The Newsvendor problem: analysis of the cost structure under normally distributed demand

We briefly review selected mathematical models that describe the dynamics of pattern formation phenomena in dip-coating and Langmuir-Blodgett transfer experiments, where solutions or suspensions are transferred onto a substrate producing patterned deposit layers with structure length from hundreds of nanometres to tens of micrometres. The models are presented with a focus on their gradient dynamics formulations that clearly shows how the dynamics is governed by particular free energy functionals and facilitates the comparison of the models. In particular, we include a discussion of models based on long-wave hydrodynamics as well as of more phenomenological models that focus on the pattern formation processes in such systems. The models and their relations are elucidated and examples of resulting patterns are discussed before we conclude with a discussion of implications of the gradient dynamics formulation and of some related open issues

Thin film dynamics with surfactant phase transition

A thin liquid film covered with an insoluble surfactant in the vicinity of a first-order phase transition is discussed. Within the lubrication approximation we derive two coupled equations to describe the height profile of the film and the surfactant density. Thermodynamics of the surfactant is incorporated via a Cahn-Hilliard type free-energy functional which can be chosen to describe a transition between two stable phases of different surfactant density. Within this model, a linear stability analysis of stationary homogeneous solutions is performed, and drop formation in a film covered with surfactant in the lower density phase is investigated numerically in one and two spatial dimensions

Continuation for thin film hydrodynamics and related scalar problems

This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues

Effects of continuous milking during a field trial on productivity, milk protein yield and health in dairy cows

The objective of this field study with an automatic milking system was to evaluate the effects of omitting the dry period on health and productivity during the subsequent lactation in dairy cows. A total of 98 German Simmental cows of six Southern German farms were assigned randomly to two experimental groups: The first group was dried-off 56 days before calving (D for dried-off, n=49), and the second group was milked continuously during this period until calving (CM for continuous milking, n=49). From the latter a third group emerged, including cows that dried-off themselves spontaneously (DS for dried-off spontaneously, n=14). Blood serum values of glucose, β-hydroxybutyrate (BHBA), non-esterified fatty acids (NEFA) and IGF-1 showed most pronounced fluctuations in D cows. Over the entire study period, the concentrations of BHBA and NEFA were markedly lower in the CM and DS groups. Furthermore, IGF-1 concentration was lowest for D cows and also decrease in back fat thickness was more pronounced. Mean concentration of milk protein was markedly higher in CM and DS cows (3.70% and 3.71%) compared with D cows (3.38%). Owing to the lower 305-day milk yield (−15.6%) and the lower total milk yield (−3.1%), the total amount of produced protein in the subsequent lactation was 2.5% (6.8 kg) lower, although the additional protein amount in CM cows from week −8 to calving was 35.7 kg. The greatest benefit resulted from positive effects on fertility and the lower incidence of diseases: CM cows had their first oestrus 1 week earlier compared with D cows, they also conceived earlier and showed a significantly lower risk of developing hypocalcaemia, ketosis and puerperal disorders. The present study showed that the costs of medical treatment and milk losses were twice as high in D cows, compared with CM and DS cows, and thus the reduced costs because of the more stable health outweighed the financial losses of milk yield by +18.49 € per cow and lactation

Active wetting of epithelial tissues

Development, regeneration and cancer involve drastic transitions in tissue morphology. In analogy with the behavior of inert fluids, some of these transitions have been interpreted as wetting transitions. The validity and scope of this analogy are unclear, however, because the active cellular forces that drive tissue wetting have been neither measured nor theoretically accounted for. Here we show that the transition between 2D epithelial monolayers and 3D spheroidal aggregates can be understood as an active wetting transition whose physics differs fundamentally from that of passive wetting phenomena. By combining an active polar fluid model with measurements of physical forces as a function of tissue size, contractility, cell-cell and cell-substrate adhesion, and substrate stiffness, we show that the wetting transition results from the competition between traction forces and contractile intercellular stresses. This competition defines a new intrinsic lengthscale that gives rise to a critical size for the wetting transition in tissues, a striking feature that has no counterpart in classical wetting. Finally, we show that active shape fluctuations are dynamically amplified during tissue dewetting. Overall, we conclude that tissue spreading constitutes a prominent example of active wetting --- a novel physical scenario that may explain morphological transitions during tissue morphogenesis and tumor progression

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where "surface fields" may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given

Probable Innocence and Independent Knowledge

International audienceWe analyse the \textsc{Crowds} anonymity protocol under the novel assumption that the attacker has independent knowledge on behavioural patterns of individual users. Under such conditions we study, reformulate and extend Reiter and Rubin's notion of probable innocence, and provide a new formalisation for it based on the concept of protocol vulnerability. Accordingly, we establish new formal relationships between protocol parameters and attackers' knowledge expressing necessary and sufficient conditions to ensure probable innocence

The history of attention deficit hyperactivity disorder

The contemporary concept of attention deficit hyperactivity disorder (ADHD) as defined in the DSM-IV-TR (American Psychiatric Association 2000) is relatively new. Excessive hyperactive, inattentive, and impulsive children have been described in the literature since the nineteenth century. Some of the early depictions and etiological theories of hyperactivity were similar to current descriptions of ADHD. Detailed studies of the behavior of hyperactive children and increasing knowledge of brain function have changed the concepts of the fundamental behavioral and neuropathological deficits underlying the disorder. This article presents an overview of the conceptual history of modern-day ADHD