Nonlinear Stability at the Zigzag Boundary

We investigate the dynamics of roll solutions at the zigzag boundary of the planar Swift-Hohenberg equation. Linear analysis shows an algebraic decay of small perturbation with a $t^{- 1/4}$ rate, instead of the classical $t^{- 1/2}$ diffusive decay rate, due to the degeneracy of the quadratic term of the continuation of the translational mode of the linearized operator in the Bloch-Fourier spaces. The proof is based on a decomposition of the neutral mode and the faster decaying modes in the Bloch-Fourier space, and a fixed-point argument, demonstrating the irrelevancy of the nonlinear terms.Comment: 29 pages. Results of 2019 Ohio University Mathematics REU with undergraduates Abhijit Chowdhary and Mason Haberle under advisor Qiliang W

Protecting the Giant Pandas: Newspaper Censorship of Negative News

We investigate newspaper censorship of firm-level negative news using a rare setting in which many companies were involved in similar tunneling scandals. We find that the Chinese censorship authorities restrict the dissemination of tunneling news on state-owned enterprises, firms with greater numbers of employees, and large taxpayers. An examination of the difference in censorship behaviors between the central and provincial authorities reveal three incentives that direct the censorship practices: strong local protectionism, cross-provincial competition, and the concern for the relative positions in the political power system. Finally, we show that the tunneling news that is reported leads to negative market reactions and greater trading volumes, indicating that the news that survives the censorship has information content

Weak Diffusive Stability of Roll Solutions at the Zigzag Boundary

Roll solutions at the zigzag boundary, typically selected by patterns and defects in numerical simulations, are shown to be nonlinearly stable. This result also serves as an example that linear decay weaker than the classical diffusive decay, together with quadratic nonlinearity, still gives nonlinear stability of spatially periodic patterns. Linear analysis reveals that, instead of the classical $t^{-1}$ diffusive decay rate, small perturbations of roll solutions at the zigzag boundary decay with a $t^{-3/4}$ rate along with time, due to the degeneracy of the quadratic term of the continuation of the translational mode of the linearized operator in the Bloch-Fourier spaces. The nonlinear stability proof is based on a decomposition of the neutral translational mode and the faster decaying modes in the Bloch-Fourier space, and a fixed-point argument, demonstrating the irrelevancy of the nonlinear terms.Comment: 54 pages, 1 figur

Preface: Special issue on advances in the mathematical study of pattern formation

Natural physical mechanisms are capable of forming an incredible array of self-organized and regular spatio-temporal structure. Often referred to as patterns, such structures have elicited interest by scientists, engineers, and mathematicians alike. Inspired by pioneers like Liesegang, Haeckel, Wentworth Thompson, and Turing, researchers seek to understand how the combination of simple mechanisms, such as diffusion, reaction, convection, or transport, combine to create and mediate regular periodic patterns. Classic examples (for which many interesting questions are still unanswered) arise in the formation of roll states in convective fluids, stripes and spots in animal coats, ordered cell differentiation in biological morphogenesis, and spiral arrangements of primordia in flowers. As such diverse systems often produce qualitatively similar forms, it is of interest to distill any universal properties of patterns across these systems

Comparative study on the thermal performance and economic efficiency of vertical and horizontal ground heat exchangers

The ground-coupled heat pump is a shallow geothermal exploitation method taking soil as the thermal energy source. The ground heat exchanger is an important component of this system, which includes vertical or horizontal configurations. However, to the best of our knowledge, few studies exist involving the comparison of thermal performances and installation costs of two heat exchanger types considering the influence of ground climate, which makes the selection of heat exchanger configuration challenging for a specific field application. Hence, a 3-dimensional numerical model considering the variations of atmospheric conditions and soil water content is constructed in this paper. Based on this model, the thermal performances and economical efficiencies of vertical and horizontal ground heat exchangers are compared. The results indicate that the thermal performance difference between the two heat exchangers is greater in winter than in summer. The thermal performance is hardly influenced by the injection mass flow rate, while it is considerably affected by the length of heat exchanger. The thermal power rises linearly with the increase in heat exchanger length, and the increment of the vertical ground heat exchanger is higher. In addition, when the heat exchanger length is shorter than 40 m, the installation cost and thereby the total cost of the horizontal ground heat exchanger is considerably higher. With regard to both the thermal performance and economic efficiency, a vertical ground heat exchanger is only recommended when installing a single shallow ground heat exchanger.Cited as: Cui, Q., Shi, Y., Zhang, Y., Wu, R., Jiao, Y. Comparative study on the thermal performance and economic efficiency of vertical and horizontal ground heat exchangers. Advances in Geo-Energy Research, 2023, 7(1): 7-19. https://doi.org/10.46690/ager.2023.01.0

3D-printed polycaprolactone-chitosan based drug delivery implants for personalized administration

Fused deposition molding (FDM) can complete most complex preparation of drug delivery implants to meet the personalized needs of patients. However, the drug activity has strict requirements on processing temperature and preparation method of filaments, the implant also has strict biocompatibility requirements for the materials. In this study, a drug delivery implant was prepared with good biocompatibility, controlled and efficient drug release using FDM printing for personalized administration. Drug-loaded filaments were developed for FDM process by hot-melt extrusion (HME). Polycaprolactone was used as a drug delivery carrier, and ibuprofen as the model drug. Notably, chitosan was dissolved to form controlled and efficient release channels. The printability, changes in physical and chemical properties during HME and FDM processes of the filament, and drug release behavior, mechanism and biocompatibility of the implants were investigated. The results showed that the filament tensile strength decreased with the increase of drug and chitosan content. No obvious degradation and chemical change occurred during the whole process. The drug release efficiency could reach\u3e99% and lasted for 120 h mainly via the diffusion - erosion mechanism. The viability of cells cultured for 24 h in 72 h, 100% implant extract was 75.3%