Characterisation of cylindrical curves

We employ moving frames along pairs of curves at constant separation to derive various conditions for a curve to belong to the surface of a circular cylinder

Equilibrium Shapes with Stress Localisation for Inextensible Elastic Mobius and Other Strips

We formulate the problem of finding equilibrium shapes of a thin inextensible elastic strip, developing further our previous work on the Möbius strip. By using the isometric nature of the deformation we reduce the variational problem to a second-order one-dimensional problem posed on the centreline of the strip. We derive Euler–Lagrange equations for this problem in Euler–Poincaré form and formulate boundary-value problems for closed symmetric one- and two-sided strips. Numerical solutions for the Möbius strip show a singular point of stress localisation on the edge of the strip, a generic response of inextensible elastic sheets under torsional strain. By cutting and pasting operations on the Möbius strip solution, followed by parameter continuation, we construct equilibrium solutions for strips with different linking numbers and with multiple points of stress localisation. Solutions reveal how strips fold into planar or self-contacting shapes as the length-to-width ratio of the strip is decreased. Our results may be relevant for curvature effects on physical properties of extremely thin two-dimensional structures as for instance produced in nanostructured origami

Sensitivity of multi-product two-stage economic lotsizing models and their dependency on change-over and product cost ratio's

This study considers the production and inventory management problem of a two-stage semi-process production system. In case both production stages are physically connected it is obvious that materials are forced to flow. The economic lotsize depends on the holding cost of the end-product and the combined change-over cost of both production stages. On the other hand this 'flow shop' is forced to produce at the speed of the slowest stage. The benefit of this approach is the low amount of Work In Process inventory. When on the other hand, the involved stages are physically disconnected, a stock of intermediates acts as a decoupling point. Typically for the semi-process industry are high change-over costs for the process oriented first stage, which results in large lotsize differences for the different production stages. Using the stock of intermediates as a decoupling point avoids the complexity of synchronising operations but is an additional reason to augment the intermediate stock position. The disadvantage of this model is the high amount of Work-In-Process inventory. This paper proposes the 'synchronised planning model' realising a global optimum instead of the combination of two locally optimised settings. The mathematical model proves (for a two-stage single-product setting) that the optimal two-stage production frequency corresponds with the single EOQ solution for the first stage. A sensitivity study reveals, within these two-stage lotsizing models, the economical cost dependency on product and change-over cost ratio‟s. The purpose of this paper is to understand under which conditions the „joined setup‟ or the „two-stage individual eoq model‟ remain close to the optimal model. Numerical examples prove that the conclusions about the optimal settings remain valid when extending the model to a two-stage multi-product setting. The research reveals that two-stage individually optimized EOQ lotsizing should only be used when the end-product stage has a high added value and small change-over costs, compared to the first stage. Physically connected operations should be used when the end-product stage has a small added value and low change-over costs, or high added value and large change-over costs compared to the first production stage. The paper concludes with suggesting a practical common cycle approach to tackle a two-stage multi-product production and inventory management problem. The common cycle approach brings the benefit of a repetitive and predictable production schedule

Collective Diffusion of Colloidal Hard Rods in Smectic Liquid Crystals: Effect of Particle Anisotropy

We study the layer-to-layer diffusion in smectic-A liquid crystals of colloidal hard rods with different length-to-diameter ratios using computer simulations. The layered arrangement of the smectic phase yields a hopping-type diffusion due to the presence of permanent barriers and transient cages. Remarkably, we detect stringlike clusters composed of inter-layer rods moving cooperatively along the nematic director. Furthermore, we find that the structural relaxation in equilibrium smectic phases shows interesting similarities with that of out-of-equilibrium supercooled liquids, although there the particles are kinetically trapped in transient rather than permanent cages. Additionally, at fixed packing fraction we find that the barrier height increases with increasing particle anisotropy, and hence the dynamics is more heterogeneous and non-Gaussian for longer rods, yielding a lower diffusion coefficient along the nematic director and smaller clusters of inter-layer particles that move less cooperatively. At fixed barrier height, the dynamics becomes more non-Gaussian and heterogeneous for longer rods that move more collectively giving rise to a higher diffusion coefficient along the nematic director.Comment: 24 pages, 10 figure

Emerging trends in 'smart probiotics' : functional consideration for the development of novel health and industrial applications

The link between gut microbiota and human health is well-recognized and described. This ultimate impact on the host has contributed to explain the mutual dependence between humans and their gut bacteria. Gut microbiota can be manipulated through passive or active strategies. The former includes diet, lifestyle, and environment, while the latter comprise antibiotics, pre- and probiotics. Historically, conventional probiotic strategies included a phylogenetically limited diversity of bacteria and some yeast strains. However, biotherapeutic strategies evolved in the last years with the advent of fecal microbiota transplant (FMT), successfully applied for treating CDI, IBD, and other diseases. Despite the positive outcomes, long-term effects resulting from the uncharacterized nature of FMT are not sufficiently studied. Thus, developing strategies to simulate the FMT, using characterized gut colonizers with identified phylogenetic diversity, may be a promising alternative. As the definition of probiotics states that the microorganism should have beneficial effects on the host, several bacterial species with proven efficacy have been considered next generation probiotics. Non-conventional candidate strains include Akkermansia muciniphila, Faecalibacterium prausnitzii, Bacteroides fragilis, and members of the Clostridia clusters IV, XIVa, and XVIII. However, viable intestinal delivery is one of the current challenges, due to their stringent survival conditions. In this review, we will cover current perspectives on the development and assessment of next generation probiotics and the approaches that industry and stakeholders must consider for a successful outcome

Dynamical Heterogeneities and Cooperative Motion in Smectic Liquid Crystals

Using simulations of hard rods in smectic-A states, we find non-gaussian diffusion and heterogeneous dynamics due to the equilibrium periodic smectic density profiles, which give rise to permanent barriers for layer-to-layer diffusion. This relaxation behavior is surprisingly similar to that of non-equilibrium supercooled liquids, although there the particles are trapped in transient (instead of permanent) cages. Interestingly, we also find stringlike clusters of up to 10 inter-layer rods exhibiting dynamic cooperativity in this equilibrium state.Comment: 10 pages, 4 figure

The essence of fertilization: oocyte meets sperm

The problem of reduced fertility in high yielding dairy cattle is a very complicated one, and the relationship between various measures of fertility and level of milk production remains controversial. In this brief review the essence of the problem is considered: what is the oocyte's and the sperm's contribution, and what is the importance of the resulting embryo in the declining fertility of the Holstein Friesian cow

Stability of Sasaki-extremal metrics under complex deformations

We consider the stability of Sasaki-extremal metrics under deformations of the complex structure on the Reeb foliation. Given such a deformation preserving the action of a compact subgroup of the automorphism group of a Sasaki-extremal structure, a sufficient condition is given involving the nondegeneracy of the relative Futaki invariant for the deformations to contain Sasaki-extremal structures. Deformations of Sasaki-Einstein metrics are also considered, where it suffices that the deformation preserve a maximal torus. As an application, new families of Sasaki-Einstein and Sasaki-extremal metrics are given on deformations of well known 3-Sasaki 7-manifolds.Comment: Added the obstruction to the existence of Sasaki structures under transversal complex deformations. 30 pages and 1 figur