Saturating Exponential Function Research Articles

Aspect ratio-dependent etching in silicon using XeF2: experimental investigation and comparative analysis with dry etching methods

Abstract Silicon machining plays a crucial role in shaping three-dimensional structures for Micro-Electro-Mechanical Systems (MEMS) applications. This study investigates Aspect Ratio Dependent Etching (ARDE) across various silicon etching processes, with a particular focus on Xenon Difluoride (XeF2) etching, in comparison to Reactive Ion Etching (RIE) and Deep Reactive Ion Etching (DRIE).By exploring different etching parameters, the study highlights the presence of ARDE in both plasma and non-plasma etching processes. Additionally, it is demonstrated that ARDE can be modeled by a saturating exponential function through experimental adjustment of parameters, enabling the prediction of etching profiles.

Reliability of trap-filling parameters read from OSL dose-response curves measured by procedures with sensitivity correction

As is known from the early stimulated luminescence studies, dose-response curves (DRCs) are not consistent with the curves of the dependence of the electron concentration in the traps on the irradiation dose delivered to a crystal, even for a system consisting of one trap and one recombination centre. However, for the optically stimulated luminescence (OSL) signal originating from more complex trap and recombination centre systems, it is often observed that the DRC can be described by a simple single saturating exponential (SSE) or a double saturating exponential (DSE) function. Using simulations, we show that although good fit compliance can often be achieved, the parameters obtained only in some cases correctly describe the relationship between the occupancy of individual traps and the dose. Simulations performed for the DRC construction procedure included a step allowing for the correction of possible changes in sensitivity. A model of two traps active in the OSL process and two recombination centres was tested. The modelling shows that the results of the DRC analysis using SSE functions strongly depend not only on the relationship of the trapping probability coefficients of traps but also on their concentrations and the concentrations of recombination centres. The shape of the DRC, and therefore the fitting parameters, also change with the annealing temperature used in the DRC measurement protocol.

Photoluminescence studies of different types of feldspars and the implications to the dating application using a Raman system

In recent years, the infrared photoluminescence (PL) of feldspar has been explored for geological dating because it offers a great increase in signal intensity with increasing radiation dose. However, a comprehensive understanding of the PL emission spectra of different types of feldspar minerals remains poorly understood and the uncommonly available instruments have hindered its research. In this study, we investigated PL characteristics (e.g., emission spectra and the dependence of PL emission on irradiation dose) of single-crystal alkali and plagioclase feldspars using a commercial Raman microscope instrument configured to excite samples with 532 and 785 nm lasers. The results show that despite being sample-dependent, 2–3 PL bands peaking at ∼2.10 eV (590 nm), 1.75 eV (710 nm), and 1.43 eV (865 nm) under 532 nm laser excitation, and 0–2 peaks ranging from ∼1.44 eV (863 nm) to ∼1.34 eV (925 nm) under 785 nm laser excitation, are broadly observed. These variations in PL bands may be attributed to subtle differences in chemical composition and crystal structure among the feldspar minerals. The sensitivity of PL emission to irradiation dose varies greatly depending on feldspar types and peak positions. The PL intensities of the peaks at ∼1.43 eV (865 nm) are particularly sensitive in K-feldspar, demonstrating their potential applicability for dating applications. Additionally, solar bleaching experiments demonstrate that PL signals of these peaks can be effectively reset by 1.5 h of solar exposure. The dose-response curves obtained using 860–870 nm PL signals of K-feldspar conform to a relationship of a single saturating exponential function between the signal and irradiation dose. Furthermore, this study demonstrates that a commonly available Raman system can be utilized for PL measurements of single grains.

Characteristics of soil moisture limitation and non-limitation in the response of sap flow to transpiration driving factors

Transpiration is a significant part of water cycle in forest ecosystems, influenced by meteorological factors and potentially constrained by soil moisture. We used Granier-type thermal dissipation probes to monitor xylem sap flow dynamics of three tree species (Quercus liaotungensis, Platycladus orientalis, and Robinia pseudoacacia) in a semi-arid loess hilly region, and to continuously monitor the key meteorological factors and soil water content (SWC). We established the SWC thresholds delineating soil moisture-limited and -unlimited sap flow responses to transpiration drivers. The results showed that mean sap flux density (Js) of Q. liaotungensis and R. pseudoacacia was significantly higher during period with higher soil moisture compared to lower soil moisture, while the difference in Js for P. orientalis between the two periods was not significant. We used an exponential saturation function to fit the relationship between the Js of each tree species and the integrated transpiration variable (VT) which reflected solar radiation and vapor pressure deficit. The difference in the fitting curve parameters indicated that there were distinct response patterns between Js and VT under different soil moisture conditions. There was a threshold in soil moisture limitation on sap flow for each species, which was identified as 0.129 m3·m-3 for Q. liaotungensis, 0.116 m3·m-3 for P. orientalis, and 0.108 m3·m-3 for R. pseudoacacia. Below the thresholds, Js was limited by soil moisture. Above these points, the normalized sensitivity index (NSI) for Q. liaotungensis and P. orientalis reached saturation, while that of R. pseudoacacia did not reach saturation but exhibited a significant reduction in moisture limitation. Among the three species, P. orientalis was the most capable of overcoming soil moisture constraints.

Thickness-dependent electronic relaxation dynamics in solution-phase redox-exfoliated MoS2 heterostructures.

Electronic relaxation dynamics of solution-phase redox-exfoliated molybdenum disulfide (MoS2) monolayer and multilayer ensembles are described. MoS2 was exfoliated using polyoxometalate (POM) reductants. This process yields a colloidal heterostructure consisting of MoS2 2D sheet multilayers with surface-bound POM complexes. Using two-dimensional electronic spectroscopy, transient bleaching and photoinduced absorption signals were detected at excitation/detection energies of 1.82/1.87 and 1.82/1.80eV, respectively. Approximate 100-fs bandgap renormalization (BGR) and subsequent defect- and phonon-mediated relaxation on the picosecond timescale were resolved for several MoS2 thicknesses spanning from 1 to 2 L to ∼20 L. BGR rates were independent of sample thickness and slightly slower than observations for chemical vapor deposition-grown MoS2 monolayers. However, defect-mediated relaxation accelerated ∼10-fold with increased sample thicknesses. The relaxation rates increased from 0.33 ± 0.05 to 1.2 ± 0.1 and 3.1 ± 0.4ps-1 for 1-2 L, 3-4 L, and 20 L fractions. The thicknesses-dependent relaxation rates for POM-MoS2 heterostructures were modeled using a saturating exponential function that showed saturation at thirteen MoS2 layers. The results suggest that the increased POM surface coverage leads to larger defect density in the POM-MoS2 heterostructure. These are the first descriptions of the influence of sample thickness on electronic relaxation rates in solution-phase redox-exfoliated POM-MoS2 heterostructures. Outcomes of this work are expected to impact the development of solution-phase exfoliation of 2D metal-chalcogenide heterostructures.

Defining Mammalian Lifespan through Epigenetic Aging Timescales

The lifespans of mammalian species vary across orders of magnitude, with the shortest on the order of a year and the longest more than one hundred years. These lifespans are influenced by both genetic and environmental factors. Here we asked whether we can define a molecular process that can be used to define the intrinsic molecular lifespan of a species that is largely independent of environmental factors. To address this question, we have focused on ‘epigenetic clocks’ - highly accurate age-predicting biomarkers based on DNA methylation. Our previous research has demonstrated that the alterations in DNA methylation related to age are non-linear, changing rapidly early in life and slowing down with advancing age. We have proposed the use of saturating exponential functions to represent these changes, which tend to stabilize at terminal methylation levels towards the end of an organism's lifespan. Our current study expands upon this by examining the exponential aging timescales across various mammalian species. We show that the DNA methylation trajectories of a broad range of species, ranging from mice to humans, adhere to a saturating exponential function. Furthermore, we find the timescale of this exponential decay to be about one third of a species’ lifespan. This striking and novel observation implies that we can define an intrinsic molecular lifespan of a species that is largely unaffected by environmental factors. Although the exact mechanisms behind the variation in species-specific rates remain unclear, we hypothesize that they may be linked to the distinct metabolic rates found in each species.

Dynamic modeling of Haidinger's brush phenomenon and analysis of the cornea effect based on the model

Starting from the dynamic feature of the vision process and taking into account the time constants of the polarization-dependent process of cones, this study proposed a physical model that can mathematically describe the transient nature of Haidinger’s brushes (HB). A saturated exponential growth function was proposed to describe the dynamic process, and the corresponding formulas were derived and discussed. The sensitivities of both static and rotating HB were considered in the model, and the visibility of HB was also investigated. Additionally, the impact of the cornea on the visions of HB was examined by using this model. Analytical results reveal that there exist two types of patterns in the rotating HB phenomenon. The visual perception of the rotating HB is related to the magnitude and interaction of these two patterns, as well as the corneal phase shift. The rotation orientation reversal at large corneal phase shifts observed by some researchers can also be explained by the model. The results are consistent with experimental observations and might help with the clinical diagnosis of macula disorders and corneal abnormalities.

Recombination centres' competition impact on the OSL dose-response curve determined by the procedure with sensitivity correction

The shape of the dose-response curve (DRC) of the OSL signal in the high dose range limits the dating range. No agreement between natural and laboratory DRC for doses close to saturation is indicated in OSL dating using quartz. The natural curve rises slower to a saturation level that is clearly lower than the saturation level of the laboratory curve. The latter is often a sum of a single saturating exponential function and a linear increase up to several kGy. Previous studies have shown that by changing the procedure for the DRC determining, one can extend the range of agreement of the curves, obtaining a slower growth of the laboratory curve. Processes occurring in the sample during the DRC determination procedure strongly influence its shape. The present study concerns the dependency of the DRC shape for doses close to saturation on the concentrations and parameters of centres participating in the OSL process. The research is for a model involving two OSL traps, one deep trap not emptied during the construction of the DRC and two recombination centres. One simulated the entire procedure of the DRC determination with OSL sensitivity control. Studies show that the DRC shape in the high dose range is primarily due to the competition of recombination centres.

Electron spin resonance (ESR) study on gamma irradiated some modern paper samples

In this work, we use paramagnetic defects induced by gamma radiation in some modern paper samples to determine their main dosimetric properties in the decontamination dose range (0.5–10 kGy) of ancient papers. Electron spin resonance (ESR) spectra of photo paper, cigarette paper, white paper napkin (napkin), cash register receipt, straw paper and white photocopy paper recorded before and after irradiation with gamma rays were reported. Photo paper, cigarette paper and napkin samples displayed the radiation-induced cellulose-like ESR signals well known from the literature on cellulose-containing foods. Cash register receipt, straw paper, and white photocopy paper are another set of samples where different ESR spectra were recorded. The ESR signals of these three paper samples were shown to originate from carbonate mineral filler grains. Inorganic mineral fillers are commonly used in paper manufacturing. The dose-response curves associated with the radiation-induced sharp ESR signals originating from the CaCO3 filler of the cash register receipt (g = 2.0027), the straw paper (g = 1.9995), and the white photocopy paper (g = 1.9996) were found to follow a single exponential saturation function. Despite the observed decreases with time in the signal intensities of cash register receipt and white photocopy paper, detectable ESR signals were obtained even 100 days after irradiation for them and straw paper. The radiation-induced free radicals responsible for the ESR spectrum of straw paper were more stable than those of cash register receipt and white photocopy paper. The results indicate that free radicals induced in mineral CaCO3 filler grains incorporated within papers have the potential to be used for application to retrospective ESR dosimetry in the range of 0.5–10 kGy.

A new analytical model for the response curve in megavoltage photon beams of the radiochromic EBT3 films measured with flatbed scanners.

PurposeThe aim of this work is to study a new analytical model which describes the dose–response curve in megavoltage photon beams of the radiochromic EBT3 film measured with two commercially available flatbed scanners. This model takes into account the different increase of the number of two types of absorbents in the film with absorbed dose and it allows to identify parameters that depend on the flatbed scanner and the film model, and parameters that exclusively depend on the production lot. In addition, the new model is also compared with other models commonly used in the literature in terms of its performance in reducing systematic calibration uncertainties.Methods and materialsThe new analytical model consists on a linear combination of two saturating exponential functions for every color channel. The exponents modeling the growing of each kind of absorbent are film model and scanner model‐dependent, but they do not depend on the manufacturing lot. The proposed model considers the different dose kinetics of each absorbent and the apparent effective behavior of one of the absorbents in the red color channel of the scanner.The dose–response curve has been measured using EBT3 films, a percentage depth dose (PDD) calibration method in a dose range between 0.5 and 25 Gy, and two flatbed scanners: a Microtek 1000 XL and an EPSON 11000 XL. The PDD calibration method allows to obtain a dense collection of calibration points which have been fitted to the proposed response curve model and to other published models. The fit residuals were used to evaluate the performance of each model compared with the new analytical model.ResultsThe model presented here does not introduce any systematic deviations up to the degree of accuracy reached in this work. The residual distribution is normally shaped and with lower variance than the distributions of the other published models. The model separates the parameters reflecting specific characteristics of the dosimetry system from the linear parameters which depend only on the production lot and are related to the relative abundance of each type of absorbent. The calibration uncertainty is reduced by a mean factor of two by using this model compared with the other studied models.ConclusionsThe proposed model reduces the calibration uncertainty related to systematic deviations introduced by the response curve. In addition, it separates parameters depending on the flatbed scanner and the film model from those depending on the production lot exclusively and therefore provides a better characterization of the dosimetry system and increases its reliability.

ESR dosimetric properties of gamma irradiated different origin eyeglass samples

In the present research, mineral and organic origin eyeglasses (CR-39) were examined with respect to their potential application in the dosimetry of ionizing radiation by using electron spin resonance (ESR) technique. Before irradiation, organic and mineral origin eyeglasses did not exhibit any ESR signal. But they do produce radiation-induced ESR spectra after gamma irradiation. The variations of the radiation-induced resonance signals of organic and mineral origin eyeglasses with microwave power and modulation amplitude were investigated and the optimum spectrometer operating conditions were determined. The dose-response curves of the organic and mineral origin eyeglasses exposed to gamma radiations were found to be described well by a linear and single exponential saturation functions in the dose ranges of 0.1–10 and 0.05–10 kGy, respectively. For mineral eyeglasses this behavior was linear at lower doses (0.05–1 kGy). Despite the observed fading with time in the signal intensity, measurable ESR signals were obtained even 54 days after irradiation for organic origin eyeglass, while the corresponding value for the mineral eyeglass was 154 days. The study also showed that the thermal stability of the radiation-induced ESR signal of mineral eyeglass sample was higher than the signal of organic origin eyeglass.

Dose rate correction for a silicon diode detector array.

PurposeA signal dependence on dose rate was reported for the ArcCHECK array due to recombination processes within the diodes. The purpose of our work was to quantify the necessary correction and apply them to quality assurance measurements.MethodsStatic 10 × 10 cm2 6‐MV fields delivered by a linear accelerator were applied to the detector array while decreasing the average dose rate, that is, the pulse frequency, from 500 to 30 MU/min. An ion chamber was placed inside the ArcCHECK cavity as a reference. Furthermore, the instantaneous dose rate dependence (DRD) was studied. The position of the detector was adjusted to change the dose‐per‐pulse, varying the distance between the focus and the diode closest to the focus between 69.6 and 359.6 cm. Reference measurements were performed with an ion chamber placed inside a PMMA slab phantom at the same source‐to‐detector distances (SDDs). Exponential saturation functions were fitted to the data, with different parameters to account for two generations of ArcCHECK detectors (types 2 and 3) and both DRDs. Corrections were applied to 12 volumetric modulated arc therapy plans.ResultsThe sensitivity decreased by up to 2.8% with a decrease in average dose rate and by 9% with a decrease in instantaneous dose rate. Correcting the average DRD, the mean gamma pass rates (2%/2‐mm criterion) of the treatment plans were improved by 5 percentage points (PP) for diode type 3 and 0.4 PP for type 2. Correcting the instantaneous DRD, the improvement was 8.4 PP for type 3 and 0.9 PP for type 2.ConclusionsThe instantaneous DRD was identified as the prevailing effect on the diode sensitivity. We developed and validated a method to correct this behavior. The number of falsely not passed treatment plans could be considerably reduced.

Assessment of myelination in infants and young children by T1 relaxation time measurements using the magnetization-prepared 2 rapid acquisition gradient echoes sequence

BackgroundAxonal myelination is an important maturation process in the developing brain. Increasing myelin content correlates with the longitudinal relaxation rate (R1=1/T1) in magnetic resonance imaging (MRI).ObjectiveBy using magnetization-prepared 2 rapid acquisition gradient echoes (MP2RAGE) on a 3-T MRI system, we provide R1 values and myelination rates for infants and young children.Materials and methodsAverage R1 values in white and grey matter regions in 94 children without pathological MRI findings (age range: 3 months to 6 years) were measured and fitted by a saturating-exponential growth model. For comparison, R1 values of 36 children with different brain pathologies are presented. The findings were related to a qualitative evaluation using T2, magnetization-prepared rapid acquisition gradient echo (MP-RAGE) and MP2RAGE.ResultsR1 changes rapidly in the first 16 months of life, then much slower thereafter. R1 is highest in pre-myelinated structures in the youngest subjects, such as the posterior limb of the internal capsule (0.74–0.76±0.04 s−1) and lowest for the corpus callosum (0.37–0.44±0.03 s−1). The myelination rate is fastest in the corpus callosum and slowest in the deep grey matter. R1 is decreased in hypo- and dysmyelination disorders. Myelin maturation is clearly visible on MP2RAGE, especially in the first year of life.ConclusionMP2RAGE permits a quantitative R1 mapping method with an examination time of approximately 6 min. The age-dependent R1 values for children without MRI-identified brain pathologies are well described by a saturating-exponential function with time constants depending on the investigated brain region. This model can serve as a reference for this age group and to search for indications of subtle pathologies. Moreover, the MP2RAGE sequence can also be used for the qualitative assessment of myelinated structures.

Kinetics of nanoscale probe-based contact electrification between metal and polymethyl methacrylate under bias

Contact electrification (CE) has the potential to be a renewable energy resource, because it converts mechanical energy to electrical energy. The kinetics of probe-based CE between metal and polymeric slab was studied by scanning probe microscopy. The CE static charges were produced on polymethyl methacrylate (PMMA) films by a Pt-coated probe under a bias (VB) and characterized by electrostatic force microscopy. The metal/PMMA CE was attributed to the charge transfer between the Fermi level of the metal (Ef) and the neutral level of the surface states of PMMA (En). The kinetics of the probe-based metal/PMMA CE was described by a saturating exponential function and the saturated charge QS was proportional to the net bias, VB − Vnull, where the nulling bias Vnull = −(En − Ef)/e. The kinetics was regarded as the charging to a conductor–capacitor series circuit. QS established a potential to cancel the net bias and ceased the CE. CE was a reversible process, and its transmission coefficient was asymmetric with the polarity of bias because of the heterogeneous nature of the metal/polymer contact.

Effects of environment and canopy structure on stem sap flow in a Larix principis-rupprechtii plantation.

Accurately quantifying the impacts of environmental factors and canopy structure on stem sap flow is of great significance for deeply understanding water use strategies of trees in changing environment. The stem sap flow of Larix principis-rupprechtii plantation was observed using thermal diffusion probes from June to September of 2019 in the Xiangshuihe small watershed of Liupan Mountains, with the meteorological conditions, root-zone soil water content and canopy structure being simultaneously recorded. We first analyzed the relationships of sap flow rate (Jc) to potential evapotranspiration (PET), relative extract water (REW) and canopy leaf area index (LAI), and then quantified their relative contribution to Jc. The results showed that the response of Jc to PET, LAI, and REW conformed to binomial, linearly increase and saturated exponential function, respectively. The Jc model coupling multiple factors was established as a continuous multiplication of the response functions of Jc to PET, REW and LAI, which had good simulation precision. PET was the main factor leading to the difference of Jc in different weather conditions. The average contribution rate of PET had obvious difference in sunny (with a contribution rate of 40.3%), cloudy (4.3%), and rainy days (-26.3%). PET and LAI were the leading factors affecting the Jc variation among months. The ranges of the contribution rates of PET and LAI were from -23.1% to 16.8% and from -12.3% to 11.0%, respectively. The Jc model coupling the multi-factor effect developed in this study could be used to predict Jc, and quantify the impacts of each leading factor, which had the potential to be an effective tool to analyze the water use of trees in the changing environment.

Separating meteorological condition and soil moisture controls on the variation in stand evapotranspiration of a larch plantation during three hydrological years

Evapotranspiration (ET) is an essential component of the forest stand water budget, and the main factors controlling ET variations are meteorological conditions and soil moisture. A deep understanding of their impacts on ET is crucial for forest water management and sustainable development in changing environments. However, the independent effects of meteorological conditions and soil moisture on ET are not clear because their impacts occur concurrently under natural environmental conditions. In this study, a relatively simple but mechanism-based forest stand ET model that couples the effects of the reference ET (ETo) and relative extractable water (REW) in the 0–60 cm soil layer was developed to quantify the independent impacts of ETo and REW on ET. The model was established based on observed stand transpiration, forest floor ET, meteorological conditions, and soil water content obtained on non-rainfall days of the 2015, 2016, and 2019 growing seasons from a larch (Larix principis-rupprechtii) plantation in Northwest China. The following key results were obtained. (1) At this sub-humid site, the weather-dependent ET increased linearly with rising ETo; daily ET initially increased rapidly with rising REW, and then gradually reached a threshold; thereafter, it tended to be stable. The response could be described by an exponential saturation function. (2) The daily stand ET model that coupled these response functions to individual factors was determined as ET = 0. 785 × [ETo × (1 – EXP(–13.567REW))]. (3) The contributions of ETo and REW were further determined using the new ET model, and the results show that ETo was the main driving factor affecting the ET variations in three different hydrological years compared with REW and the interaction of ETo and REW. Compared with those in the normal year 2015, REW and ETo limited the ET variation in the dry year 2016 by 13.1% and 7.3%, respectively, and ETo limited the ET variation in the wet year 2019 by 8.8%. Our study provides a simple and feasible method for separating the meteorological conditions (i.e., ETo) and soil moisture controls on ET variations, and can improve the understanding of the impacts of varying environments on ET.

Estimate canopy transpiration in larch plantations via the interactions among reference evapotranspiration, leaf area index, and soil moisture

Accurately modelling and predicting forest transpiration under changing environment and canopy structure are essential for understanding the interactions among the atmosphere, soil, and vegetation and precisely integrating forest water management. To enhance water management in larch plantations, the canopy transpiration (T), reference evapotranspiration (ETo), canopy leaf area index (LAI), and relative extractable water (REW) of the 0–60 cm soil layer were synchronously monitored during the growing season (May–September) in 2016 and 2018. The response functions of the basal crop coefficient (Kcb) in an ETo-based transpiration model to individual driving factors (LAI and REW) were determined using upper boundary lines and then coupled to form the T model using the crop coefficient method. The results showed that (1) the mean (and range) of the daily canopy T was 0.83 (0.003–1.60) mm·d−1 in dry year of 2016, and 0.70 (0.02–1.55) mm·d−1 in wet year of 2018. (2) The Kcb increased with rising LAI, following a positive linear relation. With rising REW, Kcb first increased rapidly and then stabilized gradually following a saturated exponential function. (3) The daily T model was fitted as T=(0.056 + 0.083(1-exp(-3.915REW))) (0.961LAI) ETo and had good performance in both the calibration period (R2 = 0.78; NSE = 0.77) and validation period (R2 = 0.85; NSE = 0.75). (4) The relative importance of ETo, LAI, and REW on T were analysed based on the developed T model. The results showed that the average contribution of ETo, LAI, and REW to T differed in various years. The dominant factor contributing to the changes in T was ETo followed by REW and LAI in dry year of 2016 and LAI followed by ETo and REW in wet year of 2018 compared with the reference T under the long-term means of the daily ETo, LAI, and REW. The newly developed simple T model in this study represents a key step for the comprehensive integrated management of forests and water and accurately predicts the response of the daily canopy T to varying LAI values under a given REW and ETo, which is helpful for designing precise adjustments of stand structure.

Responses of transpiration to variation in evaporative demands and soil water in a larch plantation at the south side of Liupan Mountains, China

Quantifying the response of tree transpiration (T) to the variation of soil water supply capability and atmospheric evaporative demand is beneficial for a better prediction of water use and hydrological cycles in forests and deepen the understanding of the relationship between forest and water. Larix principis-rupprechtii in the Xiangshuihe watershed at the south side of Liupan Mountains was used as the research object. We simultaneously monitored sap flow density by thermal diffusion probe and the environmental factors. The response of the T to the soil volumetric water content (VWC) and potential evapotranspiration (PET) was analyzed. The results showed the response curve of T to VWC was quite similar under any different PET levels. With increasing VWC, T increased rapidly and then slowly, and began to be stable when VWC reached a threshold. This process could be well fitted by the saturated exponential function. However, the VWC threshold was different, and its value increased with rising PET. The relationship of daily T to PET was a quadra-tic equation, and PET also had a threshold effect. A stand transpiration model considering the effect of soil water supply capacity and atmospheric evaporative potential was founded which coupled the response relationship of T to PET and VWC in the rapid growth season. This model could well estimate the diurnal variation of transpiration, and provide guidance for the management of plantation water control.

A new analytical equation for the dose response of dosimetric materials, based on the Lambert W function

The dose response of dosimetric materials is of fundamental importance in luminescence dosimetry and luminescence dating applications. In this paper we present a new analytical equation describing the trap filling process during irradiation of insulators, starting from the one trap and one recombination center model (OTOR). Even though this model has been studied extensively during the past 50 years, there are no published analytical solutions for the dose response n(D) in this model, where n is the concentration of filled traps and D is the irradiation dose. The new analytical equation contains the well-known Lambert function W, which has been used extensively during the past 20 years in diverse research areas. Under certain conditions, the new n(D) equation leads to the empirical saturating exponential function (SE). The new equation contains a smaller number of fitting parameters than two other commonly used fitting functions, the saturating exponential plus a linear function (SEL), and the double saturating exponential (DSE). In addition, the new equation contains physically meaningful parameters. Examples are shown of using the new equation to fit a variety of experimental signals, namely thermoluminescence (TL), optically simulated luminescence (OSL), isothermal TL (ITL) and electron spin resonance (ESR).

Phenomenological model of aluminium-hole ([AlO4/h+]0) defect formation in sedimentary quartz upon room temperature irradiation: electron spin resonance (ESR) study

The mechanism governing the production of the paramagnetic [AlO4/h+]0 centres (denoted also as Al-hole or Al-h) in quartz as a function of given dose is of great importance in electron spin resonance (ESR) dating, as the analytical function used to characterise the evolution of this centre with accumulated dose is used to derive the equivalent dose by extrapolation to the abscissa-axis. The single saturating exponential model fails to accurately represent the dose response curve especially at high doses, and consequently, empirical functions, such as a saturating exponential plus a linear term, are widely used in the dating community. Herein, a physical phenomenological model is presented to describe the Al-hole formation under gamma irradiation in sedimentary quartz. Based on previous studies it is known that the Al-hole centre is formed via the dissociation of the Al centres compensated with alkali ions [AlO4/M+]0 (generally denoted as Al-M) where M+ could be Li+, Na+ or K+, as well as by the dissociation of Al compensated with hydrogen ions [AlO4/H+]0, (denoted as Al–H). When irradiation moves interstitial alkali ions away from the aluminium ions, they can be replaced by H+ ions beside the conversion to Al-hole centres. By assuming that the rate of the dissociation process is proportional to the concentration of the defects themselves, a sum of saturating exponential functions is obtained for describing the growth of Al-hole with dose. The model is applied on data obtained on sedimentary quartz specimens of different origins for describing the dose response of the paramagnetic Al-hole ESR signal. We are showing that the signal of Al-hole does not reach full saturation at doses even as high as 100 kGy and can it be well represented by two exponential components as predicted by the model. As such, the additional linear term reported by other works when describing the dose response is just a first order approximation of one of the saturating exponential functions.