Let
D
be an indefinite quaternion division algebra over
Q
. We approach the problem of bounding the sup-norms of automorphic forms
ϕ
on
D
×
(
A
)
that belong to irreducible automorphic ...representations and transform via characters of unit groups of orders of
D
. We obtain a non-trivial upper bound for
‖
ϕ
‖
∞
in the level aspect that is valid for
arbitrary
orders. This generalizes and strengthens previously known upper bounds for
‖
ϕ
‖
∞
in the setting of newforms for Eichler orders. In the special case when the index of the order in a maximal order is a
squarefull
integer
N
, our result specializes to
‖
ϕ
‖
∞
≪
π
∞
,
ϵ
N
1
/
3
+
ϵ
‖
ϕ
‖
2
. A key application of our result is to automorphic forms
ϕ
which correspond at the ramified primes to either minimal vectors, in the sense of Hu et al. (Commun Math Helv, to appear) or
p
-adic microlocal lifts, in the sense of Nelson in “Microlocal lifts and and quantum unique ergodicity on
GL
2
(
Q
p
)
” (Algebra Number Theory 12(9):2033–2064,
2018
). For such forms, our bound specializes to
‖
ϕ
‖
∞
≪
ϵ
C
1
6
+
ϵ
‖
ϕ
‖
2
where
C
is the conductor of the representation
π
generated by
ϕ
. This improves upon the previously known
local bound
‖
ϕ
‖
∞
≪
λ
,
ϵ
C
1
4
+
ϵ
‖
ϕ
‖
2
in these cases.
Recent experiments (Wu et al., 2014) demonstrated that ignition of a combustible mixture by a high-energy kernel can be facilitated by turbulence for certain conditions. This is contrary to the ...common notion that ignition in turbulence is more difficult than in quiescence because of the increased dissipation of the deposited energy. In this study, we extend our investigation to a larger range of mixtures and turbulence intensities to explore possible limitations of such facilitated behavior. First, we calibrate our ignition system to quantify the deposited ignition energy. Next, using a lean hydrocarbon/air mixture with Le > 1, we show that: (1) it is possible to ignite a mixture in a turbulent environment with an ignition energy that is not sufficient to ignite the same mixture in a quiescent environment, and (2) there exists an upper limit of turbulence intensity beyond which such facilitation is not feasible. Through detailed experiments an ignition map for such mixtures is constructed, which shows a window of ignition energy within which this non-monotonic transition is observed. The study also identifies a minimum ignition energy required to achieve either quiescent or turbulence-facilitated ignition for the Le > 1 mixtures, and demonstrates that Le < 1 mixtures do not show such facilitation. These results are further validated with diluted hydrogen/oxygen mixtures.
We compare the difficulty of such equidistribution problems to that of corresponding subconvexity problems by deriving explicit extensions of Watson's formula to certain triple product integrals ...involving forms of nonsquarefree level. By a theorem of Ichino and a lemma of Michel-Venkatesh, this amounts to a detailed study of Rankin-Selberg integrals \int \vert f\vert^2 E of arbitrary level and Eisenstein series E We find that the local factors of such integrals participate in many amusing analogies with global -functions. For instance, we observe that the mass equidistribution conjecture with a power savings in the depth aspect is equivalent to knowing either a global subconvexity bound or what we call a ``local subconvexity bound''; a consequence of our local calculations is what we call a ``local Lindel>ö
The Naga Hills Ophiolite (NHO) belt in the Indo-Myanmar range (IMR) represents a segment of Tethyan oceanic crust and upper mantle that was involved in an eastward convergence and collision of the ...Indian Plate with the Burmese Plate during the Late Cretaceous-Eocene. Here, we present a detailed petrological and geochemical account for the mantle and crustal sections of NHO, northeastern India to address (i) the mantle processes and tectonic regimes involved in their genesis and (ii) their coherence in terms of the thermo-tectonic evolution of Tethyan oceanic crust and upper mantle. The NHO suite comprises well preserved crustal and mantle sections discretely exposed at Moki, Ziphu, Molen, Washelo and Lacham areas. The ultramafic-mafic lithologies of NHO are mineralogically composed of variable proportions of olivine, orthopyroxene, clinopyroxene and plagioclase. The primary igneous textures for the mantle peridotites have been overprinted by extensive serpentinisation whereas the crustal section rocks reflect crystal cumulation in a magma chamber. Chondrite normalised REE profiles for the cumulate peridotite-olivine gabbro-gabbro assemblage constituting the crustal section of NHO show flat to depleted LREE patterns consistent with their generation from depleted MORB-type precursor melt in an extensional tectonic setting, while the mantle peridotites depict U-shaped REE patterns marked by relative enrichment of LREE and HREE over MREE. These features collectively imply a dual role of depleted MORB-type and enriched arc-type mantle components for their genesis with imprints of melt-rock and fluid-rock interactions. Tectonically, studied lithologies from NHO correspond to a boninitic to slab-proximal Island Arc Tholeiite affinity thereby conforming to an intraoceanic supra subduction zone (SSZ) fore-arc regime coherent with the subduction initiation process. The geochemical attributes for the crustal and mantle sections of NHO as mirrored by Zr/Hf, Zr/Sm, Nb/Ta, Zr/Nb, Nb/U, Ba/Nb, Ba/Th, Ba/La and Nd/Hf ratios propound a two-stage petrogenetic process: (i) a depleted fore arc basalt (FAB) type tholeiitic melt parental to the crustal lithologies was extracted from the upwelling asthenospheric mantle at SSZ fore-arc extensional regime thereby rendering a refractory residual upper mantle; (ii) the crust and upper mantle of the SSZ fore arc were progressively refertilised by boninitic melts generated in response to subduction initiation and slab-dehydration. The vestiges of Tethyan oceanic lithosphere preserved in NHO represent an accreted intra-oceanic fore arc crust and upper mantle section which records a transitional geodynamic evolution in a SSZ regime marked by subduction initiation, fore arc extension and arc-continent accretion.
Display omitted
•NHO preserves an accreted Neotethyan supra subduction zone fore arc•MORB-type tholeiite to boninite melt coherent with subduction initiation and fore-arc extension•Boninitic signature underpins pervasive melt-rock interaction and mantle refertilization•A transitional anhydrous decompression to fluid-fluxed mantle melting domain
We, herein, present a new model based on the framework of synchronization to describe a thermoacoustic system and capture the multiple bifurcations that such a system undergoes. Instead of applying ...flame describing function to depict the unsteady heat release rate as the flame’s response to acoustic perturbation, the new model considers the acoustic field and the unsteady heat release rate as a pair of nonlinearly coupled damped oscillators. By varying the coupling strength, multiple dynamical behaviors, including limit cycle oscillation, quasi-periodic oscillation, strange nonchaos, and chaos, can be captured. Furthermore, the model was able to qualitatively replicate the different behaviors of a laminar thermoacoustic system observed in experiments by Kabiraj et al. (Chaos (Woodbury, N Y) 22:023129, 2012). By analyzing the temporal variation of phase difference between heat release rate oscillations and pressure oscillations under different dynamical states, we show that the characteristics of the dynamical states depend on the nature of synchronization between the two signals, which is consistent with previous experimental findings.
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