Validity of various semi-empirical formulae and analytical functions for the efficiency of Ge(Li) detectors

1976 ◽  
Vol 136 (3) ◽  
pp. 543-549 ◽  
Author(s):  
Raghuvir Singh
Author(s):  
Ratnesh K. Sharma ◽  
Manish Marwah ◽  
Wilfredo Lugo

Heat transfer phenomena in complex physical systems like multiphase environments, multidimensional geometries can be difficult to capture in terms of correlations, analytical functions or numerical models using conventional techniques. Such systems are designed based on approximations, thumb-rules or semi-empirical correlations between parameters based on averaged values and are operated likewise using another set of rules derived from bulk thermodynamic performance parameters. With the development of nano-scale sensors and advanced data aggregation techniques, there is a need for analytical techniques that can discover the complex interrelationships between the thermodynamic parameters of the process, geometry constraints and the governing outcomes of the process. Such techniques can leverage the possibility of deployment of thousands of sensors to extract the key relationships that drive the transport phenomena for advanced development of process control tools and methodologies. Heat and mass transfer equipment design and operation can benefit from knowledge discovered through analytics applied on thermo-physical data obtained from real time processes. We present illustrative use cases of application of data analytics and knowledge discovery techniques to a richly instrumented data center where computer room air conditioning (CRAC) units provide cooling for IT equipment arranged in rows of racks. Sensors located at each rack provide temperature measurements which are analyzed in real-time and also archived. Rack temperatures, together with operating parameters of CRAC units such as supply air temperature (SAT), and variable speed drive (VFD) settings, are analyzed together to derive design insights and detect anomalies.


2012 ◽  
Vol 12 (3) ◽  
pp. 6745-6803
Author(s):  
V. I. Khvorostyanov ◽  
J. A. Curry

Abstract. A new analytical parameterization of homogeneous ice nucleation is developed based on extended classical nucleation theory including new equations for the critical radii of the ice germs, free energies and nucleation rates as the functions of the temperature and water saturation ratio simultaneously. By representing these quantities as separable products of the analytical functions of the temperature and supersaturation, analytical solutions are found for the integral-differential supersaturation equation and concentration of nucleated crystals. Parcel model simulations are used to illustrate the general behavior of various nucleation properties under various conditions, for justifications of the further key analytical simplifications, and for verification of the resulting parameterization. The final parameterization is based upon the values of the supersaturation that determines the current or maximum concentrations of the nucleated ice crystals. The crystal concentration is analytically expressed as a function of time and can be used for parameterization of homogeneous ice nucleation both in the models with small time steps and for substep parameterization in the models with large time steps. The crystal concentration is expressed analytically via the error functions or elementary functions and depends only on the fundamental atmospheric parameters and parameters of classical nucleation theory. The diffusion and kinetic limits of the new parameterization agree with previous semi-empirical parameterizations.


2012 ◽  
Vol 12 (19) ◽  
pp. 9275-9302 ◽  
Author(s):  
V. I. Khvorostyanov ◽  
J. A. Curry

Abstract. A new analytical parameterization of homogeneous ice nucleation is developed based on extended classical nucleation theory including new equations for the critical radii of the ice germs, free energies and nucleation rates as simultaneous functions of temperature and water saturation ratio. By representing these quantities as separable products of the analytical functions of temperature and supersaturation, analytical solutions are found for the integral-differential supersaturation equation and concentration of nucleated crystals. Parcel model simulations are used to illustrate the general behavior of various nucleation properties under various conditions, for justifications of the further key analytical simplifications, and for verification of the resulting parameterization. The final parameterization is based upon the values of the supersaturation that determines the current or maximum concentrations of the nucleated ice crystals. The crystal concentration is analytically expressed as a function of time and can be used for parameterization of homogeneous ice nucleation both in the models with small time steps and for substep parameterization in the models with large time steps. The crystal concentration is expressed analytically via the error functions or elementary functions and depends only on the fundamental atmospheric parameters and parameters of classical nucleation theory. The diffusion and kinetic limits of the new parameterization agree with previous semi-empirical parameterizations.


1986 ◽  
Vol 47 (7) ◽  
pp. 1149-1154
Author(s):  
Le Quang Rang ◽  
D. Voslamber

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