This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is ...firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.
Breast cancer incidence rates are increasing among Asian women, likely due to the changes in risk factors caused by globalization. Trends in breast cancer rates among Chinese women may differ from ...other Asian regions due to the implementation of a nationwide family planning program and resulting changes in women's reproductive practices. Appraisal of cancer trends can direct cancer control and public health planning, but relevant studies in China are scarce due to a lack of long-term data. We sought to evaluate secular time trends in breast cancer incidence and mortality using 40 years of cancer registry data for women in urban Shanghai.
Data on invasive breast cancer incidence and mortality were collected by the Shanghai Cancer Registry. Age-standardized rates (ASRs) for incidence and mortality were calculated using the Segi/Doll 1960 world standard population. Age, period, and birth cohort effects were evaluated using age–period–cohort (APC) Poisson regression models. Overall linear trends, interpreted as the estimated annual percentage change (EAPC), were derived from the net drift in age–drift models.
A total of 53 885 breast cancer cases and 17 235 breast cancer-specific deaths were documented among women in urban Shanghai between 1 January 1973 and 31 December 2012. Breast cancer incidence and mortality ASRs increased by 141.2% and 26.6%, respectively. Significant age, cohort, and period effects were identified in both incidence and mortality APC models; cohort effects were pronounced. Overall, a substantial increase in breast cancer incidence (EAPC = 2.96%/year) and a moderate increase in breast cancer mortality (EAPC = 0.87%/year) was observed. A notable downward trend in mortality was identified among younger women born after 1960.
Forty years of cancer registry data document a tremendous increase in incidence and a slight increase in mortality for breast cancer among women in Shanghai. Effective, appropriate, and affordable breast cancer prevention and control strategies are urgently needed in China.
A local radial point interpolation method (LRPIM) is presented to deal with boundary-value problems for free vibration analyses of two-dimensional solids. Local weak forms are developed using ...weighted residual method locally from the partial differential equation of free vibration. A technique to construct shape functions using radial function basis is proposed. The shape functions so formulated possess delta function property. Essential boundary conditions can be implemented with ease as in the finite-element method. Some important parameters on the performance of LRPIM are also investigated thoroughly. Numerical examples for free vibration analyses of two-dimensional solids to demonstrate the validity and efficiency of the present LRPIM are presented.
In this paper, a new one-dimensional space-fractional Boussinesq equation is proposed. Two novel numerical methods with a nonlocal operator (using nodal basis functions) for the space-fractional ...Boussinesq equation are derived. These methods are based on the finite volume and finite element methods, respectively. Finally, some numerical results using fractional Boussinesq equation with the maximally positive skewness and the maximally negative skewness are given to demonstrate the strong potential of these approaches. The novel simulation techniques provide excellent tools for practical problems. These new numerical models can be extended to two- and three-dimensional fractional space-fractional Boussinesq equations in future research where we plan to apply these new numerical models for simulating the tidal water table fluctuations in a coastal aquifer.
To understand how to assess optimally the risks of inhaled particles on respiratory health, it is necessary to comprehend the uptake of ultrafine particulate matter by inhalation during the complex ...transport process through a non-dichotomously bifurcating network of conduit airways. It is evident that the highly toxic ultrafine particles damage the respiratory epithelium in the terminal bronchioles. The wide range of in silico available and the limited realistic model for the extrathoracic region of the lung have improved understanding of the ultrafine particle transport and deposition (TD) in the upper airways. However, comprehensive ultrafine particle TD data for the real and entire lung model are still unavailable in the literature. Therefore, this study is aimed to provide an understanding of the ultrafine particle TD in the terminal bronchioles for the development of future therapeutics. The Euler-Lagrange (E-L) approach and ANSYS fluent (17.2) solver were used to investigate ultrafine particle TD. The physical conditions of sleeping, resting, and light activity were considered in this modelling study. A comprehensive pressure-drop along five selected path lines in different lobes was calculated. The non-linear behaviour of pressure-drops is observed, which could aid the health risk assessment system for patients with respiratory diseases. Numerical results also showed that ultrafine particle-deposition efficiency (DE) in different lobes is different for various physical activities. Moreover, the numerical results showed hot spots in various locations among the different lobes for different flow rates, which could be helpful for targeted therapeutical aerosol transport to terminal bronchioles and the alveolar region.
The cross section of the e+e−→Λc+Λ¯c− process is measured with unprecedented precision using data collected with the BESIII detector at /¯s=4574.5, 4580.0, 4590.0 and 4599.5 MeV. The nonzero cross ...section near the Λc+Λ¯c− production threshold is cleared. At center-of-mass energies /¯s=4574.5 and 4599.5 MeV, the higher statistics data enable us to measure the Λc polar angle distributions. From these, the Λc electric over magnetic form-factor ratios (|GE/GM|) are measured for the first time. They are found to be 1.14±0.14±0.07 and 1.23±0.05±0.03, respectively, where the first uncertainties are statistical and the second are systematic.
Purpose
To assess the efficacy and safety of drug-eluting beads transarterial chemoembolization (DEB-TACE) in liver cancer patients with different times of previous conventional transarterial ...chemoembolization (cTACE) treatments.
Methods
367 liver cancer patients about to receive DEB-TACE treatment were enrolled in this prospective cohort study. All patients were divided into no previous cTACE group (NPC group), 1–2 times previous cTACE group (PC group) and triple or above previous cTACE group (TPC group) according to the times of previous cTACE treatments.
Results
There was no difference in complete response (CR) (
P
= 0.671) and objective response rate (ORR) (
P
= 0.062) among three groups. Additionally, no difference in overall survival (OS) among groups (
P
= 0.899) was found. As to liver function, most liver function indexes were deteriorative at 1 week after DEB-TACE operation, but returned to baseline at 1–3 months after DEB-TACE operation in all three groups, while percentage of abnormal total bile acid (TBA) patients was higher in TPC group than NPC and PC groups at 1–3 month post-DEB-TACE (
P
= 0.018). As for safety profiles, the incidence of pain during DEB-TACE operation was lower in TPC group compared to NPC and PC groups (
P
= 0.005), while no difference of other adverse events was found during and 1 month post-DEB-TACE treatment among three groups.
Conclusion
DEB-TACE treatment was equally efficient and tolerated in liver cancer patients with different times of previous cTACE treatments.
A fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous ...time random walks with heavy tailed random waiting times.
In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBFs) to discretize the space variable. In contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems.
Finally the convergence order is verified from a numerical example which is presented to describe a fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating fractional differential equations, and it has good potential in the development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.
The neutral heating efficiency is commonly defined as the fraction of the solar extreme ultraviolet and X-ray energy absorbed by a planetary atmosphere that ends up as local heat. It is a crucial ...parameter that determines the upper atmospheric temperature and, consequently, the thermal escape rate on both solar system bodies and exoplanets. Combining the Mars Atmosphere and Volatile Evolution measurements of a variety of atmospheric parameters, we calculate the neutral heating efficiency in the dayside Martian upper atmosphere based on a complicated network of microscopic processes, including photon and photoelectron impact processes, as well as exothermic chemical reactions. Our calculations indicate that neutral heating is mainly contributed by photon impact at low altitudes, of which the bulk occurs via CO2 photodissociation, and exothermic chemistry at high altitudes, of which the bulk occurs via and dissociative recombination. Collisional quenching of metastable neutrals and ions, which is of great interest in the literature, contributes to local heating by no more than 10% at all altitudes. In the dayside median sense, the neutral heating efficiency remains roughly constant at 20% from 150 to 200 km and increases steadily to 32% near 250 km. The heating efficiency at 150-200 km shows a weak correlation with solar zenith angle, increases modestly with increasing solar activity, and is clearly enhanced over strong crustal magnetic anomalies. Throughout the study, strict local heating is assumed, but nonlocal heating does not affect our results near or below 200 km.
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