Stochastic reconstruction of snow microstructure from x-ray microtomography images

Thesis (M.S.) University of Alaska Fairbanks, 2007The three-dimensional (3D) high-resolution digitized snow microstructure (pixel size 6 micron) was obtained by X-ray microtomography. The experimental result was verified by measuring the density of the snow sample. Statistical characteristics (porosity, local porosity, two-point correlation function) were extracted from cross-sectional images. The one-level-cut Gaussian random field model was used to stochastically reconstruct snow microstructure from X-ray microtomography images. Efficient computer programs were developed in MATLAB for the whole stochastic reconstruction procedure, including the numerical inversion of the correlation function and the generation of 3D large-scale Gaussian random fields by 3D inverse fast Fourier transform. The quality of the reconstruction was assessed by comparing the two-point correlation function and cross-sectional images.1. Introduction -- 2. Snow images by X-ray microtomography -- 2.1. Introduction of computed tomography -- 2.2. Acquisition and reconstruction -- 2.3. Binary images and 3D visualization -- 2.4. Statistical characteristics of the snow sample -- 3. Stochastic reconstruction of porous materials -- 3.1. Weak sense stationary gaussian random fields -- 3.2. The power spectral density function -- 3.3. The one-level-cut gaussian random field model -- 3.4. Generation of gaussian random fields -- 3.5. Stochastic reconstruction procedure -- 4. Reconstruction results -- 5. Conclusions -- References -- Appendices

A full contraction-reaction-diffusion model for pattern formation in geometrically confined microtissues

The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Recently, mechanical cues, such as the cellular stresses and strains, have been found to dictate the pattern formation in human stem cell differentiation. As a result, the traditional reaction-diffusion models are modified by adding mechanically related terms to consider the role played by the mechanical cues. However, these models either do not consider the activeness of the cellular tissues or neglect their poroelastic nature that biological tissues are made by both cells and interstitial fluid. Hence, the current models suffer from the lacks of biophysical relevance. Here we propose a modified reaction-diffusion model that couples with the active contraction of cellular tissues. The cellular tissue is modelled as a piece of biphasic poroelastic material, where mechanical forces naturally regulate the transport of chemical cues. Such chemical cues direct cell fate and hence yield certain types of pattern formations observed in previous experiments

The effect of viscous force on the prediction of muscle contractility in biohybrid cantilever-based experiments

The biohybrid cantilevers have been recently reported for high-throughput measurement of muscle contractility. In previous works, mechanical models were used to predict the contractile stress from the cantilever bending curvature. To derive those models, the cantilever bending process was considered as quasi-static and the viscous force was neglected. To ascertain the effect of the viscous force on the prediction of the muscle contractility in biohybrid cantilever-based experiments, we extend the modified Stoney’s equation to a dynamic model that takes into account both the viscous force and the inertia force. Parametric studies show that, because the viscous force hinders the movement of the cantilever, use of static models result in a system error between the calculated and true contractile stresses. When using static models, the diastolic stress will be over-estimated while the peak systolic stress will be under-estimated. The present work suggests that dynamic models can be used in biohybrid cantilever assays to calculate the muscle contractility with higher accuracy, or can be used to optimize the experimental parameters such that the error due to the use of static models is minimized

The Effect of Thermal Fluctuation on the Receptor-Mediated Adhesion of a Cell Membrane to an Elastic Substrate

Mechanics of the bilayer membrane play an important role in many biological and bioengineering problems such as cell–substrate and cell–nanomaterial interactions. In this work, we study the effect of thermal fluctuation and the substrate elasticity on the cell membrane–substrate adhesion. We model the adhesion of a fluctuating membrane on an elastic substrate as a two-step reaction comprised of the out-of-plane membrane fluctuation and the receptor–ligand binding. The equilibrium closed bond ratio as a function of substrate rigidity was computed by developing a coupled Fourier space Brownian dynamics and Monte Carlo method. The simulation results show that there exists a crossover value of the substrate rigidity at which the closed bond ratio is maximal

Long Term Spectral Evolution of Tidal Disruption Candidates Selected by Strong Coronal Lines

We present results of follow-up optical spectroscopic observations of seven rare, extreme coronal line emitting galaxies reported by Wang et al. (2012) with Multi-Mirror Telescope (MMT). Large variations in coronal lines are found in four objects, making them strong candidates of tidal disruption events (TDE). For the four TDE candidates, all the coronal lines with ionization status higher than [Fe VII] disappear within 5-9 years. The [Fe VII] faded by a factor of about five in one object (J0952+2143) within 4 years, whereas emerged in other two without them previously. A strong increment in the [O III] flux is observed, shifting the line ratios towards the loci of active galactic nucleus on the BPT diagrams. Surprisingly, we detect a non-canonical [O III]5007/[O III]4959 2 in two objects, indicating a large column density of O$^{2+}$ and thus probably optical thick gas. This also requires a very large ionization parameter and relatively soft ionizing spectral energy distribution (e.g. blackbody with $T < 5\times 10^4$ K). Our observations can be explained as echoing of a strong ultraviolet to soft X-ray flare caused by tidal disruption events, on molecular clouds in the inner parsecs of the galactic nuclei. Re-analyzing the SDSS spectra reveals double-peaked or strongly blue-shouldered broad lines in three of the objects, which disappeared in the MMT spectra in two objects, and faded by a factor of ten in 8 years in the remaining object with a decrease in both the line width and centroid offset. We interpret these broad lines as arising from decelerating biconical outflows. Our results demonstrate that the signatures of echoing can persist for as long as ten years, and can be used to probe the gas environment in the quiescent galactic nuclei.Comment: 30 Pages, 10 Figures, 2 Tables, Accepted for Publication in Ap

A minimal mechanics model for mechanosensing of substrate rigidity gradient in durotaxis

Durotaxis refers to the phenomenon in which cells can sense the spatial gradient of the substrate rigidity in the process of cell migration. A conceptual two-part theory consisting of the focal adhesion force generation and mechanotransduction has been proposed previously by Lo et al. to explain the mechanism underlying durotaxis. In the present work, we are concerned with the first part of the theory: how exactly is the larger focal adhesion force generated in the part of the cell adhering to the stiffer region of the substrate? Using a simple elasticity model and by assuming the cell adheres to the substrate continuously underneath the whole cell body, we show that the mechanics principle of static equilibrium alone is sufficient to account for the generation of the larger traction stress on the stiffer region of the substrate. We believe that our model presents a simple mechanistic understanding of mechanosensing of substrate stiffness gradient at the cellular scale, which can be incorporated in more sophisticated mechanobiochemical models to address complex problems in mechanobiology and bioengineering

A structure-preserving integrator for incompressible finite elastodynamics based on a grad-div stabilized mixed formulation with particular emphasis on stretch-based material models

We present a structure-preserving scheme based on a recently-proposed mixed formulation for incompressible hyperelasticity formulated in principal stretches. Although there exist Hamiltonians introduced for quasi-incompressible elastodynamics based on different variational formulations, the one in the fully incompressible regime has yet been identified in the literature. The adopted mixed formulation naturally provides a new Hamiltonian for fully incompressible elastodynamics. Invoking the discrete gradient formula, we are able to design fully-discrete schemes that preserve the Hamiltonian and momenta. The scaled mid-point formula, another popular option for constructing algorithmic stresses, is analyzed and demonstrated to be non-robust numerically. The generalized Taylor-Hood element based on the spline technology conveniently provides a higher-order, robust, and inf-sup stable spatial discretization option for finite strain analysis. To enhance the element performance in volume conservation, the grad-div stabilization, a technique initially developed in computational fluid dynamics, is introduced here for elastodynamics. It is shown that the stabilization term does not impose additional restrictions for the algorithmic stress to respect the invariants, leading to an energy-decaying and momentum-conserving fully discrete scheme. A set of numerical examples is provided to justify the claimed properties. The grad-div stabilization is found to enhance the discrete mass conservation effectively. Furthermore, in contrast to conventional algorithms based on Cardano's formula and perturbation techniques, the spectral decomposition algorithm developed by Scherzinger and Dohrmann is robust and accurate to ensure the discrete conservation laws and is thus recommended for stretch-based material modeling

Identification of a New γ\gamma-ray-emitting narrow-line Seyfert 1 Galaxy, at Redshift ∼1\sim1

We report on the identification of a new $\gamma$-ray-emitting narrow-line Seyfert 1 (NLS1) galaxy, SDSS J122222.55+041315.7, which increases the number of known objects of this remarkable but rare type of active galactic nuclei (AGN) to seven. Its optical spectrum, obtained in the Sloan Digital Sky Survey-Baryon Oscillation Spectroscopic Survey, reveals a broad H $\beta$ emission line with a width (FWHM) of 1734$\pm$104 km s$^{-1}$. This, along with strong optical Fe II multiplets [$R_{4570}=0.9$] and a weak [O III] $\lambda 5007$ emission line, makes the object a typical NLS1. On the other hand, the source exhibits a high radio brightness temperature, rapid infrared variability, and a flat X-ray spectrum extending up to $\sim$200 keV. It is associated with a luminous $\gamma$-ray source detected significantly with {\it Fermi}/LAT. Correlated variability with other wavebands has not yet been tested. The spectral energy distribution can be well modelled by a one-zone leptonic jet model. This new member is by far the most distant $\gamma$-ray-emitting NLS1, at a redshift of $z=0.966$.Comment: 5 pages, published on MNRA