The nonlinear rheology of entangled polymers is strongly influenced by molecular architecture, yet architectural complexity does not necessarily translate into superior processing performance. Here, we investigate the transient shear and uniaxial elongation responses of symmetric star-branched and linear polystyrene chains of similar span length, using recent experimental data of Liu et al. (2025). Predictions are performed with the clustered fixed slip-link model (CFSM), a coarse-grained implementation of the discrete slip-link model, recently revised to accurately describe the mean-field constraint dynamics in star-branched polymers (Katzarova et al. Macromolecules, 59(1):564–574 2026). The model quantitatively reproduces the transient shear response for both architectures at moderately large Rouse-Weissenberg numbers ( Wi_R≲ 2 ) and captures elongational stress growth up to Hencky strains of approximately two, achieving a level of agreement with experiment that is unprecedented for coarse-grained models in these nonlinear regimes. Consistent with prior experimental interpretations, we confirm theoretically that the Rouse-stretch time of symmetric star polymers can be estimated in the same manner as for linear chains, provided the span length is taken as twice the arm molecular weight. The results further suggest that, far-from-equilibrium, branch-point diffusion in star polymers plays a diminished role in the nonlinear response, highlighting an architectural effect relevant to polymer processing flows.

Recent molecular dynamics simulations of entangled polymer melts suggest that chains reëntangle on the (Rouse) time scale of chain retraction, rather than on the longest, disengagement relaxation time, upon cessation of flow [O'Connor et al. Macromolecules 2019, 52, 8540-8550]. Inspired by these results, it has been suggested by using a tube model that reëntanglement kinetics are chemistry specific [Dolata et al. ACS Macro Lett. 2024, 13, 896-902]. Here we argue that their conclusions arise from interpreting simulations with a model that does not have a sufficiently detailed level of description. We employ the discrete-slip-link model, which is more detailed and so contains important fluctuations. We show that this universal level of description can describe the results without resorting to chemistry specificity. Our results suggest that a significant amount of reëntanglement happens on the Rouse time, which obscures the fact that it finishes only on the disengagement time, resolving the apparent paradox.

Recent experiments have revealed that puller-type Janus microswimmers exhibit upstream swimming in the presence of an externally applied flow [Sharan et al., “Upstream rheotaxis of catalytic Janus spheres,” ACS Nano 16, 4599–4608 (2022)]. Previous theoretical studies had shown that hydrodynamic interactions with adjacent walls can stabilize the upstream motion of puller-type microswimmers. A thermodynamically admissible model that allows coupling fuel consumption with the swimmer's motion is used here to study a swarm. We show that hydrodynamic interactions between the swimmers in the swarm can also stabilize the upstream swimming of puller-type microswimmers. Moreover, stability is maintained for a longer time when the volume fraction of microswimmers is larger.

Entangled, linear polymers exhibit a famous molecular-weight scaling of the longest relaxation time with exponent 3.4. However, star-branched polymers exhibit a much stronger dependence closer to exp(gamma M a/M e), where M a is the arm molecular weight, and M e is an entanglement molecular weight. Several tube models have been proposed to describe star-branched polymer melts. The initial purpose was to predict gamma, and later modifications sought to improve the predictions for the shape of the dynamic modulus and to achieve consistency between the parameter values used for linear and star-branched chains. However, a survey of tube models reveals that the addition of new ad hoc terms leads to overall poor and inconsistent predictions. The alternative entanglement theory, slip-links, is more expensive to calculate than tubes, because of the large ratio of longest to entanglement relaxation times and the inclusion of fluctuations not present in tube models. Here, we introduce a corrected algorithm for star-branched relaxation calculations that is orders of magnitude faster than previous studies, allowing a much more complete study. We examine the relaxation spectrum and zero-shear-rate viscosity of stars with up to 12 entanglements per arm. Comparison with existing zero-shear-rate data for several polymer chemistries shows that the slip-link theory can correctly describe the observed molecular-weight dependence.

Equibiaxial elongational deformations are omnipresent in polymer processing technologies. The challenge of generating well-controlled equibiaxial elongational deformations in the laboratory has, however, severely inhibited progress on understanding the rheology of polymeric liquids and other complex fluids in this flow. More recently, a novel technique known as continuous lubricated squeezing flow has been developed that allows for rheological measurements in equibiaxial elongational deformations. In the present study, we examine the rheological behavior of two entangled polyisobutylene (PIB) melts with different molecular weight distributions in constant strain rate equibiaxial elongation flows. These new data are compared with predictions from two molecular models for entangled polymer melts inspired by the idea that entanglements dominate the relaxation dynamics. One model is the discrete slip-link model (DSM), and the other is known as the Rolie Double Poly (RDP) model. For the PIB with a relatively narrow molecular weight distribution, the predictions of both models are in good agreement with experiments and the DSM gives nearly quantitative agreement. For the broad molecular weight distribution PIB, both the DSM and RDP model predict strain hardening, which is not observed in the experiments.

Abstract Funding Acknowledgements Type of funding sources: Public Institution(s). Main funding source(s): Research reported in this abstract was supported by the National Heart, Lung, And Blood Institute of the National Institutes of Health under Award Number R44HL158375 (the content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health). Background Placing lesions at the same point (stacking lesions) in the left atrium during radiofrequency (RF) ablation can increase the risk of collateral injury. The use of active esophageal cooling has been shown to significantly reduce the risk of thermal injury to the esophagus, but stacking of lesions may overcome these protective effects. Longer pauses between lesions may reduce this risk, but the effect of very short pauses has not been previously quantified. Purpose To examine the impact of ultra-short pauses between stacked lesions with and without active esophageal cooling. Methods Using a computational model of the left atrium, we measured the effect of RF ablation in the left atrium on injury formation in the esophagus. Models with and without active esophageal cooling, using a dedicated esophageal cooling device, were created. Using a power of 50 W for 10 s, with up to 3 sequential lesions placed in the same location, we used the Arrhenius equation to quantify the fraction of damage (FOD) in the esophageal wall. The time between lesions was set to as short as 1 s, and results were compared to prior studies using longer pauses of up to 20 s. To account for thermal latency, measures of esophageal damage were taken both immediately after RF ablation, and again 90 s afterwards. Results With active cooling in place, esophageal injury was eliminated with active esophageal cooling after the first lesion placement, but reached 21% transmurality without cooling. Lesion transmurality increased after each lesion due to thermal latency, but active esophageal cooling prevented this effect when only one lesion was placed. Subsequent lesions resulted in esophageal injury when placed in the same location. After 3 lesions with 1 s pauses between each, esophageal injury transmurality reached 91% without cooling in place, and 22% with active cooling in place (Figure 1). In contrast, analysis of the intended lesions in the atrial wall demonstrated minimal effects from cooling (Figure 2). Conclusions Active esophageal cooling significantly reduces esophageal injury from RF ablation, but placing additional lesions at the same point can overcome the heat extraction capacity of a dedicated cooling device. Decreased time between lesions exacerbates this risk, with an ultra-short pause of one second posing the greatest risk.

The dynamics and stability of a swarm of microswimmers is examined here using a thermodynamically compliant microswimmer model. The theory presented in this work is a mean-field model in which the swarm is considered to be a uniform solution of swimmers that are moving, on average, in the same direction. The hydrodynamic interaction between swimmers is modeled accurately assuming a crystalline arrangement to the swarm. A swimmer in the swarm can swim up to 12 times faster than when alone in an infinite sea, when the volume fraction of swimmers in the swarm is about 0.14. Moreover, we have also studied the stability of the swarm around a uniform crystalline arrangement by calculating the hydrodynamic torques generated by the swarm as a function of the volume fraction of swimmers. The predictions presented here agree with recent multiparticle simulations that have shown that hydrodynamic torques have a stabilizing effect in swarms of pullers while swarms of pushers are generally destabilized by hydrodynamic interactions. The thermodynamically admissible coupling between the swimmer's motion and fuel consumption allows us to study the full dynamics instead of artificially constrained steady-states only. By accounting for fuel consumption and high order hydrodynamic interactions, we are able to examine the swarm's stability as functions of fuel concentration and the volume fraction of swimmers. We find that at high concentrations of fuel, swarms of pullers are stabilized by hydrodynamic torques for volume fractions of swimmers as low as 0.02 but at lower volume fractions Brownian forces make the swarm unstable.

Prior studies have extensively shown that the discrete slip-link model (DSM) accurately predicts the linear and nonlinear rheology of various entangled polymer systems. The only publicly available implementation of the DSM algorithm is written in the CUDA C++ programming language. In this work we discuss the implementation of the fixed slip-link model and the clustered fixed slip-link model in Python. Our work shows that Python can also utilize GPUs for fast quantitative rheological predictions. Our simulation code, named pyDSM, allows an easy-to-read and beginner-friendly approach for users wanting to utilize the efficiency of GPU computing while also enabling an open-source Python package that can easily couple or interact with other simulation or data analysis software. We demonstrate pyDSM's versatility by implementing MUnCH, a recently published algorithm that allows estimation of the statistical uncertainty in the autocorrelations for any time series data, properly accounting for the correlation in the data. An on-the-fly version of MUnCH is applied to calculate the uncertainty in the relaxation modulus and the chain center-of-mass mean squared displacement. Moreover, the uncertainty quantification in the relaxation modulus allows propagation of error through a multi-mode Maxwell fit to determine the uncertainty in the dynamic modulus. Lastly, as an example of a novel application of the pyDSM code we calculate the re-entanglement dynamics after cessation of flow which are fundamental to the weld quality in fused-filament 3D printing. Program summary Program Title: pyDSM - Discrete Slip-link Model (DSM) in Python for Fast Quantitative Rheology Predictions of Entangled Polymers CPC Library link to program files: https://doi .org /10 .17632 /v828b9cjp9 .1 Developer's repository link: https://github .com /jgethier /pyDSM Licensing provisions: GPLv3 Programming language: Python Nature of problem: Predicting stress relaxation in entangled polymer systems is crucial for understanding the macroscopic properties of the material. Many existing models do not capture the physics of polymer entanglements in linear, star-branched, and other entangled polymeric systems. The discrete slip-link model has been shown to predict quantitatively the rheological behavior of polymers, but only one version of the model is publicly available using CUDA C++ programming. Solution method: We implement a less-detailed version of the discrete-slip link model to predict the linear and nonlinear rheology of entangled polymers in Python. Uncertainty in the predictions is implemented with the MUnCH algorithm. We implement GPU-based calculations for fast and accurate predictions of the linear and nonlinear rheology behavior, as well as re-entanglement dynamics after cessation of flow. (c) 2023 Elsevier B.V. All rights reserved.

Abstract Funding Acknowledgements Type of funding sources: None. Background Thermal latency, or delayed heating, is increasingly recognized as an important factor in the formation of both intentional and unintentional lesions during radiofrequency (RF) ablation for the treatment of atrial fibrillation (AF). High-power short-duration (HPSD) ablation appears to have greater thermal latency than low or medium power ablation. Proactive esophageal cooling (PEC) has been shown to reduce esophageal lesion formation under a variety of conditions by directly reducing the effects of thermal latency, but the influence of anatomic dimensions on the protective efficacy of cooling during HPSD ablation has not been investigated. Purpose Determine the impact of changes in pericardial tissue thickness on thermal latency in order to quantify the protective efficacy of PEC across a range of anatomic dimensions. Methods We created a mathematical model of the left atrium undergoing HPSD ablation, both with and without a PEC device in place, using a range of pericardial tissue thicknesses (0.5, 0.75, and 1 mm). HPSD ablation was set at 50 W for 10 s, or 90 W for 4 s. We then examined the temperature dynamics at a range of thickness, focusing on the layer of mostly fatty tissue between the atrial and esophageal walls by varying the thickness of this layer while quantifying the degree of esophageal damage using the Arrhenius equation to determine the fraction of damage after peak heating has occurred. Results Under control conditions, the growth of lesions from RF ablation at both 50 W and 90 W was found to continue for greater than 10 seconds beyond the cessation of RF energy application. Esophageal lesion formation ranged from 71% to 96% transmurality after 50 W ablation for 10 s, and from 50% to 72% transmurality after 90 W ablation for 4 s. With PEC in place, esophageal lesion transmurality was markedly reduced, with a maximum transmurality ranging from 12% to 32% with 50 W ablation, and from 2% to 20% with 90 W ablation (Figure). Increasing thickness of pericardial tissue (with simulations of 0.5, 0.75, and 1 mm) resulted in decreasing esophageal lesion transmurality (67%, 74%, and 83% at 50 W power, and 72%, 82%, and 96% at 90 W power, respectively, with the 0.5, 0.75, and 1 mm simulations). Conclusions Thermal latency with HPSD ablation contributes to lesion growth and can cause esophageal injury. Proactive esophageal cooling counteracts this effect across a range of pericardial tissue thicknesses, and reduces esophageal lesion transmurality by an average of 79%.

Background: Recent data suggest that luminal esophageal temperature (LET) monitoring during high-power short-duration (HPSD) ablation may be inadequate to prevent esophageal thermal injury during radiofrequency (RF) ablation. This is due in part to delayed responses to thermal latency and the continued temperature rise that occurs in tissues even after the cessation of RF energy with HPSD settings. Proactive esophageal cooling has been shown to reduce severe esophageal thermal injury during medium-power medium-duration RF ablation, but less is known about the effects in HPSD ablation. Objective: We aimed to quantify the time course of esophageal damage in scenarios with and without proactive esophageal cooling, hypothesizing a reduction in the resulting tissue damage with proactive esophageal cooling. Methods: Using a computer model of RF ablation in the left atrium adjacent to the esophagus, we calculated temperature over time using ablation power of 50 W for 10 s and 90 W for 4 s. We then determined the fraction of resulting damage to esophageal tissue via the Arrhenius equation and by the percentage of tissue above lethal isotherm temperature of 50°C. Transmurality of injury was then plotted over time, and results were compared between ablation with and without proactive esophageal cooling. Results: Esophageal damage increased even after the cessation of RF energy, suggesting significant thermal latency effects under HPSD ablation. Lesion growth continued for >10 s after cessation of 50 W ablation energy, and for >12 s after cessation of 90 W ablation energy without cooling. With proactive cooling, lesion growth after cessation of ablation energy was essentially halted. Without esophageal cooling, maximum injury transmurality reached 79% with 50 W, and 58% with 90 W. With esophageal cooling, injury transmurality remained below 20% with 50 W, and 10% with 90 W, representing reductions of 75% and 83%, respectively. Conclusions: RF ablation using HPSD settings demonstrates significant latency of effect, with tissue damage and lesion growth continuing beyond the cessation of application of RF energy. Proactive esophageal cooling significantly dampens this effect, reducing esophageal injury by up to 83%.

Background Proactive cooling with a novel cooling device has been shown to reduce endoscopically identified thermal injury during radiofrequency (RF) ablation for the treatment of atrial fibrillation using medium power settings. We aimed to evaluate the effects of proactive cooling during high-power short-duration (HPSD) ablation. Methods A computer model accounting for the left atrium (1.5 mm thickness) and esophagus including the active cooling device was created. We used the Arrhenius equation to estimate the esophageal thermal damage during 50 W/ 10 s and 90 W/ 4 s RF ablations. Results With proactive esophageal cooling in place, temperatures in the esophageal tissue were significantly reduced from control conditions without cooling, and the resulting percentage of damage to the esophageal wall was reduced around 50%, restricting damage to the epi-esophageal region and consequently sparing the remainder of the esophageal tissue, including the mucosal surface. Lesions in the atrial wall remained transmural despite cooling, and maximum width barely changed (<0.8 mm). Conclusions Proactive esophageal cooling significantly reduces temperatures and the resulting fraction of damage in the esophagus during HPSD ablation. These findings offer a mechanistic rationale explaining the high degree of safety encountered to date using proactive esophageal cooling, and further underscore the fact that temperature monitoring is inadequate to avoid thermal damage to the esophagus.

Background: Active esophageal cooling during radiofrequency (RF) ablation of the left atrium (LA) has been shown to reduce esophageal injury. Although no atrioesophageal fistula has been reported in over 12 thousand uses to date, the first pericardio-esophageal fistula to occur despite cooling reinforces the fact that a threshold may exist at which heat extraction capacity may be surpassed. We aimed to examine this threshold by measuring the transmurality of esophageal injury after sequential lesion placement. Hypothesis: Reduced rest time between stacked lesions increases tissue lesion depth by enhancing thermal latency effects. Methods: Using a computational model of the left atrium, we determined esophageal lesion depth between sequentially placed RF lesions using high-power, short duration power settings (50 W for 10 s). Lesion depth was determined via Arrhenius equation, and anatomical dimensions were:1.5 mm for atrial myocardium, 0.75 mm for pericardial tissue, and 2 mm for the esophagus. Three lesions were placed on the myocardium with either 5 s or 10 s pauses in between. Final lesion transmurality was measured 45 s after the last placement to fully account for latent heating. Results: Active esophageal cooling reduced esophageal lesion transmurality by 80% after the first lesion. Sequential lesions increased esophageal lesion transmurality, with thermal latency contributing to increased lesion depth even after cessation of RF energy. Shorter timing between lesions allowed further growth in transmurality: 4% for 90 W, and 8.5% for 50 W power settings (Figure 1), showing that the efficacy of cooling against thermal latency effects decreased with the placement of each subsequent lesion. Conclusions: Active esophageal cooling reduces esophageal lesion transmurality by 80% when single lesions are placed. Stacking additional lesions at the same point reduces this safety benefit, with shorter intervals between lesions resulting in less protective effect.

The possibility of nonuniversality in the nonlinear rheology of polymer melts during the inception of shear flow at large strain rates has recently been questioned, and hence it is examined here using the discrete slip-link model (DSM). An expression for the Rouse relaxation time, tau(R), as a function of entanglement activity and number of Kuhn steps is found from a master curve of strain maxima, as predicted by the theory. In contrast to tube theories, this expression is then shown to collapse all entangled polymer solution and melt data to universal behavior for the maximum shear stress, tau(max)(xy), and the strain at maximum stress. The transition of these quantities from strain-rate-free values to values that scale with dimensionless strain rate as similar to(tau(R)(gamma) over dot)(0.33) is shown to correspond to primitive path stretching. Furthermore, the scaling exponents for melt (0.1-0.15) and solution (0.2-0.3) data do not show the same scaling for steady-state shear stress, tau(ss)(xy), but the melts are in agreement with DSM (0.1). There is a small amount of data for the scaling of stress at undershoot, tau(us)(xy), and strain at undershoot, which are predicted to scale as 0.1 and 0.33 for DSM, in agreement for melt data. Of the other comparisons made here with data, only the melt theory of Xie and Schweizer (XS) does almost as well in predicting the scalings. However, the magnitudes for tau(max)(xy), tau(ss)(xy), and tau(us)(xy) predicted by XS are about a factor of 2 greater compared to experiments. Moreover, XS overpredicts the steady-state shear scaling (0.3, for tau(R)(gamma)over dot> 6), which is also predicted by some coarse-grained molecular simulations and closer to what is observed in solutions. Finally, we find that DSM predicts only a very weak dependence of Rouse time on chemistry.

A complete propagation of error procedure for passive microrheology is illustrated using synthetic data from generalized Brownian dynamics. Moreover, measurement errors typical of bead tracking done with laser interferometry are employed. We use the blocking transformation method of Flyvbjerg and Petersen (J Chem Phys 91(1):461–466 1989) applicable to estimating statistical uncertainty in autocorrelations for any time series data, to account properly for the correlation in the bead position data. These contributions to uncertainty in correlations have previously been neglected when calculating the error in the mean-squared displacement of the probe bead (MSD). The uncertainty in the MSD can be underestimated by a factor of about 20 if the correlation in the bead position data is neglected. Using the generalized Stokes-Einstein relation, the uncertainty in the MSD is then propagated to the dynamic modulus. Uncertainties in the bead radius and the trap stiffness are also taken into account. A simple code used to aid in the calculations is provided.

We use straightforward energy and entropy balances to test the thermodynamic consistency of microstructural rheological models. The method utilizes the same mathematical methods as classical transport phenomena, so it is much simpler to use than the much more rigorous GENERIC formalism. The cost of this simplicity is that fewer restrictions are actually tested than those in either the single-generator or the two-generator formalisms. The proposed test does provide, however, a separation of energy and entropy, leading to an interesting internal energy balance. More importantly, it leads to two requirements for non-negative entropy production: one closely related to a virtual work argument, important during flow, and a second that guarantees adherence to the second law of thermodynamics during microstructural relaxation. These criteria do not appear to be in conflict with the requirements of the more rigorous formulations and are much simpler to implement. Several illustrative examples are given with models using the conformation tensor level of description. As expected, the models that use a relaxation function that is proportional to the free energy gradient are straightforward to check. These include the Hookean dumbbell, the FENE-P, and the Giesekus models, which are shown to satisfy the first and second laws. With a little more work, models with relaxation functions not driven by the free energy gradient only can also be checked for thermodynamic compliance with the proposed formalism. Examples of these are the GLaMM and Rolie–Poly models; they violate the first and second laws of thermodynamics, respectively. A recently proposed FENE-mode model is also checked, which superficially satisfies both laws, but fails to have an analytic free energy. Finally, the application of the formalism to a nonlinear dumbbell model that uses the probability density for chain conformations is also illustrated. In that case, satisfaction of the fluctuation-dissipation theorem and a positive mobility guarantee compliance with the first and second laws.

Collagen is heavily hydroxylated. Experiments show that proline hydroxylation is important to triple helix (monomer) stability, fibril assembly, and interaction of fibrils with other molecules. Nevertheless, experiments also show that even without hydroxylation, type I collagen does assemble into its native D-banded fibrillar structure. This raises two questions. Firstly, even though hydroxylation removal marginally affects macroscopic structure, how does such an extensive chemical change, which is expected to substantially reduce hydrogen bonding capacity, affect local structure? Secondly, how does such a chemical perturbation, which is expected to substantially decrease electrostatic attraction between monomers, affect collagen's mechanical properties? To address these issues, we conduct a benchmarked molecular dynamics study of rat type I fibrils in the presence and absence of hydroxylation. Our simulations reproduce the experimental observation that hydroxylation removal has a minimal effect on collagen's D-band length. We also find that the gap-overlap ratio, monomer width and monomer length are minimally affected. Surprisingly, we find that de-hydroxylation also has a minor effect on the fibril's Young's modulus, and elastic stress build up is also accompanied by tightening of triple-helix windings. In terms of local structure, de-hydroxylation does result in a substantial drop (23%) in inter-monomer hydrogen bonding. However, at the same time, the local structures and inter-monomer hydrogen bonding networks of non-hydroxylated amino acids are also affected. It seems that it is this intrinsic plasticity in inter-monomer interactions that preclude fibrils from undergoing any large changes in macroscopic properties. Nevertheless, changes in local structure can be expected to directly impact collagen's interaction with extra-cellular matrix proteins. In general, this study highlights a key challenge in tissue engineering and medicine related to mapping collagen chemistry to macroscopic properties but suggests a path forward to address it using molecular dynamics simulations.

We evaluate the thermodynamic consistency of the anisotropic mobile slip-link model for entangled flexible polymers. The level of description is that of a single chain, whose interactions with other chains are coarse grained to discrete entanglements. The dynamics of the model consist of the motion of entanglements through space and of the chain through the entanglements, as well as the creation and destruction of entanglements, which are implemented in a mean-field way. Entanglements are modeled as discrete slip links, whose spatial positions are confined by quadratic potentials. The confinement potentials move with the macroscopic velocity field, hence the entanglements fluctuate around purely affine motion. We allow for anisotropy of these fluctuations, described by a set of shape tensors. By casting the model in the form of the general equation for the nonequilibrium reversible-irreversible coupling from nonequilibrium thermodynamics, we show that (i) since the confinement potentials contribute to the chain free energy, they must also contribute to the stress tensor, (ii) these stress contributions are of two kinds: one related to the virtual springs connecting the slip links to the centers of the confinement potentials and the other related to the shape tensors, and (iii) these two kinds of stress contributions cancel each other if the confinement potentials become anisotropic in flow, according to a lower-convected evolution of the confinement strength or, equivalently, an upper-convected evolution of the shape tensors of the entanglement spatial fluctuations. In previous publications, we have shown that this cancellation is necessary for the model to obey the stress-optical rule and the Green-Kubo relation, and simultaneously to agree with plateau modulus predictions of multichain models and simulations.

In single-particle microrheology, the viscoelastic properties of a complex fluid can be extracted using the generalized Stokes-Einstein (GSE) relation by embedding a micrometer-sized particle and tracking its motion through the fluid. Applying the same analysis to molecular dynamics simulations can result in overestimated G * values because of the hydrodynamic interaction between the probe bead and its periodic images. We derive a simple correction to the GSE equation by implementing an analytical solution for Stokes drag on a periodic array of spheres, which allows smaller box sizes to be simulated while still retaining accuracy. Fluid and particle inertia are neglected, although the approach used here might be generalized to include them. The correction is applied to molecular dynamics simulations of a coarse-grained polymer melt. For several bead-to-box-size ratios R / L and two probe sizes, we measure the mean squared displacement and calculate G * using both the original GSE and the corrected hydrodynamic Stokes-Einstein (HSE) equations. These results are compared to small amplitude oscillatory non-equilibrium molecular dynamics (NEMD) simulations, which show that the HSE analysis correctly predicts the G * values at low frequencies but breaks down when either fluid inertia is important or the bead size is too small to "see " a continuum. For small R / L, the GSE and HSE results are similar, although a small correction is still required for the finite box size and computational cost is significantly larger. The HSE equation allows the use of smaller box sizes, reducing computational costs by more than an order of magnitude. (c) 2021The Society of Rheology