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We present a study of atmospheric disturbances at Jezero Crater, Mars, using ground-based measurements of surface pressure by the Perseverance rover in combination with orbital images from the Mars Express and Mars Reconnaissance Orbiter missions. The study starts at Ls $\sim$ 13.3{\deg} in MY36 (March 6th, 2021) and extends up to Ls $\sim$ 30.3{\deg} in MY37 (February 28th, 2023). We focus on the characterization of the major atmospheric phenomena at synoptic and planetary-scales. These are the thermal tides (measured up to the sixth component), long-period pressure oscillations (periods > 1 sol), the Aphelion Cloud Belt, and the occasional development of regional dust storms over Jezero. We present the seasonal evolution of the amplitudes and phases of the thermal tides and their relation with the atmospheric dust content (optical depth). Three regional dust storms and one polar storm extending over Jezero produced an increase in the diurnal and semidiurnal amplitudes but resulted in inverse responses in their phases. We show that the primary regular wave activity is due to baroclinic disturbances with periods of 2-4 sols and amplitudes $\sim$ 1-15 Pa increasing with dust content, in good agreement with theoretical predictions by model calculations. The spacecraft images show a number of arc-shaped, spiral and irregular cyclonic vortices, traced by dust and clouds at the edge of the North Polar Cap, that could be behind some of the pressure oscillations measured at Jezero.

The pressure sensors on Mars rover Perseverance measure the pressure field in the Jezero crater on regular hourly basis starting in sol 15 after landing. The present study extends up to sol 460 encompassing the range of solar longitudes from Ls 13{\deg} - 241{\deg} (Martian Year (MY) 36). The data show the changing daily pressure cycle, the sol-to-sol seasonal evolution of the mean pressure field driven by the CO2 sublimation and deposition cycle at the poles, the characterization of up to six components of the atmospheric tides and their relationship to dust content in the atmosphere. They also show the presence of wave disturbances with periods 2-5 sols, exploring their baroclinic nature, short period oscillations (mainly at night-time) in the range 8-24 minutes that we interpret as internal gravity waves, transient pressure drops with duration 1-150 s produced by vortices, and rapid turbulent fluctuations. We also analyze the effects on pressure measurements produced by a regional dust storm over Jezero at Ls 155{\deg}.

In this study, the classical two-dimensional potential $V_N=\frac{1}{2}\,m\,\omega^2\,r^2 + \frac{1}{N}\,r^N\,\sin(N\,\theta)$, $N \in {\mathbb Z}^+$, is considered. At $N=1,2$, the system is superintegrable and integrable, respectively, whereas for $N>2$ it exhibits a richer chaotic dynamics. For instance, at $N=3$ it coincides with the H\'enon-Heiles system. The periodic, quasi-periodic and chaotic motions are systematically characterized employing time series, Poincar\'e sections, symmetry lines and the largest Lyapunov exponent as a function of the energy $E$ and the parameter $N$. Concrete results for the lowest cases $N=3,4$ are presented in complete detail. This model is used as a benchmark system to estimate the accuracy of the Sparse Identification of Nonlinear Dynamical Systems (SINDy) method, a data-driven algorithm which reconstructs the underlying governing dynamical equations. We pay special attention at the transition from regular motion to chaos and how this influences the precision of the algorithm. In particular, it is shown that SINDy is a robust and stable tool possessing the ability to generate non-trivial approximate analytical expressions for periodic trajectories as well.

In this work, we consider the hydrogen atom confined inside a penetrable spherical potential. The confining potential is described by an inverted-Gaussian function of depth $\omega_0$, width $\sigma$ and centered at $r_c$. In particular, this model has been used to study atoms inside a $C_{60}$ fullerene. For the lowest values of angular momentum $l=0,1,2$, the spectra of the system as a function of the parameters ($\omega_0,\sigma,r_c$) is calculated using three distinct numerical methods: (i) Lagrange-mesh method, (ii) fourth order finite differences and (iii) the finite element method. Concrete results with not less than 11 significant figures are displayed. Also, within the Lagrange-mesh approach the corresponding eigenfunctions and the expectation value of $r$ for the first six states of $s, p$ and $d$ symmetries, respectively, are presented. Our accurate energies are taken as initial data to train an artificial neural network as well. It generates an efficient numerical interpolation. The present numerical results improve and extend those reported in the literature.

In the past, laser propagation in a fluid with heat transfer has been modeled using simplistic conduction and convection conditions yielding inaccurate predictions. Here we present a detailed numerical study describing the thermal profile of the fluid and its interaction with the laser. Furthermore, we evaluate the diffraction field in the far field produced by a pump beam impinging in the fluid and the interferometric pattern obtained normal to the propagation direction to test our model. Direct comparison between experimental results and numerical simulation allows for a complete understanding of the energy transfer from the laser to the liquid and the subsequent effect on the laser propagation. Spatial self-phase modulation and propagation control from small-phase diffraction to aberration-controlled diffraction and up to diffraction oscillation are observed and explained with our modeling.

The classical three-body harmonic system in $\mathbb{R}^d$ ($d>1$) with finite rest lengths and zero total angular momentum $L=0$ is considered. This model describes the dynamics of the $L=0$ near-equilibrium configurations of three point masses $(m_1,m_2,m_3)$ with arbitrary pairwise potential $V(r_{ij})$ that solely depends on the relative distances between bodies. It exhibits an interesting mixed regular and chaotic dynamics as a function of the energy and the system parameters. The corresponding harmonic quantum system plays a fundamental role in atomic and molecular physics. In this work we report on a novel electronic experimental realization of the model as a complementary tool to analyze the rich dynamics of the classical system. Our setup allows us to experimentally explore different regions of behavior due to the fact that the system parameters and initial conditions are independently controlled via voltage signals. Chaotic and periodic motions are characterized employing time series, phase planes, and the largest Lyapunov exponents as a function of the energy and system parameters. The results show an excellent qualitative as well as quantitative agreement between theory and experiment., Comment: 7 pages, 6 figures