All Stories

  1. Improved upper bounds on the energy dissipation rate for shear flow with injection and suction

    Article • Physics of Fluids, August 2019, American Institute of Physics

    Professor Charles R Doering, Harry Lee

  2. Nucleation pressure threshold in acoustic droplet vaporization

    Article • Journal of Applied Physics, July 2016, American Institute of Physics

    Professor Charles R Doering

  3. Gene expression dynamics with stochastic bursts: Construction and exact results for a coarse-grained model

    Article • February 2016, American Physical Society (APS)

    Professor Charles R Doering

  4. Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Bénard convection

    Article • Physical Review E, October 2015, American Physical Society (APS)

    Professor Charles R Doering

  5. Transport bounds for a truncated model of Rayleigh–Bénard convection

    Article • Physica D Nonlinear Phenomena, July 2015, Elsevier

    Professor Charles R Doering

  6. Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field

    Article • Journal of Fluid Mechanics, May 2015, Cambridge University Press

    Professor Charles R Doering

  7. Maximal transport in the Lorenz equations

    Article • Physics Letters A, March 2015, Elsevier

    Professor Charles R Doering

  8. Wall to wall optimal transport

    Article • Journal of Fluid Mechanics, June 2014, Cambridge University Press

    Professor Charles R Doering

  9. Demographic stochasticity and evolution of dispersion I. Spatially homogeneous environments

    Article • Journal of Mathematical Biology, March 2014, Springer Science + Business Media

    Professor Charles R Doering

  10. Demographic stochasticity and evolution of dispersion II: Spatially inhomogeneous environments

    Article • Journal of Mathematical Biology, March 2014, Springer Science + Business Media

    Professor Charles R Doering

  11. Discrete and Continuum Dynamics of Reacting and Interacting Individuals

    Article • January 2014, Springer Science + Business Media

    Professor Charles R Doering

  12. Computational approaches to aspect-ratio-dependent upper bounds and heat flux in porous medium convection

    Article • Physics Letters A, December 2013, Elsevier

    Professor Charles R Doering

  13. Bounds on Surface Stress-Driven Shear Flow

    Article • Journal of Nonlinear Science, July 2013, Springer Science + Business Media

    Professor Charles R Doering

  14. Erratum: “Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows” [J. Math. Phys. 53, 115611 (2012)]

    Article • Journal of Mathematical Physics, July 2013, American Institute of Physics

    Professor Charles R Doering

  15. 2012 program of study : coherent structures

    Article • January 2013, MBLWHOI Library

    Dr Colm-cille Patrick Caulfield, Professor Charles R Doering

  16. Introduction to Special Issue: Incompressible Fluids, Turbulence and Mixing

    Article • Journal of Mathematical Physics, November 2012, American Institute of Physics

    Professor Charles R Doering

  17. Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows

    Article • Journal of Mathematical Physics, October 2012, American Institute of Physics

    Professor Charles R Doering

  18. Rigid bounds on heat transport by a fluid between slippery boundaries

    Article • Journal of Fluid Mechanics, July 2012, Cambridge University Press

    Professor Charles R Doering

  19. New upper bounds and reduced dynamical modeling for Rayleigh–Bénard convection in a fluid saturated porous layer

    Article • Communications in Nonlinear Science and Numerical Simulation, May 2012, Elsevier

    Professor Charles R Doering

  20. Features of Fast Living: On the Weak Selection for Longevity in Degenerate Birth-Death Processes

    Article • Journal of Statistical Physics, April 2012, Springer Science + Business Media

    Professor Charles R Doering

  21. Noise-induced statistically stable oscillations in a deterministically divergent nonlinear dynamical system

    Article • Communications in Mathematical Sciences, January 2012, International Press of Boston

    Professor Charles R Doering

  22. Corrigendum to “Stirring up trouble: Multi-scale mixing measures for steady scalar sources” [Physica D 231 (2007) 143–164]

    Article • Physica D Nonlinear Phenomena, November 2011, Elsevier

    Professor Charles R Doering

  23. Internal heating driven convection at infinite Prandtl number

    Article • Journal of Mathematical Physics, September 2011, American Institute of Physics

    Professor Charles R Doering

  24. Symmetric factorization of the conformation tensor in viscoelastic fluid models

    Article • Journal of Non-Newtonian Fluid Mechanics, June 2011, Elsevier

    Professor Charles R Doering

  25. Ultimate State of Two-Dimensional Rayleigh-Bénard Convection between Free-Slip Fixed-Temperature Boundaries

    Article • Physical Review Letters, June 2011, American Physical Society (APS)

    Professor Charles R Doering

  26. Optimal stirring strategies for passive scalar mixing

    Article • Journal of Fluid Mechanics, March 2011, Cambridge University Press

    Professor Charles R Doering

  27. The mixing efficiency of open flows

    Article • Physica D Nonlinear Phenomena, January 2011, Elsevier

    Professor Charles R Doering

  28. Low-dimensional models from upper bound theory

    Article • Physica D Nonlinear Phenomena, January 2011, Elsevier

    Professor Charles R Doering

  29. A Fast Explicit Operator Splitting Method for Passive Scalar Advection

    Article • Journal of Scientific Computing, June 2010, Springer Science + Business Media

    Professor Charles R Doering

  30. Demographic stochasticity versus spatial variation in the competition between fast and slow dispersers

    Article • Theoretical Population Biology, June 2010, Elsevier

    Professor Charles R Doering

  31. Bounds on heat transport in Bénard-Marangoni convection

    Article • Physical Review E, April 2010, American Physical Society (APS)

    Professor Charles R Doering

  32. Models measures of mixing effective diffusion

    Article • Discrete and Continuous Dynamical Systems, April 2010, American Institute of Mathematical Sciences (AIMS)

    Professor Charles R Doering

  33. Destabilizing Taylor–Couette flow with suction

    Article • Physics of Fluids, March 2010, American Institute of Physics

    Professor Charles R Doering

  34. Extreme vorticity growth in Navier–Stokes turbulence

    Article • Physics Letters A, January 2010, Elsevier

    Professor Bruno Eckhardt, Professor Charles R Doering

  35. Comparison of Turbulent Thermal Convection between Conditions of Constant Temperature and Constant Flux

    Article • Physical Review Letters, February 2009, American Physical Society (APS)

    Professor Charles R Doering

  36. The 3D Navier-Stokes Problem

    Article • Annual Review of Fluid Mechanics, January 2009, Annual Reviews

    Professor Charles R Doering

  37. A comparison of turbulent thermal convection between conditions of constant temperature and constant heat flux boundaries

    Article • January 2009, Springer Science + Business Media

    Professor Charles R Doering

  38. Enstrophy amplification events in three-dimensional turbulence

    Article • Chaos An Interdisciplinary Journal of Nonlinear Science, December 2008, American Institute of Physics

    Professor Bruno Eckhardt, Professor Charles R Doering

  39. Mixing effectiveness depends on the source–sink structure: simulation results

    Article • Journal of Statistical Mechanics Theory and Experiment, July 2008, Institute of Physics Publishing

    Professor Bruno Eckhardt, Professor Charles R Doering

  40. DREAMS VERSUS REALITY: PLENARY DEBATE SESSION ON QUANTUM COMPUTING

    Article • Fluctuation and Noise Letters, June 2008, World Scientific Pub Co Pte Lt

    Professor Charles R Doering

  41. Limits on enstrophy growth for solutions of the three-dimensional Navier-Stokes equations

    Article • Indiana University Mathematics Journal, January 2008, Indiana University Mathematics Journal

    Professor Charles R Doering

  42. Enstropy Generation and Regularity of Solutions to the 3D Navier-Stokes Equations

    Article • January 2008, Springer Science + Business Media

    Professor Charles R Doering

  43. Rayleigh-Bénard convection with imposed heat flux

    Article • Chaos An Interdisciplinary Journal of Nonlinear Science, December 2007, American Institute of Physics

    Professor Charles R Doering

  44. Mathematical Geophysics: An Introduction to Rotating Fluids and the Navier-Stokes Equations. By J.-Y. Chemin, B. Desjardins, I. Gallagher & E. Grenier. Oxford University Press, 2006. 272 pp. ISBN 019857133X. £47

    Article • Journal of Fluid Mechanics, August 2007, Cambridge University Press

    Professor Charles R Doering

  45. Stirring up trouble: Multi-scale mixing measures for steady scalar sources

    Article • Physica D Nonlinear Phenomena, July 2007, Elsevier

    Professor Charles R Doering

  46. Introduction to Special Issue: Mathematical Fluid Dynamics

    Article • Journal of Mathematical Physics, June 2007, American Institute of Physics

    Professor Charles R Doering

  47. Energy dissipation in fractal-forced flow

    Article • Journal of Mathematical Physics, June 2007, American Institute of Physics

    Professor Charles R Doering

  48. Asymptotics of rare events in birth–death processes bypassing the exact solutions

    Article • Journal of Physics Condensed Matter, January 2007, Institute of Physics Publishing

    Professor Charles R Doering

  49. Energy and enstrophy dissipation in steady state 2d turbulence

    Article • Physics Letters A, December 2006, Elsevier

    Professor Charles R Doering

  50. Introduction: Third Annual Gallery of Nonlinear Images (Baltimore, Maryland, 2006)

    Article • Chaos An Interdisciplinary Journal of Nonlinear Science, December 2006, American Institute of Physics

    Professor Charles R Doering

  51. Multiscale mixing efficiencies for steady sources

    Article • Physical Review E, August 2006, American Physical Society (APS)

    Professor Charles R Doering

  52. Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh–Bénard convection

    Article • Journal of Fluid Mechanics, July 2006, Cambridge University Press

    Professor Charles R Doering

  53. Links between dissipation, intermittency, and helicity in the GOY model revisited

    Article • Physica D Nonlinear Phenomena, June 2006, Elsevier

    Professor Bruno Eckhardt, Professor Charles R Doering

  54. Failure of energy stability in Oldroyd-B fluids at arbitrarily low Reynolds numbers

    Article • Journal of Non-Newtonian Fluid Mechanics, May 2006, Elsevier

    Professor Bruno Eckhardt, Professor Charles R Doering

  55. 2005 program of studies : fast times and fine scales

    Article • January 2006, MBLWHOI Library

    Professor Charles R Doering

  56. Introduction: Second Annual Gallery of Nonlinear Images (Los Angeles, California, 2005)

    Article • Chaos An Interdisciplinary Journal of Nonlinear Science, December 2005, American Institute of Physics

    Professor Charles R Doering

  57. A numerical method for some stochastic differential equations with multiplicative noise

    Article • Physics Letters A, September 2005, Elsevier

    Professor Charles R Doering

  58. On Travelling Waves for the Stochastic Fisher–Kolmogorov–Petrovsky–Piscunov Equation

    Article • Journal of Statistical Physics, August 2005, Springer Science + Business Media

    Professor Charles R Doering

  59. Intermittency and Regularity Issues in 3D Navier-Stokes Turbulence

    Article • Archive for Rational Mechanics and Analysis, June 2005, Springer Science + Business Media

    Professor Charles R Doering

  60. Extinction Times for Birth-Death Processes: Exact Results, Continuum Asymptotics, and the Failure of the Fokker--Planck Approximation

    Article • Multiscale Modeling and Simulation, January 2005, Society for Industrial & Applied Mathematics (SIAM)

    Professor Charles R Doering

  61. Mean Extinction Time for Birth-Death Processes & Failure of the Fokker-Planck Approximation

    Article • January 2005, American Institute of Physics

    Professor Charles R Doering

  62. A bound on mixing efficiency for the advection–diffusion equation

    Article • Journal of Fluid Mechanics, December 2004, Cambridge University Press

    Professor Charles R Doering

  63. Bounds on convection driven by internal heating

    Article • Journal of Mathematical Physics, July 2004, American Institute of Physics

    Professor Charles R Doering

  64. High-Rayleigh-number convection in a fluid-saturated porous layer

    Article • Journal of Fluid Mechanics, January 2004, Cambridge University Press

    Professor Charles R Doering

  65. Dreams Versus Reality: Plenary Debate Session on Quantum Computing

    Article • Quantum Information Processing, December 2003, Springer Science + Business Media

    Professor Charles R Doering

  66. Bounds on dissipation in magnetohydrodynamic problems in plane shear geometry

    Article • Physics of Plasmas, November 2003, American Institute of Physics

    Professor Charles R Doering

  67. Bounds on dissipation in magnetohydrodynamic Couette and Hartmann shear flows

    Article • Physics of Plasmas, November 2003, American Institute of Physics

    Professor Charles R Doering

  68. Smooth and rough boundaries in turbulent Taylor-Couette flow

    Article • September 2003, American Physical Society (APS)

    Professor Charles R Doering

  69. Interacting particles, the stochastic Fisher–Kolmogorov–Petrovsky–Piscounov equation, and duality

    Article • Physica A Statistical Mechanics and its Applications, July 2003, Elsevier

    Professor Charles R Doering

  70. Intermittency in solutions of the three-dimensional Navier–Stokes equations

    Article • Journal of Fluid Mechanics, March 2003, Cambridge University Press

    Professor Charles R Doering

  71. Conceptual models of the climate : 2002 program of study, Bounds on turbulent transport

    Article • January 2003, MBLWHOI Library

    Dr Colm-cille Patrick Caulfield, Professor Charles R Doering

  72. Noisy Wavefront Propagation in the Fisher-Kolmogorov-Petrovsky-Piscounov Equation

    Article • January 2003, American Institute of Physics

    Professor Charles R Doering

  73. Bounds on Rayleigh–Bénard convection with an imposed heat flux

    Article • Journal of Fluid Mechanics, December 2002, Cambridge University Press

    Professor Charles R Doering

  74. Energy dissipation in body-forced turbulence

    Article • Journal of Fluid Mechanics, September 2002, Cambridge University Press

    Professor Charles R Doering

  75. Bounds on moments of the energy spectrum for weak solutions of the three-dimensional Navier–Stokes equations

    Article • Physica D Nonlinear Phenomena, May 2002, Elsevier

    Professor Charles R Doering

  76. On upper bounds for infinite Prandtl number convection with or without rotation

    Article • Journal of Mathematical Physics, January 2001, American Institute of Physics

    Professor Charles R Doering

  77. Bulk Dissipation in Shear Layers with Suction

    Article • January 2001, Springer Science + Business Media

    Professor Charles R Doering

  78. Energy dissipation in a shear layer with suction

    Article • Physics of Fluids, August 2000, American Institute of Physics

    Professor Charles R Doering

  79. Laminar and turbulent dissipation in shear flow with suction

    Article • January 2000, American Institute of Physics

    Professor Charles R Doering

  80. Bounds for heat transport in a porous layer

    Article • Journal of Fluid Mechanics, December 1998, Cambridge University Press

    Professor Charles R Doering

  81. Attractor dimension estimates for two-dimensional shear flows

    Article • Physica D Nonlinear Phenomena, November 1998, Elsevier

    Professor Charles R Doering

  82. Constructive role of noise: Fast fluctuation asymptotics of transport in stochastic ratchets

    Article • Chaos An Interdisciplinary Journal of Nonlinear Science, September 1998, American Institute of Physics

    Professor Charles R Doering

  83. Stochastic ratchets

    Article • Physica A Statistical Mechanics and its Applications, May 1998, Elsevier

    Professor Charles R Doering

  84. Energy stability bounds on convective heat transport:mNumerical study

    Article • June 1997, American Physical Society (APS)

    Professor Charles R Doering

  85. Reentrant transitions in globally coupled active rotators with multiplicative and additive noises

    Article • Physics Letters A, January 1997, Elsevier

    Professor Charles R Doering

  86. Convection, stability, and low dimensional dynamics

    Article • January 1997, American Institute of Physics

    Professor Charles R Doering

  87. Rigorous estimates of small scales in turbulent flows

    Article • Journal of Mathematical Physics, December 1996, American Institute of Physics

    Professor Charles R Doering

  88. Heat transfer in convective turbulence

    Article • Nonlinearity, July 1996, Institute of Physics Publishing

    Professor Charles R Doering

  89. Variational bounds on energy dissipation in incompressible flows. III. Convection

    Article • June 1996, American Physical Society (APS)

    Professor Charles R Doering

  90. Numerical and analytical studies of nonequilibrium fluctuation-induced transport processes

    Article • Journal of Statistical Physics, May 1996, Springer Science + Business Media

    Professor Charles R Doering

  91. Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics

    Article • April 1996, American Physical Society (APS)

    Professor Charles R Doering

  92. Fluctuations and Stability of Fisher Waves

    Article • Physical Review Letters, July 1995, American Physical Society (APS)

    Professor Charles R Doering

  93. Exponential decay rate of the power spectrum for solutions of the Navier–Stokes equations

    Article • Physics of Fluids, June 1995, American Institute of Physics

    Professor Charles R Doering

  94. Applied Analysis of the Navier-Stokes Equations

    Article • April 1995, Cambridge University Press

    Professor Charles R Doering

  95. Variational bounds in dissipative systems

    Article • Physica D Nonlinear Phenomena, April 1995, Elsevier

    Professor Charles R Doering

  96. Variational bounds on energy dissipation in incompressible flows. II. Channel flow

    Article • April 1995, American Physical Society (APS)

    Professor Charles R Doering

  97. On the shape and dimension of the Lorenz attractor

    Article • Dynamics and Stability of Systems, January 1995, Taylor & Francis

    Professor Charles R Doering

  98. Editors' note

    Article • Physics Letters A, November 1994, Elsevier

    Professor Charles R Doering

  99. Nonequilibrium fluctuation-induced transport

    Article • Physical Review Letters, May 1994, American Physical Society (APS)

    Professor Charles R Doering

  100. Variational bounds on energy dissipation in incompressible flows: Shear flow

    Article • May 1994, American Physical Society (APS)

    Professor Charles R Doering

  101. Weak and strong solutions of the complex Ginzburg-Landau equation

    Article • Physica D Nonlinear Phenomena, March 1994, Elsevier

    Professor Charles R Doering

  102. Stability of reaction-diffusion-convection systems: the case of linear shear flow

    Article • Physics Letters A, November 1993, Elsevier

    Professor Charles R Doering

  103. Scaling of turbulent spike amplitudes in the complex Ginzburg-Landau equation

    Article • Physics Letters A, July 1993, Elsevier

    Professor Charles R Doering

  104. Thermally activated escape over fluctuating barriers

    Article • June 1993, American Physical Society (APS)

    Professor Charles R Doering

  105. Energy Dissipation in Shear Driven Turbulence

    Article • Physical Review Letters, November 1992, American Physical Society (APS)

    Professor Charles R Doering

  106. Resonant activation over a fluctuating barrier

    Article • Physical Review Letters, October 1992, American Physical Society (APS)

    Professor Charles R Doering

  107. Energy dissipation in shear driven turbulence

    Article • Physical Review Letters, September 1992, American Physical Society (APS)

    Professor Charles R Doering

  108. Microscopic spatial correlations induced by external noise in a reaction-diffusion system

    Article • Physica A Statistical Mechanics and its Applications, September 1992, Elsevier

    Professor Charles R Doering

  109. Fluctuations and correlations in a diffusion-reaction system: Unified description of internal fluctuations and external noise

    Article • Physical Review A, April 1992, American Physical Society (APS)

    Professor Charles R Doering

  110. Long transmission times for transport through a weakly scattering slab

    Article • Physical Review A, January 1992, American Physical Society (APS)

    Professor Charles R Doering

  111. Fluctuations and correlations in a diffusion-reaction system: Exact hydrodynamics

    Article • Journal of Statistical Physics, December 1991, Springer Science + Business Media

    Professor Charles R Doering

  112. Note on the Constantin-Foias-Temam attractor dimension estimate for two-dimensional turbulence

    Article • Physica D Nonlinear Phenomena, March 1991, Elsevier

    Professor Charles R Doering

  113. Joint density closure schemes for a diffusion-limited reaction

    Article • Chemical Physics, October 1990, Elsevier

    Professor Charles R Doering

  114. On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equation

    Article • Physica D Nonlinear Phenomena, September 1990, Elsevier

    Professor Charles R Doering

  115. Statics and dynamics of a diffusion-limited reaction: Anomalous kinetics, nonequilibrium self-ordering, and a dynamic transition

    Article • Journal of Statistical Physics, September 1990, Springer Science + Business Media

    Professor Charles R Doering

  116. Long crossover times in a finite system

    Article • Physical Review Letters, January 1990, American Physical Society (APS)

    Professor Charles R Doering

  117. Hard turbulence in a finite dimensional dynamical system?

    Article • Physics Letters A, December 1989, Elsevier

    Professor Charles R Doering

  118. Mean Exit times for Particles Driven by Weakly Colored Noise

    Article • SIAM Journal on Applied Mathematics, October 1989, Society for Industrial & Applied Mathematics (SIAM)

    Professor Charles R Doering

  119. Transition in the relaxation dynamics of a reversible diffusion-limited reaction

    Article • Physical Review Letters, August 1989, American Physical Society (APS)

    Professor Charles R Doering

  120. Diffusion-Limited Coagulation in the Presence of Particle Input: Exact Results in One Dimension

    Article • Physical Review Letters, July 1989, American Physical Society (APS)

    Professor Charles R Doering

  121. Diffusion-limited coagulation in the presence of particle input: Exact results in one dimension

    Article • Physical Review Letters, May 1989, American Physical Society (APS)

    Professor Charles R Doering

  122. Mean exit times over fluctuating barriers

    Article • Physics Letters A, April 1989, Elsevier

    Professor Charles R Doering

  123. External noise and its interaction with spatial degrees of freedom in nonlinear dissipative systems

    Article • Journal of Statistical Physics, March 1989, Springer Science + Business Media

    Professor Charles R Doering

  124. the distribution of exit times for weakly colored noise

    Article • Journal of Statistical Physics, March 1989, Springer Science + Business Media

    Professor Charles R Doering

  125. Interparticle distribution functions and rate equations for diffusion-limited reactions

    Article • September 1988, American Physical Society (APS)

    Professor Charles R Doering

  126. Doering et al. Reply

    Article • Physical Review Letters, June 1988, American Physical Society (APS)

    Professor Charles R Doering

  127. Equilibrium of two-species annihilation with input

    Article • June 1988, American Physical Society (APS)

    Professor Charles R Doering

  128. Exact Lyapunov Dimension of the Universal Attractor for the Complex Ginzburg-Landau Equation

    Article • Physical Review Letters, December 1987, American Physical Society (APS)

    Professor Charles R Doering

  129. Nonlinear parabolic stochastic differential equations with additive colored noise onR d �R +: A regulated stochastic quantization

    Article • Communications in Mathematical Physics, December 1987, Springer Science + Business Media

    Professor Charles R Doering

  130. Bistability driven by weakly colored Gaussian noise: The Fokker-Planck boundary layer and mean first-passage times

    Article • Physical Review Letters, November 1987, American Physical Society (APS)

    Professor Charles R Doering

  131. Random walk in a quasicontinuum

    Article • July 1987, American Physical Society (APS)

    Professor Charles R Doering

  132. A stochastic partial differential equation with multiplicative noise

    Article • Physics Letters A, June 1987, Elsevier

    Professor Charles R Doering

  133. Comment on first-passage times for processes driven by dichotomous fluctuations

    Article • April 1987, American Physical Society (APS)

    Professor Charles R Doering

  134. Optimal signal-to-noise in digital phase lock amplifiers

    Article • Applied Optics, February 1987, Optical Society of America (OSA)

    Professor Charles R Doering

  135. Stability and dynamics of a noise-induced stationary state

    Article • September 1986, American Physical Society (APS)

    Professor Charles R Doering

  136. Nonperturbative bounds on 〈 φ n 〉 in cutoff (λ φ n ) d field theory

    Article • Physical Review Letters, October 1985, American Physical Society (APS)

    Professor Charles R Doering

  137. Random walks, resonance, and ratchets

    Article • Cambridge University Press

    Professor Charles R Doering

  138. Low-Wavenumber Forcing and Turbulent Energy Dissipation

    Article • Springer Science + Business Media

    Professor Charles R Doering

  139. Regularity and length scales for the 2d and 3d Navier-Stokes equations

    Article • Cambridge University Press

    Professor Charles R Doering

  140. Preface

    Article • Cambridge University Press

    Professor Charles R Doering

  141. Turbulence

    Article • Cambridge University Press

    Professor Charles R Doering

  142. Inequalities

    Article • Cambridge University Press

    Professor Charles R Doering

  143. References

    Article • Cambridge University Press

    Professor Charles R Doering

  144. The equations of motion

    Article • Cambridge University Press

    Professor Charles R Doering

  145. Dimensionless parameters and stability

    Article • Cambridge University Press

    Professor Charles R Doering

  146. Effect of Boundary Condition Fluctuations on Smoluchowski Reaction Rates

    Article • Springer Science + Business Media

    Professor Charles R Doering

  147. Degrees of freedom, dynamical systems, and attractors

    Article • Cambridge University Press

    Professor Charles R Doering

  148. On the existence, uniqueness, and regularity of solutions

    Article • Cambridge University Press

    Professor Charles R Doering

  149. Ladder results for the Navier-Stokes equations

    Article • Cambridge University Press

    Professor Charles R Doering

  150. Exponential decay of the Fourier power spectrum

    Article • Cambridge University Press

    Professor Charles R Doering

  151. The attractor dimension for the Navier-Stokes equations

    Article • Cambridge University Press

    Professor Charles R Doering

  152. Energy dissipation rate estimates for boundary-driven flows

    Article • Cambridge University Press

    Professor Charles R Doering