scispace - formally typeset
Search or ask a question
Topic

Saturation (graph theory)

About: Saturation (graph theory) is a research topic. Over the lifetime, 1782 publications have been published within this topic receiving 50823 citations.


Papers
More filters
Journal ArticleDOI
Arthur Ashkin1
TL;DR: In this paper, a method of stably trapping, cooling, and manipulating atoms on a continuous-wave basis using resonance radiation pressure forces is proposed using highly focused laser beams and atomic beam injection should give a very deep trap for confining single atoms or gases at temperatures
Abstract: A method of stably trapping, cooling, and manipulating atoms on a continuous-wave basis is proposed using resonance radiation pressure forces. Use of highly focused laser beams and atomic beam injection should give a very deep trap for confining single atoms or gases at temperatures \ensuremath{\sim} ${10}^{\ensuremath{-}6}$ \ifmmode^\circ\else\textdegree\fi{}K. An analysis of the saturation properties of radiation pressure forces is given.

515 citations

Proceedings ArticleDOI
01 Oct 1990
TL;DR: In this paper, the authors studied the effect of the thermal motion of the magnetic nuclei upon the spin-spin interaction in a rigid lattice and the line width of the absorption line.
Abstract: The exchange of energy between a system of nuclear spins immersed in a strong magnetic field, and the heat reservoir consisting of the other degrees of freedom (the "lattice") of the substance containing the magnetic nuclei, serves to bring the spin system into equilibrium at a finite temperature. In this condition the system can absorb energy from an applied radiofrequency field. With the absorption of energy, however, the spin temperature tends to rise and the rate of absorption to decrease. Through this "saturation" effect, and in some cases by a more direct method, the spin-lattice relaxation time ${T}_{1}$ can be measured. The interaction among the magnetic nuclei, with which a characteristic time $T_{2}^{}{}_{}{}^{\ensuremath{'}}$ is associated, contributes to the width of the absorption line. Both interactions have been studied in a variety of substances, but with the emphasis on liquids containing hydrogen.Magnetic resonance absorption is observed by means of a radiofrequency bridge; the magnetic field at the sample is modulated at a low frequency. A detailed analysis of the method by which ${T}_{1}$ is derived from saturation experiments is given. Relaxation times observed range from ${10}^{\ensuremath{-}4}$ to ${10}^{2}$ seconds. In liquids ${T}_{1}$ ordinarily decreases with increasing viscosity, in some cases reaching a minimum value after which it increases with further increase in viscosity. The line width meanwhile increases monotonically from an extremely small value toward a value determined by the spin-spin interaction in the rigid lattice. The effect of paramagnetic ions in solution upon the proton relaxation time and line width has been investigated. The relaxation time and line width in ice have been measured at various temperatures.The results can be explained by a theory which takes into account the effect of the thermal motion of the magnetic nuclei upon the spin-spin interaction. The local magnetic field produced at one nucleus by neighboring magnetic nuclei, or even by electronic magnetic moments of paramagnetic ions, is spread out into a spectrum extending to frequencies of the order of $\frac{1}{{\ensuremath{\tau}}_{c}}$, where ${\ensuremath{\tau}}_{c}$ is a correlation time associated with the local Brownian motion and closely related to the characteristic time which occurs in Debye's theory of polar liquids. If the nuclear Larmor frequency $\ensuremath{\omega}$ is much less than $\frac{1}{{\ensuremath{\tau}}_{c}}$, the perturbations caused by the local field nearly average out, ${T}_{1}$ is inversely proportional to ${\ensuremath{\tau}}_{c}$, and the width of the resonance line, in frequency, is about $\frac{1}{{T}_{1}}$. A similar situation is found in hydrogen gas where ${\ensuremath{\tau}}_{c}$ is the time between collisions. In very viscous liquids and in some solids where $\ensuremath{\omega}{\ensuremath{\tau}}_{c}g1$, a quite different behavior is predicted, and observed. Values of ${\ensuremath{\tau}}_{c}$ for ice, inferred from nuclear relaxation measurements, correlate well with dielectric dispersion data.Formulas useful in estimating the detectability of magnetic resonance absorption in various cases are derived in the appendix.

513 citations

Journal ArticleDOI
TL;DR: In this paper, the density dependence of the symmetry energy at subnormal density was analyzed and the results from the present work were compared to constraints put forward in other recent analyses, where the results of the calculations reproduce isospin diffusion data from two different observables and the ratios of neutron and proton spectra.
Abstract: Collisions involving $^{112}\mathrm{Sn}$ and $^{124}\mathrm{Sn}$ nuclei have been simulated with the improved quantum molecular dynamics transport model. The results of the calculations reproduce isospin diffusion data from two different observables and the ratios of neutron and proton spectra. By comparing these data to calculations performed over a range of symmetry energies at saturation density and different representations of the density dependence of the symmetry energy, constraints on the density dependence of the symmetry energy at subnormal density are obtained. The results from the present work are compared to constraints put forward in other recent analyses.

483 citations

Journal ArticleDOI
TL;DR: A new mechanism is proposed, which can exist only in the tunneling regime, for such nonsequential ionization of helium ionized by 120 fs, 614 nm laser pulses.
Abstract: We have measured the ion yields for helium ionized by 120 fs, 614 nm laser pulses for intensities near ${10}^{16}$ W/${\mathrm{cm}}^{2}$. We have found that for these ultrashort pulses the ${\mathrm{He}}^{+2}$ data exhibit a feature which saturates in parallel with the ${\mathrm{He}}^{+}$ signal indicating that the ionization may proceed nonsequentially. We propose a new mechanism, which can exist only in the tunneling regime, for such nonsequential ionization.

470 citations

Journal ArticleDOI
TL;DR: Antiphase boundaries (APBs) were observed in single crystal films grown on MgO as discussed by the authors, which is an intrinsic consequence of the nucleation and growth mechanism in films.
Abstract: Antiphase boundaries (APBs) were observed in ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ single crystal films grown on MgO. The APBs are an intrinsic consequence of the nucleation and growth mechanism in films. Across an APB, the intrasublattice superexchange coupling is greatly strengthened, while the intersublattice superexchange coupling is weakened, reversing the dominant interaction from that found in the bulk. Thus the APB separates oppositely magnetized regions, consistent with Lorentz microscopy measurements. The APBs induce very large saturation fields and nearly random magnetization distribution in zero field.

456 citations


Network Information
Related Topics (5)
Indifference graph
10.8K papers, 287.9K citations
93% related
Pathwidth
8.3K papers, 252.2K citations
92% related
Chordal graph
12.8K papers, 314.2K citations
90% related
Line graph
11.5K papers, 304.1K citations
90% related
Planar graph
10K papers, 204.5K citations
89% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231,246
20222,619
2021258
2020115
201999
201872