Magnetic structure of Li2CuO2: From ab initio calculations to macroscopic simulations

The magnetic structure of the edge-sharing cuprate compound Li2CuO2 has been investigated with highly correlated ab initio electronic structure calculations. The first- and second-neighbor in-chain magnetic interactions are calculated to be 142 and -22 K, respectively. The ratio between the two parameters is smaller than suggested previously in the literature. The interchain interactions are antiferromagnetic in nature and of the order of a few K only. Monte Carlo simulations using the ab initio parameters to define the spin model Hamiltonian result in a Nel temperature in good agreement with experiment. Spin population analysis situates the magnetic moment on the copper and oxygen ions between the completely localized picture derived from experiment and the more delocalized picture based on local-density calculations.

A model of cellular dosimetry for macroscopic tumors in radiopharmaceutical therapy.

PURPOSE: In the radiopharmaceutical therapy approach to the fight against cancer, in particular when it comes to translating laboratory results to the clinical setting, modeling has served as an invaluable tool for guidance and for understanding the processes operating at the cellular level and how these relate to macroscopic observables. Tumor control probability (TCP) is the dosimetric end point quantity of choice which relates to experimental and clinical data: it requires knowledge of individual cellular absorbed doses since it depends on the assessment of the treatment's ability to kill each and every cell. Macroscopic tumors, seen in both clinical and experimental studies, contain too many cells to be modeled individually in Monte Carlo simulation; yet, in particular for low ratios of decays to cells, a cell-based model that does not smooth away statistical considerations associated with low activity is a necessity. The authors present here an adaptation of the simple sphere-based model from which cellular level dosimetry for macroscopic tumors and their end point quantities, such as TCP, may be extrapolated more reliably. METHODS: Ten homogenous spheres representing tumors of different sizes were constructed in GEANT4. The radionuclide 131I was randomly allowed to decay for each model size and for seven different ratios of number of decays to number of cells, N(r): 1000, 500, 200, 100, 50, 20, and 10 decays per cell. The deposited energy was collected in radial bins and divided by the bin mass to obtain the average bin absorbed dose. To simulate a cellular model, the number of cells present in each bin was calculated and an absorbed dose attributed to each cell equal to the bin average absorbed dose with a randomly determined adjustment based on a Gaussian probability distribution with a width equal to the statistical uncertainty consistent with the ratio of decays to cells, i.e., equal to Nr-1/2. From dose volume histograms the surviving fraction of cells, equivalent uniform dose (EUD), and TCP for the different scenarios were calculated. Comparably sized spherical models containing individual spherical cells (15 microm diameter) in hexagonal lattices were constructed, and Monte Carlo simulations were executed for all the same previous scenarios. The dosimetric quantities were calculated and compared to the adjusted simple sphere model results. The model was then applied to the Bortezomib-induced enzyme-targeted radiotherapy (BETR) strategy of targeting Epstein-Barr virus (EBV)-expressing cancers. RESULTS: The TCP values were comparable to within 2% between the adjusted simple sphere and full cellular models. Additionally, models were generated for a nonuniform distribution of activity, and results were compared between the adjusted spherical and cellular models with similar comparability. The TCP values from the experimental macroscopic tumor results were consistent with the experimental observations for BETR-treated 1 g EBV-expressing lymphoma tumors in mice. CONCLUSIONS: The adjusted spherical model presented here provides more accurate TCP values than simple spheres, on par with full cellular Monte Carlo simulations while maintaining the simplicity of the simple sphere model. This model provides a basis for complementing and understanding laboratory and clinical results pertaining to radiopharmaceutical therapy.

Asbestos Fibers in Type B Asphaltic Concrete Surface Course, MLR-67-1, 1968

The Standard Specifications for this project included requirements for placing two 500 foot test sections of Type B asphaltic concrete with 1-1/2 per cent asbestos fibres (mix size 3/8 inch, lift thickness 3/4 inch) as part of the regular construction of the surface course. These requirements were designed to provide asbestos modified mixtures for laboratory analysis and road performance evaluation. This report provides the preliminary results and analysis of test data obtained from tests on the mixtures placed on the roadway. Previous research by G. S. Zuelke (1) and J. H. Kestzman et al (2) indicated that asphaltic concrete mixtures modified with asbestos fibres improved stability, decreased permeability, and allowed the use of higher bitumen contents. This study indicated that the addition of asbestos fibres would permit the use of higher bitumen contents, theoretically improving durability, without adverse results. An indication was also obtained to the effect that asbestos mixtures were more difficult to compact in the field.

Evaluation of "FIBERMESH" Synthetic Fibers in P.C. Concrete Bridge Barrier Rail, MLR-88-17, 1988

Ten bridges were chosen to have their concrete barrier rails constructed with one rail having "Fibermesh" synthetic fibers added and the other rail without the fibers. The rails were constructed in 1985, 1986, or 1987. All the bridges were inspected in 1988 and no consistent reduction in cracking was achieved using Fibermesh fibers in the p.c. concrete bridge barrier rails.

Brittle to ductile transition in a fiber bundle with strong heterogeneity

We analyze the failure process of a two-component system with widely different fracture strength in the framework of a fiber bundle model with localized load sharing. A fraction 0≤α≤1 of the bundle is strong and it is represented by unbreakable fibers, while fibers of the weak component have randomly distributed failure strength. Computer simulations revealed that there exists a critical composition αc which separates two qualitatively different behaviors: Below the critical point, the failure of the bundle is brittle, characterized by an abrupt damage growth within the breakable part of the system. Above αc, however, the macroscopic response becomes ductile, providing stability during the entire breaking process. The transition occurs at an astonishingly low fraction of strong fibers which can have importance for applications. We show that in the ductile phase, the size distribution of breaking bursts has a power law functional form with an exponent μ=2 followed by an exponential cutoff. In the brittle phase, the power law also prevails but with a higher exponent μ=92. The transition between the two phases shows analogies to continuous phase transitions. Analyzing the microstructure of the damage, it was found that at the beginning of the fracture process cracks nucleate randomly, while later on growth and coalescence of cracks dominate, which give rise to power law distributed crack sizes.

Sedimentation of macroscopic rigid knots and its relation to gel electrophoretic mobility of DNA knots.

We address the general question of the extent to which the hydrodynamic behaviour of microscopic freely fluctuating objects can be reproduced by macrosopic rigid objects. In particular, we compare the sedimentation speeds of knotted DNA molecules undergoing gel electrophoresis to the sedimentation speeds of rigid stereolithographic models of ideal knots in both water and silicon oil. We find that the sedimentation speeds grow roughly linearly with the average crossing number of the ideal knot configurations, and that the correlation is stronger within classes of knots. This is consistent with previous observations with DNA knots in gel electrophoresis.

Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method. II. Deformed nuclei

The binding energies of deformed even-even nuclei have been analyzed within the framework of a recently proposed microscopic-macroscopic model. We have used the semiclassical Wigner-Kirkwood ̄h expansion up to fourth order, instead of the usual Strutinsky averaging scheme, to compute the shell corrections in a deformed Woods-Saxon potential including the spin-orbit contribution. For a large set of 561 even-even nuclei with Z 8 and N 8, we find an rms deviation from the experiment of 610 keV in binding energies, comparable to the one found for the same set of nuclei using the finite range droplet model of Moller and Nix (656 keV). As applications of our model, we explore its predictive power near the proton and neutron drip lines as well as in the superheavy mass region. Next, we systematically explore the fourth-order Wigner-Kirkwood corrections to the smooth part of the energy. It is found that the ratio of the fourth-order to the second-order corrections behaves in a very regular manner as a function of the asymmetry parameter I=(N−Z)/A. This allows us to absorb the fourth-order corrections into the second-order contributions to the binding energy, which enables us us to simplify and speed up the calculation of deformed nuclei.

Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method

The semiclassical Wigner-Kirkwood ̄h expansion method is used to calculate shell corrections for spherical and deformed nuclei. The expansion is carried out up to fourth order in ̄h. A systematic study of Wigner-Kirkwood averaged energies is presented as a function of the deformation degrees of freedom. The shell corrections, along with the pairing energies obtained by using the Lipkin-Nogami scheme, are used in the microscopic-macroscopic approach to calculate binding energies. The macroscopic part is obtained from a liquid drop formula with six adjustable parameters. Considering a set of 367 spherical nuclei, the liquid drop parameters are adjusted to reproduce the experimental binding energies, which yields a root mean square (rms) deviation of 630 keV. It is shown that the proposed approach is indeed promising for the prediction of nuclear masses.

Accelerated Microstructure Imaging via Convex Optimization (AMICO) in crossing fibers

Mapping the microstructure properties of the local tissues in the brain is crucial to understand any pathological condition from a biological perspective. Most of the existing techniques to estimate the microstructure of the white matter assume a single axon orientation whereas numerous regions of the brain actually present a fiber-crossing configuration. The purpose of the present study is to extend a recent convex optimization framework to recover microstructure parameters in regions with multiple fibers.

Modeling the transport phenomena within arterial wall: porous media approach

The transport of macromolecules, such as low-density lipoprotein (LDL), and their accumulation in the layers of the arterial wall play a critical role in the creation and development of atherosclerosis. Atherosclerosis is a disease of large arteries e.g., the aorta, coronary, carotid, and other proximal arteries that involves a distinctive accumulation of LDL and other lipid-bearing materials in the arterial wall. Over time, plaque hardens and narrows the arteries. The flow of oxygen-rich blood to organs and other parts of the body is reduced. This can lead to serious problems, including heart attack, stroke, or even death. It has been proven that the accumulation of macromolecules in the arterial wall depends not only on the ease with which materials enter the wall, but also on the hindrance to the passage of materials out of the wall posed by underlying layers. Therefore, attention was drawn to the fact that the wall structure of large arteries is different than other vessels which are disease-resistant. Atherosclerosis tends to be localized in regions of curvature and branching in arteries where fluid shear stress (shear rate) and other fluid mechanical characteristics deviate from their normal spatial and temporal distribution patterns in straight vessels. On the other hand, the smooth muscle cells (SMCs) residing in the media layer of the arterial wall respond to mechanical stimuli, such as shear stress. Shear stress may affect SMC proliferation and migration from the media layer to intima. This occurs in atherosclerosis and intimal hyperplasia. The study of blood flow and other body fluids and of heat transport through the arterial wall is one of the advanced applications of porous media in recent years. The arterial wall may be modeled in both macroscopic (as a continuous porous medium) and microscopic scales (as a heterogeneous porous medium). In the present study, the governing equations of mass, heat and momentum transport have been solved for different species and interstitial fluid within the arterial wall by means of computational fluid dynamics (CFD). Simulation models are based on the finite element (FE) and finite volume (FV) methods. The wall structure has been modeled by assuming the wall layers as porous media with different properties. In order to study the heat transport through human tissues, the simulations have been carried out for a non-homogeneous model of porous media. The tissue is composed of blood vessels, cells, and an interstitium. The interstitium consists of interstitial fluid and extracellular fibers. Numerical simulations are performed in a two-dimensional (2D) model to realize the effect of the shape and configuration of the discrete phase on the convective and conductive features of heat transfer, e.g. the interstitium of biological tissues. On the other hand, the governing equations of momentum and mass transport have been solved in the heterogeneous porous media model of the media layer, which has a major role in the transport and accumulation of solutes across the arterial wall. The transport of Adenosine 5´-triphosphate (ATP) is simulated across the media layer as a benchmark to observe how SMCs affect on the species mass transport. In addition, the transport of interstitial fluid has been simulated while the deformation of the media layer (due to high blood pressure) and its constituents such as SMCs are also involved in the model. In this context, the effect of pressure variation on shear stress is investigated over SMCs induced by the interstitial flow both in 2D and three-dimensional (3D) geometries for the media layer. The influence of hypertension (high pressure) on the transport of lowdensity lipoprotein (LDL) through deformable arterial wall layers is also studied. This is due to the pressure-driven convective flow across the arterial wall. The intima and media layers are assumed as homogeneous porous media. The results of the present study reveal that ATP concentration over the surface of SMCs and within the bulk of the media layer is significantly dependent on the distribution of cells. Moreover, the shear stress magnitude and distribution over the SMC surface are affected by transmural pressure and the deformation of the media layer of the aorta wall. This work reflects the fact that the second or even subsequent layers of SMCs may bear shear stresses of the same order of magnitude as the first layer does if cells are arranged in an arbitrary manner. This study has brought new insights into the simulation of the arterial wall, as the previous simplifications have been ignored. The configurations of SMCs used here with elliptic cross sections of SMCs closely resemble the physiological conditions of cells. Moreover, the deformation of SMCs with high transmural pressure which follows the media layer compaction has been studied for the first time. On the other hand, results demonstrate that LDL concentration through the intima and media layers changes significantly as wall layers compress with transmural pressure. It was also noticed that the fraction of leaky junctions across the endothelial cells and the area fraction of fenestral pores over the internal elastic lamina affect the LDL distribution dramatically through the thoracic aorta wall. The simulation techniques introduced in this work can also trigger new ideas for simulating porous media involved in any biomedical, biomechanical, chemical, and environmental engineering applications.