Mechanics Of Fluctuating Elastic Plates And Fiber Networks

Lipid membranes and fiber networks in biological systems perform important mechanical functions at the cellular and tissue levels. In this thesis I delve into two detailed problems -- thermal fluctuation of membranes and non-linear compression response of fiber networks. Typically, membrane fluctuations are analysed by decomposing into normal modes or by molecular simulations. In the first part of my thesis, I propose a new semi-analytic method to calculate the partition function of a membrane. The membrane is viewed as a fluctuating von Karman plate and discretized into triangular elements. Its energy is expressed as a function of nodal displacements, and then the partition function and co-variance matrix are computed using Gaussian integrals. I recover well-known results for the dependence of the projected area of a lipid bilayer membrane on the applied tension, and recent simulation results on the ependence of membrane free energy on geometry, spontaneous curvature and tension. As new applications I use this technique to study a membrane with heterogeneity and different boundary conditions. I also use this technique to study solid membranes by taking account of the non-linear coupling of in-plane strains with out-of-plane deflections using a penalty energy, and apply it to graphene, an ultra-thin two-dimensional solid. The scaling of graphene fluctuations with membrane size is recovered. I am able to capture the dependence of the thermal expansion coefficient of graphene on temperature. Next, I study curvature mediated interactions between inclusions in membranes. I assume the inclusions to be rigid, and show that the elastic and entropic forces between them can compete to yield a local maximum in the free energy if the membrane bending modulus is small. If the spacing between the inclusions is less than this local maximum then the attractive entropic forces dominate and the separation between the inclusions will be determined by short range interactions; if the spacing is more than the local maximum then the elastic repulsive forces dominate and the inclusions will move further apart. This technique can be extended to account for entropic effects in other methods which rely on quadratic energies to study the interactions of inclusions in membranes. In the second part of this thesis I study the compression response of two fiber network materials -- blood clots and carbon nanotube forests. The stress-strain curve of both materials reveals four characteristic regions, for compression-decompression: 1) linear elastic region; 2) upper plateau or softening region; 3) non-linear elastic region or re-stretching of the network; 4) lower plateau in which dissociation of some newly made connections occurs. This response is described by a phase transition based continuum model. The model is inspired by the observation of one or more moving interfaces across which densified and rarefied phases of fibers co-exist. I use a quasi-static version of the Abeyaratne-Knowles theory of phase transitions for continua with a stick-slip type kinetic law and a nucleation criterion based on the critical stress for buckling to describe the formation and motion of these interfaces in uniaxial compression experiments. Our models could aid the design of biomaterials and carbon nanotube forests to have desired mechanical properties and guide further understanding of their behavior under large deformations

Angle constrained paths in sensor networks

Short-length paths in geometric graphs are not necessarily feasible in sensor networks and robotics. Paths with sharp-turn angles cannot be used by robotic vehicles and tend to consume more energy in sensor networks; In this thesis, we investigate the development of short-length paths without sharp-turn angles. We present a critical review of existing algorithms for generating angle constrained paths. We then consider the construction of routes having directional properties---d-monotone routes which are special cases of angle constrained paths. We develop a centralized algorithm for computing shortest d-monotone paths in triangulated networks. Since local computations are highly desired in sensor networks, we also consider localized online algorithms for computing length-reduced d-monotone paths in Delaunay Triangulation networks; The proposed algorithms are implemented in the Java programming language. Performances of the proposed algorithms are evaluated by examining the routes constructed by them on several randomly-generated Delaunay networks

Disentangled Phonetic Representation for Chinese Spelling Correction

Chinese Spelling Correction (CSC) aims to detect and correct erroneous characters in Chinese texts. Although efforts have been made to introduce phonetic information (Hanyu Pinyin) in this task, they typically merge phonetic representations with character representations, which tends to weaken the representation effect of normal texts. In this work, we propose to disentangle the two types of features to allow for direct interaction between textual and phonetic information. To learn useful phonetic representations, we introduce a pinyin-to-character objective to ask the model to predict the correct characters based solely on phonetic information, where a separation mask is imposed to disable attention from phonetic input to text. To avoid overfitting the phonetics, we further design a self-distillation module to ensure that semantic information plays a major role in the prediction. Extensive experiments on three CSC benchmarks demonstrate the superiority of our method in using phonetic information.Comment: Accepted to ACL 2023 Main Conferenc

The Complex Phase Transformation of Austenite in High Strength Linepipe Steels and Its Influence on the Mechanical Properties

During processing of low carbon high strength linepipe steels, complex microstructures are usually obtained. Toughness of the steels is found to be strongly dependent on the complex microstructures. Since the microstructural and chemical condition of austenite is very important for the subsequent microstructures, austenite grain coarsening and recrystallization temperatures were determined. The results showed addition of 0.3wt% more chromium can reduce about 100°C of the grain coarsening temperature. Thus, the alloy design should be considered together with thermomechanical processing to avoid the mixture of austenite grain size. It was found that Bs temperatures of steel have a wide range from 400°C to 580°C, depending on cooling rates. The formation of martensite-austenite (MA) constituents and bainitic transformation were investigated in isothermal treatment and continuous cooling conditions. The carbon diffusion was discussed from the view point of thermodynamics and kinetics to explain the formation of MA during bainitic transformation. It was found that controlling carbon diffusion is most important point for the formation of MA. Some experiments were designed and the results confirmed the thermodynamics analysis. In addition, the crystallographic orientations of bainite formed at different bainite transformation temperatures were also determined by EBSD analysis. The orientations of bainite are irrational, but two typical orientations were found. The orientation is near at a higher transformation temperature and the orientation is near at a lower transformation temperature. The crystallographic packet size of bainite is large when the orientation is near . Coincident Site Lattice (CSL) grain boundaries were introduced to explain its relationship to toughness. As proposed in this thesis, the size and volume fraction of MA, crystallographic packet size and CSL grain boundaries are the three predominant factors affecting the impact toughness of steels. Thus, some methods were proposed for impact toughness improvement. In this regard, a schematic CCT diagram was developed based on the classification of bainite and the distribution of MA within each classification. These results could provide some guidance for improved understanding of the complex microstructures of these steels

Quantization of the Lie bialgebra of string topology

Let M be a smooth, simply-connected, closed oriented manifold, and LM the free loop space of M. Using a Poincare duality model for M, we show that the reduced equivariant homology of LM has the structure of a Lie bialgebra, and we construct a Hopf algebra which quantizes the Lie bialgebra.Comment: 16 page