On Singularity Formation of a Nonlinear Nonlocal System

We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional system of the 3D model that was recently proposed by Hou and Lei in [13] for axisymmetric 3D incompressible Navier-Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier-Stokes equations is that the convection term is neglected in the 3D model. In the nonlocal system we consider in this paper, we replace the Riesz operator in the 3D model by the Hilbert transform. One of the main results of this paper is that we prove rigorously the finite time singularity formation of the nonlocal system for a large class of smooth initial data with finite energy. We also prove the global regularity for a class of smooth initial data. Numerical results will be presented to demonstrate the asymptotically self-similar blow-up of the solution. The blowup rate of the self-similar singularity of the nonlocal system is similar to that of the 3D model.Comment: 28 pages, 9 figure

Ion energy distributions in RF sheaths with dust particles

We study ion energy distributions functions (IEDFs) within an rf sheath with dust particles in SiH₄ radio-frequency discharges and compare results with ones in Ar rf discharges. The simulations are carried by PIC/MCC method over a wide range of pressure, dust density and dust radius. Our model includes electron-neutral collisions, various kinds of collisions of ions with neutrals, positive-negative ion collisions. Results of calculations show that IEDFs for positive ions SiH⁺³ in silane rf-discharge essentially differ from IEDFS for positive ions in Ar discharges. Ions near electrodes get greater energy in electronegative discharge in consequence of inessential charge exchange processes in the rfsheath. Peaks of high energy ions are appeared in IEDFs, which are caused by significant decreasing of the radiofrequency sheath width and the ratio of ion penetrating time through sheath to the radio-frequency discharge period. Results of calculations show that big dust particles slow down ions in rf-sheaths, but the presence small dust particles can increase energy of ions. It is explained by the increasing of the potential drop near electrode.Досліджуються функції розподілу іонів за енергією в приелектродному шарі з пиловими частинками в ємнісному РЧ-розряді в силані та результати порівнюються з результатами, одержаними в аргоновому розряді. Моделювання виконувалось за допомогою PIC/MCC методу для широкого діапазону тиску, концентрації та радіусу пилових частинок. Наша модель включає зіткнення електронів з нейтралами, різні види зіткнень іонів з нейтралами, зіткнення позитивних та негативних іонів. Результати обчислень показали, що функції розподілу іонів за енергією для позитивних іонів SiH⁺³ в силановому РЧ-розряді відрізняються від функцій розподілу іонів в аргоновому розряді. Іони біля електроду одержують більшу енергію в електронегативному розряді внаслідок несуттєвої ролі процесів обміну зарядом в цих розрядах. В іонних функціях розподілу з’являються піки, які пов’язані зі значним зменшенням ширини РЧ- приелектродного шару і відношення часу прольоту іонів через приелектродний шар до періоду розрядуИсследуются функции распределения ионов по энергии в приэлектродном слое с пылевыми частицами в емкостном РЧ-разряде в силане и результаты сравниваются с результатами, полученными в аргоновом разряде. Моделирование выполнялось при помощи PIC/MCC метода в широком диапазоне давлений, концентраций и радиусов пылевых частиц. Наша модель включает столкновения электронов с нейтралами, различные виды столкновений ионов с нейтралами, столкновения позитивных и негативных ионов. Результаты вычислений показали, что функции распределения ионов по энергии для позитивных ионов SiH⁺³ в силановом РЧ-разряде отличаются от функций распределения ионов в аргоновом разряде. Ионы вблизи электрода имеют большую энергию в электроотрицательном газе вследствие несущественной роли процессов перезарядки в этих разрядах. В ионных функциях распределения появляются пики, которые связаны со значительным уменьшением ширины РЧ-приэлектродного слоя и отношения времени пересечения ионами приэлектродного слоя к периоду разряда

The significance of sample mass in the analysis of steroid estrogens in sewage sludges and the derivation of partition coefficients in wastewaters

Optimization of an analytical method for determination of steroid estrogens, through minimizing sample size, resulted in recoveries >84%, with relative standard deviations <3% and demonstrated the significance of sample size on method performance. Limits of detection were 2.1–5.3 ng/g. Primary sludges had estrogen concentrations of up to one order of magnitude less than those found in biological sludges (up to 994 ng/g). However, partition coefficients were higher in primary sludges (except estriol), with the most hydrophobic compound (ethinylestradiol) exhibiting the highest Kp value, information which may be of value to those involved in modeling removal during wastewater treatment

Fast Accurate and Automatic Brushstroke Extraction

Brushstrokes are viewed as the artist’s “handwriting” in a painting. In many applications such as style learning and transfer, mimicking painting, and painting authentication, it is highly desired to quantitatively and accurately identify brushstroke characteristics from old masters’ pieces using computer programs. However, due to the nature of hundreds or thousands of intermingling brushstrokes in the painting, it still remains challenging. This article proposes an efficient algorithm for brush Stroke extraction based on a Deep neural network, i.e., DStroke. Compared to the state-of-the-art research, the main merit of the proposed DStroke is to automatically and rapidly extract brushstrokes from a painting without manual annotation, while accurately approximating the real brushstrokes with high reliability. Herein, recovering the faithful soft transitions between brushstrokes is often ignored by the other methods. In fact, the details of brushstrokes in a master piece of painting (e.g., shapes, colors, texture, overlaps) are highly desired by artists since they hold promise to enhance and extend the artists’ powers, just like microscopes extend biologists’ powers. To demonstrate the high efficiency of the proposed DStroke, we perform it on a set of real scans of paintings and a set of synthetic paintings, respectively. Experiments show that the proposed DStroke is noticeably faster and more accurate at identifying and extracting brushstrokes, outperforming the other methods

Neutron beam test of CsI crystal for dark matter search

We have studied the response of Tl-doped and Na-doped CsI crystals to nuclear recoils and $\gamma$'s below 10 keV. The response of CsI crystals to nuclear recoil was studied with mono-energetic neutrons produced by the $^3$H(p,n)$^3$He reaction. This was compared to the response to Compton electrons scattered by 662 keV $\gamma$-ray. Pulse shape discrimination between the response to these $\gamma$'s and nuclear recoils was studied, and quality factors were estimated. The quenching factors for nuclear recoils were derived for both CsI(Na) and CsI(Tl) crystals.Comment: 21pages, 14figures, submitted to NIM

Additive effect of cerebral atrophy on cognition in dementia-free elderly with cerebrovascular disease

Objective: To explore the additive effect of neurodegenerative diseases, measured by atrophy, on neurocognitive function in Asian dementia-free elderly with cerebrovascular disease (CeVD). Methods: The present study employed a cross-sectional design and was conducted between 2010 and 2015 among community-dwelling elderly participants recruited into the study. Eligible participants were evaluated with an extensive neuropsychological battery and neuroimaging. The weighted CeVD burden scale comprising markers of both small- and large-vessel diseases was applied, with a score of ≥2, indicating significant CeVD burden. Cortical atrophy (CA) and medial temporal atrophy (MTA) were graded using the global cortical atrophy scale and Schelten's scale, respectively. Global and domain-specific (attention, executive function, language, visuomotor speed, visuoconstruction, visual memory, and verbal memory) neurocognitive performance was measured using a locally validated neuropsychological battery (Vascular Dementia Battery, VDB). Results: A total of 819 dementia-free participants were included in the analysis. Among none-mild CeVD subjects, there was no significant difference in the global cognitive performance across atrophy groups (no atrophy, CA, and CA+MTA). However, in moderate-severe CeVD subjects, CA+MTA showed significantly worse global cognitive performance compared with those with CA alone (mean difference=-0.35, 95% CI -0.60 to -0.11, p=0.002) and those without atrophy (mean difference=-0.46, 95% CI -0.74 to -0.19, p<0.001, p<0.001). In domain-specific cognitive performance, subjects with CA+MTA performed worse than other groups in visual memory (p=0.005), executive function (p=0.001) and visuomotor speed (p<0.001) in moderate-severe CeVD but not in none-mild CeVD. Conclusions and relevance: Atrophy and moderate-severe CeVD burden showed an additive effect on global and domain-specific cognitive performance. This study highlights the importance of investigating the mechanisms of clinico-pathological interactions between neurodegenerative processes and vascular damage, particularly in the pre-dementia stage

The Impact of Strategic White Matter Hyperintensity Lesion Location on Language

Objective: The impact of white matter hyperintensities (WMH) on language possibly depends on lesion location through disturbance of strategic white matter tracts. We examined the impact of WMH location on language in elderly Asians. Design: Cross-sectional. Setting: Population-based. Participants: Eight-hundred nineteen residents of Singapore, ages (≥65 years). Measurements: Clinical, cognitive and 3T magnetic resonance imaging assessments were performed on all participants. Language was assessed using the Modified Boston Naming Test (MBNT) and Verbal Fluency (VF). Hypothesis-free region-of-interest-based (ROI) analyses based on major white matter tracts were used to determine the association between WMH location and language. Conditional dependencies between the regional WMH volumes and language were examined using Bayesian-network analysis. Results: ROI-based analyses showed that WMH located within the anterior thalamic radiation (mean difference: −0.12, 95% confidence interval [CI]: −0.22; −0.02, p = 0.019) and uncinate fasciculus (mean difference: −0.09, 95% CI: −0.18; −0.01, p = 0.022) in the left hemisphere were significantly associated with worse VF but did not survive multiple testing. Conversely, WMH volume in the left cingulum of cingulate gyrus was significantly associated with MBNT performance (mean difference: −0.09, 95% CI: −0.17; −0.02, p = 0.016). Bayesian-network analyses confirmed the left cingulum of cingulate gyrus as a direct determinant of MBNT performance. Conclusion: Our findings identify the left cingulum of cingulate gyrus as a strategic white matter tract for MBNT, suggesting that language – is sensitive to subcortical ischemic damage. Future studies on the role of sporadic ischemic lesions and vascular cognitive impairment should not only focus on total WMH volume but should also take WMH lesion location into account when addressing language

The energy spectrum of all-particle cosmic rays around the knee region observed with the Tibet-III air-shower array

We have already reported the first result on the all-particle spectrum around the knee region based on data from 2000 November to 2001 October observed by the Tibet-III air-shower array. In this paper, we present an updated result using data set collected in the period from 2000 November through 2004 October in a wide range over 3 decades between $10^{14}$ eV and $10^{17}$ eV, in which the position of the knee is clearly seen at around 4 PeV. The spectral index is -2.68 $\pm$ 0.02(stat.) below 1PeV, while it is -3.12 $\pm$ 0.01(stat.) above 4 PeV in the case of QGSJET+HD model, and various systematic errors are under study now.Comment: 12 pages, 7 figures, accepted by Advances in space researc

Posterior eye shape measurement with retinal OCT compared to MRI

PURPOSE. Posterior eye shape assessment by magnetic resonance imaging (MRI) is used to study myopia. We tested the hypothesis that optical coherence tomography (OCT), as an alternative, could measure posterior eye shape similarly to MRI. METHODS. Macular spectral-domain OCT and brain MRI images previously acquired as part of the Singapore Epidemiology of Eye Diseases study were analyzed. The right eye in the MRI and OCT images was automatically segmented. Optical coherence tomography segmentations were corrected for optical and display distortions requiring biometry data. The segmentations were fitted to spheres and ellipsoids to obtain the posterior eye radius of curvature (Rc) and asphericity (Qxz). The differences in Rc and Qxz measured by MRI and OCT were tested using paired t-tests. Categorical assignments of prolateness or oblateness using Qxz were compared. RESULTS. Fifty-two subjects (67.8 ± 5.6 years old) with spherical equivalent refraction from +0.50 to -5.38 were included. The mean paired difference between MRI and original OCT posterior eye Rc was 24.03 ± 46.49 mm (P = 0.0005). For corrected OCT images, the difference in Rc decreased to -0.23 ± 2.47 mm (P = 0.51). The difference between MRI and OCT asphericity, Qxz, was -0.052 ± 0.343 (P = 0.28). However, categorical agreement was only moderate (j = 0.50). CONCLUSIONS. Distortion-corrected OCT measurements of Rc and Qxz were not statistically significantly different from MRI, although the moderate categorical agreement suggests that individual differences remained. This study provides evidence that with distortion correction, noninvasive office-based OCT could potentially be used instead of MRI for the study of posterior eye shape