Aharonov–Bohm‐inspired tomographic imaging via compressive sensing

Valagiannopoulos, Constantinos A.; Marengo, Edwin A.; Dimakis, Alexandros G.; Alù, Andrea

doi:10.1049/iet-map.2017.0609

Cited by 9 publications

(4 citation statements)

References 32 publications

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“…If a solenoid with a magnetic field B = ∇ × A (where A is the electromagnetic vector potential) is placed between the two slits of a double-slit experiment the phase of the wave-function of the electrons going through the slits and following some path to the screen [29,24]. We refer to [5] for a rigorous study of the magnetic field in quantum mechanics and to [15,31,32] for other physical aspects with many references therein.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Well-posedness and scattering for a 2D inhomogeneous NLS with Aharonov-Bohm magnetic potential

Majdoub¹,

Saanouni²

2023

Preprint

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We consider the magnetic nonlinear inhomogeneous Schrödinger equationwhere α ∈ R \ Z, ̺ > 0, p > 1. We prove a dichotomy of global existence and scattering versus blow-up of energy solutions under the ground state threshold in the inter-critical regime. The scattering is obtained by using the new approach of Dodson-Murphy (A new proof of scattering below the ground state for the 3D radial focusing cubic NLS, Proc. Am. Math. Soc. ( 2017)). This method is based on Tao's scattering criteria and Morawetz estimates. The novelty here is twice: we investigate the case ̺α = 0 and we consider general energy initial data (not necessarily radially symmetric). The particular case α = 0, known as INLS, was widely investigated in the few recent years. Moreover, the particular case ̺ = 0, which gives the homogeneous regime, was considered recently by X. Gao and C. Xu (Scattering theory for NLS with inverse-square potential in 2D, J. Math. Anal. Appl. ( 2020)), where the scattering is proved for spherically symmetric datum. In the radial framework, the above problem translate to the INLS with inverse square potential, which was widely investigated in space dimensions higher than three. The Hardy inequality |x|fails in two space dimensions. Thus, it is not clear how to treat the NLS with inverse square potential in H 1 for two space dimensions. This article seems to be the first one dealing with the NLS with Aharonov-Bohm magnetic potential in the inhomogeneous regime, namely ̺ = 0.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Well-posedness and scattering for a 2D inhomogeneous NLS with Aharonov-Bohm magnetic potential

Majdoub¹,

Saanouni²

2023

Preprint

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“…[47]. We believe that our work provides a better insight into the famous Aharonov-Bohm effect for multiband systems, and could be experimentally applicable, for example, to strained or gapped graphenes, or to tomographic imaging [48]. Finally, the extension of our integral representation of the AB scattering state to anisotropic multiband systems, or to the case of a finite radius solenoid is a further relevant research direction.…”

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confidence: 79%

Unified Description of the Aharonov--Bohm Effect in Isotropic Multiband Electronic Systems

Németh¹,

Cserti²

2023

Preprint

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We present a unified treatment of the Aharonov-Bohm (AB) effect for two-dimensional multiband electronic systems possessing isotropic band structures. We propose an integral representation of the AB scattering state of an electron scattered by an infinitely thin solenoid. Moreover, we derive the asymptotic form of the AB scattering state and obtain the differential cross section from that. We found a remarkable result, namely that this cross section is the same for all isotropic systems and agrees with that obtained first by Aharonov and Bohm for spinless free particle systems. To demonstrate the generality of our theory, we consider several specific multiband systems relevant to condensed matter physics.

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“…The strength of concrete determined by a compression test, which involves smashing cubical concrete in a compression testing machine is known as compressive strength. It assesses the ability of concrete to bear a load before failing [16] and twelve cubes [8] were cast with 150 mm dimensions, and the concrete's compressive strength was measured. As shown in figure 8, compression test of cubes after water curing for 7, 14 and 28 days.…”

Section: Test Of Compressive Forcementioning

confidence: 99%

Influence Of Helical Confinement On Crack Development In RCC Beams

Abdelbaki,

Kuckian,

Obaidi

et al. 2023

IOP Conf. Ser.: Mater. Sci. Eng.

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Structures made of reinforced concrete are susceptible to developing cracks when they are in the path of earthquakes, strong winds, or increased structural loading. It is therefore possible that it will be necessary to manage structural cracking in the Service Limit State to maximise the lifetime and strength of the structural components under any stress. Helical containment is superior to rectangular containment in terms of its ability to strengthen and ductile the Reinforced Concrete (RC) structural member. In the current work, six distinct beams were each subjected to a series of tests to see how they behaved in terms of cracking when subjected to bending loads. Each of these tests used a unique helical pitch space distance. The beams all measured 150 mm by 150 mm and 750 mm in length. They were designed in accordance with the criteria of Euro code 2, with the identical dimensions. Both 50 and 100 mm were used to take the measurement for the helical pitch. The findings indicate that the utilisation of helical elements does influence the cracking behaviour of the beams. The most important finding was that the measurement of the crack’s thickness was slightly reduced when the beams were restricted to a helical zone with a closer spacing between them. The fact that the theoretical crack is longer than the actual crack that was measured experimentally demonstrates that the Euro code 2 standard provides a more accurate forecast as well as a higher factor of safety. This is demonstrated by the fact that the theoretical crack is larger than the actual crack that was measured.

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Aharonov–Bohm‐inspired tomographic imaging via compressive sensing

Cited by 9 publications

References 32 publications

Well-posedness and scattering for a 2D inhomogeneous NLS with Aharonov-Bohm magnetic potential

Well-posedness and scattering for a 2D inhomogeneous NLS with Aharonov-Bohm magnetic potential

Unified Description of the Aharonov--Bohm Effect in Isotropic Multiband Electronic Systems

Influence Of Helical Confinement On Crack Development In RCC Beams

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