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Sidewall effects on the onset of interfacial Holmboe waves in stratified exchange flows at high Schmidt number
Guilherme Siqueira de Aquino, Metten M. de Lange, Adrien Lefauve, Matias Duran-Matute
https://arxiv.org/abs/2607.19565 https://arxiv.org/pdf/2607.19565 https://arxiv.org/html/2607.19565
arXiv:2607.19565v1 Announce Type: new
Abstract: Predicting the onset of interfacial instabilities is central to understanding turbulent mixing in natural and engineered stratified shear flows. Here, we study the onset of travelling Holmboe waves in confined exchange flows along a slope. Earlier stratified inclined duct experiments have mapped this transition, and stability analyses based on measured or prescribed profiles have explained their emergence. However, a predictive criterion linking forcing, geometry, base flow, and wave onset was still lacking. We closed this gap with a long-duct, sharp-interface asymptotic theory for the three-dimensional laminar exchange flow, including the effects of sidewall friction. The resulting analytical solution naturally identifies a confinement-adjusted Froude number, $Fr^*$, which unifies the effects of forcing and confinement into a single measure of the effective laminar exchange flow. Using this solution to parameterise sidewall drag in a practical width-averaged model, we perform linear stability analyses and numerical simulations at high Schmidt number. Together, linear stability analysis, direct numerical simulations, and existing experiments across a range of duct widths show that wave onset is accurately predicted by an approximately constant critical value of $Fr^*$. Deviations arise only in very narrow ducts, where sidewalls influence instability not only by modifying the laminar exchange flow but also by directly damping perturbations and delaying wave onset. These findings provide a predictive criterion for wave onset, reconcile long-standing discrepancies among experimental configurations, and establish lateral confinement as a fundamental control on the transition from laminar exchange to wave-driven mixing in stratified shear flows.
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The Positive Experience Principle: Forecasting Conscious Choices with AI Embeddings
Zheng Su, Mingyan Fang
https://arxiv.org/abs/2607.16659 https://arxiv.org/pdf/2607.16659 https://arxiv.org/html/2607.16659
arXiv:2607.16659v1 Announce Type: new
Abstract: A fundamental challenge in the science of consciousness is the lack of a universal, predictive framework for motivated behavior. While existing theories excel at describing specific mechanisms, from neural pathways to computational models, they do not provide a foundational principle that explains the consistent direction of conscious systems toward certain states and away from others. To address this gap, we propose the Positive Experience Principle (PEP), a unifying principle stating that conscious systems have an inherent tendency to move toward states of higher positive subjective experience. This tendency is quantified by a Positive Experience Value (PEV), a scalar metric derived from the physical configurations defined by our earlier Universal Consciousness Code (UCC) theory. The PEP bridges physics, neuroscience, and psychology by positing that diverse behaviors are manifestations of a single, fundamental drive to optimize PEV. The PEP generates testable predictions for the dynamics of conscious systems, offering a path toward a unified science of behavior.
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Uniform-Loss Automated Market Making for Prediction Markets
Ciamac C. Moallemi, Dan Robinson, Brian Zhu
https://arxiv.org/abs/2607.17428 https://arxiv.org/pdf/2607.17428 https://arxiv.org/html/2607.17428
arXiv:2607.17428v1 Announce Type: new
Abstract: Automated market makers (AMMs) for prediction markets descend from market scoring rules, where a mechanism operator subsidizes a market to aggregate beliefs about uncertain events. The existing literature has focused on bounding the total worst-case loss to the subsidizer, but has not addressed how that loss is distributed across price states or over time. We use the framework of loss-versus-rebalancing (LVR) to study this distribution and introduce \textit{uniform AMMs}, defined by the property that instantaneous LVR is proportional to pool value and independent of the current token price. In a static setting, we show that for a broad class of \textit{win-martingales} -- processes that converge to 0 or 1 at a fixed resolution time -- there exists a pricing function that achieves uniform LVR under that process, and conversely, that any sufficiently regular pricing function induces a win-martingale under which it is uniform. We then extend the framework to dynamic liquidity management, showing that liquidity levels can be adjusted over time to implement a prescribed target expected cumulative loss schedule. This theory is illustrated with canonical examples of win-martingales and pricing functions. Our results can inform AMM designers and liquidity providers on how the inevitable cost of subsidizing price discovery can be shaped and controlled across both price and time.
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Electrolyte flows under magnetic fields: Manning-like counterion condensation in one dimension
Yoav Tsori, Hannes Uecker
https://arxiv.org/abs/2605.18076 https://arxiv.org/pdf/2605.18076 https://arxiv.org/html/2605.18076
arXiv:2605.18076v1 Announce Type: new
Abstract: We present a theoretical framework for unidirectional electromagnetohydrodynamic flow of dilute electrolytes under perpendicular magnetic fields. Starting from the Navier--Stokes equation coupled with the Poisson--Nernst--Planck formulation, we show that the problem admits a sequential decoupling: the Stokes equation is solved first to obtain the velocity profile, which defines a hydrodynamic potential entering the Nernst--Planck description of ions. This Lorentz-force-induced potential competes with electrostatic attraction and significantly alters ionic distributions. We analyze this mechanism in two canonical geometries. In planar Couette shear, it produces a Manning--Oosawa-like condensation transition in one dimension, a phenomenon absent in classical electrostatics. We derive an eigenvalue equation predicting a sharp threshold between counterion enrichment and depletion at the charged wall. In cylindrical Taylor--Couette flow, the same effect shifts the classical Manning criterion by a magnetic parameter, enabling tunable control of condensation. These findings extend Manning--Oosawa phenomenology to driven, non-equilibrium systems and provide a basis for magnetic manipulation of screening in electrolytes, with implications for microfluidics, electrochemical systems, and nonlinear boundary-value theory.
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