D'ALEMBERT PRINCIPLE IN THE VELOCITY SPACE

According to Newton's dynamical equation of the system of particles, the force is considered to be the function of the coordinate r, velocity and time t, and the various formulae for D'Alembert principle of the velocity space in both the holonomic and nonholonomic systems are deduced by introducing the concept of kinetic energy in the velocity space (i.e. the accelerated energy).

Debris cloud structure and hazardous fragments distribution under hypervelocity yaw impact

This study investigates how the debris cloud structure and hazardous fragment distribution vary with attack angle by simulating a circular cylinder projectile hypervelocity impinging on a thin plate using the finite element-smoothed particle hydrodynamics(FE-SPH)adaptive method.Based on the comparison and analysis of the experimental and simulation results,the FE-SPH adaptive method was applied to address the hypervelocity yaw impact problem,and the variation law of the debris cloud structure with the attack angle was obtained.The screening criterion of the hazardous fragment at yaw impact is given by analyzing the debris formation obtained by the FE-SPH adaptive method,and the distribution characteristics of hazardous fragments and their relationship with the attack angle are given.Moreover,the velocity space was used to evaluate the distribution range and damage capability of asymmetric hazardous fragments.The maximum velocity angle was extended from fully symmetrical working conditions to asymmetrical cases to describe the asymmetrical debris cloud distribution range.In this range,the energy density was calculated to quantitatively analyze how much damage hazardous fragments inflict on the rear plate.The results showed that the number of hazardous fragments generated by the case near the 35°attack angle was the largest,the distribution range was the smallest,and the energy density was the largest.These results suggest that in this case,debris cloud generated by the impact had the strongest damage to the rear plate.

Distribution and Form of Iron and Calcium Compounds Before and After Residue Hydrogenation Under Different Space Velocities

The distribution and form of iron and calcium compounds were studied using hydrogenation feedstock and hydrogenation products with different space velocities as the research object.The content of metallic elements,such as calcium and iron in hydrogenation feedstock,and extract samples were determined via flame atomic absorption spectrometry.The water-soluble iron and calcium species in oil samples were determined by an IC2010 high-throughput ion chromatograph.Nearly 60%-80%of the iron or calcium compounds were mainly concentrated in resins and asphaltenes.Iron and calcium compounds mainly exist in the form of oil-soluble metal species in hydrogenation feedstock and hydrogenation products.Under certain conditions of reaction temperature,pressure,and volume ratio of hydrogen to oil,when the reaction space velocity was 0.6 h^(−1),about 30%of the iron or calcium compounds were converted from oil-soluble to water-soluble species after hydrogenation.When the reaction space velocity was decreased from 1.70 to 0.60 h^(−1),the proportion of iron compounds converted from oil-soluble to water-soluble increased from 8.4%to 28%.Moreover,the proportion of calcium compounds converted from oil-soluble to water-soluble increased from 10%to 37%.This denotes that with decreasing reaction space velocity,the ratio of oil-soluble to water-soluble species increases.Water-soluble iron and calcium compounds are present in the form of inorganic salts,such as chlorate and sulfate.This study helps in understanding the removal mechanism of iron and calcium compounds and optimizing the operating conditions of residue hydrogenation.

Zeno and the Wrong Understanding of Motion—A Philosophical-Mathematical Inquiry into the Concept of Finitude as a Peculiarity of Infinity

In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .

Spacecraft Doppler tracking with possible violations of LLI and LPI: preliminary bounds on LLI from Mars Express

Three-way spacecraft Doppler tracking is currently widely used and it plays an important role in the control and navigation of deep space missions. Using the theory of three-way Doppler tracking, including possible violations of the local Lorentz invariance （LLI） and the local position invariance （LPI）, we analyze the post-fit residuals of three-way Doppler tracking data of Mars Express. These Doppler observations were carried out from August 7th to 8th in 2009, with an uplink station administered by the European Space Agency at New Norcia in Australia and three downlink stations at Shanghai, Kunming and Urumqi in China. We find that, although these observations impose preliminary bounds on LLI at the level of 10^-2, they are not suitable for testing LPI because of the configuration of these stations and the accuracy of the observations. To our knowledge, this is one of the first attempts in China to apply radio science to the field of fundamental physics.

Spacecraft Doppler tracking with possible violations of LLI and LPI:upper bounds from one-way measurements on MEX

We analyze the post-fit residuals of one-way Doppler tracking data from the Mars Express （MEX） spacecraft to test possible violations of local Lorentz invariance （LLI） and local position invariance （LPI）. These one-way Doppler observations were carried out on 2011 August 7 for about 20 minutes at Sheshan Station of Shanghai Astronomical Observatory in China. These downlink signals were sent by MEX for telemetry at X-band. Because we are not able to decode the data in the form of teleme- try and separate them from the carrier frequency, this makes the post-fit residuals of the Doppler data degrade to the level of 0.1 m s^-1. Even so, the residuals can still impose upper bounds on LLI and LPI at 10^-1, which is consistent with the prediction based on our analysis of the detectability. Although the upper bounds given by three-way Doppler tracking of MEX are better than those obtained in the present work, one-way Doppler measurements still provide a unique chance to test possible violations of LLI and LPI far from the ground stations.

Construction of Non-Equilibrium Gas Distribution Functions through Expansions in Peculiar Velocity Space

Gas distribution function plays a crucial role in the description of gas flows at the mesoscopic scale.In the presence of non-equilibrium flow,the distribution function loses its rotational symmetricity,making the mathematical derivation difficult.From both the Chapman-Enskog expansion and the Hermite polynomial expansion(Grad’s method),we observe that the non-equilibrium effect is closely related to the peculiar velocity space(C).Based on this recognition,we propose a new methodology to construct the non-equilibrium distribution function from the perspective of polynomial expansion in the peculiar velocity space of molecules.The coefficients involved in the non-equilibrium distribution function can be exactly determined by the compatibility conditions and the moment relationships.This new framework allows constructing non-equilibrium distribution functions at any order of truncation,and the ones at the third and the fourth order have been presented in this paper for illustration purposes.Numerical validations demonstrate that the new method is more accurate than the Grad’s method at the same truncation error for describing non-equilibrium effects.Two-dimensional benchmark tests are performed to shed light on the applicability of the new method to practical engineering problems.

Evaluation on the natural gas hydrate formation process

Gas hydrates have endowed with great potential in gas storage,and rapid formation of gas hydrates is critical to use this novel technology.This work evaluated the natural gas hydrate formation process,which was compared from six parameters,including conversion of water to hydrate,storage capacity,the rate of hydrate formation,space velocity(SV)of hydrate reaction,energy consumption and hydrate removal.The literature was selected by analyzing and comparing these six parameters mentioned above,meanwhile placing emphasis on the three parameters of storage capacity,the rate of hydrate formation and space velocity of hydrate reaction.Through analysis and comparison,four conclusions could be obtained as follows.Firstly,the overall performance of the stirring process and the spraying process were better than other processes after analyzing the six parameters.Secondly,the additive types,the reactor structure and the reactor size had influence on the natural gas hydrate formation process.Thirdly,the energy consumption via reciprocating impact in the hydrate formation process was higher than that via stirring,spraying and static higee.Finally,it was one key for hydrate removal to realize the hydrate industrial production.

Dehydroaromatization of Methane with a Small Amount of Ethane for Higher Yield of Benzene

The dehydroaromatization of methane was investigated with addition of a few ethane. A high benzene yield was achieved at a higher space velocity. The addition of CO2 could improve the stability.

Hydrogen Effect on Coke Removal and Catalytic Performance in Pre-Carburization and Methane Dehydro-Aromatization Reaction on Mo/HZSM-5

In this study, the effects of pre-carburization of catalyst, hydrogen addition to methane feed and the space velocity of methane on the catalytic performance in methane to benzene （MTB） reaction were discussed in detail over Mo/HZSM-5 catalyst at 1023 K and 0.3 MPa. Compared with the non-precarburized catalyst, the Mo catalyst pre-carburized under the flow of CHa＋4H2 at 973 K was found to have the higher activity and better stability. Further 6% H2 addition to the methane feed suppressed the aromatic type of coke formation effectively, and improved the stability of catalyst markedly, moreover gave a much longer reaction life of catalyst （53 h at 1023 K and 5400 ml/（g-h）） and much more formation amounts of benzene and hydrogen. With increase of methane space velocity, both the naphthalene formation selectivity and the coke formation selectivity were decreased by the shortened contact time; the benzene formation selectivity and total formation amount before the complete deactivation of catalyst were increased markedly, while the total naphthalene and coke formation amounts did not change much. At high methane space velocity （≥5400 ml/（g·h））, a new middle temperature coke derived from the high temperature aromatic coke was formed on the catalyst; all the coke formed could be burnt off at lower temperature in oxygen, compared with those obtained at low space velocity. Considering the benzene formation amount and catalyst stability together, 5400 ml/（g·h） was proved to be the most efficient methane space velocity for benzene production.

High NO_2/NO_X emissions downstream of the catalytic diesel particulate filter:An influencing factor study

Diesel vehicles are responsible for most of the traffic-related nitrogen oxide（NO x） emissions,including nitric oxide（NO） and nitrogen dioxide（NO2）. The use of after-treatment devices increases the risk of high NO2/NO x emissions from diesel engines. In order to investigate the factors influencing NO2/NO x emissions, an emission experiment was carried out on a high pressure common-rail, turbocharged diesel engine with a catalytic diesel particulate filter（CDPF）. NO2 was measured by a non-dispersive ultraviolet analyzer with raw exhaust sampling. The experimental results show that the NO2/NO x ratios downstream of the CDPF range around 20%–83%, which are significantly higher than those upstream of the CDPF. The exhaust temperature is a decisive factor influencing the NO2/NO x emissions. The maximum NO2/NO x emission appears at the exhaust temperature of 350°C. The space velocity,engine-out PM/NO x ratio（mass based） and CO conversion ratio are secondary factors. At a constant exhaust temperature, the NO2/NO x emissions decreased with increasing space velocity and engine-out PM/NO x ratio. When the CO conversion ratios range from 80% to 90%,the NO2/NO x emissions remain at a high level.

Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems

A parametric reduced order model based on proper orthogonal decomposition with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power reactor cooling systems.Thermal mixing of different temperature coolants in T-junction pipes leads to temperature fluctuations and this could potentially cause thermal fatigue in the pipe walls.The novelty of this paper is the development of a parametric ROM consider-ing the three dimensional,incompressible,unsteady Navier-Stokes equations coupled with the heat transport equation in a finite volume regime.Two different parametric cases are presented in this paper:parametrization of the inlet temperatures and parametrization of the kinematic viscosity.Different training spaces are considered and the results are compared against the full order model.The first test case results to a computational speed-up factor of 374 while the second test case to one of 211.