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Radial basis function collocation method for a rotating Bose-Einstein condensation with vortex lattices

Y.T. Shih, C.C. Tsai, K.T. Chen
2012 Interaction and multiscale mechanics  
We study a radial basis function collocation method (RBFCM) to discretize a coupled nonlinear Schrödinger equation (CNLSE) that governs a two dimensional rotating Bose-Einstein condensate (BEC) with an  ...  We exploit a RBFCM-continuation method (RBFCM-CM) to trace the solution curve of the CNLSE. We compare the performance of the RBFCM-CM with the FEM-CM.  ...  Lin of the National Chung-Hsing University for his contributions in developing the FEM-continuation software for rotating BEC.  ... 
doi:10.12989/imm.2012.5.2.131 fatcat:p2d5765dwfbebnb4jymuke4gvm

A time-splitting pseudospectral method for the solution of the Gross–Pitaevskii equations using spherical harmonics with generalised-Laguerre basis functions

Hayder Salman
2014 Journal of Computational Physics  
We present a method for numerically solving a Gross-Pitaevskii system of equations with a harmonic and a toroidal external potential that governs the dynamics of one-and two-component Bose-Einstein condensates  ...  This is accomplished by developing an efficient algorithm that accurately performs the generalised-Laguerre transforms of rotating Bose-Einstein condensates for different orders of the Laguerre polynomials  ...  basis for simulating the dynamics of Bose-Einstein condensates.  ... 
doi:10.1016/ fatcat:bgqzofroezeefedobtlxk7llty

On the Gross-Pitaevskii equation with pumping and decay: stationary states and their stability [article]

Jesús Sierra, Aslan Kasimov, Peter Markowich, Rada-Maria Weishäupl
2013 arXiv   pre-print
We investigate the behavior of solutions of the complex Gross-Pitaevskii equation, a model that describes the dynamics of pumped decaying Bose-Einstein condensates.  ...  Using numerical continuation, we calculate not only the ground state of the system, but also a number of excited states.  ...  [30] in a Bose-Einstein condensation of exciton-polaritons.  ... 
arXiv:1310.2388v1 fatcat:x2hedfr3h5heheruw7pvyyqdgq

Spectral methods in general relativistic astrophysics

S. Bonazzola, E. Gourgoulhon, J.-A. Marck
1999 Journal of Computational and Applied Mathematics  
We present spectral methods developed in our group to solve three-dimensional partial di erential equations.  ...  Josà e-Maria Ibà añez and an anonymous referee for their careful reading of the manuscript.  ...  Galerkin method The Galerkin method consists in choosing the set of functions used for the expansion of a set of functions satisfying the required BC.  ... 
doi:10.1016/s0377-0427(99)00167-3 fatcat:jpfy5bkfjng7hp4utury4vprg4

Spectral methods in general relativistic astrophysics [article]

S. Bonazzola, E. Gourgoulhon and J.-A. Marck (DARC, CNRS, Observatoire de Paris)
1998 arXiv   pre-print
We present spectral methods developed in our group to solve three-dimensional partial differential equations.  ...  If the photon density becomes larger than a critical value, then the photons condense at the frequency ν = 0 (Bose condensation).  ...  Galerkin method The Galerkin method consists in choosing the set of functions used for the expansion a set of function satisfying the required BC.  ... 
arXiv:gr-qc/9811089v1 fatcat:ut4oboyg7rcipi336ly6xwrepa

Hydrodynamic simulations of pulsar glitch recovery

G. Howitt, B. Haskell, A. Melatos
2016 Monthly notices of the Royal Astronomical Society  
Superfluid flow in a model neutron star is simulated by solving the equations of motion of a two-component superfluid consisting of a viscous proton-electron plasma and an inviscid neutron condensate in  ...  It is also found that mutual friction determines the fraction of the frequency jump which is later recovered, a quantity known as the 'healing parameter'.  ...  NUMERICAL METHOD Pseudospectral solver To solve the equations of motion (3)-(5), a pseudospectral collocation method is used to discretize the spatial coordinates, and a fractional timestep algorithm  ... 
doi:10.1093/mnras/stw1043 fatcat:fpbdrqyxgra5hicix6ramwjefi

Structure, dynamics, and reconnection of vortices in a nonlocal model of superfluids

Jason Reneuve, Julien Salort, Laurent Chevillard
2018 Physical Review Fluids  
We then follow and track the phenomenon of reconnection starting from a set of two perpendicular vortices.  ...  We begin by choosing a functional shape of the interaction potential that allows to reproduce in an approximative way the so-called roton minimum observed in experiments, without leading to spurious local  ...  Castaing for numerous fruitful discussions and the PSMN for computer time. Authors are partially funded by ANR Grants No. LIOUVILLE ANR-15-CE40-0013 and No. ECOUTURB ANR-16-CE30-0016.  ... 
doi:10.1103/physrevfluids.3.114602 fatcat:euhduelhijg63jvxnmcszr7gvi

Solitary Waves in the Nonlinear Dirac Equation [chapter]

Jesús Cuevas-Maraver, Nabile Boussaïd, Andrew Comech, Ruomeng Lan, Panayotis G. Kevrekidis, Avadh Saxena
2018 Understanding Complex Systems  
We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy.  ...  The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations.  ...  Acknowledgments The research of Andrew Comech was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Foundation for Sciences  ... 
doi:10.1007/978-3-319-66766-9_4 fatcat:molwfsw6ongnhkjvcscsw2pvya

Electronic and Molecular Dynamics by the Quantum Wave Packet Method [chapter]

Zhigang Sun
2016 Research Advances in Quantum Dynamics  
dynamics, state-to-state tetra-atomic reaction dynamics using transition wave packet method and reactant coordinate method, and electronic dynamics in H 2 + and H 2 molecules will be presented.  ...  A solution to the time-dependent Schrödinger equation is required in a variety of problems in physics and chemistry.  ...  , and the production of solitons and quantum vortices in Bose-Einstein condensates.  ... 
doi:10.5772/63999 fatcat:66hssjizajey7ny5lqi6xwfyka

Numerical Bifurcation Methods and their Application to Fluid Dynamics: Analysis beyond Simulation

Henk A. Dijkstra, Fred W. Wubs, Andrew K. Cliffe, Eusebius Doedel, Ioana F. Dragomirescu, Bruno Eckhardt, Alexander Yu. Gelfgat, Andrew L. Hazel, Valerio Lucarini, Andy G. Salinger, Erik T. Phipps, Juan Sanchez-Umbria (+3 others)
2014 Communications in Computational Physics  
We describe the two basic classes of methods of numerical bifurcation analysis, which differ in the explicit or implicit use of the Jacobian matrix of the dynamical system.  ...  Many of these problems are characterized by high-dimensional dynamical systems which undergo transitions as parameters are changed.  ...  This method has been used to calculate bifurcation diagrams in many physical systems, such as spherical Couette flow [73] , cylindrical Rayleigh-Bénard convection [14, 133] , Bose-Einstein condensation  ... 
doi:10.4208/cicp.240912.180613a fatcat:zyheg6354bbr7kbtaab5hbfrdq

Mathematical theory and numerical methods for Bose-Einstein condensation

Weizhu Bao, Yongyong Cai
2012 Kinetic and Related Models  
In this paper, we mainly review recent results on mathematical theory and numerical methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation (GPE).  ...  Extensions of these results for one-component BEC are then carried out for rotating BEC by GPE with an angular momentum rotation, dipolar BEC by GPE with long range dipole-dipole interaction, and two-component  ...  Now, it is possible to explore quantum world in experiments due to the remarkable discovery of a new state of matter, Bose-Einstein condensate (BEC).  ... 
doi:10.3934/krm.2013.6.1 fatcat:gpiywv4omrhflfzm6cnx24lqhy

The Lagrange-mesh method

Daniel Baye
2015 Physics reports  
This method is quite simple to use and, more importantly, can be very accurate with small number of mesh points for a number of problems.  ...  Keywords: Lagrange-mesh method Gauss quadrature Orthogonal polynomials Schrödinger and Dirac equations Two-body bound states and continuum Three-body bound states a b s t r a c t The Lagrange-mesh method  ...  Bose-Einstein condensates The Gross-Pitaevskii equation describes the behaviour of a Bose-Einstein condensate at zero temperature within the mean-field approximation [234] .  ... 
doi:10.1016/j.physrep.2014.11.006 fatcat:vtixiqjunrhu5i6hambbjzuy3y

Gravitational systems in asymptotically anti-de Sitter space-times [article]

Grégoire Martinon
2017 arXiv   pre-print
Even with arbitrarily small initial data, a singularity almost invariably emerges. However, some configurations allow for perfectly regular and quasi-periodic solutions.  ...  We also detail how several features of such space-times can be used as precision monitors and help us to validate numerics.  ...  It is a Bose-Einstein condensate of a spin-2 field, namely glueball excitations. Credits: G.  ... 
arXiv:1707.00952v3 fatcat:a4c7fenlazdcrirpuc7er2kgl4

Activities and osmotic coefficients of tropospheric aerosols: (NH4)2SO4(aq) and NaCl(aq)

Moonis R. Ally, Simon L. Clegg, Jerry Braunstein, John M. Simonson
2001 Journal of Chemical Thermodynamics  
On completing this module, students will be able to analyze a problem and compose a parallel solution using domain or functional decomposition.  ...  The basis of the independent particle model on which the adiabatic potential rests, ceases to be valid.  ...  finite element grid method with spectral or DVR element functions of local support, or a meshless method using "radial basis" functions, etc.  ... 
doi:10.1006/jcht.2000.0825 fatcat:fcxdkwqsgrdpnn5lv2ty2lt7jm

Vortex and texture defects in radiation and matter wavefields

Gary Ruben
Numerical modelling of the nonlinear system is performed for both trapped and untrapped Bose-Einstein condensates (BECs) in two and three spatial dimensions, for BEC pieces initially positioned at the  ...  Findings from this study are then applied to the time evolution of a nonlinear Bose-Einstein condensate of atoms, which shares the property of coherence that enables its description by a related model  ...  Stationary vortex clusters in nonrotating Bose-Einstein condensates. Physical Review A , . Mueller E J ( ). Spin textures in slowly rotating Bose-Einstein condensates. Physical Review A , .  ... 
doi:10.4225/03/5927d9ca51105 fatcat:55xjhqaaxvh6ve6qmbiknap7ry
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