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This paper deals with surface and interface sloshing in a tank containing two fluids of different desities. Scientific interest in this ploblem includes the need to quantify allowance loads on oil water separators and chemical plants. In this study, we give a Hamiltonian formulation of a system of two incompressible irrotational fluids with a dynamic free surface and interface. This study aims to analyze the linearized time history response and the linear properties (vibration mode and effect of surface tension on the natural frequency). As a result, it was revealed that this system has two different vibration modes (surface and interfacial mode) with same wave number and the surface tension causes natural frequency increases. The validity of the theory is verified by experimental results. This procedure can be directly applied to the nonlinear problem of this system.

This paper deals with a nonlinear surface and interface sloshing in layered two immiscible fluids of different desities. Scientific interest in surface and interface sloshing includes the need to quantify allowance loads on separators or agitators in chemical plants and so on. We propose the analytical method for nonlinear sloshing in this problem by using Hamiltonian formulation. In theoretical analysis, the governing equations and canonical form (Hamiltonian equations) of a system of two fluids with a dynamic free surface and interface are given by applying Hamilton's principle. Moreover, the nonlinear ordinary differential system which governs liquid surface and interfacial wave motions is derived by using Dirichlet-Neumann operators and the generalized Fourier series expansion. Solving these ordinary differential system yields the time histories and the transitions of surface and interfacial wave motions in a rectangular tank. The validly of the theoretical analysis is verified through the experiments.

Alterations in KRAS, CDKN2A (p16), TP53, and SMAD4 genes have been major drivers of pancreatic carcinogenesis. The clinical course of patients with pancreatic cancer in relation to these driver alterations has not been fully characterised in large populations. We hypothesised that pancreatic carcinomas with different combinations of KRAS mutation and aberrant expression of CDKN2A, p53, and SMAD4 might show distinctive recurrence patterns and post‐operative survival outcomes. To test this hypothesis, we utilised a multi‐institutional cohort of 1,146 resected pancreatic carcinomas and assessed KRAS mutations by droplet digital polymerase chain reaction and CDKN2A, p53, and SMAD4 expression by immunohistochemistry. Multivariable hazard ratios (HRs) and 95% confidence intervals (CIs) for disease‐free survival (DFS) and overall survival (OS) were computed according to each molecular alteration and the number of altered genes using the Cox regression models. Multivariable competing risks regression analyses were conducted to assess the associations of the number of altered genes with specific patterns of recurrence. Loss of SMAD4 expression was associated with short DFS (multivariable HR, 1.24; 95% CI, 1.09–1.43) and OS times (multivariable HR, 1.27; 95% CI, 1.10–1.46). Compared to cases with 0–2 altered genes, cases with three and four altered genes had multivariable HRs for OS of 1.28 (95% CI, 1.09–1.51) and 1.47 (95% CI, 1.22–1.78), respectively (ptrend < 0.001). Patients with an increasing number of altered genes were more likely to have short DFS time (ptrend = 0.003) and to develop liver metastasis (ptrend = 0.006) rather than recurrence at local or other distant sites. In conclusion, loss of SMAD4 expression and an increasing number of altered genes were associated with unfavourable outcomes in pancreatic cancer patients. This study suggests that the accumulation of the four major driver alterations can confer a high metastatic potential to the liver, thereby impairing post‐operative survival among patients with pancreatic cancer.

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