A Computational Procedure to Detect a New Type of High Dimensional Chaotic Saddle and its Application to the 3-D Hill's Problem

A computational procedure that allows the detection of a new type of high-dimensional chaotic saddle in Hamiltonian systems with three degrees of freedom is presented. The chaotic saddle is associated with a so-called normally hyperbolic invariant manifold (NHIM). The procedure allows to compute appropriate homoclinic orbits to the NHIM from which we can infer the existence a chaotic saddle. NHIMs control the phase space transport across an equilibrium point of saddle-centre-...-centre stability type, which is a fundamental mechanism for chemical reactions, capture and escape, scattering, and, more generally, ``transformation'' in many different areas of physics. Consequently, the presented methods and results are of broad interest. The procedure is illustrated for the spatial Hill's problem which is a well known model in celestial mechanics and which gained much interest e.g. in the study of the formation of binaries in the Kuiper belt.Comment: 12 pages, 6 figures, pdflatex, submitted to JPhys

Telling time with an intrinsically noisy clock

Intracellular transmission of information via chemical and transcriptional networks is thwarted by a physical limitation: the finite copy number of the constituent chemical species introduces unavoidable intrinsic noise. Here we provide a method for solving for the complete probabilistic description of intrinsically noisy oscillatory driving. We derive and numerically verify a number of simple scaling laws. Unlike in the case of measuring a static quantity, response to an oscillatory driving can exhibit a resonant frequency which maximizes information transmission. Further, we show that the optimal regulatory design is dependent on the biophysical constraints (i.e., the allowed copy number and response time). The resulting phase diagram illustrates under what conditions threshold regulation outperforms linear regulation.Comment: 10 pages, 5 figure

Preface "Nonlinear processes in oceanic and atmospheric flows"

Nonlinear phenomena are essential ingredients in many oceanic and atmospheric processes, and successful understanding of them benefits from multidisciplinary collaboration between oceanographers, meteorologists, physicists and mathematicians. The present Special Issue on ``Nonlinear Processes in Oceanic and Atmospheric Flows'' contains selected contributions from attendants to the workshop which, in the above spirit, was held in Castro Urdiales, Spain, in July 2008. Here we summarize the Special Issue contributions, which include papers on the characterization of ocean transport in the Lagrangian and in the Eulerian frameworks, generation and variability of jets and waves, interactions of fluid flow with plankton dynamics or heavy drops, scaling in meteorological fields, and statistical properties of El Ni\~no Southern Oscillation.Comment: This is the introductory article to a Special Issue on "Nonlinear Processes in Oceanic and Atmospheric Flows'', published in the journal Nonlinear Processes in Geophysics, where the different contributions are summarized. The Special Issue itself is freely available from http://www.nonlin-processes-geophys.net/special_issue103.htm

Extreme Supernova Models for the Superluminous Transient ASASSN-15lh

The recent discovery of the unprecedentedly superluminous transient ASASSN-15lh (or SN 2015L) with its UV-bright secondary peak challenges all the power-input models that have been proposed for superluminous supernovae. Here we examine some of the few viable interpretations of ASASSN-15lh in the context of a stellar explosion, involving combinations of one or more power inputs. We model the lightcurve of ASASSN-15lh with a hybrid model that includes contributions from magnetar spin-down energy and hydrogen-poor circumstellar interaction. We also investigate models of pure circumstellar interaction with a massive hydrogen-deficient shell and discuss the lack of interaction features in the observed spectra. We find that, as a supernova ASASSN-15lh can be best modeled by the energetic core-collapse of a ~40 Msun star interacting with a hydrogen-poor shell of ~20 Msun. The circumstellar shell and progenitor mass are consistent with a rapidly rotating pulsational pair-instability supernova progenitor as required for strong interaction following the final supernova explosion. Additional energy injection by a magnetar with initial period of 1-2 ms and magnetic field of 0.1-1 x 10^14 G may supply the excess luminosity required to overcome the deficit in single-component models, but this requires more fine-tuning and extreme parameters for the magnetar, as well as the assumption of efficient conversion of magnetar energy into radiation. We thus favor a single-input model where the reverse shock formed in a strong SN ejecta-CSM interaction following a very powerful core-collapse SN explosion can supply the luminosity needed to reproduce the late-time UV-bright plateau.Comment: 8 pages, 3 figure

Axial-Force Reduction by Interference Between Jet and Neighboring Afterbody

Experimental results are presented for an exploratory investigation of the effectiveness of interference between jet and afterbody in reducing the axial force on an afterbody with a neighboring jet. In addition to the interference axial force., measurements are presented of the interference normal force and the center of pressure of the interference normal force. The free-stream Mach number was 2.94, the jet-exit Mach number was 2.71, and the Reynolds number was 0.25 x 10, based on body diameter. The variables investigated include static-pressure ratio of the jet (up to 9), nacelle position relative to afterbody, angle of attack (-5 deg to 10 deg), and afterbody shape. Two families of afterbody shapes were tested. One family consisted of tangent-ogive bodies of revolution with varying length and base areas. The other family was formed by taking a planar slice off a circular cylinder with varying angle between the plane and cylinder. The trends with these variables are shown for conditions near maximum jet-afterbody interference. The interference axial forces are large and favorable. For several configurations the total afterbody axial force is reduced to zero by the interference

Self-organized Beating and Swimming of Internally Driven Filaments

We study a simple two-dimensional model for motion of an elastic filament subject to internally generated stresses and show that wave-like propagating shapes which can propel the filament can be induced by a self-organized mechanism via a dynamic instability. The resulting patterns of motion do not depend on the microscopic mechanism of the instability but only of the filament rigidity and hydrodynamic friction. Our results suggest that simplified systems, consisting only of molecular motors and filaments could be able to show beating motion and self-propulsion.Comment: 8 pages, 2 figures, REVTe

Control of Integrable Hamiltonian Systems and Degenerate Bifurcations

We discuss control of low-dimensional systems which, when uncontrolled, are integrable in the Hamiltonian sense. The controller targets an exact solution of the system in a region where the uncontrolled dynamics has invariant tori. Both dissipative and conservative controllers are considered. We show that the shear flow structure of the undriven system causes a Takens-Bogdanov birfurcation to occur when control is applied. This implies extreme noise sensitivity. We then consider an example of these results using the driven nonlinear Schrodinger equation.Comment: 25 pages, 11 figures, resubmitted to Physical Review E March 2004 (originally submitted June 2003), added content and reference

Reduction of a metapopulation genetic model to an effective one island model

We explore a model of metapopulation genetics which is based on a more ecologically motivated approach than is frequently used in population genetics. The size of the population is regulated by competition between individuals, rather than by artificially imposing a fixed population size. The increased complexity of the model is managed by employing techniques often used in the physical sciences, namely exploiting time-scale separation to eliminate fast variables and then constructing an effective model from the slow modes. Remarkably, an initial model with 2$\mathcal{D}$ variables, where $\mathcal{D}$ is the number of islands in the metapopulation, can be reduced to a model with a single variable. We analyze this effective model and show that the predictions for the probability of fixation of the alleles and the mean time to fixation agree well with those found from numerical simulations of the original model.Comment: 16 pages, 4 figures. Supplementary material: 22 pages, 3 figure

The role of dredge-up in double white dwarf mergers

We present the results of an investigation of the dredge-up and mixing during the merger of two white dwarfs with different chemical compositions by conducting hydrodynamic simulations of binary mergers for three representative mass ratios. In all the simulations, the total mass of the two white dwarfs is $\lesssim1.0~{\rm M_\odot}$. Mergers involving a CO and a He white dwarf have been suggested as a possible formation channel for R Coronae Borealis type stars, and we are interested in testing if such mergers lead to conditions and outcomes in agreement with observations. Even if the conditions during the merger and subsequent nucleosynthesis favor the production of $^{18}{\mathrm O}$, the merger must avoid dredging up large amounts of $^{16}{\mathrm O}$, or else it will be difficult to produce sufficient $^{18}{\mathrm O}$ to explain the oxygen ratio observed to be of order unity. We performed a total of 9 simulations using two different grid-based hydrodynamics codes using fixed and adaptive meshes, and one smooth particle hydrodynamics (SPH) code. We find that in most of the simulations, $>10^{-2}~{\rm M_\odot}$ of $^{16}{\mathrm O}$ is indeed dredged up during the merger. However, in SPH simulations where the accretor is a hybrid He/CO white dwarf with a $\sim 0.1~{\rm M_\odot}$ layer of helium on top, we find that no $^{16}{\mathrm O}$ is being dredged up, while in the $q=0.8$ simulation $<10^{-4}~{\rm M_\odot}$ of $^{16}{\mathrm O}$ has been brought up, making a WD binary consisting of a hybrid CO/He WD and a companion He WD an excellent candidate for the progenitor of RCB stars.Comment: Accepted for publication in Ap

Resonance Zones and Lobe Volumes for Volume-Preserving Maps

We study exact, volume-preserving diffeomorphisms that have heteroclinic connections between a pair of normally hyperbolic invariant manifolds. We develop a general theory of lobes, showing that the lobe volume is given by an integral of a generating form over the primary intersection, a subset of the heteroclinic orbits. Our definition reproduces the classical action formula in the planar, twist map case. For perturbations from a heteroclinic connection, the lobe volume is shown to reduce, to lowest order, to a suitable integral of a Melnikov function.Comment: ams laTeX, 8 figure