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Finite growth models

Kyungjin Kim, Hao Luo, Ting Zhu, Olivier N Pierron, Samuel Graham
This work is concerned with the long-term behavior of environmentally-assisted subcritical cracking of PECVD SiNx barrier films on polyethylene terephthalate (PET) and polyimide (PI) substrates. While environmentally-assisted channel cracking in SiNx has been previously demonstrated, with constant crack growth rates over short periods of time (<1 hour) during which no substrate damage was observed, the present experiments over longer periods reveal a regime where cracking also develops in the polymer substrate...
March 14, 2018: Scientific Reports
Hyung Joon Cho, Scott S Verbridge, Rafael V Davalos, Yong W Lee
To analyze complex inflammatory responses in an in vitro system, we constructed a new 3D in vitro brain tissue model that exhibits in vivo-like tissue responses (e.g. immune cell phenotypes, and molecular response) to inflammatory stimuli. Finite element modeling of oxygen diffusion and cellular oxygen consumption predicted the oxygen profile within 3D structures, consisting of Type I collagen hydrogel embedded with murine microglia. Viability and cytotoxicity analyses supported the mathematical analysis, determining optimal cell growth conditions for 3D construct development...
March 2, 2018: Annals of Biomedical Engineering
Irénée Frérot, Piero Naldesi, Tommaso Roscilde
The relaxation of uniform quantum systems with finite-range interactions after a quench is generically driven by the ballistic propagation of long-lived quasiparticle excitations triggered by a sufficiently small quench. Here we investigate the case of long-range (1/r^{α}) interactions for a d-dimensional lattice spin model with uniaxial symmetry, and show that, in the regime d<α<d+2, the entanglement and correlation buildup is radically altered by the existence of a nonlinear dispersion relation of quasiparticles, ω∼k^{z<1}, at small wave vectors, leading to a divergence of the quasiparticle group velocity and superballistic propagation...
February 2, 2018: Physical Review Letters
José Antonio Carrillo, Annachiara Colombi, Marco Scianna
The description of the cell spatial pattern and characteristic distances is fundamental in a wide range of physio-pathological biological phenomena, from morphogenesis to cancer growth. Discrete particle models are widely used in this field, since they are focused on the cell-level of abstraction and are able to preserve the identity of single individuals reproducing their behavior. In particular, a fundamental role in determining the usefulness and the realism of a particle mathematical approach is played by the choice of the intercellular pairwise interaction kernel and by the estimate of its parameters...
February 21, 2018: Journal of Theoretical Biology
Marjan Faizi, Tomáš Zavrel, Cristina Loureiro, Jan Cerveny, Ralf Steuer
Photoautotrophic growth depends upon an optimal allocation of finite cellular resources to diverse intracellular processes. Commitment of a certain mass fraction of the proteome to a specific cellular function typically reduces the proteome available for other cellular functions. Here, we develop a semi-quantitative kinetic model of cyanobacterial phototrophic growth to describe such trade-offs of cellular protein allocation. The model is based on coarse-grained descriptions of key cellular processes, in particular carbon uptake, metabolism, photosynthesis, and protein translation...
February 21, 2018: Bio Systems
Victor S Alvarez, Svein Kleiven
Finite element (FE) models are a powerful tool that can be used to understand injury mechanisms and develop better safety systems. This study aims to extend the understanding of pediatric spine biomechanics, where there is a paucity of studies available. A newly developed and continuously scalable FE model was validated and scaled to 1.5-, 3-, 6-, 10-, 14- and 18-year-old using a non-linear scaling technique, accounting for local topological changes. The oldest and youngest ages were also scaled using homogeneous geometric scaling...
February 8, 2018: Journal of Biomechanics
Schuyler B Nicholson, Jonah S Greenberg, Jason R Green
According to the asymptotic equipartition property, sufficiently long sequences of random variables converge to a set that is typical. While the size and probability of this set are central to information theory and statistical mechanics, they can often only be estimated accurately in the asymptotic limit due to the exponential growth in possible sequences. Here we derive a time-inhomogeneous dynamics that constructs the properties of the typical set for all finite length sequences of independent and identically distributed random variables...
January 2018: Physical Review. E
Luca Gagliardi, Olivier Pierre-Louis
We present a continuum model describing dissolution and growth of a crystal contact confined against a substrate. Diffusion and hydrodynamics in the liquid film separating the crystal and the substrate are modeled within the lubrication approximation. The model also accounts for the disjoining pressure and surface tension. Within this framework, we obtain evolution equations which govern the nonequilibrium dynamics of the crystal interface. Based on this model, we explore the problem of dissolution under an external load, known as pressure solution...
January 2018: Physical Review. E
Hadi S Hosseini, Larry A Taber
In the vertebrate embryo, the eyes develop from optic vesicles that grow laterally outward from the brain tube and contact the overlying surface ectoderm. Within the region of contact, each optic vesicle and the surface ectoderm thicken to form placodes, which then invaginate to create the optic cup and lens pit, respectively. Eventually, the optic cup becomes the retina, while the lens pit closes to form the lens vesicle. Here, we review current hypotheses for the physical mechanisms that create these structures and present novel three-dimensional computer (finite-element) models to illustrate the plausibility and limitations of these hypotheses...
February 9, 2018: Progress in Biophysics and Molecular Biology
Katherine A Staines, Kamel Madi, Behzad Javaheri, Peter D Lee, Andrew A Pitsillides
The epiphyseal growth plate is a developmental region responsible for linear bone growth, in which chondrocytes undertake a tightly regulated series of biological processes. Concomitant with the cessation of growth and sexual maturation, the human growth plate undergoes progressive narrowing, and ultimately disappears. Despite the crucial role of this growth plate fusion "bridging" event, the precise mechanisms by which it is governed are complex and yet to be established. Progress is hindered by the current methods for growth plate visualization; these are invasive and largely rely on histological procedures...
January 23, 2018: Frontiers in Materials
Dara Azar, Donya Ohadi, Alexander Rachev, John F Eberth, Mark J Uline, Tarek Shazly
An aortic aneurysm (AA) is a focal dilatation of the aortic wall. Occurrence of AA rupture is an all too common event that is associated with high levels of patient morbidity and mortality. The decision to surgically intervene prior to AA rupture is made with recognition of significant procedural risks, and is primarily based on the maximal diameter and/or growth rate of the AA. Despite established thresholds for intervention, rupture occurs in a notable subset of patients exhibiting sub-critical maximal diameters and/or growth rates...
2018: PloS One
Ling Wang, Jianfeng Kang, Lei Shi, Jun Fu, Dichen Li, Zheng Guo, Chaozong Liu, Shuangpeng Dong, Xi Jiang
Most vertebral body implants that are currently designed and produced in batches have difficulty meeting the patient-specific demands. Moreover, several complications, including a low fusion rate, subsidence occurrence, and rod displacement, are associated with these implants. This study aims to investigate the effects of patient-specific geometric and clinical parameters on the biomechanics of a vertebral body replacement. A three-dimensional patient-specific vertebral body replacement model was established as the basic model for parametric studies, including the anatomic design of the endplates, tilting angle, thickness, and dislocation of the vertebral body implant...
January 1, 2018: Proceedings of the Institution of Mechanical Engineers. Part H, Journal of Engineering in Medicine
Philipp Meyer, Eli Barkai, Holger Kantz
In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time- and ensemble-averaged mean-squared displacement are remarkably different. The ensemble-averaged diffusivity is obtained from a scaling Green-Kubo relation, which connects the scale-invariant nonstationary velocity correlation function with the transport coefficient. Here we obtain the relation between time-averaged diffusivity, usually recorded in single-particle tracking experiments, and the underlying scale-invariant velocity correlation function...
December 2017: Physical Review. E
Roland Lauter, Aditi Mitra, Florian Marquardt
Phase oscillator lattices subject to noise are one of the most fundamental systems in nonequilibrium physics. We have discovered a dynamical transition which has a significant impact on the synchronization dynamics in such lattices, as it leads to an explosive increase of the phase diffusion rate by orders of magnitude. Our analysis is based on the widely applicable Kuramoto-Sakaguchi model, with local couplings between oscillators. For one-dimensional lattices, we observe the universal evolution of the phase spread that is suggested by a connection to the theory of surface growth, as described by the Kardar-Parisi-Zhang (KPZ) model...
July 2017: Physical Review. E
Mahmood Mohammadi-Shad, Taehun Lee
The main objective of this paper is to extend an isothermal incompressible two-phase lattice Boltzmann equation method to model liquid-vapor phase change problems using a sharp-interface energy solver. Two discrete particle distribution functions, one for the continuity equation and the other for the pressure evolution and momentum equations, are considered in the current model. The sharp-interface macroscopic internal energy equation is discretized with an isotropic finite difference method to find temperature distribution in the system...
July 2017: Physical Review. E
Nahal Sharafi, Marc Timme, Sarah Hallerberg
Critical transitions occur in a variety of dynamical systems. Here we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for critical transitions, we consider changes in growth rates and directions of covariant Lyapunov vectors. Studying critical transitions in several models of fast-slow systems, i.e., a network of coupled FitzHugh-Nagumo oscillators, models for Josephson junctions, and the Hindmarsh-Rose model, we find that tangencies between covariant Lyapunov vectors are a common and maybe generic feature during critical transitions...
September 2017: Physical Review. E
Patrick Charbonneau, Yue Cathy Li, Henry D Pfister, Sho Yaida
Lyapunov exponents characterize the chaotic nature of dynamical systems by quantifying the growth rate of uncertainty associated with the imperfect measurement of initial conditions. Finite-time estimates of the exponent, however, experience fluctuations due to both the initial condition and the stochastic nature of the dynamical path. The scale of these fluctuations is governed by the Lyapunov susceptibility, the finiteness of which typically provides a sufficient condition for the law of large numbers to apply...
September 2017: Physical Review. E
Jonathan J Smart, André E Punt, William T White, Colin A Simpfendorfer
Leslie matrix models are an important analysis tool in conservation biology that are applied to a diversity of taxa. The standard approach estimates the finite rate of population growth (λ) from a set of vital rates. In some instances, an estimate of λ is available, but the vital rates are poorly understood and can be solved for using an inverse matrix approach. However, these approaches are rarely attempted due to pre-requisites of information on the structure of age or stage-classes. This study addressed this issue by using a combination of Monte Carlo simulations and the sample-importance-resampling (SIR) algorithm to solve the inverse matrix problem without data on population structure...
January 18, 2018: Ecological Applications: a Publication of the Ecological Society of America
Tao Zhang, Lei Li, Shi-Hong Lu, Hai Gong, Yun-Xin Wu
Asymmetrical shear rolling with velocity asymmetry and geometry asymmetry is beneficial to enlarge deformation and refine grain size at the center of the thick plate compared to conventional symmetrical rolling. Dynamic recrystallization (DRX) plays a vital role in grain refinement during hot deformation. Finite element models (FEM) coupled with microstructure evolution models and cellular automata models (CA) are established to study the microstructure evolution of plate during asymmetrical shear rolling. The results show that a larger DRX fraction and a smaller average grain size can be obtained at the lower layer of the plate...
January 17, 2018: Materials
Yong-Chang Zheng, Jun-Hong Wu, Zhi-Zhu He, Shao-Jiong Huang
BACKGROUND: Thermally significant blood flows into locally cooled diseased tissues and warm them during cryosurgery so that the iceball is often hard to cover the whole diseased volume. This paper is aimed at investigating the effects of large arterial bifurcation on the temperature distribution during cryosurgery through simulation method. METHODS: A parametric geometry model is introduced to construct a close-to-real arterial bifurcation. The three-dimensional transient conjugate heat transfer between bifurcated artery and solid tissues with phase change during cryosurgery is performed by finite volume method...
January 16, 2018: Biomedical Engineering Online
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