scholarly journals Toy model of harmonic and sum frequency generation in 2D dielectric nanostructures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jie Xu ◽  
Vassili Savinov ◽  
Eric Plum

AbstractOptical nonlinearities of matter are often associated with the response of individual atoms. Here, using a toy oscillator model, we show that in the confined geometry of a two-dimensional dielectric nanoparticle a collective nonlinear response of the atomic array can arise from the Coulomb interactions of the bound optical electrons, even if the individual atoms exhibit no nonlinearity. We determine the multipole contributions to the nonlinear response of nanoparticles and demonstrate that the odd order and even order nonlinear electric dipole moments scale with the area and perimeter of the nanoparticle, respectively.

Author(s):  
Clément Luneau ◽  
Jean Barbier ◽  
Nicolas Macris

Abstract We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method originally invented for rank-one factorization. Here we show how to extend the adaptive interpolation to finite-rank and even-order tensors. This requires new non-trivial ideas with respect to the current analysis in the literature. We also underline where the proof falls short when dealing with odd-order tensors.


2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Selwin Hageraats ◽  
Mathieu Thoury ◽  
Stefan Stanescu ◽  
Katrien Keune

X-ray linear dichroism (XLD) is a fundamental property of many ordered materials that can for instance provide information on the origin of magnetic properties and the existence of differently ordered domains. Conventionally, measurements of XLD are performed on single crystals, crystalline thin films, or highly ordered nanostructure arrays. Here, it is demonstrated how quantitative measurements of XLD can be performed on powders, relying on the random orientation of many particles instead of the controlled orientation of a single ordered structure. The technique is based on a scanning X-ray transmission microscope operated in the soft X-ray regime. The use of a Fresnel zone plate allows X-ray absorption features to be probed at ∼40 nm lateral resolution – a scale small enough to probe the individual crystallites in most powders. Quantitative XLD parameters were then retrieved by determining the intensity distributions of certain diagnostic dichroic absorption features, estimating the angle between their transition dipole moments, and fitting the distributions with four-parameter dichroic models. Analysis of several differently produced ZnO powders shows that the experimentally obtained distributions indeed follow the theoretical model for XLD. Making use of Monte Carlo simulations to estimate uncertainties in the calculated dichroic model parameters, it was established that longer X-ray exposure times lead to a decrease in the amplitude of the XLD effect of ZnO.


Author(s):  
J. W. P. Hirschfeld ◽  
J. F. Voloch

AbstractIn a finite Desarguesian plane of odd order, it was shown by Segre thirty years ago that a set of maximum size with at most two points on a line is a conic. Here, in a plane of odd or even order, sufficient conditions are given for a set with at most three points on a line to be a cubic curve. The case of an elliptic curve is of particular interest.


1992 ◽  
Vol 01 (03) ◽  
pp. 493-531 ◽  
Author(s):  
E.R. YOUNGDALE ◽  
J.R. MEYER ◽  
F.J. BARTOLI ◽  
C.A. HOFFMAN

We review recent experimental and theoretical work on optical nonlinearities in semimetals and narrow-gap semiconductors. A strong nonlinear response due to optical modulation of the free carrier susceptibility is seen to be a common feature of these materials, with large third-order nonlinear susceptibilities being reported for Hg 1−x Cd x Te , Hg 1−x Mn x Te , Hg-based superlattices, α- Sn 1−x Ge x, Pb 1−x Sn x Se , and Bi 1−x Sb x. Effects of differences in the various band structures are discussed for nonlinearities due to nonparabolicity, thermal carrier generation, and nonequilibrium carrier generation. Mechanisms leading to either partial or severe saturation are also considered. Optimized nonlinearities for the various mechanisms and materials are critically compared, and promising future directions for the field are suggested.


Blood ◽  
1986 ◽  
Vol 67 (2) ◽  
pp. 299-309 ◽  
Author(s):  
CM Payne ◽  
L Glasser

Abstract Our purpose in this study was to establish ultrastructural morphometric criteria that can be used to define pathologic giant and fusion platelet granules and to determine whether patients with neoplastic myeloproliferative disorders (MPD) can be distinguished from other patients. We have morphometrically analyzed 2,391 giant and fusion granule profiles from 46 patients with neoplastic MPD, 127 other diseased control subjects, and 30 normal subjects using a computerized image analyzer. The largest granule profile observed in normal subjects had an area of 0.51 mu 2 and a perimeter of 3.21 mu. The most irregularly shaped of the large granule profiles photographed from normal subjects had a form factor (FF) value of 0.31. FF values indicate the degree of deviation of a given granule contour from a circle and is expressed by the formula 4 pi A/P2. A pathologic granule profile was then defined as a granule that exceeded any of these limits. Fifty-seven percent of the patients with neoplastic MPD were determined to have abnormal platelet granule profiles using the aforementioned morphometric criteria. It was determined, however, that morphometrically defined giant- and fusion-type granule profiles were nonspecific and were also found in 20% of the other diseased patients with no clinical evidence of an underlying neoplastic MPD. Morphometry has allowed us to define the upper limits of normal for the area and perimeter of individual platelet granules. Morphometrically defined giant fusion granules were determined to be more prevalent in the neoplastic MPD group, but because of their nonspecificity, may only have diagnostic significance for the individual patient in specific clinical settings. The pathogenesis of platelet fusion granules is discussed.


Clay Minerals ◽  
1992 ◽  
Vol 27 (4) ◽  
pp. 475-486 ◽  
Author(s):  
S. Hillier ◽  
B. Velde

AbstractX-ray diffraction (XRD) patterns of a pore-lining diagenetic chlorite (14 Å) from a reservoir sandstone, offshore Norway, show broad odd-order and sharp even-order basal reflections indicating that it contains 7 Å layers. Using NEWMOD, simulated XRD patterns with 15% 7 Å serpentine layers and a maximum crystallite thickness of 30 layers match the natural mineral well. Microprobe analyses of the 7 Å-14 Å mineral indicate that it is Fe-rich and aluminous suggesting that it is interstratified berthierine-chamosite. Apparent octahedral vacancies, however, suggest a significant dioctahedral component, and an alternative interpretation is interstratified kaolinite-chlorite. Indeed, chemical analyses of the mineral suggest a mixture of chlorite with 15% kaolinite, precisely the proportion of 7 Å layers indicated by XRD. Two other examples from the literature, previously identified as diagenetic chlorite, are probably also 7 Å-14 Å interstratified minerals, and the proportion of 7 Å layers indicated by XRD is also correlated with their structural formulae, if the 7 Å layers are, in fact, kaolinitic. This type of interstratification could explain why Fe-rich diagenetic chlorites appear to be compositionally distinct from metamorphic chlorites. The structure and chemistry of the Norwegian chlorite tend to support the idea that pore-lining chlorites form early in the diagenetic history, inhibiting the precipitation of later diagenetic minerals, and hence preserving abnormally high porosity at greater depths.


2015 ◽  
Vol 1802 ◽  
pp. 19-24 ◽  
Author(s):  
Nasrin Hooshmand ◽  
Justin A Bordley ◽  
Mostafa A El-Sayed

ABSTRACTAg or Au nanocubes are known to be plasmonic nanoparticles with strong plasmonic fields concentrated around their corners1. When these nanoparticles aggregate the individual plasmonic oscillations of each particle begin to couple. The coupling between the two plasmonic nanoparticles is assumed to be dipolar in nature which results in an exponential red shift dependence of their localized surface plasmon resonance (LSPR) on the dimer separation2. Unfortunately, this exponential behavior is shown to fail as the separation distance between the two 42 nm nanocube dimer becomes 6nm or smaller3. Hooshmand et al4 have noted that these separation distances are marked by the formation of hot spots between the facets of the dimer.This dipolar exponential behavior results from a treatment of the coupling between the two excited nanocubes as a coupling between two oscillating dipole moments2. As a result, the vectorial addition of all the oscillating electronic dipoles is assumed to interact with the nearest nanoparticle as a single oscillating electronic dipole. Herein we suggest that as the separation distance becomes increasingly small, the coupling between the individual oscillating dipoles on the different nanocubes becomes significant. Thus, the dipolar exponential behavior fails to accurately predict the near field coupling between two nanoparticles with small separation distances.This leads to the realization that the interaction between the individual oscillating dipoles on the two nanocubes changes in a complicated manner as a function of separation distance. At 2nm, a good fraction of the oscillating dipoles are between the adjacent facets of the nanocubes as well as between the the corners. While at 3 nm less are in between the two facets of the nanocubes and a larger portion are localized at the corners. Thus, the coupling is not only dependent on the separation distance but also on what the separation does to the net interaction between the oscillating dipoles on each facet of the two coupled nanocubes. This results in the failure of the exponential behavior as the dipole moment on each nanocube is changing with distance in a complicated manner.


1970 ◽  
Vol 41 (1) ◽  
pp. 169-178 ◽  
Author(s):  
C. W. Van Atta ◽  
T. T. Yeh

Three-point odd-order correlations and four-point even-order correlations of the longitudinal velocity fluctuations in grid-generated turbulence have been measured using linearized hot-wire anemometry, digital sampling, and a high-speed digital computer. The measured correlations are compared with relations between higher-order correlations corresponding to non-Gaussian Gram-Charlier joint probability densities for three and four variables. The fourth-order, three-point Gram-Charlier distribution accurately describes the relation between measured odd-order three-point correlations. The measured fourth-order even-order correlations may be accurately predicted from the two-point correlation using Millionshtchikov's joint-Gaussian hypothesis, except for small values of the separations. The disagreement at small separations cannot be reduced through use of the Gram-Charlier approximation.


Open Physics ◽  
2006 ◽  
Vol 4 (1) ◽  
pp. 30-41 ◽  
Author(s):  
Kamil Walczak ◽  
Gloria Platero

AbstractCoherent electronic transport through a molecular device is studied using non-equilibrium Green's function (NEGF) formalism. Such device is made of atomic nanowire which is connected to ferromagnetic electrodes. The molecule itself is described with the help of Hubbard model (Coulomb interactions are treated by means of the Hartree-Fock approximation), while the coupling to the electrodes is modeled through the use of a broad-band theory. It was shown that magnetoresistance varies periodically with increasing length of the atomic wire (in the linear response regime) and oscillates with increasing bias voltage (in the nonlinear response regime). Since the TMR effect for analyzed structures is predicted to be large (tens of percent), these junctions seem to be suitable for application as magnetoresistive elements in future electronic circuits.


Author(s):  
Yongjian Yu ◽  
Guoding Chen ◽  
Jishun Li ◽  
Yujun Xue

As the rotation of roller bearings is carried out under geometrical constraint of the inner ring, outer ring and multiple rollers, the motion error of the bearing should also be resulted from geometric errors of bearing parts. Therefore, it is crucial to establish the relationship between geometric errors of bearing components and motion error of assembled bearing, which contributes to improve rotational accuracy of assembled bearing in the design and machining of the bearing. For this purpose, considering roundness error and dimension error of the inner raceway, the outer raceway and rollers, a prediction method for rotational accuracy of cylindrical roller bearings is proposed, and the correctness of the proposed prediction method is verified by experimental results. The influences of roller's geometric error distribution, roller's roundness error and the number of rollers on the runout value of inner ring are investigated. The results show that, the roller arrangement with different geometric errors has a significant impact on rotational accuracy of cylindrical roller bearings. The rotational accuracy could be improved remarkably when multiple rollers with different dimension error are distributed alternately according to the size error. Even-order roundness error of rollers has a significant effect on the rotational accuracy, and the decrease level depends on the orders of roundness errors of bearing parts and the number of rollers. But odd-order roundness error of rollers has almost no effect on the rotational accuracy. The rotational accuracy of assembled bearing would be significantly improved or decreased when even order harmonic of rollers and the number of rollers satisfy specific relationships. The greater the order of roundness error of the rollers, the more severe the influence of the roller number on rotational accuracy of assembled bearing. The rotational accuracy can not be always improved with the increase of the number of rollers.


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