Positive solutions and eigenvalue intervals of nonlocal boundary value problems with delays

AbstractThe paper is concerned with the delay differential equation u″+λb(t)f(u(t−τ))=0 satisfying u(t)=0 for −τ⩽t⩽0 and u(1)=g(∫01u(t)dβ(t)), where ∫01u(t)dβ(t) denotes the Riemann–Stieltjes integral. By applying the fixed point theorem in cones, we show the relationship between the asymptotic behaviors of the quotient f(u)u (at zero and infinity) and the open intervals (eigenvalue intervals) of the parameter λ such that the problem has zero, one and two positive solution(s). If g(t)=t, by using a property of the Riemann–Stieltjes integral, the above nonlocal boundary value problem educes a three-point boundary value problem with delay, for which some similar results are established

A novel super-elastic carbon nanofiber with cup-stacked carbon nanocones and a screw dislocation

Carbon nanofibers (NFs) have been envisioned with broad promising applications, such as nanoscale actuators and energy storage medium. This work reports for the first-time super-elastic tensile characteristics of NFs constructed from a screw dislocation of carbon nanocones (NF-S). The NF-S exhibits three distinct elastic deformation stages under tensile, including an initial homogeneous deformation, delamination, and further stretch of covalent bonds. The delamination process endows the NF-S extraordinary tensile deformation capability, which is not accessible from its counterpart with a normal cup-stacked geometry. The failure of NF-S is governed by the inner edges of the nanocone due to the strain concentration, leading to a common failure force for NF-S with varying geometrical parameters. Strikingly, the delamination process is dominated by the inner radius and the apex angle of the nanocone. For a fixed apex angle, the yielding strain increases remarkably when the inner radius increases, which can exceed 1000%. It is also found that the screw dislocation allows the nanocones flattening and sliding during compression. This study provides a comprehensive understanding on the mechanical properties of NFs as constructed from carbon nanocones, which opens new avenues for novel applications, such as nanoscale actuators.Comment: 10 pages, 10 figure

Clinical and radiological characteristics of pediatric COVID-19 before and after the Omicron outbreak: a multi-center study

IntroductionThe emergence of the Omicron variant has seen changes in the clinical and radiological presentations of COVID-19 in pediatric patients. We sought to compare these features between patients infected in the early phase of the pandemic and those during the Omicron outbreak.MethodsA retrospective study was conducted on 68 pediatric COVID-19 patients, of which 31 were infected with the original SARS-CoV-2 strain (original group) and 37 with the Omicron variant (Omicron group). Clinical symptoms and chest CT scans were examined to assess clinical characteristics, and the extent and severity of lung involvement.ResultsPediatric COVID-19 patients predominantly had normal or mild chest CT findings. The Omicron group demonstrated a significantly reduced CT severity score than the original group. Ground-glass opacities were the prevalent radiological findings in both sets. The Omicron group presented with fewer symptoms, had milder clinical manifestations, and recovered faster than the original group.DiscussionThe clinical and radiological characteristics of pediatric COVID-19 patients have evolved with the advent of the Omicron variant. For children displaying severe symptoms warranting CT examinations, it is crucial to weigh the implications of ionizing radiation and employ customized scanning protocols and protective measures. This research offers insights into the shifting disease spectrum, aiding in the effective diagnosis and treatment of pediatric COVID-19 patients

Collective dynamics and control of a 3-D small-world network with time delays

The paper presents a detailed analysis on the collective dynamics and delayed state feedback control of a three-dimensional delayed small-world network. The trivial equilibrium of the model is first investigated, showing that the uncontrolled model exhibits complicated unbounded behavior. Then three control strategies, namely a position feedback control, a velocity feedback control, and a hybrid control combined velocity with acceleration feedback, are then introduced to stabilize this unstable system. It is shown in these three control schemes that only the hybrid control can easily stabilize the 3-D network system. And with properly chosen delay and gain in the delayed feedback path, the hybrid controlled model may have stable equilibrium, or periodic solutions resulting from the Hopf bifurcation, or complex stranger attractor from the period-doubling bifurcation. Moreover, the direction of Hopf bifurcation and stability of the bifurcation periodic solutions are analyzed. The results are further extended to any "d" dimensional network. It shows that to stabilize a "d" dimensional delayed small-world network, at least a "d – 1" order completed differential feedback is needed. This work provides a constructive suggestion for the high dimensional delayed systems

Positive solutions for nonlinear discrete second-order boundary value problems with parameter dependence

AbstractIn this paper, we consider the nonlinear discrete boundary value problem{−Δ[p(t−1)Δu(t−1)]+q(t)u(t)=λf(t,u(t)),t∈Z[1,T],u(0)=u(T),p(0)Δu(0)=p(T)Δu(T), where λ is a positive parameter. By using the fixed point index theory, the criteria of the existence, multiplicity and nonexistence of positive solutions are established in terms of different values of λ

Numerical investigation of mechanical properties of nanowires: a review

Nanowires (NWs) have attracted intensive researches owing to the broad applications that arise from their remarkable properties. Over the last decade, immense numerical studies have been conducted for the numerical investigation of mechanical properties of NWs. Among these numerical simulations, the molecular dynamics (MD) plays a key role. Herein we present a brief review on the current state of the MD investigation of nanowires. Emphasis will be placed on the FCC metal NWs, especially the Cu NWs. MD investigations of perfect NWs’ mechanical properties under different deformation conditions including tension, compression, torsion and bending are firstly revisited. Following in succession, the studies for defected NWs including the defects of twin boundaries (TBs) and pre-existing defects are discussed. The different deformation mechanism incurred by the presentation of defects is explored and discussed. This review reveals that the numerical simulation is an important tool to investigate the properties of NWs. However, the substantial gaps between the experimental measurements and MD results suggest the urgent need of multi-scale simulation technique

A novel quadratic Edge-based Smoothed Conforming Point Interpolation Method (ES-CPIM) for elasticity problems

his paper formulates an edge-based smoothed conforming point interpolation method (ES-CPIM) for solid mechanics using the triangular background cells. In the ES-CPIM, a technique for obtaining conforming PIM shape functions (CPIM) is used to create a continuous and piecewise quadratic displacement field over the whole problem domain. The smoothed strain field is then obtained through smoothing operation over each smoothing domain associated with edges of the triangular background cells. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. Numerical studies have demonstrated that the ES-CPIM possesses the following good properties: (1) ES-CPIM creates conforming quadratic PIM shape functions, and can always pass the standard patch test; (2) ES-CPIM produces a quadratic displacement field without introducing any additional degrees of freedom; (3) The results of ES-CPIM are generally of very high accuracy