The Persian calendar for 3000 years

Using the analytical theory of the motion of the Earth around the Sun the times of the vernal (Spring) equinox has been calculated over the period from the Hijra (AD 622) to AD 3800. These data alone allow to decide whether a particular Persian (or Jalaali) calendar year is common or leap. Presented analysis shows that an algorithm implemented in the so called Khayam program is valid for the year 1799 to 2256 (1178 to 1634 Jalaali). A concise algorithm has been worked out that reconstructs the pattern of leap years over time span of about 3000 years. FORTRAN routines for conversion between the Jalaali, Gregorian and Julian calendars and the Julian Day Number are presented.     

Seismic signals in geothermal areas of active volcanism: a case study from ‘La Fossa’, Vulcano (Italy)

Since the last eruption (1888–1890) volcanism at Vulcano, Aeolian Archipelago, southern Tyrrhenian Sea, has taken the form of persistent fumarolic activity. The gas-vapour phases of the geothermal systems are mainly discharged within two restricted areas about 1 km apart from each other, in the northern part of the island. These areas are La Fossa crater, and the beach fumaroles of the Baia di Levante. Fluids released at the two main fumarolic fields display quite different chemical and temperature characteristics, implying different origins. The local seismicity essentially takes the form of discrete shocks of shallow origin (depth1 km) at La Fossa, usually with energy < 10¹³ ergs. They are thought to be related to the uprise of pressurized hot gases and vapours discharged at the crater fumaroles. The present investigation points to the existence of two principal categories of seismic events (called M-shocks and N-shocks). These are short events (normally < 10 s). M-type shocks are thought to be due to resonance vibrations within the interior of the volcano, probably driven by the excitation of shock-waves within cavities deeply affected by deposition and alteration of self-sealant hydrothermal minerals. N-type events display features that resemble those of volcano-tectonic earthquakes, but have no recognizable S-phases. Here they are tentatively attributed to microfracturing of rocks which have been extensively hydrothermally altered. Results of the present study permit a preliminary conceptual model of the local shallow seismic processes in the framework of geochemical modelling of fumarolic activity and geological inferences from geothermal drilling.     

The upper mantle structure of the yakutian kimberlite province,eastern Russia

Deep seismic sounding in the region of the Mirnyi kimberlite field indicates that the boundary velocity of the uppermost mantle is elevated (v _b=8.6–8.8 km/sec) and extremely variable near the Mir kimberlite pipe. These velocity heterogeneities are probably associated with the kimberlite magmatism and may be useful in the identification of other kimberlite fields.     

Integrability of the Yang-Mills Hamiltonian system

This paper considers the integrability of generalized Yang-Mills system with the HamiltonianH _a (p, q)=1/2(p ₁ ² +p ₂ ² +a ₁ q ₁ ² +a ₂ q ₂ ² )+1/4q ₁ ⁴ +1/4a ₃ q ₂ ⁴ + 1/2a ₄ q ₁ ² q ₂ ² . We prove that the system is integrable for the cases: (A)a ₁=a ₂,a ₃=a ₄=1; (b)a ₁=a ₂,a ₃=1,a ₄=3; (C)a ₁=a ₂/4,a ₃=16,a ₄=6. Our main result is the presentation of these integrals. Only for cases A and B does the Yang-Mills Hamiltonian possess the Painlevé property. Therefore the Painlevé test does not take account of the integrability for the case C.     

Generalized Lyapunov exponents indicators in Hamiltonian dynamics: An application to a double star system

The Lyapunov characteristic numbers (LCNs) which are defined as the mean value of the distribution of the local variations of the tangent vectors to the flow (=ln _k ⁱ ) (see Froeschlé, 1984) have been found to be sensitive indicators of stochasticity. So we computed the distribution of these local variations and determined the moments of higher order for the integrable and stochastic regions in a binary star system with =0.5.     

The role of bathymetry and directional wave conditions on observed crescentic bar dynamics

Nearshore sandbars are important features in the surf zone of many beaches because they strongly influence the mean circulation and evolving morphology. Due to variations in wave conditions, sandbars can experience cross-shore migration and vary in shape from alongshore uniform (shore-parallel) to alongshore rhythmic (crescentic). Sandbar dynamics have been studied extensively, but existing observational studies usually do not quantify the processes leading to crescentic bar formation and straightening. This study analyses the dynamics of crescentic bar events at the fetch-limited beach of Castelldefels (northwestern Mediterranean Sea, Spain) using 7.5 years of hourly time-exposure video images and detailed wave conditions. The results show that, despite the generally calm wave conditions, the sandbars were very dynamic in the cross-shore and longshore directions. They often migrated rapidly offshore during storms (up to 70 m in one day) and more slowly onshore during post-storm conditions. Crescentic bars were often present at the study site (48% of the time), but only when the sandbar was at least 10 m from the shoreline. They displayed a large variability in wavelengths (100–700 m), alongshore migration speeds (0–50 m/day) and cross-shore amplitudes (5–20 m). Wavelengths increased for larger bar–shoreline distances and the alongshore migration speeds were strongly correlated with the alongshore component of the radiation stresses. Crescentic patterns typically developed during low–medium energetic waves with limited obliquity ( $\theta \lesssim 20$° at 10 m depth), while bar straightening occurred during medium–high energetic waves with strong oblique angles of incidence ( $\theta \gtrsim 15$°). Overall, this study provides further proof for the important role of wave direction in crescentic bar dynamics and highlights the strong dependence of crescentic bar development on the initial bathymetric configuration.     

Hamiltonian perturbation theory on a manifold

This paper deals with Hamiltonian perturbation theory for systems which, like Euler-Poinsot (the rigid body with a fixed point and no torques), are degenerate and do not possess a global system of action-angle coordinates. It turns out that the usual methods of perturbation theory, which are essentially local being based on the construction of normal forms within the domain of a local coordinate system, are not immediately usable to study perturbations of these systems, since degeneracy makes impossible to control that the system does not fall into a singularity of the coordinates. To overcome this difficulty, we develop a global formulation of Hamiltonian perturbation theory, in which the normal forms are globally defined on the phase space manifold. The key for this study lies in the geometry of the fibration by the invariant tori of an integrable degenerate Hamiltonian system, which is described by some generalizations of the Liouville-Arnol'd theorem and is reviewed in the paper. As an application, we provide a global formulation of Nekhoroshev's theorem on the stability for exponentially long times.     

Possible ways to decipher spatial distribution of mineral resources

Regularity of structural patterns can be connected to planetary disjunctive systems (paleosystems). A computerized universal model of these systems should be developed that may be helpful to predict unknown localities of mineral resources controlled by tectonic processes. The specific character of tectonic phenomena is to be respected in geomathematical models. Some suggestions for applications are given.     

On Szebehely's problem for holonomic systems involving generalized potential functions

We consider the problem of finding the generalized potential function V = U _i(q ¹, q ²,..., q ⁿ)q ⁱ + U(q ¹, q ²,...;q ⁿ) compatible with prescribed dynamical trajectories of a holonomic system. We obtain conditions necessary for the existence of solutions to the problem: these can be cast into a system of n – 1 first order nonlinear partial differential equations in the unknown functions U ₁, U ₂,...;, U _n, U. In particular we study dynamical systems with two degrees of freedom. Using adapted coordinates on the configuration manifold M ₂ we obtain, for potential function U(q ¹, q ²), a classic first kind of Abel ordinary differential equation. Moreover, we show that, in special cases of dynamical interest, such an equation can be solved by quadrature. In particular we establish, for ordinary potential functions, a classical formula obtained in different way by Joukowsky for a particle moving on a surface.Work performed with the support of the Gruppo Nazionale di Fisica Matematica (G.N.F.M.) of the Italian National Research Council.