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Materials Engineering of Columnar and Living Liquid Crystals via Experimental Characterization, Mathematical Modelling and Simulations

Project Personnel

Maria-Carme Calderer

Principal Investigator

University of Minnesota, Twin Cities

Noel Walkington

Carnegie Mellon University

Lothar Reichel

Kent State University

Sergij Shiyanovskii

Kent State University

Dmitry Golovaty

University of Akron

Oleg Lavrentovich

Kent State University

Funding Divisions

Division of Materials Research (DMR), Division of Mathematical Sciences (DMS)

The principal research objectives of this project are to explore morphogenetic complexity of the equilibrium biphasic states of lyotropic chromonic liquid crystals (LCLCs) that require an implicit balance between the interfacial and bulk energy and to understand the mechanisms of coupling between the out-of-equilibrium behavior of living liquid crystals (LCs) and anisotropic interactions between the constituents, including the interplay of bacterial activity, bacterial concentration, vector field of velocities, and orientational order. These goals will be achieved through controlled experiments and theoretical modeling. In the case of an equilibrium behavior, a challenge is in finding the shapes of orientationally- and translationally-ordered structures in confined geometries, exemplified by the nuclei of the chromonic hexagonal columnar phase in the isotropic environment. The complex shapes observed in experiments need to be described through minimization of both the internal elastic bulk energy and the anisotropic surface anchoring energy. In the studies of dynamics of living liquid crystals (LLCs) the challenge is in simultaneous tracking of a number of scalar, vector, and tensor fields. The project aims to advance our ability to use mathematical algorithms for fast acquisition of big data characterizing dynamic systems with complex structure. It will also enhance predictive capabilities via the development and analysis of associated mathematical models.

Publications

Bend instabilities and topological turbulence in shear-aligned living liquid crystal
H. Baza, F. Chen, T. Turiv, S. V. Shiyanovskii, and O. D. Lavrentovich
1/1/2026
Impact of gas/liquid phase change of CO 2 during injection for sequestration
M. Karimi, E. S. Cochran, M. Massoudi, N. Walkington, M. Pozzi, and K. Dayal
10/1/2025
Radau- and Lobatto-type averaged Gauss rules
L. Reichel, and M. M. Spalević
2/1/2024
Aggregation phenomena in lyotropic chromonic liquid crystals
L. Mrad, L. Zhao, M. I. Español, L. Xu, and M. C. Calderer
6/1/2023
Numerical approximation of nonlinear SPDE’s
M. Ondreját, A. Prohl, and N. J. Walkington
9/12/2022
Averaged Gauss quadrature formulas: Properties and applications
L. Reichel, and M. M. Spalević
8/1/2022
Three-dimensional soliton-like distortions in flexoelectric nematic liquid crystals: modelling and linear analysis
A. Earls, and M. C. Calderer
1/11/2022
Energetic formulation of large‐deformation poroelasticity
M. Karimi, M. Massoudi, N. Walkington, M. Pozzi, and K. Dayal
1/10/2022
Toroidal nuclei of columnar lyotropic chromonic liquid crystals coexisting with an isotropic phase
R. Koizumi, D. Golovaty, A. Alqarni, S. W. Walker, Y. A. Nastishin, M. C. Calderer, and O. D. Lavrentovich
1/1/2022
Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind
D. L. Djukić, R. M. Mutavdžić Djukić, L. Reichel, and M. M. Spalević
12/1/2021
Accretion and ablation in deformable solids with an Eulerian description: examples using the method of characteristics
S. K. Naghibzadeh, N. Walkington, and K. Dayal
11/18/2021
Computation of error bounds via generalized Gauss–Radau and Gauss–Lobatto rules
J. Alahmadi, M. Pranić, and L. Reichel
11/1/2021
Saturn ring defect around a spherical particle immersed in a nematic liquid crystal
S. Alama, L. Bronsard, D. Golovaty, and X. Lamy
9/19/2021
Surface growth in deformable solids using an Eulerian formulation
S. K. Naghibzadeh, N. Walkington, and K. Dayal
9/1/2021
Ion-dependent DNA configuration in bacteriophage capsids
P. Liu, J. Arsuaga, M. C. Calderer, D. Golovaty, M. Vazquez, and S. Walker
8/1/2021
Models of bacteria swimming in a nematic liquid crystal
M. Duan, and N. Walkington
7/9/2021
A one-dimensional variational problem for cholesteric liquid crystals with disparate elastic constants
D. Golovaty, M. Novack, and P. Sternberg
6/1/2021
On the choice of regularization matrix for an ℓ2-ℓ minimization method for image restoration
A. Buccini, G. Huang, L. Reichel, and F. Yin
6/1/2021
A novel modified TRSVD method for large-scale linear discrete ill-posed problems
X. Bai, G. Huang, X. Lei, L. Reichel, and F. Yin
6/1/2021
Chromonic liquid crystals and packing configurations of bacteriophage viruses
L. Hiltner, M. Carme Calderer, J. Arsuaga, and M. Vázquez
5/24/2021
Gauss–Laurent-type quadrature rules for the approximation of functionals of a nonsymmetric matrix
J. Alahmadi, H. Alqahtani, M. S. Pranić, and L. Reichel
5/8/2021
Golub–Kahan vs. Monte Carlo: a comparison of bidiagonlization and a randomized SVD method for the solution of linear discrete ill-posed problems
X. Bai, A. Buccini, and L. Reichel
3/31/2021
Generalized cross validation for ℓp-ℓq minimization
A. Buccini, and L. Reichel
3/29/2021
On the block Lanczos and block Golub–Kahan reduction methods applied to discrete ill‐posed problems
A. Alqahtani, S. Gazzola, L. Reichel, and G. Rodriguez
3/27/2021
Centrality measures for node-weighted networks via line graphs and the matrix exponential
O. De la Cruz Cabrera, M. Matar, and L. Reichel
1/7/2021
Lanczos-based fast blind deconvolution methods
L. Dykes, R. Ramlau, L. Reichel, K. M. Soodhalter, and R. Wagner
1/1/2021
The extended global Lanczos method, Gauss–Radau quadrature, and matrix function approximation
C. Jagels, K. Jbilou, and L. Reichel
1/1/2021
A new nonstationary preconditioned iterative method for linear discrete ill‐posed problems with application to image deblurring
A. Buccini, M. Donatelli, L. Reichel, and W. Zhang
12/3/2020
Large-scale regression with non-convex loss and penalty
A. Buccini, O. De la Cruz Cabrera, M. Donatelli, A. Martinelli, and L. Reichel
11/1/2020
Stability analysis of flow of active extensile fibers in confined domains
L. Zhao, L. Yao, D. Golovaty, J. Ignés-Mullol, F. Sagués, and M. Carme Calderer
11/1/2020
Design of Chiral Domains by Surface Confinement of Liquid Crystals
O. D. Lavrentovich
10/27/2020
Directional self-locomotion of active droplets enabled by nematic environment
M. Rajabi, H. Baza, T. Turiv, and O. D. Lavrentovich
10/12/2020
Global existence of the non-isothermal Poisson–Nernst–Planck–Fourier system
C. Hsieh, T. Lin, C. Liu, and P. Liu
10/1/2020
Linearized Krylov subspace Bregman iteration with nonnegativity constraint
A. Buccini, M. Pasha, and L. Reichel
9/7/2020
An ℓp-ℓq minimization method with cross-validation for the restoration of impulse noise contaminated images
A. Buccini, and L. Reichel
9/1/2020
A spectral method for bipartizing a network and detecting a large anti-community
A. Concas, S. Noschese, L. Reichel, and G. Rodriguez
8/1/2020
Generalized singular value decomposition with iterated Tikhonov regularization
A. Buccini, M. Pasha, and L. Reichel
8/1/2020
Modulus-based iterative methods for constrained ℓ p – ℓ q minimization
A. Buccini, M. Pasha, and L. Reichel
8/1/2020
Comparison of A-posteriori parameter choice rules for linear discrete ill-posed problems
A. Buccini, Y. Park, and L. Reichel
8/1/2020
Ferroelectric nematic liquid crystal, a century in waiting
O. D. Lavrentovich
6/15/2020
Topology control of human fibroblast cells monolayer by liquid crystal elastomer
T. Turiv, J. Krieger, G. Babakhanova, H. Yu, S. V. Shiyanovskii, Q. Wei, M. Kim, and O. D. Lavrentovich
5/15/2020
Iterative Tikhonov regularization of tensor equations based on the Arnoldi process and some of its generalizations
F. P. A. Beik, M. Najafi–Kalyani, and L. Reichel
5/1/2020
A novel iterative method for discrete Helmholtz decomposition
J. Ku, and L. Reichel
5/1/2020
Golub–Kahan bidiagonalization for ill-conditioned tensor equations with applications
F. P. A. Beik, K. Jbilou, M. Najafi-Kalyani, and L. Reichel
4/2/2020
A novel Landau-de Gennes model with quartic elastic terms
D. GOLOVATY, M. NOVACK, and P. STERNBERG
3/24/2020
Polar jets of swimming bacteria condensed by a patterned liquid crystal
T. Turiv, R. Koizumi, K. Thijssen, M. M. Genkin, H. Yu, C. Peng, Q. Wei, J. M. Yeomans, I. S. Aranson, A. Doostmohammadi, and O. D. Lavrentovich
3/2/2020
Simple stopping criteria for the LSQR method applied to discrete ill-posed problems
L. Reichel, H. Sadok, and W. Zhang
1/22/2020
Phase transitions in nematics: textures with tactoids and disclinations
D. Golovaty, Y. Kim, O. D. Lavrentovich, M. Novack, and P. Sternberg
1/1/2020
Rational averaged gauss quadrature rules
L. Reichel, M. Spalevic, and J. Tomanovic
1/1/2020
Shear-induced polydomain structures of nematic lyotropic chromonic liquid crystal disodium cromoglycate
H. Baza, T. Turiv, B. Li, R. Li, B. M. Yavitt, M. Fukuto, and O. D. Lavrentovich
1/1/2020
Multi-component Multiphase Porous Flow
B. Seguin, and N. J. Walkington
11/28/2019
Three-dimensional solitary waves with electrically tunable direction of propagation in nematics
B. Li, R. Xiao, S. Paladugu, S. V. Shiyanovskii, and O. D. Lavrentovich
8/21/2019
Analysis of directed networks via the matrix exponential
O. De la Cruz Cabrera, M. Matar, and L. Reichel
8/1/2019
Arnoldi decomposition, GMRES, and preconditioning for linear discrete ill-posed problems
S. Gazzola, S. Noschese, P. Novati, and L. Reichel
8/1/2019
Internality of generalized averaged Gaussian quadrature rules and truncated variants for measures induced by Chebyshev polynomials
D. L. Djukić, L. Reichel, and M. M. Spalević
8/1/2019
Generalized block anti-Gauss quadrature rules
H. Alqahtani, and L. Reichel
7/30/2019
Nanoparticle-laden droplets of liquid crystals: Interactive morphogenesis and dynamic assembly
Y. Li, N. Khuu, E. Prince, M. Alizadehgiashi, E. Galati, O. D. Lavrentovich, and E. Kumacheva
7/5/2019
Edge importance in a network via line graphs and the matrix exponential
O. De la Cruz Cabrera, M. Matar, and L. Reichel
4/30/2019
Sub‐5 nm Dendrimer Directed Self‐Assembly with Large‐Area Uniform Alignment by Graphoepitaxy
K. Park, W. Jung, K. Kwon, O. D. Lavrentovich, and H. Jung
4/26/2019
Computing unstructured and structured polynomial pseudospectrum approximations
S. Noschese, and L. Reichel
4/1/2019
Effect of Crowding Agent Polyethylene Glycol on Lyotropic Chromonic Liquid Crystal Phases of Disodium Cromoglycate
R. Koizumi, B. Li, and O. D. Lavrentovich
3/19/2019
Multi-Component Multiphase Flow Through a Poroelastic Medium
B. Seguin, and N. J. Walkington
2/6/2019
Eigenvector sensitivity under general and structured perturbations of tridiagonal Toeplitz‐type matrices
S. Noschese, and L. Reichel
1/21/2019
The extended global Lanczos method for matrix function approximation
A. H. Bentbib, M. E. Ghomari, C. Jagels, K. Jbilou, and L. Reichel
1/1/2019
Optimally Conditioned Vandermonde-Like Matrices
M. Kuian, L. Reichel, and S. Shiyanovskii
1/1/2019
Control Volume Approximation of Degenerate Two-Phase Porous Flows
T. J. Murphy, and N. J. Walkington
1/1/2019
Internality of generalized averaged Gaussian quadrature rules and truncated variants for modified Chebyshev measures of the second kind
D. L. Djukić, L. Reichel, M. M. Spalević, and J. D. Tomanović
1/1/2019
Parameter determination for Tikhonov regularization problems in general form
Y. Park, L. Reichel, G. Rodriguez, and X. Yu
12/1/2018
Simple efficient solvers for certain ill-conditioned systems of linear equations, including H(div) problems
J. Ku, and L. Reichel
12/1/2018
Physics of liquid crystals of bent-shaped molecules
A. Jákli, O. D. Lavrentovich, and J. V. Selinger
11/20/2018
Numerical aspects of the nonstationary modified linearized Bregman algorithm
A. Buccini, Y. Park, and L. Reichel
11/1/2018
Effect of UV-light irradiation on phase diagram of lyotropic chromonic liquid crystal
Y. A. Nastishin, V. I. Savaryn, E. Lychkovskyy, M. Y. Yakovlev, P. I. Vankevych, O. M. Krupych, V. I. Hrabchak, O. P. Boiko, V. G. Nazarenko, and O. D. Lavrentovich
10/1/2018
An $$\ell ^2-\ell ^q$$ Regularization Method for Large Discrete Ill-Posed Problems
A. Buccini, and L. Reichel
9/1/2018
Electrically driven three-dimensional solitary waves as director bullets in nematic liquid crystals
B. Li, V. Borshch, R. Xiao, S. Paladugu, T. Turiv, S. V. Shiyanovskii, and O. D. Lavrentovich
7/25/2018
Fast factorization of rectangular Vandermonde matrices with Chebyshev nodes
M. Kuian, L. Reichel, and S. V. Shiyanovskii
6/28/2018
Prepatterned liquid crystal elastomers as a step toward artificial morphogenesis
O. D. Lavrentovich
6/28/2018
Accuracy optimization of combined multiparameter measuring systems with application to polarized light microscopy
M. Kuian, L. Reichel, and S. V. Shiyanovskii
6/25/2018
Sorting and separation of microparticles by surface properties using liquid crystal-enabled electro-osmosis
C. Peng, T. Turiv, Y. Guo, Q. Wei, and O. D. Lavrentovich
6/14/2018
Multiple orthogonal polynomials applied to matrix function evaluation
H. Alqahtani, and L. Reichel
5/12/2018
On the choice of subspace for large-scale Tikhonov regularization problems in general form
G. Huang, L. Reichel, and F. Yin
5/3/2018
Solution methods for linear discrete ill-posed problems for color image restoration
A. H. Bentbib, M. El Guide, K. Jbilou, E. Onunwor, and L. Reichel
4/12/2018
Regularization matrices for discrete ill‐posed problems in several space dimensions
L. Dykes, G. Huang, S. Noschese, and L. Reichel
3/15/2018
Order parameters and time evolution of mesophases in the lyotropic chromonic liquid crystal Sunset Yellow FCF by DNMR
S. D. Berart, L. Tortora, D. Finotello, B. Zupancic, B. Zalar, L. Green, and O. D. Lavrentovich
1/1/2018

View All Publications

Research Highlights

Shear-induced Polydomain Structures of Nematic Lyotropic Chromonic Liquid Crystal
Oleg Lavrentovich (Kent State University)
4/27/2026
Toroidal Nuclei of Columnar Lyotropic Chromonic Liquid Crystals Coexisting with an Isotropic Phase
Dmitry Golovaty (U. Akron), M. Carme Calderer (U. MN), Oleg Lavrentovich (Kent St. U.)
4/27/2026
Bend Instabilities and Topological Turbulence in Shear-aligned Living Liquid Crystal
Sergij Shiyanovskii and Oleg Lavrentovich (Kent State University)
4/27/2026
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