Publications of the Mathematics Department at LBNL

Journals

To appear

G.I. Barenblatt, Transfer of a passive additive in a turbulent boundary layer at very large Reynolds numbers, Proc. Natl. Acad. Sci. USA, (2003), to appear.
R. Kupferman, A.M. Stuart, J.R. Terry, and P.F. Tupper, Long term behaviour of large mechanical systems with random initial data, Stoch. Dyn. (2003), to appear.
P. Stinis, Prediction and hybrid algorithms for the Burgers equation, Discrete Contin. Dyn. Syst., (2003), to appear.
R. Kupferman and A.M. Stuart, Fitting SDE models to nonlinear Kac-Zwanzig heat bath models, submitted to Physica D.
R. Kupferman, Fractional kinetics in Kac-Zwanzig heat bath models, J. Stat. Phys. (in press).
R. Kupferman and M.M. Denn, Simulation of the evolution of concentrated shear layers in a Maxwell fluid with a fast high-resolution finite-difference scheme, J. Non-Newt. Fluid Mech. (in press).
R. Kupferman and M.M Denn, Emergence of structure in a model of liquid crystalline polymers with elastic coupling, J. Non-Newt. Fluid Mech. (in press).

2003

G.I. Barenblatt, Transport of a passive additive in a turbulent boundary layer at very large Reynolds numbers, Proceedings, National Academy of Sciences, 100 (2003), pp. 1481-1483.
A. Chorin, Averaging and renormalization for the Korteveg-deVries-Burgers equation, Proc. Nat. Acad. Sci. USA, 100, (2003), pp. 9674-9679.
A. Chorin, Conditional expectations and renormalization, Multiscale Modeling and Simulation, 1, (2003), pp. 105-118.
T.W. Patzek, D.B. Silin, S.M. Benson, and G.I. Barenblatt, On vertical diffusion of gases in a horizontal reservoir, Transp. Porous Media, 51 (2003), pp. 141-156.

2002

G.I. Barenblatt, Fluid mechanics in the XX century, Eur. J. Mech. B Fluids, (2002), to appear.
G.I. Barenblatt, A.J. Chorin, and V.M. Prostokishin, A model of turbulent boundary layer with a non-zero pressure gradient, Proc. Natl. Acad. Sci. USA, 99 (2002), pp. 5772-5776.
G.I. Barenblatt, T.W. Patzek, V.M. Prostokishin, and D.B. Silin, Oil deposits in diatomites: a new challenge for subterranean mechanics, SPE Paper 75230, Society of Petroleum Engineers, 2002, pp. 1-9.
G.I. Barenblatt, T.W. Patzek, and D.B. Silin The mathematical model of non-equilibrium effects in water-oil displacement, SPE Paper 75169, Society of Petroleum Engineers, 2002, pp. 1-10.
A. Chertock, On the stability of a class of self-similar solutions to the filtration-absorption equation, Euro. J. Appl. Math., 13 (2002), pp. 179-194.
A. Chertock and D. Levy, Particle methods for the KdV equation, J. Sci. Comput., 17 (2002), pp. 491-499.

2001

G.I. Barenblatt, Self-similar asymptotics for nonlinear degenerate parabolic free-boundary problems which occur in image processing, Proc. Natl. Acad. Sci. USA, 98 (2001), pp. 12878-12881.
R. Kupferman, A central-difference scheme for a pure stream function formulation of incompressible viscous flow, SIAM J. Sci. Comput., 23 (2001), pp. 1-18.

2000

G.I. Barenblatt, M. Bertsch, A.E. Chertock, and V.M. Prostokishin, Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation, Proc. Natl. Acad. Sci. USA, 97 (2000), pp. 9844-9848.
G.I. Barenblatt, A.J. Chorin, and V.M. Prostokishin, Self-similar intermediate structures in turbulent boundary layers at large Reynolds numbers, J. Fluid Mech., 410 (2000), pp. 263-283.
G.I. Barenblatt, A.J. Chorin, and V.M. Prostokishin, The characteristic length scale of the intermediate structure in zero-pressure-gradient boundary layer flow, Proc. Natl. Acad. Sci. USA, 97 (2000), pp. 3799-3802.
G.I. Barenblatt, A.J. Chorin, and V.M. Prostokishin, A note on the intermediate region in turbulent boundary layers, Phys. Fluids, 12 (2000), pp. 2159-2161.
G.I. Barenblatt, E.A. Ingerman, H. Shvets, and J.L. Vazquez, Very intense pulse in the groundwater flow in fissurized-porous stratum, Proc. Natl. Acad. Sci. USA, 97 (2000), pp. 1366-1369.
Y. Brenier and D. Levy, Dissipative behavior of some fully non-linear KdV-type equations, Physica D, 137 (2000), pp. 277-294.
R. Kupferman, M.N. Kawaguchi, and M.M. Denn, Emergence of structure in a model of liquid crystalline polymers with elastic coupling, J. Non-Newtonian Fluid Mech., 91 (2000) 255-271.
A. Kurganov and D. Levy, A third-order semi-discrete central scheme for conservation laws and convection-diffusion equations, SIAM J. Sci. Comput. 22 (2000), pp. 1461-1488.

1999

R. Kupferman and A.J. Chorin, One-sided polarization and renormalization flow in the Kosterlitz-Thouless phase transition, SIAM J. Appl. Math. 59 (1999), pp. 1843-1866.

Conferences

2003

G.I. Barenblatt, Turbulent boundary layers at very large Reynolds numbers. LBNL-53465, 2003. Plenary invited lecture submitted for publication in the Proceedings of the International Conference "A.N. Kolmogorov and Modern Mathematics", dedicated to the100th Anniversary of A.N. Kolmogorov.
G.I. Barenblatt and J.L. V\341zquez, Nonlinear diffusion and image contour enhancement, Preprint No. 802, Center for Pure and Applied Mathematics, UC Berkeley, 2003, LBNL-51989. Submitted for publication in the Journal Free Boundaries and Interfaces.

2003

2002

G.I. Barenblatt, Damage accumulation: a non-local model, Structured Media, Trecop '01 in memory of Prof. Ekkehart Kr\366ner. B.T. Maruszewski, ed., Poznan Univ. Publishing House, 2002, pp. 19-28.

2001

A. Chertock and D. Levy, Particle methods for dispersive equations, J. Comput. Phys., 171 (2001), pp. 708-730.

2000

J. Bell, A.J. Chorin, and W. Crutchfield, Stochastic optimal prediction with application to averaged Euler equations, Proc. 7th Nat. Conf. Comput. Fluid Mech., C.A. Lin, ed., Pingtung, Taiwan, (2000), pp. 1-13.

A. Chorin, A. Kast, and R. Kupferman. Unresolved computation and optimal prediction, Comm. Pure Appl. Math. 52 (1999), pp. 1231-1254. A. Chorin, A. Kast, and R. Kupferman, On the prediction of large-scale dynamics using unresolved computations, Contemp. Math. 238 (1999), pp. 53-75. A.J. Chorin, R. Kupferman, and D Levy, Optimal prediction for Hamiltonian partial differential equations, J. Comput. Phys., 162 (2000), pp. 267-297. A.J. Chorin, O. Hald, and R. Kupferman, Optimal prediction and the Mori-Zwanzig representation of irreversible processes, Proc. Natl. Acad. Sci. USA, 97 (2000), pp. 2968-2973. A. Chorin, O. Hald, and R. Kupferman, Non-Markovian optimal prediction, Monte Carlo Meth. & Appl., 7 (2001), pp. 99-109. A. Chorin, O. Hald and R. Kupferman, Optimal prediction with memory, Physica D, 166, (2002), pp. 239-257. F.A. Grunbaum, Diffuse tomography: using time of flight information in a two dimensional model, Int. J. Imaging Systems Technology, 11 (2001), pp. 283-286. F.A. Grunbaum, A nonlinear inverse problem inspired by three-dimensional diffuse tomography, Inverse Problems, 17 (2001), pp. 1907-1922. F.A. Grunbaum and L.F. Matusevich, Explicit inversion formulas for a model of diffuse tomography, Adv. in Appl. Math., (2002), pp.172-183. O. H. Hald, Optimal prediction and the Klein-Gordon equation, Proc. Natl. Acad. Sci. USA 96 (1999), 4774-4779. O. Hald and R. Kupferman, Convergence of optimal prediction for nonlinear Hamiltonian systems, SIAM J. Num. Anal., 39 (2001), pp. 983-1000. O.H. Hald and R. Kupferman, Asymptotic and numerical analyses for mechanical models of heat baths, J. Statist. Phys., 106 (2002), pp. 1121-1184. A. Kast, Optimal prediction of stiff oscillatory mechanics, Proc. Natl. Acad. Sci. USA, 97 (2000), pp. 6253-6257. T. Katsaounis and D. Levy, A modified structured central scheme for 2D hyperbolic conservation laws, Appl. Math. Lett. 12 (1999), 89-96. D. Levy, G. Puppo, and G. Russo, On the behavior of the total variation in CWENO methods for conservation laws, to appear in Appl. Numer. Math. D. Levy, G. Puppo, and G. Russo, A third order central WENO scheme for 2D conservation laws, Appl. Numer. Math., 33 (2000), pp. 407-414. D. Levy, G. Puppo, and G. Russo, On the behavior of the total variation in CWENO methods for conservation laws, Appl. Numer. Math., 33 (2000), pp. 415-421. D. Levy, G. Puppo, and G. Russo, Compact central WENO schemes for multidimensional conservation laws, SIAM J. Sci. Comput., 22 (2000), pp. 656-672.

1999

G.I. Barenblatt and A. Chorin, A new formulation of the near-equilibrium theory of turbulence, ESAIM Proceedings, Vol. 7, A. Giovannini, et al., eds., http://www.emath.fr/Maths/Proc (1999), pp. 22-35.

Books

G.I. Barenblatt, Scaling, Cambridge University Press, Cambridge 2002 (in press). A.J. Chorin, Probability, Mechanics, and Irreversibility, Lecture notes, UC Berkeley Math. Dept., 2000. A.J. Chorin, Stochastic Methods in Applied Mathematics and Physics, Lecture notes, UCB Math. Dept, 2002.

Ph.D Thesis

2003

K. Lin, Random perturbations of SRB measures and numerical studies of chaotic dynamics, Ph.D. thesis, LBNL 53522, 2003.
P. Stinis, Optimal prediction of Kuramoto-Sivashinsky equations, Ph.D. thesis, LBNL-53641, 2003.

2002

C. Cameron, Comparative analysis of sampling methods for stationary stochastic processes, Ph.D. thesis, Math. Dept., UC Berkeley, LBNL-41994, 2002.
E. Ingerman, Modeling the growth of uncertainty in optimal prediction, Ph.D. thesis, Math. Dept. UC Berkeley, LBNL-51995, 2002.

1999

A.D. Gottlieb, Markov transitions and the propagation of chaos, Ph.D. Thesis, LBNL-42839, 1998, Center for Pure and Applied Mathematics of the University of California at Berkeley Report No. 756, 1999.
J. Wright, Faraday oscillations in an incompressible fluid, Ph.D. thesis, UC Berkeley, LBNL-44867, 1999.

Technical Reports

2003

G.I. Barenblatt, A model of non-local damage accumulation, LBNL-53466, 2003. Plenary invited lecture submitted for publication in the Proceedings of the International Conference on Fracture.

2002

G.I. Barenblatt and J.L. Vazquez, Nonlinear diffusion and image enhancement, LBNL-51989, 2002.
A. Chorin, Conditional averaging and renormalization for the KdV-Burgers equation, LBNL-51990, 2002.
D. Givon, O.H. Hald, and R. Kupferman, Existence proof for orthogonal dynamics and the Mori-Zwanzig formalism, LBNL-52136, 2002, submitted to SIAM J. Math. Anal.
O.H. Hald and A.I. Shestakov, Stability of stationary solutions of the multifrequency radiation diffusion equations, LBNL-52134, 2002.
A.I. Shestakov, Solving the multifrequency radiation diffusion equations using Branching Brownian motion, LBNL-52133, 2002.
A.I. Shestakov, Solution of the nonlinear multigroup radiation diffusion equation using multigrid and pseudo transient continuation, LBNL-52135, 2002.

2001

G.I. Barenblatt, Damage accumulation: a non-local model, LBNL 48943, 2001.
G.I. Barenblatt, A.J. Chorin, and V.M. Prostokishin, Analysis of experimental investigations of self-similar intermediate structures in zero-pressure-gradient boundary layers at large Reynolds numbers, LBNL- 49523, 2001.
G.I. Barenblatt, A.J. Chorin, and V.M. Prostokishin, A note concerning the turbulent boundary layer drag at large Reynolds numbers, LBNL- 49524, 2001.
G.I. Barenblatt, A.J. Chorin, and V.M. Prostokishin, A note concerning the model of turbulent boundary layer with non-zero-pressure-gradient, LBNL-49493, 2001.
G.I. Barenblatt, T.W. Patzek, and D.B. Silin, Mathematical model of non-equilibrium effects in water-oil displacement, LBNL-49484, 2001.
A. Chertock, Self-similar intermediate asymptotics for free boundary problems occurring in image processing, LBNL- 49490, 2001.
A. Chertock, Particle methods for statistical initial value problems, LBNL- 49520, 2001.
A. Chorin, Conditional expectations and fast renormalization, LBNL-49522, 2001.
F.A. Grunbaum, Diffuse tomography as a source of challenging nonlinear problems, LBNL-49519, 2001.
P. Okunev, Comparative performance of three different algorithms for the non-Markovian optimal prediction applied to the Hald system, LBNL-48802, 2001.

2000

A. Chertock and D. Levy, Particle methods for dispersive equations, LBNL-47063, 2000.
A. Wiegmann, The contact zone of a frictionless rigid punch and an elastic object, LBNL-44836, 2000.
A. Wiegmann and K.P. Bube, The explicit-jump immersed interface method: finite difference methods for PDE with piecewise smooth solutions, SIAM J. Numer. Anal., 2000, to appear.

1999

G.I. Barenblatt, Scaling laws for turbulent wall bounded shear flows at very large Reynolds numbers, LBNL-43427, 1999.
T. Burin des Roziers, The optimal prediction method, LBNL-44236, 1999.
T. Burin des Roziers and A.D. Gottlieb, Experiments in first-order optimal prediction, LBNL-44191, 1999.
A. Constantin and D. Levy, Statistical mechanics of the periodic Camassa-Holm equations, LBNL-44441, 1999.
D. Givon, R. Kupferman and A.M Stuart, Extracting macroscopic dynamics: model problems & algorithms, submitted to Nonlinearity.
D. Givon and R. Kupferman, White noise limits for discrete dynamical systems driven by fast deterministic dynamics (in preparation).
A.D. Gottlieb, The propagation of molecular chaos by Markov transitions, LBNL-43105, 1999.
A. D. Gottlieb, The propagation of molecular chaos by systems of interacting quantum particles, LBNL-45081, 1999, submitted to Comm. in Math. Physics.
A. Gottlieb, Propagation of molecular chaos by quantum systems and the dynamics of the Curie-Weiss model, LBNL-44120, 1999.
D.A. Kessler, Steady-state cracks in visoelastic lattice models II, LBNL-44075, 1999.
D.A. Kessler and H. Levine, Arrested cracks in nonlinear lattice models of brittle fracture, LBNL-42870, 1999.
I. Kliakhandler, Inverse cascade in film flows, LBNL-44832, 1999, submitted to J. Fluid Mech.
I. Kliakhandler, Selection of scales in pattern-forming dynamics, LBNL-44833, 1999, submitted to Phys. Rev. Lett.
I. Kliakhandler, Long interfacial waves in multilayer thin films and coupled Kuramoto-Sivashinsky equations, J. Fluid Mech., 391 (1999), 45-65.
A. Kurganov and D. Levy, Third-order semi-discrete central scheme for conservation laws and convection-diffusion equations, LBNL-43528, 1999, to appear in SIAM J. of Sci. Comp.
D. Levy, G. Puppo, and G. Russo, Central WENO schemes for hyperbolic systems of conservation laws, Mathematical Modelling and Numerical Analysis, 33 (1999), 547-571.
D.S. Nolan, Vortex stabilization by axial stretching, presented at the 12th Conference on Atmospheric and Oceanic Fluid Dynamics, New York, NY, 1999.
D.S. Nolan and B.F. Farrell, Generalized stability analyses of asymmetric disturbances in one- and two-celled vortices maintained by radial flow, J. Atmos. Sci. 56 (1999), 1282-1307.
D.S. Nolan and B.F. Farrell, On the structure and dynamics of tornado-like vortices, J. Atmos. Sci. 56 (1999), 2908-2936.
D.S. Nolan and B.F. Farrell, The intensification of two-dimensional swirling flows by stochastic asymmetric forcing, J. Atmos. Sci. 56 (1999), 3937-3962.
D.S. Nolan, A.S. Almgren, and J.B. Bell, High Reynolds number simulations of axisymmetric tornado-like vortices with adaptive mesh refinement, LBNL-42860, 1999, submitted to J. Atmospheric Sci.
P. Rosenau and D. Levy, Compactons in a class of nonlinearly quintic equations, Phys. Lett. A. 252 (1999), 297-306.
C.F. Tolmasky and A. Wiegmann, Recovery of small perturbations of an interface for an elliptic inverse problem via linearization, Inverse Problems 15 (1999), 465-487.
A. Wiegmann. A multi-interface transmission problem and crack approximation, LBNL-42875, 1999.
A. Wiegmann, Analytic solutions to a multi-interface transmission problem and crack approximation, Inverse Problems, to appear.
A. Wiegmann, Fast Poisson, fast Helmholtz and fast linear elastostatic solvers on rectangular parallelepipeds, LBNL-43565, 1999.
A. Wiegmann, Fast elliptic solvers on rectangular parallelepipeds, submitted to SIAM J. Sci. Comp., 1999.
A. Wiegmann, The immersed interface method in bioengineering, to appear in Proceedings of the Bologna-Berkeley Conference on Partial Differential Equations in Bioengineering, ed. R. Malladi, 1999.
A. Wiegmann and K.P. Bube, The immersed interface method and integral formulas, LBNL-43566, 1999, submitted to Numerische Mathematik.
A. Wiegmann, Z. Li, and R. LeVeque, Jump conditions for cracks in elliptic problems, Appl. Math. Lett. 12 (1999), 81-88.

1998

D.A. Kessler and H. Levine, Steady-state cracks in visoelastic lattice models, LBNL-42618, 1998.
D. Levy and E. Tadmor, Non-oscillatory boundary treatment for staggered central schemes, LBNL-42864, 1998.
D. Levy, G. Puppo, and G. Russo, Central WENO schemes for multi-dimensional hyperbolic systems of conservation laws, LBNL-42866, 1998.
D. Levy, G. Puppo, and G. Russo, Central WENO schemes for balance laws, LBNL-42865, 1998.
A. Wiegmann and A. Sarti, Explicit-jump image segmentation, LBNL-42841, 1998, to be submitted to SIAM J. Appl. Math.