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تسجيل مستخدم جديدBidimensional intermittent search processes: an alternative to Levy flights strategies
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Levy flights are known to be optimal search strategies in the particular case of revisitable targets. In the relevant situation of non revisitable targets, we propose an alternative model of bidimensional search processes, which explicitly relies on the widely observed intermittent behavior of foraging animals. We show analytically that intermittent strategies can minimize the search time, and therefore do constitute real optimal strategies. We study two representative modes of target detection, and determine which features of the search time are robust and do not depend on the specific characteristics of detection mechanisms. In particular, both modes lead to a global minimum of the search time as a function of the typical times spent in each state, for the same optimal duration of the ballistic phase. This last quantity could be a universal feature of bidimensional intermittent search strategies.
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This review examines intermittent target search strategies, which combine phases of slow motion, allowing the searcher to detect the target, and phases of fast motion during which targets cannot be detected. We first show that intermittent search str
ategies are actually widely observed at various scales. At the macroscopic scale, this is for example the case of animals looking for food ; at the microscopic scale, intermittent transport patterns are involved in reaction pathway of DNA binding proteins as well as in intracellular transport. Second, we introduce generic stochastic models, which show that intermittent strategies are efficient strategies, which enable to minimize the search time. This suggests that the intrinsic efficiency of intermittent search strategies could justify their frequent observation in nature. Last, beyond these modeling aspects, we propose that intermittent strategies could be used also in a broader context to design and accelerate search processes.
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The convergence to the ground state is fast due to a polynomial decrease rate of the temperature.
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cle of an `instant temperature sigma(t) in an external force field. The temperature is supposed to decrease polynomially fast, i.e. sigma(t)approx t^{-theta} for some theta>0. We discover two different cooling regimes. If theta<1/alpha (slow cooling), the jump diffusion Z(t) has a non-trivial limiting distribution as tto infty, which is concentrated at the potentials local minima. If theta>1/alpha (fast cooling) the Levy particle gets trapped in one of the potential wells.
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iance of Levy Flights diverges and the trajectory is characterised by occasional extremely long jumps. Such long jumps significantly decrease the probability to revisit previous points of visitation, rendering Levy Flights efficient search processes in one and two dimensions. To further quantify their precise property as random search strategies we here study the first-passage time properties of Levy Flights in one-dimensional semi-infinite and bounded domains for symmetric and asymmetric jump length distributions. To obtain the full probability density function of first-passage times for these cases we employ two complementary methods. One approach is based on the space-fractional diffusion equation for the probability density function, from which the survival probability is obtained for different values of the stable index $alpha$ and the skewness (asymmetry) parameter $beta$. The other approach is based on the stochastic Langevin equation with $alpha$-stable driving noise. Both methods have their advantages and disadvantages for explicit calculations and numerical evaluation, and the complementary approach involving both methods will be profitable for concrete applications. We also make use of the Skorokhod theorem for processes with independent increments and demonstrate that the numerical results are in good agreement with the analytical expressions for the probability density function of the first-passage times.
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