Energy Variance Research Articles

Trail-Needs pseudopotentials in quantum Monte Carlo calculations with plane-wave/blip basis sets

We report a systematic analysis of the performance of a widely used set of Dirac-Fock pseudopotentials for quantum Monte Carlo (QMC) calculations. We study each atom in the periodic table from hydrogen (Z=1) to mercury (Z=80), with the exception of the 4f elements (57 <= Z <= 70). We demonstrate that ghost states are a potentially serious problem when plane-wave basis sets are used in density functional theory (DFT) orbital-generation calculations, but that this problem can be almost entirely eliminated by choosing the s channel to be local in the DFT calculation; the d channel can then be chosen to be local in subsequent QMC calculations, which generally leads to more accurate results. We investigate the achievable energy variance per electron with different levels of trial wave function and we determine appropriate plane-wave cutoff energies for DFT calculations for each pseudopotential. We demonstrate that the so-called "T-move" scheme in diffusion Monte Carlo is essential for many elements. We investigate the optimal choice of spherical integration rule for pseudopotential projectors in QMC calculations. The information reported here will prove crucial in the planning and execution of QMC projects involving beyond-first-row elements.

Structural Match of Heterogeneously Nucleated Mn(OH)2(s) Nanoparticles on Quartz under Various pH Conditions.

The early nucleation stage of Mn (hydr)oxide on mineral surfaces is crucial to understand its occurrence and the cycling of nutrients in environmental systems. However, there are only limited studies on the heterogeneous nucleation of Mn(OH)2(s) as the initial stage of Mn (hydr)oxide precipitation. Here, we investigated the effect of pH on the initial nucleation of Mn(OH)2(s) on quartz. Under various pH conditions of 9.8, 9.9, and 10.1, we analyzed the structural matches between quartz and heterogeneously nucleated Mn(OH)2(s). The structural matches were calculated by measuring the lateral and vertical dimensions using grazing incidence small angle X-ray scattering and atomic force microscopy (AFM), respectively. We found that a poorer structural match occurred at a higher pH than at a lower pH. The faster nucleation under a higher pH condition accounted for the poorer structural match observed. By fitting the structural match using classical nucleation theory, we also calculated the interfacial energy between Mn(OH)2(s) and water: γnf = 71 ± 7 mJ/m2. The calculated m values and γnf provided the variance of interfacial energy between quartz and Mn(OH)2(s): γsn = 262-272 mJ/m2. This study provides new qualitative and quantitative information on heterogeneous nucleation on an environmentally abundant mineral surface, quartz, and it offers important underpinnings for understanding the fate and transport of trace ions in environmental systems.

Acoustic measurements of vertical velocity and temperature fluctuations of a hydrothermal plume with comparisons to large eddy simulations

The acoustic scintillation method is used to study the hydrothermal plume of Dante within the Main Endeavour vent field (MEF) at the Endeavour segment of the Juan de Fuca Ridge. Forty days of vertical velocity and temperature fluctuations were obtained from the rising plume above the Dante edifice in an environment where the flow is dominated by strong (5cm/s) semi-diurnal tidal currents and a northerly mean residual current (3cm/s). These acoustic measurements provide a window on deep-sea hydrothermal plume dynamics in strong oscillatory cross flows. A large eddy simulation, parameterized with anisotropic mixing coefficients, taking into account ambient stratification and time-dependent background flows and calibrated by the acoustic measurements, yields insight into turbulent processes, entrainment, plume bending, rise height, and, inferentially, mound heat flux. The turbulent dissipation rates for kinetic energy (ε) and thermal variance (εθ) is approximated by computing the Reynolds averaged sub-grid scale turbulent production from shear and buoyancy (ε = P-B) and from temperature fluxes (εθ = Pθ), respectively, which are needed to compare to the acoustic derived turbulence levels. A new cabled observatory reciprocal acoustic scintillation system on the NEPTUNE observatory that will allow real time measurements of mean and turbulent flow of a hydrothermal plume will also be introduced.

Fluctuations of the fission energy generated in a multiplying system

The purpose of this work is to elaborate a master equation formalism for the evolution of the probability distribution of the cumulative energy generated by fissions in a multiplying system with delayed neutrons. The formalism accounts for the fact that the fission energy χ is also a random variable, thus the fluctuations of the total energy generated are due to both the fluctuations of the number of fissions, as well as to the fluctuations of the energy per fission. By comparing to the case where the fission energy is taken as constant, the significance of the fluctuations of the fission energy can be assessed. The first two moments of the cumulative fission energy are determined explicitly, and the time dependence of the expectation and the variance is calculated for different reactivities. As expected, the variance of the energy per fission does not play a significant role in the variance of the cumulative fission energy.

Joint entropy-based motion segmentation for 3D animations

With the recent advancement of data acquisition techniques, 3D animation is becoming a new challenging subject for data processing. In this paper, we present a joint entropy-based key-frame extraction method, which further derives a motion segmentation method for 3D animations. We start by applying an existing deformation-based feature descriptor to measure the degree of deformation of each triangle within each frame, from which we compute the statistical joint probability distribution of triangles’ deformation between two consecutive subsequences of frames with a fixed length. Then, we further compute joint entropy between the two subsequences. This allows us to extract key-frames by taking the local maximal from the joint entropy curve (or energy curve) of a given 3D animation. Furthermore, we classify the extracted key-frames by grouping the key-frames with similar motions into the same cluster. Finally, we compute a boundary frame between each of the two neighboring frames with different motions, which is achieved by minimizing the variance of energy between the two motions. The experimental results show that our method successfully extracts representative key-frames of different motions, and the comparisons with existing methods show the effectiveness and the efficiency of our method.

Energy and Variance Budgets of a Diffusive Staircase with Implications for Heat Flux Scaling

AbstractThe steady-state energy and thermal variance budgets form the basis for most current methods for evaluating turbulent fluxes of buoyancy, heat, and salinity. This study derives these budgets for a double-diffusive staircase and quantifies them using direct numerical simulations; 10 runs with different Rayleigh numbers are considered. The energy budget is found to be well approximated by a simple three-term balance, while the thermal variance budget consists of only two terms. The two budgets are also combined to give an expression for the ratio of the heat and salt fluxes. The heat flux scaling is also studied and found to agree well with earlier estimates based on laboratory experiments and numerical simulations at high Rayleigh numbers. At low Rayleigh numbers, however, the authors find large deviations from earlier scaling laws. Last, the scaling theory of Grossman and Lohse, which was developed for Rayleigh–Bénard convection and is based on the partitioning of the kinetic energy and tracer variance dissipation, is adapted to the diffusive regime of double-diffusive convection. The predicted heat flux scalings are compared to the results from the numerical simulations and earlier estimates.

Horizontal variability of high‐frequency nonlinear internal waves in Massachusetts Bay detected by an array of seafloor pressure sensors

AbstractA two‐dimensional array of 14 seafloor pressure sensors was deployed to measure properties of tidally generated, nonlinear, high‐frequency internal waves over a 14 km by 12 km area west of Stellwagen Bank in Massachusetts Bay during summer 2009. Thirteen high‐frequency internal wave packets propagated through the region over 6.5 days (one packet every semidiurnal cycle). Propagation speed and direction of wave packets were determined by triangulation, using arrival times and distances between triads of sensor locations. Wavefront curvature ranged from straight to radially spreading, with wave speeds generally faster to the south. Waves propagated to the southwest, rotating to more westward with shoreward propagation. Linear theory predicts a relationship between kinetic energy and bottom pressure variance of internal waves that is sensitive to sheared background currents, water depth, and stratification. By comparison to seafloor acoustic Doppler current profiler measurements, observations nonetheless show a strong relationship between kinetic energy and bottom pressure variance. This is presumably due to phase‐locking of the wave packets to the internal tide that dominates background currents and to horizontally uniform and relatively constant stratification throughout the study. This relationship was used to qualitatively describe variations in kinetic energy of the high‐frequency wave packets. In general, high‐frequency internal wave kinetic energy was greater near the southern extent of wavefronts and greatly decreased upon propagating shoreward of the 40 m isobath.

A Linearized $$k-\epsilon $$ k - ϵ Model of Forest Canopies and Clearings

A linearized analysis of the Reynolds-averaged Navier–Stokes (RANS) equations is proposed where the $$k-\epsilon $$ turbulence model is used. The flow near the forest is obtained as the superposition of the undisturbed incoming boundary layer plus a velocity perturbation due to the forest presence, similar to the approach proposed by Belcher et al. (J Fluid Mech 488:369–398, 2003). The linearized model has been compared against several non-linear RANS simulations with many leaf-area index values and large-eddy simulations using two different values of leaf-area index. All the simulations have been performed for a homogeneous forest and for four different clearing configurations. Despite the model approximations, the mean velocity and the Reynolds stress $$\overline{u'w'}$$ have been reasonably reproduced by the first-order model, providing insight about how the clearing perturbs the boundary layer over forested areas. However, significant departures from the linear predictions are observed in the turbulent kinetic energy and velocity variances. A second-order correction, which partly accounts for some non-linearities, is therefore proposed to improve the estimate of the turbulent kinetic energy and velocity variances. The results suggest that only a region close to the canopy top is significantly affected by the forest drag and dominated by the non-linearities, while above three canopy heights from the ground only small effects are visible and both the linearized model and the simulations have the same trends there.

Energetic Mechanism of Cytochrome c-Cytochrome c Oxidase Electron Transfer Complex Formation under Turnover Conditions Revealed by Mutational Effects and Docking Simulation

Based on the mutational effects on the steady-state kinetics of the electron transfer reaction and our NMR analysis of the interaction site (Sakamoto, K., Kamiya, M., Imai, M., Shinzawa-Itoh, K., Uchida, T., Kawano, K., Yoshikawa, S., and Ishimori, K. (2011) Proc. Natl. Acad. Sci. U.S.A. 108, 12271-12276), we determined the structure of the electron transfer complex between cytochrome c (Cyt c) and cytochrome c oxidase (CcO) under turnover conditions and energetically characterized the interactions essential for complex formation. The complex structures predicted by the protein docking simulation were computationally selected and validated by the experimental kinetic data for mutant Cyt c in the electron transfer reaction to CcO. The interaction analysis using the selected Cyt c-CcO complex structure revealed the electrostatic and hydrophobic contributions of each amino acid residue to the free energy required for complex formation. Several charged residues showed large unfavorable (desolvation) electrostatic interactions that were almost cancelled out by large favorable (Columbic) electrostatic interactions but resulted in the destabilization of the complex. The residual destabilizing free energy is compensated by the van der Waals interactions mediated by hydrophobic amino acid residues to give the stabilized complex. Thus, hydrophobic interactions are the primary factors that promote complex formation between Cyt c and CcO under turnover conditions, whereas the change in the electrostatic destabilization free energy provides the variance of the binding free energy in the mutants. The distribution of favorable and unfavorable electrostatic interactions in the interaction site determines the orientation of the binding of Cyt c on CcO.

Changes to intrinsic weather forecast uncertainty in one scenario of extreme future climate

Future extreme climate scenarios may harbour flows that have notably different intrinsic uncertainty from those of the present day. Here, ensemble perturbation analysis is used to explore this possibility for tropospheric flow on weather time‐scales for a climate scenario from the National Center for Atmospheric Research (NCAR) Community Climate Modeling System version 4 (CCSM4). Statistically significant changes are found in terms of basic uncertainty metrics including ensemble‐average perturbation total energy, ensemble variance, and the growth rate of perturbation total energy and ensemble variance. Strong seasonal, geographic, and vertical variation in the changes are observed. For the winter season, the poles and the jet levels are regions that exhibit notable increases in ensemble uncertainty under the extreme scenario. These increases are accompanied in some cases by substantially larger peak growth rates. For the summer season, there are prominent increases in uncertainty under the extreme scenario in terms of moist metrics. Meanwhile, there are noteworthy reductions in uncertainty for many synoptic variables. These changes in uncertainty properties are accompanied by significant changes in measures of both baroclinic and convective flow stability. Collectively, the results suggest the changes in intrinsic uncertainty under the extreme climate scenario have a fairly nuanced character. Since the CCSM4 exhibits one of the lowest climate sensitivities of available climate models, the results define a conservative estimate of the changes to intrinsic uncertainty that might be expected from extreme climate change.

A stable energy efficient clustering protocol for wireless sensor networks

Sensor networks comprise of sensor nodes with limited battery power that are deployed at different geographical locations to monitor physical events. Information gathering is a typical but an important operation in many applications of wireless sensor networks (WSNs). It is necessary to operate the sensor network for longer period of time in an energy efficient manner for gathering information. One of the popular WSN protocol, named low energy adaptive clustering hierarchy (LEACH) and its variants, aim to prolong the network lifetime using energy efficient clustering approach. These protocols increase the network lifetime at the expense of reduced stability period (the time span before the first node dies). The reduction in stability period is because of the high energy variance of nodes. Stability period is an essential aspect to preserve coverage properties of the network. Higher is the stability period, more reliable is the network. Higher energy variance of nodes leads to load unbalancing among nodes and therefore lowers the stability period. Hence, it is perpetually attractive to design clustering algorithms that provides higher stability, lower energy variance and are energy efficient. In this paper to overcome the shortcomings of existing clustering protocols, a protocol named stable energy efficient clustering protocol is proposed. It balances the load among nodes using energy-aware heuristics and hence ensures higher stability period. The results demonstrate that the proposed protocol significantly outperforms LEACH and its variants in terms of energy variance and stability period.

Coherent states of su(1,1): correlations, fluctuations, and the pseudoharmonic oscillator

We extend recent results on expectation values of coherent oscillator states and SU(2) coherent states to the case of the discrete representations of su(1,1). Systematic semiclassical expansions of products of arbitrary operators are derived. In particular, the leading order of the energy uncertainty of an arbitrary Hamiltonian is found to be given purely in terms of the time dependence of the classical variables. The coherent states considered here include the Perelomov–Gilmore (PG) coherent states. As an important application we discuss the pseudoharmonic oscillator and compare the PG states with the states introduced by Barut and Girardello. The latter ones turn out to be closer to the classical limit as their relative energy variance decays with the inverse square root of energy, while in the former case a constant is approached.

Large eddy simulation study of turbulent kinetic energy and scalar variance budgets and turbulent/non-turbulent interface in planar jets

Spatially developing planar jets with passive scalar transports are simulated for various Reynolds (Re = 2200, 7000, and 22 000) and Schmidt numbers (Sc = 1, 4, 16, 64, and 128) by the implicit large eddy simulation (ILES) using low-pass filtering as an implicit subgrid-scale model. The budgets of resolved turbulent kinetic energy k and scalar variance are explicitly evaluated from the ILES data except for the dissipation terms, which are obtained from the balance in the transport equations. The budgets of k and in the ILES agree well with the DNS and experiments for both high and low Re cases. The streamwise decay of the mean turbulent kinetic energy dissipation rate obeys the power low obtained by the scaling argument. The mechanical-to-scalar timescale ratio Cϕ is evaluated in the self-similar region. For the high Re case, Cϕ is close to the isotropic value (Cϕ = 2) near the jet centerline. However, when Re is not large, Cϕ is smaller than 2 and depends on the Schmidt number. The T/NT interface is also investigated by using the scalar isosurface. The velocity and scalar fields near the interface depend on the interface orientation for all Re. The velocity toward the interface is observed near the interface facing in the streamwise, cross-streamwise, and spanwise directions in the planar jet in the resolved velocity field.

Rotating highly mixed Gaussian packets with minimal energy

We study two-dimensional quantum mixed Gaussian packets with a fixed value of mean angular momentum. Highly mixed packets, minimizing the mean energy of an isotropic oscillator with fixed mean angular momentum $\mathcal{L}$, are found under the condition that the inverse purity ${\mathcal{P}}^{\ensuremath{-}1}$ exceeds the sum $1+2\mathcal{L}$. These states can be considered rotating thermal states. Their statistical properties (such as variances of angular momentum and energy) are studied. The case of a charged particle in a homogeneous magnetic field is considered as well.

Importance-truncated large-scale shell model

We propose an importance-truncation scheme for the large-scale nuclear shell model that extends its range of applicability to larger valence spaces and mid-shell nuclei. It is based on a perturbative measure for the importance of individual basis states that acts as an additional truncation for the many-body model space in which the eigenvalue problem of the Hamiltonian is solved numerically. Through a posteriori extrapolations of all observables to vanishing importance threshold, the full shell-model results can be recovered. In addition to simple threshold extrapolations, we explore extrapolations based on the energy variance. We apply the importance-truncated shell model for the study of 56-Ni in the pf valence space and of 60-Zn and 64-Ge in the pfg9/2 space. We demonstrate the efficiency and accuracy of the approach, which pave the way for future shell-model calculations in larger valence spaces with valence-space interactions derived in ab initio approaches.

Exploring Stratocumulus Cloud-Top Entrainment Processes and Parameterizations by Using Doppler Cloud Radar Observations

Abstract Observations made at the Atmospheric Radiation Measurement (ARM) Program’s Southern Great Plains (SGP) site during uniform nonprecipitating stratocumulus cloud conditions for a 14-h period are used to examine cloud-top entrainment processes and parameterizations. The observations from a vertically pointing Doppler cloud radar provide estimates of vertical velocity variance and energy dissipation rate (EDR) terms in the parameterized turbulent kinetic energy (TKE) budget of the entrainment zone. Hourly averages of the vertical velocity variance term in the TKE entrainment formulation correlated strongly (r = 0.72) with the dissipation rate term in the entrainment zone, with an increased correlation (r = 0.92) when accounting for the nighttime decoupling of the boundary layer. Independent estimates of entrainment rates were obtained from an inversion-height budget using the local time derivative and horizontal advection of cloud-top height together with large-scale vertical velocity at the boundary layer inversion from the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis model. The mean entrainment rate from the inversion-height budget during the 14-h period was 0.74 ± 0.15 cm s−1 and was used to calculate bulk coefficients for entrainment parameterizations based on convective velocity scale w* and TKE budgets of the entrainment zone. The hourly values of entrainment rates calculated using these coefficients exhibited good agreement with those calculated from the inversion-height budget associated with substantial changes in surface buoyancy production and cloud-top radiative cooling. The results indicate a strong potential for making entrainment rate estimates directly from radar vertical velocity variance and the EDR measurements.

Energy compensation of slow extracted beams with RF acceleration

In a conventional carbon-ion radiotherapy facility, a carbon-ion beam is typically accelerated up to an optimum energy, slowly extracted from a synchrotron ring by a resonant slow extraction method, and ultimately delivered to a patient through a beam-delivery system. At Japan’s Gunma University, a method employing slow-beam extraction along with beam-acceleration has been adopted. This method slightly alters the extracted-beam’s energy owing to the acceleration component of the process, which subsequently results in a residual-range variation of approximately 2mm in water-equivalent length. However, this range variation does not disturb a distal dose distribution with broad-beam methods such as the single beam-wobbling method. With the pencil-beam 3D scanning method, however, such a range variation disturbs a distal dose distribution because the variation is comparable to slice thickness. Therefore, for pencil-beam 3D scanning, an energy compensation method for a slow extracted beam is proposed in this paper. This method can compensate for the aforementioned energy variances by controlling net energy losses through a rotatable energy absorber set fixed between the synchrotron exit channel and the isocenter. Experimental results demonstrate that beam energies can be maintained constant, as originally hypothesized. Moreover, energy-absorber positions were found to be significantly enhanced by optimizing beam optics for reducing beam-size growth by implementation of the multiple-scattering effect option.

A Correlation-based Coverage Aware and Energy Balanced Probabilistic Flooding Algorithm

Aiming at the costly explicit and implicit acknowledgements (ACKs) and the serious energy imbalance of the existing flooding algorithm, a correlation-based coverage-aware and energy-balanced probabilistic flooding algorithm (CCEP) is proposed in this paper. CCEP distinguishes previous flooding algorithms with three features: (1) it exploits the link correlation between neighbours; the one-hop neighbours that have high link correlation are assigned to an aggregate explicit or implicit acknowledgement (aggregate ACK), thus effectively ameliorating the ACK implosion problem and saves energy on both data transmit and ACKs; (2) it balances the residual energy of sensor nodes; (3) it achieves target reliability and energy efficiency by tracking real-time aggregate ACKs and probabilistically deciding whether to retransmit a packet. The simulation results reveal that CCEP saves more than 50% energy on explicit and implicit ACKs in most cases while achieving target reliability; CCEP simultaneously reduces network variance of residual energy, thus prolonging the network lifetime.

A potential game based topology control algorithm for wireless sensor networks

In real-world applications, wireless sensor networks often consist of a large number of sensor nodes with constraint battery resources. How to reduce the power consumption of sensor nodes and maximize the network life, becomes the most important goal of topology control schemes in wireless sensor networks. During the operation of networks, sensor nodes may spend different levels of energy, and result in the uneven distribution of residual energy of sensor nodes. In order to extend the network life, it is essential to adjust the network burden of sensor nodes dynamically, so as to achieve energy balance among nodes under the consideration of different energy levels at nodes. In this paper, we introduce the game theory and the concept of game potential. By synthetically considering the factors of the residual energy and transmission power of nodes, a potential game based mathematical model of topology control is constructed. We prove the existence of Nash equilibrium. Through designing a payoff function, which takes into account both network connectivity and energy balance of nodes, the connectivity of sensor networks can be maintained while the power of sensor nodes is reduced. By increasing the average value of residual energy of neighbors, it enables to select nodes with more energy that reserves in neighborhood as neighbors, to improve the energy balance among nodes. Based on that, a distributed energy-balanced topology control algorithm (DEBA) is proposed. Theoretical analysis proves that the algorithm can maintain network connectivity. Compared with other existing game theory based algorithms DIA and MLPT, the topologies formed by the proposed algorithm have fewer bottleneck nodes which feature heavy traffic load and low residual energy, and smaller variance of node residual energy, thus achieving a longer life.

Circulation in the Arctic Ocean: Results from a high-resolution coupled ice-sea nested Global-FVCOM and Arctic-FVCOM system

A high-resolution unstructured-grid global-regional nested ice-current coupled FVCOM system was configured for the Arctic Ocean and used to examine the impact of model resolution and geometrical fitting on the basin-coastal scale circulation and transport in the pan-Arctic. With resolving steep bottom slope and irregular coastal geometry, the model was capable of simulating the multi-scale circulation and its spatial variability in the Arctic Basin and flow through the Bering Strait, Fram Strait and Canadian Archipelago. The model-simulated annual-mean velocities were in good agreement with observations within the measurement uncertainty and variability due to insufficient sampling. The errors in the flow direction varied with the flow speed, larger in the weak velocity zone and smaller as the velocity increased. In the upper 50-m layer, the annual-mean circulation pattern was dominated by the wind- and ice-drifting-induced anticyclonic circulation in the Arctic Basin and a relatively strong cyclonic slope current along the edge of the continental shelf. In the deep 200–600-m layer, a relatively permanent cyclonic circulation occurred along the steep bottom slope. These annual-mean circulations accounted for ∼85% of the total kinetic energy variance. De-trending the mean flow, an empirical orthogonal function (EOF) analysis showed that the semi-annual and seasonal variability of the sub-tidal flow was dominated by the first and second modes that accounted for ∼46% and ∼30% of the total variance in the upper 50-m layer and ∼58% and 20% in the deep 200–600-m layer. Consistent with observations, the AO-FVCOM-simulated cyclonic slope flow was characterized by a large positive topostrophy. Sensitivity experiment results with various grid configurations suggested that the currents over slopes, narrow straits and water passages featured topographic and baroclinic frontal dynamical scales associated with bathymetric slope and internal Rossby deformation radius. Over the Arctic slope, since these two scales are in the same order, the along-slope current could be captured, as the cross-isobath model resolution was refined to resolve the steep bottom topography. Under this condition, there is no need to add Neptune forcing into the momentum equations. The accuracy of the estimation of the transport through the strait and narrow water passage was affected by the model resolution. In Fram Strait where the flow is characterized by strong lateral current shear resulting from the Atlantic inflow and Arctic outflow, the transport estimation could have a significant uncertainty due to both horizontal and vertical sampling resolutions.