Analysis Scheme for Density Modulation Experiments to Study Particle Confinements

Density modulation experiments are powerful experimental schemes for the study of particle transport. The diffusion coefficients （D） and convection velocity （V）, which cannot be evaluated from the particle balance in the equilibrium state, can be obtained separately. Further, the estimated values of D and V are determined independent of the absolute value of the particle source rate, which is difficult to obtain experimentally. However, the sensitivities and interpretation of D and V from the modulation experiments need to be considered. This paper describes numerical techniques for solving the particle balance equation of the modulation components. Examples of the analysis are shown regarding the data of LHD experiments, and the results of the modulation experiments are discussed.

Diffuse reduction of spleen density is a novel prognostic marker for intrahepatic cholangiocarcinoma after curative resection

BACKGROUND Diffuse reduction of spleen density(DROSD)is related to cancer prognosis;however,its role in intrahepatic cholangiocarcinoma(ICC)remains unclear.AIM To assess the predictive value of DROSD in the prognosis of ICC after curative resection.METHODS In this multicenter retrospective cohort study,we enrolled patients with ICC who underwent curative hepatectomy between 2012 and 2019.Preoperative spleen density was measured using computed tomography.Overall survival(OS)and recurrence-free survival(RFS)rates were calculated and compared utilizing the Kaplan-Meier method.Univariable and multivariable Cox regression analyses were applied to identify independent factors for OS and RFS.A nomogram was created with independent risk factors to predict prognosis of patients with ICC.RESULTS One hundred and sixty-seven ICC patients were enrolled.Based on the diagnostic cut-off values(spleen density≤45.5 Hounsfield units),55(32.9%)patients had DROSD.Kaplan-Meier analysis indicated that patients with DROSD had worse OS and RFS than those without DROSD(P<0.05).Cox regression analysis revealed that DROSD,carcinoembryonic antigen level,carbohydrate antigen 19-9 level,length of hospital stay,lymph node metastasis,and postoperative complications were independent predictors for OS(P<0.05).The nomogram created with these factors was able to predict the prognosis of patients with ICC with good reliability(OS C-index=0.733).The area under the curve for OS was 0.79.CONCLUSION ICC patients with DROSD have worse OS and RFS.The nomogram is a simple and practical method to identify high-risk ICC patients with poor prognosis.

Travelling Waves for a Density Dependent Diffusion Nagumo Equation over the Real Line

We consider the density dependent diffusion Nagumo equation, where the diffusion coefficient is a simple power function. This equation is used in modelling electrical pulse propagation in nerve axons and in population genetics (amongst other areas). In the present paper, the δ-expansion method is applied to a travelling wave reduction of the problem, so that we may obtain globally valid perturbation solutions (in the sense that the perturbation solutions are valid over the entire infinite domain, not just locally; hence the results are a generalization of the local solutions considered recently in the literature). The resulting boundary value problem is solved on the real line subject to conditions at z →±∞. Whenever a perturbative method is applied, it is important to discuss the accuracy and convergence properties of the resulting perturbation expansions. We compare our results with those of two different numerical methods (designed for initial and boundary value problems, respectively) and deduce that the perturbation expansions agree with the numerical results after a reasonable number of iterations. Finally, we are able to discuss the influence of the wave speed c and the asymptotic concentration value α on the obtained solutions. Upon recasting the density dependent diffusion Nagumo equation as a two-dimensional dynamical system, we are also able to discuss the influence of the nonlinear density dependence (which is governed by a power-law parameter m) on oscillations of the travelling wave solutions.