Cusp-scaling behavior in fractal dimension of chaotic scattering

A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal dimension of the chaotic set for such a bifurcation. Our analysis and numerical computations in both two- and three-degrees-of-freedom systems suggest a striking feature associated with these subtle bifurcations: the dimension typically exhibits a sharp, cusplike local minimum at the bifurcation.Comment: 4 pages, 4 figures, Revte

CFD analysis of jet mixing in low NOx flametube combustors

The Rich-burn/Quick-mix/Lean-burn (RQL) combustor was identified as a potential gas turbine combustor concept to reduce NO(x) emissions in High Speed Civil Transport (HSCT) aircraft. To demonstrate reduced NO(x) levels, cylindrical flametube versions of RQL combustors are being tested at NASA Lewis Research Center. A critical technology needed for the RQL combustor is a method of quickly mixing by-pass combustion air with rich-burn gases. Jet mixing in a cylindrical quick-mix section was numerically analyzed. The quick-mix configuration was five inches in diameter and employed twelve radial-inflow slots. The numerical analyses were performed with an advanced, validated 3-D Computational Fluid Dynamics (CFD) code named REFLEQS. Parametric variation of jet-to-mainstream momentum flux ratio (J) and slot aspect ratio was investigated. Both non-reacting and reacting analyses were performed. Results showed mixing and NO(x) emissions to be highly sensitive to J and slot aspect ratio. Lowest NO(x) emissions occurred when the dilution jet penetrated to approximately mid-radius. The viability of using 3-D CFD analyses for optimizing jet mixing was demonstrated

Frailty and the Burden of Concurrent and Incident Disability in Patients With Cirrhosis: A Prospective Cohort Study.

Frailty results from the chronic effects of malnutrition and muscle wasting in patients with cirrhosis. It is well-established that frailty is strongly associated with mortality in this population. However, little is known of its relationship with physical disability, a critical patient-centered outcome. Adults with cirrhosis underwent outpatient testing of frailty using the Liver Frailty Index (LFI) and disability using activities of daily living (ADL; range 0-6) and Instrumental ADL (IADL; range 0-8) scales at one center between 2012 and 2016. We used adjusted multilevel logistic mixed-effects regression to test the association between frailty and current disability (impairment with ≥1 ADL or IADL) and incident disability at 6 months among those without baseline disability. Of the 983 participants, 20% were robust, 32% were less robust, 33% were prefrail, and 15% were frail; 587 (60%) had at least 1 assessment. The percentage of participants with at least 1 baseline ADL or IADL impairment was 28% and 37%, respectively. In adjusted regression models, each point LFI increase was associated with a 3.3 and 4.6 higher odds of current difficulty with at least 1 ADL and IADL (P < 0.001 for each), respectively. Among participants without baseline disability, each point LFI increase was associated with a 2.6 and 1.7 higher odds of having difficulty with at least 1 ADL and IADL at 6 months, respectively. Conclusion: Frailty is strongly associated with concurrent and incident disability in patients with cirrhosis. In the clinic, the LFI can be used to identify those in greatest need for additional support/resources to maintain functional independence. In research settings, the LFI may help to identify an enriched population for clinical trials of interventions aimed at those most vulnerable to disability

Dissipative chaotic scattering

We show that weak dissipation, typical in realistic situations, can have a metamorphic consequence on nonhyperbolic chaotic scattering in the sense that the physically important particle-decay law is altered, no matter how small the amount of dissipation. As a result, the previous conclusion about the unity of the fractal dimension of the set of singularities in scattering functions, a major claim about nonhyperbolic chaotic scattering, may not be observable.Comment: 4 pages, 2 figures, revte

Validity of numerical trajectories in the synchronization transition of complex systems

We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown {\it via} unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly non-hyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization state. There are potentially severe consequences of these facts on the validity of the computer-generated trajectories obtained from dynamical systems whose synchronization manifolds share the same non-hyperbolic properties.Comment: 4 pages, 4 figure

Post-Newtonian Models of Binary Neutron Stars

Using an energy variational method, we calculate quasi-equilibrium configurations of binary neutron stars modeled as compressible triaxial ellipsoids obeying a polytropic equation of state. Our energy functional includes terms both for the internal hydrodynamics of the stars and for the external orbital motion. We add the leading post-Newtonian (PN) corrections to the internal and gravitational energies of the stars, and adopt hybrid orbital terms which are fully relativistic in the test-mass limit and always accurate to PN order. The total energy functional is varied to find quasi-equilibrium sequences for both corotating and irrotational binaries in circular orbits. We examine how the orbital frequency at the innermost stable circular orbit depends on the polytropic index n and the compactness parameter GM/Rc^2. We find that, for a given GM/Rc^2, the innermost stable circular orbit along an irrotational sequence is about 17% larger than the innermost secularly stable circular orbit along the corotating sequence when n=0.5, and 20% larger when n=1. We also examine the dependence of the maximum neutron star mass on the orbital frequency and find that, if PN tidal effects can be neglected, the maximum equilibrium mass increases as the orbital separation decreases.Comment: 53 pages, LaTex, 9 figures as 10 postscript files, accepted by Phys. Rev. D, replaced version contains updated reference

Knight Field Enabled Nuclear Spin Polarization in Single Quantum Dots

We demonstrate dynamical nuclear spin polarization in the absence of an external magnetic field, by resonant circularly polarized optical excitation of a single electron or hole charged quantum dot. Optical pumping of the electron spin induces an effective inhomogeneous magnetic (Knight) field that determines the direction along which nuclear spins could polarize and enables nuclear-spin cooling by suppressing depolarization induced by nuclear dipole-dipole interactions. Our observations suggest a new mechanism for spin-polarization where spin exchange with an electron reservoir plays a crucial role. These experiments constitute a first step towards quantum measurement of the Overhauser field.Comment: 5 pages, 3 figure

Solving the Darwin problem in the first post-Newtonian approximation of general relativity

We analytically calculate the equilibrium sequence of the corotating binary stars of incompressible fluid in the first post-Newtonian(PN) approximation of general relativity. By calculating the total energy and total angular momentum of the system as a function of the orbital separation, we investigate the innermost stable circular orbit for corotating binary(we call it ISCCO). It is found that by the first PN effect, the orbital separation of the binary at the ISCCO becomes small with increase of the compactness of each star, and as a result, the orbital angular velocity at the ISCCO increases. These behaviors agree with previous numerical works.Comment: 33 pages, revtex, 4 figures(eps), accepted for publication in Phys. Rev.