An official website of the United States government
Abstract LetL/Kbe a Galois extension of number fields with Galois groupG. We show that if the density of prime ideals inKthat split totally inLtends to 1/∣G∣ with a power saving error term, then the density of prime ideals inKwhose Frobenius is a given conjugacy classC⊂Gtends to ∣C∣/∣G∣ with the same power saving error term. We deduce this by relating the poles of the corresponding Dirichlet series to the zeros ofζL(s)/ζK(s).
more »
« less
A regularity result for the free boundary compressible Euler equations of a liquid
Abstract We derivea prioriestimates for the compressible free boundary Euler equations in the case of a liquid without surface tension. We provide a new weighted functional framework which leads to the improved regularity of the flow map by using the Hardy inequality. One of main ideas is to decompose the initial density function. It is worth mentioning that in our analysis we do not need the higher order wave equation for the density.
more »
« less
- Award ID(s):
- 2009458
- PAR ID:
- 10491449
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Nonlinearity
- Volume:
- 37
- Issue:
- 3
- ISSN:
- 0951-7715
- Format(s):
- Medium: X Size: Article No. 035019
- Size(s):
- Article No. 035019
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract The extent and magnitude of parasitism often vary among closely related host species and across populations within species. Determining the ecological basis for this species and population‐level variation in parasitism is critical for understanding infection dynamics in multi‐host–parasite systems. To investigate such ecological underpinnings of variation in parasitism, we studiedEnallagmadamselfly host species and their water mite (Arrenurusspp.) ectoparasites in lakes.We first evaluated how host identity and density could shape parasitism. To test the effects of con‐ and heterospecific host density on parasitism, we used a field experiment withEnallagma basidensandE. signatum. We found that parasitism did not vary with con‐ or heterospecific density and was determined by host identity alone, with no spillover effects.We also evaluated the potential role of local adaptation and resource availability in shaping parasitism. To do so, we usedE. signatumin a reciprocal transplant experiment crossed with a prey resource‐level manipulation. This experiment revealed that parasitism declined sharply for one host population in its non‐local lake, but not the other source population, with no effects of prey levels. This asymmetry implies that damselflies express enhanced defences against parasitism that are neither population‐specific nor dependent on resource abundance, or that mites developed heightened local host specificity.The results of multivariate modeling from an observational study generally supported these experimental findings: neither host density nor resource abundance strongly explained among‐population variation in parasitism. Instead, local abiotic conditions (pH) had the strongest relationship with parasitism, with minimal associations with predator density, temperature and a measure of immune function.Collectively, our findings suggest a crucial role for the local environment in shaping host–parasite interactions within multi‐host–parasite systems. More generally, these results show that research at the intersection of community ecology and disease ecology is critical for understanding host–parasite dynamics within natural communities.more » « less
-
Abstract Conspecific plant density and heterospecific frequency are key drivers of herbivore damage. However, most studies have investigated their effects separately and for single (rather than multiple) focal plant species.We conducted an experiment involving three tree species, namely:Cordia dodecandra(Boraginaceae),Manilkara zapota(Zapotaceae), andPiscidia piscipula(Fabaceae). We manipulated understory densities ofM. zapotaandC. dodecandra(focal species) and their frequency relative toP. piscipula.Three months after planting, we surveyed insect leaf chewer and sucking damage on the former two. Because these species are attacked by different herbivores, we predicted a negative effect of heterospecific frequency on herbivory.Density and frequency varied in the direction and function of their effects on herbivory depending on the plant species and attacking herbivore. As expected,Piscidia piscipulafrequency had a negative linear effect onM. zapotaleaf‐chewer damage, whereas conspecific density did not affect chewer damage on this species. In contrast, density and frequency had non‐linear effects onC. dodecandrachewer damage, namely positive (hump‐shaped) and negative (U‐shaped) relationships, respectively. In addition, density and frequency had positive linear effects onC. dondecandradamage by leafhoppers.These findings call for more work jointly assessing plant inter‐specific variation in density‐ and frequency‐dependent variation in herbivory and its underlying drivers.more » « less
-
Abstract We have performed hybrid kinetic-fluid simulations of a positive column in alternating current (AC) argon discharges over a range of driving frequenciesfand gas pressurepfor the conditions when the spatial nonlocality of the electron energy distribution function (EEDF) is substantial. Our simulations confirmed that the most efficient conditions of plasma maintenance are observed in the dynamic regime when time modulations of mean electron energy (temperature) are substantial. The minimal values of the root mean square electric field and the electron temperature have been observed atf/pvalues of about 3 kHz Torr−1in a tube of radiusR= 1 cm. The ionization rate and plasma density reached maximal values under these conditions. The numerical solution of a kinetic equation allowed accounting for the kinetic effects associated with spatial and temporal nonlocality of the EEDF. Using thekineticenergy of electrons as an independent variable, we solved an anisotropic tensor diffusion equation in phase space. We clarified the role of different flux components during electron diffusion in phase space over surfaces of constanttotalenergy. We have shown that the kinetic theory uncovers a more exciting and rich physics than the classical ambipolar diffusion (Schottky) model. Non-monotonic radial distributions of excitation rates, metastable densities, and plasma density have been observed in our simulations atpR >6 Torr cm. The predicted off-axis plasma density peak in the dynamic regime has never been observed in experiments so far. We hope our results stimulate further experimental studies of the AC positive column. The kinetic analysis could help uncover new physics even for such a well-known plasma object as a positive column in noble gases.more » « less
-
Abstract A perturbative solution of simplified primitive equations for nonlinear weakly stratified upwelling over a frictional slope is found that resolves the vertical structure of velocity fields and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The solution uses assumptions consistent with the model proposed by Lentz and Chapman, including a steady-state, constant cross-shore density gradient, no alongshore gradients, laterally inviscid, and consideration of cross-shore advection of alongshore momentum. The solution resolves the vertical structure of velocity fields (including subsurface maxima of compensational flow, not resolved by Lentz and Chapman) and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The dynamics are similar to Lentz and Chapman; bottom stress balances alongshore wind stress in a homogeneous density ocean and is replaced by nonlinear cross-shore transport of alongshore momentum as the Burger number (S=αN/f, whereα,N, andfare the bottom slope, buoyancy frequency, Coriolis frequency, respectively) increases. When the solution uses the empirical relation between cross-shore and vertical density gradients proposed by Lentz and Chapman, vorticity conservation is not satisfied and the nonlinear momentum transport estimated by the solution linearly increases withS, asymptotically matching Lentz and Chapman forS< 1. When the solution conserves interior potential vorticity, the momentum transport is proportional toS2forS< 1 and is in better agreement with numerical simulations.more » « less
