Pure Diffusion Model Research Articles

Relationship between current response and time in ion transport problem including diffusion and convection. 1. An analytical approach

The mathematical models of the ion transport problem in a potential field are anayzed. Ion transport is regarded as the superposition of diffusion and convection. In the case of pure diffusion model the classical Gottrell’s result is studied for a constant as well as for the time dependent Dirichlet data at the electrode. Comparative analysis of the current response \({\mathcal I}_{\rm D}={\mathcal I}_{\rm D}(t)\) and the classical Gottrellian \({\mathcal I}_{\rm G}={\mathcal I}_{\rm G}(t)\) is given on the obtained explicit formulas. The approach is extended to find out the current response \({\mathcal I}_c={\mathcal I}_c(t)\) corresponding to the diffusion-convection model. The relationship between the current response \({\mathcal I}_c={\mathcal I}_c(t)\) and Gottrellian \({\mathcal I}_{\rm G}={\mathcal I}_{\rm G}(t)\) is obtained in explicit form. This relationship permits one to compare pure diffusion and diffusion-convection models, including asymptotic behaviour of current response and an influence of the convection coefficient. The theoretical result are illustrated by numerical examples.

Measurement of implanted helium particle transport by a flowing liquid lithium film

Due to its low atomic number, low sputtering yield, high sputtered ion fraction and excellent thermal properties, liquid lithium has been proposed as a potential candidate for advanced plasma-facing components (PFC). Using a liquid material opens the possibility of a continuously flowing, self-regenerating plasma-facing surface with a small residence time. This would allow such component to handle very high heat loads that are expected. There are, however, multiple unanswered questions regarding how such a liquid PFC would interact with the plasma in the reactor. The issue of particle control is critical, and it can be a factor to determine the feasibility of these advanced concepts. Hydrogen and helium are important in this regard: hydrogen transport by a flowing PFC impacts the reactor fuel recycling regime and tritium inventory; helium transport can help quantify ash removal by the flowing PFC. The flowing liquid-metal retention experiment (FLIRE) was built at the University of Illinois to answer some of the questions regarding particle transport by flowing liquid films exposed to plasmas. Experimental results regarding helium transport by a flowing lithium film after irradiation with an energetic He ion beam are presented in this work. Retained fraction values up to 2% were measured for the experimental conditions, and the retention was found to increase linearly with implanted ion energy. A pure diffusion model was used to describe the helium transport by the Li film, and it was found that such model predicts a diffusion coefficient of (2.8 ± 0.6) × 10 −11 m 2/s, based on the experimental retention measurements. Preliminary evidence of long-term trapping of helium will also be presented.

Contrasting effects of long distance seed dispersal on genetic diversity during range expansion

Currently many attempts are made to reconstruct the colonization history of plant species after the last ice age. A surprising finding is that during the colonization phase genetic diversity did not decrease as much as expected. In this paper we examine whether long distance seed dispersal events could play a role in the unexpected maintenance of genetic diversity during range expansion. This study is based on simulations carried out with a maternally inherited haploid locus using a cellular automaton. The simulations reveal a close relationship between the frequency of long distance seed dispersal events and the amount of genetic diversity preserved during colonization. In particular, when the colonized region is narrow, a complete loss of genetic diversity results from the occurrence of very rare long distance dispersal (LDD) events. We call this phenomenon the 'embolism effect'. However, slightly higher rates of LDD events reverse this effect, up to the point that diversity is better preserved than in a pure diffusion model. This phenomenon is linked to the reorganization of the genetic structure during colonization and is called the 'reshuffling effect'.

Modelling conditional heteroscedasticity and jumps in Australian short‐term interest rates

AbstractThe present paper explores a class of jump–diffusion models for the Australian short‐term interest rate. The proposed general model incorporates linear mean‐reverting drift, time‐varying volatility in the form of LEVELS (sensitivity of the volatility to the levels of the short‐rates) and generalized autoregressive conditional heteroscedasticity (GARCH), as well as jumps, to match the salient features of the short‐rate dynamics. Maximum likelihood estimation reveals that pure diffusion models that ignore the jump factor are mis‐specified in the sense that they imply a spuriously high speed of mean‐reversion in the level of short‐rate changes as well as a spuriously high degree of persistence in volatility. Once the jump factor is incorporated, the jump models that can also capture the GARCH‐induced volatility produce reasonable estimates of the speed of mean reversion. The introduction of the jump factor also yields reasonable estimates of the GARCH parameters. Overall, the LEVELS–GARCH–JUMP model fits the data best.

International mergers and acquisitions: A jump diffusion model application

This paper empirically investigates international mergers and acquisitions (M&As) of foreign targets and bidders by analyzing the stock price behavior of the firms involved. The jump diffusion model is employed to study the effects of the M&A announcements on stock prices. The results indicate that acquisition announcements are perceived as a surprise by the market, but prices seem to adjust rather rapidly, supporting the semi-strong form of the market efficiency hypothesis. In addition, a comparison of the pure diffusion and jump diffusion models indicates that the jump diffusion model is statistically superior to the traditional event study methodology (pure diffusion model). (JEL G34)

Mass-transfer in membrane based solvent extraction and stripping of 5-methyl-2-pyrazinecarboxylic acid and co-transport of sulphuric acid in HF contactors

Simultaneous membrane based solvent extraction (MBSE) and membrane based solvent stripping (MBSS) of 5-methyl-2-pyrazine carboxylic acid (MPCA) in hollow fibre contactors with solvent containing trioctylamine (TOA) have been studied. An effective transport of MPCA was achieved. The analysis of mass-transfer resistances showed, that the kinetics of the acid-carrier complexes formation and/or decomposition should be taken into account. The contribution of the mass-transfer resistances based on reaction kinetics to the overall resistances in MBSE and/or MBSS is from 40 to 80%. The proposed reaction-diffusion model gives a much better fit to the experimental values than a pure diffusion model. The mean value of the lumped rate constant of the extraction reaction for MPCA is 14.2$̂× 10−6 m.s−1. Depending on the stripping solution composition, i.e. aqueous solution of NaOH or aqueous solution of NaOH with an addition of NH4OH with lower basicity, the mean value of the lumped rate constant of the stripping reaction is 6.02 × 10−6 m.s−1 and 2.65 × 10−6 m.s−1, respectively. It has been found that sulphuric acid is cotransported with MPCA. An excess of H2SO4 in the feed decreases the selectivity of MPCA separation. The molar ratio of the transported H2SO4 to MPCA decreases with increasing the MPCA concentration in the solvent. When the feed solution pH was kept at 2.2 the value of this ratio ranged from 1 to 2.5, while when it was kept at 2.5 and NH4OH was added to the stripping solution, the molar ratio of the transported H2SO4 to MPCA was in the interval from 0.2 to 1.5.

The surprise element: jumps in interest rates

That information surprises result in discontinuous interest rates is no surprise to participants in the bond markets. We develop a class of Poisson–Gaussian models of the Fed Funds rate to capture surprise effects, and show that these models offer a good statistical description of short rate behavior, and are useful in understanding many empirical phenomena. Jump (Poisson) processes capture empirical features of the data which would not be captured by Gaussian models, and there is strong evidence that existing Gaussian models would be well-enhanced by jump and ARCH-type processes. The analytical and empirical methods in the paper support many applications, such as testing for Fed intervention effects, which are shown to be an important source of surprise jumps in interest rates. The jump model is shown to mitigate the non-linearity of interest rate drifts, so prevalent in pure-diffusion models. Day-of-week effects are modelled explicitly, and the jump model provides evidence of bond market overreaction, rejecting the martingale hypothesis for interest rates. Jump models mixed with Markov switching processes predicate that conditioning on regime is important in determining short rate behavior.

Determination of the optical properties of two-layer turbid media by use of a frequency-domain hybrid Monte Carlo diffusion model

The general two-layer inverse problem in biomedical photon migration is to estimate the absorption and scattering coefficients of each layer as well as the top-layer thickness. We attempted to solve this problem, using experimental and simulated spatially resolved frequency-domain (FD) reflectance for optical properties typical of skin overlying muscle or skin overlying fat in the near infrared. Two forward models of light propagation were used: a two-layer diffusion solution [Appl. Opt. 37, 779 (1998)] and a hybrid Monte Carlo (MC) diffusion model [Appl. Opt. 37, 7401 (1998)]. MC-simulated FD reflectance data were fitted as relative measurements to the hybrid and the pure diffusion models. It was found that the hybrid model could determine all the optical properties of the two-layer media studied to ~5%. Also, the same accuracy could be achieved by means of fitting MC-simulated cw reflectance data as absolute measurements, but fitting them as relative ones is an ill-posed problem. In contrast, two-layer diffusion could not retrieve the top-layer optical properties as accurately for FD data and was ill-posed for both relative and absolute cw data. The hybrid and the pure diffusion models were also fitted to experimental FD reflectance measurements from two-layer tissue-simulating phantoms representative of skin-on-fat and skin-on-muscle baseline optical properties. Both the hybrid and the diffusion models could determine the optical properties of the lower layer. The hybrid model demonstrated its potential to retrieve quantitatively the transport scattering coefficient of skin (the upper layer), which was not possible with the pure diffusion model. Systematic discrepancies between model and experiment may compromise the accuracy of the deduced top-layer optical properties. Identifying and eliminating such discrepancies is critical to practical application of the method.

Use of an upwelling-diffusion energy balance climate model to simulate and diagnose A/OGCM results

We demonstrate that a hemispherically averaged upwelling-diffusion energy-balance climate model (UD/EBM) can emulate the surface air temperature change and sea-level rise due to thermal expansion, predicted by the HadCM2 coupled atmosphere-ocean general circulation model, for various scenarios of anthropogenic radiative forcing over 1860–2100. A climate sensitivity of 2.6 °C is assumed, and a representation of the effect of sea-ice retreat on surface air temperature is required. In an extended experiment, with CO2 concentration held constant at twice the control run value, the HadCM2 effective climate sensitivity is found to increase from about 2.0 °C at the beginning of the integration to 3.85 °C after 900 years. The sea-level rise by this time is almost 1.0 m and the rate of rise fairly steady, implying that the final equilibrium value (the `commitment') is large. The base UD/EBM can fit the 900-year simulation of surface temperature change and thermal expansion provided that the time-dependent climate sensitivity is specified, but the vertical profile of warming in the ocean is not well reproduced. The main discrepancy is the relatively large mid-depth warming in the HadCM2 ocean, that can be emulated by (1) diagnosing depth-dependent diffusivities that increase through time; (2) diagnosing depth-dependent diffusivities for a pure-diffusion (zero upwelling) model; or (3) diagnosing higher depth-dependent diffusivities that are applied to temperature perturbations only. The latter two models can be run to equilibrium, and with a climate sensitivity of 3.85 °C, they give sea-level rise commitments of 1.7 m and 1.3 m, respectively.

Solid-State NMR and Small-Angle X-ray Scattering Study of Microphase Structure of Amorphous and Semicrystalline Poly(styrene−ethylene oxide) Diblock Copolymers

The microphase structure of a series of poly(styrene−ethylene oxide) (SEO) block copolymers has been studied by solid-state NMR and small-angle X-ray scattering (SAXS) techniques. The differential scanning calorimetry studies indicate that the majority of SEO samples are semicrystalline. For the completely amorphous SEO, solid-state NMR 1H spin diffusion was used to determine the sizes of various domains, interfacial thickness, and interdomain distances by the initial-rate approximation and by numerical simulation with a pure spin diffusion model. The results obtained from the above two methods, the initial-rate approximation and the numerical simulation, are generally in good agreement, but the interdomain distance estimated from NMR is relatively lower than that obtained from SAXS. The discrepancy is probably caused by the simulation model used in the NMR data interpretation. For the semicrystalline SEO samples, the relative locations of multiple Bragg peaks and the location of the first-order maximum i...

Activation energy for Ga diffusion on the GaAs(0 0 1)-(2×4) surface: an MBE-STM study

The pure migration of individual Ga atoms on the technologically important GaAs(0 0 1)-(2×4) reconstructed surface has been studied as a function of substrate temperature using a combined molecular beam epitaxy and scanning tunneling microscopy (STM) ultra-high vacuum, multi-chamber facility. We have successfully deposited 1 10 of a plane of Ga atoms onto a pristine GaAs surface under a constant As 4 beam equivalent pressure of 10 −6 Torr, at various substrate temperatures. After deposition the substrate was quenched to room temperature and transferred to the surface analysis chamber for STM imaging. A plot of the number density of islands formed as a function of deposition temperature follows an Arrhenius relationship. Assuming either a pure one-dimensional diffusion model or a pure isotropic two-dimensional diffusion model, the activation energy for diffusion is 2.3 or 1.7 eV, respectively.

The 1994–1995 Mexican Currency Crisis and U.S. Bank Stock Returns

We investigate the impact of the 1994–1995 Mexican currency crisis on U.S. bank stock returns. We use a jump-diffusion model rather than a pure diffusion model to describe daily stock returns, because the public release of unexpected information generally is associated with discrete jumps in prices. Traditional event study models pool both announcement effects and trading effects and may lead to inefficient estimators. The jump-diffusion model can separate the impact of informed trading from unanticipated public announcements. Our results indicate that the variance of the jumps is large and increases with bank size and portion of loans to Mexico.

Determination of the Diffusion Coefficient and Phase‐Transfer Rate Parameter in LaNi5 and MmNi3.6Co0.8Mn0.4Al0.3 Using Microelectrodes

A potential‐step method for determining the diffusion coefficient and phase‐transfer parameter in metal hydrides by using microelectrodes was investigated. It was shown that a large potential step is not enough to ensure a completely diffusion‐limited mass transfer if a surface‐phase transfer reaction takes place at a finite rate. It was shown, using a kinetic expression for the surface phase‐transfer reaction, that the slope of the logarithm of the current vs. time curve will be constant both in the case of the mass‐transfer limited by diffusion or by diffusion and a surface‐phase transfer. The diffusion coefficient and phase‐transfer rate parameter were accurately determined for using a fit to the whole transient. The diffusion coefficient was found to be . The fit was good and showed that a pure diffusion model was not enough to explain the observed transient. The diffusion coefficient and phase‐transfer rate parameter were also estimated for pure . A fit of the whole curve showed that neither a pure diffusion model nor a model including phase transfer could explain the whole transient.

Jump Diffusion Processes and Emerging Bond and Stock Markets: An Investigation Using Daily Data

The underlying stochastic processes that drive returns in several emerging bond and stock markets are investigated using the pure diffusion, the jump diffusion, the ARCH pure diffusion, and the ARCH jump diffusion models. The results indicate that jump diffusion models fit the data better than pure diffusion models. Possible sources and linkages of information surprises in emerging stock and bond markets are also investigated. Bond and stock returns of the same country exhibit simultaneous jumps, indicating a possible linkage of the two markets. U.S. equity returns respond to jumps in emerging bond markets but not to jumps in emerging stock markets

Feasibility of using sand dunes as archives of old air

Large unaltered samples of the atmosphere covering the past century would complement the history of atmospheric gases obtained from bubbles in ice cores, enabling measurement of geochemically important species such as O2, 14CH4, and 14CO. Sand dunes are a porous media with interstitial air in diffusive contact with the atmosphere, somewhat analogous to the unconsolidated layer of firn atop glaciers. Recent studies have demonstrated the value of firn as an archive of old air [Battle et al., 1996; Bender et al., 1994a]. Unlike firn, sand dunes are incompressible and so remain permeable to greater depths and may extend the firn record into the past century. To evaluate the feasibility of using sand dunes as archives of old air, we drilled 60 m deep test holes in the Algodones Dunes, Imperial Valley, California. The main objective was to see if the air in a sand dune is as old as predicted by a diffusion model, or if the dune is rapidly flushed by advective pumping during windstorms and barometric pressure changes. We dated the air with chlorofluorocarbons and krypton‐85, anthropogenic tracers whose atmospheric concentrations are known and have been increasing rapidly in the past half century. These tracer data match the pure diffusion model well, showing that advection in this dune is negligible compared to diffusion as a transport mechanism and that the mean age of the air at 61 m depth is ∼10 years. Dunes therefore do contain old air. However, dunes appear to suffer from two serious drawbacks as archives. Microbial metabolism is evident in elevated CO2 and N2O and depressed CH4 and O2 concentrations in this dune, corrupting the signals of interest in this and probably most dunes. Second, isotopic analyses of N2 and O2 from the dune show that fractionation of the gases occurs due to diffusion of water vapor, complicating the interpretation of the O2 signal beyond the point of viability for an air archive. Sand dunes may be useful for relatively inert gases with large atmospheric concentration changes such as chlorofluorocarbons.

Discrete-time bond and option pricing for jump-diffusion processes

This paper provides a methodology for numerically pricing generalized interest rate contingent claims for jump-diffusion processes. The method enhances the standard finite-differencing approach to deal with partial differential-difference equations derived in a jump-diffusion setting. Numerical illustrations compare jump-diffusion and pure-diffusion models.

Role of thermosolutal convection in liquid phase electroepitaxial growth of gallium arsenide

This article investigates the effect of thermosolutal convection in liquid phase electroepitaxial (LPEE) growth of GaAs through a two-dimensional numerical simulation model. The model accounts for heat transfer and electric current distribution with Peltier and Joule effects, diffusive and convective mass transport including the effect of electromigration, and fluid flow coupled with temperature and concentration fields. Simulations are performed for two growth cell configurations and the results are analyzed to determine growth rates, substrate shape evolution, and relative contributions of Peltier cooling and electromigration. The simulations predict and help explain a number of experimentally observed features which previous diffusion-based models fail to reproduce. In general, electromigration is found to be the dominant growth mechanism, but the contribution of Peltier cooling to the overall growth rate is found to be significantly enhanced by thermosolutal convection in the solution, and Peltier cooling can in fact become the dominant growth mechanism for certain growth conditions and growth cell configurations. The overall growth rate is found to increase with increasing furnace temperature and applied electric current density. The thermosolutal convection model predicts increased non-uniformity of the grown layers compared with the pure-diffusion model. The shape of the grown layers is also shown to be very sensitive to changes in growth cell configurations.

Stellar models with microscopic diffusion and rotational mixing. 2: Application to open clusters

Stellar models with masses ranging from 05.5 to 1.3 solar mass were constructed for comparison with young cluster observations of Li and of rotation velocities. The amount of Li depletion in cool stars is sensitive to the amount of overshoot at the base of the surface convection zone, and the exact metallicity of the models. Even when this is taken into account, the Li observations are a severe constraint for the models and rule out standard models and pure diffusion models. Stellar models which include diffusion and rotational mixing in the radiative regions of stars are able to simultaneously match the Li abundances observed in the Pleiades, the UMa Group, The Hyades, Praesepe, NGC 752, and M67. They also match the observed rotation periods in the Hyades. However, these models are unable to simultaneously explain the presence of the rapidly rotating late G and K stars in the Pleiades and the absence of rapidly rotating late F and early G stars.

Transient temperature and sea level response of a two‐dimensional ocean‐climate model to greenhouse gas increases

A two‐dimensional dynamical ocean model is coupled to an energy balance climate model and used to investigate the transient surface temperature and sea level response to greenhouse gas increases. For most experiments a step function surface‐troposphere heating perturbation of 6 W m−2 is applied. A transient reduction in the thermohaline overturning flux of 15–30% occurs in most experiments, although in some cases a near‐total circulation collapse occurs within the first 100 years and lasts 700–1000 years. The transient circulation decrease is attributed to the greater rate of downward penetration of the heating anomaly in downwelling rather than in upwelling regions and is not a result of reduced convection. For experiments in which the steady state circulation is qualitatively unchanged after a heating perturbation, the surface temperature response is roughly uniform with latitude, in the absence of ice and snow. However, in some cases a heating perturbation induces the transition from a one‐cell to a two‐cell overturning circulation, or causes a complete reversal in the direction of overturning when a single cell spans both hemispheres, causing marked latitudinal variations in the surface temperature response. The e‐folding response time scale τe for global mean surface temperature ranges from 10 to 142 years as the vertical diffusion coefficient Kν varies from 1×10−5 m2 s−1 to 5×10−4 m2 s−1, but the variation of τe with Kν is not uniform due to changes in the transient circulation response as Kν is varied. The one‐dimensional upwelling diffusion and pure diffusion models have a significantly faster surface transient response than the two‐dimensional (2‐D) model, due to transient weakening of thermohaline overturning in the 2‐D model, which dampens surface temperature warming. The presence of convection has a small effect on the transient response. Transient sea level rise is highly sensitive to Kν, with faster sea level rise associated with larger Kν and hence with slower surface warming. The steady state ocean warming is approximately uniform with depth and equal to the global mean surface warming (3°C for 6 W m−2 forcing) in most experiments, which produces a sea level rise of 2 to 3 m due to thermal expansion. The times required to reach 50% and 75% of the steady state sea level rise are 200–1100 years and 500–2400 years, respectively. However, if the unperturbed circulation consists of a single overturning cell and a second thermohaline overturning cell develops in response to a heating perturbation, vertical mean steady state deep ocean warming and associated sea level rise can be reduced by almost a factor of 10.

Estimating the Effects of Information Surprises and Trading on Stock Returns Using a Mixed Jump-Diffusion Model

I present a methodology that uses the mixed jump-diffusion model for stock returns to estimate the separate effects of information surprises and strategic trading around corporate events. Using simulation techniques, I show that for events with multiple announcements spread over a long time, the estimators derived from the mixed jump-diffusion model are more powerful compared to the traditional cumulative abnormal return estimators. The new methodology is used to study the separate effects of information surprises and strategic trading associated with blockholdings and subsequent targeted repurchases. I find that for more than 93 percent of the firms in our sample the mixed jump-diffusion model is statistically superior to the pure diffusion model in describing stock returns. More important, I find a statistically significant negative effect due to trading, while the average effect around announcements is statistically insignificant. In contrast, the standard cumulative abnormal return is not statistically different from zero. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.