Novel Method For Solution Research Articles

A Novel Method for Solution of Fractional Order Two-Dimensional Nonlocal Heat Conduction Phenomena

In this paper, we have extended the operational matrix method for approximating the solution of the fractional-order two-dimensional elliptic partial differential equations (FPDEs) under nonlocal boundary conditions. We use a general Legendre polynomials basis and construct some new operational matrices of fractional order operations. These matrices are used to convert a sample nonlocal heat conduction phenomenon of fractional order to a structure of easily solvable algebraic equations. The solution of the algebraic structure is then used to approximate a solution of the heat conduction phenomena. The proposed method is applied to some test problems. The obtained results are compared with the available data in the literature and are found in good agreement.Dedicated to my father Mr. Sher Mumtaz, (1955-2021), who gave me the basic knowledege of mathematics.

Natural-Gas-Derived Hydrogen in the Presence of Carbon Fuel Taxes and Concentrated Solar Power

This work focuses on the incorporation of renewable energy resources into the natural-gas-based production of hydrogen, via steam methane reforming (SMR). The novel concept of “energetically enhanced steam methane reforming” (EESMR) is introduced, which changes the endothermicity level of the SMR process through incorporation of carbon monoxide and steam into the SMR feed. Novel EESMR flow sheets are presented in which the aforementioned resources are internally generated and recycled, so as to create a natural-gas-based hydrogen production system with methane as raw material and a hybrid (methane/solar) energy supply. The current worldwide carbon tax legislative environment is briefly reviewed, and its potential impact on SMR-versus-EESMR economic viability is quantified. A novel method for solution of linear parametric programming problems is proposed based on the concept of dimensionality reduction—this allows the analytic quantification of the optimum objective function value and associated optimum va...

Multi‐verse optimisation: a novel method for solution of load frequency control problem in power system

In this article, a maiden attempt has been made to derive an optimal and effective outcome of load frequency control problem (LFC) using a novel evolutionary algorithm called multi-verse optimisation. The main inspiration of this algorithm is based on three concepts in cosmology: white hole, black hole, and wormhole. To show the effectiveness, a four-area hydrothermal power plant with distinct proportional-integral-derivative (PID) controller is investigated at the first instant and then the study is forwarded to the five-area thermal power plant. To enhance the dynamic stability, an optimal PID plus double-derivative controller (PID + DD) is designed and included in the control areas. The superiority of the proposed method has been established over some recently addressed control algorithms by transient analysis method. To add some degree of non-linearity, generation rate constraint and governor dead band are included in the model and their impacts on the system dynamics have been examined. Finally, a random load perturbation is given to the test systems to affirm the robustness of the designed controllers.

A Novel Method for Solution of the Division Operation on ARM7 Microcontroller

Before architecture V7, the hardware of ARM microcontroller family does not support division operation. Although it is easy to program on ARM processors with C language which can implement division operation with library functions, the procedure has much trouble and the efficiency is lower when the function code written in C language is called in assembly program. This paper introduces an algorithm for the division operation on ARM7 processor and also gives corresponding subroutines which can be used directly in assembly program design. The algorithm is similar to the operation theory of the digital circuit which uses subtraction circuit to do division operation. The given subroutines can deal with the division operation between two 32-bit unsigned integers and the division between a 64-bit unsigned integer and a 32-bit unsigned integer.

Novel method for solution of coupled radial Schrödinger equations

One of the major problems in numerical solution of coupled differential equations is the maintenance of linear independence for different sets of solution vectors. A novel method for solution of radial Schrodinger equations is suggested. It consists of rearrangement of coupled equations in a way that is appropriate to avoid usual numerical instabilities associated with components of the wave function in their classically forbidden regions. Applications of the new method for nuclear structure calculations within the hyperspherical harmonics approach are given. RAMOWITZ M, 1964

A novel method of solution for the fluid-loaded plate

We study the equations governing a fluid-loaded plate. We first reformulate these equations as a system of two equations, one of which is an explicit non-local equation for the wave height and the velocity potential on the free surface. We then concentrate on the linearized equations and show that the problems formulated either on the full or the half-line can be solved by employing the unified approach to boundary value problems introduced by one of the authors in the late 1990s. The problem on the full line was analysed by Crighton & Oswell (Crighton & Oswell 1991 Phil. Trans. R. Soc. Lond. A 335 , 557–592 (doi:10.1098/rsta.1991.0060)) using a combination of Laplace and Fourier transforms. The new approach avoids the technical difficulty of the a priori assumption that the amplitude of the plate is in L d t 1 ( R + ) and furthermore yields a simpler solution representation that immediately implies that the problem is well-posed. For the problem on the half-line, a similar analysis yields a solution representation, which, however, involves two unknown functions. The main difficulty with the half-line problem is the characterization of these two functions. By employing the so-called global relation, we show that the two functions can be obtained via the solution of a complex-valued integral equation of the convolution type. This equation can be solved in a closed form using the Laplace transform. By prescribing the initial data η 0 to be in H 〈5〉 5 ( R + ), or equivalently four times continuously differentiable with sufficient decay at infinity, we show that the solution depends continuously on the initial data, and, hence, the problem is well-posed.

A Solution for Lightly Loaded Adhesive Rough Surfaces With Application to MEMS

The stiction forces that exist in microelectromechanical systems (MEMS) are characterized by surface energy and surface roughness. To simulate this contact condition, a three-dimensional fractal surface geometry and an adhesive contact model for a single asperity are used together to create a numerical adhesive rough surface solution methodology. This novel method of solution determines the characteristic adhesive contact type for each individual asperity uniquely at the time of load and area integration. Such a simulation more accurately represents the physics of the asperity-based contact. Numerical results for the adherence force are presented as a function of surface topography, interface compliance, and the work of adhesion for a MEMS interface. The magnitude of the force required to separate an adhesive rough surface interface is given in relation to a polysilicon system.

LIMM: A technique for determination of the spatial distribution of the spontaneous polarization in ferroelectric thin films

The Laser Intensity Modulation Method (LIMM) is used to determine the spatial distribution of polarization in the direction of the polar axis of a ferroelectric sample. It is based upon measurement of the pyroelectric current generated by the material when it is heated with a laser beam which is intensity-modulated over a range of frequencies. A modification of this technique has been developed which will permit detailed profiling of the polarization distribution in a thin-film electroded ferroelectric layer on a substrate, such as a ferroelectric memory. The theory of the technique is discussed and it is shown that the determination of the polarization distributions requires the solution of a Fredholm integral equation of the 1st kind using experimental data. A novel method of solution of this problem using neural networks is described.

New Results for Directed Vesicles and Chains near an Attractive Wall

In this paper we present new exact results for single fully directed walks and fully directed vesicles near an attractive wall. This involves a novel method of solution for these types of problems. The major advantage of this method is that it, unlike many other single-walker methods, generalizes to an arbitrary number of walkers. The method of solution involves solving a set of partial difference equations with a Bethe Ansatz. The solution is expressed as a “constant-term” formula which evaluates to sums of products of binomial coefficients. The vesicle critical temperature is found at which a binding transition takes place, and the asymptotic forms of the associated partition functions are found to have three different entropic exponents depending on whether the temperature is above, below, or at its critical value. The expected number of monomers adsorbed onto the surface is found to become proportional to the vesicle length at temperatures below critical. Scaling functions near the critical point are determined.

SPORTS - A simple non-linear thermalhydraulic stability code

A simple code, called SPORTS ∗ ∗ SPORTS - Special Predictions Of Reactor Transients and Stability. , has been developed for two-phase stability studies. A novel method of solution of the finite difference equations was deviced and incorporated, and many of the approximations that are common in other stability codes are avoided. SPORTS is believed to be accurate and efficient, as small and large time-steps are permitted, and hence suitable for micro-computers.

A novel solution of a lateral connection problem

Weber's parabolic cylinder equation, ( d 2y dz 2 ) + [v + 1 2 − ( z 2 4 )] y = 0 , (∗) has as solutions the parabolic cylinder functions, D v(z) ~ z v exp(− z 2 4 ) , z → + ∞. (∗∗) The expansion (∗∗) is generally not valid for z → − ∞. This situation leads to the so-called “lateral connection problem” for (∗). A novel method of solution of this problem based on the Hadamard factorization theorem applied to the “lateral connection coefficient” is given. Unlike previous methods, explicit contour integrals for D v ( z) are not required.

Relativistic Non-linear Theory of Plasma Oscillations†

ABSTRACT Non-linear theory of plasma oscillations is extended into the threshold relativistic region where radiation damping can be neglected. A general characterization of the stationary oscillatory modes is performed in terms of a phase-space analysis with a comparison of the non-relativistic behaviour. Two procedures are offered for delineation of the amplitude-dependent frequency of the fundamental vibration. One of these is readily adopted to the zero-current limit, allowing a development already featured for the relativistic harmonic oscillator. Thus regimes requiring relativistic classical or quantum mechanical treatment are identified. In general, very high density plasmas require classical relativistic treatment, although tenuous astrophysical plasmas, where extremely large amplitudes of ion-electron motion can be accommodated, also may be included; the relativistic quantum analysis enters when the plasmon energy 𝒦ωp approaches the rest mass energy of the vibrating charge. A critique of recent disclosures on non-linear plasma oscillations is set forth and a novel method for solution of a related class of non-linear differential equations presented.

On the design of the transition region of axisymmetric, magnetically focused beam valves

Assumption of a particular magnetic-field variation in the transition region of an axially symmetric beam-type device (e.g., klystron, travelling-wave tube) leads to the solution of the equations of electron motion by means of an analogue computer. To illustrate this novel method of solution, beam envelopes are presented for Brillouin flow, periodic magnetic focusing, and space-charge-balanced flow. By matching the beam envelopes with those obtained from the theory of the Pierce gun, dimensions are obtained for an electron gun that produces the required beam.