AN INNOVATION DIFFUSION MODEL IN PARTIAL COMPETITIVE AND COOPERATIVE MARKET: ANALYSIS WITH TWO INNOVATIONS

CHUGH, S.,GUHA, R.K.,DHAR, JOYDIP The Korean Society for Computational and Applied M 2022 Journal of applied and pure mathematics Vol.4 No.1/2

An innovation diffusion model is proposed model consists of three classes, namely, a non-adopter class, adopter class innovation-I, and adopter class innovation-II in a partially competitive and cooperative market. The proposed model is analyzed with the help of the qualitative theory of a system of ordinary differential equations. Basic influence numbers associated with first and second innovation $R_{0_1}$ and $R_{0_2}$ respectively in the absence of each other are quantified. Then the overall basic influence number (R₀) of the system is assessed for analyzing stability in the market in different situations. Sensitivity analysis of basic influence numbers associated with first and second innovation in the absence of each other is carried out. Numerical simulation supports our analytical findings.

An innovation diffusion model in partial competitive and cooperative market: analysis with two innovations

S. Chugh,R.K. Guha,Joydip Dhar 한국전산응용수학회 2022 Journal of Applied and Pure Mathematics Vol.4 No.1

An innovation diffusion model is proposed model consists of three classes, namely, a non-adopter class, adopter class innovation-I, and adopter class innovation-II in a partially competitive and cooperative market. The proposed model is analyzed with the help of the qualitative theory of a system of ordinary differential equations. Basic influence numbers associated with first and second innovation {R}_{0_1} and {R}_{0_2} respectively in the absence of each other are quantified. Then the overall basic influence number ({R}_{0}) of the system is assessed for analyzing stability in the market in different situations. Sensitivity analysis of basic influence numbers associated with first and second innovation in the absence of each other is carried out. Numerical simulation supports our analytical findings.

Internal pressure dynamics of a leaky and quasi-statically flexible building with a dominant opening

Guha, T.K.,Sharma, R.N.,Richards, P.J. Techno-Press 2013 Wind and Structures, An International Journal (WAS Vol.16 No.1

An analytical model of internal pressure response of a leaky and quasi-statically flexible building with a dominant opening is provided by including the effect of the envelope external pressure fluctuations on the roof, in addition to the fluctuating external pressure at the dominant opening. Wind tunnel experiments involving a flexible roof and different building porosities were carried out to validate the analytical predictions. While the effect of envelope flexibility is shown to lower the Helmholtz frequency of the building volume-opening combination, the lowering of the resonant peak in the internal and net roof pressure coefficient spectra is attributed to the increased damping in the system due to inherent background leakage and envelope flexibility. The extent of the damping effects of "skin" flexibility and background leakage in moderating the internal and net pressure response under high wind conditions is quantified using the linearized admittance functions developed. Analytical examples provided for different combinations of background leakage and envelope flexibility show that alleviation of internal and net pressure fluctuations due to these factors by as much as 40 and 15% respectively is possible compared to that for a nominally sealed rigid building of the same internal volume and opening size.

Field studies of wind induced internal pressure in a warehouse with a dominant opening

Guha, T.K.,Sharma, R.N.,Richards, P.J. Techno-Press 2013 Wind and Structures, An International Journal (WAS Vol.16 No.1

A field study of wind-induced internal pressures in a flexible and porous industrial warehouse with a single dominant opening, of various sizes for a range of moderate wind speeds and directions, is reported in this paper. Comparatively weak resonance of internal pressure for oblique windward opening situations, and hardly discernible at other wind directions, is attributed to the inherent leakage and flexibility in the envelope of the building in addition to the moderate wind speeds encountered during the tests. The measured internal pressures agree well with the theoretical predictions obtained by numerically simulating the analytical model of internal pressure for a porous and flexible building with a dominant opening. Ratios of the RMS and peak internal to opening external pressures obtained in the study are presented in a non-dimensional format along with other published full scale measurements and compared with the non-dimensional design equation proposed in recent literature.

Wind induced internal pressure overshoot in buildings with opening

Guha, T.K.,Sharma, R.N.,Richards, P.J. Techno-Press 2013 Wind and Structures, An International Journal (WAS Vol.16 No.1

The wind-induced transient response of internal pressure following the creation of a sudden dominant opening during the occurrence of high external pressure, in low-rise residential and industrial buildings was numerically investigated. The values of the ill-defined parameters namely the flow contraction coefficient, loss coefficient and the effective slug length were calibrated by matching the analytical response with the computational fluid dynamics predictions. The effect of a sudden i.e., "instantaneously created" windward opening in the Texas Technical University (TTU) test building envelope was studied for two different envelope flexibility-leakage combinations namely: (1) a quasi-statically flexible and non-porous envelope and (2) a quasi-statically flexible and porous envelope. The responses forced by creating the openings at different time leads/lags with respect to the occurrence of the peak external pressure showed that for cases where the openings are created in close temporal proximity to the peak pressure, the transient overshoot values of internal pressure could be higher than the peak values of internal pressure in the pre-sequent or subsequent resonant response. In addition, the influence of time taken for opening creation on the level of overshoot was also investigated for the TTU building for the two different envelope characteristics. Non-dimensional overshoot factors are presented for a variety of cavity volume-opening area combinations for (1) buildings with rigid/quasi-statically flexible non-porous envelope, and (2) buildings with rigid/quasi-statically flexible and porous envelope (representing most low rise residential and industrial buildings). While the factors appear slightly on the high side due to conservative assumptions made in the analysis, a careful consideration regarding the implication of the timing and magnitude of such overshoots during strong gusts, in relation to the steady state internal pressure response in cyclonic regions, is warranted.

Field studies of wind induced internal pressure in a warehouse with a dominant opening

T.K. Guha,R.N. Sharma,P.J. Richards 한국풍공학회 2013 Wind and Structures, An International Journal (WAS Vol.16 No.1

A field study of wind-induced internal pressures in a flexible and porous industrial warehouse with a single dominant opening, of various sizes for a range of moderate wind speeds and directions, is reported in this paper. Comparatively weak resonance of internal pressure for oblique windward opening situations, and hardly discernible at other wind directions, is attributed to the inherent leakage and flexibility in the envelope of the building in addition to the moderate wind speeds encountered during the tests. The measured internal pressures agree well with the theoretical predictions obtained by numerically simulating the analytical model of internal pressure for a porous and flexible building with a dominant opening. Ratios of the RMS and peak internal to opening external pressures obtained in the study are presented in a non-dimensional format along with other published full scale measurements and compared with the non-dimensional design equation proposed in recent literature.

Optical and Electrical Properties of Bulk-grown Ternary In_xGa_(1−x)As

Y. K. Yeo,A. C. Bergstrom,R. L. Hengehold,J. W. Wei,S. Guha,L. P. Gonzalez,G. Rajagopalan,류미이 한국물리학회 2011 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.58 No.51

Bulk ternary In_xGa_(1−x)As polycrystals were grown using the vertical Bridgman technique. The optical and electrical properties of these bulk In_xGa_(1−x)As were investigated as a function of indium mole fraction from 0.75 to 0.99 by using photoluminescence (PL) and Hall-effect measurements. All samples showed good infrared transmission. A free exciton (FX) transition peak was observed from all bulk In_xGa_(1−x)As samples, and it redshifted from 0.568 to 0.412 eV as the indium mole fraction increased from 0.75 to 0.99. Bandgaps estimated from the indium compositionand temperature-dependent FX peaks generally followed the theoretically calculated bandgaps. All as-grown In_xGa_(1−x)As samples showed n-type conductivity. Although all bulk In_xGa_(1−x)As samples showed good optical transmissions and PL transitions, as well as high carrier mobilitites, they exhibited some random compositional fluctuations across the sample area.

Internal pressure dynamics of a leaky and quasi-statically flexible building with a dominant opening

T.K. Guha,R.N. Sharma,P.J. Richards 한국풍공학회 2013 Wind and Structures, An International Journal (WAS Vol.16 No.1

An analytical model of internal pressure response of a leaky and quasi-statically flexible building with a dominant opening is provided by including the effect of the envelope external pressure fluctuations on the roof, in addition to the fluctuating external pressure at the dominant opening. Wind tunnel experiments involving a flexible roof and different building porosities were carried out to validate the analytical predictions. While the effect of envelope flexibility is shown to lower the Helmholtz frequency of the building volume-opening combination, the lowering of the resonant peak in the internal and net roof pressure coefficient spectra is attributed to the increased damping in the system due to inherent background leakage and envelope flexibility. The extent of the damping effects of “skin” flexibility and background leakage in moderating the internal and net pressure response under high wind conditions is quantified using the linearized admittance functions developed. Analytical examples provided for different combinations of background leakage and envelope flexibility show that alleviation of internal and net pressure fluctuations due to these factors by as much as 40 and 15% respectively is possible compared to that for a nominally sealed rigid building of the same internal volume and opening size.

Wind induced internal pressure overshoot in buildings with opening

T. K. Guha,R.N. Sharma,P.J. Richards 한국풍공학회 2013 Wind and Structures, An International Journal (WAS Vol.16 No.1

The wind-induced transient response of internal pressure following the creation of a sudden dominant opening during the occurrence of high external pressure, in low-rise residential and industrial buildings was numerically investigated. The values of the ill-defined parameters namely the flow contraction coefficient, loss coefficient and the effective slug length were calibrated by matching the analytical response with the computational fluid dynamics predictions. The effect of a sudden i.e., “instantaneously created”windward opening in the Texas Technical University (TTU) test building envelope was studied for two different envelope flexibility-leakage combinations namely: (1) a quasi-statically flexible and non-porous envelope and (2) a quasi-statically flexible and porous envelope. The responses forced by creating the openings at different time leads/lags with respect to the occurrence of the peak external pressure showed that for cases where the openings are created in close temporal proximity to the peak pressure, the transient overshoot values of internal pressure could be higher than the peak values of internal pressure in the pre-sequent or subsequent resonant response. In addition, the influence of time taken for opening creation on the level of overshoot was also investigated for the TTU building for the two different envelope characteristics. Non-dimensional overshoot factors are presented for a variety of cavity volume-opening area combinations for (1) buildings with rigid/quasi-statically flexible non-porous envelope, and (2) buildings with rigid/quasi-statically flexible and porous envelope (representing most low rise residential and industrial buildings). While the factors appear slightly on the high side due to conservative assumptions made in the analysis, a careful consideration regarding the implication of the timing and magnitude of such overshoots during strong gusts, in relation to the steady state internal pressure response in cyclonic regions, is warranted.