ABSTRACT: **Dissipative** **particle** **dynamics** (DPD) and smoothed **dissipative** **particle** dy- namics (sDPD) have become most popular numerical techniques for simulating mesoscopic flow phenomena in fluid systems. Several DPD/sDPD simulations in the literature indi- cate that the model fluids should be designed with their dynamic response, measured by the Schmidt number, in a relevant range in order to reach a good agreement with the experimen- tal results. In this paper, we propose a new **dissipative** weighting function (or a new kernel) for the DPD (or the sDPD) formulation, which allows both the viscosity and the Schmidt number to be independently specified as input parameters. We also show that some existing **dissipative** functions/kernels are special cases of the proposed one, and the imposed viscosity of the present DPD/sDPD system has a lower and upper limit. Numerical verification of the proposed function/kernel is conducted in viscometric flows.

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Abstract. This paper is concerned with the use of oscillating particles instead of the usual frozen particles to model a suspended **particle** (solid body) in a **Dissipative** **Particle** **Dynamics** (DPD) **particle**-based simulation method. A suspended **particle** is represented by a set of basic DPD particles connected to reference sites by linear springs. The reference sites are moved as a whole with the imposed displacement that is calculated using data from the previous time step, while the velocities of their associated DPD particles are found by solving the DPD equations at the current time step. In this way, a specified Boltzmann temperature can also be maintained in the region occupied by the suspended particles and this parameter can be utilised to control the size of suspended particles.

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Key words: **dissipative** **particle** **dynamics**, particulate suspensions, spring model, soft potential, thermodynamic temperature
Abstract. This paper is concerned with the use of oscillating particles instead of the usual frozen particles to model a suspended **particle** (solid body) in a **Dissipative** **Particle** **Dynamics** (DPD) **particle**-based simulation method. A suspended **particle** is represented by a set of basic DPD particles connected to reference sites by linear springs. The reference sites are moved as a whole with the imposed displacement that is calculated using data from the previous time step, while the velocities of their associated DPD particles are found by solving the DPD equations at the current time step. In this way, a specified Boltzmann temperature can also be maintained in the region occupied by the suspended particles and this parameter can be utilised to control the size of suspended particles.

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I. INTRODUCTION
**Dissipative** **Particle** **Dynamics** (DPD) is one of the most promising methods for modelling complex multi-phase materials developed in the last 20 years. It was developed in the early 1990s by Hoogerbrugge and Koelman [1] as a tool for simulating fluids from the mesoscale (10-100 nm and 10-100 ns) to the continuum limit. The method represents matter as a set of point particles, the distribution and density of which is determined by a set of prescribed forces. Each of these point particles represents a "bead" of fluid. The molecular structure of the fluid has been eliminated in the coarse grained description of matter. The method shares features of both Molecular **Dynamics** and Lattice Gas Automata and closely resembles the structure of a Brownian **Dynamics** algorithm, having stochastic, **dissipative** and conservative forces. The conservative forces act to distribute the beads in space as evenly as possible to minimise free energy. The **dissipative** force represents friction and acts to reduce velocity differences between the beads. The stochastic force represents the degrees of freedom that have been eliminated in the coarse graining of matter. The magnitude of the stochastic and **dissipative** forces is coupled by fluctuation-dissipation theorem and this acts as a system thermostat.

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Mesoscale simulation techniques have helped to bridge the length scales and time scales needed to predict the microstructures of cured epoxies, but gaps in computational cost and experimental relevance have limited their impact. In this work we develop an open- source plugin epoxpy for HOOMD-Blue that enables epoxy crosslinking simulations of millions of particles to be routinely performed on a single modern graphics card. We demonstrate the first implementation of custom temperature-time curing profiles with **dissipative** **particle** **dynamics** and show that reaction kinetics depend sensitively on the stochastic bonding rates. We provide guidelines for modeling first-order reaction dy- namics in a classic epoxy/hardener/toughener system and show structural sensitivity to the temperature-time profile during cure. We conclude with a discussion of how these efficient large-scale simulations can be used to evaluate ensembles of epoxy processing protocols to quantify the sensitivity of microstructure on processing.

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revised (2), February 2014
Abstract This paper is concerned with the use of oscillating particles instead of the usual frozen particles to model a suspended **particle** in the **Dissipative** **Particle** **Dynamics** (DPD) method. A suspended **particle** is represented by a set of basic DPD particles connected to reference sites by linear springs of very large stiffness. The reference sites, collectively modelling a rigid body, move as a rigid body motion calculated through their Newton-Euler equations, using data from the previous time step, while the velocities of their associated DPD particles are found by solving the DPD equations at the current time step. In this way, a specified Boltzmann temperature (specific kinetic energy of the particles) can be maintained throughout the computational domain, including the region occupied by the suspended particles. This parameter can also be used to adjust the size of the suspended and solvent particles, which in turn affect the strength of the shear-thinning behaviour and the effective maximal packing fraction. Furthermore, the suspension, comprised of suspended particles in a set of solvent particles all interacting under a quadratic soft repulsive potential, can be simulated using a relatively large time step. Several numerical examples are presented to demonstrate attractiveness of the proposed model.

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Keywords: **dissipative** **particle** **dynamics**; reaction; polydispersity.
1. Introduction
As an effective simulation technique, **dissipative** **particle** **dynamics** (DPD) had been successfully applied in mesoscopic simulations for several years. Because DPD can cover large length and time scales and reproduce the correct hydrodynamic behavior of fluids, it appears to be the most suitable tool to study the behavior of complex fluids. In some cases, independent kinetic processes, e.g. chemical reactions, may accompany with the dynamic behavior of complex fluids. A lot of experimental results showed that the reactions may greatly disturb the behavior of diffusion [1]. Therefore, how to associate the hydrodynamic process of the fluids with the chemical reactions becomes an important problem in the study of the complex fluids. Especially in polymeric systems, it is of great significance how to simulate the reaction equilibrium at the mesoscopic level, since most of the dynamical problems are generally related to the mesoscopic length and time scales. Moreover, designing the polymer chains with controllable polydispersity and chain length distribution is a critical issue in polymer sciences. These problems urgently demand computational models in which the chemical reactions can be taken into account. One of the attempts on this issue was done by Lisal and the co-workers [2,3], who had proposed a reaction ensemble DPD method to study the polydisperse polymer systems and supramolecular diblock copolymers. Their work shows that DPD is an ideal method for simulating polymerization.

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The purpose of this study is to determine the e ﬀ ect of the interaction diﬀerence between the two diﬀerent hy- drophilic end groups on the self-assembly in a bolaam- phiphilic solution. To investigate the self-assembly in a bolaamphiphilic solution at the molecular level, we per- form **dissipative** **particle** **dynamics** (DPD) simulations of a bolaamphiphilic solution and analyze the formation pro- cesses of micelles and vesicles.

Jdpd is an open Java simulation kernel for Molecular Fragment **Dissipative** **Particle** **Dynamics** with parallelizable force calculation, efficient caching options and fast property calculations. It is characterized by an interface and factory- pattern driven design for simple code changes and may help to avoid problems of polyglot programming. Detailed input/output communication, parallelization and process control as well as internal logging capabilities for debug- ging purposes are supported. The new kernel may be utilized in different simulation environments ranging from flexible scripting solutions up to fully integrated “all-in-one” simulation systems.

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257801)) recently showed that nucleated pores in a homopolymer film can increase or decrease in size, depending on whether they are larger or smaller than a critical size which scales linearly with film thickness. Using **dissipative** **particle** **dynamics**, a **particle**-based simulation method, we investigate the same scenario for a lipid bilayer membrane whose structure is determined by lipid–water interactions. We simulate a perforated membrane in which holes larger than a critical radius grow, while holes smaller than the critical radius close, as in the experiment of Ilton et al. (Ilton et al. 2016 Phys.

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The self-assembly of dissolved symmetric bolaamphiphilic molecules is studied using **dissipative** **particle** **dynamics** simulations. Specifically, we investigate how interactions between the dual hydrophilic ends of the molecules aﬀect the self-assembly process. Simulations show that four types of self-assembled structures (spher- ical micelles, tubes, vesicles, and wormlike micelles) are obtained from a random configuration of symmetric bolaamphiphilic molecules in solution. We find that the self-assembled structures change from spherical micelles to tubes, then to vesicles, and finally to wormlike micelles as the repulsive interactions between the hydrophilic ends increase. The molecular shapes in vesicles tend to be more rodlike than those in spherical micelles, tubes, or wormlike micelles.

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Yao-Chun Wang 1 , Shin-Pon Ju 1* , Tien Jung Huang 2 and Hung-Hsiang Wang 1
Abstract
**Dissipative** **particle** **dynamics** (DPD), a mesoscopic simulation approach, is used to investigate the effect of volume fraction of polyethylene (PE) and poly(l-lactide) (PLLA) on the structural property of the immiscible PE/PLLA/carbon nanotube in a system. In this work, the interaction parameter in DPD simulation, related to the Flory-Huggins interaction parameter c , is estimated by the calculation of mixing energy for each pair of components in molecular **dynamics** simulation. Volume fraction and mixing methods clearly affect the equilibrated structure. Even if the volume fraction is different, micro-structures are similar when the equilibrated structures are different. Unlike the blend system, where no relationship exists between the micro-structure and the equilibrated structure, in the di- block copolymer system, the micro-structure and equilibrated structure have specific relationships.

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2 ABSTRACT
Local distribution and orientation of anisotropic nanoparticles in microphase-separated symmetric diblock copolymers has been simulated using **dissipative** **particle** **dynamics** and analyzed with a molecular theory. It has been demonstrated that nanoparticles are characterized by a non-trivial orientational ordering in the lamellar phase due to their anisotropic interactions with isotropic monomer units. In the simulations, the maximum concentration and degree of ordering are attained for non- selective nanorods near the domain boundary. In this case the nanorods have a certain tendency to align parallel to the interface in the boundary region and perpendicular to it inside the domains. Similar orientation ordering of spherical nanoparticles located at the lamellar interface is predicted by the molecular theory which takes into account that the nanoparticles interact with monomer units via both isotropic and anisotropic potentials. Computer simulations enable one to study the effects of the nanorod concentration, length, stiffness, and selectivity of their interactions with the copolymer components on the phase stability and orientational order of nanoparticles. If the volume fraction of the nanorods is lower than 0.1, they have no effect on the copolymer transition from the disordered state into a lamellar microstructure. Increasing nanorod concentration or nanorod length results in clustering of the nanorods and eventually leads to a macrophase separation, whereas the copolymer preserves its lamellar morphology. Segregated nanorods of length close to the width of the diblock copolymer domains are stacked side by side into smectic layers that fill domain space. Thus, spontaneous organization and orientation of nanorods leads to a spatial modulation of anisotropic composite properties creating an opportunity to align block copolymers by external fields which may be important for various applications.

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Abstract: Petroleum systems have a high level of complexity due to the presence of a huge variety of organic compounds, mainly hydrocarbons. These characteristics, not only make difficult its recovery but also its study. In this sense, the study of parameters, such as the local variation of interfacial tension (IFT) is essential to understanding the behavior of different interfaces that arise through the extraction, transport and oil refining processes. Accordingly, in the present study, theoretical estimations of IFTs of linear-hydrocarbon-water, linear-hydrocarbon-glycerol, and mixtures of 11 types of organic-liquid with water were performed. The system elements were built by using coarse-graining technique and the **dynamics** were carried out by the **Dissipative** **Particle** **Dynamics** (DPD). With this technique was possible to reproduce, in a systematic way, an important set of IFT values for systems of oil industrial interest, which reproduced trends obtained from experimental analogous conditions.

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Abstract. The aim of this study is to simulate the self-assembly of the surfactant molecules with special chemical structure and bending stiness into bilayer membranes using a mesoscopic **Dissipative** **Particle** **Dynamics** (DPD) method. The surfactants are modeled with special chemical structure and bending stiness. To conrm that the novel model is physical, we determine the interaction parameters based on matching the compressibility and solubility of the DPD system with real physics of the uid. To match the mutual solubility for binary uids, we use the relation between DPD parameters and -parameters in Flory-Huggins-type models. Unsaturated bonds can change the stiness of a lipid membrane, which is modeled by introducing a bond bending potential. To verify our model, we investigate the eect of surfactant structure, like chain length and stiness of the molecules, on the properties of the modeled membrane as area per surfactant. To validate our results, we also compare them with the theoretical calculations as well as with the experimental and other existing simulations results. We show that there is a good coincidence between all of the results.

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modelled as a chain of beads which are connected to each other with the spring forces. In this method, the size of the spherical beads is determined by the assumption of Stokes law and use of the frictional coecients. In DPD method, a standard model of linear polymer is a chain of DPD particles which are connected together by the spring forces and immersed in a solution of free DPD particles. Since these models of polymeric solutions are equivalent, it is necessary to introduce an intrinsic size for DPD particles to show that BD beads and DPD particles are equivalent as well. Then, two eective radii in DPD are inferred, which can be calculated independently; Stokes-Einstein radius (R SE ), which is shown in this paper as the radius of a sphere impenetrable around each DPD **particle**, is calculated by means of the coecients of self-diusion and viscosity [5] and the Stokes-Einstein equation. On the other hand, the second radius (R S ) is calculated from the Stokes law in simulating the ow past a single xed DPD **particle**. For small Reynolds numbers, it is proved that the two radii approach each other. By considering the Stokes-Einstein radius for DPD particles and representing congruous hydro- dynamic behaviour with the analytical Stokes law, it is concluded that each DPD **particle** has an intrinsic size, which behaves as a solid sphere. In the follow- ing sections, the relations governing these radii are described. This conclusion can lead to a considerable decrease in the number of particles in DPD simulating, because each **particle** represents a blu body. The eect of number of particles on computational time will be shown quantitatively, which proves that reduction in the number of particles results in more economical simulations.

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and (ii) the investigation of the dependence of the DPD transport properties on the length and time scales, which are introduced from the physical phenomenon under examination.
Transverse-current auto-correlation functions (TCAF) in Fourier space are employed to study the effects of the length scale, while analytic expressions of the shear stress in a simple small amplitude oscillatory shear flow are utilised to study the effects of the time scale. A direct mechanism for imposing the **particle** diffusion time and fluid viscosity in the hydrodynamic limit on the DPD system is also proposed.

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438B Alexandra Road, #01-03 Alexandra Technopark, Singapore 119968
Submitted to Applied Mathematical Modelling, 5/Feb/2015; revised, 8/Nov/2015; revised (2), 4/Dec/2015
Abstract In this paper, a numerical scheme is used to study strongly-overdamped Dissi- pative Particles **Dynamics** (DPD) systems for the modelling of fluid-solid systems. In the scheme, the resultant set of algebraic equations for the velocities are directly solved in an iterative manner. Different test problems, e.g., viscometric flows, particulate suspensions and flows past a periodic square array of cylinders, are used to verify the proposed method.

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6 Concluding remarks
We have reduced the mass of DPD particles to induce an incompressible slow viscous ﬂow in a DPD ﬂuid and to enhance its dynamic response. This approach appears eﬀective as the simplicity of the DPD algorithm still retains and an eﬃcient solution is still achieved with the help of an ETD algorithm. Numerical simulations for the Couette ﬂow have showed that the present method works eﬀectively for relatively-large time steps and, for a given a small time step for which the velocity-Verlet algorithm works, the ETD algorithm produces more accurate results than the velocity-Verlet algorithm. We have also investigated the use of a single DPD **particle** to represent a rigid sphere suspended in a Newtonian ﬂuid. Detailed results show that (i) the cut-oﬀ radius for the conservative force and the eﬀective radius of solvent particles are the key factors in deciding the size of the suspended sphere, and (ii) the strength and the cut-oﬀ radius of the **dissipative** force are instrumental in ﬁtting the computed drag force and the size of the sphere into the Stokes drag model. Extension of the method to colloidal suspensions is underway and results will be reported in future work.

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