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# Interval Arithmetic with Applications to Physical Phenomena

Submission Deadline: 01 February 2021 (closed)

### Guest Editors

Dr. Ali Ahmadian, National University of Malaysia, Malaysia.
Dr. Soheil Salahshour Soheil Salahshour, Bahcesehir University, Turkey.
Prof. Ahmad Azar, Prince Sultan University, Kingdom Saudi Arabia.

### Summary

One of the important topics in the applied science is dynamic systems and their applications. If these systems are involved with complex-uncertain data then they will be more important and practical. Because the real-life problems work with this type of data and most of them cannot be solved exactly and easily and sometimes they are impossible to solve. In this regard, role of employing differential equations with uncertain parameters are inevitable. Interval mathematical modeling has not been considered enough for a long time. However, in the recent years, the scientists found the applicability of this significant notion measure uncertainties in the mathematical modeling with interval parameters. Therefore, a number of researches have been done in this regard to analyze the mathematical systems based on the interval parameters and study the real-world systems based on fuzzy mathematical modeling.

Specific topics of interest include (but are not limited to):

• Foundation of Interval arithmetic (Interval arithmetic operations, Generalized Hukuhara difference, Differentiation of interval-valued functions, variant of constraint interval arithmetic, etc.)

• Interval ordinary differential equations (Existence, Uniqueness and Stability of the solution)

• Interval integral differential equations in combination with machine learning algorithms

• Fractional calculus for interval-valued functions

• Interval dynamical systems and their relevant approximate solutions

• Spectral solutions of interval integer and fractional models arising in the physical models

• Interval arithmetic to model the viscoelastic behavior of the dynamic systems

• Numerical solutions of Hybrid Interval differential equations

• Approximate solutions of interval integro-differential equations

• Interval functional, stochastic, fractional and random differential equations with their numerical solutions

### Keywords

Interval arithmetic, dynamical systems, physical problems, fractional calculus, numerical simulations, mathematical modeling, machine learning algorithms

### Published Papers

• Open Access

ARTICLE

Experimental Study of Heat Transfer Enhancement in Solar Tower Receiver Using Internal Fins

CMC-Computers, Materials & Continua, Vol.68, No.2, pp. 1693-1711, 2021, DOI:10.32604/cmc.2021.016741
（This article belongs to this Special Issue: Interval Arithmetic with Applications to Physical Phenomena)
Abstract The receiver is an important element in solar energy plants. The principal receiver’s tubes in power plants are devised to work under extremely severe conditions, including excessive heat fluxes. Half of the tube’s circumference is heated whilst the other half is insulated. This study aims to improve the heat transfer process and reinforce the tubes’ structure by designing a new receiver; by including longitudinal fins of triangular, circular and square shapes. The research is conducted experimentally using Reynolds numbers ranging from 28,000 to 78,000. Triangular fins have demonstrated the best improvement for heat transfer. For Reynolds number value near 43,000… More >

• Open Access

ARTICLE

A Novel Design of Octal-Valued Logic Full Adder Using Light Color State Model

CMC-Computers, Materials & Continua, Vol.67, No.3, pp. 3487-3503, 2021, DOI:10.32604/cmc.2021.015759
（This article belongs to this Special Issue: Interval Arithmetic with Applications to Physical Phenomena)
Abstract Due to the demand of high computational speed for processing big data that requires complex data manipulations in a timely manner, the need for extending classical logic to construct new multi-valued optical models becomes a challenging and promising research area. This paper establishes a novel octal-valued logic design model with new optical gates construction based on the hypothesis of Light Color State Model to provide an efficient solution to the limitations of computational processing inherent in the electronics computing. We provide new mathematical definitions for both of the binary OR function and the PLUS operation in multi valued logic that… More >

• Open Access

ARTICLE

Accurate Fault Location Modeling for Parallel Transmission Lines Considering Mutual Effect

CMC-Computers, Materials & Continua, Vol.67, No.1, pp. 491-518, 2021, DOI:10.32604/cmc.2021.014493
（This article belongs to this Special Issue: Interval Arithmetic with Applications to Physical Phenomena)
Abstract A new accurate algorithms based on mathematical modeling of two parallel transmissions lines system (TPTLS) as influenced by the mutual effect to determine the fault location is discussed in this work. The distance relay measures the impedance to the fault location which is the positive-sequence. The principle of summation the positive-, negative-, and zero-sequence voltages which equal zero is used to determine the fault location on the TPTLS. Also, the impedance of the transmission line to the fault location is determined. These algorithms are applied to single-line-to-ground (SLG) and double-line-to-ground (DLG) faults. To detect the fault location along the transmission… More >