Old and new results for superenergy tensors from dimensionally dependent tensor identities

It is known that some results for spinors, and in particular for superenergy spinors, are much less transparent and require a lot more effort to establish, when considered from the tensor viewpoint. In this paper we demonstrate how the use of dimensionally dependent tensor identities enables us to derive a number of 4-dimensional identities by straightforward tensor methods in a signature independent manner. In particular, we consider the quadratic identity for the Bel-Robinson tensor ${\cal T}_{abcx}{\cal T}^{abcy} = \delta_x^y {\cal T}_{abcd}{\cal T}^{abcd}/4$ and also the new conservation laws for the Chevreton tensor, both of which have been obtained by spinor means; both of these results are rederived by {\it tensor} means for 4-dimensional spaces of any signature, using dimensionally dependent identities, and also we are able to conclude that there are no {\it direct} higher dimensional analogues. In addition we demonstrate a simple way to show non-existense of such identities via counter examples; in particular we show that there is no non-trivial Bel tensor analogue of this simple Bel-Robinson tensor quadratic identity. On the other hand, as a sample of the power of generalising dimensionally dependent tensor identities from four to higher dimensions, we show that the symmetry structure, trace-free and divergence-free nature of the four dimensional Bel-Robinson tensor does have an analogue for a class of tensors in higher dimensions.Comment: 18 pages; TeX fil

Development of high temperature SiC based field effect sensors for internal combustion engine exhaust gas monitoring

While the car fleet becomes increasingly larger it is important to lower the amounts of pollutants from each individual diesel or gasoline engine to almost zero levels. The pollutants from these engines predominantly originate from high NOx emissions and particulates, in the case when diesel is utilized, and emissions at cold start from gasoline engines. One way of treating the high NOx levels is to introduce ammonia in the diesel exhausts and let it react with the NOx to form nitrogen gas and water, which is called SCR (Selective Catalytic Reduction). However, in order to make this system reduce NOx efficiently enough for meeting future legislations, closed loop control is required. To realize this type of system an NOx or ammonia sensor is needed. The cold start emissions from gasoline vehicles are primarily due to a high light-off time for the catalytic converter. Another reason is the inability to quickly heat the sensor used for controlling the air-to-fuel ratio in the exhausts, also called the lambda value, which is required to be in a particular range for the catalytic converter to work properly. This problem may be solved utilizing another, more robust sensor for this purpose. This thesis presents the efforts made to test the SiC-based field effect transistor (SiC-FET) sensor technology both as an ammonia sensor for SCR systems and as a cold start lambda sensor. The SiC-FET sensor has been shown to be highly sensitive to ammonia both in laboratory and engine measurements. As a lambda sensor it has proven to be both sensitive and selective, and its properties have been studied in lambda stairs both in engine exhausts and in the laboratory. The influence of metal gate restructuring on the linearity of the sensor has also been investigated. The speed of response for both sensor types has been found to be fast enough for closed loop control in each application.On the day of the public defence of the doctoral thesis, the status of article III was: in press. Report code: LiU-Tek-Lic-2003:50.</p

Studies of MISiC-FET sensors for car exhaust gas monitoring

The increasing size of the car fleet makes it important to find ways of lowering the amounts of pollutants from each individual diesel or gasoline engine to almost zero levels. The pollutants from these engines predominantly originate from emissions at cold start, in the case when gasoline is utilized, and high NOx emissions and particulates from diesel engines. The cold start emissions from gasoline vehicles are primarily due to a high light-off time for the catalytic converter. Another reason is the inability to quickly heat the sensor used for controlling the air-to-fuel ratio in the exhausts, also called the lambda value, which is required to be in a particular range for the catalytic converter to work properly. This problem may be solved utilizing another, more robust sensor for this purpose. One way of treating the high NOx levels from diesel engines is to introduce ammonia in the exhausts and let it react with the NOx in a special catalytic converter to form nitrogen gas and water, which is called SCR (selective catalytic reduction). However, in order to make this system reduce NOx efficiently enough for meeting future legislations, closed loop control is required. To realize this type of system an NOx or ammonia sensor is needed. This thesis presents the efforts made to test the SiC-based field effect sensor device both as a cold start lambda sensor for gasoline engines and as an NH3 sensor for SCR systems in diesel engines. The MISiC (metal insulator silicon carbide) lambda sensor has proven to be both sensitive and selective to lambda, and its properties have been studied in lambda stairs both in gasoline engine exhausts and in the laboratory. There is, however, a small cross-sensitivity to CO. The influence of metal gate restructuring on the linearity of the sensor has also been investigated. The metal tends to form islands by time, which decreases the catalytic activity and thereby gives the sensor, which is binary when fresh, a linear behavior. Successful attempts to prevent the restructuring through depositing a protective layer of insulator on top of the metal were made. The influence of increasing the catalytic activity in the measurement cell was also studied. It was concluded that the location of the binary switch point of MISiC lambda sensors could be moved towards the stoichiometric value if the consumption of gases in the measurement cell was increased. The MISiC NH3 sensor for SCR systems has been shown to be highly sensitive to ammonia both in laboratory and diesel engine measurements. The influence of other diesel exhaust gas components, such as NOx, water or N2O has been found to be low. In order to make the ammonia sensor more long-term stable experiments on samples with different types of co-sputtered Pt or Ir/SiO2 gas-sensitive layers were performed. These samples turned out to be sensitive to NH3 even though they were dense and NH3 detection normally requires porous films. The speed of response for both sensor types has been found to be fast enough for closed loop control in each application.On the day of the ublic defence of the doctoral thesis, the status of article IV was: accepted, article V was: submitted and article VII was: manuscript.</p

Development of high temperature SiC

based field effect sensors for internal combustion engine exhaust gas monitorin