Stokes equations under nonlinear slip boundary conditions coupled with the heat equation: A priori error analysis

In this work, we consider the heat equation coupled with Stokes equations under threshold type boundary condition. The conditions for existence and uniqueness of the weak solution are made clear. Next we formulate the finite element problem, recall the conditions of its solvability, and study its convergence by making use of Babuska–Brezzi's conditions for mixed problems. Third we formulate an Uzawa's type iterative algorithm that separates the fluid from heat conduction, study its feasibility, and convergence. Finally the theoretical findings are validated by numerical simulations.     

The use of proton transfer reaction mass spectrometry for high throughput screening of terpene synthases

In this work, we introduce the application of proton transfer reaction mass spectrometry (PTR-MS) for the selection of improved terpene synthase mutants. In comparison with gas chromatography mass spectrometry (GC-MS)-based methods, PTR-MS could offer advantages by reduction of sample preparation steps and analysis time. The method we propose here allows for minimal sample preparation and analysis time and provides a promising platform for the high throughput screening (HTS) of large enzyme mutant libraries. To investigate the feasibility of a PTR-MS-based screening method, we employed a small library of Callitropsis nootkatensis valencene synthase (CnVS) mutants. Bacterial cultures expressing enzyme mutants were subjected to different growth formats, and headspace terpenes concentrations measured by PTR-Qi-ToF-MS were compared with GC-MS, to rank the activity of the enzyme mutants. For all cultivation formats, including 96 deep well plates, PTR-Qi-ToF-MS resulted in the same ranking of the enzyme variants, compared with the canonical format using 100 mL flasks and GC-MS analysis. This study provides a first basis for the application of rapid PTR-Qi-ToF-MS detection, in combination with multi-well formats, in HTS screening methods for the selection of highly productive terpene synthases.     

Investigation of hormone activity in butterfly imaginal wing discs by protein expression pattern changes

In a proteomic approach using 2-DE, the changes in protein expression patterns in wing imaginal discs induced by hormone treatment have been studied. Here we show the response of butterfly imaginal wing disc tissue taken from late fifth instar larvae of the African-Mocker swallowtail Papilio dardanus (Lepidoptera) to the insect hormones 20-hydroxyecdysone (20-HE) and juvenile hormone (JH). The tissues were cultured in the presence of one hormone or a combination of both and their protein expression was compared to the pattern obtained from untreated wing discs. All the treatments resulted in changes in the expression pattern distinct from the uninduced control, indicating a distinct protein regulation induced by the hormones. The treatment with both of the hormones, which are known to have antagonistic physiological effects, did show a unique pattern, presumably the result, in part, of synergistic effects on protein expression mediated by the combined effects of both the hormones. The extent of the interaction between JH and 20-HE indicates a complex molecular regulation, far beyond a simple antagonistic effect.     

Rheological properties of cross-linked hyaluronan-gelatin hydrogels for tissue engineering

Hydrogels that mimic the natural extracellular matrix (ECM) are used in three-dimensional cell culture, cell therapy, and tissue engineering. A semi-synthetic ECM based on cross-linked hyaluronana offers experimental control of both composition and gel stiffness. The mechanical properties of the ECM in part determine the ultimate cell phenotype. We now describe a rheological study of synthetic ECM hydrogels with storage shear moduli that span three orders of magnitude, from 11 to 3 500 Pa, a range important for engineering of soft tissues. The concentration of the chemically modified HA and the cross-linking density were the main determinants of gel stiffness. Increase in the ratio of thiol-modified gelatin reduced gel stiffness by diluting the effective concentration of the HA component.     

Lyapunov functions for a dengue disease transmission model

In this paper, we study a model for the dynamics of dengue fever when only one type of virus is present. For this model, Lyapunov functions are used to show that when the basic reproduction ratio is less than or equal to one, the disease-free equilibrium is globally asymptotically stable, and when it is greater than one there is an endemic equilibrium which is also globally asymptotically stable.     

Robustness in biological regulatory networks II: Application to genetic threshold Boolean random regulatory networks (getBren)

An important example of biological regulatory networks is constituted by the genetic threshold Boolean random regulatory networks (getBren), which are very useful for explaining the precise mechanisms of the genetic control. This article shows the mathematical relationships between parameter sensitivity of the evolutionary entropy and network frustration in the particular context of the getBrens.     

Robustness in biological regulatory networks I: Mathematical approach

Numerous indices of complexity are used in biological regulatory networks like the number of their components, their connectance (or connectivity), or the number of the strong connected components of their interaction graph. Concerning the stability of a biological network, it corresponds to its ability to recover from dynamical or parametric disturbance. Complexity is here quantified by the evolutionary entropy, which describes the way the asymptotic presence distribution of the corresponding dynamical system is spread over the state space and the stability (or robustness) is characterized by the rate at which the system returns to this equilibrium distribution after a perturbation. This article shows the mathematical relationships between entropy and stability rate in the general framework of a Markov chain.     

Pool boiling heat transfer performance of Newtonian nanofluids

Experimental measurements were carried out on the boiling heat transfer characteristics of γ-Al₂O₃/water and SnO₂/water Newtonian nanofluids. Nanofluids are liquid suspensions containing nanoparticles with sizes smaller than 100 nm. In this research, suspensions with different concentrations of γ-Al₂O₃ and SnO₂ nanoparticles in water were studied under nucleate pool boiling heat transfer conditions. Results show that nanofluids possess noticeably higher boiling heat transfer coefficients than the base fluid. The boiling heat transfer coefficients depend on the type and concentration of nanoparticles.     

A novel methodology for investigating foamy oil stability by an oil-based analogue model

A novel methodology was developed based on oil-based foam to systematically investigate foamy oil stability. The first step was to generate an oil-based analogue model that has similar characteristics of foamy oil. Then, the effects of the key factors were investigated with the created oil-based foam by a new experimental procedure. Moreover, a statistical approach was utilized to ensure reliability of the experimental data. Finally, we proposed a new method to describe foamy oil rupture and simulate its defoaming kinetics. The results showed that the oil-based foam can be precursors to studies on actual foamy oil and other petroleum foams.