Monodomain Liquid Crystals of Two-Dimensional Sheets by Boundary-Free Sheargraphy

Eliminating topological defects to achieve monodomain liquid crystals is highly significant for the fundamental studies of soft matter and building long-range ordered materials.However,liquid crystals are metastable and sensitive to external stimuli,such as flow,confinement,and electromagnetic fields,which cause their intrinsic polycrystallinity and topological defects.Here,we achieve the monodomain liquid crystals of graphene oxide over 30 cm through boundary-free sheargraphy.The obtained monodomain liquid crystals exhibit large-area uniform alignment of sheets,which has the same optical polarized angle and intensity.The monodomain liquid crystals provide bidirectionally ordered skeletons,which can be applied as lightweight thermal management materials with bidirectionally high thermal and electrical conductivity.Furthermore,we extend the controllable topology of two-dimensional colloids by introducing singularities and disclinations in monodomain liquid crystals.Topological structures with defect strength from−2 to+2 were realized.This work provides a facile methodology to study the structural order of soft matter at a macroscopic level,facilitating the fabrication of metamaterials with tunable and highly anisotropic architectures.

Modified Fletcher-Reeves and Dai-Yuan Conjugate Gradient Methods for Solving Optimal Control Problem of Monodomain Model

In this paper, we present the numerical solution for the optimal control problem of monodomain modelwith Rogers-modified FitzHugh-Nagumo ion kinetic. The monodomain model, which is a well-known mathematical model for simulation of cardiac electrical activity, appears as the constraint in our problem. Our control objective is to dampen the excitation wavefront of the transmembrane potential in the observation domain using optimal applied current. Various conjugate gradient methods have been applied by researchers for solving this type of optimal control problem. For the present paper, we adopt the modified Fletcher-Reeves method and modified Dai-Yuan methodfor computing the optimal applied current. Numerical results show that the excitation wavefront is successfully dampened out by the optimal applied current when the modified Fletcher-Reeves method is used. However, this is not the case when the modified Dai-Yuan method is employed. Numerical results indicate that the modified Dai-Yuan method failed to converge to the optimal solution when the Armijo line search is used.

Stable large-area monodomain in as-grown bulk ferroelectric single crystal Sn_(2)P_(2)S_(6)

Driven by the minimization of total energy,the multi-domain morphology is preferred in as-grown ferroelectrics to reduce the depolarization and strain energy during the paraelectric to ferroelectric phase transition.However,the complicated multi-domain is not desirable for certain high-performance ferroelectric electro-optic devices.In this work,we achieve a reproducible and stable large-area monodomain in as-grown bulk ferroelectric single crystal Sn_(2)P_(2)S_(6).The monodomain dominates the entire single crystal,which is attributed to the internal charge carriers from the photoexcited disproportionation reaction of Sn ions.The charge carriers effectively screen the depolarization field and therefore decrease the depolarization energy and facilitate the formation of monodomain.This work offers a potential approach for engineering bulk ferroelectrics with a stable monodomain,which is desirable for the high-performance ferroelectric electro-optic devices.

A 2-D Kinetic Theory for Flows of Monodomain Polymer-Rod Nanocomposites

We merge classical kinetic theories [M. Doi and S. F. Edwards, The Theoryof Polymer Dynamics, 1986] for viscous dispersions of rigid rods, extended to semi-flexibility [A. R. Khokhlov and A. N. Semenov, Macromolecules, 17 (1984), pp. 2678-2685], and for Rouse flexible chains to model the hydrodynamics of polymer nano-rodcomposites (PNCs). A mean-field potential for the polymer-rod interface provides thekey coupling between the two phases. We restrict this first study to two-dimensionalconformational space. We solve the coupled set of Smoluchowski equations for threebenchmark experiments. First we explore how rod semi-flexibility and the polymer-rod interface alter the Onsager equilibrium phase diagram. Then we determine mon-odomain phase behavior of PNCs for imposed simple elongation and shear, respec-tively. These results inform the effects that each phase has on the other as parametricstrengths of the interactions are varied in the context of the most basic rheological ex-periments.

On the electrophysiology of the atrial fast conduction system:an uncertain quantification study

Cardiac modeling entails the epistemic uncertainty of the input parameters,such as bundles and chambers geometry,electrical conductivities and cell parameters,thus calling for an uncertainty quantification(UQ)analysis.Since the cardiac activation and the subsequent muscular contraction is provided by a complex electrophysiology system made of interconnected conductive media,we focus here on the fast conductivity structures of the atria(internodal pathways)with the aim of identifying which of the uncertain inputs mostly influence the propagation of the depolarization front.Firstly,the distributions of the input parameters are calibrated using data available from the literature taking into account gender differences.The output quantities of interest(Qols)of medical relevance are defined and a set of metamodels(one for each Qol)is then trained according to a polynomial chaos expansion(PCE)in order to run a global sensitivity analysis with non-linear variance-based SoboF indices with confidence intervals evaluated through the bootstrap method.The most sensitive parameters on each Qol are then identified for both genders showing the same order of importance of the model inputs on the electrical activation.Lastly,the probability distributions of the Qols are obtained through a forward sensitivity analysis using the same trained metamodels.It results that several input parameters-including the position of the internodal pathways and the electrical impulse applied at the sinoatrial node一have a little influence on the Qols studied.Vice-versa the electrical activation of the atrial fast conduction system is sensitive on the bundles geometry and electrical conductivities that need to be carefully measured or calibrated in order for the electrophysiology model to be accurate and predictive.