Search results for "BIF"
showing 10 items of 539 documents
Two-photon laser dynamics.
1995
Degenerate as well as nondegenerate three-level two-photon laser (TPL) models are derived. In the limit of equal cavity losses for both fields, it is shown that the nondegenerate model reduces to the degenerate one. We also demonstrate the isomorphism existing between our degenerate TPL model and that of a dressed-state TPL. All these models contain ac-Stark and population-induced shifts at difference from effective Hamiltonian models. The influence of the parameters that control these shifts on the nonlinear dynamics of a TPL is investigated. In particular, the stability of the periodic orbits that arise at the Hopf bifurcation of the system and the extension of the self-pulsing domains of…
Invariant circles in the Bogdanov-Takens bifurcation for diffeomorphisms
1996
AbstractWe study a generic, real analytic unfolding of a planar diffeomorphism having a fixed point with unipotent linear part. In the analogue for vector fields an open parameter domain is known to exist, with a unique limit cycle. This domain is bounded by curves corresponding to a Hopf bifurcation and to a homoclinic connection. In the present case of analytic diffeomorphisms, a similar domain is shown to exist, with a normally hyperbolic invariant circle. It follows that all the ‘interesting’ dynamics, concerning the destruction of the invariant circle and the transition to trivial dynamics by the creation and death of homoclinic points, takes place in an exponentially small part of the…
Progress in Modelling Coherently Pumped Far-Infrared Laser Dynamics
1990
Coherently pumped lasers (CPL) operating in the far-infrared spectral region shown a wealth of instabilities1, including a behavior remarkably similar2,3 with the predictions of the paradigmatic Lorenz-Haken model of a single-mode homogeneously broadened laser4,5. The qualitative agreement; between theory and experiments2,3 was rather surprising, for the model4,5 refers to a two-level system whereas the CPL operate on a three-level scheme, where the pumping and lasing transitions share a common upper level. Dupertuis et al.6 have identified conditions for the mathematical reduction of the CPL equations to the Lorenz-Haken equations4, but these conditions were not all fulfilled in the experi…
Turing Instability and Pattern Formation for the Lengyel–Epstein System with Nonlinear Diffusion
2014
In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel---Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show how nonlinear diffusion intensifies the tendency to pattern formation; in particular, unlike the case of classical linear diffusion, the Turing instability can occur even when diffusion of the inhibitor is significantly slower than activator's one. In the Turing pattern region we perform the WNL multiple scales analysis to derive the equations for the amplitude of the stationary pattern, both in the supercritical and in the subcritical case. Moreover, we c…
How to Get a Model in Pedestrian Dynamics to Produce Stop and Go Waves
2016
Stop and go waves in granular flow can often be described mathematically by a dynamical system with a Hopf bifurcation. We show that a certain class of microscopic, ordinary differential equation-based models in crowd dynamics fulfil certain conditions of Hopf bifurcations. The class is based on the Gradient Navigation Model. An interesting phenomenon arises: the number of pedestrians in the system must be greater than nine for a bifurcation—and hence for stop and go waves to be possible at all, independent of the density. Below this number, no parameter setting will cause the system to exhibit stable stop and go behaviour. The result is also interesting for car traffic, where similar model…
AICA-ribosiduria due to ATIC deficiency: Delineation of the phenotype with three novel cases, and long-term update on the first case.
2020
5-Amino-4-imidazolecarboxamide-ribosiduria (AICA)-ribosiduria is an exceedingly rare autosomal recessive condition resulting from the disruption of the bifunctional purine biosynthesis protein PURH (ATIC), which catalyzes the last two steps of de novo purine synthesis. It is characterized biochemically by the accumulation of AICA-riboside in urine. AICA-ribosiduria had been reported in only one individual, 15 years ago. In this article, we report three novel cases of AICA-ribosiduria from two independent families, with two novel pathogenic variants in ATIC. We also provide a clinical update on the first patient. Based on the phenotypic features shared by these four patients, we define AICA-…
Non-equivalent hyperbolic knots
2002
We construct, for each integer n 3, pairs of non-equivalent hyperbolic knots with the same 2fold and n-fold cyclic branched covers. We also discuss necessary conditions for such pairs of knots to exist. 2001 Elsevier Science B.V. All rights reserved. MSC: primary 57M25; secondary 57M12, 57M50
Organocatalytic Enantioselective Friedel–Crafts Aminoalkylation of Indoles in the Carbocyclic Ring
2016
The first general catalytic method for the, so far elusive, enantioselective Friedel−Crafts functionalization of indoles in the carbocyclic ring is presented. This transformation contrasts with the usual tendency of these heterocycles to react at the azole ring. For this purpose, the four regioisomeric hydroxy carbocyclic-substituted indoles were reacted with several isatinderived ketimines, using a Cinchona alkaloid-based squaramide, in a low 0.5−5 mol % catalyst loading, as a bifunctional catalyst. This methodology allows the functionalization of indoles in every position of the carbocyclic ring in a regio- and enantioselective fashion, by switching only the position of the hydroxy group …
Synthesis of oligomeric chains with 9,10‐dihydroanthracene units by carbanion alkylation
1988
Deprotonation of 9,10-dihydroanthracene (2) affords the monoanion 6 which is subjected to alkylation reactions with mono and bifunctional electrophiles. Crucial intermediates in syntheses using 6 are 9-(3-bromopropyl)-9,10-dihydroanthracene (7) and 1,3-bis(9,10-dihydro-9-anthryl)propane (9) since they provide access to linear oligomers in which 9,10-dihydroanthracene units are linked by trimethylene groups. The alkylation processes of these species can be extended to the structurally related polymer 4. The regio- and stereoselectivity of the alkylation reactions are investigated by 1H- and 13C-NMR spectroscopy. Oligomere Ketten mit 9,10-Dihydroanthracen-Einheiten durch Carbanionalkylierung …
Preclinical immunomodulation by the probiotic Bifidobacterium breve M-16V in early life
2016
This study aimed to investigate the effect of supplementation with the probiotic Bifidobacterium breve M-16V on the maturation of the intestinal and circulating immune system during suckling. In order to achieve this purpose, neonatal Lewis rats were supplemented with the probiotic strain from the 6th to the 18th day of life. The animals were weighed during the study, and faecal samples were obtained and evaluated daily. On day 19, rats were euthanized and intestinal wash samples, mesenteric lymph node (MLN) cells, splenocytes and intraepithelial lymphocytes (IEL) were obtained. The probiotic supplementation in early life did not modify the growth curve and did not enhance the systemic immu…