Publications

     
  1. Non-Oscillatory Central Schemes for the Incompressible 2D Euler Equations, Mathematical Research Letters, 4, 1997, pp. 321-340. (with E. Tadmor)
  2. On a Class of a Thermal Blow-up Patterns, Physics Letters A., 236, 1997, pp. 483-493. (with P. Rosenau)
  3. From Semi-Discrete to Fully-Discrete: The Stability of Runge-Kutta Schemes by the Energy Method, SIAM Review, 40, no.1, 1998, pp. 40-73. (with E. Tadmor)
  4. On Burgers-type Equations with Non-Monotonic Dissipative Fluxes, Communications on Pure and Applied Mathematics, 51, no. 5, 1998, pp. 443-473. (with A. Kurganov and P. Rosenau)
  5. High-Resolution Non-Oscillatory Central Schemes with Non-Staggered Grids for Hyperbolic Conservation Laws, SIAM Journal on Numerical Analysis, 35, no. 6, 1998, pp. 2147-2168. (with G.-S. Jiang, C.-T. Lin, S. Osher and E. Tadmor)
  6. Third-order 2D Central Schemes for Hyperbolic Conservation Laws, INRIA School on Hyperbolic Systems, Vol. I, 1998, pp. 489-504.
  7. Self-Focusing in the Complex Ginzburg-Landau Limit of the Critical Nonlinear Schrodinger Equation, Physics Letters A., 249, 1998, pp. 286-294. (with G. Fibich)
  8. Compactons in a Class of Nonlinearly Quintic Equations, Physics Letters A., 252, 1999, pp. 297-306. (with P. Rosenau)
  9. A Modified Structured Central Scheme for 2D Hyperbolic Conservation Laws, Applied Math Letters, 12, no. 6, 1999, pp. 89-96. (with T. Katsaounis)
  10. Central WENO Schemes for Hyperbolic Systems of Conservation Laws, Mathematical Modeling and Numerical Analysis, 33, no. 3, 1999, pp. 547-571. (with G. Puppo and G. Russo)
  11. Dissipative Behavior of Some Fully Non-Linear KdV-Type Equations, Physica D., 137, 2000, pp. 277-294 (with Y. Brenier)
  12. A Third Order Central WENO Scheme for 2D Conservation Laws, Applied Numerical Mathematics, 33, 2000, pp. 407-414. (with G. Puppo and G. Russo)
  13. On the Behavior of the Total Variation in CWENO Methods for Conservation Laws, Applied Numerical Mathematics, 33, 2000, pp. 415-421. (with G. Puppo and G. Russo)
  14. Optimal Prediction for Hamiltonian Partial Differential Equations, Journal of Computational Physics, 162, 2000, pp. 267-297. (with A.J. Chorin and R. Kupferman)
  15. Compact Central WENO Schemes for MultiDimensional Conservation Laws, SIAM Journal on Scientific Computing, 22, 2000, pp. 656-672. (with G. Puppo and G. Russo)
  16. A Third-Order Semi-Discrete Central Scheme for Conservation Laws and Convection-Diffusion Equations, SIAM Journal on Scientific Computing, 22, 2000, pp. 1461-1488. (with A. Kurganov)
  17. Particle Methods for Dispersive Equations, Journal of Computational Physics, 171, 2001, pp. 708-730. (with A. Chertock)
  18. Central-Upwind Schemes for the Saint-Venant System, Mathematical Modelling and Numerical Analysis, 36, 2002, pp. 397-425. (with A. Kurganov)
  19. A Fourth Order Central WENO Scheme for Multi-Dimensional Hyperbolic Systems of Conservation Laws, SIAM Journal on Scientific Computing, 24, 2002, pp. 480-506. (with G. Puppo and G. Russo)
  20. A Particle Method for the KdV Equation, Journal of Scientific Computing, 17, 2002, pp. 491-499. (with A. Chertock)
  21. High-order Central WENO Schemes for 1D Hamilton-Jacobi Equations, in F. Brezzi et al. (Eds.), ``Numerical Mathematics and Advanced Applications'', Proc. ENUMATH 2001, Ischia, Italy; Springer-Verlag, Italy, 2003, pp.45--54. (with S. Bryson)
  22. High-Order Central WENO Schemes for Multi-dimensional Hamilton-Jacobi Equations, in T.Y. Hou and E. Tadmor (Eds.), ``Hyperbolic Problems: Theory, Numerics, Applications'', Proc. Ninth International Conference on Hyperbolic Problems, CalTech, 2002; Springer-Verlag, Berlin, 2003, pp.387--396. (with S. Bryson)
  23. High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations, Journal of Computational Physics, 189, 2003, pp. 63-87. (with S. Bryson)
  24. High-Order Central WENO Schemes for Multi-Dimensional Hamilton-Jacobi Equations, SIAM Journal of Numerical Analysis, 41, 2003, pp. 1339-1369. (with S. Bryson)
  25. Central Schemes for Multi-Dimensional Hamilton-Jacobi Equations, SIAM Journal on Scientific Computing, 25, 2003, pp. 769-791. (with S. Bryson)
  26. Local Discontinuous Galerkin Methods for Nonlinear Dispersive Equations, Journal of Computational Physics, 196, 2004, pp. 751-772. (with C.-W. Shu and J. Yan)
  27. Central Schemes for Hamilton-Jacobi Equations on Unstructured Grids, in M. Feistauer et al. (Eds.), ``Numerical Mathematics and Advanced Applications'', Proceedings of ENUMATH 2003, Prague, Czech Republic; Springer-Verlag, Berlin, 2004, pp.623--630. (with S. Nayak)
  28. On Wavelet-Based Numerical Homogenization, Multiscale Modeling and Simulation, 3, 2004, pp. 65-88. (with A. Chertock)
  29. Registration-based Morphing of Active Contours for Segmentation of CT Scans, Mathematical Biosciences and Engineering, 2, 2005, pp. 79-96. (with Y.-N. Young)
  30. Semi-Discrete Central-Upwind Schemes with Reduced Dissipation for Hamilton-Jacobi Equations, IMA Journal of Numerical Analysis, 25, 2005, pp. 113-138. (with S. Bryson, A. Kurganov, and G. Petrova)
  31. High-Order Shock-Capturing Methods for Modeling Dynamics of the Solar Atmosphere, Physica D., 201, 2005, pp. 1-26. (with S. Bryson and A. Kosovichev)
  32. Quantitation of the a Priori Dosimetric Capabilities of Spatial Points in Inverse Planning and its Significant Implication in Defining IMRT Solution Space, Physics in Medicine and Biology, 50, 2005, pp. 1469-1482. (with Z. Shou, Y. Yang, C. Cotrutz and L. Xing)
  33. PDE-based Segmentation for Radiotherapy Treatment Planning, Mathematical Biosciences and Engineering, 2, 2005, pp. 209-226. (with F. Gibou, C. Cardenas, P. Liu, and A. Boyer)
  34. Approximate Model Equations for Water Waves, Communications in Mathematical Sciences, 3, 2005, pp. 159-170 (with R. Fetecau)
  35. Post Transplantation Dynamics of the Immune Response to Chronic Myelogenous Leukemia, Journal of Theoretical Biology, 236, 2005, pp. 39-59 (with R. DeConde, P. Kim, and P. Lee)
  36. A Stable Semi-Discrete Central Scheme for the Two-Dimensional Incompressible Euler Equations, IMA Journal of Numerical Analysis, 25, 2005, pp. 507-522.
  37. Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids, SIAM Journal on Scientific Computing, 27, 2005, pp. 532-552. (with S. Bryson)
  38. Multiscale Image Registration, Mathematical Biosciences and Engineering, 3, 2006, pp. 389-418. (with D. Paquin, E. Schreibmann, and L. Xing)
  39. On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws, Journal of Scientific Computing, 27, 2006, pp. 163-175. (with S. Bryson)
  40. Mapped WENO and Weighted Power ENO Reconstructions in Semi-Discrete Central Schemes for Hamilton-Jacobi Equations, Applied Numerical Mathematics, 56, 2006, pp. 1211-1224. (with S. Bryson)
  41. Central WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes, SIAM Journal on Scientific Computing, 28, 2006, pp. 2229-2247 (with S. Nayak, C.-W. Shu, and Y.-T. Zhang)
  42. On the Stability Crossing Boundaries of Some Delay Systems Modeling Immune Dynamics in Leukemia, Proc 17th Int Symp on Mathematical Theory of Networks and Systems, Kyoto, 2006 (with S.-I. Niculescu, P. Kim, and K. Gu)
  43. Modeling Regulation Mechanisms in the Immune System, Journal of Theoretical Biology, 246, 2007, pp. 33-69 (with P. Kim and P. Lee)
  44. On Stability of a Combined Gleevec and Immune Model of Chronic Myelogenous Leukemia: Exploiting Delay System Structure.   Proceedings of 2007 IFAC Symposium on Nonlinear Control (NOLCOS'07), Pretoria (South Africa), (with S. Niculescu, P. Kim and P. Lee)
  45. Mini-Transplants for Chronic Myelogenous Leukemia: A Modeling Perspective, in Queinnec et al. (eds.) "Biology and Control Theory: Current Challenges", Lecture notes in control and information sciences, LNCIS 357, Springer, Berlin, 2007, pp. 3-20. (with P. Kim and P. Lee)
  46. Hybrid Multiscale Landmark and Deformable Registration, Mathematical Biosciences and Engineering, 4, 2007, pp. 711-737. (with D. Paquin and L. Xing)
  47. Group Dynamics of Phototaxis: Interacting Stochastic Many-Particle Systems and their Continuum Limit, in S. Benzoni-Gavage and D. Serre (Eds.), "Hyperbolic Problems: Theory, Numerics, Application", Proceedings of HYP 2006, Lyon, France; Springer-Verlag, Berlin, 2008, pp. 145-169. (with D. Bhaya and T. Requiejo)
  48. Modeling Imatinib-Treated Chronic Myelogenous Leukemia: Reducing the Complexity of Agent-Based Models, Bulletin of Mathematical Biology, 70, pp. 724-744. (with P. Kim and P. Lee) 
  49. Modeling Group Dynamics of Phototaxis: From Particles to PDEs, Discrete and Continuous Dynamical Systems B, 9, 2008, pp. 108-128 (with T. Requiejo)
  50. Multiscale Deformable Registration of Noisy Medical Images, Mathematical Biosciences and Engineering, 5, 2008, pp. 125-144 (with D. Paquin and L. Xing)
  51. Dynamics and Potential Impact of the Immune Response to Chronic Myelogenous Leukemia, PLOS Computational Biology, 4, 2008, e1000095 doi:10.1371/journal.pcbi.1000095 (with P. Kim and P. Lee)
  52. Stochastic Models for Phototaxis, Bulletin of Mathematical Biology, to appear (with T. Requeijo)
  53. Multiscale Registration of Planning CT and Daily Cone Beam CT Images for Adaptive Radiation Therapy, Medical Physics, to appear (with D. Paquin and L. Xing)
  54. A PDE Model for Imatinib-Treated Chronic Myelogenous Leukemia, Bulletin of Mathematical Biology, to appear (with P. Kim and P. Lee)
  55. Stability Crossing Boundaries of Delay Systems Modeling Immune Dynamics in Leukemia, Submitted (with K. Gu, P. Kim, P. Lee, and S. Niculescu)
  56. Dynamics and Functional Discrepancies in CD4 and CD8 T Cell Responses to EBV in Acute Infectious Mononucleosis, Submitted (with A. Johannsen, N. Yan, P. Kim, D. Paquin, and P. Lee)
  57. Analysis of Models of Chronic Myelogenous Leukemia with Treatment Options using Structural Methods and Computation: Sensitivity to Nonlinearity and Delay, Submitted (with M. Peet, P. Kim, S.-I. Niculesco, and A. Papachristodoulou)
  58. Particle, Kinetic, and Fluid Models for Phototaxis, Submitted (with S.-Y. Ha)
  59. On the Role of Adaptive Regulatory Cells in the Immune System, In preparation (with P. Kim and P. Lee)
 

                                         © Doron Levy 2008