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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.

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.

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.

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.

We present a reservoir simulation framework for coupled thermal-compositional-mechanics processes. We use finite-volume methods to discretize the mass and energy conservation equations and finite-element methods for the mechanics problem. We use the first-order backward Euler for time. We solve the resulting set of nonlinear algebraic equations using fully implicit (FI) and sequential-implicit (SI) solution schemes. The FI approach is attractive for general-purpose simulation due to its unconditional stability. However, the FI method requires the development of a complex thermo-compositional-mechanics framework for the nonlinear problems of interest, and that includes the construction of the full Jacobian matrix for the coupled multi-physics discrete system of equations. On the other hand, SI-based solution schemes allow for relatively fast development because different simulation modules can be coupled more easily. The challenge with SI schemes is that the nonlinear convergence rate depends strongly on the coupling strength across the physical mechanisms and on the details of the sequential updating strategy across the different physics modules. The flexible automatic differentiation-based framework described here allows for detailed assessment of the robustness and computational efficiency of different coupling schemes for a wide range of multi-physics subsurface problems.

In this paper we aim to show continuous differentiability of weak solutions to a one-Laplace system perturbed by p -Laplacian with 1 < p < ∞ . The main difficulty on this equation is that uniform ellipticity breaks near a facet, the place where a gradient vanishes. We would like to prove that derivatives of weak solutions are continuous even across the facets. This is possible by estimating Hölder continuity of the Jacobian matrix multiplied with its modulus truncated near zero. To show this estimate, we consider an approximated system, and use standard methods including De Giorgi’s truncation and freezing coefficient arguments.