Circulation problems
Searched over 200M research papers for "circulation problems"
Summary
10 papers analyzed
These studies suggest that circulation problems can be addressed through various methods including algorithmic approaches for network flow, expert systems for diagnosing lost circulation in wells, and models for ocean and atmospheric circulation.
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Circulation Problems: A Comprehensive Overview
Minimum-Cost Circulation Problems in Network Flow
Successive Approximation Techniques
The minimum-cost circulation problem is a fundamental issue in network flow optimization. A novel approach combines maximum flow problem-solving methods with successive approximation techniques based on cost scaling. This method measures solution accuracy by the degree of violation of complementary slackness conditions. The proposed algorithm can run in (O(n^3 \log nC)) time on an (n)-vertex network with integer arc costs of absolute value at most (C). By incorporating advanced data structures, the time complexity can be reduced to (O(nm \log^2 n / m \log nC)) on a network with (m) arcs. This approach also yields strongly polynomial algorithms for minimum-cost circulation problems, suggesting that these problems are not significantly harder than maximum flow problems.
Flow Circulation Sharing Problem
The flow circulation sharing problem is another variant, defined as a network flow circulation problem with a maximin objective function. This model is particularly useful in equitable resource allocation over time, as demonstrated in examples like coal strikes and submarine assignments. The problem involves regular and tradeoff arcs, each with specific flow bounds and tradeoff functions. Optimality conditions are developed, and efficient algorithms are proposed for both continuous and integer versions of the problem.
Circulation in Atmospheric and Oceanic Systems
General Circulation of the Atmosphere
The seminal work by Yeh and Chu (1958) on the general circulation of the atmosphere remains highly relevant. Their insights into the role of large-scale eddies in mean meridional circulation, the formation of westerly jets, and the transport processes of angular momentum, heat, and kinetic energy continue to inform current theoretical research. These foundational concepts are crucial for understanding the general circulation's role in climate change.
Ocean Circulation Models
A numerical model for studying ocean circulation problems considers the complex outline and bottom topography of the World Ocean. This model uses the "rigid-lid" approximation to filter out surface gravity-inertial waves, allowing for the study of low-frequency, large-scale current systems. The model is designed to be energy-consistent, ensuring no fictitious energy generation or decay in the momentum equations. This approach is particularly effective for resolving features like the Equatorial Undercurrent.
Circulation Issues in Industrial and Economic Contexts
Newspaper Circulation Management
Circulation management in the newspaper industry faces significant challenges. Despite efforts to gain new subscriptions, many newspapers end the year with a net loss or only modest gains. The primary reasons for subscription cancellations are irregular delivery and poor condition of the newspapers upon arrival. Effective implementation of marketing concepts requires an organizational structure that addresses these distribution issues.
Lost Circulation in Drilling Operations
Lost circulation is a frequent and costly problem in drilling operations, leading to increased non-productive time and safety hazards. Machine learning techniques, such as artificial neural networks (ANNs) and support vector machines (SVM), have been developed to predict and mitigate lost circulation. These models analyze drilling operation parameters and fluid characteristics to suggest appropriate solutions, thereby aiding drilling engineers in making informed decisions .
Settlement Fund Circulation in Banking
In economic activities, the central bank plays a crucial role in covering payments when banks are short of funds. The settlement fund circulation problem involves determining the optimal sequence of payments to minimize or maximize the total funds required. This problem is NP-hard, but several polynomial-time solvable cases have been identified, providing insights into efficient fund management.
Conclusion
Circulation problems span a wide range of fields, from network flow optimization and atmospheric science to industrial management and economic activities. Advances in algorithms and machine learning techniques offer promising solutions to these complex issues, highlighting the importance of interdisciplinary research and innovative approaches.
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