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Register a new userOptimal Control Strategies for Active Particle Navigation
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The quest for the optimal navigation strategy in a complex environment is at the heart of microswimmer applications like cargo carriage or drug targeting to cancer cells. Here, we formulate a variational Fermats principle for microswimmers determining the optimal path regarding travelling time, energy dissipation or fuel consumption. For piecewise constant forces (or flow fields), the principle leads to Snells law, showing that the optimal path is piecewise linear, as for light rays, but with a generalized refraction law. For complex environments, like general 1D-, shear- or vortex-fields, we obtain exact analytical expressions for the optimal path, showing, for example, that microswimmers sometimes have to temporarily navigate away from their target to reach it fastest. Our results might be useful to benchmark algorithmic schemes for optimal navigation.
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Mosquitoes are responsible for the transmission of many diseases such as dengue fever, zika or chigungunya. One way to control the spread of these diseases is to use the sterile insect technique (SIT), which consists in a massive release of sterilized male mosquitoes. This strategy aims at reducing the total population over time, and has the advantage being specific to the targeted species, unlike the use of pesticides. In this article, we study the optimal release strategies in order to maximize the efficiency of this technique. We consider simplified models that describe the dynamics of eggs, males, females and sterile males in order to optimize the release protocol. We determine in a precise way optimal strategies, which allows us to tackle numerically the underlying optimization problem in a very simple way. We also present some numerical simulations to illustrate our results.
We consider a production-inventory control model with finite capacity and two different production rates, assuming that the cumulative process of customer demand is given by a compound Poisson process. It is possible at any time to switch over from the different production rates but it is mandatory to switch-off when the inventory process reaches the storage maximum capacity. We consider holding, production, shortage penalty and switching costs. This model was introduced by Doshi, Van Der Duyn Schouten and Talman in 1978. Our aim is to minimize the expected discounted cumulative costs up to infinity over all admissible switching strategies. We show that the optimal cost functions for the different production rates satisfy the corresponding Hamilton-Jacobi-Bellman system of equations in a viscosity sense and prove a verification theorem. The way in which the optimal cost functions solve the different variational inequalities gives the switching regions of the optimal strategy, hence it is stationary in the sense that depends only on the current production rate and inventory level. We define the notion of finite band strategies and derive, using scale functions, the formulas for the different costs of the band strategies with one or two bands. We also show that there are examples where the switching strategy presented by Doshi et al. is not the optimal strategy.
Foams made of complex fluids such as particle suspensions have a great potential for the development of advanced aerated materials. In this paper we study the rheological behavior of liquid foams loaded with granular suspensions. We focus on the effect of small particles, i.e. particle-to-bubble size ratio smaller than 0.1, and we measure the complex modulus as a function of particle size and particle volume fraction. With respect to previous work, the results highlight a new elastic regime characterized by unequaled modulus values as well as independence of size ratio. A careful investigation of the material microstructure reveals that particles organize through the network between the gas bubbles and form a granular skeleton structure with tightly packed particles. The latter is proven to be responsible for the reported new elastic regime. Rheological probing performed by strain sweep reveals a two-step yielding of the material: the first one occurs at small strain and is clearly attributed to yielding of the granular skeleton; the second one corresponds to the yielding of the bubble assembly, as observed for particle-free foams. Moreover the elastic modulus measured at small strain is quantitatively described by models for solid foams in assuming that the granular skeleton possesses a bulk elastic modulus of order 100 kPa. Additional rheology experiments performed on the bulk granular material indicate that this surprisingly high value can be understood as soon as the magnitude of the confinement pressure exerted by foam bubbles on packed grains is considered.
What is the fastest way of finding a randomly hidden target? This question of general relevance is of vital importance for foraging animals. Experimental observations reveal that the search behaviour of foragers is generally intermittent: active search phases randomly alternate with phases of fast ballistic motion. In this letter, we study the efficiency of this type of two states search strategies, by calculating analytically the mean first passage time at the target. We model the perception mecanism involved in the active search phase by a diffusive process. In this framework, we show that the search strategy is optimal when the average duration of motion phases varies like the power either 3/5 or 2/3 of the average duration of search phases, depending on the regime. This scaling accounts for experimental data over a wide range of species, which suggests that the kinetics of search trajectories is a determining factor optimized by foragers and that the perception activity is adequately described by a diffusion process.
We derive equations of motion for the mean-squared displacement (MSD) of an active Brownian particle (ABP) in a crowded environment modeled by a dense system of passive Brownian particles, and of a passive tracer particle in a dense active-Brownian particle system, using a projection-operator scheme. The interaction of the tracer particle with the dense host environment gives rise to strong memory effects. Evaluating these approximately in the framework of a recently developed mode-coupling theory for the glass transition in active Brownian particles (ABP-MCT), we discuss the various regimes of activity-induced super-diffusive motion and density-induced sub-diffusive motion. The predictions of the theory are shown to be in good agreement with results from an event-driven Brownian dynamics simulation scheme for the dynamics of two-dimensional active Brownian hard disks.
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