Abstract Historically, imaging quality was limited by hardware-intensive data collection. Compressed sensing has shifted this burden to software, using optimization to reconstruct images from sparse, incoherent measurements. While modalities such as MRI, CT, and array imaging rely on linear models, physical constraints often result in highly underdetermined systems that defy traditional reconstruction. This work moves beyond ”black-box” optimization by treating the model matrix !!!x1D49C; as a rigorous encoding of wave propagation and sensor geometry. We show that mathematical properties like mutual coherence are direct manifestations of physical laws, and that exploiting this structure through sparsity-promoting regularization is essential for reliable recovery. By analyzing hardware-specific constraints and non-periodic sensor placement, we bridge the gap between abstract mathematical theory and the fundamental physical bounds of imaging.
This study is a first step towards using data-informed differential models to predict and control the dynamics of cancer-on-chip experiments. We consider a conceptualized one-dimensional device, containing a cancer and a population of white blood cells. The interaction between the cancer and the population of cells is modeled by a chemotaxis model inspired by Keller-Segel-type equations, which is solved by a Hybridized Discontinuous Galerkin method. Our goal is using (synthetic) data to tune the parameters of the governing equations and to assess the uncertainty on the predictions of the dynamics due to the residual uncertainty on the parameters remaining after the tuning procedure. To this end, we apply techniques from uncertainty quantification for parametric differential models. We first perform a global sensitivity analysis using both Sobol and Morris indices to assess how parameter uncertainty impacts model predictions, and fix the value of parameters with negligible impact. Subsequently, we conduct an inverse uncertainty quantification analysis by Bayesian techniques to compute a data-informed probability distribution of the remaining model parameters. Finally, we carry out a forward uncertainty quantification analysis to compute the impact of the updated (residual) parametric uncertainties on the quantities of interest of the model. The whole procedure is sped up by using surrogate models, based on sparse-grids, to approximate the mapping of the uncertain parameters to the quantities of interest.
We introduce a mathematical model of bread leavening in a warm chamber by coupling heat transfer, yeast growth, and carbon dioxide production and diffusion with the deformation of baking paste. We analyze the corresponding system of partial differential equations. The system is discretized by using a semi-implicit Euler method and the finite-element method in the time and space domain, respectively. Numerical simulations are employed to identify the energy consumption necessary to achieve a target volume under different settings of the leavening chamber and different concentrations of yeast in the baking paste, thereby providing a tool for the identification of cost-effective protocols.
This paper presents research conducted at the University of Trento addressing an industrial challenge from Fater S.p.A. regarding the thermal bonding of non-woven fabrics for diaper production. The problem consists in a possible analysis of the behavior of the bonding process of a non-woven fabric. In particular, the bonding process is not given by the use of some kind of glue, but just by the pressure of two fiber webs through two high-velocity steel-made rollers. The research comprised the formulation and theoretical as well as numerical analysis of analytical, mechanical and thermal models for the stress-strain behavior of the non-woven fabric's fibers and for the bonding process with heating effects.
The present study focuses on particular properties of transonic flows through a planar channel featuring a circular bump on the lower wall. The selected geometry is reminiscent of the region surrounding the trailing edge of an airfoil at zero angle of attack and the resulting flow pattern is indeed similar to the fishtail shock-pattern that characterizes airfoils flying at nearly sonic speed. Numerical simulations have been conducted by solving the inviscid Euler equations using both a commercial and an in-house CFD code; discontinuities are modeled using shock-capturing in the former and shock-fitting in the latter. Numerical experiments reveal different shock-patterns obtained by independently varying the inlet Mach number and the outlet-to-inlet static pressure ratio. When shock-interactions occur, shock-polar analysis reveals that the branching point can be modeled using either von Neumann’s three-shock-theory or Guderley’s four-wave-theory, depending on the inlet Mach number. Furthermore, for certain pairs of boundary conditions, multiple solutions have been observed.
