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At least 73 records · Page 4

Evaporation in equilibrium, in vacuum, and in hydrogen gas

Evaporation experiments were conducted for SiO2 in three different conditions: in equilibrium, in vacuum, and in hydrogen gas. Evaporation rate in vacuum is about two orders of magnitude smaller than that in equilibrium, which is consistent with previous works. The rate in hydrogen gas changes depending on hydrogen pressure. The rate at 10 exp -7 bar of hydrogen pressure is as small as that of free evaporation, but at 10 exp -5 bar of hydrogen pressure it is larger than that in equilibrium. In equilibrium and in vacuum, the evaporation rate is limited by decomposition of SiO2 on the crystal surface, but it is limited by a diffusion process for evaporation in hydrogen gas. Therefore, evaporation rate of minerals in the solar nebula can be shown neither by that in equilibrium nor by that in vacuum. The maximum temperature of the solar nebula at the midplane at 2-3 AU where chondrites are believed to have originated is calculated to be as low as 150 K, 1500 K, or in between them. The temperature is, in any case, not high enough for total evaporation of the interstellar materials. Therefore, evaporation of interstellar materials is one of the most important processes for the origin and fractionation of solid materials. The fundamental process of evaporation of minerals has been intensively studied for these several years. Those experiments were carried out either in equilibrium or in vacuum; however, evaporation in the solar nebula is in hydrogen (and much smaller amount of helium) gas. In order to investigate evaporation rate and compositional (including isotopic) fractionation during evaporation, vaporization experiments for various minerals in various conditions are conducted. At first, SiO2 was adopted for a starting material, because thermochemical data and its nature of congruent vaporization are well known. Experiments were carried out in a vacuum furnace system.

Nagahara, Hiroko↗

A Heuristic Approach to Examining Volatile Equilibrium at Titan's Surface

R. D. Lorenz, J. I. Lunine, and C. P. McKay have shown in a manuscript accepted for publication that, for a given ethane abundance and surface temperature, the nitrogen and methane abundances in Titan's atmosphere can be calculated, yielding a surface pressure that can be compared with the observed value. This is potentially a very valuable tool for examining the evolution of Titan's climatology. Its validity does depend on two important assumptions, however: 1) that the atmosphere of Titan is in global radiative equilibrium, and 2) that volatiles present are in vapor equilibrium with the surface. The former assumption has been shown to be likely, but the latter has not. Water vapor in the Earth's atmosphere, in fact, is generally not very close to equilibrium in a global sense. In the present work a heuristic approach is used to examine the likelihood that methane vapor is in equilibrium with Titan's surface. Plausible climate scenerios are examined that are consistent with methane vapor abundances derived from Voyager IRIS data. Simple precipitation and surface diffusion models are incorporated into the analysis. It is tentatively inferred that methane may be in surface equilibrium near the poles, but that equilibrium at low latitudes is more difficult to establish.

Samuelson, Robert E.↗

Methane on Mars: Thermodynamic Equilibrium and Photochemical Calculations

The detection of methane (CH4) in the atmosphere of Mars by Mars Express and Earth-based spectroscopy is very surprising, very puzzling, and very intriguing. On Earth, about 90% of atmospheric ozone is produced by living systems. A major question concerning methane on Mars is its origin - biological or geological. Thermodynamic equilibrium calculations indicated that methane cannot be produced by atmospheric chemical/photochemical reactions. Thermodynamic equilibrium calculations for three gases, methane, ammonia (NH3) and nitrous oxide (N2O) in the Earth s atmosphere are summarized in Table 1. The calculations indicate that these three gases should not exist in the Earth s atmosphere. Yet they do, with methane, ammonia and nitrous oxide enhanced 139, 50 and 12 orders of magnitude above their calculated thermodynamic equilibrium concentration due to the impact of life! Thermodynamic equilibrium calculations have been performed for the same three gases in the atmosphere of Mars based on the assumed composition of the Mars atmosphere shown in Table 2. The calculated thermodynamic equilibrium concentrations of the same three gases in the atmosphere of Mars is shown in Table 3. Clearly, based on thermodynamic equilibrium calculations, methane should not be present in the atmosphere of Mars, but it is in concentrations approaching 30 ppbv from three distinct regions on Mars.

Levine, J. S.↗

Investigation of Non-Equilibrium Radiation for Earth Entry

This paper presents measurements and simulations of non-equilibrium shock layer radiation relevant to high-speed Earth entry data obtained in the NASA Ames Research Center's Electric Arc Shock Tube (EAST) facility. The experiments were aimed at measuring the spatially and spectrally resolved radiance at relevant entry conditions for both an approximate Earth atmosphere (79 N2 : 21 O2) as well as a more accurate composition featuring the trace species Ar and CO2 (78.08 N2 : 20.95 O2 : 0.04 CO2 : 0.93 Ar). The experiments were configured to target a wide range of conditions, of which shots from 8 to 11.5 km/s at 0.2 Torr (26.7 Pa) are examined in this paper. The non-equilibrium component was chosen to be the focus of this study as it can account for a significant percentage of the emitted radiation for Earth entry, and more importantly, non-equilibrium has traditionally been assigned a large uncertainty for vehicle design. The main goals of this study are to present the shock tube data in the form of a non-equilibrium metric, evaluate the level of agreement between the experiment and simulations, identify key discrepancies and to promote discussion about various aspects of modeling non-equilibrium radiating flows. Radiance profiles integrated over discreet wavelength regions, ranging from the VUV through to the NIR, were compared in order to maximize both the spectral coverage and the number of experiments that could be used in the analysis. A previously defined non-equilibrium metric has been used to allow comparisons with several shots and reveal trends in the data. Overall, LAURAHARA is shown to under-predict EAST by as much as 50 and over-predict by as much as 20 depending on the shock speed. DPLRNEQAIR is shown to under-predict EAST by as much as 40 and over-predict by as much as 12 depending on the shock speed. In terms of an upper bound estimate for the absolute error in wall-directed heat flux, at the lower speeds investigated in this paper, 8 to 9 km/s, even though there are some large relative differences, the absolute error in radiance will be less then 1 Wcm2. At the highest shock speed of 11 km/s, the error will be less than 20 W/ sq cm.

Radiation↗

Accelerating Thermochemical Equilibrium Calculations for Nuclear Reactor Applications

Thermochemical properties play a key role in modeling and simulation of several key phenomena in nuclear reactors. There has been an increasing interest in incorporating CALPHAD-based formulations in multiphysics simulations including for Molten Salt Reactors where knowledge of phase evolution of the salt and the chemical potentials of various elements are of utmost importance in source term analyses and redox control. However, the size of such simulations is often limited by the high computational cost of full thermodynamic equilibrium calculations. This work discusses the current efforts aimed at accelerating thermochemical equilibrium calculations for multiphysics simulations performed using the open-source finite element / finite volume code Multiphysics Object Oriented Simulation Environment (MOOSE) [1]. While several methods have been proposed for accelerating phase equilibrium calculations [2], most focus on relatively small systems and often rely on a- priori knowledge of the state-space of the system. Nuclear materials, however, are often multi-component systems owing to the evolution of composition under irradiation and an approach based on a-priori mapping of phase diagram is often not enough. This work is aimed at demonstrating an on-the-fly surrogate modeling framework that uses active learning to reduce the number of full equilibrium calculations that must be performed. By combining with efficient coupling approaches, the surrogate framework helps in reducing the computational cost of thermodynamic equilibrium informed multiphysics simulations of nuclear materials. The performance is benchmarked against full coupling with the thermochemistry library Thermochimica [3]. This work uses a machine learning based approach for constructing surrogate models to predict the stable phases in a multicomponent system. The surrogates were constructed using neural networks and Gaussian process classification. In this work, we compare the relative performance of the two methods. We also demonstrate the use of caching previous calculations by interpolating the values from nearest neighbors. References [1] Lindsay, A.D., et al. "2.0 – MOOSE: Enabling massively parallel multiphysics simulation", SoftwareX, 20 (2022): 101202. [2] Roos, W.A. and Zietsman J.H. "Accelerating complex chemical equilibrium calculations – A Review", Calphad, 77 (2022): 102380. [3] Piro, M.H.A., et al. "The thermochemistry library Thermochimica", Computational Materials Science, 67 (2013): 266-272.

36 MATERIALS SCIENCE↗

Optimal Equilibrium Selection of Price-Maker Agents in Performance-Based Regulation Market

This paper analyzes the oligopolistic equilibrium of multiple price-maker agents in performance-based regulation (PBR) markets. In these markets, there are price-maker agents representing some frequency regulation (FR) providers and a number of independent price-taker FR providers. An equilibrium problem with equilibrium constraints (EPEC) model is employed in this paper to study the equilibria of a PBR market in the presence of price-maker agents and pricetaker FR providers. Due to the incorporation of the FR providers' dynamics, the proposed model is reformulated as a mixed-integer linear programming (MILP) problem over innovative mathematical techniques. An optimal equilibrium point is also selected for the market, where none of the agents is unique deviator and the dynamic performance of power system is improved simultaneously. The effectiveness of proposed optimal equilibrium point is evaluated in the numerical results section by comparing the outputs with conventional optimal dispatches of the FR providers.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Thermodynamic Equilibrium in the Origin of Organic Matter

Theoretical and experimental support is presented for the hypothesis that organic compounds occurring in carbonaceous chondrites may have formed under equilibrium or near equilibrium conditions. The equilibrium distributions of organic compounds at temperature between 300 and 1000 K and pressures of 10(exp 16) to 50 atmospheres for the C-H-O system have been computed. At high temperatures and low pressures aromatic compounds may form even in the presence of excess hydrogen. Equilibrium concentrations of numerous compounds possible at 1000 K when N, S, and C1 are added to the system have also been determined. A limited equilibrium method is employed in which those few compounds which form with most difficulty are excluded from the computations. This approach is shown to be useful in the interpretation of certain experimental data. In preliminary experiments it has been found that gases, converted to the plasma state by high energy radio frequency discharge, yield product mixtures which are in qualitative agreement with those predicted.

CHEMICAL EQUILIBRIUM↗

Effects of Injected Current Streams on MHD Equilibrium Reconstruction of Local Helicity Injection Plasmas in a Spherical Tokamak

Open field line currents are intrinsic to DC helicity injection plasma startup and pose a challenge for inferring the plasma equilibrium with standard reconstruction analysis. Local helicity injection (LHI) is a type of DC helicity injection which uses small, modular current sources to drive force-free current along helical field lines to produce tokamak plasmas. MHD modeling and magnetic measurements during LHI indicate the injected current streams remain coherent as helical structures on the outboard edge of a core toroidal plasma that is tokamak-like in a toroidally averaged sense. To extract core plasma equilibrium properties, external magnetic diagnostics corrected for contributions from the injected current streams are fitted by a standard Grad-Shafranov equilibrium code. An iterative approach for estimating and subtracting the stream contributions from the diagnostic signals is described and applied to a model equilibrium database to reduce systematic errors introduced by the streams. Convergence is usually attained with 2 to 4 iterations, with derived equilibrium parameters matching the prescribed axisymmetric core values to within estimated experimental uncertainties. Accurate recovery of core parameters occurs when the ratio of the net toroidal windup current from the streams to the core plasma current is less than 0.2, which is typically satisfied in most experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Self-consistent equilibrium and transport simulations for NSTX-U plasmas enhanced via machine learning surrogate models

The Control-Oriented Transport SIMulator (COTSIM) is an advanced equilibrium and transport code designed for simulating tokamak discharges at computational speeds suitable for control applications. COTSIM’s modular framework enables users to select models that balance accuracy with speed according to specific needs, allowing the code to operate from fast to faster-than-real-time performance levels. This work presents recent enhancements to COTSIM’s predictive accuracy for NSTX-U scenarios, achieved by integrating neural-network-based surrogate models and self-consistent equilibrium calculations. To improve source deposition predictions, a surrogate model for NUBEAM has been incorporated. Additionally, a surrogate model for the Multi-Mode Module (MMM) now supports predictions of anomalous thermal, momentum, and particle diffusivities—key factors for modeling the evolution of temperature and rotation. Each surrogate model was specifically trained for the NSTX-U operational regime to enhance COTSIM’s accuracy while maintaining computational efficiency. Moreover, COTSIM now couples fixed-boundary equilibrium solvers with its transport solvers, enabling self-consistent predictions of plasma profiles and equilibrium evolution over the discharge. Simulation results demonstrate strong agreement between COTSIM and TRANSP predictions for NSTX-U discharges. These substantial advancements expand COTSIM’s utility in model-based control applications for NSTX-U. Potential applications include simultaneous optimization of equilibrium and transport scenarios, integration into digital twins, real-time profile estimation (e.g., temperature and rotation) from limited or noisy measurements, and advanced feedback-based scenario control.

Equilibrium and transport modeling↗

Plasma-Catalytic Ammonia Synthesis beyond the Equilibrium Limit

In this work, we explore the consequences of nonthermal plasma-activation on product yields in catalytic ammonia synthesis, a reaction that is equilibrium-limited at elevated temperatures. We employ a minimal microkinetic model that incorporates the influence of plasma-activation on N 2 dissociation rates to predict NH 3 yields into and across the equilibrium-limited regime. NH 3 yields are predicted to exceed bulk thermodynamic equilibrium limits on materials that are thermal-rate-limited by N 2 dissociation. In all cases, yields revert to bulk equilibrium at temperatures at which thermal reaction rates exceed plasma-activated ones. Beyond-equilibrium NH 3 yields are observed in a packed bed dielectric barrier discharge reactor and exhibit sensitivity to catalytic material choice in a way consistent with model predictions. The approach and results highlight the opportunity to exploit synergies between nonthermal plasmas and catalysts to affect transformations at conditions inaccessible through thermal routes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Projected Multi-Agent Consensus Equilibrium (PMACE) With Application to Ptychography

Multi-Agent Consensus Equilibrium (MACE) formulates an inverse imaging problem as a balance among multiple update agents such as data-fitting terms and denoisers. However, each such agent operates on a separate copy of the full image, leading to redundant memory use and slow convergence when each agent affects only a small subset of the full image. In this article, we extend MACE to Projected Multi-Agent Consensus Equilibrium (PMACE), in which each agent updates only a projected component of the full image, thus greatly reducing memory use for some applications. We describe PMACE in terms of an equilibrium problem and an equivalent fixed-point problem and show that in most cases the PMACE equilibrium is not the solution of an optimization problem. To demonstrate the value of PMACE, we apply it to the problem of ptychography, in which a sample is reconstructed from the diffraction patterns resulting from coherent X-ray illumination at multiple overlapping spots. In our PMACE formulation, each spot corresponds to a separate data-fitting agent, with the final solution found as an equilibrium among all the agents. In conclusion, our results demonstrate that the PMACE reconstruction algorithm generates more accurate reconstructions at a lower computational cost than existing ptychography algorithms when the spots are sparsely sampled.

97 MATHEMATICS AND COMPUTING↗

Construction of an Exact Pressure-Equilibrium Scheme for the Five-Equation Two-Phase Flow Model With Thermal Relaxation

Numerical simulation of compressible multiphase flows based on the four-equation (homogeneous relaxation) model is known to suffer from two fundamental difficulties with (a) wave propagation and (b) pressure equilibrium preservation. First, the mixture sound speed exhibits non-monotonic dependency with respect to the volume fraction, which leads to robustness issues in the resolution of shocks and acoustic wave propagation across two-phase regions. This difficulty can be mitigated by solving Allaire’s five-equation model augmented with infinitely fast phasic temperature equilibrium, from which solutions of the four-equation model can be recovered. However, when temperature is non-uniform, this augmented five-equation formulation still fails to preserve pressure equilibrium across material interfaces. In this work, we propose a fully conservative numerical scheme that exactly preserves pressure equilibrium at the discrete level for the augmented five-equation model, for arbitrary initial distributions of temperature and volume fraction. Combined with the monotonic sound speed property of the five-equation formulation, the proposed pressure-equilibrium preserving scheme significantly improves robustness in the presence of strong multiphase interactions, including shock–interface interactions and advection of material interfaces.

ESG↗

Impact of equilibrium radial electric field on energy loss process after pedestal collapse

An impact of the equilibrium radial electric field on energy loss processes after pedestal collapse is numerically investigated using the BOUT++ framework. Using linear stability analysis, the resistive ballooning mode is shown to be stabilized by the radial shear of the equilibrium radial electric field. On the other hand, the energy loss level after the pedestal collapse increases if the equilibrium radial electric field is taken into account. The spatio-temporal and phase diagram analyses show that the equilibrium radial electric field partially cancels the fluctuation-driven toroidally axisymmetric radial electric field and weakens the E × B shearing rate after pedestal collapse, weakening the turbulence suppression by vortex shearing. Finally, the equilibrium radial electric field therefore increases turbulence intensity in nonlinear cyclic oscillations among pressure gradient, E × B shearing rate, and turbulence intensity, which gives rise to subsequent bursts of turbulent transport and increases the energy loss level.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Equilibrium Fe isotope fractionation between olivine, pyroxene, spinel and MORB glass: Implications for mantle partial melting to generate MORBs

Primitive mid-ocean ridge basalts (MORBs) exhibit Fe isotopic compositions heavier than the upper mantle by +0.074 ± 0.028 ‰ for δ 56 Fe. The processes responsible for this isotopic difference remain unclear. Modeling of Fe isotope fractionation during mantle partial melting requires reliable equilibrium Fe isotope fractionation factors between minerals and melts, for which consistent data are still lacking. Here, in this study, we used Nuclear Resonant Inelastic X-ray Scattering (NRIXS) technique to measure Fe force constants for a MORB glass (ALV 519-4-1) and natural mantle minerals (olivine, orthopyroxene, clinopyroxene, and spinel) to determine the equilibrium Fe isotope fractionation factors between them. The force constants determined in this study, in increasing order, are 167 ± 26 N/m for spinel, 175 ± 17 N/m for olivine, 176 ± 20 N/m for MORB glass, 205 ± 26 N/m for clinopyroxene, and 219 ± 36 N/m for orthopyroxene. We evaluated the previously proposed mechanisms for the heavy Fe isotopic composition of MORBs, including (i) mantle partial melting, (ii) mantle lithological heterogeneity, with pyroxenite in the source, (iii) mantle metasomatism by low-degree melts, and (iv) fractional crystallization of olivine from melts. For (i), we used the pMELTS program to simulate adiabatic decompression melting of mantle peridotites, and calculated Fe isotope fractionation based on Fe 3+ –Fe 2+ equilibrium-controlled fractionation, where Fe 3+ forms stronger bonds and is more incompatible than Fe 2+ . At 10 wt% peridotite melting, corresponding to MORB generation, only +0.03 ‰ Fe isotope fractionation between the melt and the original bulk composition (Δ 56 Fe = δ 56 Fe melt - δ 56 Fe 0 ) was produced, insufficient to account for the observed MORB-upper mantle difference. For (ii), melting of pyroxenites yields smaller Fe isotope fractionation than melting of peridotites, making it unlikely the cause for the MORB-upper mantle isotopic difference. For (iii), both the Fe 3+ /ΣFe ratio and the δ 56 Fe of melts increase with the degree of partial melting, indicating that low-degree melts are not isotopically heavy enough to significantly alter the isotopic composition of lithospheric mantle through metasomatism. For (iv), equilibrium isotope fractionation between olivine and melt is near zero. These results suggest that equilibrium Fe isotope fractionation alone cannot explain the MORB isotopic signature, highlighting the potential role of kinetic isotope fractionation. Using a diffusion model, we calculated kinetic Fe and Mg isotope fractionations associated with (iv) olivine crystallization from a melt, and found that the predicted Fe and Mg isotope fractionations were inconsistent with observations in MORBs. Qualitatively, two processes could have induced kinetic Fe isotope fractionation during MORB generation: (a) Fe-Mg interdiffusion between melt and solid during melt migration and (b) reactive melt-rock interactions during melt focusing. However, a quantitative understanding of their role in modifying the melt isotopic composition remains limited and requires further investigation.

Fe isotopes↗

Adsorption Equilibrium, Kinetics, and Column Breakthrough Data of Acetic Acid, Butyric Acid, and Lactic Acid on IRN-78 Ion-exchange Resin at Initial pH ~3 – 7 and Temperature 25 – 55 °C

This work presents systematic aqueous-phase adsorption equilibrium, kinetics, and column breakthrough measurements with three key biointermediates that are common compounds in many bioprocesses. Adsorption equilibrium experiments were carried out with acetic acid, butyric acid, and lactic acid on a commercial ion-exchange resin, Amberlite IRN-78, at wide ranges of acid concentration (8-500 mmol/L), initial pH (similar to 3-7), and temperature (25-55 degrees C), simulating the effluent characteristics from different fermenter operations. The kinetics and column breakthrough experiments were conducted at an initial pH of 6 and a concentration of 200 mmol/L. The equilibrium study shows a higher loading at the initial pH < pK(a) and a lower loading at the initial pH > pK(a). Overall removal varies between 16 and 99% depending on the initial pH, temperature, and organic acid concentration and type. The study further indicates monolayer adsorption at the equilibrium pH > 10 and multilayer adsorption at the equilibrium pH < 6. The thermodynamic modeling of adsorption isotherm data was carried out using Langmuir and Freundlich isotherms. IRN-78 presents fast adsorption kinetics as the maximum loading was attained in <= 10 min and nearly the same breakthrough time for all three organic acids involved in this study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Two-dimensional non-equilibrium melting of charged colloids

Thermodynamic two-dimensional melting has been extensively studied in experiments and simulations, and is well predicted by theory. For systems in equilibrium, this transition is well described by the Kosterlitz–Thouless–Halperin–Nelson–Young theory, where melting is directly linked to the unbinding of topological defects. For driven, non-equilibrium melting and other non-equilibrium phase transitions, the picture is less clear. Here, in this work, we study the two-dimensional melting of a crystal of charged colloids. By randomly replacing some charged colloids with magnetic colloids, we can melt our system by rotating a fraction of the particles to create non-equilibrium, hydrodynamic random flows and local stresses. We can also melt it thermally by changing the particle number density. We find that an effective temperature approach cannot explain the results of our driven system. Rather, in both experiments and simulations, we observe that plotting the hexatic order parameter and the hexatic correlation’s exponent versus the density of disclinations and dislocations, respectively, yields universal curves. This implies that in our systems, two-dimensional melting depends directly on the density of topological defects and is independent of whether thermal or non-equilibrium forces generate them.

critical phenomena↗

Experimental evidence of non-equilibrium phase separation in supercritical fluids

Supercritical fluids (SCFs), widely utilized in many industries, have long been regarded as homogeneous single-phase media. Recent simulation studies identified different phases (more gas-like or liquid-like) in SCFs at equilibrium, expanding the previous notion but still not addressing non-equilibrium properties of SCFs. Here we reveal the existence of long-lived liquid-like clusters in non-equilibrium SCFs by time-resolved small-angle neutron scattering measurements. Since SCFs in industrial applications frequently operate under dynamic, non-equilibrium conditions rather than strict thermodynamic equilibrium, our findings offer crucial information for improving the use of SCFs in industrial settings, like semiconductor cleaning and plant thermal-hydraulic engineering.

Lee, Juho [Pohang Univ. of Science and Technology ↗

Out-of-equilibrium interactions and collective locomotion of colloidal spheres with squirming of nematoelastic multipoles

Many living and artificial systems show similar emergent behavior and collective motions on different scales, starting from swarms of bacteria to synthetic active particles, herds of mammals, and crowds of people. What all these systems often have in common is that new collective properties like flocking emerge from interactions between individual self-propelled or driven units. Such systems are naturally out-of-equilibrium and propel at the expense of consumed energy. Mimicking nature by making self-propelled or externally driven particles and studying their individual and collective motility may allow for deeper understanding of physical underpinnings behind collective motion of large groups of interacting objects or beings. Here, in this work, using a soft matter system of colloids immersed into a liquid crystal, we show that resulting so-called nematoelastic multipoles can be set into a bidirectional locomotion by external oscillating electric fields. Out-of-equilibrium elastic interactions between such colloidal objects lead to collective flock-like behaviors emerging from time-varying elasticity-mediated interactions between externally driven propelling particles. Repulsive elastic interactions in the equilibrium state can be turned into attractive interactions in the out-of-equilibrium state under applied external electric fields. We probe this behavior at different number densities of colloidal particles and show that particles in dense dispersions collectively select the same direction of a coherent motion due to elastic interactions between near neighbors. In our experimentally implemented design, their motion is highly ordered and without clustering or jamming often present in other colloidal transport systems, which is promising for technological and fundamental-science applications, like nano-cargo transport, out-of-equilibrium assembly, and microrobotics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗