The Raychaudhuri equation is derived by assuming geometric flow in space–time M of n+1 dimensions. turns into a harmonic oscillator form under suitable transformations. Thereby, relation between geometrical entropy and mean geodesic deviation established. This has connection to chaos theory where the trajectories diverge exponentially. We discuss its application cosmology black holes. Thus, we ...

B-spline curves and their rational generalizations (NURBS curves) play central role and are widely used in computer aided design today. A B-spline curve is uniquely defined by its degree, control points and knot values, while in terms of NURBS curves the weight vector has to be specified in addition. The modification of a curve is also an essential problem in CAD systems, hence numerous methods...

in this study, geometrical, gravimetrical and frictional properties of four common varieties of iranian canola seeds (namely: slm, hyola, okapi, orient), containing the mean moisture value of 6.5% (w.b.) were investigated. geometrical and gravimetrical properties included length, diameter, geometric mean diameter, sphericity, thousand seed mass, volume, true density, bulk density and porosity. ...

The study of the damage of aeronautical materials is important because it may change the microscopic surface structure profiles. The modification of geometrical surface properties can cause small instabilities and then a displacement of the boundary layer. One of the irregularities we can often find is surface roughness. Due to an increase of roughness and other effects, there may be extra mome...

Modification to the behavior of geometrical density at short scales is a key result of loop quantum cosmology, responsible for an interesting phenomenology in the very early universe. We demonstrate the way matter with arbitrary scale factor dependence in Hamiltonian incorporates this change in its effective dynamics in the loop modified phase. For generic matter, the equation of state starts v...

The structural evolution from void modification to self-assembled nanogratings in fused silica is observed for moderate (NA > 0.4) focusing conditions. Void formation, appears before the geometrical focus after the initial few pulses and after subsequent irradiation, nanogratings gradually occur at the top of the induced structures. Nonlinear Schrödinger equation based simulations are conducted...

The renormalisation group equation for N -point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has components given by the βfunctions of the theory. It is argued that this simple picture requires modification whenever any one of the points at which the ampli...

We study the coupling of massive fermions to the quantum mechanical dynamics of spacetime emerging from the spinfoam approach in three dimensions. We first recall the classical theory before constructing a spinfoam model of quantum gravity coupled to spinors. The technique used is based on a finite expansion in inverse fermion masses leading to the computation of the vacuum to vacuum transition...

Angiogenesis, the formation of new blood vessels by sprouting from pre-existing ones, is critical for the establishment and maintenance of complex tissues. Angiogenesis is usually triggered by soluble growth factors such as VEGF. However, geometrical cues also play an important role in this process. Here we report the induction of angiogenesis solely by SVVYGLR peptide micropatterning on polyme...

Radiotherapy wedges constitute an important group within the generic classification of so-called Beam Modification Devices (BMD). Wedges are subdivided into Static, Dynamic, and Omni Wedges sug-groups. The standard static wedge attenuates the beam progressively, in such a way that the dose delivery is higher at the thin side, and lower at the broader side. The slope of the inferior surface has ...