A new error correction method for the stationary Navier-Stokes equations based on two local Gauss integrations

summary:A new error correction method for the stationary Navier-Stokes equations based on two local Gauss integrations is presented. Applying the orthogonal projection technique, we introduce two local Gauss integrations as a stabilizing term in the error correction method, and derive a new error correction method. In both the coarse solution computation step and the error computation step, a locally stabilizing term based on two local Gauss integrations is introduced. The stability and convergence of the new error correction algorithm are established. Numerical examples are also presented to verify the theoretical analysis and demonstrate the efficiency of the proposed method

Blow up solutions to a viscoelastic fluid system and a coupled Navier-Stokes/Phase-Field system in R^2

We find explicit solutions to both the Oldroyd-B model with infinite Weissenberg number and the coupled Navier-Stokes/Phase-Field system. The solutions blow up in finite time.Comment: 5 page

Research and Application of Access Control Technique in 3D Virtual Reality System OpenSim

Access control in 3-D virtual reality systems is a wide and still growing topic. A good access control model is a premise for data security, and makes the whole system play its functions reliably. We compare access control techniques in 3D system OpenSim with that of other virtual reality systems. By using a general extended scheme, we analyze the model and the rule of access control in OpenSim. In this scheme, we provide a method of expanding network services for special proposes. Meanwhile, it verifies the feasibility of developing OpenSim's services on the basis of data security

Model-Free 3D Shape Control of Deformable Objects Using Novel Features Based on Modal Analysis

Shape control of deformable objects is a challenging and important robotic problem. This paper proposes a model-free controller using novel 3D global deformation features based on modal analysis. Unlike most existing controllers using geometric features, our controller employs a physically-based deformation feature by decoupling 3D global deformation into low-frequency mode shapes. Although modal analysis is widely adopted in computer vision and simulation, it has not been used in robotic deformation control. We develop a new model-free framework for modal-based deformation control under robot manipulation. Physical interpretation of mode shapes enables us to formulate an analytical deformation Jacobian matrix mapping the robot manipulation onto changes of the modal features. In the Jacobian matrix, unknown geometry and physical properties of the object are treated as low-dimensional modal parameters which can be used to linearly parameterize the closed-loop system. Thus, an adaptive controller with proven stability can be designed to deform the object while online estimating the modal parameters. Simulations and experiments are conducted using linear, planar, and solid objects under different settings. The results not only confirm the superior performance of our controller but also demonstrate its advantages over the baseline method.Comment: Accepted by the IEEE Transactions on Robotics. The paper will appear in the IEEE Transactions on Robotics. IEEE copyrigh

Thermodynamics of the Reissner-Nordstr\"om-de Sitter Spacetime with Quintessence

For Anti-de Sitte (AdS) black holes, the isochoric heat capacity of system is vanished, while the isobaric heat capacity is not. However, this situation does not hold on for de Sitter (dS) black holes. In this work, by introducing the interaction between the black hole horizon and the cosmological horizon of the Reissner-Nordstr\"om-de Sitter (RNdS) spacetime with quintessence, we discuss the phase transition of this system. The results show that the spacetime not only has the similar phase transition behavior to that of Van der Waals (VdW) system, and the non-vanishing isochoric heat capacity fulfills the whole thermodynamics system. Through the discussion of the entropic force between two horizons, we find out the role of entropic force in the evolution of spacetime. In addition, we also study the influence of various parameters on the phase transition and entropic force, which will provide a new method for exploring the interaction among black hole molecules from a micro perspective

AutoML-GPT: Large Language Model for AutoML

With the emerging trend of GPT models, we have established a framework called AutoML-GPT that integrates a comprehensive set of tools and libraries. This framework grants users access to a wide range of data preprocessing techniques, feature engineering methods, and model selection algorithms. Through a conversational interface, users can specify their requirements, constraints, and evaluation metrics. Throughout the process, AutoML-GPT employs advanced techniques for hyperparameter optimization and model selection, ensuring that the resulting model achieves optimal performance. The system effectively manages the complexity of the machine learning pipeline, guiding users towards the best choices without requiring deep domain knowledge. Through our experimental results on diverse datasets, we have demonstrated that AutoML-GPT significantly reduces the time and effort required for machine learning tasks. Its ability to leverage the vast knowledge encoded in large language models enables it to provide valuable insights, identify potential pitfalls, and suggest effective solutions to common challenges faced during model training