Instability of the solitary waves for the Generalized Benjamin-Bona-Mahony Equation

In this work, we consider the generalized Benjamin-Bona-Mahony equation $$\partial_t u+\partial_x u+\partial_x( |u|^pu)-\partial_t \partial_x^{2}u=0, \quad(t,x) \in \mathbb{R} \times \mathbb{R},$$ with $p>4$. This equation has the traveling wave solutions $\phi_{c}(x-ct),$ for any frequency $c>1.$ It has been proved by Souganidis and Strauss \cite{Strauss-1990} that, there exists a number $c_{0}(p)>1$, such that solitary waves $\phi_{c}(x-ct)$ with $1<c<c_{0}(p)$ is orbitally unstable, while for $c>c_{0}(p),$ $\phi_{c}(x-ct)$ is orbitally stable. The linear exponential instability in the former case was further proved by Pego and Weinstein \cite{Pego-1991-eigenvalue}. In this paper, we prove the orbital instability in the critical case $c=c_{0}(p)$.Comment: 32 pages, 1 fictur

Lovastatin arrests CHO cells between the origin decision point and the restriction point

AbstractAsynchronously growing Chinese hamster ovary (CHO) cells treated with the pro-drug, β-lactone ring form of lovastatin were arrested in G1-phase. Subsequent removal of lovastatin resulted in the synchronous entry of cells into S-phase regardless of the presence of mevalonic acid. Lovastatin-arrested cells contained hypophosphorylated retinoblastoma protein (Rb) and required serum mitogens to enter S-phase after lovastatin removal, indicating that cell-cycle arrest is prior to the restriction point (R-point). However, in contrast to quiescent cells, intact nuclei prepared from lovastatin-arrested cells were competent for DNA replication when introduced into Xenopus egg extracts. Initiation of replication by Xenopus egg cytosol took place specifically within the dihydrofolate reductase (DHFR) origin locus, demonstrating that cells were arrested after the origin decision point (ODP). We conclude that the β-lactone ring form of lovastatin is an effective reagent with which to synchronize CHO cells between the ODP and R-point, without resulting in the withdrawal of cells from the cell-cycle into a quiescent state

Evolutionary Paths Caused by Feedback between Environment and Finite Population

Natural selection imply that any organisms including human being will evolve to improve its fitness advantage and the selected genotype or phenotype in equilibrium state will not vary over the time. However, evolutionary process of biological organisms in reality is greatly affected by the environmental change and historical accidents. In this paper, we present a framework for analyzing the feedback between species and their environment. The framework accounts for the deterministic effect that species have on their environment, as well as the stochastic effects that arise due to finite populations. Through a simple example, we demonstrate that negative feedback between species and environment negates any advantages that a particular species may possess and results in species coexistence. In the absence of feedback, the dominant species takes over the population if the population is large enough. Conversely, we find that positive feedback generates unpredictable outcomes that depend on the evolutionary path. Even inferior species can take over the population if they achieve sufficient abundance early in the process, after which the evolutionary path becomes locked in. Our results highlight the importance of evolutionary path and the unpredictability caused by positive feedback between species and environment

Exploiting the Power of Human-Robot Collaboration: Coupling and Scale Effects in Bricklaying

As an important contributor to GDP growth, the construction industry is suffering from labor shortage due to population ageing, COVID-19 pandemic, and harsh environments. Considering the complexity and dynamics of construction environment, it is still challenging to develop fully automated robots. For a long time in the future, workers and robots will coexist and collaborate with each other to build or maintain a facility efficiently. As an emerging field, human-robot collaboration (HRC) still faces various open problems. To this end, this pioneer research introduces an agent-based modeling approach to investigate the coupling effect and scale effect of HRC in the bricklaying process. With multiple experiments based on simulation, the dynamic and complex nature of HRC is illustrated in two folds: 1) agents in HRC are interdependent due to human factors of workers, features of robots, and their collaboration behaviors; 2) different parameters of HRC are correlated and have significant impacts on construction productivity (CP). Accidentally and interestingly, it is discovered that HRC has a scale effect on CP, which means increasing the number of collaborated human-robot teams will lead to higher CP even if the human-robot ratio keeps unchanged. Overall, it is argued that more investigations in HRC are needed for efficient construction, occupational safety, etc.; and this research can be taken as a stepstone for developing and evaluating new robots, optimizing HRC processes, and even training future industrial workers in the construction industry

Absence of a transport signature of spin-orbit coupling in graphene with indium adatoms

Enhancement of the spin-orbit coupling in graphene may lead to various topological phenomena and also find applications in spintronics. Adatom absorption has been proposed as an effective way to achieve the goal. In particular, great hope has been held for indium in strengthening the spin-orbit coupling and realizing the quantum spin Hall effect. To search for evidence of the spin-orbit coupling in graphene absorbed with indium adatoms, we carry out extensive transport measurements, i.e., weak localization magnetoresistance, quantum Hall effect and non-local spin Hall effect. No signature of the spin-orbit coupling is found. Possible explanations are discussed.Comment: 5 pages, 4 figures, with supplementary material