Related papers: Stability analysis of planetary systems via second…
The backbone of nonequilibrium thermodynamics is the stability structure, where entropy is related to a Lyapunov function of thermodynamic equilibrium. Stability is the background of natural selection: unstable systems are temporary, and…
The full non-linear evolution of the tidal instability is studied numerically in an ellipsoidal fluid domain relevant for planetary cores applications. Our numerical model, based on a finite element method, is first validated by reproducing…
Quantum advantage is widely understood to rely on key quantum resources beyond entanglement, among which nonstabilizerness (quantum ``magic'') plays a central role in enabling universal quantum computation. However, the exact evaluation of…
In this work we try to understand the late time acceleration of the universe by assuming some modification in the geometry of the space and using dynamical system analysis. This technique allows to understand the behavior of the universe…
Euler's three-body problem is the problem of solving for the motion of a particle moving in a Newtonian potential generated by two point sources fixed in space. This system is integrable in the Liouville sense. We consider the Euler problem…
We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…
Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this…
We solve equations, describing in a simplified way the newtonian dynamics of a selfgravitating nonrotating spheroidal body after loss of stability. We find that contraction to a singularity happens only in a pure spherical collapse, and…
This paper is twofold. In the first part, we present a refinement of the R\'enyi Entropy Power Inequality (EPI) recently obtained in \cite{BM16}. The proof largely follows the approach in \cite{DCT91} of employing Young's convolution…
We present a novel quantum Monte Carlo method for evaluating the $\alpha$-stabilizer R\'enyi entropy (SRE) for any integer $\alpha\ge 2$. By interpreting $\alpha$-SRE as partition function ratios, we eliminate the sign problem in the…
We develop a nonequilibrium increment method in quantum Monte Carlo simulations to obtain the R\'enyi entanglement entropy of various quantum many-body systems with high efficiency and precision. To demonstrate its power, we show the…
Numerical continuation techniques are powerful tools that have been extensively used to identify particular solutions of nonlinear dynamical systems and enable trajectory design in chaotic astrodynamics problems such as the Circular…
We study the evolution of a system consisting of two protoplanets still embedded in a protoplanetary disk. Results of two different numerical approaches are presented. In the first kind of model the motion of the disk material is followed…
We present an analytical study of the quantum phase transition between the topologically ordered toric-code-model ground state and the disordered spin-polarized state. The phase transition is induced by applying an external magnetic field,…
We determine the onset point of secular instability for the nonaxisymmetric bar mode in rigidly rotating equilibrium configurations in the Post-Newtonian approximation, in order to apply it to neutron stars. The treatment is based on a…
We compute the low-temperature configurational entropy of a two-dimensional supercooled liquid. Our method, based on a higher-dimensional version of the Grassberger--Procaccia algorithm, can be implemented in a manner that is entirely…
We investigate the motion in space of an infinitesimal particle in the gravitational field generated by three primary bodies positioned at the vertices of a fixed equilateral triangle. We assume that the distances between the primaries are…
Entropy is a fundamental concept in equilibrium statistical mechanics, yet its origin in the non-equilibrium dynamics of isolated quantum systems is not fully understood. A strong consensus is emerging around the idea that the stationary…
Self-consistent N-body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global…
This paper presents a study of the use of numerical simulation and Bayesian optimisation techniques to investigate the dynamics of celestial systems. Initially, the study focuses on Lagrange points in restricted three-body systems where a…