**Abstracts of talks**

You will find on this page abstracts of talks that I am currently giving. This information is provided for the convenience of institutions where I am giving seminars or colloquia. Talks marked as COLLOQUIUM are suitable for a general audience including graduate students and advanced undergraduates, although I have given them as seminars too. Talks marked as SEMINAR are intended for a more specialised audience.

**COLLOQUIUM or SEMINAR (can be fine-tuned for the expertise of the audience) **

**The ecology of transitional turbulence **

*Nigel Goldenfeld*

Department of Physics

University of Illinois at Urbana-Champaign

Loomis Laboratory

1110 West Green St

Urbana

IL 61801

ABSTRACT

How do fluids become turbulent as their flow velocity is increased? In recent years, careful experiments in pipes and Taylor-Couette systems have revealed that the lifetime of transient turbulent regions in a fluid appears to diverge with flow velocity just before the onset of turbulence, faster than any power law or exponential function. I show how this superexponential scaling of the turbulent lifetime in pipe flow is related to extreme value statistics, which I show is a manifestation of a mapping between transitional turbulence and the statistical mechanics model of directed percolation. This mapping itself arises from a further surprising and remarkable connection: laminar and turbulent regions in a fluid behave as a predator-prey ecosystem. Such ecosystems are governed by individual fluctuations in the population and being naturally quantized, are solvable by path integral techniques from field theory. I explain the evidence for this mapping, and propose how a unified picture of the transition to turbulence emerges in systems ranging from turbulent convection to magnetohydrodynamics.

**COLLOQUIUM**

**The statistical mechanics of hallucinations and the evolution of the visual cortex **

*Nigel Goldenfeld*

Department of Physics

University of Illinois at Urbana-Champaign

Loomis Laboratory

1110 West Green St

Urbana

IL 61801

ABSTRACT

In the normal state of vision, neural excitation patterns are driven by external stimuli. However, accepted models of the visual cortex bear formal similarities to statistical mechanical models describing spatially-extended ecosystems with activation and inhibition. As such, they are subject to fluctuation-induced Turing instabilities, which generically give rise to spatial patterns of neural excitation that would be perceived as hallucinations, masking the true external stimuli. Organisms operating under such conditions would not survive --- for example, they would be easy victims of predators. How is this devastating failure mode finessed by the visual cortex? We analyze the phase diagram of the visual cortex model as a function of its long-range connectivity, and show that the neuronal connections in the visual cortex have evolved precisely the global architecture necessary to mitigate the failure mode: sparse long-range inhibition. These results imply that sparse long-range inhibition plays a previously unrecognized role in stabilizing the normal vision state, and in addition, accounts for the observed regularity of geometric visual hallucinations.

**COLLOQUIUM**

** How networks drove the rapid evolution of early life: clues from the canonical genetic code **

**OR**

**Phase Transitions in Early Life: Clues from the Genetic Code ***(Preferred for some physics-oriented audiences) *

Nigel GoldenfeldDepartment of Physics

University of Illinois at Urbana-Champaign

1110 West Green St

Urbana

IL 61801

Relics of early life, preceding even the last universal common ancestor of all life on Earth, are present in the structure of the modern day canonical genetic code --- the map between DNA sequence and amino acids that form proteins. The code is not random, as often assumed, but instead is now known to have certain error minimisation properties. How could such a code evolve, when it would seem that mutations to the code itself would cause the wrong proteins to be translated, thus killing the organism? Using digital life simulations, I show how a unique and optimal genetic code can emerge over evolutionary time, but only if horizontal gene transfer --- a network effect --- was a much stronger characteristic of early life than it is now. These results suggest a natural scenario in which evolution exhibits three distinct dynamical regimes, differentiated respectively by the way in which information flow, genetic novelty and complexity emerge. Possible observational signatures of these predictions are discussed.

Reference: K. Vetsigian, C.R. Woese and Nigel Goldenfeld. Communal evolution of the genetic code. *Proc. Natl. Acad. Sci.* **103** , 10696-10701 (2006) .

**COLLOQUIUM**

**Roughness-induced criticality and the statistical mechanics of turbulence in pipes and soap films **

*Nigel Goldenfeld*

Department of Physics

University of Illinois at Urbana-Champaign

Loomis Laboratory

1110 West Green St

Urbana

IL 61801

ABSTRACT

Are fluid turbulence and critical phenomena analogous to one another? In this talk, I explain that this connection may be deeper than has been previously thought. Indeed, I argue that one can use these insights to understand turbulence, in an attempt to emulate the pattern of discovery which led to the solution of the phase transition problem. I show that these ideas lead to the prediction of a novel scaling law --- a manifestation of what I term roughness-induced criticality --- that has been verified by analyzing experimental data on turbulent pipe flows, taken by Nikuradze in 1933. I review how the friction experienced by turbulent fluids can be captured quantitatively as a function of flow velocity and wall-roughness, by momentum-transfer arguments due to Gioia and Chakraborty, and describe how this theory and the roughness-induced criticality theory are currently being tested by direct numerical simulations and experiments on two-dimensional turbulent flows in soap films.

References:

- Nigel Goldenfeld. Roughness-induced criticality in a turbulent flow.
*Phys. Rev. Lett.***96**, 044503:1-4 (2006). - N. Guttenberg and Nigel Goldenfeld. The friction factor of two-dimensional rough-boundary turbulent soap film flows arXiv:0808.1451v4 (2008)
- G. Gioia and P. Chakraborty. Turbulent friction in rough pipes and the energy spectrum of the phenomenological theory.
*Phys. Rev. Lett.*96, 044502:1-4 (2006).

**COLLOQUIUM**

**Statistical Physics, Biological Complexity and Pattern Formation at Yellowstone's Hot
Springs**

*Nigel Goldenfeld
*Department of Physics

University of Illinois at Urbana-Champaign

1110 West Green St

Urbana

IL 61801

Abstract

Biocomplexity is the term that is becoming used to describe efforts to understand strongly-interacting dynamical systems with a biological, ecological or even social component. I provide a brief overview of why this field is not only interesting for physicists, but can benefit substantially from their participation. In particular, microbes represent a fascinating opportunity for physicists to contribute to biology, because their strong interactions, via both signalling and exchange of genes, means that the techniques of statistical mechanics are ideally suited to exploring the ecology of microbial communities and the evolutionary dynamics of microbial genomes.

As a case study of biocomplexity, I present my own work on geobiological pattern formation at Yellowstone's Mammoth Hot Springs, where heat-loving microbes may play a role in the dynamics of landscape evolution. I'll describe my group's recent field, experimental and theoretical work on the possible role of microbes in creating scale-invariant travertine terraces at geothermal hot springs. The ability to distinguish both ancient and modern geological features that are biologically influenced from those that are purely abiotic in origin can potentially advance our understanding of the timing and pattern of evolution, and may even provide a tool with which to identify evidence for life on other planets.

Work performed in collaboration with: G. Bonheyo, J. Frias-Lopez, H. Garcia Martin, J.
Veysey, B. Fouke.

Work supported by the US National Science Foundation.

**COLLOQUIUM**

**Patterns, universality and computational algorithms**

Nigel GoldenfeldDepartment of Physics

University of Illinois at Urbana-Champaign

1110 West Green St

Urbana

IL 61801http://guava.physics.uiuc.edu/~nigel

Can we use computational algorithms to make accurate predictions of physical phenomena? In this talk, intended for non-experts, I will give examples where complicated space-time phenomena can be exquisitely captured with simple computational algorithms, that not only produce patterns resembling those seen in experiment, but also make accurate predictions about probes of dynamics and spatial organisation, such as correlation functions. I use examples from condensed matter physics, as well as from geophysics.

Because many patterns involve structure on multiple length and time scales, I also discuss how one can develop multiscale methods for real materials processing from the nanoscale on up. I show that a computationally-efficient multiscale approach can be developed systematically by using renormalization group or equivalent techniques to derive appropriate coupled phase and amplitude equations, which can then be solved by adaptive mesh refinement algorithms.

Work supported by National Science Foundation and NASA.

**SEMINAR**

**Statistical mechanics of genes: an emergent mechanism for speciation in microbes**

*Nigel Goldenfeld
*Department of Physics

University of Illinois at Urbana-Champaign

1110 West Green St

Urbana

IL 61801

I show that strongly-interacting communities of microbes exhibit a non-trivial phase diagram that depends upon the details of homologous recombination and the competition with point mutation. Possible phases include one that is genetically uniform, and another that is biodiverse. A comparative genomic study of sequenced, closely-related microbial genomes finds evidence for the predicted signature of this phase transition in Bacillus. This work highlights the important role that emergent, collective effects can play in determining microbial community structure and speciation.

**SEMINAR**

**Beyond phase field models: renormalization group approach to multiscale modeling in materials science **

*Nigel Goldenfeld
*Department of Physics

University of Illinois at Urbana-Champaign

1110 West Green St

Urbana

IL 61801

Dendritic growth, and the formation of material microstructure in general, necessarily involves a wide range of length scales from the atomic up to sample dimensions. Phase field models, enhanced by optimal asymptotic methods and adaptive mesh refinement, cope with this range of scales, and provide a very efficient way to move phase boundaries. However, they fail to preserve memory of the underlying crystallographic anisotropy. Elder and Grant have convincingly shown how one can use the phase field crystal (PFC) equation -- a conserving analogue of the Swift-Hohenberg equation -- to create field equations with periodic solutions that model elasticity, the formation of solid phases, and accurately reproduce the nonequilibrium dynamics of phase transitions in real materials. In this talk, I show that a computationally-efficient multiscale approach to the PFC can be developed systematically by using the renormalization group or equivalent techniques to derive the appropriate coupled phase and amplitude equations, which can then be solved by adaptive mesh refinement algorithms.

**SEMINAR**

**Renormalization Group Approach to Global Asymptotic Analysis**

*Nigel Goldenfeld*

University of Illinois at Urbana-Champaign

Loomis Laboratory

1110 West Green St

Urbana

IL 61801

Renormalization and the renormalization group (RG) were originally developed by physicists attempting to understand the divergent terms in perturbation theory and the short distance behaviour of quantum electrodynamics. During the last few years, these methods have been used to study the divergent terms in perturbation theory and the long time behaviour of a variety of nonlinear partial differential equations. Problems studied include similarity solutions, especially intermediate asymptotics of the second kind (Barenblatt classification), and travelling waves. Examples include: porous medium equation, propagation of turbulence and the Fisher-Kolmogorov-Petrovsky-Piskunov equation.

Most recently, singular perturbation problems for nonlinear differential equations have been treated, with particular attention paid to multiple-scale analysis, boundary layers and WKB, and matched asymptotics.

The RG method starts from a regular perturbation expansion in the small parameter, and automatically generates an asymptotic sequence without requiring the user to make insightful guesses as to the presence of "unexpected" powers, logarithms, etc. The RG-generated uniform approximation is practically more useful than that generated by matched asymptotics, even when extended to values of the small parameter of order unity.

Reference:

- L.Y. Chen, N. D. Goldenfeld and Y. Oono. The renormalization group and singular perturbations: multiple-scales, boundary layers and reductive perturbation theory. Phys. Rev. E 54, 376-394 (1996).

Work performed in collaboration with Yoshitsugu Oono, L.-Y. Chen, O. Martin, F. Liu.

**Please note: A longer and more detailed version of the material in this
talk and that in my talk on Under-resolved Computation has also been given as a
mini-course of 3 lectures, including topics such as similarity solutions and anomalous
dimensions, front propagation and RG.**

Back to Nigel Goldenfeld's Home Page

*Updated August 2014
Nigel Goldenfeld*