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The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.
Constraining the behavior of cosmic ray data observed at Earth requires a precise understanding of how the cosmic rays propagate in the interstellar medium. The interstellar medium is not homogeneous; although turbulent magnetic fields dominate over large scales, small coherent regions of magnetic field exist on scales relevant to particle propagation in the nearby Galaxy. Guided propagation through a coherent field is significantly different from random particle diffusion and could be the explanation of spatial anisotropies in the observed cosmic rays. We present a Monte Carlo code to propagate cosmic particle through realistic magnetic field structures. We discuss the details of the model as well as some preliminary studies which indicate that coherent magnetic structures are important effects in local cosmic-ray propagation, increasing the flux of cosmic rays by over two orders of magnitude at anisotropic locations on the sky. Furthermore, the features induced by coherent magnetic structure could be the cause of the observed TeV cosmic-ray anisotropy.
Laminar boundary layer diffusion in liquids with a variable diffusivity
Objective: To evaluate the feasibility of using PET/CT and diffusion-weighted magnetic resonance imaging (DW-MRI) to monitor the early response of pancreatic ductal adenocarcinoma (PDAC) xenografts to brachytherapy, and to determine whether maximum standardized uptake value (SUVmax) correlate with apparent diffusion coefficient (ADC). Materials and Methods: SW1990 human PDAC were subcutaneously implanted in 20 nude mice. They were randomly divided into 125-Iodine ({sup 125}I) seeds and blank seeds group. PET/CT and DW-MRI were performed at pretreatment and 5 days after therapy. SUVmax and ADC values were calculated, respectively. The correlation between SUVmax and ADC values was analyzed by the Pearson correlation test. Results: The SUVmax were significantly decreased between pretreatment and 5 days after {sup 125}I seeds treatment (p < 0.001) and between two groups (p < 0.001). And the ADC values were significantly increased between pretreatment and 5 days after {sup 125}I seeds treatment (p < 0.001) and between two groups (p < 0.001). While in the bank seeds group, there were no significantly difference between pretreatment and after treatment in SUVmax and ADC values (p = 0.057; p = 0.397). SUVmax and ADC correlated significantly and negatively before treatment in both groups (r = − 0.964, R{sup 2} = 0.929, p < 0.001; r = − 0.917, R{sup 2} = 0.841, p < 0.001) and after treatment in the blank seeds group (r = − 0.944, R{sup 2} = 0.891, p < 0.001). But after {sup 125}I seeds treatment there was no significant correlation between SUVmax and ADC (r = − 0.388, R{sup 2} = 0.151, p = 0.268). Conclusion: The PET/CT and DW-MRI are capable of monitoring the early response of PDAC xenografts to brachytherapy. The significantly inverse correlation between pretreatment SUVmax and ADC suggests that PET/CT and DW-MRI might play complementary roles for therapy assessment.
Purpose: To assess the accuracy, criteria, and clinical significance of diffusion-weighted imaging (DWI) signal intensity and apparent diffusion coefficient (ADC) quantification for diagnosing acute appendicitis. Methods: Fifty-one patients with right lower abdominal pain [uncomplicated appendicitis (n = 25), complicated appendicitis (n = 10), and non-appendicitis (n = 16)] who underwent MR examination were enrolled in this retrospective study. Two radiologists independently measured appendiceal diameter and wall thickness. They assessed whether a wall defect, an abscess, extraluminal air, or an appendicolith was present on axial T2WI; evaluated intensity on DWI using a 5-point scale; and determined the ADC values of the appendix and peri-appendiceal tissue. Statistical analysis was performed to assess imaging findings for the diagnosis of appendicitis and complicated appendicitis. Cut-off values were determined using receiver operating characteristic analysis. Results: For diagnosing acute appendicitis, the accuracy improved from 78.4% using only T2WI to 86.3% using combined T2WI and DWI for reader 1 and from 82.4 to 86.3% for reader 2. For the appendix, the cut-off ADC values that diagnosed appendicitis were 1.41 × 10{sup −3} and 1.26 × 10{sup −3} mm{sup 2}/s with accuracies of 78.4% and 76.5%, respectively. For the peri-appendiceal tissue, these values of 1.03 × 10{sup −3} and 0.91 × 10{sup −3} mm{sup 2}/s differentiated between uncomplicated and complicated appendicitis with an accuracy of 97.1%. Conclusions: Combined DWI and T2WI provided high accuracy for diagnosing appendicitis. The inflamed appendix had lower ADC value than the normal appendix. The peri-appendiceal tissue presenting low ADC value was a notable finding of complicated appendicitis.
In this paper we develop a set of stochastic numerical schemes for hyperbolic and transport equations with diffusive scalings and subject to random inputs. The schemes are asymptotic preserving (AP), in the sense that they preserve the diffusive limits of the equations in discrete setting, without requiring excessive refinement of the discretization. Our stochastic AP schemes are extensions of the well-developed deterministic AP schemes. To handle the random inputs, we employ generalized polynomial chaos (gPC) expansion and combine it with stochastic Galerkin procedure. We apply the gPC Galerkin scheme to a set of representative hyperbolic and transport equations and establish the AP property in the stochastic setting. We then provide several numerical examples to illustrate the accuracy and effectiveness of the stochastic AP schemes.
A study of signals originating near the lithium-diffused n+ contact of p-type point contact (PPC) high purity germanium detectors (HPGe) is presented. The transition region between the active germanium and the fully dead layer of the n+ contact is examined. Energy depositions in this transition region are shown to result in partial charge collection. This provides a mechanism for events with a well defined energy to contribute to the continuum of the energy spectrum at lower energies. A novel technique to quantify the contribution from this source of background is introduced. Experiments that operate germanium detectors with a very low energy threshold may benefit from the methods presented herein.
Olivine lithium iron phosphate is a technologically important electrode material for lithium-ion batteries and a model system for studying electrochemically driven phase transformations. Despite extensive studies, many aspects of the phase transformation and lithium transport in this material are still not well understood. Here we combine operando hard X-ray spectroscopic imaging and phase-field modeling to elucidate the delithiation dynamics of single-crystal lithium iron phosphate microrods with long-axis along the [010] direction. Lithium diffusivity is found to be two-dimensional in microsized particles containing ~3%lithium-iron anti-site defects. Our study provides direct evidence for the previously predicted surface reaction-limited phase-boundary migration mechanism and the potential operation of a hybrid mode of phase growth, in which phase-boundary movement is controlled by surface reaction or lithium diffusion in different crystallographic directions. These findings uncover the rich phase-transformation behaviors in lithium iron phosphate and intercalation com-pounds in general and can help guide the design of better electrodes.
The formation of stable radiation damage in crystalline solids often proceeds via complex dynamic annealing processes, involving migration and interaction of ballistically-generated point defects. The dominant dynamic annealing processes, however, remain unknown even for crystalline Si. Here, we use a pulsed ion beam method to study defect dynamics in Si bombarded in the temperature range from -20 to 140 °C with 500 keV Ar ions. Results reveal a defect relaxation time constant of ~10–0.2 ms, which decreases monotonically with increasing temperature. The dynamic annealing rate shows an Arrhenius dependence with two well-defined activation energies of 73 ± 5 meV and 420 ± 10 meV, below and above 60 °C, respectively. Rate theory modeling, bench-marked against this data, suggests a crucial role of both vacancy and interstitial diffusion, with the dynamic annealing rate limited by the migration and interaction of vacancies.
Enhanced oxide ion diffusion by 3 to 5 orders of magnitude along grain boundary core in Sr-doped LaMnO 3 .
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MD simulation results for model size-symmetric and asymmetric electrolytes at high densities and temperatures (well outside the liquid-gas coexistence region) are generated and analyzed focusing on thermodynamic and diffusion properties. An extension of the mean spherical approximation for electrolytes originally derived for charged hard sphere fluids is adapted to these systems by exploiting the separation of short range and Coulomb interaction contributions intrinsic to these theoretical models and is found to perform well for predicting equation of state quantities. The diffusion coefficients of these electrolytes can also be reasonably well predicted using entropy scaling ideas suitably adapted to charged systems and mixtures. Thus, this approach may provide an avenue for studying dense electrolytes or complex molecular systems containing charged species at high pressures and temperatures.
The evolution of diffusive and non-diffusive transport during pedestal buildup following a low-high (L-H) transition has been interpreted from a particle-momentum-energy balance analysis of the measured density, temperature, and rotation velocity profiles in the plasma edge (0.82<{rho}<1.0) of a DIII-D [Luxon, Nucl. Fusion 42, 614 (2002)] discharge. In the discharge examined, there was an edge-localized-mode-free period of more than 600 ms following the L-H transition, and the majority of edge pedestal development occurred within the first 100 ms following the L-H transition. There appears to be a spatio-temporal correlation among the measured toroidal and poloidal rotation, the formation of a negative well in the measured radial electric field, the creation of a large inward particle pinch, the calculated intrinsic rotation due to ion orbit loss, and the measured formation of steep gradients in density and temperature in the outer region ({rho}>0.95) of the edge pedestal.
Zinc oxide (ZnO) is a wide band gap semiconductor and a potential candidate for next generation white solid state lighting applications. In this work, hydrogen-related complexes in lithium diffused ZnO single crystals were studied. In addition to the well-known Li-OH complex, several other hydrogen defects were observed. When a mixture of Li{sub 2}O and ZnO is used as the dopant source, zinc vacancies are suppressed and the bulk Li concentration is very high (>10{sup 19 }cm{sup −3}). In that case, the predominant hydrogen complex has a vibrational frequency of 3677 cm{sup −1}, attributed to surface O-H species. When Li{sub 2}CO{sub 3} is used, a structured blue luminescence band and O-H mode at 3327 cm{sup −1} are observed at 10 K. These observations, along with positron annihilation measurements, suggest a zinc vacancy–hydrogen complex, with an acceptor level ∼0.3 eV above the valence-band maximum. This relatively shallow acceptor could be beneficial for p-type ZnO.
Here, inherent advantages of wide bandgap materials make GaN-based devices attractive for power electronics and applications in radiation environments. Recent advances in the availability of wafer-scale, bulk GaN substrates have enabled the production of high quality, low defect density GaN devices, but fundamental studies of carrier transport and radiation hardness in such devices are lacking. Here, we report measurements of the hole diffusion length in low threading dislocation density (TDD), homoepitaxial n-GaN, and high TDD heteroepitaxial n-GaN Schottky diodes before and after irradiation with 2.5 MeV protons at fluences of 4–6 × 10 13 protons/cm 2 . We also characterize the specimens before and after irradiation using electron beam-induced-current (EBIC) imaging, cathodoluminescence, deep level optical spectroscopy (DLOS), steady-state photocapacitance, and lighted capacitance-voltage (LCV) techniques. We observe a substantial reduction in the hole diffusion length following irradiation (50%–55%) and the introduction of electrically active defects which could be attributed to gallium vacancies and associated complexes (V Ga -related), carbon impurities (C-related), and gallium interstitials (Ga i ). EBIC imaging suggests long-range migration and clustering of radiation-induced point defects over distances of ~500 nm, which suggests mobile Ga i . Following irradiation, DLOS and LCV reveal the introduction of a prominent optical energy level at 1.9 eV below the conduction band edge, consistent with the introduction of Ga i .
By combining density-functional theory (DFT) and wave function theory via the range separation (RS) of the interelectronic Coulomb operator, we obtain accurate fixed-node diffusion Monte Carlo (FN-DMC) energies with compact multi-determinant trial wave functions. In particular, we combine here short-range exchange-correlation functionals with a flavor of selected configuration interaction known as configuration interaction using a perturbative selection made iteratively (CIPSI), a scheme that we label RS-DFT-CIPSI. One of the take-home messages of the present study is that RS-DFT-CIPSI trial wave functions yield lower fixed-node energies with more compact multi-determinant expansions than CIPSI, especially for small basis sets. Indeed, as the CIPSI component of RS-DFT-CIPSI is relieved from describing the short-range part of the correlation hole around the electron-electron coalescence points, the number of determinants in the trial wave function required to reach a given accuracy is significantly reduced as compared to a conventional CIPSI calculation. Importantly, by performing various numerical experiments, we evidence that the RS-DFT scheme essentially plays the role of a simple Jastrow factor by mimicking short-range correlation effects, hence avoiding the burden of performing a stochastic optimization. Considering the 55 atomization energies of the Gaussian-1 benchmark set of molecules, we show that using a fixed value of mu = 0.5 bohr(-1) provides effective error cancellations as well as compact trial wave functions, making the present method a good candidate for the accurate description of large chemical systems.