Coarse-grained Particles Research Articles

Dissipative particle dynamics model of homogalacturonan based on molecular dynamics simulations

In this study we present an alternative dissipative particle dynamics (DPD) parametrization strategy based on data extracted from the united-atom molecular simulations. The model of the homogalacturonan was designed to test the ability of the formation of large-scale structures via hydrogen bonding in water. The extraction of coarse-grained parameters from atomistic molecular dynamics was achieved by means of the proposed molecule aggregation algorithm based on an iterative nearest neighbour search. A novel approach to a time-scale calibration scheme based on matching the average velocities of coarse-grained particles enabled the DPD forcefield to reproduce essential structural features of homogalacturonan molecular chains. The successful application of the proposed parametrization method allowed for the reproduction of the shapes of radial distribution functions, particle velocities and diffusivity of the atomistic molecular dynamics model using DPD force field. The structure of polygalacturonic acid molecules was mapped into the DPD force field by means of the distance and angular bond characteristics, which closely matched the MD results. The resulting DPD trajectories showed that randomly dispersed homogalacturonan chains had a tendency to aggregate into highly organized 3D structures. The final structure resembled a three-dimensional network created by tightly associated homogalacturonan chains organized into thick fibres.

Accumulated densities of sedimenting particles in turbulent flows

We study the effect of turbulence on a sedimenting layer of particles by means of direct numerical simulations. A Lagrangian model in which particles are considered as tracers with an additional downward settling velocity is integrated together with an isotropic homogeneous turbulent flow. We study the spatial distribution of particles when they are collected on a plane at non-asymptotic times. We relate the resulting coarse-grained particle density to the history of the stretching rate along the particle trajectory and the projection of the density onto the accumulation plane and analyze the deviation from homogeneity in terms of the Reynolds number and the settling velocity. We identify two regimes that arise during the early and well-mixed stages of advection. In the former regime, more inhomogeneity in the particle distribution is introduced for decreasing settling velocity or increasing Reynolds number, while the tendencies are opposite in the latter regime. A resonant-like crossover is found between these two regimes where inhomogeneity is maximal.

EFFECT OF PIPE INCLINATION ON COARSE-GRAINED PARTICLE-WATER MIXTURES FLOW

The effect of the mixture velocity, solid concentration, and pipe inclination on the coarse-grained particle–water mixtures flow behaviour, concentration distribution, and pressure drops were experimentally studied in horizontal, vertical, and inclined pipes of inner diameter D=100 mm. Graded basalt gravel was used as a solid phase. The local concentration distribution was studied with the application of a gamma-ray densitometer. The study revealed the stratified flow pattern of the coarse particle-water mixture in horizontal and inclined pipes. The particles moved principally close to the pipe invert, and particle saltation becomes the dominant mode of particle conveying for higher and moderate flow velocities. The frictional pressure droops in ascending pipe increases with increasing pipe inclination up to about 30 degrees, then gradually decreases. For the pipe inclination lower than about 30°, the effect of pipe inclination on local concentration distribution was not significant. The in-situ concentration reached higher values in the ascending than in the descending sections.

On the scaling law of JKR contact model for coarse-grained cohesive particles

The computational cost of using discrete element method (DEM) simulations for particulate processes with fine and cohesive particles is enormously large. To overcome this limitation, various coarse-grain DEM models have been developed which use a smaller number of larger sized particles. Although the computational cost is significantly reduced, the accuracy of the simulations depends on the underlying scaling law. We propose a scaling of the Johnson-Kendall-Roberts (JKR) contact model for adhesive viscoelastic particles. A scaling law using a single Bond number or Cohesion number criterion is insufficient to keep the motion of the coarse-grained particles the same as the original particles. The scaling law in this work is developed based on mass, momentum and energy conservation, and achieves good consistency between the kinematic characteristics of the coarse-grained and original particles. The simulated effective coefficients of restitution were compared for a range of particle-wall impact velocities and validated against experimental data.

Sound-Absorption Coefficient of Bark-Based Insulation Panels

The objective of this study was to investigate the sound absorption coefficient of bark-based insulation panels made of softwood barks Spruce (Picea abies (L.) H. Karst.) and Larch (Larix decidua Mill.) by means of impedance tube, with a frequency range between 125 and 4000 Hz. The highest efficiency of sound absorption was recorded for spruce bark-based insulation boards bonded with urea-formaldehyde resin, at a level of 1000 and 2000 Hz. The potential of noise reduction of larch bark-based panels glued with tannin-based adhesive covers the same frequency interval. The experimental results show that softwood bark, an underrated material, can substitute expensive materials that involve more grey energy in sound insulation applications. Compared with wood-based composites, the engineered spruce bark (with coarse-grained and fine-grained particles) can absorb the sound even better than MDF, particleboard or OSB. Therefore, the sound absorption coefficient values strengthen the application of insulation panels based on tree bark as structural elements for the noise reduction in residential buildings, and concurrently they open the new ways for a deeper research in this field.

Geochemical background and dispersion pattern of the world's largest REE deposit of Bayan Obo, China

The Bayan Obo deposit is the largest deposit of rare earth elements (REEs) in the world, with its light REE (LREE) reserve constituting approximately 45% of the world's total LREEs. This study identifies the geochemical background of REEs in the Bayan Obo region and investigates REE dispersion pattern along a stream, the fractionation between parent rocks and soils, as well as REE distribution in a weathering profile, to reveal the geochemical behavior of REEs during hypergene processes in semi-arid grasslands. Results show that the REE content in the slates of the Bilute, Jianshan, and Dulahala Formations, which are surrounding rocks of the Bayan Obo deposit, is far higher than those observed in ordinary slate and the continental crust of the North China Craton. These surrounding rocks may have provided sufficient REE sources to form the current, huge REE deposit. The total REE content of stream sediments in the Bayan Obo region ranges from 46.9 to 799.8 μg/g, with a median of 170.8 μg/g. Two large-scale REE anomalies were discovered to the west of the Bayan Obo region. The REE content in soil is primarily determined by the parent rock, and no fractionation occurs between heavy REEs (HREEs) and LREEs after the parent rock weathers in semi-arid grasslands. Across the soil profile in Bayan Obo region, REEs typically enrich the surface and deep layers; the middle layer typically contains low REE content owing to the existence of caliche. Along streams, REEs primarily migrate with fine-grained particles over long distances (7 km or longer) via mechanical means. In contrast, coarse-grained particles mainly remain in situ. Affected by aeolian sand, the REE content is relatively low in the 40–80 mesh fraction.

Multiscale Eulerian CFD of Chemical Processes: A Review

This review covers the scope of multiscale computational fluid dynamics (CFD), laying the framework for studying hydrodynamics with and without chemical reactions in single and multiple phases regarded as continuum fluids. The molecular, coarse-grained particle, and meso-scale dynamics at the individual scale are excluded in this review. Scoping single-scale Eulerian CFD approaches, the necessity of multiscale CFD is highlighted. First, the Eulerian CFD theory, including the governing and turbulence equations, is described for single and multiple phases. The Reynolds-averaged Navier–Stokes (RANS)-based turbulence model such as the standard k-ε equation is briefly presented, which is commonly used for industrial flow conditions. Following the general CFD theories based on the first-principle laws, a multiscale CFD strategy interacting between micro- and macroscale domains is introduced. Next, the applications of single-scale CFD are presented for chemical and biological processes such as gas distributors, combustors, gas storage tanks, bioreactors, fuel cells, random- and structured-packing columns, gas-liquid bubble columns, and gas-solid and gas-liquid-solid fluidized beds. Several multiscale simulations coupled with Eulerian CFD are reported, focusing on the coupling strategy between two scales. Finally, challenges to multiscale CFD simulations are discussed. The need for experimental validation of CFD results is also presented to lay the groundwork for digital twins supported by CFD. This review culminates in conclusions and perspectives of multiscale CFD.

Freud: A software suite for high throughput analysis of particle simulation data

The freud Python package is a library for analyzing simulation data. Written with modern simulation and data analysis workflows in mind, freud provides a Python interface to fast, parallelized C++ routines that run efficiently on laptops, workstations, and supercomputing clusters. The package provides the core tools for finding particle neighbors in periodic systems, and offers a uniform API to a wide variety of methods implemented using these tools. As such, freud users can access standard methods such as the radial distribution function as well as newer, more specialized methods such as the potential of mean force and torque and local crystal environment analysis with equal ease. Rather than providing its own trajectory data structure, freud operates either directly on NumPy arrays or on trajectory data structures provided by other Python packages. This design allows freud to transparently interface with many trajectory file formats by leveraging the file parsing abilities of other trajectory management tools. By remaining agnostic to its data source, freud is suitable for analyzing any particle simulation, regardless of the original data representation or simulation method. When used for on-the-fly analysis in conjunction with scriptable simulation software such as HOOMD-blue, freud enables smart simulations that adapt to the current state of the system, allowing users to study phenomena such as nucleation and growth. Program summaryProgram Title:freudProgram Files doi:http://dx.doi.org/10.17632/v7wmv9xcct.1Licensing provisions: BSD 3-ClauseProgramming language: Python, C++Nature of problem: Simulations of coarse-grained, nano-scale, and colloidal particle systems typically require analyses specialized to a particular system. Certain more standardized techniques – including correlation functions, order parameters, and clustering – are computationally intensive tasks that must be carefully implemented to scale to the larger systems common in modern simulations.Solution method:freud performs a wide variety of particle system analyses, offering a Python API that interfaces with many other tools in computational molecular sciences via NumPy array inputs and outputs. The algorithms in freud leverage parallelized C++ to scale to large systems and enable real-time analysis. The library’s broad set of features encode few assumptions compared to other analysis packages, enabling analysis of a broader class of data ranging from biomolecular simulations to colloidal experiments.Additional comments including restrictions and unusual features:1. freud provides very fast parallel implementations of standard analysis methods like RDFs and correlation functions.2. freud includes the reference implementation for the potential of mean force and torque (PMFT).3. freud provides various novel methods for characterizing particle environments, including the calculation of descriptors useful for machine learning. The source code is hosted on GitHub (https://github.com/glotzerlab/freud), and documentation is available online (https://freud.readthedocs.io/). The package may be installed via pip install freud-analysis or conda install -c conda-forge freud.

Granular Effects on Depositional Processes of Debris Avalanches

Debris avalanches generally have massive mobility and extensive deposited area, which have strong relation to the granular effect. The granular effect is an outcome from the interaction (based on frictional mechanism) among particles. Discrepancy of grain composition, for instance the difference of particle size and their proportion of particles, is a key factor to influence granular effect. A series of laboratory tests have been conducted to research the granular effects on depositional processes of debris avalanches containing fine- and coarse-grained particles. The velocity of debris front, the morphology characteristics and runout distance of the debris avalanche are considered in detail, and the mass parameter and the size parameter are introduced in analysis for the research of granular effect. The experimental results indicate that the granular effects can decrease the dissipation of momentum and increase the accumulation region, leading to further runout distance and more extensive deposited areas. Further, the velocity, the range of depositions of debris avalanches are larger than that in other conditions when the proportion of fine-grained particles is 30%, especially the materials consist of heterogeneous granular. It means there have a critical mass parameter in experiments which lead to the high efficiency of granular effects, and the granular effect is weakening in homogeneous granular composition.

Leaching behavior and potential ecological risk of heavy metals in Southwestern China soils applied with sewage sludge compost under acid precipitation based on lysimeter trials

The ecological risk of heavy metals (HM) resulting from the use of sewage sludge compost (SSC) as an amendment to flower garden soil (FGS) and to abandoned phosphate mine soil (APMS) influenced by acid rain were simulated in lysimeter trials and the potential ecological risk index (PERI) was evaluated with minor modifications. The use of SSC indeed increased the mobility and release of HMs in FGS and APMS under conditions of acid rain. The leaching dynamics of HMs was found to be influenced by Fe/Al oxides and organic matter (OM) in the soil. The application of SSC as a fertilizer to barren APMS dramatically decreased the mobility of Cr, Cu and Pb by 51–56% due to their retention by particulate organic matter, while the leaching of As, Cd and Ni was increased as the result of competition with OM for available Fe/Al oxides (As) and proton-metal exchange reactions that occurred in HM-OM complexes (Cd and Ni). The ecological risk of FGS and APMS resulting from HM migration was actually low (PERI = 0.07–0.12), but the increased potential ecological risk resulting from the use of SSC were estimated to be moderate (a 16.0–33.5% increase in PERI for SSC-amended FGS) or high (a 140% increase in PERI for SSC-amended APMS). Ni, Cd and Cu were identified as the three main HMs responsible for increasing the ecological risk in soil which was mainly composed of fine-grained particles, whereas Cd and As were key ecological risks HMs in soil that was mainly composed of coarse-grained particles.

Assessing effectiveness of thermal treatment and mixing with coarse-grained particles in stabilization of marly soils

Marly soils can show problematic behaviors such as swelling and dispersion when subjected to water. It can cause problems for various civil constructions, including building foundations, water conveyance canals, highways, and airport runways; so appropriate measurements should be taken to stabilize these soils. In this study, two stabilization methods, including thermal treatment and mixing with coarse-grained particles, were utilized to limit swelling of marly soil samples collected from around the Sonqor city and also to improve their strength properties. The results of experimental tests showed that thermal treatment in high temperatures (after 100 °C) led to a decrease and an increase in liquid and plastic limits, respectively, and subsequently plasticity index decreased. However, after 475 °C, the Atterberg limits were almost unchanged. Also, it was found that with increasing heating levels, the swelling potential of the soil samples decreases as free swelling index values of the samples changed from 13.9% (high swelling potential) at 100 °C to 0.89% (low swelling potential) at 500 °C. Based on the experiments, it was observed that by adding 30% of coarse particles to the marly soil samples, engineering properties such as maximum dry density (γdmax), California bearing ratio, and unconfined compressive strength have been improved up to 10%, 59%, and 30%, respectively. Therefore, the stabilized marly soils could be considered as appropriate construction materials.

A new interpretation of three-dimensional particle geometry: M-A-V-L

This study provides a new interpretation of 3D particle geometry that unravels the 'interrelation' of the four geometry parameters, i.e., morphology M, surface area A, volume V, and size L, for which a new formula, M = A/V$\times$L/6, is introduced to translate the 3D particle morphology as a function of surface area, volume, and size. The A/V$\times$L of a sphere is invariably 6, which is placed in the denominator of the formula, and therefore M indicates a relative morphological irregularity compared to the sphere. The minimum possible value of M is clearly one, and M may range approximately to three for coarse-grained mineral particles. Furthermore, the proposed formula, M = A/V$\times$L/6, enables to graphically preserve the four parameters' relations when plotting the geometry parameter distributions. This study demonstrates the approach with two plot spaces that represent (i) L vs. M and (ii) A/V vs. V, where A/V works as the messenger between these two spaces as A/V = M/L$\times$6. Therefore, this approach helps comprehensively address the four-dimensional aspects of the 3D particle geometry and better understand the parameters' combined influence on the mechanical behavior of granular materials. Keywords: 3D particle geometry; Morphology; Surface area; Volume; Size;

Manufacturing large 2219 Al–Cu alloy rings by a cold rolling process

ABSTRACTTransition rings made of 2219 Al–Cu alloy for tanks with diameters exceeding 5 m require enhanced performance. However, a coarse-grained structure and residual Al2Cu particles deteriorate the mechanical properties of large 2219 Al–Cu alloy rings. A cold rolling (0–6%) process was performed before solution treatment to improve the mechanical properties of such rings. The results showed that increasing the cold rolling deformation led to a higher dislocation density, yielding finer recrystallized grains after heat treatment; moreover, finer grains led to deeper and longer intergranular cracks, thereby increasing the elongation. Increasing the cold rolling deformation also facilitated the fragmentation of Al2Cu particles and enhanced the degree of supersaturation after solution heat treatment, which increased the driving force required for aging precipitation; the yield strength first increased (0–4%) and then decreased (4–6%) with respect to the variation in the characteristics of the precipitated phases. The radial tensile sample that was 6% cold-rolled may experience brittle fracture, which may lead to a significant decrease in the mean tensile strength and elongation. Overall, using the cold rolling process is feasible, and the 4% cold-rolled sample exhibited the best mechanical properties.

Long-time simulation of catalytic MTO reaction in a fluidized bed reactor with a coarse-grained discrete particle method — EMMS-DPM

Long-time behaviors widely exist in gas–solid reactors, e.g., the coke deposition and catalyst deactivation in the methanol to olefins (MTO) process. Due to the limitation of the computational cost, previous simulations of MTO reactors were mainly conducted with two-fluid model at short-time scales and assumed that the catalyst are perfectly mixed. Efficient simulation methods are, therefore, highly desirable, even for evaluating the assumptions through very long-time investigation. In this study, the MTO reaction kinetics is incorporated into a coarse-grained discrete particle method, namely EMMS-DPM, to simulate a pilot-scale reactor for 8 h of physical time. The simulation is validated by comparing the obtained gaseous products and coke contents with the experimental data. The perfect mixing assumption is validated by observing the residence time distribution of the catalyst for the whole reactor. The detailed coke content could provide more accurate data for accelerating steady state simulations. Furthermore, the relation between the coke content and age of the catalyst is directly obtained for the first time, which is valuable to effective use of the catalyst before discharging. The coke content is positively correlated to the age, but is also influenced by local conditions. For example, near the distributor, the catalyst particles are not well mixed and the maximum reaction rate fluctuates significantly even at large time scales. Thus, long-time particle-scale simulation would provide more dynamic details to characterize the reaction in the critical regions of the reactor, thus being very helpful to optimize operating conditions and the reactor designs.

Influence of pore morphology on the diffusion of water in triblock copolymer membranes.

Understanding the transport properties of water in self-assembled block copolymer morphologies is important for furthering the use of such materials as water-purifying membranes. In this study, we used coarse-grained dissipative particle dynamics simulations to clarify the influence of pore morphology on the self-diffusion of water in linear-triblock-copolymer membranes. We considered representative lamellar, cylindrical, and gyroid morphologies and present results for both the global and local diffusivities of water in the pores. Our results suggest that the diffusivity of water in the confined, polymer-coated pores differs from that in the unconfined bulk. Explicitly, in confinement, the mobility of water is reduced by the hydrodynamic friction arising from the hydrophilic blocks coating the pore walls. We demonstrate that in lamella and cylindrical morphologies, the latter effects can be rendered as a universal function of the pore size relative to the brush height of the hydrophilic blocks.

Mechanical High-Temperature Properties and Damage Behavior of Coarse-Grained Alumina Refractory Metal Composites.

The present study provides the mechanical properties of a new generation of refractory composites based on coarse-grained Al2O3 ceramic and the refractory metals Nb and Ta. The materials were manufactured by refractory castable technology and subsequently sintered at 1600 °C for 4 h. The mechanical properties and the damage behavior of the coarse-grained refractory composites were investigated at high temperatures between 1300 and 1500 °C. The compressive strength is given as a function of temperature for materials with two different volume fractions of the refractory metals Ta and Nb. It is demonstrated that these refractory composites do not fail in a completely brittle manner in the studied temperature range. The compressive strength for all materials significantly decreases with increasing temperature. Failure occurred due to the formation of cracks along the ceramic/metal interfaces of the coarse-grained Al2O3 particles. In microstructural observations of sintered specimens, the formation of tantalates, as well as niobium oxides, were observed. The lower compressive strength of coarse-grained Nb-Al2O3 refractory composites compared to Ta-Al2O3 is probably attributed to the formation of niobium oxides. The formation of tantalates, however, seems to have no detrimental effect on compressive strength.

Coarse-grained DEM study of solids sedimentation in water

The so-called coarse-grained discrete element method (DEM) is used here for efficient simulations of large-scale particle systems as its effectiveness has been successfully verified previously on the processes such as spouted beds, pneumatic conveying systems and bubbling fluidized beds. In this study, the coarse-grained DEM method is used to study the solid-liquid flow in the process of sedimentation of solids in water. Four specific types of particle systems are considered to verify the effectiveness of the coarse-grained model qualitatively and quantitatively, the particle systems considered being: the original-sized particle system; the coarse-grained particle systems in two different coarse graining ratios, and the simple large particle system. For qualitative evaluations of these systems, the evolutions of the sedimentation state, characterized by fluid velocity distributions and contour maps of void fractions, are compared using a range of snapshots at different times. For quantitative comparisons, the physical indexes such as the change of particle volume fraction, the potential energy of particles and liquid pressure changes are evaluated. These systems are also compared using four cases with different variable values for further investigation of the effectiveness of the coarse graining DEM method under different conditions. The four cases consist of one base case and three parametric cases which are different in terms of the particle number and height of the computational domain. These comparisons show that, for all four cases, the coarse-grained system in fact produces results that are in good agreement with those of the original-sized particle system both qualitatively and quantitatively. However, the simple large particle system fails to achieve a reasonable agreement with the original-sized particle system. It can be thus concluded that the coarse-grained model is a cost-effective and reliable tool to simulate the process of large-scale solids sedimentation in water.

Micro-Mechanism of Spherical Gypsum Particle Breakage under Ball–Plane Contact Condition

Coarse-grained soils are used extensively in engineering applications. The breakage of coarse-grained soil particles may have a great effect on their mechanical characteristics. It is important to fully understand the phenomenon of particle breakage and comprehend its effect on engineering properties. The aim of this study was to investigate the process and mechanism of spherical particle breakage under ball–plane contact conditions. Particle contact tests and corresponding simulations based on the discrete element method were performed. The mechanical properties and breaking morphologies of gypsum balls, as well as the significant feature of the existence of a cone core under the contact point, were obtained by the experiments. To enable particle crushing in a numerical simulation, noncrushable elementary particles were bonded together to represent the specimen. The numerical model, which was validated by the unconfined compression test and splitting test, was well fitted with the experiment by applying flat-joint contact. More importantly, the combination of the simulation and experiment demonstrated the role that the cone core plays during particle breakage and revealed the mechanism of the formation of the cone core and its effect on particle breakage.

Resolution limit of data-driven coarse-grained models spanning chemical space.

Increasing the efficiency of materials design remains a significant challenge given the large size of chemical compound space (CCS). The use of a chemically transferable coarse-grained model enables different molecular fragments to map to the same bead type, significantly increasing screening efficiency. Here, we propose new criteria for the design of coarse-grained models allowing for the optimization of their chemical transferability and evaluate the Martini model within this framework. We further investigate the scope of this transferability by parameterizing three Martini-like models in which the number of bead types ranges from 5 to 16. These force fields are fully compatible with existing Martini environments because they are parameterized by interpolating the Martini interaction matrix. We then implement a Bayesian approach to determining which chemical groups are likely to be present on fragments corresponding to specific bead types for each model. We demonstrate that a level of accuracy comparable to Martini is obtained with a force field with fewer bead types, using the water/octanol partitioning free energy (ΔGW→Ol) as our metric for comparison. However, the advantage of including more bead types is a reduction of uncertainty when back-mapping these bead types to specific chemistries. Just as reducing the size of the coarse-grained particles leads to a finer mapping of conformational space, increasing the number of bead types yields a finer mapping of CCS. Finally, we note that, due to the large size of fragments mapping to a single Martini bead, a resolution limit arises when using ΔGW→Ol as the only descriptor when coarse-graining CCS.

Microscopic derivation of coarse-grained, energy-conserving generalized Langevin dynamics.

Properly simulating nonequilibrium phenomena such as thermal transport and shock wave propagation in complex condensed matter systems require the conservation of system's internal energy. This precludes the application of the coarse-grained (CG) generalized Langevin equation (GLE) dynamics due to the presence of dissipative interactions. Attempts to address this issue have been pursued both phenomenologically and from entropy-based first principles for dissipative particle dynamics (DPD, a Markovian variant of the CG GLE dynamics) by introducing an energy conserving extension of DPD (DPD-E). We present here a rigorous microscopic derivation of two energy conserving variants of the CG GLE dynamics by extending the CG equations of motion to include the GLE for certain internal energy observables of the microscopic system. We consider two choices of such observables: the total internal energy and a set of internal energies of the CG particles. The derivation is performed using the Mori-Zwanzig projection operator method in the Heisenberg picture for time evolution of thermodynamic expectations and the recently introduced interpretation of the Zwanzig projection operator [S. Izvekov, J. Chem. Phys. 146(12), 124109 (2017)] which allows an exact calculation of the memory and projected terms. We begin with equilibrium conditions and show that the GLE dynamics for the internal energy observables is purely dissipative. Our extension of the GLE dynamics to quasiequilibrium conditions (necessary to observe heat transport) is based on the generalized canonical ensemble approach and transport equation using the nonequilibrium statistical operator (NSO) method. We derive closed microscopic expressions for conductive heat transfer coefficients in the limit of neglecting dissipation in heat transfer and in the lowest order of deviation from equilibrium. After employing the Markov approximation, we compare the equations of motion to the published DPD-E equations. Our equations contain additional energy transfer terms not reported in the previous works. Additionally, we show that, despite neglecting dissipative processes in heat transport, the heat transfer coefficients and random force are related in a way reminiscent of the fluctuation-dissipation relation. The formalism presented here is sufficiently general for the rigorous formulation of the GLE dynamics for arbitrary microscopic phase space observables as well as sampling different microscopic ensembles in CG simulations.