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تسجيل مستخدم جديدMoving, reproducing, and dying beyond Flatland: Malthusian flocks in dimensions $d>2$
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We show that Malthusian flocks -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being born and dying during their motion -- belong to a new universality class in spatial dimensions $d>2$. We calculate the universal exponents and scaling laws of this new universality class to $O(epsilon)$ in an $epsilon=4-d$ expansion, and find these are different from the canonical exponents previously conjectured to hold for immortal flocks (i.e., those without birth and death) and shown to hold for incompressible flocks in $d>2$. Our expansion should be quite accurate in $d=3$, allowing precise quantitative comparisons between our theory, simulations, and experiments.
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We show that Malthusian flocks -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being born and dying during their motion -- belong to a new universality class in spatial dimensions $d>2$. We calcu
late the universal exponents and scaling laws of this new universality class to $O(epsilon)$ in a $d=4-epsilon$ expansion, and find these are different from the canonical exponents previously conjectured to hold for immortal flocks (i.e., those without birth and death) and shown to hold for incompressible flocks with spatial dimensions in the range of $2 < d leq 4$. We also obtain a universal amplitude ratio relating the damping of transverse and longitudinal velocity and density fluctuations in these systems. Furthermore, we find a universal separatrix in real (${bf r}$) space between two regions in which the equal time density correlation $langledeltarho({bf r}, t)deltarho(0, t)rangle$ has opposite signs. Our expansion should be quite accurate in $d=3$, allowing precise quantitative comparisons between our theory, simulations, and experiments.
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