We present computer simulations of the response of a flexoelectric blue phase network, either in bulk or under confinement, to an applied field. We find a transition in the bulk between the blue phase I disclination network and a parallel array of disclinations along the direction of the applied field. Upon switching off the field, the system is unable to reconstruct the original blue phase but gets stuck in a metastable phase. Blue phase II is comparatively much less affected by the field.

CHIARA (Convolution of High-resolution Interferograms for Advanced Retrieval in the Atmosphere) is an integrated tool intended for the simulation and inversion of spectra. In this paper application of CHIARA to IMG spectra is presented and discussed.

This paper deals with finite-difference approximations of Euler equations arising in the variational formulation of image segmentation problems. We illustrate how they can be defined by the following steps: (a) definition of the minimization problem for the Mumford-Shah functional (MSf), (b) definition of a sequence of functionals Gamma-convergent to the MSf, and (c) definition and numerical solution of the Euler equations associated to the k-th functional of the sequence.

We consider a geometric motion associated with the minimization of a curvature dependent functional, which is related to the Willmore functional. Such a functional arises in connection with the image segmentation problem in computer vision theory. We show by using formal asymptotics that the geometric motion can be approximated by the evolution of the zero level set of the solution of a nonlinear fourth-order equation related to the Cahn-Hilliard and Allen-Cahn equations.

Variational methods for image segmentation try to recover a piecewise smooth function together with a discontinuity set which represents the boundaries of the segmentation. This paper deals with a variational method that constrains the formation of discontinuities along smooth contours. The functional to be minimized, which involves the computation of the geometrical properties of the boundaries, is approximated by a sequence of functionals which can be discretized in a straightforward way. Computer examples of real images are presented to illustrate the feasibility of the method.

Drug-coated balloons (DCBs) are used commonly for delivering drug into diseased arteries. When applied on the inner surface of an artery, drug is transported from the balloon into the multilayer arterial wall through diffusion and advection, where it is ultimately absorbed through binding reactions. Mathematical modeling of these mass transport processes has the potential to help understand and optimize balloon-based drug delivery, thereby ensuring both safety and efficacy.

Objective: Customization of the rate of drug delivered based on individual patient requirements is of paramount importance in the design of drug delivery devices. Advances in manufacturing may enable multilayer drug delivery devices with different initial drug distributions in each layer. However, a robust mathematical understanding of how to optimize such capabilities is critically needed. The objective of this work is to determine the initial drug distribution needed in a spherical drug delivery device such as a capsule in order to obtain a desired drug release profile.

In this paper, the modal analysis model, made up by a linear combination of complex exponential functions, is considered. Padè approximants to the Z-transform of a noisy sample are then considered, and the asymptotic locus of their poles is studied. It turns out that this locus is strongly related to the complex exponentials of the model. By exploiting these properties, powerful methods for estimating the model parameters can be devised, which have both denoising and super-resolution capabilities.

We study some numerical properties of a nonconvex variational problem which arises as the continuous limit of a discrete optimization method designed for the smoothing of images with preservation of discontinuities. The functional that has to be minimized fails to attain a minimum value. Instead, minimizing sequences develop gradient oscillations which allow them to reduce the value of the functional. The oscillations of the gradient exhibit analogies with microstructures in ordered materials. The pattern of the oscillations is analysed numerically by using discrete parametrized measures.