---
_id: '2664'
abstract:
- lang: eng
text: 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:
- first_name: Francesco
full_name: Ferraguti, Francesco
last_name: Ferraguti
- first_name: Ryuichi
full_name: Ryuichi Shigemoto
id: 499F3ABC-F248-11E8-B48F-1D18A9856A87
last_name: Shigemoto
orcid: 0000-0001-8761-9444
citation:
ama: Ferraguti F, Shigemoto R. Metabotropic glutamate receptors. *Cell and Tissue
Research*. 2006;326(2):483-504. doi:10.1007/s00441-006-0266-5
apa: Ferraguti, F., & Shigemoto, R. (2006). Metabotropic glutamate receptors.
*Cell and Tissue Research*. Springer. https://doi.org/10.1007/s00441-006-0266-5
chicago: Ferraguti, Francesco, and Ryuichi Shigemoto. “Metabotropic Glutamate Receptors.”
*Cell and Tissue Research*. Springer, 2006. https://doi.org/10.1007/s00441-006-0266-5.
ieee: F. Ferraguti and R. Shigemoto, “Metabotropic glutamate receptors,” *Cell
and Tissue Research*, vol. 326, no. 2. Springer, pp. 483–504, 2006.
ista: Ferraguti F, Shigemoto R. 2006. Metabotropic glutamate receptors. Cell and
Tissue Research. 326(2), 483–504.
mla: Ferraguti, Francesco, and Ryuichi Shigemoto. “Metabotropic Glutamate Receptors.”
*Cell and Tissue Research*, vol. 326, no. 2, Springer, 2006, pp. 483–504,
doi:10.1007/s00441-006-0266-5.
short: F. Ferraguti, R. Shigemoto, Cell and Tissue Research 326 (2006) 483–504.
date_created: 2018-12-11T11:58:57Z
date_published: 2006-11-01T00:00:00Z
date_updated: 2020-07-14T12:45:44Z
day: '01'
doi: 10.1007/s00441-006-0266-5
extern: 1
intvolume: ' 326'
issue: '2'
month: '11'
page: 483 - 504
publication: Cell and Tissue Research
publication_status: published
publisher: Springer
publist_id: '4234'
quality_controlled: 0
status: public
title: Metabotropic glutamate receptors
type: review
volume: 326
year: '2006'
...
---
_id: '2745'
abstract:
- lang: eng
text: '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:
- first_name: Alexander
full_name: Elgart, Alexander
last_name: Elgart
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
- first_name: Horng
full_name: Yau, Horng-Tzer
last_name: Yau
citation:
ama: Elgart A, Erdös L, Schlein B, Yau H. Gross-Pitaevskii equation as the mean
field limit of weakly coupled bosons. *Archive for Rational Mechanics and Analysis*.
2006;179(2):265-283. doi:10.1007/s00205-005-0388-z
apa: Elgart, A., Erdös, L., Schlein, B., & Yau, H. (2006). Gross-Pitaevskii
equation as the mean field limit of weakly coupled bosons. *Archive for Rational
Mechanics and Analysis*, *179*(2), 265–283. https://doi.org/10.1007/s00205-005-0388-z
chicago: 'Elgart, Alexander, László Erdös, Benjamin Schlein, and Horng Yau. “Gross-Pitaevskii
Equation as the Mean Field Limit of Weakly Coupled Bosons.” *Archive for Rational
Mechanics and Analysis* 179, no. 2 (2006): 265–83. https://doi.org/10.1007/s00205-005-0388-z.'
ieee: A. Elgart, L. Erdös, B. Schlein, and H. Yau, “Gross-Pitaevskii equation as
the mean field limit of weakly coupled bosons,” *Archive for Rational Mechanics
and Analysis*, vol. 179, no. 2, pp. 265–283, 2006.
ista: Elgart A, Erdös L, Schlein B, Yau H. 2006. Gross-Pitaevskii equation as the
mean field limit of weakly coupled bosons. Archive for Rational Mechanics and
Analysis. 179(2), 265–283.
mla: Elgart, Alexander, et al. “Gross-Pitaevskii Equation as the Mean Field Limit
of Weakly Coupled Bosons.” *Archive for Rational Mechanics and Analysis*,
vol. 179, no. 2, Springer, 2006, pp. 265–83, doi:10.1007/s00205-005-0388-z.
short: A. Elgart, L. Erdös, B. Schlein, H. Yau, Archive for Rational Mechanics and
Analysis 179 (2006) 265–283.
date_created: 2018-12-11T11:59:22Z
date_published: 2006-02-01T00:00:00Z
date_updated: 2019-04-26T07:22:19Z
day: '01'
doi: 10.1007/s00205-005-0388-z
extern: 1
intvolume: ' 179'
issue: '2'
month: '02'
page: 265 - 283
publication: Archive for Rational Mechanics and Analysis
publication_status: published
publisher: Springer
publist_id: '4147'
quality_controlled: 0
status: public
title: Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons
type: journal_article
volume: 179
year: '2006'
...
---
_id: '2746'
abstract:
- lang: eng
text: 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.
alternative_title:
- LNP
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Manfred
full_name: Salmhofer, Manfred
last_name: Salmhofer
- first_name: Horng
full_name: Yau, Horng-Tzer
last_name: Yau
citation:
ama: 'Erdös L, Salmhofer M, Yau H. Towards the quantum Brownian motion. In: Vol
690. World Scientific Publishing; 2006:233-257. doi:10.1007/3-540-34273-7_18'
apa: 'Erdös, L., Salmhofer, M., & Yau, H. (2006). Towards the quantum Brownian
motion (Vol. 690, pp. 233–257). Presented at the QMath: Mathematical Results in
Quantum Physics, World Scientific Publishing. https://doi.org/10.1007/3-540-34273-7_18'
chicago: Erdös, László, Manfred Salmhofer, and Horng Yau. “Towards the Quantum Brownian
Motion,” 690:233–57. World Scientific Publishing, 2006. https://doi.org/10.1007/3-540-34273-7_18.
ieee: 'L. Erdös, M. Salmhofer, and H. Yau, “Towards the quantum Brownian motion,”
presented at the QMath: Mathematical Results in Quantum Physics, 2006, vol. 690,
pp. 233–257.'
ista: 'Erdös L, Salmhofer M, Yau H. 2006. Towards the quantum Brownian motion. QMath:
Mathematical Results in Quantum Physics, LNP, vol. 690. 233–257.'
mla: Erdös, László, et al. *Towards the Quantum Brownian Motion*. Vol. 690,
World Scientific Publishing, 2006, pp. 233–57, doi:10.1007/3-540-34273-7_18.
short: L. Erdös, M. Salmhofer, H. Yau, in:, World Scientific Publishing, 2006, pp.
233–257.
conference:
name: 'QMath: Mathematical Results in Quantum Physics'
date_created: 2018-12-11T11:59:23Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2019-04-26T07:22:19Z
day: '01'
doi: 10.1007/3-540-34273-7_18
extern: 1
intvolume: ' 690'
month: '01'
page: 233 - 257
publication_status: published
publisher: World Scientific Publishing
publist_id: '4146'
quality_controlled: 0
status: public
title: Towards the quantum Brownian motion
type: conference
volume: 690
year: '2006'
...
---
_id: '2747'
abstract:
- lang: eng
text: 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:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
- first_name: Horng
full_name: Yau, Horng-Tzer
last_name: Yau
citation:
ama: Erdös L, Schlein B, Yau H. Derivation of the Gross-Pitaevskii hierarchy for
the dynamics of Bose-Einstein condensate. *Communications on Pure and Applied
Mathematics*. 2006;59(12):1659-1741. doi:10.1002/cpa.20123
apa: Erdös, L., Schlein, B., & Yau, H. (2006). Derivation of the Gross-Pitaevskii
hierarchy for the dynamics of Bose-Einstein condensate. *Communications on Pure
and Applied Mathematics*, *59*(12), 1659–1741. https://doi.org/10.1002/cpa.20123
chicago: 'Erdös, László, Benjamin Schlein, and Horng Yau. “Derivation of the Gross-Pitaevskii
Hierarchy for the Dynamics of Bose-Einstein Condensate.” *Communications on
Pure and Applied Mathematics* 59, no. 12 (2006): 1659–1741. https://doi.org/10.1002/cpa.20123.'
ieee: L. Erdös, B. Schlein, and H. Yau, “Derivation of the Gross-Pitaevskii hierarchy
for the dynamics of Bose-Einstein condensate,” *Communications on Pure and Applied
Mathematics*, vol. 59, no. 12, pp. 1659–1741, 2006.
ista: Erdös L, Schlein B, Yau H. 2006. Derivation of the Gross-Pitaevskii hierarchy
for the dynamics of Bose-Einstein condensate. Communications on Pure and Applied
Mathematics. 59(12), 1659–1741.
mla: Erdös, László, et al. “Derivation of the Gross-Pitaevskii Hierarchy for the
Dynamics of Bose-Einstein Condensate.” *Communications on Pure and Applied Mathematics*,
vol. 59, no. 12, Wiley-Blackwell, 2006, pp. 1659–741, doi:10.1002/cpa.20123.
short: L. Erdös, B. Schlein, H. Yau, Communications on Pure and Applied Mathematics
59 (2006) 1659–1741.
date_created: 2018-12-11T11:59:23Z
date_published: 2006-12-01T00:00:00Z
date_updated: 2019-04-26T07:22:19Z
day: '01'
doi: 10.1002/cpa.20123
extern: 1
intvolume: ' 59'
issue: '12'
month: '12'
page: 1659 - 1741
publication: Communications on Pure and Applied Mathematics
publication_status: published
publisher: Wiley-Blackwell
publist_id: '4145'
quality_controlled: 0
status: public
title: Derivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein
condensate
type: journal_article
volume: 59
year: '2006'
...
---
_id: '2791'
abstract:
- lang: eng
text: 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:
- first_name: Björn
full_name: Björn Hof
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
- first_name: Jerry
full_name: Westerweel, Jerry
last_name: Westerweel
- first_name: Tobias
full_name: Schneider, Tobias M
last_name: Schneider
- first_name: Bruno
full_name: Eckhardt, Bruno
last_name: Eckhardt
citation:
ama: Hof B, Westerweel J, Schneider T, Eckhardt B. Finite lifetime of turbulence
in shear flows. *Nature*. 2006;443(7107):59-62. doi:10.1038/nature05089
apa: Hof, B., Westerweel, J., Schneider, T., & Eckhardt, B. (2006). Finite lifetime
of turbulence in shear flows. *Nature*, *443*(7107), 59–62. https://doi.org/10.1038/nature05089
chicago: 'Hof, Björn, Jerry Westerweel, Tobias Schneider, and Bruno Eckhardt. “Finite
Lifetime of Turbulence in Shear Flows.” *Nature* 443, no. 7107 (2006): 59–62.
https://doi.org/10.1038/nature05089.'
ieee: B. Hof, J. Westerweel, T. Schneider, and B. Eckhardt, “Finite lifetime of
turbulence in shear flows,” *Nature*, vol. 443, no. 7107, pp. 59–62, 2006.
ista: Hof B, Westerweel J, Schneider T, Eckhardt B. 2006. Finite lifetime of turbulence
in shear flows. Nature. 443(7107), 59–62.
mla: Hof, Björn, et al. “Finite Lifetime of Turbulence in Shear Flows.” *Nature*,
vol. 443, no. 7107, Nature Publishing Group, 2006, pp. 59–62, doi:10.1038/nature05089.
short: B. Hof, J. Westerweel, T. Schneider, B. Eckhardt, Nature 443 (2006) 59–62.
date_created: 2018-12-11T11:59:37Z
date_published: 2006-09-07T00:00:00Z
date_updated: 2019-04-26T07:22:20Z
day: '07'
doi: 10.1038/nature05089
extern: 1
intvolume: ' 443'
issue: '7107'
month: '09'
page: 59 - 62
publication: Nature
publication_status: published
publisher: Nature Publishing Group
publist_id: '4098'
quality_controlled: 0
status: public
title: Finite lifetime of turbulence in shear flows
type: journal_article
volume: 443
year: '2006'
...