Odd Coefficients Research Articles

Irreversible Boltzmann samplers in dense liquids: Weak-coupling approximation and mode-coupling theory.

Exerting a nonequilibrium drive on an otherwise equilibrium Langevin process brings the dynamics out of equilibrium but can also speed up the approach to the Boltzmann steady state. Transverse forces are a minimal framework to achieve dynamical acceleration of the Boltzmann sampling. We consider a simple liquid in three space dimensions subjected to additional transverse pairwise forces, and quantify the extent to which transverse forces accelerate the dynamics. We first explore the dynamics of a tracer in a weak coupling regime describing high temperatures. The resulting acceleration is correlated with a monotonous increase of the magnitude of odd transport coefficients (mobility and diffusivity) with the amplitude of the transverse drive. We then develop a nonequilibrium version of the mode-coupling theory able to capture the effect of transverse forces, and more generally of forces created by additional degrees of freedom. Based on an analysis of transport coefficients, both odd and longitudinal, both for the collective modes and for a tracer particle, we find a systematic acceleration of the dynamics. Quantitatively, the gain, which is guaranteed throughout the ergodic phase, turns out to be a decreasing function of temperature beyond a temperature crossover, in particular as the glass transition is approached. Our theoretical results are in good agreement with available numerical results.

Research and application of the flatness target curve discrete dynamic programming based on two-dimensional decision making

The flatness target curve (FTC) is a fundamental process model in cold rolling flatness control, which directly affects the quality control effect of the strip. The accurate and efficient setting of the flatness target curve is the key to ensuring continuous rolling and is a common problem faced by various production companies. This paper establishes a discrete dynamic planning (DDP) setting method for FTC with two-dimensional decision-making. To quantitatively analyze the roles of the coefficients in the FTC, the preprocessing process is established using standardized processing methods and statistical analysis methods. The flatness target curve discrete dynamic programming (FTC-DDP) is based on Bellman optimization theory with a dual structure of local and system decision-making. The decision-making functions are established based on the effect of each coefficient on FTC geometric characteristics. The concepts of “curvature factor” and “wedge factor” are innovatively proposed to obtain the decision-making value functions. The regression analysis establishes the solution equations of even number coefficients, odd number coefficients, and gain coefficients, respectively. Roll bending and tilting roll analyze the FTC’s ability to correct flatness defects. Meanwhile, utilizing a 1450 mm five-stand six-roll cold rolling mill, it is verified that FTC-DDP can quickly and accurately set the FTC, which provides an effective solution for obtaining high-precision and high-quality cold-rolled strips. Application results show that FTC-DDP can reduce the difficulty of setting up FTC by more than 70 %, reduce the setup time to milliseconds, and improve the setup accuracy by more than 50 %.

P-087 Obstetrical and perinatal outcomes from intracytoplasmic sperm injection couples with oocyte donation are not affected by advanced paternal age measured as a continuous variable

Abstract Study question Does paternal age (PA), considered a continuous variable, have any effect on obstetrical and perinatal outcomes in intracytoplasmic sperm injection (ICSI) with donated oocytes? Summary answer PA does not affect clinically relevant obstetrical and perinatal outcomes, but it significantly increases the pregnancy’s duration in ICSI with autologous sperm and donated oocytes. What is known already Currently there has been an evident delay in childbearing, therefore studies relating advanced PA with reproductive risks are increasing and results are controversial. These studies frequently study PA by dividing it in groups arbitrarily constructed, but probably a more precise evaluation is obtained using PA as a continuous variable. Furthermore, oocyte donation standardizes female factor, to some extent, allowing a more realistic male factor evaluation. In this regard, we aimed to evaluate the effect of PA at conception (continuous variable) on obstetrical and perinatal outcomes in ICSI couples with autologous sperm and donated oocytes in a large population of patients. Study design, size, duration This retrospective observational multicentric cohort study evaluated data from couples that performed an ICSI between January 2008 and March 2020 using autologous sperm and donated oocytes. We included only singleton deliveries and the first delivery of each couple. PA was analysed as a continuous variable, considered more informative in comparison to its analysis as categorical. Data available and included consisted of 15,696 patients who had a delivery with or without a live birth. Participants/materials, setting, methods PA ranged from 21-54 years. Clinical database was constructed with reproductive outcomes from electronic medical records. Erroneous or incomplete data were removed. Statistical analysis included a descriptive analysis, followed by univariate and multivariate models using binary logistic regression or linear regression. We adjusted for maternal age and body mass index, PA, fresh sperm concentration and progressive motility, cycle type, gestational age, transfer on day 5 and delivery type (when appropriate). P < 0.05 was considered statistically significant. Main results and the role of chance Mean PA was 41.45 (41.38-41.51). We included a total of 15,696 deliveries and 15,673 live births. Results from multivariate models are presented as adjusted odd ratio or regression coefficient with 95% confidence intervals and adjusted p. In terms of obstetrical outcomes, PA results were 1.086 (0.959-1.229) p = 0.194 for gestational diabetes, 0.963 (0.849-1.093) p = 0.561 for anemia, 0.947 (0.837-1.072) p = 0.388 for hypertension, 0.959 (0.878-1.048) p = 0.356 for preterm birth and 0.986 (0.929-1.046) p = 0.641 for caesarean delivery. Regarding perinatal outcomes, PA results were 0.442 (0.005-0.879) p = 0.047 for gestational age, -0.216 (-15.559-15.126) p = 0.978 for infant weight, 1.101 (0.941-1.288) p = 0.231 for low birth weight (<2,500 g), 0.710 (0.463-1.088) p = 0.116 for very low birth weight (<1,500g), 0.988 (0.933-1.047) p = 0.684 for female sex, 0.002 (-0.076-0.08) p = 0.96 for length, -0.012 (-0.088-0.064) p = 0.763 for cranial perimeter, 0.991 (0.876-1.12) p = 0.88 for NICU admission, and 0.027 (-0.028-0.083) p = 0.337, 0.025 (-0.012-0.061) p = 0.18 and -0.045 (-0.096-0.007) p = 0.089 for Apgar 1, 5 and 10 minutes, respectively. According to our results, PA does not affect clinically relevant outcomes for the health during pregnancy and of the infant. However, PA significantly increases the duration of the pregnancy in ICSI with autologous sperm and donated oocytes. Limitations, reasons for caution The study’s major strengths are the consideration of PA as a continuous variable, the use of oocyte donation (controlling female factors) and the inclusion of a huge sample size. However, due to its retrospective nature there are some biases derived from the clinical practice and the presence of missing data. Wider implications of the findings Current evident delay in childbearing merits further research on the effect of PA on reproductive outcomes, addressed in this study. Our study suggests that PA is not associated with obstetrical and perinatal outcomes, except for gestational age, which sends a hopeful message to fathers of advanced paternal age. Trial registration number not applicable

Sampling Efficiency of Transverse Forces in Dense Liquids.

Sampling the Boltzmann distribution using forces that violate detailed balance can be faster than with the equilibrium evolution, but the acceleration depends on the nature of the nonequilibrium drive and the physical situation. Here, we study the efficiency of forces transverse to energy gradients in dense liquids through a combination of techniques: Brownian dynamics simulations, exact infinite-dimensional calculation, and a mode-coupling approximation. We find that the sampling speedup varies nonmonotonically with temperature, and decreases as the system becomes more glassy. We characterize the interplay between the distance to equilibrium and the efficiency of transverse forces by means of odd transport coefficients.

Taylor halos and Taylor spears in odd viscous liquids

A body placed in a rigidly rotating fluid becomes circumscribed by a fictitious cylinder with generators parallel to the axis of rotation, a Taylor column. Slowly moving liquid impinging on the body will swerve around the cylinder. Thus, Taylor columns may form when a breeze impinges on a mountain or when slowly moving oceanic water impinges on a seamount, both due to the Earth's rotation. Here, we show that classical non-rotating liquids endowed with an odd or Hall coefficient of viscosity, exhibiting nondissipative behavior, also give rise to Taylor column structures resembling halos or spears. Steady three-dimensional flow of such a liquid becomes effectively two dimensional, swirling around the Taylor column imitating its rigidly rotating counterparts. Formation of Taylor halos and spears is attributed to the propagation of data along characteristics that may be parallel or oblique to a center axis, respectively.

Instability of liquid film with odd viscosity and slip effect under the action of external electric field

The influence of odd viscosity on the instability of a liquid film flowing along a porous inclined plane under a normal electric field is investigated. It is assumed that the flow at the porous inclined plane satisfies the Beavers–Joseph slip boundary condition. By utilizing the long-wave approximation and employing the method of systematic asymptotic expansion, a nonlinear evolution equation for the film thickness under the influence of the electric field is derived. The stability analysis of this evolution equation reveals that the odd viscosity of the film has a stabilizing effect, while the electric field has a destabilizing effect. Additionally, the permeability of the porous inclined plane enhances the instability of the liquid film flow. Numerical simulations are conducted using a fast Fourier transform algorithm to solve the nonlinear evolution equations. The numerical results demonstrate that, within the stable region and with all parameters fixed, the wave amplitude decreases as the evolution time increases, indicating a gradual stabilization of the liquid film flow. Conversely, in the unstable region, the opposite behavior is observed. As the evolution time increases, the fluctuation amplitude grows larger, resulting in a gradual destabilization of the liquid film flow. Furthermore, when the evolution time is kept constant and the odd viscosity coefficient is nonzero, the film exhibits greater stability. The amplitude of the wave increases with the electrical parameter E. In the unstable region, an increase in the permeability β of the porous medium leads to a tendency for the film flow to stabilize.

Thermocapillary thin film flows on a slippery substrate with odd viscosity effects

This study investigates the behavior of a thin liquid with odd viscosity effects as it flows down a uniformly heated, slippery inclined plane, where the liquid’s time-reversal symmetry is broken. The breaking of symmetry results in interesting effects, as the antisymmetric part of the fluid stress tensor does not vanish. Two models, the Benney-type equation model (BEM) and the weighted residual model (WRM), are constructed to account for the combined effects of slip length, thermocapillarity, and odd viscosity. A detailed stability analysis determines both models’ critical Reynolds numbers Rec. For small slip lengths, the first-order WRM is better at capturing the instability threshold than the first-order BEM. While both models account for the effects of odd viscosity and thermocapillarity, only the Rec of WRM incorporates the wall slip effects. Another significant finding is that the BEM effectively avoids the issue of finite-time blow-up by incorporating odd viscosity. Additionally, employing a weakly nonlinear stability analysis with multiple scales uncovers four flow regions in BEM: supercritical stable, subcritical unstable, unconditional stable, and explosive zones. Two separate bifurcation scenarios emerge for various wave numbers: supercritical within a specific range and subcritical for larger wave numbers. The presence of odd viscosity alleviates the reduction of the unconditional stable zone and the increase in the explosive zone, which are caused by the combined influence of slip and thermal effects. Numerical investigation of traveling wave solutions of WRM shows that wave height is promoted by slip and thermal effects but reduced with increasing odd viscosity coefficient. Further numerical simulations of WRM on a larger domain demonstrate the stabilizing effects of odd viscosity and its interaction with destabilizing slip and thermocapillary effects.

Trends in the distribution of socioeconomic inequalities in smoking and cessation: evidence among adults aged 18 ~ 59 from China Family Panel Studies data

IntroductionCigarette smoking is usually more prevalent among those with a lower socioeconomic status (SES), which can be driven by inequalities in the initiation and cessation of smoking, giving rise to SES disparities in health. This study aimed to gauge the SES inequalities in smoking related behaviours and their evolving trends based on a nationally representative database.MethodData were extracted from repeated cross-sectional China Family Panel Studies (CFPS) of adults aged ≥18 and <60 years in 2012, 2014, 2016 and 2018. SES was constructed by principal component analysis based on income, education and occupation. Regression-based odds ratios and coefficients as the relative effect index of inequality were applied to quantify the degree of socioeconomic inequality in smoking related behaviours and to adjust for possible confounding factors. Multivariable regressions were utilized to explore the temporal trends in smoking inequalities.ResultsThe smoking prevalence among men decreased from 61.16% to 2012 to 57.88% in 2018, cigarette consumption among current smokers declined from 16.71 to 15.49 cigs/per day, and the cessation rate increased from 17.55% to 24.08%. Cigarette consumption for women decreased from 13.39 in 2012 to 11.01 cigs/per day in 2018. Smoking prevalence showed significant SES inequalities among men and women from 2012 to 2018 (men: OR2012 (95%CI)= 0.72 (0.63, 0.83), OR2014 = 0.60 (0.52, 0.69), OR2016 = 0.58 (0.50, 0.67), OR2018 = 0.56 (0.48, 0.66); women: OR2012 = 0.63 (0.41, 0.97), OR2014 = 0.50 (0.32, 0.79), OR2016 = 0.44 (0.26, 0.73), OR2018 = 0.50 (0.30, 0.85)). Cigarette consumption showed significant SES inequalities among men from 2012 to 2018 (β2012=-1.39 (-2.22, -0.57), β2014=-2.37 (-3.23, -1.50), β2016=-2.35 (-3.25, -1.44), β2018=-2.91 (-3.86, -1.97)). In 2018, inequality emerged in smoking cessation rates among men and smoking intensity among women. However, all tests for trends in changes over time were not statistically significant (P varied from 0.072 to 0.602).ConclusionThe smoking prevalence declined between 2012 and 2018 in China. However, SES inequalities in smoking persist, while socioeconomic inequalities in smoking were not alleviated among adults aged 18 ~ 59 in China. Tobacco control measures should be implemented by giving more attention to people with lower SES who are more vulnerable to tobacco use.

Body surface mapping to detect STT-wave changes during invasive coronary function testing

Drugs belonging to diverse therapeutic classes can prolong myocardial refractoriness or slow conduction. These drugs may be effective and well-tolerated, but the risk of sudden cardiac death from torsades de pointes (TdP) remains a major concern. The corrected QT interval has significant limitations when used for risk stratification. Measurement of global electrical heterogeneity (GEH) could help identify the substrate vulnerable to drug-induced ventricular arrhythmias.The purpose of this study was to improve risk stratification for drug-induced TdP by measuring GEH on the electrocardiogram (ECG).We analyzed ECG data from a case-control study of patients with a history of drug-induced TdP as well as age- and sex-matched controls. Vectorcardiograms were constructed from ECGs. GEH was measured via the spatial ventricular gradient (SVG) vector (magnitude, azimuth, and elevation). Log odds coefficients for TdP were estimated using multivariable logistic regression.Among 17 cases (47% male; age 58.9 ± 12.5 years) and 17 controls (29% male; age 61.0 ± 12.2 years), 34 ECGs were analyzed. SVG azimuth was significantly different between cases and controls (3.4 vs 22.0 degrees, respectively; P = 0.02). After adjusting for sex and QTc interval, odds of TdP increased by a factor of 3.2 for each 1 SD change in SVG azimuth from the control group mean (95% confidence interval 1.07–9.14; P = .04). QTc was not significant in the multivariable analysis (P = .20).SVG azimuth is correlated with a history of drug-induced TdP independent of QTc. GEH measurement may help identify patients at high risk for drug-induced arrhythmias.

Hydrodynamic instability of odd-viscosity-induced shear-imposed falling film

In this paper, an analysis of linear and weakly nonlinear stability for an odd-viscosity-induced shear-imposed falling film over an inclined plane is performed. Using the Chebyshev spectral collocation approach, the linear effect for disturbance of arbitrary wavenumbers is numerically examined by solving the Orr–Sommerfeld eigenvalue problem within the framework of normal mode analysis. The study reveals that instability rises with increasing external shear in the streamwise direction. However, as external shear rises in the reverse flow direction, wave energy is dissipated, and the surface wave stabilizes. Furthermore, the longwave expansion method is applied to calculate the nonlinear surface deformation expression, and it is found that the odd viscosity has the ability to stabilize the fluid flow instability caused by a positive shear force. The investigation of weakly nonlinear stability is also performed using the multiple scale method, which led to the Ginzburg–Landau equation of the nonlinear surface deformation equation. The corresponding results confirm the significant effect of both imposed shear and odd viscosity coefficient on the existent subcritical unstable and supercritical stable zones along with unconditional and explosive zones near the threshold of the film flow instability. The bandwidth of the subcritical stable zone mitigates for the higher viscosity ratio while it enhances the flow-directed potent imposed shear. Additionally, the amplitude and phase speed of nonlinear waves in the supercritical stable regime rise with increasing induced shear in the fluid flow direction and gradually decrease with increasing the value of the odd viscosity coefficient.

Hele-Shaw flow for parity odd three-dimensional fluids

We derive the governing equation of flow for a three-dimensional fluid with a parity-broken viscosity tensor when confined to a Hele-Shaw cell. When such a fluid is pushed through a channel, a transverse force is exerted on the walls, and when a bubble of air expands into a region of such fluid, a circulation develops in the far field. The Saffman-Taylor stability condition is also modified, with these terms tending to stabilize the two fluid interface. Such experiments can in principle facilitate the measurement of parity odd coefficients in both synthetic and natural active matter systems.

Diffusive regimes in a two-dimensional chiral fluid

Diffusion is a fundamental aspect of transport processes in biological systems, and thus, in the development of life itself. And yet, the diffusive dynamics of active fluids with directed rotation, known as chiral fluids, has not been analyzed in detail so far. Here, we describe the diffusive regimes of a two-dimensional chiral fluid, composed in this case of a set of identical disk-shaped rotors. We found strong experimental evidence of odd diffusion. This odd diffusion emerges in the form of a two-dimensional tensor with an antisymmetric part. In particular, we show that chiral diffusion is complex, featuring transitions between super, quasi-normal, and sub diffusion, and very slowly aging. Moreover, we show that the diffusion tensor elements, including off-diagonal elements; i.e., odd diffusion coefficient, change sign according to flow vorticity. Therefore, the chiral fluid has a self regulated diffusion, controlled by its vorticity.

Time-correlation functions for odd Langevin systems.

We investigate the statistical properties of fluctuations in active systems that are governed by nonsymmetric responses. Both an underdamped Langevin system with an odd resistance tensor and an overdamped Langevin system with an odd elastic tensor are studied. For a system in thermal equilibrium, the time-correlation functions should satisfy time-reversal symmetry and the antisymmetric parts of the correlation functions should vanish. For the odd Langevin systems, however, we find that the antisymmetric parts of the time-correlation functions can exist and that they are proportional to either the odd resistance coefficient or the odd elastic constant. This means that the time-reversal invariance of the correlation functions is broken due to the presence of odd responses in active systems. Using the short-time asymptotic expressions of the time-correlation functions, one can estimate an odd elastic constant of an active material such as an enzyme or a motor protein.

Partial Fraction Expansion of Meromorphic Maps

Partial fraction expansion of a meromorphic function or map is a way of expressing it as an infinite series of rational functions and polynomials. This representation is particularly useful in the summation of series in mathematical analysis and has at its heart the Mittag-Leffler’s expansion theorem which holds for arbitrary domains. In this article, the Mittag-Leffler’s expansion theorem was used to obtain partial fraction expansions of the functions tan⁡z and coth⁡z which are meromorphic in the entire complex plane. The expansion of tan⁡z was then used to obtain the Laurent series for it where except for the odd coefficients, all the even coefficients in the series were shown to vanish identically. By comparing these coefficients with those of the well-known Maclaurin series for tan⁡z the exact sum of the odd terms in the important p-series ∑_(n=1)^∞▒1/n^p (p=2,4,6) were obtained in closed form and consequently, those of the series ∑_(n=1)^∞▒1/n^p (p=2,4,6) for all values of n. The partial fraction expansion of coth⁡z was also gainfully employed in finding the exact sum (in closed form) of the p-series ∑_(n=1)^∞▒1/n^2 and ∑_(n=-∞)^∞▒〖1/(n^2+z^2 ) (z≠ni,n=0,1,2,…)〗 to also show its usefulness in application. Finally, since closed form expressions were obtained for those series found from the partial fraction expansions of the functions considered in this article, we suggest that further research in this area should focus on the application of the Mittag-Leffler’s theorem to other meromorphic functions such as sec⁡z, cot⁡z etc to find similar results on the summation of series as done here.

Role of odd viscosity in falling viscous fluid

The aim of the present study is to investigate the linear and nonlinear wave dynamics of a falling incompressible viscous fluid when the fluid undergoes an effect of odd viscosity. In fact, such an effect arises in classical fluids when the time-reversal symmetry is broken. The motivation to study this dynamics was raised by recent studies (Ganeshan &amp; Abanov, Phys. Rev. Fluids, vol. 2, 2017, p. 094101; Kirkinis &amp; Andreev, J. Fluid Mech., vol. 878, 2019, pp. 169–189) where the odd viscosity coefficient suppresses thermocapillary instability. Here, we explore the linear surface wave and shear wave dynamics for the isothermal case by solving the Orr–Sommerfeld eigenvalue problem numerically with the aid of the Chebyshev spectral collocation method. It is found that surface and shear instabilities can be weakened by the odd viscosity coefficient. Furthermore, the growth rate of the wavepacket corresponding to the linear spatio-temporal response is reduced as long as the odd viscosity coefficient increases. In addition, a coupled system of a two-equation model is derived in terms of the fluid layer thickness $h(x,t)$ and the flow rate $q(x,t)$. The nonlinear travelling wave solution of the two-equation model reveals the attenuation of maximum amplitude and speed in the presence of an odd viscosity coefficient, which ensures the delay of transition from the primary parallel flow with a flat surface to secondary flow generated through the nonlinear wave interactions. This physical phenomenon is further corroborated by performing a nonlinear spatio-temporal simulation when a harmonic forcing is applied at the inlet.

Generation of dissipative solitons in a doped optical fiber modeled by the higher-order dispersive cubic-quintic-septic complex Ginzburg-Landau equation

The generation of dissipative optical solitons is explored in doped fibers with correction effects under the activation of modulational instability (MI). The model, described by the cubic-quintic-septic complex Ginzburg-Landau equation, includes higher-order dispersion and nonlinear gradient terms. The Lange-Newell's criterion for MI of Stokes wave, boundary domains of MI, and integrated gain of MI are obtained via the linear stability analysis. Particular attention is given to the physical effect on the critical frequency detuning, especially in the normal regime, when varying the values of odd dispersion coefficients. Numerical simulations are undertaken and confronted with analytical predictions. Beyond the agreement between the linear stability analysis and trains of soliton generation, the soliton map induced by MI, along with the subsequent physical effects, is debated via bifurcation diagrams. This allows accurate prediction of transitions between various types of localized modes and well-calibrated generation of a wide variety of solitons with different energies. It is argued that knowing the center of mass and the energy of the generated structures can better characterize the long-time evolution of MI and, eventually, its nonlinear manifestations.

Measurement of the transverse polarization of electrons emitted in neutron decay – nTRV experiment

This paper recalls the main achievements of the nTRV experiment which measured two components of the transverse polarization (\sigma_{T_{1}}σT1, \sigma_{T_{2}}σT2) of electrons emitted in the \betaβ-decay of polarized, free neutrons and deduced two correlation coefficients, RR and NN, that are sensitive to physics beyond the Standard Model. The value of time-reversal odd coefficient RR, 0.004\pm±0.012\pm±0.005, significantly improved limits on the relative strength of imaginary scalar coupling constant in the weak interaction. The value obtained for the time-reversal even correlation coefficient NN, 0.067\pm±0.011\pm±0.004, agrees with the Standard Model expectation, providing an important sensitivity test of the electron polarimeter. One of the conclusions of this pioneering experiment was that the transverse electron polarization in the neutron \betaβ-decay is worth more systematic exploring by measurements of yet experimentally not attempted correlation coefficients such as HH, LL, SS, UU and VV. This article presents a brief outlook on that questions.

P–200 To transfer or to discard: A retrospective analysis of ploidy, implantation and birthweight outcomes of grade “C” blastocysts following preimplantation genetic testing for aneuploidy (PGT-A)

Abstract Study question What’s the ploidy status of grade “C” blastocysts and what are their implantation potential and birthweight outcomes when tested euploid? Summary answer Grade “C” blastocysts were less likely to be euploid compared to grades “A/B”. Euploid “C”s led to reduced but reasonable implantation potential with similar birthweights. What is known already In contrast to grade “A” or “B”, grade “C” blastocysts are generally considered borderline quality in most in vitro fertilization programs, with inconsistent policies between clinics. Little evidence has been reported regarding their euploidy rate, implantation potential, and birthweight outcomes. Study design, size, duration This retrospective cohort study included 426 consecutive autologous-oocyte patients undergoing PGT-A (biopsy at day 5/6) at two associated private clinics between January 2013 and August 2020. A total of 1418 resulting blastocysts (tested either euploid or aneuploid) were analysed. Implantation outcomes were assessed in a subset of 520 singly transferred euploid blastocysts. Birthweight outcomes were evaluated in 209 singleton newborns using a gestation-adjusted Z score taking into account gestational age and baby gender. Participants/materials, setting, methods Blastocysts were graded “A/B/C” according to a combination of inner cell mass and trophectoderm morphology. Endpoints included ploidy, implantation and birthweight outcomes. Multiple regression (logistic or linear) was performed to investigate relative prognosis of grade “C” blastocysts using different endpoints in reference to grade “A/B” blastocysts, expressed as either adjusted odds ratio (aOR) or coefficients (β) with 95% confidence intervals (CI). Maternal age and biopsy day (5/6) were included as potential confounders at regression analysis. Main results and the role of chance Grade “C” blastocysts (n = 466) were associated with a lower euploidy rate in reference to either grade “A” (n = 179, aOR=0.412, 95% CI: 0.278–0.611, P = 0.000) or “B” blastocysts (n = 773, aOR=0.535, 95% CI: 0.418–0.685, P = 0.000). Euploid “C” grade blastocysts (n = 128) led to significantly reduced chance to implant when compared to either grade “A” (n = 90, aOR=0.387, 95% CI: 0.215–0.696, P = 0.002) or “B” blastocysts (n = 302, aOR=0.617, 95% CI: 0.404–0.944, P = 0.026); although implantation rate was still considered at a reasonable level (44.5%) as opposed to grades “A” (66.7%) or “B” (57.6%). However, no significant difference was observed in the birthweight (g, mean ± standard deviation) following the transfer of a single euploid grade “C” blastocyst (n = 42, 3310.8±704.1) in comparison to a single euploid grade “A” (n = 48, 3367.8±519.3, P &amp;gt; 0.05) or “B” blastocyst (n = 119, 3284.5±535.5, P &amp;gt; 0.05). Taking into account maternal age, biopsy day, gestational age and baby gender; further multiple linear regression analysis also showed similar results using either birthweight itself (C vs A, β=–52.395, 95% CI: –148.83–43.893, P = 0.282; C vs B, β=–104.338, 95% CI: –272.653–63.977, P = 0.223), or the gestation-adjusted Z score as an endpoint (C vs A, β = 0.101, 95% CI: –0.001–0.164, P = 0.052; C vs B, β = 0.084, 95% CI: -–0.073 – 0.241, P = 0.290). Limitations, reasons for caution The retrospective design of this study does not allow control for unknown confounders. Inner cell mass or trophectoderm was not graded separately making it difficult to further break down the “C” grade blastocysts. Only blastocysts suitable for biopsy were included for analysis, so results may not extrapolate to untested blastocysts. Wider implications of the findings: Grade “C” blastocysts may still hold its clinical value despite reduced euploidy rate. PGT-A may be considered as a potential approach to utilize grade “C” blastocysts more effectively, without affecting birthweight outcomes. This is also potentially useful in patient counselling. Trial registration number Not applicable

Odd-viscosity-induced instability of a thin film with variable density

The stability of a two-dimensional gravity-driven thin viscous Newtonian fluid with broken time-reversal-symmetry draining down a uniformly heated inclined plane is discussed. The presence of the odd part of the Cauchy stress tensor with an odd viscosity coefficient brings new characteristics in fluid flow. A theoretical model is implemented, which captures the dependence of the surface tension on temperature, and the model also allows for variation in the density of the liquid with a thermal difference. The coupled effect of odd viscosity, variable density, and surface tension has been investigated both analytically and numerically. A nonlinear evolution equation of the free surface is derived by the method of systematic asymptotic expansion. A linear stability analysis is carried out, which yields the critical conditions for the onset of instability in long-wave perturbations. New interesting results illustrating how the critical Reynolds number depends on the odd viscosity as well as other various dimensionless parameters have been obtained. In addition, a weakly nonlinear stability analysis is performed based on the method of multiple scales from which a complex Ginzburg–Landau equation is obtained. It is observed that the film not only has supercritical stable and subcritical unstable zones, but also unconditional stable and explosive zones. It has been also shown that the spatial uniform solution corresponding to the sideband disturbance may be stable in the unstable region. Employing the Crank–Nicolson method in a periodic domain, the spatiotemporal evolution of the model has been analyzed numerically for different values of the odd viscosity as well as other flow parameters. Nonlinear simulations are found to be in good agreement with the linear and weakly nonlinear stability analysis. The results are conducive to the further development of related experiments.

Interfacial phase change effect on a viscous falling film having odd viscosity down an inclined plane

We investigate the phase change effect at the thin film interface with broken time-reversal-symmetry falling down an inclined flat wall. We consider the impact of evaporation and as well as condensation at the fluid-vapor interface separately. The non-zero odd part of the Cauchy stress tensor with the odd viscosity coefficient, which arises due to broken-time-reversal-symmetry, adds an attractive characteristic in the flow by stabilizing the effect of evaporation/condensation. We study the long-wave instabilities of the ununiform film by deriving a non-linear evolution equation in the classical long wave expansion method framework. The one-equation model can track the free surface evolution and accounts for viscosity, gravity, surface tension, and phase change (evaporation/condensation) effects. Linear stability analysis confirms that the odd viscosity has no significant impact on the instability threshold of an evaporating film as a contrast of condensate film, where the critical Reynolds number increases with the odd-viscosity parameter μ. While studying the weakly non-linear waves, we use the method of multiple scales to obtain the Complex Ginzburg Landau equation that shows both supercritical and subcritical solutions are possible for evaporating and condensate film. Interestingly, while one subcritical region is visible for an evaporating film, two subcritical unstable regions are found for condensate film. The numerical solution of the free-surface equation illustrates the finite-amplitude behavior that tends to dry out for evaporating film and rapidly increase film thickness for condensate film. The presence of odd viscosity slows down both the film thinning process for evaporation and the film thickening process for condensation. Furthermore, odd-viscosity cannot prevent film rupture in case of evaporation.