Linearized Stability of Partial Differential Equations with Application to Stabilization of the Kuramoto--Sivashinsky Equation

This is a final draft of a work, prior to publisher editing and production, that appears in Siam J. Control Optim. Vol. 56, No 1, pp 120-147. http://dx.doi.org/10.1137/140993417.Linearization is a useful tool for analyzing the stability of nonlinear differential equations. Unfortunately, the proof of the validity of this approach for ordinary differential equations does not generalize to all nonlinear partial differential equations. General results giving conditions for when stability (or instability) of the linearized equation implies the same for the nonlinear equation are given here. These results are applied to stability and stabilization of the Kuramoto--Sivashinsky equation, a nonlinear partial differential equation that models reaction-diffusion systems. The stability of the equilibrium solutions depends on the value of a positive parameter $\nu$. It is shown that if $\nu>1$, then the set of constant equilibrium solutions is globally asymptotically stable. If $\nu<1$, then the equilibria are unstable. It is also shown that stabilizing the linearized equation implies local exponential stability of the equation. Stabilization of the Kuramoto--Sivashinsky equation using a single distributed control is considered and it is described how to use a finite-dimensional approximation to construct a stabilizing controller. The results are illustrated with simulations.Natural Sciences and Engineering Research Council of Canada (NSERC

Bounded Control of the Kuramoto-Sivashinsky equation

Feedback control is used in almost every aspect of modern life and is essential in almost all engineering systems. Since no mathematical model is perfect and disturbances occur frequently, feedback is required. The design of a feedback control has been widely investigated in finite-dimensional space. However, many systems of interest, such as fluid flow and large structural vibrations are described by nonlinear partial differential equations and their state evolves on an infinite-dimensional Hilbert space. Developing controller design methods for nonlinear infinite-dimensional systems is not trivial. The objectives of this thesis are divided into multiple tasks. First, the well-posedness of some classes of nonlinear partial differential equations defined on a Hilbert space are investigated. The following nonlinear affine system defined on the Hilbert space H is considered z ̇(t)=F(z(t))+Bu(t), t≥0 z (0) = z0, where z(t) ∈ H is the state vector and z0 is the initial condition. The vector u(t) ∈ U, where U is a Hilbert space, is a state-feedback control. The nonlinear operator F : D ⊂ H → H is densely defined in H and the linear operator B : U → H is a linear bounded operator. Conditions for the closed-loop system to have a unique solution in the Hilbert space H are given. Next, finding a single bounded state-feedback control for nonlinear partial differential equations is discussed. In particular, Lyapunov-indirect method is considered to control nonlinear infinite-dimensional systems and conditions on when this method achieves the goal of local asymptotic stabilization of the nonlinear infinite-dimensional system are given. The Kuramoto-Sivashinsky (KS) equation defined in the Hilbert space L2(−π,π) with periodic boundary conditions is considered. ∂z/∂t =−ν∂4z/∂x4 −∂2z/∂x2 −z∂z/∂x, t≥0 z (0) = z0 (x) , where the instability parameter ν > 0. The KS equation is a nonlinear partial differential equation that is first-order in time and fourth-order in space. It models reaction-diffusion systems and is related to various pattern formation phenomena where turbulence or chaos appear. For instance, it models long wave motions of a liquid film over a vertical plane. When the instability parameter ν < 1, this equation becomes unstable. This is shown by analyzing the stability of the linearized system and showing that the nonlinear C0- semigroup corresponding to the nonlinear KS equation is Fr ́echet differentiable. There are a number of papers establishing the stabilization of this equation via boundary control. In this thesis, we consider distributed control with a single bounded feedback control for the KS equation with periodic boundary conditions. First, it is shown that sta- bilizing the linearized KS equation implies local asymptotical stability of the nonlinear KS equation. This is done by establishing Fr ́echet differentiability of the associated nonlinear C0-semigroup and showing that it is equal to the linear C0-semigroup generated by the linearization of the equation. Next, a single state-feedback control that locally asymptot- ically stabilizes the KS equation is constructed. The same approach to stabilize the KS equation from one equilibrium point to another is used. Finally, the solution of the uncontrolled/state-feedback controlled KS equation is ap- proximated numerically. This is done using the Galerkin projection method to approximate infinite-dimensional systems. The numerical simulations indicate that the proposed Lyapunov-indirect method works in stabilizing the KS equation to a desired state. Moreover, the same approach can be used to stabilize the KS equation from one constant equilibrium state to another

Distributed Control of the Generalized Korteweg-de Vries-Burgers Equation

The paper deals with the distributed control of the generalized Kortweg-de Vries-Burgers equation (GKdVB) subject to periodic boundary conditions via the Karhunen-Loève (K-L) Galerkin method. The decomposition procedure of the K-L method is presented to illustrate the use of this method in analyzing the numerical simulations data which represent the solutions to the GKdVB equation. The K-L Galerkin projection is used as a model reduction technique for nonlinear systems to derive a system of ordinary differential equations (ODEs) that mimics the dynamics of the GKdVB equation. The data coefficients derived from the ODE system are then used to approximate the solutions of the GKdVB equation. Finally, three state feedback linearization control schemes with the objective of enhancing the stability of the GKdVB equation are proposed. Simulations of the controlled system are given to illustrate the developed theory

Investigation the Coating of Hydroxyapatite on Titanium Substrate by Pulse Laser Deposition

بحثت هذه الدراسة وأعدت طلاء مركب للمزروعات الجراحية باستخدام المواد السيراميكيه النشطه بايولوجيا (bioactive) مثل الهيدروكسيابتايت كطلاءات للمزروعات المعدنيه التي تشجع النمو الطبيعي للعظام عند نقاط التماس بينها وبين العظم الحي. ان الهيدروكسيابتايت (Ca10(PO4)6(OH)2)) او فوسفات الكالسيوم يستخدم كطلاء للمعادن بسبب توافقيته الحياتيه الممتازه كما انه ذو هيكل مشابه للانسجه الصلبه في جسم الانسان. إن تطبيق الطلاء HA على ركائز التيتانيوم أنتجت باستخدام تقنية الترسيب بالليزر النبضي (Pulsed Laser Deposition). في هذا البحث استخدم (HA) كهدف ((Target تم كبسه عند ضغط (150MPa) مع حجم حبيبي مقداره 2.745 µm)) واستخدامه في عملية الطلاء بواسطة تقنية(PLD). أجريت عدة اختبارات لتوصيف طبقة الطلاء مثل XRD وSEM وAFM وEDX لتحديد كمية كلا من الكالسيوم (Ca) والفسفور (P) في طبقة الطلاء. وبعدها تم اختبار الصلاده وخشونة السطح لطبقه الطلاء HA)). تم اجراء اختبار التآكل باستخدام طريقة استكمال منحني تافل في محلول Hank's solution لكل النماذج المطليه وغير المطليه، حيث حصلنا في هذا الاختبار على تحسن كبير في مقاومة التآكل للعينات المطليه عند عدد نبضات 4000 نبضة بمقدار 99.88%.This study investigated and prepared a coating for surgical implants by using hydroxyapatite (HA) empowers characteristic bone that developed at a medium for prosthetic the parts of human body. HA is the generally manufactured from both Calcium (Ca) and Phosphate (P) to produce (Ca10(PO4)6(OH)2) that used as a base material for covering mineral embeds because of its incredible biocompatibility and comparable the synthesis and structure to sclerous tissues of the human body. HA, coatings on titanium substrates have been produced by Pulses laser deposition (PLD) techniques. HA used in this search pressed at pressure (150MPa) with particle size (2.745 µm) and used as a target in coating by (PLD) techniques. Surface characterization studies of the coatings such as XRD, SEM, AFM and EDX to detect the amount of (Ca) and (P) in coating layer were carried out. Then test the micro-hardness, surface roughness for HA coating .Corrosion behavior for uncoated and coated samples with various number of pulses in Hank’s solution by using OCP and the potentially static polarization test were achieved also, , in this test we obtained a greatly improved in corrosion resistance of the samples B1 after coating by 99.88%

Parental Attitudes and Hesitancy About COVID-19 vs. Routine Childhood Vaccinations: A National Survey

Objectives: To quantify parental acceptance of the COVID-19 vaccine and assess the vaccine hesitancy (VH) for COVID-19 vs. childhood vaccines. Methods: Eight vaccine hesitancy scale (VHS) items, adopted from WHO's Strategic Advisory Group of Immunization (SAGE), were used to assess VH for COVID-19 vaccine vs. routine childhood vaccines. We distributed the online survey to parents with the commence of the national childhood COVID-19 vaccination program in Saudi Arabia. Results: Among 3,167 parents, 47.6% are decided to vaccinate their children against COVID-19. The most common reasons for refusal were inadequate safety information (69%) and worry about side effects (60.6%). Parents have a significantly greater positive attitudes toward children's routine vaccines vs. the COVID-19 vaccine, with higher mean VHS (±SD) = 2.98 ± 0.58 vs. 2.63 ± 0.73, respectively (p-value < 0.001). Parents agreed more that routine childhood vaccines are more essential and effective as compared to the COVID-19 vaccine (Cohen's D: 0.946, and 0.826, consecutively; T-test p-value < 0.00). There is more parental anxiety about serious side effects of the COVID-19 vaccine vs. routine childhood vaccines (Cohen's D = 0.706, p-value < 0.001). Parents who relied on the Ministry of Health information were more predicted (OR = 1.28, p-value = 0.035) to intend to vaccinate as opposed to those who used the WHO website (OR = 0.47, −53%, p-value < 0.001). In a multivariate logistic regression analysis, the factors associated with intention to vaccinate children were parents who received COVID-19 vaccine, older parents, having children aged 12–18, and parents with lower education levels. Conclusions: Significant proportion of parents are hesitant about the COVID-19 vaccine because they are less confident in its effectiveness, safety, and whether it is essential for their children. Relying on the national official healthcare authority's website for the source of information was associated with increased acceptance of childhood COVID-19 vaccination. As parental intention to vaccinate children against COVID-19 is suboptimal, healthcare authorities could boost vaccine uptake by campaigns targeting hesitant parents

Antimicrobial resistance among migrants in Europe: a systematic review and meta-analysis

BACKGROUND: Rates of antimicrobial resistance (AMR) are rising globally and there is concern that increased migration is contributing to the burden of antibiotic resistance in Europe. However, the effect of migration on the burden of AMR in Europe has not yet been comprehensively examined. Therefore, we did a systematic review and meta-analysis to identify and synthesise data for AMR carriage or infection in migrants to Europe to examine differences in patterns of AMR across migrant groups and in different settings. METHODS: For this systematic review and meta-analysis, we searched MEDLINE, Embase, PubMed, and Scopus with no language restrictions from Jan 1, 2000, to Jan 18, 2017, for primary data from observational studies reporting antibacterial resistance in common bacterial pathogens among migrants to 21 European Union-15 and European Economic Area countries. To be eligible for inclusion, studies had to report data on carriage or infection with laboratory-confirmed antibiotic-resistant organisms in migrant populations. We extracted data from eligible studies and assessed quality using piloted, standardised forms. We did not examine drug resistance in tuberculosis and excluded articles solely reporting on this parameter. We also excluded articles in which migrant status was determined by ethnicity, country of birth of participants' parents, or was not defined, and articles in which data were not disaggregated by migrant status. Outcomes were carriage of or infection with antibiotic-resistant organisms. We used random-effects models to calculate the pooled prevalence of each outcome. The study protocol is registered with PROSPERO, number CRD42016043681. FINDINGS: We identified 2274 articles, of which 23 observational studies reporting on antibiotic resistance in 2319 migrants were included. The pooled prevalence of any AMR carriage or AMR infection in migrants was 25·4% (95% CI 19·1-31·8; I2 =98%), including meticillin-resistant Staphylococcus aureus (7·8%, 4·8-10·7; I2 =92%) and antibiotic-resistant Gram-negative bacteria (27·2%, 17·6-36·8; I2 =94%). The pooled prevalence of any AMR carriage or infection was higher in refugees and asylum seekers (33·0%, 18·3-47·6; I2 =98%) than in other migrant groups (6·6%, 1·8-11·3; I2 =92%). The pooled prevalence of antibiotic-resistant organisms was slightly higher in high-migrant community settings (33·1%, 11·1-55·1; I2 =96%) than in migrants in hospitals (24·3%, 16·1-32·6; I2 =98%). We did not find evidence of high rates of transmission of AMR from migrant to host populations. INTERPRETATION: Migrants are exposed to conditions favouring the emergence of drug resistance during transit and in host countries in Europe. Increased antibiotic resistance among refugees and asylum seekers and in high-migrant community settings (such as refugee camps and detention facilities) highlights the need for improved living conditions, access to health care, and initiatives to facilitate detection of and appropriate high-quality treatment for antibiotic-resistant infections during transit and in host countries. Protocols for the prevention and control of infection and for antibiotic surveillance need to be integrated in all aspects of health care, which should be accessible for all migrant groups, and should target determinants of AMR before, during, and after migration. FUNDING: UK National Institute for Health Research Imperial Biomedical Research Centre, Imperial College Healthcare Charity, the Wellcome Trust, and UK National Institute for Health Research Health Protection Research Unit in Healthcare-associated Infections and Antimictobial Resistance at Imperial College London

Surgical site infection after gastrointestinal surgery in high-income, middle-income, and low-income countries: a prospective, international, multicentre cohort study

Background: Surgical site infection (SSI) is one of the most common infections associated with health care, but its importance as a global health priority is not fully understood. We quantified the burden of SSI after gastrointestinal surgery in countries in all parts of the world. Methods: This international, prospective, multicentre cohort study included consecutive patients undergoing elective or emergency gastrointestinal resection within 2-week time periods at any health-care facility in any country. Countries with participating centres were stratified into high-income, middle-income, and low-income groups according to the UN's Human Development Index (HDI). Data variables from the GlobalSurg 1 study and other studies that have been found to affect the likelihood of SSI were entered into risk adjustment models. The primary outcome measure was the 30-day SSI incidence (defined by US Centers for Disease Control and Prevention criteria for superficial and deep incisional SSI). Relationships with explanatory variables were examined using Bayesian multilevel logistic regression models. This trial is registered with ClinicalTrials.gov, number NCT02662231. Findings: Between Jan 4, 2016, and July 31, 2016, 13 265 records were submitted for analysis. 12 539 patients from 343 hospitals in 66 countries were included. 7339 (58·5%) patient were from high-HDI countries (193 hospitals in 30 countries), 3918 (31·2%) patients were from middle-HDI countries (82 hospitals in 18 countries), and 1282 (10·2%) patients were from low-HDI countries (68 hospitals in 18 countries). In total, 1538 (12·3%) patients had SSI within 30 days of surgery. The incidence of SSI varied between countries with high (691 [9·4%] of 7339 patients), middle (549 [14·0%] of 3918 patients), and low (298 [23·2%] of 1282) HDI (p < 0·001). The highest SSI incidence in each HDI group was after dirty surgery (102 [17·8%] of 574 patients in high-HDI countries; 74 [31·4%] of 236 patients in middle-HDI countries; 72 [39·8%] of 181 patients in low-HDI countries). Following risk factor adjustment, patients in low-HDI countries were at greatest risk of SSI (adjusted odds ratio 1·60, 95% credible interval 1·05–2·37; p=0·030). 132 (21·6%) of 610 patients with an SSI and a microbiology culture result had an infection that was resistant to the prophylactic antibiotic used. Resistant infections were detected in 49 (16·6%) of 295 patients in high-HDI countries, in 37 (19·8%) of 187 patients in middle-HDI countries, and in 46 (35·9%) of 128 patients in low-HDI countries (p < 0·001). Interpretation: Countries with a low HDI carry a disproportionately greater burden of SSI than countries with a middle or high HDI and might have higher rates of antibiotic resistance. In view of WHO recommendations on SSI prevention that highlight the absence of high-quality interventional research, urgent, pragmatic, randomised trials based in LMICs are needed to assess measures aiming to reduce this preventable complication

Effect of remote ischaemic conditioning on clinical outcomes in patients with acute myocardial infarction (CONDI-2/ERIC-PPCI): a single-blind randomised controlled trial.

BACKGROUND: Remote ischaemic conditioning with transient ischaemia and reperfusion applied to the arm has been shown to reduce myocardial infarct size in patients with ST-elevation myocardial infarction (STEMI) undergoing primary percutaneous coronary intervention (PPCI). We investigated whether remote ischaemic conditioning could reduce the incidence of cardiac death and hospitalisation for heart failure at 12 months. METHODS: We did an international investigator-initiated, prospective, single-blind, randomised controlled trial (CONDI-2/ERIC-PPCI) at 33 centres across the UK, Denmark, Spain, and Serbia. Patients (age >18 years) with suspected STEMI and who were eligible for PPCI were randomly allocated (1:1, stratified by centre with a permuted block method) to receive standard treatment (including a sham simulated remote ischaemic conditioning intervention at UK sites only) or remote ischaemic conditioning treatment (intermittent ischaemia and reperfusion applied to the arm through four cycles of 5-min inflation and 5-min deflation of an automated cuff device) before PPCI. Investigators responsible for data collection and outcome assessment were masked to treatment allocation. The primary combined endpoint was cardiac death or hospitalisation for heart failure at 12 months in the intention-to-treat population. This trial is registered with ClinicalTrials.gov (NCT02342522) and is completed. FINDINGS: Between Nov 6, 2013, and March 31, 2018, 5401 patients were randomly allocated to either the control group (n=2701) or the remote ischaemic conditioning group (n=2700). After exclusion of patients upon hospital arrival or loss to follow-up, 2569 patients in the control group and 2546 in the intervention group were included in the intention-to-treat analysis. At 12 months post-PPCI, the Kaplan-Meier-estimated frequencies of cardiac death or hospitalisation for heart failure (the primary endpoint) were 220 (8·6%) patients in the control group and 239 (9·4%) in the remote ischaemic conditioning group (hazard ratio 1·10 [95% CI 0·91-1·32], p=0·32 for intervention versus control). No important unexpected adverse events or side effects of remote ischaemic conditioning were observed. INTERPRETATION: Remote ischaemic conditioning does not improve clinical outcomes (cardiac death or hospitalisation for heart failure) at 12 months in patients with STEMI undergoing PPCI. FUNDING: British Heart Foundation, University College London Hospitals/University College London Biomedical Research Centre, Danish Innovation Foundation, Novo Nordisk Foundation, TrygFonden