Abstract:
A commercial computational fluid dynamics (CFD) package is used for numerical analysis of the oscillating fluid flow in a pulse tube cryocooler. This model uses helium as a working medium to achieve temperatures in cryogenic range by employing two pulse tubes with 180° phase difference in the mass flow rate and the pressure at the cold end heat exchanger. The cryocooler comprises of compressor, after cooler, regenerator, pulse tube with cold and hot heat exchanger and the inertance tube. A two-dimensional axis symmetric model was used for simulation. This simulation demonstrates the variation in temperature and pressure with respect to time at the cold heat exchanger.

Abstract:
The thermodynamic performance of a Stirling cryocooler is closely linked to the movements of the two reciprocating components i.e. the compressor piston and displacer. In mechanically constrained units, such as crank-driven models or those with a rhombic drive, performance prediction is simplified by the fact that strokes of the piston and the displacer are fully determined by the geometry of the machines, and so is the phase difference between them. Hence, these are unaffected by the machine speed and gas pressure in the spaces andare thus constant in the analysis. However free piston free displacer units, since the reciprocating parts are constrained only by mechanical springs, the analysis is much more complicated. A number of dynamic and Thermodynamic variables exist which are mutually dependent i.e. strokes, pressures, temperatures and phase shift. Some researchers have coupled the thermodynamics and dynamics giving real picture of the processes. The thermodynamic processes have been assumed to be isothermal in their models. In the present paper theperformance parameters have been evaluated by assuming the real processes.

Abstract:
We developed a system that continuously maintains a cryocooler for long periods on a rotating table. A cryostat that holds the cryocooler is set on the table. A compressor is located on the ground and supplies high-purity (> 99.999%) and high-pressure (1.7 MPa) helium gas and electricity to the cryocooler. The operation of the cryocooler and other instruments requires the development of interface components between the ground and rotating table. A combination of access holes at the center of the table and two rotary joints allows simultaneous circulation of electricity and helium gas. The developed system provides two innovative functions under the rotating condition; cooling from room temperature and the maintenance of a cold condition for long periods. We have confirmed these abilities as well as temperature stability under a condition of continuous rotation at 20 revolutions per minute. The developed system can be applied in various fields; e.g., in tests of Lorentz invariance, searches for axion, radio astronomy and cosmology, and application of radar systems. In particular, there is a plan to use this system for a radio telescope observing cosmic microwave background radiation.

Abstract:
Here presented is a unified approach to Stirling numbers and their generalizations as well as generalized Stirling functions by using generalized factorial functions, $k$-Gamma functions, and generalized divided difference. Previous well-known extensions of Stirling numbers due to Riordan, Carlitz, Howard, Charalambides-Koutras, Gould-Hopper, Hsu-Shiue, Tsylova Todorov, Ahuja-Enneking, and Stirling functions introduced by Butzer and Hauss, Butzer, Kilbas, and Trujilloet and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations and generating functions are discussed. Three algorithms for calculating the Stirling numbers based on our generalization are also given, which include a comprehensive algorithm using the characterization of Riordan arrays.

Abstract:
A superconducting nanowire single photon detector (SNSPD) system for telecommunication wavelength using a GM cryocooler was developed and its performance was verified. The cryocooler based SNSPD system can operate continuously with a 100 V AC power supply without any cryogen. The packaged SNSPD device was cooled to 2.96 K within a thermal fluctuation range of 10 mK. An SNSPD with an area of 20 x 20 $\mu m^2$ showed good system detection efficiency (DE) at 100 Hz dark count rate of 2.6% and 4.5% at wavelengths of 1550 and 1310 nm, respectively. An SNSPD with an area of 10 x 10 $\mu m^2$ and kinetic inductance lower than that of the large area device showed good system DE of 2.6% at a wavelength of 1550 nm. The SNSPD system could be operated for over 10 h with constant system DE and dark count rate.

Abstract:
In this paper, algorithms are developed for computing the Stirling transform and the inverse Stirling transform; specifically, we investigate a class of sequences satisfying a two-term recurrence. We derive a general identity which generalizes the usual Stirling transform and investigate the corresponding generating functions also. In addition, some interesting consequences of these results related to classical sequences like Fibonacci, Bernoulli and the numbers of derangements have been derived.

Abstract:
For the Chebyshev-Stirling numbers, a special case of the Jacobi-Stirling numbers, asymptotic formulae are derived in terms of a local central limit theorem. The underlying probabilistic approach also applies to the classical Stirling numbers of the second kind. Thereby a supplement of the asymptotic analysis for these numbers is established.

Abstract:
It is known that the $S(n,k)$ Stirling numbers as well as the ordered Stirling numbers $k!S(n,k)$ form log-concave sequences. Although in the first case there are many estimations about the mode, for the ordered Stirling numbers such estimations are not known. In this short note we study this problem and some of its generalizations.

Abstract:
The purpose of this article is to introduce q-deformed Stirling numbers of the first and second kinds. Relations between these numbers, Riemann zeta function and q-Bernoulli numbers of higher order are given. Some relations related to the classical Stirling numbers and Bernoulli numbers of higher order are found. By using derivative operator to the generating function of the q-deformed Stirling numbers of the second kinds, a new function is defined which interpolates the q-deformed Stirling numbers of the second kinds at negative integers. The recurrence relations of the Stirling numbers of the first and second kind are given. In addition, relation between q-deformed Stirling numbers and q-Bell numbers is obtained.