Optical diffraction on fractal lattices

Bogolyubov, A. N.; Petukhov, Alexey; Shapkina, N. E.

doi:10.3103/s0027134908020021

Cited by 6 publications

(5 citation statements)

References 3 publications

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“…In [2,3] Bogolyubov considered the Hamiltonian (2) in the case of zero temperature θ. In the main perturbation order he found that µ(θ = 0) = |c| 2 ν(0), where |c| 2 = ρ 0 is the density of Bose condensate.…”

Section: -1mentioning

confidence: 99%

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Asymptotic exactness of c-number substitution in Bogolyubov's theory of superfluidity

Bogolyubov¹,

Sankovich²

2010

Condens. Matter Phys.

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The Bogolyubov model of liquid helium is considered. The validity of substituting a c-number for the k = 0 mode operatorâ0 is established rigorously. The domain of stability of the Bogolyubov's Hamiltonian is found. We derive sufficient conditions which ensure the appearance of the Bose condensate in the model. For some temperatures and some positive values of the chemical potential, there is a gapless Bogolyubov spectrum of elementary excitations, leading to a proper microscopic interpretation of superfluidity. Jp, 03.75.Fi, The modelLet us consider a system of N spinless identical nonrelativistic bosons of mass m enclosed in a centered cubic box Λ ⊂ R 3 of volume V = |Λ| = L 3 with periodic boundary conditions for wave functions. The Hamiltonian of the system can be written in the second quantized form aŝHereâ # k = {â † k orâ k } are the usual boson (creation or annihilation) operators for the one-particle state ψ k (x) = V −1/2 exp(ikx), k ∈ Λ * , x ∈ Λ, acting on the Fock spacesymm is the symmetrized n-particle Hilbert space appropriate for bosons, andThe sums in (1) run over the dual set2m) is the one-particle energy spectrum of free bosons in the modes k ∈ Λ * (we propose = 1),N Λ = k∈Λ * â † kâ k is the total particle-number operator, µ is the chemical potential, ν(k) is the Fourier transform of the interaction pair potential Φ(x). We suppose that Φ(x) = Φ(|x|) ∈ L 1 (R 3 ) and ν(k) is a real function with a compact support such that 0 ν(k) = ν(−k) ν(0) for all k ∈ R 3 . Under these conditions the Hamiltonian (1) is superstable [1]. So long as the rigorous analysis of the Hamiltonian (1) is very knotty problem, Bogolyubov introduced the model Hamiltonian of superfluidity theory [2,3]. He proposed to disregard the terms of the third and fourth order in operatorsâ # k , k = 0 in the Hamiltonian (1),c N.N. Bogolyubov, Jr., D.P. Sankovich

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Section: -1mentioning

confidence: 99%

“…Under these conditions the Hamiltonian (1) is superstable [1]. So long as the rigorous analysis of the Hamiltonian (1) is very knotty problem, Bogolyubov introduced the model Hamiltonian of superfluidity theory [2,3]. He proposed to disregard the terms of the third and fourth order in operatorsâ # k , k = 0 in the Hamiltonian (1),…”

mentioning

confidence: 99%

Asymptotic exactness of c-number substitution in Bogolyubov's theory of superfluidity

Bogolyubov¹,

Sankovich²

2010

Condens. Matter Phys.

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“…It can also be directly used to destroy pathogens in infected wounds. UV-B radiation has significantly lower biocidal potential than UV-C, but it is characterized by a maximum erythemal effect, which can expand capillary vessels, increase the permeability of their walls, and increase local blood flow, leading to a local intensification of metabolic processes and stimulating the wound-healing process [3,4,17,20]. Unlike UV-C and UV-B, UV-A radiation is weakly absorbed by DNA; instead, it excites other endogenous chromophores (porphyrins, etc.…”

Section: Introductionmentioning

confidence: 99%

“…In clinical practice, the basis for UV radiation dosimetry is the minimum erythemal dose (MED)-the lowest energy dose of skin irradiation (in mJ/cm 2 )-which causes minimal-intensity erythema but with clearly defined boundaries. The MED is determined individually, using biodosimeters [4,20]. According to international recommendations, the MED for sensitive skin is 25 mJ/cm 2 [22].…”

Section: Introductionmentioning

confidence: 99%

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Preclinical Studies of the Antimicrobial and Wound-Healing Effects of the High-Intensity Optical Irradiation “Zarnitsa-A” Apparatus

Bagrov,

Bukhtiyarov,

Volodin

et al. 2023

Applied Sciences

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In this paper, a new approach to treating infected wounds is proposed. It is based on treating the wound surface with high-intensity pulsed optical radiation with a continuous spectrum, continuously covering the entire UV range (from 200 to 400 nm) and the visible and near-infrared regions of the spectrum. A pulsed xenon lamp is used as a radiation source. A description of the design and technical characteristics of the device, “Zarnitsa-A”, is presented, implementing the proposed medical technology for wound therapy. The results of our studies of the apparatus in vitro and in vivo are also presented. The article shows that exposure to the apparatus leads to pronounced bactericidal- and wound-healing properties. The apparatus’s action reliably provides higher rates of wound healing compared with only a typical antibacterial or wound healing agent, such as “levomekol” ointment.

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Small-Angle Scattering from Nanoscale Fat Fractals

et al. 2017

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Small-angle scattering (of neutrons, x-ray, or light; SAS) is considered to describe the structural characteristics of deterministic nanoscale fat fractals. We show that in the case of a polydisperse fractal system, with equal probability for any orientation, one obtains the fractal dimensions and scaling factors at each structural level. This is in agreement with general results deduced in the context of small-angle scattering analysis of a system of randomly oriented, non-interacting, nano-/micro-fractals. We apply our results to a two-dimensional fat Cantor-like fractal, calculating analytic expressions for the scattering intensities and structure factors. We explain how the structural properties can be computed from experimental data and show their correlation to the variation of the scaling factor with the iteration number. The model can be used to interpret recorded experimental SAS data in the framework of fat fractals and can reveal structural properties of materials characterized by a regular law of changing of the fractal dimensions. It can describe successions of power-law decays, with arbitrary decreasing values of the scattering exponents, and interleaved by regions of constant intensity.

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Optical diffraction on fractal lattices

Cited by 6 publications

References 3 publications

Asymptotic exactness of c-number substitution in Bogolyubov's theory of superfluidity

Asymptotic exactness of c-number substitution in Bogolyubov's theory of superfluidity

Preclinical Studies of the Antimicrobial and Wound-Healing Effects of the High-Intensity Optical Irradiation “Zarnitsa-A” Apparatus

Small-Angle Scattering from Nanoscale Fat Fractals

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