Atmospheric and Oceanic Physics
Evaluation of medium range machine learning models for sub-seasonal prediction
Catherine de Burgh-Day, Chen Li, Debra Hudson et al. (+4 more)
The performance of two machine learning (ML) atmosphere models - GraphCast and FourCastNetV2 - is evaluated in the context of sub-seasonal prediction, including their ability to represent key
climate drivers of variability, namely the Madden-Julian Oscillation and the Southern Annular Mode. Model skill is assessed over both a 38-year hindcast period and a 2.5-year hindcast period. The longer period overlaps with the training windows of the ML models but provides a larger sample for robust evaluation, while the shorter period is independent of the ML model training period. This dual evaluation illustrates a compromise approach to the problem of insufficient independent data for evaluation of the models for sub-seasonal prediction. The ML models are compared against the Bureau of Meteorology's physics-based seasonal prediction system, ACCESS-S2, for the 38-year period, and a more recent physics-based coupled model for the shorter hindcast period. Across the two evaluation periods, both ML models have surprisingly good skill for sub-seasonal timescales, given they were designed for
forecasting on medium range timescales. In general, the ML models are as skilful as the physical model ensemble mean at shorter lead times and comparable to the physical model ensemble members at longer lead times.
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All authors Catherine de Burgh-Day, Chen Li, Debra Hudson, Li Shi, Harrison Cook, Robin Wedd, Griffith Young
Instrumentation and Detectors
NeuXtalViz: Interactive Three-Dimensional Visualization and Analysis for Single-Crystal Neutron Diffraction
Zachary Morgan, Zhongcan Xiao, Sylwia Pawledzio et al. (+7 more)
NeuXtalViz (
Neutron Single-
Crystal Visualization) is a Python-based software package developed at Oak Ridge National Laboratory to provide interactive three-dimensional visualization and analysis tools for single-
crystal neutron diffraction experiments. Built on the Mantid framework for data reduction, and leveraging PyVista and Matplotlib within a Python Qt environment, NeuXtalViz adopts a model-view-presenter architecture that separates the user interface from the core processing components. The software provides a unified interface for tasks central to single-
crystal diffraction, including UB-
matrix determination, experiment planning, visualization of normalized reciprocal-space volumes, and real-space
crystal-structure calculations. It also integrates with widely used community tools and has been deployed on instrument and analysis servers, where it is now being adopted by instrument teams and users. By
embedding advanced three-dimensional visualization directly into the experimental workflow, NeuXtalViz enhances the planning, execution, and analysis cycle for single-
crystal neutron diffraction experiments, while providing a flexible framework for future development.
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All authors Zachary Morgan, Zhongcan Xiao, Sylwia Pawledzio, Iris Ye, Kathleen Loughlin, Shiyun Jin, Vickie Lynch, Thomas Proffen, Christina Hoffmann, Xiaoping Wang
Fluid Dynamics
Mitigating adjoint chaos in wall turbulence
Qi Wang and Tamer A. Zaki
Estimating past events in wall
turbulence based solely on surface measurements and first principles is an ill-posed problem that is complicated by chaos. The sensitivity of a measurement to the earlier flow state is described by the adjoint Navier-Stokes equations, which are solved in reverse time starting from the measurement kernel at the sensing position and time. The resulting adjoint field is the spatio-temporal domain of dependence (DOD) of the sensor, which is a dual to the concept of the domain of influence (DOI) of an actuator in the linearized forward equations. In channel
turbulence, the energy of each adjoint realization grows exponentially in backward time according to the Lyapunov exponent, even though the energy of the ensemble average should decay. We introduce a linear eddy-viscosity closure model in the ensemble-averaged adjoint equations, and directly compute the mean DOD and compare our prediction to the ensemble average. Furthermore, we demonstrate that the DOD of a wall-stress measurement and the DOI resulting from a wall-stress perturbation exhibit respective universal behaviors across Reynolds numbers. However, their spatio-temporal structures differ qualitatively, due to the time-asymmetry of the governing equations. The DOD field has a two-part structure: one component is associated with the Orr mechanism, characterized by rapid reorientation under mean shear, and the other is related to self-similar expanding streaky structures. These two components jointly define the sensitivity of the wall-stress measurement to past flow events.
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Optics · Cross-listed from quant-ph
Y. Fang, J. Kuttruff, Z. Zhao et al. (+3 more)
Determining the
quantum state of a given
quantum-mechanical system is a fundamental task in physics.
Quantum-state
tomography has been pivotal for establishing
quantum optics [1-4] and for revealing the properties of bound charges in materials [5-7]. An emerging other object for studying and utilizing
quantum effects are free electrons, elementary particles that are central to high-resolution microscopy [8,9], electron-based
quantum optics [10-17], ul-trafast electron microscopy [18-24] and particle accelerators [25-27]. However, free electrons are intrinsically incoherent, and we lack a broadly applicable method to measure and control their
quantum state beyond special cases with discrete energy sidebands [28,29]. Here, we report a universal approach to measure arbitrary free-electron
quantum states in continuous variables. Two monochromatic but spectrally shifted
laser waves produce interfering quan-tum paths that directly reveal the density
matrix and thus all essential properties of the pure wavepackets, the ensemble, and their interlinks. As a first application, we show how the
quantum state of a single electron is modified by many-body Coulomb interactions of a sur-rounding electron gas. The reported concepts and results provide insight into otherwise hid-den correlations in electron beams and enable the controlled optimization of exceptional
quantum states for free-electron
quantum optics or
quantum electron microscopy.
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All authors Y. Fang, J. Kuttruff, Z. Zhao, L. Moehrle, P. Hommelhoff, P. Baum
Applied Physics
Direct stress imaging from shear wave propagation
Yiwei Duan, Michel Destrade, Wenchang Tan et al. (+1 more)
Quantitative imaging of stress fields in heterogeneous solids remains challenging because stress is not directly measurable and is typically inferred from deformation using constitutive models. Here we present Acoustoelastic Imaging (AEI), a non-destructive framework for reconstructing stress fields from shear wave propagation. AEI exploits the acoustoelastic effect, whereby pre-existing stress modifies local wave dynamics, and formulates stress recovery as an inverse problem of the governing wave equations. Using full shear waveform inversion with physics-informed learning, AEI reconstructs wave-equation coefficients from full-field wave measurements, enabling estimation of stress magnitude and principal directions without explicit constitutive model specification or material-parameter calibration. We demonstrate sub-wavelength spatial resolution (< 0.28 {\lambda}) and accurate reconstruction of nonuniform stress fields in heterogeneous materials through numerical simulations and ultrasound shear wave elastography experiments. These results establish a general framework for high-resolution stress imaging and provide a route toward non-invasive mapping of internal mechanical states in complex materials and biological tissues.
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All authors Yiwei Duan, Michel Destrade, Wenchang Tan, Guo-Yang Li
Applied Physics
Wide-field NV magnetometry under simultaneous high-pressure and high-temperature conditions
Masahiro Ohkuma, Eikichi Kimura, Shumpei Ohyama et al. (+7 more)
We demonstrate wide-field optically detected
magnetic resonance (ODMR) under simultaneous high-pressure and high-temperature conditions using nitrogen-vacancy (NV) centers. Although NV-center magnetometry has been widely used for spatially resolved
magnetic-field imaging, its application to extreme environments combining pressure and temperature remains challenging. In this work, we show that ODMR can be observed at 5 GPa and 500 K, demonstrating the feasibility of NV
spin readout under such combined extreme conditions. We further perform wide-field ODMR of iron at 7 GPa and 500 K, where the stray
magnetic field from the sample is spatially visualized through the pressure
cell. These results establish NV-center magnetometry as a promising platform for imaging
magnetic phenomena in materials under high-pressure and high-temperature environments.
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All authors Masahiro Ohkuma, Eikichi Kimura, Shumpei Ohyama, Miu Tezuka, Ryo Matsumoto, Shinobu Onoda, Yoshihiko Takano, Shintaro Azuma, Kenji Ohta, Keigo Arai
Fluid Dynamics
A Free Sphere Reverses the Rebound Direction of a Near-Wall Cavitation Bubble
Chun-Zhu Ren, Jun Wen, Hai-Bao Hu et al. (+2 more)
A near-wall cavitation bubble is generally expected to acquire a wallward Kelvin-impulse bias and to rebound or jet toward the wall. Here we show that this canonical direction can be reversed by a wall-supported free sphere. High-speed imaging reveals a transition from away-from-wall to wallward rebound as the initial bubble–sphere separation is increased. By reconstructing the Kelvin impulse on a closed bubble boundary that includes both the visible free interface and the bubble-side contact closure, we find that the reversal is not governed primarily by the instantaneous velocity of the sphere. Instead, sphere displacement creates a contact closure on which the bubble-source contribution supplies an away-from-wall impulse. This contact-source impulse competes with a wallward background formed by the wall-image source and the quadrupolar component of the sphere-induced field. The resulting balance yields a calibrated
geometric criterion, $\mathcal{M}_K$, and, in the comparable-size bubble–sphere regime, reduces to a contact number $a_z z_b/R_K^2$. These results identify a contact-
geometric mechanism by which a movable particle can redirect the first-cycle jet and rebound bias of a near-wall cavitation bubble.
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All authors Chun-Zhu Ren, Jun Wen, Hai-Bao Hu, A-Man Zhang, Xiao Huang
Plasma Physics
Nanosecond-resolved 266 nm Mach-Zehnder interferometry for electron-density measurements of dense plasmas generated in supercritical fluids
Kyusang Cho, Juho Lee and Gunsu Yun
We developed a nanosecond-resolved 266 nm Mach-Zehnder interferometer for electron-density measurements of dense
laser-produced
plasmas generated in 100-bar supercritical-fluid (SCF) helium. A 1064 nm pump pulse was focused into the SCF helium medium, and the
plasma-induced phase shift of a 266 nm UV probe beam was recorded using an ICCD-based interferometric imaging system.
Plasma-arm-only and reference-arm-only images were used to normalize raw interferograms and improve the effective fringe visibility. The corrected interferograms were analyzed using a two-dimensional
Fourier-transform method to reconstruct phase-shift maps, which were converted into line-integrated electron-density distributions through the
plasma dispersion relation. Assuming cylindrical
symmetry, Abel inversion was applied to the
plasma with the largest line-integrated electron density, yielding a maximum local electron density of approximately \(2.5\times10^{18}~\mathrm{cm^{-3}}\). The measurement fidelity was evaluated by considering free-free absorption of the probe beam, probe-beam refraction by
plasma electron density gradients, and effect of finite-collision-frequency effects on the
plasma dielectric response. These estimates indicate that the inferred electron density is not altered by more than an order of magnitude under the present experimental conditions. The present system demonstrates the applicability of 266 nm UV interferometry to nanosecond-resolved density diagnostics of dense
plasmas in high-pressure supercritical fluids.
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Computational Physics · Cross-listed from math-ph
Physics-Informed Neural Networks for the Time-Domain Maxwell Equations with Split-Field Perfectly Matched Layers
Xiaodong Liu, Lingquan Li, Gregory Moss et al. (+1 more)
Physics informed neural networks (PINNs) incorporate Maxwell's equations, initial conditions, boundary conditions, and measurement data directly into the learning process, transforming the solution of partial differential equations into a constrained optimization problem. As such, PINNs are attracting increased
attention in computational electromagnetics as an alternative to traditional time-domain solvers. This paper presents a PINN formulation for the time-domain Maxwell's equations incorporating split-field perfectly matched layers (PMLs). A key advantage of the split-field PML formulation is that the same governing equations can be applied in both the physical and PML regions, simplifying the PINN formulation and loss construction. The proposed approach is validated using one-dimensional and two-dimensional Gaussian pulse problems with PML. The PINN solutions show good agreement with analytical and finite-difference time-domain (FDTD) reference solutions, demonstrating the feasibility of combining PINNs with split-field PMLs for open-domain time-domain electromagnetic simulations.
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All authors Xiaodong Liu, Lingquan Li, Gregory Moss, Scott Langdon
Fluid Dynamics · Cross-listed from math.AP
Residual-Work Compatibility Criteria and Defect-Measure Compactness for Positive-Cone Viscoelastic Reynolds States
Sai Peng
We prove a residual-work compatibility theory for positive-cone viscoelastic Reynolds states. In Oldroyd–B, the
entropy cancellation eliminates incompressible transport and upper-convected stretching against polymeric stress work. After quotienting pressure tensors and spatial means, positive pressure-free residual work can be paid only by the conformation residual through the
entropy-dual lever (G=I-A^{-1}). This yields the closed residual-work cone (P+(\alpha/2)\int_{\mathbb T^d}G:S,dx\le 0), exact windowed tests, and the least-cost
Hilbert-space repair; constrained closures pay through the projected lever. Strong residual-data limits preserve this cone, while weak–weak limits require the product-defect measure carried by (G:S). The augmented
topology is sharp, as shown by localized residual packets. For FENE-P, the lever (G_b(C)=((b-d)/(b-\operatorname{tr}C))I-C^{-1}) makes the finite-extensibility boundary a genuine residual-work boundary.
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Physics and Society
Zipf's law before the monetary economy and written administration: volume distribution of kofun, ancient Japanese burial mounds
Hayafumi Watanabe
We analyze the volume distribution of kofun, large mounded tombs constructed in the Japanese archipelago mainly from the mid-third through the seventh century CE. We ask whether the distribution of collectively mobilized resources in an ancient society without a monetary economy or written administration could follow Zipf's law, as observed in modern firm sales. Here, Zipf's law refers to a power-law distribution with an exponent close to one. Using a nationwide database, we estimate kofun volumes as a proxy for labor and resources mobilized by the constructing groups, and the volume distributions archipelago-wide and by region, period, and mound type. We find that the volume distribution of keyhole-shaped kofun exhibits a Zipf-like upper tail with a cumulative power-law exponent close to unity, while its central part is close to log-normal—a shape that resembles the distribution of modern firm sales. Moreover, many regional and temporal differences appear primarily as scale differences: after median normalization, most distributions collapse onto a common curve and remain approximately Zipf-like. However, some exceptional groups exist—such as the politically central Kinki region—that show heavier-than-Zipf tails (cumulative exponents below unity), indicating stronger concentration among the largest kofun. To interpret these regularities, we introduce a Kesten-type
stochastic growth model with stopping and reorganization. The model provides a unified account in which the log-normal-like body, Zipf-like tail, and regional/temporal variations arise from a common growth process. Together, these findings raise the possibility that collectively mobilized resources exhibited a Zipf-like structure already in the Kofun period.
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Physics and Society · Cross-listed from econ.GN
Competitive satellite placement and the economic geography of the geostationary orbit
Akhil Rao and Nikodem Szumilo
The geostationary orbit (GEO) carries most of the world's satellite communications revenue. The International Telecommunication Union (ITU) coordinates and records frequency assignments and associated orbital positions through national administrations, without creating a
market price or property title for longitude. We ask how commercial operators locate along GEO within this administrative regime. Using a spatial sorting model, we show that commercial satellites are placed in proportion to the reachable income below a GEO longitude, discounted by viewing angle at a spatial discount rate. We estimate a placement elasticity close to one, so that satellite counts above a longitude rise proportionately with reachable income. Government satellites, by contrast, are placed in proportion to the population a GEO longitude covers. We validate the commercial model by showing that parameters estimated on 2012 placements predict the 2021 distribution well and that the model rejects treating Chinese GDP as fully addressable to the international commercial fleet. Counterfactuals suggest that competition from low-Earth orbit (LEO) systems may tilt GEO usage toward Asia-Pacific, while higher spatial discounting may concentrate it over high-GDP countries.
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Chemical Physics
Sustainable photocatalytic CO2 conversion using microalgae as a carbon-negative scavenger
Ho Truong Nam Hai, Augusto Ducati Luchessi, Makoto Arita et al. (+2 more)
Photocatalytic CO2 conversion driven by
solar energy is a highly promising approach in addressing rising atmospheric CO2 levels; however, its practical application remains limited by low conversion efficiency. In this study, a new strategy to enhance CO2 reduction toward CO and CH4 is proposed through the employment of microalgae as a sacrificial
agent, and the efficiency is compared with conventional CO2 conversion without and with the use of microplastics as sacrificial
agents. To realize this strategy, an AB2O6-type high-
entropy oxide (HEO), (Cs1/7Ba4/7Bi2/7)(Nb1/2Ta1/2)2O6, with bi-polymorphy of layered perovskite and pyrochlore, is rationally designed. The HEO incorporates alkali metal cesium and alkaline earth metal barium to increase surface basicity for CO2 chemisorption, bismuth with its stereochemically active lone pairs for localized polarization and charge separation, and tantalum and niobium to form octahedral crystalline frameworks for charge transport. The utilization of microalgae during photocatalytic reactions leads to a remarkable enhancement in CO2 conversion compared to catalysis with or without using microplastics, with CO and CH4 production increasing by 10- and 4-fold, respectively, compared to the system using only HEO. These findings not only demonstrate a new family of polymorphic AB2-type HEOs for photocatalysis but also show the potential of microalgae as a sustainable sacrificial
agent, offering an environmentally friendly pathway for efficient CO2 capture (through photosynthesis by microalgae) and CO2 conversion (through photocatalysis by HEOs).
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All authors Ho Truong Nam Hai, Augusto Ducati Luchessi, Makoto Arita, Qixin Guo, Kaveh Edalati
Applied Physics
GaN Power Devices and Converter Architectures for AI Data Centers: Efficiency, Reliability, and Deployment Pathways
Donald Intal and Abasifreke Ebong
The growth of artificial-intelligence workloads is increasing the electrical and thermal demands on data-center power-delivery systems, making conversion efficiency, power density, and reliability critical design priorities. This review examines how gallium-nitride (GaN) power devices can be matched to specific stages of the grid-to-load conversion chain, including power-factor correction, isolated DC/DC conversion, 48-V intermediate-bus conversion, and point-of-load regulation. Si, SiC, and GaN are compared using converter-relevant metrics, and lateral, vertical, and specialized GaN architectures are evaluated in terms of voltage scalability, switching behavior, reverse conduction, thermal pathways, gate control, and technology maturity. The analysis shows that GaN provides a stage-dependent rather than universal advantage. Commercial lateral GaN HEMTs are particularly effective in high-frequency, low-to-mid-voltage stages, while specialized and hybrid devices support bidirectional operation, normally-off control, extreme conversion ratios, and integration. Vertical GaN remains an emerging option for higher-voltage and higher-power conversion. A quantitative framework links cascaded converter efficiency to electrical-loss reduction, cooling demand, annual facility energy use, and operational carbon emissions. Broad deployment further requires low-parasitic packaging, disciplined gate-drive and EMI co-design, mission-profile reliability qualification, scalable manufacturing, and supply-chain resilience. GaN is therefore best treated as a stage-specific system lever whose value depends on coordinated device,
topology, package, and thermal co-design.
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Computational Physics
A convolutional neural network surrogate for hierarchical homogenization: fast elastic moduli prediction of digital rocks
Hanfeng Zhai, Rasool Ahmad, Tapan Mukerji et al. (+1 more)
Digital rock physics (DRP) aims to estimate effective rock properties (e.g., elastic
moduli) directly from 3D micro-CT images. However, direct numerical simulations (DNS) on high-resolution large 3D scans are often computationally prohibitive and severely limit the application of DRP. To address this bottleneck, we combine a lightweight 3D convolutional neural network (CNN) with hierarchical homogenization (HHM) and apply it to determine effective elastic
moduli. In this scheme, a large rock image is divided into subcubes. The CNN replaces costly DNS by directly predicting subcube elastic
moduli, while HHM upscales subcube-level predictions to the full rock. Using a shared convolutional backbone, we systematically compare three training targets: (i) full anisotropic $6\times6$ stiffness tensors, (ii) isotropic bulk and shear
moduli $(K, G)$, and (iii) Hashin–Shtrikman (HS)-normalized factors. Across multiple rock types, all three models agree well with DNS results while substantially reducing the computational cost. Moreover, training from scratch on each rock type is fast enough that transfer learning is unnecessary. Across all three targets, the accuracy is comparable. In our comparative study, the HS-normalized factor offers the best overall speed–accuracy trade-off while guaranteeing physical consistency, making it a convenient default. The isotropic $(K, G)$ target is a slightly more accurate alternative.
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All authors Hanfeng Zhai, Rasool Ahmad, Tapan Mukerji, Wei Cai
Atomic Physics · Cross-listed from quant-ph
Rapid and robust laser-frequency auto-locking using Bayesian-optimization and discrete-wavelet-transformation algorithms
Min Jiang, Xiao-Li Chen, Si-Bin Lu et al. (+8 more)
Rapid and robust
laser-frequency auto-locking is essential for the field deployment of
quantum communications,
quantum computing, and precision-measurement technologies; however, achieving this remains a considerable challenge. Here, we propose and demonstrate an auto-locking scheme employing
Bayesian optimization and discrete biorthogonal wavelet transformation. First, the reference is rapidly sought by making intelligent use of historical observations, eliminating the inherent blindness of the traditional parameter-scanning method. Second, the frequency reference is robustly identified by pinpointing transition signals with the discrete biorthogonal wavelet transformation and analyzing their immutable frequency differences and relative magnitudes, which are determined by the inherent atomic structure and remain resistant to environmental disturbances. This proposed approach achieves a fivefold acceleration in reference searching compared to conventional scanning methods in the case where the
laser frequency drifts far away from the reference. Crucially, it achieves an identification accuracy of more than 99.5 %, even under severe 50 %
laser-intensity fluctuations, $9.95^\circ$ photodiode misalignment, and $18^\circ$C Rb
cell temperature elevation. Finally, locking the
laser frequency to the identified reference with a lead zirconate titanate-current double-servo loop narrows the linewidth to 20 kHz. We believe that this rapid, robust, and high-performance auto-locking technique will be pivotal towards the deployment of the next generation of practical
quantum technologies in demanding field environments.
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All authors Min Jiang, Xiao-Li Chen, Si-Bin Lu, Jia-Hao Fu, Zhan-Wei Yao, Shao-Kang Li, Min Ke, San-Ming Song, Run-Bing Li, Jin Wang, Ming-Sheng Zhan
Physics Education
Diversity, Equity and Inclusivity in the Australian and New Zealand Medical Physics Workforce
Emily Simpson-Page, Megan Anderson, Scott B. Crowe et al. (+4 more)
The consideration of diversity, equity and inclusivity (DEI) is an important part of promoting a robust and respectful workforce, and is critical to the continued success of organisations, including healthcare providers, academic institutions and professional societies. Many professional bodies representing medical physicists have made commitments to DEI principles in the form of mission statements, policies, steering groups, frameworks and workforce surveys. In the Australian and New Zealand medical physics community, DEI work has included reflecting on the impact of stereotypes, surveys on workforce experiences, and capturing workforce diversity metrics (including gender, nationality, age and professional background). These projects have been conducted with the support of the Australasian College of Physical Sciences and Engineering in Medicine (ACPSEM) and have contributed to the enhancement of DEI in the ACPSEM workforce. Most of this work has been focused on gender diversity, reflecting increasing involvement in the Australian and New Zealand workforce: women accounted for 41% of medical physics trainees and 32% of registered medical physicists in a 2020 survey. In 2021, the ACPSEM Professional Standards Board (PSB) incepted the creation of a DEI working group. This movement was supported not only by the ACPSEM Board but also the wider medical physics community, both nationally and inter-nationally. The establishment of this group will support best-practice governance, define the diversity metrics most relevant to our profession and use data collected on these metrics to effect positive change within the ACPSEM boards and committees as well as
embedding DEI in policies and procedures for internal and external activities. The DEI working group will enhance the ACPSEM's reputation and ultimately ensure all members feel empowered, respected and represented.
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All authors Emily Simpson-Page, Megan Anderson, Scott B. Crowe, Tanya Kairn, Ian Smith, Christine Thompson, Paul Keall
Computational Physics
A Neural Surrogate Approach for Simulating Natural Convection Problems
Nurshat Menglik, Alex Shao and David Hyde
This paper presents a neural surrogate approach for improving the accuracy of natural convection problems simulated with a Boussinesq flow model (incompressible flow with heat transfer). Our approach, based on
Fourier neural operators, uses training data consisting of matched pairs of simulations run under the computationally cheaper yet less accurate Boussinesq flow model and a more computationally expensive and more accurate compressible flow model. In both cases, we implement our parallelized simulation codes based on an implicit monolithic mixed finite element method (FEM) approach using the open-source FEniCSx framework. Our implementations are validated against a commercial software package, COMSOL, as well as standard test problems from the literature. We include a careful discussion and analysis of data set generation and present learning results in two and three spatial dimensions. Using compressible flow results as high-fidelity reference solutions, our learning approach, with a single model evaluation per simulation, substantially improves the per-channel accuracy of Boussinesq predictions, with structural similarity (SSIM) close to unity across all flow variables and test distributions and corresponding mean-squared error reductions of one to nearly three orders of magnitude. All code and data is released as open-source.
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Fluid Dynamics · Cross-listed from math.AP
Pressure Quotients and Endpoint Velocity-Clock Criteria for Non-Diffusive Viscoelastic Flows
Sai Peng
We prove endpoint continuation criteria for stress-
diffusion-free incompressible viscoelastic flows by working modulo pressure. In two space dimensions, the pressure-free part of any smooth spectral isotropic stress reduces to a single active deviatoric channel (q_1(a,|Y|^2)Y), where (C=aI+Y) and (\operatorname{tr}Y=0). This scalar quotient structure allows a weighted active-deviatoric energy to cancel the top-order coupling between
polymer stretching and the divergence of the active stress. On compact conformation windows the resulting high-order estimate depends only on an endpoint velocity clock and a logarithmic conformation norm. For Oldroyd–B this gives continuation of strong two-dimensional solutions under (\nabla u\in L^1_tB^0_{\infty,1}), while for FENE-P it gives continuation under (\nabla u\in L^2_tB^0_{\infty,1}). In both models the compact conformation window and logarithmic bound are derived from the velocity clock and the model barriers, rather than imposed as independent hypotheses. The criteria are formulated in integer Sobolev strong-solution classes and do not assert Leray-type weak-solution or critical-space local well-posedness results. We also identify a static operator obstruction showing the functional necessity of the logarithmic threshold for the pressure-free stress map. In three dimensions the quotient contains an additional residual channel (q_2(Y^2)^\circ), so the exact scalar closure is intrinsically two-dimensional. On prescribed compact windows this residual can be absorbed by viscosity; for Oldroyd–B and FENE-P it vanishes because (q_2\equiv0).
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