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Uncovering thermodynamic origin of counterflow and coflow instabilities in miscible binary superfluids
No full textInternational audienceIn this paper, we explore instabilities in binary superfluids with a nonvanishing relative superflow, particularly focusing on counterflow and coflow instabilities. We extend recent results on the thermodynamic origin of finite superflow instabilities in single-component superfluids to binary systems and derive a criterion for the onset of instability through a hydrodynamic analysis. To verify this result, we utilize both the Gross-Pitaevskii equation (GPE) for weakly interacting Bose-Einstein condensates (BEC) and a holographic binary superfluid model, which naturally incorporates strong coupling, finite temperature, and dissipation. We find that the counterflow and coflow instabilities in binary superfluids are all essentially thermodynamic. Except the one due to order competing via global thermodynamic instability, the others are caused by an eigenvalue of the free energy Hessian diverging and changing sign. We also observe that the critical velocities of these instabilities follow a general scaling law related to the interaction strength between superfluid components. The nonlinear stages of the instabilities are also studied by full time evolution, where vortex dynamics is found to play a significant role, resulting in the reduction of superfluid velocity back to a stable phase
RNA Triplet Repeats: Improved Algorithms for Structure Prediction and Interactions
No full textExtended version of WABI 2024, under review at Algorithms for Molecular BiologyInternational audienceRNAs composed of Triplet Repeats (TR) have recently attracted much attention in the field of synthetic biology. We study the mimimum free energy (MFE) secondary structures of such RNAs and give improved algorithms to compute the MFE and the partition function. Furthermore, we study the interaction of multiple RNAs and design a new algorithm for computing MFE and partition function for RNA-RNA interactions, improving the previously known factorial running time to exponential. In the case of TR, we show computational hardness but still obtain a parameterized algorithm. Finally, we propose a polynomial-time algorithm for computing interactions from a base set of RNA strands and conduct experiments on the interaction of TR based on this algorithm. For instance, we study the probability that a base pair is formed between two strands with the same triplet pattern, allowing an assessment of a notion of orthogonality between TR
Numerical approximation of ergodic BSDEs using non linear Feynman-Kac formulas
No full textInternational audienceIn this work we study the numerical approximation of a class of ergodic Backward Stochastic Differential Equations. These equations are formulated in an infinite horizon framework and provide a probabilistic representation for elliptic Partial Differential Equations of ergodic type. In order to build our numerical scheme, we put forward a new representation of the PDE solution by using a classical probabilistic representation of the gradient. Then, based on this representation, we propose a fully implementable numerical scheme using a Picard iteration procedure, a grid space discretization and a Monte-Carlo approximation. Up to a limiting technical condition that guarantees the contraction of the Picard procedure, we obtain an upper bound for the numerical error. We also provide some numerical experiments that show the efficiency of this approach for small dimensions
Mega-Hertz Gravitational Waves from Neutron Star Mergers
No full textInternational audienceNeutron star mergers provide a unique laboratory for the study of strong-field gravity coupled to Quantum Chromodynamics in extreme conditions. The frequencies and amplitudes of the resulting gravitational waves encode invaluable information about the merger. Simulations to date have shown that these frequencies lie in the kilo-Hertz range. They have also shown that, if Quantum Chromodynamics possesses a first-order phase transition at high baryon density, then this is likely to be accessed during the merger dynamics. Here we show that this would result in the nucleation of superheated and/or supercompressed bubbles whose subsequent dynamics would produce gravitational waves in the Mega-Hertz range. We estimate the amplitude of this signal and show that it may fall within the expected sensitivity of future superconducting radio-frequency cavity detectors for mergers at distances up to tens of Mega-parsecs
Simple Scaling Laws for Energy Correlators in Nuclear Matter
No full textInternational audienceCollider experiments involving nuclei provide a direct means of studying exotic states of nuclear matter. Recent measurements of energy correlators in both proton-nucleus (p-A) and nucleus-nucleus (A-A) collisions reveal sizable modifications, attributable to nuclear effects, compared to proton-proton (p-p) collisions. Energy correlators, and their associated light-ray operator product expansion (OPE), allow scaling behaviors of the measured spectrum to be directly mapped to properties of the underlying quantum field theory. Here, we demonstrate for the first time how this mapping occurs in nuclear collisions, and highlight how the light-ray OPE characterizes leading nuclear effects. We show that the leading modification to the energy correlator distribution is characterized by an enhancement of the expectation value of twist-4 light-ray operators, resulting in a scaling for the ratio of the two-point correlator in nuclear matter to that in vacuum of up to quantum corrections. We verify that this leading twist-4 correction accurately describes recent A-A and p-A data, and is thus sufficient to capture the scaling behavior within the angular range measured for jet radii used in nuclear experiments. Our light-ray OPE based approach lays the groundwork for a rigorous characterization of nuclear modification to energy correlator observables
On the simulation of extreme events with neural networks
No full textInternational audienceThis article aims at investigating the use of generative methods based on neural networks to simulate extreme events. Although very popular, these methods are mainly invoked in empirical works. Therefore, providing theoretical guidelines for using such models in extreme values context is of primal importance. To this end, we propose an overview of most recent generative methods dedicated to extremes, giving some theoretical and practical tips on their tail behaviour thanks to both extreme-value and copula tools
Asymptotic approaches in inverse problems for depolymerization estimation
No full textInternational audienceDepolymerization reactions constitute frequent experiments, for instance in biochemistry for the study of amyloid fibrils. The quantities experimentally observed are related to the time dynamics of a quantity averaged over all polymer sizes, such as the total polymerised mass or the mean size of particles. The question analysed here is to link this measurement to the initial size distribution. To do so, we first derive, from the initial reaction systemtwo asymptotic models: at first order, a backward transport equation, and at second order, an advection-diffusion/Fokker-Planck equation complemented with a mixed boundary condition at x = 0. We estimate their distance to the original system solution. We then turn to the inverse problem, i.e., how to estimate the initial size distribution from the time measurement of an average quantity, given by a moment of the solution. This question has been already studied for the first order asymptotic model, and we analyse here the second order asymptotic. Thanks to Carleman inequalities and to log-convexity estimates, we prove observability results and error estimates for a Tikhonov regularization.We then develop a Kalman-based observer approach, and implement it on simulated observations. Despite its severely ill-posed character, the secondorder approach appears numerically more accurate than the first-order one.</p
Hydrodynamics in the Carrollian regime
No full textInternational audienceCarroll hydrodynamics arises in the limit of relativistic hydrodynamics. Instances of its relevance include the Bjorken and Gubser flow models of heavy-ion collisions, where the ultrarelativistic nature of the flow makes the physics effectively Carrollian. In this paper, we explore the structure of hydrodynamics in what can be termed as the Carrollian regime, where instead of keeping only the leading terms in the limit of relativistic hydrodynamics, we perform a small- expansion and retain the subleading terms as well. We do so both for perfect fluids as well as viscous fluids incorporating first order derivative corrections. As apposite applications of the formalism, we utilize the subleading terms to compute modifications to the Bjorken and Gubser flow equations which bring in, in particular, dependence on rapidity
Integration of physical bound constraints to alleviate shortcomings of statistical models for extreme temperatures
No full textInternational audienceHeatwaves have devastating impacts on societies and ecosystems. Their frequencies and intensities are increasing globally with anthropogenic climate change. Statistical models using Extreme Value Theory (EVT) have been used for quantifying risks of extreme temperatures but recent very intense events have cast doubt on their ability to represent the tail probabilities of temperatures. Using outputs from a large ensemble of a climate model, we show that physics-based estimates of the upper-bound of temperatures in the mid-latitudes are 3–8°C higher than suggested by EVT-based models. We propose a new method to bridge the gap between the physical and statistical estimates by forcing the EVT-based models to have an upper bound coherent with the bound provided by the instability of the air column. We show that our method reduces the underestimation of tail risks while not deteriorating the performance of the statistical models on the core of the distribution of extreme temperatures
Quantum vorticity: a not so effective field theory
No full textInternational audienceWe provide a comprehensive picture for the formulation of the perfect fluid in the modern effective field theory formalism at both the classical and quantum level. Due to the necessity of decomposing the hydrodynamical variables into other internal degrees of freedom, the procedure is inherently not unique. We discuss and compare the different inequivalent formulations. These theories possess a peculiarity: the presence of an infinite dimensional symmetry implying a vanishing dispersion relation for the transverse modes. This sets the stage for UV-IR mixing in the quantum theory, which we study in the different formulations focussing on the incompressible limit. We observe that the dispersion relation gets modified by quantum effects to become , where the fundamental excitations can be viewed as vortex-anti-vortex pairs. The spectrum exhibits infinitely many types of degenerate quanta. The unusual sensitivity to UV quantum fluctuations renders the implementation of the defining infinite symmetry somewhat subtle. However we present a lattice regularization that preserves a deformed version of such symmetry