Rankine-Hugoniot Relations for Lennard-Jones Liquids

1994 ◽  
Vol 116 (3) ◽  
pp. 625-630 ◽  
Author(s):  
Akira Satoh
Keyword(s):  
Shock Waves ◽  
Ideal Gas ◽  
The State ◽  
Lennard Jones ◽  
Internal Structures ◽  
Shock Mach Number ◽  
Basic Equations ◽  
Dynamics Simulations ◽  
Approximate Expressions ◽  
Shock Fronts

The purpose of the present study is to clarify the Rankine-Hugoniot relations for Lennard-Jones liquids. First, Monte Carlo simulations are conducted to evaluate the state quantities such as the pressures, the internal energies, and the sound velocities. These computed values are used to obtain the approximate expressions for the state quantities by the method of least squares. The Rankine-Hugoniot relations are then clarified numerically as a function of the shock Mach number by solving the basic equations together with those approximate expressions. For liquid shock waves, not only the pressure but also the temperature increases much larger than those for an ideal gas. The results obtained here enable us to conduct more efficient molecular dynamics simulations such as simulating shock fronts alone for the investigation of the internal structures of liquid shock waves.

Molecular Dynamics Simulations on Internal Structures of Normal Shock Waves in Lennard-Jones Liquids

1995 ◽  
Vol 117 (1) ◽  
pp. 97-103 ◽  
Author(s):  
Akira Satoh
Keyword(s):  
Molecular Dynamics ◽  
Boundary Condition ◽  
Mach Number ◽  
Shock Waves ◽  
Molecular Dynamics Simulations ◽  
Normal Shock ◽  
Lennard Jones ◽  
Internal Structures ◽  
Dynamics Simulations ◽  
Shock Fronts

The present paper describes a highly efficient method for simulating the generation of shock waves in liquids by using the periodic-shell boundary condition, which is an outer boundary condition for molecular dynamics simulations. This method is used to simulate normal shock waves in Lennard-Jones liquids, clarifying the internal structures of shock fronts and the dependence of shock thicknesses on the shock Mach number. The present method significantly decreases computation times because it enables us to simulate only the shock fronts. Some of the main results derived by these simulations of molecular dynamics are that an overshoot in the profile of longitudinal temperature arises in liquid shock waves as well as in gas shock waves, that the thickness of shock front decreases with increasing Mach number, and that this thickness is about two times the diameter of molecules when the Mach number is 4.

Equation of state of a Lennard-Jones 12-6 pairwise additive fluid

1980 ◽  
Vol 45 (4) ◽  
pp. 977-983 ◽  
Author(s):  
Jan Sýs ◽  
Anatol Malijevský
Keyword(s):  
Equation Of State ◽  
Empirical Equation ◽  
The State ◽  
Critical Properties ◽  
Lennard Jones ◽  
State Behaviour ◽  
Compressibility Factors

An empirical equation of state was proposed, which is based on pseudoexperimental data on the state behaviour. The equation can be used at reduced temperatures from the range 0.7-100.0 and reduced densities up to 2. Calculated compressibility factors and critical properties agree well with available literature data.

Multicanonical Molecular Dynamics Simulation Study of the Liquid-Solid and Solid-Solid Transitions in Lennard-Jones Clusters

2011 ◽  
Author(s):  
Toshihiro Kaneko ◽  
Kenji Yasuoka ◽  
Ayori Mitsutake ◽  
Xiao Cheng Zeng
Keyword(s):  
Molecular Dynamics ◽  
Heat Capacity ◽  
Transition Temperature ◽  
Peak Position ◽  
Temperature Curve ◽  
Dynamics Simulation ◽  
Lennard Jones ◽  
Dynamics Simulations ◽  
First Time ◽  
Good Agreement

Multicanonical molecular dynamics simulations are applied, for the first time, to study the liquid-solid and solid-solid transitions in Lennard-Jones (LJ) clusters. The transition temperatures are estimated based on the peak position in the heat capacity versus temperature curve. For LJ31, LJ58 and LJ98, our results on the solid-solid transition temperature are in good agreement with previous ones. For LJ309, the predicted liquid-solid transition temperature is also in agreement with previous result.

Molecular Dynamics Study of Ion Impact Phenomena and Compressive Stress in Thin Films

1993 ◽  
Vol 317 ◽  
Author(s):  
N.A. Marks ◽  
P. Guan ◽  
D.R. Mckenzie ◽  
B.A. PailThorpe
Keyword(s):  
Molecular Dynamics ◽  
Three Dimensional ◽  
Carbon Films ◽  
Loss Mechanism ◽  
Ion Energy ◽  
Lennard Jones ◽  
Impact Phenomena ◽  
Ion Impact ◽  
Dynamics Simulations ◽  
The Impact

ABSTRACTMolecular dynamics simulations of nickel and carbon have been used to study the phenomena due to ion impact. The nickel and carbon interactions were described using the Lennard-Jones and Stillinger-Weber potentials respectively. The phenomena occurring after the impact of 100 e V to 1 keV ions were studied in the nickel simulations, which were both two and three-dimensional. Supersonic focussed collision sequences (or focusons) were observed, and associated with these focusons were unexpected sonic bow waves, which were a major energy loss mechanism for the focuson. A number of 2D carbon films were grown and the stress in the films as a function of incident ion energy was Measured. With increasing energy the stress changed from tensile to compressive and reached a maximum around 50 eV, in agreement with experiment.

scholarly journals Shear-rate dependence of thermodynamic properties of the Lennard-Jones truncated and shifted fluid by molecular dynamics simulations

2021 ◽  
Author(s):  
Martin P. Lautenschlaeger ◽  
Hans Hasse
Keyword(s):  
Molecular Dynamics ◽  
Shear Stress ◽  
Shear Rate ◽  
Molecular Dynamics Simulations ◽  
Local Structure ◽  
Rate Dependence ◽  
Lennard Jones ◽  
Fluid Properties ◽  
Dynamics Simulations ◽  
Shear Rate Dependence

It was shown recently that using the two-gradient method, thermal, caloric, and transport properties of fluids under quasi-equilibrium conditions can be determined simultaneously from nonequilibrium molecular dynamics simulations. It is shown here that the influence of shear stresses on these properties can also be studied using the same method. The studied fluid is described by the Lennard-Jones truncated and shifted potential with the cut-off radius r*c = 2.5σ. For a given temperature T and density ρ, the influence of the shear rate on the following fluid properties is determined: pressure p, internal energy u, enthalpy h, isobaric heat capacity cp, thermal expansion coefficient αp, shear viscosity η, and self-diffusion coefficient D. Data for 27 state points in the range of T ∈ [0.7, 8.0] and ρ ∈ [0.3, 1.0] are reported for five different shear rates (γ ̇ ∈ [0.1,1.0]). Correlations for all properties are provided and compared with literature data. An influence of the shear stress on the fluid properties was found only for states with low temperature and high density. The shear-rate dependence is caused by changes in the local structure of the fluid which were also investigated in the present work. A criterion for identifying the regions in which a given shear stress has an influence on the fluid properties was developed. It is based on information on the local structure of the fluid. For the self-diffusivity, shear-induced anisotropic effects were observed and are discussed.

scholarly journals APPLICATION OF THE LENNARD-JONES POTENTIAL IN MODELLING ROBOT MOTION

2019 ◽  
Vol 9 (4) ◽  
pp. 14-17
Author(s):  
Piotr Wójcicki ◽  
Tomasz Zientarski
Keyword(s):  
Interaction Strength ◽  
Robot Motion ◽  
Lennard Jones Potential ◽  
Ordered Group ◽  
Jones Potential ◽  
Lennard Jones ◽  
Optimal Value ◽  
Potential Impact ◽  
Moving Groups ◽  
Dynamics Simulations

The article proposes a method of controlling the movement of a group of robots with a model used to describe the interatomic interactions. Molecular dynamics simulations were carried out in a system consisting of a moving groups of robots and fixed obstacles. Both the obstacles and the group of robots consisted of uniform spherical objects. Interactions between the objects are described using the Lennard-Jones potential. During the simulation, an ordered group of robots was released at a constant initial velocity towards the obstacles. The objects’ mutual behaviour was modelled only by changing the value of the interaction strength of the potential. The computer simulations showed that it is possible to find the optimal value of the potential impact parameters that enable the implementation of the assumed robotic behaviour scenarios. Three possible variants of behaviour were obtained: stopping, dispersing and avoiding an obstacle by a group of robots.

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