By Professor Alexander S. Mikhailov, Dr. Vera Calenbuhr (auth.)
This ebook indicates how, via relatively easy types, we will be able to achieve impressive insights into the habit of advanced structures. it's dedicated to the dialogue of sensible self-organization in huge populations of interacting energetic parts. the potential kinds of self-organization in such platforms diversity from coherent collective motions within the actual coordinate house to the mutual synchronization of inner dynamics, the advance of coherently working teams, the increase of hierarchical buildings, and the emergence of dynamical networks. Such procedures play a tremendous position in organic and social phenomena. The authors have selected a sequence of versions from physics, biochemistry, biology, sociology and economics, and may systematically speak about their common homes. The booklet addresses researchers and graduate scholars in quite a few disciplines, equivalent to physics, chemistry, biology and the social sciences.
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This mode describes a velocity modulation in the direction of motion. 33), the sound waves have frequency w = -Janok sin 7/J and speed s = w/k = Yanosin7/J. We see that this speed depends on the propagation direction, decreasing for the sound waves that propagate closer to the x-axis. The speed s vanishes and the respective modes become purely dissipative at 7/J = o. This behavior is different from the properties of sound waves in classical isotropic fluids, where the Galilean invariance prohibits any dependence of the sound on the angle between the wavevector and the flow direction.
Suppose that each particle represents a solid disk of radius Ro. The surfactant is continuously produced at rate J per unit time inside the particle and released into the liquid through a small hole located at the center of the disk bottom. This surfactant diffuses through the liquid with the diffusion constant D and modifies its surface tension. The capillary coefficient T, which gives the magnitude of the capillary force acting per unit length of the solid-liquid contact line, depends as T = To - J-LC on the local surfactant concentration c.
In reality, the pheromone concentration in the air close to the ground fluctuates because of the turbulence in the atmosphere. This can be taken phenomenologically into account by replacing the calculated concentration field c(r, t) with c(r, t)(l+c~(r, t)), where ~(r, t) is white noise of unit intensity and c is a parameter that specifies the mean amplitude of fluctuations. The ants sense the pheromone concentration in a thin air layer close to the surface (z -+ 0). e. tlC = l(k· V'c), where l is the distance between the left and right antennae and k is the unit vector with the components kx = sin () and ky = - cos ().
From Cells to Societies: Models of Complex Coherent Action by Professor Alexander S. Mikhailov, Dr. Vera Calenbuhr (auth.)