A Mathematical Model of Meat Cooking Based on Polymer-solvent Analogy

Mathematical modelling of transport phenomena in food processes is vital to understand the process dynamics. In this work, we study the process of double sided cooking of meat by developing a mathematical model for the simultaneous heat and mass transfer. The constitutive equations for the heat and mass transport are based on Fourier conduction, and the Flory–Huggins theory respectively, formulated for a two-phase transport inside a porous medium. We investigate a reduced one-dimensional case to verify the model, by applying appropriate boundary conditions. The results of the simulation agree well with experimental findings reported in literature. Finally, we comment upon the sensitivity of the model to the porosity of meat

Improvement of Energy Efficiency for Wastewater Treatment

Wastewater treatment requires the elimination of pathogens and reduction of organic matter in the treated sludge to acceptable levels. One process used to achieve this is Autothermal Thermophylic Aerobic Digestion (ATAD), which relies on promoting non-pathogenic thermophilic bacteria to digest organic matter and kill pathogens through metabolic heat generation. This process requires continuous aeration that may be energy consuming, and the final aim of the study is to identify how the process design can minimize the energy input per mass of treated sludge. Appropriate modeling of the reactor process is an essential ingredient, so we explore properties of an existing model and propose a simplified alternative model

Improved detection of biomarkers in cervico-vaginal mucus (CVM) from postpartum cattle

peer-reviewedBackground In the postpartum cow, early diagnosis of uterine disease is currently problematic due to the lack of reliable, non-invasive diagnostic methods. Cervico-vaginal mucus (CVM) is an easy to collect potentially informative source of biomarkers for the diagnosis and prognosis of uterine disease in cows. Here, we report an improved method for processing CVM from postpartum dairy cows for the measurement of immune biomarkers. CVM samples were collected from the vagina using gloved hand during the first two weeks postpartum and processed with buffer alone or buffer containing different concentrations of the reducing agents recommended in standard protocols: Dithiothriotol (DTT) or N-Acetyl-L-Cysteine (NAC). Total protein was measured using the bicinchoninic acid (BCA) assay; interleukin 6 (IL-6), IL-8 and α1-acid glycoprotein (AGP) were measured by ELISA. Results We found that use of reducing agents to liquefy CVM affects protein yield and the accuracy of biomarker detection. Our improved protocol results in lower protein yields but improved detection of cytokines and chemokines. Using our modified method to measure AGP in CVM we found raised levels of AGP at seven days postpartum in CVM from cows that went on to develop endometritis. Conclusion We conclude that processing CVM without reducing agents improves detection of biomarkers that reflect uterine health in cattle. We propose that measurement of AGP in CVM during the first week postpartum may identify cows at risk of developing clinical endometritis

Numerical computations of a theoretical model of ribbed moraine formation

We develop numerical solutions of a theoretical model which has been proposed to explain the formation of subglacial bedforms. The model has been shown to have the capability of producing bedforms in two dimensions, when they may be interpreted as ribbed moraine. However, these investigations have left unanswered the question of whether the theory is capable of producing fully three‐dimensional bedforms such as drumlins. We show that, while the three‐dimensional calculations show realistic quasi‐three‐dimensional features such as dislocations in the ribbing pattern, they do not produce genuine three‐dimensional drumlins. We suggest that this inadequacy is due to the treatment of subglacial drainage in the theory as a passive variable, and thus that the three‐dimensional forms may be associated with conditions of sufficient subglacial water flux

Analysis and dynamically consistent nonstandard discretization for a rabies model in humans and dogs

Rabies is a fatal disease in dogs as well as in humans. A possible model to represent rabies transmission dynamics in human and dog populations is presented. The next generation matrix operator is used to determine the threshold parameter R0, that is the average number of new infective individuals produced by one infective individual intro- duced into a completely susceptible population. If R0 < 1, the disease-free equilibrium is globally asymptotically stable, while it is unstable and there exists a locally asymptot- ically stable endemic equilibrium when R0 > 1. A nonstandard nite di erence scheme that replicates the dynamics of the continuous model is proposed. Numerical tests to support the theoretical analysis are provided.DST/NRF SARChI Chair in Mathematics Models and Methods in Bioengineering and Biosciences.http://link.springer.com/journal/133982017-09-30hb2016Mathematics and Applied Mathematic

Nonstandard finite difference schemes for Michaelis-Menten type reaction-diffusion equations

We compare and investigate the performance of the exact scheme of the Michaelis-Menten (M-M) ordinary differential equation with several new non-standard finite difference (NSFD) schemes that we construct by using Mickens’ rules. Furthermore, the exact scheme of the M-M equation is used to design several dynamically consistent NSFD schemes for related reactiondiffusion equations, advection-reaction equations and advection-reaction-diffusion equations. Numerical simulations that support the theory and demonstrate computationally the power of NSFD schemes are presented.South African National Research Foundationhttp://www3.interscience.wiley.com/journal/35979/homehb201

From enzyme kinetics to epidermiological models with Michealis-Menten contact rate : design of nonstandard finite difference schemes

We consider the basic SIR epidemiological model with the Michaelis-Menten formulation of the contact rate. From the study of the Michaelis-Menten basic enzymatic reaction, we design two types of Nonstandard Finite Difference (NSFD) schemes for the SIR model: Exact-related schemes based on the Lambert W function and schemes obtained by using Mickens’s rules of more complex denominator functions for discrete derivatives and nonlocal approximations of nonlinear terms. We compare and investigate the performance of the two types of schemes by showing that they are dynamically consistent with the continuous model. Numerical simulations that support the theory and demonstrate computationally the power of NSFD schemes are presented.The South African National Research Foundationhttp://www.elsevier.com/locate/camw

Positivity-preserving nonstandard finite difference schemes for cross-diffusion equations in biosciences

We design nonstandard finite difference (NSFD) schemes which are unconditionally dynamically consistent with respect to the positivity property of solutions of cross-diffusion equations in biosciences. This settles a problem that was open for quite some time. The study is done in the setting of three concrete and highly relevant cross-diffusion systems regarding tumor growth, convective predator–prey pursuit and evasion model and reaction–diffusion–chemotaxis model. It is shown that NSFD schemes used for classical reaction–diffusion equations, such as the Fisher equation, for which the solutions enjoy the positivity property, are not appropriate for cross-diffusion systems. The reliable NSFD schemes are therefore obtained by considering a suitable implementation on the crossdiffusive term of Mickens’ rule of nonlocal approximation of nonlinear terms, apart from his rule of complex denominator function of discrete derivatives. We provide numerical experiments that support the theory as well as the power of the NSFD schemes over the standard ones. In the case of the cancer growth model, we demonstrate computationally that our NSFD schemes replicate the property of traveling wave solutions of developing shocks observed in Marchant et al. (2000).South African Research Chairs Initiative of the Department of Science and Technology and National Research Foundation : SARChI Chair in Mathematical Models and Methods in Bioengineering and Biosciences.http://www.elsevier.com/locate/camwa2015-11-30hb201

Global endometrial transcriptomic profiling: transient immune activation precedes tissue proliferation and repair in healthy beef cows

peer-reviewedBackground: All cows experience bacterial contamination and tissue injury in the uterus postpartum, instigating a local inflammatory immune response. However mechanisms that control inflammation and achieve a physiologically functioning endometrium, while avoiding disease in the postpartum cow are not succinctly defined. This study aimed to identify novel candidate genes indicative of inflammation resolution during involution in healthy beef cows. Previous histological analysis of the endometrium revealed elevated inflammation 15 days postpartum (DPP) which was significantly decreased by 30 DPP. The current study generated a genome-wide transcriptomic profile of endometrial biopsies from these cows at both time points using mRNA-Seq. The pathway analysis tool GoSeq identified KEGG pathways enriched by significantly differentially expressed genes at both time points. Novel candidate genes associated with inflammatory resolution were subsequently validated in additional postpartum animals using quantitative real-time PCR (qRT-PCR). Results: mRNA-Seq revealed 1,107 significantly differentially expressed genes, 73 of which were increased 15 DPP and 1,034 were increased 30 DPP. Early postpartum, enriched immune pathways (adjusted P < 0.1) included the T cell receptor signalling pathway, graft-versus-host disease and cytokine-cytokine receptor interaction pathways. However 30 DPP, where the majority of genes were differentially expressed, the enrichment (adjusted P < 0.1) of tissue repair and proliferative activity pathways was observed. Nineteen candidate genes selected from mRNA-Seq results, were independently assessed by qRT-PCR in additional postpartum cows (5 animals) at both time points. SAA1/2, GATA2, IGF1, SHC2, and SERPINA14 genes were significantly elevated 30 DPP and are functionally associated with tissue repair and the restoration of uterine homeostasis postpartum. Conclusions: The results of this study reveal an early activation of the immune response which undergoes a temporal functional change toward tissue proliferation and regeneration during endometrial involution in healthy postpartum cows. These molecular changes mirror the activation and resolution of endometrial inflammation during involution previously classified by the degree of neutrophil infiltration. SAA1/2, GATA2, IGF1, SHC2, and SERPINA14 genes may become potential markers for resolution of endometrial inflammation in the postpartum cow

Coupling finite volume and nonstandard finite difference schemes for a singularly perturbed Schrödinger equation

The Schrödinger equation is a model for many physical processes in quantum physics. It is a singularly perturbed differential equation where the presence of the small reduced Planck’s constant makes the classical numerical methods very costly and inefficient. We design two new schemes. The first scheme is the nonstandard finite volume method, whereby the perturbation term is approximated by nonstandard technique, the potential is approximated by its mean value on the cell and the complex dependent boundary conditions are handled by exact schemes. In the second scheme, the deficiency of classical schemes is corrected by the inner expansion in the boundary layer region. Numerical simulations supporting the performance of the schemes are presented.South African NRF and DST/NRF SARChI Chair on Mathematical Models and Methods in Bioengineering and Biosciences (M3B2).http://www.tandfonline.com/loi/gcom202016-08-30hb201