Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

Tables of complex hyperbolic and circular functions,

Bibliography: p. 209-212.

On the classification of mixed construction and demolition waste aggregate by porosity and its impact on the mechanical performance of concrete

The properties of recycled aggregate produced from mixed (masonry and concrete) construction and demolition (C&D) waste are highly variable, and this restricts the use of such aggregate in structural concrete production. The development of classification techniques capable of reducing this variability is instrumental for quality control purposes and the production of high quality C&D aggregate. This paper investigates how the classification of C&D mixed coarse aggregate according to porosity influences the mechanical performance of concrete. Concretes using a variety of C&D aggregate porosity classes and different water/cement ratios were produced and the mechanical properties measured. For concretes produced with constant volume fractions of water, cement, natural sand and coarse aggregate from recycled mixed C&D waste, the compressive strength and Young modulus are direct exponential functions of the aggregate porosity. Sink and float technique is a simple laboratory density separation tool that facilitates the separation of cement particles with lower porosity, a difficult task when done only by visual sorting. For this experiment, separation using a 2.2 kg/dmA(3) suspension produced recycled aggregate (porosity less than 17%) which yielded good performance in concrete production. Industrial gravity separators may lead to the production of high quality recycled aggregate from mixed C&D waste for structural concrete applications.

Observação e controlo da segurança estrutural de barragens de betão: utilização integrada de modelos numéricos e de modelos de separação de efeitos

Dissertação de Natureza Científica elabora da no âmbito do protocolo de cooperação entre o ISEL e o LNEC para obtenção do grau de Mestre em Engenharia Civil

A critical analysis of dimensions and curve fitting practice in economics

When dealing with sustainability we are concerned with the biophysical as well as the monetary aspects of economic and ecological interactions. This multidimensional approach requires that special attention is given to dimensional issues in relation to curve fitting practice in economics. Unfortunately, many empirical and theoretical studies in economics, as well as in ecological economics, apply dimensional numbers in exponential or logarithmic functions. We show that it is an analytical error to put a dimensional unit x into exponential functions ( a x ) and logarithmic functions ( x a log ). Secondly, we investigate the conditions of data sets under which a particular logarithmic specification is superior to the usual regression specification. This analysis shows that logarithmic specification superiority in terms of least square norm is heavily dependent on the available data set. The last section deals with economists’ “curve fitting fetishism”. We propose that a distinction be made between curve fitting over past observations and the development of a theoretical or empirical law capable of maintaining its fitting power for any future observations. Finally we conclude this paper with several epistemological issues in relation to dimensions and curve fitting practice in economics

Does the mechanical work in running change during the VO2 slow component?

PURPOSE: The origin of the slow component is not fully understood. The mechanical hypothesis is one of the potential factors, because an increase in external mechanical work with fatigue was previously reported for a constant velocity run. The purpose of this study was to determine whether a change in mechanical work could occur during the development of the VO2 slow component under the effect of fatigue. METHODS: Twelve regional-level competitive runners performed a square-wave transition, corresponding to 95% of the speed associated with peak VO2 obtained during an incremental test. The VO2 response was fit with a classical model including two exponential functions. A specific treadmill with three-dimensional force transducers was used to measure the ground reaction force. Kinetic work (W(kin)), potential work (W(pot)), external work (W(ext)), and an index of internal work (W(int)) per unit of distance were quantified continuously. RESULTS: During the slow component of VO2, a significant increase in W (P< 0.01), no change in W, and a significant decrease in W and W index (P< 0.05, P< 0.001, respectively) were observed. CONCLUSION: The present study showed that the slow component of VO2 did not result partly from a change in mechanical work under the effect of fatigue. Nevertheless, the decrease in stride frequency (P< 0.001) and contact time (P< 0.001) suggested an alternative mechanical explanation. The slow component during running may be due to the cost of generating force or to alterations in the storage and recoil of elastic energy, and not to the external mechanical work.

Effects of increased intensity of intermittent training in runners with differing VO2 kinetics.

The purpose of this study was to test the hypothesis that athletes having a slower oxygen uptake ( VO(2)) kinetics would benefit more, in terms of time spent near VO(2max), from an increase in the intensity of an intermittent running training (IT). After determination of VO(2max), vVO(2max) (i.e. the minimal velocity associated with VO(2max) in an incremental test) and the time to exhaustion sustained at vVO(2max) ( T(lim)), seven well-trained triathletes performed in random order two IT sessions. The two IT comprised 30-s work intervals at either 100% (IT(100%)) or 105% (IT(105%)) of vVO(2max) with 30-s recovery intervals at 50% of vVO(2max) between each repeat. The parameters of the VO(2) kinetics (td(1), tau(1), A(1), td(2), tau(2), A(2), i.e. time delay, time constant and amplitude of the primary phase and slow component, respectively) during the T(lim) test were modelled with two exponential functions. The highest VO(2) reached was significantly lower ( P<0.01) in IT(100%) run at 19.8 (0.9) km(.)h(-1) [66.2 (4.6) ml(.)min(-1.)kg(-1)] than in IT(105%) run at 20.8 (1.0) km(.)h(-1) [71.1 (4.9) ml(.)min(-1.)kg(-1)] or in the incremental test [71.2 (4.2) ml(.)min(-1.)kg(-1)]. The time sustained above 90% of VO(2max) in IT(105%) [338 (149) s] was significantly higher ( P<0.05) than in IT(100%) [168 (131) s]. The average T(lim) was 244 (39) s, tau(1) was 15.8 (5.9) s and td(2) was 96 (13) s. tau(1) was correlated with the difference in time spent above 90% of VO(2max) ( r=0.91; P<0.01) between IT(105%) and IT(100%). In conclusion, athletes with a slower VO(2) kinetics in a vVO(2max) constant-velocity test benefited more from the 5% rise of IT work intensity, exercising for longer above 90% of VO(2max) when the IT intensity was increased from 100 to 105% of vVO(2max).

Oxygen uptake kinetics and middle distance swimming performance.

OBJECTIVE: The aim of this study was to determine whether V˙O(2) kinetics and specifically, the time constant of transitions from rest to heavy (τ(p)H) and severe (τ(p)S) exercise intensities, are related to middle distance swimming performance. DESIGN: Fourteen highly trained male swimmers (mean ± SD: 20.5 ± 3.0 yr; 75.4 ± 12.4 kg; 1.80 ± 0.07 m) performed an discontinuous incremental test, as well as square wave transitions for heavy and severe swimming intensities, to determine V˙O(2) kinetics parameters using two exponential functions. METHODS: All the tests involved front-crawl swimming with breath-by-breath analysis using the Aquatrainer swimming snorkel. Endurance performance was recorded as the time taken to complete a 400 m freestyle swim within an official competition (T400), one month from the date of the other tests. RESULTS: T400 (Mean ± SD) (251.4 ± 12.4 s) was significantly correlated with τ(p)H (15.8 ± 4.8s; r=0.62; p=0.02) and τ(p)S (15.8 ± 4.7s; r=0.61; p=0.02). The best single predictor of 400 m freestyle time, out of the variables that were assessed, was the velocity at V˙O(2max)vV˙O(2max), which accounted for 80% of the variation in performance between swimmers. However, τ(p)H and V˙O(2max) were also found to influence the prediction of T400 when they were included in a regression model that involved respiratory parameters only. CONCLUSIONS: Faster kinetics during the primary phase of the V˙O(2) response is associated with better performance during middle-distance swimming. However, vV˙O(2max) appears to be a better predictor of T400.

Effects of aerobic fitness on oxygen uptake kinetics in heavy intensity swimming.

This study aimed to characterise both the [Formula: see text] kinetics within constant heavy-intensity swimming exercise, and to assess the relationships between [Formula: see text] kinetics and other parameters of aerobic fitness, in well-trained swimmers. On separate days, 21 male swimmers completed: (1) an incremental swimming test to determine their maximal oxygen uptake [Formula: see text], first ventilatory threshold (VT), and the velocity associated with [Formula: see text] [Formula: see text] and (2) two square-wave transitions from rest to heavy-intensity exercise, to determine their [Formula: see text] kinetics. All the tests involved breath-by-breath analysis of freestyle swimming using a swimming snorkel. [Formula: see text] kinetics was modelled with two exponential functions. The mean values for the incremental test were 56.0 ± 6.0 ml min(-1) kg(-1), 1.45 ± 0.08 m s(-1); and 42.1 ± 5.7 ml min(-1) kg(-1) for [Formula: see text], [Formula: see text] and VT, respectively. For the square-wave transition, the time constant of the primary phase (τ(p)) averaged 17.3 ± 5.4 s and the relevant slow component (A'(sc)) averaged 4.8 ± 2.9 ml min(-1) kg(-1) [representing 8.9% of the end-exercise [Formula: see text] (%A'(sc))]. τ(p) was correlated with [Formula: see text] (r = -0.55, P = 0.01), but not with either [Formula: see text] (r = 0.05, ns) or VT (r = 0.14, ns). The %A'(sc) did not correlate with either [Formula: see text] (r = -0.14, ns) or [Formula: see text] (r = 0.06, ns), but was inversely related with VT (r = -0.61, P < 0.01). This study was the first to describe the [Formula: see text] kinetics in heavy-intensity swimming using specific swimming exercise and appropriate methods. As has been demonstrated in cycling, faster [Formula: see text] kinetics allow higher aerobic power outputs to be attained. The slow component seems to be reduced in swimmers with higher ventilatory thresholds.

Biokinetics and dosimetry of (111)In-DOTA-NOC-ATE compared with (111)In-DTPA-octreotide.

PURPOSE: The biokinetics and dosimetry of (111)In-DOTA-NOC-ATE (NOCATE), a high-affinity ligand of SSTR-2 and SSTR-5, and (111)In-DTPA-octreotide (Octreoscan?, OCTREO) were compared in the same patients. METHODS: Seventeen patients (10 men, 7 women; mean age 60 years), referred for an OCTREO scan for imaging of a neuroendocrine tumour (15), thymoma (1) or medullary thyroid carcinoma (1), agreed to undergo a second study with NOCATE. Whole-body anterior-posterior scans were recorded 0.5 (100 % reference scan), 4, 24 and 48 h (17 patients) and 120 h (5 patients) after injection. In 16 patients the OCTREO scan (178 ± 15 MBq) was performed 16 ± 5 days before the NOCATE scan (108 ± 14 MBq) with identical timing; 1 patient had the NOCATE scan before the OCTREO scan. Blood samples were obtained from 14 patients 5 min to 48 h after injection. Activities expressed as percent of the initial (reference) activity in the whole body, lung, kidney, liver, spleen and blood were fitted to biexponential or single exponential functions. Dosimetry was performed using OLINDA/EXM. RESULTS: Initial whole-body, lung and kidney activities were similar, but retention of NOCATE was higher than that of OCTREO. Liver and spleen uptakes of NOCATE were higher from the start (p < 0.001) and remained so over time. Whole-body activity showed similar α and β half-lives, but the β fraction of NOCATE was double that of OCTREO. Blood T (1/2)β for NOCATE was longer (19 vs. 6 h). As a result, the effective dose of NOCATE (105 μSv/MBq) exceeded that of OCTREO (52 μSv/MBq), and the latter result was similar to the ICRP 106 value of 54 μSv/MBq. Differential activity measurement in blood cells and plasma showed an average of <5 % of NOCATE and OCTREO attached to globular blood components. CONCLUSION: NOCATE showed a slower clearance from normal tissues and its effective dose was roughly double that of OCTREO.

The effects of moisture, cation concentration, temperature, density and composition of soils on their electrical resistivity

The effects. of moisture, cation concentration, dens ity , temper~ t ure and grai n si ze on the electrical resistivity of so il s are examined using laboratory prepared soils. An i nexpen si ve method for preparing soils of different compositions was developed by mixing various size fractions i n the laboratory. Moisture and cation c oncentration are related to soil resistivity by powe r functions, whereas soil resistiv ity and temperature, density, Yo gravel, sand , sil t, and clay are related by exponential functions . A total of 1066 cases (8528 data) from all the experiments were used in a step-wise multiple linear r egression to determine the effect of each variable on soil resistivity. Six variables out of the eight variables studied account for 92.57/. of the total variance in so il resistivity with a correlation coefficient of 0.96. The other two variables (silt and gravel) did not increase the · variance. Moisture content was found to be - the most important Yo clay. variable- affecting s oil res istivi ty followed by These two variables account for 90.81Yo of the total variance in soil resistivity with a correlation ~oefficient ·.of 0 . 95. Based on these results an equation to ' ~~ed{ ct soil r esist ivi ty using moisture and Yo clay is developed . To t est the predicted equation, resistivity measurements were made on natural soils both in s i tu a nd i n the laboratory. The data show that field and laboratory measurements are comparable. The predicted regression line c losely coinciqes with resistivity data from area A and area B soils ~clayey and silty~clayey sands). Resistivity data and the predicted regression line in the case of c layey soils (clays> 40%) do not coincide, especially a t l ess than 15% moisture. The regression equation overestimates the resistivity of so i l s from area C and underestimates for area D soils. Laboratory prepared high clay soils give similar trends. The deviations are probably caused by heterogeneous distribution of mo i sture and difference in the type o f cl ays present in these soils.

Semi-dwarfing (Rht-B1b) improves nitrogen-use efficiency in wheat, but not at economically optimal levels of nitrogen availability

A UK field experiment compared a complete factorial combination of three backgrounds (cvs Mercia, Maris Huntsman and Maris Widgeon), three alleles at the Rht-B1 locus as Near Isogenic Lines (NILs: rht-B1a (tall), Rht-B1b (semi-dwarf), Rht-B1c (severe dwarf)) and four nitrogen (N) fertilizer application rates (0, 100, 200 and 350 kg N/ha). Linear+exponential functions were fitted to grain yield (GY) and nitrogen-use efficiency (NUE; GY/available N) responses to N rate. Averaged over N rate and background Rht-B1b conferred significantly (P<0.05) greater GY, NUE, N uptake efficiency (NUpE; N in above ground crop / available N) and N utilization efficiency (NUtEg; GY / N in above ground crop) compared with rht-B1a and Rht-B1c. However the economically optimal N rate (Nopt) for N:grain price ratios of 3.5:1 to 10:1 were also greater for Rht-B1b, and because NUE, NUpE and NUtE all declined with N rate, Rht-Blb failed to increase NUE or its components at Nopt. The adoption of semi-dwarf lines in temperate and humid regions, and the greater N rates that such adoption justifies economically, greatly increases land-use efficiency, but not necessarily, NUE.

Uma proposta alternativa para o ensino progressões relacionadas a funções

Generally, arithmetic and geometric progressions are taught separately from ane and exponential functions, only by the use of memorized formulas and without any concern of showing students how these contents are related. This paper aims at presenting a way of teaching such contents in an integrated way, starting with the definition of ane and exponential functions relating them to situations from the daily life of the students. Then, characteristics and graphics of those functions are presented and, subsequently, arithmetic and geometric progression are shown as a restriction of the ane and exponential functions. Thus, the study of the progressions is introduced based on the functions mentioned above using situations from students daily lives as examples

Temperature dependence of photoinduced birefringence in mixed Langmuir-Blodgett (LB) films of azobenzene-containing polymers

The temperature dependence of photoinduced birefringence was investigated for mixed Langmuir-Blodgett (LB) films from the homopolymer poly[4'-[[2-(methacryloyloxy)ethyl]ethyl-amino]-2-chloro-4-nitroazobenzene] (HPDR13) and cadmium stearate (Cdst) and from the copolymer 4-[N-ethyl-N-(2-hydroxyethyl)]amino-2'-chloro-4'-nitroazobenzene (MMA-DR13) and CdSt. Birefringence was achieved by impinging a linearly polarized light on the LB films. The maximum birefringence achieved decreased with temperature as thermal relaxation of the chromophores was facilitated. The buildup curves for birefringence were fitted with biexponential functions representing distinctly different mechanisms with time constants. The first, fast process is thermally activated and may be represented by an Arrhenius process. The decay of birefringence after switching off the laser source was described by a Kohlraush-Williams-Watts (KWW) function, consistent with a distribution of relaxation times for the polymer system. Activation energies were obtained from Arrhenius plots of the rate constant of the exponential functions and KWW function, which showed that the buildup of birefringence was very similar for the two polymer systems. The decay, however, was slower for the LB film from MMA-DR13/CdSt. (C) 2002 Published by Elsevier B.V. Ltd.

Kinetics of photoinduced birefringence in the guest-host system of poly(methyl methacrylate) doped with azobenzene-containing crown ethers

The kinetics of the buildup and decay of photoinduced birefringence was examined in a series of host-guest systems: azobenzene-containing crown ethers, differing in the size of the crowns, dissolved in a poly (methyl methacrylate) matrix. In all samples, the kinetics of the buildup of the birefringence was reasonably described by a sum of two exponential functions, the time constants being inversely proportional to the intensity of the pumping light and the magnitudes of the signals at the saturation level depending on the pumping light intensity and sample thickness. The dark decays were best described by the stretched exponential function, with the characteristic parameters (time constant and stretch coefficient) being practically independent of the type of crown ether. The time constants of the signal decay were orders of magnitude shorter than the respective constants of the dark isomerization of the azo crown ethers, thus indicating that the process controlling the decay was a relaxation of the polymer matrix and/or a rearrangement of the flexible parts of the crowns. (C) 2007 Wiley Periodicals, Inc.