Trapped modes in finite quantum waveguides

The Laplace operator in infinite quantum waveguides (e.g., a bent strip or a twisted tube) often has a point-like eigenvalue below the essential spectrum that corresponds to a trapped eigenmode of finite L2 norm. We revisit this statement for resonators with long but finite branches that we call "finite waveguides". Although now there is no essential spectrum and all eigenfunctions have finite L2 norm, the trapping can be understood as an exponential decay of the eigenfunction inside the branches. We describe a general variational formalism for detecting trapped modes in such resonators. For finite waveguides with general cylindrical branches, we obtain a sufficient condition which determines the minimal length of branches for getting a trapped eigenmode. Varying the branch lengths may switch certain eigenmodes from non-trapped to trapped states. These concepts are illustrated for several typical waveguides (L-shape, bent strip, crossing of two stripes, etc.). We conclude that the well-established theory of trapping in infinite waveguides may be incomplete and require further development for being applied to microscopic quantum devices

Differentially Private Publication of Sparse Data

The problem of privately releasing data is to provide a version of a dataset without revealing sensitive information about the individuals who contribute to the data. The model of differential privacy allows such private release while providing strong guarantees on the output. A basic mechanism achieves differential privacy by adding noise to the frequency counts in the contingency tables (or, a subset of the count data cube) derived from the dataset. However, when the dataset is sparse in its underlying space, as is the case for most multi-attribute relations, then the effect of adding noise is to vastly increase the size of the published data: it implicitly creates a huge number of dummy data points to mask the true data, making it almost impossible to work with. We present techniques to overcome this roadblock and allow efficient private release of sparse data, while maintaining the guarantees of differential privacy. Our approach is to release a compact summary of the noisy data. Generating the noisy data and then summarizing it would still be very costly, so we show how to shortcut this step, and instead directly generate the summary from the input data, without materializing the vast intermediate noisy data. We instantiate this outline for a variety of sampling and filtering methods, and show how to use the resulting summary for approximate, private, query answering. Our experimental study shows that this is an effective, practical solution, with comparable and occasionally improved utility over the costly materialization approach

Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids

In a three-dimensional Fermi liquid, quasiparticles near the Fermi surface may possess a Berry curvature. We show that if the Berry curvature has a nonvanishing flux through the Fermi surface, the particle number associated with this Fermi surface has a triangle anomaly in external electromagnetic fields. We show how Landau's Fermi liquid theory should be modified to take into account the Berry curvature. We show that the "chiral magnetic effect" also emerges from the Berry curvature flux.Comment: 5 pages, published versio

Global solutions of the Landau--Lifshitz--Baryakhtar equation

The Landau--Lifshitz--Baryakhtar (LLBar) equation is a generalisation of the Landau--Lifshitz--Gilbert and the Landau--Lifshitz--Bloch equations which takes into account contributions from nonlocal damping and is valid at moderate temperature below the Curie temperature. Therefore, it is used to explain some discrepancies between the experimental observations and the known theories in various problems on magnonics and magnetic domain-wall dynamics. In this paper, the existence and uniqueness of global weak, strong, and regular solutions to LLBar equation are proven. H\"older continuity of the solution is also discussed.Comment: title changed, existence & uniqueness of global weak and strong solutions are show

Stable C1C^1-conforming finite element methods for the Landau--Lifshitz--Baryakhtar equation

The Landau--Lifshitz--Baryakhtar equation describes the evolution of magnetic spin field in magnetic materials at elevated temperature below the Curie temperature, when long-range interactions and longitudinal dynamics are taken into account. We propose two linear fully-discrete $C^1$-conforming methods to solve the problem, namely a semi-implicit Euler method and a semi-implicit BDF method, and show that these schemes are unconditionally stable. Error analysis is performed which shows optimal convergence rates in each case. Numerical results corroborate our theoretical results

Synthesis of Silver Nanoparticles using Non-Fouling Microfluidic Devices with Fast Mixing

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.Silver nanoparticles were synthesized in an impinging jet reactor using silver nitrate as a precursor, trisodium citrate as a stabilizer and sodium borohydride as a reducing agent. The effect of mixing time on the nanoparticle morphology was investigated by means of UV-Vis spectroscopy, used as a characterization tool. It was observed that as the mixing time became shorter the nanoparticles retained a similar average diameter but produced more aggregates. The mixing time was characterized using the ‘Villermaux-Dushmann’ reaction system together with the Interaction by Exchange with the Mean mixing model. The mixing time achieved was of the order of a few ms for flowrates in the range 18-28 ml/min. The synthesis of silver nanoparticles was carried out at the same flowrates to link mixing time to silver nanoparticle morphology

Simple Combined Model for Nonlinear Excitations in DNA

We propose a new simple model for DNA denaturation bases on the pendulum model of Englander\cite{A1} and the microscopic model of Peyrard {\it et al.},\cite{A3} so called "combined model". The main parameters of our model are: the coupling constant $k$ along each strand, the mean stretching $y^\ast$ of the hydrogen bonds, the ratio of the damping constant and driven force $\gamma/F$. We show that both the length $L$ of unpaired bases and the velocity $v$ of kinks depend on not only the coupling constant $k$ but also the temperature $T$. Our results are in good agreement with previous works.Comment: 6 pages, 10 figures, submitted to Phys. Rev.

Indochinese Mental Health In North America: Measures, Status, and Treatments

The massive influx of Indochinese refugees and immigrants to North America since the end of the Indochina war, especially to the United States of America, has resulted in numerous multi-disciplinary efforts to document and study their mental well-being. As a group, Indochinese Americans arrived from war-torn countries where many had experienced various forms of trauma, poverty, and oppression. Their pre-migration experiences, and experiences in adjusting and adapting to the new life in the host society have influenced their mental health status and overall quality of life in various ways. This paper analyzes and synthesizes a wealth of multi-disciplinary research on the mental health of Indochinese Americans over the course of two decades. The content of the paper encompasses three important dimensions: measures, status, and treatment. Practical implications are presented and discussed around each dimension of mental health research