hydrodynamic equations
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Author(s):  
Hsiu-Chung Yeh ◽  
Dimitri M Gangardt ◽  
A Kamenev

Abstract We study large deviations in interacting quantum liquids with the polytropic equation of state P (ρ) ∼ ργ, where ρ is density and P is pressure. By solving hydrodynamic equations in imaginary time we evaluate the instanton action and calculate the emptiness formation probability (EFP), the probability that no particle resides in a macroscopic interval of a given size. Analytic solutions are found for a certain infinite sequence of rational polytropic indexes γ and the result can be analytically continued to any value of γ ≥ 1. Our findings agree with (and significantly expand on) previously known analytical and numerical results for EFP in quantum liquids. We also discuss interesting universal spacetime features of the instanton solution.


2022 ◽  
Vol 258 ◽  
pp. 05008
Author(s):  
Alexander Soloviev

The evolution of a heavy ion collision passes close to the O(4) critical point of QCD, where fluctuations of the order parameter are expected to be enhanced. Using the appropriate stochastic hydrodynamic equations in mean field near the the pseudo-critical point, we compute how these enhanced fluctuations modify the transport coefficients of QCD. Finally, we estimate the expected critical enhancement of soft pion yields, which provides a plausible explanation for the excess seen in experiment relative to ordinary hydrodynamic computations.


Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 20
Author(s):  
Moise Bonilla-Licea ◽  
Dieter Schuch

Madelung showed how the complex Schrödinger equation can be rewritten in terms of two real equations, one for the phase and one for the amplitude of the complex wave function, where both equations are not independent of each other, but coupled. Although these equations formally look like classical hydrodynamic equations, they contain all the information about the quantum system. Concerning the quantum mechanical uncertainties of position and momentum, however, this is not so obvious at first sight. We show how these uncertainties are related to the phase and amplitude of the wave function in position and momentum space and, particularly, that the contribution from the phase essentially depends on the position–momentum correlations. This will be illustrated explicitly using generalized coherent states as examples.


MAUSAM ◽  
2021 ◽  
Vol 48 (2) ◽  
pp. 323-328
Author(s):  
P.S. MUKHOPADHYAY ◽  
G. K. MANDAL ◽  
G. K. SEN ◽  
D. K. SINHA

ABSTRACT. In this paper we have tried to set up a mathematical model that will show the contribution of wind-induced surface waves of the ocean, on surges in shallow basin of Bay of Bengal. For this, the energy balance equation, excluding non-linear forcing term, is considered and solved by Lax-Wendroff integration scheme. Wind is specified over all the grid points following Cardone' s formulation. The hydrodynamic equations in linearised form as used by Jelesnianski have been considered and using Shuman's algorithm, those equations have been solved. In the process of solving these equations, the output of the energy balance equation is included as wave set up term to incorporate energy contribution of wind waves to surges. The estimated surge height is compared with and without considering wave contribution.      


Author(s):  
Vitaliy Stelmashuk ◽  
Jiri Schmidt

Abstract We present a study that was undertaken to calculate the resistance of low current corona discharge in saline water. A novel empirical model was obtained, based on several assumptions, which allowed us to determine the corona resistance using the measured current. This resistance could be then exploited to compute the power deposited to the corona as a function of time. The wall motion of a bubble freely oscillating in saline water was calculated using hydrodynamic equations and the calculated power function. A comparison of numerical simulations with experimental results showed that good agreement was achieved.


2021 ◽  
Vol 1201 (1) ◽  
pp. 012017
Author(s):  
A S Lokhov ◽  
M G Gubaidullin ◽  
V B Korobov

Abstract A volumetric model of accidental oil spills on the land surface was developed, based on numerical methods for solving hydrodynamic equations, and taking into account the processes of oil spreading over the surface, its filtration into the soil and evaporation into the atmosphere. Based on the results of calculations using the hydrodynamic model for the most probable scenarios of oil spills, it is possible to obtain an estimate of the spatial-temporal scale of the spill, which, together with data on the terrain and the presence of water bodies, is the input data for the expert model. Based on the joint use of the hydrodynamic model of the oil spill and expert technologies, the territory of the Nenets Autonomous Okrug and the South Khylchuyu-Varandey oil pipeline were zoned in more detail. It makes it possible to predict the scale and areas most susceptible to negative impact in the event of an accidental oil spill, and to make the necessary decisions for the location of the spill response facilities, as well as the facilities themselves, already at the stage of selection and design of the pipeline route.


2021 ◽  
Vol 31 (2) ◽  
pp. 75-83

Autonomous Underwater Vehicles (AUV) is an unmanned underwater device with capability of performing a variety of missions in the water environment such as ocean operation, offshore waters, polluted water investigation including: marine scientific research, maritime monitoring, exploration, marine economics, oil and gas, security and defense, surveillance and measurement and in rescue and salve. In this article, the authors developed a model of AUV with retractable wings and evaluate the efficiency of solar energy collection. The establishment of the controller to adapt the stability requirements, in accordance with the model of equipment S-AUV (Solar - Autonomous Underwater Vehicles) was built. The hydrodynamic equations with the predefined conditions were modeled and solved. The Hierarchical Sliding Mode Controller (HSMC) for the S-AUV were applied in this research. Experimental results showed that the efficiency of the collection of the solar cell has been significantly improved comparing to a diving equipment without retractable energy wings. In addition, the simulation results showed that the developed controller performed much better control quality, adhering to the set value with the error within the permissible limit.


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