8,477 research outputs found
The GENGA Code: Gravitational Encounters in N-body simulations with GPU Acceleration
We describe an open source GPU implementation of a hybrid symplectic N-body
integrator, GENGA (Gravitational ENcounters with Gpu Acceleration), designed to
integrate planet and planetesimal dynamics in the late stage of planet
formation and stability analyses of planetary systems. GENGA uses a hybrid
symplectic integrator to handle close encounters with very good energy
conservation, which is essential in long-term planetary system integration. We
extended the second order hybrid integration scheme to higher orders. The GENGA
code supports three simulation modes: Integration of up to 2048 massive bodies,
integration with up to a million test particles, or parallel integration of a
large number of individual planetary systems. We compare the results of GENGA
to Mercury and pkdgrav2 in respect of energy conservation and performance, and
find that the energy conservation of GENGA is comparable to Mercury and around
two orders of magnitude better than pkdgrav2. GENGA runs up to 30 times faster
than Mercury and up to eight times faster than pkdgrav2. GENGA is written in
CUDA C and runs on all NVIDIA GPUs with compute capability of at least 2.0.Comment: Accepted by ApJ. 18 pages, 17 figures, 4 table
Bose-Einstein Condensates in Optical Quasicrystal Lattices
We analyze the physics of Bose-Einstein condensates confined in 2D
quasi-periodic optical lattices, which offer an intermediate situation between
ordered and disordered systems. First, we analyze the time-of-flight
interference pattern that reveals quasi-periodic long-range order. Second, we
demonstrate localization effects associated with quasi-disorder as well as
quasiperiodic Bloch oscillations associated with the extended nature of the
wavefunction of a Bose-Einstein condensate in an optical quasicrystal. In
addition, we discuss in detail the crossover between diffusive and localized
regimes when the quasi-periodic potential is switched on, as well as the
effects of interactions
Fluxes and Warping for Gauge Couplings in F-theory
We compute flux-dependent corrections in the four-dimensional F-theory
effective action using the M-theory dual description. In M-theory the 7-brane
fluxes are encoded by four-form flux and modify the background geometry and
Kaluza-Klein reduction ansatz. In particular, the flux sources a warp factor
which also depends on the torus directions of the compactification fourfold.
This dependence is crucial in the derivation of the four-dimensional action,
although the torus fiber is auxiliary in F-theory. In M-theory the 7-branes are
described by an infinite array of Taub-NUT spaces. We use the explicit metric
on this geometry to derive the locally corrected warp factor and M-theory
three-from as closed expressions. We focus on contributions to the 7-brane
gauge coupling function from this M-theory back-reaction and show that terms
quadratic in the internal seven-brane flux are induced. The real part of the
gauge coupling function is modified by the M-theory warp factor while the
imaginary part is corrected due to a modified M-theory three-form potential.
The obtained contributions match the known weak string coupling result, but
also yield additional terms suppressed at weak coupling. This shows that the
completion of the M-theory reduction opens the way to compute various
corrections in a genuine F-theory setting away from the weak string coupling
limit.Comment: 46 page
Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach
The extinction of a single species due to demographic stochasticity is
analyzed. The discrete nature of the individual agents and the Poissonian noise
related to the birth-death processes result in local extinction of a metastable
population, as the system hits the absorbing state. The Fokker-Planck
formulation of that problem fails to capture the statistics of large deviations
from the metastable state, while approximations appropriate close to the
absorbing state become, in general, invalid as the population becomes large. To
connect these two regimes, a master equation based on a real space WKB method
is presented, and is shown to yield an excellent approximation for the decay
rate and the extreme events statistics all the way down to the absorbing state.
The details of the underlying microscopic process, smeared out in a mean field
treatment, are shown to be crucial for an exact determination of the extinction
exponent. This general scheme is shown to reproduce the known results in the
field, to yield new corollaries and to fit quite precisely the numerical
solutions. Moreover it allows for systematic improvement via a series expansion
where the small parameter is the inverse of the number of individuals in the
metastable state
Bose Einstein Condensate in a Box
Bose-Einstein condensates have been produced in an optical box trap. This
novel optical trap type has strong confinement in two directions comparable to
that which is possible in an optical lattice, yet produces individual
condensates rather than the thousands typical of a lattice. The box trap is
integrated with single atom detection capability, paving the way for studies of
quantum atom statistics.Comment: 4 pages, 5 figure
Speeding up the GENGA N-body integrator on consumer-grade graphics cards
Context. Graphics processing unit (GPU) computing has become popular due to the enormous calculation potential that can be harvested from a single card. The N-body integrator Gravitational ENcounters with GPU Acceleration (GENGA) is built to harvest the computing power from such cards, but it suffers a severe performance penalty on consumer-grade Nvidia GPUs due to their artificially truncated double precision performance.
Aims. We aim to speed up GENGA on consumer-grade cards by harvesting their high single-precision performance.
Methods. We modified GENGA to have the option to compute the mutual long-distance forces between bodies in single precision and tested this with five experiments. First, we ran a high number of simulations with similar initial conditions of on average 6600 fully self-gravitating planetesimals in both single and double precision to establish whether the outcomes were statistically different. These simulations were run on Tesla K20 cards. We supplemented this test with simulations that (i) began with a mixture of planetesimals and planetary embryos, (ii) planetesimal-driven giant planet migration, and (iii) terrestrial planet formation with a dissipating gas disc. All of these simulations served to determine the accuracy of energy and angular momentum conservation under various scenarios with single and double precision forces. Second, we ran the same simulation beginning with 40 000 self-gravitating planetesimals using both single and double precision forces on a variety of consumer-grade and Tesla GPUs to measure the performance boost of computing the long-range forces in single precision.
Results. We find that there are no statistical differences when simulations are run with the gravitational forces in single or double precision that can be attributed to the force prescription rather than stochastic effects. The accumulations in uncertainty in energy are almost identical when running with single or double precision long-range forces. However, the uncertainty in the angular momentum using single rather than double precision long-range forces is about two orders of magnitude greater, but still very low. Running the simulations in single precision on consumer-grade cards decreases running time by a factor of three and becomes within a factor of three of a Tesla A100 GPU. Additional tuning speeds up the simulation by a factor of two across all types of cards.
Conclusions. The option to compute the long-range forces in single precision in GENGA when using consumer-grade GPUs dramatically improves performance at a little penalty to accuracy. There is an additional environmental benefit because it reduces energy usage
The spin-1/2 XXZ Heisenberg chain, the quantum algebra U_q[sl(2)], and duality transformations for minimal models
The finite-size scaling spectra of the spin-1/2 XXZ Heisenberg chain with
toroidal boundary conditions and an even number of sites provide a projection
mechanism yielding the spectra of models with a central charge c<1 including
the unitary and non-unitary minimal series. Taking into account the
half-integer angular momentum sectors - which correspond to chains with an odd
number of sites - in many cases leads to new spinor operators appearing in the
projected systems. These new sectors in the XXZ chain correspond to a new type
of frustration lines in the projected minimal models. The corresponding new
boundary conditions in the Hamiltonian limit are investigated for the Ising
model and the 3-state Potts model and are shown to be related to duality
transformations which are an additional symmetry at their self-dual critical
point. By different ways of projecting systems we find models with the same
central charge sharing the same operator content and modular invariant
partition function which however differ in the distribution of operators into
sectors and hence in the physical meaning of the operators involved. Related to
the projection mechanism in the continuum there are remarkable symmetry
properties of the finite XXZ chain. The observed degeneracies in the energy and
momentum spectra are shown to be the consequence of intertwining relations
involving U_q[sl(2)] quantum algebra transformations.Comment: This is a preprint version (37 pages, LaTeX) of an article published
back in 1993. It has been made available here because there has been recent
interest in conformal twisted boundary conditions. The "duality-twisted"
boundary conditions discussed in this paper are particular examples of such
boundary conditions for quantum spin chains, so there might be some renewed
interest in these result
Extracting Atoms on Demand with Lasers
We propose a scheme that allows to coherently extract cold atoms from a
reservoir in a deterministic way. The transfer is achieved by means of
radiation pulses coupling two atomic states which are object to different
trapping conditions. A particular realization is proposed, where one state has
zero magnetic moment and is confined by a dipole trap, whereas the other state
with non-vanishing magnetic moment is confined by a steep microtrap potential.
We show that in this setup a predetermined number of atoms can be transferred
from a reservoir, a Bose-Einstein condensate, into the collective quantum state
of the steep trap with high efficiency in the parameter regime of present
experiments.Comment: 11 pages, 8 figure
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