Journal articles: 'Diffusion timescales'

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RAGOT, BRIGITTE R. "Nonlinear particle dynamics in a broadband turbulence wave spectrum." Journal of Plasma Physics 60, no. 2 (September 1998): 299–329. http://dx.doi.org/10.1017/s0022377898006795.

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In the statistical quasilinear theory of weak plasma turbulence, charged particles moving in electrostatic fluctuations diffuse in velocity, i.e. the velocity variance 〈Δv2(t)〉 increases linearly with time t, for times long compared with the auto-correlation time τac of the field, which may be estimated as the reciprocal of the spectral width of the fluctuations. Recent test-particle simulations have revealed a new regime at very long timescales t[Gt ]τac where quasilinear theory breaks down, for intermediate field amplitudes. As this behaviour is not consistent with a diffusion on quasilinear timescales, the problem of the motion of particles in a broadband wave field, for the case of a slowly growing field, is considered here from a purely dynamical point of view, introducing no statistics on the field and no restriction on the amplitude of this field. By determining, on a given timescale, and in the frame of wave–particle interaction, the spectral width over which waves interact efficiently with a particle, a new timescale is found: the nonlinear time of wave–particle interaction τNL∝ (spectral density of energy)−1/3[Gt ]τac. This is the correlation time of the dynamics. For times shorter than τNL, the particles trajectories remain globally regular, and do not separate: they follow a quasifractal set of dimension 2. For times long compared with τNL, there appears a ‘true’ diffusive regime with mixing and decorrelation, due to nonlinear mixing in phase space and the localization of the wave–particle interaction. These theoretical results are confirmed by a numerical study of the velocity variance as a function of time. In particular, the particle dynamics really do become diffusive on timescales several orders of magnitude longer than that predicted by quasilinear theory (namely [Gt ]τNL[Gt ]τac). Finally, deviations from the quasilinear value of the diffusion coefficient and wave growth rate, discussed in the literature, are explained.

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Wu, Youjun, Bingjie Han, Younan Li, Edwin Munro, David J. Odde, and Erik E. Griffin. "Rapid diffusion-state switching underlies stable cytoplasmic gradients in the Caenorhabditis elegans zygote." Proceedings of the National Academy of Sciences 115, no. 36 (July 24, 2018): E8440—E8449. http://dx.doi.org/10.1073/pnas.1722162115.

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Protein concentration gradients organize cells and tissues and commonly form through diffusion away from a local source of protein. Interestingly, during the asymmetric division of the Caenorhabditis elegans zygote, the RNA-binding proteins MEX-5 and PIE-1 form opposing concentration gradients in the absence of a local source. In this study, we use near-total internal reflection fluorescence (TIRF) imaging and single-particle tracking to characterize the reaction/diffusion dynamics that maintain the MEX-5 and PIE-1 gradients. Our findings suggest that both proteins interconvert between fast-diffusing and slow-diffusing states on timescales that are much shorter (seconds) than the timescale of gradient formation (minutes). The kinetics of diffusion-state switching are strongly polarized along the anterior/posterior (A/P) axis by the PAR polarity system such that fast-diffusing MEX-5 and PIE-1 particles are approximately symmetrically distributed, whereas slow-diffusing particles are highly enriched in the anterior and posterior cytoplasm, respectively. Using mathematical modeling, we show that local differences in the kinetics of diffusion-state switching can rapidly generate stable concentration gradients over a broad range of spatial and temporal scales.

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Javanainen, Matti, Hector Martinez-Seara, Christopher V. Kelly, Pavel Jungwirth, and Balázs Fábián. "Anisotropic diffusion of membrane proteins at experimental timescales." Journal of Chemical Physics 155, no. 1 (July 7, 2021): 015102. http://dx.doi.org/10.1063/5.0054973.

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Bauer, Evan B., and Lars Bildsten. "Polluted White Dwarfs: Mixing Regions and Diffusion Timescales." Astrophysical Journal 872, no. 1 (February 14, 2019): 96. http://dx.doi.org/10.3847/1538-4357/ab0028.

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Costa, F., T. Shea, and T. Ubide. "Diffusion chronometry and the timescales of magmatic processes." Nature Reviews Earth & Environment 1, no. 4 (April 2020): 201–14. http://dx.doi.org/10.1038/s43017-020-0038-x.

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Shevchenko, Ivan I. "LYAPUNOV AND DIFFUSION TIMESCALES IN THE SOLAR NEIGHBORHOOD." Astrophysical Journal 733, no. 1 (May 2, 2011): 39. http://dx.doi.org/10.1088/0004-637x/733/1/39.

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Bradshaw, Richard W., and Adam J. R. Kent. "The analytical limits of modeling short diffusion timescales." Chemical Geology 466 (September 2017): 667–77. http://dx.doi.org/10.1016/j.chemgeo.2017.07.018.

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Fallon, John, Phillip G. D. Ward, Linden Parkes, Stuart Oldham, Aurina Arnatkevičiūtė, Alex Fornito, and Ben D. Fulcher. "Timescales of spontaneous fMRI fluctuations relate to structural connectivity in the brain." Network Neuroscience 4, no. 3 (January 2020): 788–806. http://dx.doi.org/10.1162/netn_a_00151.

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Intrinsic timescales of activity fluctuations vary hierarchically across the brain. This variation reflects a broad gradient of functional specialization in information storage and processing, with integrative association areas displaying slower timescales that are thought to reflect longer temporal processing windows. The organization of timescales is associated with cognitive function, distinctive between individuals, and disrupted in disease, but we do not yet understand how the temporal properties of activity dynamics are shaped by the brain’s underlying structural connectivity network. Using resting-state fMRI and diffusion MRI data from 100 healthy individuals from the Human Connectome Project, here we show that the timescale of resting-state fMRI dynamics increases with structural connectivity strength, matching recent results in the mouse brain. Our results hold at the level of individuals, are robust to parcellation schemes, and are conserved across a range of different timescale- related statistics. We establish a comprehensive BOLD dynamical signature of structural connectivity strength by comparing over 6,000 time series features, highlighting a range of new temporal features for characterizing BOLD dynamics, including measures of stationarity and symbolic motif frequencies. Our findings indicate a conserved property of mouse and human brain organization in which a brain region’s spontaneous activity fluctuations are closely related to their surrounding structural scaffold.

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Madhavi, W. A. Monika, Samantha Weerasinghe, and Konstantin I. Momot. "Effects of Hydrogen Bonding on the Rotational Dynamics of Water-Like Molecules in Liquids: Insights from Molecular Dynamics Simulations." Australian Journal of Chemistry 73, no. 8 (2020): 734. http://dx.doi.org/10.1071/ch19537.

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Rotational motion of molecules plays an important role in determining NMR spin relaxation properties of liquids. The textbook theory of NMR spin relaxation predominantly uses the assumption that the reorientational dynamics of molecules is described by a continuous time rotational diffusion random walk with a single rotational diffusion coefficient. Previously we and others have shown that reorientation of water molecules on the timescales of picoseconds is not consistent with the Debye rotational-diffusion model. In particular, multiple timescales of molecular reorientation were observed in liquid water. This was attributed to the hydrogen bonding network in water and the consequent presence of collective rearrangements of the molecular network. In order to better understand the origins of the complex reorientational behaviour of water molecules, we carried out molecular dynamics (MD) simulations of a liquid that has a similar molecular geometry to water but does not form hydrogen bonds: hydrogen sulfide. These simulations were carried out at T=208K and p=1 atm (~5K below the boiling point). Ensemble-averaged Legendre polynomial functions of hydrogen sulfide exhibited a Gaussian decay on the sub-picosecond timescale but, unlike water, did not exhibit oscillatory behaviour. We attribute these differences to hydrogen sulfide’s absence of hydrogen bonding.

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Duffy, Peter. "Bohm Diffusion and Cosmic-Ray-Modified Shocks." International Astronomical Union Colloquium 142 (1994): 981–83. http://dx.doi.org/10.1017/s0252921100078428.

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AbstractA numerical solution to the problem of self-consistent diffusive shock acceleration is presented. The cosmic rays are scattered, accelerated and exert a back-reaction on the gas through their interaction with turbulence frozen into the local fluid frame. Using a grid with a hierarchical spacetime structure the physically interesting limit of Bohm diffusion (к ∝ pv), which introduces a wide range of diffusion lengthscales and acceleration timescales, can be studied. Some implications for modified shocks and particle acceleration are presented.Subject headings: acceleration of particles — cosmic rays — diffusion — shock waves

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Münch, Thomas, and Thomas Laepple. "What climate signal is contained in decadal- to centennial-scale isotope variations from Antarctic ice cores?" Climate of the Past 14, no. 12 (December 20, 2018): 2053–70. http://dx.doi.org/10.5194/cp-14-2053-2018.

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Abstract. Ice-core-based records of isotopic composition are a proxy for past temperatures and can thus provide information on polar climate variability over a large range of timescales. However, individual isotope records are affected by a multitude of processes that may mask the true temperature variability. The relative magnitude of climate and non-climate contributions is expected to vary as a function of timescale, and thus it is crucial to determine those temporal scales on which the actual signal dominates the noise. At present, there are no reliable estimates of this timescale dependence of the signal-to-noise ratio (SNR). Here, we present a simple method that applies spectral analyses to stable-isotope data from multiple cores to estimate the SNR, and the signal and noise variability, as a function of timescale. The method builds on separating the contributions from a common signal and from local variations and includes a correction for the effects of diffusion and time uncertainty. We apply our approach to firn-core arrays from Dronning Maud Land (DML) in East Antarctica and from the West Antarctic Ice Sheet (WAIS). For DML and decadal to multi-centennial timescales, we find an increase in the SNR by nearly 1 order of magnitude (∼0.2 at decadal and ∼1.0 at multi-centennial scales). The estimated spectrum of climate variability also shows increasing variability towards longer timescales, contrary to what is traditionally inferred from single records in this region. In contrast, the inferred variability spectrum for WAIS stays close to constant over decadal to centennial timescales, and the results even suggest a decrease in SNR over this range of timescales. We speculate that these differences between DML and WAIS are related to differences in the spatial and temporal scales of the isotope signal, highlighting the potentially more homogeneous atmospheric conditions on the Antarctic Plateau in contrast to the marine-influenced conditions on WAIS. In general, our approach provides a methodological basis for separating local proxy variability from coherent climate variations, which is applicable to a large set of palaeoclimate records.

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Bartels-Rausch, T., S. N. Wren, S. Schreiber, F. Riche, M. Schneebeli, and M. Ammann. "Diffusion of volatile organics through porous snow: impact of surface adsorption and grain boundaries." Atmospheric Chemistry and Physics Discussions 13, no. 3 (March 7, 2013): 6131–64. http://dx.doi.org/10.5194/acpd-13-6131-2013.

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Abstract. Release of trace gases from surface snow on Earth drives atmospheric chemistry, especially in the polar regions. The gas-phase diffusion of methanol and of acetone through the interstitial air of snow was investigated in a well-controlled laboratory study in the temperature range of 223 to 263 K. The aim of this study was to evaluate how the structure of the snowpack, the interaction of the trace gases with the snow surface, and the grain boundaries influence the diffusion on timescales up to 1 h. The diffusive loss of these two volatile organics into packed snow samples was measured using a chemical ionization mass spectrometer. The structure of the snow was analyzed by means of X-ray computed micro-tomography. The observed diffusion profiles could be well described based on gas-phase diffusion and the known structure of the snow sample at temperatures &geq; 253 K. At colder temperatures surface interactions start to dominate the diffusive transport. Parameterizing these interactions in terms of adsorption to the solid ice surface, i.e. using temperature dependent air–ice partitioning coefficients, better described the observed diffusion profiles than the use of air–liquid partitioning coefficients. No changes in the diffusive fluxes were observed by increasing the number of grain boundaries in the snow sample by a factor of 7, indicating that for these volatile organic trace gases, uptake into grain boundaries does not play a role on the timescale of diffusion through porous surface snow. In conclusion, we have shown that the diffusivity can be predicted when the structure of the snowpack and the partitioning of the trace gas to solid ice is known.

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Price, H. C., B. J. Murray, J. Mattsson, D. O'Sullivan, T. W. Wilson, K. J. Baustian, and L. G. Benning. "Quantifying water diffusion in high-viscosity and glassy aqueous solutions using a Raman isotope tracer method." Atmospheric Chemistry and Physics Discussions 13, no. 11 (November 8, 2013): 29375–411. http://dx.doi.org/10.5194/acpd-13-29375-2013.

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Abstract. Recent research suggests that under certain temperature and relative humidity conditions atmospheric aerosol may be present in the form of a glassy solid. In order to understand the impacts that this may have on aerosol-cloud interactions and atmospheric chemistry, knowledge of water diffusion within such aerosol particles is required. Here, a method is described in which Raman spectroscopy is used to observe D2O diffusion in high-viscosity aqueous solutions, enabling a quantitative assessment of water diffusion coefficients, Dwater, as a function of relative humidity. Results for sucrose solutions compare well with literature data at 23.5 ± 0.3 °C, and demonstrate that water diffusion is slow (Dwater~5 ×10−17m2s−1), but not arrested, just below the glass transition. Room temperature water diffusion coefficients are also presented for aqueous levoglucosan and an aqueous mixture of raffinose, dicarboxylic acids and ammonium sulphate: at low humidity, diffusion is retarded but still occurs on millisecond to second timescales in atmospherically relevant-sized particles. The effect of gel formation on diffusion in magnesium sulfate solutions is shown to be markedly different from the gradual decrease in diffusion coefficients of highly viscous liquids. We show that using the Stokes–Einstein equation to determine diffusion timescales from viscosity leads to values which are more than five orders of magnitude too big, which emphasises the need to make measurements of diffusion coefficients. In addition, comparison of bounce fraction data for levoglucosan with measured diffusion data reveals that even when particles bounce the equilibration timescales for water are a fraction of a second for a 100 nm particle. This suggests a high bounce fraction does not necessarily indicate retarded water diffusion.

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Price, H. C., B. J. Murray, J. Mattsson, D. O'Sullivan, T. W. Wilson, K. J. Baustian, and L. G. Benning. "Quantifying water diffusion in high-viscosity and glassy aqueous solutions using a Raman isotope tracer method." Atmospheric Chemistry and Physics 14, no. 8 (April 16, 2014): 3817–30. http://dx.doi.org/10.5194/acp-14-3817-2014.

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Abstract. Recent research suggests that under certain temperature and relative humidity conditions atmospheric aerosol may be present in the form of a glassy solid. In order to understand the impacts that this may have on aerosol–cloud interactions and atmospheric chemistry, knowledge of water diffusion within such aerosol particles is required. Here, a method is described in which Raman spectroscopy is used to observe D2O diffusion in high-viscosity aqueous solutions, enabling a quantitative assessment of water diffusion coefficients, Dwater, as a function of relative humidity. Results for sucrose solutions compare well with literature data at 23.5 ± 0.3 °C, and demonstrate that water diffusion is slow (Dwater ~5 × 10−17 m2 s−1), but not arrested, just below the glass transition at a water activity of 0.2. Room temperature water diffusion coefficients are also presented for aqueous levoglucosan and an aqueous mixture of raffinose, dicarboxylic acids and ammonium sulphate: at low humidity, diffusion is retarded but still occurs on millisecond to second timescales in atmospherically relevant-sized particles. The effect of gel formation on diffusion in magnesium sulfate solutions is shown to be markedly different from the gradual decrease in diffusion coefficients of highly viscous liquids. We show that using the Stokes–Einstein equation to determine diffusion timescales from viscosity leads to values which are more than 5 orders of magnitude too big, which emphasises the need to make measurements of diffusion coefficients. In addition, comparison of bounce fraction data for levoglucosan with measured diffusion data reveals that even when particles bounce the diffusion timescales for water are a fraction of a second for a 100 nm particle. This suggests a high bounce fraction does not necessarily indicate retarded water diffusion.

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Bartels-Rausch, T., S. N. Wren, S. Schreiber, F. Riche, M. Schneebeli, and M. Ammann. "Diffusion of volatile organics through porous snow: impact of surface adsorption and grain boundaries." Atmospheric Chemistry and Physics 13, no. 14 (July 18, 2013): 6727–39. http://dx.doi.org/10.5194/acp-13-6727-2013.

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Abstract. Release of trace gases from surface snow on earth drives atmospheric chemistry, especially in the polar regions. The gas-phase diffusion of methanol and of acetone through the interstitial air of snow was investigated in a well-controlled laboratory study in the temperature range of 223 to 263 K. The aim of this study was to evaluate how the structure of the snowpack, the interaction of the trace gases with the snow surface, and the grain boundaries influence the diffusion on timescales up to 1 h. The diffusive loss of these two volatile organics into packed snow samples was measured using a chemical ionization mass spectrometer. The structure of the snow was analysed by means of X-ray-computed micro-tomography. The observed diffusion profiles could be well described based on gas-phase diffusion and the known structure of the snow sample at temperatures &geq; 253 K. At colder temperatures, surface interactions start to dominate the diffusive transport. Parameterizing these interactions in terms of adsorption to the solid ice surface, i.e. using temperature-dependent air–ice partitioning coefficients, better described the observed diffusion profiles than the use of air–liquid partitioning coefficients. No changes in the diffusive fluxes were observed by increasing the number of grain boundaries in the snow sample by a factor of 7, indicating that for these volatile organic trace gases, uptake into grain boundaries does not play a role on the timescale of diffusion through porous surface snow. For this, a snow sample with an artificially high amount of ice grains was produced and the grain boundary surface measured using thin sections. In conclusion, we have shown that the diffusivity can be predicted when the structure of the snowpack and the partitioning of the trace gas to solid ice is known.

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Lee, Eunsang, and YounJoon Jung. "Slow Dynamics of Ring Polymer Melts by Asymmetric Interaction of Threading Configuration: Monte Carlo Study of a Dynamically Constrained Lattice Model." Polymers 11, no. 3 (March 19, 2019): 516. http://dx.doi.org/10.3390/polym11030516.

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Abnormally slower diffusional processes than its internal structure relaxation have been observed in ring polymeric melt systems recently. A key structural feature in ring polymer melts is topological constraints which allow rings to assume a threading configuration in the melt phase. In this work, we constructed a lattice model under the assumption of asymmetric diffusivity between two threading rings, and investigated a link between the structural correlation and its dynamic behavior via Monte Carlo simulations. We discovered that the hierarchical threading configurations render the whole system to exhibit abnormally slow dynamics. By analyzing statistical distributions of timescales of threading configurations, we found that the decoupling between internal structure relaxation and diffusion is crucial to understand the threading effects on the dynamics of a ring melt. In particular, in the limit of small but threaded rings, scaling exponents of the diffusion coefficient D and timescale τ diff with respect to the degree of polymerization N agree well with that of the annealed tree model as well as our mean-field analysis. As N increases, however, the ring diffusion abruptly slows down to the glassy behavior, which is supported by a breakdown of the Stokes–Einstein relation.

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Wang, Zhiqiang, Lili Wang, and Rui Xu. "Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms." Mathematical Problems in Engineering 2017 (2017): 1–22. http://dx.doi.org/10.1155/2017/6987436.

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We study the exponential synchronization problem for a class of stochastic competitive neural networks with different timescales, as well as spatial diffusion, time-varying leakage delays, and discrete and distributed time-varying delays. By introducing several important inequalities and using Lyapunov functional technique, an adaptive feedback controller is designed to realize the exponential synchronization for the proposed competitive neural networks in terms of p-norm. According to the theoretical results obtained in this paper, the influences of the timescale, external stimulus constants, disposable scaling constants, and controller parameters on synchronization are analyzed. Numerical simulations are presented to show the feasibility of the theoretical results.

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Rout, Smruti Sourav, Burkhard C. Schmidt, and Gerhard Wörner. "Constraints on non-isothermal diffusion modeling: An experimental analysis and error assessment using halogen diffusion in melts." American Mineralogist 105, no. 2 (February 1, 2020): 227–38. http://dx.doi.org/10.2138/am-2020-7193.

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Abstract Diffusion chronometry on zoned crystals allows constraining duration of magmatic evolution and storage of crystals once temperatures are precisely known. However, non-isothermal diffusion is common in natural samples, and thus timescales may not be determined with confidence while assuming isothermal conditions. The “non-isothermal diffusion incremental step (NIDIS) model” (Petrone et al. 2016) is proposed for such cases for a non-isothermal diffusive analysis. We conducted diffusion experiments with stepwise temperature changes to analyze and test the model, evaluated the associated errors and improved the accuracy by suggesting an alternative algorithm to model diffusion times. We used Cl and F (≤0.4 wt%) as the diffusing elements in nominally anhydrous (H2O ≤ 0.3 wt%) phonolitic melt with composition of Montana Blanca (Tenerife, Spain) in an experimental setup that successively generates multiple diffusive interfaces for different temperatures by adding glass blocks of different Cl and F concentrations. This compound set of two diffusion interfaces represents distinct compositional zones that diffusively interact at different temperatures, which can be taken as an equivalent to non-isothermal diffusion in zoned magmatic crystals. The starting temperature ranged from 975 to 1150 °C, and each set of experiments included a temperature change of 85–150 °C and a total duration of 8–12 h. The experiments were carried out in an internally heated pressure vessel equipped with a rapid quench device at 1 kbar pressure. Cl and F concentration profiles were obtained from the quenched samples by electron microprobe analysis. Although the estimated diffusion times from the NIDIS-model matched well with true experimental values, the errors on estimated timescales, due to errors in curve-fitting and uncertainty in temperature, were ±10–62% (1σ). The errors are much larger at 61–288% (1σ) when the uncertainty in diffusivity parameters is included. We discuss the efficiency and limitations of the model, assess the contribution from different sources of error, and their extent of propagation. A simpler alternative algorithm is proposed that reduces errors on the estimates of diffusion time to 10–32% (1σ) and 60–75% (1σ), with and without including uncertainty in diffusivity parameters, respectively. Using this new algorithm, we recalculated the individual diffusion times for the clinopyroxene crystals analyzed by Petrone et al. (2016) and obtained a significantly reduced error of 26–40% compared to the original error of 61–100%. We also analyzed a sanidine megacryst from Taapaca volcano (N. Chile) as a test case for non-isothermal modeling and obtained diffusion times of 1.5–9.4 ky, which is significantly different from isothermal analyses including a previous study on similar sample. In this analysis, the error estimated by our new method is reduced by 63–70%.

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O'Meara, Simon, David O. Topping, and Gordon McFiggans. "The rate of equilibration of viscous aerosol particles." Atmospheric Chemistry and Physics 16, no. 8 (April 28, 2016): 5299–313. http://dx.doi.org/10.5194/acp-16-5299-2016.

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Abstract. The proximity of atmospheric aerosol particles to equilibrium with their surrounding condensable vapours can substantially impact their transformations, fate and impacts and is the subject of vibrant research activity. In this study we first compare equilibration timescales estimated by three different models for diffusion through aerosol particles to assess any sensitivity to choice of model framework. Equilibration times for diffusion coefficients with varying dependencies on composition are compared for the first time. We show that even under large changes in the saturation ratio of a semi-volatile component (es) of 1–90 % predicted equilibration timescales are in agreement, including when diffusion coefficients vary with composition. For condensing water and a diffusion coefficient dependent on composition, a plasticising effect is observed, leading to a decreased estimated equilibration time with increasing final es. Above 60 % final es maximum equilibration times of around 1 s are estimated for comparatively large particles (10 µm) containing a relatively low diffusivity component (1 × 10−25 m2 s−1 in pure form). This, as well as other results here, questions whether particle-phase diffusion through water-soluble particles can limit hygroscopic growth in the ambient atmosphere. In the second part of this study, we explore sensitivities associated with the use of particle radius measurements to infer diffusion coefficient dependencies on composition using a diffusion model. Given quantified similarities between models used in this study, our results confirm considerations that must be taken into account when designing such experiments. Although quantitative agreement of equilibration timescales between models is found, further work is necessary to determine their suitability for assessing atmospheric impacts, such as their inclusion in polydisperse aerosol simulations.

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SIMPSON, MATTHEW J., ADAM J. ELLERY, SCOTT W. MCCUE, and RUTH E. BAKER. "CRITICAL TIMESCALES AND TIME INTERVALS FOR COUPLED LINEAR PROCESSES." ANZIAM Journal 54, no. 3 (January 2013): 127–42. http://dx.doi.org/10.1017/s1446181113000059.

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AbstractIn 1991, McNabb introduced the concept of mean action time (MAT) as a finite measure of the time required for a diffusive process to effectively reach steady state. Although this concept was initially adopted by others within the Australian and New Zealand applied mathematics community, it appears to have had little use outside this region until very recently, when in 2010 Berezhkovskii and co-workers [A. M. Berezhkovskii, C. Sample and S. Y. Shvartsman, “How long does it take to establish a morphogen gradient?”Biophys. J. 99(2010) L59–L61] rediscovered the concept of MAT in their study of morphogen gradient formation. All previous work in this area has been limited to studying single-species differential equations, such as the linear advection–diffusion–reaction equation. Here we generalize the concept of MAT by showing how the theory can be applied to coupled linear processes. We begin by studying coupled ordinary differential equations and extend our approach to coupled partial differential equations. Our new results have broad applications, for example the analysis of models describing coupled chemical decay and cell differentiation processes.

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Schervish, Meredith, and Manabu Shiraiwa. "Impact of phase state and non-ideal mixing on equilibration timescales of secondary organic aerosol partitioning." Atmospheric Chemistry and Physics 23, no. 1 (January 5, 2023): 221–33. http://dx.doi.org/10.5194/acp-23-221-2023.

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Abstract. Evidence has accumulated that secondary organic aerosols (SOAs) exhibit complex morphologies with multiple phases that can adopt amorphous semisolid or glassy phase states. However, experimental analysis and numerical modeling on the formation and evolution of SOA still often employ equilibrium partitioning with an ideal mixing assumption in the particle phase. Here we apply the kinetic multilayer model of gas–particle partitioning (KM-GAP) to simulate condensation of semi-volatile species into a core–shell phase-separated particle to evaluate equilibration timescales of SOA partitioning. By varying bulk diffusivity and the activity coefficient of the condensing species in the shell, we probe the complex interplay of mass transfer kinetics and the thermodynamics of partitioning. We found that the interplay of non-ideality and phase state can impact SOA partitioning kinetics significantly. The effect of non-ideality on SOA partitioning is slight for liquid particles but becomes prominent in semisolid or solid particles. If the condensing species is miscible with a low activity coefficient in the viscous shell phase, the particle can reach equilibrium with the gas phase long before the dissolution of concentration gradients in the particle bulk. For the condensation of immiscible species with a high activity coefficient in the semisolid shell, the mass concentration in the shell may become higher or overshoot its equilibrium concentration due to slow bulk diffusion through the viscous shell for excess mass to be transferred to the core phase. Equilibration timescales are shorter for the condensation of lower-volatility species into semisolid shell; as the volatility increases, re-evaporation becomes significant as desorption is faster for volatile species than bulk diffusion in a semisolid matrix, leading to an increase in equilibration timescale. We also show that the equilibration timescale is longer in an open system relative to a closed system especially for partitioning of miscible species; hence, caution should be exercised when interpreting and extrapolating closed-system chamber experimental results to atmosphere conditions. Our results provide a possible explanation for discrepancies between experimental observations of fast particle–particle mixing and predictions of long mixing timescales in viscous particles and provide useful insights into description and treatment of SOA in aerosol models.

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Li, Ying, and Manabu Shiraiwa. "Timescales of secondary organic aerosols to reach equilibrium at various temperatures and relative humidities." Atmospheric Chemistry and Physics 19, no. 9 (May 7, 2019): 5959–71. http://dx.doi.org/10.5194/acp-19-5959-2019.

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Abstract. Secondary organic aerosols (SOA) account for a substantial fraction of air particulate matter, and SOA formation is often modeled assuming rapid establishment of gas–particle equilibrium. Here, we estimate the characteristic timescale for SOA to achieve gas–particle equilibrium under a wide range of temperatures and relative humidities using a state-of-the-art kinetic flux model. Equilibration timescales were calculated by varying particle phase state, size, mass loadings, and volatility of organic compounds in open and closed systems. Model simulations suggest that the equilibration timescale for semi-volatile compounds is on the order of seconds or minutes for most conditions in the planetary boundary layer, but it can be longer than 1 h if particles adopt glassy or amorphous solid states with high glass transition temperatures at low relative humidity. In the free troposphere with lower temperatures, it can be longer than hours or days, even at moderate or relatively high relative humidities due to kinetic limitations of bulk diffusion in highly viscous particles. The timescale of partitioning of low-volatile compounds into highly viscous particles is shorter compared to semi-volatile compounds in the closed system, as it is largely determined by condensation sink due to very slow re-evaporation with relatively quick establishment of local equilibrium between the gas phase and the near-surface bulk. The dependence of equilibration timescales on both volatility and bulk diffusivity provides critical insights into thermodynamic or kinetic treatments of SOA partitioning for accurate predictions of gas- and particle-phase concentrations of semi-volatile compounds in regional and global chemical transport models.

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Behrens, Christoph, Elco Luijendijk, Phillip Kreye, Florian Panitz, Merle Bjorge, Marlene Gelleszun, Alexander Renz, Shorash Miro, and Wolfram Rühaak. "TransPyREnd: a code for modelling the transport of radionuclides on geological timescales." Advances in Geosciences 58 (January 18, 2023): 109–19. http://dx.doi.org/10.5194/adgeo-58-109-2023.

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Abstract. The German site selection procedure for a high-level nuclear waste repository is entering a stage in which preliminary safety assessments have to be conducted and the release of radionuclides has to be estimated for a large number of potential sites. Here, we present TransPyREnd, a 1D finite-differences code for modeling the transport of radionuclides in the subsurface at geological timescales. The code simulates the processes advection, diffusion, equilibrium sorption, decay of radionuclides, and the build-up of daughter nuclides. We summarize the modeled physical processes, their mathematical description and our numerical approach to solve the governing equations. Finally, two simple tests are shown, one considering diffusion, sorption, and radioactive decay, the other involving diffusion and a radioactive decay chain. In both tests, the code shows good agreement with the reference solutions. Caveats of the model and future additions are discussed.

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Hessman, F. V. "Dynamo-Induced Mass-Transfer Variations in MCVs." International Astronomical Union Colloquium 190 (2004): 360–64. http://dx.doi.org/10.1017/s0252921100002323.

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AbstractThe fully convective secondary stars in short-period CVs are rapidly rotating and thus should have a characteristic global magnetic field produced by an α2-Dynamo. This field is expected to be dipole-like, with an axis lying in the orbital plane, and to rotate slowly through the mass of the star on magnetic diffusion timescales of years to decades. When one of the poles of this field is near the inner Lagrange point, the reduction in the sound speed, scale-height and possibly the density in the giant “starspot” will modulate the mass-transfer to the primary. Given the extremely high Coriolis numbers (low Rosby numbers) of CV secondaries, this is a generic mechanism which is capable of explaining the extended high- and low-states in the mean light curves of shorter period MCVs and perhaps the lightcurves of non-magnetic CVs (where a disk may make it difficult to see this effect). The diffusion timescale and hence the period of rotation of the field within the secondary is of order the synchronization timescale, so shorter period polar’s are unlikely to be in rotational equilibrium.

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Fowler, Kathryn, Paul J. Connolly, David O. Topping, and Simon O'Meara. "Maxwell–Stefan diffusion: a framework for predicting condensed phase diffusion and phase separation in atmospheric aerosol." Atmospheric Chemistry and Physics 18, no. 3 (February 5, 2018): 1629–42. http://dx.doi.org/10.5194/acp-18-1629-2018.

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Abstract. The composition of atmospheric aerosol particles has been found to influence their micro-physical properties and their interaction with water vapour in the atmosphere. Core–shell models have been used to investigate the relationship between composition, viscosity and equilibration timescales. These models have traditionally relied on the Fickian laws of diffusion with no explicit account of non-ideal interactions. We introduce the Maxwell–Stefan diffusion framework as an alternative method, which explicitly accounts for non-ideal interactions through activity coefficients. e-folding time is the time it takes for the difference in surface and bulk concentration to change by an exponential factor and was used to investigate the interplay between viscosity and solubility and the effect this has on equilibration timescales within individual aerosol particles. The e-folding time was estimated after instantaneous increases in relative humidity to binary systems of water and an organic component. At low water mole fractions, viscous effects were found to dominate mixing. However, at high water mole fractions, equilibration times were more sensitive to a range in solubility, shown through the greater variation in e-folding times. This is the first time the Maxwell–Stefan framework has been applied to an atmospheric aerosol core–shell model and shows that there is a complex interplay between the viscous and solubility effects on aerosol composition that requires further investigation.

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Sheng, Nan, YuSong Tu, Pan Guo, RongZheng Wan, and HaiPing Fang. "Asymmetrical free diffusion with orientation-dependence of molecules in finite timescales." Science China Physics, Mechanics and Astronomy 56, no. 6 (May 7, 2013): 1047–52. http://dx.doi.org/10.1007/s11433-013-5081-x.

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Marschall, Horst R., and Ming Tang. "High-Temperature Processes: Is it Time for Lithium Isotopes?" Elements 16, no. 4 (August 1, 2020): 247–52. http://dx.doi.org/10.2138/gselements.16.4.247.

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The field of high-temperature Li isotope geochemistry has been rattled by major paradigm changes. The idea that Li isotopes could be used to trace the sources of fluids, rocks, and magmas had to be largely abandoned, because Li diffusion causes its isotopes to fractionate at metamorphic and magmatic temperatures. However, diffusive fractionation of Li isotopes can be used to determine timescales of geologic processes using arrested diffusion profiles. High diffusivity and strong kinetic isotope fractionation favors Li isotopes as a tool to constrain the durations of fast processes in the crust and mantle, where other geochronometers fall short. Time may be the parameter that high-temperature Li isotope studies will be able to shed much light on.

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Guzik, Joyce Ann. "Element Diffusion in Pulsating Variables." International Astronomical Union Colloquium 139 (1993): 243–51. http://dx.doi.org/10.1017/s0252921100117506.

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AbstractCan pulsation studies yield information on the operation of element diffusion in stars? Can diffusion explain unusual properties of pulsating variables? Element diffusion theory and recent research relevant to these questions will be reviewed, with emphasis on the Sun and δ Scuti stars. High-degree solar p-modes that are sensitive to helium ionization support a reduced convection zone helium abundance consistent with that expected from diffusion. Intermediate-degree p-modes can be used to probe the structure of the convection zone base and constrain possible diffusion-produced composition gradients. δ Scuti variables have shallow convection zones and relatively short diffusion timescales. Helium diffusion may explain unusual period ratios, influence period changes, and affect the amplitudes and light curve shapes of δ Scuti stars.

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Gao, Xueping, Yuanyuan Chen, and Chen Zhang. "Water renewal timescales in an ecological reconstructed lagoon in China." Journal of Hydroinformatics 15, no. 3 (January 29, 2013): 991–1001. http://dx.doi.org/10.2166/hydro.2013.136.

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To improve water quality and construct a landscape lagoon in China, an ecological reconstruction plan for the Qilihai Lagoon (Changli County, Hebei) is proposed. A three-dimensional numerical model (EFDC) was used to study the water renewal capacity in the reconstructed lagoon by using residence time, exposure time and connectivity as timescales. The influences of wind and the depth of the tidal inlet of the lagoon on water renewal capacity were also investigated. The results show that the transport and diffusion processes in the lagoon were strongly influenced by wind and the modification of the tidal inlet. The lagoon under a no wind condition exhibited a low water renewal capacity, especially at the end areas (exposure time, 700–1,000 days). The wind action notably enhanced the water renewal capacity in the lagoon, and the exposure times were all lower than 400 days in the whole region. The optimal inlet depth for the water renewal in the lagoon was predicted to be 4.0 m. The connectivity matrices identified which areas of the domain would be most affected by a pollution source under different conditions. This study examines transport and diffusion processes in a reconstructed lagoon, which could be informative for ecological reconstruction planning.

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Smith, Albert A., Nicolas Bolik-Coulon, Matthias Ernst, Beat H. Meier, and Fabien Ferrage. "How wide is the window opened by high-resolution relaxometry on the internal dynamics of proteins in solution?" Journal of Biomolecular NMR 75, no. 2-3 (March 2021): 119–31. http://dx.doi.org/10.1007/s10858-021-00361-1.

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AbstractThe dynamics of molecules in solution is usually quantified by the determination of timescale-specific amplitudes of motions. High-resolution nuclear magnetic resonance (NMR) relaxometry experiments—where the sample is transferred to low fields for longitudinal (T1) relaxation, and back to high field for detection with residue-specific resolution—seeks to increase the ability to distinguish the contributions from motion on timescales slower than a few nanoseconds. However, tumbling of a molecule in solution masks some of these motions. Therefore, we investigate to what extent relaxometry improves timescale resolution, using the “detector” analysis of dynamics. Here, we demonstrate improvements in the characterization of internal dynamics of methyl-bearing side chains by carbon-13 relaxometry in the small protein ubiquitin. We show that relaxometry data leads to better information about nanosecond motions as compared to high-field relaxation data only. Our calculations show that gains from relaxometry are greater with increasing correlation time of rotational diffusion.

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Rodríguez-Sánchez, Jesús, Teresa Liberto, Catherine Barentin, and Dag Kristian Dysthe. "Mechanisms of Phase Transformation and Creating Mechanical Strength in a Sustainable Calcium Carbonate Cement." Materials 13, no. 16 (August 13, 2020): 3582. http://dx.doi.org/10.3390/ma13163582.

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Calcium carbonate cements have been synthesized by mixing amorphous calcium carbonate and vaterite powders with water to form a cement paste and study how mechanical strength is created during the setting reaction. In-situ X-ray diffraction (XRD) was used to monitor the transformation of amorphous calcium carbonate (ACC) and vaterite phases into calcite and a rotational rheometer was used to monitor the strength evolution. There are two characteristic timescales of the strengthening of the cement paste. The short timescale of the order 1 h is controlled by smoothening of the vaterite grains, allowing closer and therefore adhesive contacts between the grains. The long timescale of the order 10–50 h is controlled by the phase transformation of vaterite into calcite. This transformation is, unlike in previous studies using stirred reactors, found to be mainly controlled by diffusion in the liquid phase. The evolution of shear strength with solid volume fraction is best explained by a fractal model of the paste structure.

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Shea, Thomas, Fidel Costa, Daniel Krimer, and Julia Eve Hammer. "Accuracy of timescales retrieved from diffusion modeling in olivine: A 3D perspective." American Mineralogist 100, no. 10 (October 2015): 2026–42. http://dx.doi.org/10.2138/am-2015-5163.

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Verbitsky, Mikhail Y., and Michel Crucifix. "ESD Ideas: The Peclet number is a cornerstone of the orbital and millennial Pleistocene variability." Earth System Dynamics 12, no. 1 (January 12, 2021): 63–67. http://dx.doi.org/10.5194/esd-12-63-2021.

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Abstract. We demonstrate here that a single physical phenomenon, specifically, a naturally changing balance between intensities of temperature advection and diffusion in the viscous ice media, may influence the entire spectrum of the Pleistocene variability from orbital to millennial timescales.

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Fouvry, J. B., C. Pichon, and P. H. Chavanis. "The secular evolution of discrete quasi-Keplerian systems." Astronomy & Astrophysics 609 (January 2018): A38. http://dx.doi.org/10.1051/0004-6361/201731088.

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A discrete self-gravitating quasi-Keplerian razor-thin axisymmetric stellar disc orbiting a massive black hole sees its orbital structure diffuse on secular timescales as a result of a self-induced resonant relaxation. In the absence of collective effects, such a process is described by the recently derived inhomogeneous multi-mass degenerate Landau equation. Relying on Gauss’ method, we computed the associated drift and diffusion coefficients to characterise the properties of the resonant relaxation of razor-thin discs. For a disc-like configuration in our Galactic centre, we showed how this secular diffusion induces an adiabatic distortion of orbits and estimate the typical timescale of resonant relaxation. When considering a disc composed of multiple masses similarly distributed, we have illustrated how the population of lighter stars will gain eccentricity, driving it closer to the central black hole, provided the distribution function increases with angular momentum. The kinetic equation recovers as well the quenching of the resonant diffusion of a test star in the vicinity of the black hole (the “Schwarzschild barrier”) as a result of the divergence of the relativistic precessions. The dual stochastic Langevin formulation yields consistent results and offers a versatile framework in which to incorporate other stochastic processes.

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Tcaciuc, A. Patricia, Raffaella Borrelli, Luciano M. Zaninetta, and Philip M. Gschwend. "Passive sampling of DDT, DDE and DDD in sediments: accounting for degradation processes with reaction–diffusion modeling." Environmental Science: Processes & Impacts 20, no. 1 (2018): 220–31. http://dx.doi.org/10.1039/c7em00501f.

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Watkins, James M., and Michael A. Antonelli. "Beyond Equilibrium: Kinetic Isotope Fractionation in High-Temperature Environments." Elements 17, no. 6 (December 1, 2021): 383–88. http://dx.doi.org/10.2138/gselements.17.6.383.

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Igneous and metamorphic rocks exhibit greater isotopic heterogeneity than expected from equilibrium. Large nonequilibrium isotope effects can arise from diffusion and chemical reactions, such as crystal growth and dissolution. The effects are time-dependent and can, therefore, be used to probe timescales of igneous and metamorphic processes that are inaccessible to direct observation. New discoveries of isotopic variability in nature, informed by diffusion and reaction modeling, can provide unique insights into the formation of rocks in the interiors of planetary bodies.

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Hamster, C. H. S., and H. J. Hupkes. "Stability of Traveling Waves on Exponentially Long Timescales in Stochastic Reaction-Diffusion Equations." SIAM Journal on Applied Dynamical Systems 19, no. 4 (January 2020): 2469–99. http://dx.doi.org/10.1137/20m1323539.

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38

Shi, Yanchao, and Peiyong Zhu. "Synchronization of Stochastic Competitive Neural Networks with Different Timescales and Reaction-Diffusion Terms." Neural Computation 26, no. 9 (September 2014): 2005–24. http://dx.doi.org/10.1162/neco_a_00629.

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We propose a feedback controller for the synchronization of stochastic competitive neural networks with different timescales and reaction-diffusion terms. By constructing a proper Lyapunov-Krasovskii functional, as well as employing stochastic analysis theory, the LaShall-type invariance principle for stochastic differential delay equations, and a linear matrix inequality (LMI) technique, a feedback controller is designed to achieve the asymptotical synchronization of coupled stochastic competitive neural networks. A simulation example is given to show the effectiveness of the theoretical results.

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Jollands, Michael C., Antony D. Burnham, Hugh St C. O'Neill, Joerg Hermann, and Qing Qian. "Beryllium diffusion in olivine: A new tool to investigate timescales of magmatic processes." Earth and Planetary Science Letters 450 (September 2016): 71–82. http://dx.doi.org/10.1016/j.epsl.2016.06.028.

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Chakraborty, S. "Diffusion modeling as a tool for constraining timescales of evolution of metamorphic rocks." Mineralogy and Petrology 88, no. 1-2 (August 8, 2006): 7–27. http://dx.doi.org/10.1007/s00710-006-0152-6.

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41

Furbish, David Jon, Siobhan L. Fathel, Mark W. Schmeeckle, Douglas J. Jerolmack, and Rina Schumer. "The elements and richness of particle diffusion during sediment transport at small timescales." Earth Surface Processes and Landforms 42, no. 1 (December 19, 2016): 214–37. http://dx.doi.org/10.1002/esp.4084.

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42

Evans, L., M. K. Cameron, and P. Tiwary. "Computing committors via Mahalanobis diffusion maps with enhanced sampling data." Journal of Chemical Physics 157, no. 21 (December 7, 2022): 214107. http://dx.doi.org/10.1063/5.0122990.

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The study of phenomena, such as protein folding and conformational changes in molecules, is a central theme in chemical physics. Molecular dynamics (MD) simulation is the primary tool for the study of transition processes in biomolecules, but it is hampered by a huge timescale gap between the processes of interest and atomic vibrations that dictate the time step size. Therefore, it is imperative to combine MD simulations with other techniques in order to quantify the transition processes taking place on large timescales. In this work, the diffusion map with Mahalanobis kernel, a meshless approach for approximating the Backward Kolmogorov Operator (BKO) in collective variables, is upgraded to incorporate standard enhanced sampling techniques, such as metadynamics. The resulting algorithm, which we call the target measure Mahalanobis diffusion map (tm-mmap), is suitable for a moderate number of collective variables in which one can approximate the diffusion tensor and free energy. Imposing appropriate boundary conditions allows use of the approximated BKO to solve for the committor function and utilization of transition path theory to find the reactive current delineating the transition channels and the transition rate. The proposed algorithm, tm-mmap, is tested on the two-dimensional Moro–Cardin two-well system with position-dependent diffusion coefficient and on alanine dipeptide in two collective variables where the committor, the reactive current, and the transition rate are compared to those computed by the finite element method (FEM). Finally, tm-mmap is applied to alanine dipeptide in four collective variables where the use of finite elements is infeasible.

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Charlesworth, Edward J., Ann-Kristin Dugstad, Frauke Fritsch, Patrick Jöckel, and Felix Plöger. "Impact of Lagrangian transport on lower-stratospheric transport timescales in a climate model." Atmospheric Chemistry and Physics 20, no. 23 (December 8, 2020): 15227–45. http://dx.doi.org/10.5194/acp-20-15227-2020.

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Abstract. We investigate the impact of model trace gas transport schemes on the representation of transport processes in the upper troposphere and lower stratosphere. Towards this end, the Chemical Lagrangian Model of the Stratosphere (CLaMS) was coupled to the ECHAM/MESSy Atmospheric Chemistry (EMAC) model and results from the two transport schemes (Lagrangian critical Lyapunov scheme and flux-form semi-Lagrangian, respectively) were compared. Advection in CLaMS was driven by the EMAC simulation winds, and thereby the only differences in transport between the two sets of results were caused by differences in the transport schemes. To analyze the timescales of large-scale transport, multiple tropical-surface-emitted tracer pulses were performed to calculate age of air spectra, while smaller-scale transport was analyzed via idealized, radioactively decaying tracers emitted in smaller regions (nine grid cells) within the stratosphere. The results show that stratospheric transport barriers are significantly stronger for Lagrangian EMAC-CLaMS transport due to reduced numerical diffusion. In particular, stronger tracer gradients emerge around the polar vortex, at the subtropical jets, and at the edge of the tropical pipe. Inside the polar vortex, the more diffusive EMAC flux-form semi-Lagrangian transport scheme results in a substantially higher amount of air with ages from 0 to 2 years (up to a factor of 5 higher). In the lowermost stratosphere, mean age of air is much smaller in EMAC, owing to stronger diffusive cross-tropopause transport. Conversely, EMAC-CLaMS shows a summertime lowermost stratosphere age inversion – a layer of older air residing below younger air (an “eave”). This pattern is caused by strong poleward transport above the subtropical jet and is entirely blurred by diffusive cross-tropopause transport in EMAC. Potential consequences from the choice of the transport scheme on chemistry–climate and geoengineering simulations are discussed.

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English, Niall J., and Christian J. Burnham. "Intra-Cage Structure, Vibrations and Tetrahedral-Site Hopping of H2 and D2 in Doubly-Occupied 51264 Cages in sII Clathrate Hydrates from Path-Integral and Classical Molecular Dynamics." Applied Sciences 11, no. 1 (December 23, 2020): 54. http://dx.doi.org/10.3390/app11010054.

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The intra-cage behaviour of guest H2 and D2 molecules in doubly occupied 51264 cages in structure-II (sII) clathrate hydrates were investigated using classical and path-integral molecular dynamics at 100 K. We probed the structure of tetrahedral sites, proton vibrations, localised molecular rattling timescales at sites, and the jump-diffusion travel of H2 and D2 molecules between sites. The site-diffusion model was correlated with experimental neutron scattering data, and the cage occupancies were then discussed in light of recent state-of-the-art experimental and theoretical findings in the literature.

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Mourenas, D., A. V. Artemyev, J. F. Ripoll, O. V. Agapitov, and V. V. Krasnoselskikh. "Timescales for electron quasi-linear diffusion by parallel and oblique lower-band chorus waves." Journal of Geophysical Research: Space Physics 117, A6 (June 2012): n/a. http://dx.doi.org/10.1029/2012ja017717.

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Li, Yongkun, and Xiaofang Meng. "Synchronisation of generalised stochastic neural networks with delays and reaction-diffusion terms on timescales." International Journal of Dynamical Systems and Differential Equations 5, no. 3 (2015): 248. http://dx.doi.org/10.1504/ijdsde.2015.071005.

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Chakraborty, Sumit. "Diffusion in Solid Silicates: A Tool to Track Timescales of Processes Comes of Age." Annual Review of Earth and Planetary Sciences 36, no. 1 (May 2008): 153–90. http://dx.doi.org/10.1146/annurev.earth.36.031207.124125.

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McDannell, Kalin T., and Rebecca M. Flowers. "Vestiges of the Ancient: Deep-Time Noble Gas Thermochronology." Elements 16, no. 5 (October 1, 2020): 325–30. http://dx.doi.org/10.2138/gselements.16.5.325.

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Ancient rocks have survived plate tectonic recycling for billions of years, but key questions remain about how and when they were exhumed to the surface. Constraining exhumation histories over long timescales is a challenge because much of the rock record has been lost to erosion. Argon and helium noble gas thermochronology can reconstruct deep-time <350 °C thermal histories by using the distinct temperature sensitivities of minerals such as feldspar, zircon, and apatite, while exploiting grain size and radiation damage effects on diffusion kinetics. Resolution of unique time–temperature paths over long timescales requires multiple chronometers, appropriate kinetic models, and inverse simulation techniques to fully explore and constrain possible solutions. Results suggest that surface histories of ancient continental interiors are far from uninteresting and may merely be misunderstood.

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Butler-Caddle, Edward, Nicholas E. Grant, Sophie L. Pain, John D. Murphy, K. D. G. Imalka Jayawardena, and James Lloyd-Hughes. "Terahertz photoconductance dynamics of semiconductors from sub-nanosecond to millisecond timescales." Applied Physics Letters 122, no. 1 (January 2, 2023): 012101. http://dx.doi.org/10.1063/5.0130721.

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Optical pump terahertz probe spectroscopy (OPTP) is a versatile non-contact technique that measures transient photoconductance decays with femtosecond temporal resolution. However, its maximum temporal range is limited to only a few nanoseconds by the mechanical delay lines used. We extended the temporal range of OPTP to milliseconds and longer while retaining sub-nanosecond resolution. A separate pump laser was electrically synchronized to the probe pulses, allowing the pump–probe delay to be controlled with an electronic delay generator. We demonstrated the capabilities of this technique by examining the photoconductance decays of semiconductors with lifetimes ranging over six orders of magnitude: III-Vs, metal halide perovskites, germanium, and silicon. A direct comparison of results on silicon from OPTP and inductively coupled photoconductance decay highlighted the higher spatial and temporal resolution of OPTP, which allowed in-plane and out-of-plane carrier diffusion to be studied.

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Ho, Wynn C. G., Nils Andersson, and Vanessa Graber. "Onset of superconductivity and retention of magnetic fields in cooling neutron stars." Proceedings of the International Astronomical Union 13, S337 (September 2017): 213–16. http://dx.doi.org/10.1017/s174392131700970x.

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AbstractA superconductor of paired protons is thought to form in the core of neutron stars soon after their birth. Minimum energy conditions suggest that magnetic flux is expelled from the superconducting region due to the Meissner effect, such that the neutron star core retains or is largely devoid of magnetic fields for some nuclear equation of state and proton pairing models. We show via neutron star cooling simulations that the superconducting region expands faster than flux is expected to be expelled because cooling timescales are much shorter than timescales of magnetic field diffusion. Thus magnetic fields remain in the bulk of the neutron star core for at least 106 − 107yr. We estimate the size of flux free regions at 107yr to be ≲ 100m for a magnetic field of 1011G and possibly smaller for stronger field strengths.

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Journal articles on the topic 'Diffusion timescales'

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