Summary

Research in soft matter physics, machine learning, and nonlinear dynamics

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This is what I usually do when I am in my office:

1. Confined diblock copolymers
2. Machine Learning
3. Solitary waves in granular matter

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A demonstration of my research activities:

Publications

Peer Reviewed (Citations click here)

1. E.Avalos, T. Teramoto, Y, Hirai, H. Yabu and Y. Nishiura, "Controlling the Formation of Polyhedral Block Copolymer Nanoparticles: Insights from Process Variables and Dynamic Modeling" ACS Omega 9, 15, 17276 (2024) [Link].
2. E.Avalos, K. Akagi and Y. Nishiura, "Visible fingerprint of X-ray images of epoxy resins using singular value decomposition of deep learning features" COMMAT 186 (2021) 109996 [Link].
3. E. Ávalos, A.Datta, Rosato, Blackmore and S. Sen, "Dynamics of confined particles in a chain with 1/r repulsive magnetic interaction". Physica  A, 124651 (2020)  [Link].
4. E. Avalos, S. Xie,  K. Akagi and Y. Nishiura, "Bridging a mesoscopic inhomogeneity to macroscopic performance of amorphous materials in the framework of the phase field modeling". Physica D, 409, 132470 (2020) [Link].
5. Y. Hirai, E. Avalos, T. Teramoto,Y. Nishiura and H.Yabu, Ashura. Particles:Experimental and Theoretical Approaches for Creating Phase Separated Structures of Ternary Blended Polymers in Three-Dimensionally Confined Spaces, ACS Omega 4 (8), 13106 (2019) [Link].
6. E. Ávalos,  T. Teramoto, H. Komiyama, H. Yabu and Y. Nishiura, “Transformation of block copolymer nanoparticles from ellipsoids with striped lamellae into onion-like spheres and dynamical control via coupled CahnHilliard equations”, ACS Omega 3, 1, 1304 (2018) [Link]. 
7. E. Ávalos, T. Higuchi, T. Teramoto, H. Yabu and Y. Nishiura, Frustrated phases under three-dimensional confinement simulated by a set of coupled Cahn-Hilliard equations, Soft Matter 12, 5905 (2016)[Link].
8. E. Ávalos and S. Sen, Granular chain between asymmetric boundaries and the quasiequilibrium state, Phys. Rev. E, 89, 053202 (2014)[Link].
9. E. Ávalos, D. W. Huang and W. N. Huang, A study of city traffic in afternoon rush hours, Int. J. Mod. Phys. C. 24, 1350040 (2013)[Link] [Personal copy].
10. E. Ávalos, D. Sun, R. L. Doney and S. Sen, Sustained strong fluctuations in a nonlinear chain at acoustic vacuum, Phys. Rev. E, 84, 046610 (2011)[Link].
11. E. Ávalos, C. K. Chan and P. Y. Lai, Spiral waves in the heterogeneous excitable Kuramoto model, EPL, 94, 60006 (2011)[Link].
12. A. Rocha, F. del Rio and E. Ávalos, Equation of state and liquid-vapour equilibrium of polarizable Stockmayer fluids, J. Chem. Phys, 133, 224301 (2010)[Link].
13. E. Ávalos, P. Y. Lai and C. K. Chan, Zero refractoriness spirals in phase-coupled excitable media, Phys. Rev. E 80, 065202 (2009)[Link]. This paper was highlighted in Virtual Journal of Biological Physics Research.
14. E. Ávalos and S. Sen, How solitary waves collide in discrete granular alignments, Phys. Rev. E 79, 046607 (2009) [Link].
15. D. K. Sun, E. Ávalos, R. L. Doney, R. P. Simion, A. Sokolow and S. Sen, Nonlinear, Statistical and Applied Physics of Solitary Wave-like Objects in Granular Systems, Powders and Grains, 1145, p431-434 (2009)[Link].
16. W. Chen, S. C. Cheng, E. Ávalos, O. Drugova, P. Y. Lai, G. Osipov, C. K. Chan, Synchronization in growing heterogeneous media, Europhysics Letters, 86, 18001 (2009)[Link].
17. S. Sen, J.Hong, J. Bang, E. Ávalos and R. L. Doney, Solitary waves in the granular chain, Physics Reports, 462 (2), p.21-66, Jun (2008)[Link].
18. E. Ávalos, R. L. Doney and S. Sen, Interaction of solitary waves in confined granular alignments and the quasi-equilibrium state, Chin. J. Phys. 45, 6-II (2007) [Link] [Personal copy].
19. E. Ávalos, Jan M.M. Pfannes, T.R. Krishna Mohan and S. Sen, A numerical study of the dynamics of the surface grain in a granular chain and the role of gravity. Phys. D, 225, 2 (2007) [Link].
20. F. del Río, I. A. McLure, J. Chávez, J. E. Ramos and E. Ávalos, Interaction potentials and thermodynamics of small polar molecules, Mol. Phys., 104, 3757, (2006) [Link].
21. S. Sen, T.R. Krishna Mohan, D. P. Visco, Jr., Saravanan Swaminathan, A. Sokolow, E. Ávalos and M. Nakagawa, Using mechanical energy as a probe for the detection and imaging of shallow buried inclusions in dry granular beds, Int. J. Mod. Phys. B, 19, 2951, (2005) [Link].
22. F. del Río, Enrique Díaz Herrera, E. Ávalos and J. Alejandre, Liquid-vapor equilibrium and surface tension of nonconformal molecular fluids, J. Chem. Phys, 122, 034504, (2005) [Link].
23. E. Ávalos, F. del Río and S. Lago, Non-conformal Interaction Models and Thermodynamics of Polar Fluids, J. Phys. Chem. B, 109, 508, (2005) [Link].
24. F. del Río and E. Ávalos, Effective Potentials and Second Virial Coefficients for Polar Fluids, Developments in Mathematical and Experimental Physics, Volume B: Statistical Physics and Beyond. Edited by Macias et. Al., Kluwer Academic/Plenun, (2003) [Link].
25. F. del Río, E. Ávalos, R. Espíndola, L. F. Rull, G. Jackson and S. Lago. Vapour-liquid equilibrium of the square-well fluid of variable range via a hybrid simulation approach, Mol. Phys., 100, 2531, (2002) [Link].
26. E. Ávalos, Quantum World, Cemanáhuac, 44, January, 29th 1998.

Monographs

1. Propagacion de Impulsos en Medios Granulados
2. Termodinamica de Fluidos Polares
3. El mundo cuantico

Micellaneous

1. Research Statement
2. Teaching Statement
3. Teaching Clip

Research Agenda

Dr. Avalos obtained his PhD in March 2005, where he developed an interaction model for dipolar molecules that matches simulation results and predicts thermodynamic properties of polar substances of industrial interest (e.g., hydrogen chloride, methylamine, chloroform); this work contributed to a Mexican–Spanish collaborative effort producing six publications (*1). [2,3,4,5,7,15]

After a brief stay in Spain, in summer 2005 he joined the University at Buffalo and consolidated his work on granular matter, investigating backscattering from gravitationally loaded granular chains to probe energy propagation in granular assemblies. [6,8,10]

He also studied the interaction of solitary waves in unloaded granular media, advancing understanding of energy transmission and nonlinear wave dynamics in these arrays. [9,10,12,13,17]

In 2006 he began work in Taiwan on wave propagation in excitable media using the single-variable Kuramoto excitable phase model (originally proposed for phase synchronization) and demonstrated that it can support undamped plane and spiral waves in both homogeneous and heterogeneous media. [11][14][16,18]

His granular-matter research further shows that purely nonlinear granular systems in acoustic vacuum can sustain large energy fluctuations while exhibiting persistent cold spots—locations of near-zero energy. [17]

He has also modeled city traffic with a cellular automaton to study and better understand urban rush-hour dynamics. [19]

Dr. Avalos is currently dedicated to applying phase field theories to model the dynamic behavior of confined copolymers, with a particular focus on solving coupled Cahn-Hilliard equations to study their behavior in various contexts, including nanoparticles [20, 21].

In recent years he has turned to machine learning methods (dimensionality reduction, clustering in eigenspace, decision boundaries, and neural networks) to classify polymeric materials from X-ray images. [23]

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(*1) Reference numbers correspond to Dr. Avalos’s publication list.

Recent Presentations

Talks and Seminars

1. Classification of x-ray images of epoxy resins. AIMR Math-AI Seminar. Sendai, Japan, February 2019.
2. Machine learning classification of x-ray images. Kyoto, Japan, December 2018.
3. Tokyo, Japan, October 2018.
4. Biei, Japan, July 2018.
5. Xiamen, China, April 2018.
6. Simulation of three-dimensional confinement of diblock copolymers. Mathematical Science Group Seminar, Tohoku University, Japan. August 2015.
7. Propagation of Impulses in Granular Beds. Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan. June 2011.
8. Collision of solitary waves in granular alignments. Sapporo Winter School 2010 for Nonlinear Nano-system Science, Hokkaido University, Sapporo, Japan. February 17–19, 2010.
9. Spiral wave propagation on the excitable Kuramoto lattice. International Conference for Nonlinear Sciences, Hokkaido University, Sapporo, Japan. February 10–14, 2009.
10. Spiral wave propagation on a Kuramoto lattice. International Symposium on Non-Equilibrium Soft Matter, Kyoto University, Kyoto, Japan. June 2–5, 2008.
11. Pulse and spiral wave propagation on a lattice made of non-uniform oscillators. Annual Meeting of The Physical Society of Republic of China, National Chiao Tung University, Hsinchu, Taiwan. January 28–30, 2008.
12. Spiral clusters in coupled non-uniform oscillators. Opportunities and Challenges for Physicists in Quantitative and Systemic Biology, The Chinese University of Hong Kong, Hong Kong. December 4–9, 2006.
13. Interaction of solitary waves in granular arrays. 2006 Workshop of Nonlinear Physics, Huisun Forest Station, Nantou, Taiwan. November 3–5, 2006.

Non-linear & Biophysical Systems

Spiral waves in phase-coupled excitable media

Some cardiac arrhythmias occur when the collective motion of cells in excitable tissues in the heart deviates from the normal and healthy regime. These pathological movements are usually related to the spontaneous appearance of spiral waves on the ventricle.

We use many Kuramoto-type phase-coupled oscillators to represent excitable media capable of convey signals and support plane and spiral waves.

The figure below shows a spiral wave on a 2D lattice made of both, excitable and dead cells. Currently we study the effect of diversity and excitability on the spiral waves.

Related peer-reviewed article:
1. E. Avalos, P. Y. Lai and C. K. Chan, Zero refractoriness spirals in phase-coupled excitable media, Phys. Rev. E 80, 065202 (2009). [Link]
2. E. Avalos, C. K. Chan and P. Y. Lai, Spiral waves in the heterogeneous excitable Kuramoto model, EPL, 94, 60006 (2011). [Link]

Spiral Waves Movies

These are some movies of spiral waves in the Kuramoto excitable model. Go to my Video Play List and see more exciting movies.

1. Spiral wave in inhomogeneous excitable lattice.

2. Spiral wave in homogeneous excitable lattice.




3. Spiral wave breaks up in a excitable lattice.

Machine Learning

We employ SVD, SVM, Convolutional networks  (CNN) and dynamic mode decomposition (DMD).  Applications include discrimination of polymeric materials and dynamic systems.Using a combination of SVD and SVM we construct clusters to differentiate classes of materials.

CNN are useful not only for classification but also we are able to visualize the features that make materials different from one another.

We use DMD to construct a data driven model for diverse systems. For instance, breathers found in convective cells and also in the complex Ginzburg Landau equation. This section shows some results.

1. Data Analysis of Polymeric Materials

[Download Handout: Oct 2018]
      [Peer-reviewed paper in Physica D (2020)]

We apply tools of machine learning to study X-ray images of epoxy resins.

Polymeric materials contain a considerable variety of inhomogeneities. Correctly identifying the role of such inhomogeneities on the material properties is an extraordinary challenge. We propose a methodology to categorize samples of different types of epoxy resins.

Figure 1 shows X-ray images of different types of materials. These images represent patterns of density that are that are undistinguishable to human eye. The goal is to accurately group these images into different categories.

These images are concatenated into a matrix X as it is shown in Figure 2 and then SVD is used to extract the eigenvectors U. We then project each slice of the material onto a space of reduced dimension by computing the inner product of each slice and the eigenvectors in U. The result is shown in Figure 2c.

Decision Boundaries. The figure shows different methods of classification. (a) k-means consists of the iterative process of (i) labeling and (ii) computing the center of mass (unsupervised). These two steps were iterated seven times until convergence. (b) For the k-nearest neighbors we use k = 17. The process consists of finding the distances of a test set to the k-nearest neighbors and labeling it accordingly (supervised). The solid circles are the training set (80%) and the open circles are the test set (20%). Confusion matrix is shown for k-means classification. 

Currently we explore the early layers of a convolutional neural network in an attempt to discover what are the features that the network uses for classification.  Peer reviewed paper in Computational Materials Science [Link].

2. Data driven modeling

Dynamic mode decomposition (DMD) allows to construct  a data driven model to predict the future state of a nonlinear system.

The figure above shows an 2D breather in  a convective cell. The data driven model based on DMD is able to capture the dynamics of the nonlinear system.

Reservoir Computing is a powerful yet lightweight method for replicating time series of complex nonlinear phenomena. I used RC to reproduce the 2D breather above, complementing the DMD method.

We employed the DMD method to describe the propagation of solitary waves [Physica A (2020)]. This system is strongly non-linear and our data-driven model is able to capture the dynamics at future times nonetheless.

3. Extraction of eigenvectors of deep learning features

Convolutional Neural Network.  We developed a  CNN consisting of five layers and 1.3M parameters. 1000 images were used to process the network to be able classify the four different types of materials described above in Fig1.  We split the data as 80% for training and 20% for validation. However, data augmentation (random translation and reflection) is used to expand the data base of images.

Some few details: stochastic gradient descent is implemented to minimize the loss function (cross entropy loss). To prevent overfitting, standard techniques including L2 regularization and dropout were used. The Nvidia Quadro  GP100 GPU card was used for the calculations. Over 90% classification accuracy was achieved.

We use singular value decomposition to extract the most representative features that a Neural Network uses for classification. The figure below shows the process of feature extraction in the CNN. Peer reviewed paper in Computational Materials Science [Link].

I developed a software package containing the neural network described above, which has been trained using over a thousand of images. Below is an example of the use of this app that can be dowloaded and installed for free.

Copolymers

We use coupled partial differential equations to model confined diblock copolymers. This work contributes to the design of functional nanoparticles. The figure above shows 3D-printed models of some multipods that we are working on. These energy minimizers are solutions to four-degree coupled PDE's (Cahn-Hilliard equations). 

The two figures above show a wall energy potential (top) related to confined particles of copolymer (bottom).The contour plot of the potential illustrates  the case when both positive and negative values of the concentration parameter, v, are equally accepted. This is the case of layered nanoparticles. 

The figure above shows simulation of nanoparticles with multiple pods These particles are made solving coupled Cahn-Hilliard equations in three dimensions.

Recently, I have been using different spectral implementations to solve the multi-dimensional Cahn-Hilliard equations.

*Related peer-reviewed articles:

1. Frustrated phases under three-dimensional confinement simulated by a set of coupled Cahn-Hilliard equations (2016)


2. Transformation of block copolymer nanoparticles from ellipsoids with striped lamellae into onion-like spheres and dynamical control via coupled CahnHilliard equations (2017).

3. Ashura Particles: Experimental and Theoretical Approaches for Creating Phase-Separated Structures of Ternary Blended Polymers in Three-Dimensionally Confined Spaces (2019).

4. Controlling the Formation of Polyhedral Block Copolymer Nanoparticles: Insights from Process Variables and Dynamic Modeling (2024).

Granular Matter

Interaction of Solitary Waves

This is a cooperative work with Prof. Surajit Sen in the Physics Department at SUNY Buffalo, NY. This research is about granular matter. We research impulse acoustics to probe shallow soil properties. The aim is to develop numerical simulations to understand the propagation of impulses and their backscattering from buried inclusions in nominally dry disordered granular beds.

In particular, we are interested in the following problems: (i) simulating the effects of gravitational compaction on backscattered energy from the surface of a granular column when a mechanical pulse is applied, and (ii) studying the creation of secondary solitary waves during collisions of solitary waves in one-dimensional granular arrays.

The figure below shows multiple cold spots in a granular chain. The presence of multiple perturbations enriches the nature of fluctuations in these systems.

Traffic in cities

E. Avalos, D.W. Huang and W.N Huang. We propose a cellular automaton to simulate the traffic in cities in afternoon rush hours. The objective of this project is to optimize the travel time and traffic flow in urban and suburban environments. Within the city the traffic is regulated by the operation of traffic lights, which have a green/red cycle of period T, and there is a delay between consecutive traffic lights. We discuss some strategies to optimize travel time and traffic flow. Peer-reviewed paper here.

Previous projects

• Optics
• Polar Fluids
• Gravity Waves
• Trafic in Cities

PhD Thesis

Nonconformal Interaction Models and Thermodynamics of Polar Fluids

(Def: Dec, 03, 2004. Grad: March 2005).

• HTML related paper (English)
• PhD Thesis

Supongo que usted es estudiante de doctorado y está pensando en escribir su tesis. De acuerdo a mi experiencia personal le puedo aconsejar que lo antes posible tenga lista una versión digna de ser revisada por el jurado de su Universidad. El objetivo aquí, permítame ser franco, es que usted reciba su doctorado tan pronto como sea posible. Por dos razones: la primera es que la principal diferencia entre ser estudiante de licenciatura o maestría y ser estudiante de doctorado, es que la evaluación de un alumno de doctorado es binaria: o aprueba o no los cursos, o pasa o no los exámenes generales, los artículos de investigación se los aceptan o no, y así sucesivamente. La segunda razón es que si usted es un buen estudiante, a su asesor le interesa tenerlo a usted como colaborador por algo más de cuatro o cinco años. Por otro lado, si usted no es de los alumnos más aventajados, a su asesor también le interesa tenerlo por algo más de tiempo para mejorar su entrenamiento doctoral. De manera que el tiempo óptimo para acabar el doctorado sólo depende de usted, así que cuanto antes mejor. Uno o dos años después de haber recibido pronto su grado de doctor, usted gozará de un buen número de ventajas al ser un joven doctor.

Es muy posible que su investigación ya tenga al menos dos o tres años de edad y tendrá un montón de resultados, con esto podemos empezar. De acuerdo a mi experiencia, el mejor formato para escribir su tesis es Latex y no Word. La razón básicamente es que Latex le permitirá hacer rápidamente correcciones, añadiduras, referencias cruzadas e inserción de figuras, de manera muy simple. Todo lo anterior también es posible hacerlo en Word, pero le puedo garantizar que Latex le ofrecerá una considerable ventaja de tiempo y esfuerzo. Por otra parte, casi todo lo importante que usted escribirá en el futuro lo hará en Latex, así que si aun no ha empezado a hacerlo, ahora es el mejor momento.

Ahora necesitamos una primera versión de su tesis. Lo primero que hay que hacer es organizar sus mejores resultados. Para esto, imprima las mejores cinco gráficas y figuras que tenga. Ya vendrá el momento de poner figuras adicionales cuando sea necesario. El objetivo por ahora es explicar estas cinco figuras con dos párrafos por figura. Escríbalo rápidamente. Lo siguiente será darle contexto a la explicación de las figuras anteriores con dos párrafos adicionales. Con esto y con las figuras ya tenemos unas diez páginas listas y esto es un buen comienzo.

Vamos ahora a sus bitácoras. Si usted ha tenido una buena práctica con sus bitácoras, al final de tres años usted debe tener unas cinco o seis libretas llenas de información. Lo que usted debe que hacer en los siguientes días será exprimir y destilar todas esas bitácoras de manera muy ordenada y congruente. Al ir leyendo página por página lo que usted hizo en los pasados tres años le traerá más cosas a la mente. Lo que usted debe hacer no es pasar a limpio sus bitácoras, sino más bien, explicar detenidamente lo que hay en ellas. Empiece por la primera libreta. Vaya de una en una, página por página. Esto le tomará un par de semanas. Nuevas secciones y sub-secciones surgirán progresivamente de manera natural y su misión aquí es que la transición entre estas nuevas secciones sea suave e ilustrativa. En cada momento en su escritura, usted debe enfatizar el “Qué” y no el “Cómo”. Su tesis no es un manual, sino una referencia de hechos.

Yo le recomiendo escribir una primera versión de cada sección de su tesis como una lista enumerada de oraciones (sentence outline). Esto le ayudará a distribuir cada sección en trozos pequeños de información que tomarán más volumen hasta formar párrafos completos y bien estructurados. Una vez que la lista de oraciones tenga una estructura lógica y autocontenida, ensamble todo en párrafos. Cada párrafo debe empezar con una oración que ilustre el contenido de cada párrafo. Cada párrafo debe concluir con una oración que resuma lo que se dijo en el párrafo. Escriba la primera versión de su tesis a doble espacio y con dos o tres párrafos por página. Siga este mismo método de listar oraciones para escribir cada sección de su tesis.

Posteriormente, en las semanas siguientes, lo que sigue básicamente es pulir su escritura. Es imperativo que no haya un solo error ortográfico. La verdadera razón de esto es la siguiente: Usted tiene muy buenos resultados y ha trabajado largo y duro en su investigación. Sin embargo, si algún revisor encuentra un error ortográfico, el revisor podría pensar que si usted no es capaz de cuidar las más básicas reglas ortográficas, él también podría suponer que usted no es cuidadoso al hacer su investigación. La gente piensa así y hay que vivir con eso.

El estilo que debe usted mantener en su tesis es formal y vivo. Si usted disfruta de la escritura de su tesis, el revisor lo notará y eso es bueno. Lea varias tesis de doctorado de las mejores universidades del mundo, siga un estilo similar al de los ganadores y usted también será un ganador. Escriba entre 100 y 150 páginas y preséntelas de manera, pulcra, elegante y muy formal. Listo.

CV

PDF version
(two pages)

LinkedIn profile:
linkedin.com

Web of Science ResearcherID: QIT-6304-2026
webofscience.com

Education

PhD in Physics, Metropolitan Autonomous University, March 2005.

Research and teaching experience

1. Assistant Professor, Tohoku University, Sendai, Japan.
2. Research Visitor, Hokkaido University, Sapporo, Japan.
3. Research Fellow, Chung Yuan Christian University, Jhongli, Taiwan.
4. Research Fellow, National Central University, Jhongli, Taiwan.
5. Research Fellow, The State University of New York, Buffalo, USA.
6. Research Fellow, Universidad Pablo de Olavide, Spain.
7. Graduate Research, Universidad Pablo de Olavide, Spain.
8. Graduate Research, Metropolitan Autonomous University, Mexico.
9. Assistant Lecturer, Metropolitan Autonomous University, Mexico.
10. Research Visitor, Materials Science and Technology Division, LANL, USA.
11. Teaching Assistant, Metropolitan Autonomous University, Mexico.

Selected fellowships and awards

1. Fulbright Scholar
2. Leon Lederman Award in Physics
3. National Researchers System Fellowship, México

Peer review

Physics Reports (20.394), Journal of Physical Chemistry B (3.696), Computational Materials Science (2.863), Europhysics Letters (2.171), Physical Review E (2.255), Soft Matter (3.889), ACS Omega, Journal of Chemical Physics (3.333), Physica A (2.924), COMMAT (2.863), Physica D (1.807), Molecular Physics (1.819), International Journal of Modern Physics C (1.022), International Journal of Modern Physics B (0.647), Chinese Journal of Physics (0.515). (*)=Impact factor

pdf version (2 pages)