In this article we propose to investigate the analogy between early cortical folding process and cortical smoothing by mean curvature flow. First, we introduce a one-parameter model that is able to fit a developmental trajectory as represented in a Volume-Area plot and we propose an efficient optimization strategy for parameter estimation. Second, we validate the model on forty cortical surface...

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 ...

We consider geometrical optimization problems related to optimizing the error probability in the presence of a Gaussian noise. One famous questions in the field is the “weak simplex conjecture”. We discuss possible approaches to it, and state related conjectures about the Gaussian measure, in particular, the conjecture about minimizing of the Gaussian measure of a simplex. We also consider anti...

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. ...

MINDO-Forces calculations with complete geometry optimization have been performed on nitromethane, aci-nitromethane and X-substituted nitromethane and aci-nitromethane (X = F, OH, NH2, CH3, CN, CF3, NO2, CHO). It is found that nitromethane is more stable than aci-nitromethane by 9.337 kcal/mol. This agrees with theoretical calculations. Thermodynamically, substituted acinitro tautomers are more...

Extreme ultraviolet (EUV) lithography uses reflective ring-field projection systems. Geometrical obstruction limits the possible system configurations to small domains of the parameter space. We present an analysis, a search method, and a classification of these unobstructed domains. The exhaustive search method based on paraxial analysis provides an effective means for determining all possible...

An original parameters extraction strategy has been developed using a physical and scalable 2π equivalent on-chip spiral inductors RLC circuit model. This strategy based on optimization only, was used to model spice model parameters as a function of geometrical inductor parameters. The data used in this paper were obtained by using a 3D electromagnetic Field Solver combined with a Design of Exp...

Abstract: The paper can be considered as a complement to previous papers of the authors. An insight into applied asymptotic analysis of boundary value problems in singularly perturbed domains is presented. As a result, the asymptotic expansions of eigenvalues are obtained and discussed in terms of integral attributes of the geometrical perturbations including the virtual mass tensor, polarizati...

The paper describes the propagation of a thin laser beam which passes through a hot turbulent jet, perpendicularly to the flow direction, using geometrical optics approximation. From the modelling of the random propagation direction of the laser beam along its whole path, the diffusion coefficient of the turbulent jet is determined by means of a shape optimization technique in which a genetic a...

This paper deals with eigenvalue optimization problems for a family of natural Schrödinger operators arising in some geometrical or physical contexts. These operators, whose potentials are quadratic in curvature, are considered on closed surfaces immersed in space forms and we look for geometries that maximize the eigenvalues. We show that under suitable assumptions on the potential, the first ...