Blow-up behavior of collocation solutions to Hammerstein-type volterra integral equations

We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein-type Volterra integral equations (VIEs) whose solutions may blow up in finite time. To approximate such solutions (and the corresponding blow-up time), we will introduce an adaptive stepsize strategy that guarantees the existence of collocation solutions whose blow-up behavior is the same as the one for the exact solution. Based on the local convergence of the collocation methods for VIEs, we present the convergence analysis for the numerical blow-up time. Numerical experiments illustrate the analysis

Glass Polymorphism in TIP4P/2005 Water: A Description Based on the Potential Energy Landscape Formalism

The potential energy landscape (PEL) formalism is a statistical mechanical approach to describe supercooled liquids and glasses. Here we use the PEL formalism to study the pressure-induced transformations between low-density amorphous ice (LDA) and high-density amorphous ice (HDA) using computer simulations of the TIP4P/2005 molecular model of water. We find that the properties of the PEL sampled by the system during the LDA-HDA transformation exhibit anomalous behavior. In particular, at conditions where the change in density during the LDA-HDA transformation is approximately discontinuous, reminiscent of a first-order phase transition, we find that (i) the inherent structure (IS) energy, $e_\text{IS}(V)$, is a concave function of the volume, and (ii) the IS pressure, $P_\text{IS}(V)$, exhibits a van der Waals-like loop. In addition, the curvature of the PEL at the IS is anomalous, a non-monotonic function of $V$. In agreement with previous studies, our work suggests that conditions (i) and (ii) are necessary (but not sufficient) signatures of the PEL for the LDA-HDA transformation to be reminiscent of a first-order phase transition. We also find that one can identify two different regions of the PEL, one associated to LDA and another to HDA. Our computer simulations are performed using a wide range of compression/decompression and cooling rates. In particular, our slowest cooling rate (0.01 K/ns) is within the experimental rates employed in hyperquenching experiments to produce LDA. Interestingly, the LDA-HDA transformation pressure that we obtain at $T=80$ K and at different rates extrapolates remarkably well to the corresponding experimental pressure.Comment: Manuscript and Supplementary Materia

No Hubble Bubble in the Local Universe

Zehavi et al. (1998) have suggested that the Hubble flow within 70/h Mpc may be accelerated by the existence of a void centered on the Local Group. Its underdensity would be ~20 %, which would result in a local Hubble distortion of about 6.5 %. We have combined the peculiar velocity data of two samples of clusters of galaxies, SCI and SCII, to investigate the amplitude of Hubble distortions to 200/h Mpc. Our results are not supportive of that conclusion. The amplitude of a possible distortion in the Hubble flow within 70/h Mpc in the SCI+SCII merged data is 0.010\pm0.022. The largest, and still quite marginal, geocentric deviation from smooth Hubble flow consistent with that data set is a shell with (Delta H)/H =0.027\pm0.023, centered at hd = 101 Mpc and extending over some 30/h Mpc. Our results are thus consistent with a Hubble flow that, on distances in excess of about 50/h Mpc, is remarkably smooth.Comment: 11 pages, 1 tables, 1 figure; uses AAS LaTex; to appear in ApJ Nov 9

EarthN: A new Earth System Nitrogen Model

The amount of nitrogen in the atmosphere, oceans, crust, and mantle have important ramifications for Earth's biologic and geologic history. Despite this importance, the history and cycling of nitrogen in the Earth system is poorly constrained over time. For example, various models and proxies contrastingly support atmospheric mass stasis, net outgassing, or net ingassing over time. In addition, the amount available to and processing of nitrogen by organisms is intricately linked with and provides feedbacks on oxygen and nutrient cycles. To investigate the Earth system nitrogen cycle over geologic history, we have constructed a new nitrogen cycle model: EarthN. This model is driven by mantle cooling, links biologic nitrogen cycling to phosphate and oxygen, and incorporates geologic and biologic fluxes. Model output is consistent with large (2-4x) changes in atmospheric mass over time, typically indicating atmospheric drawdown and nitrogen sequestration into the mantle and continental crust. Critical controls on nitrogen distribution include mantle cooling history, weathering, and the total Bulk Silicate Earth+atmosphere nitrogen budget. Linking the nitrogen cycle to phosphorous and oxygen levels, instead of carbon as has been previously done, provides new and more dynamic insight into the history of nitrogen on the planet.Comment: 36 pages, 12 figure

Comparing Laser Diffraction and Optical Microscopy for Characterizing Superabsorbent Polymer Particle Morphology, Size, and Swelling Capacity

In this study, we determined the accuracy and practicality of using optical microscopy (OM) and laser diffraction (LD) to characterize hydrogel particle morphology, size, and swelling capacity (Q). Inverse-suspension-polymerized polyacrylamide particles were used as a model system. OM and LD showed that the average particle diameter varied with the mixing speed during synthesis for the dry (10–120 lm) and hydrated (34–240 lm) particles. The LD volume and number mean diameters showed that a few large particles were responsible for the majority of the water absorption. Excess water present in the gravimetric swelling measurements led to larger Qs (8.2 6 0.37 g/g), whereas the volumetric measurements with OM and LD resulted in reduced capacities (6.5 6 3.8 and 5.7 6 3.9 g/g, respectively). Results from the individual particle swelling measurements with OM (5.2 6 0.66 g/g) statistically confirmed that the volumetric methods resulted in a reduced and more accurate measurement of the Q than the gravimetric method

On perfect neighborhood sets in graphs

AbstractLet G = (V, E) be a graph and let S ⊆ V.. The set S is a dominating set of G is every vertex of V − S is adjacent to a vertex of S. A vertex v of G is called S-perfect if |N[ν]∩S| = 1 where N[v] denotes the closed neighborhood of v. The set S is defined to be a perfect neighborhood set of G if every vertex of G is S-perfect or adjacent with an S-perfect vertex. We prove that for all graphs G, Θ(G) = Γ(G) where Γ(G) is the maximum cardinality of a minimal dominating set of G and where Θ(G) is the maximum cardinality among all perfect neighborhood sets of G

Anion Photoelectron Spectroscopy of Deprotonated ortho-, meta-, and para-methylphenol

The anion photoelectron spectra of ortho-, meta-, and para-methylphenoxide, as well as methyl deprotonated meta-methylphenol, were measured. Using the Slow Electron Velocity Map Imaging technique, the Electron Affinities (EAs) of the o-, m-, and p-methylphenoxyl radicals were measured as follows: 2.1991±0.0014, 2.2177±0.0014, and 2.1199±0.0014 eV, respectively. The EA of m-methylenephenol was also obtained, 1.024±0.008 eV. In all four cases, the dominant vibrational progressions observed are due to several ring distortion vibrational normal modes that were activated upon photodetachment, leading to vibrational progressions spaced by ∼500 cm−1. Using the methylphenol O–H bond dissociation energies reported by King et al. and revised by Karsili et al., a thermodynamic cycle was constructed and the acidities of the methylphenol isomers were determined as follows: ΔacidH0298K=348.39±0.25, 348.82±0.25, 350.08±0.25, and 349.60±0.25 kcal/mol for cis-ortho-, trans-ortho-, m-, and p-methylphenol, respectively. The excitation energies for the ground doublet state to the lowest excited doublet state electronic transition in o-, m-, and p-methylphenoxyl were also measured as follows: 1.029±0.009, 0.962±0.002, and 1.029±0.009 eV, respectively. In the photoelectron spectra of the neutral excited states, C–O stretching modes were excited in addition to ring distortion modes. Electron autodetachment was observed in the cases of both m- and p-methylphenoxide, with the para isomer showing a lower photon energy onset for this phenomenon