Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMoving, reproducing, and dying beyond Flatland: Malthusian flocks in dimensions $d>2$
94
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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 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.
We study the multi-scale description of large-time collective behavior of agents driven by alignment. The resulting multi-flock dynamics arises naturally with realistic initial configurations consisting of multiple spatial scaling, which in turn peak at different time scales. We derive a `master-equation which describes a complex multi-flock congregations governed by two ingredients: (i) a fast inner-flock communication; and (ii) a slow(-er) inter-flock communication. The latter is driven by macroscopic observables which feature the up-scaling of the problem. We extend the current mono-flock theory, proving a series of results which describe rates of multi-flocking with natural dependencies on communication strengths. Both agent-based, kinetic, and hydrodynamic descriptions are considered, with particular emphasis placed on the discrete and macroscopic descriptions.
Holomorphic fields play an important role in 2d conformal field theory. We generalize them to d>2 by introducing the notion of Cauchy conformal fields, which satisfy a first order differential equation such that they are determined everywhere once we know their value on a codimension 1 surface. We classify all the unitary Cauchy fields. By analyzing the mode expansion on the unit sphere, we show that all unitary Cauchy fields are free in the sense that their correlation functions factorize on the 2-point function. We also discuss the possibility of non-unitary Cauchy fields and classify them in d=3 and 4.
The chiral spin-glass Potts system with q=3 states is studied in d=2 and 3 spatial dimensions by renormalization-group theory and the global phase diagrams are calculated in temperature, chirality concentration p, and chirality-breaking concentration c, with determination of phase chaos and phase-boundary chaos. In d=3, the system has ferromagnetic, left-chiral, right-chiral, chiral spin-glass, and disordered phases. The phase boundaries to the ferromagnetic, left- and right-chiral phases show, differently, an unusual, fibrous patchwork (microreentrances) of all four (ferromagnetic, left-chiral, right-chiral, chiral spin-glass) ordered ordered phases, especially in the multicritical region. The chaotic behavior of the interactions, under scale change, are determined in the chiral spin-glass phase and on the boundary between the chiral spin-glass and disordered phases, showing Lyapunov exponents in magnitudes reversed from the usual ferromagnetic-antiferromagnetic spin-glass systems. At low temperatures, the boundaries of the left- and right-chiral phases become thresholded in p and c. In the d=2, the chiral spin-glass system does not have a spin-glass phase, consistently with the lower-critical dimension of ferromagnetic-antiferromagnetic spin glasses. The left- and right-chirally ordered phases show reentrance in chirality concentration p.
We study incompressible systems of motile particles with alignment interactions. Unlike their compressible counterparts, in which the order-disorder (i.e., moving to static) transition, tuned by either noise or number density, is discontinuous, in incompressible systems this transition can be continuous, and belongs to a new universality class. We calculate the critical exponents to $O(epsilon)$in an $epsilon=4-d$ expansion, and derive two exact scaling relations. This is the first analytic treatment of a phase transition in a new universality class in an active system.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
