Theoretical Analysis and Numerical Simulation of Spectral Radiative Properties of Combustion Gases in Oxy/Air-Fired Combustion Systems

Energy efficiency is one of the major objectives which should be achieved in order to implement the limited energy resources of the world in a sustainable way. Since radiative heat transfer is the dominant heat transfer mechanism in most of fossil fuel combustion systems, more accurate insight and models may cause improvement in the energy efficiency of the new designed combustion systems. The radiative properties of combustion gases are highly wavelength dependent. Better models for calculating the radiative properties of combustion gases are highly required in the modeling of large scale industrial combustion systems. With detailed knowledge of spectral radiative properties of gases, the modeling of combustion processes in the different applications can be more accurate. In order to propose a new method for effective non gray modeling of radiative heat transfer in combustion systems, different models for the spectral properties of gases including SNBM, EWBM, and WSGGM have been studied in this research. Using this detailed analysis of different approaches, the thesis presents new methods for gray and non gray radiative heat transfer modeling in homogeneous and inhomogeneous H2O–CO2 mixtures at atmospheric pressure. The proposed method is able to support the modeling of a wide range of combustion systems including the oxy-fired combustion scenario. The new methods are based on implementing some pre-obtained correlations for the total emissivity and band absorption coefficient of H2O–CO2 mixtures in different temperatures, gas compositions, and optical path lengths. They can be easily used within any commercial CFD software for radiative heat transfer modeling resulting in more accurate, simple, and fast calculations. The new methods were successfully used in CFD modeling by applying them to industrial scale backpass channel under oxy-fired conditions. The developed approaches are more accurate compared with other methods; moreover, they can provide complete explanation and detailed analysis of the radiation heat transfer in different systems under different combustion conditions. The methods were verified by applying them to some benchmarks, and they showed a good level of accuracy and computational speed compared to other methods. Furthermore, the implementation of the suggested banded approach in CFD software is very easy and straightforward.

Novel Methods for Error Modeling and Parameter Identification of a Redundant Serial-Parallel Hybrid Robot

To obtain the desirable accuracy of a robot, there are two techniques available. The first option would be to make the robot match the nominal mathematic model. In other words, the manufacturing and assembling tolerances of every part would be extremely tight so that all of the various parameters would match the “design” or “nominal” values as closely as possible. This method can satisfy most of the accuracy requirements， but the cost would increase dramatically as the accuracy requirement increases. Alternatively, a more cost-effective solution is to build a manipulator with relaxed manufacturing and assembling tolerances. By modifying the mathematical model in the controller, the actual errors of the robot can be compensated. This is the essence of robot calibration. Simply put, robot calibration is the process of defining an appropriate error model and then identifying the various parameter errors that make the error model match the robot as closely as possible. This work focuses on kinematic calibration of a 10 degree-of-freedom (DOF) redundant serial-parallel hybrid robot. The robot consists of a 4-DOF serial mechanism and a 6-DOF hexapod parallel manipulator. The redundant 4-DOF serial structure is used to enlarge workspace and the 6-DOF hexapod manipulator is used to provide high load capabilities and stiffness for the whole structure. The main objective of the study is to develop a suitable calibration method to improve the accuracy of the redundant serial-parallel hybrid robot. To this end, a Denavit–Hartenberg (DH) hybrid error model and a Product-of-Exponential (POE) error model are developed for error modeling of the proposed robot. Furthermore, two kinds of global optimization methods, i.e. the differential-evolution (DE) algorithm and the Markov Chain Monte Carlo (MCMC) algorithm, are employed to identify the parameter errors of the derived error model. A measurement method based on a 3-2-1 wire-based pose estimation system is proposed and implemented in a Solidworks environment to simulate the real experimental validations. Numerical simulations and Solidworks prototype-model validations are carried out on the hybrid robot to verify the effectiveness, accuracy and robustness of the calibration algorithms.

Self-perception of sexual life and associated factors: a population study conducted in women aged 50 or more years

PURPOSE: To evaluate the prevalence of women aged 50 years or more who are sexually active and their self-perception with respect to their sexual lives. Associated factors were also assessed. METHODS: A cross-sectional, population-based, self-reported household survey involving 622 Brazilian women aged 50 years or more. Sociodemographic, clinical, and behavioral factors were evaluated. The sexual life self-perception was classified as very good, good, fair, poor, or very poor. Data were analyzed using the χ² test, Fisher's exact test, and Poisson multiple regression analysis. Prevalence ratios and their 95% confidence intervals were also calculated. RESULTS: Of the women in this sample, 228 (36.7%) reported having a sexual life and, of these, 53.5% classified it as very good or good, while 46.5% considered it fair, poor, or very poor. The bivariate analysis indicated that being postmenopausal (p=0.025) and using natural remedies to treat the menopause (p=0.035) were factors associated with the woman classifying their sexual lives as fair, poor, or very poor. Multiple regression analysis showed that more women who had used or were currently using natural remedies for the menopause scored their sexual lives as fair, poor, or very poor. CONCLUSIONS: More than half the women aged 50 years or more in this study were not sexually active. A poorer sexual life self-perception was associated with the use of natural remedies to treat menopausal symptoms. This may indicate a need to improve the way in which these women are evaluated and treated. Women's assessment of their own sexual lives may prove a useful tool in clinical practice.

Limestone Reactions in a Fluidized Bed Heat Exchanger of an Oxy-fuel Circulating Fluidized Bed Boiler

Oxy-fuel combustion in a circulating fluidized bed (CFB) boiler appears to be a promising option for capturing CO2 in power plants. Oxy-fuel combustion is based on burning of fuel in the mixture of oxygen and re-circulated flue gas instead of air. Limestone (CaCO3) is typically used for capturing of SO2 in CFB boilers where limestone calcines to calcium oxide (CaO). Because of high CO2 concentration in oxy-fuel combustion, calcination reaction may be hindered or carbonation, the reverse reaction of calcination, may occur. Carbonation of CaO particles can cause problems especially in the circulation loop of a CFB boiler where temperature level is lower than in the furnace. The aim of the thesis was to examine carbonation of CaO in a fluidized bed heat exchanger of a CFB boiler featuring oxy-fuel combustion. The calculations and analyzing were based on measurement data from an oxy-fuel pilot plant and on 0-dimensional (0D) gas balance of a fluidized bed heat exchanger. Additionally, the objective was to develop a 1-dimensional (1D) model of a fluidized bed heat exchanger by searching a suitable pre-exponential factor for a carbonation rate constant. On the basis of gas measurement data and the 0D gas balance, it was found that the amount of fluidization gas decreased as it flew through the fluidized bed heat exchanger. Most likely the reason for this was carbonation of CaO. It was discovered that temperature has a promoting effect on the reaction rate of carbonation. With the 1D model, a suitable pre-exponential factor for the equation of carbonation rate constant was found. However, during measurements there were several uncertainties, and in the calculations plenty of assumptions were made. Besides, the temperature level in the fluidized bed heat exchanger was relatively low during the measurements. Carbonation should be considered when fluidized bed heat exchangers and the capacity of related fans are designed for a CFB boiler with oxy-fuel combustion.

Oxidation rates of carbon and nitrogen in char residues from solid fuels

Computational fluid dynamics (CFD) modeling is an important tool in designing new combustion systems. By using CFD modeling, entire combustion systems can be modeled and the emissions and the performance can be predicted. CFD modeling can also be used to develop new and better combustion systems from an economical and environmental point of view. In CFD modeling of solid fuel combustion, the combustible fuel is generally treated as single fuel particles. One of the limitations with the CFD modeling concerns the sub-models describing the combustion of single fuel particles. Available models in the scientific literature are in many cases not suitable as submodels for CFD modeling since they depend on a large number of input parameters and are computationally heavy. In this thesis CFD-applicable models are developed for the combustion of single fuel particles. The single particle models can be used to improve the combustion performance in various combustion devices or develop completely new technologies. The investigated fields are oxidation of carbon (C) and nitrogen (N) in char residues from solid fuels. Modeled char-C oxidation rates are compared to experimental oxidation rates for a large number of pulverized solid fuel chars under relevant combustion conditions. The experiments have been performed in an isothermal plug flow reactor operating at 1123-1673 K and 3-15 vol.% O2. In the single particle model, the char oxidation is based on apparent kinetics and depends on three fuel specific parameters: apparent pre-exponential factor, apparent activation energy, and apparent reaction order. The single particle model can be incorporated as a sub-model into a CFD code. The results show that the modeled char oxidation rates are in good agreement with experimental char oxidation rates up to around 70% of burnout. Moreover, the results show that the activation energy and the reaction order can be assumed to be constant for a large number of bituminous coal chars under conditions limited by the combined effects of chemical kinetics and pore diffusion. Based on this, a new model based on only one fuel specific parameter is developed (Paper III). The results also show that reaction orders of bituminous coal chars and anthracite chars differ under similar conditions (Paper I and Paper II); reaction orders of bituminous coal chars were found to be one, while reaction orders of anthracite chars were determined to be zero. This difference in reaction orders has not previously been observed in the literature and should be considered in future char oxidation models. One of the most frequently used comprehensive char oxidation models could not explain the difference in the reaction orders. In the thesis (Paper II), a modification to the model is suggested in order to explain the difference in reaction orders between anthracite chars and bituminous coal chars. Two single particle models are also developed for the NO formation and reduction during the oxidation of single biomass char particles. In the models the char-N is assumed to be oxidized to NO and the NO is partly reduced inside the particle. The first model (Paper IV) is based on the concentration gradients of NO inside and outside the particle and the second model is simplified to such an extent that it is based on apparent kinetics and can be incorporated as a sub-model into a CFD code (Paper V). Modeled NO release rates from both models were in good agreement with experimental measurements from a single particle reactor of quartz glass operating at 1173-1323 K and 3-19 vol.% O2. In the future, the models can be used to reduce NO emissions in new combustion systems.

The Impact of European Macroeconomic News Announcements on CIVETS Stock Markets

The purpose of this research is to investigate how CIVETS (Colombia, Indonesia, Vietnam, Egypt, Turkey and South Africa) stock markets are integrated with Europe as measured by the impact of euro area (EA) scheduled macroeconomic news announcements, which are related to macroeconomic indicators that are commonly used to indicate the direction of the economy. Macroeconomic announcements used in this study can be divided into four categories; (1) prices, (2) real economy, (3) money supply and (4) business climate and consumer confidence. The data set consists of daily market data from CIVETS and scheduled macroeconomic announcements from the EA for the years 2007-2012. The econometric model used in this research is Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH). Empirical results show diverse impacts of macroeconomic news releases and surprises for different categories of news supporting the perception of heterogeneity among CIVETS. The analyses revealed that in general EA macroeconomic news releases and surprises affect stock market volatility in CIVETS and only in some cases asset pricing. In conclusion, all CIVETS stock markets reacted to the incoming EA macroeconomic news suggesting market integration to some extent. Thus, EA should be considered as a possible risk factor when investing in CIVETS.

Numerical study on mixed convection in a horizontal flow past a square porous cavity using UNIFAES scheme

Mixed convection on the flow past a heated length and past a porous cavity located in a horizontal wall bounding a saturated porous medium is numerically simulated. The cavity is heated from below. The steady-state regime is studied for several intensities of the buoyancy effects due to temperature variations. The influences of Péclet and Rayleigh numbers on the flow pattern and the temperature distributions are examined. Local and global Nusselt numbers are reported for the heated surface. The convective-diffusive fluxes at the volume boundaries are represented using the UNIFAES, Unified Finite Approach Exponential-type Scheme, with the Power-Law approximation to reduce the computing time. The conditions established by Rivas for the quadratic order of accuracy of the central differencing to be maintained in irregular grids are shown to be extensible to other quadratic schemes, including UNIFAES, so that accuracy estimates could be obtained.

Identification of research trends in the field of separation processes. Application of epidemiological model, citation analysis, text mining, and technical analysis of the financial markets

Choice of industrial development options and the relevant allocation of the research funds become more and more difficult because of the increasing R&D costs and pressure for shorter development period. Forecast of the research progress is based on the analysis of the publications activity in the field of interest as well as on the dynamics of its change. Moreover, allocation of funds is hindered by exponential growth in the number of publications and patents. Thematic clusters become more and more difficult to identify, and their evolution hard to follow. The existing approaches of research field structuring and identification of its development are very limited. They do not identify the thematic clusters with adequate precision while the identified trends are often ambiguous. Therefore, there is a clear need to develop methods and tools, which are able to identify developing fields of research. The main objective of this Thesis is to develop tools and methods helping in the identification of the promising research topics in the field of separation processes. Two structuring methods as well as three approaches for identification of the development trends have been proposed. The proposed methods have been applied to the analysis of the research on distillation and filtration. The results show that the developed methods are universal and could be used to study of the various fields of research. The identified thematic clusters and the forecasted trends of their development have been confirmed in almost all tested cases. It proves the universality of the proposed methods. The results allow for identification of the fast-growing scientific fields as well as the topics characterized by stagnant or diminishing research activity.

Market integration, return and volatility dynamics; empirical evidence from African stock markets

Frontier and Emerging economies have implemented policies with the objective of liberalizing their equity markets. Equity market liberalization opens the domestic equity market to foreign investors and as well paves the way for domestic investors to invest in foreign equity securities. Among other things, equity market liberalization results in diversification benefits. Moreover, equity market liberalization leads to low cost of equity capital resulting from the lower rate of return by investors. Additionally, foreign and local investors share any potential risks. Liberalized equity markets also become liquid considering that there are more investors to trade. Equity market liberalization results in financial integration which explains the movement of two markets. In crisis period, increased volatility and co-movement between two markets may result in what is termed contagion effects. In Africa, major moves toward financial liberalization generally started in the late 1980s with South Africa as the pioneer. Over the years, researchers have studied the impact of financial liberalization on Africa’s economic development with diverse results; some being positive, others negative and still others being mixed. The objective of this study is to establish whether African stock-markets are integrated into the United States (US) and World market. Furthermore, the study helps to see if there are international linkages between the Africa, US and the world markets. A Bivariate- VAR- GARCH- BEKK model is employed in the study. In the study, the effect of thin trading is removed through series of econometric data purification. This is because thin trading, also known as non-trading or inconsistency of trading, is a main feature of African markets and may trigger inconsistency and biased results. The study confirmed the widely established results that the South Africa and Egypt stock markets are highly integrated with the US and World market. Interestingly, the study adds to knowledge in this research area by establishing the fact that Kenya is very integrated with the US and World markets and that it receives and exports past innovations as well as shocks to and from the US and World market.

Suomen peliteollisuuden kasvu ja kansainvälistyminen

Suomen peliteollisuus on ollut erittäin puhuttu aihe mediassa viime vuosien ajan. Työmme pyrkii selvittämään Suomen peliteollisuuden kasvun ja kansainvälistymisprosessin taustalla olleita tekijöitä sekä niiden suhteita toisiinsa. Työssä keskitytään analysoimaan jo tapahtunutta kasvua ja kansainvälistymistä, joiden tarkastelussa käytetään hyväksi Porterin jalostamaa Klusteri -teoriaa sekä kasvuyritysten uutta kansainvälistymisilmiötä, Born Global -teoriaa. Suomen peliteollisuuden klusterista esitetään hahmotelma pelialan kattavan kokonaiskuvan rakentamiseksi. Lopuksi kootaan havaintoja ja johtopäätöksiä Suomen peliteollisuusalan kasvuprosessista eri aikakausilta sekä analysoidaan kansainvälistymisprosessin kulkua ja metodologiaa. Myös näkemyksiä Suomen peliteollisuuden tulevaisuudesta esitetään. Suomen peliteollisuuden kasvua arvioidessa voidaan havaita, että sen kasvunopeus on lisääntynyt huomattavasti viimeisen muutaman vuoden aikana. Alan yritysten kasvu painottuu erittäin vahvasti globaaleille markkinoille. Peliteollisuus on kuitenkin edelleen erittäin pieni teollisuudenala Suomessa. Tulevaisuudessa sen koko ja merkitys tulevat kasvamaan, ja varsinkin Suomen mobiilipeliteollisuuden tulevaisuus näyttää valoisalta.

Cultural distance and negotiation behavior : Perception of entrepreneurs operating in Turku

This thesis investigates the influence of cultural distance on entrepreneurs’ negotiation behaviour. For this purpose, Turku was chosen as the unit of analysis due to the exponential demographic change experienced during the last two decades that has derived in a more diversified local environment. The research aim set for this study was to identify to what extent entrepreneurs face cultural distance, how cultural distance influences the entrepreneur’s negotiation behaviour and how can it be addressed in order to turn dissimilarities into opportunities. This study presented the relation and apparent dichotomy of cultural distance and global culture, including the component of diversity. The impact of cultural distance in the entrepreneurial mindset and its consequent effect in negotiation behaviour was presented too. Addressing questions about the way individuals perceive, behave and interact allowed the use of interviews for this qualitative research study. In the empirical part of this study it was found that negotiation behaviour differed in terms of how congenial entrepreneurs felt when managing cultural distance, encompassing their performance. It was also acknowledged that after time and effort, some of the personal traits were enhanced while others reduced, allowing for more flexibility and adaptation. Furthermore, depending on the level of trust and shared interests, entrepreneurs determined their attitudinal approach, being adaptive or reactive subject to situational aspects. Additionally, it was found that the acquisition of cultural savvy not necessarily conveyed to more creativity. This experiential learning capability led to the proposition of new ways of behaviour. Likewise, it was proposed that growing cultural intelligence bridge distances, reducing mistrusts and misunderstandings. The capability of building more collaborative relationships allows entrepreneurs to see cultural distance as a cultural perspective instead of as a threat. Therefore it was recommended to focus on proximity rather than distance to better identify and exploit untapped opportunities and better perform when negotiating in whichever cultural conditions.

Interdependence of International Stock Markets, European Government Bond Market and Gold Market

This thesis examines the interdependence of international stock markets (the USA, Europe, Japan, emerging markets, and frontier markets), European government bond market, and gold market during the 21st century. Special focus is on the dynamics of the correlations between the markets, as well as on, spillovers in mean returns and volatility. The mean return spillovers are examined on the basis of the bivariate VAR(1) model, whereas the bivariate BEKK-GARCH(1, 1) model is employed for the analysis of the volatility spillovers. In order to analyze the spillover effects in different market conditions, the full sample period from 2000 to 2013 is divided into the pre-crisis period (2000–2006) and the crisis period (2007–2013). The results indicate an increasing interdependence especially within international stock markets during the periods of financial turbulence, and are thus consistent with the existing literature. Hence, bond and gold markets provide the best diversification benefits for equity investors, particularly during the periods of market turmoil.

Thermal-Aware Networked Many-Core Systems

Advancements in IC processing technology has led to the innovation and growth happening in the consumer electronics sector and the evolution of the IT infrastructure supporting this exponential growth. One of the most difficult obstacles to this growth is the removal of large amount of heatgenerated by the processing and communicating nodes on the system. The scaling down of technology and the increase in power density is posing a direct and consequential effect on the rise in temperature. This has resulted in the increase in cooling budgets, and affects both the life-time reliability and performance of the system. Hence, reducing on-chip temperatures has become a major design concern for modern microprocessors. This dissertation addresses the thermal challenges at different levels for both 2D planer and 3D stacked systems. It proposes a self-timed thermal monitoring strategy based on the liberal use of on-chip thermal sensors. This makes use of noise variation tolerant and leakage current based thermal sensing for monitoring purposes. In order to study thermal management issues from early design stages, accurate thermal modeling and analysis at design time is essential. In this regard, spatial temperature profile of the global Cu nanowire for on-chip interconnects has been analyzed. It presents a 3D thermal model of a multicore system in order to investigate the effects of hotspots and the placement of silicon die layers, on the thermal performance of a modern ip-chip package. For a 3D stacked system, the primary design goal is to maximise the performance within the given power and thermal envelopes. Hence, a thermally efficient routing strategy for 3D NoC-Bus hybrid architectures has been proposed to mitigate on-chip temperatures by herding most of the switching activity to the die which is closer to heat sink. Finally, an exploration of various thermal-aware placement approaches for both the 2D and 3D stacked systems has been presented. Various thermal models have been developed and thermal control metrics have been extracted. An efficient thermal-aware application mapping algorithm for a 2D NoC has been presented. It has been shown that the proposed mapping algorithm reduces the effective area reeling under high temperatures when compared to the state of the art.

Flexible multibody dynamics and intelligent control of a hydraulically driven hybrid redundant robot machine

The assembly and maintenance of the International Thermonuclear Experimental Reactor (ITER) vacuum vessel (VV) is highly challenging since the tasks performed by the robot involve welding, material handling, and machine cutting from inside the VV. The VV is made of stainless steel, which has poor machinability and tends to work harden very rapidly, and all the machining operations need to be carried out from inside of the ITER VV. A general industrial robot cannot be used due to its poor stiffness in the heavy duty machining process, and this will cause many problems, such as poor surface quality, tool damage, low accuracy. Therefore, one of the most suitable options should be a light weight mobile robot which is able to move around inside of the VV and perform different machining tasks by replacing different cutting tools. Reducing the mass of the robot manipulators offers many advantages: reduced material costs, reduced power consumption, the possibility of using smaller actuators, and a higher payload-to-robot weight ratio. Offsetting these advantages, the lighter weight robot is more flexible, which makes it more difficult to control. To achieve good machining surface quality, the tracking of the end effector must be accurate, and an accurate model for a more flexible robot must be constructed. This thesis studies the dynamics and control of a 10 degree-of-freedom (DOF) redundant hybrid robot (4-DOF serial mechanism and 6-DOF 6-UPS hexapod parallel mechanisms) hydraulically driven with flexible rods under the influence of machining forces. Firstly, the flexibility of the bodies is described using the floating frame of reference method (FFRF). A finite element model (FEM) provided the Craig-Bampton (CB) modes needed for the FFRF. A dynamic model of the system of six closed loop mechanisms was assembled using the constrained Lagrange equations and the Lagrange multiplier method. Subsequently, the reaction forces between the parallel and serial parts were used to study the dynamics of the serial robot. A PID control based on position predictions was implemented independently to control the hydraulic cylinders of the robot. Secondly, in machining, to achieve greater end effector trajectory tracking accuracy for surface quality, a robust control of the actuators for the flexible link has to be deduced. This thesis investigates the intelligent control of a hydraulically driven parallel robot part based on the dynamic model and two schemes of intelligent control for a hydraulically driven parallel mechanism based on the dynamic model: (1) a fuzzy-PID self-tuning controller composed of the conventional PID control and with fuzzy logic, and (2) adaptive neuro-fuzzy inference system-PID (ANFIS-PID) self-tuning of the gains of the PID controller, which are implemented independently to control each hydraulic cylinder of the parallel mechanism based on rod length predictions. The serial component of the hybrid robot can be analyzed using the equilibrium of reaction forces at the universal joint connections of the hexa-element. To achieve precise positional control of the end effector for maximum precision machining, the hydraulic cylinder should be controlled to hold the hexa-element. Thirdly, a finite element approach of multibody systems using the Special Euclidean group SE(3) framework is presented for a parallel mechanism with flexible piston rods under the influence of machining forces. The flexibility of the bodies is described using the nonlinear interpolation method with an exponential map. The equations of motion take the form of a differential algebraic equation on a Lie group, which is solved using a Lie group time integration scheme. The method relies on the local description of motions, so that it provides a singularity-free formulation, and no parameterization of the nodal variables needs to be introduced. The flexible slider constraint is formulated using a Lie group and used for modeling a flexible rod sliding inside a cylinder. The dynamic model of the system of six closed loop mechanisms was assembled using Hamilton’s principle and the Lagrange multiplier method. A linearized hydraulic control system based on rod length predictions was implemented independently to control the hydraulic cylinders. Consequently, the results of the simulations demonstrating the behavior of the robot machine are presented for each case study. In conclusion, this thesis studies the dynamic analysis of a special hybrid (serialparallel) robot for the above-mentioned special task involving the ITER and investigates different control algorithms that can significantly improve machining performance. These analyses and results provide valuable insight into the design and control of the parallel robot with flexible rods.

Growth and development of sourgrass based on days or thermal units

This work was carried out with the objective of evaluating growth and development of sourgrass (Digitaris insularis) based on days or thermal units (growing degree days - GDD). Two independent trials were developed aiming to quantify the species' phenological development and total dry matter accumulation in increasing or decreasing photoperiod conditions. Plants were grown in 4 L plastic pots, filled with commercial substrate, adequately fertilized. In each trial, nine growth evaluations were carried out, with three replicates. Phenological development of sourgrass was correctly fit to time scale in days or GDD, through linear equation of first degree. Sourgrass has slow initial growth, followed by exponential dry matter accumulation, in increasing photoperiod condition. Maximum total dry matter was 75 and 6 g per plant for increasing and decreasing photoperiod conditions, respectively. Thus, phenological development of sourgrass may be predicted by mathematical models based on days or GDD; however, it should be noted that other environmental variables interfere on the species' growth (mass accumulation), especially photoperiod.