Why Is Charles R. Doering Influential?
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
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1960 1970 1980 1990 2000 2010 2020 0 100 200 300 400 500 600 700 800 900 1000 Published Papers Applied analysis of the Navier-Stokes equations (554) Low-dimensional behaviour in the complex Ginzburg-Landau equation Applied analysis of the Navier-Stokes equations: Index Extinction Times for Birth-Death Processes: Exact Results, Continuum Asymptotics, and the Failure of the Fokker-Planck Approximation Statics and dynamics of a diffusion-limited reaction: Anomalous kinetics, nonequilibrium self-ordering, and a dynamic transition Weak and strong solutions of the complex Ginzburg-Landau equation Energy dissipation in body-forced turbulence Infinite Prandtl Number Convection Comparison of turbulent thermal convection between conditions of constant temperature and constant flux. On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equation Interacting particles, the stochastic Fisher–Kolmogorov–Petrovsky–Piscounov equation, and duality Optimal stirring strategies for passive scalar mixing High-Rayleigh-number convection in a fluid-saturated porous layer Exponential decay rate of the power spectrum for solutions of the Navier--Stokes equations Symmetric factorization of the conformation tensor in viscoelastic fluid models Dynamically stretched vortices as solutions of the 3D Navier—Stokes equations Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh–Bénard convection Ultimate state of two-dimensional Rayleigh-Bénard convection between free-slip fixed-temperature boundaries. Bounds on Rayleigh–Bénard convection with an imposed heat flux Escape over a fluctuating barrier: The white noise limit On upper bounds for infinite Prandtl number convection with or without rotation Bounds for heat transport in a porous layer Heat transfer in convective turbulence Numerical and analytical studies of nonequilibrium fluctuation-induced transport processes Smooth and rough boundaries in turbulent Taylor-Couette flow. Randomly rattled ratchets Mean exit times over fluctuating barriers On Travelling Waves for the Stochastic Fisher–Kolmogorov–Petrovsky–Piscunov Equation Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows Gene expression dynamics with stochastic bursts: Construction and exact results for a coarse-grained model. Stirring up trouble: Multi-scale mixing measures for steady scalar sources Mean exit times for particles driven by weakly colored noise A bound on mixing efficiency for the advection–diffusion equation Limits on enstrophy growth for solutions of the three-dimensional Navier-Stokes equations Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion Exponentially growing solutions in homogeneous Rayleigh-Bénard convection. On the shape and dimension of the Lorenz attractor Multiscale mixing efficiencies for steady sources. Computational approaches to aspect-ratio-dependent upper bounds and heat flux in porous medium convection New upper bounds and reduced dynamical modeling for Rayleigh–Bénard convection in a fluid saturated porous layer Fluctuations and correlations in a diffusion-reaction system: Exact hydrodynamics Features of Fast Living: On the Weak Selection for Longevity in Degenerate Birth-Death Processes Energy dissipation in a shear layer with suction Wall to wall optimal transport Length scales in solutions of the Navier-Stokes equations A numerical method for some stochastic differential equations with multiplicative noise Variational bounds in dissipative systems Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems Energy and enstrophy dissipation in steady state 2d turbulence Asymptotics of rare events in birth-death processes bypassing the exact solutions A stochastic partial differential equation with multiplicative noise Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field Joint density closure schemes for a diffusion-limited reaction Note on the Constantin-Foias-Temam attractor dimension estimate for two-dimensional turbulence Nonlinear parabolic stochastic differential equations with additive colored noise onRd ×R+: A regulated stochastic quantization Extreme vorticity growth in Navier-Stokes turbulence Bounds for convection between rough boundaries Microscopic spatial correlations induced by external noise in a reaction-diffusion system The small-world effect is a modern phenomenon (28) Feedbacks of windthrow for Norway spruce and Scots pine stands under changing climate. Rigorous estimates of small scales in turbulent flows Rigid bounds on heat transport by a fluid between slippery boundaries the distribution of exit times for weakly colored noise Variations on Kolmogorov flow: turbulent energy dissipation and mean flow profiles Energy dissipation in body-forced plane shear flow Nucleation pressure threshold in acoustic droplet vaporization Hard turbulence in a finite dimensional dynamical system Internal heating driven convection at infinite Prandtl number Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Bénard convection. Bounds on moments of the energy spectrum for weak solutions of the three-dimensional Navier-Stokes equations Optimal Wall-to-Wall Transport by Incompressible Flows. Unsolved Problems of Noise (23) Wall-to-wall optimal transport in two dimensions The Dynamics of Organized Structures in the Axisymmetric Jet Mixing Layer Bounds on convection driven by internal heating Failure of energy stability in Oldroyd-B fluids at arbitrarily low Reynolds numbers Diffusion-limited mixing by incompressible flows Destabilizing Taylor-Couette flow with suction Intermittency and Regularity Issues in 3D Navier-Stokes Turbulence Attractor dimension estimates for two-dimensional shear flows Ladder theorems for the 2D and 3D Navier-Stokes equations on a finite periodic domain Energy dissipation in fractal-forced flow Maximal transport in the Lorenz equations The formation of massive stars along the W5 ionization front Demographic stochasticity versus spatial variation in the competition between fast and slow dispersers. Linear decay in multilevel quantum systems A Fast Explicit Operator Splitting Method for Passive Scalar Advection External noise and its interaction with spatial degrees of freedom in nonlinear dissipative systems Absence of Evidence for the Ultimate Regime in Two-Dimensional Rayleigh-Bénard Convection. Links between dissipation, intermittency, and helicity in the GOY model revisited Mixing effectiveness depends on the source–sink structure: simulation results Demographic stochasticity and evolution of dispersion II: Spatially inhomogeneous environments Constructive role of noise: Fast fluctuation asymptotics of transport in stochastic ratchets. Applied analysis of the Navier-Stokes equations: Energy dissipation rate estimates for boundary-driven flows Steady Rayleigh–Bénard convection between stress-free boundaries Bounds on heat transport in Bénard-Marangoni convection. Bounds on dissipation in magnetohydrodynamic Couette and Hartmann shear flows ENERGY STABILITY BOUNDS ON CONVECTIVE HEAT TRANSPORT : NUMERICAL STUDY Demographic stochasticity and evolution of dispersion I. Spatially homogeneous environments Resonant activation of population extinctions. Transport bounds for a truncated model of Rayleigh-Bénard convection On the Optimal Design of Wall‐to‐Wall Heat Transport Reentrant transitions in globally coupled active rotators with multiplicative and additive noises Intermittency in solutions of the three-dimensional Navier–Stokes equations Thermal forcing and ‘classical’ and ‘ultimate’ regimes of Rayleigh–Bénard convection Bounds on Surface Stress-Driven Shear Flow Low-Wavenumber Forcing and Turbulent Energy Dissipation Noise-Induced statistically stable oscillations in a deterministically divergent nonlinear dynamical system Scaling of turbulent spike amplitudes in the complex Ginzburg-Landau equation Optimal bounds and extremal trajectories for time averages in dynamical systems (9) Thermal convection over fractal surfaces Random walker models for durotaxis. Turning up the heat in turbulent thermal convection Variational bounds on the energy dissipation rate in body-forced shear flow Mean Extinction Time for Birth‐Death Processes & Failure of the Fokker‐Planck Approximation Nonperturbative bounds on in cutoff (λΦn)d field theory Low-dimensional models from upper bound theory A comparison between transitions induced by random and periodic fluctuations Absence of Evidence for the Ultimate State of Turbulent Rayleigh-Bénard Convection. Optimal Heat Transfer and Optimal Exit Times Bounds on dissipation in magnetohydrodynamic problems in plane shear geometry Wall-to-wall optimal transport in two dimensions Effect of Boundary Condition Fluctuations on Smoluchowski Reaction Rates: Dedicated to Lutz Schimansky-Geier, half a century wise A Shell Model for Optimal Mixing Temperature dependence of 1/f noise (7) Rayleigh-Bénard convection with imposed heat flux. Bounds on the enstrophy growth rate for solutions of the 3-d Navier-Stokes equations (7) Models and measures of mixing and effective diffusion (6) Stability of reaction-diffusion-convection systems: the case of linear shear flow The mixing efficiency of open flows Aspect-Ratio-Dependent Upper Bounds for Two-Dimensional Rayleigh--B\'{e}nard Convection between Stress-Free Isothermal Boundaries (6) Steady Rayleigh–Bénard convection between no-slip boundaries Models & measures of mixing & effective diffusion Finite dimensionality in the laser equations in the good cavity limit Dreams Versus Reality: Plenary Debate Session on Quantum Computing Maximum palinstrophy amplification in the two-dimensional Navier–Stokes equations Unsolved Problems of Noise: Physics, Biology, Electronic Technology and Information Technology Improved upper bounds on the energy dissipation rate for shear flow with injection and suction Numerical assessment of the effect of forest structure changes on CO2 flux footprints for the flux tower in Solling, Germany Finite dimensionality in the complex Ginzburg-Landau equation Noisy Wavefront Propagation in the Fisher‐Kolmogorov‐Petrovsky‐Piscounov Equation Nucleation pressure threshold in acoustic droplet vaporization Applied analysis of the Navier-Stokes equations: Dimensionless parameters and stability Introduction to special issue: Mathematical fluid dynamics Discrete and Continuum Dynamics of Reacting and Interacting Individuals History of the Structure of Acetone Heat transport bounds for a truncated model of Rayleigh–Bénard convection via polynomial optimization Enstrophy amplification events in three-dimensional turbulence. Erratum: "Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows" [J. Math. Phys. 53, 115611 (2012)] Exact relations between Rayleigh–Bénard and rotating plane Couette flow in two dimensions Applied analysis of the Navier-Stokes equations: Preface Extinction Times for Birth-Death Processes: Continuum Asymptotics and the failure of the Fokker-Planck Approximation (2) Optimal time averages in non-autonomous nonlinear dynamical systems (2) On mix-norms and the rate of decay of correlations Lectures on Stirring, Mixing and Transport Weak and Strong Turbulence in the CGL Equation Applied analysis of the Navier-Stokes equations: On the existence, uniqueness, and regularity of solutions Bounds on dissipation in MHD problems in plane shear geometry (1) Modeling Complex Systems: Stochastic Processes, Stochastic Differential Equations, and Fokker-Planck Equations Applied analysis of the Navier-Stokes equations: Ladder results for the Navier-Stokes equations Absence of evidence for transition to the 'ultimate' regime of Rayleigh-Bénard convection (1) Erratum: Energy dissipation in shear driven turbulence(Physical Review Letters(1992), 69, 20,(3000)) A Comparison of Turbulent Thermal Convection Between Conditions of Constant Temperature and Constant Flux: Simulation Methods (1) Corrigendum to “Stirring up trouble: Multi-scale mixing measures for steady scalar sources” [Physica D 231 (2007) 143–164] Laminar and turbulent dissipation in shear flow with suction Does turbulence saturate global transport estimates Variation on the Kolmogorov Forcing: Asymptotic Dissipation Rate Driven by Harmonic Forcing Introduction to Special Issue: Incompressible Fluids, Turbulence and Mixing Erratum: Diffusion-limited coagulation in the presence of particle input: Exact results in one dimension [Phys. Rev. Lett. 62, 2563 (1989)] Maxial Enstrophy Generation in the 3D Navier-Stokes Equations (1) Optimal signal-to-noise in digital phase lock amplifiers. Enstropy Generation and Regularity of Solutions to the 3D Navier-Stokes Equations Strong enstrophy events and maximal growth estimates in turbulence simulations (0) Fokker-Planck boundary layer, recurrence times, and Wang & Uhlenbeck's unsolved problems (0) A MINIMUM POPULATION EXTINCTION TIME DRIVEN BY STOCHASTIC ENVIRONMENTAL FORCING Introduction to Special Issue: Nonlinear Partial Differential Equations in Mathematical Fluid Dynamics A comparison of turbulent thermal convection between conditions of constant temperature and constant heat flux boundaries The Effect of Random and Periodic Fluctuations on Nonlinear Systems Convection, stability, and low dimensional dynamics Introduction: Second Annual Gallery of Nonlinear Images (Los Angeles, California, 2005) Galerkin Dynamical Modeling of Porous Medium Convection using an Eigenbasis from Upper Bound Theory (0) The role of intergrain contacts in the resistance noise of HTSC (0) Diffusive transport in modern polymeric materials Convection, Stability, and Turbulence (0) Bounds on convective heat transport (0) Future trends and geographical distribution of potential evapotranspiration in Germany throughout the 21st century (0) Applied analysis of the Navier-Stokes equations: The equations of motion Shell model of optimal passive-scalar mixing (0) DREAMS VERSUS REALITY: PLENARY DEBATE SESSION ON QUANTUM COMPUTING Research highlights Thermal convection over a fractal surface (0) Ja n 20 06 Failure of energy stability in Oldroyd-B fluids at arbitrarily low Reynolds numbers (0) Applied analysis of the Navier-Stokes equations: Exponential decay of the Fourier power spectrum Projected dynamics of abiotic risks in boreal forest ecosystems (SRES A1B, B1) (0) BOUNDS ON THE HEAT TRANSFER RATE VIA PASSIVE ADVECTION (0) Bounds on the Nusselt Number for Marangoni Convection (0) On 1/f noise and frequency independent loss tangent (0) Optimal Mixing, Part II (0) Optimal heat transport (0) Applied analysis of the Navier-Stokes equations: Regularity and length scales for the 2 d and 3 d Navier-Stokes equations Optimal transport in truncated models of Rayleigh-B\'enard convection (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)]. (0) Applied analysis of the Navier-Stokes equations: Degrees of freedom, dynamical systems, and attractors APPLIED NONLINEAR STOCHASTIC DYNAMICS A pr 2 00 4 Low-wavenumber forcing and turbulent energy dissipation (0) Advection, diffusion \& dispersion: effective diffusion for transient mixing vs. stirring with steady sources \& sinks (0) Proceedings of the First International Conference on Unsolved Prolems of Noise in Physics, Biology, Electronic Technology and Information Technology (0) Convection , Stability and Turbulence Lecturer : (0) Defects and the delt-n-delta-mu controversy in semiconductor 1/f noise (0) Introduction: Third Annual Gallery of Nonlinear Images (Baltimore, Maryland, 2006) Applied analysis of the Navier-Stokes equations: Turbulence Applied analysis of the Navier-Stokes equations: Inequalities A ug 2 01 9 Thermal Convection over Fractal Surfaces (0) Upper Bounds on the Dissipation Rate of MHD Flows in Plane Geometry (0) Parameterizing turbulent transport of reactive tracers (0) DY 10: Nonlinear Stochastic Systems (0) A Novel Model Reduction Strategy Using Upper Bound Theory (0) Multiscale mixing efficiencies for passive scalars (0) The attractor dimension for the Navier-Stokes equations Improved upper bounds on energy dissipation rates in plane Couette flow with boundary injection and suction (0) Data-Driven Methods for Detecting Traffic Jams in Vehicular Traffic Systems Nonequilibrium Statistical Mechanics in One Dimension: Random walks, resonance, and ratchets Do steady rolls maximize heat transport in truncated models of Rayleigh–-B\'enard convection? (0) New variational bounds on convective transport. I. Formulation and analysis (0) Bounds on heat transport in Rayleigh's and related models of B\'enard convection (0) Maximum Production of Enstrophy in Swirling Viscous Flows (0) New upper bounds for convection in a fluid-saturated porous layer (0) Bounding heat transport for a model of Rayleigh-Benard convection using sum-of-squares optimization (0) Energy Dissipation in Fractal-Forced Flows (0) 2008 Program of Study: Perspectives and Challenges in GFD (Geophysical Fluid Dynamics) (0) Effect of Boundary Condi t ion F luc tuat ions on Smoluchowski React ion Rates (0) Instability theory of swirling flows with suction (0) New variational bounds on convective transport. II. Computations and implications (0) Measuring mixing efficiency (0) Current controlled percolation exponents in the noise of high-temperature superconductor thin films (0) A new diagnostic for the relative accuracy of Euler codes (0) Effects of Velocity and Temperature Boundary Conditions in Turbulent Thermal Convection (0) On the growth of enstrophy in axisymmetric 3D Euler flows with swirl (0) Stability and Resilience of Transportation Systems: Is a Traffic Jam About to Occur? Bulk Dissipation in Shear Layers with Suction Demographic Fluctuations versus Spatial Variation in the Competition between Fast and Slow Dispersers (0) The Positivity of the Jacobi Operator on Configuration Space and Phase Space (0) Optimizing exit times (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 More Papers This paper list is powered by the following services:
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