Peripheral phonons and phonon conductivity of the doped semiconductor

The percentage contribution of the peripheral phonons towards the total phonon conductivity of P-doped Ge has been studied with the help of the Ziman expression of the electron-phonon scattering relaxation rate and the Callaway integral of the lattice thermal conductivity. It is found that the percentage contribution of the peripheral phonons increases with the increase of temperature. The entire study is limited to the temperature range 1–5 K.     

On the uniqueness of the Shapley value

L.S. Shapley [1953] showed that there is a unique value defined on the classD of all superadditive cooperative games in characteristic function form (over a finite player setN) which satisfies certain intuitively plausible axioms. Moreover, he raised the question whether an axiomatic foundation could be obtained for a value (not necessarily theShapley value) in the context of the subclassC (respectivelyC′, C″) of simple (respectively simple monotonic, simple superadditive) gamesalone. This paper shows that it is possible to do this. Theorem I gives a new simple proof ofShapley's theorem for the classG ofall games (not necessarily superadditive) overN. The proof contains a procedure for showing that the axioms also uniquely specify theShapley value when they are restricted to certain subclasses ofG, e.g.,C. In addition it provides insight intoShapley's theorem forD itself. Restricted toC′ orC″, Shapley's axioms donot specify a unique value. However it is shown in theorem II that, with a reasonable variant of one of his axioms, a unique value is obtained and, fortunately, it is just theShapley value again.     

Diffusion-induced modulational instability in magnetised semiconductor plasmas: effect of carrier heating

The present paper is aimed to the exploration of modulational amplification in transversely magnetised diffusive semiconductors. By considering that the origin of modulational interaction lies in the third-order optical susceptibility c⁽³⁾\chi^{(3)} arising from the nonlinear diffusion current density and using coupled mode theory, an analytical investigation of frequency modulational interaction between co-propagating laser beams and internally generated acoustic mode is presented. We have studied the steady state and transient amplification characteristics of modulated waves arising in the transversely magnetised semiconductor plasmas. The effect of carrier heating adds new dimensions to the present study. The heating effect reduces the required threshold amplitude of wave and enhances steady-state as well as transient gain of the generated acoustic mode.     

Bursts in m-metric array codes

Fire [P. Fire, A class of multiple-error-correcting binary codes for non-independent errors, Sylvania Reports RSL-E-2, Sylvania Reconnaissance Systems, Mountain View, California, 1959] introduced the concept of bursts for classical codes where codes are subsets/subspaces of the space , the space of all n-tuples with entries from a finite field F_q. In this paper, we introduce the notion of bursts for m-metric array codes where m-metric array codes are subsets/subspaces of the space Mat_m×s(F_q), the linear space of all m × s matrices with entries from a finite field F_q, endowed with a non-Hamming metric. We also obtain some bounds (analogous to Fire’s bound [P. Fire, A class of multiple-error-correcting binary codes for non-independent errors, Sylvania Reports RSL-E-2, Sylvania Reconnaissance Systems, Mountain View, California, 1959], Rieger’s bound [S.H. Reiger, Codes for the correction of clustered errors, IRE-Trans., IT-6 (1960), 16-21] etc. in classical codes) on the parameters of m-metric array codes for the detection and correction of burst errors.     

Coherence characteristics of light-emitting diodes

We report the measurement of coherence characteristics of light-emitting diodes (LEDs). Experiments were performed using red and green color LEDs directly illuminating the Young's double slit kept in the far-zone. Fourier transform fringe analysis technique was used for the measurement of the visibility of interference fringes from which the modulus of degree of spectral coherence was determined. Low degree of spectral coherence, typically 0.4 for red and 0.2 for green LED with double-slit separation of 400 μm was observed. A variable slit was then kept in front of the LEDs and the double slit was illuminated with the light coming out of the slit. Experiments were performed with various slit sizes and the visibility of the interference fringes was observed. It was found that visibility of the interference fringes changes drastically in presence of variable slit kept in front of LEDs and a high degree of spectral coherence, typically 0.85 for red and 0.8 for green LED with double-slit separation of 400 μm and rectangular slit opening of 500 μm was observed. The experimental results are compared with the theoretical counterparts. Coherence lengths of both the LEDs were also determined and it was obtained 5.8±2 and 24±4 μm for green and red LEDs, respectively.