Empirical Model Research Articles

Ground-Motion Modeling of the 2016 Mw 6.2 Amatrice, Italy, Earthquake, by a Broadband Hybrid Kinematic Approach, Including Empirical Site Effects

Abstract The region of Central Italy is well known for its moderate to large earthquakes. Events such as the 2016 Mw 6.2 Amatrice earthquake generated in the shallow extensional tectonic regime motivate numerical simulations to gain insights into source-related ground-motion complexities in the near-source region. We utilize a hybrid integral-composite kinematic rupture model by Gallovič and Brokešová (2007) to simulate the Amatrice earthquake in a broadband frequency range (up to 10 Hz). In the first step, we optimize the input source parameters using a grid-search method by minimizing the spectral acceleration bias between synthetic and recorded strong-motion data at reference rock stations within 50 km of the source. To verify the robustness of the optimal model, we simulate the ground motions at 400 virtual stations and compare their spectral accelerations with the predictions of an empirical nonergodic ground-motion model (GMM) for rock sites in Central Italy (Sgobba et al., 2021). The synthetics show a good agreement with the empirical model regarding both median and variability. Finally, we account for local site effects at nonreference stations by combining the simulations on rock with empirical site terms derived by the nonergodic GMM. The site-corrected spectral responses generally improve the match with the observations, demonstrating a successful fusion of numerical simulations with empirical estimates toward reproducing near-source ground motions.

New Data-Driven Models of Mass Flow Rate and Isentropic Efficiency of Dynamic Compressors

Dynamic compressors are widely used in many industrial sectors, such as air, land, and marine vehicle engines, aircraft environmental control systems (ECS), air-conditioning and refrigeration, gas turbines, gas compression and injection, etc. The data-driven formulas of mass flow rate and isentropic efficiency of dynamic compressors are required for the design, energy analysis, performance simulation, and control- and/or diagnosis-oriented dynamic simulation of such compressors and the related systems. This work develops data-driven models for predicting the performance of dynamic compressors, including empirical models for mass flow rate and isentropic efficiency, which have high prediction accuracy and broad application range. The performance maps of two multi-stage axial compressors of an aero engine and a centrifugal compressor of an aircraft ECS were chosen for evaluation of the existing empirical formulas and testing of the new models. There are 16 empirical models of mass flow rate and 14 empirical models of isentropic efficiency evaluated, and the results show that it is necessary to develop highly accurate empirical formulas both for mass flow rate and isentropic efficiency. With the data-driven method, two empirical models for mass flow rate and one for isentropic efficiency are developed. They are in general form, with some terms removable to make them simple while enhancing their applicability and prediction accuracy. The new models have much higher prediction accuracy than the best existing counterparts. The new mass flow rate models predict for the three compressors a mean absolute relative deviation (MAD) not greater than 1.3%, while the best existing models all have MAD > 2.0%. The new efficiency model predicts for the three compressors an MAD of 1.0%, 0.4%, and 1.9%, respectively, while the best existing model predicts for the three compressors an MAD of 1.8%, 0.8%, and 3.2%, respectively.

Laboratory observations for examining estimates of soil dry surface layer thickness with parsimonious models

ABSTRACT Soil dry surface layer (DSL) thickness is often considered a key parameter for land surface resistance to gas exchange. Commonly used, simple models for DSL thickness are typically empirical in nature and based on limited observational evidence. Laboratory experiments were performed to test soil condition and boundary effects on DSL formation. DSL thickness was analyzed in soil columns with varying texture, initial water content, and potential evaporation rate. DSLs formed to greater depth in fine-textured compared to coarse-textured soils, when beginning from similar initial water content. Based on experiments, we compared a simple but physically-based mass balance DSL model to an empirical DSL model from the literature. The mass balance model performed better than the empirical relative-wetness-based model, and is similar in structure to the current DSL parameterization in the Community Land Model. Results suggest soil resistance parameterizations can be improved by employing simple, but texture-dependent, physically-based DSL formulations.

Numerical investigation on sample population requirement for mean particle diameter analysis

The determination of the minimum particle number needed to meet error specifications and confidence levels poses a fundamental challenge in particle size analysis. Conventional models, primarily designed for log-normal distributions, may yield inaccuracies when applied to other distribution functions. This study introduces a numerical approach to explore the necessary sample size for measuring different types of mean diameters. The methodology involves distribution conversion, sample generation, repeated sampling, and error estimation. Specifically, Gates–Gaudin–Schuhmann (GGS) and Rosin–Rammler (RR) distributions serve as representative models in this investigation. The impact of sample size, span ratio, and boundary sizes on relative errors is examined. Additionally, an empirical model is formulated, simplifying the calculation of the requisite sample size when the relative error and mass-based span ratio are provided. The proposed method is also verified using experimental particle size data that follow the RR distribution.

Experimental study on impact behaviour of normal strength mortar at cryogenic temperatures and after freeze-thaw cycles

Concrete structures employed for the storage of Liquefied Natural Gases (LNG) currently undergo temperature as low as −170 °C. These critical engineering structures may also experience dynamic loads such as impact or explosion during service life. Therefore, it is crucial to explore the mechanical response of concrete at intermediate to high strain rates together with low temperatures or cryogenic freeze-thaw (FT) cycles. This study presents experimental research into the combined effects of low temperatures and strain rate on normal strength mortar, providing a preliminary analysis of the dynamic performance of concrete at low and cryogenic temperatures. A Split Hopkinson Pressure Bar (SHPB) device was used to investigate the characteristics of dynamic compression (at strain rates of 40, 80, 120 and 160 s−1) and dynamic split tension (at strain rates of 20, 40, 60 and 80 s−1) of Normal Strength Mortar (NSM) at different low temperatures. In addition, the dynamic compression (at strain rates of 80, 130 and 180 s−1) after cryogenic FT cycles was also explored. The findings revealed that the failure pattern of NSM samples exposed to coupled low temperature or cryogenic FT cycles and high strain rate loading notably varied from that observed under room temperature condition. Both the dynamic compressive and split tensile strengths of NSM increased with the strain rates at all temperatures. At −160 °C, the dynamic compressive and splitting tensile strengths of NSM specimens were greater than those at room temperature (by 10.94 % and 28.29 %, respectively) and −70 °C (by 3.13 % and 4.12 %, respectively). Cryogenic freeze-thaw cycles evidently impacted the material static and dynamic performance. An empirical model was developed to predict the dynamic increase factors (DIFs) for both dynamic compression and splitting tensile strengths of NSM at low/cryogenic temperatures and after freeze-thaw cycles. Scanning electron microscopy (SEM) technique was performed to study and comprehend the microscopic processes and microstructural changes after FT cycles.

Correction to: Empirical dynamic modeling for sustainable benchmarks of short-lived species

Correction to: Empirical dynamic modeling for sustainable benchmarks of short-lived species

CFO co-option and dividend payments: the moderating role of CFO talent

Purpose This study aims to investigate the association between the co-option of the chief financial officer (CFO) and dividend payments, assessing whether the talent of the CFO affects this association. Design/methodology/approach The empirical analyses were based on hand-collected data for 922 firm-year observations from 157 European listed firms, during the period 2013–2019. Empirical models, based on a two-step estimation procedure, involved the use of instrumental variables and the generalised moment method. Findings The results show that CFO co-option is negatively associated with the level of dividend payments. It was also found that the degree of CFO talent moderates the negative association between CFO co-option and dividend payments. Research limitations/implications This investigation responds to the call for literature which examines how chief executive officer (CEO) – CFO relationships influence firms’ policies and outcomes. The study offers novel evidence for the individual-level characteristics of CFOs which are likely to reduce the effectiveness of CEO power and increase monitoring on corporate decisions on dividends. Practical implications The study sheds light on the effect of the interactions between CEOs and CFOs, which are important for investors’ expectations. In this regard, investors may be interested in the CFO profiles which may reduce CEO power over dividend policies. Originality/value Unlike previous research, which focused on CEOs, the authors are the first to shed light on the role of CFOs as key decision makers in influencing the dividend policies in modern corporations.

Relationship between the SST diurnal cycle over the Tropical Western Pacific Ocean and subseasonal/seasonal oscillations: Associations with wind speed and outgoing longwave radiation

In this study, the relationship between SST diurnal cycle,10 m wind speed (W10) and Outgoing Longwave Radiation (OLR) is investigated. A wavelet spectral analysis was applied to SST hourly data to identify the SST diurnal cycle over the Tropical Western Pacific Ocean (TWPO). The SST diurnal cycle was identified as a prominent spectrum peak in waves with an oscillation period of 1 day. An inverse energy cascade hypothesis suggests that the energy from the SST diurnal cycle propagates and gets absorbed by waves within the subseasonal timescale. Three windows were selected to represent the diurnal (0–2 days), subseasonal (15–60 days), and seasonal (80–200 days) timescales. A wavelet-filtered analysis was performed in these windows, revealing inverse SST/ wind speed and direct SST/ OLR correlations over TWPO. These findings are consistent with empirical parametric models. Additionally, this study demonstrates the rectification mechanism of SST through a wavelet-filtered approach, identifying statistically significant correlations at the 5 % level within the diurnal window (0–2 days), particularly in the central tropical Pacific. Wavelet-filtered anomalies of SST, W10, and OLR along 50–160°E reveal the alternating dry and wet phase propagation across the Indo-Pacific in the subseasonal window, which is associated with the Madden-Julian Oscillation (MJO). Furthermore, westward propagating anomalies in the Indian Ocean and eastward propagating anomalies east of the Maritime Continent (MC) and within the Pacific were identified in the seasonal window, resembling patterns of Rossby and equatorial Kelvin waves, respectively.

Chitosan-Based Oleogels: Emulsion Drying Kinetics and Physical, Rheological, and Textural Characteristics of Olive Oil Oleogels.

Oleogels are of high interest as promising substitutes for trans fats in foods. An emulsion-templated method was used to trap olive oil in the chitosan crosslinked with vanillin matrix. Oil in water emulsions (50:50 w/w) with different chitosan content (0.7 and 0.8% w/w) with a constant vanillin/chitosan ratio (1.3) were air-dried at different temperatures (50, 60, 70, and 80 °C) and freeze-dried (-26 °C and 0.1 mbar) to produce oleogels. Only falling rate periods were determined during air-drying kinetics and were successfully modeled with empirical and diffusional models. At a drying temperature of 70 °C, the drying kinetics were the fastest. The viscoelasticity of oleogels showed that the elastic modulus significantly increased after drying at 60 and 70 °C, and those dried at 50 °C and freeze-dried were weaker. All oleogels showed high oil binding capacity (>91%), but the highest values (>97%) were obtained in oleogels with a threshold elastic modulus (50,000 Pa). The oleogels' color depended on the drying temperature and chitosan content (independent of the drying method). Significant differences were observed between air-dried and freeze-dried oleogels with respect to oxidative stability. Oxidation increased with the air-drying time regardless of chitosan content. The found results indicated that drying conditions must be carefully selected to produce oleogels with specific features.

Psychometric analysis of the kansas city cardiomiopathy questionnaire-23 in a european population

Abstract Background People affected by heart failure (HF) often exhibit poor quality of life, which places a great deal of burden on the healthcare systems. The Kansas City Cardiomyopathy Questionnaire (KCCQ)-23 is one of the most widespread instruments to measure quality of life in this population. So far, its psychometric properties have been investigated by a broad array of research, but the overall findings reveal inconsistency of the factorial structure and lack of rigorous psychometric testing. Objective The aim of this study was to evaluate the psychometric properties of the KCCQ-23 in a European cohort of HF patients. Methods The data used for this study were collected for the MOTIVATE-HF study, which was a three-arm, multicenter, randomized controlled trial to evaluate the effect of motivational interviewing for improving self-care in HF. A group of 510 patients (median age 74 years, IQR=18, 58% males) completed the KCCQ-23 along with clinical and psychosocial measures. Factorial validity was established with confirmatory factor analysis (CFA); omega and model-based internal consistency indexes were computed to examine the internal consistency of the scale. Convergent validity was established by correlating the KCCQ-23 scores with several clinical and psychosocial measures. Measurement invariance testing was conducted within a multigroup framework across patients with preserved vs those with reduced ejection fraction. Results Two CFA solutions were tested, which confirmed the theoretical and empirical models postulated by the original author. The internal consistency coefficients for the latent dimensions were adequate (Omega range =0.77-0.93; internal consistency coefficient =0.89-96)- KCCQ-23 scores were found to be correlated with ejection fraction, NYHA levels, quality of life, self-care confidence, anxiety and depression, and symptom burden, supporting its convergent validity. Finally, the KCCQ-23 was invariant across ejection fraction levels, both in the theoretical and empirical factor solution. Conclusion Overall, this study provides for the first time evidence that the KCCQ-23 has satisfactory psychometric properties, promoting its use in clinical settings and research to investigate the quality of life in patients with HF.

Parametric Analysis and Optimization on Fiber Laser Micro-Milling on AZ31 Magnesium Alloy

One of the proficient machining technologies to create micro-features in a variety of materials is the laser micro-milling process. This procedure involves irradiating a highly concentrated laser beam on the sample and performing laser cutting at various cutting patterns to change the surface conditions and enhance the characteristics of that surface tribology. In this work, an effort has been made to mill magnesium alloy (AZ31) material using a laser. The pulse frequency, laser beam power, cutting speed, number of passes, and transverse feed are among the different process variables taken into account for the current research effort. Measured results include depth of cut and surface roughness. To ensure the validity of the established empirical models, this paper also presents experimental data. Several surface plots have been used to examine the test data. To get the lowest values of surface roughness and depth of cut, multiperformance optimization is also utilized. The influence of process factors on response has also been examined using optical microscopic images. Gray relational analysis approach is also applied to obtain the multiobjective optimization parametric combination and based on the calculated results of gray relational grade, it is revealed that improvement in the value of gray relational grade at predictive setting is 0.054 compared to the initial parametric combination.

Effect of Chinese outward FDI on youth unemployment in sub-Saharan Africa.

This paper investigates the effect of Chinese outward foreign direct investment (FDI) on youth unemployment in sub-Saharan Africa (SSA) by using a modified labour demand model to identify the investment sources that are helpful for reducing youth unemployment in the region. The model is applied to a panel of 42 countries for the period 2003-2021 using random-effect, and generalized method of moment (GMM) estimators for robustness check. Our results suggest that Chinese FDI has direct short-term reducing effect on youth unemployment in SSA. The direction of China's capital investment to infrastructure development and other labour-intensive activities leads to immediate reduction in youth unemployment. However, overtime, due to absence of linkages with domestic firms, and thus lack of demand effects, Chinese FDI becomes insignificant for employment creation. Our results also indicate that Other FDI does not lead to significant reduction in youth unemployment both currently and overtime. Our analysis gives partial support to the argument that the impact of Chinese FDI may differ from those of developed countries. Finally, we could not find evidence that the effect of FDI on employment depends on host country human capital and institutional quality. Several specifications of the empirical model are tested, and explanations are provided for the results. Policy implications are highlighted, especially the need to attract more job absorbing FDI and improve domestic absorptive capacity.

Machine learning versus empirical models to predict daily global solar irradiation in an average year: Homogeneous parallel ensembles prevailed

Abstract Accurate predictive daily global horizontal irradiation models are essential for diverse solar energy applications. Their long-term performances can be assessed using average years. This study scrutinized 70 machine learning and 44 empirical models using two disjoint five-year average daily training and validation datasets, each comprising 365 records and 10 features. The features included day number, minimum and maximum air temperature, air temperature amplitude, theoretical and observed sunshine hours, theoretical extraterrestrial horizontal irradiation, relative sunshine, cloud cover and relative humidity. Fourteen machine learning algorithms, namely, multiple linear regression, ridge regression, lasso regression, elastic net regression, Huber regression, k-nearest neighbors, decision tree, support vector machine, multilayer perceptron, extreme learning machine, generalized regression neural network, extreme gradient boosting, gradient boosting machine and light gradient boosting machine were trained, validated and instantiated as base learners in 4 strategically designed homogeneous parallel ensembles—variants of pasting, random subspace, bagging and random patches—which also were scrutinized, producing 70 models. Specific hyperparameters from the algorithms were optimized. Validation showed that at least two ensembles outperformed its individual model. Huber-subspace ranked first with a root mean square error of 1.495 MJ/m2/day. The multilayer perceptron was most robust to the random perturbations of the ensembles which extrapolates to good tolerance to ground truth data noise. The best empirical model returned a validation root mean square error of 1.595 MJ/m2/day but was outperformed by 93% of the machine learning models with the homogeneous parallel ensembles producing superior predictive accuracies.

Towards a Canadian National River Water Quality-Modelling System: State of Science and Future Prospects

Water quality is of significant concern and ultimately critical to every Canadian’s quality of life and security. Canada has diverse and vast landscapes and stressors that impact various waterbodies differentially, with influencing factors including contaminant and nutrient loads from human activity (mining effluent, wastewater, agricultural runoff, plastics), landscape change (wetland drainage, urbanization) and climate change (warming water temperatures, longer open water seasons, extreme hydrological events, intensifying wildfires). Canadian rivers are especially important to the overall biogeochemistry, hydrology, biodiversity, and ultimate health of aquatic and terrestrial ecosystems. While each of Canada’s provinces and territories has extensive river water quality (physical, chemical, biotic) data and monitoring programs, Environment and Climate Change Canada coordinates various national programs that contribute to the collection and consolidation of these data and conducts extensive research into the study and modelling of key river water quality processes. Despite program-specific efforts, there remains poor capacity to predict current and future conditions in monitored and unmonitored Canadian rivers, particularly remote or northern rivers, due to a myriad of factors including lack of coordination amongst groups and examination of areas in which modelling efforts might be integrated. Herein, we review and analyse the current state of data availability, process studies, and modelling systems for Canadian river water quality. Our synthesis reveals that specific physical processes (water temperature, ice formation, permafrost thaw, sediment dynamics), biogeochemical processes (dissolved oxygen, dissolved organic matter, nutrient cycling, metals/contaminants) and ecological/biological features (biota mass, functional indicators) are well understood, though complex, and are amenable to empirical or mechanistic modelling. Review of this information assists us in identifying opportunities and challenges for developing a national water quality modelling system (NWQMS), that would eventually include similar modelling activities for parallel processes in lakes and integrated watersheds. We identify needs for stronger coordination of monitoring programs in remote areas, recommend use of novel remote sensing technologies, and development of a flexible, iterative ‘process’ for integrated modelling to which stakeholders beyond government can contribute. Such a platform would support short and long-term predictive models of Canadian water quality and ecosystem health, inform effluent concentration limits, and be an early warning system for source waters.

A coupled three-dimensional wormhole modeling in heterogenous carbonate lithology in limited-entry and openhole completions

Wormhole propagation in carbonate formation is a well-researched area with several proposed empirical, analytical, and numerical models to predict the process efficiency. The most reliable and up-to-date model is the two-scale continuum (TSC) model, based on numerical simulation of reactive transport in a porous medium. The model has been utilized in two and occasionally in three-dimensional space but has yet to consider the lithology impact in three-dimensional space (3D). This study demonstrated the impact of lithology considering both openhole and limited-entry completion in 3D space. Moreover, the model considered the acid temperature impact on acidizing efficiency. Results showed that limited entry results in a longer wormhole at the expense of its coverage along the wellbore. Similarly, the higher the number of perforations, the lower the wormhole radius but the higher the coverage. Increasing acid temperature results in better dolomite and lower limestone acid stimulation efficiency. In mixed mineralogy, the positive impact of temperature appears at 50 °C and higher. Wormholes propagate in the limestone sections in layered formation with openhole completion, leaving the dolomite under-stimulated, even at high acid temperatures. Limited entry completion in dolomite layers did not prevent the acid from traveling to the limestone layers but provided limited stimulation in the dolomite section. This is the first study to utilize the TSC model to predict the acid stimulation outcomes at field conditions in 3D space.

A Unified Adsorption Kinetic Model Inspired by Epidemiological Model: Based on Adsorbates "Infect" Adsorbents.

Adsorption is a unit operation used in various fields, including the environmental, chemical, and pharmaceutical industries. Understanding the adsorption kinetics is crucial to designing efficient adsorption systems. However, existing empirical adsorption models are limited in providing insights into the mass transfer mechanisms. Additionally, the absence of a unified adsorption kinetic model hampers the effective comparison of different adsorption systems. Here, we viewed the adsorption as an "infectious process of adsorbates by adsorbents" akin to epidemiology. In epidemiology, individuals can be divided into susceptible, infected, and recovered compartments, ignoring the complexities of movement among individuals. Analogously, we have categorized the adsorbates as adsorbable, adsorbed, and removed compartments. Thus, we proposed a unified adsorption kinetic model (the monolayer-multilayer-adsorbable-adsorbed-removed model) that accommodates monolayer/multilayer adsorption. The model was designed to encompass diverse adsorption setups, including continuous and batch processes with fixed/dispersed adsorbents. The versatility and applicability of the model were demonstrated through validation using a diverse set of experimental data. This validation underscored its effectiveness in water/wastewater treatment, salt reduction, metal recovery, and drug purification. A MATLAB-based program for solving this model was made available to researchers for their utilization and further investigations. Overall, this study developed a versatile adsorption kinetic model that offers a comprehensive and unified understanding of adsorption kinetics across various applications.

Mitigating the brittle behavior of compression cast concrete using polypropylene fibers

Compression casting enhances mechanical properties, durability, and microstructure of concrete while reducing cement usage and carbon emissions. However, its brittleness restricts its widespread use. This study aims to mitigate the brittleness of compression cast concrete (CCC) through fiber reinforcement. Eleven concrete mixes with varied volumetric ratios (0, 0.05, 0.1, 0.15, 0.2, and 2 %) and aspect ratios (250, 313, and 396) of polypropylene fibers were prepared. Both compressed and uncompressed specimens were analyzed for compressive stress-strain behavior, compressive strength, modulus of elasticity, toughness, specific toughness, and microstructure. Results show that CCC specimens have steeper and shorter descending segments on their compressive stress-strain curves than uncompressed concrete, indicating brittleness. Adding polypropylene fibers significantly reduces this brittleness by enhancing the post-peak compressive stress-strain behavior of CCC. Fiber reinforced CCC specimens exhibit significant enhancements in compressive strength, modulus of elasticity, and toughness (up to 68 %, 34 %, and 38 % respectively) compared to uncompressed plain concrete. Mercury intrusion porosimetry, scanning electron microscopy, and backscattered electron imaging confirm that compression casting strengthens the interfacial transition zone of both plain and fiber reinforced CCC. Proposed empirical models accurately forecast the modulus of elasticity, compressive strength, and peak compression strain for both types of CCC. Comparisons with existing models show that Nematzadeh and GB50010–2010 models effectively predict the ascending part of the compressive stress-strain curves of plain and fiber reinforced CCC. These findings affirm that polypropylene fibers effectively reduce the brittleness of CCC, promoting its practical application.

Empirical Model Variability: Developing a new global optimisation approach to populate compression and compaction mixture rules

This study systematically evaluated the predictive accuracy of common empirical models for pharmaceutical powder compaction. A dataset of nine placebo and twelve active pharmaceutical ingredient (API) loaded blend formulations (four APIs at three drug loadings) was fitted to the widely used empirical tablet compression (Gurnham, Heckel, and Kawakita) and compaction (Ryshkewitch-Duckworth and Leuenberger) models. At low API loadings (<20w/w%), all models achieved R2 above 90 % and RRMSE (relative root mean squared error) below 0.1. However, as API loads increased, overall model performance decreased, notably in the Heckel model. A parameter variability analysis identified multiple parameter pairs achieving acceptable fits. Consequently, a novel global optimization approach was developed populating arithmetic, geometric, and harmonic mixture rules for empirical tuning parameters. This method outperformed the traditional line of best fit approach. A cross validation study revealed that this method is capable of predicting tuning parameters which achieve an acceptable Goodness of Fit for new blends. Finally, with the restriction of maintaining consistent parameters for the placebo blend, the proposed method could substantially reduce the experimental requirements and API consumption for the exploration of new blends.

Mathematical modeling of the enzymatic hydrolysis of lignocellulosic waste in membrane bioreactor considering transport phenomena

Enzymatic hydrolysis is a crucial step in processing lignocellulosic biomass into biofuels and other valuable products in biorefineries. Applying a membrane reactor to realize this process allows for continuous separation of inhibitory end-products, thus improving process efficiency. Developed so far models have generally been dedicated to describing the reaction kinetics without considering transport phenomena and flux decline prediction. In the present paper, a new mathematical model simulating the hydrolysis process course in membrane bioreactor was established. Compared to previous reports, our study presents a novel approach to modeling the process accounting for the reaction course and permeate flux decline depending on reaction hydrodynamics. A surface renewal theory and empirical reaction kinetic model were implemented to simulate the influences of the operating parameters on the permeate flux and the monosaccharide concentration in the permeate. A procedure to determine the model parameters with experimental data was also presented. The proposed model simulated experimental data with good accuracy (R2>0.97). The total mass of glucose and xylose produced during 10 h of the hydrolysis performed under mixing conditions equaled 2.37 g and 2.39 g for the pressure of 0.4 and 0.6 bar, respectively. They correspond to the high hydrolysis yield, equaled in average to 99.1 %.

Suitable Model for Rehydration of Dried Red Beets: Effect of Solid-to-Liquid Ratio on Rehydration Characteristics

Rehydration of food products was carried out in various amounts of liquid. The effects of the solid-to-liquid ratio on rehydration characteristics of dried red beets were investigated. Six values of the solid-to-liquid ratio (1:20, 1:15, 1:10, 1:5, 1:3, and 1:1) were taken into consideration. Red beets cubes (10 mm) were dried in a forced convection (2 m/s; 60 °C) and then rehydrated in distilled water at a temperature of 20 °C. The kinetics of mass gain, dry matter loss, water gain, moisture content increase, and volume increase were modeled using the empirical Peleg model which parameters have physical meanings. Equations were formulated to make the Peleg model parameters dependent on the solid-to-liquid ratio. The obtained results indicated that the amount of rehydrating water influenced the values of the model parameters and the course of dried red beets rehydration and helped explain the rehydration kinetics. The Peleg model can be recommended for describing the kinetics of mass gain (R2 = 0.9662–0.9895), dry matter loss (R2 = 0.7042–0.9881), water gain (R2 = 0.9732–0.9913), moisture content increase (R2 = 0.9770–0.9929), and volume increase (R2 = 0.9374–0.9847) during the rehydration of dried red beet cubes at all considered values of the solid-to-liquid ratio.