1,721,280 research outputs found
Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability
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A boundary-value problem for nematic liquid crystals with a variable degree of orientation
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Biofabrication via integrated additive manufacturing and electrofluidodynamics
No full textStemming from the first pioneering works carried out in the late 1990s, a fast-growing body of scientific literature has been focused on the investigation of various additive manufacturing techniques (e.g., fused deposition modeling and stereolithography) for the development of customized polymeric devices for different biomedical applications, such as tissue engineering scaffolds and permanent endoprostheses. In addition, the combination of additive manufacturing with other polymer processing techniques has been investigated as a powerful tool for the enhancement of polymeric scaffold structural and functional features including resolution, surface topography, local porosity, and multiscale architectural design. This chapter is aimed at providing a comprehensive overview of the current progress integrating additive manufacturing and electrofluidodynamic techniques. The main technological aspects of additive manufacturing as a biofabrication approach to developing tissue-engineered constructs are first outlined by presenting and discussing different strategies involving the processing of cell-laden materials or the fabrication of scaffolds able to steer cell behavior through structural stimuli. The different technological solutions developed to integrate additive manufacturing and electrofluidodynamics are then analyzed through an overview of significant literature aimed at imparting nanoscale features to microarchitectures or patterning nanostructures (i.e., nanofibers or nanoparticles) into 3D-layered architectures
Weak differentiability of BV functions on stratified groups
No full textWe prove the almost everywhere approximate differentiability of functions with bounded variation in stratified groups and we study their approximate discontinuity set. We introduce functions of bounded higher order variation and obtain a weak version of Alexandroff differentiability theorem in this context. We present a nontrivial class of functions with second order bounded variation, arising from inf-convolution formula of a suitable "cost'' function
On the Bakry–Émery Condition, the Gradient Estimates and the Local-to-Global Property of RCD∗(K, N) Metric Measure Spaces
Full text linkWe prove higher summability and regularity of Gamma(f) for functions f in spaces satisfying the Bakry–Émery condition BE(K,∞). As a byproduct, we obtain various equivalent weak formulations of BE( K , N ) and we prove the Local-to-Global property of the RCD∗(K, N) condition in locally compact metric measure spaces (X, d, m), without assuming a priori the non-branching condition on the metric space
Comparison of structural behaviour of natural Inter-vertebral disc and a PHEMA-PCL-PET system using a finite Element Analysis
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