Pub Date : 2018-01-01DOI: 10.12921/CMST.2018.0000042
J. Sprott
Gibbs’ canonical ensemble describes the exponential equilibrium distribution f(q, p, T ) ∝ e−H(q,p)/kT for an ergodic Hamiltonian system interacting with a ‘heat bath’ at temperature T . The simplest deterministic heat bath can be represented by a single ‘thermostat variable’ ζ. Ideally, this thermostat controls the kinetic energy so as to give the canonical distribution of the coordinates and momenta {q, p}. The most elegant thermostats are time-reversible and include the extra variable(s) needed to extract or inject energy. This paper describes a single-variable ‘signum thermostat.’ It is a limiting case of a recently proposed ‘logistic thermostat.’ It has a single adjustable parameter and can access all of Gibbs’ microstates for a wide variety of one-dimensional oscillators.
{"title":"Ergodicity of One-dimensional Oscillators with a Signum Thermostat","authors":"J. Sprott","doi":"10.12921/CMST.2018.0000042","DOIUrl":"https://doi.org/10.12921/CMST.2018.0000042","url":null,"abstract":"Gibbs’ canonical ensemble describes the exponential equilibrium distribution f(q, p, T ) ∝ e−H(q,p)/kT for an ergodic Hamiltonian system interacting with a ‘heat bath’ at temperature T . The simplest deterministic heat bath can be represented by a single ‘thermostat variable’ ζ. Ideally, this thermostat controls the kinetic energy so as to give the canonical distribution of the coordinates and momenta {q, p}. The most elegant thermostats are time-reversible and include the extra variable(s) needed to extract or inject energy. This paper describes a single-variable ‘signum thermostat.’ It is a limiting case of a recently proposed ‘logistic thermostat.’ It has a single adjustable parameter and can access all of Gibbs’ microstates for a wide variety of one-dimensional oscillators.","PeriodicalId":10561,"journal":{"name":"computational methods in science and technology","volume":"220 1","pages":"169-176"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85890680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-01-01DOI: 10.12921/CMST.2018.0000054
Jarosław Jung, R. Kiełbik, K. Rudnicki, K. Hałagan, P. Polanowski, A. Sikorski
The designing, production and testing of the mDLL machine led to the development of such a structure in which operational cells (e.g. KDLL) were located in the nodes of a three-dimensional torus network and the device was scalable. Thus, the future expansion of this device with additional Printed Circuit Boards (PCB) will not result in lengthened wire connections between Field-Programmable Gate Arrays (FPGA) or slow down the operation of the machine. The conducted tests confirmed the correctness of the adopted design assumptions and showed that by using mDLL one can effectively perform molecular simulations. Despite some structural shortcomings, the mDLL machine was a prototype that has already been sufficiently tested to allow the technology used in it to be used to build a device with a number of 1 million to 5 million KDLL cells. Such a device would already be suitable for simulating multi-particle systems with unprecedented speed.
{"title":"From the Dynamic Lattice Liquid Algorithm to the Dedicated Parallel Computer – mDLL Machine","authors":"Jarosław Jung, R. Kiełbik, K. Rudnicki, K. Hałagan, P. Polanowski, A. Sikorski","doi":"10.12921/CMST.2018.0000054","DOIUrl":"https://doi.org/10.12921/CMST.2018.0000054","url":null,"abstract":"The designing, production and testing of the mDLL machine led to the development of such a structure in which operational cells (e.g. KDLL) were located in the nodes of a three-dimensional torus network and the device was scalable. Thus, the future expansion of this device with additional Printed Circuit Boards (PCB) will not result in lengthened wire connections between Field-Programmable Gate Arrays (FPGA) or slow down the operation of the machine. The conducted tests confirmed the correctness of the adopted design assumptions and showed that by using mDLL one can effectively perform molecular simulations. Despite some structural shortcomings, the mDLL machine was a prototype that has already been sufficiently tested to allow the technology used in it to be used to build a device with a number of 1 million to 5 million KDLL cells. Such a device would already be suitable for simulating multi-particle systems with unprecedented speed.","PeriodicalId":10561,"journal":{"name":"computational methods in science and technology","volume":"53 4 1","pages":"235-247"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86782574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-01-01DOI: 10.12921/CMST.2018.0000029
J. Ghosh, U. Ghosh, S. Sarkar
This paper describes a SIRS model with the logistic growth rate of susceptible class. The effect of an inhibitory factor in the infection is also taken into consideration. We have analysed local as well as global stabilities of the equilibrium points (both hyperbolic and non-hyperbolic) of the system and investigated the Transcritical bifurcation at the disease free equilibrium point with respect to the inhibitory factor. The occurrence of Hopf bifurcation of the system is examined and it was observed that this Hopf bifurcation is either supercritical or subcritical depending on parameters. Some numerical simulations are carried out for the validity of theoretical results.
{"title":"Qualitative Analysis of Both Hyperbolic and Non-hyperbolic Equilibria of a SIRS Model with Logistic Growth Rate of Susceptibles and Inhibitory Effect in the Infection","authors":"J. Ghosh, U. Ghosh, S. Sarkar","doi":"10.12921/CMST.2018.0000029","DOIUrl":"https://doi.org/10.12921/CMST.2018.0000029","url":null,"abstract":"This paper describes a SIRS model with the logistic growth rate of susceptible class. The effect of an inhibitory factor in the infection is also taken into consideration. We have analysed local as well as global stabilities of the equilibrium points (both hyperbolic and non-hyperbolic) of the system and investigated the Transcritical bifurcation at the disease free equilibrium point with respect to the inhibitory factor. The occurrence of Hopf bifurcation of the system is examined and it was observed that this Hopf bifurcation is either supercritical or subcritical depending on parameters. Some numerical simulations are carried out for the validity of theoretical results.","PeriodicalId":10561,"journal":{"name":"computational methods in science and technology","volume":"10 1","pages":"285-300"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88559985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-01-01DOI: 10.12921/cmst.2018.0000025
Mariusz Uchroński, P. Potasz, Agnieszka Szymańska-Kwiecień, M. Hruszowiec
This work is focused on parallel simulation of electron-electron interactions in materials with non-trivial topological order (i.e. Chern insulators). The problem of electron-electron interaction systems can be solved by diagonalizing a many-body Hamiltonian matrix in a basis of configurations of electrons distributed among possible single particle energy levels – the configuration interaction method. The number of possible configurations exponentially increases with the number of electrons and energy levels; 12 electrons occupying 24 energy levels corresponds to the dimension of Hilbert space about 10. Solving such a problem requires effective computational methods and highly efficient optimization of the source code. The work is focused on many-body effects related to strongly interacting electrons on flat bands with non-trivial topology. Such systems are expected to be useful in study and understanding of new topological phases of matter, and in further future they can be used to design novel nanomaterials. Heterogeneous architecture based on GPU accelerators and MPI nodes will be used for improving performance and scalability in parallel solving problem of electron-electron interaction systems.
{"title":"Using GPU Accelerators for Parallel Simulations in Material Physics","authors":"Mariusz Uchroński, P. Potasz, Agnieszka Szymańska-Kwiecień, M. Hruszowiec","doi":"10.12921/cmst.2018.0000025","DOIUrl":"https://doi.org/10.12921/cmst.2018.0000025","url":null,"abstract":"This work is focused on parallel simulation of electron-electron interactions in materials with non-trivial topological order (i.e. Chern insulators). The problem of electron-electron interaction systems can be solved by diagonalizing a many-body Hamiltonian matrix in a basis of configurations of electrons distributed among possible single particle energy levels – the configuration interaction method. The number of possible configurations exponentially increases with the number of electrons and energy levels; 12 electrons occupying 24 energy levels corresponds to the dimension of Hilbert space about 10. Solving such a problem requires effective computational methods and highly efficient optimization of the source code. The work is focused on many-body effects related to strongly interacting electrons on flat bands with non-trivial topology. Such systems are expected to be useful in study and understanding of new topological phases of matter, and in further future they can be used to design novel nanomaterials. Heterogeneous architecture based on GPU accelerators and MPI nodes will be used for improving performance and scalability in parallel solving problem of electron-electron interaction systems.","PeriodicalId":10561,"journal":{"name":"computational methods in science and technology","volume":"2 1","pages":"249-258"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84289995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-09-30DOI: 10.12921/CMST.2017.00000012
B. Hafskjold
A one-component Lennard-Jones/spline fluid at equilibrium was perturbed by a sudden change of the temperature at one of the system’s boundaries. The system’s response was determined by non-equilibrium molecular dynamics (NEMD). The results show that heat was transported by two mechanisms: (1) Heat diffusion and conduction, and (2) energy dissipation associated with the propagation of a pressure (shock) wave. These two processes occur at different time scales, which makes it possible to separate them in one single NEMD run. The system was studied in gas, liquid, and supercritical states with various forms and strengths of the thermal perturbation. Near the heat source, heat was transported according to the transient heat equation. In addition, there was a much faster heat transport, correlated with a pressure wave. This second mechanism was similar to the thermo-mechanical “piston effect” in near-critical fluids and could not be explained by the Joule-Thomson effect. For strong perturbations, the pressure wave travelled faster than the speed of sound, turning it into a shock wave. The system’s local measurable heat flux was found to be consistent with Fourier’s law near the heat source, but not in the wake of the shock. The NEMD results were, however, consistent with the Cattaneo-Vernotte model. The system was found to be in local equilibrium in the transient phase, even with very strong perturbations, except for a low-density gas. For dense systems, we did not find that the local equilibrium assumption used in classical irreversible thermodynamics is inconsistent with the Cattaneo-Vernotte model.
{"title":"Transient Heat Flow in a One-component Lennard-Jones/spline Fluid. A Non-equilibrium Molecular Dynamics Study","authors":"B. Hafskjold","doi":"10.12921/CMST.2017.00000012","DOIUrl":"https://doi.org/10.12921/CMST.2017.00000012","url":null,"abstract":"A one-component Lennard-Jones/spline fluid at equilibrium was perturbed by a sudden change of the temperature at one of the system’s boundaries. The system’s response was determined by non-equilibrium molecular dynamics (NEMD). The results show that heat was transported by two mechanisms: (1) Heat diffusion and conduction, and (2) energy dissipation associated with the propagation of a pressure (shock) wave. These two processes occur at different time scales, which makes it possible to separate them in one single NEMD run. The system was studied in gas, liquid, and supercritical states with various forms and strengths of the thermal perturbation. Near the heat source, heat was transported according to the transient heat equation. In addition, there was a much faster heat transport, correlated with a pressure wave. This second mechanism was similar to the thermo-mechanical “piston effect” in near-critical fluids and could not be explained by the Joule-Thomson effect. For strong perturbations, the pressure wave travelled faster than the speed of sound, turning it into a shock wave. The system’s local measurable heat flux was found to be consistent with Fourier’s law near the heat source, but not in the wake of the shock. The NEMD results were, however, consistent with the Cattaneo-Vernotte model. The system was found to be in local equilibrium in the transient phase, even with very strong perturbations, except for a low-density gas. For dense systems, we did not find that the local equilibrium assumption used in classical irreversible thermodynamics is inconsistent with the Cattaneo-Vernotte model.","PeriodicalId":10561,"journal":{"name":"computational methods in science and technology","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78495143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-09-30DOI: 10.12921/CMST.2017.0000018
F. Bresme
{"title":"Non-equilibrium Computer Simulations of Coupling Effects under Thermal Gradients","authors":"F. Bresme","doi":"10.12921/CMST.2017.0000018","DOIUrl":"https://doi.org/10.12921/CMST.2017.0000018","url":null,"abstract":"","PeriodicalId":10561,"journal":{"name":"computational methods in science and technology","volume":"13 4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77559407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-09-30DOI: 10.12921/CMST.2016.0000066
S. Sarman, Yong-lei Wang, A. Laaksonen
: The purpose of this review article is to summarize observations accumulated over the years on director alignment phenomena in nematic and cholesteric liquid crystals by molecular dynamics simulation of molecular model systems and by experiment on real systems. The main focus is on the alignment angle between the director and external dissipative fields such as velocity gradients in various flow geometries and temperature gradients doing irreversible work on the system. A general observation is that the director attains an orientation relative to the field where the energy dissipation rate is minimal in the steady state. In the case of planar elongational flow, it can be proven by using symmetry arguments that the energy dissipation rate must be either maximal or minimal and simulations have shown that is minimal. In planar Couette flow both simulations and experiments imply that the energy dissipation rate is minimal in the steady state. Finally, in the case of heat conduction, symmetry arguments imply that the energy dissipation rate must be either minimal or maximal and simulations and experiments indicate that it is minimal. All these observations can be explained by applying a recently proven theorem according to which the energy dissipation rate is minimal in the steady state in the linear regime at low fields.
{"title":"Minimal Energy Dissipation Rate and Director Orientation Relative to External Dissipative Fields such as Temperature and Velocity Gradients in Nematic and Cholestric Liquid Crystals","authors":"S. Sarman, Yong-lei Wang, A. Laaksonen","doi":"10.12921/CMST.2016.0000066","DOIUrl":"https://doi.org/10.12921/CMST.2016.0000066","url":null,"abstract":": The purpose of this review article is to summarize observations accumulated over the years on director alignment phenomena in nematic and cholesteric liquid crystals by molecular dynamics simulation of molecular model systems and by experiment on real systems. The main focus is on the alignment angle between the director and external dissipative fields such as velocity gradients in various flow geometries and temperature gradients doing irreversible work on the system. A general observation is that the director attains an orientation relative to the field where the energy dissipation rate is minimal in the steady state. In the case of planar elongational flow, it can be proven by using symmetry arguments that the energy dissipation rate must be either maximal or minimal and simulations have shown that is minimal. In planar Couette flow both simulations and experiments imply that the energy dissipation rate is minimal in the steady state. Finally, in the case of heat conduction, symmetry arguments imply that the energy dissipation rate must be either minimal or maximal and simulations and experiments indicate that it is minimal. All these observations can be explained by applying a recently proven theorem according to which the energy dissipation rate is minimal in the steady state in the linear regime at low fields.","PeriodicalId":10561,"journal":{"name":"computational methods in science and technology","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91054880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-09-30DOI: 10.12921/cmst.2017.0000038
K. Travis, F. Bresme
{"title":"Advances in Theory and Simulation of Non-equilibrium Systems : foreword","authors":"K. Travis, F. Bresme","doi":"10.12921/cmst.2017.0000038","DOIUrl":"https://doi.org/10.12921/cmst.2017.0000038","url":null,"abstract":"","PeriodicalId":10561,"journal":{"name":"computational methods in science and technology","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82966614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-09-30DOI: 10.12921/CMST.2017.0000016
A. Menzel, P. Daivis, B. D. Todd
The behaviour of polymer solutions in highly confined geometries remains a subject of interest in rheology and fluid dynamics. In this paper, we investigate how well the classical hydrodynamic description based on the Navier-Stokes equations, Fourier's Law and Fick's Law describes the flow of a highly confined polymer solution. In particular, we examine the effects of depletion of polymer concentration at the wall-fluid interface and strain rate coupling to the heat flux. We present data from molecular dynamics simulations of a model polymer solution in explicit solvent undergoing planar Poiseuille flow for channel widths ranging from around 10 solvent atomic diameters to around 80 solvent atomic diameters. We find that the classical continuum approach works very well for channels wider than 20 solvent atomic diameters. For narrower channels, we observe deviations in the velocity, temperature and concentration profiles due to density oscillations near the walls, the polymer depletion effect, and possible weak strain rate coupling. For the narrowest channel, the wall effects extend to the centre of the channel but the underlying profiles are quite well described by the classical continuum picture. By allowing very long times of order 104 reduced time units for relaxation to the steady state and averaging over very long runs of order 105 reduced time units and 16 independent ensemble members, we are able to conclude that previously reported deviations from the classical continuum predictions (I.K. Snook, P.J. Daivis, T. Kairn, J. Physics-Condensed Matter 20, 404211 (2008)) were probably the result of insufficient equilibration time. Our results are also sufficiently accurate and precise to verify the expected quartic temperature profile predicted by classical hydrodynamic theory, with only a very small deviation which we can attribute to nonlinear coupling of the heat flux vector to the strain rate.
聚合物溶液在高度受限几何中的行为仍然是流变学和流体动力学中感兴趣的主题。在本文中，我们研究了基于Navier-Stokes方程、傅里叶定律和菲克定律的经典流体力学描述如何很好地描述高受限聚合物溶液的流动。特别地，我们研究了在壁-流体界面处聚合物浓度的损耗和应变速率耦合对热流的影响。我们展示了一种模型聚合物溶液在显式溶剂中进行平面泊泽维尔流动的分子动力学模拟数据，通道宽度从大约10个溶剂原子直径到大约80个溶剂原子直径不等。我们发现经典的连续介质方法对于超过20个溶剂原子直径的通道非常有效。对于较窄的通道，我们观察到由于壁附近的密度振荡、聚合物耗损效应和可能的弱应变速率耦合而导致的速度、温度和浓度分布的偏差。对于最窄的通道，壁效应延伸到通道的中心，但是底层的剖面可以用经典的连续谱图很好地描述。通过允许很长时间的104阶简化时间单位松弛到稳定状态，并在很长时间内平均105阶简化时间单位和16个独立的集合成员，我们能够得出这样的结论:先前报道的与经典连续统预测的偏差(I.K. Snook, P.J. Daivis, T. Kairn, J. Physics-Condensed Matter 20,404211(2008))可能是平衡时间不足的结果。我们的结果也足够精确，足以验证经典流体力学理论预测的四次温度分布，只有很小的偏差，我们可以将其归因于热流矢量与应变率的非线性耦合。
{"title":"Deviations From Classical Hydrodynamic Theory in Highly Confined Planar Poiseuille Flow of a Polymer Solution","authors":"A. Menzel, P. Daivis, B. D. Todd","doi":"10.12921/CMST.2017.0000016","DOIUrl":"https://doi.org/10.12921/CMST.2017.0000016","url":null,"abstract":"The behaviour of polymer solutions in highly confined geometries remains a subject of interest in rheology and fluid dynamics. In this paper, we investigate how well the classical hydrodynamic description based on the Navier-Stokes equations, Fourier's Law and Fick's Law describes the flow of a highly confined polymer solution. In particular, we examine the effects of depletion of polymer concentration at the wall-fluid interface and strain rate coupling to the heat flux. We present data from molecular dynamics simulations of a model polymer solution in explicit solvent undergoing planar Poiseuille flow for channel widths ranging from around 10 solvent atomic diameters to around 80 solvent atomic diameters. We find that the classical continuum approach works very well for channels wider than 20 solvent atomic diameters. For narrower channels, we observe deviations in the velocity, temperature and concentration profiles due to density oscillations near the walls, the polymer depletion effect, and possible weak strain rate coupling. For the narrowest channel, the wall effects extend to the centre of the channel but the underlying profiles are quite well described by the classical continuum picture. By allowing very long times of order 104 reduced time units for relaxation to the steady state and averaging over very long runs of order 105 reduced time units and 16 independent ensemble members, we are able to conclude that previously reported deviations from the classical continuum predictions (I.K. Snook, P.J. Daivis, T. Kairn, J. Physics-Condensed Matter 20, 404211 (2008)) were probably the result of insufficient equilibration time. Our results are also sufficiently accurate and precise to verify the expected quartic temperature profile predicted by classical hydrodynamic theory, with only a very small deviation which we can attribute to nonlinear coupling of the heat flux vector to the strain rate.","PeriodicalId":10561,"journal":{"name":"computational methods in science and technology","volume":"1 1","pages":"219-231"},"PeriodicalIF":0.0,"publicationDate":"2017-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78307022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-09-30DOI: 10.12921/CMST.2017.0000033
K. Travis
We demonstrate that the main features of DPD may be obtained using molecular dynamics employing a deterministic thermostat. This apparent isomorphism holds as long as the MD pair potentials are sufficiently smooth and short ranged, which gives rise to a quadratic equation of state (pressure as a function of density). This is advantageous because it avoids the need to use stochastic forces, enabling a wider choice of integration algorithms, involves fully time reversible motion equations and offers a simpler algorithm to achieve the same objective. The isomorphism is explored and shown to hold in 2 and 3 physical dimensions as well as for binary and ternary systems for two different choices of pair potential. The mapping between DPD and Hildebrand’s regular solution theory (a consequence of the quadratic equation of state) is extended to multicomponent mixtures. The procedure for parametrization of MD (identical to that of DPD) is outlined and illustrated for a equimolar binary mixture of SnI4 and isooctane (2,2,4-trimethylpentane).
{"title":"Dissipative particle dynamics via molecular dynamics","authors":"K. Travis","doi":"10.12921/CMST.2017.0000033","DOIUrl":"https://doi.org/10.12921/CMST.2017.0000033","url":null,"abstract":"We demonstrate that the main features of DPD may be obtained using molecular dynamics employing a deterministic thermostat. This apparent isomorphism holds as long as the MD pair potentials are sufficiently smooth and short ranged, which gives rise to a quadratic equation of state (pressure as a function of density). This is advantageous because it avoids the need to use stochastic forces, enabling a wider choice of integration algorithms, involves fully time reversible motion equations and offers a simpler algorithm to achieve the same objective. The isomorphism is explored and shown to hold in 2 and 3 physical dimensions as well as for binary and ternary systems for two different choices of pair potential. \u0000 \u0000The mapping between DPD and Hildebrand’s regular solution theory (a consequence of the quadratic equation of state) is extended to multicomponent mixtures. The procedure for parametrization of MD (identical to that of DPD) is outlined and illustrated for a equimolar binary mixture of SnI4 and isooctane (2,2,4-trimethylpentane).","PeriodicalId":10561,"journal":{"name":"computational methods in science and technology","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76283628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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