Local ill-posedness of the 1D Zakharov system

Ginibre-Tsutsumi-Velo (1997) proved local well-posedness for the Zakharov system for any dimension $d$, in the inhomogeneous Sobolev spaces $(u,n)\in H^k(\mathbb{R}^d)\times H^s(\mathbb{R}^d)$ for a range of exponents $k$, $s$ depending on $d$. Here we restrict to dimension $d=1$ and present a few results establishing local ill-posedness for exponent pairs $(k,s)$ outside of the well-posedness regime. The techniques employed are rooted in the work of Bourgain (1993), Birnir-Kenig-Ponce-Svanstedt-Vega (1996), and Christ-Colliander-Tao (2003) applied to the nonlinear Schroedinger equation

On the Scale-Invariant Distribution of the Diffusion Coefficient for Classical Particles Diffusing in Disordered Media.-

The scaling form of the whole distribution P(D) of the random diffusion coefficient D(x) in a model of classically diffusing particles is investigated. The renormalization group approach above the lower critical dimension d=0 is applied to the distribution P(D) using the n-replica approach. In the annealed approximation (n=1), the inverse gaussian distribution is found to be the stable one under rescaling. This identification is made based on symmetry arguments and subtle relations between this model and that of fluc- tuating interfaces studied by Wallace and Zia. The renormalization-group flow for the ratios between consecutive cumulants shows a regime of pure diffusion for small disorder, in which P(D) goes to delta(D-), and a regime of strong disorder where the cumulants grow infinitely large and the diffusion process is ill defined. The boundary between these two regimes is associated with an unstable fixed-point and a subdiffusive behavior: =Ct**(1-d/2). For the quenched case (n goes to 0) we find that unphysical operators are generated raisng doubts on the renormalizability of this model. Implications to other random systems near their lower critical dimension are discussed.Comment: 21 pages, 1 fig. (not included) Use LaTex twic

Linear hyperbolic PDEs with non-commutative time

Motivated by wave or Dirac equations on noncommutative deformations of Minkowski space, linear integro-differential equations of the form $(D+\lambda W)f=0$ are studied, where $D$ is a normal or prenormal hyperbolic differential operator on ${\mathbb R}^n$, $\lambda\in\mathbb C$ is a coupling constant, and $W$ is a regular integral operator with compactly supported kernel. In particular, $W$ can be non-local in time, so that a Hamiltonian formulation is not possible. It is shown that for sufficiently small $|\lambda|$, the hyperbolic character of $D$ is essentially preserved. Unique advanced/retarded fundamental solutions are constructed by means of a convergent expansion in $\lambda$, and the solution spaces are analyzed. It is shown that the acausal behavior of the solutions is well-controlled, but the Cauchy problem is ill-posed in general. Nonetheless, a scattering operator can be calculated which describes the effect of $W$ on the space of solutions of $D$. It is also described how these structures occur in the context of noncommutative Minkowski space, and how the results obtained here can be used for the analysis of classical and quantum field theories on such spaces.Comment: 33 pages, 5 figures. V2: Slight reformulation

Problem Behavior in Children of Chronically Ill Parents: A Meta-Analysis

The aim of this meta-analysis is to examine whether children of chronically ill parents differ from norm groups in problem behavior. We report moderator effects and overall effect sizes for internalizing, externalizing and total problem behavior assessed by children and parents. In fixed effect models, we found a significant overall effect size for internalizing problem behavior (number of studies k = 19, total sample size N = 1,858, Cohen’s d = .23, p < .01) and externalizing problem behavior (k = 13, N = 1,525, d = .09, p < .01) but not for total problem behavior (k = 7; N = 896). Effects for internalizing and externalizing problem behavior were larger in non-cancer studies, in samples including younger children and younger ill parents, in samples defined by low average SES and in studies including parents with longer illness duration. In addition, effects for externalizing problem behavior were larger in studies characterized by a higher percentage of ill mothers and single parents. With exclusive self-report, effect sizes were significant for all problem behaviors. Based on these results, a family-centered approach in health care is recommended

The nucleus ^198 Au investigated with neutron capture and transfer reactions I. Experiments and evaluation

The transfer reaction ^197 Au(d,p)^198 Au was measured at the Tandem Accelerator in Munich. The ^197 Au(n,gamma)^198 Au and ^197 Au(n,e)^198 Au reactions were performed at the High Flux Reactor of ILL, Grenoble. Up to 1560 keV a total of 111 levels were observed by the (d,p) reaction and 125 by the (n,gamma) reaction. For many of the levels, spins and parities were assigned. Additional information was obtained from summed (n,gamma gamma) coincidences measured in Dubna

Superconformal Multi-Black Hole Quantum Mechanics

The quantum mechanics of N slowly-moving charged BPS black holes in five-dimensional ${\cal N}=1$ supergravity is considered. The moduli space metric of the N black holes is derived and shown to admit 4 supersymmetries. A near-horizon limit is found in which the dynamics of widely separated black holes decouples from that of strongly-interacting, near-coincident black holes. This decoupling suggests that the quantum states supported in the near-horizon moduli space can be interpreted as internal states of a single composite black hole carrying all of the charge. The near-horizon theory is shown to have an enhanced D(2,1;0) superconformal symmetry. Eigenstates of the Hamiltonian H of the near-horizon theory are ill-defined due to noncompact regions of the moduli space corresponding to highly redshifted near-coincident black holes. It is argued that one should consider, instead of H eigenstates, eigenstates of $2 L_0 = H+K$, where K is the generator of special conformal transformations. The result is a well-defined Hilbert space with a discrete spectrum describing the N-black hole dynamics.Comment: 17 pages AMSLaTeX with JHEP.cls, using epsf.tex for 3 eps figures. Typos corrected. References adde