@inproceedings{2746,
abstract = {We consider random Schrödinger equations on Rd or Zd for d ≥ 3 with uncorrelated, identically distributed random potential. Denote by λ the coupling constant and ψt the solution with initial data ψ0.},
author = {László Erdös and Salmhofer, Manfred and Yau, Horng-Tzer},
pages = {233 -- 257},
publisher = {World Scientific Publishing},
title = {{Towards the quantum Brownian motion}},
doi = {10.1007/3-540-34273-7_18},
volume = {690},
year = {2006},
}
@article{2747,
abstract = {Consider a system of N bosons on the three-dimensional unit torus interacting via a pair potential N 2V(N(x i - x j)) where x = (x i, . . ., x N) denotes the positions of the particles. Suppose that the initial data ψ N,0 satisfies the condition 〈ψ N,0, H 2 Nψ N,0) ≤ C N 2 where H N is the Hamiltonian of the Bose system. This condition is satisfied if ψ N,0 = W Nφ N,t where W N is an approximate ground state to H N and φ N,0 is regular. Let ψ N,t denote the solution to the Schrödinger equation with Hamiltonian H N. Gross and Pitaevskii proposed to model the dynamics of such a system by a nonlinear Schrödinger equation, the Gross-Pitaevskii (GP) equation. The GP hierarchy is an infinite BBGKY hierarchy of equations so that if u t solves the GP equation, then the family of k-particle density matrices ⊗ k |u t?〉 〈 t | solves the GP hierarchy. We prove that as N → ∞ the limit points of the k-particle density matrices of ψ N,t are solutions of the GP hierarchy. Our analysis requires that the N-boson dynamics be described by a modified Hamiltonian that cuts off the pair interactions whenever at least three particles come into a region with diameter much smaller than the typical interparticle distance. Our proof can be extended to a modified Hamiltonian that only forbids at least n particles from coming close together for any fixed n.},
author = {László Erdös and Schlein, Benjamin and Yau, Horng-Tzer},
journal = {Communications on Pure and Applied Mathematics},
number = {12},
pages = {1659 -- 1741},
publisher = {Wiley-Blackwell},
title = {{Derivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein condensate}},
doi = {10.1002/cpa.20123},
volume = {59},
year = {2006},
}
@article{2791,
abstract = {Generally, the motion of fluids is smooth and laminar at low speeds but becomes highly disordered and turbulent as the velocity increases. The transition from laminar to turbulent flow can involve a sequence of instabilities in which the system realizes progressively more complicated states, or it can occur suddenly. Once the transition has taken place, it is generally assumed that, under steady conditions, the turbulent state will persist indefinitely. The flow of a fluid down a straight pipe provides a ubiquitous example of a shear flow undergoing a sudden transition from laminar to turbulent motion. Extensive calculations and experimental studies have shown that, at relatively low flow rates, turbulence in pipes is transient, and is characterized by an exponential distribution of lifetimes. They also suggest that for Reynolds numbers exceeding a critical value the lifetime diverges (that is, becomes infinitely large), marking a change from transient to persistent turbulence. Here we present experimental data and numerical calculations covering more than two decades of lifetimes, showing that the lifetime does not in fact diverge but rather increases exponentially with the Reynolds number. This implies that turbulence in pipes is only a transient event (contrary to the commonly accepted view), and that the turbulent and laminar states remain dynamically connected, suggesting avenues for turbulence control.},
author = {Björn Hof and Westerweel, Jerry and Schneider, Tobias M and Eckhardt, Bruno},
journal = {Nature},
number = {7107},
pages = {59 -- 62},
publisher = {Nature Publishing Group},
title = {{Finite lifetime of turbulence in shear flows}},
doi = {10.1038/nature05089},
volume = {443},
year = {2006},
}
@article{2792,
abstract = {Transition to turbulence in pipe flow has posed a riddle in fluid dynamics since the pioneering experiments of Reynolds[1]. Although the laminar flow is linearly stable for all flow rates, practical pipe flows become turbulent at large enough flow speeds. Turbulence arises suddenly and fully without distinct steps and without a clear critical point. The complexity of this problem has puzzled mathematicians, physicists and engineers for more than a century and no satisfactory explanation of this problem has been given. In a very recent theoretical approach it has been suggested that unstable solutions of the Navier Stokes equations may hold the key to understanding this problem. In numerical studies such unstable states have been identified as exact solutions for the idealized case of a pipe with periodic boundary conditions[2, 3]. These solutions have the form of waves extending through the entire pipe and travelling in the streamwise direction at a phase speed close to the bulk velocity of the fluid. With the aid of a recently developed high-speed stereoscopic Particle Image Velocimetry (PIV) system, we were able to observe transients of such unstable solutions in turbulent pipe flow[4].},
author = {Björn Hof and van Doorne, Casimir W and Westerweel, Jerry and Nieuwstadt, Frans T},
journal = {Fluid Mechanics and its Applications},
pages = {109 -- 114},
publisher = {Springer},
title = {{Observation of nonlinear travelling waves in turbulent pipe flow}},
doi = {10.1007/1-4020-4159-4_11},
volume = {78},
year = {2006},
}
@article{2894,
abstract = {IL-10 is a potent anti-inflammatory and immunomodulatory cytokine, exerting major effects in the degree and quality of the immune response. Using a newly generated IL-10 reporter mouse model, which easily allows the study of IL-10 expression from each allele in a single cell, we report here for the first time that IL-10 is predominantly monoallelic expressed in CD4+ T cells. Furthermore, we have compelling evidence that this expression pattern is not due to parental imprinting, allelic exclusion, or strong allelic bias. Instead, our results support a stochastic regulation mechanism, in which the probability to initiate allelic transcription depends on the strength of TCR signaling and subsequent capacity to overcome restrictions imposed by chromatin hypoacetylation. In vivo Ag-experienced T cells show a higher basal probability to transcribe IL-10 when compared with naive cells, yet still show mostly monoallelic IL-10 expression. Finally, statistical analysis on allelic expression data shows transcriptional independence between both alleles. We conclude that CD4+ T cells have a low probability for IL-10 allelic activation resulting in a predominantly monoallelic expression pattern, and that IL-10 expression appears to be stochastically regulated by controlling the frequency of expressing cells, rather than absolute protein levels per cell.},
author = {Calado, Dinis P and Tiago Paixao and Holmberg, Dan and Haury, Matthias},
journal = {Journal of Immunology},
number = {8},
pages = {5358 -- 5364},
publisher = {American Association of Immunologists},
title = {{Stochastic Monoallelic Expression of IL 10 in T Cells}},
doi = {10.4049/jimmunol.177.8.5358 },
volume = {177},
year = {2006},
}