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On non-autonomous parabolic equations with measure-valued right hand sides and applications to optimal control
No full textThe main aim of this paper is to develop a theory for non-autonomous parabolic equations with time-dependent measures on the spatial domain appearing as right hand sides. Restricting these measures to ones which have their supports on ‘curves’ or ‘surfaces’ – the latter understood in the sense of geometric measure theory – we succeed in interpreting them as distributional objects from a (negative indexed) Sobolev-Slobodetskii space Ws,2(Ω) with s close to −1. For these indices s a tailor suited parabolic theory is established, based on results of Disser et al. [Ann. Sci. Norm. Super. Pisa, Cl. Sci. 17 (2017) 65-79] and Haller-Dintelmann et al. [Ann. Mat. Pura Appl. 198 (2019) 1227-1241]. The proposed frame work is well-suited for optimal control problems with controls acting on sub-manifolds
Achieving broadband directivity control with dual corona discharge transducers
No full textLoudspeakers inherit their directivity from their geometry and dimensions. Enclosed loudspeakers are omnidirectional in the low frequency range, but their directivity depends on frequency for wavelengths smaller than the radiator size, precluding the directional control over the whole bandwidth. Loudspeakers pairs allow achieving simultaneously monopolar (in-phase) and dipolar (out-of-phase) sources, thus allowing directivity control. However, they are limited by their bulkiness, preventing extending controllable directivities over high frequencies. The Corona Discharge transducer (CDT) concept relies on ionizing an ultra-thin layer of air and oscillating it through an alternating electric field, generating sound without resorting to a mechanical membrane. This transducer combines a monopolar source linked to heat exchanges, and a dipolar linked to electrostatic forces, although these two sources strengths are interconnected, yielding a given unidirectional directivity. In this paper, we propose to leverage the combination of monopole and dipole at the heart of the CDT concept to achieve controllable directivities by stacking two independent CDTs. The very thin dimensions of the CDT allows achieving coincident controllable monopolar and dipolar sound sources making the control of directivity over the whole operating frequency ranges. An analytical model of the dual CDTs concept is first compared to full-wave simulations, and an experimental prototype is finally assessed in anechoic conditions. Our findings open the way to a new range of broadband directionally-controllable transducers that have application to sound generation, active noise reduction, or even non-reciprocal active acoustic metamaterials
A discrete-time Matsumoto–Yor theorem
No full textWe study a random walk on the subgroup of lower triangular matrices of SL2, with i.i.d. increments. We prove that the process of the lower corner of the random walk satisfies a Rogers–Pitman criterion to be a Markov chain if and only if the increments are distributed according to a Generalized Inverse Gaussian (GIG) law on their diagonals. For this, we prove a new characterization of these laws. We prove a discrete-time version of the Dufresne identity. We show how to recover the Matsumoto–Yor theorem by taking the continuous limit of the random walk
Finite element discretization of nonlinear models of ultrasound heating
No full textHeating generated by high-intensity focused ultrasound waves is central to many emerging medical applications, including non-invasive cancer therapy and targeted drug delivery. In this study, we aim to gain a fundamental understanding of numerical simulations in this context by analyzing conforming finite element approximations of the underlying nonlinear models that describe ultrasound- heat interactions. These models are based on a coupling of a nonlinear Westervelt–Kuznetsov acoustic wave equation to the heat equation with a pressure-dependent source term. A particular challenging feature of the system is that the acoustic medium parameters may depend on the temperature. The core of our new arguments in the a priori error analysis lies in devising energy estimates for the coupled semi-discrete system that can accommodate the nonlinearities present in the model. To derive them, we exploit the parabolic nature of the system thanks to the strong damping present in the acoustic component. Theoretically obtained optimal convergence rates in the energy norm are confirmed by the numerical experiments. In addition, we conduct a further numerical study of the problem, where we simulate the propagation of acoustic waves in liver tissue for an initially excited profile and under high-frequency sources
Multiple short-term cycles in
No full textContext. Solar and stellar magnetic activity may have similar properties, which can be used to understand the stellar magnetic evolution.
Aims. This paper examines the multiple short-term cycles in the total irradiance of the Sun and in the light curve of a Kepler star, KIC 6876668.
Methods. We study the light curve variations of KIC 6876668, which exhibits a rotation period of 5−6 d. In order to detect cyclic patterns across rotational and Rieger timescales, we used wavelet and Lomb-Scargle (LS) methodologies.
Results. We found that the light curve of the star exhibits periodicities at ∼47, 59 and 72 d, which are fully consistent with the Rieger period range. Through LS and wavelet analysis, we also found variations in the total irradiance of the Sun as a star in cycle 23 of ∼185, 240, and 380 d. The ratios of stellar and solar cyclic periods over their rotation periods revealed striking similarities of ∼8, ∼10, and 12−15. The observed cycles are interpreted as the spherical harmonics of magnetic Rossby waves in dynamo layers of the star and the Sun. The corresponding magnetic field strengths are estimated as 40 kG and 10 kG in the stellar and solar interiors, respectively. The relationship observed between the Rieger cycle and the rotation period of a young star suggests that the processes in its inner layers driving stellar cycles resemble those found in the Sun.
Conclusions. These results provide an insight into the internal magnetic processes in a Sun-like star, KIC 6876668, where a short cycle and a strong magnetic field indicate stronger activity. Sun-like stars as well as other stars may show similar variations in magnetic activity to the Sun. Therefore, the cycles can be used to extract plasma parameters in their interior. Our analysis shows that the ratio of the rotation angular frequency and the estimated magnetic field strength might stay constant (Ω/B = constant) throughout stellar evolution
The investment and reinsurance game on asset-liability management with common shock dependence under CEV model
No full textThis paper investigates the non-zero-sum stochastic differential game problem of optimal asset-liability management (ALM) between insurers and reinsurers. Combining the investment-reinsurance problem with the ALM, this paper innovatively studies the investment-reinsurance ALM non-zero-sum game within the framework of the constant elasticity of variance (CEV) model under common shock dependence. We allow the insurance companies to purchase proportional reinsurance from reinsurance companies, and both companies can invest in a financial market composed of one risk-free asset and one risk asset whose price process follows the CEV model. By innovatively introducing a class of stochastic liability processes associated with the volatility of risky assets, we obtain the dynamic evolution of net wealth. Using stochastic control theory, we obtain an explicit expression of Nash equilibrium strategy for the problem and a closed-form expression for the corresponding equilibrium value function by maximizing the expected utility from the terminal net wealth. Finally, we illustrate the effect of relevant parameters on the optimal investment-reinsurance strategy by means of numerical examples
Experimental demonstration of optical energy transfer between the 0th and −1st orders diffracted by an all-dielectric resonant waveguide grating
No full textThe energy transfer between the reflected 0th and −1st orders diffracted by a grating in the vicinity of the Littrow angle is experimentally demonstrated for the first time with an all-dielectric resonant waveguide grating under TE polarization. This effect has already been described in a theoretical approach but never proved by measurements. Contrary to classical configuration, the dielectric resonant diffractive structure is probed here from the grating backside to avoid signal disturbance. A transparent layer of very high refractive index (hydrogenated amorphous silicon: a-Si:H) is structured by e-beam lithography and plasma etching to create a resonant grating waveguide on a BK7 substrate. Agreement between modeling and experimental characterizations validates the energy transfer effect, opening the way to all-dielectric sensing devices
Lunar reference systems and their realisations using INPOP ephemerides
No full textContext. The definition of a reference system plays a crucial role in quantifying geodetic effects and in surface body cartography. Today, the development and specification of the lunar reference system is stimulated by future space missions, some of which will be manned, and by the needs of lunar space navigation.
Aims. This paper aims to describe the lunar reference system in use and determine the accuracy of its realisation in space and time. At present, two lunar reference systems are defined: the Principal Axis system (PA system), based on the Moon’s principal axes of inertia, and the Mean Earth/Polar Axis (ME system), defined by the Earth’s mean position on the Moon surface. A first step towards a relativistic definition of the lunar time scale is also introduced in agreement with that proposed by the International Astronomical Union (IAU) and other recent realisations.
Methods. We based the realisation of a PA lunar reference system on the choice of an ephemeris, which relied on the coordinates of the laser retro-reflectors on the Moon surface. We related the ME system and frame to the PA system and frame through a rotation transformation. This study provides a new method to determine the transformation procedure between the two systems, based on a series decomposition of librations and pole motion.
Results. We used the comparisons of the position of the lunar laser retro-reflectors obtained with different ephemerides to estimate the internal and external uncertainties of the different realisations of the PA and ME systems. It also includes comparisons between Euler angles and the propagation of their uncertainties.
Conclusions. This work provides the full expression of the transformation and a new series of libration and polar motion for the lunar motion. We also introduce possible realisations of lunar timescales, applicable depending on their use. The proposed procedure, with opportunities for future improvements, can help set new standards for lunar reference systems and their realisations
Center-to-limb variations of the He I 10 830 Å triplet
No full textWe present high-resolution spectroscopic observations of the quiet-Sun center-to-limb variations (CLV) of the He
New ab initio constrained extended Skyrme equations of state for simulations of neutron stars, supernovae, and binary mergers
No full textContext. Numerical simulations of core-collapse supernovae, mergers of binary neutron stars, and the formation of stellar black holes, using standard Skyrme interactions, have established clear correlations between the evolution of these processes, the characteristics of hot compact objects, as well as neutrino and gravitational wave signals, and the value of effective nucleon mass at the saturation density. However, the density dependence of the effective nucleon mass in these models does not align with the predictions of ab initio models with three-body forces.
Aims. We investigated the thermal response for a set of extended Skyrme interactions that feature widely different density dependencies of the effective mass of nucleons.
Methods. We studied thermal contributions to the energy density and pressure, along with several thermal coefficients, over wide domains of density, temperature, and isospin asymmetry that are relevant for the physics of hot compact objects.
Results. For some of the effective interactions, the thermal pressure is negative at high densities. This results in hot compact stars supporting less mass before collapsing into a black hole compared to their cold counterparts. Moreover, the higher the temperature, the lower the maximum mass that the hot star can support