Search results for "Mathematica"
showing 10 items of 7971 documents
Nonlinear topological symmetry protection in a dissipative system
2023
We report an experimental and theoretical investigation of a system whose dynamics is dominated by an intricate interplay between three key concepts of modern physics: topology, nonlinearity, and spontaneous symmetry breaking. The experiment is based on a two-mode coherently-driven optical resonator in which photons interact through the Kerr nonlinearity. In presence of a phase defect between the modes, a nonlinear attractor develops, which confers a synthetic M\"obius topology to the modal structure of the system. That topology is associated with an inherently protected exchange symmetry between the modes, enabling the realization of spontaneous symmetry breaking in ideal, bias-free, condi…
Spatiotemporal optical solitons in nonlinear dissipative media: From stationary light bullets to pulsating complexes
2007
Nonlinear dissipative systems display the full (3+1) D spatiotemporal dynamics of stable optical solitons. We review recent results that were obtained within the complex cubic-quintic Ginzburg-Landau equation model. Numerical simulations reveal the existence of stationary bell-shaped (3+1) D solitons for both anomalous and normal chromatic dispersion regimes, as well as the formation of double soliton complexes. We provide additional insight concerning the possible dynamics of these soliton complexes, consider collision cases between two solitons, and discuss the ways nonstationary evolution can lead to optical pattern formation. © 2007 American Institute of Physics.
Modèles quantiques à deux états avec croisements de niveaux décrits par les fonctions de Heun
2019
The thesis is devoted to the fundamental problem of excitation and manipulation of quantum systems, having discrete energy spectrum, via external laser fields. We examine the semiclassical time- dependent quantum two-state problem, when the external electromagnetic field is resonant or quasi-resonant for some two of many levels of the system. The focus of the thesis is on the analytic description of the non- adiabatic evolution of quantum systems subject to excitation by level-crossing field configurations. In the present thesis we classify the complete set of the semiclassical time-dependent quantum two-state models solvable in terms of the five function of the Heun class.Main results of t…
Optical bullets and "rockets" in nonlinear dissipative systems and their transformations and interactions
2006
We demonstrate the existence of stable optical light bullets in nonlinear dissipative media for both cases of normal and anomalous chromatic dispersion. The prediction is based on direct numerical simulations of the (3+1)-dimensional complex cubic-quintic GinzburgLandau equation. We do not impose conditions of spherical or cylindrical symmetry. Regions of existence of stable bullets are determined in the parameter space. Beyond the domain of parameters where stable bullets are found, unstable bullets can be transformed into >rockets> i.e. bullets elongated in the temporal domain. A few examples of the interaction between two optical bullets are considered using spatial and temporal interact…
Decay and Fission Hindrance of Two- and Four-Quasiparticle K Isomers in 254Rf
2015
International audience; Two isomers decaying by electromagnetic transitions with half-lives of 4.7(1.1) and 247(73) mu s have been discovered in the heavy (254)Rf nucleus. The observation of the shorter-lived isomer was made possible by a novel application of a digital data acquisition system. The isomers were interpreted as the K-pi = 8(-), nu(2)(7/2(+)[624]; 9/2(-)[734]) two-quasineutron and the K-pi = 16(+), 8(-)nu(2)(7/2(+)[624]; 9/2(-)[734] circle times 8(-)pi(2) (7/2(-)[514]; 9/2(+)[624]) four-quasiparticle configurations, respectively. Surprisingly, the lifetime of the two-quasiparticle isomer is more than 4 orders of magnitude shorter than what has been observed for analogous isomer…
Quantizations from reproducing kernel spaces
2012
Abstract The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of L 2 ( C , d 2 z / π ) based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family depending on a nonnegative parameter s . We examine some interesting issues, mainly related to CS quantization, like the existence of the usual harmonic oscillator spectrum despite the absence of canonical commutation rules. The question of mathematical and physical equivalences between the s -dependent quantizations is also considered.
18 parameter deformations of the Peregrine breather of order 10 solutions of the NLS equation
2015
We present here new solutions of the focusing one-dimensional nonlinear Schrödinger (NLS) equation which appear as deformations of the Peregrine breather of order 10 with 18 real parameters. With this method, we obtain new families of quasi-rational solutions of the NLS equation, and we obtain explicit quotients of polynomial of degree 110 in x and t by a product of an exponential depending on t. We construct new patterns of different types of rogue waves and recover the triangular configurations as well as rings and concentric rings as found for the lower-orders.
Isotope removal experiment in JET-ILW in view of T-removal after the 2nd DT campaign at JET
2022
Abstract A sequence of fuel recovery methods was tested in JET, equipped with the ITER-like beryllium main chamber wall and tungsten divertor, to reduce the plasma deuterium concentration to less than 1% in preparation for operation with tritium. This was also a key activity with regard to refining the clean-up strategy to be implemented at the end of the 2nd DT campaign in JET (DTE2) and to assess the tools that are envisaged to mitigate the tritium inventory build-up in ITER. The sequence began with 4 days of main chamber baking at 320 °C, followed by a further 4 days in which Ion Cyclotron Wall Conditioning (ICWC) and Glow Discharge Conditioning (GDC) were applied with hydrogen fuelling,…
Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives
2022
The keloids are fibroproliferative disorders described by an excessive growth of fibrotic tissue, which also invades adjacent areas (beyond the original wound borders). Since these disorders are specific to humans (no other animal species naturally develop keloid-like tissue), the experimental in vivo/in vitro research has not lead to significant advances in this field. One possible approach could be to combine in vitro human models with calibrated in silico mathematical approaches (i.e., models and simulations) to generate new testable biological hypotheses related to biological mechanisms and improved treatments. Since these combined approaches do not really exist for keloid disorders, in…
Un finage dans la longue durée: Saint-Martin-du-Mont (Côte-d’Or)
2010
On évalue ici les effets de la transmission des structures et formes agraires dans la longue durée. Nous postulons que, depuis la protohistoire, la forme des parcellaires, celle de la voirie ou de l’habitat n’ont jamais été fondamentalement remises en cause. L’organisation actuelle du finage de la commune de Saint-Martin-du-Mont (Bourgogne) est un héritage, probablement une construction médiévale et moderne adossée à une potentialité antique. Les opérations foncières successives se sont coulées dans le moule planimétrique préexistant.