A perturbative approach to the spectral zeta functions of strings, drums and quantum billiards

We have obtained an explicit expression for the spectral zeta functions and for the heat kernel of strings, drums and quantum billiards working to third order in perturbation theory, using a generalization of the binomial theorem to operators. The perturbative parameter used in the expansion is either the small deformation of a reference domain (for instance a square), or a small variation of the density around a constant value (in two dimensions both cases can apply). This expansion is well defined even in presence of degenerations of the unperturbed spectrum. We have discussed several examples in one, two and three dimensions, obtaining in some cases the analytic continuation of the series, which we have then used to evaluate the corresponding Casimir energy. For the case of a string with piecewise constant density, subject to different boundary conditions, and of two concentric cylinders of very close radii, we have reproduced results previously published, thus obtaining a useful check of our method.Comment: 23 pages, 5 figures, 2 tables; version accepted on Journal of Mathematical Physic

Resistant protein. Forms and functions

Several global health risks are related to our dietary lifestyle. As a consequence of the overconsumption of ultra-processed and highly digestible protein (150–200% of the recommended value), excess dietary proteins reach the colon, are hydrolysed to peptides and amino acids by bacterial proteases and fermented to various potentially toxic end products. A diet reformulation strategy with reduced protein content in food products appears to be the most effective approach. A potential approach to this challenge is to reduce food digestibility by introducing resistant protein into the diet that could positively influence human health and gut microbiome functionality. Resistant protein is a dietary constituent not hydrolysed by digestive enzymes or absorbed in the human small intestine. The chemical conformation and the amino acid composition strictly influence its structural stability and resistance to in vivo proteolysis and denaturation. Responding to the important gap in our knowledge regarding the digestibility performance of alternative proteins, we hypothesise that resistant proteins can beneficially alter food functionality via their role in improving metabolic properties and health benefits in human nutrition, similar to fibres and resistant starches. A multidisciplinary investigation of resistant protein will generate tremendous scientific impact for other interlinked societal, economic, technological and health and wellbeing aspects of human life

From waste to taste. Application of fermented spent rootlet ingredients in a bread system

The process of upcycling and incorporating food by-products into food systems as functional ingredients has become a central focus of research. Barley rootlets (BR) are a by-product of the malting and brewing industries that can be valorised using lactic acid bacteria fermentation. This research investigates the effects of the inclusion of unfermented (BR-UnF), heat-sterilised (BR-Ster), and five fermented BR ingredients (using Weissella cibaria MG1 (BR-MG1), Leuconostoc citreum TR116 (BR-TR116), Lactiplantibacillus plantarum FST1.7 (BR-FST1.7), Lactobacillus amylovorus FST2.11 (BR-FST2.11), and Limosilactobacillus reuteri R29 (BR-R29) in bread. The antifungal compounds in BR ingredients and the impact of BR on dough rheology, gluten development, and dough mixing properties were analysed. Additionally, their effects on the techno-functional characteristics, in vitro starch digestibility, and sensory quality of bread were determined. BR-UnF showed dough viscoelastic properties and bread quality comparable to the baker's flour (BF). BR-MG1 inclusion ameliorated bread specific volume and reduced crumb hardness. Breads containing BR-TR116 had comparable bread quality to BF, while the inclusion of BR-R29 substantially slowed microbial spoilage. Formulations containing BR-FST2.11 and BR-FST1.7 significantly reduced the amounts of sugar released from breads during a simulated digestion and resulted in a sourdough-like flavour profile. This study highlights how BR fermentation can be tailored to achieve desired bread characteristics

Functional properties of brewer’s spent grain protein isolate. The missing piece in the plant protein portfolio

Plant protein sources, as a part of developing sustainable food systems, are currently of interest globally. Brewer’s spent grain (BSG) is the most plentiful by-product of the brewing industry, representing ~85% of the total side streams produced. Although nutritionally dense, there are very few methods of upcycling these materials. High in protein, BSG can serve as an ideal raw material for protein isolate production. This study details the nutritional and functional characteristics of BSG protein isolate, EverPro, and compares these with the technological performance of the current gold standard plant protein isolates, pea and soy. The compositional characteristics are determined, including amino acid analysis, protein solubility, and protein profile among others. Related physical properties are determined, including foaming characteristics, emulsifying properties, zeta potential, surface hydrophobicity, and rheological properties. Regarding nutrition, EverPro meets or exceeds the requirement of each essential amino acid per g protein, with the exception of lysine, while pea and soy are deficient in methionine and cysteine. EverPro has a similar protein content to the pea and soy isolates, but far exceeds them in terms of protein solubility, with a protein solubility of ~100% compared to 22% and 52% for pea and soy isolates, respectively. This increased solubility, in turn, affects other functional properties; EverPro displays the highest foaming capacity and exhibits low sedimentation activity, while also possessing minimal gelation properties and low emulsion stabilising activity when compared to pea and soy isolates. This study outlines the functional and nutritional properties of EverPro, a brewer’s spent grain protein, in comparison to commercial plant protein isolates, indicating the potential for the inclusion of new, sustainable plant-based protein sources in human nutrition, in particular dairy alternative applications

Investigation of different dietary-fibre-ingredients for the design of a fibre enriched bread formulation low in FODMAPs based on wheat starch and vital gluten

Consumption of fermentable oligo-, di-, monosaccharides and polyols (FODMAPs) often induces symptoms of irritable bowel syndrome (IBS). Since FODMAPs and dietary fbre (DF) share certain characteristics, IBS-patients have a limited intake of DF. Therefore, enrichment of a low FODMAP model bread (based on 84% wheat starch and 16% vital gluten) with various fbres (bamboo, cellulose, psyllium, guar gum) in two diferent concentrations (3 g/100 g and 6 g/100 g) was investigated. Physico-chemical properties of doughs and breads were analysed (fermentation quality, gluten development, specifc volume and hardness), as well as the release of reducing sugars during in vitro digestion. High performance anion exchange chromatography with coupled pulsed amperometric detection (HPAEC-PAD) was used to determine the FODMAP levels (contents of mannitol, sorbitol, fructose in excess of glucose, fructans and α-galactooligosaccharides) of both dough and bread. Prototypes were compared with wheat four-based breads (bakers’ four with and without wheat bran addition) to assess the performance of these prototypes. Prototypes showed a decreased quality compared to a baker’s four control, however, a quality comparable to commercial wheat bran breads was found. This in combination with a lower release of reducing sugars during in vitro digestion underline the potential of fbre enriched breads as part of a healthier and more palateable low FODMAP diet. Furthermore, this study highlights the importance of the type (viscous and insoluble) and the concentration of fbres used. Application of psyllium in a concentration of 3 g/100 g showed the most benefcial impact on both physical (specifc volume, hardness after 0 h and 24 h) and nutritional aspects of bread

Quality analysis of fresh and dried mangoes

[EN] Organic acids, sugar and colour define the quality and the taste of mangoes. The quality deteriorates during drying on a single-layer-dryer. Quality losses can be reduced by using drying parameters that influence the quality less. In this research, the contents of ascorbic acid, organic acids and sugar as well as colour changes and shrinkage are analysed. Analyses are carried out at different temperatures, dew point temperatures and air velocities using HPLC, IC and UV/Vis- spectrometry. The quality criteria showed the lowest changes at a temperature of 60°C, dew point temperature of 20°C and an air velocity of 0.9 m/s.The underlying RELOAD-Project for this report is funded by the German Federal Ministry of Education and Research, grant number 031A247C. The responsibility for the content of this publication lies with the author.Arendt, S.; Jodicke, K.; Hofacker, W.; Speckle, W. (2018). Quality analysis of fresh and dried mangoes. En IDS 2018. 21st International Drying Symposium Proceedings. Editorial Universitat Politècnica de València. 1591-1598. https://doi.org/10.4995/IDS2018.2018.7526OCS1591159

Diamagnetic Susceptibility and Current Distributions in Granular Superconductors at Percolation

Comments: 4 pages RevTeX, 4 Postscript figures. References added. We study a two-dimensional granular superconducting network at the percolation threshold under the influence of an external perpendicular magnetic field. By numerical simulations on the full nonlinear problem, we determine the scaling exponent for the magnetic susceptibility. Further, we report on the scaling properties of the current distribution. The scaling of the current is found to be independent of the value of the magnetic field. Our results are in contradiction with previous numerical results based on linearized equations. We find a value for the susceptibility exponent which does not agree with existing theoretical suggestions, but agrees perfectly with renormalization group calculations

Steady states in a structured epidemic model with Wentzell boundary condition

We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a special compartment that carries mass, hence the model is equipped with generalized Wentzell (or dynamic) boundary conditions. Our model is intended to describe the spread of infection of a vertically transmitted disease, for example Wolbachia in a mosquito population. Therefore the (infinite dimensional) nonlinearity arises in the recruitment term. First we establish global existence of solutions and the Principle of Linearised Stability for our model. Then, in our main result, we formulate simple conditions, which guarantee the existence of non-trivial steady states of the model. Our method utilizes an operator theoretic framework combined with a fixed point approach. Finally, in the last section we establish a sufficient condition for the local asymptotic stability of the positive steady state

Well-Posedness and Symmetries of Strongly Coupled Network Equations

We consider a diffusion process on the edges of a finite network and allow for feedback effects between different, possibly non-adjacent edges. This generalizes the setting that is common in the literature, where the only considered interactions take place at the boundary, i. e., in the nodes of the network. We discuss well-posedness of the associated initial value problem as well as contractivity and positivity properties of its solutions. Finally, we discuss qualitative properties that can be formulated in terms of invariance of linear subspaces of the state space, i. e., of symmetries of the associated physical system. Applications to a neurobiological model as well as to a system of linear Schroedinger equations on a quantum graph are discussed.Comment: 25 pages. Corrected typos and minor change

Water absorption as a prediction tool for the application of hydrocolloids in potato starch-based bread

To create visco-elastic networks in gluten-free doughs, hydrocolloids have been used most commonly to compensate for the lack of gluten. This study applies a prediction tool in form of an equation, considering the right water absorption level, to obtain optimised conditions for the use of six different hydrocolloids (guar gum, hydroxypropyl methyl cellulose, locust bean gum, pectin, sodium alginate, xanthan gum). For this purpose, the water holding capacity of each hydrocolloid was determined and the water amount in the formulation was adjusted accordingly to it. The hydrocolloids were analysed in five concentrations (0.25%, 0.5%, 1%, 1.5%, 2.0%). Analysis of water adjusted doughs included rheological properties, pasting properties and the baking performance. With the aid of the prediction tool, it was possible to obtain bread-like products for each hydrocolloid. However, the various hydrocolloids showed different concentration levels, where they performed best. In this study, the main influencing factors on bread quality were linked to the charge and the molecular weight of the various hydrocolloids. The negative charge of some hydrocolloids was hypothesised to created repelling forces between it and the negative charged phosphate groups of potato starches, affected those parameters. Bread baked with sodium alginate reached the highest specific volume at a concentration level of 1% and 2% xanthan gum had the softest bread crumb. Based on the source of used hydrocolloid, the analysis of the rheological and pasting properties revealed connections between dough properties and bread quality parameters