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Stergios Adamopoulos - One of the best experts on this subject based on the ideXlab platform.
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Crack formation, strain distribution and fracture surfaces around Knots in thermally modified timber loaded in static bending
Wood Science and Technology, 2020Co-Authors: Joran Blokland, Anders Olsson, Jan Oscarsson, Geoffrey Daniel, Stergios AdamopoulosAbstract:The effect of thermal modification (TM) on the chemistry, anatomy and mechanical properties of wood is often investigated using small clear samples. Little is known on the effect of growth-related and processing defects, such as Knots and checks, on the bending strength and stiffness of thermally modified timber (TMT). Nine boards of Norway spruce with different combinations of knot types were used to study the combined effects of checks and Knots on the bending behaviour of TMT. Digital image correlation (DIC) measurements on board surfaces at sites of Knots subjected to bending allowed to study strain distribution and localise cracks prior to and after TM, and to monitor development of fracture (around Knots) in TMT to failure. DIC confirmed that checking in Knots was increased after TM compared to kiln-dried timber, specifically for intergrown Knots and intergrown parts of encased Knots. Effects appear local and do not affect board bending stiffness at these sites. Bending failure in TMT initiated mainly at knot interfaces or besides Knots and fractures often propagated from checks. Scanning electron microscopy analyses of fracture surfaces confirmed this, and fractures were typically initiated around Knots and at knot interfaces due to crack propagation along the grain in the longitudinal–radial plane (TL fracture) under mixed mode I and II loading, such that boards failed in simple tension like unmodified timber. Images of fracture surfaces at the ultrastructural level revealed details of the brittle behaviour of TM wood. This was especially apparent from the smooth appearance of transwall failure under mode I loading across the grain.
Anton Morozov - One of the best experts on this subject based on the ideXlab platform.
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universal racah matrices and adjoint knot polynomials arborescent Knots
Physics Letters B, 2016Co-Authors: A Mironov, Anton MorozovAbstract:Abstract By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso–Jones formula then implies a universal description of the adjoint knot polynomials for torus Knots, which in particular unifies the HOMFLY ( SU N ) and Kauffman ( SO N ) polynomials. For E 8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) Knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the “eigenvalue conjecture”, which expresses the Racah and mixing matrices through the eigenvalues of the quantum R -matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6 × 6 case. The adjoint polynomials do not distinguish between mutants and therefore are not very efficient in knot theory, however, universal polynomials in higher representations can probably be better in this respect.
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tabulating knot polynomials for arborescent Knots
arXiv: High Energy Physics - Theory, 2016Co-Authors: A Mironov, Anton Morozov, An Morozov, P Ramadevi, Vivek Kumar Singh, A SleptsovAbstract:Arborescent Knots are the ones which can be represented in terms of double fat graphs or equivalently as tree Feynman diagrams. This is the class of Knots for which the present knowledge is enough for lifting topological description to the level of effective analytical formulas. The paper describes the origin and structure of the new tables of colored knot polynomials, which will be posted at the dedicated site. Even if formal expressions are known in terms of modular transformation matrices, the computation in finite time requires additional ideas. We use the "family" approach, and apply it to arborescent Knots in the Rolfsen table by developing a Feynman diagram technique associated with an auxiliary matrix model field theory. Gauge invariance in this theory helps to provide meaning to Racah matrices in the case of non-trivial multiplicities and explains the need for peculiar sign prescriptions in the calculation of [21]-colored HOMFLY polynomials.
Theunis Piersma - One of the best experts on this subject based on the ideXlab platform.
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differential responses of red Knots calidris canutus to perching and flying sparrowhawk accipiter nisus models
Animal Behaviour, 2009Co-Authors: Kimberley J Mathot, Piet J Van Den Hout, Theunis PiersmaAbstract:According to the threat-sensitive predator avoidance hypothesis, prey should match the intensity of their antipredation response to the degree of threat posed by predators. We used controlled indoor experiments to investigate the ability of red Knots to discern between high- and low-threat encounters with a representative predator, the sparrowhawk. The behaviour of Knots was compared across three conditions: no predators present (very low predation threat), presentation of a perching sparrowhawk model (low predation threat) and presentation of a gliding sparrowhawk model (high predation threat). In all behavioural parameters measured, red Knots showed evidence of discriminating between the different levels of predation risk. Knots responded immediately to the presence of sparrowhawks with escape flights, and the duration of escape flights was longer following the gliding sparrowhawk events than following perching events. Similarly, the proportion of time spent vigilant increased with increasing level of predation threat, while the proportion of time spent feeding decreased. These results show that Knots recognize variations in the level of predation threat, and adjust their antipredator responses accordingly. Furthermore, model sparrowhawks were introduced into the experimental arena at similar distances to the Knots, which suggests that Knots are able to use cues other than distance to predator to gauge the immediate level of threat that a predator poses.
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modelling phenotypic flexibility an optimality analysis of gizzard size in red Knots calidris canutus
Ardea, 2006Co-Authors: Jan A Van Gils, Theunis Piersma, Anne Dekinga, Phil F BattleyAbstract:Reversible phenotypic changes, such as those observed in nutritional organs of long-distance migrants, increasingly receive the attention of ornithologists. In this paper we review the cost-benefit studies that have been performed on the flexible gizzard of Red Knots Calidris canutus. By varying the hardness of the diet on offer gizzard mass could experimentally be manipulated, which allowed quantification of the energetic costs and benefits as a function of gizzard size. These functions were used to construct an optimality model of gizzard mass for Red Knots on migration and during winter. Two possible currencies were assumed, one in which Knots aim to balance their energy budget on a daily basis (satisficers), and one in which Knots aim to maximise their daily energy budget (net rate maximisers). The model accurately predicted variation in gizzard mass that we observed (1) between years, (2) within years, and (3) between sites. Knots maintained satisficing gizzards during winter and rate-maximising gizzards when fuelling for migration. The model-exercise revealed the importance of digestive constraints and quality of prey in the life of Knots.
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unraveling the intraspecific phylogeography of Knots calidris canutus a progress report on the search for genetic markers
Journal of Ornithology, 1994Co-Authors: Theunis Piersma, Allan J Baker, Lene RosenmeierAbstract:Mitochondrial DNA control region sequences of 25 Knots sampled from 10 populations and possibly four subspecies (canutus, islandica, rogersi, rufa) were obtained by PCR and direct sequencing. Only 7 haplotypes were found worldwide, all closely related to one another and differing by 1–3 substitutions. Knots have most probably expanded to their current population size from a refugial population that was severely bottlenecked late in the Pleistocene. Preliminary results from RAPDs are consistent with this prediction, in that Knots from North America appear to be genetically distinct from Knots elsewhere.
Hwa Jeong Lee - One of the best experts on this subject based on the ideXlab platform.
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Quantum Knots and the number of knot mosaics
Quantum Information Processing, 2015Co-Authors: Kyungpyo Hong, Ho Lee, Hwa Jeong LeeAbstract:Lomonaco and Kauffman developed a knot mosaic system to introduce a precise and workable definition of a quantum knot system. This definition is intended to represent an actual physical quantum system. A knot $$(m,n)$$ ( m , n ) -mosaic is an $$m \times n$$ m × n matrix of mosaic tiles ( $$T_0$$ T 0 through $$T_{10}$$ T 10 depicted in the introduction) representing a knot or a link by adjoining properly that is called suitably connected. $$D^{(m,n)}$$ D ( m , n ) is the total number of all knot $$(m,n)$$ ( m , n ) -mosaics. This value indicates the dimension of the Hilbert space of these quantum knot system. $$D^{(m,n)}$$ D ( m , n ) is already found for $$m,n \le 6$$ m , n ≤ 6 by the authors. In this paper, we construct an algorithm producing the precise value of $$D^{(m,n)}$$ D ( m , n ) for $$m,n \ge 2$$ m , n ≥ 2 that uses recurrence relations of state matrices that turn out to be remarkably efficient to count knot mosaics. $$\begin{aligned} D^{(m,n)} = 2 \, \Vert (X_{m-2}+O_{m-2})^{n-2} \Vert \end{aligned}$$ D ( m , n ) = 2 ‖ ( X m - 2 + O m - 2 ) n - 2 ‖ where $$2^{m-2} \times 2^{m-2}$$ 2 m - 2 × 2 m - 2 matrices $$X_{m-2}$$ X m - 2 and $$O_{m-2}$$ O m - 2 are defined by $$\begin{aligned} X_{k+1} = \begin{bmatrix} X_k&O_k \\ O_k&X_k \end{bmatrix} \ \hbox {and } \ O_{k+1} = \begin{bmatrix} O_k&X_k \\ X_k&4 \, O_k \end{bmatrix} \end{aligned}$$ X k + 1 = X k O k O k X k and O k + 1 = O k X k X k 4 O k for $$k=0,1, \cdots , m-3$$ k = 0 , 1 , ⋯ , m - 3 , with $$1 \times 1$$ 1 × 1 matrices $$X_0 = \begin{bmatrix} 1 \end{bmatrix}$$ X 0 = 1 and $$O_0 = \begin{bmatrix} 1 \end{bmatrix}$$ O 0 = 1 . Here $$\Vert N\Vert $$ ‖ N ‖ denotes the sum of all entries of a matrix $$N$$ N . For $$n=2$$ n = 2 , $$(X_{m-2}+O_{m-2})^0$$ ( X m - 2 + O m - 2 ) 0 means the identity matrix of size $$2^{m-2} \times 2^{m-2}$$ 2 m - 2 × 2 m - 2 .
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quantum Knots and the number of knot mosaics
arXiv: Geometric Topology, 2014Co-Authors: Kyungpyo Hong, Ho Lee, Hwa Jeong LeeAbstract:Lomonaco and Kauffman developed a knot mosaic system to introduce a precise and workable definition of a quantum knot system. This definition is intended to represent an actual physical quantum system. A knot (m,n)-mosaic is an $m \times n$ matrix of mosaic tiles ($T_0$ through $T_{10}$ depicted in the introduction) representing a knot or a link by adjoining properly that is called suitably connected. $D^{(m,n)}$ is the total number of all knot (m,n)-mosaics. This value indicates the dimension of the Hilbert space of these quantum knot system. $D^{(m,n)}$ is already found for $m,n \leq 6$ by the authors. In this paper, we construct an algorithm producing the precise value of $D^{(m,n)}$ for $m,n \geq 2$ that uses recurrence relations of state matrices that turn out to be remarkably efficient to count knot mosaics. $$ D^{(m,n)} = 2 \, \| (X_{m-2}+O_{m-2})^{n-2} \| $$ where $2^{m-2} \times 2^{m-2}$ matrices $X_{m-2}$ and $O_{m-2}$ are defined by $$ X_{k+1} = \begin{bmatrix} X_k & O_k \\ O_k & X_k \end{bmatrix} \ \mbox{and } \ O_{k+1} = \begin{bmatrix} O_k & X_k \\ X_k & 4 \, O_k \end{bmatrix} $$ for $k=0,1, \cdots, m-3$, with $1 \times 1$ matrices $X_0 = \begin{bmatrix} 1 \end{bmatrix}$ and $O_0 = \begin{bmatrix} 1 \end{bmatrix}$. Here $\|N\|$ denotes the sum of all entries of a matrix $N$. For $n=2$, $(X_{m-2}+O_{m-2})^0$ means the identity matrix of size $2^{m-2} \times 2^{m-2}$.
Joran Blokland - One of the best experts on this subject based on the ideXlab platform.
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Crack formation, strain distribution and fracture surfaces around Knots in thermally modified timber loaded in static bending
Wood Science and Technology, 2020Co-Authors: Joran Blokland, Anders Olsson, Jan Oscarsson, Geoffrey Daniel, Stergios AdamopoulosAbstract:The effect of thermal modification (TM) on the chemistry, anatomy and mechanical properties of wood is often investigated using small clear samples. Little is known on the effect of growth-related and processing defects, such as Knots and checks, on the bending strength and stiffness of thermally modified timber (TMT). Nine boards of Norway spruce with different combinations of knot types were used to study the combined effects of checks and Knots on the bending behaviour of TMT. Digital image correlation (DIC) measurements on board surfaces at sites of Knots subjected to bending allowed to study strain distribution and localise cracks prior to and after TM, and to monitor development of fracture (around Knots) in TMT to failure. DIC confirmed that checking in Knots was increased after TM compared to kiln-dried timber, specifically for intergrown Knots and intergrown parts of encased Knots. Effects appear local and do not affect board bending stiffness at these sites. Bending failure in TMT initiated mainly at knot interfaces or besides Knots and fractures often propagated from checks. Scanning electron microscopy analyses of fracture surfaces confirmed this, and fractures were typically initiated around Knots and at knot interfaces due to crack propagation along the grain in the longitudinal–radial plane (TL fracture) under mixed mode I and II loading, such that boards failed in simple tension like unmodified timber. Images of fracture surfaces at the ultrastructural level revealed details of the brittle behaviour of TM wood. This was especially apparent from the smooth appearance of transwall failure under mode I loading across the grain.
