The Effectiveness Mechanisms of Carbon Nanotubes (CNTs) as Reinforcements for Magnesium-Based Composites for Biomedical Applications: A Review.

As a smart implant, magnesium (Mg) is highly biocompatible and non-toxic. In addition, the elastic modulus of Mg relative to other biodegradable metals (iron and zinc) is close to the elastic modulus of natural bone, making Mg an attractive alternative to hard tissues. However, high corrosion rates and low strength under load relative to bone are some challenges for the widespread use of Mg in orthopedics. Composite fabrication has proven to be an excellent way to improve the mechanical performance and corrosion control of Mg. As a result, their composites emerge as an innovative biodegradable material. Carbon nanotubes (CNTs) have superb properties like low density, high tensile strength, high strength-to-volume ratio, high thermal conductivity, and relatively good antibacterial properties. Therefore, using CNTs as reinforcements for the Mg matrix has been proposed as an essential option. However, the lack of understanding of the mechanisms of effectiveness in mechanical, corrosion, antibacterial, and cellular fields through the presence of CNTs as Mg matrix reinforcements is a challenge for their application. This review focuses on recent findings on Mg/CNT composites fabricated for biological applications. The literature mentions effective mechanisms for mechanical, corrosion, antimicrobial, and cellular domains with the presence of CNTs as reinforcements for Mg-based nanobiocomposites.

Recent Advances in Magnesium-Magnesium Oxide Nanoparticle Composites for Biomedical Applications.

Magnesium (Mg) is considered an attractive option for orthopedic applications due to its density and elastic modulus close to the natural bone of the body, as well as biodegradability and good tensile strength. However, it faces serious challenges, including a high degradation rate and, as a result, a loss of mechanical properties during long periods of exposure to the biological environment. Also, among its other weaknesses, it can be mentioned that it does not deal with bacterial biofilms. It has been found that making composites by synergizing its various components can be an efficient way to improve its properties. Among metal oxide nanoparticles, magnesium oxide nanoparticles (MgO NPs) have distinct physicochemical and biological properties, including biocompatibility, biodegradability, high bioactivity, significant antibacterial properties, and good mechanical properties, which make it a good choice as a reinforcement in composites. However, the lack of comprehensive understanding of the effectiveness of Mg NPs as Mg matrix reinforcements in mechanical, corrosion, and biological fields is considered a challenge in their application. While introducing the role of MgO NPs in medical fields, this article summarizes the most important results of recent research on the mechanical, corrosion, and biological performance of Mg/MgO composites.

Geometry of commutes in the universality of percolating traffic flows.

Traffic congestion is a major problem in megacities which increases vehicle emissions and degrades ambient air quality. Various models have been developed to address the universal features of traffic jams. These models range from microscopic car-following models to macroscopic collective dynamic models. Here, we study the macrostructure of congested traffic influenced by the complex geometry of the commute. Our main focus is on the dynamics of traffic patterns in Paris and Los Angeles, each with distinct urban structures. We analyze the complexity of the giant traffic clusters based on a percolation framework during rush hours in the mornings, evenings, and holidays. We uncover that the universality described by several critical exponents of traffic patterns is highly correlated with the geometry of commute and the underlying urban structure. Our findings might have broad implications for developing a greener, healthier, and more sustainable future city.

Emergence of rigidity percolation in flowing granular systems.

Jammed granular media and glasses exhibit spatial long-range correlations as a result of mechanical equilibrium. However, the existence of such correlations in the flowing matter, where the mechanical equilibrium is unattainable, has remained elusive. Here, we investigate this problem in the context of the percolation of interparticle forces in flowing granular media. We find that the flow rate introduces an effective long-range correlation, which plays the role of a relevant perturbation giving rise to a spectrum of varying exponents on a critical line as a function of the flow rate. Our numerical simulations along with analytical arguments predict a crossover flow rate [Formula: see text] below which the effect of induced disorder is weak and the universality of the force chain structure is shown to be given by the standard rigidity percolation. We also find a power-law behavior for the critical exponents with the flow rate [Formula: see text].

A Comprehensive Review of the Current Research Status of Biodegradable Zinc Alloys and Composites for Biomedical Applications.

Zinc (Zn)-based biodegradable materials show moderate degradation rates in comparison with other biodegradable materials (Fe and Mg). Biocompatibility and non-toxicity also make them a viable option for implant applications. Furthermore, Pure Zn has poor mechanical behavior, with a tensile strength of around 100-150 MPa and an elongation of 0.3-2%, which is far from reaching the strength required as an orthopedic implant material (tensile strength is more than 300 MPa, elongation more than 15%). Alloy and composite fabrication have proven to be excellent ways to improve the mechanical performance of Zn. Therefore, their alloys and composites have emerged as an innovative category of biodegradable materials. This paper summarizes the most important recent research results on the mechanical and biological characteristics of biodegradable Zn-based implants for orthopedic applications and the most commonly added components in Zn alloys and composites.

MWCNTs-TiO2 Incorporated-Mg Composites to Improve the Mechanical, Corrosion and Biological Characteristics for Use in Biomedical Fields.

This study attempts to synthesize MgZn/TiO2-MWCNTs composites with varying TiO2-MWCNT concentrations using mechanical alloying and a semi-powder metallurgy process coupled with spark plasma sintering. It also aims to investigate the mechanical, corrosion, and antibacterial properties of these composites. When compared to the MgZn composite, the microhardness and compressive strength of the MgZn/TiO2-MWCNTs composites were enhanced to 79 HV and 269 MPa, respectively. The results of cell culture and viability experiments revealed that incorporating TiO2-MWCNTs increased osteoblast proliferation and attachment and enhanced the biocompatibility of the TiO2-MWCNTs nanocomposite. It was observed that the corrosion resistance of the Mg-based composite was improved and the corrosion rate was reduced to about 2.1 mm/y with the addition of 10 wt% TiO2-1 wt% MWCNTs. In vitro testing for up to 14 days revealed a reduced degradation rate following the incorporation of TiO2-MWCNTs reinforcement into a MgZn matrix alloy. Antibacterial evaluations revealed that the composite had antibacterial activity, with an inhibition zone of 3.7 mm against Staphylococcus aureus. The MgZn/TiO2-MWCNTs composite structure has great potential for use in orthopedic fracture fixation devices.

Bredigite-CNTs Reinforced Mg-Zn Bio-Composites to Enhance the Mechanical and Biological Properties for Biomedical Applications.

Magnesium (Mg) and its compounds have been investigated as biodegradable metals for bone implants. However, high corrosion rates and low bioactivity that cause loss of mechanical properties are factors that have limited their biomedical applications. The purpose of this work is to remedy the weaknesses of the Mg-Zn (MZ) alloy matrix. For this purpose, we have synthesized Mg-based composites with different concentrations of bredigite (Br; Ca7MgSi4O16)-carbon nanotubes (CNTs) using mechanical alloying and semi-powder metallurgy processes with spark plasma sintering. Then, we studied the effect of the simultaneous addition of Br-CNTs on in vitro degradation, as well as its effect on the composites' mechanical and antibacterial properties. Increases of 57% and 72% respectively were observed in the microhardness and compressive strength of the MZ/Br-CNTs composite in comparison to the MZ alloy. In addition, the rate of degradation of Mg-based composites in simulated body fluids (SBF) was almost 2 times lower. An assessment of antibacterial behavior disclosed that the simultaneous adding of Br-CNTs to Mg can meaningfully prevent the growth and invasion of E. coli and S. aureus. These research findings demonstrate the potential application of MZ/Br-CNTs composites to implants and the treatment of bone infections.

The effect of Co-encapsulated GNPs-CNTs nanofillers on mechanical properties, degradation and antibacterial behavior of Mg-based composite.

Magnesium (Mg)-based composites, as one group of the biodegradable materials, enjoy high biodegradability, biocompatibility, and non-toxicity making them a great option for implant applications. In this paper, by the semi powder metallurgy (SPM) technique, the graphene nano-platelets (GNPs) and carbon nanotubes (CNTs) nanosystems, as reinforcements, are dispersed homogenously in the Mg-Zn (MZ) alloy matrix. Subsequently, the composite is successfully produced employing the spark plasma sintering (SPS) process. Compared to the unreinforced MZ sample, GNPs + CNTs mixture reinforced composite exhibits higher compressive strength (∼75%). Notably, adding only 1 wt % of GNPs + CNTs to the MZ matrix reduces the rate of the degradation in the Mg-based composite by almost 2- fold. Examining the antibacterial activity demonstrate that the incorporation of GNPs + CNTs into the Mg-based matrix is likely to prevent the infiltration and development of Staphylococcus aureus (S. aureus) and Escherichia coli (E. coli) significantly. While the MTT with 0.5 and 1 wt % GNPs + CNTs does not demonstrate cytotoxicity to the MG63 cells, the excessive GNPs + CNTs results in a certain degree of poisonousness. In general, the findings of the present research attest to the viable application of MZ/GNPs + CNTs composites for implants as well as bone infection treatment.

A 2D Lévy-flight model for the complex dynamics of real-life financial markets.

We report on the emergence of scaling laws in the temporal evolution of the daily closing values of the S&P 500 index prices and its modeling based on the Lévy flights in two dimensions (2D). The efficacy of our proposed model is verified and validated by using the extreme value statistics in the random matrix theory. We find that the random evolution of each pair of stocks in a 2D price space is a scale-invariant complex trajectory whose tortuosity is governed by a 2/3 geometric law between the gyration radius Rg(t) and the total length ℓ(t) of the path, i.e., Rg(t)∼ℓ(t)2/3. We construct a Wishart matrix containing all stocks up to a specific variable period and look at its spectral properties for over 30 years. In contrast to the standard random matrix theory, we find that the distribution of eigenvalues has a power-law tail with a decreasing exponent over time-a quantitative indicator of the temporal correlations. We find that the time evolution of the distance of 2D Lévy flights with index α=3/2 from origin generates the same empirical spectral properties. The statistics of the largest eigenvalues of the model and the observations are in perfect agreement.

Exact finite-size scaling for the random-matrix representation of bond percolation on square lattice.

We report on the exact treatment of a random-matrix representation of a bond-percolation model on a square lattice in two dimensions with occupation probability p. The percolation problem is mapped onto a random complex matrix composed of two random real-valued matrices of elements +1 and -1 with probability p and 1-p, respectively. We find that the onset of percolation transition can be detected by the emergence of power-law divergences due to the coalescence of the first two extreme eigenvalues in the thermodynamic limit. We develop a universal finite-size scaling law that fully characterizes the scaling behavior of the extreme eigenvalue's fluctuation in terms of a set of universal scaling exponents and amplitudes. We make use of the relative entropy as an index of the disparity between two distributions of the first and second-largest extreme eigenvalues to show that its minimum underlies the scaling framework. Our study may provide an inroad for developing new methods and algorithms with diverse applications in machine learning, complex systems, and statistical physics.

Universal scaling and criticality of extremes in random matrix theory.

We present a random matrix realization of a two-dimensional percolation model with the occupation probability p. We find that the behavior of the model is governed by the two first extreme eigenvalues. While the second extreme eigenvalue resides on the moving edge of the semicircle bulk distribution with an additional semicircle functionality on p, the first extreme exhibits a disjoint isolated Gaussian statistics which is responsible for the emergence of a rich finite-size scaling and criticality. Our extensive numerical simulations along with analytical arguments unravel the power-law divergences due to the coalescence of the first two extreme eigenvalues in the thermodynamic limit. We develop a scaling law that provides a universal framework in terms of a set of scaling exponents uncovering the full finite-size scaling behavior of the extreme eigenvalue's fluctuation. Our study may provide a simple practical approach to capture the criticality in complex systems and their inverse problems with a possible extension to the interacting systems.

Effects of foliar spray of agricultural grade mineral oil in springtime, in combination with potassium and calcium sulfates on the phenological and biophysical indices of clusters, and foliar nutritional levels in grapevine (Vitis vinifera L.) cv. Sultana (Id. Thompson seedless, Sultanina).

BACKGROUND: Improving the nutritional condition of grapevine in spring to regulate bloom, fruit set, and yield is among the management goals of vineyards. METHODS: In the present study, the early season spray of calcium sulfate (C; 0.00 and 2.00%), potassium sulfate (K; 0.00 and 3.00%), and agricultural grade mineral oil (V; 0.00 and 1.00%) on flower and fruit phenology, nutrient concentration, and cluster biophysical indices and yield of Sultana grapevine (Vitis vinifera L.) were investigated for two consecutive years. RESULTS: Based on the results, the spray of this nutrient combined with mineral oil significantly affected all the treatments except cluster length, berry length, and phosphorus concentration. The highest concentrations of potassium, calcium, and magnesium were obtained in the vines treated with V0K1C1, and the highest concentrations of zinc and iron were obtained only in the vines treated with mineral oil. In treatments containing mineral oil, especially in combination with the second level of calcium and potassium (V1K1C1), bloom time, berries pea-sized time, and harvest time were delayed by 3, 3, and 6 days compared with control vines. While in vines treated with a combination of the second level of potassium and calcium (V0K1C1), bloom time, berries pea-sized time, and harvest time were advanced by 5, 4, and 1.50 days, respectively, compared with control vines. Regarding the biophysical indices of the cluster, it was found that the vines treated with V1K1C1 had higher cluster weight, berry weight, fruit, and raisins yield than other treatments. Also, the highest berry quality, including total soluble solids, titratable acidity, and total phenol content, were obtained in the vines treated with V0K1C1. However, the lowest berry quality was observed in the vines treated with mineral oil. CONCLUSIONS: Therefore, the combination of nutrients with mineral oil can alleviate the adverse effect of mineral oil solely on some phenological indices and berry quality-related traits in vineyards.

Geometrically regulating evolutionary dynamics in biofilms.

The theoretical understanding of evolutionary dynamics in spatially structured populations often relies on nonspatial models. Biofilms are among such populations where a more accurate understanding is of theoretical interest and can reveal new solutions to existing challenges. Here, we studied how the geometry of the environment affects the evolutionary dynamics of expanding populations, using the Eden model. Our results show that fluctuations of subpopulations during range expansion in two- and three-dimensional environments are not Brownian. Furthermore, we found that the substrate's geometry interferes with the evolutionary dynamics of populations that grow upon it. Inspired by these findings, we propose a periodically wedged pattern on surfaces prone to develop biofilms. On such patterned surfaces, natural selection becomes less effective and beneficial mutants would have a harder time establishing. Additionally, this modification accelerates genetic drift and leads to less diverse biofilms. Both interventions are highly desired for biofilms.

Superlinear growth reveals the Allee effect in tumors.

Integrating experimental data into ecological models plays a central role in understanding biological mechanisms that drive tumor progression where such knowledge can be used to develop new therapeutic strategies. While the current studies emphasize the role of competition among tumor cells, they fail to explain recently observed superlinear growth dynamics across human tumors. Here we study tumor growth dynamics by developing a model that incorporates evolutionary dynamics inside tumors with tumor-microenvironment interactions. Our results reveal that tumor cells' ability to manipulate the environment and induce angiogenesis drives superlinear growth-a process compatible with the Allee effect. In light of this understanding, our model suggests that, for high-risk tumors that have a higher growth rate, suppressing angiogenesis can be the appropriate therapeutic intervention.

Percolation analysis of the atmospheric structure.

The atmosphere is a thermo-hydrodynamical complex system and provides oxygen to most animal life at the Earth's surface. However, the detection of complexity for the atmosphere remains elusive and debated. Here we develop a percolation-based framework to explore its structure by using the global air temperature field. We find that the percolation threshold is much delayed compared with the prototypical percolation model and the giant cluster eventually emerges explosively. A finite-size-scaling analysis reveals that the observed transition in each atmosphere layer is genuine discontinuous. Furthermore, at the percolation threshold, we uncover that the boundary of the giant cluster is self-affine, with fractal dimension d_{f}, and can be utilized to quantify the atmospheric complexity. Specifically, our results indicate that the complexity of the atmosphere decreases superlinearly with height, i.e., the complexity is higher at the surface than at the top layer and vice versa, due to the atmospheric boundary forcings. The proposed methodology may evaluate and improve our understanding regarding the critical phenomena of the complex Earth system and can be used as a benchmark tool to test the performance of Earth system models.

Universality class of epidemic percolation transitions driven by random walks.

Inspired by the recent viral epidemic outbreak and its consequent worldwide pandemic, we devise a model to capture the dynamics and the universality of the spread of such infectious diseases. The transition from a precritical to the postcritical phase is modeled by a percolation problem driven by random walks on a two-dimensional lattice with an extra average number ρ of nonlocal links per site. Using finite-size scaling analysis, we find that the effective exponents of the percolation transitions as well as the corresponding time thresholds, extrapolated to the infinite system size, are ρ dependent. We argue that the ρ dependence of our estimated exponents represents a crossover-type behavior caused by the finite-size effects between the two limiting regimes of the system. We also find that the universal scaling functions governing the critical behavior in every single realization of the model can be well described by the theory of extreme values for the maximum jumps in the order parameter and by the central limit theorem for the transition threshold.

Effects of foliar spray of agricultural grade mineral oil in springtime, in combination with potassium and calcium sulfates on the phenological and biophysical indices of clusters, and foliar nutritional levels in grapevine ( Vitis vinifera L.) cv. Sultana (Id. Thompson seedless, Sultanina)

BACKGROUND: Improving the nutritional condition of grapevine in spring to regulate bloom, fruit set, and yield is among the management goals of vineyards. METHODS: In the present study, the early season spray of calcium sulfate (C; 0.00 and 2.00%), potassium sulfate (K; 0.00 and 3.00%), and agricultural grade mineral oil (V; 0.00 and 1.00%) on flower and fruit phenology, nutrient concentration, and cluster biophysical indices and yield of Sultana grapevine ( Vitis vinifera L.) were investigated for two consecutive years. RESULTS: Based on the results, the spray of this nutrient combined with mineral oil significantly affected all the treatments except cluster length, berry length, and phosphorus concentration. The highest concentrations of potassium, calcium, and magnesium were obtained in the vines treated with V0K1C1, and the highest concentrations of zinc and iron were obtained only in the vines treated with mineral oil. In treatments containing mineral oil, especially in combination with the second level of calcium and potassium (V1K1C1), bloom time, berries pea-sized time, and harvest time were delayed by 3, 3, and 6 days compared with control vines. While in vines treated with a combination of the second level of potassium and calcium (V0K1C1), bloom time, berries pea-sized time, and harvest time were advanced by 5, 4, and 1.50 days, respectively, compared with control vines. Regarding the biophysical indices of the cluster, it was found that the vines treated with V1K1C1 had higher cluster weight, berry weight, fruit, and raisins yield than other treatments. Also, the highest berry quality, including total soluble solids, titratable acidity, and total phenol content, were obtained in the vines treated with V0K1C1. However, the lowest berry quality was observed in the vines treated with mineral oil. CONCLUSIONS: Therefore, the combination of nutrients with mineral oil can alleviate the adverse effect of mineral oil solely on some phenological indices and berry quality-related traits in vineyards.

Random walks on intersecting geometries.

We present an analytical approach to study simple symmetric random walks on a crossing geometry consisting of a plane square lattice crossed by n_{l} number of lines that all meet each other at a single point (the origin) on the plane. The probability density to find the walker at a given distance from the origin either in a line or in the plane geometry is exactly calculated as a function of time t. We find that the large-time asymptotic behavior of the walker for any arbitrary number n_{l} of lines is eventually governed by the diffusion of the walker on the plane after a crossover time approximately given by t_{c}∝n_{l}^{2}. We show that this competition can be changed in favor of the line geometry by switching on an arbitrarily small perturbation of a drift term in which even a weak biased walk is able to drain the whole probability density into the line at long-time limit. We also present the results of our extensive simulations of the model which perfectly support our analytical predictions. Our method can, however, be simply extended to other crossing geometries with a single common point.

Regulation of migration of chemotactic tumor cells by the spatial distribution of collagen fiber orientation.

Collagen fibers, an important component of the extracellular matrix (ECM), can both inhibit and promote cellular migration. In vitro studies have revealed that the fibers' orientations are crucial to cellular invasion, while in vivo investigations have led to the development of tumor-associated collagen signatures (TACS) as an important prognostic factor. Studying biophysical regulation of cell invasion and the effect of the fibers' orientation not only deepens our understanding of the phenomenon, but also helps classify the TACSs precisely, which is currently lacking. We present a stochastic model for random or chemotactic migration of cells in fibrous ECM, and study the role of the various factors in it. The model provides a framework for quantitative classification of the TACSs, and reproduces quantitatively recent experimental data for cell motility. It also indicates that the spatial distribution of the fibers' orientations and extended correlations between them, hitherto ignored, as well as dynamics of cellular motion all contribute to regulation of the cells' invasion length, which represents a measure of metastatic risk. Although the fibers' orientations trivially affect randomly moving cells, their effect on chemotactic cells is completely nontrivial and unexplored, which we study in this paper.

Percolation framework of the Earth's topography.

Self-similarity and long-range correlations are the remarkable features of the Earth's surface topography. Here we develop an approach based on percolation theory to study the geometrical features of Earth. Our analysis is based on high-resolution, 1 arc min, ETOPO1 global relief records. We find some evidence for abrupt transitions that occurred during the evolution of the Earth's relief network, indicative of a continental/cluster aggregation. We apply finite-size-scaling analysis based on a coarse-graining procedure to show that the observed transition is most likely discontinuous. Furthermore, we study the percolation on two-dimensional fractional Brownian motion surfaces with Hurst exponent H as a model of long-range correlated topography, which suggests that the long-range correlations may play a key role in the observed discontinuity on Earth. Our framework presented here provides a theoretical model to better understand the geometrical phase transition on Earth, and it also identifies the critical nodes that will be more exposed to global climate change in the Earth's relief network.