@article{2707,
abstract = {We give a nonrigorous derivation of the nonlinear Boltzmann equation from the Schrödinger evolution of interacting fermions. The argument is based mainly on the assumption that a quasifree initial state satisfies a property called restricted quasifreeness in the weak coupling limit at any later time. By definition, a state is called restricted quasifree if the four-point and the eight-point functions of the state factorize in the same manner as in a quasifree state.},
author = {László Erdös and Salmhofer, Manfred and Yau, Horng-Tzer},
journal = {Journal of Statistical Physics},
number = {1-4},
pages = {367 -- 380},
publisher = {Springer},
title = {{On the quantum Boltzmann equation}},
doi = {10.1023/B:JOSS.0000037224.56191.ed},
volume = {116},
year = {2004},
}
@article{2741,
abstract = {The Pauli operator describes the energy of a nonrelativistic quantum particle with spin 1/2 in a magnetic field and an external potential. A new Lieb-Thirring type inequality on the sum of the negative eigenvalues is presented. The main feature compared to earlier results is that in the large field regime the present estimate grows with the optimal (first) power of the strength of the magnetic field. As a byproduct of the method, we also obtain an optimal upper bound on the pointwise density of zero energy eigenfunctions of the Dirac operator. The main technical tools are: (i) a new localization scheme for the square of the resolvent of a general class of second order elliptic operators; (ii) a geometric construction of a Dirac operator with a constant magnetic field that approximates the original Dirac operator in a tubular neighborhood of a fixed field line. The errors may depend on the regularity of the magnetic field but they are uniform in the field strength.},
author = {László Erdös and Solovej, Jan P},
journal = {Annales Henri Poincare},
number = {4},
pages = {671 -- 741},
publisher = {Birkhäuser},
title = {{Uniform Lieb-Thirring inequality for the three-dimensional Pauli operator with a strong non-homogeneous magnetic field}},
doi = {10.1007/s00023-004-0180-x},
volume = {5},
year = {2004},
}
@article{2742,
abstract = {We consider a system of N weakly interacting fermions with a real analytic pair interaction. We prove that for a general class of initial data there exists a fixed time T such that the difference between the one particle density matrix of this system and the solution of the nonlinear Hartree equation is of order N−1 for any time t⩽T.},
author = {Elgart, Alexander and László Erdös and Schlein, Benjamin and Yau, Horng-Tzer},
journal = {Journal de Mathématiques Pures et Appliquées},
number = {10},
pages = {1241 -- 1273},
publisher = {Elsevier},
title = {{Nonlinear Hartree equation as the mean field limit of weakly coupled fermions}},
doi = {10.1016/j.matpur.2004.03.006},
volume = {83},
year = {2004},
}
@article{2786,
abstract = {Transition to turbulence in pipe flow is one of the most fundamental and longest- standing problems in fluid dynamics. Stability theory suggests that the flow remains laminar for all flow rates, but in practice pipe flow becomes turbulent even at moderate speeds. This transition drastically affects the transport efficiency of mass, momentum, and heat. On the basis of the recent discovery of unstable traveling waves in computational studies of the Navier-Stokes equations and ideas from dynamical systems theory, a model for the transition process has been suggested. We report experimental observation of these traveling waves in pipe flow, confirming the proposed transition scenario and suggesting that the dynamics associated with these unstable states may indeed capture the nature of fluid turbulence.},
author = {Björn Hof and van Doorne, Casimir W and Westerweel, Jerry and Nieuwstadt, Frans T and Faisst, Holger and Eckhardt, Bruno and Wedin, Håkan and Kersweli, Richard R and Waleffe, Fabian},
journal = {Science},
number = {5690},
pages = {1594 -- 1598},
publisher = {American Association for the Advancement of Science},
title = {{Experimental observation of nonlinear traveling waves in turbulent pipe flow}},
doi = {10.1126/science.1100393},
volume = {305},
year = {2004},
}
@article{2787,
abstract = {The results of experimental and numerical investigations of the onset of oscillatory convection in a sidewall heated rectangular cavity of molten gallium are reported. Detailed comparisons are made between experimental observations and calculations from numerical simulations of a three-dimensional Boussinesq model. The onset of time-dependence takes place through supercritical Hopf bifurcations and the loci of critical points in the (Gr, Pr)-plane are qualitatively similar with excellent agreement between the frequencies of the oscillatory motion. This provides a severe test of the control of the experiment since the mode of oscillation is extremely sensitive to imperfections. Detailed numerical investigations reveal that there are a pair of Hopf bifurcations which exist on two asymmetric states which themselves arise at a subcritical pitchfork from the symmetric state. There is no evidence for this in the experiment and this qualitative difference is attributed to non-Boussinesq perturbations which increase with Gr. However, the antisymmetric spatial structure of the oscillatory state is robust and is present in both the experiment and the numerical model. Moreover, the detailed analysis of the numerical results reveals the origins of the oscillatory instability.},
author = {Björn Hof and Juel, Anne and Zhao, Li and Henry, Daniel and Ben Hadid, Hamda and Mullin, Tom P},
journal = {Journal of Fluid Mechanics},
pages = {391 -- 413},
publisher = {Cambridge University Press},
title = {{On the onset of oscillatory convection in molten gallium}},
doi = {10.1017/S0022112004000527},
volume = {515},
year = {2004},
}