Delta-shocks and vacuums in zero-pressure gas dynamics by the flux approximation

In this paper, firstly, by solving the Riemann problem of the zero-pressure flow in gas dynamics with a flux approximation, we construct parameterized delta-shock and constant density solutions, then we show that, as the flux perturbation vanishes, they converge to the delta-shock and vacuum state solutions of the zero-pressure flow, respectively. Secondly, we solve the Riemann problem of the Euler equations of isentropic gas dynamics with a double parameter flux approximation including pressure. Further we rigorously prove that, as the two-parameter flux perturbation vanishes, any Riemann solution containing two shock waves tends to a delta shock solution to the zero-pressure flow; any Riemann solution containing two rarefaction waves tends to a two-contact-discontinuity solution to the zero-pressure flow and the nonvacuum intermediate state in between tends to a vacuum state.Comment: 17 pages, 4 figures, accepted for publication in SCIENCE CHINA Mathematic

Determination of adsorption and activation volumes and apparent transfer coefficients by pressure and potential modulation

In this thesis the following investigations were carried out on Pt or Pt based electrodes: the determination of the apparent transfer coefficient (α′) for CO oxidation using an ac method, the determination of the molar adsorption volume of hydrogen and the effect of cations thereupon combining the methods of pressure modulation and ac voltammetry, and the determination of the activation volume for CO oxidation by pressure modulation. The ac method for the determination of apparent transfer coefficients or Tafel slopes has been developed in this thesis; it’s used here for CO oxidation on noble metals. This method involves a sinusoidal modulation of the potential and the simultaneous recording of the ac and the dc current. It allows to record α′ quasi continuously as a function of potential or time (i.e., in cyclic voltammetry or in potentiostatic experiments), with the reaction rate varying with time, much more accurately than the traditional method that can only measure the transfer coefficient or Tafel slope over a large range of potentials. Since the mechanism for CO oxidation on noble metals is in the focus of electrocatalytic research in recent years, I applied this ac method to the determination of the apparent transfer coefficient for the oxidation of pre-adsorbed CO at Pt electrodes in sulfuric acid. Electrodes of polycrystalline platinum and single crystalline Pt(111), Pt(665) and Pt(332) were investigated using either potential sweeps or potential steps while superimposing an ac voltage. The apparent transfer coefficients were measured and the transition of values from 1.5 to 0.5 with potential increase, which had been predicted in a simulation by Koper et al., was clearly observed experimentally for the first time. Some assumptions on the mechanism of CO oxidation on Pt by other authors could thus be rejected. The measurement of the apparent transfer coefficient by the ac method is also extended to CO oxidation on Ru and Sn decorated Pt and contributes to the understanding of those processes, as well. The ac method for the determination of the apparent transfer coefficient, which I used here, will be of great help also in many other cases, especially under steady state conditions, where the major limitations of the method are avoided. The volume of adsorbed hydrogen on Pt and the cation effects on it were investigated combining pressure modulation method and ac voltammetry. The pressure modulation method has been developed in our group by Loewe et al for the measurement of reaction and adsorption volumes and was further improved in this work. Instead of the traditional way of using high pressure in a complicated device, modulation by less than 1 bar is sufficient for the measurement of pressure dependences. The adsorption of hydrogen on noble metal surfaces is important for many other reactions, the partial molar volume of adsorbed hydrogen is of fundamental interest. In this thesis, the molar adsorption volume of hydrogen is measured to be 3.3±1 cm3·mol-1 on polycrystalline Pt in sulphuric acid. Cation were observed to largely influence the molar volume of adsorbed hydrogen in Li+, K+ and Cs+ containing electrolytes. A preliminary explanation for these cation effects is proposed. This work will be of importance in understanding the surface structure of the double layer in the hydrogen adsorption region and the involvement of cations in the interface. The pressure modulation method has been extended in this work to the determination of the activation volume for CO oxidation. Activation volume is one of the few parameters that can be measured for the activated complex. Instead of the traditional way of using complicated high pressure method, in this thesis I introduced the pressure modulation method to the measurement of the activation volume of the oxidation of adsorbed CO on polycrystalline Pt. Reasonable values are obtained at low sweep rates and low step potentials with an average of -18.2 cm3·mol-1. A preliminary structure for this activated complex is put forward. The applicability of pressure modulation method for measuring the activation volume of electrochemical processes is thus demonstrated

Modification Problems Toward Proper (Helly) Circular-Arc Graphs

We present a $9^k\cdot n^{O(1)}$-time algorithm for the proper circular-arc vertex deletion problem, resolving an open problem of van 't Hof and Villanger [Algorithmica 2013] and Crespelle et al. [arXiv:2001.06867]. Our structural study also implies parameterized algorithms for modification problems toward proper Helly circular-arc graphs

Cordyceps Mushroom: a Potent Anticancer Nutraceutical

The Cordyceps mushrooms have a long history as medicinal fungi. In Traditional Chinese Medicine, Cordyceps have been used to treat several conditions including cancers for thousand of years. Extracts from both mycelium and fruiting bodies of C. sinensis, C. militaris and other Cordyceps species showed significant anticancer activities by various mechanisms such as, modulating immune system and inducing cell apoptosis. Some polysaccharide components and cordycepin (3\u27 -deoxyadenosine) have been isolated from C. sinensis and C. militaris, which acted as potent anticancer components. This review article aims to further elucidate the importance of Cordyceps mushrooms by summarizing the findings of some of the important research works concerning possible mechanism of anticancer activity of this mushroom

RESenv: A Realistic Earthquake Simulation Environment based on Unreal Engine

Earthquakes have a significant impact on societies and economies, driving the need for effective search and rescue strategies. With the growing role of AI and robotics in these operations, high-quality synthetic visual data becomes crucial. Current simulation methods, mostly focusing on single building damages, often fail to provide realistic visuals for complex urban settings. To bridge this gap, we introduce an innovative earthquake simulation system using the Chaos Physics System in Unreal Engine. Our approach aims to offer detailed and realistic visual simulations essential for AI and robotic training in rescue missions. By integrating real seismic waveform data, we enhance the authenticity and relevance of our simulations, ensuring they closely mirror real-world earthquake scenarios. Leveraging the advanced capabilities of Unreal Engine, our system delivers not only high-quality visualisations but also real-time dynamic interactions, making the simulated environments more immersive and responsive. By providing advanced renderings, accurate physical interactions, and comprehensive geological movements, our solution outperforms traditional methods in efficiency and user experience. Our simulation environment stands out in its detail and realism, making it a valuable tool for AI tasks such as path planning and image recognition related to earthquake responses. We validate our approach through three AI-based tasks: similarity detection, path planning, and image segmentation