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- ItemMonitoring Thermal and Non-Thermal Treatments during Processing of Muscle Foods : A Comprehensive Review of Recent Technological Advances(Basel : MDPI, 2020) Hassoun, Abdo; Ojha, Shikha; Tiwari, Brijesh; Rustad, Turid; Nilsen, Heidi; Heia, Karsten; Cozzolino, Daniel; Bekhit, Alaa El-Din; Biancolillo, Alessandra; Wold, Jens PetterMuscle food products play a vital role in human nutrition due to their sensory quality and high nutritional value. One well-known challenge of such products is the high perishability and limited shelf life unless suitable preservation or processing techniques are applied. Thermal processing is one of the well-established treatments that has been most commonly used in order to prepare food and ensure its safety. However, the application of inappropriate or severe thermal treatments may lead to undesirable changes in the sensory and nutritional quality of heat-processed products, and especially so for foods that are sensitive to thermal treatments, such as fish and meat and their products. In recent years, novel thermal treatments (e.g., ohmic heating, microwave) and non-thermal processing (e.g., high pressure, cold plasma) have emerged and proved to cause less damage to the quality of treated products than do conventional techniques. Several traditional assessment approaches have been extensively applied in order to evaluate and monitor changes in quality resulting from the use of thermal and non-thermal processing methods. Recent advances, nonetheless, have shown tremendous potential of various emerging analytical methods. Among these, spectroscopic techniques have received considerable attention due to many favorable features compared to conventional analysis methods. This review paper will provide an updated overview of both processing (thermal and non-thermal) and analytical techniques (traditional methods and spectroscopic ones). The opportunities and limitations will be discussed and possible directions for future research studies and applications will be suggested.
- ItemQuantum diffusion(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2015) Knowles, AnttiIf you place a drop of ink into a glass of water, the ink will slowly dissipate into the surrounding water until it is perfectly mixed. If you record your experiment with a camera and play the film backwards, you will see something that is never observed in the real world. Such diffusive and irreversible behaviour is ubiquitous in nature. Nevertheless, the fundamental equations that describe the motion of individual particles – Newton’s and Schrödinger’s equations – are reversible in time: a film depicting the motion of just a few particles looks as realistic when played forwards as when played backwards. In this snapshot, we discuss how one may try to understand the origin of diffusion starting from the fundamental laws of quantum mechanics.
- ItemTowards a Mathematical Theory of Turbulence in Fluids(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Bedrossian, JacobFluid mechanics is the theory of how liquids and gases move around. For the most part, the basic physics are well understood and the mathematical models look relatively simple. Despite this, fluids display a dazzling mystery to their motion. The random-looking, chaotic behavior of fluids is known as turbulence, and it lies far beyond our mathematical understanding, despite a century of intense research.
- ItemQuantum symmetry(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2020) Caspers, MartijnThe symmetry of objects plays a crucial role in many branches of mathematics and physics. It allowed, for example, the early prediction of the existence of new small particles. “Quantum symmetry” concerns a generalized notion of symmetry. It is an abstract way of characterizing the symmetry of a much richer class of mathematical and physical objects. In this snapshot we explain how quantum symmetry emerges as matrix symmetries using a famous example: Mermin’s magic square. It shows that quantum symmetries can solve problems that lie beyond the reach of classical symmetries, showing that quantum symmetries play a central role in modern mathematics.
- ItemOperator theory and the singular value decomposition(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Knese, GregThis is a snapshot about operator theory and one of its fundamental tools: the singular value decomposition (SVD). The SVD breaks up linear transformations into simpler mappings, thus unveiling their geometric properties. This tool has become important in many areas of applied mathematics for its ability to organize information. We discuss the SVD in the concrete situation of linear transformations of the plane (such as rotations, reflections, etc.).
- ItemDeterminacy versus indeterminacy(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2020) Berg, ChristianCan a continuous function on an interval be uniquely determined if we know all the integrals of the function against the natural powers of the variable? Following Weierstrass and Stieltjes, we show that the answer is yes if the interval is finite, and no if the interval is infinite.
- ItemEmergence in biology and social sciences(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2022) Hoffmann, Franca; Merino-Aceituno, SaraMathematics is the key to linking scientific knowledge at different scales: from microscopic to macroscopic dynamics. This link gives us understanding on the emergence of observable patterns like flocking of birds, leaf venation, opinion dynamics, and network formation, to name a few. In this article, we explore how mathematics is able to traverse scales, and in particular its application in modelling collective motion of bacteria driven by chemical signalling.
- ItemTouching the transcendentals: tractional motion from the bir th of calculus to future perspectives(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2019) Milici, PietroWhen the rigorous foundation of calculus was developed, it marked an epochal change in the approach of mathematicians to geometry. Tools from geometry had been one of the foundations of mathematics until the 17th century but today, mainstream conception relegates geometry to be merely a tool of visualization. In this snapshot, however, we consider geometric and constructive components of calculus. We reinterpret “tractional motion”, a late 17th century method to draw transcendental curves, in order to reintroduce “ideal machines” in math foundation for a constructive approach to calculus that avoids the concept of infinity.
- ItemNews on quadratic polynomials(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2017) Pottmeyer, LukasMany problems in mathematics have remained unsolved because of missing links between mathematical disciplines, such as algebra, geometry, analysis, or number theory. Here we introduce a recently discovered result concerning quadratic polynomials, which uses a bridge between algebra and analysis. We study the iterations of quadratic polynomials, obtained by computing the value of a polynomial for a given number and feeding the outcome into the exact same polynomial again. These iterations of polynomials have interesting applications, such as in fractal theory.
- ItemExpander graphs and where to find them(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2019) Khukhro, AnaGraphs are mathematical objects composed of a collection of “dots” called vertices, some of which are joined by lines called edges. Graphs are ideal for visually representing relations between things, and mathematical properties of graphs can provide an insight into real-life phenomena. One interesting property is how connected a graph is, in the sense of how easy it is to move between the vertices along the edges. The topic dealt with here is the construction of particularly well-connected graphs, and whether or not such graphs can happily exist in worlds similar to ours.