Takens-Bogdanov bifurcation of travelling wave solutions in pipe flow

The appearance of travelling-wave-type solutions in pipe Poiseuille flow that are disconnected from the basic parabolic profile is numerically studied in detail. We focus on solutions in the 2-fold azimuthally-periodic subspace because of their special stability properties, but relate our findings to other solutions as well. Using time-stepping, an adapted Krylov-Newton method and Arnoldi iteration for the computation and stability analysis of relative equilibria, and a robust pseudo-arclength continuation scheme we unfold a double-zero (Takens-Bogdanov) bifurcating scenario as a function of Reynolds number (Re) and wavenumber (k). This scenario is extended, by the inclusion of higher order terms in the normal form, to account for the appearance of supercritical modulated waves emanating from the upper branch of solutions at a degenerate Hopf bifurcation. These waves are expected to disappear in saddle-loop bifurcations upon collision with lower-branch solutions, thereby leaving stable upper-branch solutions whose subsequent secondary bifurcations could contribute to the formation of the phase space structures that are required for turbulent dynamics at higher Re.Comment: 26 pages, 15 figures (pdf and png). Submitted to J. Fluid Mec

Statistical analysis of coherent structures in transitional pipe flow

Numerical and experimental studies of transitional pipe flow have shown the prevalence of coherent flow structures that are dominated by downstream vortices. They attract special attention because they contribute predominantly to the increase of the Reynolds stresses in turbulent flow. In the present study we introduce a convenient detector for these coherent states, calculate the fraction of time the structures appear in the flow, and present a Markov model for the transition between the structures. The fraction of states that show vortical structures exceeds 24% for a Reynolds number of about Re=2200, and it decreases to about 20% for Re=2500. The Markov model for the transition between these states is in good agreement with the observed fraction of states, and in reasonable agreement with the prediction for their persistence. It provides insight into dominant qualitative changes of the flow when increasing the Reynolds number.Comment: 11 pages, 26 (sub)figure

From travelling waves to mild chaos: a supercritical bifurcation cascade in pipe flow

We study numerically a succession of transitions in pipe Poiseuille flow that leads from simple travelling waves to waves with chaotic time-dependence. The waves at the origin of the bifurcation cascade possess a shift-reflect symmetry and are both axially and azimuthally periodic with wave numbers {\kappa} = 1.63 and n = 2, respectively. As the Reynolds number is increased, successive transitions result in a wide range of time dependent solutions that includes spiralling, modulated-travelling, modulated-spiralling, doubly-modulated-spiralling and mildly chaotic waves. We show that the latter spring from heteroclinic tangles of the stable and unstable invariant manifolds of two shift-reflect-symmetric modulated-travelling waves. The chaotic set thus produced is confined to a limited range of Reynolds numbers, bounded by the occurrence of manifold tangencies. The states studied here belong to a subspace of discrete symmetry which makes many of the bifurcation and path-following investigations presented technically feasible. However, we expect that most of the phenomenology carries over to the full state-space, thus suggesting a mechanism for the formation and break-up of invariant states that can sustain turbulent dynamics.Comment: 38 pages, 35 figures, 1 tabl

Irf4 is a positional and functional candidate gene for the control of serum IgM levels in the mouse

Natural IgM are involved in numerous immunological functions but the genetic factors that control the homeostasis of its secretion and upholding remain unknown. Prompted by the finding that C57BL/6 mice had significantly lower serum levels of IgM when compared with BALB/c mice, we performed a genome-wide screen and found that the level of serum IgM was controlled by a QTL on chromosome 13 reaching the highest level of association at marker D13Mit266 (LOD score¼3.54). This locus was named IgMSC1 and covered a region encompassing the interferon-regulatory factor 4 gene (Irf4). The number of splenic mature B cells in C57BL/6 did not differ from BALB/c mice but we found that low serum levels of IgM in C57BL/6 mice correlated with lower frequency of IgM-secreting cells in the spleen and in the peritoneal cavity. These results suggested that C57BL/6 mice have lower efficiency in late B-cell maturation, a process that is highly impaired in Irf4 knockout mice. In fact, we also found reduced Irf4 gene expression in B cells of C57BL/6 mice. Thus, we propose Irf4 as a candidate for the IgMSC1 locus, which controls IgM homeostatic levels at the level of B-cell terminal differentiation

Differences in management approaches for lupus nephritis within the UK

\ua9 The Author(s) 2024. Published by Oxford University Press on behalf of the British Society for Rheumatology.Objectives: Outcomes of therapy for LN are often suboptimal. Guidelines offer varied options for treatment of LN and treatment strategies may differ between clinicians and regions. We aimed to assess variations in the usual practice of UK physicians who treat LN. Methods: We conducted an online survey of simulated LN cases for UK rheumatologists and nephrologists to identify treatment preferences for class IV and class V LN. Results: Of 77 respondents, 48 (62.3%) were rheumatologists and 29 (37.7%) were nephrologists. A total of 37 (48.0%) reported having a joint clinic between nephrologists and rheumatologists, 54 (70.0%) reported having a multidisciplinary team meeting for LN and 26 (33.7%) reported having a specialized lupus nurse. Of the respondents, 58 (75%) reported arranging a renal biopsy before starting the treatment. A total of 20 (69%) of the nephrologists, but only 13 (27%) rheumatologists, reported having a formal departmental protocol for treating patients with LN (P < 0.001). The first-choice treatment of class IV LN in pre-menopausal patients was MMF [41 (53.2%)], followed by CYC [15 (19.6%)], rituximab [RTX; 12 (12.5%)] or a combination of immunosuppressive drugs [9 (11.7%)] with differences between nephrologists’ and rheumatologists’ choices (P \ubc 0.026). For class V LN, MMF was the preferred initial treatment, irrespective of whether proteinuria was in the nephrotic range or not. RTX was the preferred second-line therapy for non-responders. Conclusion: There was variation in the use of protocols, specialist clinic service provision, biopsies and primary and secondary treatment choices for LN reported by nephrologists and rheumatologists in the UK

Rheumatoid arthritis - treatment: 180. Utility of Body Weight Classified Low-Dose Leflunomide in Japanese Rheumatoid Arthritis

Background: In Japan, more than 20 rheumatoid arthritis (RA) patients died of interstitial pneumonia (IP) caused by leflunomide (LEF) were reported, but many of them were considered as the victims of opportunistic infection currently. In this paper, efficacy and safety of low-dose LEF classified by body weight (BW) were studied. Methods: Fifty-nine RA patients were started to administrate LEF from July 2007 to July 2009. Among them, 25 patients were excluded because of the combination with tacrolimus, and medication modification within 3 months before LEF. Remaining 34 RA patients administered 20 to 50 mg/week of LEF were followed up for 1 year and enrolled in this study. Dose of LEF was classified by BW (50 mg/week for over 50 kg, 40 mg/week for 40 to 50 kg and 20 to 30 mg/week for under 40 kg). The average age and RA duration of enrolled patients were 55.5 years old and 10.2 years. Prednisolone (PSL), methotrexate (MTX) and etanercept were used in 23, 28 and 2 patients, respectively. In case of insufficient response or adverse effect, dosage change or discontinuance of LEF were considered. Failure was defined as dosages up of PSL and MTX, or dosages down or discontinuance of LEF. Last observation carried forward method was used for the evaluation of failed patients at 1 year. Results: At 1 year after LEF start, good/ moderate/ no response assessed by the European League Against Rheumatism (EULAR) response criteria using Disease Activity Score, including a 28-joint count (DAS28)-C reactive protein (CRP) were showed in 14/ 10/ 10 patients, respectively. The dosage changes of LEF at 1 year were dosage up: 10, same dosage: 5, dosage down: 8 and discontinuance: 11 patients. The survival rate of patients in this study was 23.5% (24 patients failed) but actual LEF continuous rate was 67.6% (11 patients discontinued) at 1 year. The major reason of failure was liver dysfunction, and pneumocystis pneumonia was occurred in 1 patient resulted in full recovery. One patient died of sepsis caused by decubitus ulcer infection. DAS28-CRP score was decreased from 3.9 to 2.7 significantly. Although CRP was decreased from 1.50 to 0.93 mg/dl, it wasn't significant. Matrix metalloproteinase (MMP)-3 was decreased from 220.0 to 174.2 ng/ml significantly. Glutamate pyruvate transaminase (GPT) was increased from 19 to 35 U/l and number of leukocyte was decreased from 7832 to 6271 significantly. DAS28-CRP, CRP, and MMP-3 were improved significantly with MTX, although they weren't without MTX. Increase of GPT and leukopenia were seen significantly with MTX, although they weren't without MTX. Conclusions: It was reported that the risks of IP caused by LEF in Japanese RA patients were past IP history, loading dose administration and low BW. Addition of low-dose LEF is a potent safe alternative for the patients showing unsatisfactory response to current medicines, but need to pay attention for liver function and infection caused by leukopenia, especially with MTX. Disclosure statement: The authors have declared no conflicts of interes