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Simulating Bulk Gap in Chiral Projected Entangled-Pair States
No full textInternational audienceProjected entangled-pair states (PEPS) have proven effective in capturing chiral spin liquid ground states, yet the presence of long-range ``gossamer'' correlation tails raises concerns about their ability to accurately describe bulk gaps. Here, we address this challenge and demonstrate that PEPS can reliably characterize gapped bulk excitations in chiral topological phases. Using a variational principle for excited states within a local mode approximation, we establish that correlation functions decaying faster than are not necessarily related to gapless modes and thus long-range ``gossamer'' correlation tails in chiral PEPS do not contradict the presence of a bulk gap. This framework is validated in the spin- Kitaev model with a chiral term, where PEPS yields excitation gaps that agree well with exact solutions. Extending our approach to the Kitaev model, we present compelling evidence for its chiral ground state and accurately resolve its gapped excitations. These findings thus solidify PEPS as a powerful tool for studying both ground and excited states in chiral topological systems, thereby bridging a key gap in the understanding of their bulk properties
Landscape k-complexity of isotropic centered Gaussian fields
No full textIn large dimension, we study the asymptotic behavior of the mean number of critical points with index k below a level u for an isotropic centered Gaussian random field defined on a family of subsets of depending on d. We prove the existence of three regimes depending on the speed of growth of the volume the parameter set. In the first regime the mean number of critical points decreases exponentially with the dimension. For the second regime, there exists a critical level such that the mean number of critical points with index k below a level u with increases exponentially with the dimension d independently of the index k and decreases exponentially with d when . In the third regime, there exists a layered structure depending on the level u considered and on the index k of the critical points. This behavior is similar to the one encountered on the sphere by Auffinger et al. [5]. In the particular case of the Bargmann-Fock field, only two regimes coexist
Performance Isolation in Multi Tenant Cloud Data Centers
No full textInternational audienceEnsuring network performance isolation in multitenant cloud data centers is critical for maintaining Service Level Agreement (SLA) compliance while supporting diverse and dynamic workloads. Traditional approaches predominantly emphasize flow-level fairness, which, although effective in certain scenarios, often fails to address the broader needs of tenant-based fairness essential for SLA-driven environments. My research introduces a novel framework leveraging control theory and AI-enhanced decision-making to achieve adaptive and intelligent network resource management. By shifting the focus to tenantbased fairness, the proposed solution ensures that resources are allocated equitably among tenants while meeting SLA requirements under fluctuating conditions. Preliminary investigations demonstrate the potential of this approach to enhance reliability, scalability, and efficiency, addressing the limitations of fairnesscentric methods focused solely on flows. This work lays the groundwork for intelligent, automated resource management in cloud data centers, advancing the capabilities of multi-tenant infrastructure to meet future demands
Symmetric SAGE and SONC forms, exactness and quantitative gaps
No full textInternational audienceThe classes of sums of arithmetic-geometric exponentials (SAGE) and of sums of nonnegative circuit polynomials (SONC) provide nonnegativity certificates which are based on the inequality of the arithmetic and geometric means. We study the cones of symmetric SAGE and SONC forms and their relations to the underlying symmetric nonnegative cone. As main results, we provide several symmetric cases where the SAGE or SONC property coincides with nonnegativity and we present quantitative results on the differences in various situations. The results rely on characterizations of the zeroes and the minimizers for symmetric SAGE and SONC forms, which we develop. Finally, we also study symmetric monomial mean inequalities and apply SONC certificates to establish a generalized version of Muirhead's inequality
Afflecto: A Web Server to Generate Conformational Ensembles of Flexible Proteins from Alphafold Models
No full textIntrinsically disordered proteins and regions (IDPs/IDRs) leverage their structural flexibility to fulfill essential cellular functions, with dysfunctions often linked to severe diseases. However, the relationships between their sequences, structural dynamics and functional roles remain poorly understood. Understading these complex relationships is crucial for therapeutic development, highlighting the need for methods that generate ensembles of plausible IDP/IDR conformers. While AlphaFold (AF) excels at modeling structured domains, it fails to accurately represent disordered regions, leaving a significant portion of proteomes inaccurately modeled. We present AFflecto, a user-friendly web server for generating large conformational ensembles of proteins that include both structured domains and IDRs from AF structural models. AFflecto identifies IDRs as tails, linkers or loops by analyzing their structural context. Additionally, it incorporates a method to identify conditionally folded IDRs that AF may incorrectly predict as natively folded elements. The conformational space is globally explored using efficient stochastic sampling algorithms. AFflecto's web interface allows users to customize the modeling, by modifying boundaries between ordered and disordered regions, and selecting among several sampling strategies. The web server is freely available at https://moma.laas.fr/applications/AFflecto/.</div
Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness
No full textWe characterize the Leray--Hopf solutions of the 2D inhomogeneous Navier--Stokes system that become strong for positive times. This characterization relies on the strong energy inequality and the regularity properties of the pressure. As an application, we establish a weak-strong uniqueness result and provide a unified framework for several recent advances in the field
Connected McMullen-like Julia sets in a Chebyshev-Halley Family
No full textInternational audienceIn this paper we study a one parameter family of rational maps obtained by applying the Chebyshev-Halley root finding algorithms. We show that the dynamics near parameters where the family presents some degeneracy might be understood from the point of view of singular perturbations. More precisely, we relate the dynamics of those maps with the one of the McMullen family , using quasi-conformal surgery
Derivation and numerical resolution of 2D shallow water equations for multi-regime flows of Herschel–Bulkley fluids
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Electrohydrodynamic characteristics of a needle-to-ring positive corona discharges: self-consistent modeling and turbulence effects
No full textInternational audienceAbstract We report on the voltage–current characteristics as well as the voltage–velocity characteristics of a needle-to-ring configuration by self-consistent, 2D-axisymmetric, multi-physics plasma-fluid simulations. Parametric studies are performed to investigate the effects of background ionization level on the plasma electrical characteristics as well as turbulence parameters on the resulting flow. Our results show that the discharge and the flow exhibit an annular structure around the needle (anode) tip, with a maximum positive ion density from 1.5 × 10 18 –2.7 × 10 18 m − 3 and a maximum flow velocity from 10–15 m s − 1 , for overvoltages between 4−12 kV and an anode–cathode distance of 20 mm . Good overall agreement with experimental findings is achieved, noting that background ionization level can be used as a tuning parameter to better match experimentally measured current values even with a simplified plasma-chemistry. A better agreement between simulation and experiments is achieved concerning the voltage–velocity curves. Therefore, the latter are likely to be better indicators for assessing and validating electrohydrodynamic effects of corona actuators through numerical modeling. The flow dynamics indicate that positive-corona-induced ionic winds are most likely laminar to turbulent transitional flows, with a ratio between eddy viscosity and air viscosity varying between 0 − 200
Anomalous propagators and the particle-particle channel: Bethe-Salpeter equation
No full text19 pages, 8 figuresInternational audienceThe Bethe-Salpeter equation has been extensively employed to compute the two-body electron-hole propagator and its poles which correspond to the neutral excitation energies of the system. Through a different time-ordering, the two-body Green's function can also describe the propagation of two electrons or two holes. The corresponding poles are the double ionization potentials and double electron affinities of the system. In this work, a Bethe-Salpeter equation for the two-body particle-particle propagator is derived within the linear-response formalism using a pairing field and anomalous propagators. This framework allows us to compute kernels corresponding to different self-energy approximations (, -matrix, and second-Born) as in the usual electron-hole case. The performance of these various kernels is gauged for singlet and triplet valence double ionization potentials using a set of 23 small molecules. The description of double core hole states is also analyzed