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A REMARK ON SELF-ADJOINT PROBLEMS IN THE OPTIMIZATION OF NON-LINEAR MODELS
No full textInternational audienceThis article considers optimization problems under nonlinear partial differential equation (p.d.e.) constraints. It is assumed that the p.d.e. arises from minimizing a convex energy. We prove that the optimization problem is self-adjoint when the objective function is the dual energy. In other words, the differential of the objective function with respect to the optimization variable does not involve any adjoint state. This result generalizes the well-known fact that the so-called compliance is self-adjoint in the linear case. We also prove that in a large class of objective functions the dual energy is the only one which is self-adjoint
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
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
Bipartite Current Fluctuations in Quantum Wires through Charge Fractionalization
No full textInternational audienceQuantum information measures of many-body systems often imply a measure with multi- or two regions such as bipartite charge fluctuations within the ground state revealing the logarithmic profile of the entanglement entropy in a quantum wire. Here, we introduce a new method from the bipartite current fluctuations and the divergence theorem. They reveal the fractional charges related to ground-state energetics and the proximity to Mott physics in the same ballistic quantum wires. This also encodes the behavior of the electron Green's function in space. With metallic gates on both sides of an interface to implement the protocol introducing the two macroscopic domains, bipartite current fluctuations can reveal an additional localized bound state associated to the topological Jackiw-Rebbi model, coexisting with the fractional charges. Through the Density Matrix Renormalization Group (DMRG) algorithm we introduce a quantum spin chain analogue
On a geometric graph-covering problem related to optimal safety-landing-site location
No full textInternational audienceWe propose integer-programming formulations for an optimal safety-landing site (SLS) location problem that arises in the design of urban air-transportation networks. We first develop a set-cover based approach for the case where the candidate location set is finite and composed of points, and we link the problems to solvable cases that have been studied. We then use a mixed-integer second-order cone program to model the situation where the locations of SLSs are restricted to convex sets only. Finally, we introduce strong fixing, which we found to be very effective in reducing the size of integer programs.</div
Constraining the nature of the most extreme Galactic particle accelerator. H.E.S.S. observations of the microquasar V4641 Sgr
No full textInternational audienceMicroquasars have emerged as promising candidates to explain the cosmic-ray flux at petaelectronvolt energies. LHAASO observations revealed V4641~Sgr as the most extreme example so far. Using 100~h of H.E.S.S. data, we performed a spectro-morphological study of the gamma-ray emission around V4641~Sgr. We employed HI and dedicated CO observations of the region to infer the target material for cosmic-ray interactions. We detected multi-TeV emission around V4641~Sgr with a high significance. The emission region is elongated. We found a power-law spectrum with an index 1.8, and together with results from other gamma-ray instruments, this reveals a spectral energy distribution that peaks at energies of 100~TeV for the first time. We found indications (3) of a two-component morphology, with indistinguishable spectral properties. The position of V4641~Sgr is inconsistent with the best-fit position of the single-component model and with the dip between the two components. We found no significant evidence of an energy-dependent morphology. No dense gas was found at any distance towards V4641~Sgr. The peak of the SED at 100~TeV identifies V4641~Sgr as a candidate cosmic-ray accelerator beyond the so-called knee. The absence of dense target gas places stringent energetic constraints on hadronic interpretations, however. The H.E.S.S. measurement requires an unusually hard () spectral index for the protons. A leptonic scenario faces fewer obstacles if the particle transport is fast enough to avoid losses and to reproduce the observed energy-independent morphology. The absence of bright \xray emission across the gamma-ray emission region requires a magnetic field strength ~G, however. Our findings favour a leptonic origin of the gamma-ray emission. This conclusion does not exclude hadron acceleration in the V4641~Sgr system
Hubble Constant and Mass Determination of Centaurus A and M83 from TGRB Distances
No full textInternational audienceAn independent determination of the Hubble constant is crucial in light of the persistent tension between early- and late-Universe measurements. In this study, we analyze the dynamics of the Centaurus A (CenA) and M83 galaxies, along with their associated dwarf companions identified via Tip of the Red Giant Branch (TRGB) distance measurements, to constrain both the group mass and the local value of . By examining the motions of these galaxies relative to the system's barycenter, we apply both the minor and major infall models, which provide bounds on the true radial velocity dispersion. Averaging these approaches, we obtain a virial mass estimate of and a Hubble flow-based mass of . Modeling the cold Hubble flow around the group center of mass, we derive a corresponding value of the Hubble constant as . These results offer an independent, dynamically motivated constraint on the local value of , explicitly accounting for the impact of peculiar velocities in the nearby Universe. We also discuss the mild tension between the virial and Hubble flow-based mass estimates, which likely arises from the fact that M83 is close to the velocity surface and breaks the Hubble flow model assumptions. While the Hubble flow fit emphasizes galaxies that follow smooth expansion on the lower branch of the velocity-distance relation, the virial estimate includes the broader spread of bound galaxies near the group core, which seems to fit better for the CenA/M83 total mass
Distinguishing Majorana bound states from accidental zero-energy modes with a microwave cavity
No full textInternational audienceTransport measurements of hybrid nanowires often rely on the observation of a zero-bias conductance peak as a hallmark of Majorana bound states (MBSs). However, such signatures can also be produced by trivial zero-energy Andreev bound states (ABSs) or by quasi-Majorana bound states (QMBSs), complicating their unambiguous identification. Here we propose microwave absorption visibility, extracted from parity-dependent cavity-nanowire susceptibility measurements, as a complementary probe of MBSs nonlocality. We study a Rashba spin-orbit nanowire consisting of a proximitized superconducting segment and an uncovered quantum-dot region, capacitively coupled to a single-mode microwave cavity. We show that true MBSs yield finite visibility only when both MBSs are simultaneously coupled to the cavity, reflecting their intrinsic nonlocality. In contrast, ABSs and QMBSs exhibit visibility extrema even when the cavity couples only locally to part of the nanowire. We further demonstrate that this distinction persists in the presence of Gaussian disorder, which may otherwise generate trivial subgap states. Motivated by recent experiments, we also analyze ``poor man's" Majoranas in double-quantum-dot setups, where analytical results confirm the same nonlocal visibility criterion. Finally, we discuss a cavity-driven scheme for initializing the electronic system in a given parity state. Our results establish cavity-based visibility as a robust and versatile probe of MBSs, providing a clear route to distinguish them from trivial zero-energy states in hybrid superconducting platforms
Analysis of ATLAS pp elastic measurements at =13 TeV and comparison with TOTEM measurements
No full textInternational audienceA comparative description is made of the measurements at LHC of pp elastic scattering at 13 TeV by the ATLAS and TOTEM Collaborations. In the total and differential cross sections we show that the differences are justified through single numerical factor. It seems that there is no fundamental physical difference, but only a difference of normalization between the two experiments. We study the real and imaginary amplitudes disentangled with the KFK (Kohara-Ferreira-Kodama) model and show that the properties are similar in qualitative aspects for both experiments. The real and imaginary parts have different slopes at the origin and present zeros, with distributions that are common to several models, with three zeros in the real part and one zero in the imaginary amplitude. A zero in the real part, known as Martin's zero, influences the determination of the parameter