Potential Energy in a Three-Dimensional Vibrated Granular Medium Measured by NMR Imaging

Hydrogels hold promise in agriculture as reservoirs of water in dry soil, potentially alleviating the burden of irrigation. However, confinement in soil can markedly reduce the ability of hydrogels to absorb water and swell, limiting their widespread adoption. Unfortunately, the underlying reason remains unknown. By directly visualizing the swelling of hydrogels confined in three-dimensional granular media, we demonstrate that the extent of hydrogel swelling is determined by the competition between the force exerted by the hydrogel due to osmotic swelling and the confining force transmitted by the surrounding grains. Furthermore, the medium can itself be restructured by hydrogel swelling, as set by the balance between the osmotic swelling force, the confining force, and intergrain friction. Together, our results provide quantitative principles to predict how hydrogels behave in confinement, potentially improving their use in agriculture as well as informing other applications such as oil recovery, construction, mechanobiology, and filtration.

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On the 3D → 2D Isomerization of Hexaborane(12)

Chemistry ◽

10.3390/chemistry3010003 ◽

2021 ◽

Vol 3 (1) ◽

pp. 28-38

Author(s):

Josep M. Oliva-Enrich ◽

Ibon Alkorta ◽

José Elguero ◽

Maxime Ferrer ◽

José I. Burgos

Keyword(s):

Potential Energy ◽

Potential Energy Surface ◽

Energy Surface ◽

Transition States ◽

Three Dimensional ◽

Reaction Coordinate ◽

Intrinsic Reaction Coordinate ◽

Limiting Factor ◽

Two Dimensional ◽

Axis Of Rotation

By following the intrinsic reaction coordinate connecting transition states with energy minima on the potential energy surface, we have determined the reaction steps connecting three-dimensional hexaborane(12) with unknown planar two-dimensional hexaborane(12). In an effort to predict the potential synthesis of finite planar borane molecules, we found that the reaction limiting factor stems from the breaking of the central boron-boron bond perpendicular to the C2 axis of rotation in three-dimensional hexaborane(12).

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An energy landscape approach to locomotor transitions in complex 3D terrain

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1918297117 ◽

2020 ◽

Vol 117 (26) ◽

pp. 14987-14995 ◽

Cited By ~ 2

Author(s):

Ratan Othayoth ◽

George Thoms ◽

Chen Li

Keyword(s):

Potential Energy ◽

Complex Terrain ◽

Statistical Physics ◽

Energy Landscape ◽

Three Dimensional ◽

Single Mode ◽

Physical Interaction ◽

Landscape Approach ◽

3D Terrain ◽

Potential Energy Landscape

Effective locomotion in nature happens by transitioning across multiple modes (e.g., walk, run, climb). Despite this, far more mechanistic understanding of terrestrial locomotion has been on how to generate and stabilize around near–steady-state movement in a single mode. We still know little about how locomotor transitions emerge from physical interaction with complex terrain. Consequently, robots largely rely on geometric maps to avoid obstacles, not traverse them. Recent studies revealed that locomotor transitions in complex three-dimensional (3D) terrain occur probabilistically via multiple pathways. Here, we show that an energy landscape approach elucidates the underlying physical principles. We discovered that locomotor transitions of animals and robots self-propelled through complex 3D terrain correspond to barrier-crossing transitions on a potential energy landscape. Locomotor modes are attracted to landscape basins separated by potential energy barriers. Kinetic energy fluctuation from oscillatory self-propulsion helps the system stochastically escape from one basin and reach another to make transitions. Escape is more likely toward lower barrier direction. These principles are surprisingly similar to those of near-equilibrium, microscopic systems. Analogous to free-energy landscapes for multipathway protein folding transitions, our energy landscape approach from first principles is the beginning of a statistical physics theory of multipathway locomotor transitions in complex terrain. This will not only help understand how the organization of animal behavior emerges from multiscale interactions between their neural and mechanical systems and the physical environment, but also guide robot design, control, and planning over the large, intractable locomotor-terrain parameter space to generate robust locomotor transitions through the real world.

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Three dimensional models of the potential energy of triatomic systems

Transactions of the Faraday Society ◽

10.1039/tf9343000060 ◽

1934 ◽

Vol 30 ◽

pp. 60 ◽

Cited By ~ 6

Author(s):

C. F. Goodeve

Keyword(s):

Potential Energy ◽

Three Dimensional ◽

Dimensional Models ◽

Three Dimensional Models

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THEORETICAL TRANSITION PROBABILITIES FOR THE $\tilde{A}^{2}A_{1} -\tilde{X}^{2}B_{1}$ SYSTEM OF H2O+ AND D2O+ AND RELATED FRANCK–CONDON FACTORS BASED ON GLOBAL POTENTIAL ENERGY SURFACES

Journal of Theoretical and Computational Chemistry ◽

10.1142/s0219633605001428 ◽

2005 ◽

Vol 04 (01) ◽

pp. 225-245 ◽

Cited By ~ 1

Author(s):

IKUO TOKUE ◽

KATSUYOSHI YAMASAKI ◽

SATOSHI MINAMINO ◽

SHINKOH NANBU

Keyword(s):

Potential Energy ◽

Photoelectron Spectroscopy ◽

Potential Energy Surfaces ◽

Least Squares Method ◽

Transition Probabilities ◽

Three Dimensional ◽

Equilibrium Geometry ◽

Condon Factors ◽

Energy Surfaces ◽

Franck Condon

To elucidate the ionization dynamics, in particular the vibrational distribution, of H 2 O +(Ã) produced by photoionization and the Penning ionization of H 2 O and D 2 O with He *(2 3S) atoms, Franck–Condon factors (FCFs) were given for the [Formula: see text] ionization, and the transition probabilities were presented for the [Formula: see text] emission. The FCFs were obtained by quantum vibrational calculations using the three-dimensional potential energy surfaces (PESs) of [Formula: see text] and [Formula: see text] electronic states. The global PESs were determined by the multi-reference configuration interaction calculations with the Davidson correction and the interpolant moving least squares method combined with the Shepard interpolation. The obtained FCFs exhibit that the [Formula: see text] state primarily populates the vibrational ground state, as its equilibrium geometry is almost equal to that of [Formula: see text], while the bending mode (ν2) is strongly enhanced for the H 2 O +(Ã) state; the maximums in the population of H 2 O + and D 2 O + are approximately v2 = 11–12 and 15–17, respectively. These results are consistent with the distributions observed by photoelectron spectroscopy. Transition probabilities for the [Formula: see text] system of H 2 O + and D 2 O + show that the bending progressions consist primarily of the [Formula: see text] emission, with combination bands from the (1, v′2 = 4–8, 0) level being next most important.

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