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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Strangeness enhancement at its extremes: multiple (multi-)strange hadron production in pp collisions at \(\sqrt{s}=5.02\) TeV

The probability to observe a specific number of strange and multi-strange hadrons (nS), denoted as P(nS), is measured by ALICE at midrapidity (|y| < 0.5) in $$\sqrt{s}=5.02$$ TeV proton-proton (pp) collisions, dividing events into several multiplicity-density classes. Exploiting, for the first time, a technique based on counting the number of strange-particle candidates event-by-event, this measurement allows one to extend the study of strangeness production beyond the mean of the distribution. This constitutes a new test bench for production mechanisms, probing events with a large imbalance between strange and non-strange content. The analysis of a large-statistics data sample makes it possible to extract P(nS) up to a maximum nS of 7 for $${\text{K}}_{\text{S}}^{0}$$, 5 for Λ and $$\overline{\Lambda }$$, 4 for Ξ− and $${\overline{\Xi } }^{+}$$, and 2 for Ω− and $${\overline{\Omega } }^{+}$$. From this, the probability of producing strange hadron multiplets per event is calculated, thereby enabling the extension of the study of strangeness enhancement to extreme situations where several strange quarks hadronize in a single event at midrapidity. Moreover, comparing hadron combinations with different u and d quark compositions and equal overall s quark content, the contribution to the enhancement pattern coming from non-strangeness related mechanisms is isolated. The results are compared with state-of-the-art phenomenological models implemented in commonly used Monte Carlo event generators, including PYTHIA 8 Monash 2013, PYTHIA 8 with QCD-based Color Reconnection and Rope Hadronization (QCD-CR + Ropes), and EPOS LHC, which incorporates both partonic interactions and hydrodynamic evolution. These comparisons show that the new approach dramatically enhances the sensitivity to the different underlying physics mechanisms modeled by each generator.

Abualrob, I J↗
DOE OSTI2020

Nature of Non-Adiabatic Electron-Ion Forces in Liquid Metals

We report that an accurate description of electron-ion interactions in materials is crucial for our understanding of their equilibrium and non-equilibrium properties. Here, we assess the properties of frictional forces experienced by ions in non-crystalline metallic systems, including liquid metals and warm dense plasmas, that arise from electronic excitations driven by the nuclear motion due to the presence of a continuum of low-lying electronic states. To this end, we perform detailed ab-initio calculations of the full friction tensor that characterizes the set of friction forces. The nonadiabatic electron-ion interactions introduce hydrodynamic couplings between the ionic degrees of freedom, which are sizeable between nearest neighbors. The friction tensor is generally inhomogeneous, anisotropic and non-diagonal, especially at lower densities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Antielectrophoretic Response-Driven Bending–Tilting Deformation of Cationic Polyelectrolyte Brushes Drives Nonlinear Electroosmotic Transport in Brush-Grafted Nanochannels

In this paper, we use all-atom molecular dynamics (MD) simulations to describe a non-linearly enhanced electroosmotic (EOS) flow, where, in a nanochannel grafted with cationic PMETAC ([Poly(2-(Methacryloyloxy)Ethyl) Trimethylammonium Chloride]) brushes, a two-fold increase in the electric field strength leads to a several-fold (more than two-fold) increase in the EOS flow strength and volume flow rate. The electric field enforces the PMETAC brushes to undergo a bending-tilting driven deformation with a significant portion of the brush layer becoming parallel to the grafting surface. In response, a substantial fraction of the counterions leave the brush layer (hence become more mobile), but instead of going into the bulk, accumulate at the brush-bulk interface, i.e., stay in proximity of the brush segments aligned parallel to the grafting surface. This creates an interesting situation, where the counterions are not completely within the brush layer, yet they fully screen the brush charges. Such “freer” conditions enable the counterions to achieve very high velocity, thereby ensuring that the water solvating the counterions themselves move very fast triggering the significantly augmented EOS transport. Probing deeper we can identify that the bending-tilting driven brush deformation, enforcing the brushes to align parallel to the substrate, results from the anti-electrophoretic behavior of the brushes, where despite being positively charged, the brushes move against the electric field direction. Such an anti-electrophoretic behavior of the PE brushes, which has not been reported before, can be associated with the very fast velocities of the negatively charged counterions and the electrostatic and hydrodynamic coupling of the counterions with the positive functional groups of the brushes. Here, we anticipate that the findings of this paper will shed light on strategies for nanochannel flow, the anti-electrophoretic response of charged polymer chains, and the significance of capturing the detailed chemical architecture of polyelectrolytes in nanoscale science and engineering.

36 MATERIALS SCIENCE↗
DOE OSTI2024

On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions

The statistics of velocity and density fields are crucial for cosmic structure formation and evolution. Here, this paper extends our previous work on the two-point second-order statistics for the velocity field [Phys. Fluids 35, 077105 (2023)] to one-point probability distributions for both density and velocity fields. The scale and redshift variation of density and velocity distributions are studied by a halo-based non-projection approach. First, all particles are divided into halo and out-of-halo particles so that the redshift variation can be studied via generalized kurtosis of distributions for halo and out-of-halo particles, respectively. Second, without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: (i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; (ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade on small scales with a constant rate $\varepsilon_u$; (iii) On small scales, the even order moments of pairwise velocity $\Delta u_L$ follow a two-thirds law $\propto{(-\varepsilon_ur)}^{2/3}$, while the odd order moments follow a linear scaling $\langle(\Delta u_L)^{2n+1}\rangle=(2n+1)\langle(\Delta u_L)^{2n}\rangle\langle\Delta u_L\rangle\propto{r}$; (iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{'}$, pairwise velocity (velocity difference) $\Delta u_L$=$u_L^{'}$-$u_L$ and velocity sum $\Sigma u_L$=$u^{'}_L$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; (v) On small scales, $u_L$ and $\Sigma u_L$ can be modeled by a $X$ distribution to maximize the entropy of the system. The distribution of $\Delta u_L$ can be different; (vi) On large scales, $\Delta u_L$ and $\Sigma u_L$ can be modeled by a logistic or a $X$ distribution, while $u_L$ has a different distribution; (vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $\alpha(z)$ decreasing with time.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

A review of five decades of strategic decisions and key results on the path to ignition on the National Ignition Facility

Successful demonstration of an implosion that meets the physics metrics for ignition on the National Ignition Facility (NIF) in August 2021 and demonstration of G > 1 in December 2022 represented the culmination of five decades of research. This review covers the key strategic decisions and physics results from the 20 J Janus laser to the 2 MJ NIF laser. NIF's specifications were set in order to have a margin in performance to account for uncertainty in the physics challenges leading to ignition, particularly for laser–plasma interaction and hydrodynamic instabilities including long-wavelength modes responsible for implosion symmetry. The ignition experiments utilized all that margin. Achieving the laser and target performance utilized in the Hybrid-E experiments that achieved ignition and G > 1 proved to be a challenge that consumed a decade.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Checking nonflow assumptions and results via PHENIX published correlations in p+p, p+Au, d+Au, and 3 He+Au at √ s NN=200 GeV

Recently the PHENIX Collaboration has made available two-particle correlation Fourier coefficients for multiple detector combinations in minimum bias p+p and 0–5% central p+Au, d+Au, and 3 He+Au collisions at √ s NN = 200 GeV [Phys. Rev. C 105, 024901 (2022)]. Using these coefficients for three sets of two-particle correlations, azimuthal anisotropy coefficients v 2 and v 3 are extracted for midrapidity charged hadrons as a function of transverse momentum. In this paper, we use the available coefficients to explore various nonflow hypotheses as well as to compare the results with theoretical model calculations. The nonflow methods fail basic closure tests with ampt and pythia/angantyr, particularly when including correlations with particles in the low multiplicity light-projectile going direction. In data, the nonflow adjusted v 2 results are modestly lower in p+Au and the adjusted v 3 results are more significantly higher in p+Au and d+Au. However, the resulting higher values for the ratio v 3 /v 2 in p+Au at RHIC compared to p+Pb at the LHC is additional evidence for a significant overcorrection. Incorporating these additional checks, the conclusion that these flow coefficients are dominated by initial geometry coupled with final-state interactions (e.g., hydrodynamic expansion of quark-gluon plasma) remains true, and explanations based solely on initial-state glasma are ruled out. The detailed balance between intrinsic and fluctuation-driven geometry and the exact role of weakly versus strongly coupled prehydrodynamic evolution remains an open question for triangular flow, requiring further theoretical and experimental investigation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

MFIX DEM Enhancement for Industry-Relevant Flows (Final Report)

The overall goal of this two-phase project is to implement performance improvements of the Multiphase Flow with Interphase Exchanges (MFIX) Discrete Element Model (DEM) code that enable a transformative shift for industrial use. Prior to this effort, the largest simulations performed using MFIX are O(10 7 ) particles. This falls short of the O(10 9 ) particle simulations that must be completed on a timescale of days or weeks (vs. months or years) to enable simulations with physically-relevant domain sizes to be incorporated into industrial design cycles within five years. This was accomplished by tailoring best-in-class practices to bear on the unique challenges posed by the MFIX-DEM algorithm and code base. Scientific simulations (e.g., in cosmology, turbulent combustion) routinely use massively parallel computing to update far more particles in short wall clock times. Results from Phase 1 (1.5 years in duration) indicated significant gains in speed were possible for a wide range of benchmark cases. Moreover, a survey sent to >35 companies indicates that the timing is ideal for such an enhanced tool, with >80% of the respondents indicating that DEM is already value-added or will be within the next 5 years, and >70% of the respondents indicating that improved speed is the top computational priority. In Phase 2 (3.5 years in duration), the two major barriers that hinder industry from effectively using multiphase Computational Fluid Dynamics (CFD) to cut costs and improve performance, namely computational overhead and confidence in predictions, continued to be addressed. Regarding the former, the results from Phase 1 to guide the effort, with enhancements focused on an improved time-stepping algorithm and particle sorting. Four target problems of 1 billion particles each and increasing complexity were identified: homogeneous cooling, tumbler with continuous particle size distribution, discharge from a rectangular hopper and a cylindrical riser. Each of these were successfully simulated for relevant time scales (on order of seconds) using less than 24 hours of wall clock time. These represent the first 1-billion particle DEM simulations performed with MFIX, namely using the MFIX-Exa code. This code is currently under development at NETL in collaboration with Lawrence Berkeley National Laboratory. Regarding the second barrier on predictive uncertainty, experiments from Phase 1 (interacting nozzles - hydrodynamics only) and Phase 2 (very small-scale segregation experiments) were used to demonstrate the ability of two simplified approaches to uncertainty quantification (UQ). By limiting the number of particles, UQ based on the simplified treatment was compared to standard UQ, which was shown to have much higher computational demands. Experiments were also performed on a pilot-scale stripper unit to provide validation data for future CFD-DEM simulations and UQ.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2025

Underground Hydrogen Storage: Transforming Subsurface Science into Sustainable Energy Solutions

As the global economy moves toward net-zero carbon emissions, large-scale energy storage becomes essential to tackle the seasonal nature of renewable sources. Underground hydrogen storage (UHS) offers a feasible solution by allowing surplus renewable energy to be transformed into hydrogen and stored in deep geological formations such as aquifers, salt caverns, or depleted reservoirs, making it available for use on demand. This study thoroughly evaluates UHS concepts, procedures, and challenges. This paper analyzes the most recent breakthroughs in UHS technology and identifies special conditions needed for its successful application, including site selection guidelines, technical and geological factors, and the significance of storage characteristics. The integrity of wells and caprock, which is important for safe and efficient storage, can be affected by the operating dynamics of the hydrogen cycle, notably the fluctuations in pressure and stress within storage formations. To evaluate its potential for broader adoption, we also examined economic elements such as cost-effectiveness and the technical practicality of large-scale storage. We also reviewed current UHS efforts and identified key knowledge gaps, primarily in the areas of hydrogen–rock interactions, geochemistry, gas migration control, microbial activities, and geomechanical stability. Resolving these technological challenges, regulatory frameworks, and environmental sustainability are essential to UHS’s long-term and extensive integration into the energy industry. This article provides a roadmap for UHS research and development, emphasizing the need for further research to fully realize the technology’s promise as a pillar of the hydrogen economy.

25 ENERGY STORAGE↗
DOE OSTI2020

Star Formation in Splash Bridges

Splash bridges are created from the direct collision of two gas-rich disk galaxies. These direct collisions can eject gas masses on the order of 10 10 M ⊙ stripped from the stellar disks of each galaxy. The Taffy Galaxy system (UGC 1294/5) is a prototypical example of a splash bridge system. CO observations of the Taffy revealed that its splash bridge contains a mass of H 2 equal to the Milky Way's H 2 mass. However, the little visible star formation occurring within the bridge highlights the need for models of direct gas-rich disk collisions. The Arp 194 system displays what may be another splash bridge resulting from the collision between two disk galaxies. The region between the two stellar disks contains bright clumps of active star formation. We aim to better understand the conditions for star formation in splash bridges by employing a Jeans criterion to determine where gravitational instabilities occur in the shocked and cooling gas of gas-rich disk collisions. The splash bridge results are obtained from our previous work using a sticky particle code and post-processed. We find that the inclination between the gas disks and the collision velocity with which the gas collides strongly affects the fraction of gas that will become gravitationally unstable. Low inclinations between gas disks produce starbursts whereas high inclinations result in steady-rate star formation. The offset of the gas disks at impact will determine how many gas elements directly collide but does not strongly affect the resulting star formation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

C HIMERA : A Massively Parallel Code for Core-collapse Supernova Simulations

Herein we provide a detailed description of the C HIMERA code, a code developed to model core collapse supernovae (CCSNe) in multiple spatial dimensions. The CCSN explosion mechanism remains the subject of intense research. Progress to date demonstrates that it involves a complex interplay of neutrino production, transport, and interaction in the stellar core, three-dimensional stellar core fluid dynamics and its associated instabilities, nuclear burning, and the fundamental physics of the neutrino–stellar core weak interactions and the equations of state of all stellar core constituents—particularly, the nuclear equation of state associated with core nucleons, both free and bound in nuclei. C HIMERA , by incorporating detailed neutrino transport, realistic neutrino–matter interactions, three-dimensional hydrodynamics, realistic nuclear, leptonic, and photonic equations of state, and a nuclear reaction network, along with other refinements, can be used to study the role of neutrino radiation, hydrodynamic instabilities, and a variety of input physics in the explosion mechanism itself. It can also be used to compute observables such as neutrino signatures, gravitational radiation, and the products of nucleosynthesis associated with CCSNe. The code contains modules for neutrino transport, multidimensional compressible hydrodynamics, nuclear reactions, a variety of neutrino interactions, equations of state, and modules to provide data for post-processing observables such as the products of nucleosynthesis, and gravitational radiation. C HIMERA is an evolving code, being updated periodically with improved input physics and numerical refinements. We detail here the current version of the code, from which future improvements will stem, which can in turn be described as needed in future publications.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Effective dissipation rate in a Liouvillian-graph picture of high-temperature quantum hydrodynamics

At high temperature, generic strongly interacting spin systems are expected to display hydrodynamics: local transport of conserved quantities, governed by classical partial differential equations like the diffusion equation. I argue that the emergence of this dissipative long-wavelength dynamics from the system's unitary microscopic dynamics is controlled by the structure of the Liouvillian graph of the system's Hamiltonian, that is, the graph induced on Pauli strings by commutation with that Hamiltonian. The Liouvillian graph decomposes naturally into subgraphs of Pauli strings of constant diameter, and the coherent dynamics of these subgraphs determines the rate at which operator weight spreads to long operators. In conclusion, this argument provides a quantitative theory of the emergence of a dissipative effective dynamics from unitary microscopic dynamics; it also leads to an effective model with Hilbert space dimension linear in system size and exponential in the UV cutoff for diffusion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Investigating the Interaction Between Circulating Tumor Cells and Local Hydrodynamics via Experiment and Simulations

Introduction: The biological and mechanical properties of circulating tumor cells (CTCs) in combination with the hemodynamics affect the preference of metastatic sites in the vasculature. Despite the extensive literature on the effects of biological properties on cell adhesion, the effects of hydrodynamic forces on primary attachment remains an active area of research. Here, using simulations in conjunction with experimentation, we provide new insight into the interplay of CTCs dynamics and local hydrodynamics. Methods: A flow experiment of CTC attachment was performed within a bioprinted, double branching endothelialized vessel. Simulations of fluid flow and CTC transport in the reconstructed and idealized bifurcated vessel were respectively performed by HARVEY, our in-house massively parallel computational fluid dynamics solver. HARVEY is based on the lattice Boltzmann and finite element methods to model the fluid and cells dynamics. The immersed boundary method is employed for resolving the fluid–structure interaction. Results: CTC attachment was quantified experimentally at all regions of the complex vessel. The results demonstrate a clear preference for CTCs to attach at the branch points. To elucidate the effect of the vessel topology on the location of attachment, a fluid-only simulation was performed assessing the differences in the hydrodynamics along the vessel. CTC transport in idealized bifurcated vessels was subsequently studied to examine the effects of cell deformability on the local hydrodynamics patterns and, thus, the preference of attachment sites. Conclusions: The current work provides evidence on the correlation of the hydrodynamics forces arising from the vessel topology and CTC properties on the attachment regions.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Chemical pumps and flexible sheets spontaneously form self-regulating oscillators in solution

The synchronization of self-oscillating systems is vital to various biological functions, from the coordinated contraction of heart muscle to the self-organization of slime molds. Through modeling, we design bioinspired materials systems that spontaneously form shape-changing self-oscillators, which communicate to synchronize both their temporal and spatial behavior. Here, catalytic reactions at the bottom of a fluid-filled chamber and on mobile, flexible sheets generate the energy to “pump” the surrounding fluid, which also transports the immersed sheets. The sheets exert a force on the fluid that modifies the flow, which in turn affects the shape and movement of the flexible sheets. This feedback enables a single coated (active) and even an uncoated (passive) sheet to undergo self-oscillation, displaying different oscillatory modes with increases in the catalytic reaction rate. Two sheets (active or passive) introduce excluded volume, steric interactions. This distinctive combination of the hydrodynamic, fluid–structure, and steric interactions causes the sheets to form coupled oscillators, whose motion is synchronized in time and space. We develop a heuristic model that rationalizes this behavior. These coupled self-oscillators exhibit rich and tunable phase dynamics, which depends on the sheets’ initial placement, coverage by catalyst and relative size. Moreover, through variations in the reactant concentration, the system can switch between the different oscillatory modes. This breadth of dynamic behavior expands the functionality of the coupled oscillators, enabling soft robots to display a variety of self-sustained, self-regulating moves.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Dust distribution around low-mass planets on converging orbits

Context : Super-Earths can form at large orbital radii and migrate inward due to tidal interactions with the circumstellar disk. In this scenario, convergent migration may occur and lead to the formation of resonant pairs of planets. Aim : We explore the conditions under which convergent migration and resonance capture take place, and what dynamical consequences can be expected on the dust distribution surrounding the resonant pair. Methods : We combine hydrodynamic planet–disk interaction models with dust evolution calculations to investigate the signatures produced in the dust distribution by a pair of planets in mean-motion resonances. Results : We find that convergent migration takes place when the outer planet is the more massive. However, convergent migration also depends on the local properties of the disk, and divergent migration may result as well. For similar disk parameters, the capture in low degree resonances (e.g., 2:1 or 3:2) is preferred close to the star where the resonance strength can more easily overcome the tidal torques exerted by the gaseous disk. Farther away from the star, convergent migration may result in capture in high degree resonances. The dust distribution shows potentially observable features typically when the planets are trapped in a 2:1 resonance. In other cases, with higher degree resonances (e.g., 5:4 or 6:5) dust features may not be sufficiently pronounced to be easily observable. Conclusions : The degree of resonance established by a pair of super-Earths may be indicative of the location in the disk where capture occurred. There can be significant differences in the dust distribution around a single super-Earth and a pair of super-Earths in resonance.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Hydrodynamics of nonintegrable systems from a relaxation-time approximation

We develop a general kinetic theory framework to describe the hydrodynamics of strongly interacting, nonequilibrium quantum systems in which integrability is weakly broken, leaving a few residual conserved quantities. This framework is based on a generalized relaxation-time approximation; it gives a simple, but surprisingly accurate, prescription for computing nonequilibrium transport even in strongly interacting systems. We validate the predictions of this approximation against matrix product operator calculations on chaotic quantum spin chains, finding surprisingly good agreement. Lastly, we show that despite its simplicity, our framework can capture phenomena distinctive to strongly interacting systems, such as widely separated charge and energy diffusion constants.

1-dimensional spin chains↗
DOE OSTI2023

Sucrose transport inside the phloem: Bridging hydrodynamics and geometric characteristics

In plants, the delivery of the products of photosynthesis is achieved through a hydraulic system labeled as phloem. This semi-permeable plant tissue consists of living cells that contract and expand in response to fluid pressure and flow velocity fluctuations. The Münch pressure flow theory, which is based on osmosis providing the necessary pressure gradient to drive the mass flow of carbohydrates, is currently the most accepted model for such sucrose transport. When this hypothesis is combined with the conservation of fluid mass and momentum as well as sucrose mass, many simplifications must be invoked to mathematically close the problem and to resolve the flow. Here this study revisits such osmotically driven flows by developing a new two-dimensional numerical model in cylindrical coordinates for an elastic membrane and a concentration-dependent viscosity. It is demonstrated that the interaction between the hydrodynamic and externally supplied geometrical characteristic of the phloem has a significant effect on the front speed of sucrose transport. These results offer a novel perspective about the evolutionary adaptation of plant hydraulic traits to optimize phloem soluble compounds transport efficiency.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Incorporating the molecular-scale into a hydrodynamic description of confined aqueous systems

Hydrodynamics provides a continuum-level description of fluid motion, but its applicability at the nanoscale becomes uncertain due to the emerging importance of molecular-level effects such as spatial heterogeneity. Hydrodynamic boundary conditions that incorporate molecular details allow us to partition the system into a near-wall region and a bulk fluid region. We identify a hydrodynamic wall located inside the fluid that determines where slip begins. By extending the hydrodynamic wall with the slip length, the position of the extrapolated wall is established. This offers a unified description of both slip and stagnant flow behaviors, with wall hydrophobicity characterized by the relative location of the extrapolated wall with respect to the physical wall. Employing this concept in analyses of equilibrium molecular dynamics (MD) and non-equilibrium MD simulations of Couette and Poiseuille flows, our results demonstrate consistency between equilibrium and non-equilibrium approaches across different flow types and confinement levels. This demonstrates the robust nature of linear response theory. We then explore the effects of fluid-wall and bulk fluid interactions on the hydrodynamic properties. These findings enhance the effectiveness of molecular-based simulations for investigating complex confined systems in nanofluidics, biology, and colloidal science, offering a complementary molecular-scale perspective to traditional continuum approaches.

flow simulations↗