Recent development in kinetic theory of granular materials: analysis and numerical methods

33 pagesOver the past decades, kinetic description of granular materials has received a lot of attention in mathematical community and applied fields such as physics and engineering. This article aims to review recent mathematical results in kinetic granular materials, especially for those which arose since the last review by Villani on the same subject. We will discuss both theoretical and numerical developments. We will finally showcase some important open problems and conjectures by means of numerical experiments based on spectral methods

The effects of supercritical CO2 on the seepage characteristics and microstructure of water-bearing bituminous coal at in-situ stress conditions

CO2 geological storage (CGS) is considered to be an important technology for achieving carbon peak and carbon neutralization goals. Injecting CO2 into deep unminable coal seams can achieve both CGS and enhance coalbed methane (ECBM) production. Therefore, the deep unminable coal seams are considered as promising geological reservoirs. CO2 exists in a supercritical CO2 (ScCO2) when it was injected into deep unminable coal seams. The injection of ScCO2 can induce changes in the seepage characteristics and microstructure of deep water-bearing coal seams. In this study, typical bituminous coal from Shenmu, Shanxi Province was used to investigate the effects of ScCO2 on seepage characteristics, pore characteristics, and mineral composition through experiments such as seepage tests, low-temperature liquid nitrogen adsorption, and X-ray diffraction (XRD). The results indicate that ScCO2 treatment of dry and saturated coal samples caused a significant increase in clay mineral content due to the dissolution of carbonates, leading to the conversion of adsorption pores to seepage pores and an improvement in seepage pore connectivity. Therefore, the Brunauer-Emmett-Teller (BET) specific surface area and pore volume of the two coal samples both decreased after ScCO2 treatment. Moreover, the permeability of dry and saturated coal samples increased by 191.53% and 231.71% at 10 MPa effective stress respectively. In semi-saturated coal samples, a large amount of dolomite dissolved, leading to the precipitation of Ca2+ and CO32- to form calcite. This caused pore throats to clog and macropores to divide. The results show that the pore volume and average pore size of coal samples decrease, while the specific surface area increases after ScCO2 treatment, providing more space for gas adsorption. However, the pore changes also reduced the permeability of the coal samples by 32.21% and 7.72% at effective stresses of 3 MPa and 10 MPa, respectively. The results enhance our understanding of carbon sequestration through ScCO2 injection into water-bearing bituminous coal seams

Optical flow-based vascular respiratory motion compensation

This paper develops a new vascular respiratory motion compensation algorithm, Motion-Related Compensation (MRC), to conduct vascular respiratory motion compensation by extrapolating the correlation between invisible vascular and visible non-vascular. Robot-assisted vascular intervention can significantly reduce the radiation exposure of surgeons. In robot-assisted image-guided intervention, blood vessels are constantly moving/deforming due to respiration, and they are invisible in the X-ray images unless contrast agents are injected. The vascular respiratory motion compensation technique predicts 2D vascular roadmaps in live X-ray images. When blood vessels are visible after contrast agents injection, vascular respiratory motion compensation is conducted based on the sparse Lucas-Kanade feature tracker. An MRC model is trained to learn the correlation between vascular and non-vascular motions. During the intervention, the invisible blood vessels are predicted with visible tissues and the trained MRC model. Moreover, a Gaussian-based outlier filter is adopted for refinement. Experiments on in-vivo data sets show that the proposed method can yield vascular respiratory motion compensation in 0.032 sec, with an average error 1.086 mm. Our real-time and accurate vascular respiratory motion compensation approach contributes to modern vascular intervention and surgical robots.Comment: This manuscript has been accepted by IEEE Robotics and Automation Letter

Iterative PnP and its application in 3D-2D vascular image registration for robot navigation

This paper reports on a new real-time robot-centered 3D-2D vascular image alignment algorithm, which is robust to outliers and can align nonrigid shapes. Few works have managed to achieve both real-time and accurate performance for vascular intervention robots. This work bridges high-accuracy 3D-2D registration techniques and computational efficiency requirements in intervention robot applications. We categorize centerline-based vascular 3D-2D image registration problems as an iterative Perspective-n-Point (PnP) problem and propose to use the Levenberg-Marquardt solver on the Lie manifold. Then, the recently developed Reproducing Kernel Hilbert Space (RKHS) algorithm is introduced to overcome the ``big-to-small'' problem in typical robotic scenarios. Finally, an iterative reweighted least squares is applied to solve RKHS-based formulation efficiently. Experiments indicate that the proposed algorithm processes registration over 50 Hz (rigid) and 20 Hz (nonrigid) and obtains competing registration accuracy similar to other works. Results indicate that our Iterative PnP is suitable for future vascular intervention robot applications.Comment: Submitted to ICRA 202

Generating Giant and Tunable Nonlinearity in a Macroscopic Mechanical Resonator from Chemical Bonding Force

Nonlinearity in macroscopic mechanical system plays a crucial role in a wide variety of applications, including signal transduction and processing, synchronization, and building logical devices. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow the Hooke's law and response linearly to external force, unless strong drive is used. Here we propose and experimentally realize a record-high nonlinear response in macroscopic mechanical system by exploring the anharmonicity in deforming a single chemical bond. We then demonstrate the tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize a cubic elastic constant of \mathversion{bold}$2 \times 10^{18}~{\rm N}/{\rm m^3}$, many orders of magnitude larger in strength than reported previously. This enables us to observe vibrational bistate transitions of the resonator driven by the weak Brownian thermal noise at 6~K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics