Arrest of Domain Coarsening via Antiperiodic Regimes in Delay Systems

Motionless domains walls representing heteroclinic temporal or spatial orbits typically exist only for very specific parameters. This report introduces a novel mechanism for stabilizing temporal domain walls away from the Maxwell point opening up new possibilities to encode information in dynamical systems. It is based on anti-periodic regimes in a delayed system close to a bistable situation, leading to a cancellation of the average drift velocity. The results are demonstrated in a normal form model and experimentally in a laser with optical injection and delayed feedback.Comment: 6 pages, 5 figures, resubmitted manuscrip

Finsler geodesics in the presence of a convex function and their applications

We obtain a result about the existence of only a finite number of geodesics between two fixed non-conjugate points in a Finsler manifold endowed with a convex function. We apply it to Randers and Zermelo metrics. As a by-product, we also get a result about the finiteness of the number of lightlike and timelike geodesics connecting an event to a line in a standard stationary spacetime.Comment: 16 pages, AMSLaTex. v2 is a minor revision: title changed, references updated, typos fixed; it matches the published version. This preprint and arXiv:math/0702323v3 [math.DG] substitute arXiv:math/0702323v2 [math.DG

A note on the existence of standard splittings for conformally stationary spacetimes

Let $(M,g)$ be a spacetime which admits a complete timelike conformal Killing vector field $K$. We prove that $(M,g)$ splits globally as a standard conformastationary spacetime with respect to $K$ if and only if $(M,g)$ is distinguishing (and, thus causally continuous). Causal but non-distinguishing spacetimes with complete stationary vector fields are also exhibited. For the proof, the recently solved "folk problems" on smoothability of time functions (moreover, the existence of a {\em temporal} function) are used.Comment: Metadata updated, 6 page

Collective Atomic Recoil Laser as a synchronization transition

We consider here a model previously introduced to describe the collective behavior of an ensemble of cold atoms interacting with a coherent electromagnetic field. The atomic motion along the self-generated spatially-periodic force field can be interpreted as the rotation of a phase oscillator. This suggests a relationship with synchronization transitions occurring in globally coupled rotators. In fact, we show that whenever the field dynamics can be adiabatically eliminated, the model reduces to a self-consistent equation for the probability distribution of the atomic "phases". In this limit, there exists a formal equivalence with the Kuramoto model, though with important differences in the self-consistency conditions. Depending on the field-cavity detuning, we show that the onset of synchronized behavior may occur through either a first- or second-order phase transition. Furthermore, we find a secondary threshold, above which a periodic self-pulsing regime sets in, that is immediately followed by the unlocking of the forward-field frequency. At yet higher, but still experimentally meaningful, input intensities, irregular, chaotic oscillations may eventually appear. Finally, we derive a simpler model, involving only five scalar variables, which is able to reproduce the entire phenomenology exhibited by the original model

Can we make a Finsler metric complete by a trivial projective change?

A trivial projective change of a Finsler metric $F$ is the Finsler metric $F + df$. I explain when it is possible to make a given Finsler metric both forward and backward complete by a trivial projective change. The problem actually came from lorentz geometry and mathematical relativity: it was observed that it is possible to understand the light-line geodesics of a (normalized, standard) stationary 4-dimensional space-time as geodesics of a certain Finsler Randers metric on a 3-dimensional manifold. The trivial projective change of the Finsler metric corresponds to the choice of another 3-dimensional slice, and the existence of a trivial projective change that is forward and backward complete is equivalent to the global hyperbolicity of the space-time.Comment: 11 pages, one figure, submitted to the proceedings of VI International Meeting on Lorentzian Geometry (Granada

Rigorous design of distillation columns using surrogate models based on Kriging interpolation

The economic design of a distillation column or distillation sequences is a challenging problem that has been addressed by superstructure approaches. However, these methods have not been widely used because they lead to mixed-integer nonlinear programs that are hard to solve, and require complex initialization procedures. In this article, we propose to address this challenging problem by substituting the distillation columns by Kriging-based surrogate models generated via state of the art distillation models. We study different columns with increasing difficulty, and show that it is possible to get accurate Kriging-based surrogate models. The optimization strategy ensures that convergence to a local optimum is guaranteed for numerical noise-free models. For distillation columns (slightly noisy systems), Karush–Kuhn–Tucker optimality conditions cannot be tested directly on the actual model, but still we can guarantee a local minimum in a trust region of the surrogate model that contains the actual local minimum.The authors gratefully acknowledge the financial support of the Ministry of Economy and Competitiveness of Spain, under the project CTQ2012-37039-C02-02

Structural considerations in zeotropic distillation sequences with multiple feeds

The separation of multiple feed streams with some common components using sequences of distillation columns produces a rich space of alternatives that must be considered. In this work, we present the main structural characteristics of sequences generated when we want to take advantage of the synergies of common components in multiple feed streams to reduce both, energy consumption and the total number of distillation columns. In general, the sequence of separation tasks of the whole system can be obtained from the sequences of separation tasks of each one of the feeds. However, the integration in actual columns is not so straightforward and we must consider aspects like the optimal location of feeds in multiple-feed columns; and the alternatives of integration of common sub-mixtures (when possible) in actual columns. Besides, the optimal sequence of separation tasks for each feed is not necessarily the same when all of them are considered simultaneously. We show that the minimum number of actual columns, without considering further intensification, depends on the number of components in each feed and on the possibilities of integration of common sub-mixtures, so we extend the concepts of regular and basic column sequences to deal with these new situations. The examples show the potential savings in energy and number of columns compared to maintain isolated each feed; mixing the feed streams or an incorrect integration.The authors acknowledge financial support to the “Generalitat Valenciana” under project PROMETEO 2020/064