Invasion occurs in environments that are normally spatially disordered, however, the effect of such a randomness on the dynamics of the invasion front has remained less understood. Here, we study Fisher’s equation in disordered environments both analytically and numerically. Using the Effective Medium Approximation, we show that disorder slows down invasion velocity and for ensemble average of invasion velocity in disordered environment we have $$\bar{v}=v_0 (1-|\xi |^2/6)$$ v ¯ = v 0 ( 1 - | ξ | 2 / 6 ) where $$|\xi |$$ | ξ | is the amplitude of disorder and $$v_0$$ v 0 is the invasion velocity in the corresponding homogeneous environment given by $$v_0=2\sqrt{RD_0}$$ v 0 = 2 R D 0 . Additionally, disorder imposes fluctuations on the invasion front. Using a perturbative approach, we show that these fluctuations are Brownian with a diffusion constant of: $$D_{C}= \dfrac{1}{8} \xi ^2\sqrt{RD_0 (1-|\xi |^2/3)}$$ D C = 1 8 ξ 2 R D 0 ( 1 - | ξ | 2 / 3 ) . These findings were approved by numerical analysis. Alongside this continuum model, we use the Stepping Stone Model to check how our findings change when we move from the continuum approach to a discrete approach. Our analysis suggests that individual-based models exhibit inherent fluctuations and the effect of environmental disorder becomes apparent for large disorder intensity and/or high carrying capacities.
In this paper, an in silico proof of concept of a spinristor is proposed and provided; a new electronic component that combines a spin-filter and a memristor in a single molecule, useful for in-memory processing. It builds on the idea of an open-shell transition metal ion enclosed within an elliptical fullerene connected to a pair of electrodes. The spin-and electronic-polarization induced by the enclosed open-shell metallic ion leads to differential rectification of the electrons at low voltages applied between the source-drain electrodes, V SD . The position of the encapsulated ion can be switched by a high V SD which leads to a change in the direction of the rectification and the spin-filtering ratio. The system can thus be used as a switching rectifier, that is, a memristor and a spin-filter; therefore, a spinristor. The effect of different linkers on the function of the proposed device is further analyzed to show that linkers reduce the overall conductivity by an order of magnitude, but improve the spin-filtering ratio. The computations suggest that nitrile and isocyanide linkers enhance the rectification, too. To the best of the authors' knowledge, spinristor has no macroscopic counterpart in electronics, so far.
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