Many of the static and dynamic properties of an atomic Bose-Einstein condensate (BEC) are usually studied by solving the mean-field Gross-Pitaevskii (GP) equation, which is a nonlinear partial differential equation for short-range atomic interaction.
More recently, BEC of atoms with long-range dipolar atomic interaction are used in theoretical and experimental studies. For dipolar atomic interaction, the GP equation is a partial integro-differential equation, requiring complex algorithm for its numerical solution. Here we present numerical algorithms for both stationary and non-stationary solutions of the full three-dimensional (3D) GP equation for a dipolar BEC, including the contact interaction. We also consider the simplified one- (1D) and two-dimensional (2D) GP equations satisfied by cigar- and disk-shaped dipolar BECs. We employ the split-step Crank-Nicolson method with real- and imaginary-time propagations, respectively, for the numerical solution of the GP equation for dynamic and static properties of a dipolar BEC. The atoms are considered to be polarized along the z axis and we consider ten different cases, e.g., stationary and non-stationary solutions of the GP equation for a dipolar BEC in 1D (along x and z axes), 2D (in x-y and x-z planes), and 3D, and we provide working codes in Fortran 90/95 and C for these ten cases (twenty programs in all). We present numerical results for energy, chemical potential, root-mean-square sizes and density of the dipolar BECs and, where available, compare them with results of other authors and of variational and Thomas-Fermi approximations.
The Spitzer Space Telescope mapped the Perseus molecular cloud complex with IRAC and MIPS as part of the c2d Spitzer Legacy project. This paper combines the observations from both instruments giving an overview of low-mass star formation across Perse
us from 3.6 to 70 micron. We provide an updated list of young stellar objects with new classifications and source fluxes from previous works, identifying 369 YSOs in Perseus with the Spitzer dataset. By synthesizing the IRAC and MIPS maps of Perseus and building on the work of previous papers in this series (Jorgensen et al. 2006, Rebull et al. 2007), we present a current census of star formation across the cloud and within smaller regions. 67% of the YSOs are associated with the young clusters NGC 1333 and IC 348. The majority of the star formation activity in Perseus occurs in the regions around the clusters, to the eastern and western ends of the cloud complex. The middle of the cloud is nearly empty of YSOs despite containing regions of high visual extinction. The western half of Perseus contains three-quarters of the total number of embedded YSOs (Class 0+I and Flat SED sources) in the cloud and nearly as many embedded YSOs as Class II and III sources. Class II and III greatly outnumber Class 0+I objects in eastern Perseus and IC 348. These results are consistent with previous age estimates for the clusters. Across the cloud, 56% of YSOs and 91% of the Class 0+I and Flat sources are in areas where Av > 5 mag, indicating a possible extinction threshold for star formation.
We describe the first nearly linear-time approximation algorithms for explicitly given mixed packing/covering linear programs, and for (non-metric) fractional facility location. We also describe the first parallel algorithms requiring only near-linea
r total work and finishing in polylog time. The algorithms compute $(1+epsilon)$-approximate solutions in time (and work) $O^*(N/epsilon^2)$, where $N$ is the number of non-zeros in the constraint matrix. For facility location, $N$ is the number of eligible client/facility pairs.
Spectra for 2D stars in the 1.5D approximation are created from synthetic spectra of 1D non-local thermodynamic equilibrium (NLTE) spherical model atmospheres produced by the PHOENIX code. The 1.5D stars have the spatially averaged Rayleigh-Jeans flu
x of a K3-4 III star, while varying the temperature difference between the two 1D component models ($Delta T_{mathrm{1.5D}}$), and the relative surface area covered. Synthetic observable quantities from the 1.5D stars are fitted with quantities from NLTE and local thermodynamic equilibrium (LTE) 1D models to assess the errors in inferred $T_{mathrm{eff}}$ values from assuming horizontal homogeneity and LTE. Five different quantities are fit to determine the $T_{mathrm{eff}}$ of the 1.5D stars: UBVRI photometric colors, absolute surface flux SEDs, relative SEDs, continuum normalized spectra, and TiO band profiles. In all cases except the TiO band profiles, the inferred $T_{mathrm{eff}}$ value increases with increasing $Delta T_{mathrm{1.5D}}$. In all cases, the inferred $T_{mathrm{eff}}$ value from fitting 1D LTE quantities is higher than from fitting 1D NLTE quantities and is approximately constant as a function of $Delta T_{mathrm{1.5D}}$ within each case. The difference between LTE and NLTE for the TiO bands is caused indirectly by the NLTE temperature structure of the upper atmosphere, as the bands are computed in LTE. We conclude that the difference between $T_{mathrm{eff}}$ values derived from NLTE and LTE modelling is relatively insensitive to the degree of the horizontal inhomogeneity of the star being modeled, and largely depends on the observable quantity being fit.
We present a study of the morphology and intensity of star formation in the host galaxies of eight Palomar-Green quasars using observations with the Hubble Space Telescope. Our observations are motivated by recent evidence for a close relationship be
tween black hole growth and the stellar mass evolution in its host galaxy. We use narrow-band [O II] $lambda$3727, H$beta$, [O III] $lambda$5007 and Pa$alpha$ images, taken with the WFPC2 and NICMOS instruments, to map the morphology of line-emitting regions, and, after extinction corrections, diagnose the excitation mechanism and infer star-formation rates. Significant challenges in this type of work are the separation of the quasar light from the stellar continuum and the quasar-excited gas from the star-forming regions. To this end, we present a novel technique for image decomposition and subtraction of quasar light. Our primary result is the detection of extended line-emitting regions with sizes ranging from 0.5 to 5 kpc and distributed symmetrically around the nucleus, powered primarily by star formation. We determine star-formation rates of order a few tens of M$_odot$/yr. The host galaxies of our target quasars have stellar masses of order $10^{11}$ M$_odot$ and specific star formation rates on a par with those of M82 and luminous infrared galaxies. As such they fall at the upper envelope or just above the star-formation mass sequence in the specific star formation vs stellar mass diagram. We see a clear trend of increasing star formation rate with quasar luminosity, reinforcing the link between the growth of the stellar mass of the host and the black hole mass found by other authors.
We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual solutions
whose costs are within a factor of 1+eps of the optimal cost in time O((r+c)log(n)/eps^2 + n).
Spin qubits have been successfully realized in electrostatically defined, lateral few-electron quantum dot circuits. Qubit readout typically involves spin to charge information conversion, followed by a charge measurement made using a nearby biased q
uantum point contact. It is critical to understand the back-action disturbances resulting from such a measurement approach. Previous studies have indicated that quantum point contact detectors emit phonons which are then absorbed by nearby qubits. We report here the observation of a pronounced back-action effect in multiple dot circuits where the absorption of detector-generated phonons is strongly modified by a quantum interference effect, and show that the phenomenon is well described by a theory incorporating both the quantum point contact and coherent phonon absorption. Our combined experimental and theoretical results suggest strategies to suppress back-action during the qubit readout procedure.
This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards) covering c
onstraints, each of which constrains at most D variables of the problem. (A simple example is Vertex Cover, with D = 2.) The algorithm generalizes previous approximation algorithms for fundamental covering problems and online paging and caching problems.
We use numerical simulations to investigate, for the first time, the joint effect of feedback from supernovae (SNe) and active galactic nuclei (AGN) on the evolution of galaxy cluster X-ray scaling relations. Our simulations are drawn from the Millen
nium Gas Project and are some of the largest hydrodynamical N-body simulations ever carried out. Feedback is implemented using a hybrid scheme, where the energy input into intracluster gas by SNe and AGN is taken from a semi-analytic model of galaxy formation. This ensures that the source of feedback is a population of galaxies that closely resembles that found in the real universe. We show that our feedback model is capable of reproducing observed local X-ray scaling laws, at least for non-cool core clusters, but that almost identical results can be obtained with a simplistic preheating model. However, we demonstrate that the two models predict opposing evolutionary behaviour. We have examined whether the evolution predicted by our feedback model is compatible with observations of high-redshift clusters. Broadly speaking, we find that the data seems to favour the feedback model for z<0.5, and the preheating model at higher redshift. However, a statistically meaningful comparison with observations is impossible, because the large samples of high-redshift clusters currently available are prone to strong selection biases. As the observational picture becomes clearer in the near future, it should be possible to place tight constraints on the evolution of the scaling laws, providing us with an invaluable probe of the physical processes operating in galaxy clusters.
