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A mathematical model of the evolution of plane perturbations in the cosmological statistical system of completely degenerated scalar-charged fermions with the Higgs scalar interaction is formulated. A complete closed system of differential…
We construct steady states of the Euler-Poisson system with a barotropic equation of state as minimizers of a suitably defined energy functional. Their minimizing property implies the non-linear stability of such states against general,…
We present a method for the steady state optimization of nonlinear delay differential equations. The method ensures stability and robustness, where a system is called robust if it remains stable despite uncertain parameters. Essentially, we…
The hydrodynamics of stellar collisions and mergers is discussed in the context of blue straggler formation. Emphasis is placed on the very important question of hydrodynamic mixing during the merger process. Recent results of…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
Full self-consistent stationary Vlasov-Maxwell solutions of magnetically confined plasmas are built for systems with cylindrical symmetries. The stationary solutions are thermodynamic equilibrium solutions. These are obtained by computing…
The collinear eZe configuration of helium, with the electrons on opposite sides of the nucleus, is studied in the presence of an external electromagnetic (laser or microwave) field. We show that the classically unstable "asymmetric stretch"…
The paper addresses an existence problem for infinite horizon optimal control when the system under control is exponentially stabilizable or stable. Classes of nonlinear control systems for which infinite horizon optimal controls exist are…
Incremental stability is a property of dynamical systems ensuring the uniform asymptotic stability of each trajectory rather than a fixed equilibrium point or trajectory. Here, we introduce a notion of incremental stability for stochastic…
We introduce a novel set of stability conditions for vacua with broken Lorentz symmetry. The first class of conditions require that the energy be minimized under small geometric deformations, which translates into requiring the positivity…
We address the issue of designing robust stabilization terms for the nonconforming virtual element method. To this end, we transfer the problem of defining the stabilizing bilinear form from the elemental nonconforming virtual element…
We continue the study of the existence and stability of static spherical membrane configurations in curved spacetimes. We first consider higher order membranes described by a Lagrangian which, besides the Dirac term, includes a term…
We report that defocusing cubic media with spatially inhomogeneous nonlinearity, whose strength increases rapidly enough toward the periphery, can support stable bright localized modes. Such nonlinearity landscapes give rise to a variety of…
We study the equivalence of two - order-by-order Einstein's equation and Reduced action - approaches to cosmological perturbation theory at all orders for different models of inflation. We point out a crucial consistency check which we…
The linear gyrokinetic stability properties of magnetically confined electron-positron plasmas are investigated in the parameter regime most likely to be relevant for the first laboratory experiments involving such plasmas, where the…
We propose a method for quantifying charge-driven instabilities in clusters, based on equilibrium simulations under confinement at constant external pressure. This approach makes no assumptions about the mode of decay and allows different…
General-relativistic equilibria of differentially rotating stars are expected in a number of astrophysical scenarios, from core-collapse supernovae to the remnant of binary neutron-star mergers. The latter, in particular, have been the…
The rapid deposition of energy by Edge Localised Modes (ELMs) onto plasma facing components, is a potentially serious issue for large Tokamaks such as ITER and DEMO. The trigger for ELMs is believed to be the ideal Magnetohydrodynamic…
For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the…
The mesoscopic properties of a plasma in a cylindrical magnetic field are investigated from the view point of test-particle dynamics. When the system has enough time and spatial symmetries, a Hamiltonian of a test particle is completely…