On the quenching behaviour of a semilinear wave equation modelling MEMS technology

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - Series A following peer review. The definitive publisher-authenticated version 2015, 35(3), pp. 1009-1037 is available online at: http://dx.doi.org/10.3934/dcds.2015.35.100

A study of a nonlocal problem with Robin boundary conditions arising from technology

From Wiley via Jisc Publications RouterHistory: received 2020-08-03, rev-recd 2021-02-18, accepted 2021-02-22, pub-electronic 2021-05-04Article version: VoRPublication status: PublishedIn the current work, we study a nonlocal parabolic problem with Robin boundary conditions. The problem arises from the study of an idealized electrically actuated MEMS (micro‐electro‐mechanical system) device, when the ends of the device are attached or pinned to a cantilever. Initially, the steady‐state problem is investigated estimates of the pull‐in voltage are derived. In particular, a Pohožaev's type identity is also obtained, which then facilitates the derivation of an estimate of the pull‐in voltage for radially symmetric N‐dimensional domains. Next a detailed study of the time‐dependent problem is delivered and global‐in‐time as well as quenching results are obtained for generic and radially symmetric domains. The current work closes with a numerical investigation of the presented nonlocal model via an adaptive numerical method. Various numerical experiments are presented, verifying the previously derived analytical results as well as providing new insights on the qualitative behavior of the studied nonlocal model

Correction to: Two years later: Is the SARS-CoV-2 pandemic still having an impact on emergency surgery? An international cross-sectional survey among WSES members

Background: The SARS-CoV-2 pandemic is still ongoing and a major challenge for health care services worldwide. In the first WSES COVID-19 emergency surgery survey, a strong negative impact on emergency surgery (ES) had been described already early in the pandemic situation. However, the knowledge is limited about current effects of the pandemic on patient flow through emergency rooms, daily routine and decision making in ES as well as their changes over time during the last two pandemic years. This second WSES COVID-19 emergency surgery survey investigates the impact of the SARS-CoV-2 pandemic on ES during the course of the pandemic. Methods: A web survey had been distributed to medical specialists in ES during a four-week period from January 2022, investigating the impact of the pandemic on patients and septic diseases both requiring ES, structural problems due to the pandemic and time-to-intervention in ES routine. Results: 367 collaborators from 59 countries responded to the survey. The majority indicated that the pandemic still significantly impacts on treatment and outcome of surgical emergency patients (83.1% and 78.5%, respectively). As reasons, the collaborators reported decreased case load in ES (44.7%), but patients presenting with more prolonged and severe diseases, especially concerning perforated appendicitis (62.1%) and diverticulitis (57.5%). Otherwise, approximately 50% of the participants still observe a delay in time-to-intervention in ES compared with the situation before the pandemic. Relevant causes leading to enlarged time-to-intervention in ES during the pandemic are persistent problems with in-hospital logistics, lacks in medical staff as well as operating room and intensive care capacities during the pandemic. This leads not only to the need for triage or transferring of ES patients to other hospitals, reported by 64.0% and 48.8% of the collaborators, respectively, but also to paradigm shifts in treatment modalities to non-operative approaches reported by 67.3% of the participants, especially in uncomplicated appendicitis, cholecystitis and multiple-recurrent diverticulitis. Conclusions: The SARS-CoV-2 pandemic still significantly impacts on care and outcome of patients in ES. Well-known problems with in-hospital logistics are not sufficiently resolved by now; however, medical staff shortages and reduced capacities have been dramatically aggravated over last two pandemic years

Impacts of noise on quenching of some models arising in MEMS technology

In the current work, we study a stochastic parabolic problem. The presented problem is motivated by the study of an idealised electrically actuated MEMS (Micro-Electro-Mechanical System) device in the case of random fluctuations of the potential difference, a parameter that actually controls the operation of MEMS device. We first present the construction of the mathematical model, and then, we deduce some local existence results. Next for some particular versions of the model, relevant to various boundary conditions, we derive quenching results as well as estimations of the probability for such singularity to occur. Additional numerical study of the problem in one dimension follows, which also allows the further investigation the problem with respect to its quenching behaviour

On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control

We consider a nonlocal parabolic model for a micro-electro-mechanical system. Specifically, for a radially symmetric problem with monotonic initial data, it is shown that the solution quenches, so that touchdown occurs in the device, in a situation where there is no steady state. It is also shown that quenching occurs at a single point and a bound on the approach to touchdown is obtained. Numerical simulations illustrating the results are given

A stochastic parabolic model of MEMS driven by fractional Brownian motion

In this paper, we study a stochastic parabolic problem that emerges in the modeling and control of an electrically actuated MEMS (micro-electro-mechanical system) device. The dynamics under consideration are driven by an one dimensional fractional Brownian motion with Hurst index [Formula: see text]. We derive conditions under which the resulting SPDE has a global in time solution, and we provide analytic estimates for certain statistics of interest, such as quenching times and the corresponding quenching probabilities. Our results demonstrate the non-trivial impact of the fractional noise on the dynamics of the system. Given the significance of MEMS devices in biomedical applications, such as drug delivery and diagnostics, our results provide valuable insights into the reliability of these devices in the presence of positively correlated noise