Smoothing effect for the Schrödinger evolution equations with electric fields

1990 ◽  
pp. 226-235 ◽  
Author(s):  
Tohru Ozawa
Keyword(s):  
Electric Fields ◽  
Evolution Equations ◽  
Smoothing Effect

Film Flows in the Presence of Electric Fields

2019 ◽  
Vol 51 (1) ◽  
pp. 155-187 ◽  
Author(s):  
Demetrios T. Papageorgiou
Keyword(s):  
Electric Fields ◽  
Evolution Equations ◽  
Nonlinear Models ◽  
Practical Importance ◽  
Three Dimensional ◽  
Spatiotemporal Chaos ◽  
Reduced Dimension ◽  
Drive Systems ◽  
Nonlocal Terms ◽  
Film Flows

The presence of electric fields in immiscible multifluid flows induces Maxwell stresses at sharp interfaces that can produce electrohydrodynamic phenomena of practical importance. Electric fields can be stabilizing or destabilizing depending on their strength and orientation. In microfluidics, fields can be used to drive systems out of equilibrium to produce hierarchical patterning, mixing, and phase separation. We describe nonlinear theories of electrohydrodynamic instabilities in immiscible multilayer flows in several geometries, including flows over or inside planar or topographically structured substrates and channels and flows in cylinders and cylindrical annuli. Matched asymptotic techniques are developed for two- and three-dimensional flows, and reduced-dimension nonlinear models are derived and studied. When all regions are slender, electrostatic extensions to lubrication or shallow-wave theories are derived. In the presence of nonslender layers, nonlocal terms emerge naturally to modify the evolution equations. Analysis and computations provide a plethora of dynamics, including nonlinear traveling waves, spatiotemporal chaos, and singularity formation. Direct numerical simulations are used to evaluate the models and go beyond their range of validity to quantify phenomena such as electric field–induced directed patterning, suppression of Rayleigh–Taylor instabilities, and electrostatically induced pumping in microchannels. Comparisons of theory and simulations with available experiments are included throughout.

scholarly journals Identification of hysteretic control influence operators representing smart actuators part I: Formulation

1997 ◽  
Vol 3 (4) ◽  
pp. 287-328 ◽  
Author(s):  
H. T. Banks ◽  
A. J. Kurdila ◽  
G. Webb
Keyword(s):  
Shape Memory ◽  
Electric Fields ◽  
Evolution Equations ◽  
Identification Problem ◽  
Least Square ◽  
Structural Level ◽  
Input Output ◽  
Hysteretic Control ◽  
Actuation Devices ◽  
Hysteresis Operators

A large class of emerging actuation devices and materials exhibit strong hysteresis characteristics during their routine operation. For example, when piezoceramic actuators are operated under the influence of strong electric fields, it is known that the resulting input–output behavior is hysteretic. Likewise, when shape memory alloys are resistively heated to induce phase transformations, the input–output response at the structural level is also known to be strongly hysteretic. This paper investigates the mathematical issues that arise in identifying a class of hysteresis operators that have been employed for modeling both piezoceramic actuation and shape memory alloy actuation. Specifically, the identification of a class of distributed hysteresis operators that arise in the control influence operator of a class of second order evolution equations is investigated. In Part I of this paper we introduce distributed,hysteretic control influence operators derived from smoothed Preisach operators and generalized hysteresis operators derived from results of Krasnoselskii and Pokrovskii. For these classes, the identification problem in which we seek to characterize the hysteretic control influence operator can be expressed as an ouput least square minimization over probability measures defined on a compact subset of a closed half-plane. In Part II of this paper, consistent and convergent approximation methods for identification of the measure characterizing the hysteresis are derived.

Control of Metal Alloy Oxidation with Electric Fields

1973 ◽  
Vol 31 ◽  
pp. 164-165
Author(s):  
R. R. Dils ◽  
P. S. Follansbee
Keyword(s):  
Electric Fields ◽  
Oxidation Process ◽  
Base Alloy ◽  
Oxide Surface ◽  
Platinum Electrodes ◽  
Insulating Layer ◽  
Iron Base Alloy ◽  
Alloy Oxidation ◽  
Aluminum Oxide Layer ◽  
And Control

Electric fields have been applied across oxides growing on a high temperature alloy and control of the oxidation of the material has been demonstrated. At present, three-fold increases in the oxidation rate have been measured in accelerating fields and the oxidation process has been completely stopped in a retarding field.The experiments have been conducted with an iron-base alloy, Pe 25Cr 5A1 0.1Y, although, in principle, any alloy capable of forming an adherent aluminum oxide layer during oxidation can be used. A specimen is polished and oxidized to produce a thin, uniform insulating layer on one surface. Three platinum electrodes are sputtered on the oxide surface and the specimen is reoxidized.

Electron-Mirror Microscopic Aspects of Ferroelectric Domains of BaTiO3 And Ca2Sr (C2H5CO2)6

1970 ◽  
Vol 28 ◽  
pp. 478-479
Author(s):  
Teruo Someya ◽  
Jinzo Kobayashi
Keyword(s):  
Surface Layer ◽  
Electric Fields ◽  
Quantitative Study ◽  
Recent Progress ◽  
Ferroelectric Domain ◽  
Resolving Power ◽  
Surface Pattern ◽  
Crystal Surfaces ◽  
One Dimensional ◽  
Ferroelectric Domains

Recent progress in the electron-mirror microscopy (EMM), e.g., an improvement of its resolving power together with an increase of the magnification makes it useful for investigating the ferroelectric domain physics. English has recently observed the domain texture in the surface layer of BaTiO3. The present authors ) have developed a theory by which one can evaluate small one-dimensional electric fields and/or topographic step heights in the crystal surfaces from their EMM pictures. This theory was applied to a quantitative study of the surface pattern of BaTiO3).

Electron Microscope Observations of Magnetic and Electric Effects

1970 ◽  
Vol 28 ◽  
pp. 430-431
Author(s):  
John Silcox
Keyword(s):  
Electron Microscope ◽  
Electric Fields ◽  
Magnetic Image ◽  
Magnetic Effects ◽  
Ferromagnetic Films ◽  
Diffraction Contrast ◽  
Microscope Images ◽  
Electric Effects ◽  
Image Detail

Several aspects of magnetic and electric effects in electron microscope images are of interest and will be discussed here. Clearly electrons are deflected by magnetic and electric fields and can give rise to image detail. We will review situations in ferromagnetic films in which magnetic image effects are the predominant ones, others in which the magnetic effects give rise to rather subtle changes in diffraction contrast, cases of contrast at specimen edges due to leakage fields in both ferromagnets and superconductors and some effects due to electric fields in insulators.

Electron microscopy studies of PZT ferroelectric film capacitor structures

1992 ◽  
Vol 50 (2) ◽  
pp. 1364-1365
Author(s):  
V. Kaushik ◽  
P. Maniar ◽  
J. Olowolafe ◽  
R. Jones ◽  
A. Campbell ◽  
...  
Keyword(s):  
Electric Fields ◽  
Sol Gel ◽  
Ferroelectric Material ◽  
Dielectric Constants ◽  
Dielectric Films ◽  
Lead Zirconium Titanate ◽  
Si Substrate ◽  
Film Capacitor ◽  
Pzt Films ◽  
High Dielectric

Lead zirconium titanate films (Pb (Zr,Ti) O3 or PZT) are being considered for potential application as dielectric films in memory technology due to their high dielectric constants. PZT is a ferroelectric material which shows spontaneous polarizability, reversible under applied electric fields. We report herein some results of TEM studies on thin film capacitor structures containing PZT films with platinum-titanium electrodes.The wafers had a stacked structure consisting of PZT/Pt/Ti/SiO2/Si substrate as shown in Figure 1. Platinum acts as electrode material and titanium is used to overcome the problem of platinum adhesion to the oxide layer. The PZT (0/20/80) films were deposited using a sol-gel method and the structure was annealed at 650°C and 800°C for 30 min in an oxygen ambient. XTEM imaging was done at 200KV with the electron beam parallel to <110> zone axis of silicon.Figure 2 shows the PZT and Pt layers only, since the structure had a tendency to peel off at the Ti-Pt interface during TEM sample preparation.

Current Status of Solid-State X-Ray Systems

1985 ◽  
Vol 43 ◽  
pp. 158-161
Author(s):  
Martin Peckerar ◽  
Anastasios Tousimis
Keyword(s):  
Solid State ◽  
Electric Fields ◽  
Spectral Lines ◽  
Current Status ◽  
Mobile Charge ◽  
Electron Hole ◽  
X Ray ◽  
Sensing Systems ◽  
Transmission Electron ◽  
Electron Microscopes

Solid state x-ray sensing systems have been used for many years in conjunction with scanning and transmission electron microscopes. Such systems conveniently provide users with elemental area maps and quantitative chemical analyses of samples. Improvements on these tools are currently sought in the following areas: sensitivity at longer and shorter x-ray wavelengths and minimization of noise-broadening of spectral lines. In this paper, we review basic limitations and recent advances in each of these areas. Throughout the review, we emphasize the systems nature of the problem. That is. limitations exist not only in the sensor elements but also in the preamplifier/amplifier chain and in the interfaces between these components.Solid state x-ray sensors usually function by way of incident photons creating electron-hole pairs in semiconductor material. This radiation-produced mobile charge is swept into external circuitry by electric fields in the semiconductor bulk.

Atomic Spectroscopy in the FIM

1986 ◽  
Vol 44 ◽  
pp. 758-761
Author(s):  
J. J. Hren ◽  
S. D. Walck
Keyword(s):  
Electron Microscope ◽  
Electric Fields ◽  
Atom Probe ◽  
Atomic Spectroscopy ◽  
Single Atom ◽  
Statistical Sampling ◽  
Commercial Instrument ◽  
Available Technology ◽  
High Electric Fields ◽  
Field Ion Microscope

The field ion microscope (FIM) has had the ability to routinely image the surface atoms of metals since Mueller perfected it in 1956. Since 1967, the TOF Atom Probe has had single atom sensitivity in conjunction with the FIM. “Why then hasn't the FIM enjoyed the success of the electron microscope?” The answer is closely related to the evolution of FIM/Atom Probe techniques and the available technology. This paper will review this evolution from Mueller's early discoveries, to the development of a viable commercial instrument. It will touch upon some important contributions of individuals and groups, but will not attempt to be all inclusive. Variations in instrumentation that define the class of problems for which the FIM/AP is uniquely suited and those for which it is not will be described. The influence of high electric fields inherent to the technique on the specimens studied will also be discussed. The specimen geometry as it relates to preparation, statistical sampling and compatibility with the TEM will be examined.

Off-axis electron holography applied to the study of interfaces

1992 ◽  
Vol 50 (1) ◽  
pp. 244-245
Author(s):  
J.K. Weiss ◽  
M. Gajdardziska-Josifovska ◽  
M. R. McCartney ◽  
David J. Smith
Keyword(s):  
Electric Fields ◽  
Resolution Enhancement ◽  
Interfacial Structure ◽  
Atomic Scale ◽  
Bulk Property ◽  
Electron Holography ◽  
Specimen Thickness ◽  
Composition And Structure ◽  
Chemical Segregation ◽  
Diffraction Effects

Interfacial structure is a controlling parameter in the behavior of many materials. Electron microscopy methods are widely used for characterizing such features as interface abruptness and chemical segregation at interfaces. The problem for high resolution microscopy is to establish optimum imaging conditions for extracting this information. We have found that off-axis electron holography can provide useful information for the study of interfaces that is not easily obtained by other techniques.Electron holography permits the recovery of both the amplitude and the phase of the image wave. Recent studies have applied the information obtained from electron holograms to characterizing magnetic and electric fields in materials and also to atomic-scale resolution enhancement. The phase of an electron wave passing through a specimen is shifted by an amount which is proportional to the product of the specimen thickness and the projected electrostatic potential (ignoring magnetic fields and diffraction effects). If atomic-scale variations are ignored, the potential in the specimen is described by the mean inner potential, a bulk property sensitive to both composition and structure. For the study of interfaces, the specimen thickness is assumed to be approximately constant across the interface, so that the phase of the image wave will give a picture of mean inner potential across the interface.

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