Diffusion Fundamentals (E-Journal)

Bastidon, Cécile

Durlauf, Steven N.

Parent, Antoine

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   diffusion-fundamentals.org, Vol. 37 (2023) 3, URL: https://diffusion-fundamentals.org/journal/37/2023/3.pdf 
Diffusion in Cliometrics and Complexity: The role of popular societies in 
the dynamic spread of revolutionary ideas in 1789 France 
Cécile Bastidon1,4, Steven Durlauf2, Antoine Parent3,4,* 
1 LEAD, Univ. Toulon and CAC-IXXI 
2 Steans Professor, Harris School of Public Policy, Univ. of Chicago 
Director, Stone Center for Research on Wealth Inequality and Mobility 
Chair, Committee on Quantitative Research Methods in Social, Behavioral and Health Sciences 
3 LED, Univ. Paris 8; OFCE – Sciences-Po 
4 CAC-IXXI, Institut des Systèmes Complexes, Lyon 
* Presenting author: antoine.parent02@univ-paris8.fr
(Received: 2023/06/20, Published online: 2023/06/24) 
In this lecture, we consider whether popular societies were a place of diffusion of a plural thought 
during the French revolution. The motivation for this research is the following: should we believe the 
classic Cochin thesis (1921), advocated in modern times by Furet (1979) and Furet and Ozouf 
(1988), that Jacobin clubs were places of “brainwashing” and as such precursors of what was seen 
in the Soviet Union and Peoples Republic of China? Do historiographical sources on the popular 
societies corroborate this perspective, which constit utes the dominant historiographical view today? 
Our examination of the historical evidence produces a far more nuanced picture than that drawn by 
these authors. The first step of our research has consisted in reading the collection of monographs of 
“Popular societies” gathered by historians for the bicentenary of the French Revolution under the 
title « Les Sociétés populaires à travers leurs procès-verbaux », published by the Editions du Comité 
des travaux historiques et scientifiques in 2018, to identify the patterns of Revolutionary thought. To 
the best of our knowledge, this source is the most complete for understanding, at the local level, the 
way these societies of thought functioned in revolutionary France, from their beginning in 1789 to 
their end in 1795. These sources include the minutes of the deliberations, the correspondence, the list of 
newspaper subscriptions, the list of members, etc. They are an irreplaceable source for understanding 
intellectual currents at the local level, exhibiting the political and philosophical debates of the 
clubs and the sociological composition of their members. This source demonstrates that these 
popular societies were (i) places of philosophical and political debate about the ideal city, (ii) 
representative of the diversity of professions of French society at the time. 
Reading the monographs of Sociétés populaires challenges the conventional wisdom of Cochin 
(1921), Furet (1979), and Furet and Ozouf (1988). These authors reject a democratic vision of 
the French revolution in favor of a vision of the Revolution as illiberal and ultimately 
authoritarian. These monographs reveal (i) an undeniable pluralism of ideas within the clubs and 
between the clubs, and (ii) a profound diversity in the sociological composition of these clubs. Deep 
heterogeneities and differences existed between the clubs. The clubs, even those affiliated with the 
Jacobin Club of Paris, were places of hearing, exchange, reflection, and transmission of ideas with 
significant philosophical differences existing between clubs in the same location. When single club 
was present in a location, we find intra-club pluralism. Our findings help challenges the conventional 
view that societies of thought were the vehicle of a uniform Jacobin thought. On the contrary, the 
monographs of popular societies provide evidence of a democratic impulse underlying debates over 
ideas. This intellectual diversity reflects a sociological diversity among club members that contrasts 
with the fixed society of ancient regime. We give evidence that these two characteristics of 
popular societies coincide with the diffusion of revolutionary ideas outside popular societies. 
The open question we address to the community in 
1 
2 
Diffusions fundamentals is the following: Were these two inner characteristics a necessary and 
sufficient condition for the diffusion of revolutionary ideas outside clubs? Discussions with physicists 
and scientists specialized in diffusion fundamentals will help envisage innovative tools to analyze the 
process of diffusion of ideas outside clubs, more specifically how the internal characteristics of these 
clubs facilitated the external diffusion of revolutionary ideas, at the tipping point of the French 
Revolution. Interactions with physicists should help defining new methods to enrich the cliometric and 
complexity approach to revolutions and revisit conventional historical wisdom on the French revolution. 
References 
A. Cochin, 1921. Les sociétés de pensée et la démocratie. Etudes d'histoire révolutionnaire. Paris. Plon.
F. Furet, M. Ozouf (Eds). 1988. Dictionnaire critique de la Révolution française. Flammarion.
F. Furet. 1979. Penser la Révolution française. Gallimard.
P. Gueniffey, R. Halevi. 1988. “Clubs et sociétés populaires” in Dictionnaire critique de la Révolution française, Furet F. et M.
Ozouf  (Eds), Flammarion.
S. Bianchi (sous la dir.). 2018. Les sociétés populaires à travers leurs procès-verbaux, éd. électronique, Paris, Éd. du Comité
des travaux historiques et scientifiques (Actes des congrès nationaux des sociétés historiques et scientifiques).


English

Diffusion in Cliometrics and Complexity: The role of popular societies in the dynamic spread of revolutionary ideas in 1789 France

Weber, Shlomo

Wiesmeth, Hans

Kärger, Jörg

This work is licensed under a Creative Commons Attribution 4.0 International License. 
   diffusion-fundamentals.org, Vol. 37 (2023) 1, URL: https://diffusion-fundamentals.org/journal/37/2023/Editorial.pdf 1 
Foreword: Special issue "Diffusion Fundamentals X" 
Shlomo Weber, Hans Wiesmeth, Jörg Kärger 
(Received: 2023/11/20, Published online: 2023/11/23) 
This Foreword opens a Special Issue: 
A collection of abstracts of invited lectures 
The Diffusion Fundamentals conference is a well-established biennial event that has been initiated in 
2005 - the year of the 150th anniversary of Adolf Fick's and the 100th anniversary of Albert Einstein's 
fundamental papers on diffusion. This first conference has taken place at Leipzig where these two 
seminal papers have been published. Continuing a very successful series of conferences in Europe 
(L'Aquila 2007, Athens 2009, Leipzig 2013, Dresden 2015, Moscow 2017, Erlangen 2019, Krakow 
2022) and the Americas (Troy, NY, USA, 2011) the 10th jubilee conference has now been held in 
September 2023 in Tashkent, Uzbekistan, as its first visit to Asia. After the organization of DF IX was 
delayed by a year due to the COVID pandemic, the conference series has thus returned to its traditional 
rhythm of being held in odd-numbered years. 
Tashkent, the capital of Uzbekistan, is renowned for its vibrant cityscape and rich cultural heritage as 
one of the leading trade centers along the Silk Road. Together with the New Uzbekistan University as 
an upcoming stronghold of science, Tashkent has thus been an ideal host for the 10th Diffusion-
Fundamentals jubilee conference. 
The Diffusion Fundamentals (DF) conference series is dedicated to spreading phenomena wherever they 
may occur. Spreading (often, essentially synonymously, referred to as “diffusion”) may be observed 
over microscopic just as over macroscopic dimensions. It may be observed with atoms and molecules 
as the elementary constituents of our matter, with biological species in our environment and with, finally, 
us human beings and our material and immaterial “products”. As a common feature, it appears in the 
spreading behavior of the “objects” considered in the various areas. Observation, classification, and 
comprehension of these phenomena are thus among the main objectives for the scientists in the different 
disciplines, ranging from social sciences and humanities to engineering and natural sciences. By 
bringing together scholars from all these disciplines, DF X has once again succeeded in creating an 
atmosphere, ideally suited to stimulating an exciting exchange of ideas.  
Following the conference format as started with DF VIII in Erlangen, 2019, the conference comprised 
invited talks, poster presentations and workshops. The workshops were scheduled to be performed in 
the manner of “round table discussions”, following one or a couple of introductory talks. Under the title 
“Diffusion of and in Language” a workshop, jointly shared by Gero Vogl, Vienna, and Uwe Junghanns, 
Göttingen, dealt with the two-fold occurrence of spreading phenomena in our language, comprising 
language shifts caused by contacts between different speech communities and the spreading of 
properties, features and functions of a language within one and the same linguistic system. A second 
workshop, chaired by Jörg Kärger, Leipzig, was dedicated to “Diffusion in Nanoporous Materials”, in 
continuation of an initiative launched by the IUPAC (“International Union of Pure and Applied 
Chemistry”) on this topic.  
2 
The poster session included presentations, by Qu Chen, Hangzhou, on “Molecular Dynamics Simulation 
on Self-diffusion Coefficients of CO2 in Substituted Amines”,  Joaquim Pérez-Losada, Girona, on 
“Diffusion of Humans out of Africa and the Phonemic Diversity Cline”,  Patricia Seidel, Leipzig, on 
“Diffusion and Adsorption of 2-methylpentane and 3-methylpentane in Silicalite-1 Crystals” and Nicole 
Trebel, Marburg, on “Confinement Effects on Distribution and Transport of Neutral Solutes in a Small 
Hydrophobic Nanopore”. Extended abstracts of these posters may be found in the subsequent volume 
38 of the Diffusion Fundamentals Online Journal. 
Traditionally, the invited plenary lectures were at the heart of the conference. A particular pleasure for 
the conference participants was to be able to experience scientists from the host country Uzbekistan, 
including Boris Goldengorin, Servar Abdullaev and Bobomurat Ahmedov.  The present volume 37 
provides an overview of all lectures held on the core topic of the conference, i.e. on “Diffusion in Nature, 
Technology and Society”, with a compilation of the extended abstracts. Together with the contributions 
written by established representatives of the individual disciplines, it also contains the abstract of Felix 
Hagemann's presentation, to which he was invited in recognition of his nomination for the Young 
Researcher Award 2023 of the Saxon Academy of Sciences and Humanities. 
The Saxon Academy of Sciences and Humanities has taken over the patronage of the Diffusion-
Fundamentals conference series in 2015 during its 6th meeting in Dresden, simultaneously with the 
edition of a text book with the programmatic title “Diffusive Spreading in Nature, Technology and 
Society”, emerging from the contributions held during this conference. Fortunately, a greatly expanded 
new edition of this book (meanwhile honored with the Literature Prize 2019 of the Fund of Chemical 
Industry) was published prior to the 10th anniversary conference and several authors made it possible 
to attend. Special mention should be made of Jean-Philippe Platteau, Shlomo Weber and Hans 
Wiesmeth, whose contribution "The Fight against COVID-19: The Gap between Epidemiologic and 
Economic Approaches" significantly enriched the new edition with its treatment of a hot current topic 
(having led to the delay with the previous conference), and Marc-Olivier Coppens, who spoke on the 
topic of his book chapter "Nature-Inspired Optimization of Transport in Porous Media" not only within 
the frame of the conference, but also to the students in a well-attended, regular course lecture at New 
Uzbekistan University. The support of the publisher, Springer Nature, which provided us with several 
complimentary copies of this book for the conference, is gratefully acknowledged. 
In a ceremonial opening event in the large lecture hall of the New Uzbekistan University, which was 
also well attended by many local visitors, the conference participants were cordially welcomed by 
Khilola Umarova, Minister of Preschool and School Education of Uzbekistan, and Odil 
Abdurakhmanov, Advisor to the President of Uzbekistan on Youth, Education, Health, Culture and 
Sports. Their speeches were followed by Shlomo Weber, conference chair, and Hans Wiesmeth, 
President of the Saxon Academy of Sciences and Humanities, who included a special welcome to Jörg 
Kärger and Paul Heitjans in the audience as the “fathers” of the conference series by jointly organizing 
its first event in 2005 in Leipzig.  
In their closing remarks, Yuldashev Bakhtiyor, Vice-rector of the New Uzbekistan University, and 
Shlomo Weber once again expressed their sincerest thanks to all participants for coming to Tashkent 
and for contributing to the great success of this conference - followed by the invitation of attending the 
subsequent DF conference taking place in 2025 at the Northwestern University in Evanston, Il, USA. 
The hearty applause that followed was especially for also Dinara Datbayeva for her excellent work in 
dealing with all the administrative challenges that have emerged with the organization of this 
conference. 
Generous support of the conference by Ziyaev Foundation, Friedrich-Ebert-Stiftung, Center for 
Progressive Reforms of Uzbekistan, Bruker BioSpin GmbH, Springer Nature and Shell is gratefully 
acknowledged. 


Foreword: Special issue "Diffusion Fundamentals X"

Maeir, Aren M.

This work is licensed under a Creative Commons Attribution 4.0 International License. 
   diffusion-fundamentals.org, Vol. 37 (2023) 5, URL: https://diffusion-fundamentals.org/journal/37/2023/5.pdf 
1 
Movement of artifacts, people and ideas in antiquity 
Aren M. Maeir 
Bar-Ilan University, Ramat-Gan, ISRAEL 
arenmaeir@gmail.com 
(Received: 2023/07/07, Published online: 2023/07/07) 
In this lecture, I will discuss evidence for connectivity in the ancient Near East and beyond during the 
Bronze and Iron Ages (ca. 3rd to late 1st mill BCE). Based on materials finds and historical documents, 
a broad range of materials were traded over large distances, between disparate regions, from NW Europe 
to SE Asia and from northern Europe and sub-Saharan Africa. I will bring examples of evidence of these 
wide connections, many only recently revealed through new analytic techniques. I will then discuss the 
possible cultural implications of these long-term connections, and how it changes our understanding of 
the ancient concepts of geography. 
Reference 
Maeir, A. M. (2023) [in press]. “Their voice carries throughout the earth, their words to the end of the world” (Ps. 19, 5): 
Thoughts on long-range trade in organics in the Bronze and Iron Age Levant, in “And in Length of Days Understanding” 
(Job 12:12) - Essays on Archaeology in the 21st Century in Honor of Thomas E. Levy, edited by E. Ben-Yosef & I. W. N. 
Jones (Springer, Cham, 2023). 


Movement of artifacts, people and ideas in antiquity

Fritzsche, Albrecht

This work is licensed under a Creative Commons Attribution 4.0 International License. 
1 
Changing topologies of innovation diffusion and their implications for 
generativity 
Albrecht Fritzsche1, 2 
1Université Internationale de Rabat, Rabat, Morocco 
2IEDC – Bled School of Management, Bled, Slovenia 
albrecht.fritzsche@uir.ac.ma 
(Received: 2023/07/31, Published online: 2023/08/01) 
The term generativity has been coined by Erikson [1] to describe a concern in human beings for 
establishing and guiding the next generation. In cognitive science, Epstein [2],[3] has propagated the 
usage of the term to explain creativity, spontaneity, and the emergence of novelty. Innovation research 
has lately started using the term generativity to describe the ability of organizations and larger business 
ecosystems to stay innovative over time, coming up with attractive new offerings when the old ones 
have penetrated their markets [4].  
Most approaches to generativity in this field study heuristic methods of engineering design [5],[6] or 
structural properties of innovation hotspots [7], [8]. These approaches are informed by evolutionary 
models of innovation as reproduction and survival under selective pressure from the environment [9]. 
They have provided numerous interesting insights, but still leave many questions unanswered. In 
particular, they do add much to a better understanding as to why innovation hubs in developing countries 
are hardly able to reach the generativity that can be observed in industrialized countries, despite 
immense efforts put into their establishment and operation [10]. 
The work presented here therefore advocates a different approach. Inspired by earlier contributions to 
the Diffusion Fundamentals series [11] [12], it argues that generativity is not sufficiently explained by 
the description of design processes and conditions of their application. It is also necessary to give 
account of the structural changes in society that each successful innovation entails. An innovation must 
be considered as a vehicle that transports a narrative of value creation, which affects the conditions 
under which all follow-up innovations can spread through society. In other words, each innovation sets 
the stage for the diffusion of future innovations in its own way. This effect needs to be considered in the 
discussion of generativity as well. 
Formally speaking, this dynamic can be described as a change of topological structure. Using a cellular 
automaton as a model for innovation diffusion, such a change would need to be addressed on two 
different levels. On the one hand, prior innovations would need to be considered to have an effect on 
the adoption/ infection probabilities of the single cells for new innovations. On the other hand, prior 
innovations would also need to be considered to have a more radical effect, changing the neighborhood 
relations of the cells. A simple example is the spread of new means of transportation, which change the 
paths on which subsequent innovations spread. Overall, each innovation can be expected to have such 
an effect, although it might be not as obvious as in this example. Regarding the two levels of change in 
the model of the cellular automaton, it should be mathematically possible to reflect changing adoption/ 
infection probabilities and neighborhood relations in the same distance measure. This, however, will not 
further be explored here. 
To give more insight into the explanatory power of this approach to generativity, we present findings 
from a comparative case study in Morocco. For the subject matter at hand, Morocco is particularly 
interesting, because parts of the country are highly industrialized and offer standards of living 
comparable to Western Europe, while other parts are still in an earlier stage of socio-economic 
development.  Each case in this study concerns a recent Moroccan innovation, which is assessed in terms 
of its technical inventiveness and sophistication, its value proposition and target audience, as well as its 
effect on the topological structures for the spread of further innovation. The assessment is based on 
document studies and expert interviews.  
  diffusion-fundamentals.org, Vol. 37 (2023) 10, URL: https://diffusion-fundamentals.org/journal/372023/10.pdf 
2 
After initial screening or 247 candidates, 13 innovations were finally studied in detail, ranging across 
numerous application domains and value propositions. The level of technical sophistication and 
innovativeness of the innovations varies a lot, with some of them qualifying rather as user innovations, 
while others can be considered as state-of-the-art high-tech. Interestingly enough, however, none of the 
innovations were estimated to have a significant impact on the topological structures for the spread of 
further innovations. In view of these results, innovations preceding the ones studied in these cases were 
analyzed as well. Most of these preceding innovations originated in highly industrialized countries. 
Moreover, their impact on topological structures was found to be much stronger than for the others. 
The study has various implications for theory and practice. Regarding theory, it shows the added value 
of diffusion models for the study of generativity in innovation research. Such models make it possible 
to address the topological implications of subsequently spreading innovations, which have so far not 
received the attention that they deserve. Moreover, the study shows how research on diffusion processes 
can step beyond the analysis fixed structural conditions under which something spreads, using a more 
dynamic approach to space that takes the possibility of change over time into account. Where social 
phenomena are concerned, this seems to be highly important. Regarding practice, the study can inform 
future steps of policy-making to increase generativity in developing countries, as it shows that 
investments should not only be taken to increase technical sophistication and inventiveness, but also to 
anticipate future implications of the innovations that are encouraged and subsidized. 
Future work in this area will have to move from qualitative, exploratory studies to more robust, 
quantitative empirical work. Furthermore, simulations may help to learn more about the phenomena 
studied here and to distinguish different patterns of structural change of diffusion topologies.   
 
References 
[1] E.H. Erikson, Childhood and society, London: Penguin Books (1950). 
[2] R. Epstein, Skinner, creativity, and the problem of spontaneous behavior, Psychological Science, 2 (1991) 362-370. 
[3] R. Epstein, Generativity theory and education. Educational Technology, 33 (1993) 40-45. 
[4] L.D. Thomas, R. Tee, Generativity: A systematic review and conceptual framework, International Journal of Management 
Reviews, 24 (2022) 255-278. 
[5] D. Tilson, K. Lyytinen, C. Sorensen, Digital infrastructures: The missing IS research agenda, Information Systems 
Research, 21 (2010) 748–759. 
[6] P. Le Masson, A. Hatchuel, M. Le Glatin, M., B. Weil, Designing decisions in the unknown: A generative model, European 
Management Review, 16 (2019) 471-490. 
[7] J.L. Zittrain, The generative internet, Harvard Law Review, 119 (2006) 1974–2040. 
[8] J.M. Bauer, Platforms, systems competition, and innovation: Reassessing the foundations of communications policy, 
Telecommunications Policy, 38 (2014) 662–673. 
[9] D.E. Goldberg, The Design of innovation: Lessons from and for competent genetic algorithms, Boston: Kluwer (2002).  
[10] V.Y. Atiase, O. Kolade, T.A. Liedong, The emergence and strategy of tech hubs in Africa: Implications for knowledge 
production and value creation, Technological Forecasting & Social Change 161 (2020) 120307. 
[11] A. Fritzsche, Spreading Innovations, Models, Designs, and Research Directions, in: A. Bunde, J. Kärger, J. Caro, G. Vogl 
(Eds.), Diffusive Spreading in Nature, Technology and Society, Springer, Cham, 2018, pp. 277–294. 
[12] A. Grunwald, The spreading of techno-visionary futures, in: A. Bunde, J. Kärger, J. Caro, G. Vogl (Eds.), Diffusive 
Spreading in Nature, Technology and Society, Springer, Cham, 2018, pp. 295-309. 
 


Changing topologies of innovation diffusion and their implications for generativity

Seidel, Patricia

Shi, Kaihang

Chmelik, Christian

Goepel, Michael

Snurr, Randall

Gläser, Roger

This work is licensed under a Creative Commons Attribution 4.0 International License. 
   diffusion-fundamentals.org, Vol. 38 (2023) 6, URL: https://diffusion-fundamentals.org/journal/38/2023/6.pdf 
Diffusion and adsorption of 2-methylpentane and 3-methylpentane in 
silicalite-1 crystals 
Patricia Seidel1*, Kaihang Shi2, Christian Chmelik3, Michael Goepel1, Randall Snurr2, 
Jörg Kärger3, Roger Gläser1
1Institute of Chemical Technology, Universität Leipzig, 04103 Leipzig, Germany 
2Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA 
3Faculty of Physics and Earth Sciences, Universität Leipzig, 04103 Leipzig, Germany 
*Presenting author: p.seidel@uni-leipzig.de
(Received: 2023/06/19, Published online: 2023/06/24) 
Introduction 
Molecular diffusion is often a key criterion for the performance of microporous materials in 
technological applications [1]. Due to the intimate contact of guest molecules with the inner surface of 
microporous adsorbents, slight changes in the structure of the guest molecules may already lead to 
considerable changes in their diffusion behavior. One example of such behavior, which is investigated 
in this study, is the diffusion of 2-methylpentane (2MP) and 3-methylpentane (3MP) in large crystallites 
of silicalite-1 studied via IR microscopy (IRM). Furthermore, a rationalization of the observed large 
differences (factor of 3) in the transport diffusivity of 2MP and 3MP using both Grand Canonical Monte 
Carlo (GCMC) and dynamically corrected transition state theory (dcTST) simulations is attempted. 
Experimental 
Silicalite-1 was prepared via a synthesis adapted from Mueller and Unger [2] using Ludox® as silica 
precursor, aqueous ammonia solution as base and tetrapropylammonium as structure-directing agent. 
The molar composition of the synthesis gel was 59:4:123:2280 (SiO2/(TPA)2O/(NH4)2O/H2O). 
Diffusion investigations were conducted with a Bruker Hyperion 3000 IR microscope attached to a 
Bruker Vertex 80 FT-IR spectrometer with polychromatic MIR source, Michelson Interferometer and a 
single element MCT (mercury cadmium telluride) detector. Grand canonical Monte Carlo simulations 
were carried out using the RASPA2 package [3] using force field parameters from Dubbeldam [4] to 
predict the single component sorption isotherms. To estimate the self-diffusivity of 2MP and 3MP the 
dynamically corrected TST method was used [5]. 
Results and Discussion 
The adsorption isotherms in Fig. 1. show that 2MP adsorbs more strongly at loadings < 4 molecules per 
unit cell while the equilibrium loading is higher for 3MP at loadings > 4 molecules per unit cell. The 
experimental data obtained is in good agreement with GCMC simulations for silicalite-1 in its 
monoclinic state. Additionally, the loading dependent transport diffusivities were studied. The transport 
diffusivity only marginally increases below a loading of 4 molecules per unit cell, but strongly increases 
for a higher loading in the case of both 2MP and 3MP. While the trend observed for both molecular 
probes is the same, the transport diffusivity of 2MP is 2.0 – 4.5 times higher than that of 3MP. This is 
attributed to lower energy barriers for 2MP mobility, differences in the energy profiles and the 
orientation of both molecules inside the pore system with the help of dcTST simulations.
1 
10-2 10-1 100 101 102 103 104 105
0
1
2
3
4
5
6
MFI, 300 K
 2MP - IRM
 2MP - GCMC MONO
 3MP - IRM
 3MP - GCMC MONO
c 
/ (
m
ol
ec
ul
es
/u
c)
p / Pa
Fig. 1. Adsorption isotherms of 2-methylpentane and 3-methylpentane inside monoclinic silicalite-1 at 300 K, as obtained 
from IRM experiments and GCMC simulation. The loading c is given in molecules per unit cell.  
Conclusions 
Overall we see a faster hopping rate in the sinusoidal channels of silicalite-1 compared to the straight 
channels for both molecules. 2MP has a longer carbon backbone compared to 3MP when considering 
the location of the methyl-branch. The orientation of 2MP inside of an intersection is such that its longer 
‘tail’ will be oriented into either a straight or sinusoidal channel, facilitating its jump from one 
intersection to the next, while 3MP remains more confined within the preferred intersections. As such, 
the simulation data correlates nicely with our experimental findings. 
References 
[1] J. Kärger, D.M. Ruthven, D.N. Theodorou, Diffusion in Nanoporous Materials, 1. ed., (2012) 872.
[2] U. Mueller, K.K. Unger, Preliminary studies on the synthesis of alkaline-free large crystals of ZSM-5,
Zeolites 8 (1988), 154-156.
[3] D. Dubbeldam, S. Calero, D.E. Ellis, R.Q. Snurr, RASPA: molecular simulation software for adsorption and
diffusion in flexible nanoporous materials, Mol. Simul. 42 (2016), 81-101.
[4] D. Dubbeldam, S. Calero, T.J.H. Vlugt, R. Krishna, T.L.M. Maesen, B. Smit, United Atom Force Field for
Alkanes in Nanoporous Materials, J. Phys. Chem. B 108 (2004), 12301-12313.
[5] D. Chandler, Statistical mechanics of isomerization dynamics in liquids and the transition state approximation,
J. Chem. Phys. 68 (1978), 2959-2970.
2 


Diffusion and adsorption of 2-methylpentane and 3-methylpentane in silicalite-1 crystals

Straumal, Boris

Gornakova, Alena

Kuzmin, Alexei

Tyurin, Alexander

Druzhinin, Alexander

Afonikova, Natalia

Davdian, Gregory

This work is licensed under a Creative Commons Attribution 4.0 International License. 
   diffusion-fundamentals.org, Vol. 38 (2023) 8, URL: https://diffusion-fundamentals.org/journal/38/2023/8.pdf 
1 
Influence of heat treatment and high-pressure torsion on phase 
transformations in TiZrHfMoCr high-entropy alloy 
Boris Straumal1,2,3*, Alena Gornakova1, Alexei Kuzmin4, Alexander Tyurin5, Alexander 
Druzhinin1, Natalia Afonikova1 and Gregory Davdian1,2 
1Science Center in Chernogolovka at Osipyan Institute of Solid State Physics, Chernogolovka, Russia 
2National University of Science and Technology "MISIS" Moscow, Russia 
3Department of materials for agrotechnology at Cotton breeding, seed production and 
agrotechnologies research institute, Salar, Tashkent region, Uzbekistan 
4Institute of Solid State Physics, University of Latvia, Riga, Latvia 
5G.R. Derzhavin Research Institute “Nanotechnologies and Nanomaterials” TSU, Tambov, Russia 
*Presenting author: straumal@issp.ac.ru
(Received: 2023/07/04, Published online: 2023/07/07) 
The study focused on the 21.99 at.%Ti–22.49 at.%Zr–20.35 at.%Hf–17.45 at.%Mo–17.73 at.%Cr high 
entropy alloy (Fig. 1). The analytical techniques like X-ray diffraction, scanning electron microscopy 
as well as X-ray absorption spectroscopy were employed to investigate the alloy's structure, phase 
transformations, and properties. The alloy in the as-cast state contained three phases, namely the 
body-centered cubic (A2) phase, hexagonal Laves phase (C14) and cubic Laves phase (C15). The 
alloy has beeen annealed during long time at different temperatures. It led to the disappearance of the 
hexagonal Laves phase, leaving behind two primary phases, namely the cubic Laves phase (C15) and 
body-centered cubic phase (A2). At 1200°С the A2 phase almost disappeared, resulting in a 
practically single-phase sample. After high pressure torsion (HPT) treatment, the hexagonal Laves 
phase disappeared entirely, while the A2 and C15 phases remained. The grain size of the A2 and C15 
phases was refined after HPT and grains were elongated, and their configuration resembled a layered 
structure. The high hardness of the A2 and C15+C14 phases accounted for this behavior. The lattice 
parameters in the A2 and C15 phases after HPT treatment approached those observed after prolonged 
annealing at 1000°C, indicating that the composition of these phases after short-term high pressure 
torsion at ambient temperature is equivalent to the composition of these phases after long tempering at 
1000°C. The rate of diffusion-like mass transfer during severe plastic deformation was estimated to 
be many orders of magnitude higher than that for conventional bulk diffusion at the HPT treatment 
temperature and similar to that at elevated temperatures above 1000°C. X-ray absоrption spectrоscopy 
results obtained at K-edges of Ti, Cr, Zr, and Mo as well as at L3-edge of Hf indicated that the local 
environment around metal atoms before HPT is similar to that after HPT (Fig. 2). However, the static 
disorder increased after HPT, which could be attributed to an increased specific amount of metal 
atoms in the disordered grain boundary layers after HPT-driven grain refinement (Fig. 3). 
Fig. 1. SEM images of the initial microstructure of the TiZrHfMoCr alloy: (a) general view, (b) dots mark the areas of 
component analysis: light gray (1), dark gray (2), and gray (3) colors. (c) X-ray diffraction pattern of the as-cast TiZrHfMoCr 
alloy. Reprinted with permission from Ref. [1]. Copyright 2023 MDPI. 
2 
Fig. 2. XANES spectra of the original as-cast (AC) TiZrHfMoCr HEA sample and sample after HPT at the Ti, Cr, Zr, and Mo 
K-edges and Hf L3-edge. The insets show an enlarged view around the edge. The pre-edge A and the white line WL 
are indicated. Reprinted with permission from Ref. [1]. Copyright 2023 MDPI.
Fig. 3. Comparison of the Fourier transform of the EXAFS spectra for as-cast (AC) TiZrHfMoCr HEA at the K-edges of 
Ti, Cr, Zr, and Mo and L3-edge of Hf. Only the moduli of FTs are shown for clarity. Reprinted with permission from Ref. 
[1]. Copyright 2023 MDPI. 
This research was funded by the Russian Ministry of Science and Higher Education (contract no. 075-
15-2021-945 grant no. 13.2251.21.0013).
References
[1] A. Gornakova, B. Straumal, A. Kuzmin, A. Tyurin, E. Chernyaeva, A. Druzhinin, N. Afonikova, G. Davdian. Metals 13
(2023) 1030. 


Influence of heat treatment and high-pressure torsion on phase transformations in TiZrHfMoCr high-entropy alloy

Nathan, Ran

This work is licensed under a Creative Commons Attribution 4.0 International License. 
1 
The high-throughput revolution in movement ecology 
Ran Nathan 
The Hebrew University of Jerusalem, Department of Ecology, Behavior and Evolution, 
ran.nathan@mail.huji.ac.il 
(Received: 2023/07/10, Published online: 2023/07/11) 
Movement characterizes life, constitutes a basic interaction between organisms and the environment, 
and occurs in all organisms – plants, microorganisms, animals and humans – forming diverse 
manifestations, which are crucial for our environment and human life. Many major environmental 
concerns that challenge humanity, such as infectious diseases, invasive species, and climate changes, 
are directly related to the movement of organisms. In an era of dramatic global environmental changes, 
understanding the drivers of critical ecological/environmental processes necessitates delving into the 
mechanisms underlying organismal movement.  
The rapidly growing field of Movement Ecology, established 15 years ago [1], aims at elucidating 
movement patterns, the underlying movement processes and their ecological and evolutionary 
consequences across all types of organisms and movement phenomena. Focusing on the level of the 
individual, the conceptual framework of movement ecology depicts how the internal state, the motion 
and the navigation capacities of the individual, and the external environmental factors affecting its 
movement, are linked to shape the resulting movement pattern [1]. As such, movement ecology provides 
a natural platform for examining the mechanisms underlying movement processes and patterns, merging 
the random walk / diffusion paradigms with several other central research paradigms developed in 
biomechanics, cognitive sciences and economy [1].   
Technological advances are now transforming movement ecology into a big-data discipline, enabling 
rapid, cost-effective generation of large amounts of data on movements of animals in the wild. High-
throughput systems provide new research opportunities beyond simply enlarging datasets and sample 
sizes, allowing thorough investigations of fine-scale variation among individuals, the true nature of 
biological interactions, behavioral decisions in response to the physical and anthropogenic environment, 
and behavioral shifts across spatiotemporal scales [2]. 
ATLAS (Advanced Tracking and Localization of Animals in real-life Systems) is a new powerful 
wildlife tracking system that provides new opportunities for movement ecology research at a regional 
scale (10-100 km wide). This high-throughput system, developed over the past decade by the Minerva 
Center for Movement Ecology, is based on “reverse GPS” technology and is capable to automatically 
and simultaneously track multiple small animals at high sampling frequency and GPS-level accuracy. 
The first ATLAS system was established at the Hula Valley (Israel) in 2014, followed by 15 additional 
systems that have been established in 10 different countries around the world. The high-throughput 
merits of ATLAS enabled exciting new research insights, including the first comprehensive field 
evidence for the existence of a cognitive map in wild animals [3], the discovery of mobile sensory 
networks formed by insectivorous bats [4] and the elucidation of how predation risk selects for spatial 
memory in young birds during home-range development [5].  
Although the integration of organismal movement research under the movement ecology umbrella is 
fairly new, studies of movement phenomena have long benefited from insights gained from random 
walk and diffusion theories. The recent high-throughput revolution in movement ecology offers 
numerous new opportunities for further integration between physics, biology and ecology. Examples 
for recent research using tools developed in physics to analyze ATLAS-derived big data include the 
demonstration of ergodicity breaking in area-restricted search of avian predators [6], and the discovery 
   diffusion-fundamentals.org, Vol. 37 (2023) 6, URL: https://diffusion-fundamentals.org/journal/372023/6.pdf 
of a strong phase transition in the foraging movements of fruit bats, reflecting a mixture of tendencies 
to visit known resources (i.e., memory) and to search for new ones (i.e., exploration) [7]. Further 
enhancing cooperation among traditionally separated disciplines such as ecology, cognitive sciences, 
and statistical physics is crucial for understanding the key drivers of organismal movement in globally 
changing environments. 
References 
[1] R. Nathan, W.M. Getz, E. Revilla, M. Holyoak, R. Kadmon, D. Saltz, P.E. Smouse, A Movement Ecology Paradigm for
Unifying Organismal Movement Research, Proc. Natl. Acad. Sci. U.S.A. 105 (2008) 19052-19059.
[2] R. Nathan, C.T. Monk, R. Arlinghaus, T. Adam, J. Alós, M. Assaf, H. Baktoft, C.E. Beardsworth, M.G. Bertram, A.I.
Bijleveld, T. Brodin, J.L. Brooks, A. Campos-Candela, S.J. Cooke, K.Ø. Gjelland, P.R. Gupte, R. Harel, G. Hellström, F.
Jeltsch, S.S. Killen, T. Klefoth, R. Langrock, R.J. Lennox, E. Lourie, J.R. Madden, Y. Orchan, I.S. Pauwels, M. Říha, M.
Roeleke, U.E. Schlägel, D. Shohami, J. Signer, S. Toledo, O. Vilk, S. Westrelin, M.A. Whiteside, I. Jarić, Big-Data
Approaches Lead to an Increased Understanding of the Ecology of Animal Movement, Science 375 (2022) eabg1780.
[3] S. Toledo, D. Shohami, I. Schiffner, E. Lourie, Y. Orchan, Y. Bartan, R. Nathan, Cognitive Map-Based Navigation in
Wild Bats Revealed by a New High-Throughput Tracking System, Science 369 (2020) 188-193.
[4] M. Roeleke, U.E. Schlägel, C. Gallagher, J. Pufelski, T. Blohm, R. Nathan, S. Toledo, F. Jeltsch, C.C. Voigt,
Insectivorous Bats Form Mobile Sensory Networks to Optimize Prey Localization: The Case of the Common Noctule Bat,
Proc. Natl. Acad. Sci. U.S.A. 119 (2022) e2203663119.
[5] R.J.P. Heathcote, M.A. Whiteside, C.E. Beardsworth, J.O. Van Horik, P.R. Laker, S. Toledo, Y. Orchan, R. Nathan, J.R.
Madden, Spatial Memory Predicts Home Range Size and Predation Risk in Pheasants, Nat. Ecol. Evol. 7 (2023) 461-+.
[6] O. Vilk, Y. Orchan, M. Charter, N. Ganot, S. Toledo, R. Nathan, M. Assaf, Ergodicity Breaking in Area-Restricted
Search of Avian Predators, Phys. Rev. X 12 (2022) 031005.
[7] O. Vilk, D. Campos, V. Méndez, E. Lourie, R. Nathan, M. Assaf, Phase Transition in a Non-Markovian Animal
Exploration Model with Preferential Returns, Phys. Rev. Lett. 128 (2022) 148301.
2 


The high-throughput revolution in movement ecology

Pérez-Losada, Joaquim

Fort, Joaquim

This work is licensed under a Creative Commons Attribution 4.0 International License. 
   diffusion-fundamentals.org, Vol. 38 (2023) 1, URL: https://diffusion-fundamentals.org/journal/38/2023/1.pdf 
1 
Diffusion of humans out of Africa and the phonemic diversity cline 
Joaquim Pérez-Losada1*, Joaquim Fort1,2 
1Complex Systems Laboratory, University of Girona, Girona, Spain 
2Catalan Institute for Research and Advanced Studies (ICREA), Barcelona, Spain 
*Presenting author: joaquim.perez@udg.edu
(Received: 2023/06/24, Revised version: 2023/07/14, Published online: 2023/07/14) 
Introduction 
The study of the origin of human language(s) is particularly challenging due to the lack of direct data 
on ancient languages [1]. Languages spoken in Africa tend to have the largest phonemic inventories, 
while those in South America and Oceania have the smallest [2]. Atkinson [2] proposed a serial founder 
effect (SFE) mechanism to explain this global phonemic cline. According to his hypothesis, small 
populations of humans migrated carrying only part of the languages used in their original locations and 
phonemes would be lost. However, Atkinson did not present any model based on diffusion equations 
neither simulations to back his claim. Our previous simulations [3] suggested that a phonemic serial 
founder effect could explain the global phonemic cline, assuming both low initial phonemic inventories 
and a natural rate of increase in phonemic inventory size. Here we explore the alternative hypotheses 
that languages at the origin of the range expansion had large phonemic inventories, and that low-density 
populations lose phonemic diversity [1]. The latter assumption aligns with empirical evidence showing 
that cultural diversity decreases with population size and that smaller populations have higher rates of 
word loss. We aim to determine if Atkinson's proposed SFE model can generate the observed spatial 
phonemic cline. Additionally, we investigate the stability of the phonemic signal over long periods of 
time.  
A Serial Founder Effect (SFE) model based on population diffusion 
We used UPSID [4] database of languages and phonemes. Our model simulates the dispersal of hunter-
gatherer tribes from a single origin, in a two-dimensional grid representing the Earth's surface with 1,000 
x 1,000 nodes, and the subsequent evolution and spread of languages spoken by these tribes. The 
distance between adjacent nodes (r) is set at 50 km to reflect pre-industrial population dispersal patterns. 
The model considers a population density of 1.2 people/km2 for hunter-gatherer tribes, with each tribe 
consisting of approximately 300 individuals speaking a common language. Multiple tribes can speak 
the same language, and a node can accommodate up to 10 tribes. The language of each tribe is encoded 
as a binary string representing the presence (1) or absence (0) of phonemes. We assume that languages 
spoken in low-density populations, as encountered at the forefront of a wave of expansion, experience 
phonemic evolution through random phoneme loss. Each time step represents one generation, with value 
T = 32 years. The new population number density p(x, y, t + T) in each cell and time, is computed 
through four steps: (i) Dispersal: a fraction pe of tribes remains in the original node (for ethnographic 
data, pe = 0.38), while the remainder disperse randomly to neighboring nodes, i.e. [5]: 
p(x, y, t + T) = R0 �pep(x, y, t)
+ (1 − pe)�
1
4
p(x − r, y, t) +
1
4
p(x + r, y, t) +
1
4
p(x, y − r, t) +
1
4
p(x, y + r, t)�� (1) 
(ii) Reproduction: new tribes are generated at a net fecundity rate (from ethnography, R0 = 1.4), with
the resulting number adjusted to the nearest integer, (iii) Vertical transmission: information on the
number of phonemes in a language is copied from the parent tribe to the child tribe without any changes,
and finally (iv) Mutation: phonemic loss occurs in low-density cells, where a randomly selected
phoneme in the parent language is converted from "1" (present) to "0" (absent) in the child language.
This process allows new languages to emerge at nodes with a population density below saturation.
2 
The model runs for a total of 72,960 years, representing approximately 2,280 generations, which 
corresponds to a reasonable estimation of the time span since the Out-of-Africa dispersal. Two initial 
conditions are considered: (a) initial languages have around 71 phonemes, similarly to present-day 
languages with the largest phoneme inventories (e.g., click languages); (b) the initial languages have a 
range of 35 to 40 phonemes, reflecting the languages spoken today in the  region of origin of the out-
of-Africa dispersal. 
Results and discussion 
Figure 1 displays the number of phonemes versus distance from the likely origin of the Out-of-Africa 
dispersal, for a phonemic loss time of 80 generations per phoneme. As mentioned above, two scenarios 
are considered: languages with a similar number of phonemes to present-day click languages (66–76 
phonemes, open circles, blue solid line), and languages spoken today in the regions of origin of the Out-
of-Africa dispersal (35–40 phonemes, squares, red solid line). For the second case, the slope and 
intercept of the simulated cline closely matched the observed values (green dash-dotted and dashed 
lines). Note  that the initial number of phonemes had minimal impact on the slope of the simulated 
clines. This finding implies that regardless of the phonemic diversity and mixture of languages at the 
onset of the Out-of-Africa dispersal, the simulated slope agrees with the observed one. Also, the 
simulations demonstrate that the SFE signal for phonemic diversity does not disappear even over a deep 
temporal scale of 300,000 years, contradicting claims that such a signal would rapidly diminish. 
Conclusions 
A SFE model, combined with the assumption that languages have a higher probability of phonemic loss 
in low-density populations, can generate the observed global cline. These findings challenge previous 
assertions regarding the disappearance of SFE signals.  
Fig. 1. Simulated phonemic cline (i.e., number of phonemes versus distance from Atkinson’s putative origin of the Out- of-
Africa dispersal). Two instances of the same model are shown in which at the onset of the Out-of-Africa dispersal, initial 
languages had 66–76 phonemes (open circles) and 35–40 phonemes (squares). The observed global phonemic cline is also 
shown (green dash-dotted and dashed lines). Adapted from Ref. [1]. 
References 
[1] J. Pérez-Losada, J. Fort, A serial founder effect model of phonemic diversity based on phonemic loss in low-density
populations, PLoS ONE 13(6) (2018) e0198346.
[2] QD. Atkinson, Phonemic diversity supports a serial founder effect model of language expansion from Africa, Science 332
(2011) 346–349.
[3] J. Fort, J. Pérez-Losada, Can a linguistic serial founder effect originating in Africa explain the worldwide phonemic cline?,
J R Soc Interface 13 (2016) 20160185, 1–9.
[4] I. Maddieson, K. Precoda, Updating UPSID, UCLA working papers in Phonetics 74 (2011) 104–111.
[5] J. Fort, J. Pérez-Losada, and N. Isern, Fronts from integrodifference equations and persistence effects on the Neolithic
transition, Phys. Rev. E 76 (2007) 031913, 1-10.
0 5000 10000 15000 20000 25000
20
30
40
50
60
70
80
 66-76 phonemes (simulations)
 linear fit
 35-40 phonemes (simulations)
 linear fit
 observed upper bound
 observed mean regression
 observed lower bound
Nu
m
be
r o
f p
ho
ne
m
es
Distance from origin (km)
80 generations/phoneme
a


Diffusion of humans out of Africa and the phonemic diversity cline

Kagramanyan, David

Konstantinova, Elisaveta

Nekrasov, Alexei

Druzhinin, Alexandr

Shchur, Lev

This work is licensed under a Creative Commons Attribution 4.0 International License. 
   diffusion-fundamentals.org, Vol. 38 (2023) 5, URL: https://diffusion-fundamentals.org/journal/38/2023/5.pdf 
Topology of WC/Co interfaces in cemented carbides 
Boris Straumal1*, David Kagramanyan1,2, Elisaveta Konstantinova1,2, Alexei Nekrasov3, 
Alexandr Druzhinin1, Lev Shchur1,2,4 
1Science Center in Chernogolovka (SCC) at  Osipyan Institute of Solid State Physics (ISSP), Russian 
Academy of Sciences, Chernogolovka, Russia 
2HSE University, Moscow, Russia 
3Korzhinsky Institute of Experimental Mineralogy, Russian Academy of Sciences, Chernogolovka, 
Russia 
4Landau Institute for Theoretical Physics, Russian Academy of Sciences, Chernogolovka, Russia 
*Presenting author: straumal@issp.ac.ru
(Received: 2023/06/19, Published online: 2023/06/24) 
On March 23, 1923, the first patent for cemented carbides based on tungsten carbide with a 
cobalt binder was registered in Germany [1]. Further development of such alloys requires now 
the new methods for describing their microstructure, which go beyond the traditional 
approaches of quantitative metallography. Here we propose a fundamentally new approach 
to describing the microstructure of these materials, namely, the topology of the WC/Co interfaces 
in hard alloys based on tungsten carbide with a cobalt binder using computer vision elements (Fig. 1).  
B
B
C
C
C/C
C/B
CW
CW
CW
PW
PW
OA
IA
IA
IA
OA
OA
10 μm
(a) (b) 
Fig. 1 (a) SEM micrograph of a WC-Co alloy with various structural elements. Center: crack growth trajectory. The symbol 
C denotes a transgranular fracture, C/B and C/C, an intergranular fracture, and B, a fracture through a cobalt binder. To the 
left of the crack the phenomena of grain-boundary wetting are marked. The arrows and symbol CW indicate the boundaries 
between tungsten carbide grains completely wetted with a cobalt binder. The arrows and symbol PW indicate the boundaries 
between tungsten carbide grains partially wetted with a cobalt binder. To the right of the crack the structural elements of the 
"islands" of the cobalt binder are marked. Arrows and the symbol IA indicate kinks at the interface(“incoming angles”), in 
which the ridges of faceted tungsten carbide crystallites enter the region of the cobalt binder. The arrows and symbol OA 
indicate  kinks at the interface (“outgoing angles”) where the cobalt binder contacts the WC/WC boundaries between 
tungsten carbide grains. The ellipse denotes, for example, a continuous region of cobalt binder grains. For such areas, an 
analysis of the contour of the interphase boundary was carried out with the determination of incoming IA and outgoing OA 
angles. The lengths of the semiaxes of such ellipses, which characterize the dimensions of the continuous regions of the 
cobalt binder, were also determined. (b) Scheme of an ellipse around the points of the contour.   
In this work, model sections of samples imitating conventional commercial hard alloys WC-Co were 
made. The resulting sections were subjected to microscopic examination using scanning electron 
microscopy (SEM). The calculation of the angles at the interface between tungsten carbide and cobalt 
binder was based on the scalar product. For each of the three samples, one hundred micrographs were 
processed and a histogram of the angles at the interfacial boundary of the cobalt binder and tungsten 
1 
2 
carbide was plotted in Fig. 2(a). To determine the width and length of the cobalt binder regions (Fig. 
2b,c), we describe an ellipse around the cobalt regions using the Khachiyan algorithm [2] (Fig. 1c). 
Based on the obtained lengths of small and diseased semiaxes, we construct a heat maps of the 
probability distribution of a two-dimensional quantity for large grains and apply a polynomial on it, 
passing through the “warmest” pixel (Fig. 3) 
Fig. 2. (a) Distribution of angles on the contour of cobalt binder regions for three samples with different WC grain sizes. Blue 
is for small grains, orange is for medium grains, green is for large grains. The distribution of the lengths of the semiaxes of 
such ellipses for the cobalt binder for three samples with different grain sizes WC. (b) long axis, (c) short axis. The vertical 
axis shows the logarithms of the distribution probability Blue is for small grains, orange is for medium grains, green is for 
large grains. 
Fig. 3. Two-dimensional distribution densities P(a,b) of the lengths of the semiaxes a and b. (a) small grains, (b) medium 
grains, (c) large grains. The color scale on the right represents the values of P(a,b). The solid lines are for the distribution 
ridge. (d) The value of P(a,b) on the distribution ridge as a function of the major semiaxis: blue is for small grains, orange is 
for medium grains, green is for large grains. 
The work was carried out within the framework of the Russian Science Foundation project 22-22-
00511, https://rscf.ru/project/22-22-00511/. 
References 
[1] K. Schröter, DRP 420.689: Sintered hardmetal alloy and procedure for its fabrication, 1923.
[2] L.G. Khachiyan, Rounding of Polytopes in the Real Number Model of Computation. Mathematics of Operations
Research (1996).


Topology of WC/Co interfaces in cemented carbides

This work is licensed under a Creative Commons Attribution 4.0 International License. 
   diffusion-fundamentals.org, Vol. 37 (2023) 4, URL: https://diffusion-fundamentals.org/journal/37/2023/4.pdf 
Diffusion of socioeconomic influences across generations 
Steven N. Durlauf 
University of Chicago, Chicago USA 
durlauf@gmail.com 
(Received: 2023/06/20, Published online: 2023/06/24) 
In this presentation, I will provide an overview of models of intergenerational mobility. These models 
describe how the socioeconomic characteristics of parents help determine the future socioeconomic 
characteristics of their children.  Intergenerational mobility has close connections to the concept of 
equality of opportunity and so its nature and level have normative significance. I will consider both 
theoretical models of mobility that reflect various socioeconomic mechanisms as well as statistical 
models that have been used to measure mobility. Part of the talk will therefore involve the relationship 
between theoretical and statistical models of mobility. 
To provide this overview, I will proceed to work through a sequence of Markov models of 
intergenerational mobility.  Each of these models is constituted by the specification of an environment 
in which features of childhood and adolescence influence future adult outcomes through their effects on 
the preferences, constraints, and beliefs of individuals and the determination of the outcomes that 
emerge via individual choices and the interdependences between them that are induced by the social and 
political structure of the environment.  
The first class of theoretical models will relate a scalar measure of parental incomes (the average income 
of the parent over the life course) to the same measure for children. These models are based on the 
intuitive idea that parental income helps determine levels of human capital formation in children. 
Denoting the scalar measure for a parent i  as i ,ty  and for their child as i t+, 1y , the first class of models 
will produce conditional probability measures to describe family income dynamics of the form 
( )t+, 1 i t,µ iy y (1) 
I will focus on features of this conditional probability structure that are of particular interest to social 
scientists. I will emphasize the possibility that (1) produces multiple steady states for different families 
and/or slow convergence rates towards steady states.  I will indicate how contemporary empirical studies 
of mobility often use statistical models that are inappropriate for uncovering phenomena such as poverty 
traps. This occurs because of the limits in the capacity of conventional statistical frameworks to reveal 
nonlinearities in the dynamics.  
Next, I will enrich the underlying behavior foundations of models that produce (1) by incorporating 
social factors, ts  that affect children. These social factors include neighborhood and school 
characteristics and lead to family income dynamics of the form 
( )t+, 1 ,i t i t,µ iy ,y s (2) 
I will argue that this formulation produces two important implications that are new relative to the first 
model. First, the introduction of social factors demonstrates the role of segregation in creating 
persistence in socioeconomic status across generations. Second, the formulation implies that increased 
inequality within a generation can increase persistence across generations, which is consistent with an 
empirical regularity known as the Great Gatsby Curve. While nonlinearities in (1) can produce a Gatsby 
Curve, (2) provides a behavioral, as opposed to mathematical, explanation for the empirical finding. 
1 
2 
I will complete the overview by describing a new set of models that emphasize the importance of 
childhood exposures at different ages. If one denotes , ,i r ty  as family income and , ,i r ts  as social influences 
when the child is age r , these models imply income dynamics take the form 
( ), 1 ,0, ,18, ,0, ,18,, , , , ...µ +i t i t i t i t i ty y y s s (3) 
This class of models has only begun to be analysed and I will present some of the new insights the 
approach has already produced. 
As this sequence of models indicates, as one incorporates greater social science richness, 
intergenerational mobility analysis involves increasing complex stochastic processes. Hence there is the 
potential for much fruitful collaboration between mobility researchers and diffusion researchers.  
References 
[1] Y. Chang, S. Durlauf, S. Lee, and J. Park, A Trajectories-Based Approach to Measuring
Intergenerational Mobility, National Bureau of Economic Research Working Paper no. 31020, 2023.
[2] N. Cholli and S. Durlauf, Intergenerational Mobility, National Bureau of Economic Research
Working Paper no. 29760, 2022.
[3] S. Durlauf and A. Seshadri, Understanding the Great Gatsby Curve, with A. Seshadri,
Macroeconomics Annual, University of Chicago Press, 2018.
[4] S. Durlauf, C. M. Tan, and A. Kourtellos. The Great Gatsby Curve, Annual Review of Economics,
2022.


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