University of Wisconsin Fusion Design Memos (UWFDM)

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The UWFDM series of technical reports details the research of the Fusion Technology Institute from 1971 to the present. Over 800 authors have contributed more than 56000 pages to the 1300 reports. Nearly all are online.

Publications

Results: 892 to 990 of 1414 order by: Num Author Title Date Size Length
1  2  3  4  5  6  7  8  9  10   11  12  13  14  15 

UWFDM-530   Low Mode Number Stability of a Quadrupole Tandem Mirror; M.W. Phillips and J.D. Callen, July 1983. (28 pages, 1.1 MB)

UWFDM-537   Radiative Heat Transfer in Self-Shielding Vapor Layer During Tokamak Disruptions; R.R. Peterson, August 1983. (28 pages, 1.2 MB)

UWFDM-558   14-MeV Neutron Radiation-Induced Microhardness Changes in Copper Alloys; S.J. Zinkle and G.L. Kulcinski, September 1983 [presented at the ASTM Conference on Subsized Specimens, Albuquerque, NM, September 23, 1983]. (28 pages, 1.4 MB)

UWFDM-649   Modeling of Lithium-Lead/Water Interactions in a Fusion Reactor Design: Part II. Modeling Improvements; J.P. Herzog, M.L. Corradini, September 1985. (28 pages, 1.2 MB)

UWFDM-667   Microstructural Modification of 2-1/4 Cr-1 Mo Steel by Irradiation with 14 MeV Nickel Ions; R.L. Sindelar, J.J. Kai, D.L. Plumton, R.A. Dodd and G.L. Kulcinski, October 1985 [presented at the 1985 TMS-AIME Fall Meeting, 13-17 October 1985, Toronto, Ontario]. (28 pages, 8.6 MB)

UWFDM-685   Key Materials Issues for Near Term Fusion Reactors; G.L. Kulcinski, J.M. Dupouy and F. Ishino, April 1986 [Presented at the 2nd International Conference on Fusion Reactor Materials, 14-17 April 1986, Chicago, IL]. (28 pages, 1.3 MB) [more]

UWFDM-824   U.S. Aqueous Salt Blanket for ITER; I.N. Sviatoslavsky, M.E. Sawan, L.J. Wittenberg, G.L. Kulcinski, J.P. Blanchard, E.A. Mogahed, February 1990 [published in Fusion Engineering and Design 13 (1990) 33-4]. (28 pages, 4.2 MB)

UWFDM-858   Non-LTE Radiative Transfer with Lambda-Acceleration: Convergence Properties Using Exact Full and Diagonal Lambda-Operators; J.J. MacFarlane, August 1991 [Astronomy and Astrophysics 264 (1992) 153]. (28 pages, 746 kB)

UWFDM-1094   X-1 Experiment Chamber Design and Analysis: Progress Report for the Period August 1, 1998 to September 30, 1998; R.R. Peterson, G.L. Kulcinski, E.A. Mogahed, H.Y. Khater, M.E. Sawan, I.N. Sviatoslavsky, P. Cousseau, J.F. Santarius, K. Olson, T. Utschig, D.L. Henderson, M.L. Corradini, R.L. Engelstad, G.A. Moses, October 1998. (28 pages, 853 kB)

UWFDM-1408   3-D Modeling of Neutron Wall Loading, Tritium Breeding Ratio, and Nuclear Heating Distribution for ARIES-ACT-DCLL Design; A. Jaber, L. El-Guebaly, L. Mynsberge, April 2012. (28 pages, 1.8 MB)

UWFDM-113   Comparative Study of Radioactivity and Afterheat in Several Fusion Reactor Blanket Designs; R.W. Conn, T.Y. Sung, and M.A. Abdou, October 1974. (29 pages, 1.4 MB)

UWFDM-132   The Need for Neutron Radiation Damage Information from the Viewpoint of the Fusion Reactor Designer; G.L. Kulcinski, June 27, 1975 [prepared for the International Conference on Radiation Test Facilities for the CTR Surface and Materials Program, Argonne National Laboratory, 15-18 July 1975]. (29 pages, 1.4 MB)

UWFDM-254   Formulation of Constitutive Laws for Deformation During Irradiation; W. Wolfer, July 1978 [ASTM-STP-683, 581-597 (1979)]. (29 pages, 1.3 MB)

UWFDM-346   Effective Time and Resonance Width in Cyclotron Resonance Heating; J.E. Howard, May 1980. (29 pages, 1.2 MB)

UWFDM-370   Evaporation Under Intense Energy Deposition; L.L. Loebel and W.G. Wolfer, August 1980. (29 pages, 1.3 MB)

UWFDM-669   Preparation of Ion-Irradiated Foils for Cross-Section Analysis; S.J. Zinkle and R.L. Sindelar, December 1985. (29 pages, 6.8 MB)

UWFDM-784   The Effect of Tempering and Aging on a Low Activation Martensitic Steel; R.D. Griffin, R.A. Dodd, G.L. Kulcinski, D.S. Gelles, January 1989. (29 pages, 6.5 MB) [more]

UWFDM-820   Projected Ranges of Energetic Ions in Solids; J.H. Liang and G.L. Kulcinski, August 1990 [Published in J. Nucl. Matls. 183/3 (August 1991), pp. 202-215]. (29 pages, 1.2 MB)

UWFDM-901   Stress-Enhanced Swelling: Mechanisms and Implications for Fusion Reactors; M.H. Hassan, J.P. Blanchard, G.L. Kulcinski, May 1992. (29 pages, 634 kB)

UWFDM-930   MHD, Heat Transfer and Stress Analysis for the ITER Self-Cooled Blanket Design; X.R. Wang, E.A. Mogahed, I.N. Sviatoslavsky, October 1993. (29 pages, 1.5 MB)

UWFDM-973   Numerical Simulation of Target Microexplosion Dynamics for the LIBRA-SP Inertial Confinement Fusion Reactor; J.J. MacFarlane, G.A. Moses, P. Wang, M.E. Sawan, R.R. Peterson, December 1994. (29 pages, 1.1 MB)

UWFDM-977   Summary Report for ITER Design Task D10: Updating the Activation Code RACC for ITER Design Analysis; Qingming Wang and D.L. Henderson, January 1995 (revised April 1995). (29 pages, 737 kB)

UWFDM-1028   Preliminary Analysis of Aluminum K-alpha Satellite Spectra Obtained in KALIF Applied-B Diode Experiments; J.J. MacFarlane and P. Wang, July 1996. (29 pages, 810 kB)

UWFDM-1271   Evolution of Clearance Standards and Implications for Radwaste Management of Fusion Power Plants; L.A. El-Guebaly, P. Wilson, D. Paige, and the ARIES and Z-Pinch Teams, July 2005 (revised August 2005)  [ Fusion Science and Technology, 49 (2006) 62-73]. (29 pages, 1.1 MB)

UWFDM-1338   Contributon Theory for Shielding Analysis; Marat Seydaliev and D.L. Henderson, July 2008. (29 pages, 1.2 MB)

UWFDM-140   The Influence of First Wall Lifetime on the Cost of Electricity in UWMAK Type Fusion Reactors; G.L. Kulcinski and J.R. Young, October 20, 1975 [published in the Proceedings of the International Conference on Radiation and Tritium Technology for Fusion Reactors, Gatlinburg TN, 1-3 October 1975]. (30 pages, 1.3 MB) [more]

UWFDM-184   A Systematic Approach to the Radiation Damage Problem in Fission and Fusion Structural Alloys; R. Bullough, B.L. Eyre, and G.L. Kulcinski, October 1976. (30 pages, 1.7 MB) [more]

UWFDM-290   The Application of Uncertainty Analysis in Conceptual Fusion Reactor Design; T. Wu and C.W. Maynard, February 1979 [Proc. Seminar-Workshop on Theory and Uncertainty Analysis, ORNL, TN, August 1978]. (30 pages, 1.8 MB)

UWFDM-301a   Appendix - Detailed Summaries and Conclusions for Different Subsystems in SOLASE; R.W. Conn, S.I. Abdel-Khalik, G.A. Moses, F. Beranek, E.T. Cheng, G.W. Cooper, R.B. Droll, T. Henderson, J. Howard, T.O. Hunter, E.M. Larsen, G.L. Kulcinski, E.G. Lovell, G.R. Magelssen, C.W. Maynard, K.R. Okula, M. Ortman, M. Ragheb, W.B. Rensel, D. Solomon, R. Spencer, I.N. Sviatoslavsky, W.F. Vogelsang, R.D. Watson, and W.G. Wolfer, April 1979. (30 pages, 1.6 MB) [more]

UWFDM-612   Inversion Techniques for Several Banded Matrices; J.W. Johnson, January 1985. (30 pages, 1.1 MB)

UWFDM-686   SIRIUS-M: A Symmetric Illumination, Inertially Confined Direct Drive Materials Test Facility; S.I. Abdel-Khalik, H. Attaya, R.L. Engelstad, G.L. Kulcinski, J.H. Liang, E.G. Lovell, G.A. Moses, R.R. Peterson, M.E. Sawan, I.N. Sviatoslavsky and L.J. Wittenberg, April 1986 [Presented at the 2nd International Conference on Fusion Reactor Materials, 14-17 April 1986, Chicago, IL]. (30 pages, 1.4 MB)

UWFDM-721   UWEOSPAC: A Subroutine Package for Accessing MIXERG-Generated SESAME-Formatted Multigroup Opacity Tables; R.W. Holzer, March 1987. (30 pages, 1.4 MB)

UWFDM-790   Simulation of Plasma Flow in the Edge Region of a Stellarator; M.A. Hussein, G.A. Emmert, February 1989. (30 pages, 1.1 MB)

UWFDM-967   Non-Lunar 3He Resources; L.J. Wittenberg, July 1994 (revised July 1994)  [presented at the Second Wisconsin Symposium on Helium-3 and Fusion Power, 19-21 July 1993, Madison WI]. (30 pages, 600 kB)

UWFDM-976   1994 Summary Report for ITER Design Task D4. Shielding 3D Analysis. Afterheat Analysis for the Whole Machine and Cryostat Area. Part A: Neutronics and Shielding; M.E. Sawan, L.A. El-Guebaly, H.Y. Khater, January 1995. (30 pages, 859 kB)

UWFDM-1007   Summary Report on the Neutronics Activities Performed by the U.S. Home Team as Part of the Blanket Design Task D202 in 1995; M.E. Sawan, H.Y. Khater, L.A. El-Guebaly, March 1996. (30 pages, 665 kB)

UWFDM-11   Some Technological Problems in Fusion Reactor Design; H.K. Forsen, March 1972. (31 pages, 1.5 MB)

UWFDM-33   Major Technological Problems for Fusion Reactor Power Stations; G.L. Kulcinski, November 1972. (31 pages, 2.7 MB)

UWFDM-171   Decay Chain Data Library for Radioactivity Calculations; T.Y. Sung and W.F. Vogelsang, September 1976. (31 pages, 1.2 MB)

UWFDM-237   First Wall and Divertor Plate Material Selection in Fusion Reactors; Robert W. Conn, March 20, 1978. (31 pages, 1.4 MB)

UWFDM-319   Interaction of Lower Hybrid Wave Fields with Drift-Cyclotron Loss-Cone Instability; K-C. Shaing, October 1979. (31 pages, 1.1 MB)

UWFDM-372   MIXER - A Multi-Species Optical Data and Equation of State Computer Code; R.R. Peterson and G.A. Moses, September 1980. (31 pages, 1.4 MB)

UWFDM-412   A Parametric Cost Analysis for Tandem Mirror Reactors Similar to WITAMIR-I; E. Montalvo, J. Santarius, and I. Sviatoslavsky, March 1981. (31 pages, 1.1 MB)

UWFDM-425   Alpha Particle Loss and Energy Deposition in Tandem Mirrors; J.F. Santarius and J.D. Callen, November 1981 [Phys. Fluids 26 (1983) 1037]. (31 pages, 968 kB)

UWFDM-661   Microstructure of Copper Following High Dose 14-MeV Cu Ion Irradiation; S.J. Zinkle, G.L. Kulcinski and R.W. Knoll, November 1985 [presented at the 1985 TMS-AIME Fall Meeting, 13-17 October 1985, Toronto, Ontario]. (31 pages, 6.4 MB)

UWFDM-726   Radiological Dose Calculations for the Chamber and Diode Region of the Light Ion Fusion Target Development Facility; O. Yasar, M.E. Sawan, D.L. Henderson, G.A. Moses, July 1987. (31 pages, 1.5 MB)

UWFDM-764   Lunar He3, Fusion Propulsion, and Space Development; J.F. Santarius, June 1988 (revised August 1988)  [Second Conference on Lunar Bases and Space Activities of the 21st Century (NASA Conf. Pub. 3166, Vol. 2 (1992) 459]. (31 pages, 1.4 MB)

UWFDM-788   One-Dimensional Simulation of Neutral Helium Transport in Edge Plasmas; H.H. Abou-gabal, G.A. Emmert, January 1989. (31 pages, 1.2 MB)

UWFDM-1036   National Ignition Facility Target Area Studies Final Report for the Period 4/1/96 through 11/30/96; R.R. Peterson, J.F. Santarius, G.A. Moses, January 1997. (31 pages, 838 kB)

UWFDM-1065   ASCA X-ray Spectroscopy of the Unusual B0 V Star tau Scorpii; D.H. Cohen, J.P. Cassinelli, W.L. Waldron, October 1997 [published in the Astrophysical Journal, 488, 397 (October 20, 1997)]. (31 pages, 768 kB) [more]

UWFDM-207   Monte Carlo Study of Asymmetry Effects in a Lithium Oxide Blanket for a Laser Driven Reactor; M.H. Ragheb, E.T. Cheng, and R.W. Conn, June 1977. (32 pages, 1.4 MB)

UWFDM-292   The Radiation Disorder Model of Phase Stability; K-Y. Liou and P. Wilkes, February 1979. (32 pages, 1.7 MB)

UWFDM-471   Nucleation of Voids in Materials Supersaturated with Mobile Interstitials, Vacancies, and Divacancies; W.G. Wolfer and A. Si-Ahmed, May 1982 [Phil. Mag. A46, 723-736 (1982)]. (32 pages, 1.2 MB)

UWFDM-529   Fusion Reactor Design: On the Road to Commercialization; G.L. Kulcinski, May 31, 1983 [presented at the Third International Conference on Emerging Nuclear Energy Systems, Helsinki, Finland, June 6-9, 1983] [Atomkernenergie/Kerntechnik 44 (1984) 1]. (32 pages, 1.5 MB)

UWFDM-594   Fatigue Stress Analysis of the Sandia TDF Reaction Chamber; R.L. Engelstad, E.G. Lovell and G.A. Moses, September 1984. (32 pages, 1.1 MB)

UWFDM-613   Microfireball Propagation in Z-Discharge Plasma Channels in the Light Ion Fusion Target Development Facility; Robert R. Peterson, John J. Watrous and Gregory A. Moses, January 1985. (32 pages, 1.2 MB)

UWFDM-693   Stability of Vacancy Clusters in Metals II: Effect of Oxygen and Helium on Void Formation in Metals; S.J. Zinkle, W.G. Wolfer, G.L. Kulcinski, L.E. Seitzman, June 1986. (32 pages, 1.5 MB)

UWFDM-761   Non-LTE Effects in Inertial Confinement Fusion Target Chambers; J.J. MacFarlane, G.A. Moses, R.R. Peterson, April 1988 [Nucl. Fusion 29 (1989) 27]. (32 pages, 1.3 MB)

UWFDM-767   Improvements in the SOAST Code; Y. Yamauchi, G.L. Kulcinski, C.D. Croessmann, August 1988. (32 pages, 1.2 MB)

UWFDM-936   U.S. Aqueous Salt Blanket for ITER; I.N. Sviatoslavsky, M. Sawan, G.L. Kulcinski, J. Blanchard, L. El-Guebaly, L. Wittenberg, February 1989 [Presented at the U.S./Canada Workshop on Lithium Salt Blankets, Toronto, Canada, 7-9 February 1989]. (32 pages, 1.6 MB)

UWFDM-1171   Experiments on the Richtmyer-Meshkov Instability I: Preparation of a Membraneless Interface Using the Rayleigh-Taylor Instability; Bhalchandra Puranik, Jason Oakley, Mark Anderson, Riccardo Bonazza, September 2001. (32 pages, 637 kB)

UWFDM-1330   Toward the Ultimate Goal of Tritium Self-Sufficiency: Technical Issues and Requirements Imposed on ARIES Fusion Power Plants; L.A. El-Guebaly and S. Malang, April 2008 (revised August 2008)  [submitted to Fusion Engineering and Design]. (32 pages, 2.0 MB) [more]

UWFDM-199   Critical Assessment of Pulse Annealing; N. Ghoniem and G. Kulcinski, March 1977. (33 pages, 1.2 MB) [more]

UWFDM-213   Quasi-Linear Model for Ion Cyclotron Heating; J. Kesner, June 1977. (33 pages, 1.3 MB)

UWFDM-277   Fusion Reactors: Their Challenge to Materials Scientists; G.L. Kulcinski, October 1978 [Contemp. Phys. 20, 417 (1979)]. (33 pages, 2.8 MB)

UWFDM-326   Radiation-Induced Creep in Single Crystals of Face-Centered Cubic Materials; W.G. Wolfer, October 1979 [Phil. Mag. A31, 61-70 (1981)]. (33 pages, 1.2 MB)

UWFDM-386   Time Dependent Neutronics Analysis for the First Wall of the University of Wisconsin Heavy Ion Beam Fusion Reactor Design; M.E. Sawan, G.A. Moses, G.L. Kulcinski, October 1980 [Trans. ANS 38 (1981) 574, Nucl. Tech./Fusion 2 (1982) 215]. (33 pages, 1.3 MB)

UWFDM-395   Coupled Target - Blanket Neutronics and Photonics Analysis for the University of Wisconsin Heavy Ion Beam Fusion Reactor Design; M.E. Sawan, W.F. Vogelsang, and G.A. Moses, November 1980 [Trans. ANS 38 (1981) 574]. (33 pages, 1.3 MB)

UWFDM-588   Suppression of Void Nucleation by Injected Interstitials During Heavy Ion Bombardment; D.L. Plumton and W.G. Wolfer, August 1984 [J. Nucl. Mat. 120, 245-253 (1984)]. (33 pages, 1.3 MB)

UWFDM-597   A User's Guide to TRAK: A Customizable Particle Following Code; J.W. Johnson, October 1984. (33 pages, 1.7 MB)

UWFDM-614   Liquid Metal Condensation in the Cavity of the HIBALL Heavy Ion Fusion Reactor; L. Pong, M.L. Corradini, R.R. Peterson and G.A. Moses, January 1985. (33 pages, 1.2 MB)

UWFDM-710   Generation of Minimal Cut Sets Using LISP; Y. Watanabe, November 1986. (33 pages, 1.2 MB)

UWFDM-905   Calculational Models for the Treatment of Pulsed/Intermittent Activation within Fusion Energy Devices; S.E. Spangler, J.E. Sisolak, D.L. Henderson, August 1992 [published in Fusion Engineering and Design 22 (July 1993) 349]. (33 pages, 738 kB)

UWFDM-914   Generic Magnetic Fusion Rocket Model; J.F. Santarius and B.G. Logan, April 1993 (revised February 1998)  [Prepared for the 29th AIAA/SAE/ASME/ASEE Joint Propulsion Conference, Paper AIAA-93-2029, June 28-30, 1993, Monterey CA]. (33 pages, 623 kB) [more]

UWFDM-1290   Implicit Monte Carlo Method for Nonlinear Radiation Transport; J. Yuan, G.A. Moses, February 2006. (33 pages, 2.1 MB)

UWFDM-1333   Evaluation of Recent Scenarios for Managing Fusion Activated Materials: Recycling and Clearance, Avoiding Disposal; L. El-Guebaly, V. Massaut, K. Tobita, L. Cadwallader, September 2007 (revised January 2008). (33 pages, 1.8 MB) [more]

UWFDM-42   Transmutation Effects in CTR Materials; G.L. Kulcinski, R. Lott, T. Yang, March 8, 1973. (34 pages, 1.3 MB)

UWFDM-58   Irradiation and Thermal Creep in UWCTR; P.A. Sanger, May 2, 1973. (34 pages, 1.8 MB)

UWFDM-83   Potential CTR Requirements for Helium Up to the Year 2020; G.L. Kulcinski, August 28, 1973. (34 pages, 1.8 MB)

UWFDM-109   A New Fusion Reactor Design Concept; R.W. Conn and G.L. Kulcinski, August 10, 1974. (34 pages, 1.3 MB)

UWFDM-201   Fluid Simulation of Large Tokamak Plasmas Using a Variable Spatial Mesh, Variable Time Step Implicit Procedure; W.A. Houlberg and R.W. Conn, March 1977 [presented at the Mathematics and Computations Division ANS Topical Meeting, Tucson, Arizona, March 28-30, 1977]. (34 pages, 1.4 MB)

UWFDM-212   New Analysis of First Wall Lifetime Considerations for Fusion Reactors; W. Wolfer and R.W. Conn, March 1977. (34 pages, 1.3 MB)

UWFDM-263   Neutronics Optimization Studies for a Proliferation Resistant Fuel Assembly from the Fusion-Fission Fuel Factory, SOLASE-H; M.Z. Youssef, R.W. Conn, and G.A. Moses, October 1978. (34 pages, 1.6 MB)

UWFDM-340   Power Balance in a Tandem Mirror Reactor With Thermal Barriers; J.F. Santarius and R.W. Conn, January 1980. (34 pages, 1.2 MB)

UWFDM-384   A Literature Review of Radiation Damage Data for Copper; R.W. Knoll, October 1980. (34 pages, 1.8 MB)

UWFDM-602   Dislocation Evolution in Metals During Irradiation; W.G. Wolfer and B.B. Glasgow, October 1984 [submitted to Acta Met.]. (34 pages, 1.3 MB)

UWFDM-611   Stability Limit Guidelines for Superconducting Coil Design; P.L. Walstrom, January 1985. (34 pages, 1.5 MB)

UWFDM-947   X-ray-Induced Ionization in the Winds of Near-Main-Sequence O and B Stars; J.J. MacFarlane, D.H. Cohen, P. Wang, May 1994 [submitted to Astrophysical Journal]. (34 pages, 901 kB)

UWFDM-1172   Experiments on the Richtmyer-Meshkov Instability II: Nonlinear Evolution of a Shocked Membraneless Single-Mode Sinusoidal Interface; Bhalchandra Puranik, Jason Oakley, Mark Anderson, Riccardo Bonazza, September 2001. (34 pages, 685 kB)

UWFDM-1411   Environmental Aspects of W-Based Components Employed in ITER, ARIES, and PPCS Fusion Designs; M. Desecures, L. El-Guebaly, June 2012. (34 pages, 1.9 MB) [more]

UWFDM-253   The Depth Dependent Damage Profile in Nickel Irradiated with Nickel or Copper Ions; J.B. Whitley, G.L. Kulcinski, P. Wilkes, and H.V. Smith, Jr., July 1978 [J. Nucl. Matls. 79, 159 (1979)]. (35 pages, 5.2 MB)

UWFDM-410   Boundary Layer Corrections to Neoclassical Ripple Transport in Tokamaks; K-C. Shaing and J.D. Callen, March 1981. (35 pages, 1.2 MB)

UWFDM-478   Analysis and Design of ICF Target Development Facility First Wall Reinforcing Structures; R.L. Engelstad and E.G. Lovell, July 1982. (35 pages, 1.3 MB)

UWFDM-690   Approximation of General Curved Surfaces in the Fabrication of Shell Structures; P.L. Walstrom, September 1986. (35 pages, 1.4 MB)

UWFDM-692   Stability of Vacancy Clusters in Metals I: Energy Calculations for Pure Metals; S.J. Zinkle, L.E. Seitzman, W.G. Wolfer, June 1986. (35 pages, 1.5 MB)

UWFDM-998   Addition of Ga, Pb, and Li-Pb Materials to MELCOR Computer Model and Associated Enhancements; Eric Gracyalny, November 1995. (35 pages, 1.4 MB)

UWFDM-1331   Assessment of Radiation Streaming Through ARIES-CS He-Access Pipes using Two- and Three-Dimensional Analyses; A. Ibrahim, D.L. Henderson, L.A. El-Guebaly, P.P.H. Wilson, M.E. Sawan, December 2007. (35 pages, 5.1 MB)

UWFDM-43   Engineering Feasibility of a Fusion Reactor; R. Boom, G. Kulcinski, C. Maynard and W.F. Vogelsang, April 1973. (36 pages, 1.6 MB)

UWFDM-61   Effect of Neutron Irradiation on the Ductility of 316 Stainless Steel; R. Lott, April 1973. (36 pages, 2.2 MB)


Results: 892 to 990 of 1414 order by: Num Author Title Date Size Length
1  2  3  4  5  6  7  8  9  10   11  12  13  14  15