Marangoni convection caused by a photochemical reaction of the type A $\stackrel{h\nu}{\rightleftharpoons}$ B in a deep liquid layer is studied. Linear stability analysis is performed and the conditionsfor Marangoni convection to occur are obtained. It is shown that increasing the rate of thedirect reaction, for example, by increasing the light intensity, destabilizes the steady stateand causes convective motion of the fluid, whereas increasing the rate of the inverse reactionstabilizes the steady state. A weakly nonlinear analysis of the problem is performed thatgives conditions for hexagonal convective patters to occur. It is shown that, in the case ofsmall light absorption length, the hexagonal cells correspond to "down"-hexagons.

We present new a posteriori error estimates for the finite volume approximationsof elliptic problems. They are obtained by applying functional a posteriorierror estimates to natural extensions of the approximate solution and its fluxcomputed by the finite volume method. The estimates give guaranteed upper boundsfor the errors in terms of the primal (energy) norm, dual norm (for fluxes), andalso in terms of the combined primal-dual norms. It is shown that the estimatesprovide sharp upper and lower bounds of the error and their practicalcomputation requires solving only finite-dimensional problems.

The Bilevel Knapsack Problem (BKP) is a hierarchical optimization problem in which thefeasible set is determined by the set of optimal solutions of parametric Knapsack Problem.In this paper, we propose two stages exact method for solving the BKP. In the first stage,a dynamic programming algorithm is used to compute the set of reactions of the follower.The second stage consists in solving an integer program reformulation of BKP. We show thatthe integer program reformulation is equivalent to the BKP. Numerical results show theefficiency of our method compared with those obtained by the algorithm of Moore andBard

Amazon molly (Poecilia formosa) females reproduce asexually, but theyneed sperm to initiate the process. Such gynogenetic reproduction can be called spermparasitism since the DNA in the sperm is not used. Since all offspring of asexuallyreproducing females are females, they can locally outcompete sexually reproducing ones,but their persistence is threatened by the lack of males. Therefore, the existence ofAmazon mollies is puzzling. A metapopulation structure has been suggested to enable thecoexistence of gynogenetic and sexual species. Previously only Levins-type metapopulationmodels have been used to investigate this question, but they are not defined on theindividual level. Therefore we investigate the evolution of sperm parasitism in astructured metapopulation model, which incorporates both realistic local populationdynamics and individual-level dispersal. If the reproduction strategy is freely evolvingin a large well-mixed population or in the structured metapopulation model, strongdiscrimination of asexually reproducing females by males results in evolution to fullsexuality, whereas mild discrimination leads to too small probability of sexualreproduction, so that the lack of males causes the extinction of the evolving population,resulting in evolutionary suicide. This classification remains the same also when bothsexual reproduction and dispersal are freely evolving. Sexual and asexual behaviour can beobserved at the same time in this model in the presence of a trade-off between thereproduction and dispersal traits. However, we do not observe disruptive selectionresulting in the evolutionarily stable coexistence of fully sexual and fully asexualfemales. Instead, the presence of sexual and asexual behaviour is due to females with amixed reproduction trait.

We propose a novel approach to introducing hypothesis testing into the biologycurriculum. Instead of telling students the hypothesis and what kind of data to collectfollowed by a rigid recipe of testing the hypothesis with a given test statistic, we askstudents to develop a hypothesis and a mathematical model that describes the nullhypothesis. Simulation of the model under the null hypothesis allows students to comparetheir experimental data to what they would expect under the null hypothesis, thus leadingto a much more intuitive understanding of hypothesis testing. This approach has beentested both in the classroom and in faculty workshops, and we provide some suggestions forimplementations based on our experiences.

A recently proposed model for the investigation of diffusivity in planktonic systemscontaining toxin-producing phytoplanktons is here reconsidered. We show the existence ofplanktonic travelling waves. Numerical simulations validate the analytical findings, toelucidate the sensitivity of the results in dependence of the diffusion coefficients.

In this paper we study the error rate of RNA synthesis in the look-ahead model for therandom walk of RNA polymerase along DNA during transcription. The model’s centralassumption is the existence of a window of activity in whichribonucleoside triphosphates (rNTPs) bind reversibly to the template DNA strand beforebeing hydrolyzed and linked covalently to the nascent RNA chain. An unknown, butimportant, integer parameter of this model is the window size w. Here, weuse mathematical analysis and computer simulation to study the rate at whichtranscriptional errors occur as a function of w. We find dramaticreduction in the error rate of transcription as w increases, especiallyfor small values of w. The error reduction method provided by look-aheadoccurs before hydrolysis and covalent linkage of rNTP to the nascent RNAchain, and is therefore distinct from error correction mechanisms that have previouslybeen considered.

The majority of species are under predatory risk in their natural habitat and targeted bypredators as part of the food web. During the evolution of ecosystems, manifold mechanismshave emerged to avoid predation. So called secondary defences, which are used after apredator has initiated prey-catching behaviour, commonly involve the expression of toxinsor deterrent substances which are not observable by the predator. Hence, the possession ofsuch secondary defence in many prey species comes with a specific signal of that defence(aposematism). This paper builds on the ideas of existing models of such signallingbehaviour, using a model of co-evolution and generalisation of aversive information andintroduces a new methodology of numerical analysis for finite populations. This newmethodology significantly improves the accessibility of previous models.

In finite populations, investigating the co-evolution of defence and signalling requiresan understanding of natural selection as well as an assessment of the effects of drift asan additional force acting on stability. The new methodology is able to reproduce thepredicted solutions of preceding models and finds additional solutions involving negativecorrelation between signal strength and the extent of secondary defence. In addition,genetic drift extends the range of stable aposematic solutions through the introduction ofa new pseudo-stability and gives new insights into the diversification of aposematicdisplays.

In this review paper we consider physiologically structured population models that havebeen widely studied and employed in the literature to model the dynamics of a wide varietyof populations. However in a number of cases these have been found inadequate to describesome phenomena arising in certain real-world applications such as dispersion in thestructure variables due to growth uncertainty/variability. Prompted by this, we describedtwo recent approaches that have been investigated in the literature to describe thisgrowth uncertainty/variability in a physiologically structured population. One involvesformulating growth as a Markov diffusion process while the other entails imposing aprobabilistic structure on the set of possible growth rates across the entire population.Both approaches lead to physiologically structured population models with nontrivialdispersion. Even though these two approaches are conceptually quite different, they werefound in [17] to have a close relationship: in somecases with properly chosen parameters and coefficient functions, the resulting stochasticprocesses have the same probability density function at each time.

The aim of this paper is to study the steady states of the mathematical models with delaykernels which describe pathogen-immune dynamics of infectious diseases. In the study of mathematicalmodels of infectious diseases it is important to predict whether the infection disappearsor the pathogens persist. The delay kernel is described by the memory function that reflects theinfluence of the past density of pathogen in the blood and it is given by a nonnegative bounded andnormated function k defined on [ 0, ∞ ). By using the coefficient of the kernel k, as a bifurcationparameter, the models are found to undergo a sequence of Hopf bifurcation. The direction and the stability criteria of bifurcation periodic solutions are obtained by applying the normal form theory and the center manifold theorems. Some numerical simulation examples for justifying the theoretical results are also given.

National policies regarding the BCG vaccine for tuberculosis vary greatly throughout the international community and several countries are currently considering discontinuing universal vaccination. Detractors of BCG point to its uncertain effectiveness and its interference with the detection and treatment of latent tuberculosis infection (LTBI).

In order to quantify the trade-off between vaccination and treatment of LTBI, a mathematical model was designed and calibrated to data from Brazil, Ghana, Germany, India, Mexico, Romania, the United Kingdom and the United States. Country-specific thresholds for when LTBI treatment outperforms mass vaccination were found and the consequences of policy changes were estimated.

Our results suggest that vaccination outperforms LTBI treatment in all settings but with greatly reduced efficiency in low incidence countries. While national policy statements emphasize BCG’s interference with LTBI detection, we find that reinfection should be more determinant of a country’s proper policy choice.

In this note, I wish to describe the first order semiclassical approximation to thespectrum of one frequency quasi-periodic operators. In the case of a sampling functionwith two critical points, the spectrum exhibits two gaps in the leading orderapproximation. Furthermore, I will give an example of a two frequency quasi-periodicoperator, which has no gaps in the leading order of the semiclassical approximation.

In this paper, we propose a computational model to investigate the coupling between cell’s adhesions and actin fibres and how this coupling affects cell shape and stability. To accomplish that, we take into account the successive stages of adhesion maturation from adhesion precursors to focal complexes and ultimately to focal adhesions, as well as the actin fibres evolution from growing filaments, to bundles and finally contractile stress fibres.

We use substrates with discrete patterns of adhesive patches, whose inter-patches distance can be modulated in order to control the location of the adhesions and the resulting fibres architecture. We then investigate the emergence of stable cell morphologies as a function of the inter-patches distance, for two different cell phenotypes generated from the model. Force generated by the stress fibres on the focal adhesions and specifically the influence of the cell contractility are also investigated.

Our results suggest that adhesion lifetime and fibre growing rate are the key parameters in the emergence of stable cell morphologies and the limiting factors for the magnitude of the mean tension force from the fibres on the focal adhesions.

A feature often observed in epidemiological networks is significant heterogeneity indegree. A popular modelling approach to this has been to consider large populations withhighly heterogeneous discrete contact rates. This paper defines an individual-levelnon-Markovian stochastic process that converges on standard ODE models of such populationsin the appropriate asymptotic limit. A generalised Sellke construction is derived for thismodel, and this is then used to consider final outcomes in the case where heterogeneityfollows a truncated Zipf distribution.

Two-dimensional inviscid channel flow of an incompressible fluid is considered. It isshown that if the flow is steady and features no horizontal stagnation, then the flow mustnecessarily be a parallel shear flow.

In this work we deal with the design of the robust feedback control ofwastewater treatmentsystem, namely the activated sludge process. This problem is formulated by anonlinearordinary differential system. On one hand, we develop a robust analysis when thespecific growthfunction of the bacterium μ is not well known. On the other hand, when alsothe substrate concentrationin the feed stream s in is unknown, we provide an observer of system andpropose a designof robust feedback control in term of recycle rate, in order to keep thepollutant concentration lowerthan an allowed maximum level s d .

Real-world medical decisions rarely involve binary Ðsole condition present or absent-patterns of patient pathophysiology. Similarly, provider interventions are rarely unitaryin nature: the clinician often undertakes multiple interventions simultaneously.Conventional approaches towards complex physiologic derangements and their associatedmanagement focus on the frequencies of joint appearances, treating the individualderangements of physiology or elements of intervention as conceptually isolated. Thisframework is ill suited to capture either the integrated patterns of derangement displayedby a particular patient or the integrated patterns of provider intervention. Here weillustrate the application of a different approach-that of symbolic dynamics-in which theintegrated pattern of each patients derangement, and the associated provider response, arecaptured by defining words based on the elements of the pattern offailure. We will use as an example provider practices in the context of mechanicalventilation- a common, potentially harmful, and complex life support technology. We alsodelineate other domains in which symbolic dynamics approaches might aid in quantitatingpractice patterns, assessing quality of care, and identifying best practices.

Waxy Crude Oils (WCO’s) are characterized by the presence of heavy paraffins insufficiently large concentrations. They exhibit quite complex thermodynamical andrheological behaviour and present the peculiar property of giving rise to the formation ofsegregated wax deposits, when temperature falls down the so called WAT, or Wax AppearanceTemperature. In extreme cases, segregated waxes may lead to pipeline occlusion due todeposition on cold walls. In this paper we review the mathematical models formulated todescribe: (i) wax cystallization or thawing in cooling/heating cycles; (ii) the mechanismsof mass transport in saturated non-isothermal solutions; (iii) the experimental deviceused to measure wax solubility and wax diffusivity; (iv) wax deposition in pipelinescarrying a warm, wax-saturated WCO through cold regions; (v) wax deposition accompanied bygelification during the cooling of a WCO under a thermal gradient.

Experimental evidence points to a rich variety of physical scenarios that arise when alaminar flame propagates through a pre-mixture of evaporating liquid fuel and a gaseousoxidant. In this paper new results of time-dependent numerical simulations of richoff-stoichiometric spray flame propagation in a two-dimensional channel are presented. Aconstant density model is adopted, thereby eliminating the Darrieus-Landau instability. Itis demonstrated that there exists a narrow band of vaporization Damkohler numbers (theratio of a characteristic flow time to a characteristic evaporation time) for which theflame propagation is oscillatory. For values outside this range steady state propagationis attained but with a curved (cellular) flame front. The critical range for thenon-steady propagation is also found to be a function of the Lewis number of the deficientreactant.