Residual Power Research Articles

Soil moisture retrieval over crop fields based on two-component polarimetric decomposition: a comparison of generalized volume scattering models

Model-based polarimetric decomposition can separate to some extent the backscattered radar signals from the vegetation canopy and the underlying ground, hence enabling a strategy for soil moisture retrieval in vegetated agricultural fields. However, the volume scattering models used in previous studies are only applicable to specific cases, making it difficult to completely remove the volume component induced by the vegetation layer. In this paper, three generalized volume scattering models (i.e., generalized volume scattering model (GVSM), simplified adaptive volume scattering model (SAVSM), and simplified Neumann volume scattering model (SNVSM)) are incorporated in the decomposition and evaluated for soil moisture retrieval. Considering the complexity and descriptive ability of the available physical models, a modified two-component model-based decomposition is proposed as the basic decomposition framework. This decomposition is also based on the physical constraint of the dielectric constants included in the model. The employed models combine an X-Bragg surface scattering model with three continuous generalized volume scattering models. The analytic solution of the parameters is obtained, and the minimum residual power criterion is used to determine the optimal solution to fit the model. By using the proposed model-based decomposition framework, the performance of the three models to simulate the canopy scattering and, as a result, to later estimate soil moisture under agricultural vegetation is evaluated. Fully polarimetric RADARSAT-2 C-band images acquired on eight dates in 2013 and 2015 over fields covered by two crops (wheat and soybean) were employed for validation. Results show that the proposed decomposition method, using any of the three volume scattering models, can provide promising inversion results of soil moisture, with RMSEs ranging from 2.89 to 7.43 [vol.%]. Compared with the other two models, the SNVSM simulates the vegetation contribution more accurately in this framework, and it provides a stable soil moisture inversion performance at different crop phenological stages, with an optimal overall accuracy of RMSE = 4.99 [vol.%] and a correlation coefficient of R = 0.78.

Space time fractional Ito system with variable coefficients: explicit solution, conservation laws and numerical approximation

PurposeThe purpose of this paper is to present the residual power series method for solving the space time fractional variable coefficients Ito system.Design/methodology/approachA weighted algorithm based on the residual power series method is used numerical solution of the space time fractional Ito system variable coefficients. The authors show that this technique yields the analytical solution of the desired problem in the form of a rapidly convergent series with easily computable components.FindingsThe authors illustrate that the proposed method produces satisfactory results with respect to the other semi analytical methods. The reliability of the method and the reduction in the size of computational domain give this method a wider applicability.Originality/valueThis research presents, for the first time, a new modification of the proposed technique for aforementioned problems and some interesting results are obtained.

New optimum solutions of nonlinear fractional acoustic wave equations via optimal homotopy asymptotic method-2 (OHAM-2)

The second iteration of the optimal homotopy asymptotic technique (OHAM-2) has been protracted to fractional order partial differential equations in this work for the first time (FPDEs). Without any transformation, the suggested approach can be used to solve fractional-order nonlinear Zakharov–Kuznetsov equations. The Caputo notion of the fractional-order derivative, whose values fall within the closed interval [0, 1], has been taken into consideration. The method's appeal is that it provides an approximate solution after just one iteration. The suggested method's numerical findings have been contrasted with those of the variational iteration method, residual power series method, and perturbation iteration method. Through tables and graphs, the proposed method's effectiveness and dependability are demonstrated.

A Novel Analytical LRPSM for Solving Nonlinear Systems of FPDEs

This article employs the Laplace residual power series approach to study nonlinear systems of time-fractional partial differential equations with time-fractional Caputo derivative. The proposed technique is based on a new fractional expansion of the Maclurian series, which provides a rapid convergence series solution where the coefficients of the proposed fractional expansion are computed with the limit concept. The nonlinear systems studied in this work are the Broer-Kaup system, the Burgers’ system of two variables, and the Burgers’ system of three variables, which are used in modeling various nonlinear physical applications such as shock waves, processes of the wave, transportation of vorticity, dispersion in porous media, and hydrodynamic turbulence. The results obtained are reliable, efficient, and accurate with minimal computations. The proposed technique is analyzed by applying it to three attractive problems where the approximate analytical solutions are formulated in rapid convergent fractional Maclurian formulas. The results are studied numerically and graphically to show the performance and validity of the technique, as well as the fractional order impact on the behavior of the solutions. Moreover, numerical comparisons are made with other well-known methods, proving that the results obtained in the proposed technique are much better and the most accurate. Finally, the obtained outcomes and simulation data show that the present method provides a sound methodology and suitable tool for solving such nonlinear systems of time-fractional partial differential equations.

Applying the natural transform iterative technique for fractional high-dimension equations of acoustic waves

In the present study, the natural transform iterative method (NTIM) has been implemented for the solution of a fractional Zakharavo–Kuznetsov (FZK) equation. NTIM is a relatively new technique for handling non-linear fractional differential equations. The method is tested upon the two non-linear FZK equalities. The solution of the proposed technique has been compared with the existing perturbation–iteration algorithm (PIA) method and residual power series method (RPSM). From the numerical results, it is clear that the method handles non-linear differential equations very suitably and provides the results in very closed accord with the accurate solution. As a result, the NTIM approach is regarded as one of the finest analytical techniques for solving fractional-order linear and non-linear problems.

A copula-based assessment of renewable energy droughts across Europe

Meeting carbon-reduction targets will require thorough consideration of climate variability and climate change due to the increasing share of climate-sensitive renewable energy sources (RES). One of the main concerns arises from situations of low renewable production and high demand, which can hinder the power system. We analysed energy droughts, defined as periods of low energy production (wind plus solar generation) or high residual load (demand minus production), in terms of two main properties: duration and severity. We estimated the joint return periods associated with energy droughts of residual load and power production. We showed that moderate winter energy droughts of both low renewable production and high residual load occur every half a year, while summer events occur every 3.6 and 2.4 years (on average). As expected, the occurrence of energy droughts tends to decrease with the degree of the severity of the energy drought, and moderate and extreme energy droughts showed longer return periods for most countries. In general, we found a large variability across Europe in summer, with some countries (e.g. Italy) being more sensitive to energy droughts. Our results highlight the relevance of sharing RES during prolonged periods of low production and high demand.

A matching game framework for users clustering and resource allocation with wireless power transfer in a CR‐NOMA network

SummaryThis paper investigates the resource allocation in a massively deployed user cognitive radio enabled non‐orthogonal multiple access (CR‐NOMA) network considering the downlink scenario. The system performance deteriorates with the number of users who are experiencing similar channel characteristics from the base station (BS) in NOMA. To address this challenge, we propose a framework for maximizing the system throughput that is based on one‐to‐one matching game theory integrated with the machine learning technique. The proposed approach is decomposed to solve users clustering and power allocation subproblems. The selection of optimal cluster heads (CHs) and their associated cluster members is based on Gale‐Shapley matching game theoretical model with the application of Hungarian method. The CHs can harvest energy from the BS and transfer their surplus power to the primary user (PU) through wireless power transfer. In return, they are allowed to access the licensed band for secondary transmission. The power allocation to the users intended for power conservation at CHs is formulated as a probabilistic constraint, which is then solved by employing the support vector machine (SVM) algorithm. The simulation results demonstrate the efficacy of our proposed schemes that enable the CHs to transfer the residual power while ensuring maximum system throughput. The effects of different parameters on the performance are also studied.

Analytical Solutions of the Nonlinear Time-Fractional Coupled Boussinesq-Burger Equations Using Laplace Residual Power Series Technique

In this paper, we present the series solutions of the nonlinear time-fractional coupled Boussinesq-Burger equations (T-FCB-BEs) using Laplace-residual power series (L-RPS) technique in the sense of Caputo fractional derivative (C-FD). To assert the efficiency, simplicity, performance, and reliability of our proposed method, an attractive and interesting numerical example is tested analytically and graphically. In addition, our obtained results show that this algorithm is compatible and accurate for investigating the fractional-order solutions of engineering and physical applications. Finally, Mathematica software 14 is applied to compute the numerical and graphical results.

Analysis of a Fractional-Order COVID-19 Epidemic Model with Lockdown.

The outbreak of the coronavirus disease (COVID-19) has caused a lot of disruptions around the world. In an attempt to control the spread of the disease among the population, several measures such as lockdown, and mask mandates, amongst others, were implemented by many governments in their countries. To understand the effectiveness of these measures in controlling the disease, several mathematical models have been proposed in the literature. In this paper, we study a mathematical model of the coronavirus disease with lockdown by employing the Caputo fractional-order derivative. We establish the existence and uniqueness of the solution to the model. We also study the local and global stability of the disease-free equilibrium and endemic equilibrium solutions. By using the residual power series method, we obtain a fractional power series approximation of the analytic solution. Finally, to show the accuracy of the theoretical results, we provide some numerical and graphical results.

Contract-based scheme for computational resource allocation in cloud-assisted parked vehicular edge computing

Having shown promising performance with high flexibility and efficiency in vehicular edge computing (VEC) network, the parked vehicles (PVs) received an increasing number of attentions in recent years. However, PVs’ residual battery power restricts their running time. In addition, there is still no alternate resource pool for the PVs to cope with the emergencies in the previous VEC framework. To alleviate these problems, we model a cloud-assisted parked vehicular edge computing (PVEC) framework, in which the PVs are classified based on their residual battery power. PVs corporate with the cloud servers (CSs) for the computational resources provision. In addition, we formulate the utilities of the service provider (SP) and PVs and design a contract-based resource allocation problem for the maximization of the SP’s utility. Considering that it is intractable to solve the optimization problem directly, the primal problem is simplified and decoupled into two sub-problems. To design the optimal contracts, we solve the sub-problems by Lagrangian multiplier method and dual function. Simulation results prove that the utilities of PVs can reach to the maximum when they choose the contract corresponding to their types. In addition, the simulation results illustrate the superiority of proposed scheme over previous schemes in improving the utilities of the SP and social welfare.

A novel hybrid technique to obtain the solution of generalized fractional-order differential equations

The motive of the work is to propose a new hybrid technique, the Homotopy Perturbation General Transform Method (HPGTM) for obtaining an analytic solution for a wide class of time-fractional differential equations in the Caputo sense. The efficiency of HPGTM is analyzed using a comparative study with Adomian Decomposition Method (ADM), Residual Power Series Method (RPSM), and exact solution. Numerical examples including well-known equations viz. radioactive decay model, Riccati equation, backward Kolmogorov equation, Klein–Gordon equation, and Rosenau–Hyman equation are considered in arbitrary order. The outcomes of numerical simulations clearly state the effectiveness of the present method.

Analysis of thin film flows of Pseudo-Plastic and Oldroyd 6-constant fluids using modified residual power series algorithm

This manuscript presents the detailed analysis of thin film flows of two non-Newtonian fluid models by proposing a new modification of residual power series method (RPSM). The numerical algorithm is extended to boundary value problems (BVPs) in the current scenario. Major advantage of RPSM is its direct usage with discretization, linearization or perturbation. Convergence analysis of the proposed algorithm is also performed for the implication of RPSM to thin film phenomena. The governing equations of Pseudo-Plastic and Oldroyd 6-constant fluids leads to highly nonlinear ordinary differential equations (ODEs) in lifting and drainage cases. Due to highly nonlinear nature of the modeled problems, exact solutions do not exist. As a result, validity of the obtained solutions is confirmed by computing residuals in each case. Furthermore, detailed graphical analysis is performed to check the effects of different fluid parameters on the velocity profile in lifting and drainage situations. It is observed that magnetic parameter and non-Newtonian parameter have similar, while stokes number has opposite effects on the velocity in lifting and drainage of thin film of Pseudo-Plastic fluid. On the other hand, in case of Oldroyd 6-Constant fluid, gravitational parameter and involved material constants are showing opposite behavior on the velocity profile in lifting and drainage. Analysis of the numerical solutions and errors reveals that proposed modification ensure reliable solutions and hence may be used for more advanced problems in science and engineering.

A new analytical method to simulate the mutual impact of space-time memory indices embedded in (1 + 2)-physical models

Abstract In the present article, we geometrically and analytically examine the mutual impact of space-time Caputo derivatives embedded in (1 + 2)-physical models. This has been accomplished by integrating the residual power series method (RPSM) with a new trivariate fractional power series representation that encompasses spatial and temporal Caputo derivative parameters. Theoretically, some results regarding the convergence and the error for the proposed adaptation have been established by virtue of the Riemann–Liouville fractional integral. Practically, the embedding of Schrödinger, telegraph, and Burgers’ equations into higher fractional space has been considered, and their solutions furnished by means of a rapidly convergent series that has ultimately a closed-form fractional function. The graphical analysis of the obtained solutions has shown that the solutions possess a homotopy mapping characteristic, in a topological sense, to reach the integer case solution where the Caputo derivative parameters behave similarly to the homotopy parameters. Altogether, the proposed technique exhibits a high accuracy and high rate of convergence.

Numerical and Analytical Simulations of Nonlinear Time Fractional Advection and Burger’s Equations

In this paper, the higher nonlinear problems of fractional advection-diffusion equations and systems of nonlinear fractional Burger’s equations are solved by using two sophisticated procedures, namely, the q-homotopy analysis transform method and the residual power series method. The proposed methods are implemented with the Caputo operator. The present techniques are utilised in a very comprehensive and effective manner to obtain the solutions to the suggested fractional-order problems. The nonlinearity of the problem was controlled tactfully. The numerical results of a few examples are calculated and analyzed. The tables and graphs are constructed to understand the higher accuracy and applicability of the current method. The obtained results that are in good contact with the actual dynamics of the given problem, which is verified by the graphs and tables. The present techniques require fewer calculations and are associated with a higher degree of accuracy, and therefore can be extended to solve other high nonlinear fractional problems.

The CARMENES search for exoplanets around M dwarfs

Context. A challenge with radial-velocity (RV) data is disentangling the origin of signals either due to a planetary companion or to stellar activity. In fact, the existence of a planetary companion has been proposed, as well as contested, around the relatively bright, nearby M3.0 V star AD Leo at the same period as the stellar rotation of 2.23 days. Aims. We further investigate the nature of this signal. We introduce new CARMENES optical and near-IR RV data and an analysis in combination with archival data taken by HIRES and HARPS, along with more recent data from HARPS-N, GIANO-B, and HPF. Additionally, we address the confusion concerning the binarity of AD Leo. Methods. We consider possible correlations between the RVs and various stellar activity indicators accessible with CARMENES. We additionally applied models within a Bayesian framework to determine whether a Keplerian model, a red-noise quasi-periodic model using a Gaussian process, or a mixed model would explain the observed data best. We also exclusively focus on spectral lines potentially associated with stellar activity. Results. The CARMENES RV data agree with the previously reported periodicity of 2.23 days, correlate with some activity indicators, and exhibit chromaticity. However, when considering the entire RV data set, we find that a mixed model composed of a stable and a variable component performs best. Moreover, when recomputing the RVs using only spectral lines insensitive to activity, there appears to be some residual power at the period of interest. We therefore conclude that it is not possible to determinedly prove that there is no planet orbiting in synchronization with the stellar rotation given our data, current tools, machinery, and knowledge of how stellar activity affects RVs. We do rule out planets more massive than 27 M⊕ (=0.084 MJup). Likewise, we exclude any binary companion around AD Leo with M sin i greater than 3–6 MJup on orbital periods <14 yr.

Research on the active cancellation technology of spectrum symbiotic interference

In this article, an active spectrum symbiotic interference (SSI) cancellation architecture is proposed for the spectrum symbiotic wireless communication systems. To minimize the residual reception power, a joint SSI cancellation algorithm based on time -amplitude -phase-three-dimensional search is proposed, which actively utilizes the characteristics of transmitted signals in the spectrum symbiotic wireless communication systems to adjust, reconstruct, and cancel the SSI from the aspects of time, amplitude, and phase. Theoretical and simulation analyses demonstrate that the proposed architecture and algorithm can suppress the SSI to the noise level, exhibiting lower space and time complexity.

Forecasting the behavior of fractional order Bloch equations appearing in NMR flow via a hybrid computational technique

In this paper, we present an efficient computational approach named as Sumudu residual power series method (SRPSM) to solve fractional Bloch equations appearing in an NMR flow. This method is a copulation of the residual power series method (RPSM) and the Sumudu transform to construct approximate solution in shapes of sharp convergent series by adopting the notion of limit with a view of smooth calculations and time saving strategy as compared to the classical RPSM in which computations of fractional derivatives are required. This work also verifies and compares the solution obtained by the proposed technique with the classical RPSM. To assure the applicability, performance, and reliability of the introduced method, a system of fractional Bloch equations are examined along with numerical simulations. The aspect of application supported with computer simulations demonstrates that the suggested approach is precise, and appropriate to explore the solutions of linear & nonlinear initial value problems with fractional-order derivatives.

Solutions of Time Fractional fKdV Equation Using the Residual Power Series Method

The fifth-order Korteweg-de Vries (fKdV) equation is a nonlinear model in various long wave physical phenomena. The residual power series method (RPSM) is used to gain the approximate solutions of the time fractional fKdV equation in this study. Basic definitions of fractional derivatives are described in the Caputo sense. The solutions of the time fractional fKdV equation with easily computable components are calculated as a quick convergent series. When compared to exact solutions, the RPSM provides good accuracy for approximate solutions. The reliability of the proposed method is also illustrated with the aid of table and graphs. Cleary observed from the results that the suggested method is suitable and simple for similar type of the time fractional nonlinear differential equations.

Deploying mobile cluster heads in wireless sensor network using heuristic protocol

Exploiting mobile base stations in wireless sensor network increases longevity as it is very effective in dealing with the power hole problem. Mobile sinks are elements used to collect data from network sensors nodes. The movement of the sink eventually changes the sensors of a single hop which will prevent the formation of the hotspot thereby improving the life of the network to a critical level. In this paper we propose the Greedy Heuristic Protocol for Data Collection called GHPDC which selfishly selects energy-rich sites for a mobile channel. Apart from this the paper also proposes the formation of Linear Programming which enhances the station duration which will have a direct impact on prolonging the life of the network. The design of the system line takes into account the residual power of the sensor nodes to determine the amount of time for the base station to halt.

Semi-analytic solution of time-fractional Korteweg-de Vries equation using fractional residual power series method

In this paper, we have solved the non-linear Korteweg-de Vries equation by considering it in time-fraction Caputo sense and offered intrinsic properties of solitary waves. The fractional residual power series method is used to obtain the approximate solution of the aforesaid equation and compared the obtained results with Adomian Decomposition Method. Obtained results are efficient, reliable, and simple to execute on most of the non-linear fractional partial differential equations, which arise in various dynamical systems.