The Movable lunar landing leg is a novel multi - closed parallel mechanism with sub-closed loop. Moreover, there are multiple passive and active joint variables in the mobile lunar landing legged mechanism (MLLLM), Due to the complex dynamic relationship between the passive joint variables and the active joint variables, it is difficult to derive the dynamic modeling of parallel mechanisms by the non-redundant parallel mechanism using the traditional Lagrangian formulation method. In order to solve this problem, the utilization of the virtual work principle makes the application of the Lagrangian formulation for parallel mechanisms possible and efficient. The MLLLM is divided into several serial open-loop sub-chains. Explicit dynamic equations of each sub-chain can be derived by using the Lagrangian formalism straightforwardly with respect to their own local generalized coordinates. Secondly, when transforming between different generalized coordinates, the dynamic equation is transformed into different coordinate subsystems by using the principle of virtual work, and the Jacobian matrix and Hessen matrix are introduced as constraints to ensure the explicit form of the dynamic equation, by combining the differential dynamics equations of each subsystem with the virtual work principle, the explicit dynamics model of the MLLLM under the active generalized coordinates is obtained. Finally, the position error of the end-effector caused by the active and passive joints of the parallel mechanism was evaluated. Compared with the previous methods, the inverse dynamic analysis formula presented in this paper is more concise, the calculation efficiency is higher, and the position error evaluation method is more accurate than the traditional method.

We present two different methods to estimate parameters within a partial differential equation model of cancer invasion. The model describes the spatio-temporal evolution of three variables—tumour cell density, extracellular matrix density and matrix degrading enzyme concentration—in a one-dimensional tissue domain. The first method is a likelihood-free approach associated with approximate Bayesian computation; the second is a two-stage gradient matching method based on smoothing the data with a generalized additive model (GAM) and matching gradients from the GAM to those from the model. Both methods performed well on simulated data. To increase realism, additionally we tested the gradient matching scheme with simulated measurement error and found that the ability to estimate some model parameters deteriorated rapidly as measurement error increased.

Erosion wear is a common failure form of slotted screen in service. In this paper, based on CFD software and sand production data of a gas field in the Tarim Basin, the particle velocity and shear force at the slot of the flow field in the sieve tube were studied to determine the maximum area of erosion; at the same time, the velocity, viscosity, particle size and concentration of sand-carrying fluid were analyzed by orthogonal test, and the regression model of multi-factor maximum erosion rate was established. ① Through the analysis of the four factors on the degree of dependent variables, the order of the primary and secondary factors are: sand-carrying liquid flow rate, particle concentration, fluid viscosity, particle diameter, the effect of fluid viscosity and particle diameter on erosion rate is relatively small; ② According to the analysis of variance and range, the combination scheme of minimum erosion generation is obtained, and the calculation model of the erosion rate of the slotted screen is established. In order to reduce the erosion and abrasion in the actual oil and gas production process, the reasonable flow control and precise sand control method design and precision selection can be adopted; it provides a design basis for sand control and long-term effects of production in high-yield gas field.

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