arXiv subjects

Yeva Gevorgyan

Publications and source records attributed to Yeva Gevorgyan.

9 recordsLinked to original sources

arXiv2026

Bregman-projected mirror methods for regularized stationary mean-field games

We develop and analyze a Bregman-projected mirror iteration for low-order regularizations of stationary mean-field game (MFG) systems in their natural Banach space setting. For separable Hamiltonians of the form $H(x,p,m)=H_0(x,p)-g(m)$, with quadratic or super-quadratic Hamiltonian growth and linear or super-linear density couplings, we formulate a low-order $\barγ$-Laplacian regularization of the stationary MFG system as a variational inequality on $L^{\barβ}(\mathbb T^d)\times W^{1,\barγ}(\mathbb T^d)$. To approximate solutions of this regularized variational inequality, we introduce a Bregman geometry matched to the mixed Lebesgue--Sobolev exponents of the problem and analyze a constrained two-step mirror method with frozen operator evaluation. For the exact constrained iteration and each fixed regularization parameter $\epsi>0$, we derive a one-step Bregman inequality and use it to prove that the constrained iteration converges strongly to the unique solution of the regularized variational inequality under natural summability conditions on the step sizes. Numerical experiments on one- and two-dimensional models, validated against exact test solutions, illustrate residual decay under mesh refinement and suggest improved practical performance of the two-step implementation in the tested discretizations.

math.NA↗

arXiv2026

A user-friendly package and workflow for generating effective homogeneous rheologies for the study of the long-term orbital evolution of multilayered planetary bodies

We present a user-friendly, open-source Wolfram Language package that automates the construction of an effective homogeneous generalized Voigt rheology for a spherically symmetric, incompressible layered body with Maxwell solid layers. It provides a practical bridge between layered interior models and time-domain simulations of tidal evolution. The package combines three components: (i) a forward computation of the degree-2 tidal Love number based on the propagator-matrix formulation for incompressible stratified viscoelastic bodies; (ii) numerical identification of the secular relaxation poles and residues of the layered model; and (iii) inversion of the resulting response into the compliance of an equivalent homogeneous generalized Voigt body. The implementation is based on the equivalence established for multilayer Maxwell bodies and includes an optional dominant-mode selection procedure for obtaining reduced rheological models over a prescribed frequency range. The package returns the parameters of the equivalent homogeneous model, including elastic, gravitational, viscous, and Voigt-element contributions, in a format suitable for downstream numerical applications. As a case study, we apply the package to a five-layer lunar interior model and obtain its equivalent generalized Voigt representation, together with a reduced model that preserves the tidal response over the frequency interval relevant for orbital evolution while using fewer relaxation elements. This package makes the reduction from stratified viscoelastic interiors to effective homogeneous rheologies reproducible and accessible. It allows physical tidal dissipation models to be used in long-term orbital and spin-evolution studies without having to repeatedly solve the full layered boundary-value problem.

astro-ph.EP↗

arXiv2026

Synchronisation of a tidal binary by inward orbital migration. The case of Pluto and Charon

It is usually taken for granted that mutual synchronisation of a tidal two-body system is attained through tidal recession, assuming the reduced Hill sphere is not reached. However, synchronisation can be achieved also via tidal approach, provided the Roche limit is not crossed. For each of the two scenarios, we derive the condition under which the evolving synchronicity radius catches up with the tidally evolving orbit. We consider the two scenarios for the Pluto-Charon system and examine the impact-origin hypothesis of Charon's formation against capture. Based on geophysical evidence, we propose that capture appears more likely. Motivated by this conclusion, we investigate the capture scenario, wherein the orbital evolution of Charon starts at a larger distance than present and undergoes tidal descent, both analytically and numerically. We also consider the possibility that Pluto's initial prograde spin underwent a reversal by a tidally approaching retrograde Charon. Depending on the initial conditions, we observe temporary locking of Charon into higher spin-orbit resonances (3:2 to 7:2) during the first 0.5 Myr of the system's evolution. Owing to a greater initial separation between the partners, the power dissipated in each of them turns out to be much lower than in the case of tidal recession of bodies of the same internal structure. The greater initial separation also results in lower tidal stress, which may explain the absence of tidally generated fracture patterns.

astro-ph.EP↗

arXiv2025

A Simplified Model for the Forced Libration of Icy Moons with Subsurface Oceans: Application to Enceladus and Mimas

We investigate a simple two-layered viscoelastic rheological model capable of replicating the forced librations of an icy moon with a subsurface ocean. We show that the model, composed only of a prestressed icy crust lying over an effective fluid core (a fixed mantle cavity), can effectively describe the librational behavior of icy moons, thus holding the potential to predict the presence of a subsurface ocean through the analysis of longitudinal librations. The proposed model is applied to the longitudinal librations of Enceladus and Mimas, two small icy moons of Saturn for which relevant data is available from the Cassini mission.

astro-ph.EP↗

arXiv2023

Equivalence between simple multilayered and homogeneous laboratory-based rheological models in planetary science

The goal of this work is to investigate under which circumstances the tidal response of a stratified body can be approximated by that of a homogeneous body. We show that any multilayered planet model can be approximated by a homogeneous body, with the same dissipation of tidal energy as a function of the excitation frequency, as long as the rheology of the homogeneous model is sufficiently complex. Moreover we provide two straightforward methods for finding the parameters of the homogeneous rheology that would exhibit the same tidal response as the layered body. These results highlight the fact that the two models cannot be distinguished from each other only by the measurement of the second degree tidal Love number and quality factor, and that we do not need the complexity of the multilayer planet model in order to estimate its tidal dissipation. The methodology promises a great simplification of the treatment of multilayered bodies in numerical simulations because the treatment of a homogeneous body -- even with a complex rheological model -- can be computationally better handled than that of a multilayered planet.

astro-ph.EP↗

arXiv2022

Librations of a body composed of a deformable mantle and a fluid core

We present fully three-dimensional equations to describe the rotations of a body made of a deformable mantle and a fluid core. The model in its essence is similar to that used by INPOP (Integration Planétaire de l'Observatoire de Paris), e.g. Viswanathan et al. (2019), and by JPL (Jet Propulsion Laboratory), e.g. Folkner et al. (2014), to represent the Moon. The intended advantages of our model are: straightforward use of any linear-viscoelastic model for the rheology of the mantle; easy numerical implementation in time-domain (no time lags are necessary); all parameters, including those related to the "permanent deformation", have a physical interpretation. The paper also contains: 1) A physical model to explain the usual lack of hydrostaticity of the mantle (permanent deformation). 2) Formulas for free librations of bodies in and out-of spin-orbit resonance that are valid for any linear viscoelastic rheology of the mantle. 3) Formulas for the offset between the mantle and the idealized rigid-body motion (Peale's Cassini states). 4) Applications to the librations of Moon, Earth, and Mercury that are used for model validation.

astro-ph.EP↗

arXiv2021

Homogeneous model for the TRAPPIST-1e planet with an icy layer

In this work we investigate whether a multilayered planet can be approximated as a homogeneous planet, and in particular how well the dissipation rate of a multilayered planet can be reproduced with a homogeneous rheology. We study the case of a stratified body with an icy crust that, according to recent studies, displays a double peak feature in the tidal response that cannot be reproduced with a homogeneous planet with an Andrade rheology. We revisit the problem with a slightly more complex rheology for the homogeneous body, the Sundberg-Cooper rheology, which naturally has a double peak feature, and apply the model to the TRAPPIST-1e planet. Our results compare very well with the results obtained when employing a multilayered model, showing that it is possible to approximate the behavior of a multilayer icy planet with a homogeneous planet using the Sundberg-Cooper rheology. This highlights the fact that we do not need the complexity of the multilayer planet model in order to estimate the tidal dissipation of an icy planet.

astro-ph.EP↗

arXiv2019

Andrade rheology in time-domain. Application to Enceladus' dissipation of energy due to forced libration

The main purpose of this work is to present a time-domain implementation of the Andrade rheology, instead of the traditional expansion in terms of a Fourier series of the tidal potential. This approach can be used in any fully three dimensional numerical simulation of the dynamics of a system of many deformable bodies. In particular, it allows large eccentricities, large mutual inclinations, and it is not limited to quasi-periodic perturbations. It can take into account an extended class of perturbations, such as chaotic motions, transient events, and resonant librations. The results are presented by means of a concrete application: the analysis of the libration of Enceladus. This is done by means of both analytic formulas in the frequency domain and direct numerical simulations. We do not a priori assume that Enceladus has a triaxial shape, the eventual triaxiality is a consequence of the satellite motion and its rheology. As a result we obtain an analytic formula for the amplitude of libration that incorporates a new correction due to the rheology. Our results provide an estimation of the amplitude of libration of the core of Enceladus as 0.6% of that of the shell. They also reproduce the observed 10 GW of tidal heat generated by Enceladus with a value of $0.17\times 10^{14}$Pa$\cdot$s for the global effective viscosity under both Maxwell and Andrade rheology.

astro-ph.EP↗

arXiv2017

Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete logisticlike growth with and without weak Allee effects

We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with nonoverlapping generations. Beginning with a general six-parameter model, we find constraints on the transition probabilities of the PCA that guarantee that the ensuing approximations make sense in terms of population dynamics and classify the valid combinations thereof. Several possible models display a negative cubic term that can be interpreted as a weak Allee factor. We also investigate the conditions under which a one-parameter PCA derived from the more general six-parameter model can generate valid population growth dynamics. Numerical simulations illustrate the behavior of some of the PCA found.

cond-mat.stat-mech↗