Journal ArticleDOI
Quantization of Foster mesoscopic circuit and DC-pumped Josephson parametric amplifier from fractal measure arguments
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A quantum theory of the mesoscopic LC-circuit based on the product-like fractal measure which was introduced by Li and Ostoja-Starzewski is proposed in this paper.Abstract:
A quantum theory of the mesoscopic LC-circuit based on the product-like fractal measure which was introduced by Li and Ostoja-Starzewski is proposed. On the basis of the theory, the Schrodinger equation and the energy spectrum for the quantum LC circuit were derived. By introducing special forms of position-dependent LC-electric components, the associated creation and annihilation operators were obtained and analyzed. The quantization of the DC-driven Josephson circuit and its parametric amplifier were studied in details. The main outcome of this study concerns the finite form of the energy expectation value at very high temperature in contrast to the results obtained in literature which is time-dependent. Further details were analyzed and discussed.read more
Citations
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Quantum dots and cuboid quantum wells in fractal dimensions with position-dependent masses
TL;DR: In this paper, a generalized Schrodinger equation in fractal dimensions was constructed by an effective potential which is generated by a position-dependent mass, which is based on the fractal anisotropy and product-like fractal measure approach introduced by Li and Ostoja-Starzewski in their formulation of continuum media.
Journal ArticleDOI
Fractal dimensions in fluid dynamics and their effects on the Rayleigh problem, the Burger's Vortex and the Kelvin–Helmholtz instability
Rami Ahmad El-Nabulsi,W. Anukool +1 more
Journal ArticleDOI
Fractal dimensions in fluid dynamics and their effects on the Rayleigh problem, the Burger's Vortex and the Kelvin–Helmholtz instability
Rami Ahmad El-Nabulsi,W. Anukool +1 more
Journal ArticleDOI
A mapping from Schrodinger equation to Navier–Stokes equations through the product-like fractal geometry, fractal time derivative operator and variable thermal conductivity
TL;DR: In this article, the concept of the product-like fractal measure introduced by Li and Ostoja-Starzewski in their formulation of fractal continuum media is combined with the fractal time derivative operator to construct a map between the Schrodinger equation which governs the wave function of a quantum-mechanical system and the Navier-Stokes equations that describe the flow of incompressible fluids.
Journal ArticleDOI
Fractal nonlocal thermoelasticity of thin elastic nanobeam with apparent negative thermal conductivity
Rami Ahmad El-Nabulsi,W. Anukool +1 more
TL;DR: In this paper , a new model of nonlocal fractal thermoelasticity beam theory for nanomaterials characterized by an apparent negative thermal conductivity which occurs in shaped graded materials is presented.
References
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Journal ArticleDOI
Currents Induced by Electron Motion
TL;DR: In this article, the instantaneous current induced in neighboring conductors by a given specified motion of electrons is computed based on the repeated use of a simple equation giving the current due to a single electron's movement.
Journal ArticleDOI
Currents to Conductors Induced by a Moving Point Charge
TL;DR: In this article, general expressions for the currents which flow in the external circuit connecting a system of conductors when a point charge is moving among the conductors are derived for several cases of practical interest.
Book
Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media
TL;DR: In this article, the Ginzburg-Landau Equation for Fractal Media and Fokker-Planck Equation of Fractal Distributions of Probability are presented.