Stable dark and bright soliton Kerr combs can coexist in normal dispersion resonators

Using the Lugiato-Lefever model, we analyze the effects of third order chromatic dispersion on the existence and stability of dark and bright soliton Kerr frequency combs in the normal dispersion regime. While in the absence of third order dispersion only dark solitons exist over an extended parameter range, we find that third order dispersion allows for stable dark and bright solitons to coexist. Reversibility is broken and the shape of the switching waves connecting the top and bottom homogeneous solutions is modified. Bright solitons come into existence thanks to the generation of oscillations in the switching wave profiles. Finally, oscillatory instabilities of dark solitons are also suppressed in the presence of sufficiently strong third order dispersion

Documentation of the Fourth Order Band Model

A general circulation model is presented which uses quadratically conservative, fourth order horizontal space differences on an unstaggered grid and second order vertical space differences with a forward-backward or a smooth leap frog time scheme to solve the primitive equations of motion. The dynamic equations for motion, finite difference equations, a discussion of the structure and flow chart of the program code, a program listing, and three relevent papers are given

Transport efficiency and dynamics of hydraulic fracture networks

Acknowledgments This study is carried out within the framework of DGMK (German Society for Petroleum and Coal Science and Technology) research project 718 “Mineral Vein Dynamics Modeling,” which is funded by the companies ExxonMobil Production Deutschland GmbH, GDF SUEZ E&P Deutschland GmbH, RWE Dea AG and Wintershall Holding GmbH, within the basic research programme of the WEG Wirtschaftsverband Erdöl- und Erdgasgewinnung e.V. We thank the companies for their financial support and their permission to publish our results. We further acknowledge support by Deutsche Forschungsgemeinschaft and Open Access Publishing Fund of University of Tübingen.Peer reviewedPublisher PD

Interaction of solitons and the formation of bound states in the generalized Lugiato-Lefever equation

Bound states, also called soliton molecules, can form as a result of the interaction between individual solitons. This interaction is mediated through the tails of each soliton that overlap with one another. When such soliton tails have spatial oscillations, locking or pinning between two solitons can occur at fixed distances related with the wavelength of these oscillations, thus forming a bound state. In this work, we study the formation and stability of various types of bound states in the Lugiato-Lefever equation by computing their interaction potential and by analyzing the properties of the oscillatory tails. Moreover, we study the effect of higher order dispersion and noise in the pump intensity on the dynamics of bound states. In doing so, we reveal that perturbations to the Lugiato-Lefever equation that maintain reversibility, such as fourth order dispersion, lead to bound states that tend to separate from one another in time when noise is added. This separation force is determined by the shape of the envelope of the interaction potential, as well as an additional Brownian ratchet effect. In systems with broken reversibility, such as third order dispersion, this ratchet effect continues to push solitons within a bound state apart. However, the force generated by the envelope of the potential is now such that it pushes the solitons towards each other, leading to a null net drift of the solitons.Comment: 13 pages, 13 figure

OTOC, complexity and entropy in bi-partite systems

There is a remarkable interest in the study of Out-of-time ordered correlators (OTOCs) that goes from many body theory and high energy physics to quantum chaos. In this latter case there is a special focus on the comparison with the traditional measures of quantum complexity such as the spectral statistics, for example. The exponential growth has been verified for many paradigmatic maps and systems. But less is known for multi-partite cases. On the other hand the recently introduced Wigner separability entropy (WSE) and its classical counterpart (CSE) provide with a complexity measure that treats equally quantum and classical distributions in phase space. We have compared the behavior of these measures in a system consisting of two coupled and perturbed cat maps with different dynamics: double hyperbolic (HH), double elliptic (EE) and mixed (HE). In all cases, we have found that the OTOCs and the WSE have essentially the same behavior, providing with a complete characterization in generic bi-partite systems and at the same time revealing them as very good measures of quantum complexity for phase space distributions. Moreover, we establish a relation between both quantities by means of a recently proven theorem linking the second Renyi entropy and OTOCs.Comment: 6 pages, 5 figure

Quantum and classical complexity in coupled maps

We study a generic and paradigmatic two-degrees-of-freedom system consisting of two coupled perturbed cat maps with different types of dynamics. The Wigner separability entropy (WSE)—equivalent to the operator space entanglement entropy—and the classical separability entropy (CSE) are used as measures of complexity. For the case where both degrees of freedom are hyperbolic, the maps are classically ergodic and the WSE and the CSE behave similarly, growing to higher values than in the doubly elliptic case. However, when one map is elliptic and the other hyperbolic, the WSE reaches the same asymptotic value than that of the doubly hyperbolic case but at a much slower rate. The CSE only follows the WSE for a few map steps, revealing that classical dynamical features are not enough to explain complexity growth.Fil: Bergamasco, Pablo D.. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Carlo, Gabriel Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Rivas, Alejandro Mariano Fidel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentin

WHAT IS THE LENGTH OF A SNAKE?

The way that herpetologists have traditionally measuredlive snakes is by stretching them on a ruler andrecording the total length (TL). However, due to the thinconstitution of the snake, the large number of intervertebraljoints, and slim muscular mass of most snakes,it is easier to stretch a snake than it is to stretch anyother vertebrate. The result of this is that the length ofa snake recorded is infl uenced by how much the animalis stretched. Stretching it as much as possible is perhapsa precise way to measure the length of the specimenbut it might not correspond to the actual length ofa live animal. Furthermore, it may seriously injure a livesnake. Another method involves placing the snake in aclear plexiglass box and pressing it with a soft materialsuch as rubber foam against a clear surface. Measuringthe length of the snake may be done by outlining itsbody with a string (Fitch 1987; Frye 1991). However, thismethod is restricted to small animals that can be placedin a box, and in addition, no indications of accuracy of thetechnique are given. Measuring the snakes with a fl exibletape has also been reported (Blouin-Demers 2003)but when dealing with a large animals the way the tapeis positioned can produce great variance on the fi nal outcome.In this contribution we revise alternative ways tomeasuring a snake and propose a method that offers repeatableresults. We further analyze the precision of thismethod by using a sample of measurements taken fromwild populations of green anacondas (Eunectes murinus)with a large range of sizes