scholarly journals Wiener–Hopf Method Applied to the X-ray Edge Problem

1997 ◽  
Vol 11 (29) ◽  
pp. 3433-3453 ◽  
Author(s):  
V. Janiš
Keyword(s):  
Integral Equations ◽  
Time Limit ◽  
Time Interval ◽  
Infinite Time ◽  
Effective Lifetime ◽  
X Ray ◽  
Edge Problem ◽  
Long Time ◽  
The Difference ◽  
Hopf Method

We apply the Wiener–Hopf method of solving convolutive integral equations on a semi-infinite interval to the X-ray edge problem. Dyson equations for basic Green functions from the X-ray problem are rewritten as convolutive integral equations on a time-interval [0,t] with t→∞. The long-time asymptotics of solutions to these equations is derived with the aid of the Wiener–Hopf method. Although the Wiener–Hopf long-time exponents differ by a factor of two from the solution of Nozières and De Dominicis we demonstrate how the latter and the critical exponents of measurable amplitudes from the X-ray problem can be derived from the former. We explain that the difference in the exponents arises due to different ways of performing the long-time limit in the two solutions. To enable the infinite-time limit in the defining equations a new infinite-time scale τ→∞, interpreted as an effective lifetime of the core-hole, must be introduced. The ratio t/τ decides about the resulting critical exponent. The physical relevance of the Nozières and De Dominicis as well as of the Wiener–Hopf exponents is discussed.

LONG‐TIME RESPONSE PREDICTED BY EXACT ELASTIC RAY THEORY

Geophysics ◽  
1965 ◽  
Vol 30 (3) ◽  
pp. 363-368 ◽  
Author(s):  
T. W. Spencer
Keyword(s):  
Formal Solution ◽  
Intermediate Stage ◽  
Time Limit ◽  
Time Interval ◽  
Individual Response ◽  
Axially Symmetric ◽  
Long Time ◽  
The Difference ◽  
The Individual ◽  
Significant Figures

The formal solution for an axially symmetric radiation field in a multilayered, elastic system can be expanded in an infinite series. Each term in the series is associated with a particular raypath. It is shown that in the long‐time limit the individual response functions produced by a step input in particle velocity are given by polynomials in odd powers of the time. For rays which suffer m reflections, the degree of the polynomials is 2m+1. The total response is obtained by summing all rays which contribute in a specified time interval. When the rays are selected indiscriminately, the difference between the magnitude of the partial sum at an intermediate stage of computation and the magnitude of the correct total sum may be greater than the number of significant figures carried by the computer. A prescription is stated for arranging the rays into groups. Each group response function varies linearly in the long‐time limit and goes to zero when convolved with a physically realizable source function.

Relative Contributions of Viscoelasticity and Aging to the Relaxation of Rubber Vulcanizates

1963 ◽  
Vol 36 (1) ◽  
pp. 50-58 ◽  
Author(s):  
P. Thirion ◽  
R. Chasset
Keyword(s):  
Quantitative Analysis ◽  
Natural Rubber ◽  
Time Interval ◽  
Dicumyl Peroxide ◽  
Infinite Time ◽  
Negative Power ◽  
Theoretical Assumptions ◽  
The Difference ◽  
Natural Rubber Vulcanizates ◽  
Actual Stress

Abstract Relaxation in relatively stable, gum natural rubber vulcanizates has been studied to determine the effects of viscoelasticity and aging, respectively, using a dark, air-oven. A quantitative analysis of experimental results shows that, in the case of a dicumyl peroxide vulcanizate at 100° C, relaxation is caused by aging, except in its initial stages. Stress decreases as a linear function of time, in agreement with theoretical assumptions. Conversely, at 30° C, the effect of aging is negligible. At this temperature the difference between actual stress and stress extrapolated to infinite time, is proportional to a negative power of time. At intermediate temperatures, both phenomena occur simultaneously over a time interval ranging from. 3 minutes to 150 hours.

Jupiter’s polar auroral bright spots as seen by Juno-UVS

2020 ◽  
Author(s):  
Kamolporn Haewsantati ◽  
Bertrand Bonfond ◽  
Suwicha Wannawichian ◽  
George R Gladstone
Keyword(s):  
Hubble Space Telescope ◽  
Bright Spot ◽  
Time Interval ◽  
Systematic Analysis ◽  
X Ray ◽  
Bright Spots ◽  
Polar Aurora ◽  
The Difference ◽  
Magnetospheric Cusp ◽  
First Time

<p>The instruments on board the NASA Juno mission provides scientists with a wealth of unprecedented details about Jupiter. In particular, the Ultraviolet Spectrograph (UVS) is dedicated to the study of Jupiter’s aurora in the 60-200 nm wavelength range. The images taken by Juno-UVS reveals for the first time a complete view of Jupiter’s aurora, including the nightside part hidden from the Earth-orbiting Hubble Space Telescope (HST). This work aims to study Jupiter’s polar aurora using images obtained from the UVS instruments. Here we present the systematic analysis of one of the most spectacular features of Jupiter’s polar-most aurora, called the bright spot. The emitted power of the bright spots ranges from a few to a hundred GWs. Within a Juno perijove, the spots reappear at almost the same positions in system III. The time interval between two consecutive brightenings is a few tens of minutes, comparable to Jupiter’s X-ray pulsation. The comparison of the time interval with X-ray observation is under the investigation. Comparing the difference perijove sequences, the system III positions of bright spots in the northern hemisphere are concentrated in a region around 175 degrees of system III longitude and 65 degrees of latitude. On the other hand, the positions of bright spot aurora the southern hemisphere are scattered all around the pole. Previous studies suggested that the bright spot could correspond to noon facing magnetospheric cusp. However and surprisingly, we have discovered that the bright spots could map to any magnetic local time, putting this interpretation into question.</p>

scholarly journals Investigation of method of elimination of interference situation effect on GPS navigation receiver operation by smoothing of pseudorange measurements by pseudophase increment

2020 ◽  
pp. 46-53
Author(s):  
V. Y. Vovasov ◽  
D. A. Sukharev
Keyword(s):  
High Precision ◽  
Experimental Studies ◽  
Satellite System ◽  
Mobile Object ◽  
Time Interval ◽  
Urgent Task ◽  
Long Time ◽  
The Difference ◽  
Navigation Signals ◽  
Global Navigation Satellite

The wide application of high-precision GNSS (global navigation satellite system) positioning technologies for unmanned mobile object management requires the acquisition of solutions with subdecimeter accuracy and the reduction of the convergence period to such accuracy from the beginning of measurements to 20–25 minutes. Unfortunately, the accuracy of the obtained navigation solutions and the time of convergence to high-precision solutions are influenced by re-reflection of GNSS signals from the ground, buildings and structures, as well as interference from different sources of radio emissions of the urban environment. Therefore, it is an urgent task to implement methods of eliminating the influence of the interference situation on the operation of the navigation receiver of GNSS signals and investigating their effectiveness. The paper considers the results of investigation of the method of elimination of interference situation effect on GPS signal navigation receiver operation using smoothing of raw pseudorange measurements by pseudophase increment. Justification of the difference of measurement of pseudo-range by carrier phase and pseudo-range by code is given as a criterion of efficiency of estimation of interference situation influence in the area of navigation signals reception. As a result of the analysis of experimental studies, it has been shown that using the described method, starting from 900 seconds, the values of the smoothed parameter do not deviate from the averaged measurements over a long time interval by more than 0.1 meters, which indicates the efficiency of the method of smoothing by phase increments and is potentially promising for highly accurate measurements.

Relative Contributions of Viscoelasticity and Aging to the Relaxation of Cured Rubber

1964 ◽  
Vol 37 (3) ◽  
pp. 617-626 ◽  
Author(s):  
P. Thirion ◽  
R. Chasset
Keyword(s):  
Quantitative Analysis ◽  
Natural Rubber ◽  
Time Interval ◽  
Dicumyl Peroxide ◽  
Infinite Time ◽  
Negative Power ◽  
Theoretical Assumptions ◽  
The Difference ◽  
Natural Rubber Vulcanizates ◽  
Actual Stress

Abstract Relaxation in relatively stable pure gum natural rubber vulcanizates has been studied to determine the effects of viscoelasticity and aging, respectively, using a dark air oven. A quantitative analysis of experimental results shows that, in the case of a dicumyl peroxide vulcanizate and at 100° C, relaxation is caused by aging, except in its initial stages. Stress decreases as a linear function of time, in agreement with theoretical assumptions. Conversely, at 30° C, the influence of aging is negligible. At this temperature the difference between actual stress and stress extrapolated to infinite time, is proportional to a negative power of time. At intermediate temperatures, both phenomena occur simultaneously over a time interval ranging from 3 minutes to 150 hours.

Studies on the Heterostructure of Fe Film on Si Substrate

2005 ◽  
Vol 475-479 ◽  
pp. 3753-3756
Author(s):  
Y.F. Ge ◽  
Rong Zhang ◽  
Xiang Qian Xiu ◽  
Zi Li Xie ◽  
Shu Lin Gu ◽  
...  
Keyword(s):  
Single Crystal ◽  
Photoelectron Spectroscopy ◽  
Chemical Vapor ◽  
Iron Film ◽  
Organic Chemical ◽  
X Ray ◽  
Si Substrates ◽  
Long Time ◽  
The Difference ◽  
Oxidation In Air

Fe films have been grown on different oriented Si substrates by metal organic chemical vapor deposition (MOCVD), and then samples are put in the air without any protection for nearly fifteen years. In this paper, using methods such as X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and vibrating sample magnetometer (VSM), we make a detailed research on the samples. We identify the composition and structure of the epitaxial films on different oriented substrates and compare the difference both in composition and magnetic properties. Different orientation of the substrates results in different epitaxial film with different characteristic. We also confirm the existence of single crystal iron in the heteroepitaxial film grown on Si (001), and discuss the possible reason why the single crystal iron film still exists without complete oxidation in air for such a long time.

Difference Fourier Analysis of Glucose Embedded and Frozen Hydrated Purple Membrane

1982 ◽  
Vol 40 ◽  
pp. 74-75
Author(s):  
Jules S. Jaffe ◽  
Robert M. Glaeser
Keyword(s):  
Purple Membrane ◽  
Data Set ◽  
High Resolution Data ◽  
X Ray ◽  
X Ray Crystallography ◽  
Fourier Techniques ◽  
Versus Protein ◽  
The Difference ◽  
Difference Fourier ◽  
Ideal Method

Although difference Fourier techniques are standard in X-ray crystallography it has only been very recently that electron crystallographers have been able to take advantage of this method. We have combined a high resolution data set for frozen glucose embedded Purple Membrane (PM) with a data set collected from PM prepared in the frozen hydrated state in order to visualize any differences in structure due to the different methods of preparation. The increased contrast between protein-ice versus protein-glucose may prove to be an advantage of the frozen hydrated technique for visualizing those parts of bacteriorhodopsin that are embedded in glucose. In addition, surface groups of the protein may be disordered in glucose and ordered in the frozen state. The sensitivity of the difference Fourier technique to small changes in structure provides an ideal method for testing this hypothesis.

Antiphase Boundaries in Ordered Ni3FE Crystals

1969 ◽  
Vol 27 ◽  
pp. 62-63
Author(s):  
Y. H. Liu
Keyword(s):  
Domain Size ◽  
Antiphase Domain ◽  
X Ray Diffraction ◽  
X Ray ◽  
Hardening Mechanism ◽  
Superlattice Structure ◽  
Disordered Phase ◽  
Domain Boundaries ◽  
Atomic Scattering ◽  
The Difference

Ordered Ni3Fe crystals possess a LI2 type superlattice similar to the Cu3Au structure. The difference in slip behavior of the superlattice as compared with that of a disordered phase has been well established. Cottrell first postulated that the increase in resistance for slip in the superlattice structure is attributed to the presence of antiphase domain boundaries. Following Cottrell's domain hardening mechanism, numerous workers have proposed other refined models also involving the presence of domain boundaries. Using the anomalous X-ray diffraction technique, Davies and Stoloff have shown that the hardness of the Ni3Fe superlattice varies with the domain size. So far, no direct observation of antiphase domain boundaries in Ni3Fe has been reported. Because the atomic scattering factors of the elements in NijFe are so close, the superlattice reflections are not easily detected. Furthermore, the domain configurations in NioFe are thought to be independent of the crystallographic orientations.

An Adaptive and Learning System for Feedback-Controlled Evoked Response Studies

1981 ◽  
Vol 20 (03) ◽  
pp. 169-173
Author(s):  
J. Wagner ◽  
G. Pfurtscheixer
Keyword(s):  
Brain Activity ◽  
Evoked Response ◽  
Learning System ◽  
Time Interval ◽  
Electrical Brain Activity ◽  
Long Time ◽  
The Subject ◽  
Eeg Power ◽  
Stimulation System ◽  
Background Eeg

The shape, latency and amplitude of changes in electrical brain activity related to a stimulus (Evoked Potential) depend both on the stimulus parameters and on the background EEG at the time of stimulation. An adaptive, learnable stimulation system is introduced, whereby the subject is stimulated (e.g. with light), whenever the EEG power is subthreshold and minimal. Additionally, the system is conceived in such a way that a certain number of stimuli could be given within a particular time interval. Related to this time criterion, the threshold specific for each subject is calculated at the beginning of the experiment (preprocessing) and adapted to the EEG power during the processing mode because of long-time fluctuations and trends in the EEG. The process of adaptation is directed by a table which contains the necessary correction numbers for the threshold. Experiences of the stimulation system are reflected in an automatic correction of this table. Because the corrected and improved table is stored after each experiment and is used as the starting table for the next experiment, the system >learns<. The system introduced here can be used both for evoked response studies and for alpha-feedback experiments.

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