Decay and return of internal solitary waves with rotation

Author Posting. © The Author, 2007. This is the author's version of the work. It is posted here by permission of American Institute of Physics for personal use, not for redistribution. The definitive version was published in Physics of Fluids 19 (2007): 026601, doi:10.1063/1.2472509.The effect of rotation on the propagation of internal solitary waves is examined. Wave evolution is followed using a new rotating extension of a fully-nonlinear, weakly nonhydrostatic theory for waves in a two-layer system. When a solitary wave solution of the non-rotating equations is used as the initial condition the wave initially decays by radiation of longer inertia-gravity waves. The radiated inertia-gravity wave always steepens, leading to the formation a secondary solitary-like wave. This decay and re-emergence process then repeats. Eventually a nearly localized wavepacket emerges. It consists of a longwave envelope and shorter, faster solitary-like waves that propagate through the envelope. The radiation from this mature state is very weak, leading to a robust, long-lived structure that may contain as much as 50% of the energy in the initial solitary wave. Interacting packets may either pass through one another, or merge to form a longer packet. The packets appear to be modulated, fully-nonlinear versions of the steadily translating quasi-cnoidal waves.This work was supported by a Woods Hole Oceanographic Institution Mellon Independent Study Award and ONR Grant N000140610798

Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data

We provide formal definitions and efficient secure techniques for - turning noisy information into keys usable for any cryptographic application, and, in particular, - reliably and securely authenticating biometric data. Our techniques apply not just to biometric information, but to any keying material that, unlike traditional cryptographic keys, is (1) not reproducible precisely and (2) not distributed uniformly. We propose two primitives: a "fuzzy extractor" reliably extracts nearly uniform randomness R from its input; the extraction is error-tolerant in the sense that R will be the same even if the input changes, as long as it remains reasonably close to the original. Thus, R can be used as a key in a cryptographic application. A "secure sketch" produces public information about its input w that does not reveal w, and yet allows exact recovery of w given another value that is close to w. Thus, it can be used to reliably reproduce error-prone biometric inputs without incurring the security risk inherent in storing them. We define the primitives to be both formally secure and versatile, generalizing much prior work. In addition, we provide nearly optimal constructions of both primitives for various measures of ``closeness'' of input data, such as Hamming distance, edit distance, and set difference.Comment: 47 pp., 3 figures. Prelim. version in Eurocrypt 2004, Springer LNCS 3027, pp. 523-540. Differences from version 3: minor edits for grammar, clarity, and typo

Spin-torque resonance due to diffusive dynamics at a surface of topological insulator

We investigate spin-orbit torques on magnetization in an insulating ferromagnetic (FM) layer that is brought into a close proximity to a topological insulator (TI). In addition to the well-known field-like spin-orbit torque, we identify an anisotropic anti-damping-like spin-orbit torque that originates in a diffusive motion of conduction electrons. This diffusive torque is vanishing in the limit of zero momentum (i. e. for spatially homogeneous electric field or current), but may, nevertheless, have a strong effect on spin-torque resonance at finite frequency provided external field is neither parallel nor perpendicular to the TI surface. The required electric field configuration can be created by a grated top gate.Comment: 10 page main text, 3 figure

Strongly nonlinear, simple internal waves in continuously-stratified, shallow fluids

© The Author(s), 2011. This article is distributed under the terms of the Creative Commons Attribution 3.0 License. The definitive version was published in Nonlinear Processes in Geophysics 18 (2011): 91-102, doi:10.5194/npg-18-91-2011.Strongly nonlinear internal waves in a layer with arbitrary stratification are considered in the hydrostatic approximation. It is shown that "simple waves" having a variable vertical structure can emerge from a wide class of initial conditions. The equations describing such waves have been obtained using the isopycnal coordinate as a variable. Emergence of simple waves from an initial Gaussian impulse is numerically investigated for different density profiles, from two- and three-layer structure to the continuous one. Besides the first mode, examples of second- and third-mode simple waves are given.KRH is supported by the Office of Naval Research IWISE Program grant N00014-09-1-0227

Effects of rotation and topography on internal solitary waves governed by the rotating Gardner equation

© The Author(s), 2022. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Helfrich, K. R., & Ostrovsky, L. Effects of rotation and topography on internal solitary waves governed by the rotating Gardner equation. Nonlinear Processes in Geophysics, 29(2), (2022): 207–218, https://doi.org/10.5194/npg-29-207-2022.Nonlinear oceanic internal solitary waves are considered under the influence of the combined effects of saturating nonlinearity, Earth's rotation, and horizontal depth inhomogeneity. Here the basic model is the extended Korteweg–de Vries equation that includes both quadratic and cubic nonlinearity (the Gardner equation) with additional terms incorporating slowly varying depth and weak rotation. The complicated interplay between these different factors is explored using an approximate adiabatic approach and then through numerical solutions of the governing variable depth, i.e., the rotating Gardner model. These results are also compared to analysis in the Korteweg–de Vries limit to highlight the effect of the cubic nonlinearity. The study explores several particular cases considered in the literature that included some of these factors to illustrate limitations. Solutions are made to illustrate the relevance of this extended Gardner model for realistic oceanic conditions.This research has been supported by the Office of Naval Research (grant no. N00014-18-1-2542) and National Science Foundation (grant no. OCE-1736698)

Some new aspects of the joint effect of rotation and topography on internal solitary waves.

Author Posting. © American Meteorological Society, 2019. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 49(6), (2019): 1639-1649, doi: 10.1175/JPO-D-18-0154.1.Using a recently developed asymptotic theory of internal solitary wave propagation over a sloping bottom in a rotating ocean, some new qualitative and quantitative features of this process are analyzed for internal waves in a two-layer ocean. The interplay between different singularities—terminal damping due to radiation and disappearing quadratic nonlinearity, and reaching an “internal beach” (e.g., zero lower-layer depth)—is discussed. Examples of the adiabatic evolution of a single solitary wave over a uniformly sloping bottom under realistic conditions are considered in more detail and compared with numerical solutions of the variable-coefficient, rotation-modified Korteweg–de Vries (rKdV) equation.LAO is thankful to Yu. Stepanyants for broad discussions of mutual benefit. KRH was supported by Grant N00014-18-1-2542 from the Office of Naval Research.2020-06-1

Quantum Hall criticality and localization in graphene with short-range impurities at the Dirac point

We explore the longitudinal conductivity of graphene at the Dirac point in a strong magnetic field with two types of short-range scatterers: adatoms that mix the valleys and "scalar" impurities that do not mix them. A scattering theory for the Dirac equation is employed to express the conductance of a graphene sample as a function of impurity coordinates; an averaging over impurity positions is then performed numerically. The conductivity $\sigma$ is equal to the ballistic value $4e^2/\pi h$ for each disorder realization provided the number of flux quanta considerably exceeds the number of impurities. For weaker fields, the conductivity in the presence of scalar impurities scales to the quantum-Hall critical point with $\sigma \simeq 4 \times 0.4 e^2/h$ at half filling or to zero away from half filling due to the onset of Anderson localization. For adatoms, the localization behavior is obtained also at half filling due to splitting of the critical energy by intervalley scattering. Our results reveal a complex scaling flow governed by fixed points of different symmetry classes: remarkably, all key manifestations of Anderson localization and criticality in two dimensions are observed numerically in a single setup.Comment: 17 pages, 4 figure