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At least 811 records · Page 45

Induced and non-induced poset saturation problems

A subfamily G ⊆ F ⊆ 2 [ n ] of sets is a non-induced (weak) copy of a poset P in F if there exists a bijection i : P → G such that p ≤ P q implies i ( p ) ⊆ i ( q ) . In the case where in addition p ≤ P q holds if and only if i ( p ) ⊆ i ( q ) , then is an induced (strong) copy of P in G . We consider the minimum number sat ( n , P ) [resp. sat ⁎ ( n , P ) ] of sets that a family F ⊆ 2 [ n ] can have without containing a non-induced [induced] copy of P and being maximal with respect to this property, i.e., the addition of any G ∈ 2 [ n ] ∖ F creates a non-induced [induced] copy of P.

97 MATHEMATICS AND COMPUTING↗

Saturation of a floating potential of an electron emitting electrode with increased electron emission: A one-dimensional kinetic model and particle-in-cell simulation

A bounded plasma system is studied by a one-dimensional kinetic model and particle-in-cell computer simulation using the XPDP1 code. Three particle species are injected into the system from a planar source, which are the singly charged positive ions and the cool and the hot electrons. All the particle species are injected with half-Maxwellian velocity distributions with different temperatures. From the collector, the emitted electrons are injected, also with a half-Maxwellian velocity distribution, but with a much lower temperature than the cool electrons. As electron emission from the collector is increased, the floating potential of the collector increases also until the boundary of space charge limited emission is achieved. In the simulation, the emission can be increased further and it turns out that the floating potential of the collector remains constant in spite of the increased electron emission. The model on the other hand is valid only up to the boundary of space charge limited emission. The predictions of that limit and of the respective floating potential of the collector by the model are in very good agreement with the simulation. As the criterion for comparison of the model and the simulations propose the matching of the potential, electric field, and density profiles obtained from the simulation and from the numerical solution of the Poisson equation. The matching of potential and electric field profiles is usually almost perfect. On the other hand, the numerical solutions of the Poisson equation give larger ion density at the source and emitted electron density at the collector than obtained from the simulation, but the matching of the particle densities around the inflection point of the potential between the model and the simulation is excellent for all 4 particle species. The same is valid also for the hot electron density at the source. If the potentials and the electric fields are read from the simulation and inserted into the model equations, one obtains an over-determined system of 4 equations for 3 unknown parameters: the ion and the hot electron density at the source and the emitted electron density at the collector. A solution of such a system with the method of least squares is presented. The errors obtained by such a solution can be considered as a measure of how well does the model describe the simulated system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Extracted current saturation in negative ion sources

The extraction of negatively charged particles from a negative ion source is one of the crucial issues in the development of the neutral beam injector system for future experimental reactor ITER. Full 3D electrostatic particle-in-cell Monte Carlo collision code - ONIX [S. Mochalskyy et al., Nucl. Fusion 50, 105011 (2010)] - is used to simulate the hydrogen plasma behaviour and the extracted particle features in the vicinity of the plasma grid, both sides of the aperture. It is found that the contribution to the extracted negative ion current of ions born in the volume is small compared with that of ions created at the plasma grid walls. The parametric study with respect to the rate of negative ions released from the walls shows an optimum rate. Beyond this optimum, a double layer builds-up by the negative ion charge density close to the grid aperture surface reducing thus extraction probability, and therefore the extracted current. The effect of the extraction potential and magnetic field magnitudes on the extraction is also discussed. Results are in good agreement with available experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Simultaneous stimulated Raman, Brillouin, and electron-acoustic scattering reveals a potential saturation mechanism in Raman plasma amplifiers

In a Raman plasma amplifier, the aim is to create plasma conditions in which Raman backscattering is the fastest growing instability, outrunning all competing effects so that it is possible to amplify and compress a laser beam to unprecedented unfocused intensities by utilizing that instability. However, achieving high efficiencies via this scheme has proven very difficult experimentally. Recent data show the simultaneous occurrence of stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS), and stimulated electron-acoustic scattering (SEAS). The appearance of SEAS is indicative of strong particle trapping, the existence of which is hard to justify without highlighting the interplay between SRS and SBS.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Soil Water Retention and Relative Permeability for Conditions from Oven-Dry to Full Saturation

Common conceptual models for unsaturated flow often rely on the oversimplified representation of medium pores as a bundle of cylindrical capillaries and assume that the matric potential is attributed to the capillary force only. The adsorptive surface forces are ignored. It is often assumed that aqueous flow is negligible when a soil is near or at the residual water content. These models are successful at high and medium water contents but often give poor results at low water contents. These models do not apply to conditions at which the water content is less than the residual water content. We extend the lower bound of existing water-retention functions and conductivity models from residual water content to the oven-dry condition (i.e., zero water content) by defining a state-dependent, residual-water content for a soil drier than a critical value. Furthermore, a hydraulic conductivity model for smooth uniform spheres was modified by introducing a correction factor to describe the film flow-induced hydraulic conductivity for natural porous media. The total unsaturated hydraulic conductivity is the sum of those due to capillary and film flow. The extended retention and conductivity models were verified measurements. Results show that, when the soil is at high and intermediate water content, there is no difference between the un-extended and the extended models; when the soil is at low water content, the un-extended models overestimate the water content but underestimate the conductivity. The extended models match the retention and conductivity measurements well.

54 ENVIRONMENTAL SCIENCES↗

Near-saturation Conditions at the Tropical Tropopause: Results from Ticosonde

Balloon-borne frostpoint measurements have shown a high frequency of supersaturation near the tropical tropopause, and this has been attributed to forced ascent associated with wavemotions as well as diabatic heating. Long-term profile statistics are typically presented on altitude, pressure or potential temperature surfaces. For example, at Costa Rica long-term mean values of CFH RH at 16.8 km, the mean annual height of the tropopause, range from less than 60 percent in July to over 90% in October. While a plot of the annual cycle vs height shows relatively high humidities in the upper troposphere and especially so as one approaches the tropopause, the overall picture is one of subsaturation. A very different picture emerges,however, if the analysis is done in height relative to the tropopause. Here the long-term average of RH at the tropopause is 94 percent or greater throughout the year. We discuss this paradoxical result in the context of dynamical and cloud processes occurring near the tropical tropopause.

Tropical↗

Heterogeneity‐enhanced gas phase formation in shallow aquifers during leakage of CO 2 ‐saturated water from geologic sequestration sites

Abstract A primary concern for geologic carbon storage is the potential for leakage of stored carbon dioxide (CO 2 ) into the shallow subsurface where it could degrade the quality of groundwater and surface water. In order to predict and mitigate the potentially negative impacts of CO 2 leakage, it is important to understand the physical processes that CO 2 will undergo as it moves through naturally heterogeneous porous media formations. Previous studies have shown that heterogeneity can enhance the evolution of gas phase CO 2 in some cases, but the conditions under which this occurs have not yet been quantitatively defined, nor tested through laboratory experiments. This study quantitatively investigates the effects of geologic heterogeneity on the process of gas phase CO 2 evolution in shallow aquifers through an extensive set of experiments conducted in a column that was packed with layers of various test sands. Soil moisture sensors were utilized to observe the formation of gas phase near the porous media interfaces. Results indicate that the conditions under which heterogeneity controls gas phase evolution can be successfully predicted through analysis of simple parameters, including the dissolved CO 2 concentration in the flowing water, the distance between the heterogeneity and the leakage location, and some fundamental properties of the porous media. Results also show that interfaces where a less permeable material overlies a more permeable material affect gas phase evolution more significantly than interfaces with the opposite layering.

Plampin, Michelle R.↗

Dynamic fault weakening and strengthening by gouge compaction and dilatancy in a fluid-saturated fault zone

Fault gouge deformation likely plays a significant role in controlling the strength of mature, large-displacement faults. Experiments show that intact gouge deforms in an overall ductile and stable manner, readily compacting, but dilates and experiences brittle failure under large strain rate. Inelastic gouge compaction and dilatancy are modeled here using a combined Mohr-Coulomb and end-cap yield criterion in a dynamic rupture model of a strike-slip fault with strongly velocity-weakening friction. We show that large shear stress concentration ahead of the rupture associated with the rupture front causes the gouge layer to compact (e.g., by structural collapse and comminution), leading to rapidly elevated pore pressure and significant weakening of the principal fault surface. Shortly after the rupture front passes, strong dilatancy during strength drop and rapid sliding reduces pore pressure and strengthens the fault, promoting slip pulses. Large strain localization in the gouge layer occurs as a result of rapid gouge dilatancy and strain softening. The combination of prerupture weakening from compaction and restrengthening from dilatancy hardening leads to a smaller-strength drop, and limits the stress concentration outside the gouge layer. Furthermore, this leads to a reduction of inelastic shear strain in the damage zone, which is more consistent with geological observations and high-speed frictional experiments. With the presence of well-developed fault gouge, the strength of mature faults may be limited by end-cap rather than Mohr-Coulomb failure; thus, their frictional strengths are significantly smaller than Byerlee friction.

58 GEOSCIENCES↗

Uncatalyzed, Regioselective Oxidation of Saturated Hydrocarbons in an Ambient Corona Discharge

Abstract Atmospheric pressure chemical ionization (APCI) in air or in nitrogen with just traces of oxygen is shown to yield regioselective oxidation, dehydrogenation, and fragmentation of alkanes. Ozone is produced from ambient oxygen in situ and is responsible for the observed ion chemistry, which includes partial oxidation to ketones and C−C cleavage to give aldehydes. The mechanism of oxidation is explored and relationships between ionic species produced from individual alkanes are established. Unusually, dehydrogenation occurs by water loss. Competitive incorporation into the hydrocarbon chain of nitrogen versus oxygen as a mode of ionization is also demonstrated.

Ayrton, Stephen T.↗

Implementation and verification of a user-defined element (UEL) for coupled thermal-hydraulic-mechanical-chemical (THMC) processes in saturated geological media

Efficient and accurate modeling of the coupled thermal-hydraulic-mechanical-chemical (THMC) processes in various rock formations is indispensable for designing energy geo-structures such as underground repositories for high-level nuclear wastes. Here, this work focuses on developing and verifying an implicit finite element solver for generic coupled THMC problems in geological settings. Starting from the mass, momentum, and energy balance laws, a specialized set of governing equations and a thermoporoelastic constitutive model is derived. This system is then solved by an implicit finite element (FE) scheme. Specifically, the residuals and the Jacobians are scripted in a user-defined element (UEL) subroutine which is then combined with the general-purpose FE software Abaqus Standard to solve initial-boundary value problems. Considering the complexity of the system, the UEL development follows a stepwise manner by first solving the coupled hydraulic-mechanical (HM) and thermal-hydraulic-mechanical (THM) equations before moving on to the full THMC problem. Each implementation step consists of at least one verification test by comparing computed results with closed-form analytical solutions to ensure that the various coupling effects are correctly realized. To demonstrate the robustness of the algorithm and to validate the UEL, a three-dimensional case study is performed with reference to the in-situ heating test of ATLAS at Belgium in 1980s. A hypothetical radionuclide leakage event is then simulated by activating the chemical-concentration degree of freedom and prescribing a constant high concentration at the heater's surface. The model predicts a limited contaminated regime after six years considering both diffusion and advection effects on species transport.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗