Cross-scale analysis of cluster correspondence using different operational neighborhoods

Cluster correspondence analysis examines the spatial autocorrelation of multi-location events at the local scale. This paper argues that patterns of cluster correspondence are highly sensitive to the definition of operational neighborhoods that form the spatial units of analysis. A subset of multi-location events is examined for cluster correspondence if they are associated with the same operational neighborhood. This paper discusses the construction of operational neighborhoods for cluster correspondence analysis based on the spatial properties of the underlying zoning system and the scales at which the zones are aggregated into neighborhoods. Impacts of this construction on the degree of cluster correspondence are also analyzed. Empirical analyses of cluster correspondence between paired vehicle theft and recovery locations are conducted on different zoning methods and across a series of geographic scales and the dynamics of cluster correspondence patterns are discussed.      

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.     

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.     

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.     

Temporal behavior of the background seismicity rate in central Japan, 1998 to mid-2003

We studied the temporal behavior of the background shallow seismicity rate in 700 circular areas across inland Japan. To search for and test the significance of the possible rate changes in background seismicity, we developed an efficient computational method that applies the space–time ETAS model proposed by Ogata in 1998 to the areas. Also, we conducted Monte Carlo tests using a simulated catalog to validate the model we applied. Our first finding was that the activation anomalies were found so frequently that the constant background seismicity hypothesis may not be appropriate and/or the triggered event model with constraints on the parameters may not adequately describe the observed seismicity. However, quiescence occasionally occurs merely by chance. Another outcome of our study was that we could automatically find several anomalous background seismicity rate changes associated with the occurrence of large earthquakes. Very significant seismic activation was found before the M6.1 Mt. Iwate earthquake of 1998. Also, possible seismic quiescence was found in an area 150 km southwest of the focal region of the M7.3 Western Tottori earthquake of 2000. The seismicity rate in the area recovered after the mainshock.     

Towards Formulation of a Space-borne System for Early Warning of Floods: Can Cost-Effectiveness Outweigh Prediction Uncertainty?

The three most important components necessary for functioning of an operational flood warning system are: (1) a rainfall measuring system; (2) a soil moisture updating system; and, (3) a surface discharge measuring system. Although surface based networks for these systems can be largely inadequate in many parts of the world, this inadequacy particularly affects the tropics, which are most vulnerable to flooding hazards. Furthermore, the tropical regions comprise developing countries lacking the financial resources for such surface-based monitoring. The heritage of research conducted on evaluating the potential for measuring discharge from space has now morphed into an agenda for a mission dedicated to space-based surface discharge measurements. This mission juxtaposed with two other upcoming space-based missions: (1) for rainfall measurement (Global Precipitation Measurement, GPM), and (2) soil moisture measurement (Hydrosphere State, HYDROS), bears promise for designing a fully space-borne system for early warning of floods. Such a system, if operational, stands to offer tremendous socio-economic benefit to many flood-prone developing nations of the tropical world. However, there are two competing aspects that need careful assessment to justify the viability of such a system: (1) cost-effectiveness due to surface data scarcity; and (2) flood prediction uncertainty due to uncertainty in the remote sensing measurements. This paper presents the flood hazard mitigation opportunities offered by the assimilation of the three proposed space missions within the context of these two competing aspects. The discussion is cast from the perspective of current understanding of the prediction uncertainties associated with space-based flood prediction. A conceptual framework for a fully space-borne system for early-warning of floods is proposed. The need for retrospective validation of such a system on historical data comprising floods and its associated socio-economic impact is stressed. This proposal for a fully space-borne system, if pursued through wide interdisciplinary effort as recommended herein, promises to enhance the utility of the three space missions more than what their individual agenda can be expected to offer.