Numerical modelling of the quantum-tail effect on fusion rates at low energy

Results of numerical simulations of fusion rate d(d,p)t, for low-energy deuteron beam, colliding with deuterated metallic matrix (Raiola et al. Phys. Lett.B 547 (2002) 193 and Eur. Phys J. A 13 (2002) 377) confirm analytical estimate given in Coraddu et al. nucl-th/0401043, taking into account quantum tails in the momentum distribution function of target particles, and predict an enhanced astrophysical factor in the 1 keV region in qualitative agreement with experiments.Comment: 6 pages, without figure

Old chinese and friends: new approaches to historical linguistics of the Sino-Tibetan area

List J-M, Starostin G, Yunfan L. “Old Chinese and Friends”: new approaches to historical linguistics of the Sino-Tibetan area. Journal of Language Relationship. 2019;17(1-2):1-6

Equilibria of elastic cable knots and links

We present a theory for equilibria of geometrically exact braids made of two thin, uniform, homogeneous, isotropic, initially-straight, inextensible and unshear- able elastic rods of circular cross-section. We formulate a second-order variational problem for an action functional whose Euler–Lagrange equations, partly in Euler– Poincaré form, yield a compact system of ODEs for which we define boundary-value problems for braids closed into knots or links. The purpose of the chapter is to present a pathway of deformations leading to braids with a knotted axis, thereby offering a way to systematically compute elastic cable knots and links. A representative bifurca- tion diagram and selected numerical solutions illustrate our approach

Forceless folding of thin annular strips

Thin strips or sheets with in-plane curvature have a natural tendency to adopt highly symmetric shapes when forced into closed structures and to spontaneously fold into compact multi-covered configurations under feed-in of more length or change of intrinsic curvature. This disposition is exploited in nature as well as in the design of everyday items such as foldable containers. We formulate boundary-value problems (for an ODE) for symmetric equilibrium solutions of unstretchable circular annular strips and present sequences of numerical solutions that mimic different folding modes. Because of the high-order symmetry, closed solutions cannot have an internal force, i.e., the strips are forceless. We consider both wide and narrow (strictly zero-width) strips. Narrow strips cannot have inflections, but wide strips can be either inflectional or non-inflectional. Inflectional solutions are found to feature stress localisations, with divergent strain energy density, on the edge of the strip at inflections of the surface. ‘Regular’ folding gives these singularities on the inside of the annulus, while ‘inverted’ folding gives them predominantly on the outside of the annulus. No new inflections are created in the folding process as more length is inserted. We end with a discussion of an intriguing apparent connection with a deep result on the topology of curves on surfaces

Biased statistical ensembles for developable ribbons

Letter to the edito

Whisker Sensing by Force and Moment Measurements at the Whisker Base

We address the theoretical question which forces and moments measured at the base of a whisker (tactile sensor) allow for the prediction of the location in space of the point at which a whisker makes contact with an object. We deal with the general case of three-dimensional deformations as well as with the special case of planar configurations. All deformations are treated as quasi-static, and contact is assumed to be frictionless. We show that the minimum number of independent forces or moments required is three but that conserved quantities of the governing elastic equilibrium equations prevent certain triples from giving a unique solution in the case of contact at any point along the whisker except the tip. The existence of these conserved quantities depends on the material and geometrical properties of the whisker. For whiskers that are tapered and intrinsically curved, there is no obstruction to the prediction of the contact point. We show that the choice of coordinate system (Cartesian or cylindrical) affects the number of suitable triples. Tip and multiple point contact are also briefly discussed. Our results explain recent numerical observations in the literature and offer guidance for the design of robotic tactile sensory devices

The Euler Spiral of Rat Whiskers

This paper reports on an analytical study of the intrinsic shapes of 523 whiskers from 15 rats. We show that the variety of whiskers on a rat’s cheek, each of which has different lengths and shapes, can be described by a simple mathematical equation such that each whisker is represented as an interval on the Euler spiral. When all the representative curves of mystacial vibrissae for a single rat are assembled together, they span an interval extending from one coiled domain of the Euler Spiral to the other. We additionally find that each whisker makes nearly the same angle of 47 with the normal to the spherical virtual surface formed by the tips of whiskers, which constitutes the rat’s tactile sensory shroud or ‘search-space’. The implications of the linear curvature model for gaining insight into relationships between growth, form and function are discussed

Writhe formulas and antipodal points in plectonemic DNA configurations

The linking and writhing numbers are key quantities when characterizing the structure of a piece of supercoiled DNA. Defined as double integrals over the shape of the double-helix, these numbers are not always straightforward to compute, though a simplified formula exists. We examine the range of applicability of this widely-used simplified formula, and show that it cannot be employed for plectonemic DNA. We show that inapplicability is due to a hypothesis of Fuller theorem that is not met. The hypothesis seems to have been overlooked in many works.Comment: 20 pages, 7 figures, 47 reference