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At least 1,675 records · Page 93

Analytical Study of Gravity Effects on Laminar Diffusion Flames

A mathematical model is presented for the description of axisymmetric laminar-jet diffusion flames. The analysis includes the effects of inertia, viscosity, diffusion, gravity and combustion. These mechanisms are coupled in a boundary layer type formulation and solutions are obtained by an explicit finite difference technique. A dimensional analysis shows that the maximum flame width radius, velocity and thermodynamic state characterize the flame structure. Comparisons with experimental data showed excellent agreement for normal gravity flames and fair agreement for steady state low Reynolds number zero gravity flames. Kinetics effects and radiation are shown to be the primary mechanisms responsible for this discrepancy. Additional factors are discussed including elipticity and transient effects.

Edelman, R. B.↗

Microstructural Modeling of the α + β Phase in Ti-6Al-4V: A Diffusion-Based Approach

Complex heat treatment operations and advanced manufacturing processes such as laser or electron-beam welding will see the metallic workpiece experience a considerable range of temperatures and heating/cooling rates. These intrinsic conditions will have a significant bearing upon the microstructure of the material, and in turn upon the thermo-mechanical properties. In this work, a diffusion-based approach to model the growth and shrinkage of precipitates in the alpha + beta field of the common titanium alloy Ti-6Al-4V is established. Further, the numerical model is extended using a JMA-type approach to explore the dependency of the beta-transus temperature on extremely high heating rates, whereby dissolution alone is too slow to accurately describe the alpha to beta-phase transformation. Experimental heat treatments at rates of 5, 50, and 500 °C/s were performed, and metallographic analysis of the samples was used to validate the numerical modeling framework predictions for lamellar shrinkage, while data from the literature has been used to evaluate the numerical modeling framework for the growth of equiaxed microstructures. The agreement between measurements and numerical predictions was found to be good.

36 MATERIALS SCIENCE↗

Efficient Conservative Numerical Schemes for 1D Nonlinear Spherical Diffusion Equations with Applications in Battery Modeling

Mathematical models of batteries which make use of the intercalation of a species into a solid phase need to solve the corresponding mass transfer problem. Because solving this equation can significantly add to the computational cost of a model, various methods have been devised to reduce the computational time. In this paper we focus on a comparison of the formulation, accuracy, and order of the accuracy for two numerical methods of solving the spherical diffusion problem with a constant or non-constant diffusion coefficient: the finite volume method and the control volume method. Both methods provide perfect mass conservation and second order accuracy in mesh spacing, but the control volume method provides the surface concentration directly, has a higher accuracy for a given numbers of mesh points and can also be easily extended to variable mesh spacing. Variable mesh spacing can significantly reduce the number of points that are required to achieve a given degree of accuracy in the surface concentration (which is typically coupled to the other battery equations) by locating more points where the concentration gradients are highest. (C) 2013 The Electrochemical Society. All rights reserved.

Zeng, Y↗

Numerical simulation of flow through inlets/diffusers with terminal shocks

Two-dimensional Euler and Navier-Stokes solutions of the flow through three inlet/diffuser configurations with terminal shock systems are reported. Calculations without bleed indicate that the terminal shock location is very sensitive to the outflow back pressure. For cases where there are no available experimental results, it becomes difficult to estimate the back pressure that will result in a terminal shock. Estimates based on quasi-one-dimensional analysis are not found adequate for complex two-dimensional flows. It is found that since the flow downstream of the terminal shock is subsonic, and what happens at the outflow boundary affects the flow inside the inlet, enough of the subsonic diffuser must be modeled to accurately predict the terminal shock region. The diffuser portion should be fairly long with the outflow boundary occurring in a region of more or less uniform flow to be able to prescribe a uniform back pressure. The third configuration studied was investigated with and without incorporating bleed in the code. It is found that the use of bleed stabilizes the shock location and allows solutions which without bleed result in unstarting of the inlet. Comparisons are made with available experimental data.

Talcott, N. A., Jr.↗

Fullerene film on metal surface: Diffusion of metal atoms and interface model

We try to understand the fact that fullerene film behaves as n-type semiconductor in electronic devices and establish a model describing the energy level alignment at fullerene/metal interfaces. The C{sub 60}/Ag(100) system was taken as a prototype and studied with photoemission measurements. The photoemission spectra revealed that the Ag atoms of the substrate diffused far into C{sub 60} film and donated electrons to the molecules. So the C{sub 60} film became n-type semiconductor with the Ag atoms acting as dopants. The C{sub 60}/Ag(100) interface should be understood as two sub-interfaces on both sides of the molecular layer directly contacting with the substrate. One sub-interface is Fermi level alignment, and the other is vacuum level alignment.

36 MATERIALS SCIENCE↗

The effect of breaking gravity waves on the dynamics and chemistry of the mesosphere and lower thermosphere (invited review)

The influence of breaking gravity waves on the dynamics and chemical composition of the 60 to 110 km region is investigated with a two dimensional model that includes a parameterization of gravity wave momentum deposition and diffusion. The dynamical model is described by Garcia and Solomon (1983) and Solomon and Garcia (1983) and includes a complete chemical scheme for the mesosphere and lower thermosphere. The parameterization of Lindzen (1981) is used to calculate the momentum deposited and the turbulent diffusion produced by the gravity waves. It is found that wave momentum deposition drives a very vigorous mean meridional circulation, produces a very cold summer mesopause and reverse the zonal wind jets above about 85 km. The seasonal variation of the turbulent diffusion coefficient is consistent with the behavior of mesospheric turbulences inferred from MST radar echoes. The large degree of consistency between model results and various types of dynamical and chemical data supports very strongly the hypothesis that breaking gravity waves play a major role in determining the zonally-averaged dynamical and chemical structure of the 60 to 110 km region of the atmosphere.

Garcia, R. R.↗

Baffle aperture design study of hollow cathode equipped ion thrusters

A simple theoretical model which can be used as an aid in the design of the baffle aperture region of a hollow cathode equipped ion thruster was developed. An analysis of the ion and electron currents in both the main and cathode discharge chambers is presented. From this analysis a model of current flow through the aperture, which is required as an input to the design model, was developed. This model was verified experimentally. The dominant force driving electrons through the aperture was the force due to the electrical potential gradient. The diffusion process was modeled according to the Bolm diffusion theory. A number of simplifications were made to limit the amount of detailed plasma information required as input to the model to facilitate the use of the model in thruster design. This simplified model gave remarkably consistant results with experimental results obtained with a given thruster geometry over substantial changes in operating conditions. The model was uncertain to about a factor of two for different thruster cathode region geometries. The design usefulness was limited by this factor of two uncertainty and by the accuracy to which the plasma parameters required as inputs to the model were specified.

Brophy, J. R., Jr.↗

A model for the trap-assisted tunneling mechanism in diffused n-p and implanted n(+)-p HgCdTe photodiodes

A theoretical model for the trap-assisted tunneling process in diffused n-on-p and implanted n(+)-on-p HgCdTe photodiodes is presented. The model describes the traps and the trap characteristics: concentration, energy level, and capture cross sections. We have observed that the above two types of diodes differ in the voltage dependence of the trap-assisted tunneling current and dynamic resistance. Our model takes this difference into account and offers an explanation of the phenomenon. The good fit between measured and calculated DC characteristics of the photodiodes (for medium and high reverse bias and for temperatures from 65 to 140 K) supports the validity of the model.

Rosenfeld, David↗

Observation of silicon self-diffusion enhanced by the strain originated from end-of-range defects using isotope multilayers

Si self-diffusion in the presence of end-of-range (EOR) defects is investigated using {sup nat}Si/{sup 28}Si isotope multilayers. The isotope multilayers were amorphized by Ge ion implantation, and then annealed at 800–950 °C. The behavior of Si self-interstitials is investigated through the {sup 30}Si self-diffusion. The experimental {sup 30}Si profiles show further enhancement of Si self-diffusion at the EOR defect region, in addition to the transient enhanced diffusion via excess Si self-interstitials by EOR defects. To explain this additional enhanced diffusion, we propose a model which takes into account enhanced diffusion by tensile strain originated from EOR defects. The calculation results based on this model have well reproduced the experimental {sup 30}Si profiles.

36 MATERIALS SCIENCE↗

Measuring Fault Zone and Host Rock Hydraulic Properties Using Tidal Responses

Pore pressure diffusion along faults influences induced seismicity and rupture mechanics. In situ hydraulic diffusivity measurements along faults are rare and generally lower than inferred from seismicity migration. Here we use the tidal response of deep geothermal boreholes to measure fault diffusivity and permeability. Initial interpretations of the observation with a homogeneous confined aquifer model result in diffusivities of 10 -3 –10 -1 m 2 /s. However, this model mixes signals from both the conduit and the host rock. We develop a model for tidal response with a fault passing through the aquifer based on the fault-guided fracture network and solve for hydraulic properties in both the fault and the host rock. The resulting fault permeability is 2 × 10 -14 –7 × 10 -14 m 2 (90% confidence interval[CI]) and fault diffusivity is 0.08–0.33 m 2 /s (90% CI), which is 2 orders of magnitude higher than the host rock diffusivity in some wells, thus highlighting the role of faults as fluid conduits.

58 GEOSCIENCES↗

Nonlocal operators, parabolic-type equations, and ultrametric random walks

In this article, we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov, V. A. and Bikulov, A. Kh., “On the ultrametricity of the fluctuation dynamicmobility of protein molecules,” Proc. Steklov Inst. Math. 265(1), 75–81 (2009) [Tr. Mat. Inst. Steklova 265, 82–89 (2009) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Zubarev, A. P., “First passage time distribution and the number of returns for ultrametric random walks,” J. Phys. A 42(8), 085003 (2009); Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic models of ultrametric diffusion in the conformational dynamics of macromolecules,” Proc. Steklov Inst. Math. 245(2), 48–57 (2004) [Tr. Mat. Inst. Steklova 245, 55–64 (2004) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic description of characteristic relaxation in complex systems,” J. Phys. A 36(15), 4239–4246 (2003); Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., and Osipov, V. A., “p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes,” J. Phys. A 35(2), 177–189 (2002); Avetisov, V. A., Bikulov, A. Kh., and Kozyrev, S. V., “Description of logarithmic relaxation by a model of a hierarchical random walk,” Dokl. Akad. Nauk 368(2), 164–167 (1999) (in Russian). The fundamental solutions of these parabolic-type equations are transition functions of random walks on the n-dimensional vector space over the field of p-adic numbers. We study some properties of these random walks, including the first passage time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Integrated surface/subsurface permafrost thermal hydrology: Model formulation and proof-of-concept simulations

The need to understand potential climate impacts and feedbacks in Arctic regions has prompted recent interest in modeling of permafrost dynamics in a warming climate. A new fine-scale integrated surface/subsurface thermal hydrology modeling capability is described and demonstrated in proof-of-concept simulations. The new modeling capability combines a surface energy balance model with recently developed three-dimensional subsurface thermal hydrology models and new models for nonisothermal surface water flows and snow distribution in the microtopography. Surface water flows are modeled using the diffusion wave equation extended to include energy transport and phase change of ponded water. Variation of snow depth in the microtopography, physically the result of wind scour, is also modeled heuristically with a diffusion wave equation. The multiple surface and subsurface processes are implemented by leveraging highly parallel community software. Fully integrated thermal hydrology simulations on the tilted open book catchment, an important test case for integrated surface/subsurface flow modeling, are presented. Fine-scale 100-year projections of the integrated permafrost thermal hydrological system on an ice wedge polygon at Barrow Alaska in a warming climate are also presented. Finally, these simulations demonstrate the feasibility of microtopography-resolving, process-rich simulations as a tool to help understand possible future evolution of the carbon-rich Arctic tundra in a warming climate.

54 ENVIRONMENTAL SCIENCES↗

Modeling Studies of the MODIS Solar Diffuser Attenuation Screen and Comparison with On-Orbit Measurements

The MODIS instrument relies on solar calibration to achieve the required radiometric accuracy. This solar calibration occurs as the TERRA spacecraft comes up over the North Pole. The earth underneath the spacecraft is still dark for approximately one minute and the sun is just rising over the earth's north polar regions. During this time the sun moves through about 4 degrees, the scan mirror rotates about 19 times and about 50 frames (exposures) are made of the white solar diffuser. For some of MODIS'S bands the brightness of the screen is reduced, to prevent detector saturation, by means of a pinhole screen, which produces approximately 600 pinhole images of the sun within the field of view of any one detector. Previous attempts at creating a detailed radiometric model of this calibration scenario produced intensity variations on the focal planes with insufficient detail to be useful. The current computational approach produces results, which take into account the motion of the sun and the scan mirror and produces variations, which strongly resemble the observed focal plane intensity variations. The computational approach and results and a comparison with actual observational data are presented.

Waluschka, Eugene↗

Modeling Damage Complexity-Dependent Non-Homologous End-Joining Repair Pathway

Non-homologous end joining (NHEJ) is the dominant DNA double strand break (DSB) repair pathway and involves several repair proteins such as Ku, DNA-PKcs, and XRCC4. It has been experimentally shown that the choice of NHEJ proteins is determined by the complexity of DSB. In this paper, we built a mathematical model, based on published data, to study how NHEJ depends on the damage complexity. Under an appropriate set of parameters obtained by minimization technique, we can simulate the kinetics of foci track formation in fluorescently tagged mammalian cells, Ku80-EGFP and DNA-PKcs-YFP for simple and complex DSB repair, respectively, in good agreement with the published experimental data, supporting the notion that simple DSB undergo fast repair in a Ku-dependent, DNA-PKcs-independent manner, while complex DSB repair requires additional DNA-PKcs for end processing, resulting in its slow repair, additionally resulting in slower release rate of Ku and the joining rate of complex DNA ends. Based on the numerous experimental descriptions, we investigated several models to describe the kinetics for complex DSB repair. An important prediction of our model is that the rejoining of complex DSBs is through a process of synapsis formation, similar to a second order reaction between ends, rather than first order break filling/joining. The synapsis formation (SF) model allows for diffusion of ends before the synapsis formation, which is precluded in the first order model by the rapid coupling of ends. Therefore, the SF model also predicts the higher number of chromosomal aberrations observed with high linear energy transfer (LET) radiation due to the higher proportion of complex DSBs compared to low LET radiation, and an increased probability of misrejoin following diffusion before the synapsis is formed, while the first order model does not provide a mechanism for the increased effectiveness in chromosomal aberrations observed.

59 BASIC BIOLOGICAL SCIENCES↗

A Model of Charge-Transfer Excitons: Diffusion, Spin Dynamics, and Magnetic Field Effects

In this Letter, we investigate how the microscopic dynamics of charge-transfer (CT) excitons are influenced by the presence of an external magnetic field in disordered molecular semiconductors. This influence is driven by the dynamic interplay between the spin and spatial degrees of freedom of the electron–hole pair. To account for this interplay, we have developed a numerical framework that combines a traditional model of quantum spin dynamics with a stochastic coarse-grained model of charge transport. This combination gives a general and efficient methodology for simulating the effects of magnetic field on CT state dynamics, therefore providing a basis for revealing the microscopic origin of experimentally observed magnetic field effects. We reveal that simulations carried out on our model are capable of reproducing experimental results as well as generating theoretical predictions related to the efficiency of organic electronic materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗