Phase separation of binary condensates in harmonic and lattice potentials

We propose a modified Gaussian ansatz to study binary condensates, trapped in harmonic and optical lattice potentials, both in miscible and immiscible domains. The ansatz is an apt one as it leads to the smooth transition from miscible to immiscible domains without any {\em a priori} assumptions. In optical lattice potentials, we analyze the squeezing of the density profiles due to the increase in the depth of the optical lattice potential. For this we develop a model with three potential wells, and define the relationship between the lattice depth and profile of the condensate.Comment: 13 pages, 11 figures, additional references adde

Stabilization of Unstable Procedures: The Recursive Projection Method

Fixed-point iterative procedures for solving nonlinear parameter dependent problems can converge for some interval of parameter values and diverge as the parameter changes. The Recursive Projection Method (RPM), which stabilizes such procedures by computing a projection onto the unstable subspace is presented. On this subspace a Newton or special Newton iteration is performed, and the fixed-point iteration is used on the complement. As continuation in the parameter proceeds, the projection is efficiently updated, possibly increasing or decreasing the dimension of the unstable subspace. The method is extremely effective when the dimension of the unstable subspace is small compared to the dimension of the system. Convergence proofs are given and pseudo-arclength continuation on the unstable subspace is introduced to allow continuation past folds. Examples are presented for an important application of the RPM in which a “black-box” time integration scheme is stabilized, enabling it to compute unstable steady states. The RPM can also be used to accelerate iterative procedures when slow convergence is due to a few slowly decaying modes

Bosonization of non-relativistic fermions on a circle: Tomonaga's problem revisited

We use the recently developed tools for an exact bosonization of a finite number $N$ of non-relativistic fermions to discuss the classic Tomonaga problem. In the case of noninteracting fermions, the bosonized hamiltonian naturally splits into an O$(N)$ piece and an O$(1)$ piece. We show that in the large-N and low-energy limit, the O$(N)$ piece in the hamiltonian describes a massless relativistic boson, while the O$(1)$ piece gives rise to cubic self-interactions of the boson. At finite $N$ and high energies, the low-energy effective description breaks down and the exact bosonized hamiltonian must be used. We also comment on the connection between the Tomonaga problem and pure Yang-Mills theory on a cylinder. In the dual context of baby universes and multiple black holes in string theory, we point out that the O$(N)$ piece in our bosonized hamiltonian provides a simple understanding of the origin of two different kinds of nonperturbative O$(e^{-N})$ corrections to the black hole partition function.Comment: latex, 28 pages, 5 epsf figure

Stability of networks of delay-coupled delay oscillators

Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When the local dynamical stability of the network is plotted as a function of the two delays then a pattern of tongues is revealed. Exploiting a link between structure and dynamics, we identify conditions under which perturbations of the topology have a strong impact on the stability. If these critical regions are avoided the local stability of large random networks can be well approximated analytically

The effect of weight, body mass index, age, sex, and race on plasma concentrations of subcutaneous sumatriptan: a pooled analysis.

Objective/backgroundFactors such as body size (weight and body mass index [BMI]), age, sex, and race might influence the clinical response to sumatriptan. We evaluated the impact of these covariates on the plasma concentration (Cp) profile of sumatriptan administered subcutaneously.MethodsWe conducted three pharmacokinetic studies of subcutaneous sumatriptan in 98 healthy adults. Sumatriptan was administered subcutaneously (236 administrations) as either DFN-11 3 mg, a novel 0.5 mL autoinjector being developed by Dr. Reddy's Laboratories; Imitrex(®) (Sumatriptan) injection 3 mg or 6 mg (6 mg/0.5 mL); or Imitrex STATdose 4 mg or 6 mg (0.5 mL). Blood was sampled for 12 hours to determine sumatriptan Cp. Maximum Cp (Cmax), area under the curve during the first 2 hours (AUC0-2), and total area under the curve (AUC0-∞) were determined using noncompartmental methods. Post hoc analyses were conducted to determine the relationship between these exposure metrics and each of body weight, BMI, age, sex, and race (categorized as white, black, or others).ResultsBoth weight and BMI correlated negatively with each exposure metric for each treatment group. Across all treatment groups, AUC0-2 for subjects with BMI less than or equal to median value was 1.03-1.12 times the value for subjects with BMI more than median value. For subjects with BMI less than or equal to median value receiving DFN-11, median AUC0-2 was slightly less than that for subjects with BMI more than median value receiving Imitrex 4 mg and larger than that for subjects with BMI more than median value receiving Imitrex 3 mg. Results were similar for the other exposure metrics and for weight. Exposure was higher in women than in men, which can be attributed in part to differences in weight. There was no relationship between exposure and age. For DFN-11, AUC0-2 and AUC0-∞ were lower in nonwhites compared with whites; the ratio of median values was 0.84 and 0.89, respectively. A similar, nonstatistically significant, trend was observed in the other products (ratio of median values ranging from 0.84 to 0.89).ConclusionWeight and BMI appear to be important covariates for sumatriptan exposure: subjects with lower values for either metric of body size have higher systemic exposure compared with subjects with higher values. Additional studies are required to determine if doses of subcutaneous sumatriptan may be adjusted based on BMI for comparable efficacy and a potentially improved tolerability profile