Global Behavior Of Finite Energy Solutions To The dd-Dimensional Focusing Nonlinear Schr\"odinger Equation

We study the global behavior of finite energy solutions to the $d$-dimensional focusing nonlinear Schr\"odinger equation (NLS), $i \partial_t u+\Delta u+ |u|^{p-1}u=0,$ with initial data $u_0\in H^1,\; x \in R^n$. The nonlinearity power $p$ and the dimension $d$ are such that the scaling index $s=\frac{d}2-\frac2{p-1}$ is between 0 and 1, thus, the NLS is mass-supercritical $(s>0)$ and energy-subcritical $(s<1).$ For solutions with \ME[u_0]<1 (\ME[u_0] stands for an invariant and conserved quantity in terms of the mass and energy of $u_0$), a sharp threshold for scattering and blowup is given. Namely, if the renormalized gradient \g_u of a solution $u$ to NLS is initially less than 1, i.e., \g_u(0)<1, then the solution exists globally in time and scatters in $H^1$ (approaches some linear Schr\"odinger evolution as $t\to\pm\infty$); if the renormalized gradient \g_u(0)>1, then the solution exhibits a blowup behavior, that is, either a finite time blowup occurs, or there is a divergence of $H^1$ norm in infinite time. This work generalizes the results for the 3d cubic NLS obtained in a series of papers by Holmer-Roudenko and Duyckaerts-Holmer-Roudenko with the key ingredients, the concentration compactness and localized variance, developed in the context of the energy-critical NLS and Nonlinear Wave equations by Kenig and Merle.Comment: 57 pages, 4 figures and updated reference

SIMULATED IMPACT OF A REGIONAL SHIFT IN FED CATTLE PRODUCTION ON THE LOCATION OF FED CATTLE SLAUGHTER

During the past decade fed cattle slaughter has relocated to states situated in the southwest plains. Concern has developed that the economic depletion of groundwater used for irrigating feeding activity could result in reduced levels of cattle feeding in that region. A reduction in cattle feeding activity could result in slaughtering plant closures and a relocation in slaughter activity to other regions. A mixed integer programming model was developed to simulate the possible effect of a declining cattle feeding industry in the southwest plains on the location of the fed cattle slaughtering and processing industry. Solution of the model indicated that the primary readjustment to lower levels of cattle feeding in the southwest plains would be in terms of plant and aggregate area volume, not plant location readjustment.Livestock Production/Industries,

ADOPTION OF BACKGROUNDING ON COW-CALF FARMS

A discrete choice model is used to analyze the decision to feed or sell calves at weaning. After accounting for regional factors, results show that operator perceptions toward profitability, risk, and facilities as well as control over production and attention to marketing impacted retained ownership of calves. Farm size had a minimal impact.Livestock Production/Industries,

Renormalization and blow up for charge one equivariant critical wave maps

We prove the existence of equivariant finite time blow up solutions for the wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the sum of a dynamically rescaled ground-state harmonic map plus a radiation term. The local energy of the latter tends to zero as time approaches blow up time. This is accomplished by first "renormalizing" the rescaled ground state harmonic map profile by solving an elliptic equation, followed by a perturbative analysis

Low Temperature Deposition of Si02 Films by ECR

SiO films of high quality have been deposited by Electron Cyclotron Resonance (ECR) at temperatures less than 400 ° C. Chemistries of 02 and 25 % SiHqin Ar were used. Deposition rates of about 220 A/minute were obtained, studying films of typical thicknesses of 1100 A. Characteristics of the films studied include refractive index of 1.467 — 1.477, dielectric strengths of 5.0 — 9.0 MV/cm, dielectric constants of 3.8 — 4.2, and buffered HF etch rates of 19 - 21 A/second. These characteristics were shown to degrade around a deposition temperature of 200 °C, with temperatures on either side of this range yielding better characteristics. Optical emission spectroscopy was also utilized to identify the species present in the plasma

Stable self-similar blow-up dynamics for slightly L2L^2-supercritical generalized KdV equations

In this paper we consider the slightly $L^2$-supercritical gKdV equations $\partial_t u+(u_{xx}+u|u|^{p-1})_x=0$, with the nonlinearity $5<p<5+\varepsilon$ and $0<\varepsilon\ll 1$ . We will prove the existence and stability of a blow-up dynamic with self-similar blow-up rate in the energy space $H^1$ and give a specific description of the formation of the singularity near the blow-up time.Comment: 38 page