An alternative to the Allen-Cahn phase field model for interfaces in solids - numerical efficiency

The derivation of the Allen-Cahn and Cahn-Hilliard equations is based on the Clausius-Duhem inequality. This is not a derivation in the strict sense of the word, since other phase field equations can be fomulated satisfying this inequality. Motivated by the form of sharp interface problems, we formulate such an alternative equation and compare the properties of the models for the evolution of phase interfaces in solids, which consist of the elasticity equations and the Allen-Cahn equation or the alternative equation. We find that numerical simulations of phase interfaces with small interface energy based on the alternative model are more effective then simulations based on the Allen-Cahn model.Comment: arXiv admin note: text overlap with arXiv:1505.0544

Projections of scan patterns on human retina

Fundus camera tracks eye movements by using camera optics with the aid of an inverted system. Camera provides a flying-spot circular scanning light source in the normal film plane and a broadband photodetector in position normally occupied by light source

Scanning technique for tracking small eye-movements

Scanning technique images spot of blue light on fundus, measures variations in reflectance of spot and compares reflectance pattern with a stored reference pattern. Method then converts the difference from stored pattern into infrared eye motion

Contact Angle Measurement of Dental Restorative Materials by Drop Profile Image Analysis

The capability of initial microbial adhesion to dental restorative composites surface is influenced by the surface wettability of the materials. The common method to evaluate surface wettability of materials is contact angle measurement. The existing conventional method to measure contact angle is by means of a contact angle (CA)-Goniometer device, which is less practically applicable in clinical circumstances. Therefore, a more practical and applicable method is needed to measure contact angle in clinical circumstances. This research was performed to compare between contact angles measured by means of a CA-Goniometer device and a new practical method of drop profile image analysis. In addition, since there were two different formulas that can be used to calculate contact angle value from a drop profile image, then we also need to evaluate which formula is more reliable to be used. Tests were carried out using three composite discs (Clearfill-Kuraray Medical, Inc.) sample and deionised water for different measurement procedures. One drop of 3µl liquid was dropped onto the surface of the composite discs, and the drop profile image was captured by means of a customized home-made device connected to a digital camera. Two different formulas were used to calculate the contact angle value from the drop profile image, namely the “linier gradient equation” and the “tangential line”. The contact angle values obtained from the two different formulas were compared with the value obtained from the conventional method descriptively. Tests were carried out using three composite discs (Clearfill-Kuraray Medical, Inc.) sample and deionised water for different measurement procedures. One drop of 3µl liquid was dropped onto the surface of the composite discs, and the drop profile image was captured by means of a customized home-made device connected to a digital camera. Two different formulas were used to calculate the contact angle value from the drop profile image, namely the “linier gradient equation” and the “tangential line”. The contact angle values obtained from the two different formulas were compared with the value obtained from the conventional method descriptively. The differences in percentage between the contact angle value calculated by the “linier gradient equation” and “tangential line” formulas, and those calculated by means of the CA-Goniometer are 20,56% and 3,51%, respectively. It is obviously demonstrated that the value obtained by the “tangential line” formula has a smaller difference compared to those obtained by the “linier equation gradient” formula. Among the two different formulas, it is confirmed that the contact angle value calculated with the “tangential line” formula has closer similarity with the value obtained from the CA-Goniometer. This result confirms that the new practical method of drop profile image analysis is promising for measuring contact angle values in clinical circumstances. Related to the drop profile image analysis, the “tangential line” formula is more accurate compared to the “linier gradient equation” formula

Gauge Transformations in Quantum Mechanics and the Unification of Nonlinear Schr\"odinger Equations

Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we characterize directly a class of nonlinear quantum theories physically equivalent to linear quantum mechanics through nonlinear gauge transformations. We show that under two physically-motivated assumptions, these transformations are uniquely determined: they are exactly the group of time-dependent, nonlinear gauge transformations introduced previously for a family of nonlinear Schr\"odinger equations. The general equation in this family, including terms considered by Kostin, by Bialynicki-Birula and Mycielski, and by Doebner and Goldin, with time-dependent coefficients, can be obtained from the linear Schr\"odinger equation through gauge transformation and a subsequent process we call gauge generalization. We thus unify, on fundamental grounds, a rather diverse set of nonlinear time-evolutions in quantum mechanics.Comment: RevTeX, 20 pages, no figures. also available on http://www.pt.tu-clausthal.de/preprints/asi-tpa/021-96.htm

Relation between current sheets and vortex sheets in stationary incompressible MHD

Magnetohydrodynamic configurations with strong localized current concentrations and vortices play an important role for the dissipation of energy in space and astrophysical plasma. Within this work we investigate the relation between current sheets and vortex sheets in incompressible, stationary equilibria. For this approach it is helpful that the similar mathematical structure of magnetohydrostatics and stationary incompressible hydrodynamics allows us to transform static equilibria into stationary ones. The main control function for such a transformation is the profile of the Alfven-Mach number M_A, which is always constant along magnetic field lines, but can change from one field line to another. In the case of a global constant M_A, vortices and electric current concentrations are parallel. More interesting is the nonlinear case, where M_A varies perpendicular to the field lines. This is a typical situation at boundary layers like the magnetopause, heliopause, the solar wind flowing around helmet streamers and at the boundary of solar coronal holes. The corresponding current and vortex sheets show in some cases also an alignment, but not in every case. For special density distributions in 2D it is possible to have current but no vortex sheets. In 2D vortex sheets of field aligned-flows can also exist without strong current sheets, taking the limit of small Alfven Mach numbers into account. The current sheet can vanish if the Alfven Mach number is (almost) constant and the density gradient is large across some boundary layer. It should be emphasized that the used theory is not only valid for small Alfven Mach numbers M_A<<1, but also for M_A~1. Connection to other theoretical approaches and observations and physical effects in space plasmas are presented. Differences in the various aspects of theoretical investigations of current sheets and vortex sheets are given.Comment: 10 pages, 2 figures, accepted for publication in Annales Geophysica

Advanced action manipulator system (ADAMS)

Manipulator offers improved performance over other models in its category. It features larger force and reach capabilities and is readily convertible for underwater use. Unique kinematic arrangement provides extremely large working envelope. System has six degrees of motion: azimuth joint, shoulder joint, upper arm rotating joint, elbow joint, wrist pitch, and wrist twist

The group of causal automorphisms

The group of causal automorphisms on Minkowski space-time is given and its structure is analyzed

Turbulence characteristics of an axisymmetric reacting flow

Turbulent sudden expansion flows are of significant theoretical and practical importance. Such flows have been the subject of extensive analytical and experimental study for decades, but many issues are still unresolved. Detailed information on reacting sudden expansion flows is very limited, since suitable measurement techniques have only been available in recent years. The present study of reacting flow in an axisymmetric sudden expansion was initiated under NASA support in December 1983. It is an extension of a reacting flow program which has been carried out with Air Force support under Contract F33615-81-K-2003. Since the present effort has just begun, results are not yet available. Therefore a brief overview of results from the Air Force program will be presented to indicate the basis for the work to be carried out