Potential Energy Gradient Research Articles

Grain size effects on indentation-induced defect evolution and plastic deformation mechanism of ploycrystalline materials

Using molecular dynamics (MD) simulations, the defect evolution and plastic deformation mechanism of single-crystalline and polycrystalline copper under spherical nanoindentation are investigated and compared with previous nanoindentation simulations and experiments. To reveal the grain size effects on the indentation-induced internal stress and deformation behavior, the polycrystalline copper with different grain size are adopted in nanoindentation simulations, whose grain size are follow the inverse Hall-Petch relation. To study the grain boundary network effect, the grain boundary interface is further divided into three microstructural components with different dimensions. The results show that the indentation force of single-crystalline copper is larger than that of polycrystalline copper, and that of polycrystalline copper continuously decreases with the decrease of grain size due to softening phenomenon. The defect nucleation and propagation region in both single-crystalline and polycrystalline copper appear below the tool tip, due to the high internal stress and atomic potential energy induced by nanoindentation. The horizontal propagation of defects is faster and larger than the vertical propagation of that, and such defects are limited in the grains around the tool tip due to grain boundary network. An obvious stresses and potential energy gradient exist under tool tip in single-crystalline copper, and such gradients are possibly distributed along multiply direction in the polycrystalline copper. The internal stresses and atomic potential energy in the region of VP are highest, followed by that in TJ, GB and VP, resulting in the defect nucleation and propagation are more possible occur in VP than other microstructural components.

Available Potential Energy in Density Coordinates

AbstractThe vertically integrated potential energy of an incompressible stratified fluid formulated in density coordinates can be simply written as a weighted vertical sum of the squares of the vertical displacements of density surfaces, a general expression valid for arbitrary displacements. The sum of this form of potential energy and kinetic energy is then a conserved quantity for the multilayer shallow water model. The formulation in density coordinates is a natural one to find the Lorenz reference state of available potential energy (APE). We describe the method to compute the APE of an ocean state and provide two applications. The first is the classical double-gyre, wind-driven circulation simulated by a shallow water model at high resolution. We show that the eddy kinetic and eddy potential energies are localized in regions of large gradients of mean APE. These large gradients surround an APE minimum found between the two gyres. The second is the time-mean World Ocean Circulation reconstructed from hydrography (World Ocean Atlas) and reference velocities at 1000 db from the Argo float program to obtain an absolute circulation. The total available potential energy exceeds the total mean kinetic energy of the World Ocean by three orders of magnitude, pointing out the very small Burger number of the circulation. The Gulf Stream, the Kuroshio, the Agulhas retroflection, and the confluence regions are four examples that confirm the shallow water model results that large gradients of mean available potential energy can be used as predictors for the presence of high eddy kinetic energy (obtained here from satellite altimetry).

Isostasy and seismisity

A model of the Earth crust structure formed by gravitation of the planet has been considered. An important role in this structure is given to isostasy processes. Analysis of results of seismic exploration by reflected waves method allows to suggest that reflecting areas in the interior correspond to fissures and chambers in the material of rocks, which form the structures of the Earth crust. A suggestion has been made that weight loadings created by the planet gravitation are carried by the framing — bearing areas where geological bodies of different composition and form are contacting. The weight of equal volumes of crust materials varies due to differences in the density of matter, presence of fissures and chambers. Mountain structures are formed exactly due to such variations which determine the store of potential energy of masses of rocks. The presence of uplands near the valleys determines the gradients of potential energy and additional weight loadings in zones bordering mountain structures. As a result of lasting action of weight loadings bearing areas may be destroyed that leads to displacement of rock blocks; in this case potential energy is partly transformed into packets of mechanical impulse — seismic radiation characterizing the process of an earthquake. As a model of seismic processes a shock with displacement of large blocks of rocks is considered. An earthquake is represented as a result of partial destruction of mountain structures. Results of model calculations of lower edges of mountain structures for two areas of the territory of Magadan region have been presented in the paper.

Finite-Time Regulation of Robots: a Strict Lyapunov Function Approach

Motivated by the energy shaping framework and the properties of homogeneous systems, we introduce a methodology to derive strict Lyapunov functions (SLFs) for a class of global finite-time (FT) controllers for robot manipulators. These controllers are described by the gradient of the controller potential energy plus the gradient of (nonlinear) energy dissipation-like functions. Sufficient conditions on the controller potential energy and energy dissipation-like functions are provided in order to obtain, in a straightforward manner, a SLF that ensures global asymptotic stability at the desired equilibrium. Finite-time stability is concluded by constructing a local SLF. As an important practical outcome, we illustrate the proposed methodology by constructing SLFs for some particular FT controllers.

Receiver Function Imaging of Mantle Transition Zone Discontinuities Beneath the Tanzania Craton and Adjacent Segments of the East African Rift System

AbstractThe mantle transition zone (MTZ) discontinuities beneath the Tanzania Craton and the Eastern and Western Branches of the East African Rift System are imaged by stacking over 7,100 receiver functions. The mean thickness of the MTZ beneath the Western Branch and Tanzania Craton is about 252 km, which is comparable to the global average and is inconsistent with the existence of present‐day thermal upwelling originating from the lower mantle. In contrast, beneath the Eastern Branch, an up to 30 km thinning of the MTZ is observed and is attributable to upwelling of higher temperature materials from either the upper MTZ or the lower mantle. The observations are in agreement with the hypothesis that rifting in Africa is primarily driven by gradients of gravitational potential energy and lateral variations of basal traction force along zones of significant changes of lithospheric thickness such as the edges of the Tanzania Craton.

The role of asthenospheric flow during rift propagation and breakup

Continental rifting precedes the breakup of continents, leading to the formation of passive margins and oceanic lithosphere. Although rifting dynamics is classically described in terms of either active rifting caused by active mantle upwelling, or passive rifting caused by far-field extensional stresses, it was proposed that a transition from passive to active rifting can result from changes in buoyancy forces due to localized thinning of the lithosphere. Three-dimensional numerical experiments of rifting near an Euler pole allow the quantification of these buoyancy forces and show that gravitational stresses are strong enough not only to sustain rifting and drive axis-parallel motion in the asthenosphere dome, but also to promote along-axis asthenospheric flow and to drive the propagation of the rift tip toward its rotation pole. We show that gradients of gravitational potential energy due to the presence of the dome of asthenosphere induce time-dependent phases of compressional and transcurrent stress regimes, despite an overall divergent plate setting. Our experiments predict overdeepened bathymetry at the tip of the propagating rift, as well as the variability of focal mechanisms of shallow seismic events similar to those observed in such a setting. We also explain the episodes of basin inversion documented in many rifted continental margins.

Shallow‐water equations on a spherical multiple‐cell grid

The shallow‐water equations (SWEs) are discretized on a spherical multiple‐cell (SMC) grid and validated with classical tests, including steady zonal flow over flat or hill floor, the Rossby–Haurwitz wave and the unstable zonal jet. The numerical schemes follow the conventional latitude–longitude (lat‐lon) grid ones at low latitudes but switch to a fixed‐reference direction system to define vector variables at high latitudes for reduction of polar curvature errors. Semi‐implicit schemes are used for both the Coriolis terms and the potential energy gradients. A C‐grid mass‐conserving advection–diffusion scheme is used for the thickness variable and mixed A‐ and D‐grid schemes are applied on the momentum equation. Tests demonstrate that the two reference directions work fine on the SMC grid and the SWEs model is stable as long as numerical noises are suppressed with enough smoothing. This implies that other reduced grids could be used for dynamical models if the vector polar problem is properly solved. The unstructured SMC grid also supports multi‐resolutions in mesh refinement style and a refined area is included to show grid refinement effects. For steady smooth flows, the refinement is almost unnoticeable while in unstable jet case, it may stir up instability ripples in the jet flow unless strong average is applied.

Roaming mediated nonadiabatic dynamics in molecular hydrogen elimination from propane at 157 nm

The photofragmentation dynamics study using Tully’s fewest switches trajectory surface hopping calculations, based on MRCIS(6,6)/6-31++G∗∗ potential energy surfaces, energy gradients and nonadiabatic couplings, reveals the occurrence of roaming mediated nonadiabatic pathways for the elimination of molecular hydrogen from propane at 157nm. 1,2- and 1,3-molecular hydrogen eliminations, the minor dissociation channels, exclusively follow roaming (of partially dissociated H atom) mediated nonadiabatic pathway (S1→S0) to the ground electronic state followed by an atomic hydrogen abstraction from another carbon atom in the ground singlet (S0) state. 1,1- and 2,2-molecular hydrogen eliminations on the other hand, the major dissociation processes, proceed either adiabatically in the first excited singlet (S1) electronic state or through the internal conversion S1→S0 followed by direct two-body fragmentation in the ground singlet (S0) state, with equal probability.

Path optimization by a variational reaction coordinate method. II. Improved computational efficiency through internal coordinates and surface interpolation.

Reaction path optimization is being used more frequently as an alternative to the standard practice of locating a transition state and following the path downhill. The Variational Reaction Coordinate (VRC) method was proposed as an alternative to chain-of-states methods like nudged elastic band and string method. The VRC method represents the path using a linear expansion of continuous basis functions, allowing the path to be optimized variationally by updating the expansion coefficients to minimize the line integral of the potential energy gradient norm, referred to as the Variational Reaction Energy (VRE) of the path. When constraints are used to control the spacing of basis functions and to couple the minimization of the VRE with the optimization of one or more individual points along the path (representing transition states and intermediates), an approximate path as well as the converged geometries of transition states and intermediates along the path are determined in only a few iterations. This algorithmic efficiency comes at a high per-iteration cost due to numerical integration of the VRE derivatives. In the present work, methods for incorporating redundant internal coordinates and potential energy surface interpolation into the VRC method are described. With these methods, the per-iteration cost, in terms of the number of potential energy surface evaluations, of the VRC method is reduced while the high algorithmic efficiency is maintained.

Assessing the global environmental sources driving the geobiosphere: A revised emergy baseline

The empower that is derived from solar radiation, tidal momentum and geothermal sources drives the productive processes of the geobiosphere and is responsible for developing gradients of potential energy transformed into secondary energy and tertiary sources. In this paper we establish the geobiosphere emergy baseline (GEB) based on earlier methods proposed by Odum (2000) and refinements by Brown and Ulgiati (2010). After revising the solar exergy input and our previous interpretation of the sources and magnitudes of geothermal exergy, we compute a revised solar equivalent exergy and solar equivalence ratios (SERs) of geothermal and tidal inputs to the geobiosphere dynamic.A Monte Carlo simulation that includes the revised solar exergy flow of geothermal inputs and uncertainty in the flows yields SERs of 26,300seJJ−1 and 5500seJJ−1 for tidal and geothermal sources respectively. The solar exergy remains 3.6 E+24sejy−1, while the solar equivalent exergy of tidal and geothermal sources were 3.1 E+24seJy−1, and 5.4 E+24seJy−1 respectively, resulting in a GEB of 12.1 E+24seJy−1.

Indirect excitons in a potential energy landscape created by a perforated electrode

We report on the principle and realization of an excitonic device: a ramp that directs the transport of indirect excitons down a potential energy gradient created by a perforated electrode at a constant voltage. The device provides an experimental proof of principle for controlling exciton transport with electrode density gradients. We observed that the exciton transport distance along the ramp increases with increasing exciton density. This effect is explained in terms of disorder screening by repulsive exciton-exciton interactions.

Insights on continental collisional processes from GPS data: Dynamics of the peri‐Adriatic belts

AbstractWe present a new GPS velocity field covering the peri‐Adriatic tectonically active belts and the entire Balkan Peninsula. From the velocities, we calculate consistent strain rate and interpolated velocity fields. Significant features of the crustal deformation include (1) the eastward motion of the northern part of the Eastern Alps together with part the Alpine foreland and Bohemian Massif toward the Pannonian Basin, (2) shortening across the Dinarides, (3) a clockwise rotation of the Albanides‐Hellenides, and (4) a southward motion south of 44°N of the inner Balkan lithosphere between the rigid Apulia and Black Sea, toward the Aegean domain. Using this new velocity field, we derive the strain rate tensor to analyze the regional style of the deformation. Then, we devise a simple test based on the momentum balance equation, to investigate the role of horizontal gradients of gravitational potential energy in driving the deformation in the peri‐Adriatic tectonically active mountain belts: the Eastern Alps, the Dinarides, the Albanides, and the Apennines. We show that the strain rate fields observed in the Apennines and Albanides are consistent with a fluid, with viscosity η ∼ 3×1021 Pa s, deforming in response to horizontal gradients of gravitational potential energy. Conversely, both the Dinarides and Eastern Alps are probably deforming in response to the North and North‐East oriented motion of the Adria‐Apulia indenter, respectively, and as a consequence of horizontal lithospheric heterogeneity.

Femtosecond Heterodyne Transient-Grating Studies of Nonradiative Decay of the S2 (1(1)Bu(+)) State of β-Carotene: Contributions from Dark Intermediates and Double-Quantum Coherences.

Femtosecond transient-grating spectroscopy with heterodyne detection was employed to characterize the nonradiative decay pathway in β-carotene from the S2 (1(1)Bu(+)) state to the S1 (2(1)Ag(-)) state in benzonitrile solution. The results indicate definitively that the S2 state populates an intermediate state, Sx, on an ultrafast time scale prior to nonradiative decay to the S1 state. Numerical simulations using the response function formalism and the multimode Brownian oscillator model were used to fit the absorption and dispersion components of the transient-grating signal with a common set of parameters for all of the relevant Feynman pathways, including double-quantum coherences. The requirement for inclusion of the Sx state in the nonradiative decay pathway is the observed fast rise time of the dispersion component, which is predominantly controlled by the decay of the stimulated emission signal from the optically prepared S2 state. The finding that the excited-state absorption spectrum from the Sx state is significantly red-shifted from that of S2 and S1 leads to a new assignment for the spectroscopic origin of the Sx state. Rather than assigning Sx to a discrete electronic state, such as the (1)Bu(-) state suggested in previous work, it is proposed that the Sx state corresponds to a transition-state-like structure on the S2 potential surface. In this hypothesis, the 12 fs time constant for the decay of the S2 state corresponds to a vibrational displacement of the C-C and C═C bond-length alternation coordinates of the conjugated polyene backbone from the optically prepared Franck-Condon structure to a potential energy barrier on the S2 surface that divides planar and torsionally displaced structures. The lifetime of the Sx state would be associated with a subsequent relaxation along torsional coordinates over a steep potential energy gradient toward a conical intersection with the S1 state. This hypothesis leads to the idea that twisted structures with intramolecular charge-transfer character along the S2 torsional gradient are active in excitation energy-transfer mechanisms to (bacterio)chlorophyll acceptors.

Quantum Game Beats Classical Odds—Thermodynamics Implications

A quantum game is described making use of coins embodied as entangled Fermions in a potential energy well. It is shown that the odds are affected by the Pauli Exclusion Principle. They depend on the elevation in the energy well where the coins are selected, ranging from being a certainty of winning at the bottom of the well to being near classical at the top. These odds differ markedly from those in a classical game in which they are independent of elevation. The thermodynamics counterpart of the quantum game is discussed. It is shown that the temperature of a Maxwellian gas column in a potential energy gradient is independent of elevation. However, the temperature of a Fermion gas is shown to drop with elevation. The game and the gas column utilize the same components. When Fermions are used, a shifting of odds is produced in the game and a shifting of kinetic energy is produced in the thermodynamic experiment, leading to a spontaneous temperature gradient.

Gravitational spreading, bookshelf faulting, and tectonic evolution of the South Polar Terrain of Saturn’s moon Enceladus

Despite a decade of intense research the mechanical origin of the tiger-stripe fractures (TSF) and their geologic relationship to the hosting South Polar Terrain (SPT) of Enceladus remain poorly understood. Here we show via systematic photo-geological mapping that the semi-squared SPT is bounded by right-slip, left-slip, extensional, and contractional zones on its four edges. Discrete deformation along the edges in turn accommodates translation of the SPT as a single sheet with its transport direction parallel to the regional topographic gradient. This parallel relationship implies that the gradient of gravitational potential energy drove the SPT motion. In map view, internal deformation of the SPT is expressed by distributed right-slip shear parallel to the SPT transport direction. The broad right-slip shear across the whole SPT was facilitated by left-slip bookshelf faulting along the parallel TSF. We suggest that the flow-like tectonics, to the first approximation across the SPT on Enceladus, is best explained by the occurrence of a transient thermal event, which allowed the release of gravitational potential energy via lateral viscous flow within the thermally weakened ice shell.

Non-linear plasma wake growth of electron holes

An object's wake in a plasma with small Debye length that drifts across the magnetic field is subject to electrostatic electron instabilities. Such situations include, for example, the moon in the solar wind and probes in magnetized laboratory plasmas. The instability drive mechanism can equivalently be considered drift down the potential-energy gradient or drift up the density-gradient. The gradients arise because the plasma wake has a region of depressed density and electrostatic potential into which ions are attracted along the field. The non-linear consequences of the instability are analysed in this paper. At physical ratios of electron to ion mass, neither linear nor quasilinear treatment can explain the observation of large-amplitude perturbations that disrupt the ion streams well before they become ion-ion unstable. We show here, however, that electron holes, once formed, continue to grow, driven by the drift mechanism, and if they remain in the wake may reach a maximum non-linearly stable size, beyond which their uncontrolled growth disrupts the ions. The hole growth calculations provide a quantitative prediction of hole profile and size evolution. Hole growth appears to explain the observations of recent particle-in-cell simulations.

Role of mantle flow in Nubia‐Somalia plate divergence

AbstractPresent‐day continental extension along the East African Rift System (EARS) has often been attributed to diverging sublithospheric mantle flow associated with the African Superplume. This implies a degree of viscous coupling between mantle and lithosphere that remains poorly constrained. Recent advances in estimating present‐day opening rates along the EARS from geodesy offer an opportunity to address this issue with geodynamic modeling of the mantle‐lithosphere system. Here we use numerical models of the global mantle‐plates coupled system to test the role of present‐day mantle flow in Nubia‐Somalia plate divergence across the EARS. The scenario yielding the best fit to geodetic observations is one where torques associated with gradients of gravitational potential energy stored in the African highlands are resisted by weak continental faults and mantle basal drag. These results suggest that shear tractions from diverging mantle flow play a minor role in present‐day Nubia‐Somalia divergence.

Probing the π→π* photoisomerization mechanism of cis-azobenzene by multi-state ab initio on-the-fly trajectory dynamics simulation.

Based on a newly developed algorithm to compute global nonadiabatic switching probability by using only electronic adiabatic potential energy surfaces and gradients, we performed on-the-fly, trajectory-surface hopping simulations at the 5SA-CASSCF(6,6)/6-31G quantum level to probe the π→π* photoisomerization mechanism of the azobenzene within four singlet low-lying electronic states (S0, S1, S2, and S3) coupled with a complicated conical intersection network. We found that four conical intersections between the S1 and S2 states (one is near the cis-isomer region, another near the trans-isomer region, and two others between cis and trans) play the most important roles for understanding the photoisomerization mechanism of azobenzene upon S2 and S3ππ* excitation. We studied six cases to demonstrate the photoisomerization mechanism in detail by choosing eight (six) typical reactive (nonreactive) trajectories, namely, two-step fast-fast processes having lifetimes of several tenths to one hundred femtoseconds and two-step, fast-slow and slow-slow processes having lifetimes of several hundred to one thousand femtoseconds. We found for the first time from simulation that once a trajectory visits the conical intersection near the trans-isomer after ππ* excitation, it could rapidly go through the inversion pathway to trans-azobenzene, and confirms the most recent experimental observations. We performed 536 sampling trajectories (336 from S2 and 200 from S3), initially starting from the Franck-Condon region of cis-azobenzene, and obtained a total reactive quantum yield of 0.3-0.45 in very good agreement with recent experimental results of 0.24-0.50. Moreover, the current method can estimate overall nonadiabatic transition probability for each sampling trajectory from beginning to end. This can greatly accelerate convergence of nonadiabatic molecular dynamic simulation, and, for instance, results in a quantum yield of 0.53 estimated from only eight typical reactive trajectories.

Derivation of baroclinic Ertel—Rossby invariant-based thermally-coupled vorticity equation in moist flow

For the potential vorticity (PV) invariant, there is a PV-based complete-form vorticity equation, which we use heuristically in the present paper to answer the following question: for the Ertel—Rossby invariant (ERI), is there a corresponding vorticity tendency equation? Such an ERI-based thermally-coupled vorticity equation is derived and discussed in detail in this study. From the obtained new vorticity equation, the vertical vorticity change is constrained by the vertical velocity term, the term associated with the slope of the generalized momentum surface, the term related to the horizontal vorticity change, and the baroclinic or solenoid term. It explicitly includes both the dynamical and thermodynamic factors' influence on the vorticity change. For the ERI itself, besides the traditional PV term, the ERI also includes the moisture factor, which is excluded in dry ERI, and the term related to the gradients of pressure, kinetic energy, and potential energy that reflects the fast-manifold property. Therefore, it is more complete to describe the fast motions off the slow manifold for severe weather than the PV term. These advantages are naturally handed on and inherited by the ERI-based thermally-coupled vorticity equation. Then the ERI-based thermally-coupled vorticity equation is further transformed and compared with the traditional vorticity equation. The main difference between the two equations is the term which describes the contribution of the solenoid term to the vertical vorticity development. In a barotropic flow, the solenoid term disappears, then the ERI-based thermally-coupled vorticity equation can regress to the traditional vorticity equation.

Entropy changes in a thermodynamic process under potential gradients

Thermal energy applied to particles in conservative vector fields results in an increase in the potential and kinetic energy causing an increase in entropy. However, conservative fields associated with potential energy gradients of the system act in opposition to the kinetic energy gradients reducing the overall accessible states of the system and its entropy. Thus, entropy can be expressed as the ratio of difference between the input energy and potential energy of the system to its temperature. As the input energy represents the changes in Hamiltonian of the system, entropy can also be expressed as the difference in changes of its Hamiltonian and potential energy. Formulation of entropy in terms of the changes in system Hamiltonian and potential energy changes give novel insights on the role of potential fields in determining entropy rate and its impact on order and equilibrium.