Linear Proportion Research Articles

Wavefront-correction for nearly diffraction-limited focusing of dual-color laser beams to high intensities.

We demonstrate wavefront correction of terawatt-peak-power laser beams at two distinct and well-separated wavelengths. Simultaneous near diffraction-limited focusability is achieved for both the fundamental (800 nm) and second harmonic (400 nm) of Ti:sapphire-amplified laser light. By comparing the relative effectiveness of various correction loops, the optimal ones are found. Simultaneous correction of both beams of different color relies on the linear proportionality between their wavefront aberrations. This method can enable two-color experiments at relativistic intensities.

Abstract 5333: A mathematical model for the kinetics of metastasis formation based on SEER data

Abstract Metastasis is responsible for most cancer mortality, yet many questions remain about how best to describe the kinetics of metastasis formation mathematically. Because the initial step of metastasis is the detachment of cells from a tumor mass, the rate of formation of new metastases is assumed to depend on the size of the original tumor mass. A power-law dependence, rather than linear proportionality, has been assumed, since access to blood vessels and lymphatics becomes more limited as tumor mass increases. Under this assumption, the cumulative distribution of fraction of patients not showing detectable metastases at diagnosis should decrease monotonically as tumor size at detection increases. Using data from the NCI's SEER (Surveillance, Epidemiology, and End Results) 1973-2010 database, it is shown here that this relation in fact shows non-monotonic behavior at larger detection sizes. A mathematical model for tumor growth and metastasis kinetics is developed to show that this implies that proliferation rates and metastatic rates are not independently distributed across the patient population, but rather, show some correlation. The model is further applied to deduce quantitative information about the size-dependence of the rate of metastasis. Kaplan-Meier curves stratified by tumor size, also computed from SEER 1973-2010 data, provide an additional data source for determining model parameters. It is found that accounting for age dependence is necessary for fitting these curves. Two possible age-related effects: a lower lethal tumor burden threshold; and an increased coefficient of metastatic rate due to declining immunity; are considered in the model, and a comparison is made of their ability to describe the observed age-dependence. In sum, the model shows how SEER data can be used to deduce information about the kinetics of metastasis formation, and is expected to have application in optimization of the treatment of metastatic tumors as well as screening schedules. Citation Format: Ardith W. El-Kareh, Timothy W. Secomb. A mathematical model for the kinetics of metastasis formation based on SEER data. [abstract]. In: Proceedings of the 105th Annual Meeting of the American Association for Cancer Research; 2014 Apr 5-9; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2014;74(19 Suppl):Abstract nr 5333. doi:10.1158/1538-7445.AM2014-5333

Application of evolved gas analysis to cold-cap reactions of melter feeds for nuclear waste vitrification

Abstract In the vitrification of nuclear wastes, the melter feed (a mixture of nuclear waste and glass-forming and modifying additives) experiences multiple gas-evolving reactions in an electrical glass-melting furnace. We employed the thermogravimetry-gas chromatography–mass spectrometry (TGA-GC–MS) combination to perform evolved gas analysis (EGA). Along with identifying the gases evolved, we performed quantitative analysis relating the weighted sum of intensities of individual gases in linear proportion with the differential thermogravimetry. The proportionality coefficients were obtained by three methods based on the stoichiometry, least squares, and calibration. The linearity was shown to be a good first-order approximation, in spite of the complicated overlapping reactions.

Engineering properties of alkali-activated binders by use of desulfurization slag and GGBFS

In this study, industrial by-products desulphurization slag powder (DS-P) and ground granulated blast furnace slag (GGBFS) were used as the raw materials for producing non-Portland-cement binders. Material properties and microstructures of the constituents were examined. Fresh behaviors, hardening properties and microstructures of the mortars made with these binders are also investigated. Experimental results showed that DS-P can provide sufficient alkali environment for activating the pozzolanic reactions of GGBFS. The mortar compressive strengths were shown to attain 17MPa at 28days of age. A linear proportion between DS-P content and required water amount is also found in the flow test. Increasing the amount of GGBFS would result in a shortened setting time; while increasing the DS-P content would gain a shorten time interval between initial and final setting. Our results suggested that the high alkali feature of DS-P can trigger the pozzolanic reactions of GGBFS mixtures for producing non-Portland-cement binders with satisfying qualities.

Emission of Organically Bound Elements during the Pyrolysis and Char Oxidation of Lignites in Air and Oxyfuel Combustion Mode

This study aims to clarify the abundance of individual elements, particularly those in trace concentrations in lignites, and their emission dynamics during pyrolysis and char oxidation in both air and oxyfuel combustion modes. For this laboratory-scale study, the emission dynamics was represented by element release from the coal/char particle during thermal treatment in a drop-tube furnace. The main coal sample studied is a Victorian brown coal (VBC), which was compared with a Chinese lignite. Irrespective of elemental type, the VBC is rich in organically bound elements, which partly dissociated during the initial flash pyrolysis step. This dissociation extent varied broadly with elemental type. For element release during char oxidation, As release rates in both N2 and CO2 bulk gases were slower than char surface consumption rate, because of internal diffusion limitations and scavenging of a portion of As by Ca/Al/Fe-bearing discrete minerals. In contrast, the release rates of Pb from the char surface were faster than the carbon consumption rate. Releases of the remaining elements were simply in linear proportion to the char consumption rate for the two lignites studied, despite their differences in properties with no observable (element release) difference between air and oxyfuel combustion mode.

Optimization of operating conditions and structure parameters of zinc electrolytic cell based on numerical simulation for electrolyte flow

The physical and mathematical model of an operating electrowinning cell was established, and the flow of electrolyte was numerically simulated by the commercial software Fluent. The results indicate that there are two circulations at the surface flow where part of electrolyte backflows to the inlet from the side of cell, and the rest flows directly to the outlet, and the separation of two circulations with opposite direction occurs at the 20th pair of anode-cathode. This phenomenon was observed in the real operation. The electrolyte flows into the space between anode and cathode from the side portion of the cell. Meanwhile, the interelectrode effective flow rate (IEFR) is put forward to describe quantitively the flow field characteristics and is defined as the ratio of electrolyte flow between the anode and cathode to the total flow area. The influences of structure parameters and operating conditions on IEFR, such as the inlet angle, the volumetric flow rate, the inlet position and the height of steel baffles were simulated. The inlet position has a significant influence on the IEFR and its optimal value is 0.9 m below free surface. The inlet angle should be in the range from −10° to 10°. IEFR is in linear proportion with the volumetric flow rate, and the height of the steel baffle has little influence on the flow field.

Are there any gender differences in the hippocampus volume after head-size correction? A volumetric and voxel-based morphometric study

Previous findings on normal sexual dimorphism in hippocampal volume have not always been consistent. This study investigated gender differences in hippocampal volume using different head-size correction strategies. T1-weighted MR images were collected in 99 healthy, Caucasian, university students (66 female subjects; mean age: 23.1±2.3, range: 19–31 years). Sexual dimorphism in hippocampus was investigated by automated MRI volumetry and voxel-based morphometry (VBM) using both general linear model (GLM) and proportion head-size correction strategies. Absolute hippocampal volumes were larger in men than women. After adjusting for head-size, the proportion method indicated larger hippocampi in women than men, while no gender differences were found using the GLM approach. Investigating absolute hippocampal volumes in 15 head-size matched pairs of males and females indicated no gender differences. We suggest that there is no sexual dimorphism in hippocampal size and the apparent gender differences found by the proportion method may have more to do with head-size than with sex. The GLM and proportion head-size correction strategies are not interchangeable and may yield different results. The importance of the present findings is mostly related to scientific reproducibility across MRI volumetry or VBM studies.

Differential morphological responses to selection for high voluntary wheel running in the scapula and os coxae of mice (17.1)

Previous work has shown that the morphology of the scapula and ox coxae vary with locomotor differences. In addition, studies have also shown that chronic exercise produces a variety of long bone responses, including increased bone diameter and mass. Similar studies to voluntary exercise in flat bones, such as the major girdle elements (e.g. scapula, os coxae [hip bones]), are scarce, but show that the morphology of these elements may also respond to different forms of locomotor activity. We used laboratory mice from 4 replicate lines bred for high voluntary wheel running (HR) and 4 non‐selected control (C) lines to examine responses in these elements to 21 generations of selection for high voluntary wheel running and 8 weeks of a wheel/ no‐wheel treatment. Bone masses were taken and geometric morphometric techniques were employed to generate quantitative descriptors of 2D scapular and os coxae shape, centroid size, and a series of linear measurements. From the linear and mass data, we calculated ratios used to quantify scapular and coxal proportions. HR mice weighed less than C and wheel access reduced body mass for both groups. ANCOVA showed no statistical differences between the HR and C lines in scapular and coxal mass, centroid size, or ratios generated from linear data. However, HR and C mice were different in multivariate scapular and coxal shape, with the magnitudes of those differences greater in the scapula than in the os coxae. Wheel access significantly increased scapular but not coxal mass in both groups and produced scapular and coxal shape differences in both linetypes, but with no interaction between linetype and wheel access. HR mice with the mini‐muscle phenotype (HRmini) had significantly different linear proportions and larger centroid sizes in both elements than other mice. Finally, HRmini mice had significantly different scapular but not coxal shapes from all other mice.Grant Funding Source: Supported by NSF IOS‐1121273 to TG

The Efficacy of Mathematics Education

Evidence supports the notion that mathematics education in the United States is inadequate. There is also evidence that mathematics education deficiencies extend internationally. The worldwide mathematics education deficit appears large enough that improving student performance in this educational problem area could yield great economic benefit. To improve the efficacy of mathematics education, education’s root problems must first be understood. Often supposed educational root problems are considered and contrasted against potential deficiencies of mathematics methodologies and curricula that are based on mainstream educational philosophies. The educational philosophies utilized to form early-grade mathematics methodologies and related curricula are judged to be the main reasons for low levels of interest in the subject of mathematics by student populations. An exploration of available literature in regard to how the human brain learns is provided. Two unifications are resultantly hypothesized: interest and learning appear to be mentally intertwined, this unification may serve as the basis for a more effective educational methodology; children are nearly universally interested in the visual arts, arithmetic and geometric mathematical principles are intertwined with the visual arts principles of linear perspective and proportion. An early grade curriculum that relates those mathematical principles via artistic methods (similar to those developed and utilized by master artists and engineers of the Renaissance era) may prove broadly effective at equitably increasing students’ mathematical achievement. Future research in such a direction is highly recommended.

The cortisol awakening response (CAR) in male children with autism spectrum disorder

Our ability to adapt to change is fundamental. The cortisol awakening response (CAR) is a sharp rise in cortisol 30min after waking to help prepare an individual for ensuing stress. Children with autism spectrum disorder (ASD) often have difficulty adapting to change. Exploration of the CAR is warranted; yet, the few studies investigating it are inconclusive. The CAR was investigated in 94 pre-pubertal male children 8-to-12years of age with ASD (46) and typical development (TD, 48). Salivary samples were collected over three diurnal cycles involving two morning samples: M1: Immediately upon Waking and M2: 30-min Post Waking (M2−M1=CAR). The magnitude of the CAR was measured by independent two sample t-tests, variability was measured using Levene's Test, the sequence of the CAR was analyzed by a linear mixed-effects model and proportion of children exhibiting a CAR by chi-square test of independence. There were no significant differences on the CAR between the groups based on magnitude (t(92)=−0.14, p=0.89, d=0.04), variability (F(45,47)=1.11, p=0.72, η2=0.11) or the sequence over three days (F(2,88)=0.26, p=0.77, η2=0.01). No significant differences were shown in the proportion of children exhibiting a CAR across the groups based on child (χ2(1)=0.02, p=0.89) or adult criterion (χ2(1)=1.82, p=0.18). Despite group differences in the regulation and responsivity of cortisol, the CAR is indistinguishable between children with and without ASD. Inconsistencies across studies may be due to age, criterion used, and diagnostic distinctions.

Trophic Magnification and Isomer Fractionation of Perfluoroalkyl Substances in the Food Web of Taihu Lake, China

Biomagnification of perfluoroalkyl substances (PFASs) are well studied in marine food webs, but related information in fresh water ecosystem and knowledge on fractionation of their isomers along the food web are limited. The distribution, bioaccumulation, magnification, and isomer fractionation of PFASs were investigated in a food web of Taihu Lake, China. Perfluorooctanesulfonate (PFOS) and perfluorocarboxylates (PFCAs) with longer carbon chain lengths, such as perfluorodecanoate (PFDA) and perfluoroundecanoate (PFUnA), were predominant in organisms, while perfluorohexanoate (PFHxA) and perfluorooctanoate (∑PFOA) contributed more in the water phase. The consistent profile signature of PFOA isomers in water phase with 3M electrochemical fluorination (ECF) products suggests that ECF production of PFOA still exists in China. Linear proportions of PFOA, PFOS and perfluorooctane sulfonamide (PFOSA) in the biota were in the range of 91.9-100%, 78.6-95.5%, and 72.2-95.5%, respectively, indicating preferential bioaccumulation of linear isomers in biota. Trophic magnification factors (TMFs) were estimated for PFDA (2.43), perfluorododecanoate (PFDoA) (2.68) and PFOS (3.46) when all biota were included, suggesting that PFOS and long-chained PFCAs are biomagnified in the fresh water food web. The TMF of PFOS isomers descended in the order: n-PFOS (3.86) > 3+5m-PFOS (3.35) > 4m-PFOS (3.32) > 1m-PFOS (2.92) > m2-PFOS (2.67) > iso-PFOS (2.59), which is roughly identical to their elution order on a FluoroSep-RP Octyl column, suggesting that hydrophobicity may be an important contributor for isomer discrimination in biota.

Anomalous scaling of spin accumulation in ferromagnetic tunnel devices with silicon and germanium

The magnitude of spin accumulation created in semiconductors by electrical injection of spin-polarized electrons from a ferromagnetic tunnel contact is investigated, focusing on how the spin signal detected in a Hanle measurement varies with the thickness of the tunnel oxide. An extensive set of spin-transport data for Si and Ge magnetic tunnel devices reveals a scaling with the tunnel resistance that violates the core feature of available theories, namely, the linear proportionality of the spin voltage to the injected spin current density. Instead, an anomalous scaling of the spin signal with the tunnel resistance is observed, following a power law with an exponent between 0.75 and 1 over 6 decades. The scaling extends to tunnel resistance values larger than 10 9 �μ m 2 , far beyond the regime where the classical impedance mismatch or back flow into the ferromagnet play a role.Thisscalingisincompatiblewithexistingtheoryfordirecttunnelinjectionofspinsintothesemiconductor.It also demonstrates conclusively that the large spin signal does not originate from two-step tunneling via localized states near the oxide/semiconductor interface. Control experiments show that spin accumulation in localized states within the tunnel barrier or artifacts are also not responsible. Altogether, the scaling results suggest that, contrary to all existing descriptions, the spin signal is proportional to the applied bias voltage, rather than the (spin) current.

Mechanistic Models Fit to ED001 Data on >40,000 Trout Exposed to Dibenzo[A,L]pyrene Indicate Mutations Do Not Drive Increased Tumor Risk.

ED001-study data on increased liver and stomach tumor risks in >40,000 trout fed dibenzo[a,l]pyrene (DBP), one of the most potently mutagenic chemical carcinogens known, provide the greatest low-dose dose-response resolution of any experimentally induced tumor data set to date. Although multistage somatic mutation/clonal-expansion cancer theory predicts that genotoxic carcinogens increase tumor risk in linear no-threshold proportion to dose at low doses, ED001 tumor data curiously exhibit substantial low-dose nonlinearity. To explore the role that nongenotoxic mechanisms may have played to yield such nonlinearity, the liver and stomach tumor data sets were each fit by two models that each assume a genotoxic and a nongenotoxic pathway to increased tumor risk: the stochastic 2-stage (MVK) cancer model, and a model implementing the more recent dysregulated adaptive hyperplasia (DAH) theory of tumorigenesis. MVK and DAH fits to the data sets were each excellent, but unexpectedly each MVK fit implies that DBP acts to increase tumor risk by entirely non-mutagenic mechanisms. Given that DBP is such a potent mutagen, the MVK-model fits obtained appear to be biologically implausible, whereas the DAH-model fits reflect that model's assumption that chemical-induced tumorigenesis typically is driven by elevated repair-cell populations rather than mutations per se.

Scale effects and morphological diversification in hindlimb segment mass proportions in neognath birds.

IntroductionIn spite of considerable work on the linear proportions of limbs in amniotes, it remains unknown whether differences in scale effects between proximal and distal limb segments has the potential to influence locomotor costs in amniote lineages and how changes in the mass proportions of limbs have factored into amniote diversification. To broaden our understanding of how the mass proportions of limbs vary within amniote lineages, I collected data on hindlimb segment masses – thigh, shank, pes, tarsometatarsal segment, and digits – from 38 species of neognath birds, one of the most speciose amniote clades. I scaled each of these traits against measures of body size (body mass) and hindlimb size (hindlimb length) to test for departures from isometry. Additionally, I applied two parameters of trait evolution (Pagel’s λ and δ) to understand patterns of diversification in hindlimb segment mass in neognaths.ResultsAll segment masses are positively allometric with body mass. Segment masses are isometric with hindlimb length. When examining scale effects in the neognath subclade Land Birds, segment masses were again positively allometric with body mass; however, shank, pedal, and tarsometatarsal segment masses were also positively allometric with hindlimb length. Methods of branch length scaling to detect phylogenetic signal (i.e., Pagel’s λ) and increasing or decreasing rates of trait change over time (i.e., Pagel’s δ) suffer from wide confidence intervals, likely due to small sample size and deep divergence times.ConclusionsThe scaling of segment masses appears to be more strongly related to the scaling of limb bone mass as opposed to length, and the scaling of hindlimb mass distribution is more a function of scale effects in limb posture than proximo-distal differences in the scaling of limb segment mass. Though negative allometry of segment masses appears to be precluded by the need for mechanically sound limbs, the positive allometry of segment masses relative to body mass may underlie scale effects in stride frequency and length between smaller and larger neognaths. While variation in linear proportions of limbs appear to be governed by developmental mechanisms, variation in mass proportions does not appear to be constrained so.

Random Modeling of Daily Rainfall and Runoff Using a Seasonal Model and Wavelet Denoising

Instead of Fourier smoothing, this study applied wavelet denoising to acquire the smooth seasonal mean and corresponding perturbation term from daily rainfall and runoff data in traditional seasonal models, which use seasonal means for hydrological time series forecasting. The denoised rainfall and runoff time series data were regarded as the smooth seasonal mean. The probability distribution of the percentage coefficients can be obtained from calibrated daily rainfall and runoff data. For validated daily rainfall and runoff data, percentage coefficients were randomly generated according to the probability distribution and the law of linear proportion. Multiplying the generated percentage coefficient by the smooth seasonal mean resulted in the corresponding perturbation term. Random modeling of daily rainfall and runoff can be obtained by adding the perturbation term to the smooth seasonal mean. To verify the accuracy of the proposed method, daily rainfall and runoff data for the Wu-Tu watershed were analyzed. The analytical results demonstrate that wavelet denoising enhances the precision of daily rainfall and runoff modeling of the seasonal model. In addition, the wavelet denoising technique proposed in this study can obtain the smooth seasonal mean of rainfall and runoff processes and is suitable for modeling actual daily rainfall and runoff processes.

Average Case Network Lifetime on an Interval with Adjustable Sensing Ranges

Given n sensors on an interval, each of which is equipped with an adjustable sensing radius and a unit battery charge that drains in inverse linear proportion to its radius, what schedule will maximize the lifetime of a network that covers the entire interval? Trivially, any reasonable algorithm is at least a 2-approximation for this Sensor Strip Cover problem, so we focus on developing an efficient algorithm that maximizes the expected network lifetime under a random uniform model of sensor distribution. We demonstrate one such algorithm that achieves an expected network lifetime within 12 % of the theoretical maximum. Most of the algorithms that we consider come from a particular family of RoundRobin coverage, in which sensors take turns covering predefined areas until their battery runs out.

Pediatric Nephrectomy: Incidence, Indications and Use of Minimally Invasive Techniques

There is a paucity of knowledge regarding nephrectomy in contemporary United States pediatric populations. Usage patterns, indications and demographics of children undergoing nephrectomy are unknown. Given the significant increases in the use of minimally invasive nephrectomy in adults, we hypothesized similar trends may be seen in the pediatric population. An estimated total of 27,615 children undergoing nephrectomy between 1998 and 2010 was extracted from the Nationwide Inpatient Sample. Trends in use were analyzed with the estimated annual percent change methodology using linear regression and proportions by chi-square. Determinants of minimally invasive nephrectomy were evaluated using generalized linear models adjusted for clustering with generalized estimating equations. The annual incidence of pediatric nephrectomy was 2.90 per 100,000 patient-years and remained stable. Nephrectomy was most common in children 0 to 1 year old (36%) and least common in children 6 to 9 years old (14%). However, nephrectomy for malignancy was most common in children 3 to 4 years old. Minimally invasive nephrectomy usage increased from 1.1% to 11.6% during the study period (estimated annual percent change 72.82%, p = 0.007). On multivariable analysis patients with malignancy (OR 0.07, p <0.001) had a lower rate of minimally invasive nephrectomy. Increased use was associated with increasing age (OR 1.07, p <0.001), treatment at a teaching institution (OR 1.95, p = 0.008) and increasing hospital volume (OR 1.01, p = 0.001). While the annual incidence of nephrectomy is stable, the use of minimally invasive nephrectomy is expanding in the pediatric population. Benign pathology and increasing age as well as nephrectomy at high volume teaching institutions are independently associated with minimally invasive nephrectomy use.

Exploring new W–B coating materials for the aqueous corrosion–wear protection of austenitic stainless steel

The material loss of metallic surfaces through corrosion–wear is a serious concern in many application sectors, ranging from bio-medical implants to marine, oil and gas field components to transport vehicle and nuclear reactor devices. In principle, self-passivating alloys, like stainless steels, can be protected from surface degradation caused by corrosion–wear through the application of protective thin, hard surface coatings. In this work the suitability of using W matrix coating materials supersaturated with varying levels of boron were applied to austenitic stainless steel substrates (Ortron 90) and assessed for this purpose. These materials were compared to a highly corrosion–wear resistant “datum” surface engineered material (CrN coated Ti–6Al–4V) in sliding contact tests against a chemically inert aluminium oxide ball, whilst immersed in 0.9% NaCl solution at 37°C. The work demonstrated that all the coated materials to be very much more resistant to material loss through corrosion–wear (by nearly an order of magnitude) compared to uncoated stainless steel, and two coatings, W–13%B and W–23%B coated Ortron 90 were similarly resistant as CrN coated Ti–6Al–4V. Three fundamental types of corrosion–wear were discovered that represented differing levels of passive film durability. The total material loss rate (TMLR) during corrosion–wear testing showed linear proportionality with the change in open circuit potential δOCP which obeyed the governing equation: TMLR=m δOCP+C.

Large-scale fabrication and luminescence properties of GaN nanostructures by a soft UV-curing nanoimprint lithography

GaN nanorods with a period of 400 nm and diameter of 200 nm, and nano-gratings with a period of 400 nm and gap width of 100 nm are fabricated on wafers by a soft UV-curing nanoimprint lithography. These nanostructures show high periodicity and good morphology. The photoluminescence (PL) spectra exhibit that the integral PL intensity of GaN nanorods is enhanced as much as 2.5 times, compared to that of as-grown GaN films. According to finite-difference time-domain simulations and cathodoluminescence mappings, it is concluded that the enhancement for nanorods is due to the improvements of both spontaneous emission rate and light extraction efficiency caused by periodic GaN structures on the surface. By identifying the Raman shift of E1(TO) and modes of GaN films with nano-gratings and nanorods, the normal-plane strain εzz is determined. The PL emission energy is found to be proportional to the εzz, whose linear proportionality factor is calculated to be −27 meV GPa−1.

Study of Thermal Properties of Bamboo/Cotton Blended Single Jersey Knitted Fabrics

In this study, the thermal properties of bamboo/cotton blended single jersey fabrics have been studied in relation to linear density, loop length and blend proportion on thickness, air permeability, thermal conductivity, thermal resistance and water vapour permeability. Cotton, bamboo fibre and blends of the two fibres (100 % cotton, 100 % bamboo, 50:50 % bamboo/cotton) were spun into yarns of linear densities (20s, 25s, 30s Nec). Each of the yarns so produced was converted to single jersey knitted fabrics with three loop lengths. The thermal conductivity of the fabrics was generally found to decrease with increase in the proportion of bamboo fibre. The water vapour permeability and air permeability of the fabrics were observed to increase with increase in bamboo fibre content. An increasing presence of bamboo fibre in the fabric causes a reduction in fabric thickness and GSM for all linear densities of yarn. As the constituent yarn gets finer, fabric air and water-vapour permeability both increase in value while the thermal conductivity falls.