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Academic literature on the topic 'Lennard-Jones type Particles'

Author: Grafiati
Published: 7 September 2023

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Journal articles on the topic "Lennard-Jones type Particles"

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RETKUTE, RENATA, and JAMES P. GLEESON. "ROLE OF INTERACTION ON NOISE-INDUCED TRANSPORT OF TWO COUPLED PARTICLES IN BROWNIAN RATCHET DEVICES." Fluctuation and Noise Letters 06, no. 03 (September 2006): L263—L277. http://dx.doi.org/10.1142/s0219477506003409.

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The motion of elastically coupled Brownian particles in ratchet-like potentials has attracted much recent interest due to its application to transport processes in many fields, including models of DNA polymers. We consider the influence of the type of interacting force on the transport of two particles in a one-dimensional flashing ratchet. Our aim is to examine whether the common assumption of elastic coupling captures the important features of ratchet transport when the inter-particle forces are more complex. We compare Lennard-Jones type interaction to the classical case of elastically coupled particles. Numerical simulations agree with analytical formulas for the limiting cases where the coupling is very weak or very strong. Parameter values where the Lennard-Jones force is not well approximated by a linearization of the force about the equilibrium distance are identified.
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GRIDNEV, K. A., S. YU TORILOV, D. K. GRIDNEV, V. G. KARTAVENKO, and W. GREINER. "MODEL OF BINDING ALPHA-PARTICLES AND APPLICATIONS TO SUPERHEAVY ELEMENTS." International Journal of Modern Physics E 14, no. 04 (June 2005): 635–43. http://dx.doi.org/10.1142/s0218301305003387.

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A model of nuclear matter built from alpha-particles is proposed. In this model, nuclei possess the molecular-like structure. Analyzing the numbers of bonds, one gets the formula for the binding energy of a nucleus. The structure is determined by the minimum of the total potential energy, where interaction between alpha-particles is pairwise and the pair-potential is of Lennard–Jones type. The calculated binding energies show a good agreement with experiment. Calculations predict the stability island for superheavy nuclei around Z=120.
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TEWARI, S. P., GRIMA DHINGRA, and POONAM SILOTIA. "COLLECTIVE DYNAMICS OF A NANO-FLUID: FULLERENE, C60." International Journal of Modern Physics B 24, no. 22 (September 10, 2010): 4281–92. http://dx.doi.org/10.1142/s0217979210055974.

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Collective dynamics of a strongly correlated nano-fluid of fullerenes, C 60 having number density 0.945 particles/nm3 at 1850 K has been predicted using the sphericalized inter-fullerene interaction and the self-consistent microscopic theory of fluids. The dynamical structure factors have been computed to yield much different dispersion relation of the collective excitations from that of the Lennard–Jones type fluid. The wave-vector dependent longitudinal viscosity of the nano-fluid has also been reported.
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Camrud, Evan, David P. Herzog, Gabriel Stoltz, and Maria Gordina. "Weighted L 2-contractivity of Langevin dynamics with singular potentials." Nonlinearity 35, no. 2 (December 29, 2021): 998–1035. http://dx.doi.org/10.1088/1361-6544/ac4152.

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Abstract Convergence to equilibrium of underdamped Langevin dynamics is studied under general assumptions on the potential U allowing for singularities. By modifying the direct approach to convergence in L 2 pioneered by Hérau and developed by Dolbeault et al, we show that the dynamics converges exponentially fast to equilibrium in the topologies L 2(dμ) and L 2(W* dμ), where μ denotes the invariant probability measure and W* is a suitable Lyapunov weight. In both norms, we make precise how the exponential convergence rate depends on the friction parameter γ in Langevin dynamics, by providing a lower bound scaling as min(γ, γ −1). The results hold for usual polynomial-type potentials as well as potentials with singularities such as those arising from pairwise Lennard-Jones interactions between particles.
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Steinhauser, Martin O., and Erkai Watson. "Discrete Particle Methods for Simulating Quasi-Static Load and Hypervelocity Impact Phenomena." International Journal of Computational Methods 16, no. 05 (May 28, 2019): 1740009. http://dx.doi.org/10.1142/s0219876217400096.

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In this paper, we introduce a mesh-free computational model for the simulation of high-speed impact phenomena. Within the framework of particle dynamics simulations we model a macroscopic solid ceramic tile as a network of overlapping discrete particles of microscopic size. Using potentials of the Lennard–Jones type, we integrate the classical Newtonian equations of motion and perform uni-axial, quasi-static load simulations to customize our three model parameters to the typical tensile strength, Young’s modulus and the compressive strength of a ceramic. Subsequently we perform shock load simulations in a standard experimental setup, the edge-on impact (EOI) configuration. Our obtained results concerning crack initiation and propagation through the material agree well with corresponding high-speed EOI experiments with Aluminum Oxinitride (AlON), Aluminum Oxide [Formula: see text] and Silicon Carbide (SiC), performed at the Fraunhofer Ernst-Mach-Institute (EMI). Additionally, we present initial simulation results where we use our particle–based model to simulate a second type of high-speed impact experiments where an accelerated sphere strikes a thin aluminum plate. Such experiments are done at our institute to investigate the debris clouds arising from such impacts, which constitute a miniature model version of a generic satellite structure that is hit by debris in the earth’s orbit. Our findings are that a discrete particle based method leads to very stable, energy-conserving simulations of high–speed impact scenarios. Our chosen interaction model works particularly well in the velocity range where the local stresses caused by impact shock waves markedly exceed the ultimate material strength.
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Golabczak, Marcin, Andrzej Konstantynowicz, and Andrzej Golabczak. "Use of Cellular Automata for Modelling of the Carbon Nanolayer Growth on a Light Alloy Substrate." Journal of Nano Research 26 (December 2013): 159–67. http://dx.doi.org/10.4028/www.scientific.net/jnanor.26.159.

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Carbon deposition forming a nanolayer on a light alloy substrate is a physico-chemical process of the discrete type in all of its aspects. Thus, use of cellular automata, intrinsic discrete, as a mathematical tool for modelling, is fully justified. We adopted two-dimensional (i.e. surface), two-layer automation with Moore vicinity of a cell, for modelling of the carbon deposition process, starting from bonding to the light alloy substrate, leading through layer growth and finishing at the phase transition process, converting graphite into diamond form. To achieve this, we related the transition probabilities of the automaton with the Lennard-Jones potentials for carbon and metal atoms, as well as the physico-chemical conditions in the reaction environment gaseous hydrocarbons density and their particles energy distribution (Maxwell). Taking it into account allowed us to establish an automation time scale of about 1s per calculations run, which has resulted in a simulated layer thickness growth rate well matched with observed results. Using of the two-layer automation allowed us to make some survey into the mechanism of the graphite/diamond transition in the real environmental conditions we met. This demanded further thorough investigations to properly model the spatial structure of mutually interleaved areas of the graphite and diamond type carbon, giving not only a flat-surface but also a vertical structure. The overall surface morphology of the simulated nanolayer we have compared with those of AFM survey performed on real samples, observing relatively good matching in terms of statistical parameters of the surface.
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Prozorova, Evelina. "Some Consequences of Mathematical Inaccuracies in Mechanics." WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS 17 (September 16, 2022): 124–31. http://dx.doi.org/10.37394/232011.2022.17.17.

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The article is devoted to the study of some violations of the known laws of mathematics and classical mechanics in continuum mechanics and kinetics. The most common is open non-stationary systems. From the equations formulated earlier and some experiments, a connection traced between the gradients of physical quantities and the angular momentum (force). The use of Hamilton's formalism and the dependence of force only on the distance between particles limits the study. In the collision integral, for example, for a rarefied gas, the Lennard-Jones potential, which not related to the type under consideration, is often used. Hamilton's formalism traces the behavior of closed systems. The general form of boundary conditions and forces changes the theory proposed in the works of N.N. Bogolyubov. The results of the reformulation discussed. Even in the classical theory, after taking into account the moments, we come to the absence of symmetric stress tensor in Boltzmann theory. The symmetric tensor obtains after assumption of small influence from absence of symmetry at the condition of the forces balance. No symmetric tensor leads to the existence of two solutions. New examples of solving problems on hydromechanics, elasticity theory and kinetic theory are given. A correspondence between the terms of the Liouville equation with more general and traditional forces established for continues mechanics. Previously considered boundary layer problems, jet problems and the simplest problems of elasticity theory. The paper proposes a method for finding the second solution for no symmetric problems, if the solution of the symmetric problem we know. The mathematical inaccuracies of the theory of continuum mechanics and kinetics discussed.
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Thiel, Robert, and Jens Jäkel. "Simulation of a passive position control for ferromagnetic particles with multiple Halbach rings." Current Directions in Biomedical Engineering 8, no. 2 (August 1, 2022): 773–76. http://dx.doi.org/10.1515/cdbme-2022-1197.

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Abstract Various types of magnetic nanoparticles have been developed for a range of medical applications and some have the potential to treat diseases. In this paper, a new method for controlling the position of these magnetic particles by changing the magnetic field surrounding them using three Halbach ringsis investigated with the aid of a simulation. The inner ring controls the direction, and the position of the two outer rings can keep the group of particles together. In the simulation, the magnetic field is calculated analytically for each time step and the movement of the particles is simulated by applying the corresponding forces. These result from the manipulable external magnetic field, the magnetic field between the particles, the Lennard-Jones potential to model attractive interactions between the particles and the drag. In the simulation, we show how the particles are manipulated using a Levenberg-Marquard algorithm and develop a closedloop control for the position of the grouped particles by manipulating the magnetic field inside the Halbach rings by changing the angular position of these rings.
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OKABE, TSUNEYASU, and HIROAKI YAMADA. "DYNAMICAL INSTABILITY OF ONE-DIMENSIONAL MORSE SYSTEM." Modern Physics Letters B 13, no. 09n10 (April 30, 1999): 303–15. http://dx.doi.org/10.1142/s0217984999000403.

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Dynamical instability in an one-dimensional many-body system with Morse-type interaction potential is studied by computer simulation. The dynamical instability of the Morse system is caused by two kinds of instability. One is the parametric instability caused by the stochastic fluctuation of positive curvature of a Riemannian manifold and the other is the local instability approximated by the local negative eigenvalues of the Hessian matrix for the potential function. We investigate the energy dependence of the maximal Lyapunov exponent in order to emphasize the characteristic dynamical instability of the Morse system and compare the characteristics with results have been reported in Fermi–Pasta–Ulam system and Lennard–Jones system. We also investigate the energy dependence of the particle diffusion in the Morse system.
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10

Mizerski, Krzysztof A. "The detrimental effect of hydrodynamic interactions on the process of Brownian flocculation in shear flow." Journal of Fluid Mechanics 748 (April 29, 2014): 328–49. http://dx.doi.org/10.1017/jfm.2014.190.

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AbstractThe problem of Brownian flocculation of spherical particles in strong shearing flow without hydrodynamic interactions is studied in detail using the singular perturbation method. All other types of interparticle interactions, such as van der Waals or Lennard-Jones forces, are also ignored. In the limit of strong external flow, the strength of which is measured by the Péclet number ($Pe\gg 1$), a complicated boundary layer structure for the pair probability density function ($P_{2}$) is identified and the complete stationary spatial distribution of $P_{2}(\boldsymbol {x})$ in the domain is found. The results, in particular the total mass flux in the accumulation process, are compared qualitatively and quantitatively with the case where the spheres interact hydrodynamically and it is demonstrated that the hydrodynamic interactions tend to decrease the rate of flocculation. An explicit simple formula for the flocculation rate for a general form of hydrodynamic interactions is provided. The limit of small Péclet number is also discussed to confirm the conclusion on the detrimental influence of hydrodynamic interactions on the rate of Brownian flocculation in shearing flow.
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Conference papers on the topic "Lennard-Jones type Particles"

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Streator, Jeffrey L. "Micro-Scale Simulation of Adhesive Effects During Normal Impact." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-3914.

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Abstract A numerical simulation is developed to investigate the role of adhesive forces during the normal impact of a rigid body against an elastic surface. The model consists of a rigid, 2D translating body and a surface that is composed of a flexible linear array of particles, coupled to a fixed base via linear springs. Adhesive effects are incorporated in the model by ascribing a Lennard-Jones type interaction potential between the surface and the body. Dynamical equations of motion for the interface are integrated numerically during an impact event. It is found that the coefficient of restitution decreases with increasing interaction strength and decreasing approach velocity. Above a certain interaction strength for given velocity and below a certain velocity for given interaction strength, the body is found not to rebound, but sticks to the surface. The simulation results are found to be in qualitative agreement with the impact model of Dahneke (1973, 1975). Quantitative discrepancies are explained by the effects of surface “plucking.”
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