An estimate for the Morse index of a Stokes wave

Stokes waves are steady periodic water waves on the free surface of an infinitely deep irrotational two dimensional flow under gravity without surface tension. They can be described in terms of solutions of the Euler-Lagrange equation of a certain functional. This allows one to define the Morse index of a Stokes wave. It is well known that if the Morse indices of the elements of a set of non-singular Stokes waves are bounded, then none of them is close to a singular one. The paper presents a quantitative variant of this result.Comment: This version contains an additional reference and some minor change

Self-Similar Blowup Solutions to the 2-Component Camassa-Holm Equations

In this article, we study the self-similar solutions of the 2-component Camassa-Holm equations% \begin{equation} \left\{ \begin{array} [c]{c}% \rho_{t}+u\rho_{x}+\rho u_{x}=0 m_{t}+2u_{x}m+um_{x}+\sigma\rho\rho_{x}=0 \end{array} \right. \end{equation} with \begin{equation} m=u-\alpha^{2}u_{xx}. \end{equation} By the separation method, we can obtain a class of blowup or global solutions for $\sigma=1$ or $-1$. In particular, for the integrable system with $\sigma=1$, we have the global solutions:% \begin{equation} \left\{ \begin{array} [c]{c}% \rho(t,x)=\left\{ \begin{array} [c]{c}% \frac{f\left( \eta\right) }{a(3t)^{1/3}},\text{ for }\eta^{2}<\frac {\alpha^{2}}{\xi} 0,\text{ for }\eta^{2}\geq\frac{\alpha^{2}}{\xi}% \end{array} \right. ,u(t,x)=\frac{\overset{\cdot}{a}(3t)}{a(3t)}x \overset{\cdot\cdot}{a}(s)-\frac{\xi}{3a(s)^{1/3}}=0,\text{ }a(0)=a_{0}% >0,\text{ }\overset{\cdot}{a}(0)=a_{1} f(\eta)=\xi\sqrt{-\frac{1}{\xi}\eta^{2}+\left( \frac{\alpha}{\xi}\right) ^{2}}% \end{array} \right. \end{equation} where $\eta=\frac{x}{a(s)^{1/3}}$ with $s=3t;$ $\xi>0$ and $\alpha\geq0$ are arbitrary constants.\newline Our analytical solutions could provide concrete examples for testing the validation and stabilities of numerical methods for the systems.Comment: 5 more figures can be found in the corresponding journal paper (J. Math. Phys. 51, 093524 (2010) ). Key Words: 2-Component Camassa-Holm Equations, Shallow Water System, Analytical Solutions, Blowup, Global, Self-Similar, Separation Method, Construction of Solutions, Moving Boundar

Interferometer for Low-Uncertainty Vector Metrology

A simplified schematic diagram of a tilt-sensing unequal-path interferometer set up to measure the orientation of the normal vector of one surface of a cube mounted on a structure under test is described herein. This interferometer has been named a "theoferometer" to express both its interferometric nature and the intention to use it instead of an autocollimating theodolite. The theoferometer optics are mounted on a plate, which is in turn mounted on orthogonal air bearings for near-360 rotation in azimuth and elevation. Rough alignment of the theoferometer to the test cube is done by hand, with fine position adjustment provided by a tangent arm drive using linear inchwormlike motors

A Governance Perspective for System-of-Systems

The operating landscape of 21st century systems is characteristically ambiguous, emergent, and uncertain. These characteristics affect the capacity and performance of engineered systems/enterprises. In response, there are increasing calls for multidisciplinary approaches capable of confronting increasingly ambiguous, emergent, and uncertain systems. System of Systems Engineering (SoSE) is an example of such an approach. A key aspect of SoSE is the coordination and the integration of systems to enable ‘system-of-systems’ capabilities greater than the sum of the capabilities of the constituent systems. However, there is a lack of qualitative studies exploring how coordination and integration are achieved. The objective of this research is to revisit SoSE utility as a potential multidisciplinary approach and to suggest ‘governance’ as the basis for enabling ‘system-of-systems’ coordination and integration. In this case, ‘governance’ is concerned with direction, oversight, and accountability of ‘system-of-systems.’ ‘Complex System Governance’ is a new and novel basis for improving ‘system-of-system’ performance through purposeful design, execution, and evolution of essential metasystem functions.

Extracting Structural Information of a Heteropolymer from Force-Extension Curves

We present a theory for the reverse analysis on the sequence information of a single H/P two-letter random hetero-polymer (RHP) from its force-extension(f-z) curves during quasi static stretching. Upon stretching of a self-assembled RHP, it undergoes several structural transitions. The typical elastic response of a hetero-polymeric globule is a set of overlapping saw-tooth patterns. With consideration of the height and the position of the overlapping saw-tooth shape, we analyze the possibility of extracting the binding energies of the internal domains and the corresponding block sizes of the contributing conformations.Comment: 5 figures 7 page

Acoustoelectric effect in a finite-length ballistic quantum channel

The dc current induced by a coherent surface acoustic wave (SAW) of wave vector q in a ballistic channel of length L is calculated. The current contains two contributions, even and odd in q. The even current exists only in a asymmetric channel, when the electron reflection coefficients r_1 and r_2 at both channel ends are different. The direction of the even current does not depend on the direction of the SAW propagation, but is reversed upon interchanging r_1 and r_2. The direction of the odd current is correlated with the direction of the SAW propagation, but is insensitive to the interchange of r_1 and r_2. It is shown that both contributions to the current are non zero only when the electron reflection coefficients at the channel ends are energy dependent. The current exhibits geometric oscillations as function of qL. These oscillations are the hallmark of the coherence of the SAW and are completely washed out when the current is induced by a flux of non-coherent phonons. The results are compared with those obtained previously by different methods and under different assumptions.Comment: 7 pages, 2 figure

Steep sharp-crested gravity waves on deep water

A new type of steady steep two-dimensional irrotational symmetric periodic gravity waves on inviscid incompressible fluid of infinite depth is revealed. We demonstrate that these waves have sharper crests in comparison with the Stokes waves of the same wavelength and steepness. The speed of a fluid particle at the crest of new waves is greater than their phase speed.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let

Database, Features, and Machine Learning Model to Identify Thermally Driven Metal-Insulator Transition Compounds

Metal-insulator transition (MIT) compounds are materials that may exhibit insulating or metallic behavior, depending on the physical conditions, and are of immense fundamental interest owing to their potential applications in emerging microelectronics. There is a dearth of thermally-driven MIT materials, however, which makes delineating these compounds from those that are exclusively insulating or metallic challenging. Here we report a material database comprising temperature-controlled MITs (and metals and insulators with similar chemical composition and stoichiometries to the MIT compounds) from high quality experimental literature, built through a combination of materials-domain knowledge and natural language processing. We featurize the dataset using compositional, structural, and energetic descriptors, including two MIT relevant energy scales, an estimated Hubbard interaction and the charge transfer energy, as well as the structure-bond-stress metric referred to as the global-instability index (GII). We then perform supervised classification, constructing three electronic-state classifiers: metal vs non-metal (M), insulator vs non-insulator (I), and MIT vs non-MIT (T). We identify two important descriptors that separate metals, insulators, and MIT materials in a 2D feature space: the average deviation of the covalent radius and the range of the Mendeleev number. We further elaborate on other important features (GII and Ewald energy), and examine how they affect classification of binary vanadium and titanium oxides. We discuss the relationship of these atomic features to the physical interactions underlying MITs in the rare-earth nickelate family. Last, we implement an online version of the classifiers, enabling quick probabilistic class predictions by uploading a crystallographic structure file

Evidence for Alteration of Gene Regulatory Networks through MicroRNAs of the HIV-Infected Brain: Novel Analysis of Retrospective Cases

HIV infection disturbs the central nervous system (CNS) through inflammation and glial activation. Evidence suggests roles for microRNA (miRNA) in host defense and neuronal homeostasis, though little is known about miRNAs' role in HIV CNS infection. MiRNAs are non-coding RNAs that regulate gene translation through post-transcriptional mechanisms. Messenger-RNA profiling alone is insufficient to elucidate the dynamic dance of molecular expression of the genome. We sought to clarify RNA alterations in the frontal cortex (FC) of HIV-infected individuals and those concurrently infected and diagnosed with major depressive disorder (MDD). This report is the first published study of large-scale miRNA profiling from human HIV-infected FC. The goals of this study were to: 1. Identify changes in miRNA expression that occurred in the frontal cortex (FC) of HIV individuals, 2. Determine whether miRNA expression profiles of the FC could differentiate HIV from HIV/MDD, and 3. Adapt a method to meaningfully integrate gene expression data and miRNA expression data in clinical samples. We isolated RNA from the FC (n = 3) of three separate groups (uninfected controls, HIV, and HIV/MDD) and then pooled the RNA within each group for use in large-scale miRNA profiling. RNA from HIV and HIV/MDD patients (n = 4 per group) were also used for non-pooled mRNA analysis on Affymetrix U133 Plus 2.0 arrays. We then utilized a method for integrating the two datasets in a Target Bias Analysis. We found miRNAs of three types: A) Those with many dysregulated mRNA targets of less stringent statistical significance, B) Fewer dysregulated target-genes of highly stringent statistical significance, and C) unclear bias. In HIV/MDD, more miRNAs were downregulated than in HIV alone. Specific miRNA families at targeted chromosomal loci were dysregulated. The dysregulated miRNAs clustered on Chromosomes 14, 17, 19, and X. A small subset of dysregulated genes had many 3′ untranslated region (3′UTR) target-sites for dysregulated miRNAs. We provide evidence that certain miRNAs serve as key elements in gene regulatory networks in HIV-infected FC and may be implicated in neurobehavioral disorder. Finally, our data indicates that some genes may serve as hubs of miRNA activity

Functional diversification of maize RNA polymerase IV and V subtypes via alternative catalytic subunits.

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