Emergence of quasiperiodic quantum wave functions in Hausdorff dimensional crystals and improved intrinsic Carrier concentrations

El-Nabulsi, Rami Ahmad

doi:10.1016/j.jpcs.2018.12.025

Cited by 51 publications

(17 citation statements)

References 62 publications

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“…This equation was explored in literature through a = 0.50, 0 < r 2 < 0.0002 ×10 -4 Figure 19. Variations of Q(r) for α = 0.5 and for 0 < r < 0.0002 m. a = 1.00, 0 < r 1 < 0.0001 ×10 -4 Figure 23. Variations of Q(r) for α = 1 and for 0 < r < 0.0001 m. royalsocietypublishing.org/journal/rsif J. R. Soc.…”

Section: Analytical Solution Of the Time-dependent Fractal Pennes Bioheat Transfer Equationmentioning

confidence: 99%

“…Fractal kinetic theory has been explored in surface chemical reactions [4], spin dynamics [5], adsorption on mesoporous carbons [6], reaction kinetics of proteins and enzymes [7], diffusion-limited reactions [8][9][10], non-extensive thermodynamics [11], rock fractures in fluid flows [12], colloid science [13], fluids dynamics simulations [14], porous media [15] and among others. More generally, fractals have imperative implications in materials sciences [16], fluids flows [17,18], elastic and continuum media [19], electromagnetic theory [20,21], quantum mechanics [22][23][24][25][26], astrophysics [27][28][29][30][31][32][33][34][35][36], fluid mechanics and nanofluid [37,38], transport in complex porous media [39], materials sciences [40], heat transfer [41], etc.…”

Section: Introductionmentioning

confidence: 99%

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Fractal Pennes and Cattaneo–Vernotte bioheat equations from product-like fractal geometry and their implications on cells in the presence of tumour growth

El-Nabulsi

2021

J. R. Soc. Interface.

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In this study, the Pennes and Cattaneo–Vernotte bioheat transfer equations in the presence of fractal spatial dimensions are derived based on the product-like fractal geometry. This approach was introduced recently, by Li and Ostoja-Starzewski, in order to explore dynamical properties of anisotropic media. The theory is characterized by a modified gradient operator which depends on two parameters: R which represents the radius of the tumour and R 0 which represents the radius of the spherical living tissue. Both the steady and unsteady states for each fractal bioheat equation were obtained and their implications on living cells in the presence of growth of a large tumour were analysed. Assuming a specific heating/cooling by a constant heat flux equivalent to the metabolic heat generation in the tissue, it was observed that the solutions of the fractal bioheat equations are robustly affected by fractal dimensions, the radius of the tumour growth and the dimensions of the living cell tissue. The ranges of both the fractal dimensions and temperature were obtained, analysed and compared with recent studies. This study confirms the importance of fractals in medicine.

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Section: Analytical Solution Of the Time-dependent Fractal Pennes Bioheat Transfer Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractal Pennes and Cattaneo–Vernotte bioheat equations from product-like fractal geometry and their implications on cells in the presence of tumour growth

El-Nabulsi

2021

J. R. Soc. Interface.

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“…A numerical technique has been used for resolving the fractional Hamilton equation with the help of Caputo fractional operator [2], mathematical modelling of human liver with Caputo-Fabrizio fractional derivative [3], and mathematical model for Zika virus transmission [4]. Investigation of different types of soliton solutions of fractional differential equations (FDEs) can be identified through different techniques and has been examined by many authors [5][6][7][8][9]. Moreover, the application of fractionalorder differential equations has been clearly expressed by studying the hyperchaotic behaviors of a nonautonomous cardiac conduction system in both frames of integer and fractional-order differential equations [10].…”

Section: Introductionmentioning

confidence: 99%

Wave Propagations in Nonlinear Low-Pass Electrical Transmission Lines through Optical Fiber Medium

Zulfiqar

Ahmad

Rani

et al. 2022

Mathematical Problems in Engineering

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The present article discovers the new soliton wave solutions and their propagation in nonlinear low-pass electrical transmission lines (NLETLs). Based on an innovative Exp-function method, multitype soliton solutions of nonlinear fractional evolution equations of NLETLs are established. The equation is reformulated to a fractional-order derivative by using the Jumarie operator. Some new results are also presented graphically to understand the real physical importance of the studied model equation. The physical interpretation of waves is represented in the form of three-dimensional and contour graphs to visualize the underlying dynamic behavior of these solutions for particular values of the parameters. Moreover, the attained outcomes are generally new for the considered model equation, and the results show that the used method is efficient, direct, and concise which can be used in more complex phenomena.

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“…Fractal physics phenomena play an important role in different branches of sciences and engineering, e.g. fracture mechanics [3], viscoelasticity [4], turbulence [5], quantum mechanics [6], cells biology [7], astrophysics [8], continuum mechanics [9] and solid state physics [10] among others. Fractals are attractive since they are considered indispensable components in the modelling of several natural phenomena characterized by several temporal or spatial scales [11] should be noted that fractal analysis is connected to fractional calculus, and their association are used employed to model the evolution of fractal dynamical systems [12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

On a new fractional uncertainty relation and its implications in quantum mechanics and molecular physics

El-Nabulsi¹

2020

Proc. R. Soc. A.

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A new generalized uncertainty relation is constructed based on Li-Ostoja-Starzewski fractional gradient operator of order 0 < α ≤ 1 introduced recently in literature which is motivated from dimensional regularization method. The new generalized uncertainty relation leads to a new form of Schrödinger equation and emergent position-dependent mass. Special forms of position-dependent mass were studied and the problem of a particle in a box was explored. Dissimilar forms of allowed quantum energies were obtained which lead to different scenarios. We have confronted the theory with observations by evaluating the maximum wavelength obtained in the 1,3-butadiene molecule. Several features were discussed accordingly.

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Emergence of quasiperiodic quantum wave functions in Hausdorff dimensional crystals and improved intrinsic Carrier concentrations

Cited by 51 publications

References 62 publications

Fractal Pennes and Cattaneo–Vernotte bioheat equations from product-like fractal geometry and their implications on cells in the presence of tumour growth

Fractal Pennes and Cattaneo–Vernotte bioheat equations from product-like fractal geometry and their implications on cells in the presence of tumour growth

Wave Propagations in Nonlinear Low-Pass Electrical Transmission Lines through Optical Fiber Medium

On a new fractional uncertainty relation and its implications in quantum mechanics and molecular physics

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