Curvature effects on phase transitions in chiral magnets

Periodical equilibrium states of magnetization exist in chiral ferromagnetic films, if the constant of antisymmetric exchange (Dzyaloshinskii-Moriya interaction) exceeds some critical value. Here, we demonstrate that this critical value can be significantly modified in curved film. The competition between symmetric and antisymmetric exchange interactions in a curved film can lead to a new type of domain wall which is inclined with respect to the cylinder axis. The wall structure is intermediate between Bloch and N\\u27eel ones. The exact analytical solutions for phase boundary curves and the new domain wall are obtained

Curvature effects on phase transitions in chiral magnets

Periodical equilibrium states of magnetization exist in chiral ferromagnetic films, if the constant of antisymmetric exchange (Dzyaloshinskii-Moriya interaction) exceeds some critical value. Here, we demonstrate that this critical value can be significantly modified in curved film. The competition between symmetric and antisymmetric exchange interactions in a curved film can lead to a new type of domain wall which is inclined with respect to the cylinder axis. The wall structure is intermediate between Bloch and N\'eel ones. The exact analytical solutions for phase boundary curves and the new domain wall are obtained

Stripe patterns in a model for block copolymers

We consider a pattern-forming system in two space dimensions defined by an energy G_e. The functional G_e models strong phase separation in AB diblock copolymer melts, and patterns are represented by {0,1}-valued functions; the values 0 and 1 correspond to the A and B phases. The parameter e is the ratio between the intrinsic, material length scale and the scale of the domain. We show that in the limit (as e goes to 0) any sequence u_e of patterns with uniformly bounded energy G_e(u_e) becomes stripe-like: the pattern becomes locally one-dimensional and resembles a periodic stripe pattern of periodicity O(e). In the limit the stripes become uniform in width and increasingly straight. Our results are formulated as a convergence theorem, which states that the functional G_e Gamma-converges to a limit functional G_0. This limit functional is defined on fields of rank-one projections, which represent the local direction of the stripe pattern. The functional G_0 is only finite if the projection field solves a version of the Eikonal equation, and in that case it is the L^2-norm of the divergence of the projection field, or equivalently the L^2-norm of the curvature of the field. At the level of patterns the converging objects are the jump measures |grad(u_e)| combined with the projection fields corresponding to the tangents to the jump set. The central inequality from Peletier & Roeger, (Archive for Rational Mechanics and Analysis, to appear), provides the initial estimate and leads to weak measure-function-pair convergence. We obtain strong convergence by exploiting the non-intersection property of the jump set.Comment: 56 pages, 8 figures, submitte

Doctor of Philosophy

dissertationShape analysis is a well-established tool for processing surfaces. It is often a first step in performing tasks such as segmentation, symmetry detection, and finding correspondences between shapes. Shape analysis is traditionally employed on well-sampled surfaces where the geometry and topology is precisely known. When the form of the surface is that of a point cloud containing nonuniform sampling, noise, and incomplete measurements, traditional shape analysis methods perform poorly. Although one may first perform reconstruction on such a point cloud prior to performing shape analysis, if the geometry and topology is far from the true surface, then this can have an adverse impact on the subsequent analysis. Furthermore, for triangulated surfaces containing noise, thin sheets, and poorly shaped triangles, existing shape analysis methods can be highly unstable. This thesis explores methods of shape analysis applied directly to such defect-laden shapes. We first study the problem of surface reconstruction, in order to obtain a better understanding of the types of point clouds for which reconstruction methods contain difficulties. To this end, we have devised a benchmark for surface reconstruction, establishing a standard for measuring error in reconstruction. We then develop a new method for consistently orienting normals of such challenging point clouds by using a collection of harmonic functions, intrinsically defined on the point cloud. Next, we develop a new shape analysis tool which is tolerant to imperfections, by constructing distances directly on the point cloud defined as the likelihood of two points belonging to a mutually common medial ball, and apply this for segmentation and reconstruction. We extend this distance measure to define a diffusion process on the point cloud, tolerant to missing data, which is used for the purposes of matching incomplete shapes undergoing a nonrigid deformation. Lastly, we have developed an intrinsic method for multiresolution remeshing of a poor-quality triangulated surface via spectral bisection

NASA Tech Briefs, March 2010

Topics covered include: Software Tool Integrating Data Flow Diagrams and Petri Nets; Adaptive Nulling for Interferometric Detection of Planets; Reducing the Volume of NASA Earth-Science Data; Reception of Multiple Telemetry Signals via One Dish Antenna; Space-Qualified Traveling-Wave Tube; Smart Power Supply for Battery-Powered Systems; Parallel Processing of Broad-Band PPM Signals; Inexpensive Implementation of Many Strain Gauges; Constant-Differential-Pressure Two-Fluid Accumulator; Inflatable Tubular Structures Rigidized with Foams; Power Generator with Thermo-Differential Modules; Mechanical Extraction of Power From Ocean Currents and Tides; Nitrous Oxide/Paraffin Hybrid Rocket Engines; Optimized Li-Ion Electrolytes Containing Fluorinated Ester Co-Solvents; Probabilistic Multi-Factor Interaction Model for Complex Material Behavior; Foldable Instrumented Bits for Ultrasonic/Sonic Penetrators; Compact Rare Earth Emitter Hollow Cathode; High-Precision Shape Control of In-Space Deployable Large Membrane/Thin-Shell Reflectors; Rapid Active Sampling Package; Miniature Lightweight Ion Pump; Cryogenic Transport of High-Pressure-System Recharge Gas; Water-Vapor Raman Lidar System Reaches Higher Altitude; Compact Ku-Band T/R Module for High-Resolution Radar Imaging of Cold Land Processes; Wide-Field-of-View, High-Resolution, Stereoscopic Imager; Electrical Capacitance Volume Tomography with High-Contrast Dielectrics; Wavefront Control and Image Restoration with Less Computing; Polarization Imaging Apparatus; Stereoscopic Machine-Vision System Using Projected Circles; Metal Vapor Arcing Risk Assessment Tool; Performance Bounds on Two Concatenated, Interleaved Codes; Parameterizing Coefficients of a POD-Based Dynamical System; Confidence-Based Feature Acquisition; Algorithm for Lossless Compression of Calibrated Hyperspectral Imagery; Universal Decoder for PPM of any Order; Algorithm for Stabilizing a POD-Based Dynamical System; Mission Reliability Estimation for Repairable Robot Teams; Processing AIRS Scientific Data Through Level 3; Web-Based Requesting and Scheduling Use of Facilities; AutoGen Version 5.0; Time-Tag Generation Script; PPM Receiver Implemented in Software; Tropospheric Emission Spectrometer Product File Readers; Reporting Differences Between Spacecraft Sequence Files; Coordinating "Execute" Data for ISS and Space Shuttle; Database for Safety-Oriented Tracking of Chemicals; Apparatus for Cold, Pressurized Biogeochemical Experiments; Growing B Lymphocytes in a Three-Dimensional Culture System; Tissue-like 3D Assemblies of Human Broncho-Epithelial Cells; Isolation of Resistance-Bearing Microorganisms; Oscillating Cell Culture Bioreactor; and Liquid Cooling/Warming Garment