Lagrangian Based Methods for Coherent Structure Detection

There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows. (C) 2015 AIP Publishing LLC.ONR N000141210665Center for Nonlinear Dynamic

Heavy quarkonium 2S states in light-front quark model

We study the charmonium 2S states $\psi'$ and $\eta_c'$, and the bottomonium 2S states $\Upsilon'$ and $\eta_b'$, using the light-front quark model and the 2S state wave function of harmonic oscillator as the approximation of the 2S quarkonium wave function. The decay constants, transition form factors and masses of these mesons are calculated and compared with experimental data. Predictions of quantities such as Br$(\psi' \to \gamma \eta_c')$ are made. The 2S wave function may help us learn more about the structure of these heavy quarkonia.Comment: 5 latex pages, final version for journal publicatio

A multiple exp-function method for nonlinear differential equations and its application

A multiple exp-function method to exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards ease of use and capability of computer algebra systems, and provides a direct and systematical solution procedure which generalizes Hirota's perturbation scheme. With help of Maple, an application of the approach to the $3+1$ dimensional potential-Yu-Toda-Sasa-Fukuyama equation yields exact explicit 1-wave and 2-wave and 3-wave solutions, which include 1-soliton, 2-soliton and 3-soliton type solutions. Two cases with specific values of the involved parameters are plotted for each of 2-wave and 3-wave solutions.Comment: 12 pages, 16 figure

Finite dimensional integrable Hamiltonian systems associated with DSI equation by Bargmann constraints

The Davey-Stewartson I equation is a typical integrable equation in 2+1 dimensions. Its Lax system being essentially in 1+1 dimensional form has been found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the present paper, this essentially 1+1 dimensional Lax system is further nonlinearized into 1+0 dimensional Hamiltonian systems by taking the Bargmann constraints. It is shown that the resulting 1+0 dimensional Hamiltonian systems are completely integrable in Liouville sense by finding a full set of integrals of motion and proving their functional independence.Comment: 10 pages, in LaTeX, to be published in J. Phys. Soc. Jpn. 70 (2001

Prenatal ketamine exposure causes abnormal development of prefrontal cortex in rat.

Ketamine is commonly used for anesthesia and as a recreational drug. In pregnant users, a potential neurotoxicity in offspring has been noted. Our previous work demonstrated that ketamine exposure of pregnant rats induces affective disorders and cognitive impairments in offspring. As the prefrontal cortex (PFC) is critically involved in emotional and cognitive processes, here we studied whether maternal ketamine exposure influences the development of the PFC in offspring. Pregnant rats on gestational day 14 were treated with ketamine at a sedative dose for 2 hrs, and pups were studied at postnatal day 0 (P0) or P30. We found that maternal ketamine exposure resulted in cell apoptosis and neuronal loss in fetal brain. Upon ketamine exposure in utero, PFC neurons at P30 showed more dendritic branching, while cultured neurons from P0 PFC extended shorter neurites than controls. In addition, maternal ketamine exposure postponed the switch of NR2B/2A expression, and perturbed pre- and postsynaptic protein expression in the PFC. These data suggest that prenatal ketamine exposure impairs neuronal development of the PFC, which may be associated with abnormal behavior in offsprings

A Reanalysis of the Hydrodynamic Theory of Fluid, Polar-Ordered Flocks

I reanalyze the hydrodynamic theory of fluid, polar ordered flocks. I find new linear terms in the hydrodynamic equations which slightly modify the anisotropy, but not the scaling, of the damping of sound modes. I also find that the nonlinearities allowed {\it in equilibrium} do not stabilize long ranged order in spatial dimensions $d=2$; in accord with the Mermin-Wagner theorem. Nonequilibrium nonlinearities {\it do} stabilize long ranged order in $d=2$, as argued by earlier work. Some of these were missed by earlier work; it is unclear whether or not they change the scaling exponents in $d=2$.Comment: 6 pages, no figures. arXiv admin note: text overlap with arXiv:0909.195

Examining exotic structure of proton-rich nucleus 23^{23}Al

The longitudinal momentum distribution (P_{//}) of fragments after one-proton removal from ^{23} Al and reaction cross sections (\sigma_R) for ^{23,24} Al on carbon target at 74A MeV have been measured. The ^{23,24} Al ions were produced through projectile fragmentation of 135 A MeV ^{28} Si primary beam using RIPS fragment separator at RIKEN. P_{//} is measured by a direct time-of-flight (TOF) technique, while \sigma_R is determined using a transmission method. An enhancement in \sigma_R is observed for ^{23} Al compared with ^{24} Al. The P_{//} for ^{22} Mg fragments from ^{23} Al breakup has been obtained for the first time. FWHM of the distributions has been determined to be 232 \pm 28 MeV/c. The experimental data are discussed by using Few-Body Glauber model. Analysis of P_{//} demonstrates a dominant d-wave configuration for the valence proton in ground state of ^{23} Al, indicating that ^{23} Al is not a proton halo nucleus

Dynamics of Scalar Field in Polymer-like Representation

In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to gravity in this framework. A Hamiltonian operator for the scalar field can be well defined in the coupled diffeomorphism invariant Hilbert space, which is both self-adjoint and positive. On the other hand, the Hamiltonian constraint operator for the scalar field coupled to gravity can be well defined in the coupled kinematical Hilbert space. There are 1-parameter ambiguities due to scalar field in the construction of both operators. The results heighten our confidence that there is no divergence within this background independent and diffeomorphism invariant quantization approach of matter coupled to gravity. Moreover, to avoid possible quantum anomaly, the master constraint programme can be carried out in this coupled system by employing a self-adjoint master constraint operator on the diffeomorphism invariant Hilbert space.Comment: 24 pages, accepted for pubilcation in Class. Quant. Gra