Common Knots Research Articles

Knot Security 101: A Comprehensive Practical Review to Optimal Knot Configuration, Pulling Direction, Throw Count, and Tail Length.

Knots are the weakest structural point in a suture line and inevitably weaken almost all suture materials. This practical review critically evaluates the factors, such as suture material properties, gauge, configuration, throw count, and tail length, that affect knot security. A PubMed search between the years 1934 and 2023 identified relevant studies that addressed factors relating to knot security. Studies that investigated knots and sutures solely used in laparoscopic and arthroscopic surgery were excluded. Knot configurations assessed were the Aberdeen, sliding, square, and surgeon's. Eighty-six articles were included in this review article and demonstrated that knot security varies greatly between suture materials and gauge. Knot security also varies by configuration, throw count, conditions, tail length, and stitch type. Throw count differs by knot configuration, with the Aberdeen knot being most secure with three throws and one to two turns compared with three to five throws for surgeon's and square knots. The optimal tail length was 3 mm. This practical review demonstrates that there are significant differences in knot security based on a variety of factors. It is challenging to propose an ideal knot because most studies did not evaluate knot security using a broad variety of suture materials, gauges, and throws for each of the most common knots. Although this review article demonstrated several applicable findings, additional robust studies are needed to simplify proposals.

Joint inversion of seismic slopes, traveltimes and gravity anomaly data based on structural similarity

SUMMARY Attention is paid to joint inversion of multiple geophysical data because of its advantages on weakening the non-uniqueness of inversion and further enhancing comprehensive interpretation. Due to the good correlation between rock velocity and density, seismic and gravity data have been widely used in joint inversion. However, the joint inversion of pre-stack seismic reflection and gravity data remains underdeveloped at the exploration scale. Without a quantitive relation between velocity and density, we develop a structure-based joint inversion using seismic reflection traveltimes, slopes and Bouguer gravity anomaly data simultaneously for building both velocity and density models. In our method, cubic B-spline interpolation is used to parametrize the common knots of velocity and density models. Incorporating seismic slopes into the joint inversion framework, we build a composite objective function which minimizes the weighted-sum of seismic/gravity data misfits, regularization and structural constraint terms. By subdividing the knot spacing, a multiscale strategy is alternative to increase the stability of inversion. First, we describe the methodology, followed by three synthetic examples to illustrate the feasibility and benefits of the method. Examination of the convergence curves via inversion suggests that the desired solution is more likely to be obtained with gentle convergence of each term, thus it can be used as an indicator for weight adjustment. Additionally, locations of scattering points and acoustic impedance can be obtained as by-products. Compared with the inversion of the respective data, the joint inversion exhibits the complementary characteristics of seismic and gravity data, improves the distribution and structural features of the resulting physical properties, especially in deep and complex tectonic situations.

It's knot what you know

Applied Physics Why is it that some knots seem to hold tight while others readily slip apart? Patil et al. develop a theoretical analysis of the stability of knots and find links between topological parameters (twist charge, crossing numbers, handedness) and mechanical stability. The theory is confirmed using simulations and experiments on color-changing fibers that optically show localized stress differences in different parts of the knot as the two strands are pulled apart. The authors show why some common knots slip easily and untie, whereas others hold tight. Science , this issue p. [71][1] [1]: /lookup/doi/10.1126/science.aaz0135

Local T-spline surface skinning with shape preservation

Surface skinning is a surface generation method that uses a set of given cross-sectional curves, and it is widely used in free-form surface design. In the B-spline surface skinning, the given B-spline curves should be compatible, that is, the curves should have the same degree and knot sequence. While making the curves compatible, lots of control vertices are generated. Although T-spline surface skinning methods have been introduced to reduce the number of control vertices, the T-spline skinning method that was proposed by Nasri et al. (2012) can generate a wiggled surface when the given B-spline curves are not sufficiently compatible. The intermediate cross sections that were introduced for T-spline surface skinning cannot preserve the shape of the given B-spline curves if the adjacent B-spline curves do not have sufficient common knots, and it can cause wiggles on the surface. In this paper, we analyze this issue and suggest a modified method to remove the wiggles on the skinned T-spline surface. Furthermore, we propose an algorithm for shape preservation of the surface. Our approach is verified by suggesting some examples compared to the Nasri et al. (2012)’s method.

Feasibility of Knots to Reduce the Maximum Dynamic Arresting Load in Rope Systems

Impact loads to the human body due to falls from height can be mitigated by well-designed and characterized fall protection systems. While energy absorption methods using rope deformation and/or accessory components have previously been evaluated, the ability for simple knots tied in the system to alter impact loads has not been studied in detail. We quantify the effectiveness of various common knots to reduce dynamic loads in typical fall scenarios for which the systems are designed, and interpret this change in the context of rope strength reduction due to the knot. Knots are shown to significantly (45–60 %) reduce the quasistatic strength of rope when compared to a manufactured sewn-eye (40 %). A single exception to this outcome is with the quadruple overhand on a bite (30–35 %). Knots significantly reduce the maximum arresting load due to a dynamic impact event when compared to ropes without knots, providing significantly more energy absorption than the sewn-eye alone. In nearly all rope/knot combinations, the ratio of maximum arrest load (MAL) to breaking strength was lower with the knotted ropes when compared to the sewn-eye terminations. In particular, the quadruple overhand on a bite tied in the Technora–Technora rope resulted in MALs that were only 33 % of the minimum breaking strength (MBS). Ropes with sewn-eye terminations resulted in MALs that were 80 % of the MBS. From the scenarios investigated, the quadruple overhand on a bite provides a favorable reduction in arrest loads with the smallest associated loss of strength.

Some Calculations on Link Polynomials from 2-Parameter Quantum Groups

Starting with the link invariant G (p,q,z) , a skein relation is introduced which enables us to calculate the polynomial starting with G (p,q,z) = 1, for the unknot. The relation between G (p,q,z) and the known 2-variable link invariant K (l,m) is shown. Then the polynomial of some common knots is calculated, also it is shown that this invariant failed to distinguish the Birmans pairs as well as Jones invariant.

Further asymptotic properties of best approximation by splines

Let S n k, r denote the collection of polynomial splines of order k with at most ( n − 1) free knots, each of multiplicity r. This paper explicitly finds the constants C k, r, p so that lim n→∞ n k dist L p[0, 1] {ƒ, S n k,r} = C k,r,p ∥ƒ (k)∥ L σ[0,1] , where σ = p (kp + 1) and ƒ is sufficiently smooth. This completely fills the gap between previously known results for simple knots ( r = 1) and for piecewise polynomials ( r = k). We also consider similar asymptotic properties pertaining to approximation of vector functions by vector splines. We define the latter to be families of vector functions whose components are splines of order k with common knots.

Mirror Images in Knots

Abstract Most knots are asymmetric and thus can be tied in two forms which are mirror images. An individual tends to tie one of the mirror images habitually which increases the significance of an analysis of the knot. Of 103 college students, 68 surveyed tied a knot based on an overhand knot. Of these, approximately 75% of the right-handed persons tied the overhand knot in one orientation while the other 25% tied the mirror image of it. Some background information relating to analyzing common knots is discussed.