5,962 research outputs found
Boundary Harnack estimates in slit domains and applications to thin free boundary problems
We provide a higher order boundary Harnack inequality for harmonic functions
in slit domains. As a corollary we obtain the regularity of the free
boundary in the Signorini problem near non-degenerate points
The two membranes problem for different operators
We study the two membranes problem for different operators, possibly
nonlocal. We prove a general result about the H\"older continuity of the
solutions and we develop a viscosity solution approach to this problem. Then we
obtain regularity of the solutions provided that the orders of
the two operators are different. In the special case when one operator
coincides with the fractional Laplacian, we obtain the optimal regularity and a
characterization of the free boundary
Is H3+ cooling ever important in primordial gas?
Studies of the formation of metal-free Population III stars usually focus
primarily on the role played by H2 cooling, on account of its large chemical
abundance relative to other possible molecular or ionic coolants. However,
while H2 is generally the most important coolant at low gas densities, it is
not an effective coolant at high gas densities, owing to the low critical
density at which it reaches local thermodynamic equilibrium (LTE) and to the
large opacities that develop in its emission lines. It is therefore possible
that emission from other chemical species may play an important role in cooling
high density primordial gas. A particularly interesting candidate is the H3+
molecular ion. This ion has an LTE cooling rate that is roughly a billion times
larger than that of H2, and unlike other primordial molecular ions such as H2+
or HeH+, it is not easily removed from the gas by collisions with H or H2. It
is already known to be an important coolant in at least one astrophysical
context -- the upper atmospheres of gas giants -- but its role in the cooling
of primordial gas has received little previous study. In this paper, we
investigate the potential importance of H3+ cooling in primordial gas using a
newly-developed H3+ cooling function and the most detailed model of primordial
chemistry published to date. We show that although H3+ is, in most
circumstances, the third most important coolant in dense primordial gas (after
H2 and HD), it is nevertheless unimportant, as it contributes no more than a
few percent of the total cooling. We also show that in gas irradiated by a
sufficiently strong flux of cosmic rays or X-rays, H3+ can become the dominant
coolant in the gas, although the size of the flux required renders this
scenario unlikely to occur.Comment: 60 pages, 22 figures. Submitted to MNRA
Evaluating Rice Straw as a Substitute for Barley Straw in Inhibiting Algal Growth in Farm Ponds
Algal blooms disrupt aquatic ecosystems and are more common in lakes, ponds, and rivers during the summer months due to nutrient pollution. Livestock production can contribute increased quantities of nutrients to water bodies from runoff of manure. Commonly used mechanical and chemical control methods may have limited success because algae are small and propagate quickly. Barley (Hordeum vulgare) straw has been shown to inhibit the growth of algae as the straw decomposes aerobically in ponds. Therefore, barley represents a natural option for algal biomass control. However, the small amount of barley production in Arkansas limits the availability of barley straw as a solution to control algal blooms locally. Other cereal grain straws may produce similar inhibitory effects during decomposition. Rice (Oryza sativa) is produced in large quantities in Arkansas, making rice straw a locally sourced straw product. The objective of this research was to determine the efficacy of using rice compared to barley straw to inhibit algal growth in freshwater ponds. Data were collected from nine farm ponds, three treated with rice straw, three treated with barley straw, and three without amendment to serve as the experimental control. Dissolved oxygen, pH, nitrate-nitrogen (NO3--N), dissolved phosphorus (P), temperature, and turbidity were measured for 14 weeks from June 12 to September 17, 2018. Algal biomass was measured as chlorophyll-a concentration to evaluate treatment effectiveness over time. Dissolved oxygen was significantly influenced by treatment and time. The NO3--N concentration in ponds treated with rice straw was significantly greater than the control and barley treatment. Chlorophyll-a concentrations were variable, and there were no consistent trends through time within a treatment. More research under controlled conditions to understand impacts of abiotic conditions, microbial and algal community compositions, and mode of action of algal inhibition is required before cereal straw can be a reliable, locally sourced method of algal control in farm ponds
Normal heat conductivity in two-dimensional scalar lattices
The paper revisits recent counterintuitive results on divergence of heat
conduction coefficient in two-dimensional lattices. It was reported that in
certain lattices with on-site potential, for which one-dimensional chain has
convergent conductivity, for the 2D case it turns out to diverge. We
demonstrate that this conclusion is an artifact caused by insufficient size of
the simulated system. To overcome computational restrictions, a ribbon of
relatively small width is simulated instead of the square specimen. It is
further demonstrated that the heat conduction coefficient in the "long"
direction of the ribbon ceases to depend on the width, as the latter achieves
only 10 to 20 interparticle distances. So, one can consider the dynamics of
much longer systems, than in the traditional setting, and still can gain a
reliable information regarding the 2D lattice. It turns out that for all
considered models, for which the conductivity is convergent in the 1D case, it
is indeed convergent in the 2D case. In the same time, however, the length of
the system, necessary to reveal the convergence in the 2D case, may be much
bigger than in its 1D counterpart.Comment: 6 pages, 6 figure
Heat Conduction in One-Dimensional chain of Hard Discs with Substrate Potential
Heat conduction of one-dimensional chain of equivalent rigid particles in the
field of external on-site potential is considered. Zero diameters of the
particles correspond to exactly integrable case with divergent heat conduction
coefficient. By means of simple analytical model it is demonstrated that for
any nonzero particle size the integrability is violated and the heat conduction
coefficient converges. The result of the analytical computation is verified by
means of numerical simulation in a plausible diapason of parameters and good
agreement is observedComment: 14 pages, 7 figure
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