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The MOOSE (Monitoring Observations of SMC X-1 Excursions) program uses the Neutron Star Interior Composition Explorer Mission (NICER) to monitor the high mass X-ray binary SMC X-1 during its superorbital period excursions. Here we perform X-ray spectral analyses of 26 NICER observations of SMC X-1, taken at the tail-end of the excursion between 2021-04-01 and 2022-01-05. We use a single spectral model to fit spectra observed in high, intermediate and low states, using a combination of a partial covering fraction model, a black-body disc, and a power-law component. We find that the partial covering fraction varies significantly with the superorbital state during superorbital excursion. Our findings suggest that the low/high state in SMC X-1 is caused by a very high obscuration of the accretion disk., Comment: 10 pages 4 figures, accepted to MNRAS

Semi-flexible polyelectrolytes are a group of biopolymers with a wide range of applications from drag reducing agents in turbulent flows to thickening agents in food and cosmetics. In this study, we investigate the rheology of aqueous solutions of xanthan gum as a canonical semi-flexible polyelectrolyte in steady shear and transient extensional flows via torsional rheometry and dripping-onto-substrate (DoS), respectively. The high molecular weight of the xanthan gum and the numerous charged groups on the side branches attached to the backbone allow the shear and extensional rheology of the xanthan gum solutions to be tuned over a wide range by changing the ionic strength of the solvent. In steady shear flow, increasing the xanthan gum concentration increases both the zero shear viscosity and the extent of shear-thinning of the solution. Conversely, increasing the ionic strength of the solvent by addition of sodium chloride (NaCl) decreases both the zero shear viscosity and the level of shear-thinning. In transient extensional flow, increasing the xanthan gum concentration changes the dynamics of the capillary thinning from an inelastic power-law (IP) response to an elastocapillary (EC) balance, from which an extensional relaxation time can be measured based on the rate of filament thinning. Increasing the NaCl concentration decreases the extensional relaxation time and the transient extensional viscosity of the viscoelastic solution. Based on the dynamics of capillary thinning observed in the DoS experiments, we provide a relationship for the smallest extensional relaxation time that can be measured using DoS. We suggest that the change in the dynamics of capillary thinning from an IP response to an EC response can be used as an easy and robust experimental method for identifying the rheologically effective overlap concentration of a semi-flexible polyelectrolyte solution, i.e., the critical concentration at which polymer molecules start to interact with each other to produce a viscoelastic strain-stiffening response (often perceived as "stringiness") in transient extensional flows such as those involved in dripping, dispensing and filling operations.

This is an index of the contributions by the Giant Radio Array for Neutrino Detection (GRAND) Collaboration to the 10th International Workshop on Acoustic and Radio EeV Neutrino Detection Activities (ARENA 2024, University of Chicago, June 11-14, 2024). The contributions include an overview of GRAND in its present and future incarnations, methods of radio-detection that are being developed for them, and ongoing joint work between the GRAND and BEACON experiments., Comment: Note: To access the list of contributions, please follow the "HTML" link that can be found on the arXiv page

The radio interferometric closure phases can be a valuable tool for studying cosmological {H\scriptsize{I}}~from the early Universe. Closure phases have the advantage of being immune to element-based gains and associated calibration errors. Thus, calibration and errors therein, which are often sources of systematics limiting standard visibility-based approaches, can be avoided altogether in closure phase analysis. In this work, we present the first results of the closure phase power spectrum of {H\scriptsize{I}}~21-cm fluctuations using the Murchison Widefield Array (MWA), with $\sim 12$ hours of MWA-phase II observations centered around redshift, $z\approx 6.79$, during the Epoch of Reionisation. On analysing three redundant classes of baselines -- 14~m, 24~m, and 28~m equilateral triads, our estimates of the $2\sigma$ ($95\%$ confidence interval) 21-cm power spectra are $\lesssim (184)^2 pseudo \rm ~mK^2$ at ${k}_{||} = 0.36 $ $pseudo~h {\rm Mpc^{-1}}$ in the EoR1 field for the 14~m baseline triads, and $\lesssim (188)^2 pseudo \rm ~mK^2$ at $k_{||} = 0.18 $ $pseudo~h {\rm Mpc^{-1}}$ in the EoR0 field for the 24~m baseline triads. The ``$pseudo$'' units denote that the length scale and brightness temperature should be interpreted as close approximations. Our best estimates are still 3-4 orders high compared to the fiducial 21-cm power spectrum; however, our approach provides promising estimates of the power spectra even with a small amount of data. These data-limited estimates can be further improved if more datasets are included into the analysis. The evidence for excess noise has a possible origin in baseline-dependent systematics in the MWA data that will require careful baseline-based strategies to mitigate, even in standard visibility-based approaches., Comment: 24 pages, 21 figures, 4 tables (accepted for publication in PASA)

The operation of upcoming ultra-high-energy cosmic-ray, gamma-ray, and neutrino radio-detection experiments, like the Giant Radio Array for Neutrino Detection (GRAND), poses significant computational challenges involving the production of numerous simulations of particle showers and their detection, and a high data throughput. GRANDlib is an open-source software tool designed to meet these challenges. Its primary goal is to perform end-to-end simulations of the detector operation, from the interaction of ultra-high-energy particles, through -- by interfacing with external air-shower simulations -- the ensuing particle shower development and its radio emission, to its detection by antenna arrays and its processing by data-acquisition systems. Additionally, GRANDlib manages the visualization, storage, and retrieval of experimental and simulated data. We present an overview of GRANDlib to serve as the basis of future GRAND analyses., Comment: 11 pages, 9 figures, plus appendices

Trust is a subjective yet fundamental component of human-computer interaction, and is a determining factor in shaping the efficacy of data visualizations. Prior research has identified five dimensions of trust assessment in visualizations (credibility, clarity, reliability, familiarity, and confidence), and observed that these dimensions tend to vary predictably along with certain features of the visualization being evaluated. This raises a further question: how do the design features driving viewers trust assessment vary with the characteristics of the viewers themselves? By reanalyzing data from these studies through the lens of individual differences, we build a more detailed map of the relationships between design features, individual characteristics, and trust behaviors. In particular, we model the distinct contributions of endogenous design features (such as visualization type, or the use of color) and exogenous user characteristics (such as visualization literacy), as well as the interactions between them. We then use these findings to make recommendations for individualized and adaptive visualization design.

This brief note gives several new upper and lower bounds on Ramsey numbers for books and wheels, including tight lower bounds establishing the Ramsey numbers $R(B_3, B_6) = 19$, $R(B_4,B_5)=19$, $R(B_5,B_6)= 23$, and $R(B_6,B_7)= 27$, and tight upper and lower bounds establishing $R(W_5, W_7) = 15$. The new upper bound was obtained using the flag algebra method, and the lower bounds come from constructions discovered using tabu search. We also explore generalized Ramsey numbers using similar methods. Let $GR(r,K_s,t)$ denote the minimum number of vertices $n$ such that any $r$-edge-coloring of $K_n$ has a copy of $K_s$ with at most $t$ colors. We establish $GR(3,K_4,2) = 10$, $GR(4,K_4,3) = 10$, and some additional bounds., Comment: 7 pages (not including references and appendix)

Abstract Knowledge of the evolution of mechanical properties of the curing matrix is of great importance in composite parts or structure fabrication. Conventional rheometry, based on small amplitude oscillatory shear is limited by long interrogation times. In rapidly evolving materials, time sweeps can provide a meaningful measurement albeit at a single frequency. To overcome this constraint we utilize a combined frequency and amplitude-modulated chirped strain waveform in conjunction with a home-made sliding plate piezo-operated (PZR) and a dual-head commercial rotational rheometer (Anton Paar MCR 702) to probe the linear viscoelasticity of these time-evolving materials. The direct controllability of the PZR resulting from the absence of any kind of firmware and the microsecond actuator-sensor response renders this device ideal for exploring the advantages of this technique. The high frequency capability allows us to extend the upper limits of the accessible linear viscoelastic spectrum and most importantly, to shorten the length of the interrogating strain signal (OWCh-PZR) to sub-second scales, while retaining a high time-bandwidth product. This short duration ensures that the mutation number (NMu) is kept sufficiently low, even in fast curing resins. The method is validated via calibration tests in both instruments and the corresponding limitations are discussed. As a proof of concept the technique is applied to a curing vinylester resin. The linear viscoelastic (LVE) spectrum is assessed every 20 seconds to monitor the rapid evolution of the time- and frequency-dependence of the complex modulus. Finally, FTIR spectroscopy is utilized to gain insights on the evolution of the chemical network while the gap-dependence of the evolving material properties in these heterogeneous systems is also investigated.

Unleashing the synergies among rapidly evolving mobility technologies in a multi-stakeholder setting presents unique challenges and opportunities for addressing urban transportation problems. This paper introduces a novel synthetic participatory method that critically leverages large language models (LLMs) to create digital avatars representing diverse stakeholders to plan shared automated electric mobility systems (SAEMS). These calibratable agents collaboratively identify objectives, envision and evaluate SAEMS alternatives, and strategize implementation under risks and constraints. The results of a Montreal case study indicate that a structured and parameterized workflow provides outputs with higher controllability and comprehensiveness on an SAEMS plan than that generated using a single LLM-enabled expert agent. Consequently, this approach provides a promising avenue for cost-efficiently improving the inclusivity and interpretability of multi-objective transportation planning, suggesting a paradigm shift in how we envision and strategize for sustainable transportation systems.

Extensional flows of complex fluids are pivotal in industrial applications like spraying, atomisation, and microfluidic drop deposition. The Dripping-on-Substrate (DoS) technique is a conceptually simple, but dynamically-complex, probe of the extensional rheology of low-viscosity, non-Newtonian fluids. DoS involves capillary-driven thinning of a liquid bridge formed by a slowly dispensed drop onto a partially-wetting solid substrate. By following the filament thinning and pinch-off, the extensional viscosity and relaxation time can be determined. Importantly, DoS enables measurements for lower viscosity solutions than commercially available capillary break-up extensional rheometers. To understand DoS operation, we employ a computational rheology approach via adaptively-refined, time-dependent axisymmetric simulations using the open-source Eulerian code, \textit{Basilisk}. The volume-of-fluid technique is used to capture the moving interface, and the log-conformation transformation enables a stable viscoelastic solution. We focus on understanding the roles of surface tension, elasticity, and finite chain extensibility in the Elasto-Capillary (EC) regime. Additionally, we explore perturbative effects of gravity and substrate wettability in setting the evolution of the self-similar thinning and pinch-off dynamics. To illustrate the interplay of these different forces, we construct a simple one-dimensional model capturing the initial thinning rates, balancing inertia and capillarity. This model also describes the structure of the transition region to the nonlinear EC regime, where elastic stresses counteract capillary pressure in the thread as the filament thins toward breakup. Finally, we propose a fitting methodology based on the analytical solutions for FENE-P fluids to enhance accuracy in determining the effective relaxation time for unknown fluids.

Neuro-oncological surgery is the primary brain cancer treatment, yet it faces challenges with gliomas due to their invasiveness and the need to preserve neurological function. Hence, radical resection is often unfeasible, highlighting the importance of precise tumor margin delineation to prevent neurological deficits and improve prognosis. Imaging Mueller polarimetry, an effective modality in various organ tissues, seems a promising approach for tumor delineation in neurosurgery. To further assess its use, we characterized the polarimetric properties by analysing 45 polarimetric measurements of 27 fresh brain tumor samples, including different tumor types with a strong focus on gliomas. Our study integrates a wide-field imaging Mueller polarimetric system and a novel neuropathology protocol, correlating polarimetric and histological data for accurate tissue identification. An image processing pipeline facilitated the alignment and overlay of polarimetric images and histological masks. Variations in depolarization values were observed for grey and white matter of brain tumor tissue, while differences in linear retardance were seen only within white matter of brain tumor tissue. Notably, we identified pronounced optical axis azimuth randomization within tumor regions. This study lays the foundation for machine learning-based brain tumor segmentation algorithms using polarimetric data, facilitating intraoperative diagnosis and decision making., Comment: 12 pages, 9 figures. This work has been submitted to the IEEE for possible publication

The globular cluster ultraluminous X-ray source, RZ2109, is a complex and unique system which has been detected at X-ray, ultra-violet, and optical wavelengths. Based on almost 20 years of Chandra and XMM-Newton observations, the X-ray luminosity exhibits order-of-magnitude variability, with the peak flux lasting on the order of a few hours. We perform robust time series analysis on the archival X-ray observations and find that this variability is periodic on a timescale of 1.3 $\pm 0.04$ days. The source also demonstrates broad [OIII] 5007 Angstrom emission, which has been observed since 2004, suggesting a white dwarf donor and therefore an ultra-compact X-ray binary. We present new spectra from 2020 and 2022, marking eighteen years of observed [OIII] emission from this source. Meanwhile, we find that the globular cluster counterpart is unusually bright in the NUV/UVW2 band. Finally, we discuss RZ2109 in the context of the eccentric Kozai Lidov mechanism and show that the observed 1.3 day periodicity can be used to place constraints on the tertiary configuration, ranging from 20 minutes (for a 0.1 ${\rm M}_\odot$ companion) to approximately 95 minutes (for a 1 ${\rm M}_\odot$ companion), if the eccentric Kozai Lidov mechanism is at the origin of the periodic variability., Comment: Accepted to MNRAS

We present a new way to summarize and select mixture models via the hierarchical clustering tree (dendrogram) constructed from an overfitted latent mixing measure. Our proposed method bridges agglomerative hierarchical clustering and mixture modeling. The dendrogram's construction is derived from the theory of convergence of the mixing measures, and as a result, we can both consistently select the true number of mixing components and obtain the pointwise optimal convergence rate for parameter estimation from the tree, even when the model parameters are only weakly identifiable. In theory, it explicates the choice of the optimal number of clusters in hierarchical clustering. In practice, the dendrogram reveals more information on the hierarchy of subpopulations compared to traditional ways of summarizing mixture models. Several simulation studies are carried out to support our theory. We also illustrate the methodology with an application to single-cell RNA sequence analysis., Comment: 53 pages, 11 figures

Wide-field imaging Mueller polarimetry is a revolutionary, label-free, and non-invasive modality for computer-aided intervention: in neurosurgery it aims to provide visual feedback of white matter fibre bundle orientation from derived parameters. Conventionally, robust polarimetric parameters are estimated after averaging multiple measurements of intensity for each pair of probing and detected polarised light. Long multi-shot averaging, however, is not compatible with real-time in-vivo imaging, and the current performance of polarimetric data processing hinders the translation to clinical practice. A learning-based denoising framework is tailored for fast, single-shot, noisy acquisitions of polarimetric intensities. Also, performance-optimised image processing tools are devised for the derivation of clinically relevant parameters. The combination recovers accurate polarimetric parameters from fast acquisitions with near-real-time performance, under the assumption of pseudo-Gaussian polarimetric acquisition noise. The denoising framework is trained, validated, and tested on experimental data comprising tumour-free and diseased human brain samples in different conditions. Accuracy and image quality indices showed significant improvements on testing data for a fast single-pass denoising versus the state-of-the-art and high polarimetric image quality standards. The computational time is reported for the end-to-end processing. The end-to-end image processing achieved real-time performance for a localised field of view. The denoised polarimetric intensities produced visibly clear directional patterns of neuronal fibre tracts in line with reference polarimetric image quality standards; directional disruption was kept in case of neoplastic lesions. The presented advances pave the way towards feasible oncological neurosurgical translations of novel, label free, interventional feedback.

Many imaging techniques for biological systems -- like fixation of cells coupled with fluorescence microscopy -- provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. These snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems. However, experimental data is commonly a set of locations whose number is insufficient to approximate a continuous-in-space PDE solution. Here, motivated by popular subcellular imaging data of gene expression, we embrace the stochastic nature of the data and investigate the mathematical foundations of parametrically inferring demographic rates from snapshots of particles undergoing birth, diffusion, and death in a nuclear or cellular domain. Toward inference, we rigorously derive a connection between individual particle paths and their presentation as a Poisson spatial process. Using this framework, we investigate the properties of the resulting inverse problem and study factors that affect quality of inference. One pervasive feature of this experimental regime is the presence of cell-to-cell heterogeneity. Rather than being a hindrance, we show that cell-to-cell geometric heterogeneity can increase the quality of inference on dynamics for certain parameter regimes. Altogether, the results serve as a basis for more detailed investigations of subcellular spatial patterns of RNA molecules and other stochastically evolving populations that can only be observed for single instants in their time evolution., Comment: 33 pages, 6 figures

The microtubule cytoskeleton is responsible for sustained, long-range intracellular transport of mRNAs, proteins, and organelles in neurons. Neuronal microtubules must be stable enough to ensure reliable transport, but they also undergo dynamic instability, as their plus and minus ends continuously switch between growth and shrinking. This process allows for continuous rebuilding of the cytoskeleton and for flexibility in injury settings. Motivated by \textit{in vivo} experimental data on microtubule behavior in \textit{Drosophila} neurons, we propose a mathematical model of dendritic microtubule dynamics, with a focus on understanding microtubule length, velocity, and state-duration distributions. We find that limitations on microtubule growth phases are needed for realistic dynamics, but the type of limiting mechanism leads to qualitatively different responses to plausible experimental perturbations. We therefore propose and investigate two minimally-complex length-limiting factors: limitation due to resource (tubulin) constraints and limitation due to catastrophe of large-length microtubules. We combine simulations of a detailed stochastic model with steady-state analysis of a mean-field ordinary differential equations model to map out qualitatively distinct parameter regimes. This provides a basis for predicting changes in microtubule dynamics, tubulin allocation, and the turnover rate of tubulin within microtubules in different experimental environments., Comment: 34 pages, 10 figures

It is well known that inertia-free shearing flows of a viscoelastic fluid with curved streamlines, such as the torsional flow between a rotating cone and plate, or the flow in a Taylor-Couette geometry, can become unstable to a three-dimensional time-dependent instability at conditions exceeding a critical Weissenberg (Wi) number. However, the combined effects of fluid elasticity, shear thinning, and finite inertia (as quantified by the Reynolds number Re) on the onset of elasto-inertial instabilities are not fully understood. Using a set of cone-plate geometries, we experimentally explore the entire Wi - Re phase space for a series of rate-dependent viscoelastic fluids (quantified using a shear thinning parameter $\beta_P$). We tune $\beta_P$ by varying the polymer concentration in solutions. This progressively reduces shear-thinning but leads to finite inertial effects before the onset of elastic instability, thus naturally resulting in elasto-inertial coupling. Transient rheometric measurements and flow visualization experiments allow us to investigate the effects of flow geometry and document the combined effects of varying Wi, Re, and $\beta_P$ on the emergence of secondary motions at the onset of instability. The resulting critical state diagram quantitatively depicts the competition between the stabilizing effects of shear thinning and the destabilizing effects of inertia. We extend the curved streamline instability criterion of Pakdel and McKinley 1996 for the onset of purely elastic instability in curvilinear geometries by using scaling arguments to incorporate shear thinning and finite inertial effects. The augmented condition facilitates predictions of the onset of instability over a broader range of flow conditions, thus bridging the gap between purely elastic and elasto-inertial curved streamline instabilities.

Few concepts are as ubiquitous in computational fields as trust. However, in the case of information visualization, there are several unique and complex challenges, chief among them: defining and measuring trust. In this paper, we investigate the factors that influence trust in visualizations. We draw on the literature to identify five factors likely to affect trust: credibility, clarity, reliability, familiarity, and confidence. We then conduct two studies investigating these factors' relationship with visualization design features. In the first study, participants' credibility, understanding, and reliability ratings depended on the visualization design and its source. In the second study, we find these factors also align with subjective trust rankings. Our findings suggest that these five factors are important considerations for the design of trustworthy visualizations., Comment: 5 pages, IEEE visualization conference (VIS)

Neutron star high mass X-ray binaries with superorbital modulations in luminosity host warped inner accretion disks that occult the neutron star during precession. In SMC X-1, the instability in the warped disk geometry causes superorbital period "excursions:" times of instability when the superorbital period decreases from its typical value of 55 days to $\sim$40 days. Disk instability makes SMC X-1 an ideal system in which to investigate the effects of variable disk geometry on the inner accretion flow. Using the high resolution spectral and timing capabilities of the Neutron Star Interior Composition Explorer (NICER) we examined the high state of four different superorbital cycles of SMC X-1 to search forchanges in spectral shape and connections to the unstable disk geometry. We performed pulse phase-averaged and phase-resolved spectroscopy to closely compare the changes in spectral shape and any cycle-to-cycle variations. While some parameters including the photon index and absorbing column density show slight variations with superorbital phase, these changes are most evident during the intermediate state of the supeorbital cycle. Few spectral changes are observed within the high state of the superorbital cycle, possibly indicating the disk instability does not significantly change SMC X-1's accretion process., Comment: 11 pages, 5 figures. Accepted to ApJ

Soft biological tissues exhibit a remarkable resilience to large mechanical loads, a property which is associated with the strain stiffening capability of the biopolymer networks that structurally support the tissues. Yet, recent studies have shown that composite systems such as tissues and blood clots exhibit mechanical properties that contradict those of the polymer matrix - demonstrating stiffening in compression, but softening in shear and tension. The microscopic basis of this apparent paradox remains poorly understood. We show that composite hydrogels and tissues do indeed exhibit non-linear elastic stiffening in shear - which is governed by the stretching of the polymer chains in the matrix - and that it is driven by the same mechanism that drives compression stiffening. However, we show that the non-linear elastic stiffening in composite hydrogels and tissues is masked by mechanical dissipation arising from filler-polymer interactions known as the Mullins effect, and we introduce a method to characterize the non-linear elasticity of the composites in isolation from this overall strain softening response through large-amplitude oscillatory shear experiments. We present a comprehensive characterization of the non-linear elastic strain stiffening of composite hydrogels and soft tissues, and show that the strain stiffening in shear and compression are both governed by universal strain amplification factors that depend on essential properties of the composite system, such as the filler concentration and the filler-polymer interaction strength. These results elucidate the microscopic mechanisms governing the non-linear mechanics of tissues, which provides design principles for engineering tissue-mimetic soft materials, and have broad implications for cell-matrix mechanotransduction in living tissues under strain.

The thickness of the cortical band is linked to various neurological and psychiatric conditions, and is often estimated through surface-based methods such as Freesurfer in MRI studies. The DiReCT method, which calculates cortical thickness using a diffeomorphic deformation of the gray-white matter interface towards the pial surface, offers an alternative to surface-based methods. Recent studies using a synthetic cortical thickness phantom have demonstrated that the combination of DiReCT and deep-learning-based segmentation is more sensitive to subvoxel cortical thinning than Freesurfer. While anatomical segmentation of a T1-weighted image now takes seconds, existing implementations of DiReCT rely on iterative image registration methods which can take up to an hour per volume. On the other hand, learning-based deformable image registration methods like VoxelMorph have been shown to be faster than classical methods while improving registration accuracy. This paper proposes CortexMorph, a new method that employs unsupervised deep learning to directly regress the deformation field needed for DiReCT. By combining CortexMorph with a deep-learning-based segmentation model, it is possible to estimate region-wise thickness in seconds from a T1-weighted image, while maintaining the ability to detect cortical atrophy. We validate this claim on the OASIS-3 dataset and the synthetic cortical thickness phantom of Rusak et al., Comment: Accepted (early acceptance) at MICCAI 2023

The black hole candidate XTE J2012+381 underwent an outburst at the end of 2022. We analyzed 105 NICER observations and 2 NuSTAR observations of the source during the outburst. The NuSTAR observations of the $M \sim10M_\odot$ black hole indicate clear signs of relativistic disk reflection, which we modeled to measure a BH spin of $a=0.988^{+0.008}_{-0.030}$ and an inclination of $\theta=68^{+6}_{-11}$ degrees ($1\sigma$ statistical errors). In our analysis, we test an array of models and examine the effect of fitting NuSTAR spectra alone versus fitting simultaneously with NICER. We find that when the underlying continuum emission is properly accounted for, the reflected emission is similarly characterized by multiple models. We combined 52 NICER spectra to obtain a spectrum with an effective exposure of 190 ks in order to probe the presence of absorption lines that would be suggestive of disk winds, but the resulting features were not statistically significant. We discuss the implications of this measurement in relation to the overall BH spin distribution in X-ray binary systems., Comment: 17 pages, 7 figures. Accepted for publication in ApJ

We perform simulations of an impulsively-started, axisymmetric viscoelastic jet exiting a nozzle and entering a stagnant gas phase using the open-source code Basilisk. This code allows for efficient computations through an adaptively-refined volume-of-fluid technique that can accurately capture the deformation of the liquid-gas interface. We use the FENE-P constitutive equation to describe the viscoelasticity of the liquid and employ the log-conformation transformation, which provides stable solutions for the evolution of the conformation tensor as the jet thins down under the action of interfacial tension. For the first time, the entire jetting and breakup process of a viscoelastic fluid is simulated, including the pre-shearing flow through the nozzle, which results in an inhomogeneous initial radial stress distribution in the fluid thread that affects the subsequent breakup dynamics. The evolution of the velocity field and the elastic stresses in the nozzle are validated against analytical solutions where possible, and the early-stage dynamics of the jet evolution are compared favourably to the predictions of linear stability theory. We study the effect of the flow inside the nozzle on the thinning dynamics of the viscoelastic jet (which develops distinctive "beads-on-a-string" structures) and on the spatio-temporal evolution of the polymeric stresses in order to systematically explore the dependence of the filament thinning and breakup characteristics on the initial axial momentum of the jet and the extensibility of the dissolved polymer chains.

Radio interferometers can potentially detect the sky-averaged signal from the Cosmic Dawn (CD) and the Epoch of Reionisation (EoR) by studying the Moon as a thermal block to the foreground sky. The first step is to mitigate the Earth-based RFI reflections (Earthshine) from the Moon, which significantly contaminate the FM band $\approx 88-110$ MHz, crucial to CD-EoR science. We analysed MWA phase-I data from $72-180$ MHz at $40$ kHz resolution to understand the nature of Earthshine over three observing nights. We took two approaches to correct the Earthshine component from the Moon. In the first method, we mitigated the Earthshine using the flux density of the two components from the data, while in the second method, we used simulated flux density based on an FM catalogue to mitigate the Earthshine. Using these methods, we were able to recover the expected Galactic foreground temperature of the patch of sky obscured by the Moon. We performed a joint analysis of the Galactic foregrounds and the Moon's intrinsic temperature $(T_{\rm Moon})$ while assuming that the Moon has a constant thermal temperature throughout three epochs. We found $T_{\rm Moon}$ to be at $184.4\pm{2.6}\rm ~K$ and $173.8\pm{2.5}\rm ~K$ using the first and the second methods, respectively, and the best-fit values of the Galactic spectral index $(\alpha)$ to be within the $5\%$ uncertainty level when compared with the global sky models. Compared with our previous work, these results improved constraints on the Galactic spectral index and the Moon's intrinsic temperature. We also simulated the Earthshine at MWA between November and December 2023 to find suitable observing times less affected by the Earthshine. Such observing windows act as Earthshine avoidance and can be used to perform future global CD-EoR experiments using the Moon with the MWA., Comment: 17 pages, 14 figures and 8 tables, accepted for publication in PASA

Given a graph $F$, we define $\operatorname{ex}(G_{n,p},F)$ to be the maximum number of edges in an $F$-free subgraph of the random graph $G_{n,p}$. Very little is known about $\operatorname{ex}(G_{n,p},F)$ when $F$ is bipartite, with essentially tight bounds known only when $F$ is either $C_4, C_6, C_{10}$, or $K_{s,t}$ with $t$ sufficiently large in terms of $s$, due to work of F\"uredi and of Morris and Saxton. We extend this work by establishing essentially tight bounds when $F$ is a theta graph with sufficiently many paths. Our main innovation is in proving a balanced supersaturation result for vertices, which differs from the standard approach of proving balanced supersaturation for edges.

Inverse problems describe the task of recovering an underlying signal of interest given observables. Typically, the observables are related via some non-linear forward model applied to the underlying unknown signal. Inverting the non-linear forward model can be computationally expensive, as it often involves computing and inverting a linearization at a series of estimates. Rather than inverting the physics-based model, we instead train a surrogate forward model (emulator) and leverage modern auto-grad libraries to solve for the input within a classical optimization framework. Current methods to train emulators are done in a black box supervised machine learning fashion and fail to take advantage of any existing knowledge of the forward model. In this article, we propose a simple learned weighted average model that embeds linearizations of the forward model around various reference points into the model itself, explicitly incorporating known physics. Grounding the learned model with physics based linearizations improves the forward modeling accuracy and provides richer physics based gradient information during the inversion process leading to more accurate signal recovery. We demonstrate the efficacy on an ocean acoustic tomography (OAT) example that aims to recover ocean sound speed profile (SSP) variations from acoustic observations (e.g. eigenray arrival times) within simulation of ocean dynamics in the Gulf of Mexico.

For an odd integer $n = 2d-1$, let $\mathcal B_d$ be the subgraph of the hypercube $Q_n$ induced by the two largest layers. In this paper, we describe the typical structure of proper $q$-colorings of $V(\mathcal B_d)$ and give asymptotics on the number of them. The proofs use various tools including information theory (entropy), Sapozhenko's graph container method and a recently developed method of M. Jenssen and W. Perkins that combines Sapozhenko's graph container lemma with the cluster expansion for polymer models from statistical physics., Comment: 31 pages

Addition of particles to a viscoelastic suspension dramatically alters the properties of the mixture, particularly when it is sheared or otherwise processed. Shear-induced stretching of the polymers results in elastic stress that causes a substantial increase in measured viscosity with increasing shear, and an attractive interaction between particles, leading to their chaining. At even higher shear rates, the flow becomes unstable, even in the absence of particles. This instability makes it very difficult to determine the properties of a particle suspension. Here we use a fully immersed parallel plate geometry to measure the high-shear-rate behavior of a suspension of particles in a viscoelastic fluid. We find an unexpected separation of the particles within the suspension resulting in the formation of a layer of particles in the center of the cell. Remarkably, monodisperse particles form a crystalline layer which dramatically alters the shear instability. By combining measurements of the velocity field and torque fluctuations, we show that this solid layer disrupts the flow instability and introduces a new, single-frequency component to the torque fluctuations that reflects a dominant velocity pattern in the flow. These results highlight the interplay between particles and a suspending viscoelastic fluid at very high shear rates., Comment: SI Videos and future data sharing are available at https://doi.org/10.7910/DVN/K0XZ6N

Convolutional neural networks (CNNs) allow for parameter sharing and translational equivariance by using convolutional kernels in their linear layers. By restricting these kernels to be SO(3)-steerable, CNNs can further improve parameter sharing. These rotationally-equivariant convolutional layers have several advantages over standard convolutional layers, including increased robustness to unseen poses, smaller network size, and improved sample efficiency. Despite this, most segmentation networks used in medical image analysis continue to rely on standard convolutional kernels. In this paper, we present a new family of segmentation networks that use equivariant voxel convolutions based on spherical harmonics. These networks are robust to data poses not seen during training, and do not require rotation-based data augmentation during training. In addition, we demonstrate improved segmentation performance in MRI brain tumor and healthy brain structure segmentation tasks, with enhanced robustness to reduced amounts of training data and improved parameter efficiency. Code to reproduce our results, and to implement the equivariant segmentation networks for other tasks is available at http://github.com/SCAN-NRAD/e3nn_Unet, Comment: Accepted for publication at the Journal of Machine Learning for Biomedical Imaging (MELBA) https://melba-journal.org/2024:010

Solutions of polymer chains are modelled using non-equilibrium Brownian dynamics simulations, with physically associative beads which form reversible crosslinks to establish a system-spanning physical gel network. Rheological properties such as the zero-shear-rate viscosity and relaxation modulus are investigated systematically as functions of polymer concentration and the binding energy between associative sites. It is shown that a system-spanning network can form regardless of binding energy at sufficiently high concentration. However, the contribution to the stress sustained by this physical network can decay faster than other relaxation processes, even single chain relaxations. If the polymer relaxation time scales overlap with short-lived associations, the mechanical response of a gel becomes ``evanescent'', decaying before it can be rheologically observed, even though the network is instantaneously mechanically rigid. In our simulations, the concentration of elastically active chains and the dynamic modulii are computed independently. This makes it possible to combine structural and rheological information to identify the concentration at which the sol-gel transition occurs as a function of binding energy. Further, it is shown that the competition of scales between the sticker dissociation time and the single-polymer relaxation time determines if the gel is in the evanescent regime., Comment: 25 pages, 13 figures, includes supplementary information, to appear in Macromolecules

In Part I of this paper [Haward et al. submitted (2023)], we presented a new three-dimensional microfluidic device (the optimized uniaxial and biaxial extensional rheometer, OUBER) for generating near-homogeneous uniaxial and biaxial elongational flows. In this Part II of the paper, we employ the OUBER device to examine the uniaxial and biaxial extensional rheology of some model dilute polymer solutions. We also compare the results with measurements made under planar extension in the optimized-shape cross-slot extensional rheometer [or OSCER, Haward et al. Phys. Rev. Lett. (2012)]. In each case (uniaxial, planar and biaxial extension), we use micro-particle image velocimetry to measure the extension rate as a function of the imposed flow rate, and we measure the excess pressure drop across each device in order to estimate the tensile stress difference generated in the fluid. We present a new analysis, based on solving the macroscopic power balance for flow through each device, to refine the estimate of the tensile stress difference obtained from the measured pressure drop. Based on this analysis, we find that for our most dilute polymer sample, which is "ultradilute", the extensional viscosity is well described by the finitely extensible non-linear elastic dumbbell model. In this limit, the biaxial extensional viscosity at high Weissenberg numbers (Wi) is half that of the uniaxial and planar extensional viscosities. At higher polymer concentrations, the experimental measurements deviate from the model predictions, which is attributed to the onset of intermolecular interactions as polymers unravel in the extensional flows. Of practical significance (and fundamental interest), elastic instability occurs at a significantly lower Wi in uniaxial extensional flow than in either biaxial or planar extensional flow, limiting the utility of this flow type for extensional viscosity measurement.

Understanding the temporal characteristics of data from low frequency radio telescopes is of importance in devising suitable calibration strategies. Application of time series analysis techniques to data from radio telescopes can reveal a wealth of information that can aid in calibration. In this paper, we investigate singular spectrum analysis (SSA) as an analysis tool for radio data. We show the intimate connection between SSA and Fourier techniques. We develop the relevant mathematics starting with an idealised periodic dataset and proceeding to include various non-ideal behaviours. We propose a novel technique to obtain long-term gain changes in data, leveraging the periodicity arising from sky drift through the antenna beams. We also simulate several plausible scenarios and apply the techniques to a 30-day time series data collected during June 2021 from SITARA - a short-spacing two element interferometer for global 21-cm detection. Applying the techniques to real data, we find that the first reconstructed component - the trend - has a strong anti-correlation with the local temperature suggesting temperature fluctuations as the most likely origin for the observed variations in the data. We also study the limitations of the calibration in the presence of diurnal gain variations and find that such variations are the likely impediment to calibrating SITARA data with SSA., Comment: Accepted for publication in MNRAS

The rod-climbing or Weissenberg effect in which the free surface of a complex fluid climbs a thin rotating rod is a popular and convincing experiment demonstrating the existence of elasticity in polymeric fluids. The interface shape depends on the rotation rate, fluid elasticity, surface tension, and inertia. By solving the equations of motion in the low rotation rate limit for a second-order fluid, a mathematical relationship between the interface deflection and the fluid material functions, specifically the first and second normal stress differences, emerges. This relationship has been used in the past to measure the climbing constant, a combination of the first ($\Psi_{1,0}$) and second ($\Psi_{2,0}$) normal stress difference coefficients from experimental observations of rod-climbing in the low inertia limit. However, a quantitative reconciliation of such observations with the capabilities of modern-day torsional rheometers is lacking. To this end, we combine rod-climbing experiments with both small amplitude oscillatory shear flow measurements and steady shear measurements of the first normal stress difference from commercial rheometers to quantify the values of both normal stress differences for a series of polymer solutions. Furthermore, by retaining the oft-neglected inertial terms, we show that the climbing constant $\hat{\beta}=0.5\Psi_{1,0}+2\Psi_{2,0}$ can be measured even when the fluids, in fact, experience rod descending. A climbing condition derived by considering the competition between elasticity and inertial effects accurately predicts whether a fluid will undergo rod-climbing or rod-descending. The analysis and observations presented in this study establish rotating rod rheometry as a prime candidate for measuring normal stress differences in polymeric fluids at low shear rates that are often below commercial rheometers' sensitivity limits.

SMC X-1 is a high-mass X-ray binary showing superorbital modulation with an unstable period. Previous monitoring shows three excursion events in 1996--1998, 2005--2007, and 2014--2016. The superorbital period drifts from >60 days to <40 days and then evolves back during an excursion. Here we report a new excursion event of SMC X-1 in 2020--2021, indicating that the superorbital modulation has an unpredictable, chaotic nature. We trace the spin-period evolution and find that the spin-up rate accelerated one year before the onset of this new excursion, which suggests a possible inside-out process connecting the spin-up acceleration and the superorbital excursion. This results in a deviation of the spin period residual, similar to the behaviour of the first excursion in 1996--1998. In further analysis of the pulse profile evolution, we find that the pulsed fraction shows a long-term evolution and may be connected to the superorbital excursion. These discoveries deepen the mystery of SMC X-1 because they cannot be solely interpreted by the warped disc model. Upcoming pointed observations and theoretical studies may improve our understanding of the detailed accretion mechanisms taking place., Comment: 7 pages, 3 figures, Accepted for publication in MNRAS

A laser pulse focused near the closed end of a glass capillary partially filled with water creates a vapor bubble and an associated pressure wave. The pressure wave travels through the liquid toward the meniscus where it is reflected, creating a fast, focused microjet. In this study, we selectively coat the hydrophilic glass capillaries with hydrophobic strips along the capillary. The result after filling the capillary is a static meniscus which has a curvature markedly different than an unmodified capillary. This tilting asymmetry in the static meniscus alters the trajectory of the ensuing jets. The hydrophobic strips also influence the advancing contact line and receding contact line as the vapor bubble expands and collapses. We present thirteen different permutations of this system which includes three geometries and four coating schemes. The combination of geometry and coatings influences the jet breakup, the resulting drop size distribution, the trajectory of the jet tip, and the consistency of jet characteristics across trials. The inclusion of hydrophobic strips promotes jetting in line with the channel axis, with the most effective arrangement dependent on channel size.

The number of international benchmarking competitions is steadily increasing in various fields of machine learning (ML) research and practice. So far, however, little is known about the common practice as well as bottlenecks faced by the community in tackling the research questions posed. To shed light on the status quo of algorithm development in the specific field of biomedical imaging analysis, we designed an international survey that was issued to all participants of challenges conducted in conjunction with the IEEE ISBI 2021 and MICCAI 2021 conferences (80 competitions in total). The survey covered participants' expertise and working environments, their chosen strategies, as well as algorithm characteristics. A median of 72% challenge participants took part in the survey. According to our results, knowledge exchange was the primary incentive (70%) for participation, while the reception of prize money played only a minor role (16%). While a median of 80 working hours was spent on method development, a large portion of participants stated that they did not have enough time for method development (32%). 25% perceived the infrastructure to be a bottleneck. Overall, 94% of all solutions were deep learning-based. Of these, 84% were based on standard architectures. 43% of the respondents reported that the data samples (e.g., images) were too large to be processed at once. This was most commonly addressed by patch-based training (69%), downsampling (37%), and solving 3D analysis tasks as a series of 2D tasks. K-fold cross-validation on the training set was performed by only 37% of the participants and only 50% of the participants performed ensembling based on multiple identical models (61%) or heterogeneous models (39%). 48% of the respondents applied postprocessing steps.

Particle filtering methods can be applied to estimation problems in discrete spaces on bounded domains, to sample from and marginalise over unknown hidden states. As in continuous settings, problems such as particle degradation can arise: proposed particles can be incompatible with the data, lying in low probability regions or outside the boundary constraints, and the discrete system could result in all particles having weights of zero. In this paper we introduce the Lifebelt Particle Filter (LBPF), a novel method for robust likelihood estimation in low-valued count problems. The LBPF combines a standard particle filter with one (or more) lifebelt particles which, by construction, lie within the boundaries of the discrete random variables, and therefore are compatible with the data. A mixture of resampled and non-resampled particles allows for the preservation of the lifebelt particle, which, together with the remaining particle swarm, provides samples from the filtering distribution, and can be used to generate unbiased estimates of the likelihood. The main benefit of the LBPF is that only one or few, wisely chosen, particles are sufficient to prevent particle collapse. Differently from other methods, there is no need to increase the number of particles, and therefore the computational effort, in regions of the parameter space that generate less likely hidden states. The LBPF can be used within a pseudo-marginal scheme to draw inferences on static parameters, $ \boldsymbol{\theta} $, governing the system. We address here the estimation of a parameter governing probabilities of deaths and recoveries of hospitalised patients during an epidemic.

Viscoelastic stress relaxation is a basic characteristic of soft matter systems such as colloids, gels, and biological networks. Although the Maxwell model of linear viscoelasticity provides a classical description of stress relaxation, the Maxwell model is often not sufficient for capturing the complex relaxation dynamics of soft matter. In this Tutorial, we introduce and dis-cuss the physics of non-Maxwellian linear stress relaxation as observed in soft materials, the ascribed origins of this effect in different systems, and appropriate models that can be used to capture this relaxation behavior. We provide a basic toolkit that can assist the understanding and modeling of the mechanical relaxation of soft materials for diverse applications.

Soft particulate gels include materials we can eat, squeeze, or 3D print. From foods to bio-inks to cement hydrates, these gels are composed of a small amount of particulate matter (proteins, polymers, colloidal particles, or agglomerates of various origins) embedded in a continuous fluid phase. The solid components assemble to form a porous matrix, providing rigidity and control of the mechanical response, despite being the minority constituent. The rheological response and gel elasticity are direct functions of the particle volume fraction $\phi$: however, the diverse range of different functional dependencies reported experimentally has, to date, challenged efforts to identify general scaling laws. Here we reveal a hidden hierarchical organization of fractal elements that controls the viscoelastic spectrum, and which is associated with the spatial heterogeneity of the solid matrix topology. The fractal elements form the foundations of a viscoelastic master curve, which we construct using large-scale 3D microscopic simulations of model gels, and can be described by a recursive rheological ladder model over a range of particle volume fractions and gelation rates. The hierarchy of the fractal elements provides the missing general framework required to predict the gel elasticity and the viscoelastic response of these ubiquitous complex materials.

We study the locations of complex zeroes of independence polynomials of bounded degree hypergraphs. For graphs, this is a long-studied subject with applications to statistical physics, algorithms, and combinatorics. Results on zero-free regions for bounded-degree graphs include Shearer's result on the optimal zero-free disk, along with several recent results on other zero-free regions. Much less is known for hypergraphs. We make some steps towards an understanding of zero-free regions for bounded-degree hypergaphs by proving that all hypergraphs of maximum degree $\Delta$ have a zero-free disk almost as large as the optimal disk for graphs of maximum degree $\Delta$ established by Shearer (of radius $\sim 1/(e \Delta)$). Up to logarithmic factors in $\Delta$ this is optimal, even for hypergraphs with all edge-sizes strictly greater than $2$. We conjecture that for $k\ge 3$, $k$-uniform linear hypergraphs have a much larger zero-free disk of radius $\Omega(\Delta^{- \frac{1}{k-1}} )$. We establish this in the case of linear hypertrees.

Production garbage collectors make substantial compromises in pursuit of reduced pause times. They require far more CPU cycles and memory than prior simpler collectors. concurrent copying collectors (C4, ZGC, and Shenandoah) suffer from the following design limitations. 1) Concurrent copying. They only reclaim memory by copying, which is inherently expensive with high memory bandwidth demands. Concurrent copying also requires expensive read and write barriers. 2) Scalability. They depend on tracing, which in the limit and in practice does not scale. 3) Immediacy. They do not reclaim older objects promptly, incurring high memory overheads. We present LXR, which takes a very different approach to optimizing responsiveness and throughput by minimizing concurrent collection work and overheads. 1) LXR reclaims most memory without any copying by using the Immix heap structure. It then combats fragmentation with limited judicious stop-the-world copying. 2) LXR uses reference counting to achieve both scalability and immediacy, promptly reclaiming young and old objects. It uses concurrent tracing as needed for identifying cyclic garbage. 3) To minimize pause times while allowing judicious copying of mature objects, LXR introduces remembered sets for reference counting and concurrent decrement processing. 4) LXR introduces a novel low-overhead write barrier that combines coalescing reference counting, concurrent tracing, and remembered set maintenance. The result is a collector with excellent responsiveness and throughput. On the widely-used Lucene search engine with a generously sized heap, LXR has 6x higher throughput while delivering 30x lower 99.9 percentile tail latency than the popular Shenandoah production collector in its default configuration., Comment: 17 pages, 7 Figures. This extends the original publication with an LBO analysis (Section 5.5)

The formulation of rheological constitutive equations -- models that relate internal stresses and deformations in complex fluids -- is a critical step in the engineering of systems involving soft materials. While data-driven models provide accessible alternatives to expensive first-principles models and less accurate empirical models in many engineering disciplines, the development of similar models for complex fluids has lagged. The diversity of techniques for characterizing non-Newtonian fluid dynamics creates a challenge for classical machine learning approaches, which require uniformly structured training data. Consequently, early machine learning constitutive equations have not been portable between different deformation protocols or mechanical observables. Here, we present a data-driven framework that resolves such issues, allowing rheologists to construct learnable models that incorporate essential physical information, while remaining agnostic to details regarding particular experimental protocols or flow kinematics. These scientific machine learning models incorporate a universal approximator within a materially objective tensorial constitutive framework. By construction, these models respect physical constraints, such as frame-invariance and tensor symmetry, required by continuum mechanics. We demonstrate that this framework facilitates the rapid discovery of accurate constitutive equations from limited data, and that the learned models may be used to describe more kinematically complex flows. This inherent flexibility admits the application of these 'digital fluid twins' to a range of material systems and engineering problems. We illustrate this flexibility by deploying a trained model within a multidimensional computational fluid dynamics simulation -- a task that is not achievable using any previously developed data-driven rheological equation of state., Comment: 13 pages, 4 figures

Nanocomposites formed by mixing nanoparticles and polymers offer a limitless creative space for the design of functional advanced materials with a broad range of applications in materials and biological sciences. Here we focus on aqueous dispersions of hydrophobic colloidal soot particles, namely carbon black (CB) dispersed with a sodium salt of carboxymethylcellulose (CMC), a food additive known as cellulose gum that bears hydrophobic groups, which are liable to bind physically to CB particles. Varying the relative content of CB nanoparticles and cellulose gum allows us to explore a rich phase diagram that includes a gel phase. We investigate this hydrogel using rheometry and electrochemical impedance spectroscopy. CB-CMC hydrogels display two radically different types of mechanical behaviors that are separated by a critical CMC-to-CB mass ratio $r_c$. For $rr_c$ CB-CMC gels display a power-law viscoelastic spectrum that depends strongly on the CMC concentration. These relaxation spectra can be rescaled onto a master curve that exhibits a power-law scaling in the high-frequency limit, with an exponent that follows Zimm theory, showing that CMC plays a key role in the gel viscoelastic properties for $r>r_c$. Our results offer a characterization of CB-CMC dispersions that will be useful for designing nanocomposites based on hydrophobic interactions., Comment: 18 pages, 10 figures, and 6 supplemental figures

Modelling complex real-world situations such as infectious diseases, geological phenomena, and biological processes can present a dilemma: the computer model (referred to as a simulator) needs to be complex enough to capture the dynamics of the system, but each increase in complexity increases the evaluation time of such a simulation, making it difficult to obtain an informative description of parameter choices that would be consistent with observed reality. While methods for identifying acceptable matches to real-world observations exist, for example optimisation or Markov chain Monte Carlo methods, they may result in non-robust inferences or may be infeasible for computationally intensive simulators. The techniques of emulation and history matching can make such determinations feasible, efficiently identifying regions of parameter space that produce acceptable matches to data while also providing valuable information about the simulator's structure, but the mathematical considerations required to perform emulation can present a barrier for makers and users of such simulators compared to other methods. The hmer package provides an accessible framework for using history matching and emulation on simulator data, leveraging the computational efficiency of the approach while enabling users to easily match to, visualise, and robustly predict from their complex simulators., Comment: 47 pages, 16 figures; provisionally accepted for publication in Journal of Statistical Software

To the best of our knowledge this paper is the first attempt to introduce and study polynomial interpolation of the polynomial data given on arbitrary varieties. In the first part of the paper we present results on the solvability of such problems. In the second part of the paper we relate the interpolation problem to polynomial solution of some boundary values problems. In particular, we extend a result of W. K. Hayman and Z. G. Shanidze.

The FENE-P (Finitely-Extensible Nonlinear Elastic) dumbbell constitutive equation is widely used in simulations and stability analyses of free and wall-bounded viscoelastic shear flows due to its relative simplicity and accuracy in predicting macroscopic properties of dilute polymer solutions. The model contains three independent material parameters, which expressed in dimensionless form correspond to a Weissenberg number ($\textrm{Wi}$), i.e., the ratio of the dumbbell relaxation time scale to a characteristic flow time scale, a finite extensibility parameter ($L$), corresponding to the ratio of the fully extended dumbbell length to the root mean square end-to-end separation of the polymer chain under equilibrium conditions, and a solvent viscosity ratio, commonly denoted $\beta$. An exact solution for the rheological predictions of the FENE-P model in steady simple shear flow is available [Sureshkumar et al., Phys Fluids (1997)], but the resulting nonlinear and nested set of equations do not readily reveal the key shear-thinning physics that dominates at high $\textrm{Wi}$ as a result of the finite extensibility of the polymer chain. In this note we review a simple way of evaluating the steady material functions characterizing the nonlinear evolution of the polymeric contributions to the shear stress and first normal stress difference as the shear rate increases, provide asymptotic expansions as a function of $\textrm{Wi}$ , and show that it is in fact possible to construct universal master curves for these two material functions as well as the corresponding stress ratio. Steady shear flow experiments on three highly elastic dilute polymer solutions of different finite extensibilities also follow the identified master curves. The governing dimensionless parameter for these master curves is $\textrm{Wi}/L$ and it is only in strong shear flows exceeding $\textrm{Wi}/L \gtrsim 1$ that the effects of finite extensibility of the polymer chains dominate the evolution of polymeric stresses in the flow field. We suggest that reporting the magnitude of $\textrm{Wi}/L$ when performing stability analyses or simulating shear-dominated flows with the FENE-P model will help clarify finite extensibility effects.

The interplay between viscoelasticity and inertia in dilute polymer solutions at high deformation rates can result in inertio-elastic instabilities. The nonlinear evolution of these instabilities generates a state of turbulence with significantly different spatio-temporal features compared to Newtonian turbulence, termed elasto-inertial turbulence (EIT). We explore EIT by studying the dynamics of a submerged planar jet of a dilute aqueous polymer solution injected into a quiescent tank of water using a combination of schlieren imaging and laser Doppler velocimetry (LDV). We show how fluid elasticity has a nonmonotonic effect on the jet stability depending on its magnitude, creating two distinct regimes in which elastic effects can either destabilize or stabilize the jet. In agreement with linear stability analyses of viscoelastic jets, an inertio-elastic shear-layer instability emerges near the edge of the jet for small levels of elasticity, independent of bulk undulations in the fluid column. The growth of this disturbance mode destabilizes the flow, resulting in a turbulence transition at lower Reynolds numbers and closer to the nozzle compared to the conditions required for the transition to turbulence in a Newtonian jet. Increasing the fluid elasticity merges the shear-layer instability into a bulk instability of the jet column. In this regime, elastic tensile stresses generated in the shear layer act as an "elastic membrane" that partially stabilizes the flow, retarding the transition to turbulence to higher levels of inertia and greater distances from the nozzle. In the fully turbulent state far from the nozzle, planar viscoelastic jets exhibit unique spatio-temporal features associated with EIT. The time-averaged angle of jet spreading, an Eulerian measure of the degree of entrainment, and the centerline velocity of the jets both evolve self-similarly with distance from the nozzle. The autocovariance of the schlieren images in the fully turbulent region of the jets shows coherent structures that are elongated in the streamwise direction, consistent with the suppression of streamwise vortices by elastic stresses. These coherent structures give a higher spectral energy to small frequency modes in EIT characterized by LDV measurements of the velocity fluctuations at the jet centerline. Finally, our LDV measurements reveal a frequency spectrum characterized by a $-3$ power-law exponent, different from the well-known $-5/3$ power-law exponent characteristic of Newtonian turbulence.

Let $E$ be an elliptic curve defined over $\mathbb{Q}$ and without complex multiplication. For a prime $p$ of good reduction for $E$, we write $\#E_p(\mathbb{F}_p) = p + 1 - a_p(E)$ for the number of $\mathbb{F}_p$-rational points of the reduction $E_p$ of $E$ modulo $p$. Under the Generalized Riemann Hypothesis (GRH), we study the primes $p$ for which the integer $|a_p(E)|$ is a prime. In particular, we prove the following results: (i) the number of primes $p < x$ for which $|a_p(E)|$ is a prime is bounded from above by $C_1(E) \frac{x}{(\log x)^2}$ for some constant $C_1(E)$; (ii) the number of primes $p < x$ for which $|a_p(E)|$ is the product of at most 4 distinct primes, counted without multiplicity, is bounded from below by $C_2(E) \frac{x}{(\log x)^2}$ for some constant $C_2(E)$; (iii) the number of primes $p < x$ for which $|a_p(E)|$ is the product of at most 5 distinct primes, counted with multiplicity, is bounded from below by $C_3(E) \frac{x}{(\log x)^2}$ for some positive constant $C_3(E) > 0$. Under GRH, we also prove the convergence of the sum of the reciprocals of the primes $p$ for which $|a_p(E)|$ is a prime. Furthermore, under GRH, together with Artin's Holomorphy Conjecture and a Pair Correlation Conjecture for Artin L-functions, we prove that the number of primes $p < x$ for which $|a_p(E)|$ is the product of at most 2 distinct primes, counted with multiplicity, is bounded from below by $C_4(E) \frac{x}{(\log x)^2}$ for some constant $C_4(E)$. The constants $C_i(E)$, $1 \leq i \leq 4$, are defined explicitly in terms of $E$ and are factors of another explicit constant $C(E)$ that appears in the conjecture that $\#\{p < x: |a_p(E)| \ \text{is prime}\} \sim C(E) \frac{x}{(\log x)^2}$.

SMC X-1 has exhibited three super-orbital period excursions since the onset of X-ray monitoring beginning with RXTE's launch in 1995. NICER has recently probed a fourth observed excursion beginning in 2021 with our program Monitoring Observations of SMC X-1's Excursions (MOOSE). These sensitive new MOOSE data probe different super-orbital periods and phases within them. Spectral fits to the high-state continuum during April 2021 to January 2022 show that the intrinsic spectral shapes are characterised by a soft (kT~0.19 keV) disc component and a hard (Gamma~0.7) power-law tail. When the 2021-2022 NICER observations, taken during an excursion, are compared to 2016 XMM-Newton observations (outside of an excursion), we find little evidence for intrinsic spectral variability across the high-states, but find evidence for a >3 sigma change in the absorption, although we caution that there may be calibration differences between the two instruments. Thus, over different lengths of super-orbital periods, we see little evidence for intrinsic spectral changes in the high-state. Upcoming studies of the pulse profiles may shed light on the mechanism behind the excursions., Comment: accepted to MNRAS

We analyze the capillarity-driven thinning dynamics of entangled polymer solutions described by the Doi-Edwards-Marrucci-Grizzuti (DEMG) model and the Rolie-Poly (RP) model. Both models capture polymer reptation, finite rates of chain retraction and finite extensibility of single polymer molecules, while differing slightly in their final form regarding to the convective constraint release. We calculate numerically the filament thinning profiles predicted by the two models with realistic entanglement densities, assuming cylindrical filament shapes and no fluid inertia. Both results reveal an early tube-reorientation regime, followed by a brief intermediate elasto-capillary regime, and finally a finite-extensibility regime close to the pinch-off singularity. The results presented in this work reveal two critical features in the transient extensional rheology of entangled polymer solutions that have been reported from previous experimental studies, but are poorly described by the widely-used FENE-P model. First, the relaxation time obtained from capillary breakup extensional rheometry is notably smaller than that from steady-shear rheometry. Their ratio can be expressed as a universal function of the entanglement state and the polymer concentration, which agrees well with the experimental data for a range of entangled polymer solutions. Second, the filament thinning dynamics at sufficiently high polymer concentrations are governed by the tube reorientation at intermediate strain-rates, and the apparent extensional viscosity shows a noticeably rate-thinning response. We finally evaluate the filament thinning dynamics of aqueous polyethylene oxide solutions (1 MDa) over dilute and entangled regimes. As the concentration increases, the profiles deviate from the well-studied exponential-thinning trends beyond the entangled threshold, becoming increasingly power-law in character., Comment: 44 pages, 11 figures, to be published