scholarly journals High-precision numerical solution of the Fermi polaron problem and large-order behavior of its diagrammatic series

2020 ◽  
Vol 101 (4) ◽  
Author(s):  
Kris Van Houcke ◽  
Félix Werner ◽  
Riccardo Rossi
Keyword(s):  
Numerical Solution ◽  
High Precision ◽  
Large Order ◽  
Fermi Polaron

scholarly journals Numerical Solution of the Spinor-Spinor Bethe-Salpeter Equation in Functional Nonlinear Spinor Theory

1975 ◽  
Vol 30 (5) ◽  
pp. 656-671
Author(s):  
W. Bauhoff
Keyword(s):  
Angular Momentum ◽  
Excited State ◽  
Variational Method ◽  
Numerical Solution ◽  
High Precision ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
First Order ◽  
Scalar Mesons ◽  
Functional Methods

AbstractThe mass eigenvalue equation for mesons in nonlinear spinor theory is derived by functional methods. In second order it leads to a spinorial Bethe-Salpeter equation. This is solved by a variational method with high precision for arbitrary angular momentum. The results for scalar mesons show a shift of the first order results, obtained earlier. The agreement with experiment is improved thereby. An excited state corresponding to the η' is found. A calculation of a Regge trajectory is included,too.

scholarly journals Numerical Solution of High-Dimensional Nonlinear Rotor-Bearing Dynamic System with Precise Integration

2014 ◽  
Vol 8 (1) ◽  
pp. 264-269
Author(s):  
Guangtian Shi
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Solution ◽  
High Precision ◽  
Integration Method ◽  
Rotor System ◽  
Degree Of Freedom ◽  
High Dimensional ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Rotor Bearing

Through an example of rotor system which has multi-degree of freedom mounted on the nonlinear fluid film bearings, this paper analyzes the precise integration algorithm, a new numerical solution for high–dimensional nonlinear dynamics system. The precise integration method has advantages of long step, high precision and absolute stability for solving nonlinear dynamics equations. To make good use of the method, firstly, the precise integral iterative formula is given and then the mechanism of controlling high precision and efficiency is discussed. The evolution of precise integration method is an algorithm with explicit, simple form, self-start, and fast to solve nonlinear dynamics equations. High power of athwart of Hamiltonian matrix is not needed, so it is convenient in this case. The stability of period response of nonlinear rotor-bearing system is analyzed by employing the precise integration method. The bifurcation rules of the period response of the elastic rotor system with multi-degree of freedom are obtained and the chaos of the system is determined according to the fractal dimension of Poincare mapping of phase space at a certain speed.

scholarly journals Rers2014 and Mrs2014: New High-Precision Rigid Earth Rotation and Moon Rotation Series

2015 ◽  
Vol 50 (1) ◽  
pp. 35-40
Author(s):  
V.V. Pashkevich
Keyword(s):  
Numerical Solution ◽  
Numerical Investigation ◽  
High Precision ◽  
Rotational Motion ◽  
Earth Rotation ◽  
Euler Angles ◽  
Time Intervals ◽  
The Earth ◽  
Long Time ◽  
Rigid Earth

Abstract Numerical investigation of the Earth and Moon rotational motion dynamics is carried out at a long time intervals. In our previous studies (Pashkevich, 2013), (Pashkevich and Eroshkin, 2011) the high-precision Rigid Earth Rotation Series (designated RERS2013) and Moon Rotation Series (designated MRS2011) were constructed. RERS2013 are dynamically adequate to the JPL DE422/LE422 (Folkner, 2011) ephemeris over 2000 and 6000 years and include about 4113 periodical terms (without attempt to estimate new subdiurnal and diurnal periodical terms). MRS2011 are dynamically adequate to the JPL DE406/LE406 (Standish, 1998) ephemeris over 418, 2000 and 6000 years and include about 1520 periodical terms. In present research have been improved the Rigid Earth Rotation Series RERS2013 and Moon Rotation Series MRS2011, and as a result have been constructed the new high-precision Rigid Earth Rotation Series RERS2014 and Moon Rotation Series MRS2014 dynamically adequate to the JPL DE422/LE422 ephemeris over 2000 and 6000 years, respectively. The elaboration of RERS2013 is carried out by means recalculation of sub-diurnal and diurnal periodical terms. The residuals in Euler angles between the numerical solution and RERS2014 do not surpass 3 ìas over 2000 years. Improve the accuracy of the series MRS2011 is obtained by using the JPL DE422/LE422 ephemeris. The residuals in the perturbing terms of the physical librations between the numerical solution and MRS2014 do not surpass 8 arc seconds over 6000 years

Range Particle Algorithm Application in the Solving Inverse Problem of Line Source

2012 ◽  
Vol 532-533 ◽  
pp. 1492-1496
Author(s):  
Ke Guang Yu
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
High Precision ◽  
Line Source ◽  
Measured Data ◽  
Range Searching ◽  
Computational Stability ◽  
Mathematical Solution ◽  
Source Particle ◽  
Implementation Steps

Now mature and effective algorithms for the numerical solution of inverse problem of line source are few, so the researching of algorithms for the problem is urgent and necessary. Firstly, a brief introduction to the characteristics of solving the inverse problem of the line source is given, and the mathematical solution model of inverse problem is established based on the Line source equation, Secondly a new algorithm (Range Particle algorithm) based on range searching algorithm is proposed for the numerical solving the inverse problem of the line source particle and the basic implementation steps and parameter adjustment of the algorithm also be discussed. Finally, simulated and measured data were used to test the effect of the algorithm. The results show that the range particle algorithm is an algorithm of high precision, fast convergence and computational stability for the solving the inverse problem of the line source and it do can be applied in Engineering.

scholarly journals MRS2016: Rigid Moon Rotation Series in the Relativistic Approximation

2017 ◽  
Vol 52 (1) ◽  
pp. 1-8
Author(s):  
V.V. Pashkevich
Keyword(s):  
Numerical Solution ◽  
High Precision ◽  
Analytical Solutions ◽  
Analytical Methods ◽  
The Moon ◽  
Relativistic Approximation ◽  
First Time ◽  
Numerical And Analytical Methods

Abstract The rigid Moon rotation problem is studied for the relativistic (kinematical) case, in which the geodetic perturbations in the Moon rotation are taken into account. As the result of this research the high-precision Moon Rotation Series MRS2016 in the relativistic approximation was constructed for the first time and the discrepancies between the high-precision numerical and the semi-analytical solutions of the rigid Moon rotation were investigated with respect to the fixed ecliptic of epoch J2000, by the numerical and analytical methods. The residuals between the numerical solution and MRS2016 in the perturbing terms of the physical librations do not exceed 80 mas and 10 arc seconds over 2000 and 6000 years, respectively.

scholarly journals Construction of the New High-Precision Moon Rotation Series at a Long Time Intervals

2011 ◽  
Vol 46 (2) ◽  
pp. 63-73
Author(s):  
V. Pashkevich ◽  
G. Eroshkin
Keyword(s):  
Numerical Solution ◽  
High Precision ◽  
Initial Conditions ◽  
Analytical Theory ◽  
Time Interval ◽  
The Moon ◽  
Time Intervals ◽  
Good Consistency ◽  
Newtonian Case ◽  
Long Time

Construction of the New High-Precision Moon Rotation Series at a Long Time Intervals The main purposes of this research are the construction of the new high-precision Moon Rotation Series (MRS2011), dynamically adequate to the DE404/LE404 and the DE406/LE406 ephemeris, over long time intervals. The comparison of the new highprecision Moon Rotation solutions of MRS2011 with the solution of MRS2010 (Pashkevich and Eroshkin, 2010), which is dynamically adequate to the DE200/LE200 ephemeris over 418.9 year time interval, is performed. The dynamics of the rotational motion of the Moon is studied numerically by using Rodrigues-Hamilton parameters over 418.9, 2000 and 6000 years. The numerical solution of the Moon rotation is implemented with the quadruple precision of the calculations. The results of the numerical solution of the problem are compared with the composite semi-analytical theory of the Moon rotation (SMR) (Pashkevich and Eroshkin, 2010) with respect to the fixed ecliptic of epoch J2000. The initial conditions of the numerical integration are taken from SMR. The investigation of the discrepancies is carried out by the least squares and spectral analysis methods for the Newtonian case. All the secular, periodic and Poisson terms, representing the behavior of the residuals, are interpreted as corrections to SMR semi-analytical theory. As a result, the Moon Rotation Series (MRS2011) is constructed, which is dynamically adequate to the DE404/LE404 and the DE406/LE406 ephemeris over 418.9, 2000 and 6000 years. A numerical solution for the Moon rotation is obtained anew with the new initial conditions calculated by means of MRS2011. The discrepancies between the new numerical solution and the semi-analytical solution of MRS2011 do not surpass 20 mas over 418.9 year time interval, 64 mas over 2000 year time interval and 8 arc seconds over 6000 year time interval. Thus, the result of the comparison demonstrates a good consistency of MRS2011 series with the DE/LE ephemeris.

scholarly journals Numerical solution of a class of advection-reaction-diffusion system

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1503-1511
Author(s):  
Li Cao ◽  
Zhanxin Ma
Keyword(s):  
Numerical Experiment ◽  
Numerical Solution ◽  
Collocation Method ◽  
High Precision ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Collocation Methods ◽  
Barycentric Interpolation ◽  
Precision Method

In this article, the barycentric interpolation collocation methods is proposed for solving a class of non-linear advection-reaction-diffusion system. Compared with other methods, the numerical experiment shows the barycentric interpolation collocation method is a high precision method to solve the advection- reaction-diffusion system.

Automatic measurement of SAED patterns from asbestos minerals

1988 ◽  
Vol 46 ◽  
pp. 846-847
Author(s):  
J. C. Russ ◽  
T. Taguchi ◽  
P. M. Peters ◽  
E. Chatfield ◽  
J. C. Russ ◽  
...  
Keyword(s):  
Diffraction Pattern ◽  
High Precision ◽  
Diffraction Data ◽  
Automatic Measurement ◽  
Automatic Method ◽  
Important Method ◽  
X Ray ◽  
Integrated Intensity ◽  
Asbestiform Minerals ◽  
True Center

Conventional SAD patterns as obtained in the TEM present difficulties for identification of materials such as asbestiform minerals, although diffraction data is considered to be an important method for making this purpose. The preferred orientation of the fibers and the spotty patterns that are obtained do not readily lend themselves to measurement of the integrated intensity values for each d-spacing, and even the d-spacings may be hard to determine precisely because the true center location for the broken rings requires estimation. We have implemented an automatic method for diffraction pattern measurement to overcome these problems. It automatically locates the center of patterns with high precision, measures the radius of each ring of spots in the pattern, and integrates the density of spots in that ring. The resulting spectrum of intensity vs. radius is then used just as a conventional X-ray diffractometer scan would be, to locate peaks and produce a list of d,I values suitable for search/match comparison to known or expected phases.

On effects of non-systematic reflections on weak-beam images of partial dislocations

1991 ◽  
Vol 49 ◽  
pp. 688-689
Author(s):  
K. Z. Botros ◽  
S. S. Sheinin
Keyword(s):  
High Precision ◽  
Stacking Fault ◽  
Important Application ◽  
Stacking Fault Energy ◽  
Sharp Peak ◽  
Weak Beam ◽  
Partial Dislocations ◽  
Deviation Parameter ◽  
Beam Diffraction

The main features of weak beam images of dislocations were first described by Cockayne et al. using calculations of intensity profiles based on the kinematical and two beam dynamical theories. The feature of weak beam images which is of particular interest in this investigation is that intensity profiles exhibit a sharp peak located at a position very close to the position of the dislocation in the crystal. This property of weak beam images of dislocations has an important application in the determination of stacking fault energy of crystals. This can easily be done since the separation of the partial dislocations bounding a stacking fault ribbon can be measured with high precision, assuming of course that the weak beam relationship between the positions of the image and the dislocation is valid. In order to carry out measurements such as these in practice the specimen must be tilted to "good" weak beam diffraction conditions, which implies utilizing high values of the deviation parameter Sg.

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