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. Talks marked as PUBLIC LECTURES have been given successfully to a wide range of audiences, including non-technical people, high school students etc.


The life and death of turbulence


Turbulence is the last great unsolved problem of classical physics. But there is no consensus on what it would mean to actually solve this problem. In this colloquium, I propose that turbulence is most fruitfully regarded as a problem in non-equilibrium statistical mechanics, and will show that this perspective explains turbulent drag behavior measured over 80 years, and makes predictions that have been experimentally tested in 2D turbulent soap films. I will also explain how this perspective is useful in understanding the laminar-turbulence transition, establishing it as a non-equilibrium phase transition whose critical behavior has been predicted and tested experimentally.  This work connects transitional turbulence with statistical mechanics and renormalization group theory, high energy hadron scattering, the statistics of extreme events, and even population biology.

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

The emergence of collective modes, ecological collapse and directed percolation at the laminar-turbulence transition in pipe flow

or a simpler title:

Statistical Mechanics of the Laminar-Turbulence transition


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.


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


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.



Beyond chaos: the continuing enigma of turbulence


Turbulence is the last great unsolved problem of classical physics.  This seemingly random, unpredictable motion of fluids is pervasive and completely familiar to us all.  Turbulence governs the speed at which rivers flow and the air drag as you drive your car; it is the bane of air travelers.  Turbulence can kill, by causing arteries and aneurisms to burst. Turbulence makes stars twinkle.  Its random but structured patterns have inspired artists and scientists alike.  And yet, despite a century of scientific investigation, our understanding is primarily based upon a mere handful of early seminal insights.  In this talk, I'll try to explain why this problem is so difficult, much harder than chaos, and what it would mean to solve it.  In particular, I will show that regarding turbulence as a problem in non-equilibrium statistical mechanics yields novel predictions that have been tested in two-dimensional turbulence.  Finally, I'll discuss recent dramatic advances in both experiment and theory that account for the way in which fluids start to become turbulent as their flow velocity is increased, making precise mathematical contact with transitional behavior in a seemingly disconnected problem: predator-prey ecosystems.


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


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.


Stochastic Turing Patterns in the Biosphere: From Brains To Biofilms


Why are the patterns of plankton in the ocean so patchy? Why do frequently described geometrical hallucinations tend to fall into one of four different classes of pattern? Why don't we see hallucinations all the time? And why do populations in ecosystems tend to have noisy cycles in abundance? This talk explains how these phenomena all arise from the discreteness of the underlying entities, be they the on-off states of neurons or the numbers of bacteria in a fluid volume of ocean, or the number of signaling molecules in a biofilm. I explain how tools from statistical mechanics can yield insights into these phenomena, and report on a range of studies that include the operation of the primate visual cortex, the behavior of signalling molecules in a forward-engineered synthetic biofilm, and the fluctuating patterns and populations of marine organisms.


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


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

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) .


Evolutionary transitions at the dawn of life: the emergence of the genetic code and biological homochirality


Universal Biology, the Genetic Code and the First Billion Years of Life on Earth

This colloquium concerns two ideas.  First, that there are universal laws of life, which can be deduced by abstracting what we know about life on Earth.  Second, universal dynamical signatures 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 early life was dominated by collective effects, very different from the present era where individuals and species are well-defined concepts.  I will also discuss a second universal signature of life: the complete breaking of chiral symmetry in biological amino acids and sugars, and explain how such transitions can arise in principle as a result of the non-equilibrium dynamics of early-life autocatalytic replicators.


Rapid evolutionary dynamics of bacteria-phage ecosystems: role of mutations and horizontal gene transfer


I present two recent examples that demonstrate how evolution can profoundly influence ecological systems.  In the first, anomalous phase relationships between predator and prey have been observed in the dynamics of ecosystems as a fast response to strong selection among distinct strains from point mutations.  By applying statistical mechanics approach and stochastic simulation to a generic simple model of population dynamics taking into account the cost of defense, I show that the intrinsic stochastic nature of the system alone can genetically lead to the emergence of rapid evolution.  In the second example, I describe a model for how antagonistic predator-prey coevolution can lead to mutualistic adaptation to an environment, as a result of horizontal gene transfer.  Our model is a simple description of ecosystems such as marine cyanobacteria and their predator cyanophages, which carry photosynthesis genes. These genes evolve more rapidly in the virosphere than the bacterial pan-genome, and thus the bacterial population can potentially benefit from phage predation.   By modeling both the barrier to predation and horizontal gene transfer, I study this balance between individual sacrifice and collective benefits.  The outcome is an emergent mutualistic coevolution of improved photosynthesis capability, benefiting both bacteria and phage.  This form of multi-level selection can contribute to niche stratification in the cyanobacteria-phage ecosystem.


Diversity, co-evolution and stability of microbe-phage communities


This talk concerns topics evolutionary ecology related to the question of how microbe-phage communities can be stable, and what sorts of dynamics can arise from the interplay between predation and population dynamics.  If there is time, I want to emphasize two specific ideas: (1) Communities can be stabilized by coevolution, as shown in the dynamics of co-evolving predator-prey interactions, kill-the-winner dynamics and the emergent population structure.  In this class of systems, demographic stochasticity plays a large role in determining the fate and stability of the system.  These ideas are relevant to marine bacteria and their phage.  (2) There are emergent collective interactions between marine cyanobacteria and their phages associated with the important role of horizontal gene transfer.  Counter-intuitively, viral predation can stabilize a bacterial community and even assist it to expand its range.  A specific example of this is the system of marine cyanobacteria Prochlorococcus and its phage.


Is there universality in biology?


It is sometimes said that there are two reasons why physics is so successful as a science. One is that it deals with very simple problems. The other is that it attempts to account only for universal aspects of systems at a desired level of description, with lower level phenomena subsumed into a small number of adjustable parameters. It is a widespread belief that this approach seems unlikely to be useful in biology, which is intimidatingly complex, where "everything has an exception", and where there are a huge number of undetermined parameters.

I will try to argue, nonetheless, that there are important, experimentally-testable aspects of biology that exhibit universality, and should be amenable to being tackled from a physics perspective.  My suggestion is that this can lead to useful new insights into the existence and universal characteristics of living systems.  I will try to justify this point of view by contrasting the goals and practices of the field of condensed matter physics with materials science, and then by extension, the goals and practices of the newly emerging field of “Physics of Living Systems” with biology.

Specific biological examples that I will discuss include the following:

  1. Universal patterns of gene expression in cell biology

  2. Universal scaling laws in ecosystems, including the species-area law, Kleiber’s law, Paradox of the Plankton

  3. Universality of the genetic code

  4. Universality of thermodynamic utilization in microbial communities

  5. Universal scaling laws in the tree of life

The question of what can be learned from studying universal phenomena in biology will also be discussed.  Universal phenomena, by their very nature, shed little light on detailed microscopic levels of description.  Yet there is no point in seeking idiosyncratic mechanistic explanations for phenomena whose explanation is found in rather general principles, such as the central limit theorem, that every microscopic mechanism is constrained to obey.  Thus, physical perspectives may be better suited to answering certain questions such as universality than traditional biological perspectives. Concomitantly, it must be recognized that the identification and understanding of universal phenomena may not be a good answer to questions that have traditionally occupied biological scientists.

Lastly, I plan to talk about what is perhaps the central question of universality in biology: why does the phenomenon of life occur at all?  Is it an inevitable consequence of the laws of physics or some special geochemical accident?  What methodology could even begin to answer this question?  I will try to explain why traditional approaches to biology do not aim to answer this question, by comparing with our understanding of superconductivity as a physical phenomenon, and with the theory of universal computation.


Nigel Goldenfeld, Tommaso Biancalani, Farshid Jafarpour. Universal biology and the statistical mechanics of early life. Phil. Trans. R. Soc. A 375, 20160341 (14 pages) (2017).

Nigel Goldenfeld and Carl R. Woese. Life is Physics: evolution as a collective phenomenon far from equilibrium. Ann. Rev. Cond. Matt. Phys. 2, 375-399 (2011).


Even parasites have parasites: oscillatory population dynamics of mobile genetic elements in your genome


The Statistical Mechanics of Jumping Genes in Your Genome


Transposable elements (TEs), or transposons, are a class of mobile genetic elements that can either move or duplicate themselves in the genome, sometimes interfering with gene expression as a result. Some TEs can code all necessary enzymes for their transposition and are thus autonomous, while non-autonomous TEs are parasitic and must depend on the machinery of autonomous ones. We present and solve a stochastic model to describe the dynamics of non-autonomous/autonomous pairs of retrotransposons in the human genome that proliferate by a copy-and-paste mechanism. We predict noise-induced persistent oscillations in their copy numbers, analogous to predator-prey dynamics in an ecosystem. We discuss if it is experimentally feasible to measure these phenomena in the laboratory, using techniques recently developed in collaboration with Tom Kuhlman to visualize transposon activity in real time in living cells.  We also discuss the possibility to to observe these oscillations over evolutionary time through bioinformatics. This work shows that it is fruitful to regard the genome as an ecosystem that is host to diverse interacting populations.


What can theoretical physics tell us about the origin and evolution of early life?


Life on Earth is wonderfully diverse, with a multitude of life forms, structures and evolutionary mechanisms.  However, there are two aspects of life that are universal --- shared by all known organisms.  These are the genetic code, which governs how DNA is converted into the proteins making up your body, and the unexpected left-handedness of the amino acids in your body.  One would expect that your amino acids were a mixture of left and right-handed molecules, but none are right handed!  In this talk, I describe how these universal aspects of biology can be understood as arising from evolution, but generalised to an era where genes, species and individuality had not yet emerged.  I will also discuss to what extent one can find general principles of biology that can apply to all life in the universe, and what this would mean for the nascent field of astrobiology.


Patterns, universality and computational algorithms

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.  


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

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.


Renormalization Group Approach to Global Asymptotic Analysis

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.


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.

RETIRED COLLOQUIUM (I do not give this any more)

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


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.


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Updated August 2018
Nigel Goldenfeld