Boundedness of solutions of linear differential systems with periodic coefficients

Archive for Rational Mechanics and Analysis -     

Long-term evolution of mid-altitude quasi-satellite orbits

Quasi-satellite orbits are of great interest for the exploration of planetary moons because of their dynamical features and close proximity with respect to the surface of scientifically relevant objects like Phobos and Deimos. This paper explores the equations of the elliptical Hill problem, offering a new analytical insight into the long-term evolution of mid-altitude quasi-satellite orbits. Our developments are based on the Yamanaka–Ankersen solution of the Tschauner–Hempel equations and capture the effects of the secondary’s gravity and orbital eccentricity on the shape and orientation of near-equatorial retrograde relative trajectories. The analytical solution of the in-plane and out-of-plane components of the secular motion is achieved by averaging over the relative longitude of a spacecraft as seen from the co-rotating frame of the two primaries. Developments are validated against the numerical integration of quasi-periodic trajectories that densely cover the surface of three-dimensional invariant tori. This analysis confirms the stable nature of quasi-satellite orbits and provides new tools for future spacecraft missions such as the Martian Moons eXploration envisaged by JAXA.

     

Work and Thermal Fluctuations in Crystal Indentation under Deterministic and Stochastic Thermostats: The Role of System–Bath Coupling

The Jarzynski equality (JE) was originally derived under the deterministic Hamiltonian formalism, and later, it was demonstrated that stochastic Langevin dynamics also lead to the JE. However, the JE has been verified mainly in small, low-dimensional systems described by Langevin dynamics. Although the two theoretical derivations apparently lead to the same expression, we illustrate that they describe fundamentally different experimental conditions. While the Hamiltonian framework assumes that the thermal bath producing the initial canonical equilibrium switches off for the duration of the work process, the Langevin bath effectively acts on the system. Moreover, the former considers an environment with which the system may interact, whereas the latter does not. In this study, we investigate the effect of the bath on the measurable quantity of the JE through molecular dynamics simulations of crystal nanoindentation employing deterministic and stochastic thermostats. Our analysis shows that the distributions of the kinetic energy and the mechanical work produced during the indentation processes are affected by the interaction between the system and the thermostat baths. As a result, the type of thermostatting has also a clear effect on the left-hand side of the JE, which enables the estimation of the free-energy difference characterizing the process.     

Proprietà delle funzioni rappresentate mediante serie trigonometriche

Rendiconti del Circolo Matematico di Palermo Series 1 -     

Fluctuation Relations for Dissipative Systems in Constant External Magnetic Field: Theory and Molecular Dynamics Simulations

We illustrate how, contrary to common belief, transient Fluctuation Relations (FRs) for systems in constant external magnetic field hold without the inversion of the field. Building on previous work providing generalized time-reversal symmetries for systems in parallel external magnetic and electric fields, we observe that the standard proof of these important nonequilibrium properties can be fully reinstated in the presence of net dissipation. This generalizes recent results for the FRs in orthogonal fields—an interesting but less commonly investigated geometry—and enables direct comparison with existing literature. We also present for the first time a numerical demonstration of the validity of the transient FRs with nonzero magnetic field via nonequilibrium molecular dynamics simulations of a realistic model of liquid NaCl.     

Sulle trasformazioni continue

Sunto Si dimostra che ogni trasformazione piana, rappresentata da funzioni assolutamente continue secondoTonelli con dervate parziali prime integrabiliL ²→ α con α>0, sono a variazione limitata e assolutamente continue secondoBanach eVitali. Si danno inoltre esempi effettivi di trasformazioni piane, rappresentate da funzioni assolutamente continue secondoTonelli con derivate parziali prime integrabiliL ², che non sono ne a variazione limitata ne assolutamente continue secondoBanacheVitali. Lavoro eseguito nel Seminario Matematico della R. Scuola Normale Superiore di Pisa.     

Temporal asymmetry of fluctuations in nonequilibrium steady states

Temporal asymmetries of fluctuation paths in nonequilibrium microscopic shearing systems are observed for the first time. Inspired by theories that predict asymmetry of fluctuation paths in stochastic dynamics, we focus on deterministic reversible particle models, which represent a small part of a macroscopic system. We have monitored and measured the asymmetry of the fluctuation paths of various observables as they go away from and towards the mean. The understanding of such asymmetries may scatter light on how irreversibility emerges from the microscopic reversible dynamics and on the behavior of mesoscopic (nanoscale) systems.     

Iridoid glucosides from Viburnum chinshanense

The phytochemical study of the aerial parts of Viburnum chinshanense Graebn., a species growing in Western and Central China, led to the isolation of six iridoid glucosides: the novel 10,2'-diacetylpatrinoside, 1, and the known 2'-acetyldihydropenstemide, 2'-trans- p-coumaroyl-dihydropenstemide, 2'-acetylpatrinoside, decapetaloside, and patrinoside. In addition, amentoflavone and rosarin were also isolated.     

Reduction of Protein Networks Models by Passivity Preserving Projection

Reduction of complex protein networks models is of great importance.The accuracy of a passivity preserving algorithm (PRIMA) for model order reduction (MOR) is here tested on protein networks,introducing innovative variations of the standard PRIMA method to fit the problem at hand.The reduction method does not require to solve the complete system,resulting in a promising tool for studying very large-scale models for which the full solution cannot be computed.The mathematical structure of the considered kinetic equations is preserved.Keeping constant the reduction factor,the approximation error is lower for larger systems.