Article
Multidisciplinary Sciences
Richard J. Mandle, Nerea Sebastian, Josu Martinez-Perdiguero, Alenka Mertelj
Summary: The study shows that subtle changes in molecular structure can enable denser packing of molecules exhibiting polar order, indicating that the reduction of excluded volume is the origin of the polar nematic phase. Additionally, molecular dynamics simulations are identified as powerful tools for predicting, identifying, and designing materials with the polar nematic phase and its precursor phases.
NATURE COMMUNICATIONS
(2021)
Article
Physics, Fluids & Plasmas
Izabela Shwa, Pavel Maslennikov, Alex Zakharov
Summary: This article describes the physical mechanisms behind the spatially periodic and kinklike distortions that can appear in a homogeneously aligned microsized nematic volume under the influence of crossed electric and magnetic fields. Numerical studies show that when the electric field is directed close to a right angle to the magnetic field, two scenarios of director field reorientation can be realized. Additionally, under certain conditions, a distortion in the form of a kinklike wave spreading normally to the horizontal bounding surfaces with a velocity in a few meters per second can be excited in the microsized nematic volume.
Article
Multidisciplinary Sciences
Sebastian Echeverria-Alar, Marcel G. Clerc, Ignacio Bordeu
Summary: Spatial branching processes are observed in chiral nematic liquid crystals, where a cholesteric phase self-organizes into extended branching patterns. We study the spatial and temporal organization of thermally driven branching patterns in chiral nematic liquid crystal cells experimentally, and describe the observations using a mean-field model.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2023)
Article
Mathematics, Applied
Qiao Liu
Summary: In this paper, the singular points of suitable weak solutions to the 3D co-rotational Beris-Edwards system are investigated. This system models the hydrodynamical motion of nematic liquid crystal flows, and is a coupled system with the Navier-Stokes equations for the fluid and a parabolic system of Q-tensor for the liquid average orientation. The paper also establishes conditions for the finiteness of the number of singular points on a given open subset, and proves the energy equality for the solution including the blow-up time.
JOURNAL OF MATHEMATICAL FLUID MECHANICS
(2023)
Review
Chemistry, Multidisciplinary
Arbresha Holbl, Luka Mesarec, Jus Polansek, Ales Iglix, Samo Kralj
Summary: We studied general mechanisms for stabilizing localized assemblies of topological defects. Physical fields represent fundamental entities in nature and are of interest to all branches of physics. The cores of defects are energetically costly and unfavorable, but thermotropic nematic liquid crystals provide an ideal experimental platform for studying defects and have potential applications.
Article
Mathematics
Qiao Liu
Summary: This study focuses on the partial regularity of suitable weak solutions to the 3d co-rotational Beris-Edwards system, presenting an improved version of the Caffarelli-Kohn-Nirenberg criterion in terms of the velocity gradient. The findings highlight the importance of the velocity field over the Q-tensor field in the partial regularity theory of the 3d co-rotational Beris-Edwards system.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mechanics
Thomas G. J. Chandler, Saverio E. E. Spagnolie
Summary: This study examines the equilibrium configurations of a nematic liquid crystal with an immersed body in two dimensions. Analytical solutions are found using a complex variables formulation in the case of strong anchoring. Local tractions, forces, and torques on the body are discussed. For weak anchoring strengths, an effective boundary technique is proposed to determine asymptotic solutions. The energy-minimizing locations of topological defects on the body surface are also examined. Various examples, including circular and triangular bodies, and a Janus particle with hybrid anchoring conditions, are provided. Analogies to classical results in fluid dynamics are identified.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Physics, Multidisciplinary
Chau Dao, Jeffrey C. Everts, Miha Ravnik, Yaroslav Tserkovnyak
Summary: Adopting a spintronics-inspired approach, we study the reciprocal coupling between ionic charge currents and nematic texture dynamics in a uniaxial nematic electrolyte. Based on the principle of least dissipation of energy, we derive the adiabatic nematic torque exerted by ionic currents on the nematic director field as well as the reciprocal motive force on ions due to the orientational dynamics of the director. Several simple examples are discussed to illustrate the potential functionality of this coupling. Furthermore, a practical means to extract the coupling strength through impedance measurements on a nematic cell is proposed using our phenomenological framework. Exploring further applications based on this physics could foster the development of nematronics-nematic iontronics.
PHYSICAL REVIEW LETTERS
(2023)
Article
Chemistry, Multidisciplinary
Ewan Cruickshank, Rebecca Walker, John M. D. Storey, Corrie T. Imrie
Summary: This article reports the synthesis and characterization of two series of low molar mass liquid crystals in order to investigate the influence of a lateral alkyloxy chain on the formation and stability of ferroelectric nematic phase. The two series differ by the addition of a fluorine substituent. The members of both series exhibit different phase transitions depending on the length of the lateral chain, with a reduction in nematic-isotropic transition temperature and an increase in ferroelectric nematic-nematic or isotropic transition temperature observed as the chain length increases. These findings suggest that the lateral alkyloxy chain adopts specific conformations that affect the mesophase behavior.
Article
Chemistry, Physical
Jordan Hobbs, Matthew Reynolds, Mallasandra Krishnappa Srinatha, Govindaswamy Shanker, Johan Mattsson, Mamatha Nagaraj
Summary: In this study, a detailed investigation of two cyanobiphenyl-based liquid crystal (LC) tripods was conducted, focusing on their phase behavior, molecular relaxation dynamics, rheology, and dielectric properties. It was found that the length of the spacer units in the tripods affects their properties, including the wide nematic range and large birefringence. Four molecular relaxation processes were identified, and the ion transport properties were found to be influenced by the design of the tripod mesogen arm.
JOURNAL OF MOLECULAR LIQUIDS
(2023)
Article
Mathematics
Qiao Liu
Summary: We investigate regularity criteria for weak solutions to the Cauchy problem of the 3d co-rotational Beris-Edwards system for nematic liquid crystals. Our results show that if certain conditions on the associated pressure and the quantity 2Pi+|u|^2+|del Q|^2 are satisfied, then the weak solution (u, Q) to the system is globally smooth. Our findings extend previous known results from the theory of the 3d Navier-Stokes equations if Q is equal to zero.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Physics, Fluids & Plasmas
P. V. Dolganov, A. S. Zverev, K. D. Baklanova, V. K. Dolganov
Summary: The study revealed that both droplet bridge and outer bridge can exist simultaneously during droplet coalescence, fundamentally changing the coalescence process. This leads to a decrease in outer bridge size, an increase in droplet bridge size, and ultimately the formation of satellite droplets.
Article
Mathematics, Applied
Francisco Guillen-Gonzalez, Maria Angeles Rodriguez-Bellido, Giordano Tierra
Summary: In this study, a new model was proposed to represent the interaction between flows and vesicle membranes with liquid crystalline phases. A new numerical scheme was introduced to approximate the model, demonstrating good performance and showcasing the dynamics of such vesicle membranes through several numerical results.
PHYSICA D-NONLINEAR PHENOMENA
(2021)
Article
Mechanics
Sami C. C. Al-Izzi, Richard G. G. Morris
Summary: In this paper, morphodynamic equations governing the behavior of active nematic fluids on deformable curved surfaces are constructed in the large deformation limit. Objective rates are formulated to account for normal deformations while ensuring that tangential flows are Eulerian, and the surface derivative is used in the nematic free energy to couple local order to out-of-plane bending of the surface. Several illustrative instabilities are characterized by focusing on surface geometry and its dynamical interplay with hydrodynamics.
JOURNAL OF FLUID MECHANICS
(2023)
Review
Chemistry, Physical
L. Kondic, L. J. Cummings
Summary: The discussion focuses on the instabilities exhibited by nanoscale thickness free surface nematic liquid crystal (NLC) films deposited on solid substrates, particularly surface instabilities leading to dewetting. Although extensively discussed, there is still no consensus on the interpretation of experimental results, appropriate modeling approaches, or instability mechanisms. The relevance of substrate-film interaction, particularly for NLCs with an 'effective' disjoining pressure incorporating the elastic energy of the NLC film, is highlighted in relation to instability development in thin films.
CURRENT OPINION IN COLLOID & INTERFACE SCIENCE
(2021)
Article
Mathematics, Applied
Jurgen Sprekels, Hao Wu
Summary: This paper studies an optimal control problem for a two-dimensional Cahn-Hilliard-Darcy system with mass sources that is used in modeling tumor growth. The goal is to monitor the tumor fraction within a finite time interval in a way that keeps it under control and minimizes harm to the patient. The paper proves the existence of a solution to the optimal control problem and derives necessary optimality conditions in terms of adjoint variables and variational inequality.
APPLIED MATHEMATICS AND OPTIMIZATION
(2021)
Article
Mathematics, Applied
Takeshi Fukao, Hao Wu
Summary: The study focuses on a class of Cahn-Hilliard equations with specific boundary conditions, establishing global regularity of weak solutions in the case of physically relevant singular potential. Instantaneous strict separation property is proven in two dimensions, while eventual separation property for large time is obtained in three dimensions. It is shown that every global weak solution converges to a single equilibrium as t -> infinity, utilizing an extended Lojasiewicz-Simon inequality.
ASYMPTOTIC ANALYSIS
(2021)
Article
Multidisciplinary Sciences
Xian Chen, Irene Fonseca, Miha Ravnik, Valeriy Slastikov, Claudio Zannoni, Arghir Zarnescu
Summary: The article discusses various research directions in the mathematical design of new materials, including phase-transforming materials, semiconductor materials, soft matter, magnetic materials, liquid crystals, and liquid crystal colloids. It emphasizes the potential for exciting progress that mathematical approaches could bring to these design themes in both soft and hard condensed matter.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Multidisciplinary Sciences
Arghir Zarnescu
Summary: Mathematical studies of nematic liquid crystals are approached from two different perspectives: fluid mechanics and calculus of variations, focusing on dynamical and stationary problems respectively. This review aims to introduce practitioners to results and issues from the other perspective, as well as presenting research topics that bridge the gap between the two communities.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Mathematics
Jingning He, Hao Wu
Summary: This study focuses on a diffuse interface model for incompressible two-phase flows with chemotaxis effects, considering mechanisms such as active transport and nonlocal interactions of Oono's type. The research proves the existence and uniqueness of global strong solutions in a smooth bounded domain, as well as the continuous dependence of the strong solution on initial data and source terms in energy norms. Additionally, the study demonstrates the propagation of regularity for global weak solutions.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Razvan-Dumitru Ceuca, Jamie M. Taylor, Arghir Zarnescu
Summary: In this study, we investigate the impact of boundary rugosity in nematic liquid crystalline systems. A highly general formulation is employed to handle multiple liquid crystal theories simultaneously. Utilizing Gamma convergence techniques, we demonstrate that the fine-scale surface oscillations can be substituted by an effective homogenized surface energy in a simpler domain. Convergence rates are then quantitatively examined in a simplified setting.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2023)
Article
Physics, Condensed Matter
A. Earls, M-C Calderer, M. Desroches, A. Zarnescu, S. Rodrigues
Summary: We propose a minimalist phenomenological model to describe the 'interfacial water' phenomenon near hydrophilic polymeric surfaces. By combining a Ginzburg-Landau approach with Maxwell's equations, we derive a well-posed model that offers a macroscopic interpretation of experimental observations. The unknown parameters in the derived governing equations are estimated using experimental measurements, and the resulting profiles are found to be in agreement with experimental results. This proposed model serves as the first step towards a more complete and parsimonious macroscopic model, which can help elucidate the effects of interfacial water on cells, infrared neural stimulation, and drug interactions.
JOURNAL OF PHYSICS-CONDENSED MATTER
(2022)
Article
Mathematics
Nicholas D. Alikakos, Zhiyuan Geng, Arghir Zarnescu
Summary: We study globally bounded entire minimizers u : R-n -> R-m of Allen-Cahn systems for potentials W >= 0. We establish estimates and bounds for the diffuse interface I-0 and the free boundary partial derivative I-0, and provide results for the case when alpha = 1.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mathematics, Applied
Zhiyuan Geng, Arghir Zarnescu
Summary: This paper investigates the properties of the Landau-de Gennes functional on 3D domains, focusing on the structure and behavior of its minimizers near a point defect. The results obtained provide convergence and approximation properties for the minimizers in the neighborhood of the defect.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Andrea Di Primio, Maurizio Grasselli, Hao Wu
Summary: We investigate a diffuse-interface model for viscous incompressible two-phase flows with surfactant. The model consists of two coupled Cahn-Hilliard equations and a Navier-Stokes system, describing the concentration differences and fluid velocity. We prove the existence of global and unique weak solutions in two dimensions, as well as the existence of unique strong solutions under stronger regularity assumptions in both two and three dimensions. We also establish continuous dependence estimates and instantaneous regularization properties of the solutions.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Simone Rusconi, Christina Schenk, Arghir Zarnescu, Elena Akhmatskaya
Summary: Rational computer-aided design of multiphase polymer materials is crucial for various applications, and while property predictive models have been developed, they lack computational efficiency and accurate prediction of material properties. This study explores the feasibility of enhancing the performance of the LPMF PBM model by reducing its complexity through disregarding the aggregation terms. The resulting models demonstrate a significant improvement in computational efficiency compared to the original LPMF PBM.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Eduard Feireisl, Arnab Roy, Arghir Zarnescu
Summary: In this paper, we study the motion of a small rigid object immersed in a viscous compressible fluid in the 3-dimensional Eucleidean space. By assuming the object is a ball of small radius e, we demonstrate that the behavior of the fluid is independent of the object in the limit of e approaching 0. This result holds for the isentropic pressure law p(Q)=aQ(?) for any ?>3/2, with mild assumptions regarding the rigid body density. Notably, the density can be bounded as soon as ?>3. The proof utilizes a novel method for constructing test functions in the weak formulation of the problem, including a new form of the Bogovskii operator.
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Review
Mathematics
Hao Wu
Summary: The article provides a survey and review on the derivation, structure, and analytical issues of the Cahn-Hilliard equation and its variants. It focuses on the well-posedness and long-time behavior of global solutions in the classical setting, as well as recent progress on dynamic boundary conditions that describe non-trivial boundary effects.
ELECTRONIC RESEARCH ARCHIVE
(2022)
Article
Mathematics, Applied
Hao Wu, Yuchen Yang
Summary: In this paper, we study a hydrodynamic phase-field system that models the deformation of functionalized membranes in incompressible viscous fluids. We prove the existence and uniqueness of global weak solutions, as well as the existence and uniqueness of local strong solutions. We also derive some blow-up criteria and show the eventual regularity of global weak solutions for large time.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2022)
Article
Mathematics, Applied
Xiaoming Wang, Hao Wu
Summary: The study focuses on the Navier-Stokes-Darcy-Boussinesq system modeling thermal convection of a fluid overlying a saturated porous medium in a decomposed domain. Global weak solutions are proved to exist, and a weak-strong uniqueness result is established.
ADVANCES IN DIFFERENTIAL EQUATIONS
(2021)
