Charles R. Doering
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American mathematician
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Charles R. Doeringmathematics Degrees
Mathematics
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Applied Mathematics
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#195
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#65
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#706
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Mathematics Physics
Charles R. Doering's Degrees
- PhD Physics University of Texas at Austin
- Bachelors Physics University of Texas at Austin
Why Is Charles R. Doering Influential?
(Suggest an Edit or Addition)According to Wikipedia, Charles Rogers Doering was a professor of mathematics at the University of Michigan, Ann Arbor. He is notable for his research that is generally focused on the analysis of stochastic dynamical systems arising in biology, chemistry and physics, to systems of nonlinear partial differential equations. Recently he had been focusing on fundamental questions in fluid dynamics as part of the $1M Clay Institute millennium challenge concerning the regularity of solutions to the equations of fluid dynamics. With J. D. Gibbon, he notably co-authored the book Applied Analysis of the Navier-Stokes Equations, published by Cambridge University Press. He died on May 15, 2021.
Charles R. Doering's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Applied analysis of the Navier-Stokes equations (1995) (600)
- Low-dimensional behaviour in the complex Ginzburg-Landau equation (1988) (216)
- Extinction Times for Birth-Death Processes: Exact Results, Continuum Asymptotics, and the Failure of the Fokker-Planck Approximation (2004) (198)
- Applied analysis of the Navier-Stokes equations: Index (1995) (193)
- Weak and strong solutions of the complex Ginzburg-Landau equation (1994) (162)
- Infinite Prandtl Number Convection (1999) (160)
- Energy dissipation in body-forced turbulence (2001) (159)
- Statics and dynamics of a diffusion-limited reaction: Anomalous kinetics, nonequilibrium self-ordering, and a dynamic transition (1990) (155)
- Comparison of turbulent thermal convection between conditions of constant temperature and constant flux. (2008) (150)
- On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equation (1990) (147)
- Optimal stirring strategies for passive scalar mixing (2010) (127)
- Interacting particles, the stochastic Fisher–Kolmogorov–Petrovsky–Piscounov equation, and duality (2003) (123)
- High-Rayleigh-number convection in a fluid-saturated porous layer (2004) (105)
- Exponential decay rate of the power spectrum for solutions of the Navier--Stokes equations (1995) (93)
- Symmetric factorization of the conformation tensor in viscoelastic fluid models (2010) (90)
- Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh–Bénard convection (2005) (83)
- Ultimate state of two-dimensional Rayleigh-Bénard convection between free-slip fixed-temperature boundaries. (2011) (81)
- Dynamically stretched vortices as solutions of the 3D Navier—Stokes equations (1999) (81)
- Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion (2018) (76)
- Bounds for heat transport in a porous layer (1998) (74)
- Bounds on Rayleigh–Bénard convection with an imposed heat flux (2002) (71)
- On upper bounds for infinite Prandtl number convection with or without rotation (2001) (71)
- Escape over a fluctuating barrier: The white noise limit (1990) (68)
- Heat transfer in convective turbulence (1996) (68)
- Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows (2012) (64)
- Smooth and rough boundaries in turbulent Taylor-Couette flow. (2003) (63)
- Numerical and analytical studies of nonequilibrium fluctuation-induced transport processes (1996) (60)
- Exponentially growing solutions in homogeneous Rayleigh-Bénard convection. (2006) (55)
- On Travelling Waves for the Stochastic Fisher–Kolmogorov–Petrovsky–Piscunov Equation (2005) (55)
- Limits on enstrophy growth for solutions of the three-dimensional Navier-Stokes equations (2008) (55)
- Randomly rattled ratchets (1995) (55)
- Mean exit times over fluctuating barriers (1989) (54)
- Gene expression dynamics with stochastic bursts: Construction and exact results for a coarse-grained model. (2015) (54)
- Mean exit times for particles driven by weakly colored noise (1989) (53)
- Wall to wall optimal transport (2014) (51)
- A bound on mixing efficiency for the advection–diffusion equation (2003) (50)
- Stirring up trouble: Multi-scale mixing measures for steady scalar sources (2006) (50)
- On the shape and dimension of the Lorenz attractor (1995) (49)
- Computational approaches to aspect-ratio-dependent upper bounds and heat flux in porous medium convection (2013) (46)
- New upper bounds and reduced dynamical modeling for Rayleigh–Bénard convection in a fluid saturated porous layer (2012) (45)
- Multiscale mixing efficiencies for steady sources. (2005) (45)
- Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems (2017) (42)
- Features of Fast Living: On the Weak Selection for Longevity in Degenerate Birth-Death Processes (2012) (41)
- Fluctuations and correlations in a diffusion-reaction system: Exact hydrodynamics (1991) (40)
- Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field (2015) (39)
- Bounds for convection between rough boundaries (2016) (38)
- Energy dissipation in a shear layer with suction (2000) (38)
- Energy and enstrophy dissipation in steady state 2d turbulence (2006) (37)
- Note on the Constantin-Foias-Temam attractor dimension estimate for two-dimensional turbulence (1991) (36)
- Variational bounds in dissipative systems (1995) (36)
- Length scales in solutions of the Navier-Stokes equations (1993) (36)
- A numerical method for some stochastic differential equations with multiplicative noise (2005) (35)
- The small-world effect is a modern phenomenon (2013) (34)
- Asymptotics of rare events in birth–death processes bypassing the exact solutions (2007) (34)
- Extreme vorticity growth in Navier-Stokes turbulence (2009) (34)
- Nucleation pressure threshold in acoustic droplet vaporization (2016) (34)
- Nonlinear parabolic stochastic differential equations with additive colored noise onRd ×R+: A regulated stochastic quantization (1987) (33)
- A stochastic partial differential equation with multiplicative noise (1987) (32)
- Joint density closure schemes for a diffusion-limited reaction (1990) (32)
- Microscopic spatial correlations induced by external noise in a reaction-diffusion system (1992) (31)
- Rigid bounds on heat transport by a fluid between slippery boundaries (2012) (31)
- Diffusion-limited mixing by incompressible flows (2017) (31)
- Steady Rayleigh–Bénard convection between stress-free boundaries (2020) (30)
- Rigorous estimates of small scales in turbulent flows (1996) (30)
- Unsolved Problems of Noise (1997) (30)
- Optimal Wall-to-Wall Transport by Incompressible Flows. (2016) (28)
- Internal heating driven convection at infinite Prandtl number (2011) (28)
- Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Bénard convection. (2015) (28)
- Variations on Kolmogorov flow: turbulent energy dissipation and mean flow profiles (2011) (28)
- the distribution of exit times for weakly colored noise (1989) (27)
- Hard turbulence in a finite dimensional dynamical system (1989) (26)
- Energy dissipation in body-forced plane shear flow (2003) (25)
- Bounds on convection driven by internal heating (2003) (25)
- Bounds on moments of the energy spectrum for weak solutions of the three-dimensional Navier-Stokes equations (2002) (24)
- Absence of Evidence for the Ultimate Regime in Two-Dimensional Rayleigh-Bénard Convection. (2019) (23)
- The Dynamics of Organized Structures in the Axisymmetric Jet Mixing Layer (1991) (23)
- Failure of energy stability in Oldroyd-B fluids at arbitrarily low Reynolds numbers (2004) (23)
- Intermittency and Regularity Issues in 3D Navier-Stokes Turbulence (2004) (23)
- Demographic stochasticity versus spatial variation in the competition between fast and slow dispersers. (2010) (22)
- Destabilizing Taylor-Couette flow with suction (2009) (21)
- Turning up the heat in turbulent thermal convection (2020) (20)
- Attractor dimension estimates for two-dimensional shear flows (1998) (20)
- Maximal transport in the Lorenz equations (2014) (20)
- Wall-to-wall optimal transport in two dimensions (2013) (19)
- Ladder theorems for the 2D and 3D Navier-Stokes equations on a finite periodic domain (1991) (19)
- On the Optimal Design of Wall‐to‐Wall Heat Transport (2017) (18)
- External noise and its interaction with spatial degrees of freedom in nonlinear dissipative systems (1989) (18)
- A Fast Explicit Operator Splitting Method for Passive Scalar Advection (2010) (17)
- The formation of massive stars along the W5 ionization front (1984) (17)
- Energy dissipation in fractal-forced flow (2006) (17)
- Links between dissipation, intermittency, and helicity in the GOY model revisited (2005) (17)
- Applied analysis of the Navier-Stokes equations: Energy dissipation rate estimates for boundary-driven flows (1995) (16)
- Linear decay in multilevel quantum systems (1991) (16)
- Thermal forcing and ‘classical’ and ‘ultimate’ regimes of Rayleigh–Bénard convection (2019) (16)
- Bounds on dissipation in magnetohydrodynamic Couette and Hartmann shear flows (2003) (16)
- Thermal convection over fractal surfaces (2019) (16)
- Demographic stochasticity and evolution of dispersion II: Spatially inhomogeneous environments (2015) (16)
- Demographic stochasticity and evolution of dispersion I. Spatially homogeneous environments (2015) (16)
- Mixing effectiveness depends on the source–sink structure: simulation results (2008) (15)
- Steady Rayleigh–Bénard convection between no-slip boundaries (2020) (15)
- ENERGY STABILITY BOUNDS ON CONVECTIVE HEAT TRANSPORT : NUMERICAL STUDY (1997) (15)
- Constructive role of noise: Fast fluctuation asymptotics of transport in stochastic ratchets. (1998) (14)
- Bounds on heat transport in Bénard-Marangoni convection. (2010) (14)
- Transport bounds for a truncated model of Rayleigh-Bénard convection (2015) (13)
- Optimal bounds and extremal trajectories for time averages in dynamical systems (2017) (13)
- Absence of Evidence for the Ultimate State of Turbulent Rayleigh-Bénard Convection. (2019) (12)
- Random walker models for durotaxis (2018) (12)
- A Shell Model for Optimal Mixing (2018) (11)
- Heat transport bounds for a truncated model of Rayleigh–Bénard convection via polynomial optimization (2020) (11)
- Reentrant transitions in globally coupled active rotators with multiplicative and additive noises (1997) (11)
- Intermittency in solutions of the three-dimensional Navier–Stokes equations (2003) (11)
- Noise-Induced statistically stable oscillations in a deterministically divergent nonlinear dynamical system (2012) (11)
- Resonant activation of population extinctions. (2017) (10)
- Bounds on Surface Stress-Driven Shear Flow (2013) (10)
- Low-Wavenumber Forcing and Turbulent Energy Dissipation (2004) (10)
- Optimal Heat Transfer and Optimal Exit Times (2017) (10)
- Variational bounds on the energy dissipation rate in body-forced shear flow (2004) (9)
- Scaling of turbulent spike amplitudes in the complex Ginzburg-Landau equation (1993) (9)
- Low-dimensional models from upper bound theory (2011) (9)
- Temperature dependence of 1/f noise (1996) (8)
- The mixing efficiency of open flows (2010) (8)
- A comparison between transitions induced by random and periodic fluctuations (1985) (8)
- Bounds on the enstrophy growth rate for solutions of the 3-d Navier-Stokes equations (2005) (8)
- Nonperturbative bounds on in cutoff (λΦn)d field theory (1985) (8)
- Effect of Boundary Condition Fluctuations on Smoluchowski Reaction Rates: Dedicated to Lutz Schimansky-Geier, half a century wise (2000) (7)
- Rayleigh-Bénard convection with imposed heat flux. (2007) (7)
- Improved upper bounds on the energy dissipation rate for shear flow with injection and suction (2019) (7)
- Aspect-Ratio-Dependent Upper Bounds for Two-Dimensional Rayleigh--B\'{e}nard Convection between Stress-Free Isothermal Boundaries (2014) (7)
- Bounds on dissipation in magnetohydrodynamic problems in plane shear geometry (2003) (7)
- Models and measures of mixing and effective diffusion (2010) (7)
- Exact relations between Rayleigh–Bénard and rotating plane Couette flow in two dimensions (2020) (6)
- Maximum palinstrophy amplification in the two-dimensional Navier–Stokes equations (2017) (6)
- Models & measures of mixing & effective diffusion (2010) (6)
- On mix-norms and the rate of decay of correlations (2020) (6)
- Numerical assessment of the effect of forest structure changes on CO2 flux footprints for the flux tower in Solling, Germany (2011) (6)
- Stability of reaction-diffusion-convection systems: the case of linear shear flow (1993) (6)
- Unsolved Problems of Noise: Physics, Biology, Electronic Technology and Information Technology (1997) (5)
- Finite dimensionality in the laser equations in the good cavity limit (1988) (5)
- Dreams Versus Reality: Plenary Debate Session on Quantum Computing (2003) (5)
- Mean Extinction Time for Birth‐Death Processes & Failure of the Fokker‐Planck Approximation (2005) (4)
- Finite dimensionality in the complex Ginzburg-Landau equation (1987) (4)
- Stability and Resilience of Transportation Systems: Is a Traffic Jam About to Occur? (2022) (4)
- Noisy Wavefront Propagation in the Fisher‐Kolmogorov‐Petrovsky‐Piscounov Equation (2003) (4)
- Lectures on Stirring, Mixing and Transport (2017) (3)
- Enstrophy amplification events in three-dimensional turbulence. (2008) (3)
- Erratum: "Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows" [J. Math. Phys. 53, 115611 (2012)] (2013) (3)
- Modeling Complex Systems: Stochastic Processes, Stochastic Differential Equations, and Fokker-Planck Equations (2018) (3)
- Discrete and Continuum Dynamics of Reacting and Interacting Individuals (2014) (3)
- History of the Structure of Acetone (1959) (3)
- Wall-to-wall optimal transport in two dimensions (2019) (3)
- Introduction to special issue: Mathematical fluid dynamics (2007) (3)
- Optimal time averages in non-autonomous nonlinear dynamical systems (2020) (3)
- Applied analysis of the Navier-Stokes equations: Dimensionless parameters and stability (1995) (2)
- Weak and Strong Turbulence in the CGL Equation (1993) (2)
- Extinction Times for Birth-Death Processes: Continuum Asymptotics and the failure of the Fokker-Planck Approximation (2005) (2)
- Demographic stochasticity and evolution of dispersion II: Spatially inhomogeneous environments (2014) (1)
- Optimal signal-to-noise in digital phase lock amplifiers. (1987) (1)
- Applied analysis of the Navier-Stokes equations: Ladder results for the Navier-Stokes equations (1995) (1)
- Absence of evidence for transition to the 'ultimate' regime of Rayleigh-Bénard convection (2018) (1)
- Erratum: Energy dissipation in shear driven turbulence(Physical Review Letters(1992), 69, 20,(3000)) (1992) (1)
- Erratum: Diffusion-limited coagulation in the presence of particle input: Exact results in one dimension [Phys. Rev. Lett. 62, 2563 (1989)] (1989) (1)
- Introduction to Special Issue: Incompressible Fluids, Turbulence and Mixing (2012) (1)
- Variation on the Kolmogorov Forcing: Asymptotic Dissipation Rate Driven by Harmonic Forcing (2009) (1)
- Heat transport in a hierarchy of reduced-order convection models (2022) (1)
- Corrigendum to “Stirring up trouble: Multi-scale mixing measures for steady scalar sources” [Physica D 231 (2007) 143–164] (2011) (1)
- Does turbulence saturate global transport estimates (1999) (1)
- Applied analysis of the Navier-Stokes equations: On the existence, uniqueness, and regularity of solutions (1995) (1)
- Bounds on dissipation in MHD problems in plane shear geometry (2003) (1)
- Maxial Enstrophy Generation in the 3D Navier-Stokes Equations (2006) (1)
- Applied analysis of the Navier-Stokes equations: Preface (1995) (1)
- Laminar and turbulent dissipation in shear flow with suction (2000) (1)
- The role of intergrain contacts in the resistance noise of HTSC (1996) (0)
- Parameterizing turbulent transport of reactive tracers (2019) (0)
- Proceedings of the First International Conference on Unsolved Prolems of Noise in Physics, Biology, Electronic Technology and Information Technology (1997) (0)
- The Effect of Random and Periodic Fluctuations on Nonlinear Systems (1984) (0)
- Do steady rolls maximize heat transport in truncated models of Rayleigh–-B\'enard convection? (2019) (0)
- Bounds on Surface Stress-Driven Shear Flow (2013) (0)
- Bounds on heat transport in Rayleigh's and related models of B\'enard convection (2015) (0)
- A pr 2 00 4 Low-wavenumber forcing and turbulent energy dissipation (2008) (0)
- A new diagnostic for the relative accuracy of Euler codes (2010) (0)
- Bounds on the Nusselt Number for Marangoni Convection (2009) (0)
- APPLIED NONLINEAR STOCHASTIC DYNAMICS (1999) (0)
- Thermal convection over a fractal surface (2019) (0)
- A Comparison of Turbulent Thermal Convection Between Conditions of Constant Temperature and Constant Flux: Simulation Methods (2009) (0)
- Future trends and geographical distribution of potential evapotranspiration in Germany throughout the 21st century (2009) (0)
- DY 10: Nonlinear Stochastic Systems (2014) (0)
- Optimal heat transport (2015) (0)
- Measuring mixing efficiency (2007) (0)
- On the growth of enstrophy in axisymmetric 3D Euler flows with swirl (2015) (0)
- Fokker-Planck boundary layer, recurrence times, and Wang & Uhlenbeck's unsolved problems (1996) (0)
- Introduction: Third Annual Gallery of Nonlinear Images (Baltimore, Maryland, 2006) (2006) (0)
- Enstropy Generation and Regularity of Solutions to the 3D Navier-Stokes Equations (2008) (0)
- Bounding heat transport for a model of Rayleigh-Benard convection using sum-of-squares optimization (2018) (0)
- Diffusive transport in modern polymeric materials (1996) (0)
- New variational bounds on convective transport. II. Computations and implications (2016) (0)
- Ja n 20 06 Failure of energy stability in Oldroyd-B fluids at arbitrarily low Reynolds numbers (2008) (0)
- A ug 2 01 9 Thermal Convection over Fractal Surfaces (2019) (0)
- Optimal transport in truncated models of Rayleigh-B\'enard convection (2014) (0)
- Optimal Mixing, Part II (2010) (0)
- Projected dynamics of abiotic risks in boreal forest ecosystems (SRES A1B, B1) (2009) (0)
- Applied analysis of the Navier-Stokes equations: Exponential decay of the Fourier power spectrum (1995) (0)
- Demographic Fluctuations versus Spatial Variation in the Competition between Fast and Slow Dispersers (2010) (0)
- 1 2 A ug 2 01 5 Gene expression dynamics with stochastic bursts : exact results for a coarse-grained model (2015) (0)
- Convection, Stability, and Turbulence (2015) (0)
- Convection, stability, and low dimensional dynamics (1997) (0)
- A comparison of turbulent thermal convection between conditions of constant temperature and constant heat flux boundaries (2009) (0)
- The attractor dimension for the Navier-Stokes equations (1995) (0)
- Applied analysis of the Navier-Stokes equations: Turbulence (1995) (0)
- Multiscale mixing efficiencies for passive scalars (2005) (0)
- Applied analysis of the Navier-Stokes equations: The equations of motion (1995) (0)
- Applied analysis of the Navier-Stokes equations: Degrees of freedom, dynamical systems, and attractors (1995) (0)
- Instability theory of swirling flows with suction (2007) (0)
- Features of Fast Living: On the Weak Selection for Longevity in Degenerate Birth-Death Processes (2012) (0)
- Demographic stochasticity and evolution of dispersion I. Spatially homogeneous environments (2014) (0)
- Data-Driven Methods for Detecting Traffic Jams in Vehicular Traffic Systems (2020) (0)
- New upper bounds for convection in a fluid-saturated porous layer (2011) (0)
- The Positivity of the Jacobi Operator on Configuration Space and Phase Space (1984) (0)
- On 1/f noise and frequency independent loss tangent (1996) (0)
- Introduction: Second Annual Gallery of Nonlinear Images (Los Angeles, California, 2005) (2005) (0)
- 2008 Program of Study: Perspectives and Challenges in GFD (Geophysical Fluid Dynamics) (2009) (0)
- Effects of Velocity and Temperature Boundary Conditions in Turbulent Thermal Convection (2013) (0)
- Defects and the delt-n-delta-mu controversy in semiconductor 1/f noise (1996) (0)
- A Shell Model for Optimal Mixing (2017) (0)
- Applied analysis of the Navier-Stokes equations: Regularity and length scales for the 2 d and 3 d Navier-Stokes equations (1995) (0)
- Bounds on convective heat transport (2001) (0)
- Energy Dissipation in Fractal-Forced Flows (2006) (0)
- Strong enstrophy events and maximal growth estimates in turbulence simulations (2007) (0)
- Upper Bounds on the Dissipation Rate of MHD Flows in Plane Geometry (2003) (0)
- Convection , Stability and Turbulence Lecturer : (0)
- Nonequilibrium Statistical Mechanics in One Dimension: Random walks, resonance, and ratchets (1997) (0)
- Current controlled percolation exponents in the noise of high-temperature superconductor thin films (1996) (0)
- Applied analysis of the Navier-Stokes equations: Inequalities (1995) (0)
- New variational bounds on convective transport. I. Formulation and analysis (2016) (0)
- Maximum Production of Enstrophy in Swirling Viscous Flows (2016) (0)
- A MINIMUM POPULATION EXTINCTION TIME DRIVEN BY STOCHASTIC ENVIRONMENTAL FORCING (2017) (0)
- Research highlights (2006) (0)
- [Quantitative aspects of labeled plasma cell count in the demonstration of heavy and light immunoglobulin chains. (Findings in human oral squamous cell carcinomas before and after BCG treatment)]. (1982) (0)
- Optimizing exit times (2015) (0)
- Galerkin Dynamical Modeling of Porous Medium Convection using an Eigenbasis from Upper Bound Theory (2012) (0)
- Introduction to Special Issue: Nonlinear Partial Differential Equations in Mathematical Fluid Dynamics (2018) (0)
- Effect of Boundary Condi t ion F luc tuat ions on Smoluchowski React ion Rates (0)
- Bulk Dissipation in Shear Layers with Suction (2001) (0)
- Mathematical Geophysics: An Introduction to Rotating Fluids and the Navier-Stokes Equations. By J.-Y. Chemin, B. Desjardins, I. Gallagher and E. Grenier. Oxford University Press, 2006. 272 pp. ISBN 019857133X. £47 (2007) (0)
- Advection, diffusion \& dispersion: effective diffusion for transient mixing vs. stirring with steady sources \& sinks (2008) (0)
- Improved upper bounds on energy dissipation rates in plane Couette flow with boundary injection and suction (2017) (0)
- A Novel Model Reduction Strategy Using Upper Bound Theory (2009) (0)
- Shell model of optimal passive-scalar mixing (2015) (0)
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