Pseudopotentials for non-linear evolution equations in 2 + 1 dimensions

In this paper the concept of pseudopotential is generalized to non-linear evolution equations in 2 + 1 dimensions. If the equations satisfied by the pseudopotential are of a Riccati-type in the x-variable, it is shown how to obtain both the generalized AKNS system and the auto-Bäcklund transformation for the corresponding non-linear evolution equation. Several examples are given: Kadomtsev-Petviashvili, modified Kadomtsev-Petviashvili, (2 + 1 dim.)-Harry-Dym, and (2 + 1 dim.)-Sawada-Kotera equations.     

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.     

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.     

Comments on the Entropy of Nonequilibrium Steady States

We discuss the entropy of nonequilibrium steady states. We analyze the so-called spontaneous production of entropy in certain reversible deterministic nonequilibrium system, and its link with the collapse of such systems towards an attractor that is of lower dimension than the dimension of phase space. This means that in the steady state limit, the Gibbs entropy diverges to negative infinity. We argue that if the Gibbs entropy is expanded in a series involving 1, 2,... body terms, the divergence of the Gibbs entropy is manifest only in terms involving integrals whose dimension is higher than, approximately, the Kaplan–Yorke dimension of the steady state attractor. All the low order terms are finite and sum in the weak field limit to the local equilibrium entropy of linear irreversible thermodynamics.     

Applications of periodic orbit theory toN-particle systems

In recent years a number of new techniques have become available in nonequilibrium statistical mechanics, all derived from dynamical system theory, especially from the thermodynamic formalism of Ruelle. We focus here on periodic orbit theory, and we compare it with a novel approach proposed by Evans, Cohen, and Morriss, and developed further by Gallavotti and Cohen. We argue that the two approaches based on such theories are equivalent for systems of many particles if the underlying dynamics is similar to that of Anosov systems, and that such equivalence should remain in more general situations. We extend our previous explanation of irreversibility in the thermostatted Lorentz gas toN-particle diffusion and shearing systems.     

Lie integrable cases of the simplified multistrain/two-stream model for tuberculosis and dengue fever

We apply the techniques of Lie's symmetry analysis to a caricature of the simplified multistrain model of Castillo-Chavez and Feng [C. Castillo-Chavez, Z. Feng, To treat or not to treat: The case of tuberculosis, J. Math. Biol. 35 (1997) 629-656] for the transmission of tuberculosis and the coupled two-stream vector-based model of Feng and Velasco-Hernández [Z. Feng, J.X. Velasco-Hernández, Competitive exclusion in a vector-host model for the dengue fever, J. Math. Biol. 35 (1997) 523-544] to identify the combinations of parameters which lead to the existence of nontrivial symmetries. In particular we identify those combinations which lead to the possibility of the linearization of the system and provide the corresponding solutions. Many instances of additional symmetry are analyzed.