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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.

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.

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.

Autocatalytic chemical reaction networks can collectively replicate or maintain their constituents despite degradation reactions only above a certain threshold, which we refer to as the decay threshold. When the chemical network has a Jacobian matrix with the Metzler property, we leverage analytical methods developed for Markov processes to show that the decay threshold can be calculated by solving a linear problem, instead of the standard eigenvalue problem. We explore how this decay threshold depends on the network parameters, such as its size, the directionality of the reactions (reversible or irreversible), and its connectivity, then we deduce design principles from this that might be relevant to research on the Origin of Life.

Task-space control needs the inverse kinematics solution or Jacobian matrix for the transformation from task space to joint space. However, they are not always available for redundant robots because there are more joint degrees-of-freedom than Cartesian degrees-of-freedom. Intelligent learning methods, such as neural networks (NN) and reinforcement learning (RL) can learn the inverse kinematics solution. However, NN needs big data and classical RL is not suitable for multi-link robots controlled in task space. In this paper, we propose a fully cooperative multi-agent reinforcement learning (MARL) to solve the kinematic problem of redundant robots. Each joint of the robot is regarded as one agent. The fully cooperative MARL uses a kinematic learning to avoid function approximators and large learning space. The convergence property of the proposed MARL is analyzed. The experimental results show that our MARL is much more better compared with the classic methods such as Jacobian-based methods and neural networks.