Exact solutions for a class of integrable Henon-Heiles-type systems

We study the exact solutions of a class of integrable Henon-Heiles-type systems (according to the analysis of Bountis et al. (1982)). These solutions are expressed in terms of two-dimensional Kleinian functions. Special periodic solutions are expressed in terms of the well-known Weierstrass function. We extend some of our results to a generalized Henon-Heiles-type system with n+1 degrees of freedom.Comment: RevTeX4-1, 13 pages, Submitted to J. Math. Phy

Mechanical similarity as a generalization of scale symmetry

In this paper we study the symmetry known as mechanical similarity (LMS) and present for any monomial potential. We analyze it in the framework of the Koopman-von Neumann formulation of classical mechanics and prove that in this framework the LMS can be given a canonical implementation. We also show that the LMS is a generalization of the scale symmetry which is present only for the inverse square potential. Finally we study the main obstructions which one encounters in implementing the LMS at the quantum mechanical level.Comment: 9 pages, Latex, a new section adde

Breakdown of Lindstedt Expansion for Chaotic Maps

In a previous paper of one of us [Europhys. Lett. 59 (2002), 330--336] the validity of Greene's method for determining the critical constant of the standard map (SM) was questioned on the basis of some numerical findings. Here we come back to that analysis and we provide an interpretation of the numerical results by showing that no contradiction is found with respect to Greene's method. We show that the previous results based on the expansion in Lindstedt series do correspond to the transition value but for a different map: the semi-standard map (SSM). Moreover, we study the expansion obtained from the SM and SSM by suppressing the small divisors. The first case turns out to be related to Kepler's equation after a proper transformation of variables. In both cases we give an analytical solution for the radius of convergence, that represents the singularity in the complex plane closest to the origin. Also here, the radius of convergence of the SM's analogue turns out to be lower than the one of the SSM. However, despite the absence of small denominators these two radii are lower than the ones of the true maps for golden mean winding numbers. Finally, the analyticity domain and, in particular, the critical constant for the two maps without small divisors are studied analytically and numerically. The analyticity domain appears to be an perfect circle for the SSM analogue, while it is stretched along the real axis for the SM analogue yielding a critical constant that is larger than its radius of convergence.Comment: 12 pages, 3 figure

Variable δ15N Diet-Tissue Discrimination Factors among Sharks: Implications for Trophic Position, Diet and Food Web Models

The application of stable isotopes to characterize the complexities of a species foraging behavior and trophic relationships is dependent on assumptions of δ15N diet-tissue discrimination factors (∆15N). As ∆15N values have been experimentally shown to vary amongst consumers, tissues and diet composition, resolving appropriate speciesspecific ∆15N values can be complex. Given the logistical and ethical challenges of controlled feeding experiments for determining ∆ 15N values for large and/or endangered species, our objective was to conduct an assessment of a range of reported ∆ 15N values that can hypothetically serve as surrogates for describing the predator-prey relationships of four shark species that feed on prey from different trophic levels (i.e., different mean δ 15N dietary values). Overall, the most suitable species-specific ∆ 15N values decreased with increasing dietary-δ 15N values based on stable isotope Bayesian ellipse overlap estimates of shark and the principal prey functional groups contributing to the diet determined from stomach content analyses. Thus, a single ∆ 15N value was not supported for this speciose group of marine predatory fishes. For example, the ∆ 15N value of 3.7‰ provided the highest percent overlap between prey and predator isotope ellipses for the bonnethead shark (mean diet δ 15N = 9‰) whereas a ∆ 15N value \u3c 2.3‰ provided the highest percent overlap between prey and predator isotope ellipses for the white shark (mean diet δ 15N = 15‰). These data corroborate the previously reported inverse ∆ 15N-dietary δ 15N relationship when both isotope ellipses of principal prey functional groups and the broader identified diet of each species were considered supporting the adoption of different ∆ 15N values that reflect the predators’ δ 15N-dietary value. These findings are critical for refining the application of stable isotope modeling approaches as inferences regarding a species’ ecological role in their community will be influenced with consequences for conservation and management actions

Diet and trophic ecology of the tiger shark (Galeocerdo cuvier) from South African waters

Knowledge of the diet and trophic ecology of apex predators is key for the implementation of effective ecosystem as well as species-based management initiatives. Using a combination of stomach content data and stable isotope analysis (δ15N and δ13C) the current study provides information on size-based and sex-specific variations in diet, trophic position (TP) and foraging habitat of tiger sharks (Galeocerdo cuvier) caught in the KwaZulu-Natal Sharks Board bather protection program. This study presents the longest time-series and most detailed analysis of stomach content data for G. cuvier worldwide. Prey identified from 628 non-empty stomachs revealed a size-based shift in diet. Reptiles, birds, mysticetes, and large shark species increased in dietary importance with G. cuvier size, concomitant with a decrease in smaller prey such as batoids and teleosts. Seasonal and decadal shifts in diet driven primarily by changes in the importance of elasmobranchs and mammal (cetacean) prey were recorded for medium sized (150-220 cm) G. cuvier. Both stomach content and stable isotope analysis indicated that G. cuvier is a generalist feeder at the population level. Size-based δ13C profiles indicated a movement to offshore foraging habitats by larger G. cuvier. Calculated TP varied by method ranging from 4.0 to 5.0 (TPSCA for stomach contents) and from 3.6 to 4.5 (TPscaled and TPadditive for δ15N). Large (> 220 cm) G. cuvier did not feed at discrete trophic levels, but rather throughout the food web. These data provide key information on the ecological role of G. cuvier to improve the accuracy of regional food web modelling. This will enable a better understanding of the ecological impacts related to changes in the abundance of this predator

Variable δ15N Diet-Tissue Discrimination Factors among Sharks: Implications for Trophic Position, Diet and Food Web Models

The application of stable isotopes to characterize the complexities of a species foraging behavior and trophic relationships is dependent on assumptions of δ(15)N diet-tissue discrimination factors (∆(15)N). As ∆(15)N values have been experimentally shown to vary amongst consumers, tissues and diet composition, resolving appropriate species-specific ∆(15)N values can be complex. Given the logistical and ethical challenges of controlled feeding experiments for determining ∆(15)N values for large and/or endangered species, our objective was to conduct an assessment of a range of reported ∆(15)N values that can hypothetically serve as surrogates for describing the predator-prey relationships of four shark species that feed on prey from different trophic levels (i.e., different mean δ(15)N dietary values). Overall, the most suitable species-specific ∆(15)N values decreased with increasing dietary-δ(15)N values based on stable isotope Bayesian ellipse overlap estimates of shark and the principal prey functional groups contributing to the diet determined from stomach content analyses. Thus, a single ∆(15)N value was not supported for this speciose group of marine predatory fishes. For example, the ∆(15)N value of 3.7‰ provided the highest percent overlap between prey and predator isotope ellipses for the bonnethead shark (mean diet δ(15)N = 9‰) whereas a ∆(15)N value < 2.3‰ provided the highest percent overlap between prey and predator isotope ellipses for the white shark (mean diet δ(15)N = 15‰). These data corroborate the previously reported inverse ∆(15)N-dietary δ(15)N relationship when both isotope ellipses of principal prey functional groups and the broader identified diet of each species were considered supporting the adoption of different ∆(15)N values that reflect the predators' δ(15)N-dietary value. These findings are critical for refining the application of stable isotope modeling approaches as inferences regarding a species' ecological role in their community will be influenced with consequences for conservation and management actions

Dynamical derivation of Bode's law

In a planetary or satellite system, idealized as n small bodies in initially coplanar, concentric orbits around a large central body, obeying Newtonian point-particle mechanics, resonant perturbations will cause dynamical evolution of the orbital radii except under highly specific mutual relationships, here derived analytically apparently for the first time. In particular, the most stable situation is achieved (in this idealized model) only when each planetary orbit is roughly twice as far from the Sun as the preceding one, as observed empirically already by Titius (1766) and Bode (1778) and used in both the discoveries of Uranus (1781) and the Asteroid Belt (1801). ETC.Comment: 27 page

The last frontier: Catch records of white sharks (carcharodon carcharias) in the northwest pacific ocean

White sharks are highly migratory apex predators, globally distributed in temperate, sub-tropical, and tropical waters. Knowledge of white shark biology and ecology has increased recently based on research at known aggregation sites in the Indian, Atlantic, and Northeast Pacific Oceans; however, few data are available for the Northwest Pacific Ocean. This study provides a meta-analysis of 240 observations of white sharks from the Northwest Pacific Ocean between 1951 and 2012. Records comprise reports of bycatch in commercial fisheries, media accounts, personal communications, and documentation of shark-human interactions from Russia (n = 8), Republic of Korea (22), Japan (129), China (32), Taiwan (45), Philippines (1) and Vietnam (3). Observations occurred in all months, excluding October-January in the north (Russia and Republic of Korea) and July-August in the south (China, Taiwan, Philippines, and Vietnam). Population trend analysis indicated that the relative abundance of white sharks in the region has remained relatively stable, but parameterization of a 75% increase in observer effort found evidence of a minor decline since 2002. Reliably measured sharks ranged from 126– 602 cm total length (TL) and 16–2530 kg total weight. The largest shark in this study (602 cm TL) represents the largest measured shark on record worldwide. For all countries combined the sex ratio was non-significantly biased towards females (1:1.1; n = 113). Of 60 females examined, 11 were confirmed pregnant ranging from the beginning stages of pregnancy (egg cases) to near term (140 cm TL embryos). On average, 6.062.2 embryos were found per litter (maximum of 10) and gestation period was estimated to be 20 months. These observations confirm that white sharks are present in the Northwest Pacific Ocean year-round. While acknowledging the difficulties of studying little known populations of a naturally low abundance species, these results highlight the need for dedicated research to inform regional conservation and management plannin

The last frontier: Catch records of white sharks (carcharodon carcharias) in the northwest pacific ocean

White sharks are highly migratory apex predators, globally distributed in temperate, sub-tropical, and tropical waters. Knowledge of white shark biology and ecology has increased recently based on research at known aggregation sites in the Indian, Atlantic, and Northeast Pacific Oceans; however, few data are available for the Northwest Pacific Ocean. This study provides a meta-analysis of 240 observations of white sharks from the Northwest Pacific Ocean between 1951 and 2012. Records comprise reports of bycatch in commercial fisheries, media accounts, personal communications, and documentation of shark-human interactions from Russia (n = 8), Republic of Korea (22), Japan (129), China (32), Taiwan (45), Philippines (1) and Vietnam (3). Observations occurred in all months, excluding October-January in the north (Russia and Republic of Korea) and July-August in the south (China, Taiwan, Philippines, and Vietnam). Population trend analysis indicated that the relative abundance of white sharks in the region has remained relatively stable, but parameterization of a 75% increase in observer effort found evidence of a minor decline since 2002. Reliably measured sharks ranged from 126–602 cm total length (TL) and 16–2530 kg total weight. The largest shark in this study (602 cm TL) represents the largest measured shark on record worldwide. For all countries combined the sex ratio was non-significantly biased towards females (1∶1.1; n = 113). Of 60 females examined, 11 were confirmed pregnant ranging from the beginning stages of pregnancy (egg cases) to near term (140 cm TL embryos). On average, 6.0±2.2 embryos were found per litter (maximum of 10) and gestation period was estimated to be 20 months. These observations confirm that white sharks are present in the Northwest Pacific Ocean year-round. While acknowledging the difficulties of studying little known populations of a naturally low abundance species, these results highlight the need for dedicated research to inform regional conservation and management planning