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Register a new userOn the Mathematical Theory of Human Migration: Model of a Migration Channel with a Secondary and a Tertiary Arm
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We study the motion of substance in a finite channel that belongs to a network. The channel splits to two arms in a node of the network. There is an additional split of the secondary arm. We obtain analytical relationships for the distribution of the substance in the nodes of the channel for the case of stationary regime of the motion of the substance in the arms of the channel. The obtained results are discussed from the point of view of application of the model to migration dynamics: model of motion of migrants in a channel consisting of chains of countries with different probabilities for obtaining permission to stay for the migrants in the different countries of the channel
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The gravity model (GM) analogous to Newtons law of universal gravitation has successfully described the flow between different spatial regions, such as human migration, traffic flows, international economic trades, etc. This simple but powerful approach relies only on the mass factor represented by the scale of the regions and the geometrical factor represented by the geographical distance. However, when the population has a subpopulation structure distinguished by different attributes, the estimation of the flow solely from the coarse-grained geographical factors in the GM causes the loss of differential geographical information for each attribute. To exploit the full information contained in the geographical information of subpopulation structure, we generalize the GM for population flow by explicitly harnessing the subpopulation properties characterized by both attributes and geography. As a concrete example, we examine the marriage patterns between the bride and the groom clans of Korea in the past. By exploiting more refined geographical and clan information, our generalized GM properly describes the real data, a part of which could not be explained by the conventional GM. Therefore, we would like to emphasize the necessity of using our generalized version of the GM, when the information on such nongeographical subpopulation structures is available.
We study empirically how the fame of WWI fighter-pilot aces, measured in numbers of web pages mentioning them, is related to their achievement, measured in numbers of opponent aircraft destroyed. We find that on the average fame grows exponentially with achievement; the correlation coefficient between achievement and the logarithm of fame is 0.72. The number of people with a particular level of achievement decreases exponentially with the level, leading to a power-law distribution of fame. We propose a stochastic model that can explain the exponential growth of fame with achievement. Next, we hypothesize that the same functional relation between achievement and fame that we found for the aces holds for other professions. This allows us to estimate achievement for professions where an unquestionable and universally accepted measure of achievement does not exist. We apply the method to Nobel Prize winners in Physics. For example, we obtain that Paul Dirac, who is a hundred times less famous than Einstein contributed to physics only two times less. We compare our results with Landaus ranking.
We discuss an inertial migration of oblate spheroids in a plane channel, where steady laminar flow is generated by a pressure gradient. Our lattice Boltzmann simulations show that spheroids orient in the flow, so that their minor axis coincides with the vorticity direction (a log-rolling motion). Interestingly, for spheroids of moderate aspect ratios, the equilibrium positions relative to the channel walls depend only on their equatorial radius $a$. By analysing the inertial lift force we argue that this force is proportional to $a^3b$, where $b$ is the polar radius, and conclude that the dimensionless lift coefficient of the oblate spheroid does not depend on $b$, and is equal to that of the sphere of radius $a$.
Collective migration of animals in a cohesive group is rendered possible by a strategic distribution of tasks among members: some track the travel route, which is time and energy-consuming, while the others follow the group by interacting among themselves. In this paper, we study a social dynamics system modeling collective migration. We consider a group of agents able to align their velocities to a global target velocity, or to follow the group via interaction with the other agents. The balance between these two attractive forces is our control for each agent, as we aim to drive the group to consensus at the target velocity. We show that the optimal control strategies in the case of final and integral costs consist of controlling the agents whose velocities are the furthest from the target one: these agents sense only the target velocity and become leaders, while the uncontrolled ones sense only the group, and become followers. Moreover, in the case of final cost, we prove an Inactivation principle: there exist initial conditions such that the optimal control strategy consists of letting the system evolve freely for an initial period of time, before acting with full control on the agent furthest from the target velocity.
A planet is formed within a protoplanetary disk. Recent observations have revealed substructures such as gaps and rings, which may indicate forming planets within the disk. Due to disk--planet interaction, the planet migrates within the disk, which can affect a shape of the planet-induced gap. In this paper, we investigate effects of fast inward migration of the planet on the gap shape, by carrying out hydrodynamic simulations. We found that when the migration timescale is shorter than the timescale of the gap-opening, the orbital radius is shifted inward as compared to the radial location of the gap. We also found a scaling relation between the radial shift of the locations of the planet and the gap as a function of the ratio of the timescale of the migration and gap-opening. Our scaling relation also enables us to constrain the gas surface density and the viscosity when the gap and the planet are observed. Moreover, we also found the scaling relation between the location of the secondary gap and the aspect ratio. By combining the radial shift and the secondary gap, we may constrain the physical condition of the planet formation and how the planet evolves in the protoplanetary disk, from the observational morphology.
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