FY2014 Annual Report

Mathematical Soft Matter Unit

Professor Eliot Fried

Abstract

Research efforts in the Mathematical Soft Matter Unit during FY2014 focused on a various topics, including:

(a) Deriving a physically sound and mathematically tractable framework for modeling two-dimensional materials such as paper and graphene, which bend easily but are highly resistant to stretching. As a key fundamental result, we obtained an explicit representation for a generic three-times continuously differentiable isometric mapping from a planar region to a surface in space.

(b) The effect of material stretchability on the equilibrium shape of a Möbius band. Focusing on bands made from rectangular sheets, we obtained a phase diagram that explains how band shape is influenced by the aspect ratio and the Föppl-von Kármán number, which measures the importance of bending energy importance to stretching energy.

(c) Crystal formation in monolayers of magnetic colloids. In this project, we developed a numerical framework for performing simulations designed to (i) improve our understanding the processes that govern the nucleation and growth of defects and (ii) produce optimal strategies for growing defect-free single crystals. This work was closely tied to experiments conducted at Duke University.

(d) Numerical studies of how self-motile agents, such as bacteria, can be used to drive the motion of passive particles. Additionally, we developed a strategy for using spatial averaging to derive continuum equations of motion for suspensions of self-motile agents  from microscopic, particle-based models.

(e) Developing a simulation environment for studying problems involving fluid films that span flexible frames. Long-term, this environment will be applied to study a spectrum and physically and biologically relevant applications such as the maturation of discoidal high-density lipoprotein particles.

1. Staff

  • Dr. Eliot Fried, Professor
  • Dr. Ryohei Seto, Group Leader
  • Dr. Russell Todres, Staff Scientist
  • Dr. Abdul Majid, Postdoctoral Scholar
  • Ms. Agnes Oshiro, Research Administrator

2. Collaborations

  • Theme: Unstretchable two-dimensional materials Type of collaboration: Joint research
    Researchers:
    Professor Yi-Chao Chen, University of Houston, Houston, TX, USA
     
  • Theme: Facture networks in particulate systems Type of collaboration: Joint research
    Researchers:
    Professor John E. Dolbow, Duke University, Durham, NC, USA Yingjie Liu, Duke University, Durham, NC, USA Professor Mahesh Bandi, OIST, Okinawa, Japan Aryesh Mukherjee, OIST, Okinawa, Japan
     
  • Theme: Nanodomain formation and faceting of biomemembranes Type of collaboration: Joint research
    Researchers:
    Professor John E. Dolbow, Duke University, Durham, NC, USA Wen Jiang, Duke University, Durham, NC, USA
     
  • Theme: Upscaling of self-motile suspensions by spatial averaging Type of collaboration: Joint research
    Researchers:
    Dr. Denis F. Hinz, Kamstrup A/S, Skanderborg, Denmark Professor Alexander Panchenko, Washington State University, Pullman, WA, USA
     
  • Theme: Simulation of wind-driven ocean circulation Type of collaboration: Joint research
    Researchers:
    Professor Luca Heltai, International School for Advanced Studies, Trieste, Italy Dr. Wen Jiang, Fuels Modeling and Simulation, Idaho National Laboratory, Idaho Falls, ID, USA Professor Tae-Yeon Kim, Khalifa University of Science, Technology and Research, Abu Dhabi, UAE Dr. Nella Rotundo, Weierstraß-Institut, Berlin, Germany
     
  • Theme: Two-dimensional crystal formation in magnetic colloids Type of collaboration: Joint research
    Researchers:
    Professor Benjamin Yellen, Duke University, Durham, NC, USA An Pham, Duke University, Durham, NC, USA Dr. Ryohei Seto, OIST, Okinawa, Japan
     

3. Publications

3.1 Journals

  1. D. F. Hinz, A. Panchenko, T.-Y. Kim, E. Fried. Motility versus fluctuations: mixtures of self-propelled and passive particles, Soft Matter 10 (2014), 9082–9089. (doi:10.1039/c4sm01562b)
  2. A. Biria, E. Fried. Buckling of a soap film spanning a flexible loop resistant to bending and twisting, Proceedings of the Royal Society of London Series A, Mathematical, Physical and Engineering Sciences 470 (2014), 20140368. (doi:10.1098/rspa.2014.0368)
  3. T.-Y. Kim, X. Chen, J. Dolbow, E. Fried. Going to new lengths: studying the Navier–Stokes-αβ equations using the spiral vortex model, Discrete and Continuous Dynamical Systems, Series B 19 (2014), 2207–2225. (doi:10.3934/dcdsb.2014.19.2207)
  4. G. Giuisteri, E. Fried. Slender-body theory for viscous flow via dimensional reduction and hyperviscous regularization, Meccanica 49 (2014), 2153–2167. (doi:10.1007/s11012-014-9890-4)
  5. B. Seguin, D. F. Hinz, E. Fried. Extending the transport theorem to rough domains of integration, Applied Mechanics Reviews 66 (2014), 050802. (doi:10.1115/1.4026910)
  6. B. Seguin, E. Fried. Roughening it — Evolving irregular domains and transport theorems, Mathematical Models and Methods in Applied Sciences 24 (2014), 1729–1779. (doi:10.1142/S0218202514500067)
  7. Y.-C. Chen, E. Fried.  Stability and bifurcation of a soap film spanning a flexible loop. Journal of Elasticity 116 (2014), 75–100. (doi:10.1007/s10659-013-9458-x)
  8. D. F. Hinz, T.-Y. Kim, E. Fried. Statistics of the Navier–Stokes-alpha-beta regularization model for fluid turbulence, Journal of Physics A: Mathematical and Theoretical 47 (2014), 055501. (doi:10.1088/1751-8113/47/5/055501)

3.2 Books and other one-time publications

  1. B. Seguin, E. Fried, Calculating the bending moduli of the Canham–Helfrich free-energy density, to appear in: Differential Geometry and Continuum Mechanics (R.J. Knops, G.-Q. Chen, M. Grinfeld, Eds.). Springer Proceedings in Mathematics and Statistics 137 (2015). (doi:10.1007/978-3-319-18573-6_12)

3.3 Oral and Poster Presentations

  1. Fried, E. "Stability and Bifurcation of a Flexible Loop Spanned by a Fluid Film", University of Hong Kong (2015).
  2. Seto, R. "Particle scale simulations for bulk rheology: Shear thickening suspensions and yield stress suspensions", Universite Paris-Est, France (2015).
  3. Seto, R. "Beyond friction: cohesion and interlocking in shear thickening of suspensions", in Arrested Gels: Dynamics, Structure, and Applications at Gonville and Caius College, Cambridge, UK (2015).
  4. Fried, E. "Dimensionally Reduced Energy of a Möbius Band made from an Unstretchable but Bendable Sheet", University of California, Berkeley, USA (2015).
  5. Seto, R. "Particle-Scale Modeling of Colloidal Suspension Rheology: Shear Thickening", in The 7th Biennial Australian Colloid and Interface Symposium, Tasmania, Australia (2015).
  6. Seto, R. "Inter-Particle Contact Forces: Why They Matter in Flow of Suspensions", the University of Melbourne, Australia (2015).
  7. Fried, E. "Slender-body theory via dimensional reduction and hyperviscous regularization", the University of British Columbia, Canada (2015).
  8. Seto, R. "S-shaped Rheology Curves of Shear Thickening Suspension", in The 4th Soft Matter Study Group at Nagoya University, Japan (2015).
  9. Fried, E. "Stability of discoidal high-density lipoprotein particles", in CMMSC Short Course: Some Applications of Mathematics to Soft Matter at National Chiao Tung University, Taiwan (2014).
  10. Fried, E. "Slender-body theory via dimensional reduction and hyperviscous regularization", in CMMSC Short Course: Some Applications of Mathematics to Soft Matter at National Chiao Tung University, Taiwan (2014).
  11. Fried, E. "Self-propelled soft-core dumbbells for active suspensions", in CMMSC Short Course: Some Applications of Mathematics to Soft Matter at National Chiao Tung University, Taiwan (2014).
  12. Fried, E. " Isometric mappings of the plane into surfaces in three-dimensional space and the energetics of ribbons and bands", in CMMSC Short Course: Some Applications of Mathematics to Soft Matter at National Chiao Tung University, Taiwan (2014).

 

4. Intellectual Property Rights and Other Specific Achievements

Nothing to report.

5. Meetings and Events

5.1 Research Visits and Seminars

  • Title: Modeling the sedimentation of filaments in viscous fluids via dimensional reduction and hyperviscous regularization
    • Date: May 23, 2014
    • Venue: OIST Campus, Center building
    • Speaker: Dr. Giulio G. Giusteri
      Assistant Professor at the Department of Mathematics and Physics of the Catholic University of the Sacred Heart in Brescia, Italy
       
  • Title: Rigidity vs. flexibility of isometric immersions and degenerate deformations of Euclidean domains
    • Date: August 4, 2014
    • Venue: OIST Campus, Center building
    • Speaker: Dr. Reza Pakzad
      Assistant Professor, Department of Mathematics, University of Pittsburgh
       
  • Title: Shear Thickening of Brownian and non-Brownian suspensions: the Essential Role of Frictional Contact
    • Date: August 5, 2014
    • Venue: OIST Campus, Center building
    • Speaker: Dr. Ryohei Seto
      Research Associate of Benjamin Levich Institute at The City College of New York
       
  • Title: Variational models for prestrained plates with Monge-Ampère constraint
    • Date: August 8, 2014
    • Venue: OIST Campus, Center building
    • Speaker: Associate Professor Marta Lewicka
      Department of Mathematics, University of Pittsburgh
       
  • Title:  Modeling Immuno-qPCR to Estimate Protein Quantity in a Biological Sample
    • Date: August 22, 2014
    • Venue: OIST Campus, Center building
    • Speaker: Dr. Harrison Leong
      Sr. Staff Engineer, Software, Thermo Fisher Scientific Inc. U.S.A.
       
  • Title: Digital PCR (dPCR), Target-specific Quantification of Genetic Material Using a Silicon Wafer
    • Date: August 29, 2014
    • Venue: OIST Campus, Center building
    • Speaker: Dr. Harrison Leong
      Sr. Staff Engineer, Software, Thermo Fisher Scientific Inc. U.S.A.
       
  • Title: Continuous States in Dipole Clusters: Why Dipoles are Bevel Gears
    • Date: January 14, 2015
    • Venue: OIST Campus, Lab1
    • Speaker: Dr.Johannes Schoenke
       
  • Title: Active Matter in confining geometries
    • Date: January 20, 2015
    • Venue: OIST Campus, Lab1
    • Speaker: Dr. Matteo Paoluzzi
       
  • Title: How synthetic microswimmers move, turn, flip, and spread
    • Date: February 20, 2015
    • Venue: OIST Campus, Lab1
    • Speaker: Professor Daisuke Takagi
      Mathematics at the University of Hawaii at Manoa
       
  • Title: Macroscopic behavior of systems with a dynamic preferred direction
    • Date: March 6, 2015
    • Venue: OIST Campus, Lab1
    • Speaker: Professor Helmut Brand
      Department of Physics, University of Bayreuth, Germany
       
  • Title: Phase transformations in colloidal alloys
    • Date: March 12, 2015
    • Venue: OIST Campus, Lab1
    • Speaker: Professor Benjamin Yellen
      Department of Mechanical Engineering and Materials Science at Duke University, Durham, NC
       
  • Title: Magnetophoretic Circuits for Applications in Single Cell Arrays
    • Date: March 13, 2015
    • Venue: OIST Campus, Lab1
    • Speaker: Professor Benjamin Yellen
      Department of Mechanical Engineering and Materials Science at Duke University, Durham, NC