The existence and stability of solutions to nonlinear operator differential equation

Existance and stability of solutions to nonlinear operator differential equatio

Spectral techniques in jet noise theory

Spectral analysis techniques applied to Lighthill aerodynamic sound equation for unified jet noise theor

The existence and stability of nonlinear wave equations

Second order nonlinear wave equation solution on Hilbert space with stability and uniquenes

Some applications of jet noise theory

Some applications of jet noise theorie

Stability theory of nonlinear operational differential equations in Hilbert spaces

Stability theory of nonlinear operational differential equations in Hilbert space

Spectral Analysis of Elastic Waves Scattered by Objects with Smooth Surfaces

This is a summary of the research on NDE performed during the last two years by the authors and Professor W. Sachse and Messrs . S. Sancar and G. C. C. Ku of the Department of Theoretical and Applied Mechanics at Cornell University. The report is divided into three parts: (1) Theoretical Spectra-Results based on the method of wave function expansion and the method of transition matrix (T-matrix) will be presented for the scattering by a circular cylindrical, elliptic cylindrical, spherical, and spheroidal (prolate or oblate) inclusions in solids. Additional results for the scattering by two circular cylindrical inclusions will also be shown. (2) Interpretation of Spectra - Spectra of a fluid inclusion may be interpreted on the basis of the theory of normal modes, and those of a cavity from the principle of interference. Spectra for two cylindrical cavities exhibit new features which are related to the interferences of waves diffracted by each cavity. (3) Comparison with Experiments - Some of the theoretical spectra are compared with experimental results obtained by Professor W. Sachse and his associates

Hydrodynamic scaling from the dynamics of relativistic quantum field theory

Hydrodynamic behavior is a general feature of interacting systems with many degrees of freedom constrained by conservation laws. To date hydrodynamic scaling in relativistic quantum systems has been observed in many high energy settings, from cosmic ray detections to accelerators, with large particle multiplicity final states. Here we show first evidence for the emergence of hydrodynamic scaling in the dynamics of a relativistic quantum field theory. We consider a simple scalar $\lambda \phi^4$ model in 1+1 dimensions in the Hartree approximation and study the dynamics of two colliding kinks at relativistic speeds as well as the decay of a localized high energy density region. The evolution of the energy-momentum tensor determines the dynamical local equation of state and allows the measurement of the speed of sound. Hydrodynamic scaling emerges at high local energy densities.Comment: 4 pages, 4 color eps figures, uses RevTex, v2 some typos corrected and references adde

An integrated genomic analysis of lung cancer reveals loss of DUSP4 in EGFR-mutant tumors.

To address the biological heterogeneity of lung cancer, we studied 199 lung adenocarcinomas by integrating genome-wide data on copy number alterations and gene expression with full annotation for major known somatic mutations in this cancer. This showed non-random patterns of copy number alterations significantly linked to EGFR and KRAS mutation status and to distinct clinical outcomes, and led to the discovery of a striking association of EGFR mutations with underexpression of DUSP4, a gene within a broad region of frequent single-copy loss on 8p. DUSP4 is involved in negative feedback control of EGFR signaling, and we provide functional validation for its role as a growth suppressor in EGFR-mutant lung adenocarcinoma. DUSP4 loss also associates with p16/CDKN2A deletion and defines a distinct clinical subset of lung cancer patients. Another novel observation is that of a reciprocal relationship between EGFR and LKB1 mutations. These results highlight the power of integrated genomics to identify candidate driver genes within recurrent broad regions of copy number alteration and to delineate distinct oncogenetic pathways in genetically complex common epithelial cancers