Effective medium approach for stiff polymer networks with flexible cross-links

Recent experiments have demonstrated that the nonlinear elasticity of in vitro networks of the biopolymer actin is dramatically altered in the presence of a flexible cross-linker such as the abundant cytoskeletal protein filamin. The basic principles of such networks remain poorly understood. Here we describe an effective medium theory of flexibly cross-linked stiff polymer networks. We argue that the response of the cross-links can be fully attributed to entropic stiffening, while softening due to domain unfolding can be ignored. The network is modeled as a collection of randomly oriented rods connected by flexible cross-links to an elastic continuum. This effective medium is treated in a linear elastic limit as well as in a more general framework, in which the medium self-consistently represents the nonlinear network behavior. This model predicts that the nonlinear elastic response sets in at strains proportional to cross-linker length and inversely proportional to filament length. Furthermore, we find that the differential modulus scales linearly with the stress in the stiffening regime. These results are in excellent agreement with bulk rheology data.Comment: 12 pages, 8 figure

A Study of Charles-Auguste de Beriot and his Contributions to the Violin

The purpose of this research was to gain information about Charles-Auguste de Beriot (1802-1870) and his contributions to the violin. The specific problems of the study were as follows: 1.) to identify what influenced the compositions of Charles-Auguste de Beriot; 2.) to outline important developments in his writing that contributed to violin technique and Romanticism; and 3.) to analyze Concerto IX in A minor for Violin, Op. 104 in terms of melody, harmony, tonality, texture, and form. The intention of this research is to investigate Beriot’s compositions for violin and examines the Romantic aspects that appear in his Concerto IX. The appendix contains a discography of Concerto IX

Frankenstein: Man or Monster?

Since its first publication in 1818, Mary Shelley’s novel Frankenstein has left a lasting impression upon the world speaking to a multitude of audiences including artists, scientists, philosophers, and society as a whole. Considering the impact of Frankenstein through its evolution as a cultural myth in various plays and films, this thesis will provide a way to gauge the relevance of Shelley’s story as an adaptation. Only by knowing what has been done in the past and how the materials have been used by other playwrights and screenwriters can one understand how to handle them as an original work. The purpose of this project was to examine and identify the main themes of Mary Shelley’s Frankenstein in her original 1818 work; to analyze interpretations in film adaptations from 1931-1994; and to determine how Shelley’s work applies to modern culture in order to lay the groundwork for an original play (the play itself is not a part of this thesis, but an analysis of the structure is provided). The specific problems of the project are as follows: 1) To provide biographical information on Mary Shelley and general information on the influences that led to her creation of Frankenstein; 2) To explore themes of the novel addressed by literary critics; 3) To analyze the identified themes in film adaptations from 1931-94; 4) To analyze the application of Shelley’s original work and interpolation of this research into a contemporary, musical adaptation. Appendices have been added to support this project. Appendix A is a personal analysis of Shelley’s 1818 novel including notes and quotations compiled from two separate readings. Appendix B is the final revision of the original script. Appendix C contains the finalized score for the vocal and instrumental music. Appendix D is a set diagram. Appendix E contains photographs of possible costumes, images for set decoration, and a sketch of the monster’s make-up. Appendix F is the literature review for sources used in Sections I, II, and III

Electronic structure and magnetism in the frustrated antiferromagnet LiCrO2

LiCrO2 is a 2D triangular antiferromagnet, isostructural with the common battery material LiCoO2 and a well-known Jahn-Teller antiferromagnet NaNiO2. As opposed to the latter, LiCrO2 exibits antiferromagnetic exchange in Cr planes, which has been ascribed to direct Cr-Cr d-d overlap. Using LDA and LDA+U first principles calculations I confirm this conjecture and show that (a) direct d-d overlap is indeed enhanced compared to isostructural Ni and Cr compounds, (b) p-d charge transfer gap is also enhanced, thus suppressing the ferromagnetic superexchange, (c) the calculated magnetic Hamiltonian maps well onto the nearest neighbors Heisenberg exchange model and (d) interplanar inteaction is antiferromagnetic.Comment: 5 pages, 4 figure

Nonlinear elasticity of composite networks of stiff biopolymers with flexible linkers

Motivated by recent experiments showing nonlinear elasticity of in vitro networks of the biopolymer actin cross-linked with filamin, we present an effective medium theory of flexibly cross-linked stiff polymer networks. We model such networks by randomly oriented elastic rods connected by flexible connectors to a surrounding elastic continuum, which self-consistently represents the behavior of the rest of the network. This model yields a crossover from a linear elastic regime to a highly nonlinear elastic regime that stiffens in a way quantitatively consistent with experiment.Comment: 4 pages, 3 figure

Criticality and isostaticity in fiber networks

The rigidity of elastic networks depends sensitively on their internal connectivity and the nature of the interactions between constituents. Particles interacting via central forces undergo a zero-temperature rigidity-percolation transition near the isostatic threshold, where the constraints and internal degrees of freedom are equal in number. Fibrous networks, such as those that form the cellular cytoskeleton, become rigid at a lower threshold due to additional bending constraints. However, the degree to which bending governs network mechanics remains a subject of considerable debate. We study disordered fibrous networks with variable coordination number, both above and below the central-force isostatic point. This point controls a broad crossover from stretching- to bending-dominated elasticity. Strikingly, this crossover exhibits an anomalous power-law dependence of the shear modulus on both stretching and bending rigidities. At the central-force isostatic point---well above the rigidity threshold---we find divergent strain fluctuations together with a divergent correlation length $\xi$, implying a breakdown of continuum elasticity in this simple mechanical system on length scales less than $\xi$.Comment: 6 pages, 5 figure

Actively stressed marginal networks

We study the effects of motor-generated stresses in disordered three dimensional fiber networks using a combination of a mean-field, effective medium theory, scaling analysis and a computational model. We find that motor activity controls the elasticity in an anomalous fashion close to the point of marginal stability by coupling to critical network fluctuations. We also show that motor stresses can stabilize initially floppy networks, extending the range of critical behavior to a broad regime of network connectivities below the marginal point. Away from this regime, or at high stress, motors give rise to a linear increase in stiffness with stress. Finally, we demonstrate that our results are captured by a simple, constitutive scaling relation highlighting the important role of non-affine strain fluctuations as a susceptibility to motor stress.Comment: 8 pages, 4 figure

Stress relaxation in F-actin solutions by severing

Networks of filamentous actin (F-actin) are important for the mechanics of most animal cells. These cytoskeletal networks are highly dynamic, with a variety of actin-associated proteins that control cross-linking, polymerization and force generation in the cytoskeleton. Inspired by recent rheological experiments on reconstituted solutions of dynamic actin filaments, we report a theoretical model that describes stress relaxation behavior of these solutions in the presence of severing proteins. We show that depending on the kinetic rates of assembly, disassembly, and severing, one can observe both length-dependent and length-independent relaxation behavior

Critical behaviour in the nonlinear elastic response of hydrogels

In this paper we study the elastic response of synthetic hydrogels to an applied shear stress. The hydrogels studied here have previously been shown to mimic the behaviour of biopolymer networks when they are sufficiently far above the gel point. We show that near the gel point they exhibit an elastic response that is consistent with the predicted critical behaviour of networks near or below the isostatic point of marginal stability. This point separates rigid and floppy states, distinguished by the presence or absence of finite linear elastic moduli. Recent theoretical work has also focused on the response of such networks to finite or large deformations, both near and below the isostatic point. Despite this interest, experimental evidence for the existence of criticality in such networks has been lacking. Using computer simulations, we identify critical signatures in the mechanical response of sub-isostatic networks as a function of applied shear stress. We also present experimental evidence consistent with these predictions. Furthermore, our results show the existence of two distinct critical regimes, one of which arises from the nonlinear stretch response of semi-flexible polymers.

Multi-scale strain-stiffening of semiflexible bundle networks

Bundles of polymer filaments are responsible for the rich and unique mechanical behaviors of many biomaterials, including cells and extracellular matrices. In fibrin biopolymers, whose nonlinear elastic properties are crucial for normal blood clotting, protofibrils self-assemble and bundle to form networks of semiflexible fibers. Here we show that the extraordinary strain-stiffening response of fibrin networks is a direct reflection of the hierarchical architecture of the fibrin fibers. We measure the rheology of networks of unbundled protofibrils and find excellent agreement with an affine model of extensible wormlike polymers. By direct comparison with these data, we show that physiological fibrin networks composed of thick fibers can be modeled as networks of tight protofibril bundles. We demonstrate that the tightness of coupling between protofibrils in the fibers can be tuned by the degree of enzymatic intermolecular crosslinking by the coagulation Factor XIII. Furthermore, at high stress, the protofibrils contribute independently to the network elasticity, which may reflect a decoupling of the tight bundle structure. The hierarchical architecture of fibrin fibers can thus account for the nonlinearity and enormous elastic resilience characteristic of blood clots.Comment: 27 pages including 8 figures and Supplementary Dat