Theoretical analysis of the focusing of acoustic waves by two-dimensional sonic crystals

Motivated by a recent experiment on acoustic lenses, we perform numerical calculations based on a multiple scattering technique to investigate the focusing of acoustic waves with sonic crystals formed by rigid cylinders in air. The focusing effects for crystals of various shapes are examined. The dependance of the focusing length on the filling factor is also studied. It is observed that both the shape and filling factor play a crucial role in controlling the focusing. Furthermore, the robustness of the focusing against disorders is studied. The results show that the sensitivity of the focusing behavior depends on the strength of positional disorders. The theoretical results compare favorably with the experimental observations, reported by Cervera, et al. (Phys. Rev. Lett. 88, 023902 (2002)).Comment: 8 figure

New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces

We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.Comment: to appear in GAF

Classification and nondegeneracy of SU(n+1)SU(n+1) Toda system with singular sources

We consider the following Toda system \Delta u_i + \D \sum_{j = 1}^n a_{ij}e^{u_j} = 4\pi\gamma_{i}\delta_{0} \text{in}\mathbb R^2, \int_{\mathbb R^2}e^{u_i} dx -1$,$\delta_0$is Dirac measure at 0, and the coefficients$a_{ij}$form the standard tri-diagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quantization result:$$\sum_{j=1}^n a_{ij}\int_{\R^2}e^{u_j} dx = 4\pi (2+\gamma_i+\gamma_{n+1-i}), \;\;\forall\; 1\leq i \leq n.$$This generalizes the classification result by Jost and Wang for$\gamma_i=0$,$\forall \;1\leq i\leq n$. (ii) We prove that if$\gamma_i+\gamma_{i+1}+...+\gamma_j \notin \mathbb Z$for all$1\leq i\leq j\leq n$, then any solution$u_i$ is \textit{radially symmetric} w.r.t. 0. (iii) We prove that the linearized equation at any solution is \textit{non-degenerate}. These are fundamental results in order to understand the bubbling behavior of the Toda system.Comment: 28 page

An improved geometric inequality via vanishing moments, with applications to singular Liouville equations

We consider a class of singular Liouville equations on compact surfaces motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the Gaussian curvature prescription with conical singularities and Onsager's description of turbulence. We analyse the problem of existence variationally, and show how the angular distribution of the conformal volume near the singularities may lead to improvements in the Moser-Trudinger inequality, and in turn to lower bounds on the Euler-Lagrange functional. We then discuss existence and non-existence results.Comment: some references adde

Organic film thickness influence on the bias stress instability in Sexithiophene Field Effect Transistors

In this paper, the dynamics of bias stress phenomenon in Sexithiophene (T6) Field Effect Transistors (FETs) has been investigated. T6 FETs have been fabricated by vacuum depositing films with thickness from 10 nm to 130 nm on Si/SiO2 substrates. After the T6 film structural analysis by X-Ray diffraction and the FET electrical investigation focused on carrier mobility evaluation, bias stress instability parameters have been estimated and discussed in the context of existing models. By increasing the film thickness, a clear correlation between the stress parameters and the structural properties of the organic layer has been highlighted. Conversely, the mobility values result almost thickness independent

Uniqueness and Nondegeneracy of Ground States for (−Δ)sQ+Q−Qα+1=0(-\Delta)^s Q + Q - Q^{\alpha+1} = 0 in R\mathbb{R}

We prove uniqueness of ground state solutions $Q = Q(|x|) \geq 0$ for the nonlinear equation $(-\Delta)^s Q + Q - Q^{\alpha+1}= 0$ in $\mathbb{R}$, where $0 < s < 1$ and $0 < \alpha < \frac{4s}{1-2s}$ for $s < 1/2$ and $0 < \alpha < \infty$ for $s \geq 1/2$. Here $(-\Delta)^s$ denotes the fractional Laplacian in one dimension. In particular, we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for $s=1/2$ and $\alpha=1$ in [Acta Math., \textbf{167} (1991), 107--126]. As a technical key result in this paper, we show that the associated linearized operator $L_+ = (-\Delta)^s + 1 - (\alpha+1) Q^\alpha$ is nondegenerate; i.\,e., its kernel satisfies $\mathrm{ker}\, L_+ = \mathrm{span}\, \{Q'\}$. This result about $L_+$ proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for nonlinear dispersive PDEs with fractional Laplacians, such as the generalized Benjamin-Ono (BO) and Benjamin-Bona-Mahony (BBM) water wave equations.Comment: 45 page

Nonlinear Dynamical Stability of Newtonian Rotating White Dwarfs and Supermassive Stars

We prove general nonlinear stability and existence theorems for rotating star solutions which are axi-symmetric steady-state solutions of the compressible isentropic Euler-Poisson equations in 3 spatial dimensions. We apply our results to rotating and non-rotating white dwarf, and rotating high density supermassive (extreme relativistic) stars, stars which are in convective equilibrium and have uniform chemical composition. This paper is a continuation of our earlier work ([28])

Finished sequence and assembly of the DUF1220-rich 1q21 region using a haploid human genome

BackgroundAlthough the reference human genome sequence was declared finished in 2003, some regions of the genome remain incomplete due to their complex architecture. One such region, 1q21.1-q21.2, is of increasing interest due to its relevance to human disease and evolution. Elucidation of the exact variants behind these associations has been hampered by the repetitive nature of the region and its incomplete assembly. This region also contains 238 of the 270 human DUF1220 protein domains, which are implicated in human brain evolution and neurodevelopment. Additionally, examinations of this protein domain have been challenging due to the incomplete 1q21 build. To address these problems, a single-haplotype hydatidiform mole BAC library (CHORI-17) was used to produce the first complete sequence of the 1q21.1-q21.2 region.ResultsWe found and addressed several inaccuracies in the GRCh37sequence of the 1q21 region on large and small scales, including genomic rearrangements and inversions, and incorrect gene copy number estimates and assemblies. The DUF1220-encoding NBPF genes required the most corrections, with 3 genes removed, 2 genes reassigned to the 1p11.2 region, 8 genes requiring assembly corrections for DUF1220 domains (~91 DUF1220 domains were misassigned), and multiple instances of nucleotide changes that reassigned the domain to a different DUF1220 subtype. These corrections resulted in an overall increase in DUF1220 copy number, yielding a haploid total of 289 copies. Approximately 20 of these new DUF1220 copies were the result of a segmental duplication from 1q21.2 to 1p11.2 that included two NBPF genes. Interestingly, this duplication may have been the catalyst for the evolutionarily important human lineage-specific chromosome 1 pericentric inversion.ConclusionsThrough the hydatidiform mole genome sequencing effort, the 1q21.1-q21.2 region is complete and misassemblies involving inter- and intra-region duplications have been resolved. The availability of this single haploid sequence path will aid in the investigation of many genetic diseases linked to 1q21, including several associated with DUF1220 copy number variations. Finally, the corrected sequence identified a recent segmental duplication that added 20 additional DUF1220 copies to the human genome, and may have facilitated the chromosome 1 pericentric inversion that is among the most notable human-specific genomic landmarks

Existence and Nonlinear Stability of Rotating Star Solutions of the Compressible Euler-Poisson Equations

We prove existence of rotating star solutions which are steady-state solutions of the compressible isentropic Euler-Poisson (EP) equations in 3 spatial dimensions, with prescribed angular momentum and total mass. This problem can be formulated as a variational problem of finding a minimizer of an energy functional in a broader class of functions having less symmetry than those functions considered in the classical Auchmuty-Beals paper. We prove the nonlinear dynamical stability of these solutions with perturbations having the same total mass and symmetry as the rotating star solution. We also prove local in time stability of W^{1, \infty}(\RR^3) solutions where the perturbations are entropy-weak solutions of the EP equations. Finally, we give a uniform (in time) a-priori estimate for entropy-weak solutions of the EP equations

Search for TeV Scale Physics in Heavy Flavour Decays

The subject of heavy flavour decays as probes for physics beyond the TeV scale is covered from the experimental perspective. Emphasis is placed on the more traditional Beyond the Standard Model topics that have potential for impact in the short term, with the physics explained. We do unabashedly promote our own phemonenology work.Comment: 10 pages, 9 figures (now fixed); Submitted for the SUSY07 proceeding