51,308 research outputs found
Stochastic homogenization of Hamilton-Jacobi and degenerate Bellman equations in unbounded environments
We consider the homogenization of Hamilton-Jacobi equations and degenerate
Bellman equations in stationary, ergodic, unbounded environments. We prove
that, as the microscopic scale tends to zero, the equation averages to a
deterministic Hamilton-Jacobi equation and study some properties of the
effective Hamiltonian. We discover a connection between the effective
Hamiltonian and an eikonal-type equation in exterior domains. In particular, we
obtain a new formula for the effective Hamiltonian. To prove the results we
introduce a new strategy to obtain almost sure homogenization, completing a
program proposed by Lions and Souganidis that previously yielded homogenization
in probability. The class of problems we study is strongly motivated by
Sznitman's study of the quenched large deviations of Brownian motion
interacting with a Poissonian potential, but applies to a general class of
problems which are not amenable to probabilistic tools.Comment: 51 pages, 2 figures. We have added material and made some corrections
to our previous versio
Vital dye labelling demonstrates a sacral neural crest contribution to the enteric nervous system of chick and mouse embryos
We have used the vital dye, DiI, to analyze the contribution of sacral neural crest cells to the enteric nervous system in chick and mouse embryos. In order to label premigratory sacral neural crest cells selectively, DiI was injected into the lumen of the neural tube at the level of the hindlimb. In chick embryos, DiI injections made prior to stage 19 resulted in labelled cells in the gut, which had emerged from the neural tube adjacent to somites 29–37. In mouse embryos, neural crest cells emigrated from the sacral neural tube between E9 and E9.5. In both chick and mouse embryos, DiI-labelled cells were observed in the rostral half of the somitic sclerotome, around the dorsal aorta, in the mesentery surrounding the gut, as well as within the epithelium of the gut. Mouse embryos, however, contained consistently fewer labelled cells than chick embryos. DiI-labelled cells first were observed in the rostral and dorsal portion of the gut. Paralleling the maturation of the embryo, there was a rostral-to-caudal sequence in which neural crest cells populated the gut at the sacral level. In addition, neural crest cells appeared within the gut in a dorsal-to-ventral sequence, suggesting that the cells entered the gut dorsally and moved progressively ventrally. The present results resolve a long-standing discrepancy in the literature by demonstrating that sacral neural crest cells in both the chick and mouse contribute to the enteric nervous system in the postumbilical gut
A vital dye analysis of the timing and pathways of avian trunk neural crest cell migration
To permit a more detailed analysis of neural crest cell migratory pathways in the chick embryo, neural crest cells were labelled with a nondeleterious membrane intercalating vital dye, DiI. All neural tube cells with endfeet in contact with the lumen, including premigratory neural crest cells, were labelled by pressure injecting a solution of DiI into the lumen of the neural tube. When assayed one to three days later, migrating neural crest cells, motor axons, and ventral root cells were the only cells types external to the neural tube labelled with DiI. During the neural crest cell migratory phase, distinctly labelled cells were found along: (1) a dorsolateral pathway, under the epidermis, as well adjacent to and intercalating through the dermamyotome; and (2) a ventral pathway, through the rostral portion of each sclerotome and around the dorsal aorta as described previously. In contrast to those cells migrating through the sclerotome, labelled cells on the dorsolateral pathway were not segmentally arranged along the rostrocaudal axis. DiI-labelled cells were observed in all truncal neural crest derivatives, including subepidermal presumptive pigment cells, dorsal root ganglia, and sympathetic ganglia. By varying the stage at which the injection was performed, neural crest cell emigration at the level of the wing bud was shown to occur from stage 13 through stage 22. In addition, neural crest cells were found to populate their derivatives in a ventral-to-dorsal order, with the latest emigrating cells migrating exclusively along the dorsolateral pathway
Pathways of trunk neural crest cell migration in the mouse embryo as revealed by vital dye labelling
Analysis of neural crest cell migration in the mouse has been difficult due to the lack of reliable cell markers. Recently, we found that injection of DiI into the chick neural tube marks premigratory neural crest cells whose endfeet are in contact with the lumen of the neural tube (Serbedzija et al. Development 106, 809–819 (1989)). In the present study, this technique was applied to study neural crest cell migratory pathways in the trunk of the mouse embryo. Embryos were removed from the mother between the 8th and the 10th days of development and DiI was injected into the lumen of the neural tube. The embryos were then cultured for 12 to 24 h, and analyzed at the level of the forelimb. We observed two predominant pathways of neural crest cell migration: (1) a ventral pathway through the rostral portion of the somite and (2) a dorsolateral pathway between the dermamyotome and the epidermis. Neural crest cells were observed along the dorsolateral pathway throughout the period of migration. The distribution of labelled cells along the ventral pathway suggested that there were two overlapping phases of migration. An early ventrolateral phase began before E9 and ended by E9.5; this pathway consisted of a stream of cells within the rostral sclerotome, adjacent to the dermamyotome, that extended ventrally to the region of the sympathetic ganglia and the dorsal aorta
Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations
We present exponential error estimates and demonstrate an algebraic
convergence rate for the homogenization of level-set convex Hamilton-Jacobi
equations in i.i.d. random environments, the first quantitative homogenization
results for these equations in the stochastic setting. By taking advantage of a
connection between the metric approach to homogenization and the theory of
first-passage percolation, we obtain estimates on the fluctuations of the
solutions to the approximate cell problem in the ballistic regime (away from
flat spot of the effective Hamiltonian). In the sub-ballistic regime (on the
flat spot), we show that the fluctuations are governed by an entirely different
mechanism and the homogenization may proceed, without further assumptions, at
an arbitrarily slow rate. We identify a necessary and sufficient condition on
the law of the Hamiltonian for an algebraic rate of convergence to hold in the
sub-ballistic regime and show, under this hypothesis, that the two rates may be
merged to yield comprehensive error estimates and an algebraic rate of
convergence for homogenization.
Our methods are novel and quite different from the techniques employed in the
periodic setting, although we benefit from previous works in both first-passage
percolation and homogenization. The link between the rate of homogenization and
the flat spot of the effective Hamiltonian, which is related to the
nonexistence of correctors, is a purely random phenomenon observed here for the
first time.Comment: 57 pages. Revised version. To appear in J. Amer. Math. So
Developmental potential of trunk neural crest cells in the mouse
The availability of naturally occurring and engineered mutations in mice which affect the neural crest makes the mouse embryo an important experimental system for studying neural crest cell differentiation. Here, we determine the normal developmental potential of neural crest cells by performing in situ cell lineage analysis in the mouse by microinjecting lysinated rhodamine dextran (LRD) into individual dorsal neural tube cells in the trunk. Labeled progeny derived from single cells were found in the neural tube, dorsal root ganglia, sympathoadrenal derivatives, presumptive Schwann cells and/or pigment cells. Most embryos contained labeled cells both in the neural tube and at least one neural crest derivative, and numerous clones contributed to multiple neural crest derivatives. The time of injection influenced the derivatives populated by the labeled cells. Injections at early stages of migration yielded labeled progeny in both dorsal and ventral neural crest derivatives, whereas those performed at later stages had labeled cells only in more dorsal neural crest derivatives, such as dorsal root ganglion and presumptive pigment cells. The results suggest that in the mouse embryo: (1) there is a common precursor for neural crest and neural tube cells; (2) some neural crest cells are multipotent; and (3) the timing of emigration influences the range of possible neural crest derivatives
Nonlinear surface impurity in a semi-infinite 2D square lattice
We examine the formation of localized states on a generalized nonlinear
impurity located at, or near the surface of a semi-infinite 2D square lattice.
Using the formalism of lattice Green functions, we obtain in closed form the
number of bound states as well as their energies and probability profiles, for
different nonlinearity parameter values and nonlinearity exponents, at
different distances from the surface. We specialize to two cases: impurity
close to an "edge" and impurity close to a "corner". We find that, unlike the
case of a 1D semi-infinite lattice, in 2D, the presence of the surface helps
the formation of a localized state.Comment: 6 pages, 7 figures, submitted to PR
Thirteen Plus One: A Comparison of Global Climate Policy Architectures
We critically review the Kyoto Protocol and thirteen alternative policy architectures for addressing the threat of global climate change. We employ six criteria to evaluate the policy proposals: environmental outcome, dynamic efficiency, cost effectiveness, equity, flexibility in the presence of new information, and incentives for participation and compliance. The Kyoto Protocol does not fare well on a number of criteria, but none of the alternative proposals fare well along all six dimensions. We identify several major themes among the alternative proposals: Kyoto is “too little, too fast”; developing countries should play a more substantial role and receive incentives to participate; implementation should focus on market-based approaches, especially those with price mechanisms; and participation and compliance incentives are inadequately addressed by most proposals. Our investigation reveals tensions among several of the evaluative criteria, such as between environmental outcome and efficiency, and between cost-effectiveness and incentives for participation and compliance.Policy architecture, Kyoto Protocol, Efficiency, Cost effectiveness, Equity, Participation, Compliance
Absolute absorption and fluorescence measurements over a dynamic range of 10 with cavity-enhanced laser-induced fluorescence
We describe a novel experimental setup that combines the advantages of both
laser-induced fluorescence and cavity ring-down techniques. The simultaneous
and correlated measurement of the ring-down and fluorescence signals yields
absolute absorption coefficients for the fluorescence measurement. The combined
measurement is conducted with the same sample in a single, pulsed laser beam.
The fluorescence measurement extends the dynamic range of a stand-alone cavity
ring-down setup from typically three to at least six orders of magnitude. The
presence of the cavity improves the quality of the signal, in particular the
signal-to-noise ratio. The methodology, dubbed cavity-enhanced laser-induced
fluorescence (CELIF), is developed and rigorously tested against the
spectroscopy of 1,4-bis(phenylethynyl)benzene in a molecular beam and density
measurements in a cell. We outline how the method can be utilised to determine
absolute quantities: absorption cross sections, sample densities and
fluorescence quantum yields.Comment: 12 pages, 6 figures, submitted to J. Chem. Phy
Dynamical Origin of Extrasolar Planet Eccentricity Distribution
We explore the possibility that the observed eccentricity distribution of
extrasolar planets arose through planet-planet interactions, after the initial
stage of planet formation was complete. Our results are based on ~3250
numerical integrations of ensembles of randomly constructed planetary systems,
each lasting 100 Myr. We find that for a remarkably wide range of initial
conditions the eccentricity distributions of dynamically active planetary
systems relax towards a common final equilibrium distribution, well described
by the fitting formula dn ~ e exp[-1/2 (e/0.3)^2] de. This distribution agrees
well with the observed eccentricity distribution for e > 0.2, but predicts too
few planets at lower eccentricities, even when we exclude planets subject to
tidal circularization. These findings suggest that a period of large-scale
dynamical instability has occurred in a significant fraction of newly formed
planetary systems, lasting 1--2 orders of magnitude longer than the ~1 Myr
interval in which gas-giant planets are assembled. This mechanism predicts no
(or weak) correlations between semimajor axis, eccentricity, inclination, and
mass in dynamically relaxed planetary systems. An additional observational
consequence of dynamical relaxation is a significant population of planets
(>10%) that are highly inclined (>25deg) with respect to the initial symmetry
plane of the protoplanetary disk; this population may be detectable in
transiting planets through the Rossiter-McLaughlin effect.Comment: Accepted to ApJ, conclusions updated to reflect the current
observational constraint
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