Search results for "differential geometry"

Convexly generic curves in R 3

1988

We study curves immersed in R 3, with special interest in the description of their convex hull frontier structure from a global viewpoint. Genericity conditions are set for these curves by looking at the singularities of height functions on them. We define panel structures for convexly generic curves and work out numerical relations involving the number of tritangent support planes. As a consequence, a generic version of the 4-vertex theorem for convex curves in R 3 is obtained.

Approximate Closed-Form Solutions for the Shift Mechanics of Rubber Belt Variators

2009

The mechanical behavior of V-belt variators during the speed ratio shift is different from the steady operation as a gross radial motion of the belt is superimposed to the circumferential motion. The theoretical analysis involves equilibrium equations similar to the steady case, but requires a re-formulation of the mass conservation condition making use of the Reynolds transport theorem. The mathematical model of the belt-pulley coupling implies the repeated numerical solution of a strongly non-linear differential system. Nevertheless, an attentive observation of the numerical diagrams suggests simple and useful closed-form approximations for the four possible working modes of any pulley, o…

Minimal unit vector fields

2002

We compute the first variation of the functional that assigns each unit vector field the volume of its image in the unit tangent bundle. It is shown that critical points are exactly those vector fields that determine a minimal immersion. We also find a necessary and sufficient condition that a vector field, defined in an open manifold, must fulfill to be minimal, and obtain a simpler equivalent condition when the vector field is Killing. The condition is fulfilled, in particular, by the characteristic vector field of a Sasakian manifold and by Hopf vector fields on spheres.

The exterior derivative as a Killing vector field

1996

Among all the homogeneous Riemannian graded metrics on the algebra of differential forms, those for which the exterior derivative is a Killing graded vector field are characterized. It is shown that all of them are odd, and are naturally associated to an underlying smooth Riemannian metric. It is also shown that all of them are Ricci-flat in the graded sense, and have a graded Laplacian operator that annihilates the whole algebra of differential forms.

A Dido problem for domains in ?2 with a given inradius

1990

We find which are the simply connected domains in ℝ2 satisfying the Dido condition for a straight shoreline, with a given area A and a fixed inradius ϱ, which minimize the length of the free boundary. There are three different cases according to the values of A and ϱ.

Boundary behavior of quasi-regular maps and the isodiametric profile

2001

We study obstructions for a quasi-regular mapping f : M → N f:M\rightarrow N of finite degree between Riemannian manifolds to blow up on or collapse on a non-trivial part of the boundary of M M .

Support of removable partial dentures in situations with a unilaterally missing canine and a curved edentulous ridge.

1997

The load and movement of abutments and removable partial dentures were examined in situations with a unilaterally missing canine and a curved edentulous ridge. These measurements were performed on a model adapted to intraoral conditions. In this simulation, removable partial dentures supported by incisors may result in failure. Spring rest support results in significantly reduced articulation vertically and horizontally when compared with solid rest support and avoids periodontal overloading.

Finite Element Method and Von Mises Investigation on Bone Response to Dynamic Stress with a Novel Conical Dental Implant Connection

2020

The bioengineering and medical and biomedical fields are ever closer, and they manage to obtain surprising results for the development of new devices. The field of simulations and studies in silica has undergone considerable development in recent years, favoring the advancement of medicine. In this manuscript, a study was carried out to evaluate the force distribution on the implant components (In-Kone® Universal) and on the peri-implant tissues subjected to loading. With the finite element analysis and the Von Mises method, it was possible to evaluate this distribution of forces both at 0 degrees (occlusal force) and at 30 degrees; the applied force was 800 N. The obtained results on this …

Seminararbeiten von Semester 71/72, 72, 72/73

1801

On the time function of the Dulac map for families of meromorphic vector fields

2003

Given an analytic family of vector fields in Bbb R2 having a saddle point, we study the asymptotic development of the time function along the union of the two separatrices. We obtain a result (depending uniformly on the parameters) which we apply to investigate the bifurcation of critical periods of quadratic centres.