arXiv subjects

Alan C. Newell

Publications and source records attributed to Alan C. Newell.

11 recordsLinked to original sources

arXiv2021

Pattern dark matter and galaxy scaling relations

We argue that a natural explanation for a variety of robust galaxy scaling relations comes from the perspective of pattern formation and self-organization as a result of symmetry breaking. We propose a simple Lagrangian model that combines a conventional model for normal matter in a galaxy with a conventional model for stripe pattern formation in systems that break continuous translation invariance. We show that the energy stored in the pattern field acts as an effective dark matter. Our theory reproduces the gross features of elliptic galaxies as well as disk galaxies (HSB and LSB) including their detailed rotation curves, the radial acceleration relation (RAR), and the Freeman law. We investigate the stability of disk galaxies in the context of our model and obtain scaling relations for the central dispersion for elliptical galaxies. A natural interpretation of our results is that (1) `dark matter' is potentially a collective, emergent phenomenon and not necessarily an as yet undiscovered particle, and (2) MOND is an effective theory for the description of a self-organized complex system rather than a fundamental description of nature that modifies Newton's second law.

astro-ph.GA↗

arXiv2020

Computing with non-orientable defects: nematics, smectics and natural patterns

Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they appear as `unphysical' singularities, with non-integrable energy densities in coarse-grained macroscopic models. We develop a principled approach for enriching coarse-grained theories with enough of the `micro-physics' to obtain thermodynamically consistent, well-set models, that allow for the investigations of dynamics and interactions of defects in extended systems. We also develop associated numerical methods that are applicable to computing energy driven behaviors of defects across the amorphous-soft-crystalline materials spectrum. Our methods can handle order parameters that have a head-tail symmetry, i.e. director fields, in systems with a continuous translation symmetry, as in nematic liquid crystals, and in systems where the translation symmetry is broken, as in smectics and convection patterns. We illustrate our methods with explicit computations.

cond-mat.soft↗

arXiv2020

Disk galaxies and their dark halos as self-organized patterns

Galaxies are built by complex physical processes with significant inherent stochasticity. It is therefore surprising that the inferred dark matter distributions in galaxies are strongly correlated with the observed baryon distributions leading to various `Baryon-Halo conspiracies'. The fact that no dark matter candidate has been definitively identified invites a search for alternative explanations for such correlations and we present an approach motivated by the behaviors of self organized patterns. We propose a nonlocal relativistic Lagrangian theory for a `pattern field' which acts as an `effective dark matter', built on the idea that defects in this pattern field couple to the baryonic matter distribution. Our theory accounts for the gross structure of cold disk galaxies. We compute galactic rotation curves and derive various galaxy scaling relations including Renzo's rule, the radial acceleration relation, and the existence of the Freeman limit for central surface brightness.

astro-ph.GA↗

arXiv2018

Pattern Universes

In this essay we explore analogies between macroscopic patterns, which result from a sequence of phase transitions/instabilities starting from a homogeneous state, and similar phenomena in cosmology, where a sequence of phase transitions in the early universe is believed to have separated the fundamental forces from each other, and also shaped the structure and distribution of matter in the universe. We discuss three distinct aspects of this analogy: (i) Defects and topological charges in macroscopic patterns are analogous to spins and charges of quarks and leptons; (ii) Generic (3+1) stripe patterns carry an (energy) density that accounts for phenomena that are currently attributed to dark matter; (iii) Space-time patterns of interacting nonlinear waves display behaviors reminiscent of quantum phenomena including inflation, entanglement and dark energy.

nlin.PS↗

arXiv2017

Elastic sheets, phase surfaces and pattern universes

We connect the theories of the deformation of elastic surfaces and phase surfaces arising in the description of almost periodic patterns. In particular, we show parallels between asymptotic expansions for the energy of elastic surfaces in powers of the thickness $h$ and the free energy for almost periodic patterns expanded in powers of $ε$, the inverse aspect ratio of the pattern field. For sheets as well as patterns, the resulting energy can be expressed in terms of natural geometric invariants, the first and second fundamental forms of the elastic surface, respectively the phase surface. We discuss various results for these energies and also address some of the outstanding questions. We extend previous work on point (in 2D) and loop (in 3D) disclinations and connect their topological indices with the condensation of Gaussian curvature of the phase surface. Motivated by this connection with the charge and spin of pattern quarks and leptons, we lay out an ambitious program to build a multi-scale universe inspired by patterns in which the short (spatial and temporal) scales are given by a nearly periodic microstructure and whose macroscopic/slowly varying/averaged behaviors lead to a hierarchy of structures and features on much longer scales including analogues to quarks and leptons, dark matter, dark energy and inflationary cosmology. One of our new findings is an interpretation of dark matter as the energy density in a pattern field. The associated gravitational forces naturally result in galactic rotation curves that are consistent with observations, while simultaneously avoiding some of the small-scale difficulties of the standard $Λ$CDM paradigm in cosmology.

nlin.PS↗

arXiv2013

Phyllotaxis, Pushed Pattern-Forming Fronts and Optimal Packing

We demonstrate that the pattern forming partial differential equation derived from the auxin distribution model proposed by Meyerowitz, Traas and others gives rise to all spiral phyllotaxis properties observed on plants. We show how the advancing pushed pattern front chooses spiral families enumerated by Fibonacci sequences with all attendant self similar properties and connect the results with the optimal packing based algorithms previously used to explain phyllotaxis. Our results allow us to make experimentally testable predictions.

math.AP↗

arXiv2009

Dynamical Scaling and the Finite Capacity Anomaly in 3-Wave Turbulence

We present a systematic study of the dynamical scaling process leading to the establishment of the Kolmogorov--Zakharov (KZ) spectrum in weak 3-wave turbulence. In the finite capacity case, in which the transient spectrum reaches infinite frequency in finite time, the dynamical scaling exponent is anomalous in the sense that it cannot be determined from dimensional considerations. As a consequence, the transient spectrum preceding the establishment of the steady state is steeper than the KZ spectrum. Constant energy flux is actually established from right to left in frequency space after the singularity of the transient solution. From arguments based on entropy production, a steeper transient spectrum is heuristically plausible.

nlin.CD↗

arXiv2003

Localization and Coherence in Nonintegrable Systems

We study the irreversible dynamics of nonlinear, nonintegrable Hamiltonian oscillator chains approaching their statistical asympotic states. In systems constrained by more than one conserved quantity, the partitioning of the conserved quantities leads naturally to localized and coherent structures. If the phase space is compact, the final equilibrium state is governed by entropy maximization and the final coherent structures are stable lumps. In systems where the phase space is not compact, the coherent structures can be collapses represented in phase space by a heteroclinic connection to infinity.

nlin.PS↗

arXiv2003

Non-stationary Spectra of Local Wave Turbulence

The evolution of the Kolmogorov-Zakharov (K-Z) spectrum of weak turbulence is studied in the limit of strongly local interactions where the usual kinetic equation, describing the time evolution of the spectral wave-action density, can be approximated by a PDE. If the wave action is initially compactly supported in frequency space, it is then redistributed by resonant interactions producing the usual direct and inverse cascades, leading to the formation of the K-Z spectra. The emphasis here is on the direct cascade. The evolution proceeds by the formation of a self-similar front which propagates to the right leaving a quasi-stationary state in its wake. This front is sharp in the sense that the solution remains compactly supported until it reaches infinity. If the energy spectrum has infinite capacity, the front takes infinite time to reach infinite frequency and leaves the K-Z spectrum in its wake. On the other hand, if the energy spectrum has finite capacity, the front reaches infinity within a finite time, t*, and the wake is steeper than the K-Z spectrum. For this case, the K-Z spectrum is set up from the right after the front reaches infinity. The slope of the solution in the wake can be related to the speed of propagation of the front. It is shown that the anomalous slope in the finite capacity case corresponds to the unique front speed which ensures that the front tip contains a finite amount of energy as the connection to infinity is made. We also introduce, for the first time, the notion of entropy production in wave turbulence and show how it evolves as the system approaches the stationary K-Z spectrum.

physics.flu-dyn↗

arXiv2003

Dimensional Analysis and Weak Turbulence

In the study of weakly turbulent wave systems possessing incomplete self-similarity it is possible to use dimensional arguments to derive the scaling exponents of the Kolmogorov-Zakharov spectra, provided the order of the resonant wave interactions responsible for nonlinear energy transfer is known. Furthermore one can easily derive conditions for the breakdown of the weak turbulence approximation. It is found that for incompletely self-similar systems dominated by three wave interactions, the weak turbulence approximation usually cannot break down at small scales. It follows that such systems cannot exhibit small scale intermittency. For systems dominated by four wave interactions, the incomplete self-similarity property implies that the scaling of the interaction coefficient depends only on the physical dimension of the system. These results are used to build a complete picture of the scaling properties of the surface wave problem where both gravity and surface tension play a role. We argue that, for large values of the energy flux, there should be two weakly turbulent scaling regions matched together via a region of strongly nonlinear turbulence.

physics.flu-dyn↗

arXiv1997

Semiconductor Lasers and Kolmogorov Spectra

In this article, we make a prima facie case that there could be distinct advantages to exploiting a new class of finite flux equilibrium solutions of the Quantum Boltzmann equation in semiconductor lasers.

math-ph↗