The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part I. One reason of the still limited use of NNMs in structural dynamics is that their computation is often regarded as impractical. However, when resorting to numerical algorithms, we show that the NNM computation is possible with limited implementation effort, which paves the way to a practical method for determining the NNMs of nonlinear mechanical systems. The proposed algorithm relies on two main techniques, namely a shooting procedure and a method for the continuation of NNM motions. The algorithm is demonstrated using four different mechanical systems, a weakly and a strongly nonlinear two-degree-of-freedom system, a simplified discrete model of a nonlinear bladed disk and a nonlinear cantilever beam discretized by the finite element method.

Purpose: Leukocyte-and platelet-rich fibrin (L-PRF) has been used for alveolar ridge preservation (ARP) in postextraction tooth sockets. However, current reports have measured its effectiveness in linear measurements of 3-dimensional ridge preservation. The purpose of this study was to determine the effectiveness of the use of L-PRF filling versus natural clot blood healing in ARP according to the clinical, radiographic, and volumetric measurements of postextraction tooth sockets.Materials and Methods: A split-mouth randomized clinical trial was designed. Healthy patients who needed bilateral extraction of upper third molars were selected. After the tooth extraction, the socket was filled and distributed randomly with L-PRF and the contralateral socket only with the blood clot. The dimensional change of soft tissue healing around the sockets, and the length, depth, and difference of bone formation were examined using standardized periapical radiographs. Volumetric measurement variation of the sockets was evaluated by 3-dimensional scanning of dental casts. Changes of all measures were analyzed at 7 days (initial) and 3 months (final) after the tooth extraction and compared between both groups (t test; P < .05).Results: Sixteen patients (aged 24.75 AE 3.53 years; 56.25% women) participated. Measurements of wound healing and the length, depth, and difference of bone formation were similar for both study groups at initial and final times. The calculation of initial-final volumetric socket variation was 15.45 AE 13.12 mL using L-PRF and 14.12 AE 11.23 mL using blood clot (P = .78).

Mandibular reconstruction after trauma or pathology is one of the cornerstones of oral and maxillofacial surgery. 1 This reconstruction is needed in cases with a large amount of bone loss, comminute fractures, severe traumas, and infections leading to multiple bone sequestrations. 2 In the case of infections of the bone, different risk factors may enhance the speed in which the bone is lost, such as age, sex, poor oral hygiene, comorbidities (diabetes, hyperlipemia, autoimmune diseases), and drug abuse (cocaine, cannabinoid, tobacco smoking, hepatic cirrhosis due alcoholism). [3][4][5][6][7][8] The four basic principles of successful reconstruction are (a) establish an ideal orthognathic relationship; (b) a flush bone to graft/flap contact; (c) stable bony fixation; and (d) adequate, well-vascularized soft tissue coverage. 1 To achieve the previously established principles, the maxillofacial literature describes different surgical treatment

The design of scaffolds to reach similar three-dimensional structures mimicking the natural and fibrous environment of some cells is a challenge for tissue engineering, and 3D-printing and electrospinning highlights from other techniques in the production of scaffolds. The former is a well-known additive manufacturing technique devoted to the production of custom-made structures with mechanical properties similar to tissues and bones found in the human body, but lacks the resolution to produce small and interconnected structures. The latter is a well-studied technique to produce materials possessing a fibrillar structure, having the advantage of producing materials with tuned composition compared with a 3D-print. Taking the advantage that commercial 3D-printers work with polylactide (PLA) based filaments, a biocompatible and biodegradable polymer, in this work we produce PLA-based composites by blending materials obtained by 3D-printing and electrospinning. Porous PLA fibers have been obtained by the electrospinning of recovered PLA from 3D-printer filaments, tuning the mechanical properties by blending PLA with small amounts of polyethylene glycol and hydroxyapatite. A composite has been obtained by blending two layers of 3D-printed pieces with a central mat of PLA fibers. The composite presented a reduced storage modulus as compared with a single 3D-print piece and possessing similar mechanical properties to bone tissues. Furthermore, the biocompatibility of the composites is assessed by a simulated body fluid assay and by culturing composites with 3T3 fibroblasts. We observed that all these composites induce the growing and attaching of fibroblast over the surface of a 3D-printed layer and in the fibrous layer, showing the potential of commercial 3D-printers and filaments to produce scaffolds to be used in bone tissue engineering.

The power law relation between the mean population count and its variance (Taylor's Power Law, TPL) is among the few general patterns in population ecology. While the TPL has been described to be pervasive across taxa, the causes of variation of the exponent describing this relation is not well understood. We compare the TPL exponents for two species with different social systems and behavior: Piñon jays (Gymnorhinus cyanocephalus) and Western scrub-jays (Aphelocoma californica). We analyze the underlying processes that generate the expected values of population size and its variance. Using a probabilistic model, we identify and estimate important processes involved in the generation of the TPL exponents. While both species show a scaling relationship between their mean and abundance, share a common negative relation between mean abundance and colonization-extinction rates, they differ greatly in the statistical distributions of colonization, extinction, the mean number of colonists, the probability of zero abundance and population sizes. We show how different aspects of the processes that generate abundance affect the TPL exponent, thereby providing empirical guidelines to interpret differences in the scaling relation between mean and variance of population size.