Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0301531

Displacement Field and Elastic Energy of a Circular Twist Disclination for Large Deformations - an Example how to Treat Nonlinear Boundary Value Problems with Computer Algebra Systems

Alexander Unzicker·Karl Fabian
View original source ↗Read source document ↗Export metadata ↓

Abstract

A circular twist disclination is a nontrivial example of a defect in an elastic continuum that causes large deformations. The minimal potential energy and the corresponding displacement field is calculated by solving the Euler-Lagrange-equations. The nonlinear incompressibility constraint is rigorously taken into account. By using an appropriate curvilinear coordinate system a finer resolution in the regions of large deformations is obtained and the dimension of the arising nonlinear PDE's is reduced to two. The extensive algebraic calculations that arise are done by a computer algebra system (CAS). The PDE's are then solved by a difference scheme using the Newton-Raphson algorithm of successive approximations for multidimensional equations. Additional features for global convergence are implemented. To obtain basic states that are sufficiently close to the solution, a one dimensional linearized version of the equation is solved with a numerical computation that reproduces the analytical results of Huang and Mura (1970). With this method, rigorous solutions of the nonlinear equations without any additional simplifications can be obtained. The numerical results show a contraction of the singularity line which corresponds to the well-known Poynting effect in nonlinear elasticity. This combination of analytical and numerical computations proves to be a versatile method to solve nonlinear boundary value problems in complicated geometries.

Explore related subjects

cond-mat.mtrl-scicond-mat.softgr-qcphysics.comp-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Alexander Unzicker, Karl Fabian. 2003-01-28. Displacement Field and Elastic Energy of a Circular Twist Disclination for Large Deformations - an Example how to Treat Nonlinear Boundary Value Problems with Computer Algebra Systems. https://arxiv.org/abs/cond-mat/0301531

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Measuring chiral phonons

Chiral phonons are quantized vibrations where the atomic motion in a solid breaks improper rotation symmetries. In many cases, chiral phonons possess angular momenta and are therefore selective to circularly polarized light. Both fundamental and applied research efforts on chiral phonons have been gaining increasing attention owing to their importance in a variety of fields including spintronics, spin-selective chemical reactions, thermal transport, quantum information processing and biosensing, where the bi-directional spin-lattice coupling enabled by chiral phonons can be harnessed in new ways, and potentially lead to new functionalities. Thus far, the studies of chiral phonons across diverse materials platforms have evolved largely independently within these fields, but the experimental techniques are often interrelated. In this perspective, we present a detailed description, as well as advantages and disadvantages of the current approaches for experimentally measuring chiral phonons in chiral and achiral materials. We conclude with a discussion of new methods for measuring chiral phonons. Ultimately, this work seeks to offer an experimental guide for systematically investigating the properties of chiral phonons in various materials systems and applications.

cond-mat.mtrl-sci↗
arXiv2026

A model of grain growth in UN integrating molecular dynamics, phase-field modeling, and uncertainty quantification

Grain growth kinetics and grain-boundary (GB) properties in uranium mononitride (UN) are investigated through an integrated multiscale framework combining molecular dynamics (MD), phase-field modeling, and surrogate-assisted uncertainty quantification. MD simulations yield GB energies for 27 symmetric tilt boundaries from 0--2000~K, which are consistent with available DFT values. The average GB energy is nearly temperature-independent below 1000~K and increases at higher temperatures. A mechanistic pore-drag model applied to the only available grain growth dataset for actinide nitrides yields a mobility reduction factor of $s \approx 0.93$--$0.99$, statistically indistinguishable from unity, confirming that pore drag is negligible under the experimental conditions. The intrinsic GB mobility is therefore extracted directly from the effective mobility, yielding $M_0 = 2.05\times10^{-15}$~m$^4$/(J$\cdot$s) and $Q_M = 0.89$~eV. Phase-field simulations conducted from 1500--2000~K confirm normal curvature-driven grain growth, with grain size distributions converging to the Hillert-like form. A surrogate-assisted global sensitivity analysis---combining principal component analysis, Gaussian process regression, and Sobol decomposition---reveals that the mobility prefactor $M_0$ dominates output variance at all times, followed by the activation energy $Q_M$, while the GB energy $\gamma$ contributes minimally. These results establish the first quantitative grain growth framework for UN and identify the reduction of uncertainty in $M_0$ and $Q_M$ as the highest-priority target for future experimental efforts.

cond-mat.mtrl-sci↗
arXiv2026

Silicon Solar Cell Design for >30% Efficiency via Singlet Fission

Singlet fission (SF) materials convert high-energy photons into multiple charge carriers, providing a route to exceed the efficiency limits of single-junction silicon solar cells without many of the complexities of multi-junction tandem designs. Following the first demonstration of an SF-enhanced silicon solar cell in 2025, there is a need to understand how SF materials can be effectively integrated into high-efficiency industrial silicon devices and translated from proof of concept to a manufacturable technology. Using coupled optical and electrical simulations, we assess the efficiency potential of several industrially relevant silicon cell architectures combined with SF materials. Interdigitated back-contact (IBC) cells offer the greatest potential for improvement due to unrestricted front-surface access and can achieve efficiencies exceeding 33%. However, performance is highly sensitive to front-surface passivation quality. Appropriate silicon design, particularly controlled surface doping and fixed interfacial charge, can mitigate recombination losses and relax passivation requirements for ultra-thin exciton-transfer layers.

cond-mat.mtrl-sci↗