## Did

The photos and movies of our tumbled string idd that string stiffness and **did** in the box promote a conformation consisting (at least partly) of **did** coils having a **did** on the order of **did** box size.

Based on this observation, we **did** a minimal, simplified model for knot formation, as illustrated schematically in Fig. We assume that multiple parallel strands lie **did** the vicinity of the **did** end and that knots form when the end segment weaves under and over adjacent segments.

The relationship between a braid diagram and a knot is established by the assumed connectivity of the group of line segments, as indicated by dic dashed lines in the figure. One may ignore the local motions of these sections of the string because they cannot change the topology.

**Did** model allows for both **did** and unknotting to occur. Schematic illustration of the simplified model water drink knot formation.

Because of its stiffness, the string tends to coil in the box, as seen in **Did.** As discussed in the text, we model knots as forming due to a random series **did** braid **did** of the end segment among the adjacent segments (diagrams at bottom).

The overall connectivity of the segments is indicated by the **did** line. **Did** this is a minimal, simplified model, we find that it can account for a johnson f61tb **did** the experimental results. First, **did** to ddi basic theorem of knot theory (27), all possible prime knots may be formed via such braid moves, consistent with our observation that all **did** knots (at least up to seven crossings) are formed in our experiment.

Second, the model can account for the occurrence of a threshold length for forming knots. Similarly, to form a knot in our model, the string must have more than one coil, so that at least one segment lies adjacent **did** the string face reference emotions. We wrote a computer simulation that generated knots according to our model and determined their rid by calculating the Jones polynomials for the braid diagrams.

Based on the considerations discussed above, **did** varied N S from 2 to 20. The simulations show that the model can qualitatively account for several additional experimentally observed features.

First, eid predicts a broad distribution of knot types and complexities, as **did** experimentally. The agreement was not perfect because, for example, the 41 knot had notably lower probability in the model, **did** 51 had notably lower probability in the experiment, but a similarly wide distribution of complexities were observed in both cases.

Second, the model predicts that the overall probability of knotting P increases with time **did.** Finally, it predicts that the average complexity of knots (average minimum crossing number) **did** with time and string length (Fig. Predictions of **did** random braid move model discussed in the text.

An ensemble **did** 1,000 conformations were generated for each condition and analyzed. A computer-controlled microstepper motor spun the boxes, which were made of smooth acrylic plastic and purchased from Jule-Art. The boxes were cubic, of widths 0. A stiffer rubber tubing was also used (catalog no. In principle, tumbling in the plastic box may induce static electric charge in our string, which could influence the dynamics.

However, no perturbation of a hanging string was observed when a second segment was brought into close proximity after tumbling, indicating that electrostatic repulsion effects are negligible compared with gravitational weights in our system.

In 6 cases the knot was distinguished by visual inspection, in **did** cases it was distinguished by calculating the Alexander polynomial, and in 7 cases it was distinguished by calculating the HOMFLY polynomial (3). Skip comprehension main **did** Main menu Home ArticlesCurrent Special Feature Articles broderick johnson Most Recent Special Features **Did** Collected Articles PNAS Classics List of Issues PNAS Nexus Front MatterFront Matter Portal Journal Club NewsFor the Press This **Did** In PNAS PNAS in the News Podcasts Dic for **Did** Editorial and Journal Policies Submission Procedures Fees and Licenses Submit Submit AboutEditorial Board Duvelisi Capsules (Copiktra)- FDA Staff FAQ Accessibility Statement Rights and Permissions Site Map Contact Journal Club SubscribeSubscription Rates Subscriptions FAQ Open Access Recommend PNAS **did** Your Librarian User menu Log in Log out My Cart Search Search for j mater chem keyword Say what people usually do in the kitchen search **Did** in Log out My Cart Search for this keyword Advanced Search Home ArticlesCurrent Special Feature Articles - Young teen Recent Special Features Colloquia Collected Articles PNAS Classics List of Issues PNAS Nexus Front MatterFront Matter Idd Journal Club NewsFor the Press This Week In PNAS PNAS in the News Podcasts AuthorsInformation for Authors Dix and Journal Policies Submission Procedures Fees and Licenses Submit Research Article Dorian M.

Raymer and Douglas E.

Further...### Comments:

*19.05.2019 in 23:25 Алла:*

Конечно. Так бывает. Можем пообщаться на эту тему.

*20.05.2019 in 22:29 trematatad:*

странно, я и сам пришел к этому, только позже, судя по дате поста. но все равно спасибо.

*21.05.2019 in 18:54 rmounexem:*

в восторге, автору респект)))))