Floating Bodies with Surface Tension

Capillary phenomena have been studied by mathematicians and physicists for hundreds of years. In this thesis, both two-dimensional(2D) and three-dimensional(3D) bodies floating on an unbounded reservoir are studied based on the Young-Laplace equation. We reconsider the 2D floating cylinder problem studied in a groundbreaking paper of Bhatnargar and Finn from 2006. We derive the total energy relative to the undisturbed state and the total force in vertical direction. The relation between the total force and the derivative of the total energy with respect to the height of the centre of the cylinder relative to the undisturbed fluid level is found. The number of equilibria, the floating configurations and their stability are also studied. In the 2D floating square problem, we rederive the floating configurations and their stability in the no surface tension case. Allowing surface tension, one example with a special contact angle is considered. We show that there is one unstable equilibrium of the floating square with a horizontal side. In the 3D floating object problem with radial symmetry, the shooting method is applied to obtain the fluid height and radial distance from the vertical axis numerically in terms of the inclination angle parameter. In the vertical cylinder problem, the relation between the total energy and the total force in vertical direction is found to be consistent with 2D cylinder case. In the floating ball problem, a non-monotone relation between height of centre and the wetting angle is found. We also give an example of two floating configurations with the same height. More study of the 3D floating ball problem is anticipated.

A Floating Ball and Two Asymptotic Problems in Capillarity

The study of capillary phenomena can be traced back to the age of Aristotle. In this thesis, a floating ball and two asymptotic problems in capillarity are considered, all of which include surface tension and gravity. The first problem, the ascent of fluid surface outside a narrow vertical circular tube has been studied for decades. Lo obtained a five-term asymptotic expansion of the fluid height near the boundary for the small Bond number using the method of matched asymptotic expansions. Miersemann gave a rigorous proof of a two-term asymptotic expansion but the error bound he obtained is inferior to Lo's. We reconsider this problem and our goal is to establish a rigorous approach to improve Miersemann's error bound. We construct two piecewise smooth approximate solutions. Each approximate solution consists of an inner solution and an outer solution. The first approximate solution with its inner solution having zero mean curvature is shown as an upper bound. The second approximate solution with its inner solution having constant mean curvature is shown as a lower bound. The approximations are optimized in terms of the transition radius $q$ by use of Olver's theorem. This establishes the two-term asymptotic expansion. Its error bound is an improvement of Miersemann's but is inferior to Lo's. A modification of the outer solution helps improve our error bound. However, we did not achieve Lo's error bound. Interest in floating objects goes back to antiquity. In recent research, many examples of multiple equilibrium configurations have been found with or without surface tension and gravity. We consider a ball floating on an unbounded reservoir. The floating configuration is assumed to be radially symmetric. By a result of Elcrat, Neel and Siegel, the fluid interface is determined by the attachment radius $r_0$ and inclination angle $\psi_0$. Both of these are given in terms of the attachment angle $\phi_0$. However, the zero solution is not included in the parametric solution. So, the graph description of the fluid height is considered, as well. We develop $C^1$ smoothness of the attachment height $u_0$ with respect to $\phi_0$. This requires an extension of Vogel's description of solutions and monotonicity results. As a by-product, Vogel's conjecture on the smoothness of the envelope of exterior solutions is shown. In the study of the number of equilibria and their stability, both force and energy approaches are considered. We classify forces and energies and establish a relation between the total force and the total energy. This requires determining the asymptotic expansion of the interface as the inclination angle tends to zero, which is achieved through the use of Levinson's theorem. A critical point of the total energy can be either a force balanced point or a critical point of the height of the center. Both the total force and the center height contain $u_0$, which has to be found numerically by the shooting method. In order to understand the behavior of the total force and the height curves, both asymptotic analysis and numerical tests are employed. We investigate the limiting behavior of the total force and the height curves for small and large Bond number or when the attachment angle tends to its end points. We perform thousands of numerical tests with different values of Bond numbers and contact angles. Combined with the numerical observations and the results from the asymptotic analysis, we conjecture that there are at most two force balanced points. If there is only one force balanced point, it must be stable. If there are two force balanced points, the one with smaller attachment angle must be stable and the other one with larger attachment angle can be either stable or unstable. For a given contact angle, the information on the number of equilibria and their stability for the floating ball system are illustrated in Bond number versus density ratio figures. We give several such figures with typical contact angles. Finally, two examples are presented. One admits two stable equilibrium configurations. Another example shows a case with no force balanced point where there is an energy minimizer. This prompts discussion of the necessary condition for the floating configuration and a modification of changing topological structure for the floating configurations in this example

HuMiTar: A sequence-based method for prediction of human microRNA targets

<p>Abstract</p> <p>Background</p> <p>MicroRNAs (miRs) are small noncoding RNAs that bind to complementary/partially complementary sites in the 3' untranslated regions of target genes to regulate protein production of the target transcript and to induce mRNA degradation or mRNA cleavage. The ability to perform accurate, high-throughput identification of physiologically active miR targets would enable functional characterization of individual miRs. Current target prediction methods include traditional approaches that are based on specific base-pairing rules in the miR's seed region and implementation of cross-species conservation of the target site, and machine learning (ML) methods that explore patterns that contrast true and false miR-mRNA duplexes. However, in the case of the traditional methods research shows that some seed region matches that are conserved are false positives and that some of the experimentally validated target sites are not conserved.</p> <p>Results</p> <p>We present HuMiTar, a computational method for identifying common targets of miRs, which is based on a scoring function that considers base-pairing for both seed and non-seed positions for human miR-mRNA duplexes. Our design shows that certain non-seed miR nucleotides, such as 14, 18, 13, 11, and 17, are characterized by a strong bias towards formation of Watson-Crick pairing. We contrasted HuMiTar with several representative competing methods on two sets of human miR targets and a set of ten glioblastoma oncogenes. Comparison with the two best performing traditional methods, PicTar and TargetScanS, and a representative ML method that considers the non-seed positions, NBmiRTar, shows that HuMiTar predictions include majority of the predictions of the other three methods. At the same time, the proposed method is also capable of finding more true positive targets as a trade-off for an increased number of predictions. Genome-wide predictions show that the proposed method is characterized by 1.99 signal-to-noise ratio and linear, with respect to the length of the mRNA sequence, computational complexity. The ROC analysis shows that HuMiTar obtains results comparable with PicTar, which are characterized by high true positive rates that are coupled with moderate values of false positive rates.</p> <p>Conclusion</p> <p>The proposed HuMiTar method constitutes a step towards providing an efficient model for studying translational gene regulation by miRs.</p

Low-carbon economic dispatch of integrated energy system based on liquid carbon dioxide energy storage

To realize the integrated energy system (IES) low-carbon and economy dispatches and renewable energy utilization, the integrated energy system economic dispatch model introduces the liquid carbon dioxide energy storage (LCES) and carbon capture system (CCS). This paper proposes a low-carbon economic dispatch model for an integrated energy system that considers LCES and carbon capture system. The paper considers the impact of carbon trading mechanisms on systemic carbon emissions, aims to minimize the total operating cost of the system, and comparison of integrated energy system dispatch for two scenarios: integrated energy system equipped with LCES and integrated energy system equipped with battery energy storage. CPLEX simulation software simulates this comprehensive energy system. Analyzing the dispatching results from different perspectives, such as electric energy, thermal energy, and CO2 emissions. These results show that the proposed model effectively reduces carbon emissions, improves energy utilization, and achieves comprehensive low-carbon economic operation of the integrated energy system

Spatial-temporal distribution and transport flux of polycyclic aromatic hydrocarbons in a large hydropower reservoir of Southeast China: Implication for impoundment impacts

Abstract(#br)In order to investigate the impacts of dam-related water impoundment on the spatial-temporal variations and transport of anthropogenic organic pollutants, 15 priority polycyclic aromatic hydrocarbons (PAHs) were analyzed in water samples from the Shuikou Reservoir (SKR) of the Minjiang River. The SKR was formed after the construction of the Shuikou Dam, which is the largest hydropower station in Southeast China. The water samples were collected from the backwater zone of the SKR, in both the wet and dry seasons, corresponding to the drainage and impoundment periods of water flow, respectively. The concentrations of the dissolved PAHs in surface water from the wet season (average of 161 ± 97 ng L −1 ) were significantly higher (ANOVA, p < 0.01) than those from the dry season (average of 43 ± 21 ng L −1 ). PAH concentrations in the SKR decreased from upstream (industrialized cities) to downstream (rural towns or counties), indicating high PAH loads caused by intensive urbanization effects. The high proportions of 3-ring PAHs in the wet season were from local sources via surface runoff; while the elevated proportions of 4- to 6- ring PAHs in the dry season reflected atmospheric deposition emerged of these PAHs and/or volatilization of 3-ring PAHs enhanced. Molecular diagnostic ratios of PAH isomers in multimedium and principal component analysis indicated that PAH presence in the SKR was mainly attributed to pyrogenic origin. The isomeric ratios of fluoranthene to fluoranthene plus pyrene in the wet season were homogeneous, implying that there were continuous new inputs along the riverine runoff. However, these ratios showed spatial downward trend in the dry season, indicating continued degradation of PAHs occurred along the transport path during the impoundment period. The input and output fluxes of PAHs in the SKR were 5330 kg yr −1 and 2991 kg yr −1 , revealing that the reservoir retained contaminants after impoundment of the hydropower dam

Spatial-temporal distribution and transport flux of polycyclic aromatic hydrocarbons in a large hydropower reservoir of Southeast China: Implication for impoundment impacts.

In order to investigate the impacts of dam-related water impoundment on the spatial-temporal variations and transport of anthropogenic organic pollutants, 15 priority polycyclic aromatic hydrocarbons (PAHs) were analyzed in water samples from the Shuikou Reservoir (SKR) of the Minjiang River. The SKR was formed after the construction of the Shuikou Dam, which is the largest hydropower station in Southeast China. The water samples were collected from the backwater zone of the SKR, in both the wet and dry seasons, corresponding to the drainage and impoundment periods of water flow, respectively. The concentrations of the dissolved PAHs in surface water from the wet season (average of 161 ± 97 ng L-1) were significantly higher (ANOVA, p < 0.01) than those from the dry season (average of 43 ± 21 ng L-1). PAH concentrations in the SKR decreased from upstream (industrialized cities) to downstream (rural towns or counties), indicating high PAH loads caused by intensive urbanization effects. The high proportions of 3-ring PAHs in the wet season were from local sources via surface runoff; while the elevated proportions of 4- to 6- ring PAHs in the dry season reflected atmospheric deposition emerged of these PAHs and/or volatilization of 3-ring PAHs enhanced. Molecular diagnostic ratios of PAH isomers in multimedium and principal component analysis indicated that PAH presence in the SKR was mainly attributed to pyrogenic origin. The isomeric ratios of fluoranthene to fluoranthene plus pyrene in the wet season were homogeneous, implying that there were continuous new inputs along the riverine runoff. However, these ratios showed spatial downward trend in the dry season, indicating continued degradation of PAHs occurred along the transport path during the impoundment period. The input and output fluxes of PAHs in the SKR were 5330 kg yr-1 and 2991 kg yr-1, revealing that the reservoir retained contaminants after impoundment of the hydropower dam