scholarly journals Path Integral Estimates of the Quantum Fluctuations of the Relative Soliton-Soliton Velocity in a Gross-Pitaevskii Breather

Physics ◽  
2022 ◽  
Vol 4 (1) ◽  
pp. 12-20
Author(s):  
Sumita Datta ◽  
Vanja Dunjko ◽  
Maxim Olshanii
Keyword(s):  
Quantum Monte Carlo ◽  
Relative Velocity ◽  
Integration Method ◽  
Monte Carlo Calculation ◽  
Quantum Fluctuations ◽  
Suggested Approach ◽  
Bogoliubov Approximation ◽  
Path Integration Method ◽  
Good Agreement ◽  
Body Correlation

In this paper, the quantum fluctuations of the relative velocity of constituent solitons in a Gross-Pitaevskii breather are studied. The breather is confined in a weak harmonic trap. These fluctuations are monitored, indirectly, using a two-body correlation function measured at a quarter of the harmonic period after the breather creation. The results of an ab initio quantum Monte Carlo calculation, based on the Feynman-Kac path integration method, are compared with the analytical predictions using the recently suggested approach within the Bogoliubov approximation, and a good agreement is obtained.

OPTIMAL VELOCITY MODEL WITH RELATIVE VELOCITY

2006 ◽  
Vol 17 (01) ◽  
pp. 65-73 ◽  
Author(s):  
SHIRO SAWADA
Keyword(s):  
Nonlinear Analysis ◽  
Relative Velocity ◽  
Velocity Model ◽  
Fundamental Diagram ◽  
Optimal Velocity ◽  
Traffic Jam ◽  
Optimal Velocity Model ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Good Agreement

The optimal velocity model which depends not only on the headway but also on the relative velocity is analyzed in detail. We investigate the effect of considering the relative velocity based on the linear and nonlinear analysis of the model. The linear stability analysis shows that the improvement in the stability of the traffic flow is obtained by taking into account the relative velocity. From the nonlinear analysis, the relative velocity dependence of the propagating kink solution for traffic jam is obtained. The relation between the headway and the velocity and the fundamental diagram are examined by numerical simulation. We find that the results by the linear and nonlinear analysis of the model are in good agreement with the numerical results.

Stochastic dynamics of a nonlinear time-varying spur gear model using an adaptive time-stepping path integration method

2019 ◽  
Vol 447 ◽  
pp. 170-185
Author(s):  
Saeed Gheisari Hasnijeh ◽  
Mehrdad Poursina ◽  
Bernt Johan Leira ◽  
Hossein Karimpour ◽  
Wei Chai
Keyword(s):  
Path Integration ◽  
Stochastic Dynamics ◽  
Integration Method ◽  
Spur Gear ◽  
Time Varying ◽  
Time Stepping ◽  
Path Integration Method ◽  
Adaptive Time ◽  
Adaptive Time Stepping

Relationship between installation torque and uplift capacity of deep helical piles in sand

2010 ◽  
Vol 47 (6) ◽  
pp. 635-647 ◽  
Author(s):  
Cristina de Hollanda Cavalcanti Tsuha ◽  
Nelson Aoki
Keyword(s):  
Laboratory Tests ◽  
Friction Angle ◽  
Correlation Factor ◽  
Experimental Program ◽  
Uplift Capacity ◽  
Suggested Approach ◽  
Interface Friction ◽  
Helical Piles ◽  
Shear Interface ◽  
Good Agreement

The empirical torque correlation factor (KT), which relates the uplift capacity to the installation torque of helical piles, is routinely used as an on-site instrument for quality control with this type of foundation. This paper presents a theoretical relationship between uplift capacity and installation torque of deep helical piles in sand. An experimental program, including centrifuge and direct shear interface tests, was carried out to validate this expression. The experimental results were compared with the values predicted by the suggested approach and showed good agreement. As the developed model depends on the residual interface friction angle (δr) between the helix surface and the surrounding sand, results of δr, extracted from different sand samples, are presented for use in this suggested relationship on site. Also, the values of KT found in this work were compared with those of field and laboratory tests on helical piles in sand reported in the literature. From this analysis, it was found that the measured values of KT decrease with an increase in pile dimensions and, in most of cases, with an increase in sand friction angle. These results were explained by the presented model.

Experimental, DFT and quantum Monte Carlo studies of a series of peptide-based metal–organic frameworks: synthesis, structures and properties

2014 ◽  
Vol 1 (7) ◽  
pp. 526-533 ◽  
Author(s):  
Gui-lin Zhuang ◽  
Li Tan ◽  
Wu-lin Chen ◽  
Jun Zheng ◽  
Hong-zhou Yao ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Monte Carlo Calculation ◽  
Metal Organic Frameworks ◽  
Experimental Measurements ◽  
Function Structure ◽  
Structures And Properties ◽  
Structure Relation ◽  
Monte Carlo Studies ◽  
Metal Organic

Properties and the function–structure relation of four peptide-based MOFs were identified by experimental measurements, DFT and quantum Monte Carlo calculation.

Importance of coupling for inelastic collisions between protons and hydrogen atoms

1965 ◽  
Vol 283 (1392) ◽  
pp. 100-114 ◽  
Keyword(s):  
Cross Sections ◽  
Intermediate State ◽  
Relative Velocity ◽  
Inelastic Collisions ◽  
Hydrogen Atoms ◽  
Resonance Reactions ◽  
The Cross ◽  
Good Agreement

The importance of coupling for fast collisions between protons and hydrogen atoms is examined with the two-centred expansion in atomic eigenfunctions proposed by Bates (1958 a ). Cross-sections are evaluated for reactions H + + H (I s ) → H(I s ) + H + , H + + H( I s ) → H(2 s ) + H + , and H + + H(l a ) → H + + H(2 s ). The effect of a single intermediate state, either I s or 2 s , is considered. For the non-resonance processes, it is found that the cross-sections may be substantially increased by passage through intermediate state for incident energies less than about 10 keV, tending towards equality with decrease in relative velocity. Results obtained for the symmetrical resonance reactions are in good agreement with the two-state solutions of McCarroll (1961).

scholarly journals Numerical Techniques for Solving Linear Volterra Fractional Integral Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Safa’ Hamdan ◽  
Naji Qatanani ◽  
Adnan Daraghmeh
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Fractional Integral ◽  
Integration Method ◽  
Haar Wavelet ◽  
Numerical Techniques ◽  
Product Integration ◽  
Fractional Integral Equation ◽  
Product Integration Method ◽  
Good Agreement

Two numerical techniques, namely, Haar Wavelet and the product integration methods, have been employed to give an approximate solution of the fractional Volterra integral equation of the second kind. To test the applicability and efficiency of the numerical method, two illustrative examples with known exact solution are presented. Numerical results show clearly that the accuracy of these methods are in a good agreement with the exact solution. A comparison between these methods shows that the product integration method provides more accurate results than its counterpart.

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