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Recently, Stein et al. (2016) studied theoretical properties and parameter estimation of continuous time processes derived as solutions of a generalized Langevin equation (GLE). In this paper, the authors extend the model to a wider class of memory kernels and then propose a bond and bond option valuation model based on the extension of the generalized Langevin process of Stein et al. (2016).

Bond and bond option pricing based on the proposed interest rate models presents new difficulties as the standard partial differential equation method of stochastic calculus for bond pricing cannot be used directly. The authors obtain bond and bond option prices by finding the closed form expression of the conditional characteristic function of the integrated short rate process driven by a general Lévy noise.

The authors obtain zero-coupon default-free bond and bond option prices for short rate models driven by a variety of Lévy processes, which include Vasicek model and the short rate model obtained by solving a second-order Langevin stochastic differential equation (SDE) as special cases.

Bond and bond option pricing plays an important role in capital markets and risk management. In this paper, the authors derive closed form expressions for bond and bond option prices for a wider class of interest rate models including second-order SDE models. Closed form expressions may be especially instrumental in facilitating parameter estimation in these models.

This paper aims to investigate the existence and uniqueness of solution for generalized Sturm–Liouville and Langevin equations formulated using Caputo–Hadamard fractional derivative operator in accordance with three nonlocal Hadamard fractional integral boundary conditions. With regard to this nonlinear boundary value problem, three popular fixed point theorems, namely, Krasnoselskii’s theorem, Leray–Schauder’s theorem and Banach contraction principle, are employed to theoretically prove and guarantee three novel theorems. The main outcomes of this work are verified and confirmed via several numerical examples.

In order to accomplish our purpose, three fixed point theorems are applied to the problem under consideration according to some conditions that have been established to this end. These theorems are Krasnoselskii's theorem, Leray Schauder's theorem and Banach contraction principle.

In accordance to the applied fixed point theorems on our main problem, three corresponding theoretical results are stated, proved, and then verified via several numerical examples.

The existence and uniqueness of solution for generalized Sturm–Liouville and Langevin equations formulated using Caputo–Hadamard fractional derivative operator in accordance with three nonlocal Hadamard fractional integral boundary conditions are studied. To the best of the authors’ knowledge, this work is original and has not been published elsewhere.

The conventional treatment of thermal noise is based on Nyquist’s theorem. This theorem has only been derived for linear, reciprocal (we define “reciprocal networks” as networks that are built of reciprocal network elements) networks. In this paper a description of thermal noise in reciprocal non‐linear RLC networks is presented. This description is derived from first principles, i.e. from a direct application of non‐equilibrium thermodynamics (irreversible thermodynamics) to electrical networks. As an example, the class of “complete” non‐linear networks is considered. Using the idea of equivalent n‐ports, the theory’s extension to certain classes of transistor circuits should be possible.

A transport equation for the one‐point velocity probability density function (pdf) of turbulence is derived, modelled and solved. The new pdf equation is obtained by two modeling steps. In the first step, a dynamic equation for the fluid elements is proposed in terms of the fluctuating part of Navier‐Stokes equation. A transition probability density function (tpdf) is extracted from the modelled dynamic equation. Then the pdf equation of Fokker‐Planck type is obtained from the tpdf. In the second step, the Fokker‐Planck type pdf equation is modified by Lundgren’s formal pdf equation to ensure it can properly describe the turbulence intrinsic mechanism. With the new pdf equation, the turbulent plane Couette flow is solved by the direct finite difference method coupled with dimensionality reduction and QUICKER scheme. A simple boundary treatment is proposed such that the near‐wall solution is tractable and then no refined grid is required. The calculated mean velocity, friction coefficient, and turbulence structure are in good agreement with available experimental data. In the region departed from the center of flow field, the contours of isojoint pdf of V₁ and V₂ is very similar to that of experimental result of channel flow. These agreements show the validity of the new pdf model and the availability of the boundary treatment and QUICKER scheme for solving the turbulent plane Couette flow.

The purpose of this paper is to propose an accurate model for simulation of inrush current in power transformers with taking into account the magnetic core structure and hysteresis phenomenon. Determination of the required model parameters and generalization of the obtained parameters to be used in different conditions with acceptable accuracy is the secondary purpose of this work.

The duality transformation is used to construct the transformer model based on its topology. The inverse Jiles-Atherton hysteresis model is used to represent the magnetic core behavior. Measured inrush waveforms of a laboratory test power transformer are used to calculate a fitness function which is defined by comparing the measured and simulated currents. This fitness function is minimized by particle swarm optimization algorithm which calculates the optimal model parameters.

An analytical and simple approach is proposed to generalize the obtained parameters from one inrush current measurement for simulation of this phenomenon in different situations. The measurement results verify the accuracy of the proposed method. The developed model with the determined parameters can be used for accurate simulation of inrush current transient in power transformers.

A general and flexible topology-based model is developed in PSCAD/EMTDC software to represent the transformer behavior in inrush situation. The hysteresis model parameters which are obtained from one inrush current waveform are generalized using the structure parameters, switching angle, and residual flux for accurate simulation of this phenomenon in different conditions.

The purpose of this paper is to model one of the unsolved problems of magnetism, the reversal of hysteresis loops, in an analytical way. The mathematical models, describing the multiphase steel used in engineering practice, without any exception, are unsuited to provide a way to reverse the hysteretic process. In this paper, a proposal is put forward to model it by using analytical expressions, applying the reversal of the Langevin function. This model works with a high accuracy, giving useful answers to a long unsolved magnetic problem, the lack of reversibility of the hysteresis loop. The use of the proposal is shown by applying the reversal of Langevin function to a sinusoidal and a triangular waveform, the two most frequently used waveforms in research, test and industrial applications. Schematic representations are given for the wave reconstruction by using the proposed method.

The unsolved reversibility of the hysteresis loop is approached by a simple analytical formula, providing close approximation for most applications.

The proposed solution, applying the reversal of Langevin function, to the problem provides a good practical solution.

The simple analytical formula has been applied to a number of loops of widely different shapes and sizes with excellent results.

The proposed solution provides a missing mathematical tool to an unsolved problem for practical applications.

The solution proposed will reduce the work required and provide replacement for expensive complex test instrumentation.

To the best of the authors’ knowledge, this approach used in this study is the first successful approach in this field, irrespective of the required waveform, and is completely independent of the model used by the user.

The Debye theory of dielectric relaxation as corrected for inertial effects has as yet been only considered in the linear approximation. There, the rise and decay transients are identical. Here a method recently developed for the treatment of a rotator in a periodic potential is applied to calculate the transient behaviour when the linear approximation is discarded. The Kramers equation for the problem is expanded in a set of orthogonal functions which lead to a set of linear differential difference equations giving the relaxation behaviour. It is shown that the Mori formalism for the problem leads to the same set of differential difference equations as the Kramers equation.

The purpose of the paper is to conduct a numerical and experimental investigation into the properties of nanofluids containing spherical nanoparticles of random sizes flowing through a porous medium. The study aims to understand how the thermophysical properties of the nanofluid are affected by factors such as nanoparticle volume fraction, permeability of the porous medium, and pore size. The paper provides insights into the behavior of nanofluids in complex environments and explores the impact of varying conditions on key properties such as thermal conductivity, density, viscosity, and specific heat. Ultimately, the research contributes to the broader understanding of nanofluid dynamics and has potential implications for engineering and industrial applications in porous media.

This paper investigates nanofluids with spherical nanoparticles in a porous medium, exploring thermal conductivity, density, specific heat, and dynamic viscosity. Studying three compositions, the analysis employs the classical Maxwell model and Koo and Kleinstreuer’s approach for thermal conductivity, considering particle shape and temperature effects. Density and specific heat are defined based on mass and volume ratios. Dynamic viscosity models, including Brinkman’s and Gherasim et al.'s, are discussed. Numerical simulations, implemented in Python using the Langevin model, yield results processed in Origin Pro. This research enhances understanding of nanofluid behavior, contributing valuable insights to porous media applications.

This study involves a numerical examination of nanofluid properties, featuring spherical nanoparticles of varying sizes suspended in a base fluid with known density, flowing through a porous medium. Experimental findings reveal a notable increase in thermal conductivity, density, and viscosity as the volume fraction of particles rises. Conversely, specific heat experiences a decrease with higher particle volume concentration.xD; xA; The influence of permeability and pore size on particle volume fraction variation is a key focus. Interestingly, while the permeability of the medium has a significant effect, it is observed that it increases with permeability. This underscores the role of the medium’s nature in altering the thermophysical properties of nanofluids.

This paper presents a novel numerical study on nanofluids with randomly sized spherical nanoparticles flowing in a porous medium. It explores the impact of porous medium properties on nanofluid thermophysical characteristics, emphasizing the significance of permeability and pore size. The inclusion of random nanoparticle sizes adds practical relevance. Contrasting trends are observed, where thermal conductivity, density, and viscosity increase with particle volume fraction, while specific heat decreases. These findings offer valuable insights for engineering applications, providing a deeper understanding of nanofluid behavior in porous environments and guiding the design of efficient systems in various industrial contexts.

Owing to the excellent performance, giant magnetostrictive materials (GMMs) are widely used in many engineering fields. The dynamic Jiles–Atherton (J-A) model, derived from physical mechanism, is often used to describe the hysteresis characteristics of GMM. However, this model, despite cited by many different literature studies, seems not to possess unique expressions, which may cause great trouble to the subsequent application. This paper aims to provide the rational expressions of the dynamic J-A model and propose a numerical computation scheme to obtain the model results with high accuracy and fast speed.

This paper analyzes different published papers and provides a reasonable form of the dynamic J-A model based on functional properties and physical explanations. Then, a numerical computation scheme, combining the Newton method and the explicit Adams method, is designed to solve the modified model. In addition, the error source and transmission path of the numerical solution are investigated, and the influence of model parameters on the calculation error is explored. Finally, some attempts are made to study the influence of numerical scheme parameters on the accuracy and time of the computation process. Subsequently, an optimization procedure is proposed.

A rational form of the dynamic J-A model is concluded in this paper. Using the proposed numerical calculation scheme, the maximum calculation error, while computing the modified model, can remain below 2 A/m under different model parameter combinations, and the computation time is always less than 0.5 s. After optimization, the calculation speed can be enhanced with the computation accuracy guaranteed.

To the best of the authors’ knowledge, this paper is the first one trying to provide a rational form of the dynamic J-A model among different citations. No other research studies focus on designing a detailed computation scheme targeting the fast and accurate calculation of this model as well. And the performance of the proposed calculation method is validated in different conditions.

The purpose of this paper is to introduce new non‐classical implementations of neural networks (NNs). The developed implementations are performed in the quantum, nano, and optical domains to perform the required neural computing. The various implementations of the new NNs utilizing the introduced architectures are presented, and their extensions for the utilization in the non‐classical neural‐systolic networks are also introduced.

The introduced neural circuits utilize recent findings in the quantum, nano, and optical fields to implement the functionality of the basic NN. This includes the techniques of many‐valued quantum computing (MVQC), carbon nanotubes (CNT), and linear optics. The extensions of implementations to non‐classical neural‐systolic networks using the introduced neural‐systolic architectures are also presented.

Novel NN implementations are introduced in this paper. NN implementation using the general scheme of MVQC is presented. The proposed method uses the many‐valued quantum orthonormal computational basis states to implement such computations. Physical implementation of quantum computing (QC) is performed by controlling the potential to yield specific wavefunction as a result of solving the Schrödinger equation that governs the dynamics in the quantum domain. The CNT‐based implementation of logic NNs is also introduced. New implementations of logic NNs are also introduced that utilize new linear optical circuits which use coherent light beams to perform the functionality of the basic logic multiplexer by utilizing the properties of frequency, polarization, and incident angle. The implementations of non‐classical neural‐systolic networks using the introduced quantum, nano, and optical neural architectures are also presented.

The introduced NN implementations form new important directions in the NN realizations using the newly emerging technologies. Since the new quantum and optical implementations have the advantages of very high‐speed and low‐power consumption, and the nano implementation exists in very compact space where CNT‐based field effect transistor switches reliably using much less power than a silicon‐based device, the introduced implementations for non‐classical neural computation are new and interesting for the design in future technologies that require the optimal design specifications of super‐high speed, minimum power consumption, and minimum size, such as in low‐power control of autonomous robots, adiabatic low‐power very‐large‐scale integration circuit design for signal processing applications, QC, and nanotechnology.