Explore the vast range of titles available.

This paper gives an update of the RTTOV (Radiative Transfer for TOVS) fast radiative transfer model, which is widely used in the satellite retrieval and data assimilation communities. RTTOV is a fast radiative transfer model for simulating top-of-atmosphere radiances from passive visible, infrared and microwave downward-viewing satellite radiometers. In addition to the forward model, it also optionally computes the tangent linear, adjoint and Jacobian matrix providing changes in radiances for profile variable perturbations assuming a linear relationship about a given atmospheric state. This makes it a useful tool for developing physical retrievals from satellite radiances, for direct radiance assimilation in NWP models, for simulating future instruments, and for training or teaching with a graphical user interface. An overview of the RTTOV model is given, highlighting the updates and increased capability of the latest versions, and it gives some examples of its current performance when compared with more accurate line-by-line radiative transfer models and a few selected observations. The improvement over the original version of the model released in 1999 is demonstrated.

Time-lapse electrical resistivity tomography (ERT) has been proved to be a useful method for monitoring subsurface changes. Four-dimensional (4D) inversion scheme is one of the most common inversion schemes used to obtain subsurface resistivity at different moments. However, it uses the cross-time term to regulate the models at neighbouring moments and still needs to be improved. Therefore, we proposed a full-gradient difference (FGD) inversion scheme based on the 4D inversion scheme. The numerical experiment shows that the FGD inversion scheme has good imaging and anti-noise capability, which can be used in ERT monitoring.

A conventional SEIR epidemic model is proposed, with the general nonlinear incidence rate. It is hypothesized that some recovered people may become infected again in this paper. Both the basic reproduction number and its critical effect on the system have been determined. We mainly used Jacobian matrices to discuss the local stability of the system and make use of geometric methods to research the system’s global stability. Eventually, we draw a brief conclusion.

With the expansion of the scale and complexity of the power system, traditional three-phase power flow calculation methods are facing dual challenges of computational efficiency and accuracy. Power flow calculation is a mathematical method for analyzing the power flow of an electrical system. And the Newton-Raphson (NR) method is an effective algorithm for solving nonlinear problems. However, updating the Jacobian matrix in the NR method can take a lot of time. Based on the asymmetry in three-phase power systems and the time-consuming nature of the NR method, an enhanced version of the NR method is proposed in this paper that improves the efficiency of power flow calculations by simplifying the Jacobian matrix and optimizing the iteration speed. Furthermore, in order to minimize the number of iterations in the NR method, it is proposed to use the PO method to determine the ideal iteration threshold.

In this paper, we studied some conservative problems, and constructed a low memory approach to its solution. By means of component-wise approximation approach, a diagonal update to the Jacobian matrix was derived. Numerical examples are given to illustrate the proposed scheme.

We introduce Sparse Matrix Preconditioner for Iterative Refinement and Inversion Toolkit (SPIRIT), a general-purpose sparse matrix solver with a novel preconditioner designed for the large, sparse, and ill-conditioned Jacobian systems that arise in r-process nucleosynthesis simulations. The preconditioner employs a dual-threshold filtering strategy applied before factorization, yielding highly sparse yet stable approximations. Coupled with the Krylov subspace solver biconjugate gradient-stabilized method, SPIRIT dramatically accelerates the matrix inversion step during reaction network evolution. In tests on 500 Jacobian matrices of dimension 7836 × 7836 generated in an r-process run, SPIRIT outperformed traditional incomplete LU preconditioners by several orders of magnitude in both runtime and residual accuracy. Benchmarks against Intel Math Kernel Library (Intel MKL) show that SPIRIT reduced matrix inversion costs from 68% to 16% of total runtime while maintaining agreement with MKL solutions to within 10−6 error. Final abundance distributions matched those from standard solvers across all astrophysical relevant nuclear species. SPIRIT also performed reliably for smaller test cases, including trivial and small networks, as well as X-ray burst scenarios (with minor deviations). We have integrated SPIRIT into the network code SkyNet, providing a fast, robust, and open-source alternative for high-performance simulations in nuclear astrophysics and other scientific applications requiring efficient solutions of large, sparse, and ill-conditioned linear systems.

The power flow variation of the distribution network has super fluctuation, which produces equivalent random disturbance, which affects the characterization of peak frequency of the current signal, resulting in low accuracy of power flow calculation results. Therefore, a random power flow calculation method of distribution network based on improved Newton Raphson algorithm is proposed. The current signal is reconstructed based on the wavelet threshold de-noising method. The peak frequency of current signal is used to classify the random power flow data of distribution network and eliminate the non power flow signal. Newton Raphson algorithm is improved by using Jacobian matrix, and the power flow model estimated by Newton Raphson algorithm is established to realize the random power flow calculation of distribution network. The test results show that the average relative error and standard deviation of power flow calculation results for different connected power nodes are low, which can provide more accurate data for power flow control.

The incremental harmonic balance (IHB) method is a semi-analytical and semi-numerical method widely applied to solve periodic responses of strongly nonlinear systems. However, it suffers from deficiencies in convergence and computational efficiency, particularly for systems with non-polynomial nonlinearities where time-consuming numerical integration is needed. The solution process of the IHB method is transformed into a nonlinear least squares optimization problem to elucidate the fundamental reasons for its convergence deficiencies in this work. An enhanced incremental harmonic balance (EIHB) method that incorporates the fast Fourier transform (FFT) to obtain the residuals of nonlinear algebraic equations, Broyden’s method to approximate the Jacobian matrix of these equations, and an improved Levenberg–Marquardt (L–M) method with adaptive search direction adjustment and restart steps to improve convergence is then proposed. The introduction of the FFT and Broyden’s method significantly reduces computation time and greatly simplifies the process of formula derivation and programming. The proposed improved L–M method enhances convergence by introducing a new negative gradient search direction beyond the Gauss-Newton search direction of the traditional IHB method and adjusting the step sizes adaptively. It can also utilize restart steps to reinitiate iterations and escape from local minima. The proposed EIHB method, which boosts both computational efficiency and convergence, is particularly suited for systems with non-polynomial nonlinearities, where the traditional IHB method is time-consuming and often fails to ensure convergence. The effectiveness of the EIHB method is demonstrated through three examples: a dielectric elastomer balloon with negative exponent nonlinearity, an inverted rod pendulum with trigonometric nonlinearity, and a non-smooth gear transmission system with piecewise linear functions. Comparative results with those from the fourth-order Runge–Kutta method, the traditional IHB method, and a modified IHB method combining the FFT and Broyden’s method indicate that the EIHB method significantly improves convergence and computational efficiency while maintaining the same accuracy as the traditional IHB method.

This study presents the kinematic and dynamic modeling of an individual leg in a hexapod robot, along with simulation analysis. First, a kinematic model for the single leg is constructed based on the Denavit-Hartenberg (D-H) notation. The forward kinematic solution is derived, and the Jacobian matrix is employed to analyze the relationship between foot tip velocity and joint angular velocity. Subsequently, a dynamic model for the single leg is developed using the Lagrange method, and the torques at the hip and knee joints are calculated. Simulations are executed with the purpose of validate the correctness of the kinematic model and analyze the trends in foot tip velocity and joint torque. These results serve as a theoretical underpinning for improving the robot’s design and control techniques.

A new attempt of employing salp swarm algorithm (SSA) to tackle the optimal power flow (OPF) problem is demonstrated in the current study. This aforementioned problem has four fitness functions to be optimized such as (1) the sum of generating units’ fuel costs, (2) total network real power losses, (3) entire sum of voltage deviation of load buses, and (4) static voltage stability (VS) of electric power systems. At initial stage, these objective are solved one by one, and at a later stage, different vector objective functions are solved simultaneously by the SSA. The VS study based on a modal analysis is taken into consideration as an objective function. In this issue, the eigenvalues and eigenvectors of a reduced Jacobian matrix due to the reactive power change are figured. The smaller magnitude of eigenvalues indicates the vicinity to system voltage instability. As the magnitude of eigenvalues increases, the incremental voltage decreases, which means strong VS. The output active power of generating units, their voltages, transformers tap setting, and capacitor devices represent the search field. Two electric grids such as IEEE 57- and 118-bus electric networks are demonstrated to examine the performance of the SSA. The effectiveness of the SSA–OPF methodology is compared with that obtained by using other competing optimization methods. Furthermore, statistical performance measures comprising parametric and nonparametric tests are made and the simulation results are extensively verified which indicate a competition of the SSA with others algorithms in solving the OPF problem.