Hamiltonian formulation of the spin-orbit model with time-varying non-conservative forces

In a realistic scenario, the evolution of the rotational dynamics of a celestial or artificial body is subject to dissipative effects. Time-varying non-conservative forces can be due to, for example, a variation of the moments of inertia or to tidal interactions. In this work, we consider a simplified model describing the rotational dynamics, known as the spin-orbit problem, where we assume that the orbital motion is provided by a fixed Keplerian ellipse. We consider different examples in which a non-conservative force acts on the model and we propose an analytical method, which reduces the system to a Hamiltonian framework. In particular, we compute a time parametrisation in a series form, which allows us to transform the original system into a Hamiltonian one. We also provide applications of our method to study the rotational motion of a body with time-varying moments of inertia, e.g. an artificial satellite with flexible components, as well as subject to a tidal torque depending linearly on the velocity.Comment: Accepted for publication in Communications in Nonlinear Science and Numerical Simulatio

The theory of secondary resonances in the spin-orbit problem

We study the resonant dynamics in a simple one degree of freedom, time dependent Hamiltonian model describing spin-orbit interactions. The equations of motion admit periodic solutions associated with resonant motions, the most important being the synchronous one in which most evolved satellites of the Solar system, including the Moon, are observed. Such primary resonances can be surrounded by a chain of smaller islands which one refers to as secondary resonances. Here, we propose a novel canonical normalization procedure allowing to obtain a higher order normal form, by which we obtain analytical results on the stability of the primary resonances as well as on the bifurcation thresholds of the secondary resonances. The procedure makes use of the expansion in a parameter, called the detuning, measuring the shift from the exact secondary resonance. Also, we implement the so-called `book-keeping' method, i.e., the introduction of a suitable separation of the terms in orders of smallness in the normal form construction, which deals simultaneously with all the small parameters of the problem. Our analytical computation of the bifurcation curves is in excellent agreement with the results obtained by a numerical integration of the equations of motion, thus providing relevant information on the parameter regions where satellites can be found in a stable configuration.Comment: Accepted for publication in MNRA

Accurate modelling of the low-order secondary resonances in the spin-orbit problem

We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous primary resonance in the gravitational spin-orbit problem. To this end we extend the perturbative approach introduced in Gkolias et. al. (2016), based on normal form series computations. This allows to recover analytically all non-trivial features of the phase space topology and bifurcations associated with these resonances. Applications include the characterization of spin states of irregular planetary satellites or double systems of minor bodies with irregular shapes. The key ingredients of our method are: i) the use of a detuning parameter measuring the distance from the exact resonance, and ii) an efficient scheme to `book-keep' the series terms, which allows to simultaneously treat all small parameters entering the problem. Explicit formulas are provided for each secondary resonance, yielding i) the time evolution of the spin state, ii) the form of phase portraits, iii) initial conditions and stability for periodic solutions, and iv) bifurcation diagrams associated with the periodic orbits. We give also error estimates of the method, based on analyzing the asymptotic behavior of the remainder of the normal form series.Comment: Accepted for publication in Communications in Nonlinear Science and Numerical Simulatio

Recovery of lipids from spent coffee grounds for use as a biofuel

Spent coffee grounds (SCG) are the main residues of the coffee industry, and a potentially valuable source of lipids for sustainable biodiesel production. However, feedstock properties, such as the high SCG moisture content and the relatively high free fatty acid (FFA) content of recovered oil, can impact on the efficiency of the extraction and the quality of extracted oil and derived biodiesel, thus reducing the possible environmental benefits of producing biodiesel from this waste stream. Therefore, a better understanding of feedstock properties and processing steps is required to improve the efficiency of SCG valorization as a biodiesel feedstock and contribute to its future industrialization. This work presents experimental studies including feedstock characterization of SCG, laboratory and pilot plant scale solvent extraction experiments and utilization of mechanical pressing for processing of coffee residues. The solvent extraction experiments investigated effects of solvent type, SCG moisture content and particle size, SCG-to-solvent ratio, and the duration, temperature and pressure of the extraction process on oil extraction efficiency and composition. Transesterification was performed with SCG oil containing high FFA content, and the combustion of derived biodiesel was investigated in a compression-ignition engine. Instant SCG were found to possess higher lipid and FFA content than retail SCG. Solvent extraction experiments showed that longer durations, higher temperatures, low moisture presence and mixed size SCG particles generally improved extraction efficiency, while the impact of pressure depended on temperature. A correlation was observed between longer extraction durations and lower FFA content, while extraction temperature and solvent selection affected the oil composition. Pilot plant extraction showed reduced sensitivity to moisture, while mechanical pressing was efficient in removing a fraction of residual moisture. A two-step transesterification process achieved a biodiesel conversion yield of 86.7 % relative to initial oil weight. SCG biodiesel showed similar combustion and emissions characteristics to commercial soybean and rapeseed biodiesel

Chaotic transport of navigation satellites

Navigation satellites are known from numerical studies to reside in a dynamically sensitive environment, which may be of profound importance for their long-term sustainability. We derive the fundamental Hamiltonian of Global Navigation Satellite System dynamics and show analytically that near-circular trajectories lie in the neighborhood of a Normally Hyperbolic Invariant Manifold (NHIM), which is the primary source of hyperbolicity. Quasicircular orbits escape through chaotic transport, regulated by NHIM's stable and unstable manifolds, following a power-law escape time distribution P (t) ∼ t - α, with α ∼ 0.8 - 1.5. Our study is highly relevant for the design of satellite disposal trajectories, using manifold dynamics

Genome-wide Screens Implicate Loss of Cullin Ring Ligase 3 in Persistent Proliferation and Genome Instability in TP53-Deficient Cells

TP53 deficiency is the most common alteration in cancer; however, this alone is typically insufficient to drive tumorigenesis. To identify genes promoting tumorigenesis in combination with TP53 deficiency, we perform genome-wide CRISPR-Cas9 knockout screens coupled with proliferation and transformation assays in isogenic cell lines. Loss of several known tumor suppressors enhances cellular proliferation and transformation. Loss of neddylation pathway genes promotes uncontrolled proliferation exclusively in TP53-deficient cells. Combined loss of CUL3 and TP53 activates an oncogenic transcriptional program governed by the nuclear factor kappa B (NF-kappa B), AP-1, and transforming growth factor beta (TGF-beta) pathways. This program maintains persistent cellular proliferation, induces partial epithelial to mesenchymal transition, and increases DNA damage, genomic instability, and chromosomal rearrangements. Our findings reveal CUL3 loss as a key event stimulating persistent proliferation in TP53-deficient cells. These findings may be clinically relevant, since TP53-CUL3-deficient cells are highly sensitive to ataxia telangiectasia mutated (ATM) inhibition, exposing a vulnerability that could be exploited for cancer treatment