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CMR

Quantitative Technology Forecasting using Substitution Models and Lotka-Volterra Models Feb 16, 2001. TECHNOLOGY PROGRESS EXAMPLE -- NMR WELL LOGGING. 1984. 1986. 1988. 1990. 1992. 1994. 1996. 1998. 2000. NML. SCHLUMBERGER. DEAD. CMR. CMR-200. FREE FLUID INDEX. PERMEABILITY.

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CMR

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  1. Quantitative Technology Forecasting using Substitution Models andLotka-Volterra ModelsFeb 16, 2001

  2. TECHNOLOGY PROGRESS EXAMPLE -- NMR WELL LOGGING 1984 1986 1988 1990 1992 1994 1996 1998 2000 NML SCHLUMBERGER DEAD CMR CMR-200 FREE FLUID INDEX PERMEABILITY NUMAR NMR MWD ? MRIL A MRIL B MRIL C MRIL+ CAP PRESSURE ? NMR FACIES ID? CLAY TYPING HEAVY OIL ID ? T2 INVERSION METHODS DIRECT HYDROCARBON DETECTION ATTEMPTS TO APPLY ADVANCES IN MEDICAL MRI TO ROCK PHYSICS POROSITY BOUND WATER PERMEABILITY CORE TO LOG CALIBRATION NMR CORE IMAGING DEAD

  3. SPURT OF INNOVATION IN RESPONSE TO NEW TECHNOLOGY RATE OF INNOVATION OLD DOMINANT TECHNOLOGY OBSOLESENCE COMPETITION AMONG MANY, NO STANDARD PRODUCT EMERGENCE OF STANDARD PRODUCT INNOVATION NEW DOMINANT TECHNOLOGY PROCESS INNOVATION PRODUCT INNOVATION RATE OF INNOVATION TECHNOLOGY REPLACEMENT PROCESS* * Utterback, J. M., Mastering the Dynamics of Innovation, Harvard Business School Press, Boston, 1994

  4. DISCONTINUOUS TECHNOLOGY SUBSTITUTION OLD DOMINANT TECHNOLOGY OBSOLESENCE COMPETITION AMONG MANY, NO STANDARD PRODUCT EMERGENCE OF STANDARD PRODUCT INNOVATION NEW DOMINANT TECHNOLOGY

  5. INCREMENTAL TECHNOLOGY SUBSTITUTION OLD TECHNOLOGY OBSOLESENCE AS OLD UNITS FAIL REPLACE WITH NEW UNITS IMPROVED TECHNOLOGY IMPROVEMENT

  6. One Dimensional Substitution Models Market size K Unlimited growth K-x x Fisher-Pry Restricted growth Exponential Replacement by loss Replacement by wearout Gompertz

  7. Graph of Differential Equations of Substitution Models EXPONENTIAL GOMPERTZ FISHER-PRY x

  8. SUBSTITUTION MODELS EXPONENTIAL GOMPERTZ FISHER=PRY

  9. Gompertz Fisher-Pry Confined exponential

  10. Candidate Parabolic Family of Curves a x

  11. Gompertz x/K

  12. 0 .5 .75 .937 .875 1.0 .937 1.0 .5 .75 .875 0 b b

  13. 1.0 0 .875 .5 .75 .937 .875  .937 1.0 0 .5 .75 

  14. Exponent  = .6 GOMPERTZ FISHER-PRY Confined exponential

  15. Modeling Multiple Competitors Using the Lotka-Volterra Equations

  16. Nullcline Equations

  17. Decreasing x1 Decreasing x2 Increasing x1 Increasing x2

  18. Modeling Competition in Heterogeneous Market Example: Model a two dimensional market for integrated circuits. Market parameters are max operating frequency and max power consumption. Products are TTL, a fast technology which consumes a lot of power, and CMOS, a slow technology which consumes little power. Let x1 be TTL market share Let x2 CMOS market share

  19. Benefit ratio: CMOS vs TTL by frequency

  20. Benefit ratio: CMOS vs TTL by max power consumtion

  21. Calculation of I using harmonic average • Large rij won’t inflate i • Small rij suppresses i • All rij=1 then i = 1 • Possible for all i < 1 • Not possible for all I > 1

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