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41.
Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically
by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually
employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be
“close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence
many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report
results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process
can be improved to better reflect the actual properties sought.
In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend
themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms
of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling
approach may possibly lead to algorithms with improved efficiency.
AMS subject classification (2000) 65L05, 65M32, 65N21, 65N22, 65D18 相似文献
42.
E. Goering M. Justen J. Geissler U. Rüdiger M. Rabe G. Güntherodt G. Schütz 《Applied Physics A: Materials Science & Processing》2002,74(6):747-753
Highly a-axis-textured CrO2 films have been deposited on Al2O3 (0001) substrates by chemical vapor deposition. CrO2 has been found to have highly a-axis (010)-oriented columnar growth on a Cr2O3 (0001) initial layer. The six-fold surface symmetry of the Cr2O3 initial layer leads to three equivalent in-plane orientations of the a-axis-oriented CrO2 unit cell. We report Cr L2,3 X-ray magnetic circular dichroism data along the surface normal and at 60° off-normal sample orientation. For a 60° sample
alignment, a strong increase of the projected orbital moment could be observed for unoccupied majority t2g states using moment analysis. Therefore, the c axis is identified as the intrinsic magnetic easy axis of CrO2. In addition, a small spin moment and a very strong magnetic dipole term Tz have been found.
Received: 8 January 2002 / Accepted: 8 January 2002 相似文献
43.
44.
T. Hansel J. Müller C. Falldorf C. von Kopylow W. Jüptner R. Grunwald G. Steinmeyer U. Griebner 《Applied physics. B, Lasers and optics》2007,89(4):513-516
Digital holographic shape measurements using femtosecond laser pulses are reported. For contouring of very fast moving objects,
the simultaneous generation of at least two spectrally separated ultrashort pulses is required. To deliver this particular
spectral signature at high pulse energies, a chirped-pulse Ti:sapphire laser amplifier was modified to emit two spectrally
separated pulses with energies above 1 μJ each. The wavelength separation of these pulses was adjustable within the 50 nm
gain bandwidth, cutting out two distinct wavelength peaks by a variable double-slit assembly in a prism sequence. A Michelson-type
interferometer was employed to perform the two-wavelength contouring. The phases of the holograms and the phase differences
are calculated numerically, which allow us to deduce the contour lines of the topology of the object. The suitability of the
light source for digital holography is demonstrated with contouring of stationary objects and the potential for high-speed
applications is indicated.
PACS 42.40.-i; 42.60.By 相似文献
45.
46.
We present the explicit form of the symplectic structure of anti-self-dual Yang-Mills (ASDYM) equations in Yang’s J- and K-gauges in order to establish the bi-Hamiltonian structure of this completely integrable system. Dirac’s theory of constraints is applied to the degenerate Lagrangians that yield the ASDYM equations. The constraints are second class as in the case of all completely integrable systems which stands in sharp contrast to the situation in full Yang-Mills theory. We construct the Dirac brackets and the symplectic 2-forms for both J- and K-gauges. The covariant symplectic structure of ASDYM equations is obtained using the Witten-Zuckerman formalism. We show that the appropriate component of the Witten-Zuckerman closed and conserved 2-form vector density reduces to the symplectic 2-form obtained from Dirac’s theory. Finally, we present the Bäcklund transformation between the J- and K-gauges in order to apply Magri’s theorem to the respective two Hamiltonian structures. 相似文献
47.
We present a simplified computational scheme in order to calculate the effects of electron correlations on the energy bands of diamond and silicon. By adopting a quasiparticle picture we compute first the relaxation and polarization effects around an electron set into a conduction-band Wannier orbital. This is done by allowing the valence orbitals to relax within a self-consistent field (SCF) calculation. The diagonal matrix element of the Hamiltonian leads to a shift of the center of gravity of the conduction band while the off-diagonal matrix elements result in a small reduction of the conduction-electron bandwidth. This calculation is supplemented by the computation of the loss of ground-state correlations due to the blocked Wannier orbital into which the added electron has been placed. The same procedure applies to the removal of an electron, i.e., to the valence bands. But the latter have been calculated previously in some detail and previous results are used to estimate the energy gap in the two materials. The numerical data reported here show that the methods works, in principle, but that some extension of the scheme is also necessary to obtain fully satisfactory results.Dedicated to J.-P. Malrieu on the occasion of his 60th birthday 相似文献
48.
B. D. Kabulov K. A. Akhundzhanov F. U. Yunusov O. A. Shpigun S. S. Negmatov 《Russian Journal of Physical Chemistry A, Focus on Chemistry》2007,81(3):354-356
The hydrolytic polycondensation of tetraethoxysilane in the presence of various polymers (polyacrylonitrile, polycaproamide, and chitosan) as templates was performed with the use of the sol-gel technology to obtain nanohybrid composite polymer-silica sorbents-nanofractals. 相似文献
49.
J. Łukasik G. Auger M. L. Begemann-Blaich N. Bellaize R. Bittiger F. Bocage B. Borderie R. Bougault B. Bouriquet J. L. Charvet A. Chbihi R. Dayras D. Durand J. D. Frankland E. Galichet D. Gourio D. Guinet S. Hudan P. Lautesse F. Lavaud A. Le Fèvre R. Legrain O. Lopez U. Lynen W. F. J. Müller L. Nalpas H. Orth E. Plagnol E. Rosato A. Saija C. Schwarz C. Sfienti B. Tamain W. Trautmann A. Trzciński K. Turzó E. Vient M. Vigilante C. Volant B. Zwiegliński 《Acta Physica Hungarica A》2006,25(2-4):229-239
Directed and elliptic flow for the 197Au+197Au system at incident energies between 40 and 150 MeV per nucleon has been measured using the INDRA 4π multi-detector. For semi-central collisions, the excitation function of elliptic flow shows a transition from in-plane to out-of-plane emission at around 100 MeV per nucleon. The directed flow changes sign at a bombarding energy between 50 and 60 MeV per nucleon and remains negative at lower energies. Molecular dynamics calculations (CHIMERA) indicate sensitivity of the global squeeze-out transition on the σ NN and demonstrate the importance of angular momentum conservation in transport codes at low energies. 相似文献
50.