scholarly journals A Dynamical Study of Fusion Hindrance with Nakajima-Zwanzig Projection Method

2021 ◽  
Author(s):  
Yasuhisa Abe ◽  
David Boilley ◽  
Quentin Hourdillé ◽  
Caiwan Shen
Keyword(s):  
Cross Sections ◽  
Degrees Of Freedom ◽  
Operator Method ◽  
Initial Distribution ◽  
Physical Parameters ◽  
Relaxation Processes ◽  
Fast Variable ◽  
Dynamical Study ◽  
Injection Point ◽  
Slow Variables

Abstract A new framework is proposed for the study of collisions between very heavy ions which lead to the synthesis of Super-Heavy Elements (SHE), to address the fusion hindrance phenomenon. The dynamics of the reaction is studied in terms of collective degrees of freedom undergoing relaxation processes with different time scales. The Nakajima-Zwanzig projection operator method is employed to eliminate fast variable and derive a dynamical equation for the reduced system with only slow variables. There, the time evolution operator is renormalised and an inhomogeneous term appears, which represents a propagation of the given initial distribution. The term results in a slip to the initial values of the slow variables. We expect that gives a dynamical origin of the so-called “injection point s” introduced by Swiatecki et al in order to reproduce absolute values of measured cross sections for SHE. A formula for the slip is given in terms of physical parameters of the system, which confirms the results recently obtained with a Langevin equation, and permits us to compare various incident channels.

Analysis of variations in and correlations between selected physical parameters of common beech (Fagus silvatica L.) nuts

2017 ◽  
Vol 1 (21) ◽  
pp. 49-63
Author(s):  
Zdzisław Kaliniewicz ◽  
Piotr Markowski ◽  
Andrzej Anders ◽  
Paweł Tylek ◽  
Zbigniew Krzysiak ◽  
...  
Keyword(s):  
Regression Analysis ◽  
Correlation Analysis ◽  
Cross Sections ◽  
Linear Regression Analysis ◽  
Physical Parameters ◽  
Common Beech ◽  
Mesh Screen ◽  
Before And After ◽  
Fagus Silvatica ◽  
Highly Correlated

The basic dimensions and the mass of common beech nuts and seeds from five nut batches, harvested from tree stands in northern Poland, were determined. Environmental conditions had a greater influence on seed plumpness than the age of tree stands. The results of measurements were analyzed statistically by analysis of variance, correlation analysis and linear regression analysis. Despite differences in their plumpness, nuts were characterized by nearly identical cross-sections which resembled an equilateral triangle. The thickness of nuts and seeds was highly correlated with their mass, and this information can facilitate seed husking and separation into mass categories. Before and after husking, seeds should be separated with the use of a mesh screen with longitudinal openings. Medium-sized (most numerous) seeds were separated into the following plumpness categories using a screen separator with ≠6 mm and ≠7 mm openings: 84% of moderately plump seeds, 3% of seeds with reduced plumpness, and 13% of plump seeds.

Shock discontinuity zone effect: the main factor in the explosive decomposition detonation process

1992 ◽  
Vol 339 (1654) ◽  
pp. 355-364 ◽  
Keyword(s):  
Degrees Of Freedom ◽  
Thermal Ionization ◽  
Relaxation Processes ◽  
Explosive Decomposition ◽  
Time Duration ◽  
Active Particles ◽  
Condensed Explosives ◽  
Discontinuity Zone ◽  
Electronically Excited ◽  
Non Equilibrium

A new qualitative conception of the detonation mechanism in condensed explosives has been developed on the basis of experimental and numerical modelling data. According to the conception the mechanism consists of two stages: non-equilibrium and equilibrium. The mechanism regularities are explosive characteristics and they do not depend on explosive charge structure (particle size, nature of filler in the pores, explosive state, liquid or solid, and so on). The tremendous rate of loading inside the detonation wave shock discontinuity zone ( ca. 10 -13 s) is responsible for the origin of the non-equilibrium stage. For this reason, the kinetic part of the shock compression energy is initially absorbed only by the translational degrees of freedom of the explosive molecules. It involves the appearance of extremely high translational temperatures for the polyatomic molecules. In the course of the translational-vibrational relaxation processes (that is, during the first non-equilibrium stage of ca. 10 -10 s time duration) the most rapidly excited vibrational degrees of freedom can accumulate surplus energy, and the corresponding bonds decompose faster than behind the front at the equilibrium stage. In addition to this process, the explosive molecules become electronically excited and thermal ionization becomes possible inside the translational temperature overheat zone. The molecules thermal decomposition as well as their electronic excitation and thermal ionization result in some active particles (radicals, ions) being created. The active particles and excited molecules govern the explosive detonation decomposition process behind the shock front during the second equilibrium stage. The activation energy is usually low, so that during this stage the decomposition proceeds extremely rapidly. Therefore the experimentally observed dependence of the detonation decomposition time for condensed explosives is rather weak.

Effects of Nano-Nozzles Cross-Sectional Geometry on Fluid Flow: Molecular Dynamic Simulation

2017 ◽  
Vol 34 (5) ◽  
pp. 667-678 ◽  
Author(s):  
H. Nowruzi ◽  
H. Ghassemi
Keyword(s):  
Fluid Flow ◽  
Velocity Profile ◽  
Cross Sections ◽  
Md Simulation ◽  
Flow Behavior ◽  
Water Model ◽  
Physical Parameters ◽  
Cross Sectional ◽  
Behavior Characteristics ◽  
Fanning Friction Factor

AbstractNano-nozzles are an essential part of the nano electromechanical systems (NEMS). Cross-sectional geometry of nano-nozzles has a significant role on the fluid flow inside them. So, main purpose of the present study is related to the effects of different symmetrical cross-sections on the fluid flow behavior inside of nano-nozzles. To this accomplishment, five different cross-sectional geometries (equilateral triangle, square, regular hexagon, elliptical and circular) are investigated by using molecular dynamics (MD) simulation. In addition, TIP4P is used for atomistic water model. In order to evaluate the fluid flow behavior, non-dimensional physical parameters such as Fanning friction factor, velocity profile and density number are analyzed. Obtained results are shown that the flow behavior characteristics appreciably depend on the geometry of nano-nozzle's cross-section. Velocity profile and density number for five different cross sections of nano-nozzle at three various measurement gauges are presented and discussed.

Nonlinear Six-Degree-of-Freedom Dynamic Model for Risers, Pipelines, and Beams

1986 ◽  
Vol 30 (03) ◽  
pp. 177-185
Author(s):  
Michael M. Bernitsas ◽  
John E. Kokarakis
Keyword(s):  
Cross Sections ◽  
Degrees Of Freedom ◽  
Nonlinear Effects ◽  
Nonlinear Formulation ◽  
Marine Risers ◽  
Internal Fluid ◽  
Rotational Degrees Of Freedom ◽  
Six Degree Of Freedom ◽  
Structural Imperfections ◽  
Inertia Forces

A nonlinear model for the dynamic behavior of tubular beams such as marine risers, pipelines, legs of tension leg platforms, and drill strings is developed. The formulation includes three translational degrees of freedom of the riser cross section and three rotational degrees of freedom for shear and torsion. Nonlinear constitutive equations for cross sections of unequal principal stiffnesses and extensible material are derived. Initial structural imperfections which are inherent in long risers are modeled in the form of initial curvature and geometric torsion which do not induce strains. The inertia forces due to the motion of the riser and internal fluid motions are formulated. The external hydrodynamic and hydrostatic forces are integrated on the riser surface as pressure and traction forces. The model is a comprehensive consistent nonlinear formulation of the riser dynamics and can be used for evaluation of the significance of nonlinear effects.

scholarly journals EVOLUTION OF THE CARBON NANOTUBE BUNDLE STRUCTURE UNDER BIAXIAL AND SHEAR STRAINS

2020 ◽  
pp. 525
Author(s):  
Leysan Kh. Rysaeva ◽  
Dmitry V. Bachurin ◽  
Ramil T. Murzaev ◽  
Dina U. Abdullina ◽  
Elena A. Korznikova ◽  
...  
Keyword(s):  
Carbon Nanotube ◽  
Shear Strain ◽  
Cross Sections ◽  
Degrees Of Freedom ◽  
Shear Bands ◽  
Volumetric Strain ◽  
Structural Evolution ◽  
Biaxial Compression ◽  
Chain Model ◽  
Nanotube Bundle

Close packed carbon nanotube bundles are materials with highly deformable elements, for which unusual deformation mechanisms are expected. Structural evolution of the zigzag carbon nanotube bundle subjected to biaxial lateral compression with the subsequent shear straining is studied under plane strain conditions using the chain model with a reduced number of degrees of freedom. Biaxial compression results in bending of carbon nanotubes walls and formation of the characteristic pattern, when nanotube cross-sections are inclined in the opposite directions alternatively in the parallel close-packed rows. Subsequent shearing up to a certain shear strain leads to an appearance of shear bands and vortex-like displacements. Stress components and potential energy as the functions of shear strain for different values of the biaxial volumetric strain are analyzed in detail. A new mechanism of carbon nanotube bundle shear deformation through cooperative, vortex-like displacements of nanotube cross sections is reported.

scholarly journals Evolution Equation and Transport Coefficients of Swarms in Initial Relaxation Processes

1987 ◽  
Vol 40 (3) ◽  
pp. 367 ◽  
Author(s):  
Keiichi Kondo
Keyword(s):  
Evolution Equation ◽  
Transport Coefficients ◽  
Collision Operator ◽  
Operator Method ◽  
Time Dependent ◽  
Relaxation Processes ◽  
Projection Operator Method ◽  
Model Collision ◽  
The Difference ◽  
Dependent Transport

The problem of a swarm approaching the hydrodynamic regime is studied by using the projection operator method. An evolution equation for the density and the related time-dependent transport coefficient are derived. The effects of the initial condition on the transport characteristics of a swarm are separated from the intrinsic evolution of the swarms, and the difference from the continuity equation with time-dependent transport coefficients introduced by Tagashira et al. (1977, 1978) is discussed. To illustrate this method, calculations on the relaxation model collision operator have been carried out. The results are found to agree with the analysis by Robson (1975).

Evolution and stationarity of liquid toroidal drop in compressional Stokes flow

2017 ◽  
Vol 835 ◽  
pp. 1-23 ◽  
Author(s):  
B. K. Ee ◽  
O. M. Lavrenteva ◽  
I. Smagin ◽  
A. Nir
Keyword(s):  
Cross Sections ◽  
Capillary Number ◽  
Initial Conditions ◽  
Extensional Flow ◽  
Building Blocks ◽  
Physical Parameters ◽  
Ambient Fluid ◽  
Medicinal Substances ◽  
Expansion Dynamic ◽  
Axisymmetric Disturbances

Dynamics of fluid tori in slow viscous flow is studied. Such tori are of interest as future carriers of biological and medicinal substances and are also viewed as potential building blocks towards more complex particles. In this study the immiscible ambient fluid is subject to a compressional flow (i.e., bi-extensional flow), and it comprises a generalization of our earlier report on the particular case with viscosity ratio$\unicode[STIX]{x1D706}=1$(see Zabarankinet al.,J. Fluid Mech., vol. 785, 2015, pp. 372–400), where$\unicode[STIX]{x1D706}$is the ratio between the torus viscosity and that of the ambient fluid. It is found that, for all viscosity ratios, the torus either collapses towards the axis of symmetry or expands indefinitely, depending on the initial conditions and the capillary number,Ca. During these dynamic patterns the cross-sections exhibit various forms of deformation. The collapse and expansion dynamic modes are separated by a limited deformation into a deformed stationary state which appears to exist in a finite interval of the capillary number,$0<Ca<Ca_{cr}(\unicode[STIX]{x1D706})$, and is unstable to axisymmetric disturbances, which eventually cause the torus either to collapse or to expand indefinitely. The characteristic dimensions and shapes of these unstable stationary tori and their dependence on the physical parametersCaand$\unicode[STIX]{x1D706}$are reported.

scholarly journals The Dynamical Behavior of a Rigid Body Relative Equilibrium Position

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
T. S. Amer
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Relative Equilibrium ◽  
Dynamical Behavior ◽  
Vertical Plane ◽  
The Body ◽  
Physical Parameters ◽  
Pendulum Model

In this paper, we will focus on the dynamical behavior of a rigid body suspended on an elastic spring as a pendulum model with three degrees of freedom. It is assumed that the body moves in a rotating vertical plane uniformly with an arbitrary angular velocity. The relative periodic motions of this model are considered. The governing equations of motion are obtained using Lagrange’s equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. The numerical solutions are investigated using the fourth-order Runge-Kutta algorithms through Matlab packages. These solutions are represented graphically in order to describe and discuss the behavior of the body at any instant for different values of the physical parameters of the body. The obtained results have been discussed and compared with some previous published works. Some concluding remarks have been presented at the end of this work. The importance of this work is due to its numerous applications in life such as the vibrations that occur in buildings and structures.

X-Ray Fluorescence Cross-Section Measurements in the Energy Range 4-18 keV

1995 ◽  
Vol 39 ◽  
pp. 845-855
Author(s):  
Krassimir N. Stoev ◽  
Joseph F. Dlouhy
Keyword(s):  
Cross Sections ◽  
Transition Probabilities ◽  
Weighted Average ◽  
Physical Parameters ◽  
Emission Rates ◽  
Excitation Energies ◽  
X Ray ◽  
Fluorescence Cross Section ◽  
Theoretical Results

K, L and M shell x-ray fluorescence cross sections have been measured for elements 11 ≤, Z ≤, 92 at excitation energies corresponding to weighted average energies of K-lines of Ti-K (4.558 keV), Fe-K (6,480 keV), Ge-K (10.024 keV), Se-K (11.391 keV) and Mo-K (17.805 keV) . The measurements were performed with an energy-dispersive x-ray spectrometer in a vacuum chamber using thin ultra-pure targets. Rh x-ray tube and secondary targets were used for excitation of x-ray radiation. The measured x-ray fluorescence cross-sections have been compared to previously published experimental and theoretical results. Presented data can be used for determination of physical parameters such as photoionization cross-sections, fluorescence yields, x-ray emission rates, Coster-Kronig transition probabilities and jump ratios.

An Overview on a Nonideal System With Three and a Half Degrees of Freedom

2005 ◽  
Author(s):  
Karen de Lolo Guilherme ◽  
Jose´ Manoel Balthazar ◽  
Paulo Roberto Gardel Kurka ◽  
Masayoshi Tsuchida
Keyword(s):  
Degrees Of Freedom ◽  
Averaging Method ◽  
Dynamical Behavior ◽  
Mathematical Formulation ◽  
Rotation Frequency ◽  
Steady State Solution ◽  
Dc Motor ◽  
Physical Parameters ◽  
Phase Coordinates ◽  
Limited Power

The present paper studies a system comprised of two blocks connected by springs and dampers, and a DC motor with limited power supply fixed on a block, characterizing a non-ideal problem. This DC motor exciting the system causes interactions between the motor and the structure supporting it. Because of that, the non-ideal mathematical formulation of the problem has one and a half extra degree of freedom than the ideal one. A suitable choice of physical parameters leads to internal resonance conditions, that is, its natural frequencies are multiple of each other, by a known integer quantity. The purpose here is to study the dynamic behavior of the system using an analytical method based on perturbation techniques. The literature shows that the averaging method is the more flexible method concerning non-ideal problems. Summarizing, an steady state solution in amplitude and phase coordinates was obtained with averaging method showing the dependence of the structure amplitudes with the rotation frequency of the motor. Moreover, this solution shows that on of the amplitude coordinates has influence in the determination of the stationary rotation frequency. The analytical solution obtained shows the presence of the rotation frequency in expressions representing the oscillations of the structure, and the presence of amplitude coordinates in expressions describing the dynamic motion of the DC motor. These characteristics show the influence not only of the motor on structure but also of the response of the structure on dynamical behavior of the motor.

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