Abstract A variety of materials, such as polycrystalline ceramics or carbon fiber reinforced polymers, show a pronounced anisotropy in their local crack resistance. We introduce an FFT-based method to compute the effective energy heterogeneous, locally anisotropic materials. Recent theoretical works ensure existence representative volume elements for fracture mechanics described by Francfort–Ma...

Stress analysis is an important step in the design of material systems, and finite element methods (FEM) are a standard approach performing computational stresses complex systems. The significant cost associated with multi-scale FEM motivates replacement significantly faster data-driven machine learning based approach. In this study, we consider application deep tools to local stress field pred...

With the goal of non-invasively localizing cardiac ischemic disease using body-surface potential recordings, we attempted to reconstruct the transmembrane potential (TMP) throughout the myocardium with the bidomain heart model. The task is an inverse source problem governed by partial differential equations (PDE). Our main contribution is solving the inverse problem within a PDE-constrained opt...

We show that a particular noncommutative geometry, sometimes called angular or $\rho$-Minkowski, requires the spectrum of time be discrete. In this space variable is not commuting with in cylindrical coordinates. The possible values can take go from minus infinity to plus infinity, equally spaced by scale noncommmutativity. Possible self-adjoint extensions "time operator" are discussed. They gi...

In this paper, we present a topology optimization (TO) framework to simultaneously optimize the matrix and fiber distribution of functionally graded continuous fiber-reinforced composites (FRC). Current approaches in density-based TO for FRC use underlying finite element mesh both analysis design representation. This poses several limitations while enforcing sub-element spacing generating high-...

Spherical Deconvolution (SD) is commonly used for estimating fiber Orientation Distribution Functions (fODFs) from diffusion-weighted signals. Existing SD methods can be classified into two categories: 1) Continuous Representation based SD (CR-SD), where typically Spherical Harmonic (SH) representation is used for convenient analytical solutions, and 2) Discrete Representation based SD (DR-SD),...