A complete and simple solution for a discrete-time multi-server queue with bulk arrivals and deterministic service times

A complete distribution for the system content of a discrete-time multi-server queue with an infinite buffer is presented, where each customer arriving in a group requires a deterministic service time that could be greater than one slot. In addition, when the service time equals one slot, a complete distribution for the delay is also presented.     

Heat conduction in a semi-infinite solid when subjected to spatially decaying instantaneous laser source

A closed-form model for the computation of temperature and heat flux distribution in a semi-infinite solid when subjected to spatially decaying, instantaneous laser source is investigated. The appropriate dimensionless parameters are identified and the reduced temperature and heat flux as a function of these parameters are presented in the graphic form. Some special cases of practical interest are also discussed. It is demonstrated that the present analysis covers the classical case of no heat generation in the solid as well as some new solutions.

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Wärmeleitung in einem halbunendlichen Körper, der plötzlich durch eine mit zunehmender Eindringtiefe abklingende Laser-Wärmequelle beaufschlagt wird

Zusammenfassung Es wird ein geschlossenes Rechenmodell zur Ermittlung der Temperatur- und Wärmeflußverteilung in einem halbunendlichen Körper untersucht, der plötzlich durch eine mit der Eindringtiefe abklingende Laserquelle beaufschlagt wird. Die normierten Temperaturen und Wärmeflüsse sind als Funktionen relevanter Kenngrößen graphisch dargestellt. Spezialfälle von praktischem Interesse werden diskutiert. Die vorliegende Untersuchung liefert neben einigen neuen Lösungen auch das Ergebnis für den klassischen Fall, daß keine Wärmequellen wirksam sind.

     

Multiple focus formation in a Mather gun device

Along with the normally produced pulses of dI/dt, x-ray, optical emission, neutrons and ions by a Mather type plasma focus gun, one more set of pulses were observed to be generated by a low energy device at Trombay, a few 100 ns after the first set of pulses, in majority of the discharges. In a small number of discharges even three or more sets of pulses were observed. Signals from pick-up probes placed in the run down region of the device suggest formation of more than one sheath which subsequently may form more than one focus which in turn is responsible for the second and subsequent sets of pulses.     

Modes in buried planar optical waveguides with graded-index profiles

The refractive index profile of buried graded-index planar optical waveguides fabricated by ion migration can be described by a buried secant hyperbolic function. Using such a profile, we have obtained the exact propagation characteristics for such buried optical waveguides. We have also shown that profiles which deviate slightly from the above profile can be treated as perturbations and a first-order perturbation correction gives very accurate results.     

On the service system MX/G/∞

In the present paper we consider the service system M^X/G/∞ characterized by an infinite number of servers anda general service time distribution. The customers arrive at the system in groups of size X, which is a random variable, the time between group arrivals being exponentially distributed. Using simple probability arguments, we obtain probability generating functions (p.g.f.'s) of the number of busy servers at time t and the number that depart by time t. Several other properties of these random variables are also discussed.     

Relativistic α-particles emitted in Fe-emulsion interactions at 1.7A GeV

Relativistic α-particles have been studied in 423 interactions of Fe in emulsion at 1.7A GeV. Comparisons of the observed angular distribution with that from ¹⁶O-emulsion reactions at 2.1A GeV reveal that more α-particles are observed at large angles in the Fe-emulsion reactions. The α-particles at large angles cannot be explained by fragmentation from a clean-cut spectator. Comparison of the experimental data with moving relativistic Boltzmann distributions shows that a single Boltzmann distribution cannot fit the fragmentation peak and the tail simultaneously. A thermal source (fireball) explaining the tail part of the distribution needs to be formed by a mechanism other than a simple clean-cut participant-spectator process. A large transverse momentum transfer to the spectator before fragmentation may explain the tail.     

The effect of various factors on micro-analysis by circular thin-layer chromatography

Summary The effect of various factors such as thickness of layer, acidity, activation of layer, amount of sample spotted, time interval for the flow of solvent, saturation of developing chamber, etc. have been studied using circular TLC apparatus and suitable conditions for micro-analysis by circular thin-layer chromatography are recorded. Comparative study with linear TLC is made to evaluate advantages of circular TLC in microanalysis.

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Zusammenfassung Der Einfluß der Schichtdicke, der Acidität, der Aktivierung des Schichtmaterials, der aufgetragenen Probenmenge, der Dauer des Lösungsmittelflusses, der Sättigung der Kammeratmosphäre usw. auf die Dünnschicht Ringchromatographie wurde geprüft und geeignete Arbeitsbedingungen ausgearbeitet. Im Vergleich zur linearen DC wurden die Vorteile hervorgehoben.

     

Modelling of guided-wave Bragg gratings and grating sensors using the collocation method

We have used the collocation method to model the characteristics of guided-wave Bragg gratings. The collocation method being a total field method, takes into account all modes, guided as well as radiation. We have first studied the effect of the grating structural parameters such as the grating profile and the duty cycle of periodic variation and have shown that these can have significant effect on the Bragg wavelength and the reflection spectrum. We have then obtained the response characteristics of gratings for their use in strain, temperature and pressure sensing. Our results compare very well with available experimental results. Comparisons with the coupled mode theory have also been included.     

Locating order-chaos-order transition in elastic pendulum

An undamped elastic pendulum being a nonintegrable Hamiltonian system always has some chaotic trajectories observable on choosing appropriate initial conditions. This is true even if the pendulum is in libration with small amplitude; in this situation, the pendulum may be seen as a nearly integrable system. Since the measure of the set of the local chaotic trajectories in the phase space may be very small, the trajectories are hard to locate. However, the emergence of widespread chaos when the elastic pendulum is at autoparametric resonance is well-documented. The transition from the local and the widespread chaos is typically established through the Chirikov overlap criterion that approximates the phase portrait around a resonance using a one degree-of-freedom pendulum Hamiltonian. We argue in this paper that the aforementioned transition in the elastic pendulum is due to interaction between two resonances of same kind and their coexistence can be analytically located using perturbation methods, like the method of averaging, whereas the technique of the pendulum Hamiltonian is inapplicable. Furthermore, in the course of validating the result numerically, we also showcase the order-chaos-order transition in the elastic pendulum using the fast Lyapunov indicator.