Selfish Routing on Dynamic Flows

Selfish routing on dynamic flows over time is used to model scenarios that vary with time in which individual agents act in their best interest. In this paper we provide a survey of a particular dynamic model, the deterministic queuing model, and discuss how the model can be adjusted and applied to different real-life scenarios. We then examine how these adjustments affect the computability, optimality, and existence of selfish routings.Comment: Oberlin College Computer Science Honors Thesis. Supervisor: Alexa Sharp, Oberlin Colleg

Biophilic urban developments following dynamic flows of tree-shaped architectures

Latest theories and practices in Biophilic designs of the urban space regard the urban fabric as being composed of several interrelated layers of energetic structure influencing each other in a non-linear manner primarily. The interaction between two or more interfaces of the urban space layers evolves into new and non-predictable properties. Evolution and creation of new boundaries/interfaces follows laws related to fractal growth; most of the times this particular evolution is defined by laws of physics, such as Thermodynamics and Constructal Law. Designs that do not follow these laws may produce anti-natural and hostile environments, which do not fit into human beings’ evolution, and thus, fail to enhance life by all means. The author of this paper should like to illustrate how new developments of urbanism worldwide currently work upon conceptual and town planning models based not only upon cutting-edge technology, but also upon natural laws and patterns of life and human behaviours strictly related to flaws and movement dictated by natural phenomena. When abrupt interruption of the urban structure has occurred, a consequent design solution does not even guarantee flowing and freedom to morph. It is impossible to create harmonic designs which naturally “unite the animate with the inanimate”, as Adrian Bejan and Sylvie Lorente affirm, whenever urban sprawl fails to encompass Biophilic solutions related to tree-shaped architectures. The author argues that Constructal invasion into the urban space “as fundamental problems of access to flow: volume to point, area to point, line to point, and the respective reverse flow directions” can only guarantee high standard quality of life in either contemporary or future cities developments

Dynamic Flows with Adaptive Route Choice

We study dynamic network flows and introduce a notion of instantaneous dynamic equilibrium (IDE) requiring that for any positive inflow into an edge, this edge must lie on a currently shortest path towards the respective sink. We measure current shortest path length by current waiting times in queues plus physical travel times. As our main results, we show: 1. existence and constructive computation of IDE flows for single-source single-sink networks assuming constant network inflow rates, 2. finite termination of IDE flows for multi-source single-sink networks assuming bounded and finitely lasting inflow rates, 3. the existence of IDE flows for multi-source multi-sink instances assuming general measurable network inflow rates, 4. the existence of a complex single-source multi-sink instance in which any IDE flow is caught in cycles and flow remains forever in the network.Comment: 40 pages, shorter version published in the "Proceedings of the 20th Conference on Integer Programming and Combinatorial Optimization, 2019

Relativistic Kinetics of Phonon Gas in Superfluids

The relativistic kinetic theory of the phonon gas in superfluids is developed. The technique of the derivation of macroscopic balance equations from microscopic equations of motion for individual particles is applied to an ensemble of quasi-particles. The necessary expressions are constructed in terms of a Hamilton function of a (quasi-)particle. A phonon contribution into superfluid dynamic parameters is obtained from energy-momentum balance equations for the phonon gas together with the conservation law for superfluids as a whole. Relations between dynamic flows being in agreement with results of relativistic hydrodynamic consideration are found. Based on the kinetic approach a problem of relativistic variation of the speed of sound under phonon influence at low temperature is solved.Comment: 23 pages, Revtex fil

Complex Dynamic Flows in Solar Flare Sheet Structures

Observations of high-energy emission from solar flares often reveal the presence of large sheet-like structures, sometimes extending over a space comparable to the Sun's radius. Given that these structures are found between a departing coronal mass ejection and the post-eruption flare arcade, it is natural to associate the structure with a current sheet; though the relationship is unclear. Moreover, recent high-resolution observations have begun to reveal that the motions in this region are highly complex, including reconnection outflows, oscillations, and apparent wakes and eddies. We present a detailed first look at the complicated dynamics within this supra-arcade plasma, and consider implications for the interrelationship between the plasma and its embedded magnetic field

Distributed Control of Dynamic Flows in Traffic Networks

In today’s society, traffic congestion is a major problem in several aspects. Apart from the obvious problem that people are losing valuable time due to the resulting delays, it also has negative impact on as well the economy as the local and global environment. With the development of sensors and navigation support, it has now become possible and thus of interest to study optimal routing of vehicles in a traffic network, in order to reduce the congestion-related problems. In this master’s thesis, a distributed algorithm for solution of optimal dynamic traffic flow control problems is derived, implemented and tested. Traffic networks are modelled with the cell transmission model (CTM), and the solution algorithm is based on a generalization of the alternating direction method of multipliers (ADMM). The algorithm is tested for one simple and one more complicated traffic network. The tests include both cases with time-varying external inflow of traffic as well as cases where the flow capacity of a specific road segment is varied with time, in order to simulate temporary traffic incidents. The tests show that if the cost function is chosen as the sum of squares of the traffic volumes at the cells (road segments) of the network, the algorithm converges to the optimal solution if a specific parameter (the penalty parameter, or step length) is chosen sufficiently small. The report starts with a description and examples from the simpler case of static traffic flow optimization. It also contains a summary of the concepts used from optimization theory. After this, the approach for dynamic traffic flow modelling and optimization is described. Finally, a description and derivation of the algorithm is provided, after which the implementation is tested for different cases involving the two different traffic networks

Flow velocity mapping using contrast enhanced high-frame-rate plane wave ultrasound and image tracking: methods and initial in vitro and in vivo evaluation

Ultrasound imaging is the most widely used method for visualising and quantifying blood flow in medical practice, but existing techniques have various limitations in terms of imaging sensitivity, field of view, flow angle dependence, and imaging depth. In this study, we developed an ultrasound imaging velocimetry approach capable of visualising and quantifying dynamic flow, by combining high-frame-rate plane wave ultrasound imaging, microbubble contrast agents, pulse inversion contrast imaging and speckle image tracking algorithms. The system was initially evaluated in vitro on both straight and carotid-mimicking vessels with steady and pulsatile flows and in vivo in the rabbit aorta. Colour and spectral Doppler measurements were also made. Initial flow mapping results were compared with theoretical prediction and reference Doppler measurements and indicate the potential of the new system as a highly sensitive, accurate, angle-independent and full field-of-view velocity mapping tool capable of tracking and quantifying fast and dynamic flows