Simplex Design Research Articles

Nitrogen facilitation was maintained in sown Mediterranean forage mixtures despite drought stress conditions with concurrent general benefits upon plant aboveground water status and yield

There is an urge to optimise the sustainability and resilience of grasslands, especially in light of the extreme weather risks posed by climate change. Plant sown diversity could contribute to mitigating these risks by improving resource use efficiency as well as reducing reliance on fertilisation. We established a field experiment to determine forage swards’ performance in terms of water use, nitrogen (N) use, and dry matter (DM) yield in a semi-arid Mediterranean area which faced a severe drought period. Most variables were tested over three growing seasons, whilst DM yield had an extra year of sampling in which two levels of N fertilisation were tested. Following the Generalised Diversity-Interactions modelling approach, we manipulated the composition and evenness of forage swards including a grass (Festuca arundinacea), a legume (Medicago sativa), and a non-legume forb (Cichorium intybus). Communities were grown as monocultures or mixtures of three species according to a simplex design, which allowed us to estimate separately the two components of the diversity effect: the individual species effects and that due to species interactions. Models were tested both with sown proportions (Pi0) and realised proportions (PiR). The Pi0 models indicated a major beneficial effect of mixtures in contrast to the average monoculture performance for all studied variables. In contrast, PiR models revealed that some of the effects in Pi0 models are indeed explained by the growing proportion of M. sativa over time. However, beneficial interaction effects are still found in PiR models, especially concerning N2 fixation (with δ15N as proxy), which was maintained regardless of the drought stress level experienced by the swards. All things considered, mixed swards merit attention as a valuable nature-based solution that can optimise N management (by boosting N2 input through fixation) as well as water use. This would result in well-nurtured swards with a better ability to cope with drought stress and maintain productivity.

Influence of the simplex-centroid mixture design on the texture of sauces with different food

The use of different food matrices can result in products with different textures. In this context, the objective was to develop sauces with a mixture of tomato, pumpkin and mango pulp, using the centroid simplex design. The texture of the sauces was studied instrumentally (consistometer and texturometer) and sensorially (Acceptance and Acceptability Index – AI%). What adjusted the flow, measured in a consistometer (from 1.40 to 5.50 cm), firmness (from 51.90 to 112.54 N), consistency (1322.66 to 2864.35 N.s-1), cohesiveness (-30.31 to -87.10 N), viscosity index (-757.57 to -1933.60 N.s-1) and consistency acceptance (4.42 to 7.84) to the predictive model linear, while the AI was greater than 70%. The sauces were accepted for their satisfactory consistency, with no significant influence on the texture of the sauces, demonstrating the possibility of implementing different food matrices without compromising the consumer's taste.

Functional Properties and Acceptability of Potentially Medicinal Tea Infusions Based on Equisetum arvense, Desmodium molliculum, and Mentha piperita.

Natural herbal teas are one of the three most consumed beverages in the world, and despite their frequent use in the cosmetic, food, and pharmaceutical industries, there is still much to about them. This study aimed to determine the functional properties of tea infusions made from dried Equisetum arvense (EA), Desmodium molliculum (DM), and Mentha piperita (M) grown in the Peruvian Andes. Next, using a simplex design with unrestricted centroid amplified centroid, 12 combinations were obtained for the combination of dried leaves with EA: 0∼100%, DM: 0∼100%, and M: 0∼100% optimal combination of EA: 6.59%, DM: 84.62%, and M: 8.79% maximizes functional components for total polyphenols (2,831.18 mg EAG/100 g), flavonoids (37.73 mg CAT/g), and antioxidant capacity (145.99 μmol Trolox/g). It can be confirmed that dried mixtures of these plants made into tea are a significant source of bioactive molecules, have a tolerable flavor, and can be used for therapeutic purposes when consumed.

The effects of functional trait diversity on productivity of grass-legume swards across multiple sites and two levels of nitrogen fertiliser

Productive and stable forage yields are essential for the sustainability of ruminal livestock production. Grassland seed mixtures composed of species of diverse functional groups have previously been demonstrated to increase yield performance and stability compared to monocultures. In this study we conducted field trials with five grass and two legume species either grown in monocultures or a range of mixtures from two-species to seven-species mixtures sown in a simplex design. The species represented different functional groups regarding ability to fixate atmospheric nitrogen (N), rate of establishment and temporal persistence.The experiments were established with the same cultivars of species at five locations in Norway with climatically contrasting environments – from mild humid, mountainous continental to sub-arctic. The experimental plots were harvested for three years at four of the sites and two years at one of the sites, and they were fertilised according to normal practise in intensive silage grass production in the respective regions (regular N). At three of the sites, a treatment with low mineral N supply rate was also included.We found that crops sown as mixtures returned higher yields and contained less weeds than the average of monoculture crops, and these effects were consistent over all sites and study years. The grass-legume mixtures managed at low N supply rate performed equally well or better than monocultures or grass-only mixtures managed at regular N supply. We found no effects of the functional groups categorised as temporal persistence or rate of establishment on the yield performance, and there were no apparent benefits of increasing the number of species beyond the species P. pratense, F. pratensis and T. pratense over the three production years the experiments lasted.The results suggest that by using grass-clover mixtures, farmers can reduce N fertiliser rates, without compromising productivity of temporary grassland under northern conditions over the first three years of production.

Sustainable Mining: Reuse of Clay from Abandoned Areas in the South of Brazil for Ceramic Production Based on a Simplex Design.

The environmental impact of clay mining can be minimized using extractive mineral circularity practices. Combining the available knowledge of the characteristics of different clays with statistical tools was a decisive step for the improved use of mining resources. Through blends, all the mined materials can be incorporated to produce quality ceramic products. This study identified two types of clay from abandoned mining areas in the southern state of Santa Catarina, Brazil. These raw materials were valued together with plastic clay, which is widely used in the region, to develop 10 different formulations using a mixture design method. The clays were characterized using average granulometric distribution, mineralogical composition, and chemical, thermal and plasticity analyses. The specimens were shaped by extrusion, dried in an oven, fired in a muffle furnace and characterized based on their shrinkage, water absorption and compressive strength values. Two clays with varying characteristics-one with low workability and the other with a high silica content-exhibited difficulties (generating defects) in the extrusion shaping process, which compromised the final quality of the ceramic paste. Results showed that incorporating up to 45% by mass of the low-workability clay resulted in an increase in water absorption. The more siliceous clay improved dimensional control; however, its use at high contents (~80%) decreased the mechanical resistance. Nevertheless, when used in controlled amounts, these clays can be beneficial to the production of blocks and bricks because they have the potential to improve some properties of the finished ceramic products.

Experimental study of mixtures soil-industrial waste using simplex design for application in paving

The large amount of solid waste generated by industry is a concern for society. A possible solution is to incorporate these wastes into soils to improve their properties and contribute to sustainable development. The objective of this research was to conduct an experimental study on the chemical stabilization of two samples of tropical soils using two industrial wastes, electric arc furnace slag (EAFS) and fly ash (FA), using a design of experiments (DoE) of mixtures in a simplex centroid network. Seven mixtures were determined from the DoE for each soil sample. Using specimens of these mixes prepared at optimum moisture content, after a curing period of 7 days in a humid chamber, the properties were evaluated: unconfined compressive strength (UCS), California Bearing Ratio (CBR), and resilient modulus (RM). An improvement in the evaluated mechanical properties was observed with the addition of waste, especially with the addition of EAFS. The statistical software Minitab 18 allowed to obtain response surfaces for each mechanical property studied as a function of the pseudo-components of the mixtures. To determine the proportion of components that optimized the soil-waste mixtures, the desirability function was used, which resulted in the proportions of 80% soil, 20% EAFS, and 0% FA for both soil samples. Based on SEM and XRD tests, it was found that calcium silicate hydrate (C–S–H), calcium aluminate silicate hydrate (C-A-S-H), and calcium aluminate hydrate (C-A-H) were formed, which were responsible for improving the mechanical strength. The use of industrial waste to stabilize tropical soils with low bearing capacity proved to be a technically and environmentally viable alternative.

Sown diversity effects on yield and resistance to weed invasion: Clues to improve mixture design under climatic change in the Mediterranean

With the aim to improve mixture design, particularly in regions vulnerable to climate change, we tested several forage communities following the biodiversity–ecosystem function (BEF) framework. We sowed monocultures and 4-species mixtures from a pool of 7 forage species in a sub-Mediterranean region (Eastern Pyrenees) and assessed the diversity effects on yield and resistance to weed invasion. The tested species included two grasses and five legumes with contrasting temporal patterns and different climatic amplitudes. The communities differed in their specific composition (mixture types) and the relative abundance of the components, following a simplex design, which allowed us to estimate separately the two components of the diversity effect: the individual species effects and that due to species interactions. Whereas monocultures performed in a highly variable way within and across harvests, both in relation to yield and weed suppression, mixture variability was narrower. Both functions increased in mixtures (with significant interaction effects between 24% and 57% for yield and 13% and 96% for weed suppression), especially in those mixtures including Mediterranean species, which showed the highest diversity effects that persisted over the three experimental years. Extreme climatic events during the experimental period might have affected not only the species’ individual performances but also the strength of species interactions. Both components of diversity, identities and interactions, were key in maintaining high performances. We conclude that, under the current climate change scenario, it is important to include species in mixtures that increase resistance or resilience not only at the species level but also at the community level, through enhanced interaction effects.

Mining circular economy: Potential of rice husk ash as an alternative mineral source in the production of clay ceramics using simplex design

To determine the feasibility of using rice husk ash (RHA) in clay ceramic production, a design of experiments (DoEs) method was employed to test 10 different formulations. The vertex formulations (from triaxial diagram) were tested to obtain their chemical (XRF), mineralogical (XRD), and thermal properties (DSC/TG). After obtaining the optimum lower and upper limits of the materials, all formulations were further evaluated in terms of particle size (>45 µm), plasticity (Atterberg), real density (helium gas pycnometry), drying shrinkage at various humidities (Bigot’s curve), and technological properties exhibited after thermal processing namely, total shrinkage, water absorption index, apparent density, and diametral mechanical strength. The integration of RHA into ceramic paste showed positive impacts on the drying process and dimensional control - higher RHA content decreases shrinkage and stabilizes the drying more quickly; however, it reduced the density and plasticity of the formulations. The use of RHA > 25% left the plasticity index < 10, impairing the workability of the paste. The results of the mixture design method indicated that RHA could only be used in a limited capacity of 15% by mass; higher RHA contents would make the water absorption index exceed the threshold established as per the technical standard (25%).

Incorporating Derivative-Free Convexity with Trigonometric Simplex Designs for Learning-Rate Estimation of Stochastic Gradient-Descent Method

This paper proposes a novel mathematical theory of adaptation to convexity of loss functions based on the definition of the condense-discrete convexity (CDC) method. The developed theory is considered to be of immense value to stochastic settings and is used for developing the well-known stochastic gradient-descent (SGD) method. The successful contribution of change of the convexity definition impacts the exploration of the learning-rate scheduler used in the SGD method and therefore impacts the convergence rate of the solution that is used for measuring the effectiveness of deep networks. In our development of methodology, the convexity method CDC and learning rate are directly related to each other through the difference operator. In addition, we have incorporated the developed theory of adaptation with trigonometric simplex (TS) designs to explore different learning rate schedules for the weight and bias parameters within the network. Experiments confirm that by using the new definition of convexity to explore learning rate schedules, the optimization is more effective in practice and has a strong effect on the training of the deep neural network.

Development of Facial Cosmetic Formulations Using Microbial Levan in Association with Plant-Derived Compounds Using Simple Lattice Design

HIGHLIGHTS A levan-based formulation composed of Aloe vera and avocado oil was development. Biocosmetic showed antioxidant activity, retention capacity and good spreadability. Levan-based formulation was efficiently modeled within the simplex design space. Cosmetic formulations showed great stability and pH compatible with skin.

Mix design formulation range for metakaolin-based geopolymer synthesis

This article presents a range of mix design formulations to obtain metakaolin-based geopolymer synthesis. Geopolymer samples were synthesized from metakaolin, a 10 M sodium hydroxide solution, and alkaline sodium silicate. These three components were mixed in different proportions to form a paste which was molded in a cylindrical shape, set at room temperature for 24 hours, and demolded. The workability of the paste, the integrity of the samples, development of efflorescence, and the presence of undissolved metakaolin particles in the microstructure of the geopolymer matrix were observed. Since sodium and water play a vital role in the geopolymerization and were added at fixed proportions, a mix design was employed based on the molar proportions of aluminum, silicon, and sodium plus water. The simplex design plot was able to separate the regions of a mix of the components that showed different behaviors according to the observed responses. The dissolution of metakaolin, condensation of ortho-sialate and silicate species, which are expected to interact with each other according to the model of geopolymerization of Davidovits, can explain the observed results. “Good results” (no release of white powder, no efflorescence, no shrinkage, and no cracks) after 28 days of curing at room conditions were observed for the molar proportions 0.097 < Al < 0.112, 0.120 < Si < 0.178, and 0.711 < Na+H2O < 0.775 (Na/H2O = 0.185).

Measurements of soot and response optimisation of laminar pool and prevaporised jet flames for various oxygenated biofuels

In this study, the generation of soot from the combustion of biodiesels and their blend with fossil diesel are investigated under laminar pool flame and prevaporised diffusion jet flame conditions. Neat biodiesels from eight feedstocks including carotene palm, palm, soy, coconut, rice bran, waste vegetable oil, duck, and goose, alongside two methyl esters of methyl laureate and methyl myristate are blended with fossil diesel at 20% volumetric intervals to form 51 different blends. The soot volume fractions for the combustion of all blends are determined using continuous-wave laser cavity extinction (CW-LCE) calibrated 2D laser-induced incandescence (2D-LII) technique. Results show that biodiesels with higher degree of saturation produce less soot, as reflected in both laminar pool and prevaroprised diffusion jet flames. The experimental data is further analysed using design of experiments (DOE) methodology. The mixture design model (MDM) following the simplex design is used to focus on the soot generating effects arising from the chemical compositions by classifying the chemical components into hydrocarbons and saturated, monounsaturated and polyunsaturated fatty acid methyl esters (FAME). The results from the Cox response trace plot associated with DOE elucidate the effects of the individual chemical group within the fuels. Both laminar flame types for the all 51 biodiesel-diesel blends exhibit the same trends with differing magnitudes. Saturated FAME has the largest singular effect on soot generation followed by hydrocarbons. However, when only neat biodiesels are considered, the laminar pool flame and laminar diffusion jet flames show differing trends for all the chemical groups. Monounsaturated FAME and saturated FAME have the greatest influence on neat biodiesel-generated soot for laminar pool flame and laminar diffusion jet flame, respectively. From the mixture design model, an optimum synthetic biodiesel mixture containing 16.1%, 34.6% and 49.3% of saturated, monounsaturated and polyunsaturated methyl esters is recommended for the lowest soot generation.

High-dimensional normalized data profiles for testing derivative-free optimization algorithms.

This article provides a new tool for examining the efficiency and robustness of derivative-free optimization algorithms based on high-dimensional normalized data profiles that test a variety of performance metrics. Unlike the traditional data profiles that examine a single dimension, the proposed data profiles require several dimensions in order to analyze the relative performance of different optimization solutions. To design a use case, we utilize five sequences (solvers) of trigonometric simplex designs that extract different features of non-isometric reflections, as an example to show how various metrics (dimensions) are essential to provide a comprehensive evaluation about a particular solver relative to others. In addition, each designed sequence can rotate the starting simplex through an angle to designate the direction of the simplex. This type of features extraction is applied to each sequence of the triangular simplexes to determine a global minimum for a mathematical problem. To allocate an optimal sequence of trigonometric simplex designs, a linear model is used with the proposed data profiles to examine the convergence rate of the five simplexes. Furthermore, we compare the proposed five simplexes to an optimized version of the Nelder–Mead algorithm known as the Genetic Nelder–Mead algorithm. The experimental results demonstrate that the proposed data profiles lead to a better examination of the reliability and robustness for the considered solvers from a more comprehensive perspective than the existing data profiles. Finally, the high-dimensional data profiles reveal that the proposed solvers outperform the genetic solvers for all accuracy tests.

Recycling carbon-steel waste from blast cleaning by powder metallurgy employing the augmented simplex lattice design

Blasting cleaning is widely used to prepare and clean surfaces, but the waste resultant is generally contaminated and recycling is an obstacle. The present study shows a technical route to reuse the carbon-steel shot blast waste to produce a solid material by powder metallurgy. The waste was selected by sieve and the particles mixtures were analyzed and selected with the aid of a simplex lattice experimental design and tap density. The characterization of waste particles was conducted in terms of their morphological shape and their technological and physical characteristics. The density of green compacts and sintered samples reached 7.11 g.cm-3 and 7.06 g.cm-3, respectively. After quenching and tempering heat treatments, the sintered steel exhibited a martensitic microstructure with a hardness of 430 HV. The sintered bodies showed promising properties and the powder metallurgy method for recycling shot blast waste was considered viable.

High fiber content snack bars made with maize biomass flour, rice flakes and oat flakes: Physicochemical properties and sensory acceptance.

The aim of this study was to assess physicochemical properties and sensory acceptance of snack bars (SBs) made with different levels of maize biomass flour (MBF), rice flakes (RF) and oat flakes (OF). A simplex design was used, with 6 mixtures and 2 repetitions. The different levels of MBF, RF and OF used in the SBs influenced all physicochemical properties evaluated (moisture, water activity, specific volume, hardness and instrumental color). SB4 (containing 14.85:5:10.85% of MBF:RF:OF, respectively) and SB6 (containing 14:8:8% of MBF:RF:OF, respectively) were the closest to the desirable formulation according to the desirability diagram for the physicochemical properties of the SBs. SB1 (containing 20:5:5% of MBF:RF:OF, respectively) was also selected for sensory analysis as it showed the highest MBF content among all formulations. None SBs presented a microbiological risk. The SB6 presented the highest sensory acceptance and purchase intent, highlighting its rich content of dietary fiber (16.45 ± 0.1 g/100 g) and protein (7.04 ± 0.02 g/100 g) besides its low-calorie characteristic (1421.22 kJ/100 g/339.68 kcal/100 g). The development of SBs using MBF is feasible in relation to their physicochemical and sensory properties, which can stimulate the sustainable production of new goods from this by-product.

Adjustment of Strength and Air Permeation Resistance of Low Basis Weight Paper by Separated Beating

This paper reports a method for improving the air permeation resistance and strength of low basis weight paper by applying separated beating. Sw-BKP was beaten to prepare three pulp stocks with three freeness levels (713, 500, and 300 mL CSF), and the fiber properties and one pass retention of the handsheet were analyzed. In addition, using Scheffe’s three-component simplex design, this study investigated the change in the physical properties of paper according to the mixing of the three types of the pulp. The freeness of the pulp, air permeation resistance, and tensile strength of the paper were evaluated. When the freeness of the Sw-BKP decreased, the average fiber length decreased while external fibrillation and WRV increased. When 400 mL CSF pulp was prepared by mixing 300 mL CSF pulp with unbeaten pulp (713 mL CSF), the tensile strength of the handsheet was slightly lower as compared with the case when the same freeness was obtained by mixing 300 mL CSF pulp with 500 mL CSF pulp. However, the air permeation resistance was improved. The formation of the handsheet was improved when 713 mL CSF pulp and 300 mL CSF pulp were blended, and the air permeation resistance increased significantly as the fines increased. However, the tensile strength decreased because of the incorporation of unbeaten pulp, which weakened the bonds between the fibers of the handsheet. Blending pulp with low freeness and unbeaten pulp is advantageous if separate beating is applied during the manufacturing of the low basis weight paper to improve the air permeation resistance regardless of the decrease in tensile strength under certain freeness conditions.

Relationship between the composition and hydration-microstructure-mechanical properties of cement-metakaolin-limestone ternary system

This paper aims to elucidate the effect of changes in the mix composition on the properties of Portland cement (PC)-metakaolin (MK)-limestone (LS) ternary system. To achieve this, the mixture proportion was optimized using the simplex design method and its effect on the properties of the binder was evaluated experimentally and correlated via graphical visualization. Experimental results confirmed the enhancement and acceleration of kinetics of cement hydration by LS and MK. However, a higher porosity was noticed at early age and was attributed to the high reactivity of MK which hindered it from acting as an effective filler. Therefore, the correlation between the optimum mix design and compressive strength was found to be dependent on the paste age. The findings of this paper would contribute to a better understanding of the dependence of the properties of PC-MK-LS ternary system on its composition.

Plant diversity enhanced yield and mitigated drought impacts in intensively managed grassland communities

Abstract There is a global requirement to improve the environmental sustainability of intensively managed grassland monocultures that rely on high rates of nitrogen fertiliser, which is associated with negative environmental impacts. Multi‐species grass–legume mixtures are a promising tool for stimulating both productivity and sustainability in intensively managed grasslands, but questions remain about the benefit of increasing the diversity of plant functional groups. We established a plot‐scale experiment that manipulated the diversity of plant communities from a six‐species pool comprising three functional groups: grasses, legumes and herbs (two species each). Communities were grown as monocultures, or mixtures of two to six species, following a simplex design. This allowed us to quantify species’ identity effects and functional group interaction effects. To investigate the impact of severe weather events, main plots were split and two levels of water supply, ‘rainfed’ and a 2‐month experimental drought, were applied. Mineral nitrogen fertiliser was applied at 150 kg ha−1 year−1, and a Lolium perenne monoculture received 300 kg ha−1 year−1 (300N) as a highly fertilised comparison. Annual above‐ground biomass was measured for 2 years. We found a strong positive effect on yield due to functional group interactions. Multi‐species communities with three functional groups yielded more than the best‐performing monoculture over a large range of different relative abundances of the three functional groups. The highest diversity community outperformed the 300N L. perenne under rainfed conditions. Although species' monoculture yields were generally reduced by the experimental drought, the interaction effects were not affected by drought and remained sufficiently large for the six‐species mixture under drought to have similar yields to both the best‐performing monoculture and the 300N L. perenne under rainfed conditions. Synthesis and applications. Plant diversity can result in higher yields, mitigate the yield risks associated with extreme weather events and displace fertiliser inputs and their embedded greenhouse gas emissions. Multi‐species swards offer a practical, farm‐scale management action to enhance the sustainability of intensive grassland production.

Performance of reduced fat-reduced salt fermented sausage with added microcrystalline cellulose, resistant starch and oat fiber using the simplex design

The search for ingredients that improve technological and nutritional aspects of food has been intensified in recent years by both researchers and industry. Thus, the aim of this study was to evaluate fermented sausages with simultaneous reduction of fat (25%) and salt (25% KCl; 75% NaCl) using up to 2% of three different dietary fiber: microcrystalline cellulose (MCC), resistant starch (RS) and oat fiber (OF). Technological and sensory evaluations used the simplex-centroid mixture design. The dietary fiber added did not affect the weight loss, pH values and sensory acceptance. Models were obtained for water activity, lactic acid bacteria, hardness, chewiness and TBARS values. When included in combination the three dietary fiber helped reduce water activity, inclusion of MCC increased the population of lactic acid bacteria, and inclusion of OF with MCC demonstrated an antioxidant effect and improved hardness and chewiness. These dietary fibers are ingredients that can contribute to the development of reduced fat – reduced salt fermented sausage.

Repeated-value simplex designs better rotations of the classical simplex experimental design

Repeated-value simplex designs better rotations of the classical simplex experimental design