Search
9 articles for “non-linear integral equations”
-
Non-linear Integral Equations Ideal Solar Cells Analysis with One and Two Intermediate Bands
Abstract: An innovative and groundbreaking theory is proposed by using intermediate bands within the energy gap of the semiconductor in order to increase the efficiency of solar cells. Consequently, photons with energy less than the band gap may contribute to the output device by using the intermediate band or bands, in order to jump to the conduction band. This problem is reduced to the solution of non-linear integral equations and for …
Published in Journal of Alternate Energy Sources & Technologies · Vol. 4, Issue 2, 2013 · pp. 8–15 Read article
-
Non-linear Singular Integral Equations for Multiphase Flows in Petroleum Reservoir Engineering
Abstract: A very important problem of petroleum reservoir engineering is investigated by the present research. Consequently, an innovative and groundbreaking mathematical approach is introduced for the determination of the properties of the earth subsurface, when oil reserves together with water are moving through porous media. So, the multiphase flow problem of petroleum together with water is reduced to the solution of a non-linear singular integral equation, which is numerically solved by …
Published in Journal of Petroleum Engineering & Technology · Vol. 2, Issue 1-3, 2012 · pp. 73–82 Read article
-
Numerical Modeling of Elastoviscoplastic Material Model in Strain Space
Abstract: Conventional material non-linear analysis works with stress-space plasticity. It uses yield function, loading-unloading criteria, and flow rule in terms of stress parameters. It shows ambiguity in loading-unloading criteria for softening materials. During such situations, an alternative strain-space formulation becomes quite useful to carry out analysis of such materials. The viscoplastic response of materials requires the time integration of system of non-linear first order differential equations. In viscoplasiticy, the constitutive equation …
Published in Journal of Experimental & Applied Mechanics · Vol. 9, Issue 1, 2018 · pp. 9–14 Read article
-
Analytical Solution to Single Degree of Freedom Bi-Linear Spring Mass Systems Transient Vibration
Abstract: Conventional approach to solution of linear systems under transient vibration has been through Convolution integral or Duhamel integral method which employs the method of superposition of linear solutions to obtain the total solution. Principle of superposition is not possible for non-linear systems and hence transient vibration solution cannot be obtained through classical methods. Nevertheless, the solution to transient vibration for each domain can be obtained as a sum of homogeneous …
Published in Journal of Aerospace Engineering & Technology · Vol. 8, Issue 2, 2018 · pp. 7–18 Read article
-
From Differential Equations to Data Science: A Survey on Analytical Methods in Contemporary Problems
Abstract: The integration of differential equations and data science methods represents a dynamic and evolving approach to solving contemporary challenges across a wide range of disciplines, including engineering, physics, biology, economics, and finance. Differential equations have long served as fundamental tools for modeling continuous systems and processes, offering powerful insights into the behavior of natural and man-made phenomena. For example, they describe how heat diffuses through materials, how populations grow in …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 1–6 Read article
-
BIS Processes in the Human Neural Networks and Asymptotic Periodic Solutions of the Evolution Equations in the Brain Nanosystem using Jacobi Elliptic Function
Abstract: Our perseverance is dependent upon the normal functioning and fluctuation of the brain. That functioning involves complex electrical activities. These in turn generate subtle waves which were first noticed and studied by Hans Berger. These are essentially electrical rhythms in the brain which, when recorded by means of instruments called electroencephalograms or EEG on a roll of paper, appear as complex wave forms. In this paper, based on Jacobi elliptic …
Published in Current Trends in Signal Processing · Vol. 3, Issue 3, 2013 · pp. 11–18 Read article
-
Artificial Intelligence–Assisted Reduced-Order Modeling and Stability Control in Granular Couette Flow
Abstract: This study develops a reduced-order and stability-aware modeling framework for dense granular Couette flow by integrating continuum mechanics, bifurcation analysis, and data-driven stability estimation. Starting from coupled governing equations for momentum, granular temperature, and microstructural evolution, the system is nondimensionalized and reduced using a Galerkin projection consistent with shear-driven boundary conditions. This yields a low-dimensional nonlinear dynamical system that preserves the essential coupling between velocity, fluctuation energy, and structural relaxation. …
Published in Emerging Trends in Chemical Engineering · Vol. 13, Issue 3, 2026 Read article
-
AI-Assisted Kinetic Modeling of PLA Hydrolysis Under Subcritical Water Conditions for Sustainable Polymer Recycling
Abstract: The accumulation of poly (lactic acid) (PLA) in terrestrial and marine ecosystems has intensified the demand for closed-loop, green recycling technologies. Subcritical water (SCW) hydrolysis offers a promising, catalyst-free pathway for the rapid depolymerization of PLA into its constituent monomer, lactic acid. However, the complex, highly non-linear kinetics governing macro-molecular degradation under variable hydrothermal conditions limit real-time process optimization and industrial scalability. This study develops a novel artificial intelligence (AI)-assisted …
Published in Journal of Modern Chemistry & Chemical Technology · Vol. 17, Issue 2, 2026 · pp. 65–74 Read article
-
The Rise of Fractional Calculus: Novel Applications in Engineering and Biological Systems
Abstract: Fractional calculus (FC) is an advanced mathematical framework that generalizes the classical concepts of differentiation and integration to non-integer, or fractional, orders. This extension of traditional calculus allows for the modeling of complex dynamic systems that exhibit behavior not easily captured by integer-order differential equations. Over the last few decades, fractional calculus has seen a rapid rise in popularity, particularly in applied mathematics, engineering, and biological sciences, due to its …
Published in Recent Trends in Mathematics · Vol. 1, Issue 2, 2024 · pp. 7–11 Read article