Note on dust trapping in inviscid vortex pairs with unequal strengths

We investigate theoretically the motion of tiny heavy passive particles transported in a plane inviscid flow consisting of two point vortices, in order to understand particle dispersion and trapping during vortex interaction. In spite of their large density, particles are not necessarily centrifugated away from vortices. It is observed that they can have various equilibrium positions in the reference frame rotating with the vortices, provided the particle response time and the vortex strength ratio lie in appropriate ranges. A stability analysis reveals that some of these points can be asymptotically stable, and can therefore trap particles released in their basin of attraction. A complete trapping diagram is derived, showing that any vortex pair can potentially become a dust trap, provided the vortex strength ratio is different from 0 (single vortex) and -1 (translating symmetrical vortices). Trapping exists for both co-rotating or contra-rotating vortex pairs. In the latter case, particle trapping on a limit cycle is also observed, and confirmed by using Sapsis and Haller's method [Chaos, 20, 017515, 2010] generalized to non-inertial reference frames

Entrepreneurial motives and performance:Why might better educated entrepreneurs be less successful?

In a sample of newly created French firms, the impact of an entrepreneurís education on the firm's survival varies widely depending on his previous labor market situation. While it is strongly positive for the overall population, it is much weaker or insignificant for entrepreneurs who were previously unemployed or poorly matched. Our theoretical entrepreneurship model shows that these differences may be attributed to differences in unobserved human capital for better educated entrepreneurs across different initial states in the labor market. Empirical results are consistent with the theory if employers have limited information about potential entrepreneurs'human capital

Asymptotic properties of wall-induced chaotic mixing in point vortex pairs

The purpose of this work is to analyze the flow due to a potential point vortex pair in the vicinity of a symmetry line (or "wall"), in order to understand why the presence of the wall, even far from the vortices, accelerates fluid mixing around the vortex pair. An asymptotic analysis, in the limit of large distances to the wall, allows to approximate the wall effect as a constant translation of the vortex pair parallel to the wall, plus a straining flow which induces a natural blinking vortex mechanism with period half the rotation period. A Melnikov analysis of lagrangian particles, in the frame translating and rotating with the vortices, shows that a homoclinic bifurcation indeed occurs, so that the various separatrices located near the vortex pair (and rotating with it) do not survive when a wall is present. The thickness of the resulting inner stochastic layer is estimated by using the separatrix map method, and is shown to scale like the inverse of the squared distance to the wall. This estimation provides a lower-bound to the numerical thickness measured from either Poincar\'e sections or simulations of lagrangian particles transported by the exact potential velocity field in the laboratory frame. In addition, it is shown that the outer homoclinic cycle, separating the vortices from the external (open) flow, is also perturbed from inside by the rotation of the vortex pair. As a consequence, a stochastic layer is shown to exist also in the vicinity of this cycle, allowing fluid exchange between the vortices and the outer flow. However, the thickness of this outer stochastic zone is observed to be much smaller than the one of the inner stochastic zone near vortices, as soon as the distance to the wall is large enough

Human Dimensions of Natural Resources: A Case of Farmers in Northern Rwanda

As food demand increases globally, the world faces the challenge of feeding everyone without harming the environment. Meeting this challenge requires increased food production. Paradoxically, increased food production can harm the environment and natural resources. Change in consumption patterns offers an opportunity to reconcile the increase in food production and environmental protection. However, consumption patterns can only change if they are perceived first, then acted upon. Research shows that people who perceive their consumption of natural resources are more likely to conserve them as they can see how much they are consuming. This study investigated perceptions of natural resources and environmental behaviors among farmers in Musanze District, northern Rwanda. The first part of this research investigated perceptions of water and charcoal consumption among farmers. A survey was used to collect data from 323 farmers involved in a poultry development project in the district. Results indicate that the perception of charcoal consumption was associated with three variables: living in the urban section of the district, the amount of feed consumed by chickens, and the elevation at which the coop is located. To examine farmers’ environmental behaviors, the second chapter of the research employed the various existing theories to assess the influence of attitudes, subjective norms, perceived behavior control, and other factors on farmers’ behavioral intent to engage in rainwater harvesting, the use of organic fertilizer, and the use of alternative sources of energy for domestic cooking. To conduct the study, a survey was conducted from a randomly selected sample of 604 farmers from 7 sectors of the district of Musanze in northern Rwanda. A Structural Equation Model (SEM) approach was used to analyze data. Results revealed that farmers’ decision to engage in environmental behaviors depends on their attitudes, social norms, perceived behavior control, and other background factors. Overall, the results provided useful insights into understanding farmers’ decision-making towards nature and the environment. The last part of the research applied spatial analysis to examine farmers’ behaviors. Results showed that in addition to the presence of spatial dependence, there are spatial clusters of farmers’ behavioral intent in some regions of the study area

Development of numerical algorithms for practical computation of nonlinear normal modes

When resorting to numerical algorithms, we show that nonlinear normal mode (NNM) computation is possible with limited implementation effort, which paves the way to a practical method for determining the NNMs of nonlinear mechanical systems. The proposed method relies on two main techniques, namely a shooting procedure and a method for the continuation of NNM motions. In addition, sensitivity analysis is used to reduce the computational burden of the algorithm. A simplified discrete model of a nonlinear bladed disk is considered to demonstrate the developments

Existence and qualitative properties of multidimensional conical bistable fronts

International audienceTravelling fronts with conical-shaped level sets are constructed for reaction-diffusion equations with bistable nonlinearities of positive mass. The construction is valid in space dimension 2, where two proofs are given, and in arbitrary space dimensions under the assumption of cylindrical symmetry. General qualitative properties are presented under various assumptions: conical conditions at infinity, existence of a sub-level set with globally Lipschitz boundary, monotonicity in a given direction