Generic bifurcations of low codimension of planar Filippov Systems

In this article some qualitative and geometric aspects of non-smooth dynamical systems theory are discussed. The main aim of this article is to develop a systematic method for studying local (and global) bifurcations in non-smooth dynamical systems. Our results deal with the classification and characterization of generic codimension-2 typical singularities of planar Filippov systems as well as the presentation of the bifurcation diagrams and some dynamical consequencesPreprin

Critical velocity in kink-defect interaction models: rigorous results

In this work we study a model of interaction of kinks of the sine-Gordon equation with a weak defect. We obtain rigorous results concerning the so-called critical velocity derived in [7] by a geometric approach. More specifically, we prove that a heteroclinic orbit in the energy level 0 of a 2-dof Hamiltonian is destroyed giving rise to heteroclinic connections between certain elements (at infinity) for exponentially small (in e) energy levels. In this setting Melnikov theory does not apply because there are exponentially small phenomena.Peer ReviewedPostprint (published version

Dynamical Bonding Driving Mixed Valency in a Metal Boride

Samarium hexaboride is an anomaly, having many exotic and seemingly mutually incompatible properties. It was proposed to be a mixed-valent semiconductor, and later - a topological Kondo insulator, and yet has a Fermi surface despite being an insulator. We propose a new and unified understanding of SmB$_6$ centered on the hitherto unrecognized dynamical bonding effect: the coexistence of two Sm-B bonding modes within SmB$_6$, corresponding to different oxidation states of the Sm. The mixed valency arises in SmB$_6$ from thermal population of these distinct minima enabled by motion of B. Our model simultaneously explains the thermal valence fluctuations, appearance of magnetic Fermi surface, excess entropy at low temperatures, pressure-induced phase transitions, and related features in Raman spectra and their unexpected dependence on temperature and boron isotope

Exponentially small splitting of separatrices beyond Melnikov analysis: rigorous results

In this paper we study the problem of exponentially small splitting of separatrices of one degree of freedom classical Hamiltonian systems with a non-autonomous perturbation which is fast and periodic in time. We provide a result valid for general systems which are polynomials or trigonometric polynomials in the state variables. Our result consists in obtaining a rigorous proof of the asymptotic formula for the measure of the splitting. We have obtained that the splitting has the asymptotic behavior K" e−a/" identifying the constants K, and a in terms of the features of the system. The study of our problem leads us to consider several cases. In some cases, assuming the per- turbation is small enough, it turns out that the values of K, coincides with the classical Melnikov approach. We have identified the limit size of the perturbation for which this classical theory holds true. However for the limit cases, which appear naturally both in averaging theory and bifurcation theory, we encounter that, generically, neither K nor are actually well predicted by Melnikov theory.Preprin

Lean Manufacturing Model for production management to increase SME productivity in the non-primary manufacturing sector

Currently, there is a large percentage of small and medium-sized enterprises (SMEs) in the Peruvian textile market that show economic loss because of the payment of penalties to customers, which are incurred owing to the delay in the delivery of order batches. This is due to poor production management and a lack of focus. The manufacturing sector is essential because of its high contribution to the country's gross domestic product. Currently, SMEs do not employ methodologies that help improve production and process management as they do not realize how important and necessary the methodologies are, in addition to how complex these may be. Therefore, this paper will propose a production management model designed for SMEs in this sector, based on Lean methodology where the objective is time reductions and production increases as well as exerting changes to the organizational culture. Thus, this model will help organizations to avoid incurring economic losses because of the payment of penalties for orders not delivered on time. To validate the present model, a time simulation was performed in the manufacturing area of a textile company. The result of this project was positive, since there was a 25% increase in productivity and a 20% reduction of takt time with respect to the initial data

Streptozotocin-induced diabetes in the rat is associated with changes in vaginal hemodynamics, morphology and biochemical markers

BACKGROUND: Diabetes is associated with declining sexual function in women. However, the effects of diabetes on genital tissue structure, innervation and function remains poorly characterized. In control and streptozotocin-treated female rats, we investigated the effects of diabetes on vaginal blood flow, tissue morphology, and expression of arginase I, endothelial nitric oxide synthase (eNOS) and cGMP-dependent protein kinase (PKG), key enzymes that regulate smooth muscle relaxation. We further related these changes with estrogen receptor alpha (ERα) and androgen receptor (AR) expression. RESULTS: In addition to significantly elevated blood glucose levels, diabetic rats had decreased mean body weight, lower levels of plasma estradiol, and higher plasma testosterone concentration, compared to age-matched controls. Eight weeks after administration of buffer (control) or 65 mg/kg of streptozotocin (diabetic), the vaginal blood flow response to pelvic nerve stimulation was significantly reduced in diabetic rats. Histological examination of vaginal tissue from diabetic animals showed reduced epithelial thickness and atrophy of the muscularis layer. Diabetic animals also had reduced vaginal levels of eNOS and arginase I, but elevated levels of PKG, as assessed by Western blot analyses. These alterations were accompanied by a reduction in both ERα and AR in nuclear extracts of vaginal tissue from diabetic animals. CONCLUSION: In ovariectomized (estrogen deficient) animals, previous reports from our lab and others have documented changes in blood flow, tissue structure, ERα, arginase I and eNOS that parallel those observed in diabetic rats. We hypothesize that diabetes may lead to multiple disruptions in sex steroid hormone synthesis, metabolism and action. These pathological events may cause dramatic changes in tissue structure and key enzymes that regulate cell growth and smooth muscle contractility, ultimately affecting the genital response during sexual arousal

An insight into transfer hydrogenation reactions catalysed by iridium(iii) bis-n-heterocyclic carbenes

A variety of [M(L)2(L')2{kC,C'-bis(NHC)}]BF4 complexes (M = Rh or Ir; L = CH3CN or wingtip group; L' = I– or CF3COO–; NHC=N-heterocyclic carbene) have been tested as pre-catalysts for the transfer hydrogenation of ketones and imines. The conversions and TOF's obtained are closely related to the nature of the ligand system and metal centre, more strongly coordinating wingtip groups yielding more active and recyclable catalysts. Theoretical calculations at the DFT level support a classic stepwise metal-hydride pathway against the concerted Meerwein–Ponndorf–Verley (MPV) mechanism. The calculated catalytic cycle involves a series of ligand rearrangements due to the high trans effect of the carbene and hydrido ligands, which are more stable when situated in mutual cis positions. The reaction profiles obtained for the complexes featuring an iodide or a trifluoroacetate in one of the apical positions agree well with the relative activity observed for both catalysts

Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation

In this paper we study the splitting of separatrices phenomenon which arises when one considers a Hamiltonian System of one degree of freedom with a fast periodic or quasiperiodic and meromorphic in the state variables perturbation. The obtained results are different from the previous ones in the literature, which mainly assume algebraic or trigonometric polynomial dependence on the state variables. As a model, we consider the pendulum equation with several meromorphic perturbations and we show the sensitivity of the size of the splitting on the width of the analyticity strip of the perturbation with respect to the state variables. We show that the size of the splitting is exponentially small if the strip of analyticity is wide enough. Furthermore, we see that the splitting grows as the width of the analyticity strip shrinks, even becoming non-exponentially small for very narrow strips. Our results prevent from using polynomial truncations of the meromorphic perturbation to compute the size of the splitting of separatrices.Preprin

Oscillatory motions and parabolic manifolds at infinity in the planar circular restricted three body problem

Consider the Restricted Planar Circular 3 Body Problem. If the trajectory of the body of zero mass is defined for all time, it can have the following four types of asymptotic motion when time tends to infinity forward or backward in time: bounded, parabolic (goes to infinity with asymptotic zero velocity), hyperbolic (goes to infinity with asymptotic positive velocity) or oscillatory (the position of the body is unbounded but goes back to a compact region of phase space for a sequence of arbitrarily large times). We consider realistic mass ratio for the Sun-Jupiter pair and Jacobi constant which allows the massless body to cross Jupiter's orbit. This is a non-perturbative regime. We prove the existence of all possible combinations of past and future final motions. In particular, we obtain the existence of oscillatory motions. All the constructed trajectories cross the orbit of Jupiter but avoid close encounters with it. The proof relies on analyzing the stable and unstable invariant manifolds of infinity and their intersections. We construct orbits shadowing these invariant manifolds by the method of correctly aligned windows. The proof is computer assisted.M. C. has been partially supported by the NCN grant 2018/29/B/ST1/00109 2M. G. has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 757802). M. G. is supported by the Catalan Institution for Research and Advanced Studies via an ICREA Academia Prize 2019. P. M. has been partially supported by the Spanish MINECO-FEDER Grant PGC2018-100928-B-I00 and the Catalan grant 2017SGR1049 T. S. has been also partly supported by the Spanish MINECO-FEDER Grant PGC2018-098676-B100 (AEI/FEDER/UE), the Catalan grant 2017SGR1049 and by the Catalan Institution for Research and Advanced Studies via an ICREA Academia Prize 2019. P. Z. has been partially supported by the NCN grant 2019/35/B/ST1/00655Peer ReviewedPostprint (author's final draft

Oscillatory motions for the restricted planar circular three body problem

Dynamical System Prize, atorgat per la Societat Catalana de Matemàtiques© 2015, Springer-Verlag Berlin Heidelberg. The restricted three body problem models the motion of a massless body under the influence of the Newtonian gravitational force caused by two other bodies called the primaries. When they move along circular Keplerian orbits and the third body moves in the same plane, one has the restricted planar circular three body problem (RPC3BP). In suitable coordinates, it is a Hamiltonian system of two degrees of freedom. The conserved energy is usually called the Jacobi constant. Llibre and Simó [Math Ann 248(2):153–184, 1980] proved the existence of oscillatory motions for this system. That is, orbits which leave every bounded region but which return infinitely often to some fixed bounded region. To prove their existence they had to assume the ratio between the masses of the primaries to be small enough. In this paper we prove the existence of such motions for any value of the mass ratio(Formula presented.) closing the problem of existence of oscillatory motions in the RPC3BP. To obtain such motions, we restrict ourselves to the level sets of the Jacobi constant. We show that, for any value of the mass ratio and for large values of the Jacobi constant, there exist transversal intersections between the stable and unstable manifolds of infinity in these level sets. These transversal intersections guarantee the existence of a symbolic dynamics that creates the oscillatory orbits. The main achievement is to prove the existence of these orbits without assuming the mass ratio (Formula presented.) small. When (Formula presented.) is not small, this transversality can not be checked by means of classical perturbation theory. Since our method is valid for all values of v, we are able to detect a curve in the parameter space, formed by (Formula presented.) and the Jacobi constant, where cubic homoclinic tangencies between the invariant manifolds of infinity appear.Award-winningPostprint (published version