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The persistent quasi-planar nematic texture known also as the dowser texture is characterized by a 2D unitary vector field d. We show here that the dowser texture is sensitive, in first order, to electric fields. This property is due to the flexo-electric polarisation P collinear with d expected from R.B. Meyer's considerations on flexo-electricity in nematics. It is pointed out that due to the flexo-electric polarisation nematic monopoles can be manipulated by electric fields of appropriated geometry.

We deal here with three metastable systems: 1{\textdegree}- the dowser texture, 2{\textdegree}- supertwistedcholesterics and 3{\textdegree}- hypotwisted cholesterics. We outline remarkable properties of tropisms of the dowser texture stemming from its low symmetry and we show that, using setups called Dowsons Colliders, nematic monopoles can be nucleated, set into motion and brought into collisions in the dowser texture. Subsequently we point out that nucleation of dislocation loops occurs in cholesteric layers compressed or dilated between cylindrical mica sheets. Under compression, three modes of nucleation of dislocation loops have been identified: individual, serial and continuous. The serial mode generates dislocation nets made of L circular loops connected by C radial crossing into superloops. Similar superloops can also be generated under dilation. We analyse the topology of superloops in terms of the theory of knots and point out they can be reduced into the unknot by Reidemeister moves. In other words, superloops are multiply folded loops that can be continuously unfolded.

The shape of the most tight trefoil knot with N=200640 vertices found with an appropriately modified finite element method is analyzed. The high number of vertices makes plots of its curvature and torsion very precise what allows the authors to formulate new, firmly justified conjectures concerning the shape of the ideal trefoil knot., Comment: 14 figures

We reinterpret the distribution of the Hall potential in the Hall bar-with-a-hole that has been found and interpreted by Mani and Klitzing [Appl. Phys. Lett., 64 1262 (1994)]. Our reinterpretation explains all the "paradoxes" without resorting to new theoretical conceptions., Comment: 10 pages, 4 figures; Contact address: maciej.oszwaldowski@put.poznan.pl

The dynamics of the tip of the falling chain is analyzed. Results of laboratory experiments are presented and compared with results of numerical simulations. Time dependences of the velocity and the acceleration of the chain tip for a number of different initial conformations of the chain are determined. A simple analytical model of the system is also considered., Comment: 29 pages, 13 figures

A physical interpretation of the rope simulated by the SONO algorithm is presented. Properties of the tight polygonal knots delivered by the algorithm are analyzed. An algorithm for bounding the ropelength of a smooth inscribed knot is shown. Two ways of calculating the ropelength of tight polygonal knots are compared. An analytical calculation performed for a model knot shows that an appropriately weighted average should provide a good estimation of the minimum ropelength for relatively small numbers of edges., Comment: 27 pages, to appear in "Physical and Numerical Models in Knot Theory and their Application to the Life Sciences"

Numerical simulations indicate that there exist conformations of the unknot, tied on a finite piece of rope, entangled in such a manner, that they cannot be disentangled to the torus conformation without cutting the rope. The simplest example of such a gordian unknot is presented., Comment: 6 pages, 3 figures

The question: "How many different trajectories are there on a single invariant torus within the phase space of an integrable Hamiltonian system?" is posed. A rigorous answer to the question is found both for the rational and the irrational tori. The relevant notion of non-measurable sets is discussed., Comment: 8 pages, 1 figure

The most tight conformation of the trefoil knot found by the SONO algorithm is presented. Structure of the set of its self-contact points is analyzed., Comment: 11 pages, 8 figures

The most tight conformations of prime knots are found with the use of the SONO algorithm. Their curvature and torsion profiles are calculated. Symmetry of the knots is analysed. Connections with the physics of polymers are discussed., Comment: 11 pages, 8 figures

The values of writhe of the most tight conformations, found by the SONO algorithm, of all alternating prime knots with up to 10 crossings are analysed. The distribution of the writhe values is shown to be concentrated around the equally spaced levels. As predicted by Cerf and Stasiak the writhe quantum is shown to be close to the rational 4/7 value. The deviation of the writhe values from the n*(4/7) writhe levels scheme is analysed quantitatively. Consequences of the writhe quantization phenomenon are discussed., Comment: 11 pages,6 figures

Closely packed conformations of helices formed on the ideal rope are considered. The pitch versus radius relations which define a closely packed helix are determined. The relations stem from the turn-to-turn distance and curvature limiting conditions. Plots of the relations are shown to cross each other. The physical sense of the crossing point is discussed., Comment: 14 pages, 10 figures