@article{2365,
abstract = {We consider a gas of fermions with non-zero spin at temperature T and chemical potential μ. We show that if the range of the interparticle interaction is small compared to the mean particle distance, the thermodynamic pressure differs to leading order from the corresponding expression for non-interacting particles by a term proportional to the scattering length of the interparticle interaction. This is true for any repulsive interaction, including hard cores. The result is uniform in the temperature as long as T is of the same order as the Fermi temperature, or smaller.},
author = {Robert Seiringer},
journal = {Communications in Mathematical Physics},
number = {3},
pages = {729 -- 757},
publisher = {Springer},
title = {{The thermodynamic pressure of a dilute fermi gas}},
doi = {10.1007/s00220-005-1433-3},
volume = {261},
year = {2006},
}
@article{2366,
abstract = {Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential.},
author = {Frank, Rupert L and Laptev, Ari and Lieb, Élliott H and Robert Seiringer},
journal = {Letters in Mathematical Physics},
number = {3},
pages = {309 -- 316},
publisher = {Springer},
title = {{Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials}},
doi = {10.1007/s11005-006-0095-1},
volume = {77},
year = {2006},
}
@inbook{2368,
abstract = {The recent experimental success in creating Bose-Einstein condensates of alkali atoms, honored by the Nobel prize awards in 2001 [1,5], led to renewed interest in the mathematical description of interacting Bose gases.},
author = {Robert Seiringer},
booktitle = {Large Coulomb Systems},
editor = {Dereziński, Jan and Siedentop, Heinz},
pages = {249 -- 274},
publisher = {Springer},
title = {{Dilute, trapped Bose gases and Bose-Einstein condensation}},
doi = {10.1007/3-540-32579-4_6},
volume = {695},
year = {2006},
}
@inbook{2369,
abstract = {One of the most remarkable recent developments in the study of ultracold Bose gases is the observation of a reversible transition from a Bose Einstein condensate to a state composed of localized atoms as the strength of a periodic, optical trapping potential is varied. In [1] a model of this phenomenon has been analyzed rigorously. The gas is a hard core lattice gas and the optical lattice is modeled by a periodic potential of strength λ. For small λ and temperature Bose- Einstein condensation (BEC) is proved to occur, while at large λ BEC disappears, even in the ground state, which is a Mott-insulator state with a characteristic gap. The inter-particle interaction is essential for this effect. This contribution gives a pedagogical survey of these results.},
author = {Aizenman, Michael and Lieb, Élliott H and Robert Seiringer and Solovej, Jan P and Yngvason, Jakob},
booktitle = {Mathematical Physics of Quantum Mechanics},
editor = {Asch, Joachim and Joye, Alain},
pages = {199 -- 215},
publisher = {Springer},
title = {{Bose-Einstein condensation as a quantum phase transition in an optical lattice}},
doi = {10.1007/b11573432},
volume = {690},
year = {2006},
}
@inbook{2416,
author = {Bang-Jensen, Jørgen and Reed, Bruce and Schacht, Bruce and Šámal, Robert and Toft, Bjarne and Uli Wagner},
booktitle = {Topics in Discrete Mathematics},
pages = {613 -- 627},
publisher = {Springer},
title = {{On six problems posed by Jarik Nešetřil}},
doi = {10.1007/3-540-33700-8_30},
volume = {26},
year = {2006},
}
@article{2429,
abstract = {We show, with an elementary proof, that the number of halving simplices in a set of n points in 4 in general position is O(n4-2/45). This improves the previous bound of O(n4-1/134). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane. },
author = {Matoušek, Jiří and Sharir, Micha and Smorodinsky, Shakhar and Uli Wagner},
journal = {Discrete & Computational Geometry},
number = {2},
pages = {177 -- 191},
publisher = {Springer},
title = {{K-sets in four dimensions}},
doi = {10.1007/s00454-005-1200-4},
volume = {35},
year = {2006},
}
@article{2430,
abstract = {We consider an online version of the conflict-free coloring of a set of points on the line, where each newly inserted point must be assigned a color upon insertion, and at all times the coloring has to be conflict-free, in the sense that in every interval I there is a color that appears exactly once in I. We present deterministic and randomized algorithms for achieving this goal, and analyze their performance, that is, the maximum number of colors that they need to use, as a function of the number n of inserted points. We first show that a natural and simple (deterministic) approach may perform rather poorly, requiring Ω(√̃) colors in the worst case. We then derive two efficient variants of this simple algorithm. The first is deterministic and uses O(log 2 n) colors, and the second is randomized and uses O(log n) colors with high probability. We also show that the O(log 2 n) bound on the number of colors used by our deterministic algorithm is tight on the worst case. We also analyze the performance of the simplest proposed algorithm when the points are inserted in a random order and present an incomplete analysis that indicates that, with high probability, it uses only O(log n) colors. Finally, we show that in the extension of this problem to two dimensions, where the relevant ranges are disks, n colors may be required in the worst case.},
author = {Chent, Ke and Fiat, Amos and Kaplan, Haim and Levy, Meital B and Matoušek, Jiří and Mossel, Elchanan and Pach, János and Sharir, Micha and Smorodinsky, Shakhar and Uli Wagner and Welzl, Emo},
journal = {SIAM Journal on Computing},
number = {5},
pages = {1342 -- 1359},
publisher = {SIAM},
title = {{Online conflict-free coloring for intervals}},
doi = {10.1137/S0097539704446682},
volume = {36},
year = {2006},
}
@inproceedings{2431,
abstract = {We prove an upper bound, tight up to a factor of 2, for the number of vertices of level at most t in an arrangement of n halfspaces in R , for arbitrary n and d (in particular, the dimension d is not considered constant). This partially settles a conjecture of Eckhoff, Linhart, and Welzl. Up to the factor of 2, the result generalizes McMullen's Upper Bound Theorem for convex polytopes (the case ℓ = O) and extends a theorem of Linhart for the case d ≤ 4. Moreover, the bound sharpens asymptotic estimates obtained by Clarkson and Shor. The proof is based on the h-matrix of the arrangement (a generalization, introduced by Mulmuley, of the h-vector of a convex polytope). We show that bounding appropriate sums of entries of this matrix reduces to a lemma about quadrupels of sets with certain intersection properties, and we prove this lemma, up to a factor of 2, using tools from multilinear algebra. This extends an approach of Alon and Kalai, who used linear algebra methods for an alternative proof of the classical Upper Bound Theorem. The bounds for the entries of the h-matrix also imply bounds for the number of i-dimensional faces, i > 0, at level at most ℓ. Furthermore, we discuss a connection with crossing numbers of graphs that was one of the main motivations for investigating exact bounds that are valid for arbitrary dimensions.},
author = {Uli Wagner},
pages = {635 -- 645},
publisher = {IEEE},
title = {{On a geometric generalization of the Upper Bound Theorem}},
doi = {10.1109/FOCS.2006.53},
year = {2006},
}
@article{2657,
abstract = {The highest densities of the two metabotropic GABA subunits, GABA B1 and GABAB2, have been reported as occurring around the glutamatergic synapses between Purkinje cell spines and parallel fibre varicosities. In order to determine how this distribution is achieved during development, we investigated the expression pattern and the cellular and subcellular localization of the GABAB1 and GABAB2 subunits in the rat cerebellum during postnatal development. At the light microscopic level, immunoreactivity for the GABAB1 and GABAB2 subunits was very prominent in the developing molecular layer, especially in Purkinje cells. Using double immunofluorescence, we demonstrated that GABAB1 was transiently expressed in glial cells. At the electron microscopic level, immunoreactivity for GABAB receptors was always detected both pre- and postsynaptically. Presynaptically, GABAB1 and GABAB2 were localized in the extrasynaptic membrane of parallel fibres at all ages, and only rarely in GABAergic axons. Postsynaptically, GABAB receptors were localized to the extrasynaptic and perisynaptic plasma membrane of Purkinje cell dendrites and spines throughout development. Quantitative analysis and three-dimensional reconstructions further revealed a progressive developmental movement of the GABAB1 subunit on the surface of Purkinje cells from dendritic shafts to its final destination, the dendritic spines. Together, these results indicate that GABAB receptors undergo dynamic regulation during cerebellar development in association with the establishment and maturation of glutamatergic synapses to Purkinje cells.},
author = {Luján, Rafael and Ryuichi Shigemoto},
journal = {European Journal of Neuroscience},
number = {6},
pages = {1479 -- 1490},
publisher = {Wiley-Blackwell},
title = {{Localization of metabotropic GABA receptor subunits GABAB1 and GABAB2 relative to synaptic sites in the rat developing cerebellum}},
doi = {10.1111/j.1460-9568.2006.04669.x},
volume = {23},
year = {2006},
}
@article{2659,
abstract = {Transmembrane AMPA receptor regulatory proteins (TARPs), including stargazin/γ-2, are associated with AMPA receptors and participate in their surface delivery and anchoring at the postsynaptic membrane. TARPs may also act as a positive modulator of the AMPA receptor ion channel function; however, little is known about other TARP members except for stargazin/γ-2. We examined the synaptic localization of stargazin/γ-2 and γ-8 by immunoelectron microscopy and biochemical analysis. The analysis of sodium dodecyl sulfate-digested freeze-fracture replica labeling revealed that stargazin/γ-2 was concentrated in the postsynaptic area, whereas γ-8 was distributed both in synaptic and extra-synaptic plasma membranes of the hippocampal neuron. When a synaptic plasma membrane-enriched brain fraction was treated with Triton X-100 and separated by sucrose density gradient ultracentrifugation, a large proportion of NMDA receptor and stargazin/γ-2 was accumulated in raft-enriched fractions, whereas AMPA receptor and γ-8 were distributed in both the raft-enriched fractions and other Triton-insoluble fractions. Phosphorylation of stargazin/γ-2 and γ-8 was regulated by different sets of kinases and phosphatases in cultured cortical neurons. These results suggested that stargazin/γ-2 and γ-8 have distinct roles in postsynaptic membranes under the regulation of different intracellular signaling pathways.},
author = {Inamura, Mihoko and Itakura, Makoto and Okamoto, Hirotsugu and Hoka, Sumio and Mizoguchi, Akira and Fukazawa, Yugo and Ryuichi Shigemoto and Yamamori, Saori and Takahashi, Masami},
journal = {Neuroscience Research},
number = {1},
pages = {45 -- 53},
publisher = {Elsevier},
title = {{ Differential localization and regulation of stargazin-like protein, γ-8 and stargazin in the plasma membrane of hippocampal and cortical neurons}},
doi = {10.1016/j.neures.2006.01.004},
volume = {55},
year = {2006},
}
@article{2660,
abstract = {Pavlovian fear conditioning, a simple form of associative learning, is thought to involve the induction of associative, NMDA receptor-dependent long-term potentiation (LTP) in the lateral amygdala. Using a combined genetic and electrophysiological approach, we show here that lack of a specific GABAB receptor subtype, GABAB(1a,2), unmasks a nonassociative, NMDA receptor-independent form of presynaptic LTP at cortico-amygdala afferents. Moreover, the level of presynaptic GABA B(1a,2) receptor activation, and hence the balance between associative and nonassociative forms of LTP, can be dynamically modulated by local inhibitory activity. At the behavioral level, genetic loss of GABA B(1a) results in a generalization of conditioned fear to nonconditioned stimuli. Our findings indicate that presynaptic inhibition through GABAB(1a,2) receptors serves as an activity-dependent constraint on the induction of homosynaptic plasticity, which may be important to prevent the generalization of conditioned fear.},
author = {Shaban, Hamdy and Humeau, Yann and Herry, Cyril and Cassasus, Guillaume and Ryuichi Shigemoto and Ciocchi, Stéphane and Barbieri, Samuel and Van Der Putten, Herman V and Kaupmann, Klemens and Bettler, Bernhard and Lüthi, Andreas},
journal = {Nature Neuroscience},
number = {8},
pages = {1028 -- 1035},
publisher = {Nature Publishing Group},
title = {{Generalization of amygdala LTP and conditioned fear in the absence of presynaptic inhibition}},
doi = {10.1038/nn1732},
volume = {9},
year = {2006},
}
@article{2661,
abstract = {GABAB receptors are the G protein-coupled receptors for the main inhibitory neurotransmitter in the brain, γ-aminobutyric acid (GABA). Molecular diversity in the GABAB system arises from the GABAB1a and GABAB1b subunit isoforms that solely differ in their ectodomains by a pair of sushi repeats that is unique to GABAB1a. Using a combined genetic, physiological, and morphological approach, we now demonstrate that GABAB1 isoforms localize to distinct synaptic sites and convey separate functions in vivo. At hippocampal CA3-to-CA1 synapses, GABAB1a assembles heteroreceptors inhibiting glutamate release, while predominantly GABAB1b mediates postsynaptic inhibition. Electron microscopy reveals a synaptic distribution of GABAB1 isoforms that agrees with the observed functional differences. Transfected CA3 neurons selectively express GABAB1a in distal axons, suggesting that the sushi repeats, a conserved protein interaction motif, specify heteroreceptor localization. The constitutive absence of GABAB1a but not GABAB1b results in impaired synaptic plasticity and hippocampus-dependent memory, emphasizing molecular differences in synaptic GABAB functions.},
author = {Vigot, Réjan and Barbieri, Samuel and Bräuner-Osborne, Hans and Tureček, Rostislav and Ryuichi Shigemoto and Zhang, Yan Ping and Luján, Rafael and Jacobson, Laura H and Biermann, Barbara and Fritschy, Jean-Marc and Vacher, Claire-Marie and Müller, Matthias P and Sansig, Gilles and Guetg, Nicole and Cryan, John F and Kaupmann, Klemens and Gassmann, Martin and Oertner, Thomas G and Bettler, Bernhard},
journal = {Neuron},
number = {4},
pages = {589 -- 601},
publisher = {Elsevier},
title = {{Differential Compartmentalization and Distinct Functions of GABAB Receptor Variants}},
doi = {10.1016/j.neuron.2006.04.014},
volume = {50},
year = {2006},
}
@article{2662,
abstract = {G-protein-coupled inwardly rectifying K+ channels (Kir3 channels) coupled to metabotropic GABAB receptors are essential for the control of neuronal excitation. To determine the distribution of Kir3 channels and their spatial relationship to GABAB receptors on hippocampal pyramidal cells, we used a high-resolution immunocytochemical approach. Immunoreactivity for the Kir3.2 subunit was most abundant postsynaptically and localized to the extrasynaptic plasma membrane of dendritic shafts and spines of principal cells. Quantitative analysis of immunogold particles for Kir3.2 revealed an enrichment of the protein around putative glutamatergic synapses on dendritic spines, similar to that of GABA B1. Consistent with this observation, a high degree of coclustering of Kir3.2 and GABAB1 was revealed around excitatory synapses by the highly sensitive SDS-digested freeze-fracture replica immunolabeling. In contrast, in dendritic shafts receptors and channels were found to be mainly segregated. These results suggest that Kir3.2-containing K+ channels on dendritic spines preferentially mediate the effect of GABA, whereas channels on dendritic shafts are likely to be activated by other neurotransmitters as well. Thus, Kir3 channels, localized to different subcellular compartments of hippocampal principal cells, appear to be differentially involved in synaptic integration in pyramidal cell dendrites.},
author = {Kulik, Ákos and Vida, Imre and Fukazawa, Yugo and Guetg, Nicole and Kasugai, Yu and Marker, Cheryl L and Rigato, Franck and Bettler, Bernhard and Wickman, Kevin D and Frotscher, Michael and Ryuichi Shigemoto},
journal = {Journal of Neuroscience},
number = {16},
pages = {4289 -- 4297},
publisher = {Society for Neuroscience},
title = {{Compartment-dependent colocalization of Kir3.2-containing K+ channels and GABAB receptors in hippocampal pyramidal cells}},
doi = {10.1523/JNEUROSCI.4178-05.2006},
volume = {26},
year = {2006},
}
@article{2663,
abstract = {The rocker mice are hereditary ataxic mutants that carry a point mutation in the gene encoding the CaV2.1 (P/Q-type) Ca2+ channel α1 subunit, and show the mildest symptoms among the reported CaV2.1 mutant mice. We studied the basic characteristics of the rocker mutant Ca2+ channel and their impacts on excitatory synaptic transmission in cerebellar Purkinje cells (PCs). In acutely dissociated PC somas, the rocker mutant channel showed a moderate reduction in Ca2+ channel current density, whereas its kinetics and voltage dependency of gating remained nearly normal. Despite the small changes in channel function, synaptic transmission in the parallel fiber (PF)-PC synapses was severely impaired. The climbing fiber inputs onto PCs showed a moderate impairment but could elicit normal complex spikes. Presynaptic function of the PF-PC synapses, however, was unexpectedly almost normal in terms of paired-pulse facilitation, sensitivity to extracellular Ca2+ concentration and glutamate concentration in synaptic clefts. Electron microscopic analyses including freeze-fracture replica labeling revealed that both the number and density of postsynaptic α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors substantially decreased without gross structural changes of the PF-PC synapses. We also observed an abnormal arborization of PC dendrites in young adult rocker mice (∼ 1 month old). These lines of evidence suggest that even a moderate dysfunction of CaV2.1 Ca2+ channel can cause substantial changes in postsynaptic molecular composition of the PF-PC synapses and dendritic structure of PCs.},
author = {Kodama, Takashi and Itsukaichi-Nishida, Yuko and Fukazawa, Yugo and Wakamori, Minoru and Miyata, Mariko and Molnár, Elek and Mori, Yasuo and Ryuichi Shigemoto and Imoto, Keiji},
journal = {European Journal of Neuroscience},
number = {11},
pages = {2993 -- 3007},
publisher = {Wiley-Blackwell},
title = {{A CaV2.1 calcium channel mutation rocker reduces the number of postsynaptic AMPA receptors in parallel fiber-Purkinje cell synapses}},
doi = {10.1111/j.1460-9568.2006.05191.x},
volume = {24},
year = {2006},
}
@misc{2664,
abstract = {Metabotropic glutamate receptors (mGlus) are a family of G-protein-coupled receptors activated by the neurotransmitter glutamate. Molecular cloning has revealed eight different subtypes (mGlu1-8) with distinct molecular and pharmacological properties. Multiplicity in this receptor family is further generated through alternative splicing. mGlus activate a multitude of signalling pathways important for modulating neuronal excitability, synaptic plasticity and feedback regulation of neurotransmitter release. In this review, we summarize anatomical findings (from our work and that of other laboratories) describing their distribution in the central nervous system. Recent evidence regarding the localization of these receptors in peripheral tissues will also be examined. The distinct regional, cellular and subcellular distribution of mGlus in the brain will be discussed in view of their relationship to neurotransmitter release sites and of possible functional implications.},
author = {Ferraguti, Francesco and Ryuichi Shigemoto},
booktitle = {Cell and Tissue Research},
number = {2},
pages = {483 -- 504},
publisher = {Springer},
title = {{Metabotropic glutamate receptors}},
doi = {10.1007/s00441-006-0266-5},
volume = {326},
year = {2006},
}
@article{2745,
abstract = {We consider the dynamics of N boson systems interacting through a pair potential N -1 V a (x i -x j ) where V a (x)=a -3 V(x/a). We denote the solution to the N-particle Schrödinger equation by Ψ N, t . Recall that the Gross-Pitaevskii (GP) equation is a nonlinear Schrödinger equation and 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 [InlineMediaObject not available: see fulltext.] solves the GP hierarchy. Under the assumption that a = Nε for 0 < ε < 3/5, we prove that as N→∞ the limit points of the k-particle density matrices of Ψ N, t are solutions of the GP hierarchy with the coupling constant in the nonlinear term of the GP equation given by ∫ V (x)dx. The uniqueness of the solutions of this hierarchy remains an open question.},
author = {Elgart, Alexander and László Erdös and Schlein, Benjamin and Yau, Horng-Tzer},
journal = {Archive for Rational Mechanics and Analysis},
number = {2},
pages = {265 -- 283},
publisher = {Springer},
title = {{Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons}},
doi = {10.1007/s00205-005-0388-z},
volume = {179},
year = {2006},
}
@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},
}