Four field coupled dynamics for a micro resonant gas sensor

In a micro resonant gas sensor, the electrostatic excitation is used widely. For a micro resonant gas sensor with electrostatic excitation, four physical fields are involved. In this paper, for the micro resonant gas sensor, the four-field coupled dynamics equation is proposed. It includes mechanical force field, chemical density field, electrostatic force field, and the van der Waals force field. Using the method of multiple scales, the coupled dynamics equation is resolved. The effects of the four physical fields on the natural frequencies for the micro resonant gas sensor are investigated. Results show that the effects of the Van der Waals force on the natural frequencies of the micro resonant gas sensor depend on the mechanical parameters and the bias voltages; the sensitivity of the natural frequencies to the gas adsorption depends on the mechanical parameters, the bias voltages, and the Van der Waals force

Taylor-Hood like finite elements for nearly incompressible strain gradient elasticity problems

We propose a family of mixed finite elements that are robust for the nearly incompressible strain gradient model, which is a fourth-order singular perturbed elliptic system. The element is similar to [C. Taylor and P. Hood, Comput. & Fluids, 1(1973), 73-100] in the Stokes flow. Using a uniform discrete B-B inequality for the mixed finite element pairs, we show the optimal rate of convergence that is robust in the incompressible limit. By a new regularity result that is uniform in both the materials parameter and the incompressibility, we prove the method converges with $1/2$ order to the solution with strong boundary layer effects. Moreover, we estimate the convergence rate of the numerical solution to the unperturbed second-order elliptic system. Numerical results for both smooth solutions and the solutions with sharp layers confirm the theoretical prediction.Comment: 27 pages, 1 figures, 4 table

Improved fracture toughness by microalloying of Fe in Ti-6Al-4V

The widely used Ti–6Al–4V (TC4) titanium alloy has been modified through the micro-alloying of Fe. The microstructural features and mechanical properties of the designed alloy, TC4F, are compared with other alloys in Ti–6Al–4V class by combining experimental characterizations and thermodynamic calculations. TC4F alloy not only maintains strength, hardness, and elongation similar to baseline TC4 but also exhibits improved fracture toughness comparable to TC4_ELI and even superior to TC4_DT under the heat-treated condition. It opens up a new cost-reducing way to enhance fracture toughness in place of controlling interstitial contents, showing potential in engineering applications. The discerned mechanisms indicate that the trace addition of Fe gives rise to composition redistribution between V and Fe in the ß phase, boosts the lattice distortion and vibration, thereafter enhances Young''s modulus and fracture toughness. It has been validated and verified by experiments, thermodynamic calculations, and Hahn-Rosenfield empirical research. The enhanced fracture toughness also benefits from the kinked ß+a lamellar microstructure at crack tip as well as the improved fracture surface due to the Fe addition. The enlarged plastic zone, redirected crack propagation, and more dimples with even-distributed size additionally contribute to the improvement of fracture toughness

Four field coupled dynamics for a micro resonant gas sensor

In a micro resonant gas sensor, the electrostatic excitation is used widely. For a micro resonant gas sensor with electrostatic excitation, four physical fields are involved. In this paper, for the micro resonant gas sensor, the four-field coupled dynamics equation is proposed. It includes mechanical force field, chemical density field, electrostatic force field, and the van der Waals force field. Using the method of multiple scales, the coupled dynamics equation is resolved. The effects of the four physical fields on the natural frequencies for the micro resonant gas sensor are investigated. Results show that the effects of the Van der Waals force on the natural frequencies of the micro resonant gas sensor depend on the mechanical parameters and the bias voltages; the sensitivity of the natural frequencies to the gas adsorption depends on the mechanical parameters, the bias voltages, and the Van der Waals force

Four field coupled dynamics for a micro resonant gas sensor

In a micro resonant gas sensor, the electrostatic excitation is used widely. For a micro resonant gas sensor with electrostatic excitation, four physical fields are involved. In this paper, for the micro resonant gas sensor, the four-field coupled dynamics equation is proposed. It includes mechanical force field, chemical density field, electrostatic force field, and the van der Waals force field. Using the method of multiple scales, the coupled dynamics equation is resolved. The effects of the four physical fields on the natural frequencies for the micro resonant gas sensor are investigated. Results show that the effects of the Van der Waals force on the natural frequencies of the micro resonant gas sensor depend on the mechanical parameters and the bias voltages; the sensitivity of the natural frequencies to the gas adsorption depends on the mechanical parameters, the bias voltages, and the Van der Waals force

Towards Robust Text Retrieval with Progressive Learning

Retrieval augmentation has become an effective solution to empower large language models (LLMs) with external and verified knowledge sources from the database, which overcomes the limitations and hallucinations of LLMs in handling up-to-date and domain-specific information. However, existing embedding models for text retrieval usually have three non-negligible limitations. First, the number and diversity of samples in a batch are too restricted to supervise the modeling of textual nuances at scale. Second, the high proportional noise are detrimental to the semantic correctness and consistency of embeddings. Third, the equal treatment to easy and difficult samples would cause sub-optimum convergence of embeddings with poorer generalization. In this paper, we propose the PEG, a progressively learned embeddings for robust text retrieval. Specifically, we increase the training in-batch negative samples to 80,000, and for each query, we extracted five hard negatives. Concurrently, we incorporated a progressive learning mechanism, enabling the model to dynamically modulate its attention to the samples throughout the entire training process. Additionally, PEG is trained on more than 100 million data, encompassing a wide range of domains (e.g., finance, medicine, and tourism) and covering various tasks (e.g., question-answering, machine reading comprehension, and similarity matching). Extensive experiments conducted on C-MTEB and DuReader demonstrate that PEG surpasses state-of-the-art embeddings in retrieving true positives, highlighting its significant potential for applications in LLMs. Our model is publicly available at https://huggingface.co/TownsWu/PEG