scholarly journals Global Regularity of Wave Maps¶II. Small Energy in Two Dimensions

2001 ◽  
Vol 224 (2) ◽  
pp. 443-544 ◽  
Author(s):  
Terence Tao
Keyword(s):  
Global Regularity ◽  
Two Dimensions ◽  
Wave Maps ◽  
Small Energy

scholarly journals Pressureless Euler alignment system with control

2018 ◽  
Vol 28 (09) ◽  
pp. 1635-1664 ◽  
Author(s):  
Giacomo Albi ◽  
Young-Pil Choi ◽  
Axel-Stefan Häck
Keyword(s):  
Global Regularity ◽  
Blow Up ◽  
Strong Solutions ◽  
Two Dimensions ◽  
Finite Volume Scheme ◽  
Computational Results ◽  
Controlled System ◽  
Critical Thresholds ◽  
Alignment System ◽  
Non Local

We study a non-local hydrodynamic system with control. First, we characterize the control dynamics as a sub-optimal approximation to the optimal control problem constrained to the evolution of the pressureless Euler alignment system. We then discuss the critical thresholds that lead to global regularity or finite-time blow-up of strong solutions in one and two dimensions. Finally, we use a finite volume scheme, coupled with an implicit–explicit time integrator to solve numerically the stiff scale of the controlled system. Several numerical simulations are shown to validate the theoretical and computational results of the paper.

scholarly journals Small data global regularity for half-wave maps

2018 ◽  
Vol 11 (3) ◽  
pp. 661-682 ◽  
Author(s):  
Joachim Krieger ◽  
Yannick Sire
Keyword(s):  
Global Regularity ◽  
Small Data ◽  
Wave Maps ◽  
Half Wave

The tangled web of agency

2018 ◽  
Vol 41 ◽  
Author(s):  
Alain Pe-Curto ◽  
Julien A. Deonna ◽  
David Sander
Keyword(s):  
Two Dimensions ◽  
Bad Company

AbstractWe characterize Doris's anti-reflectivist, collaborativist, valuational theory along two dimensions. The first dimension is socialentanglement, according to which cognition, agency, and selves are socially embedded. The second dimension isdisentanglement, the valuational element of the theory that licenses the anchoring of agency and responsibility in distinct actors. We then present an issue for the account: theproblem of bad company.

Use of LaB6 for a High Quality, Small Energy Spread Beam in an Electron Velocity Spectrometer

1976 ◽  
Vol 34 ◽  
pp. 534-535 ◽  
Author(s):  
P. E. Batson ◽  
C. H. Chen ◽  
J. Silcox
Keyword(s):  
High Temperature ◽  
Energy Resolution ◽  
Electron Velocity ◽  
Electronic Excitations ◽  
Small Energy ◽  
Small Intensity ◽  
Good Energy ◽  
Spectrometer System ◽  
Electron Energy Loss ◽  
Very High

Electron energy loss experiments combined with microscopy have proven to be a valuable tool for the exploration of the structure of electronic excitations in materials. These types of excitations, however, are difficult to measure because of their small intensity. In a usual situation, the filament of the microscope is run at a very high temperature in order to present as much intensity as possible at the specimen. This results in a degradation of the ultimate energy resolution of the instrument due to thermal broadening of the electron beam.We report here observations and measurements on a new LaB filament in a microscope-velocity spectrometer system. We have found that, in general, we may retain a good energy resolution with intensities comparable to or greater than those available with the very high temperature tungsten filament. We have also explored the energy distribution of this filament.

Performance and applications of a field-emission gun TEM/STEM

1992 ◽  
Vol 50 (2) ◽  
pp. 942-943
Author(s):  
Judith M. Brock ◽  
Max T. Otten ◽  
Marc. J.C. de Jong
Keyword(s):  
Field Emission ◽  
High Resolution Imaging ◽  
High Quality ◽  
Small Energy ◽  
High Brightness ◽  
Small Probe ◽  
Resolution Imaging ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

A Field Emission Gun (FEG) on a TEM/STEM instrument provides a major improvement in performance relative to one equipped with a LaB6 emitter. The improvement is particularly notable for small-probe techniques: EDX and EELS microanalysis, convergent beam diffraction and scanning. The high brightness of the FEG (108 to 109 A/cm2srad), compared with that of LaB6 (∼106), makes it possible to achieve high probe currents (∼1 nA) in probes of about 1 nm, whilst the currents for similar probes with LaB6 are about 100 to 500x lower. Accordingly the small, high-intensity FEG probes make it possible, e.g., to analyse precipitates and monolayer amounts of segregation on grain boundaries in metals or ceramics (Fig. 1); obtain high-quality convergent beam patterns from heavily dislocated materials; reliably detect 1 nm immuno-gold labels in biological specimens; and perform EDX mapping at nm-scale resolution even in difficult specimens like biological tissue.The high brightness and small energy spread of the FEG also bring an advantage in high-resolution imaging by significantly improving both spatial and temporal coherence.

A transmission electron microscopic study of structural transitions in fast ionic conductors

1987 ◽  
Vol 45 ◽  
pp. 156-157
Author(s):  
R. B. Queenan ◽  
P. K. Davies
Keyword(s):  
Optical Properties ◽  
Ionic Conduction ◽  
Recent Observation ◽  
Ionic Conductivities ◽  
Sodium Aluminate ◽  
Two Dimensions ◽  
Ionic Conductors ◽  
Electron Microscopic ◽  
Transmission Electron ◽  
Trivalent Cations

Na ß“-alumina (Na1.67Mg67Al10.33O17) is a non-stoichiometric sodium aluminate which exhibits fast ionic conduction of the Na+ ions in two dimensions. The Na+ ions can be exchanged with a variety of mono-, di-, and trivalent cations. The resulting exchanged materials also show high ionic conductivities.Considerable interest in the Na+-Nd3+-ß“-aluminas has been generated as a result of the recent observation of lasing in the pulsed and cw modes. A recent TEM investigation on a 100% exchanged Nd ß“-alumina sample found evidence for the intergrowth of two different structure types. Microdiffraction revealed an ordered phase coexisting with an apparently disordered phase, in which the cations are completely randomized in two dimensions. If an order-disorder transition is present then the cooling rates would be expected to affect the microstructures of these materials which may in turn affect the optical properties. The purpose of this work was to investigate the affect of thermal treatments upon the micro-structural and optical properties of these materials.

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