Search results for "Ginzburg"
showing 10 items of 34 documents
Notes on the Electroelastic Interaction in Joint Hamiltonian and Stochastic Treatment of Polarization Response
2008
Conventional Landau theory for ferroelectric phase instability is extended by entities accounting for the violation of thermodynamic equilibrium and the impact of thermal fluctuations. The physical content concerns Ginzburg-Landau type model Hamiltonians assigned to the mean field interaction of macroscopically small and microscopically large lattice cells affected by thermal fluctuations. A special topic derived in a systematic way is long range electroelastic interaction formally given by selfconsistent solution of the polarization and strain fields. Test solution for inhomogeneous strain in a slab is presented within the framework of lattice cell picture.
Asymptotic structure factor for the two-component Ginzburg-Landau equation
1992
We derive an analytic form for the asymptotic time-dependent structure factor for the two-component Ginzburg-Landau equation in arbitrary dimensions. This form is in reasonable agreement with results from numerical simulations in two dimensions. A striking feature of our analytic form is the absence of Porod's law in the tail. This is a consequence of the continuous symmetry of the Hamiltonian, which inhibits the formation of sharp domain walls.
Three-Dimensional Superconducting Nanohelices Grown by He+-Focused-Ion-Beam Direct Writing
2019
Novel schemes based on the design of complex three-dimensional (3D) nanoscale architectures are required for the development of the next generation of advanced electronic components. He+ focused-ion-beam (FIB) microscopy in combination with a precursor gas allows one to fabricate 3D nanostructures with an extreme resolution and a considerably higher aspect ratio than FIB-based methods, such as Ga+ FIB-induced deposition, or other additive manufacturing technologies. In this work, we report the fabrication of 3D tungsten carbide nanohelices with on-demand geometries via controlling key deposition parameters. Our results show the smallest and highest-densely packed nanohelix ever fabricated s…
Propagation of spatiotemporal solitons in dissipative media
2010
This thesis presents a semi-analytical approach for the search of (3+1)D spatio-temporal soliton solutions of the complex cubic-quintic Ginzburg-Landau equation (GL3D).We use a semi-analytical method called collective coordinate approach, to obtain an approximate profile of the unknown pulse field. This ansatz function is chosen to be a function of a finite number of parameters describing the light pulse.By applying this collective corrdinate procedure to the GL3D equation, we obtain a system of variational equations which give the evolution of the light bullet parameters as a function of the propagation distance. We show that the collective coordinate approach is uncomparably faster than t…
Thermodynamics of Nanoparticles: Experimental Protocol Based on a Comprehensive Ginzburg-Landau Interpretation
2014
MATERIAUX+SMR:SDA; The effects of surface and interface on the thermodynamics of small particles require a deeper understanding. This step is crucial for the development of models that can be used for decision-making support to design nanomaterials with original properties. On the basis of experimental results for phase transitions in compressed ZnO nanoparticles, we show the limitations of classical thermodynamics approaches (Gibbs and Landau). We develop a new model based on the Ginzburg-Landau theory that requires the consideration of several terms, such as the interaction between nanoparticles, pressure gradients, defect density, and so on. This phenomenological approach sheds light on …
De Menocchio a Pinocchio. Carlo Ginzburg y la literatura
2022
Son muchas las posibles razones de una celebridad cultural, en este caso la del historiador Carlo Ginzburg. Enumeremos algunas de las circunstancias que han hecho posible su fama. La singularidad intelectual de su familia judía, gravemente diezmada por la muerte del padre, acribillado por los nazis al final de la guerra. El círculo temprano de sus mayores y sus amistades en Turín, en torno a Einaudi, un espacio de excelencia y de agitación editorial. La temprana incorporación del joven Ginzburg a la investigación y a la docencia universitarias en Bolonia, con resultados prometedores, nada rutinarios. La red de intercambios, la transferencia de conocimientos entre sus pares y colegas de dist…
Turing instability and traveling fronts for a nonlinear reaction–diffusion system with cross-diffusion
2012
In this work we investigate the phenomena of pattern formation and wave propagation for a reaction–diffusion system with nonlinear diffusion. We show how cross-diffusion destabilizes uniform equilibrium and is responsible for the initiation of spatial patterns. Near marginal stability, through a weakly nonlinear analysis, we are able to predict the shape and the amplitude of the pattern. For the amplitude, in the supercritical and in the subcritical case, we derive the cubic and the quintic Stuart–Landau equation respectively. When the size of the spatial domain is large, and the initial perturbation is localized, the pattern is formed sequentially and invades the whole domain as a travelin…
Cross-Diffusion Driven Instability in a Predator-Prey System with Cross-Diffusion
2013
In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. Finally when the pattern invades the domain as a trave…
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.
Pulsating Dissipative Light Bullets
2009
Finding domains of existence for (3+1)D spatio-temporal dissipative solitons, also called “dissipative light bullets”, by direct numerical solving of a cubic-quintic Ginzburg-Landau equation (CGLE) is a lengthy procedure [1,2]. Variational approaches pave the way for quicker soliton solution mapping, as long as tractable trial functions remain suitable approximations for exact solutions [3,4].