The Linear-Time-Invariance Notion of the Koopman Analysis-Part 2: Physical Interpretations of Invariant Koopman Modes and Phenomenological Revelations

This serial work presents a Linear-Time-Invariance (LTI) notion to the Koopman analysis, finding consistent and physically meaningful Koopman modes and addressing a long-standing problem of fluid-structure interactions: deterministically relating the fluid and structure. Part 1 (Li et al., 2022) developed the Koopman-LTI architecture and applied it to a pedagogical prism wake. By the systematic procedure, the LTI generated a sampling-independent Koopman linearization that captured all the recurring dynamics, finding six corresponding, orthogonal, and in-synch fluid excitation-structure response mechanisms. This Part 2 analyzes the six modal duplets' to underpin their physical interpretations, providing a phenomenological revelation of the subcritical prism wake. By the dynamical mode shape, results show that two mechanisms at St1=0.1242 and St5=0.0497 describe shear layer dynamics, the associated B\'ernard-K\'arm\'an shedding, and turbulence production, which together overwhelm the upstream and crosswind walls by instigating a reattachment-type of response. The on-wind walls' dynamical similarity renders them a spectrally unified fluid-structure interface. Another four harmonic counterparts, namely the subharmonic at St7=0.0683, the second harmonic at St3=0.2422, and two ultra-harmonics at St7 =0.1739 and St13=0.1935, govern the downstream wall. The 2P wake mode is also observed as an embedded harmonic of the bluff-body wake. Finally, this work discovered the vortex breathing phenomenon, describing the constant energy exchange in wake's circulation-entrainment-deposition processes. With the Koopman-LTI, one may pinpoint the exact excitations responsible for a specific structural response, or vice versa.Comment: 24 figures, 60 pages. Video files at https://drive.google.com/drive/folders/1AHdhUdAfNwlC1XUh-74PgQWW6jUHXJ5j?usp=sharin

Efficacy and safety of tigecycline monotherapy vs. imipenem/cilastatin in Chinese patients with complicated intra-abdominal infections: a randomized controlled trial

<p>Abstract</p> <p>Background</p> <p>Tigecycline, a first-in-class broad-spectrum glycylcycline antibiotic, has broad-spectrum in vitro activity against bacteria commonly encountered in complicated intra-abdominal infections (cIAIs), including aerobic and facultative Gram-positive and Gram-negative bacteria and anaerobic bacteria. In the current trial, tigecycline was evaluated for safety and efficacy vs. imipenem/cilastatin in hospitalized Chinese patients with cIAIs.</p> <p>Methods</p> <p>In this phase 3, multicenter, open-label study, patients were randomly assigned to receive IV tigecycline or imipenem/cilastatin for ≤2 weeks. The primary efficacy endpoints were clinical response at the test-of-cure visit (12-37 days after therapy) for the microbiologic modified intent-to-treat and microbiologically evaluable populations. Because the study was not powered to demonstrate non-inferiority between tigecycline and imipenem/cilastatin, no formal statistical analysis was performed. Two-sided 95% confidence intervals (CIs) were calculated for the response rates in each treatment group and for differences between treatment groups for descriptive purposes.</p> <p>Results</p> <p>One hundred ninety-nine patients received ≥1 dose of study drug and comprised the modified intent-to-treat population. In the microbiologically evaluable population, 86.5% (45 of 52) of tigecycline- and 97.9% (47 of 48) of imipenem/cilastatin-treated patients were cured at the test-of-cure assessment (12-37 days after therapy); in the microbiologic modified intent-to-treat population, cure rates were 81.7% (49 of 60) and 90.9% (50 of 55), respectively. The overall incidence of treatment-emergent adverse events was 80.4% for tigecycline vs. 53.9% after imipenem/cilastatin therapy (<it>P </it>< 0.001), primarily due to gastrointestinal-related events, especially nausea (21.6% vs. 3.9%; <it>P </it>< 0.001) and vomiting (12.4% vs. 2.0%; <it>P </it>= 0.005).</p> <p>Conclusions</p> <p>Clinical cure rates for tigecycline were consistent with those found in global cIAI studies. The overall safety profile was also consistent with that observed in global studies of tigecycline for treatment of cIAI, as well as that observed in analyses of Chinese patients in those studies; no novel trends were observed.</p> <p>Trial Registration</p> <p>ClinicalTrials.gov NCT00136201</p