after LSP. In addition, particle size, PVF and particle orientation all influence the strain rate, static residual stress, static plastic strain and energy absorption during the LSP process.

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The Matrix Operator e x and the Lucas Polynomials

Journal of Mathematics and Physics ◽

10.1002/sapm1964431332 ◽

1964 ◽

Vol 43 (1-4) ◽

pp. 332-335 ◽

Cited By ~ 11

Author(s):

Richard Barakat

Keyword(s):

Matrix Operator ◽

Lucas Polynomials ◽

The Matrix

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Matrix-operator method in problems of elasticity theory for an infinite layer

Soviet Applied Mechanics ◽

10.1007/bf00882451 ◽

1976 ◽

Vol 12 (5) ◽

pp. 458-463

Author(s):

V. A. Stolyarov

Keyword(s):

Elasticity Theory ◽

Operator Method ◽

Matrix Operator ◽

Infinite Layer

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Symmetric Determinants and the Cayley and Capelli Operator

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500024822 ◽

1948 ◽

Vol 8 (2) ◽

pp. 76-86 ◽

Cited By ~ 9

Author(s):

H. W. Turnbull

Keyword(s):

Invariant Theory ◽

Differential Operators ◽

Matrix Operator ◽

Linear Combinations ◽

Classical Invariant Theory ◽

Independent Variables ◽

The Matrix ◽

Classical Invariant ◽

Initial Discovery ◽

Special Case

The result obtained by Lars Gårding, who uses the Cayley operator upon a symmetric matrix, is of considerable interest. The operator Ω = |∂/∂xij|, which is obtained on replacing the n2 elements of a determinant |xij by their corresponding differential operators and forming the corresponding n-rowed determinant, is fundamental in the classical invariant theory. After the initial discovery in 1845 by Cayley further progress was made forty years later by Capelli who considered the minors and linear combinations (polarized forms) of minors of the same order belonging to the whole determinant Ω: but in all this investigation the n2 elements xij were regarded as independent variables. The apparently special case, undertaken by Gårding when xij = xji and the matrix [xij] is symmetric, is essentially a new departure: and it is significant to have learnt from Professor A. C. Aitken in March this year 1946, that he too was finding the symmetrical matrix operator [∂/∂xij] of importance and has already written on the matter.

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