Search results for "Milton"
showing 10 items of 720 documents
Multiple time step integrators and momentum conservation
1997
Abstract By use of the standard Liouville operator formalism, we derive a new symplectic multiple time step integrator for Hamiltonian systems with disparate masses, which, in contrast to previous algorithms, conserves the total momentum exactly, and is only moderately slower. The new scheme is tested numerically by application to Molecular Dynamics simulations of a polymer melt whose monomers have different masses, and compared to earlier algorithms.
About the role of hamiltonian singularities in controlled systems : applications in quantum mechanics and nonlinear optics
2012
This thesis has two goals: the first one is to improve the control techniques in quantum mechanics, and more specifically in NMR, by using the tools of geometric optimal control. The second one is the study of the influence of Hamiltonian singularities in controlled systems. The chapter about optimal control study three classical problems of NMR : the inversion problem, the influence of the radiation damping term, and the steady state technique. Then, we apply the geometric optimal control to the problem of the population transfert in a three levels quantum system to recover the STIRAP scheme.The two next chapters study Hamiltonian singularities. We show that they allow to control the polar…
Principal part of multi-parameter displacement functions
2012
This paper deals with a perturbation problem from a period annulus, for an analytic Hamiltonian system [J.-P. Françoise, Ergodic Theory Dynam. Systems 16 (1996), no. 1, 87–96 ; L. Gavrilov, Ann. Fac. Sci. Toulouse Math. (6) 14(2005), no. 4, 663–682. The authors consider the planar polynomial multi-parameter deformations and determine the coefficients in the expansion of the displacement function generated on a transversal section to the period annulus. Their first result gives a generalization to the Françoise algorithm for a one-parameter family, following [J.-P. Françoise and M. Pelletier, J. Dyn. Control Syst. 12 (2006), no. 3, 357–369. The second result expresses the principal terms in …
Redundant Picard–Fuchs System for Abelian Integrals
2001
We derive an explicit system of Picard-Fuchs differential equations satisfied by Abelian integrals of monomial forms and majorize its coefficients. A peculiar feature of this construction is that the system admitting such explicit majorants, appears only in dimension approximately two times greater than the standard Picard-Fuchs system. The result is used to obtain a partial solution to the tangential Hilbert 16th problem. We establish upper bounds for the number of zeros of arbitrary Abelian integrals on a positive distance from the critical locus. Under the additional assumption that the critical values of the Hamiltonian are distant from each other (after a proper normalization), we were…
The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS
2002
In this paper I propose a method for solving in closed form a general class of four-dimension non-linear modified Hamiltonian dynamic systems. This method may be used to study several intertemporal optimization problems with a predetermined structure, involving unbounded technological constraints as well as multiple controls and state variables. The method is developed here by solving the first order conditions corresponding to the socially optimal solution to the Lucas (1988) two-sector model of endogenous growth.
Far-off-resonance averaging of dipolar interactions in solids
1997
Abstract The far-off-resonance performance of several line-narrowing sequences is investigated. Both theoretically and experimentally, it is found that transverse relaxation times, dominated by dipole–dipole interactions, are most effectively prolonged not only on-resonance but also for certain, generally large, resonance offsets. These correspond to a situation when, during the basic pulse separation, the frequency offset rotates the toggling-frame Hamiltonian by multiples of 180°. The implications of these results for the study of macroscopic translational diffusion using static-field-gradient NMR are discussed.
Combining data from high-energy p p -reactions and neutrinoless double-beta decay: Limits on the mass of the right-handed boson
2016
From the recently established lower-limits on the nonobservability of the neutrinoless double-beta decay of 76Ge (GERDA collaboration) and 136Xe (EXO-200 and KamLAND-Zen collaborations), combined with the ATLAS and CMS data, we extract limits for the left-right (LR) mixing angle, of the SU(2)L ×SU(2)R electroweak Hamiltonian. For the theoretical analysis, which is a model dependent, we have adopted a minimal extension of the Standard Model (SM) of Electroweak Interactions belonging to the SU(2)L ×SU(2)R representation. The nuclear-structure input of the analysis consists of a set of matrix elements and phase-space factors, and the experimental lower-limits for the half-lives. The other inpu…
Structure of transactinide nuclei with relativistic energy density functionals
2013
A microscopic theoretical framework based on relativistic energy density functionals (REDFs) is applied to studies of shape evolution, excitation spectra, and decay properties of transactinide nuclei. Axially symmetric and triaxial relativistic Hartree-Bogoliubov (RHB) calculations, based on the functional DD-PC1 and with a separable pairing interaction, are performed for the even-even isotopic chains between Fm and Fl. The occurrence of a deformed shell gap at neutron number $N=162$ and its role on the stability of nuclei in the region around $Z=108$ is investigated. A quadrupole collective Hamiltonian, with parameters determined by self-consistent constrained triaxial RHB calculations, is…
Isospin mixing and the continuum coupling in weakly bound nuclei
2009
The isospin breaking effects due to the Coulomb interaction in weakly-bound nuclei are studied using the Gamow Shell Model, a complex-energy configuration interaction approach which simultaneously takes into account many-body correlations between valence nucleons and continuum effects. We investigate the near-threshold behavior of one-nucleon spectroscopic factors and the structure of wave functions along an isomultiplet. Illustrative calculations are carried out for the T=1 isobaric triplet. By using a shell-model Hamiltonian consisting of an isoscalar nuclear interaction and the Coulomb term, we demonstrate that for weakly bound or unbound systems the structure of isobaric analog states v…
Model nuclear energy density functionals derived from ab initio calculations
2020
We present the first application of a new approach, proposed in [Journal of Physics G: Nuclear and Particle Physics, 43, 04LT01 (2016)] to derive coupling constants of the Skyrme energy density functional (EDF) from ab initio Hamiltonian. By perturbing the ab initio Hamiltonian with several functional generators defining the Skyrme EDF, we create a set of metadata that is then used to constrain the coupling constants of the functional. We use statistical analysis to obtain such an ab initio-equivalent Skyrme EDF. We find that the resulting functional describes properties of atomic nuclei and infinite nuclear matter quite poorly. This may point out to the necessity of building up the ab init…