Nonlinear diffusion equation

By S. Motamen. 2002

249 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9b14cc2310eb08450f1961e8381df79a17147823

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In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

The Stellar Initial Mass Function from Turbulent Fragmentation (2000, methodology): “=3 for incompressible turbulence (Kolmogorov power spectrum; Kolmogorov 1941) and 2 for pressureless turbulence (Burgers power spectrum; Burgers 1974; Gotoh & Kraichnan 1993).”
Galactic Stellar and Substellar Initial Mass Function (2003, background): “…numerical simulations of compressible turbulence in a magnetized gas (Boldyrev, Nordlund & Padoan 2002a, 2002b, Padoan et al. 2003a) yield a power spectrum consistent with β = 1.74, between incompressible turbulence, β ≈ 5/3 (Kolmogorov spectrum) and pressureless turbulence, β ≈ 2 (Burgers 1974).”
Macroscopic fluctuation theory (2014, methodology): “We restrict the discussion to the one-dimensional inviscid Burgers equation (Burgers, 1974), which is a simple model for a compressible fluid.”
Burgers Turbulence (2007, methodology): “For n = 0, this t law was actually derived by Burgers himself [27].”
Travelling Waves in Nonlinear Diffusion-Convection Reaction (2004, background): “The above class of explicit travelling wave solutions of the Burgers equation was documented by the person after whom the equation is named in [59,60].”
Probing turbulence in the Coma galaxy cluster (2004, result): “Previous reports of these observations were given by Briel et al. (2001), Arnaud et al. (2001), Neumann et al.”
Crystal surfaces in and out of equilibrium: A modern view (2010, background): “2.104 , we find the Burgers equation Burgers, 1974 t = D zz + Q2 z , 2.107 where D represents the analog of viscosity and is thus assumed to be positive .”
Analytical Theory for the Initial Mass Function: CO Clumps and Prestellar Cores (2008, methodology): “Note that in the cosmological case, the Bond et al. (1991) result is exactly recovered if one assumes P (M, M ) = 1/2. Since, as demonstrated in Appendix C, it appears that the calculation of Yano et al. (1996) is also applicable in our case, we take P (M c R, M ) = 1/2.”
On the well-posedness of entropy solutions to conservation laws with a zero-flux boundary condition (2007, unknown): “1) appears as the vanishing viscosity limit of a multi-dimensional model of turbulence [5] or of a simple model of two-phase flow in porous media [21].”
The Kardar-Parisi-Zhang equation and universality class (2011, background): “These exponents had first been identified in 1977 by [73] in the study of the stochastic Burgers equation (stochastic space-time noise, not initial data as studied in [39]).”
Refined Second Law of Thermodynamics for Fast Random Processes (2012, background): “We shall describe below a relation of the minimization problem for total entropy production or the average heat release to the optimal mass transport [55] and the inviscid Burgers dynamics [13].”
Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling (2003, background): “…disturbances decay exponentially over time, but the Burgers equation can be solved analytically in its entirety, i.e., also for large disturbances (Burgers 1974).2 The result for any localized initial disturbance is that it develops into a characteristic triangular structure, which grows in width…”