Assessment of smoothed spectra using autocorrelation function

International Nuclear Information System (INIS)

Urbanski, P.; Kowalska, E.

2006-01-01

Recently, data and signal smoothing became almost standard procedures in the spectrometric and chromatographic methods. In radiometry, the main purpose to apply smoothing is minimisation of the statistical fluctuation and avoid distortion. The aim of the work was to find a qualitative parameter, which could be used, as a figure of merit for detecting distortion of the smoothed spectra, based on the linear model. It is assumed that as long as the part of the raw spectrum removed by the smoothing procedure (v s ) will be of random nature, the smoothed spectrum can be considered as undistorted. Thanks to this feature of the autocorrelation function, drifts of the mean value in the removed noise vs as well as its periodicity can be more easily detected from the autocorrelogram than from the original data

Partial autocorrelation functions of the fractional ARIMA processes with negative degree of differencing

OpenAIRE

Inoue, Akihiko; Kasahara, Yukio

2004-01-01

Let {Xn : ∈Z} be a fractional ARIMA(p,d,q) process with partial autocorrelation function α(·). In this paper, we prove that if d∈(−1/2,0) then |α(n)|~|d|/n as n→∞. This extends the previous result for the case 0

Break point on the auto-correlation function of Elsässer variable z- in the super-Alfvénic solar wind fluctuations

Science.gov (United States)

Wang, X.; Tu, C. Y.; He, J.; Wang, L.

2017-12-01

It has been a longstanding debate on what the nature of Elsässer variables z- observed in the Alfvénic solar wind is. It is widely believed that z- represents inward propagating Alfvén waves and undergoes non-linear interaction with z+ to produce energy cascade. However, z- variations sometimes show nature of convective structures. Here we present a new data analysis on z- autocorrelation functions to get some definite information on its nature. We find that there is usually a break point on the z- auto-correlation function when the fluctuations show nearly pure Alfvénicity. The break point observed by Helios-2 spacecraft near 0.3 AU is at the first time lag ( 81 s), where the autocorrelation coefficient has the value less than that at zero-time lag by a factor of more than 0.4. The autocorrelation function breaks also appear in the WIND observations near 1 AU. The z- autocorrelation function is separated by the break into two parts: fast decreasing part and slowly decreasing part, which cannot be described in a whole by an exponential formula. The breaks in the z- autocorrelation function may represent that the z- time series are composed of high-frequency white noise and low-frequency apparent structures, which correspond to the flat and steep parts of the function, respectively. This explanation is supported by a simple test with a superposition of an artificial random data series and a smoothed random data series. Since in many cases z- autocorrelation functions do not decrease very quickly at large time lag and cannot be considered as the Lanczos type, no reliable value for correlation-time can be derived. Our results showed that in these cases with high Alfvénicity, z- should not be considered as inward-propagating wave. The power-law spectrum of z+ should be made by fluid turbulence cascade process presented by Kolmogorov.

Inference for local autocorrelations in locally stationary models.

Science.gov (United States)

Zhao, Zhibiao

2015-04-01

For non-stationary processes, the time-varying correlation structure provides useful insights into the underlying model dynamics. We study estimation and inferences for local autocorrelation process in locally stationary time series. Our constructed simultaneous confidence band can be used to address important hypothesis testing problems, such as whether the local autocorrelation process is indeed time-varying and whether the local autocorrelation is zero. In particular, our result provides an important generalization of the R function acf() to locally stationary Gaussian processes. Simulation studies and two empirical applications are developed. For the global temperature series, we find that the local autocorrelations are time-varying and have a "V" shape during 1910-1960. For the S&P 500 index, we conclude that the returns satisfy the efficient-market hypothesis whereas the magnitudes of returns show significant local autocorrelations.

Velocity and stress autocorrelation decay in isothermal dissipative particle dynamics

Science.gov (United States)

Chaudhri, Anuj; Lukes, Jennifer R.

2010-02-01

The velocity and stress autocorrelation decay in a dissipative particle dynamics ideal fluid model is analyzed in this paper. The autocorrelation functions are calculated at three different friction parameters and three different time steps using the well-known Groot/Warren algorithm and newer algorithms including self-consistent leap-frog, self-consistent velocity Verlet and Shardlow first and second order integrators. At low friction values, the velocity autocorrelation function decays exponentially at short times, shows slower-than exponential decay at intermediate times, and approaches zero at long times for all five integrators. As friction value increases, the deviation from exponential behavior occurs earlier and is more pronounced. At small time steps, all the integrators give identical decay profiles. As time step increases, there are qualitative and quantitative differences between the integrators. The stress correlation behavior is markedly different for the algorithms. The self-consistent velocity Verlet and the Shardlow algorithms show very similar stress autocorrelation decay with change in friction parameter, whereas the Groot/Warren and leap-frog schemes show variations at higher friction factors. Diffusion coefficients and shear viscosities are calculated using Green-Kubo integration of the velocity and stress autocorrelation functions. The diffusion coefficients match well-known theoretical results at low friction limits. Although the stress autocorrelation function is different for each integrator, fluctuates rapidly, and gives poor statistics for most of the cases, the calculated shear viscosities still fall within range of theoretical predictions and nonequilibrium studies.

Autocorrelation in queuing network type production systems - revisited

DEFF Research Database (Denmark)

Nielsen, Erland Hejn

-production systems (Takahashi and Nakamura, 1998) establishes that autocorrelation plays definitely a non-negligible role in relation to the dimensioning as well as functioning of Kanban-controlled production flow lines . This must logically either imply that production managers are missing an important aspect...... in their production planning reasoning, or that the 'realistic' autocorrelation patterns , inherent in actual production setups , are not like those so far considered in the literature. In this paper, an attempt to characterise relevant and 'realistic' types of autocorrelation schemes as well as their levels...

Determination of the friction coefficient via the force autocorrelation function. A molecular dynamics investigation for a dense Lennard-Jones fluid

International Nuclear Information System (INIS)

Vogelsang, R.; Hoheisel, C.

1987-01-01

For a large region of dense fluid states of a Lennard-Jones system, they have calculated the friction coefficient by the force autocorrelation function of a Brownian-type particle by molecular dynamics (MD). The time integral over the force autocorrelation function showed an interesting behavior and the expected plateau value when the mass of the Brownian particle was chosen to be about a factor of 100 larger than the mass of the fluid particle. Sufficient agreement was found for the friction coefficient calculated by this way and that obtained by calculations of the self-diffusion coefficient using the common relation between these coefficients. Furthermore, a modified friction coefficient was determined by integration of the force autocorrelation function up to the first maximum. This coefficient can successfully be used to derive a reasonable soft part of the friction coefficient necessary for the Rice-Allnatt approximation for the shear velocity and simple liquids

Spectral velocity estimation using autocorrelation functions for sparse data sets

DEFF Research Database (Denmark)

2006-01-01

The distribution of velocities of blood or tissue is displayed using ultrasound scanners by finding the power spectrum of the received signal. This is currently done by making a Fourier transform of the received signal and then showing spectra in an M-mode display. It is desired to show a B......-mode image for orientation, and data for this has to acquired interleaved with the flow data. The power spectrum can be calculated from the Fourier transform of the autocorrelation function Ry (k), where its span of lags k is given by the number of emission N in the data segment for velocity estimation...

Spatial autocorrelation in farmland grasshopper assemblages (Orthoptera: Acrididae) in western France.

Science.gov (United States)

Badenhausser, I; Gouat, M; Goarant, A; Cornulier, T; Bretagnolle, V

2012-10-01

Agricultural intensification in western Europe has caused a dramatic loss of grassland surfaces in farmlands, which have resulted in strong declines in grassland invertebrates, leading to cascade effects at higher trophic levels among consumers of invertebrates. Grasshoppers are important components of grassland invertebrate assemblages in European agricultural ecosystems, particularly as prey for bird species. Understanding how grasshopper populations are distributed in fragmented landscapes with low grassland availability is critical for both studies in biodiversity conservation and insect management. We assessed the range and strength of spatial autocorrelation for two grasshopper taxa (Gomphocerinae subfamily and Calliptamus italicus L.) across an intensive farmland in western France. Data from surveys carried out over 8 yr in 1,715 grassland fields were analyzed using geostatistics. Weak spatial patterns were observed at small spatial scales, suggesting important local effects of management practices on grasshopper densities. Spatial autocorrelation patterns for both grasshopper taxa were only detected at intermediate scales. For Gomphocerinae, the range of spatial autocorrelation varied from 802 to 2,613 m according to the year, depending both on grasshopper density and on grassland surfaces in the study site, whereas spatial patterns for the Italian locust were more variable and not related to grasshopper density or grassland surfaces. Spatial patterns in the distribution of Gomphocerinae supported our hypothesis that habitat availability was a major driver of grasshopper distribution in the landscape, and suggested it was related to density-dependent processes such as dispersal.

Transforming the autocorrelation function of a time series to detect land cover change

CSIR Research Space (South Africa)

Salmon

2015-07-01

Full Text Available stream_source_info Salmon_2016.pdf.txt stream_content_type text/plain stream_size 1090 Content-Encoding ISO-8859-1 stream_name Salmon_2016.pdf.txt Content-Type text/plain; charset=ISO-8859-1 International Geoscience... and Remote Sensing Symposium (IEEE IGARSS), 10-15 July 2016, Beijing Transforming the autocorrelation function of a time series to detect land cover change Salmon, B.P., Kleynhans, W., Olivier, J.C. and Schwegmann, C.P. ABSTRACT Regional...

Wave packet autocorrelation functions for quantum hard-disk and hard-sphere billiards in the high-energy, diffraction regime.

Science.gov (United States)

Goussev, Arseni; Dorfman, J R

2006-07-01

We consider the time evolution of a wave packet representing a quantum particle moving in a geometrically open billiard that consists of a number of fixed hard-disk or hard-sphere scatterers. Using the technique of multiple collision expansions we provide a first-principle analytical calculation of the time-dependent autocorrelation function for the wave packet in the high-energy diffraction regime, in which the particle's de Broglie wavelength, while being small compared to the size of the scatterers, is large enough to prevent the formation of geometric shadow over distances of the order of the particle's free flight path. The hard-disk or hard-sphere scattering system must be sufficiently dilute in order for this high-energy diffraction regime to be achievable. Apart from the overall exponential decay, the autocorrelation function exhibits a generally complicated sequence of relatively strong peaks corresponding to partial revivals of the wave packet. Both the exponential decay (or escape) rate and the revival peak structure are predominantly determined by the underlying classical dynamics. A relation between the escape rate, and the Lyapunov exponents and Kolmogorov-Sinai entropy of the counterpart classical system, previously known for hard-disk billiards, is strengthened by generalization to three spatial dimensions. The results of the quantum mechanical calculation of the time-dependent autocorrelation function agree with predictions of the semiclassical periodic orbit theory.

Influence of the nuclear autocorrelation function on the positron production in heavy-ion collisions

International Nuclear Information System (INIS)

Tomoda, T.; Weidenmueller, H.A.

1983-01-01

The influence of a nuclear reaction on atomic positron production in heavy-ion collisions is investigated. Using statistical concepts, we describe the nuclear S matrix for a heavy-ion induced reaction as a statistically fluctuating function of energy. The positron production rate is then dependent on the autocorrelation function of this S matrix, and on the ratio of the ''direct'' versus the ''fluctuating'' part of the nuclear cross section. Numerical calculations show that in this way, current experimental results on positron production in heavy-ion collisions can be reproduced in a semiquantitative fashion

General simulation algorithm for autocorrelated binary processes.

Science.gov (United States)

Serinaldi, Francesco; Lombardo, Federico

2017-02-01

The apparent ubiquity of binary random processes in physics and many other fields has attracted considerable attention from the modeling community. However, generation of binary sequences with prescribed autocorrelation is a challenging task owing to the discrete nature of the marginal distributions, which makes the application of classical spectral techniques problematic. We show that such methods can effectively be used if we focus on the parent continuous process of beta distributed transition probabilities rather than on the target binary process. This change of paradigm results in a simulation procedure effectively embedding a spectrum-based iterative amplitude-adjusted Fourier transform method devised for continuous processes. The proposed algorithm is fully general, requires minimal assumptions, and can easily simulate binary signals with power-law and exponentially decaying autocorrelation functions corresponding, for instance, to Hurst-Kolmogorov and Markov processes. An application to rainfall intermittency shows that the proposed algorithm can also simulate surrogate data preserving the empirical autocorrelation.

General simulation algorithm for autocorrelated binary processes

Science.gov (United States)

Serinaldi, Francesco; Lombardo, Federico

2017-02-01

The apparent ubiquity of binary random processes in physics and many other fields has attracted considerable attention from the modeling community. However, generation of binary sequences with prescribed autocorrelation is a challenging task owing to the discrete nature of the marginal distributions, which makes the application of classical spectral techniques problematic. We show that such methods can effectively be used if we focus on the parent continuous process of beta distributed transition probabilities rather than on the target binary process. This change of paradigm results in a simulation procedure effectively embedding a spectrum-based iterative amplitude-adjusted Fourier transform method devised for continuous processes. The proposed algorithm is fully general, requires minimal assumptions, and can easily simulate binary signals with power-law and exponentially decaying autocorrelation functions corresponding, for instance, to Hurst-Kolmogorov and Markov processes. An application to rainfall intermittency shows that the proposed algorithm can also simulate surrogate data preserving the empirical autocorrelation.

A Quantized Analog Delay for an ir-UWB Quadrature Downconversion Autocorrelation Receiver

NARCIS (Netherlands)

Bagga, S.; Zhang, L.; Serdijn, W.A.; Long, J.R.; Busking, E.B.

2005-01-01

A quantized analog delay is designed as a requirement for the autocorrelation function in the quadrature downconversion autocorrelation receiver (QDAR). The quantized analog delay is comprised of a quantizer, multiple binary delay lines and an adder circuit. Being the foremost element, the quantizer

Positron-electron autocorrelation function study of E-center in phosphorus-doped silicon

International Nuclear Information System (INIS)

Ho, K.F.; Beling, C.D.; Fung, S.; Biasini, M.; Ferro, G.; Gong, M.

2004-01-01

Two dimensional fourier transformed angular correlation of annihilation radiation (2D-FT-ACAR) spectra have been taken for 10 19 cm -3 phosphorus-doped Si in the as grown state and after being subjected to 1.8 MeV e - fluences of 2 x 10 18 cm -2 . In the spectra of the irradiated samples, the zero-crossing points are observed to displace outwards from the bravais lattice positions. It is suggested that this results from positrons annihilating with electrons in localized orbitals at the defect site. An attempt is made to extract just the component of the defect's positron-electron autocorrelation function that relates to the localized defect orbitals. It is argued that such an extracted real-space function may provide a suitable means for obtaining a mapping of localized defect orbitals. (orig.)

Landau-Placzek ratio for heat density dynamics and its application to heat capacity of liquids.

Science.gov (United States)

Bryk, Taras; Ruocco, Giancarlo; Scopigno, Tullio

2013-01-21

Exact relation for contributions to heat capacity of liquids is obtained from hydrodynamic theory. It is shown from analysis of the long-wavelength limit of heat density autocorrelation functions that the heat capacity of simple liquids is represented as a sum of two contributions due to "phonon-like" collective excitations and heat relaxation. The ratio of both contributions being the analogy of Landau-Placzek ratio for heat processes depends on the specific heats ratio. The theory of heat density autocorrelation functions in liquids is verified by computer simulations. Molecular dynamics simulations for six liquids having the ratio of specific heats γ in the range 1.1-2.3, were used for evaluation of the heat density autocorrelation functions and predicted Landau-Placzek ratio for heat processes. The dependence of contributions from collective excitations and heat relaxation process to specific heat on γ is shown to be in excellent agreement with the theory.

New approaches for calculating Moran's index of spatial autocorrelation.

Science.gov (United States)

Chen, Yanguang

2013-01-01

Spatial autocorrelation plays an important role in geographical analysis; however, there is still room for improvement of this method. The formula for Moran's index is complicated, and several basic problems remain to be solved. Therefore, I will reconstruct its mathematical framework using mathematical derivation based on linear algebra and present four simple approaches to calculating Moran's index. Moran's scatterplot will be ameliorated, and new test methods will be proposed. The relationship between the global Moran's index and Geary's coefficient will be discussed from two different vantage points: spatial population and spatial sample. The sphere of applications for both Moran's index and Geary's coefficient will be clarified and defined. One of theoretical findings is that Moran's index is a characteristic parameter of spatial weight matrices, so the selection of weight functions is very significant for autocorrelation analysis of geographical systems. A case study of 29 Chinese cities in 2000 will be employed to validate the innovatory models and methods. This work is a methodological study, which will simplify the process of autocorrelation analysis. The results of this study will lay the foundation for the scaling analysis of spatial autocorrelation.

New approaches for calculating Moran's index of spatial autocorrelation.

Directory of Open Access Journals (Sweden)

Yanguang Chen

Full Text Available Spatial autocorrelation plays an important role in geographical analysis; however, there is still room for improvement of this method. The formula for Moran's index is complicated, and several basic problems remain to be solved. Therefore, I will reconstruct its mathematical framework using mathematical derivation based on linear algebra and present four simple approaches to calculating Moran's index. Moran's scatterplot will be ameliorated, and new test methods will be proposed. The relationship between the global Moran's index and Geary's coefficient will be discussed from two different vantage points: spatial population and spatial sample. The sphere of applications for both Moran's index and Geary's coefficient will be clarified and defined. One of theoretical findings is that Moran's index is a characteristic parameter of spatial weight matrices, so the selection of weight functions is very significant for autocorrelation analysis of geographical systems. A case study of 29 Chinese cities in 2000 will be employed to validate the innovatory models and methods. This work is a methodological study, which will simplify the process of autocorrelation analysis. The results of this study will lay the foundation for the scaling analysis of spatial autocorrelation.

Sign reversals of the output autocorrelation function for the stochastic Bernoulli-Verhulst equation

Energy Technology Data Exchange (ETDEWEB)

Lumi, N., E-mail: Neeme.Lumi@tlu.ee; Mankin, R., E-mail: Romi.Mankin@tlu.ee [Institute of Mathematics and Natural Sciences, Tallinn University, 29 Narva Road, 10120 Tallinn (Estonia)

2015-10-28

We consider a stochastic Bernoulli-Verhulst equation as a model for population growth processes. The effect of fluctuating environment on the carrying capacity of a population is modeled as colored dichotomous noise. Relying on the composite master equation an explicit expression for the stationary autocorrelation function (ACF) of population sizes is found. On the basis of this expression a nonmonotonic decay of the ACF by increasing lag-time is shown. Moreover, in a certain regime of the noise parameters the ACF demonstrates anticorrelation as well as related sign reversals at some values of the lag-time. The conditions for the appearance of this highly unexpected effect are also discussed.

Spectrum sensing algorithm based on autocorrelation energy in cognitive radio networks

Science.gov (United States)

Ren, Shengwei; Zhang, Li; Zhang, Shibing

2016-10-01

Cognitive radio networks have wide applications in the smart home, personal communications and other wireless communication. Spectrum sensing is the main challenge in cognitive radios. This paper proposes a new spectrum sensing algorithm which is based on the autocorrelation energy of signal received. By taking the autocorrelation energy of the received signal as the statistics of spectrum sensing, the effect of the channel noise on the detection performance is reduced. Simulation results show that the algorithm is effective and performs well in low signal-to-noise ratio. Compared with the maximum generalized eigenvalue detection (MGED) algorithm, function of covariance matrix based detection (FMD) algorithm and autocorrelation-based detection (AD) algorithm, the proposed algorithm has 2 11 dB advantage.

Cut contribution to momentum autocorrelation function of an impurity in a classical diatomic chain

Science.gov (United States)

Yu, Ming B.

2018-02-01

A classic diatomic chain with a mass impurity is studied using the recurrence relations method. The momentum autocorrelation function of the impurity is a sum of contributions from two pairs of resonant poles and three branch cuts. The former results in cosine function and the latter in acoustic and optical branches. By use of convolution theorem, analytical expressions for the acoustic and optical branches are derived as even-order Bessel function expansions. The expansion coefficients are integrals of elliptic functions in the real axis for the acoustic branch and along a contour parallel to the imaginary axis for the optical branch, respectively. An integral is carried out for the calculation of optical branch: ∫0 ϕ dθ/√((1 - r 1 2 sin2 θ)(1 - r 2 2 sin2 θ)) = igsn -1 (sin ϕ) ( r 2 2 > r 1 2 > 1, g is a constant).

A broadly tunable autocorrelator for ultra-short, ultra-high power infrared optical pulses

Energy Technology Data Exchange (ETDEWEB)

Szarmes, E.B.; Madey, J.M.J. [Duke Univ., Durham, NC (United States)

1995-12-31

We describe the design of a crossed-beam, optical autocorrelator that uses an uncoated, birefringent beamsplitter to split a linearly polarized incident pulse into two orthogonally polarized pulses, and a Type II, SHG crystal to generate the intensity autocorrelation function. The uncoated beamsplitter accommodates extremely broad tunability while precluding any temporal distortion of ultrashort optical pulses at the dielectric interface, and the specific design provides efficient operation between 1 {mu}m and 4 {mu}m. Furthermore, the use of Type II SHG completely eliminates any single-beam doubling, so the autocorrelator can be operated at very shallow crossed-beam angles without generating a background pedestal. The autocorrelator has been constructed and installed in the Mark III laboratory at Duke University as a broadband diagnostic for ongoing compression experiments on the chirped-pulse FEL.

Parallel auto-correlative statistics with VTK.

Energy Technology Data Exchange (ETDEWEB)

Pebay, Philippe Pierre; Bennett, Janine Camille

2013-08-01

This report summarizes existing statistical engines in VTK and presents both the serial and parallel auto-correlative statistics engines. It is a sequel to [PT08, BPRT09b, PT09, BPT09, PT10] which studied the parallel descriptive, correlative, multi-correlative, principal component analysis, contingency, k-means, and order statistics engines. The ease of use of the new parallel auto-correlative statistics engine is illustrated by the means of C++ code snippets and algorithm verification is provided. This report justifies the design of the statistics engines with parallel scalability in mind, and provides scalability and speed-up analysis results for the autocorrelative statistics engine.

The Green-Kubo formula, autocorrelation function and fluctuation spectrum for finite Markov chains with continuous time

International Nuclear Information System (INIS)

Chen Yong; Chen Xi; Qian Minping

2006-01-01

A general form of the Green-Kubo formula, which describes the fluctuations pertaining to all the steady states whether equilibrium or non-equilibrium, for a system driven by a finite Markov chain with continuous time (briefly, MC) {ξ t }, is shown. The equivalence of different forms of the Green-Kubo formula is exploited. We also look at the differences in terms of the autocorrelation function and the fluctuation spectrum between the equilibrium state and the non-equilibrium steady state. Also, if the MC is in the non-equilibrium steady state, we can always find a complex function ψ, such that the fluctuation spectrum of {φ(ξ t )} is non-monotonous in [0, + ∞)

A simple method to estimate interwell autocorrelation

Energy Technology Data Exchange (ETDEWEB)

Pizarro, J.O.S.; Lake, L.W. [Univ. of Texas, Austin, TX (United States)

1997-08-01

The estimation of autocorrelation in the lateral or interwell direction is important when performing reservoir characterization studies using stochastic modeling. This paper presents a new method to estimate the interwell autocorrelation based on parameters, such as the vertical range and the variance, that can be estimated with commonly available data. We used synthetic fields that were generated from stochastic simulations to provide data to construct the estimation charts. These charts relate the ratio of areal to vertical variance and the autocorrelation range (expressed variously) in two directions. Three different semivariogram models were considered: spherical, exponential and truncated fractal. The overall procedure is demonstrated using field data. We find that the approach gives the most self-consistent results when it is applied to previously identified facies. Moreover, the autocorrelation trends follow the depositional pattern of the reservoir, which gives confidence in the validity of the approach.

The Green-Kubo formula, autocorrelation function and fluctuation spectrum for finite Markov chains with continuous time

Energy Technology Data Exchange (ETDEWEB)

Chen Yong; Chen Xi; Qian Minping [School of Mathematical Sciences, Peking University, Beijing 100871 (China)

2006-03-17

A general form of the Green-Kubo formula, which describes the fluctuations pertaining to all the steady states whether equilibrium or non-equilibrium, for a system driven by a finite Markov chain with continuous time (briefly, MC) {l_brace}{xi}{sub t}{r_brace}, is shown. The equivalence of different forms of the Green-Kubo formula is exploited. We also look at the differences in terms of the autocorrelation function and the fluctuation spectrum between the equilibrium state and the non-equilibrium steady state. Also, if the MC is in the non-equilibrium steady state, we can always find a complex function {psi}, such that the fluctuation spectrum of {l_brace}{phi}({xi}{sub t}){r_brace} is non-monotonous in [0, + {infinity})

Detecting land cover change using a sliding window temporal autocorrelation approach

CSIR Research Space (South Africa)

Kleynhans, W

2012-07-01

Full Text Available There has been recent developments in the use of hypertemporal satellite time series data for land cover change detection and classification. Recently, an Autocorrelation function (ACF) change detection method was proposed to detect the development...

The statistics of maxima in primordial density perturbations

International Nuclear Information System (INIS)

Peacock, J.A.; Heavens, A.F.

1985-01-01

An investigation has been made of the hypothesis that protogalaxies/protoclusters form at the sites of maxima in a primordial field of normally distributed density perturbations. Using a mixture of analytic and numerical techniques, the properties of the maxima, have been studied. The results provide a natural mechanism for biased galaxy formation in which galaxies do not necessarily follow the large-scale density. Methods for obtained the true autocorrelation function of the density field and implications for Microwave Background studies are discussed. (author)

AFM topographies of densely packed nanoparticles: a quick way to determine the lateral size distribution by autocorrelation function analysis

Czech Academy of Sciences Publication Activity Database

Fekete, Ladislav; Kůsová, Kateřina; Petrák, Václav; Kratochvílová, Irena

2012-01-01

Roč. 14, č. 8 (2012), s. 1-10 ISSN 1388-0764 R&D Projects: GA AV ČR KAN200100801; GA TA ČR TA01011165; GA ČR(CZ) GAP304/10/1951; GA ČR GPP204/12/P235 Institutional research plan: CEZ:AV0Z10100520 Keywords : lateral grain size distribution * AFM * autocorrelation function * nanodiamond Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 2.175, year: 2012

Autocorrelation in queuing network-type production systems - revisited

DEFF Research Database (Denmark)

Nielsen, Erland Hejn

2007-01-01

, either production managers are missing important aspects in production planning, or the 'realistic' autocorrelation patterns inherent in actual production setups are not like those considered in the literature. In this paper, relevant and 'realistic' types of autocorrelation schemes are characterised...

Auto-correlation of velocity-fluctuations and frequency-dependent diffusion constant for hot electrons

International Nuclear Information System (INIS)

Roy, M.D.; Nag, B.R.

1981-01-01

A method has been developed for determining the auto-correlation functions of the fluctuations in the transverse and the parallel components of hot carrier-velocity in a semiconductor by Monte Carlo simulation. The functions for electrons in InSb are determined by this method for applied electric fields of 50 V/cm, 75 V/cm, and 100 V/cm. With increasing value of the time interval the transverse auto-correlation function fall nearly exponentially to zero, but the parallel function falls sharply to a negative peak, then rises to positive values and finally becomes zero. The interval beyond which the auto-correlation function is zero and the correlation time are also evaluated. The correlation time is found to be approximately 1.6 times the relaxation time calculated from the chord mobility. The effect of the flight sampling time on the value of variance of the displacement, is investigated in terms of the low frequency diffusion constants, determined from the variation of the correlation functions. It is found that the diffusion constants become independent of the sampling time if it is of the order of one hundred times the relaxation time. The frequency-dependent diffusion constants are calculated from the correlation functions. The transverse diffusion constant falls monotonically with frequency for all the field strengths studied. The parallel diffusion constant has similar variation for the lower fields (50 V/cm and 75 V/cm) but it has a peak at about 44 GHz for the field of 100 V/cm. (orig.)

Spatial Autocorrelation and Uncertainty Associated with Remotely-Sensed Data

Directory of Open Access Journals (Sweden)

Daniel A. Griffith

2016-06-01

Full Text Available Virtually all remotely sensed data contain spatial autocorrelation, which impacts upon their statistical features of uncertainty through variance inflation, and the compounding of duplicate information. Estimating the nature and degree of this spatial autocorrelation, which is usually positive and very strong, has been hindered by computational intensity associated with the massive number of pixels in realistically-sized remotely-sensed images, a situation that more recently has changed. Recent advances in spatial statistical estimation theory support the extraction of information and the distilling of knowledge from remotely-sensed images in a way that accounts for latent spatial autocorrelation. This paper summarizes an effective methodological approach to achieve this end, illustrating results with a 2002 remotely sensed-image of the Florida Everglades, and simulation experiments. Specifically, uncertainty of spatial autocorrelation parameter in a spatial autoregressive model is modeled with a beta-beta mixture approach and is further investigated with three different sampling strategies: coterminous sampling, random sub-region sampling, and increasing domain sub-regions. The results suggest that uncertainty associated with remotely-sensed data should be cast in consideration of spatial autocorrelation. It emphasizes that one remaining challenge is to better quantify the spatial variability of spatial autocorrelation estimates across geographic landscapes.

Fourier analysis of spherically averaged momentum densities for some gaseous molecules

International Nuclear Information System (INIS)

Tossel, J.A.; Moore, J.H.

1981-01-01

The spherically averaged autocorrelation function, B(r), of the position-space wavefunction, psi(anti r), is calculated by numerical Fourier transformation from spherically averaged momentum densities, rho(p), obtained from either theoretical wavefunctions or (e,2e) electron-impact ionization experiments. Inspection of B(r) for the π molecular orbitals of C 4 H 6 established that autocorrelation function differences, ΔB(r), can be qualitatively related to bond lengths and numbers of bonding interactions. Differences between B(r) functions obtained from different approximate wavefunctions for a given orbital can be qualitatively understood in terms of wavefunction difference, Δpsi(1anti r), maps for these orbitals. Comparison of the B(r) function for the 1αsub(u) orbital of C 4 H 6 obtained from (e,2e) momentum densities with that obtained from an ab initio SCF MO wavefunction shows differences consistent with expected correlation effects. Thus, B(r) appears to be a useful quantity for relating spherically averaged momentum distributions to position-space wavefunction differences. (orig.)

Spin theory of the density functional: reduced matrices and density functions

International Nuclear Information System (INIS)

Pavlov, R.; Delchev, Y.; Pavlova, K.; Maruani, J.

1993-01-01

Expressions for the reduced matrices and density functions of N-fermion systems of arbitrary order s (1<=s<=N) are derived within the frame of rigorous spin approach to the density functional theory (DFT). Using the local-scale transformation method and taking into account the particle spin it is shown that the reduced matrices and density functions are functionals of the total one-fermion density. Similar dependence is found for the distribution density of s-particle aggregates. Generalization and applicability of DFT to the case of s-particle ensembles and aggregates is discussed. 14 refs

Consequences of spatial autocorrelation for niche-based models

DEFF Research Database (Denmark)

Segurado, P.; Araújo, Miguel B.; Kunin, W. E.

2006-01-01

1.  Spatial autocorrelation is an important source of bias in most spatial analyses. We explored the bias introduced by spatial autocorrelation on the explanatory and predictive power of species' distribution models, and make recommendations for dealing with the problem. 2.  Analyses were based o...

Long-time tails of the velocity autocorrelation function in 2D and 3D lattice gas cellular automata: a test of mode-coupling theory

NARCIS (Netherlands)

Hoef, M.A. van der; Frenkel, D.

1990-01-01

We report simulations of the velocity autocorrelation function (VACF) of a tagged particle in two- and three-dimensional lattice-gas cellular automata, using a new technique that is about a million times more efficient than the conventional techniques. The simulations clearly show the algebraic

A novel auto-correlation function method and FORTRAN codes for the determination of the decay ratio in BWR stability analysis

International Nuclear Information System (INIS)

Behringer, K.

2001-08-01

A novel auto-correlation function (ACF) method has been investigated for determining the oscillation frequency and the decay ratio in BWR stability analyses. The report describes not only the method but also documents comprehensively the used and developed FORTRAN codes. The neutron signals are band-pass filtered to separate the oscillation peak in the power spectral density (PSD) from background. Two linear second-order oscillation models are considered. The ACF of each model, corrected for signal filtering and with the inclusion of a background term under the peak in the PSD, is then least-squares fitted to the ACF estimated on the previously filtered neutron signals, in order to determine the oscillation frequency and the decay ratio. The procedures of filtering and ACF estimation use fast Fourier transform techniques with signal segmentation. Gliding 'short-time' ACF estimates along a signal record allow the evaluation of uncertainties. Some numerical results are given which have been obtained from neutron signal data offered by the recent Forsmark I and Forsmark II NEA benchmark project. They are compared with those from other benchmark participants using different other analysis methods. (author)

A novel auto-correlation function method and FORTRAN codes for the determination of the decay ratio in BWR stability analysis

Energy Technology Data Exchange (ETDEWEB)

Behringer, K

2001-08-01

A novel auto-correlation function (ACF) method has been investigated for determining the oscillation frequency and the decay ratio in BWR stability analyses. The report describes not only the method but also documents comprehensively the used and developed FORTRAN codes. The neutron signals are band-pass filtered to separate the oscillation peak in the power spectral density (PSD) from background. Two linear second-order oscillation models are considered. The ACF of each model, corrected for signal filtering and with the inclusion of a background term under the peak in the PSD, is then least-squares fitted to the ACF estimated on the previously filtered neutron signals, in order to determine the oscillation frequency and the decay ratio. The procedures of filtering and ACF estimation use fast Fourier transform techniques with signal segmentation. Gliding 'short-time' ACF estimates along a signal record allow the evaluation of uncertainties. Some numerical results are given which have been obtained from neutron signal data offered by the recent Forsmark I and Forsmark II NEA benchmark project. They are compared with those from other benchmark participants using different other analysis methods. (author)

Spatial autocorrelation method using AR model; Kukan jiko sokanho eno AR model no tekiyo

Energy Technology Data Exchange (ETDEWEB)

Yamamoto, H; Obuchi, T; Saito, T [Iwate University, Iwate (Japan). Faculty of Engineering

1996-05-01

Examination was made about the applicability of the AR model to the spatial autocorrelation (SAC) method, which analyzes the surface wave phase velocity in a microtremor, for the estimation of the underground structure. In this examination, microtremor data recorded in Morioka City, Iwate Prefecture, was used. In the SAC method, a spatial autocorrelation function with the frequency as a variable is determined from microtremor data observed by circular arrays. Then, the Bessel function is adapted to the spatial autocorrelation coefficient with the distance between seismographs as a variable for the determination of the phase velocity. The result of the AR model application in this study and the results of the conventional BPF and FFT method were compared. It was then found that the phase velocities obtained by the BPF and FFT methods were more dispersed than the same obtained by the AR model. The dispersion in the BPF method is attributed to the bandwidth used in the band-pass filter and, in the FFT method, to the impact of the bandwidth on the smoothing of the cross spectrum. 2 refs., 7 figs.

ISAR Imaging of Ship Targets Based on an Integrated Cubic Phase Bilinear Autocorrelation Function

Directory of Open Access Journals (Sweden)

Jibin Zheng

2017-03-01

Full Text Available For inverse synthetic aperture radar (ISAR imaging of a ship target moving with ocean waves, the image constructed with the standard range-Doppler (RD technique is blurred and the range-instantaneous-Doppler (RID technique has to be used to improve the image quality. In this paper, azimuth echoes in a range cell of the ship target are modeled as noisy multicomponent cubic phase signals (CPSs after the motion compensation and a RID ISAR imaging algorithm is proposed based on the integrated cubic phase bilinear autocorrelation function (ICPBAF. The ICPBAF is bilinear and based on the two-dimensionally coherent energy accumulation. Compared to five other estimation algorithms, the ICPBAF can acquire higher cross term suppression and anti-noise performance with a reasonable computational cost. Through simulations and analyses with the synthetic model and real radar data, we verify the effectiveness of the ICPBAF and corresponding RID ISAR imaging algorithm.

Power properties of invariant tests for spatial autocorrelation in linear regression

NARCIS (Netherlands)

Martellosio, F.

2006-01-01

Many popular tests for residual spatial autocorrelation in the context of the linear regression model belong to the class of invariant tests. This paper derives a number of exact properties of the power function of such tests. In particular, we extend the work of Krämer (2005, Journal of Statistical

Intrinsic-density functionals

International Nuclear Information System (INIS)

Engel, J.

2007-01-01

The Hohenberg-Kohn theorem and Kohn-Sham procedure are extended to functionals of the localized intrinsic density of a self-bound system such as a nucleus. After defining the intrinsic-density functional, we modify the usual Kohn-Sham procedure slightly to evaluate the mean-field approximation to the functional, and carefully describe the construction of the leading corrections for a system of fermions in one dimension with a spin-degeneracy equal to the number of particles N. Despite the fact that the corrections are complicated and nonlocal, we are able to construct a local Skyrme-like intrinsic-density functional that, while different from the exact functional, shares with it a minimum value equal to the exact ground-state energy at the exact ground-state intrinsic density, to next-to-leading order in 1/N. We briefly discuss implications for real Skyrme functionals

Damage detection and isolation via autocorrelation: a step toward passive sensing

Science.gov (United States)

Chang, Y. S.; Yuan, F. G.

2018-03-01

Passive sensing technique may eliminate the need of expending power from actuators and thus provide a means of developing a compact and simple structural health monitoring system. More importantly, it may provide a solution for monitoring the aircraft subjected to environmental loading from air flow during operation. In this paper, a non-contact auto-correlation based technique is exploited as a feasibility study for passive sensing application to detect damage and isolate the damage location. Its theoretical basis bears some resemblance to reconstructing Green's function from diffusive wavefield through cross-correlation. Localized high pressure air from air compressor are randomly and continuously applied on the one side surface of the aluminum panels through the air blow gun. A laser Doppler vibrometer (LDV) was used to scan a 90 mm × 90 mm area to create a 6 × 6 2D-array signals from the opposite side of the panels. The scanned signals were auto-correlated to reconstruct a "selfimpulse response" (or Green's function). The premise for stably reconstructing the accurate Green's function requires long sensing times. For a 609.6 mm × 609.6 mm flat aluminum panel, the sensing times roughly at least four seconds is sufficient to establish converged Green's function through correlation. For the integral stiffened aluminum panel, the geometrical features of the panel expedite the formation of the diffusive wavefield and thus shorten the sensing times. The damage is simulated by gluing a magnet onto the panels. Reconstructed Green's functions (RGFs) are used for damage detection and damage isolation based on an imaging condition with mean square deviation of the RGFs from the pristine and the damaged structure and the results are shown in color maps. The auto-correlation based technique is shown to consistently detect the simulated damage, image and isolate the damage in the structure subjected to high pressure air excitation. This technique may be transformed into

An asymptotic theory for cross-correlation between auto-correlated sequences and its application on neuroimaging data.

Science.gov (United States)

Zhou, Yunyi; Tao, Chenyang; Lu, Wenlian; Feng, Jianfeng

2018-04-20

Functional connectivity is among the most important tools to study brain. The correlation coefficient, between time series of different brain areas, is the most popular method to quantify functional connectivity. Correlation coefficient in practical use assumes the data to be temporally independent. However, the time series data of brain can manifest significant temporal auto-correlation. A widely applicable method is proposed for correcting temporal auto-correlation. We considered two types of time series models: (1) auto-regressive-moving-average model, (2) nonlinear dynamical system model with noisy fluctuations, and derived their respective asymptotic distributions of correlation coefficient. These two types of models are most commonly used in neuroscience studies. We show the respective asymptotic distributions share a unified expression. We have verified the validity of our method, and shown our method exhibited sufficient statistical power for detecting true correlation on numerical experiments. Employing our method on real dataset yields more robust functional network and higher classification accuracy than conventional methods. Our method robustly controls the type I error while maintaining sufficient statistical power for detecting true correlation in numerical experiments, where existing methods measuring association (linear and nonlinear) fail. In this work, we proposed a widely applicable approach for correcting the effect of temporal auto-correlation on functional connectivity. Empirical results favor the use of our method in functional network analysis. Copyright © 2018. Published by Elsevier B.V.

The problem of the universal density functional and the density matrix functional theory

International Nuclear Information System (INIS)

Bobrov, V. B.; Trigger, S. A.

2013-01-01

The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.

Autocorrelation Study of Solar Wind Plasma and IMF Properties as Measured by the MAVEN Spacecraft

Science.gov (United States)

Marquette, Melissa L.; Lillis, Robert J.; Halekas, J. S.; Luhmann, J. G.; Gruesbeck, J. R.; Espley, J. R.

2018-04-01

It has long been a goal of the heliophysics community to understand solar wind variability at heliocentric distances other than 1 AU, especially at ˜1.5 AU due to not only the steepening of solar wind stream interactions outside 1 AU but also the number of missions available there to measure it. In this study, we use 35 months of solar wind and interplanetary magnetic field (IMF) data taken at Mars by the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft to conduct an autocorrelation analysis of the solar wind speed, density, and dynamic pressure, which is derived from the speed and density, as well as the IMF strength and orientation. We found that the solar wind speed is coherent, that is, has an autocorrelation coefficient above 1/e, over roughly 56 hr, while the density and pressure are coherent over smaller intervals of roughly 25 and 20 hr, respectively, and that the IMF strength is coherent over time intervals of approximately 20 hr, while the cone and clock angles are considerably less steady but still somewhat coherent up to time lags of roughly 16 hr. We also found that when the speed, density, pressure, or IMF strength is higher than average, the solar wind or IMF becomes uncorrelated more quickly, while when they are below average, it tends to be steadier. This analysis allows us to make estimates of the values of solar wind plasma and IMF parameters when they are not directly measured and provide an approximation of the error associated with that estimate.

Quantifying uncertainty in soot volume fraction estimates using Bayesian inference of auto-correlated laser-induced incandescence measurements

Science.gov (United States)

Hadwin, Paul J.; Sipkens, T. A.; Thomson, K. A.; Liu, F.; Daun, K. J.

2016-01-01

Auto-correlated laser-induced incandescence (AC-LII) infers the soot volume fraction (SVF) of soot particles by comparing the spectral incandescence from laser-energized particles to the pyrometrically inferred peak soot temperature. This calculation requires detailed knowledge of model parameters such as the absorption function of soot, which may vary with combustion chemistry, soot age, and the internal structure of the soot. This work presents a Bayesian methodology to quantify such uncertainties. This technique treats the additional "nuisance" model parameters, including the soot absorption function, as stochastic variables and incorporates the current state of knowledge of these parameters into the inference process through maximum entropy priors. While standard AC-LII analysis provides a point estimate of the SVF, Bayesian techniques infer the posterior probability density, which will allow scientists and engineers to better assess the reliability of AC-LII inferred SVFs in the context of environmental regulations and competing diagnostics.

Spin-Density Functionals from Current-Density Functional Theory and Vice Versa: A Road towards New Approximations

International Nuclear Information System (INIS)

Capelle, K.; Gross, E.

1997-01-01

It is shown that the exchange-correlation functional of spin-density functional theory is identical, on a certain set of densities, with the exchange-correlation functional of current-density functional theory. This rigorous connection is used to construct new approximations of the exchange-correlation functionals. These include a conceptually new generalized-gradient spin-density functional and a nonlocal current-density functional. copyright 1997 The American Physical Society

Autocorrelated process control: Geometric Brownian Motion approach versus Box-Jenkins approach

Science.gov (United States)

Salleh, R. M.; Zawawi, N. I.; Gan, Z. F.; Nor, M. E.

2018-04-01

Existing of autocorrelation will bring a significant effect on the performance and accuracy of process control if the problem does not handle carefully. When dealing with autocorrelated process, Box-Jenkins method will be preferred because of the popularity. However, the computation of Box-Jenkins method is too complicated and challenging which cause of time-consuming. Therefore, an alternative method which known as Geometric Brownian Motion (GBM) is introduced to monitor the autocorrelated process. One real case of furnace temperature data is conducted to compare the performance of Box-Jenkins and GBM methods in monitoring autocorrelation process. Both methods give the same results in terms of model accuracy and monitoring process control. Yet, GBM is superior compared to Box-Jenkins method due to its simplicity and practically with shorter computational time.

Laboratory Density Functionals

OpenAIRE

Giraud, B. G.

2007-01-01

We compare several definitions of the density of a self-bound system, such as a nucleus, in relation with its center-of-mass zero-point motion. A trivial deconvolution relates the internal density to the density defined in the laboratory frame. This result is useful for the practical definition of density functionals.

External field as the functional of inhomogeneous density and the density matrix functional approach

NARCIS (Netherlands)

Bobrov, V.B.; Trigger, S.A.; Vlasov, Y.P.

2012-01-01

Based on the Hohenberg-Kohn lemma and the hypotheses of the density functional existence for the external-field potential, it is shown that the strict result of the density functional theory is the equation of the external-field potential as the density functional. This result leads to the

Orbital functionals in density-matrix- and current-density-functional theory

Energy Technology Data Exchange (ETDEWEB)

Helbig, N

2006-05-15

Density-Functional Theory (DFT), although widely used and very successful in the calculation of several observables, fails to correctly describe strongly correlated materials. In the first part of this work we, therefore, introduce reduced-densitymatrix- functional theory (RDMFT) which is one possible way to treat electron correlation beyond DFT. Within this theory the one-body reduced density matrix (1- RDM) is used as the basic variable. Our main interest is the calculation of the fundamental gap which proves very problematic within DFT. In order to calculate the fundamental gap we generalize RDMFT to fractional particle numbers M by describing the system as an ensemble of an N and an N+1 particle system (with N{<=}M{<=}N+1). For each fixed particle number, M, the total energy is minimized with respect to the natural orbitals and their occupation numbers. This leads to the total energy as a function of M. The derivative of this function with respect to the particle number has a discontinuity at integer particle number which is identical to the gap. In addition, we investigate the necessary and sufficient conditions for the 1- RDM of a system with fractional particle number to be N-representable. Numerical results are presented for alkali atoms, small molecules, and periodic systems. Another problem within DFT is the description of non-relativistic many-electron systems in the presence of magnetic fields. It requires the paramagnetic current density and the spin magnetization to be used as basic variables besides the electron density. However, electron-gas-based functionals of current-spin-density-functional Theory (CSDFT) exhibit derivative discontinuities as a function of the magnetic field whenever a new Landau level is occupied, which makes them difficult to use in practice. Since the appearance of Landau levels is, intrinsically, an orbital effect it is appealing to use orbital-dependent functionals. We have developed a CSDFT version of the optimized

Spot auto-focusing and spot auto-stigmation methods with high-definition auto-correlation function in high-resolution TEM.

Science.gov (United States)

Isakozawa, Shigeto; Fuse, Taishi; Amano, Junpei; Baba, Norio

2018-04-01

As alternatives to the diffractogram-based method in high-resolution transmission electron microscopy, a spot auto-focusing (AF) method and a spot auto-stigmation (AS) method are presented with a unique high-definition auto-correlation function (HD-ACF). The HD-ACF clearly resolves the ACF central peak region in small amorphous-thin-film images, reflecting the phase contrast transfer function. At a 300-k magnification for a 120-kV transmission electron microscope, the smallest areas used are 64 × 64 pixels (~3 nm2) for the AF and 256 × 256 pixels for the AS. A useful advantage of these methods is that the AF function has an allowable accuracy even for a low s/n (~1.0) image. A reference database on the defocus dependency of the HD-ACF by the pre-acquisition of through-focus amorphous-thin-film images must be prepared to use these methods. This can be very beneficial because the specimens are not limited to approximations of weak phase objects but can be extended to objects outside such approximations.

Generalised partial autocorrelations and the mutual information between past and future

DEFF Research Database (Denmark)

Proietti, Tommaso; Luati, Alessandra

the generalized partial autocorrelations as the partial autocorrelation coefficients of an auxiliary process, we derive their properties and relate them to essential features of the original process. Based on a parameterisation suggested by Barndorff-Nielsen and Schou (1973) and on Whittle likelihood, we develop...

Local-scaling density-functional method: Intraorbit and interorbit density optimizations

International Nuclear Information System (INIS)

Koga, T.; Yamamoto, Y.; Ludena, E.V.

1991-01-01

The recently proposed local-scaling density-functional theory provides us with a practical method for the direct variational determination of the electron density function ρ(r). The structure of ''orbits,'' which ensures the one-to-one correspondence between the electron density ρ(r) and the N-electron wave function Ψ({r k }), is studied in detail. For the realization of the local-scaling density-functional calculations, procedures for intraorbit and interorbit optimizations of the electron density function are proposed. These procedures are numerically illustrated for the helium atom in its ground state at the beyond-Hartree-Fock level

Autocorrelation based reconstruction of two-dimensional binary objects

International Nuclear Information System (INIS)

Mejia-Barbosa, Y.; Castaneda, R.

2005-10-01

A method for reconstructing two-dimensional binary objects from its autocorrelation function is discussed. The objects consist of a finite set of identical elements. The reconstruction algorithm is based on the concept of class of element pairs, defined as the set of element pairs with the same separation vector. This concept allows to solve the redundancy introduced by the element pairs of each class. It is also shown that different objects, consisting of an equal number of elements and the same classes of pairs, provide Fraunhofer diffraction patterns with identical intensity distributions. However, the method predicts all the possible objects that produce the same Fraunhofer pattern. (author)

Wave-function functionals for the density

International Nuclear Information System (INIS)

Slamet, Marlina; Pan Xiaoyin; Sahni, Viraht

2011-01-01

We extend the idea of the constrained-search variational method for the construction of wave-function functionals ψ[χ] of functions χ. The search is constrained to those functions χ such that ψ[χ] reproduces the density ρ(r) while simultaneously leading to an upper bound to the energy. The functionals are thereby normalized and automatically satisfy the electron-nucleus coalescence condition. The functionals ψ[χ] are also constructed to satisfy the electron-electron coalescence condition. The method is applied to the ground state of the helium atom to construct functionals ψ[χ] that reproduce the density as given by the Kinoshita correlated wave function. The expectation of single-particle operators W=Σ i r i n , n=-2,-1,1,2, W=Σ i δ(r i ) are exact, as must be the case. The expectations of the kinetic energy operator W=-(1/2)Σ i ∇ i 2 , the two-particle operators W=Σ n u n , n=-2,-1,1,2, where u=|r i -r j |, and the energy are accurate. We note that the construction of such functionals ψ[χ] is an application of the Levy-Lieb constrained-search definition of density functional theory. It is thereby possible to rigorously determine which functional ψ[χ] is closer to the true wave function.

Density functional theory

International Nuclear Information System (INIS)

Das, M.P.

1984-07-01

The state of the art of the density functional formalism (DFT) is reviewed. The theory is quantum statistical in nature; its simplest version is the well-known Thomas-Fermi theory. The DFT is a powerful formalism in which one can treat the effect of interactions in inhomogeneous systems. After some introductory material, the DFT is outlined from the two basic theorems, and various generalizations of the theorems appropriate to several physical situations are pointed out. Next, various approximations to the density functionals are presented and some practical schemes, discussed; the approximations include an electron gas of almost constant density and an electron gas of slowly varying density. Then applications of DFT in various diverse areas of physics (atomic systems, plasmas, liquids, nuclear matter) are mentioned, and its strengths and weaknesses are pointed out. In conclusion, more recent developments of DFT are indicated

BetaBit: A fast generator of autocorrelated binary processes for geophysical research

Science.gov (United States)

Serinaldi, Francesco; Lombardo, Federico

2017-05-01

We introduce a fast and efficient non-iterative algorithm, called BetaBit, to simulate autocorrelated binary processes describing the occurrence of natural hazards, system failures, and other physical and geophysical phenomena characterized by persistence, temporal clustering, and low rate of occurrence. BetaBit overcomes the simulation constraints posed by the discrete nature of the marginal distributions of binary processes by using the link existing between the correlation coefficients of this process and those of the standard Gaussian processes. The performance of BetaBit is tested on binary signals with power-law and exponentially decaying autocorrelation functions (ACFs) corresponding to Hurst-Kolmogorov and Markov processes, respectively. An application to real-world sequences describing rainfall intermittency and the occurrence of strong positive phases of the North Atlantic Oscillation (NAO) index shows that BetaBit can also simulate surrogate data preserving the empirical ACF as well as signals with autoregressive moving average (ARMA) dependence structures. Extensions to cyclo-stationary processes accounting for seasonal fluctuations are also discussed.

A Comparison of Weights Matrices on Computation of Dengue Spatial Autocorrelation

Science.gov (United States)

Suryowati, K.; Bekti, R. D.; Faradila, A.

2018-04-01

Spatial autocorrelation is one of spatial analysis to identify patterns of relationship or correlation between locations. This method is very important to get information on the dispersal patterns characteristic of a region and linkages between locations. In this study, it applied on the incidence of Dengue Hemorrhagic Fever (DHF) in 17 sub districts in Sleman, Daerah Istimewa Yogyakarta Province. The link among location indicated by a spatial weight matrix. It describe the structure of neighbouring and reflects the spatial influence. According to the spatial data, type of weighting matrix can be divided into two types: point type (distance) and the neighbourhood area (contiguity). Selection weighting function is one determinant of the results of the spatial analysis. This study use queen contiguity based on first order neighbour weights, queen contiguity based on second order neighbour weights, and inverse distance weights. Queen contiguity first order and inverse distance weights shows that there is the significance spatial autocorrelation in DHF, but not by queen contiguity second order. Queen contiguity first and second order compute 68 and 86 neighbour list

The specification of weight structures in network autocorrelation models of social influence

NARCIS (Netherlands)

Leenders, Roger Th.A.J.

2002-01-01

Many physical and social phenomena are embedded within networks of interdependencies, the so-called 'context' of these phenomena. In network analysis, this type of process is typically modeled as a network autocorrelation model. Parameter estimates and inferences based on autocorrelation models,

Effect of nonlinear crystal thickness on the parameters of the autocorrelator of femtosecond light pulses

International Nuclear Information System (INIS)

Masalov, Anatolii V; Chudnovsky, Aleksandr V

2004-01-01

It is shown that the finite thickness of the second-harmonic crystal distorts the results of measurements in nonlinear autocorrelators intended for measuring the durations and fields of femtosecond light pulses mainly due to dispersive broadening (or compression) of the pulses being measured, as well as due to the group velocity mismatch between the fundamental and sum-frequency pulses. The refractive index dispersion of the crystal, scaled by half its thickness, distorts the pulse duration to a certain extent depending on its initial chirp and thus determines the width of the energy distribution recorded in the autocorrelator. As the crystal thickness increases, the group velocity mismatch leads to a transformation of the recorded distribution from the correlation function of intensity to the squared modulus of the field correlation function. In the case of Gaussian pulses, such a transformation does not affect significantly the recorded distribution. Errors of pulse duration measurements are estimated. (nonlinear optical phenomena)

A New Multi-Gaussian Auto-Correlation Function for the Modeling of Realistic Shot Peened Random Rough Surfaces

International Nuclear Information System (INIS)

Hassan, W.; Blodgett, M.

2006-01-01

Shot peening is the primary surface treatment used to create a uniform, consistent, and reliable sub-surface compressive residual stress layer in aero engine components. A by-product of the shot peening process is random surface roughness that can affect the measurements of the resulting residual stresses and therefore impede their NDE assessment. High frequency eddy current conductivity measurements have the potential to assess these residual stresses in Ni-base super alloys. However, the effect of random surface roughness is expected to become significant in the desired measurement frequency range of 10 to 100 MHz. In this paper, a new Multi-Gaussian (MG) auto-correlation function is proposed for modeling the resulting pseudo-random rough profiles. Its use in the calculation of the Apparent Eddy Current Conductivity (AECC) loss due to surface roughness is demonstrated. The numerical results presented need to be validated with experimental measurements

Assessment of drug-induced arrhythmic risk using limit cycle and autocorrelation analysis of human iPSC-cardiomyocyte contractility

Energy Technology Data Exchange (ETDEWEB)

Kirby, R. Jason [Sanford Burnham Prebys Medical Discovery Institute, Conrad Prebys Center for Chemical Genomics, 6400 Sanger Rd, Orlando, FL 32827 (United States); Qi, Feng [Sanford Burnham Prebys Medical Discovery Institute, Applied Bioinformatics Facility, 6400 Sanger Rd, Orlando, FL 32827 (United States); Phatak, Sharangdhar; Smith, Layton H. [Sanford Burnham Prebys Medical Discovery Institute, Conrad Prebys Center for Chemical Genomics, 6400 Sanger Rd, Orlando, FL 32827 (United States); Malany, Siobhan, E-mail: smalany@sbpdiscovery.org [Sanford Burnham Prebys Medical Discovery Institute, Conrad Prebys Center for Chemical Genomics, 6400 Sanger Rd, Orlando, FL 32827 (United States)

2016-08-15

Cardiac safety assays incorporating label-free detection of human stem-cell derived cardiomyocyte contractility provide human relevance and medium throughput screening to assess compound-induced cardiotoxicity. In an effort to provide quantitative analysis of the large kinetic datasets resulting from these real-time studies, we applied bioinformatic approaches based on nonlinear dynamical system analysis, including limit cycle analysis and autocorrelation function, to systematically assess beat irregularity. The algorithms were integrated into a software program to seamlessly generate results for 96-well impedance-based data. Our approach was validated by analyzing dose- and time-dependent changes in beat patterns induced by known proarrhythmic compounds and screening a cardiotoxicity library to rank order compounds based on their proarrhythmic potential. We demonstrate a strong correlation for dose-dependent beat irregularity monitored by electrical impedance and quantified by autocorrelation analysis to traditional manual patch clamp potency values for hERG blockers. In addition, our platform identifies non-hERG blockers known to cause clinical arrhythmia. Our method provides a novel suite of medium-throughput quantitative tools for assessing compound effects on cardiac contractility and predicting compounds with potential proarrhythmia and may be applied to in vitro paradigms for pre-clinical cardiac safety evaluation. - Highlights: • Impedance-based monitoring of human iPSC-derived cardiomyocyte contractility • Limit cycle analysis of impedance data identifies aberrant oscillation patterns. • Nonlinear autocorrelation function quantifies beat irregularity. • Identification of hERG and non-hERG inhibitors with known risk of arrhythmia • Automated software processes limit cycle and autocorrelation analyses of 96w data.

Assessment of drug-induced arrhythmic risk using limit cycle and autocorrelation analysis of human iPSC-cardiomyocyte contractility

International Nuclear Information System (INIS)

Kirby, R. Jason; Qi, Feng; Phatak, Sharangdhar; Smith, Layton H.; Malany, Siobhan

2016-01-01

Cardiac safety assays incorporating label-free detection of human stem-cell derived cardiomyocyte contractility provide human relevance and medium throughput screening to assess compound-induced cardiotoxicity. In an effort to provide quantitative analysis of the large kinetic datasets resulting from these real-time studies, we applied bioinformatic approaches based on nonlinear dynamical system analysis, including limit cycle analysis and autocorrelation function, to systematically assess beat irregularity. The algorithms were integrated into a software program to seamlessly generate results for 96-well impedance-based data. Our approach was validated by analyzing dose- and time-dependent changes in beat patterns induced by known proarrhythmic compounds and screening a cardiotoxicity library to rank order compounds based on their proarrhythmic potential. We demonstrate a strong correlation for dose-dependent beat irregularity monitored by electrical impedance and quantified by autocorrelation analysis to traditional manual patch clamp potency values for hERG blockers. In addition, our platform identifies non-hERG blockers known to cause clinical arrhythmia. Our method provides a novel suite of medium-throughput quantitative tools for assessing compound effects on cardiac contractility and predicting compounds with potential proarrhythmia and may be applied to in vitro paradigms for pre-clinical cardiac safety evaluation. - Highlights: • Impedance-based monitoring of human iPSC-derived cardiomyocyte contractility • Limit cycle analysis of impedance data identifies aberrant oscillation patterns. • Nonlinear autocorrelation function quantifies beat irregularity. • Identification of hERG and non-hERG inhibitors with known risk of arrhythmia • Automated software processes limit cycle and autocorrelation analyses of 96w data

Adaptive non-collinear autocorrelation of few-cycle pulses with an angular tunable bi-mirror

Energy Technology Data Exchange (ETDEWEB)

Treffer, A., E-mail: treffer@mbi-berlin.de; Bock, M.; König, S.; Grunwald, R. [Max Born Institute for Nonlinear Optics and Short-Pulse Spectroscopy, Max Born Strasse 2A, D-12489 Berlin (Germany); Brunne, J.; Wallrabe, U. [Laboratory for Microactuators, Department of Microsystems Engineering, IMTEK, University of Freiburg, Georges-Koehler-Allee 102, Freiburg 79110 (Germany)

2016-02-01

Adaptive autocorrelation with an angular tunable micro-electro-mechanical system is reported. A piezo-actuated Fresnel bi-mirror structure was applied to measure the second order autocorrelation of near-infrared few-cycle laser pulses in a non-collinear setup at tunable superposition angles. Because of enabling measurements with variable scaling and minimizing the influence of distortions by adaptive self-reconstruction, the approach extends the capability of autocorrelators. Flexible scaling and robustness against localized amplitude obscurations are demonstrated. The adaptive reconstruction of temporal frequency information by the Fourier analysis of autocorrelation data is shown. Experimental results and numerical simulations of the beam propagation and interference are compared for variable angles.

Biometric feature extraction using local fractal auto-correlation

International Nuclear Information System (INIS)

Chen Xi; Zhang Jia-Shu

2014-01-01

Image texture feature extraction is a classical means for biometric recognition. To extract effective texture feature for matching, we utilize local fractal auto-correlation to construct an effective image texture descriptor. Three main steps are involved in the proposed scheme: (i) using two-dimensional Gabor filter to extract the texture features of biometric images; (ii) calculating the local fractal dimension of Gabor feature under different orientations and scales using fractal auto-correlation algorithm; and (iii) linking the local fractal dimension of Gabor feature under different orientations and scales into a big vector for matching. Experiments and analyses show our proposed scheme is an efficient biometric feature extraction approach. (condensed matter: structural, mechanical, and thermal properties)

Hydrodynamic description of the long-time tails of the linear and rotational velocity autocorrelation functions of a particle in a confined geometry.

Science.gov (United States)

Frydel, Derek; Rice, Stuart A

2007-12-01

We report a hydrodynamic analysis of the long-time behavior of the linear and angular velocity autocorrelation functions of an isolated colloid particle constrained to have quasi-two-dimensional motion, and compare the predicted behavior with the results of lattice-Boltzmann simulations. Our analysis uses the singularity method to characterize unsteady linear motion of an incompressible fluid. For bounded fluids we construct an image system with a discrete set of fundamental solutions of the Stokes equation from which we extract the long-time decay of the velocity. For the case that there are free slip boundary conditions at walls separated by H particle diameters, the time evolution of the parallel linear velocity and the perpendicular rotational velocity following impulsive excitation both correspond to the time evolution of a two-dimensional (2D) fluid with effective density rho_(2D)=rhoH. For the case that there are no slip boundary conditions at the walls, the same types of motion correspond to 2D fluid motions with a coefficient of friction xi=pi(2)nu/H(2) modulo a prefactor of order 1, with nu the kinematic viscosity. The linear particle motion perpendicular to the walls also experiences an effective frictional force, but the time dependence is proportional to t(-2) , which cannot be related to either pure 3D or pure 2D fluid motion. Our incompressible fluid model predicts correct self-diffusion constants but it does not capture all of the effects of the fluid confinement on the particle motion. In particular, the linear motion of a particle perpendicular to the walls is influenced by coupling between the density flux and the velocity field, which leads to damped velocity oscillations whose frequency is proportional to c_(s)/H , with c_(s) the velocity of sound. For particle motion parallel to no slip walls there is a slowing down of a density flux that spreads diffusively, which generates a long-time decay proportional to t(-1) .

Crude oil market efficiency and modeling. Insights from the multiscaling autocorrelation pattern

International Nuclear Information System (INIS)

Alvarez-Ramirez, Jose; Alvarez, Jesus; Solis, Ricardo

2010-01-01

Empirical research on market inefficiencies focuses on the detection of autocorrelations in price time series. In the case of crude oil markets, statistical support is claimed for weak efficiency over a wide range of time-scales. However, the results are still controversial since theoretical arguments point to deviations from efficiency as prices tend to revert towards an equilibrium path. This paper studies the efficiency of crude oil markets by using lagged detrended fluctuation analysis (DFA) to detect delay effects in price autocorrelations quantified in terms of a multiscaling Hurst exponent (i.e., autocorrelations are dependent of the time scale). Results based on spot price data for the period 1986-2009 indicate important deviations from efficiency associated to lagged autocorrelations, so imposing the random walk for crude oil prices has pronounced costs for forecasting. Evidences in favor of price reversion to a continuously evolving mean underscores the importance of adequately incorporating delay effects and multiscaling behavior in the modeling of crude oil price dynamics. (author)

Crude oil market efficiency and modeling. Insights from the multiscaling autocorrelation pattern

Energy Technology Data Exchange (ETDEWEB)

Alvarez-Ramirez, Jose [Departamento de Ingenieria de Procesos e Hidraulica, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico D.F., 09340 (Mexico); Departamento de Economia, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico D.F., 09340 (Mexico); Alvarez, Jesus [Departamento de Ingenieria de Procesos e Hidraulica, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico D.F., 09340 (Mexico); Solis, Ricardo [Departamento de Economia, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico D.F., 09340 (Mexico)

2010-09-15

Empirical research on market inefficiencies focuses on the detection of autocorrelations in price time series. In the case of crude oil markets, statistical support is claimed for weak efficiency over a wide range of time-scales. However, the results are still controversial since theoretical arguments point to deviations from efficiency as prices tend to revert towards an equilibrium path. This paper studies the efficiency of crude oil markets by using lagged detrended fluctuation analysis (DFA) to detect delay effects in price autocorrelations quantified in terms of a multiscaling Hurst exponent (i.e., autocorrelations are dependent of the time scale). Results based on spot price data for the period 1986-2009 indicate important deviations from efficiency associated to lagged autocorrelations, so imposing the random walk for crude oil prices has pronounced costs for forecasting. Evidences in favor of price reversion to a continuously evolving mean underscores the importance of adequately incorporating delay effects and multiscaling behavior in the modeling of crude oil price dynamics. (author)

Density functionals from deep learning

OpenAIRE

McMahon, Jeffrey M.

2016-01-01

Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep learning is developed to approximate this functional. Deep learning allows computational models that are capable of naturally discovering intricate structure in large and/or high-dimensional data sets, with multiple levels of abstraction. As no assumptions are ...

FREQUENCY ANALYSIS OF RLE-BLOCKS REPETITIONS IN THE SERIES OF BINARY CODES WITH OPTIMAL MINIMAX CRITERION OF AUTOCORRELATION FUNCTION

Directory of Open Access Journals (Sweden)

A. A. Kovylin

2013-01-01

Full Text Available The article describes the problem of searching for binary pseudo-random sequences with quasi-ideal autocorrelation function, which are to be used in contemporary communication systems, including mobile and wireless data transfer interfaces. In the synthesis of binary sequences sets, the target set is manning them based on the minimax criterion by which a sequence is considered to be optimal according to the intended application. In the course of the research the optimal sequences with order of up to 52 were obtained; the analysis of Run Length Encoding was carried out. The analysis showed regularities in the distribution of series number of different lengths in the codes that are optimal on the chosen criteria, which would make it possible to optimize the searching process for such codes in the future.

Multicomponent density functional theory embedding formulation

Energy Technology Data Exchange (ETDEWEB)

Culpitt, Tanner; Brorsen, Kurt R.; Pak, Michael V.; Hammes-Schiffer, Sharon, E-mail: shs3@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave, Urbana, Illinois 61801 (United States)

2016-07-28

Multicomponent density functional theory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals. Herein a general theory for multicomponent embedded DFT is developed to enable the accurate treatment of larger systems. In the general theory, the total electronic density is separated into two subsystem densities, denoted as regular and special, and different electron-proton correlation functionals are used for these two electronic densities. In the specific implementation, the special electron density is defined in terms of spatially localized Kohn-Sham electronic orbitals, and electron-proton correlation is included only for the special electron density. The electron-proton correlation functional depends on only the special electron density and the proton density, whereas the electronic exchange-correlation functional depends on the total electronic density. This scheme includes the essential electron-proton correlation, which is a relatively local effect, as well as the electronic exchange-correlation for the entire system. This multicomponent DFT-in-DFT embedding theory is applied to the HCN and FHF{sup −} molecules in conjunction with two different electron-proton correlation functionals and three different electronic exchange-correlation functionals. The results illustrate that this approach provides qualitatively accurate nuclear densities in a computationally tractable manner. The general theory is also easily extended to other types of partitioning schemes for multicomponent systems.

Vibrational signatures of cation-anion hydrogen bonding in ionic liquids: a periodic density functional theory and molecular dynamics study.

Science.gov (United States)

Mondal, Anirban; Balasubramanian, Sundaram

2015-02-05

Hydrogen bonding in alkylammonium based protic ionic liquids was studied using density functional theory (DFT) and ab initio molecular dynamics (AIMD) simulations. Normal-mode analysis within the harmonic approximation and power spectra of velocity autocorrelation functions were used as tools to obtain the vibrational spectra in both the gas phase and the crystalline phases of these protic ionic liquids. The hydrogen bond vibrational modes were identified in the 150-240 cm(-1) region of the far-infrared (far-IR) spectra. A blue shift in the far-IR mode was observed with an increasing number of hydrogen-bonding sites on the cation; the exact peak position is modulated by the cation-anion hydrogen bond strength. Sub-100 cm(-1) bands in the far-IR spectrum are assigned to the rattling motion of the anions. Calculated NMR chemical shifts of the acidic protons in the crystalline phase of these salts also exhibit the signature of cation-anion hydrogen bonding.

Nanoscale and femtosecond optical autocorrelator based on a single plasmonic nanostructure

International Nuclear Information System (INIS)

Melentiev, P N; Afanasiev, A E; Balykin, V I; Tausenev, A V; Konyaschenko, A V; Klimov, V V

2014-01-01

We demonstrated a nanoscale size, ultrafast and multiorder optical autocorrelator with a single plasmonic nanostructure for measuring the spatio-temporal dynamics of femtosecond laser light. As a nanostructure, we use a split hole resonator (SHR), which was made in an aluminium nanofilm. The Al material yields the fastest response time (100 as). The SHR nanostructure ensures a high nonlinear optical efficiency of the interaction with laser radiation, which leads to (1) the second, (2) the third harmonics generation and (3) the multiphoton luminescence, which, in turn, are used to perform multi-order autocorrelation measurements. The nano-sized SHR makes it possible to conduct autocorrelation measurements (i) with a subwavelength spatial resolution and (ii) with no significant influence on the duration of the laser pulse. The time response realized by the SHR nanostructure is about 10 fs. (letter)

Thirty-two phase sequences design with good autocorrelation ...

Indian Academy of Sciences (India)

mum peak aperiodic autocorrelation sidelobe level one are called Barker Sequences. ... the generation and processing of polyphase signals have now become easy ..... Cook C E, Bernfield M 1967 An introduction to theory and application.

Magnetic fields and density functional theory

Energy Technology Data Exchange (ETDEWEB)

Salsbury Jr., Freddie [Univ. of California, Berkeley, CA (United States)

1999-02-01

A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.

Magnetic fields and density functional theory

International Nuclear Information System (INIS)

Salsbury, Freddie Jr.

1999-01-01

A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules

Density dependence of the nuclear energy-density functional

Science.gov (United States)

Papakonstantinou, Panagiota; Park, Tae-Sun; Lim, Yeunhwan; Hyun, Chang Ho

2018-01-01

Background: The explicit density dependence in the coupling coefficients entering the nonrelativistic nuclear energy-density functional (EDF) is understood to encode effects of three-nucleon forces and dynamical correlations. The necessity for the density-dependent coupling coefficients to assume the form of a preferably small fractional power of the density ρ is empirical and the power is often chosen arbitrarily. Consequently, precision-oriented parametrizations risk overfitting in the regime of saturation and extrapolations in dilute or dense matter may lose predictive power. Purpose: Beginning with the observation that the Fermi momentum kF, i.e., the cubic root of the density, is a key variable in the description of Fermi systems, we first wish to examine if a power hierarchy in a kF expansion can be inferred from the properties of homogeneous matter in a domain of densities, which is relevant for nuclear structure and neutron stars. For subsequent applications we want to determine a functional that is of good quality but not overtrained. Method: For the EDF, we fit systematically polynomial and other functions of ρ1 /3 to existing microscopic, variational calculations of the energy of symmetric and pure neutron matter (pseudodata) and analyze the behavior of the fits. We select a form and a set of parameters, which we found robust, and examine the parameters' naturalness and the quality of resulting extrapolations. Results: A statistical analysis confirms that low-order terms such as ρ1 /3 and ρ2 /3 are the most relevant ones in the nuclear EDF beyond lowest order. It also hints at a different power hierarchy for symmetric vs. pure neutron matter, supporting the need for more than one density-dependent term in nonrelativistic EDFs. The functional we propose easily accommodates known or adopted properties of nuclear matter near saturation. More importantly, upon extrapolation to dilute or asymmetric matter, it reproduces a range of existing microscopic

Microfluidic volumetric flow determination using optical coherence tomography speckle: An autocorrelation approach

Energy Technology Data Exchange (ETDEWEB)

De Pretto, Lucas R., E-mail: lucas.de.pretto@usp.br; Nogueira, Gesse E. C.; Freitas, Anderson Z. [Instituto de Pesquisas Energéticas e Nucleares, IPEN–CNEN/SP, Avenida Lineu Prestes, 2242, 05508-000 São Paulo (Brazil)

2016-04-28

Functional modalities of Optical Coherence Tomography (OCT) based on speckle analysis are emerging in the literature. We propose a simple approach to the autocorrelation of OCT signal to enable volumetric flow rate differentiation, based on decorrelation time. Our results show that this technique could distinguish flows separated by 3 μl/min, limited by the acquisition speed of the system. We further perform a B-scan of gradient flow inside a microchannel, enabling the visualization of the drag effect on the walls.

Density-functional theory for internal magnetic fields

Science.gov (United States)

Tellgren, Erik I.

2018-01-01

A density-functional theory is developed based on the Maxwell-Schrödinger equation with an internal magnetic field in addition to the external electromagnetic potentials. The basic variables of this theory are the electron density and the total magnetic field, which can equivalently be represented as a physical current density. Hence, the theory can be regarded as a physical current density-functional theory and an alternative to the paramagnetic current density-functional theory due to Vignale and Rasolt. The energy functional has strong enough convexity properties to allow a formulation that generalizes Lieb's convex analysis formulation of standard density-functional theory. Several variational principles as well as a Hohenberg-Kohn-like mapping between potentials and ground-state densities follow from the underlying convex structure. Moreover, the energy functional can be regarded as the result of a standard approximation technique (Moreau-Yosida regularization) applied to the conventional Schrödinger ground-state energy, which imposes limits on the maximum curvature of the energy (with respect to the magnetic field) and enables construction of a (Fréchet) differentiable universal density functional.

Density-density functionals and effective potentials in many-body electronic structure calculations

International Nuclear Information System (INIS)

Reboredo, Fernando A.; Kent, Paul R.

2008-01-01

We demonstrate the existence of different density-density functionals designed to retain selected properties of the many-body ground state in a non-interacting solution starting from the standard density functional theory ground state. We focus on diffusion quantum Monte Carlo applications that require trial wave functions with optimal Fermion nodes. The theory is extensible and can be used to understand current practices in several electronic structure methods within a generalized density functional framework. The theory justifies and stimulates the search of optimal empirical density functionals and effective potentials for accurate calculations of the properties of real materials, but also cautions on the limits of their applicability. The concepts are tested and validated with a near-analytic model.

Velocity auto-correlation and hot-electron diffusion constant in GaAs and InP

International Nuclear Information System (INIS)

Deb Roy, M.

1982-01-01

Auto-correlation functions of the fluctuations in the electron velocities transverse and parallel to the applied electric field are calculated by the Monte Carlo method for GaAs and InP at three different values of field strength which are around three times the threshold field for negative differential mobility in each case. From these the frequency-dependent diffusion coefficients transverse and parallel to the applied field and the figure of merit for noise performance when used in a microwave amplifying device are determined. The results indicate that the transverse auto-correlation function Csub(t)(s) falls nearly exponentially to zero with increasing interval s while the parallel function Csub(p)(s) falls sharply, attains a minimum and then rises towards zero. In each case a higher field gives a higher rate of fall and makes the correlation functions zero within a shorter interval. The transverses diffusion coefficient falls monotonically with the frequency but the parallel diffusion coefficient generally starts with a low value at low frequencies, rises to a maximum and then falls. InP, with a larger separation between the central and the satellite valleys, has a higher value of the low frequency transverse diffusion coefficient and a lower value of its parallel counterpart. The noise performance of microwave semiconductor amplifying devices depends mainly on the low frequency parallel diffusion constant and consequently devices made out of materials like InP with a large separation between valleys are likely to have better noise characteristics. (orig.)

Excited-state density functional theory

International Nuclear Information System (INIS)

Harbola, Manoj K; Hemanadhan, M; Shamim, Md; Samal, P

2012-01-01

Starting with a brief introduction to excited-state density functional theory, we present our method of constructing modified local density approximated (MLDA) energy functionals for the excited states. We show that these functionals give accurate results for kinetic energy and exchange energy compared to the ground state LDA functionals. Further, with the inclusion of GGA correction, highly accurate total energies for excited states are obtained. We conclude with a brief discussion on the further direction of research that include the construction of correlation energy functional and exchange potential for excited states.

Spectral function from Reduced Density Matrix Functional Theory

Science.gov (United States)

Romaniello, Pina; di Sabatino, Stefano; Berger, Jan A.; Reining, Lucia

2015-03-01

In this work we focus on the calculation of the spectral function, which determines, for example, photoemission spectra, from reduced density matrix functional theory. Starting from its definition in terms of the one-body Green's function we derive an expression for the spectral function that depends on the natural occupation numbers and on an effective energy which accounts for all the charged excitations. This effective energy depends on the two-body as well as higher-order density matrices. Various approximations to this expression are explored by using the exactly solvable Hubbard chains.

Ground-state densities from the Rayleigh-Ritz variation principle and from density-functional theory.

Science.gov (United States)

Kvaal, Simen; Helgaker, Trygve

2015-11-14

The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh-Ritz variation principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg-Kohn variation principle) is studied within the framework of convex conjugation, in a generic setting covering molecular systems, solid-state systems, and more. Having introduced admissible density functionals as functionals that produce the exact ground-state energy for a given external potential by minimizing over densities in the Hohenberg-Kohn variation principle, necessary and sufficient conditions on such functionals are established to ensure that the Rayleigh-Ritz ground-state densities and the Hohenberg-Kohn ground-state densities are identical. We apply the results to molecular systems in the Born-Oppenheimer approximation. For any given potential v ∈ L(3/2)(ℝ(3)) + L(∞)(ℝ(3)), we establish a one-to-one correspondence between the mixed ground-state densities of the Rayleigh-Ritz variation principle and the mixed ground-state densities of the Hohenberg-Kohn variation principle when the Lieb density-matrix constrained-search universal density functional is taken as the admissible functional. A similar one-to-one correspondence is established between the pure ground-state densities of the Rayleigh-Ritz variation principle and the pure ground-state densities obtained using the Hohenberg-Kohn variation principle with the Levy-Lieb pure-state constrained-search functional. In other words, all physical ground-state densities (pure or mixed) are recovered with these functionals and no false densities (i.e., minimizing densities that are not physical) exist. The importance of topology (i.e., choice of Banach space of densities and potentials) is emphasized and illustrated. The relevance of these results for current-density-functional theory is examined.

AFM topographies of densely packed nanoparticles: a quick way to determine the lateral size distribution by autocorrelation function analysis

International Nuclear Information System (INIS)

Fekete, L.; Kůsová, K.; Petrák, V.; Kratochvílová, I.

2012-01-01

The distribution of sizes is one of the basic characteristics of nanoparticles. Here, we propose a novel way to determine the lateral distribution of sizes from AFM topographies. Our algorithm is based on the autocorrelation function and can be applied both on topographies containing spatially separated and densely packed nanoparticles as well as on topographies of polycrystalline films. As no manual treatment is required, this algorithm can be easily automatable for batch processing. The algorithm works in principle with any kind of spatially mapped information (AFM current maps, optical microscope images, etc.), and as such has no size limitations. However, in the case of AFM topographies, the tip/sample convolution effects will be the factor limiting the smallest size to which the algorithm is applicable. Here, we demonstrate the usefulness of this algorithm on objects with sizes ranging between 20 nm and 1.5 μm.

Single-particle energies and density of states in density functional theory

Science.gov (United States)

van Aggelen, H.; Chan, G. K.-L.

2015-07-01

Time-dependent density functional theory (TD-DFT) is commonly used as the foundation to obtain neutral excited states and transition weights in DFT, but does not allow direct access to density of states and single-particle energies, i.e. ionisation energies and electron affinities. Here we show that by extending TD-DFT to a superfluid formulation, which involves operators that break particle-number symmetry, we can obtain the density of states and single-particle energies from the poles of an appropriate superfluid response function. The standard Kohn- Sham eigenvalues emerge as the adiabatic limit of the superfluid response under the assumption that the exchange- correlation functional has no dependence on the superfluid density. The Kohn- Sham eigenvalues can thus be interpreted as approximations to the ionisation energies and electron affinities. Beyond this approximation, the formalism provides an incentive for creating a new class of density functionals specifically targeted at accurate single-particle eigenvalues and bandgaps.

Performing T-tests to Compare Autocorrelated Time Series Data Collected from Direct-Reading Instruments.

Science.gov (United States)

O'Shaughnessy, Patrick; Cavanaugh, Joseph E

2015-01-01

Industrial hygienists now commonly use direct-reading instruments to evaluate hazards in the workplace. The stored values over time from these instruments constitute a time series of measurements that are often autocorrelated. Given the need to statistically compare two occupational scenarios using values from a direct-reading instrument, a t-test must consider measurement autocorrelation or the resulting test will have a largely inflated type-1 error probability (false rejection of the null hypothesis). A method is described for both the one-sample and two-sample cases which properly adjusts for autocorrelation. This method involves the computation of an "equivalent sample size" that effectively decreases the actual sample size when determining the standard error of the mean for the time series. An example is provided for the one-sample case, and an example is given where a two-sample t-test is conducted for two autocorrelated time series comprised of lognormally distributed measurements.

Density of states functions for photonic crystals

International Nuclear Information System (INIS)

McPhedran, R.C.; McOrist, J.; Sterke, C.M. de; Nicorovici, N.A.; Botten, L.C.; Asatryan, A.A.

2004-01-01

We discuss density of states functions for photonic crystals, in the context of the two-dimensional problem for arrays of cylinders of arbitrary cross section. We introduce the mutual density of states (MDOS), and show that this function can be used to calculate both the local density of states (LDOS), which gives position information for emission of radiation from photonic crystals, and the spectral density of states (SDOS), which gives angular information. We establish the connection between MDOS, LDOS, SDOS and the conventional density of states, which depends only on frequency. We relate all four functions to the band structure and propagating states within the crystal, and give numerical examples of the relation between band structure and density of states functions

Nonlocal kinetic-energy-density functionals

International Nuclear Information System (INIS)

Garcia-Gonzalez, P.; Alvarellos, J.E.; Chacon, E.

1996-01-01

In this paper we present nonlocal kinetic-energy functionals T[n] within the average density approximation (ADA) framework, which do not require any extra input when applied to any electron system and recover the exact kinetic energy and the linear response function of a homogeneous system. In contrast with previous ADA functionals, these present good behavior of the long-range tail of the exact weight function. The averaging procedure for the kinetic functional (averaging the Fermi momentum of the electron gas, instead of averaging the electron density) leads to a functional without numerical difficulties in the calculation of extended systems, and it gives excellent results when applied to atoms and jellium surfaces. copyright 1996 The American Physical Society

Exchange-correlation energies of atoms from efficient density functionals: influence of the electron density

Science.gov (United States)

Tao, Jianmin; Ye, Lin-Hui; Duan, Yuhua

2017-12-01

The primary goal of Kohn-Sham density functional theory is to evaluate the exchange-correlation contribution to electronic properties. However, the accuracy of a density functional can be affected by the electron density. Here we apply the nonempirical Tao-Mo (TM) semilocal functional to study the influence of the electron density on the exchange and correlation energies of atoms and ions, and compare the results with the commonly used nonempirical semilocal functionals local spin-density approximation (LSDA), Perdew-Burke-Ernzerhof (PBE), Tao-Perdew-Staroverov-Scuseria (TPSS), and hybrid functional PBE0. We find that the spin-restricted Hartree-Fock density yields the exchange and correlation energies in good agreement with the Optimized Effective Potential method, particularly for spherical atoms and ions. However, the errors of these semilocal and hybrid functionals become larger for self-consistent densities. We further find that the quality of the electron density have greater effect on the exchange-correlation energies of kinetic energy density-dependent meta-GGA functionals TPSS and TM than on those of the LSDA and GGA, and therefore, should have greater influence on the performance of meta-GGA functionals. Finally, we show that the influence of the density quality on PBE0 is slightly reduced, compared to that of PBE, due to the exact mixing.

A multiconfigurational hybrid density-functional theory

DEFF Research Database (Denmark)

Sharkas, Kamal; Savin, Andreas; Jensen, Hans Jørgen Aagaard

2012-01-01

We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the electron-electron interaction. This gives a straightforward extension ...

Local density approximation for exchange in excited-state density functional theory

OpenAIRE

Harbola, Manoj K.; Samal, Prasanjit

2004-01-01

Local density approximation for the exchange energy is made for treatment of excited-states in density-functional theory. It is shown that taking care of the state-dependence of the LDA exchange energy functional leads to accurate excitation energies.

Modified Exponential Weighted Moving Average (EWMA) Control Chart on Autocorrelation Data

Science.gov (United States)

Herdiani, Erna Tri; Fandrilla, Geysa; Sunusi, Nurtiti

2018-03-01

In general, observations of the statistical process control are assumed to be mutually independence. However, this assumption is often violated in practice. Consequently, statistical process controls were developed for interrelated processes, including Shewhart, Cumulative Sum (CUSUM), and exponentially weighted moving average (EWMA) control charts in the data that were autocorrelation. One researcher stated that this chart is not suitable if the same control limits are used in the case of independent variables. For this reason, it is necessary to apply the time series model in building the control chart. A classical control chart for independent variables is usually applied to residual processes. This procedure is permitted provided that residuals are independent. In 1978, Shewhart modification for the autoregressive process was introduced by using the distance between the sample mean and the target value compared to the standard deviation of the autocorrelation process. In this paper we will examine the mean of EWMA for autocorrelation process derived from Montgomery and Patel. Performance to be investigated was investigated by examining Average Run Length (ARL) based on the Markov Chain Method.

Energy vs. density on paths toward more exact density functionals.

Science.gov (United States)

Kepp, Kasper P

2018-03-14

Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a "path". Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness and "straying" from the "path" by separating errors in ρ and E[ρ]. A consistent path toward exactness involves minimizing both errors. Second, a suitably diverse test set of trial densities ρ' can be used to estimate the significance of errors in ρ without knowing the exact densities which are often inaccessible. To illustrate this, the systems previously studied by Medvedev et al., the first ionization energies of atoms with Z = 1 to 10, the ionization energy of water, and the bond dissociation energies of five diatomic molecules were investigated using CCSD(T)/aug-cc-pV5Z as benchmark at chemical accuracy. Four functionals of distinct designs was used: B3LYP, PBE, M06, and S-VWN. For atomic cations regardless of charge and compactness up to Z = 10, the energy effects of the different ρ are energy-wise insignificant. An interesting oscillating behavior in the density sensitivity is observed vs. Z, explained by orbital occupation effects. Finally, it is shown that even large "normal" problems such as the Co-C bond energy of cobalamins can use simpler (e.g. PBE) trial densities to drastically speed up computation by loss of a few kJ mol -1 in accuracy. The proposed method of using a test set of trial densities to estimate the sensitivity and significance of density errors of functionals may be useful for testing and designing new balanced functionals with more systematic improvement of densities and energies.

Covariance Estimation and Autocorrelation of NORAD Two-Line Element Sets

National Research Council Canada - National Science Library

Osweiler, Victor P

2006-01-01

This thesis investigates NORAD two-line element sets (TLE) containing satellite mean orbital elements for the purpose of estimating a covariance matrix and formulating an autocorrelation relationship...

Relativistic density functional for nuclear structure

CERN Document Server

2016-01-01

This book aims to provide a detailed introduction to the state-of-the-art covariant density functional theory, which follows the Lorentz invariance from the very beginning and is able to describe nuclear many-body quantum systems microscopically and self-consistently. Covariant density functional theory was introduced in nuclear physics in the 1970s and has since been developed and used to describe the diversity of nuclear properties and phenomena with great success. In order to provide an advanced and updated textbook of covariant density functional theory for graduate students and nuclear physics researchers, this book summarizes the enormous amount of material that has accumulated in the field of covariant density functional theory over the last few decades as well as the latest developments in this area. Moreover, the book contains enough details for readers to follow the formalism and theoretical results, and provides exhaustive references to explore the research literature.

Spatial autocorrelation analysis of tourist arrivals using municipal data: A Serbian example

Directory of Open Access Journals (Sweden)

Stankov Uglješa

2017-01-01

Full Text Available Spatial autocorrelation methodologies can be used to reveal patterns and temporal changes of different spatial variables, including tourism arrivals. The research adopts a GIS-based approach to spatially analyse tourist arrivals in Serbia, using Global Moran's I and Anselin's Local Moran's I statistics applied on the level of municipalities. To assess feasibility of this approach the article discusses spatial changes of tourist arrivals in order to identify potentially significant trends of interest for tourism development policy in Serbia. There is a significant spatial inequality in the distribution of tourism arrivals in Serbia that is not adequately addressed in tourism development plans. The results of global autocorrelation suggest the existence of low and decreasing spatial clustering for domestic tourist arrivals and high, relatively stable spatial clustering for international tourists. Local autocorrelation statistics revealed different of domestic and international tourism arrivals. In order to assess feasibility of this approach these results are discussed in their significance to tourism development policy in Serbia.

Computation and analysis of the transverse current autocorrelation function, Ct(k,t), for small wave vectors: A molecular-dynamics study for a Lennard-Jones fluid

Science.gov (United States)

Vogelsang, R.; Hoheisel, C.

1987-02-01

Molecular-dynamics (MD) calculations are reported for three thermodynamic states of a Lennard-Jones fluid. Systems of 2048 particles and 105 integration steps were used. The transverse current autocorrelation function, Ct(k,t), has been determined for wave vectors of the range 0.5viscosities which showed a systematic behavior as a function of k. Extrapolation to the hydrodynamic region at k=0 gave shear viscosity coefficients in good agreement with direct Green-Kubo results obtained in previous work. The two-exponential model fit for the memory function proposed by other authors does not provide a reasonable description of the MD results, as the fit parameters show no systematic wave-vector dependence, although the Ct(k,t) functions are somewhat better fitted. Similarly, the semiempirical interpolation formula for the decay time based on the viscoelastic concept proposed by Akcasu and Daniels fails to reproduce the correct k dependence for the wavelength range investigated herein.

Performances Of Estimators Of Linear Models With Autocorrelated ...

African Journals Online (AJOL)

The performances of five estimators of linear models with Autocorrelated error terms are compared when the independent variable is autoregressive. The results reveal that the properties of the estimators when the sample size is finite is quite similar to the properties of the estimators when the sample size is infinite although ...

Locality of correlation in density functional theory

Energy Technology Data Exchange (ETDEWEB)

Burke, Kieron [Department of Chemistry, University of California, Irvine, California 92697 (United States); Cancio, Antonio [Department of Physics and Astronomy, Ball State University, Muncie, Indiana 47306 (United States); Gould, Tim [Qld Micro- and Nanotechnology Centre, Griffith University, Nathan, Qld 4111 (Australia); Pittalis, Stefano [CNR-Istituto di Nanoscienze, Via Campi 213A, I-41125 Modena (Italy)

2016-08-07

The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that E{sub C} → −A{sub C} ZlnZ + B{sub C}Z as Z → ∞, where Z is the atomic number, A{sub C} is known, and we estimate B{sub C} to be about 37 mhartree. The local density approximation yields A{sub C} exactly, but a very incorrect value for B{sub C}, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with B{sub C} a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.

Functional derivative of noninteracting kinetic energy density functional

International Nuclear Information System (INIS)

Liu Shubin; Ayers, Paul W.

2004-01-01

Proofs from different theoretical frameworks, namely, the Hohenbergh-Kohn theorems, the Kohn-Sham scheme, and the first-order density matrix representation, have been presented in this paper to show that the functional derivative of the noninteracting kinetic energy density functional can uniquely be expressed as the negative of the Kohn-Sham effective potential, arbitrary only to an additive orbital-independent constant. Key points leading to the current result as well as confusion about the quantity in the literature are briefly discussed

Density functionals in the laboratory frame

International Nuclear Information System (INIS)

Giraud, B. G.

2008-01-01

We compare several definitions of the density of a self-bound system, such as a nucleus, in relation with its center-of-mass zero-point motion. A trivial deconvolution relates the internal density to the density defined in the laboratory frame. This result is useful for the practical definition of density functionals

Density-functional expansion methods: Grand challenges.

Science.gov (United States)

Giese, Timothy J; York, Darrin M

2012-03-01

We discuss the source of errors in semiempirical density functional expansion (VE) methods. In particular, we show that VE methods are capable of well-reproducing their standard Kohn-Sham density functional method counterparts, but suffer from large errors upon using one or more of these approximations: the limited size of the atomic orbital basis, the Slater monopole auxiliary basis description of the response density, and the one- and two-body treatment of the core-Hamiltonian matrix elements. In the process of discussing these approximations and highlighting their symptoms, we introduce a new model that supplements the second-order density-functional tight-binding model with a self-consistent charge-dependent chemical potential equalization correction; we review our recently reported method for generalizing the auxiliary basis description of the atomic orbital response density; and we decompose the first-order potential into a summation of additive atomic components and many-body corrections, and from this examination, we provide new insights and preliminary results that motivate and inspire new approximate treatments of the core-Hamiltonian.

Waveguide superconducting single-photon autocorrelators for quantum photonic applications

NARCIS (Netherlands)

Sahin, D.; Gaggero, A.; Frucci, G.; Jahanmirinejad, S.; Sprengers, J.P.; Mattioli, F.; Leoni, R.; Beetz, J.; Lermer, M.; Kamp, M.; Höfling, S.; Fiore, A.; Hasan, Z.U.; Hemmer, P.R.; Lee, H.; Santori, C.M.

2013-01-01

We report a novel component for integrated quantum photonic applications, a waveguide single-photon autocorrelator. It is based on two superconducting nanowire detectors patterned onto the same GaAs ridge waveguide. Combining the electrical output of the two detectors in a correlation card enables

Periodic subsystem density-functional theory

International Nuclear Information System (INIS)

Genova, Alessandro; Pavanello, Michele; Ceresoli, Davide

2014-01-01

By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn–Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn–Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy density functionals that go beyond the GGA level must be employed

Periodic subsystem density-functional theory

Science.gov (United States)

Genova, Alessandro; Ceresoli, Davide; Pavanello, Michele

2014-11-01

By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn-Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn-Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy density functionals that go beyond the GGA level must be employed.

Performances of estimators of linear auto-correlated error model ...

African Journals Online (AJOL)

The performances of five estimators of linear models with autocorrelated disturbance terms are compared when the independent variable is exponential. The results reveal that for both small and large samples, the Ordinary Least Squares (OLS) compares favourably with the Generalized least Squares (GLS) estimators in ...

Quantal density functional theory

CERN Document Server

Sahni, Viraht

2016-01-01

This book deals with quantal density functional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The treated time-independent QDFT constitutes a special case. In the 2nd edition, the theory is extended to include the presence of external magnetostatic fields. The theory is a description of matter based on the ‘quantal Newtonian’ first and second laws which is in terms of “classical” fields that pervade all space, and their quantal sources. The fields, which are explicitly defined, are separately representative of electron correlations due to the Pauli exclusion principle, Coulomb repulsion, correlation-kinetic, correlation-current-density, and correlation-magnetic effects. The book further describes Schrödinger theory from the new physical perspective of fields and quantal sources. It also describes traditional Hohenberg-Kohn-Sham DFT, and explains via QDFT the physics underlying the various energy functionals and functional derivatives o...

Reduced density matrix functional theory via a wave function based approach

Energy Technology Data Exchange (ETDEWEB)

Schade, Robert; Bloechl, Peter [Institute for Theoretical Physics, Clausthal University of Technology, Clausthal (Germany); Pruschke, Thomas [Institute for Theoretical Physics, University of Goettingen, Goettingen (Germany)

2016-07-01

We propose a new method for the calculation of the electronic and atomic structure of correlated electron systems based on reduced density matrix functional theory (rDMFT). The density-matrix functional is evaluated on the fly using Levy's constrained search formalism. The present implementation rests on a local approximation of the interaction reminiscent to that of dynamical mean field theory (DMFT). We focus here on additional approximations to the exact density-matrix functional in the local approximation and evaluate their performance.

A real-space stochastic density matrix approach for density functional electronic structure.

Science.gov (United States)

Beck, Thomas L

2015-12-21

The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.

Decay of autoionizing states in time-dependent density functional and reduced density matrix functional theory

Energy Technology Data Exchange (ETDEWEB)

Kapoor, Varun; Brics, Martins; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)

2013-07-01

Autoionizing states are inaccessible to time-dependent density functional theory (TDDFT) using known, adiabatic Kohn-Sham (KS) potentials. We determine the exact KS potential for a numerically exactly solvable model Helium atom interacting with a laser field that is populating an autoionizing state. The exact single-particle density of the population in the autoionizing state corresponds to that of the energetically lowest quasi-stationary state in the exact KS potential. We describe how this exact potential controls the decay by a barrier whose height and width allows for the density to tunnel out and decay with the same rate as in the ab initio time-dependent Schroedinger calculation. However, devising a useful exchange-correlation potential that is capable of governing such a scenario in general and in more complex systems is hopeless. As an improvement over TDDFT, time-dependent reduced density matrix functional theory has been proposed. We are able to obtain for the above described autoionization process the exact time-dependent natural orbitals (i.e., the eigenfunctions of the exact, time-dependent one-body reduced density matrix) and study the potentials that appear in the equations of motion for the natural orbitals and the structure of the two-body density matrix expanded in them.

Can spatial autocorrelation method be applied to arbitrary array shape; Kukan jiko sokanho no nin`i array eno tekiyo kanosei

Energy Technology Data Exchange (ETDEWEB)

Yamamoto, H; Iwamoto, K; Saito, T; Tachibana, M [Iwate University, Iwate (Japan). Faculty of Engineering

1997-05-27

Methods to learn underground structures by utilizing the dispersion phenomenon of surface waves contained in microtremors include the frequency-wave number analysis method (the F-K method) and the spatial autocorrelation method (the SAC method). Despite the fact that the SAC method is capable of exploring structures at greater depths, the method is not utilized because of its stringent restriction in arrangement of seismometers during observation that they must be arranged evenly on the same circumference. In order to eliminate this restriction in the SAC method, a research group in the Hokuriku University has proposed an expanded spatial autocorrelation (ESAC) method. Using the concept of the ESAC method as its base, a method was realized to improve phase velocity estimation by making a simulation on an array shifted to the radius direction. As a result of the discussion, it was found that the proposed improvement method can be applied to places where waves come from a number of directions, such as urban areas. If the improvement method can be applied, the spatial autocorrelation function needs not be even in the circumferential direction. In other words, the SAC method can be applied to arbitrary arrays. 1 ref., 7 figs.

Self-Interaction Error in Density Functional Theory: An Appraisal.

Science.gov (United States)

Bao, Junwei Lucas; Gagliardi, Laura; Truhlar, Donald G

2018-05-03

Self-interaction error (SIE) is considered to be one of the major sources of error in most approximate exchange-correlation functionals for Kohn-Sham density-functional theory (KS-DFT), and it is large with all local exchange-correlation functionals and with some hybrid functionals. In this work, we consider systems conventionally considered to be dominated by SIE. For these systems, we demonstrate that by using multiconfiguration pair-density functional theory (MC-PDFT), the error of a translated local density-functional approximation is significantly reduced (by a factor of 3) when using an MCSCF density and on-top density, as compared to using KS-DFT with the parent functional; the error in MC-PDFT with local on-top functionals is even lower than the error in some popular KS-DFT hybrid functionals. Density-functional theory, either in MC-PDFT form with local on-top functionals or in KS-DFT form with some functionals having 50% or more nonlocal exchange, has smaller errors for SIE-prone systems than does CASSCF, which has no SIE.

Distributions of Autocorrelated First-Order Kinetic Outcomes: Illness Severity.

Directory of Open Access Journals (Sweden)

James D Englehardt

Full Text Available Many complex systems produce outcomes having recurring, power law-like distributions over wide ranges. However, the form necessarily breaks down at extremes, whereas the Weibull distribution has been demonstrated over the full observed range. Here the Weibull distribution is derived as the asymptotic distribution of generalized first-order kinetic processes, with convergence driven by autocorrelation, and entropy maximization subject to finite positive mean, of the incremental compounding rates. Process increments represent multiplicative causes. In particular, illness severities are modeled as such, occurring in proportion to products of, e.g., chronic toxicant fractions passed by organs along a pathway, or rates of interacting oncogenic mutations. The Weibull form is also argued theoretically and by simulation to be robust to the onset of saturation kinetics. The Weibull exponential parameter is shown to indicate the number and widths of the first-order compounding increments, the extent of rate autocorrelation, and the degree to which process increments are distributed exponential. In contrast with the Gaussian result in linear independent systems, the form is driven not by independence and multiplicity of process increments, but by increment autocorrelation and entropy. In some physical systems the form may be attracting, due to multiplicative evolution of outcome magnitudes towards extreme values potentially much larger and smaller than control mechanisms can contain. The Weibull distribution is demonstrated in preference to the lognormal and Pareto I for illness severities versus (a toxicokinetic models, (b biologically-based network models, (c scholastic and psychological test score data for children with prenatal mercury exposure, and (d time-to-tumor data of the ED01 study.

Density functional theory and parallel processing

International Nuclear Information System (INIS)

Ward, R.C.; Geist, G.A.; Butler, W.H.

1987-01-01

The authors demonstrate a method for obtaining the ground state energies and charge densities of a system of atoms described within density functional theory using simulated annealing on a parallel computer

Rational Density Functional Selection Using Game Theory.

Science.gov (United States)

McAnanama-Brereton, Suzanne; Waller, Mark P

2018-01-22

Theoretical chemistry has a paradox of choice due to the availability of a myriad of density functionals and basis sets. Traditionally, a particular density functional is chosen on the basis of the level of user expertise (i.e., subjective experiences). Herein we circumvent the user-centric selection procedure by describing a novel approach for objectively selecting a particular functional for a given application. We achieve this by employing game theory to identify optimal functional/basis set combinations. A three-player (accuracy, complexity, and similarity) game is devised, through which Nash equilibrium solutions can be obtained. This approach has the advantage that results can be systematically improved by enlarging the underlying knowledge base, and the deterministic selection procedure mathematically justifies the density functional and basis set selections.

Estimating the variation, autocorrelation, and environmental sensitivity of phenotypic selection

NARCIS (Netherlands)

Chevin, Luis-Miguel; Visser, Marcel E.; Tufto, Jarle

2015-01-01

Despite considerable interest in temporal and spatial variation of phenotypic selection, very few methods allow quantifying this variation while correctly accounting for the error variance of each individual estimate. Furthermore, the available methods do not estimate the autocorrelation of

Estimating the variation, autocorrelation, and environmental sensitivity of phenotypic selection

NARCIS (Netherlands)

Chevin, Luis-Miguel; Visser, Marcel E.; Tufto, Jarle

Despite considerable interest in temporal and spatial variation of phenotypic selection, very few methods allow quantifying this variation while correctly accounting for the error variance of each individual estimate. Furthermore, the available methods do not estimate the autocorrelation of

Building a three-dimensional model of CYP2C9 inhibition using the Autocorrelator: an autonomous model generator.

Science.gov (United States)

Lardy, Matthew A; Lebrun, Laurie; Bullard, Drew; Kissinger, Charles; Gobbi, Alberto

2012-05-25

In modern day drug discovery campaigns, computational chemists have to be concerned not only about improving the potency of molecules but also reducing any off-target ADMET activity. There are a plethora of antitargets that computational chemists may have to consider. Fortunately many antitargets have crystal structures deposited in the PDB. These structures are immediately useful to our Autocorrelator: an automated model generator that optimizes variables for building computational models. This paper describes the use of the Autocorrelator to construct high quality docking models for cytochrome P450 2C9 (CYP2C9) from two publicly available crystal structures. Both models result in strong correlation coefficients (R² > 0.66) between the predicted and experimental determined log(IC₅₀) values. Results from the two models overlap well with each other, converging on the same scoring function, deprotonated charge state, and predicted the binding orientation for our collection of molecules.

Subsystem density functional theory with meta-generalized gradient approximation exchange-correlation functionals.

Science.gov (United States)

Śmiga, Szymon; Fabiano, Eduardo; Laricchia, Savio; Constantin, Lucian A; Della Sala, Fabio

2015-04-21

We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes this limitation and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method.

Incorporating spatial autocorrelation into species distribution models alters forecasts of climate-mediated range shifts.

Science.gov (United States)

Crase, Beth; Liedloff, Adam; Vesk, Peter A; Fukuda, Yusuke; Wintle, Brendan A

2014-08-01

Species distribution models (SDMs) are widely used to forecast changes in the spatial distributions of species and communities in response to climate change. However, spatial autocorrelation (SA) is rarely accounted for in these models, despite its ubiquity in broad-scale ecological data. While spatial autocorrelation in model residuals is known to result in biased parameter estimates and the inflation of type I errors, the influence of unmodeled SA on species' range forecasts is poorly understood. Here we quantify how accounting for SA in SDMs influences the magnitude of range shift forecasts produced by SDMs for multiple climate change scenarios. SDMs were fitted to simulated data with a known autocorrelation structure, and to field observations of three mangrove communities from northern Australia displaying strong spatial autocorrelation. Three modeling approaches were implemented: environment-only models (most frequently applied in species' range forecasts), and two approaches that incorporate SA; autologistic models and residuals autocovariate (RAC) models. Differences in forecasts among modeling approaches and climate scenarios were quantified. While all model predictions at the current time closely matched that of the actual current distribution of the mangrove communities, under the climate change scenarios environment-only models forecast substantially greater range shifts than models incorporating SA. Furthermore, the magnitude of these differences intensified with increasing increments of climate change across the scenarios. When models do not account for SA, forecasts of species' range shifts indicate more extreme impacts of climate change, compared to models that explicitly account for SA. Therefore, where biological or population processes induce substantial autocorrelation in the distribution of organisms, and this is not modeled, model predictions will be inaccurate. These results have global importance for conservation efforts as inaccurate

Uniform magnetic fields in density-functional theory

Science.gov (United States)

Tellgren, Erik I.; Laestadius, Andre; Helgaker, Trygve; Kvaal, Simen; Teale, Andrew M.

2018-01-01

We construct a density-functional formalism adapted to uniform external magnetic fields that is intermediate between conventional density functional theory and Current-Density Functional Theory (CDFT). In the intermediate theory, which we term linear vector potential-DFT (LDFT), the basic variables are the density, the canonical momentum, and the paramagnetic contribution to the magnetic moment. Both a constrained-search formulation and a convex formulation in terms of Legendre-Fenchel transformations are constructed. Many theoretical issues in CDFT find simplified analogs in LDFT. We prove results concerning N-representability, Hohenberg-Kohn-like mappings, existence of minimizers in the constrained-search expression, and a restricted analog to gauge invariance. The issue of additivity of the energy over non-interacting subsystems, which is qualitatively different in LDFT and CDFT, is also discussed.

Recursive Estimation for Dynamical Systems with Different Delay Rates Sensor Network and Autocorrelated Process Noises

Directory of Open Access Journals (Sweden)

Jianxin Feng

2014-01-01

Full Text Available The recursive estimation problem is studied for a class of uncertain dynamical systems with different delay rates sensor network and autocorrelated process noises. The process noises are assumed to be autocorrelated across time and the autocorrelation property is described by the covariances between different time instants. The system model under consideration is subject to multiplicative noises or stochastic uncertainties. The sensor delay phenomenon occurs in a random way and each sensor in the sensor network has an individual delay rate which is characterized by a binary switching sequence obeying a conditional probability distribution. By using the orthogonal projection theorem and an innovation analysis approach, the desired recursive robust estimators including recursive robust filter, predictor, and smoother are obtained. Simulation results are provided to demonstrate the effectiveness of the proposed approaches.

What autocorrelation tells us about motor variability: insights from dart throwing.

Directory of Open Access Journals (Sweden)

Robert J van Beers

Full Text Available In sports such as golf and darts it is important that one can produce ballistic movements of an object towards a goal location with as little variability as possible. A factor that influences this variability is the extent to which motor planning is updated from movement to movement based on observed errors. Previous work has shown that for reaching movements, our motor system uses the learning rate (the proportion of an error that is corrected for in the planning of the next movement that is optimal for minimizing the endpoint variability. Here we examined whether the learning rate is hard-wired and therefore automatically optimal, or whether it is optimized through experience. We compared the performance of experienced dart players and beginners in a dart task. A hallmark of the optimal learning rate is that the lag-1 autocorrelation of movement endpoints is zero. We found that the lag-1 autocorrelation of experienced dart players was near zero, implying a near-optimal learning rate, whereas it was negative for beginners, suggesting a larger than optimal learning rate. We conclude that learning rates for trial-by-trial motor learning are optimized through experience. This study also highlights the usefulness of the lag-1 autocorrelation as an index of performance in studying motor-skill learning.

density functional theory approach

Indian Academy of Sciences (India)

YOGESH ERANDE

2017-07-27

Jul 27, 2017 ... a key role in all optical switching devices, since their optical properties can be .... optimized in the gas phase using Density Functional Theory. (DFT).39 The ...... The Mediation of Electrostatic Effects by Sol- vents J. Am. Chem.

Strong Correlation in Kohn-Sham Density Functional Theory

NARCIS (Netherlands)

Malet, F.; Gori Giorgi, P.

2012-01-01

We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to approximate the exchange-correlation energy of the restricted Kohn-Sham scheme. Our approximation corresponds to a highly nonlocal density functional whose functional derivative can be easily constructed,

Multiconfiguration Pair-Density Functional Theory Outperforms Kohn-Sham Density Functional Theory and Multireference Perturbation Theory for Ground-State and Excited-State Charge Transfer.

Science.gov (United States)

Ghosh, Soumen; Sonnenberger, Andrew L; Hoyer, Chad E; Truhlar, Donald G; Gagliardi, Laura

2015-08-11

The correct description of charge transfer in ground and excited states is very important for molecular interactions, photochemistry, electrochemistry, and charge transport, but it is very challenging for Kohn-Sham (KS) density functional theory (DFT). KS-DFT exchange-correlation functionals without nonlocal exchange fail to describe both ground- and excited-state charge transfer properly. We have recently proposed a theory called multiconfiguration pair-density functional theory (MC-PDFT), which is based on a combination of multiconfiguration wave function theory with a new type of density functional called an on-top density functional. Here we have used MC-PDFT to study challenging ground- and excited-state charge-transfer processes by using on-top density functionals obtained by translating KS exchange-correlation functionals. For ground-state charge transfer, MC-PDFT performs better than either the PBE exchange-correlation functional or CASPT2 wave function theory. For excited-state charge transfer, MC-PDFT (unlike KS-DFT) shows qualitatively correct behavior at long-range with great improvement in predicted excitation energies.

Coded aperture imagery filtered autocorrelation decoding; Imagerie par ouverture de codage decodage par autocorrelation filtree

Energy Technology Data Exchange (ETDEWEB)

Rouyer, A. [CEA Bruyeres-le-Chatel, 91 (France)

2005-10-15

Coded aperture imagery is particularly suited for imaging objects emitting penetrating radiation (hard X rays, gamma, neutrons), or for particles with rectilinear trajectories (electrons, protons, alpha particles, etc.). It is used when methods based on classical optical principles (reflection, refraction, diffraction), are invalid, or when the source emission is too weak for the well known pinhole method to give a usable image. The optical system consists in an aperture through an absorbing screen, named coding aperture, whose transmission is calculated in such a way that the spatial resolution is similar to that of a simple pinhole device, but with a far superior radiation collecting efficiency. We present a new decoding method,, called filtered autocorrelation, and illustrate its performances on images obtained with various coding apertures. (author)

Functional renormalization group and Kohn-Sham scheme in density functional theory

Science.gov (United States)

Liang, Haozhao; Niu, Yifei; Hatsuda, Tetsuo

2018-04-01

Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the φ4 theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.

Measurement of reactor parameters of the 'Nora' reactor by noise analysis method - power spectral density

International Nuclear Information System (INIS)

Jovanovic, S.; Stormark, E.

1966-01-01

Measurements of reactor parameters the Nora reactor by Power Spectral Density (PSD) method are described. In case of critical reactor this method was applied for direct measurement of β/l ratio, β is the effective yield of delayed neutrons and l is the neutron lifetime. In case of subcritical reactor values of α+β-ρ/l were measured, ρ is the negative reactivity. Out coming PSD was measured by a filter or by ISAC. PSD was registered by ISAC as well as the auto-correlation function [sr

Density functional theory: Foundations reviewed

Energy Technology Data Exchange (ETDEWEB)

Kryachko, Eugene S., E-mail: eugene.kryachko@ulg.ac.be [Bogolyubov Institute for Theoretical Physics, Kiev, 03680 (Ukraine); Ludeña, Eduardo V., E-mail: popluabe@yahoo.es [Centro de Química, Instituto Venezolano de Investigaciones Científicas, IVIC, Apartado 21827, Caracas 1020-A (Venezuela, Bolivarian Republic of); Prometheus Program, Senescyt (Ecuador); Grupo Ecuatoriano para el Estudio Experimental y Teórico de Nanosistemas, GETNano, USFQ, N104-E, Quito (Ecuador); Escuela Politécnica Superior del Litoral, ESPOL, Guayaquil (Ecuador)

2014-11-10

Guided by the above motto (quotation), we review a broad range of issues lying at the foundations of Density Functional Theory, DFT, a theory which is currently omnipresent in our everyday computational study of atoms and molecules, solids and nano-materials, and which lies at the heart of modern many-body computational technologies. The key goal is to demonstrate that there are definitely the ways to improve DFT. We start by considering DFT in the larger context provided by reduced density matrix theory (RDMT) and natural orbital functional theory (NOFT), and examine the implications that N-representability conditions on the second-order reduced density matrix (2-RDM) have not only on RDMT and NOFT but, also, by extension, on the functionals of DFT. This examination is timely in view of the fact that necessary and sufficient N-representability conditions on the 2-RDM have recently been attained. In the second place, we review some problems appearing in the original formulation of the first Hohenberg–Kohn theorem which is still a subject of some controversy. In this vein we recall Lieb’s comment on this proof and the extension to this proof given by Pino et al. (2009), and in this context examine the conditions that must be met in order that the one-to-one correspondence between ground-state densities and external potentials remains valid for finite subspaces (namely, the subspaces where all Kohn–Sham solutions are obtained in practical applications). We also consider the issue of whether the Kohn–Sham equations can be derived from basic principles or whether they are postulated. We examine this problem in relation to ab initio DFT. The possibility of postulating arbitrary Kohn–Sham-type equations, where the effective potential is by definition some arbitrary mixture of local and non-local terms, is discussed. We also deal with the issue of whether there exists a universal functional, or whether one should advocate instead the construction of problem

Linear scaling of density functional algorithms

International Nuclear Information System (INIS)

Stechel, E.B.; Feibelman, P.J.; Williams, A.R.

1993-01-01

An efficient density functional algorithm (DFA) that scales linearly with system size will revolutionize electronic structure calculations. Density functional calculations are reliable and accurate in determining many condensed matter and molecular ground-state properties. However, because current DFA's, including methods related to that of Car and Parrinello, scale with the cube of the system size, density functional studies are not routinely applied to large systems. Linear scaling is achieved by constructing functions that are both localized and fully occupied, thereby eliminating the need to calculate global eigenfunctions. It is, however, widely believed that exponential localization requires the existence of an energy gap between the occupied and unoccupied states. Despite this, the authors demonstrate that linear scaling can still be achieved for metals. Using a linear scaling algorithm, they have explicitly constructed localized, almost fully occupied orbitals for the quintessential metallic system, jellium. The algorithm is readily generalizable to any system geometry and Hamiltonian. They will discuss the conceptual issues involved, convergence properties and scaling for their new algorithm

Density-Functional formalism

International Nuclear Information System (INIS)

Szasz, L.; Berrios-Pagan, I.; McGinn, G.

1975-01-01

A new Density-Functional formula is constructed for atoms. The kinetic energy of the electron is divided into two parts: the kinetic self-energy and the orthogonalization energy. Calculations were made for the total energies of neutral atoms, positive ions and for the He isoelectronic series. For neutral atoms the results match the Hartree-Fock energies within 1% for atoms with N 36 the results generally match the HF energies within 0.1%. For positive ions the results are fair; for the molecular applications a simplified model is developed in which the kinetic energy consists of the Weizsaecker term plus the Fermi energy reduced by a continuous function. (orig.) [de

Density-functional, density-functional tight-binding, and wave-function calculations on biomolecular systems

Czech Academy of Sciences Publication Activity Database

Kubař, Tomáš; Jurečka, Petr; Černý, Jiří; Řezáč, Jan; Otyepka, M.; Valdes, Haydee; Hobza, Pavel

2007-01-01

Roč. 111, č. 26 (2007), s. 5642-5647 ISSN 1089-5639 R&D Projects: GA MŠk LC512; GA AV ČR IAA400550510; GA ČR(CZ) GD203/05/H001; GA ČR GA203/05/0009 Institutional research plan: CEZ:AV0Z40550506 Keywords : density functional theory * empirical dispersion-energy term * non-covalent interactions Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.918, year: 2007

The force distribution probability function for simple fluids by density functional theory.

Science.gov (United States)

Rickayzen, G; Heyes, D M

2013-02-28

Classical density functional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory.

Real-time autocorrelator for fluorescence correlation spectroscopy based on graphical-processor-unit architecture: method, implementation, and comparative studies

Science.gov (United States)

Laracuente, Nicholas; Grossman, Carl

2013-03-01

We developed an algorithm and software to calculate autocorrelation functions from real-time photon-counting data using the fast, parallel capabilities of graphical processor units (GPUs). Recent developments in hardware and software have allowed for general purpose computing with inexpensive GPU hardware. These devices are more suited for emulating hardware autocorrelators than traditional CPU-based software applications by emphasizing parallel throughput over sequential speed. Incoming data are binned in a standard multi-tau scheme with configurable points-per-bin size and are mapped into a GPU memory pattern to reduce time-expensive memory access. Applications include dynamic light scattering (DLS) and fluorescence correlation spectroscopy (FCS) experiments. We ran the software on a 64-core graphics pci card in a 3.2 GHz Intel i5 CPU based computer running Linux. FCS measurements were made on Alexa-546 and Texas Red dyes in a standard buffer (PBS). Software correlations were compared to hardware correlator measurements on the same signals. Supported by HHMI and Swarthmore College

Versatile Density Functionals for Computational Surface Science

DEFF Research Database (Denmark)

Wellendorff, Jess

Density functional theory (DFT) emerged almost 50 years ago. Since then DFT has established itself as the central electronic structure methodology for simulating atomicscale systems from a few atoms to a few hundred atoms. This success of DFT is due to a very favorable accuracy-to-computational c......Density functional theory (DFT) emerged almost 50 years ago. Since then DFT has established itself as the central electronic structure methodology for simulating atomicscale systems from a few atoms to a few hundred atoms. This success of DFT is due to a very favorable accuracy...... resampling techniques, thereby systematically avoiding problems with overfitting. The first ever density functional presenting both reliable accuracy and convincing error estimation is generated. The methodology is general enough to be applied to more complex functional forms with higher-dimensional fitting...

Local and linear chemical reactivity response functions at finite temperature in density functional theory

International Nuclear Information System (INIS)

Franco-Pérez, Marco; Ayers, Paul W.; Gázquez, José L.; Vela, Alberto

2015-01-01

We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model

Autocorrelation exponent of conserved spin systems in the scaling regime following a critical quench.

Science.gov (United States)

Sire, Clément

2004-09-24

We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length L(t) approximately t(1/z), we find that for times t' and t satisfying L(t')infinity limit, we show that lambda(')(c)=d+2 and phi=z/2. We give a heuristic argument suggesting that this result is, in fact, valid for any dimension d and spin vector dimension n. We present numerical simulations for the conserved Ising model in d=1 and d=2, which are fully consistent with the present theory.

A single-shot nonlinear autocorrelation approach for time-resolved physics in the vacuum ultraviolet spectral range

International Nuclear Information System (INIS)

Rompotis, Dimitrios

2016-02-01

In this work, a single-shot temporal metrology scheme operating in the vacuum-extreme ultraviolet spectral range has been designed and experimentally implemented. Utilizing an anti-collinear geometry, a second-order intensity autocorrelation measurement of a vacuum ultraviolet pulse can be performed by encoding temporal delay information on the beam propagation coordinate. An ion-imaging time-of-flight spectrometer, offering micrometer resolution has been set-up for this purpose. This instrument enables the detection of a magnified image of the spatial distribution of ions exclusively generated by direct two-photon absorption in the combined counter-propagating pulse focus and thus obtain the second-order intensity autocorrelation measurement on a single-shot basis. Additionally, an intense VUV light source based on high-harmonic generation has been experimentally realized. It delivers intense sub-20 fs Ti:Sa fifth-harmonic pulses utilizing a loose-focusing geometry in a long Ar gas cell. The VUV pulses centered at 161.8 nm reach pulse energies of 1.1 μJ per pulse, while the corresponding pulse duration is measured with a second-order, fringe-resolved autocorrelation scheme to be 18 ± 1 fs on average. Non-resonant, two-photon ionization of Kr and Xe and three-photon ionization of Ne verify the fifth-harmonic pulse intensity and indicate the feasibility of multi-photon VUV pump/VUV probe studies of ultrafast atomic and molecular dynamics. Finally, the extended functionally of the counter-propagating pulse metrology approach is demonstrated by a single-shot VUV pump/VUV probe experiment aiming at the investigation of ultrafast dissociation dynamics of O 2 excited in the Schumann-Runge continuum at 162 nm.

The Effect of Autocorrelation on the Hotelling T-2 Control Chart

DEFF Research Database (Denmark)

Vanhatalo, Erik; Kulahci, Murat

2015-01-01

One of the basic assumptions for traditional univariate and multivariate control charts is that the data are independent in time. For the latter, in many cases, the data are serially dependent (autocorrelated) and cross-correlated because of, for example, frequent sampling and process dynamics......- correlation structures for different magnitudes of shifts in the process mean is not fully explored in the literature. In this article, the performance of the Hotelling T-2 control chart for different shift sizes and various autocorrelation and cross- correlation structures are compared based on the average...... and using the raw data with adjusted control limits calculated through Monte Carlo simulations; and (iii) constructing the control chart for the residuals from a multivariate time series model fitted to the raw data. To limit the complexity, we use a first-order vector autoregressive process and focus...

A Safari Through Density Functional Theory

Science.gov (United States)

Dreizler, Reiner M.; Lüdde, Cora S.

Density functional theory is widely used to treat quantum many body problems in many areas of physics and related fields. A brief survey of this method covering foundations, functionals and applications is presented here.

How cosmic microwave background correlations at large angles relate to mass autocorrelations in space

Science.gov (United States)

Blumenthal, George R.; Johnston, Kathryn V.

1994-01-01

The Sachs-Wolfe effect is known to produce large angular scale fluctuations in the cosmic microwave background radiation (CMBR) due to gravitational potential fluctuations. We show how the angular correlation function of the CMBR can be expressed explicitly in terms of the mass autocorrelation function xi(r) in the universe. We derive analytic expressions for the angular correlation function and its multipole moments in terms of integrals over xi(r) or its second moment, J(sub 3)(r), which does not need to satisfy the sort of integral constraint that xi(r) must. We derive similar expressions for bulk flow velocity in terms of xi and J(sub 3). One interesting result that emerges directly from this analysis is that, for all angles theta, there is a substantial contribution to the correlation function from a wide range of distance r and that radial shape of this contribution does not vary greatly with angle.

Comparison of exact-exchange calculations for solids in current-spin-density- and spin-density-functional theory

DEFF Research Database (Denmark)

Sharma, S.; Pittalis, S.; Kurth, S.

2007-01-01

The relative merits of current-spin-density- and spin-density-functional theory are investigated for solids treated within the exact-exchange-only approximation. Spin-orbit splittings and orbital magnetic moments are determined at zero external magnetic field. We find that for magnetic (Fe, Co......, and Ni) and nonmagnetic (Si and Ge) solids, the exact-exchange current-spin-density functional approach does not significantly improve the accuracy of the corresponding spin-density functional results....

Dynamical density functional theory for dense atomic liquids

International Nuclear Information System (INIS)

Archer, A J

2006-01-01

Starting from Newton's equations of motion, we derive a dynamical density functional theory (DDFT) applicable to atomic liquids. The theory has the feature that it requires as input the Helmholtz free energy functional from equilibrium density functional theory. This means that, given a reliable equilibrium free energy functional, the correct equilibrium fluid density profile is guaranteed. We show that when the isothermal compressibility is small, the DDFT generates the correct value for the speed of sound in a dense liquid. We also interpret the theory as a dynamical equation for a coarse grained fluid density and show that the theory can be used (making further approximations) to derive the standard mode coupling theory that is used to describe the glass transition. The present theory should provide a useful starting point for describing the dynamics of inhomogeneous atomic fluids

Constructive definition of functional derivatives in density-functional theory

International Nuclear Information System (INIS)

Luo Ji

2006-01-01

It is shown that the functional derivatives in density-functional theory (DFT) can be explicitly defined within the domain of electron densities restricted by the electron number, and a constructive definition of such restricted derivatives is suggested. With this definition, Kohn-Sham (KS) equations can be established for an N-electron system without extending the functional domain and introducing a Lagrange multiplier. This may clarify some of the fundamental questions raised by Nesbet (1998 Phys. Rev. A 58 R12). The definition naturally leads to the fact that the KS effective potential is determined only to within an additive constant, thus the KS levels can shift freely and the relation between the highest occupied molecular orbital (HOMO) energy and the ionization potential of the system depends on the choice of the constant. On the other hand, if the domain of functionals is indeed extended beyond the electron number restriction, conclusions depend on whether the extended functionals have unrestricted derivatives or not. It is shown that the ensemble extension of DFT to open systems of mixed states (Perdew et al 1982 Phys. Rev. Lett. 49 1691) leads to an energy functional which has no unrestricted derivative at integer electron numbers. Hence after this extension, the relation between the HOMO energy and the ionization potential for an N-electron system is still uncertain. Besides, there are different extensions of the energy functional to a domain of densities unrestricted by the integer electron number, resulting in different unrestricted derivatives and electron systems with different chemical potentials. Even for the exact exchange-correlation potential, there is still an undetermined constant, whether it is a restricted or unrestricted derivative

Density functional theory in quantum chemistry

CERN Document Server

Tsuneda, Takao

2014-01-01

This book examines density functional theory based on the foundation of quantum chemistry. Unconventional in approach, it reviews basic concepts, then describes the physical meanings of state-of-the-art exchange-correlation functionals and their corrections.

Comment on 'Kinetic energy as a density functional'

International Nuclear Information System (INIS)

Holas, A.; March, N.H.

2002-01-01

In a recent paper, Nesbet [Phys. Rev. A 65, 010502(R) (2001)] has proposed dropping ''the widespread but unjustified assumption that the existence of a ground-state density functional for the kinetic energy, T s [ρ], of an N-electron system implies the existence of a density-functional derivative, δT s [ρ]/δρ(r), equivalent to a local potential function,'' because, according to his arguments, this derivative 'has the mathematical character of a linear operator that acts on orbital wave functions'. Our Comment demonstrates that the statement called by Nesbet an 'unjustified assumption' happens, in fact, to be a rigorously proven theorem. Therefore, his previous conclusions stemming from his different view of this derivative, which undermined the foundations of density-functional theory, can be discounted

SYNTHESIS, CHARACTERIZATION AND DENSITY FUNCTIONAL ...

African Journals Online (AJOL)

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We synthesized a number of aniline derivatives containing acyl groups to compare their barriers of rotation around ... KEY WORDS: Monoacyl aniline, Synthesis, Density functional theory, Rotation barrier. INTRODUCTION. Developments in ...

Density functional approach to the many-body problem : Key concepts and exact functionals

NARCIS (Netherlands)

van Leeuwen, Robert

2003-01-01

We give an overview of the fundamental concepts of density functional theory. We give a careful discussion of the several density functionals and their differentiability properties. We show that for nondegenerate ground states we can calculate the necessary functional derivatives by means of linear

Extended screened exchange functional derived from transcorrelated density functional theory.

Science.gov (United States)

Umezawa, Naoto

2017-09-14

We propose a new formulation of the correlation energy functional derived from the transcorrelated method in use in density functional theory (TC-DFT). An effective Hamiltonian, H TC , is introduced by a similarity transformation of a many-body Hamiltonian, H, with respect to a complex function F: H TC =1FHF. It is proved that an expectation value of H TC for a normalized single Slater determinant, D n , corresponds to the total energy: E[n] = ⟨Ψ n |H|Ψ n ⟩/⟨Ψ n |Ψ n ⟩ = ⟨D n |H TC |D n ⟩ under the two assumptions: (1) The electron density nr associated with a trial wave function Ψ n = D n F is v-representable and (2) Ψ n and D n give rise to the same electron density nr. This formulation, therefore, provides an alternative expression of the total energy that is useful for the development of novel correlation energy functionals. By substituting a specific function for F, we successfully derived a model correlation energy functional, which resembles the functional form of the screened exchange method. The proposed functional, named the extended screened exchange (ESX) functional, is described within two-body integrals and is parametrized for a numerically exact correlation energy of the homogeneous electron gas. The ESX functional does not contain any ingredients of (semi-)local functionals and thus is totally free from self-interactions. The computational cost for solving the self-consistent-field equation is comparable to that of the Hartree-Fock method. We apply the ESX functional to electronic structure calculations for a solid silicon, H - ion, and small atoms. The results demonstrate that the TC-DFT formulation is promising for the systematic improvement of the correlation energy functional.

Toward sub-femtosecond pump-probe experiments: a dispersionless autocorrelator with attosecond resolution

Energy Technology Data Exchange (ETDEWEB)

Constant, E.; Mevel, E.; Zair, A.; Bagnoud, V.; Salin, F. [Bordeaux-1 Univ., Talence (FR). Centre Lasers Intenses et Applications (CELIA)

2001-07-01

We designed a dispersionless autocorrelator with a sub-femtosecond resolution suitable for the characterization of ultrashort X-UV pulses. We present a proof of feasibility experiment with 11 fs infrared pulses. (orig.)

Quantum Crystallography: Density Matrix-Density Functional Theory and the X-Ray Diffraction Experiment

Science.gov (United States)

Soirat, Arnaud J. A.

Density Matrix Theory is a Quantum Mechanical formalism in which the wavefunction is eliminated and its role taken over by reduced density matrices. The interest of this is that, it allows one, in principle, to calculate any electronic property of a physical system, without having to solve the Schrodinger equation, using only two entities much simpler than an N-body wavefunction: first and second -order reduced density matrices. In practice, though, this very promising possibility faces the tremendous theoretical problem of N-representability, which has been solved for the former, but, until now, voids any hope of theoretically determining the latter. However, it has been shown that single determinant reduced density matrices of any order may be recovered from coherent X-ray diffraction data, if one provides a proper Quantum Mechanical description of the Crystallography experiment. A deeper investigation of this method is the purpose of this work, where we, first, further study the calculation of X-ray reduced density matrices N-representable by a single Slater determinant. In this context, we independently derive necessary and sufficient conditions for the uniqueness of the method. We then show how to account for electron correlation in this model. For the first time, indeed, we derive highly accurate, yet practical, density matrices approximately N-representable by correlated-determinant wavefunctions. The interest of such a result lies in the Quantum Mechanical validity of these density matrices, their property of being entirely obtainable from X-ray coherent diffraction data, their very high accuracy conferred by this known property of the N-representing wavefunction, as well as their definition as explicit functionals of the density. All of these properties are finally used in both a theoretical and a numerical application: in the former, we show that these density matrices may be used in the context of Density Functional Theory to highly accurately determine

Density functional theory of nuclei

International Nuclear Information System (INIS)

Terasaki, Jun

2008-01-01

The density functional theory of nuclei has come to draw attention of scientists in the field of nuclear structure because the theory is expected to provide reliable numerical data in wide range on the nuclear chart. This article is organized to present an overview of the theory to the people engaged in the theory of other fields as well as those people in the nuclear physics experiments. At first, the outline of the density functional theory widely used in the electronic systems (condensed matter, atoms, and molecules) was described starting from the Kohn-Sham equation derived on the variational principle. Then the theory used in the field of nuclear physics was presented. Hartree-Fock and Hartree-Fock-Bogolyubov approximation by using Skyrme interaction was explained. Comparison of the results of calculations and experiments of binding energies and ground state mean square charge radii of some magic number nuclei were shown. The similarity and dissimilarity between the two streams were summarized. Finally the activities of the international project of Universal Nuclear Energy Density Functional (UNEDF) which was started recently lead by US scientist was reported. This project is programmed for five years. One of the applications of the project is the calculation of the neutron capture cross section of nuclei on the r-process, which is absolutely necessary for the nucleosynthesis research. (S. Funahashi)

Estimating the Autocorrelated Error Model with Trended Data: Further Results,

Science.gov (United States)

1979-11-01

Perhaps the most serious deficiency of OLS in the presence of autocorrelation is not inefficiency but bias in its estimated standard errors--a bias...k for all t has variance var(b) = o2/ Tk2 2This refutes Maeshiro’s (1976) conjecture that "an estimator utilizing relevant extraneous information

Optimal Bandwidth Selection for Kernel Density Functionals Estimation

Directory of Open Access Journals (Sweden)

Su Chen

2015-01-01

Full Text Available The choice of bandwidth is crucial to the kernel density estimation (KDE and kernel based regression. Various bandwidth selection methods for KDE and local least square regression have been developed in the past decade. It has been known that scale and location parameters are proportional to density functionals ∫γ(xf2(xdx with appropriate choice of γ(x and furthermore equality of scale and location tests can be transformed to comparisons of the density functionals among populations. ∫γ(xf2(xdx can be estimated nonparametrically via kernel density functionals estimation (KDFE. However, the optimal bandwidth selection for KDFE of ∫γ(xf2(xdx has not been examined. We propose a method to select the optimal bandwidth for the KDFE. The idea underlying this method is to search for the optimal bandwidth by minimizing the mean square error (MSE of the KDFE. Two main practical bandwidth selection techniques for the KDFE of ∫γ(xf2(xdx are provided: Normal scale bandwidth selection (namely, “Rule of Thumb” and direct plug-in bandwidth selection. Simulation studies display that our proposed bandwidth selection methods are superior to existing density estimation bandwidth selection methods in estimating density functionals.

Current Density Functional Theory Using Meta-Generalized Gradient Exchange-Correlation Functionals.

Science.gov (United States)

Furness, James W; Verbeke, Joachim; Tellgren, Erik I; Stopkowicz, Stella; Ekström, Ulf; Helgaker, Trygve; Teale, Andrew M

2015-09-08

We present the self-consistent implementation of current-dependent (hybrid) meta-generalized gradient approximation (mGGA) density functionals using London atomic orbitals. A previously proposed generalized kinetic energy density is utilized to implement mGGAs in the framework of Kohn-Sham current density functional theory (KS-CDFT). A unique feature of the nonperturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 au (∼235 kT) in strength. CDFT functionals based on the TPSS and B98 forms are investigated, and their performance is assessed by comparison with accurate coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) data. In the weak field regime, magnetic properties such as magnetizabilities and nuclear magnetic resonance shielding constants show modest but systematic improvements over generalized gradient approximations (GGA). However, in the strong field regime, the mGGA-based forms lead to a significantly improved description of the recently proposed perpendicular paramagnetic bonding mechanism, comparing well with CCSD(T) data. In contrast to functionals based on the vorticity, these forms are found to be numerically stable, and their accuracy at high field suggests that the extension of mGGAs to CDFT via the generalized kinetic energy density should provide a useful starting point for further development of CDFT approximations.

Autocorrelation as a source of truncated Lévy flights in foreign exchange rates

Science.gov (United States)

Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Da Silva, Sergio

2003-05-01

We suggest that the ultraslow speed of convergence associated with truncated Lévy flights (Phys. Rev. Lett. 73 (1994) 2946) may well be explained by autocorrelations in data. We show how a particular type of autocorrelation generates power laws consistent with a truncated Lévy flight. Stock exchanges have been suggested to be modeled by a truncated Lévy flight (Nature 376 (1995) 46; Physica A 297 (2001) 509; Econom. Bull. 7 (2002) 1). Here foreign exchange rate data are taken instead. Scaling power laws in the “probability of return to the origin” are shown to emerge for most currencies. A novel approach to measure how distant a process is from a Gaussian regime is presented.

A Novel Acoustic Liquid Level Determination Method for Coal Seam Gas Wells Based on Autocorrelation Analysis

Directory of Open Access Journals (Sweden)

Ximing Zhang

2017-11-01

Full Text Available In coal seam gas (CSG wells, water is periodically removed from the wellbore in order to keep the bottom-hole flowing pressure at low levels, facilitating the desorption of methane gas from the coal bed. In order to calculate gas flow rate and further optimize well performance, it is necessary to accurately monitor the liquid level in real-time. This paper presents a novel method based on autocorrelation function (ACF analysis for determining the liquid level in CSG wells under intense noise conditions. The method involves the calculation of the acoustic travel time in the annulus and processing the autocorrelation signal in order to extract the weak echo under high background noise. In contrast to previous works, the non-linear dependence of the acoustic velocity on temperature and pressure is taken into account. To locate the liquid level of a coal seam gas well the travel time is computed iteratively with the non-linear velocity model. Afterwards, the proposed method is validated using experimental laboratory investigations that have been developed for liquid level detection under two scenarios, representing the combination of low pressure, weak signal, and intense noise generated by gas flowing and leakage. By adopting an evaluation indicator called Crest Factor, the results have shown the superiority of the ACF-based method compared to Fourier filtering (FFT. In the two scenarios, the maximal measurement error from the proposed method was 0.34% and 0.50%, respectively. The latent periodic characteristic of the reflected signal can be extracted by the ACF-based method even when the noise is larger than 1.42 Pa, which is impossible for FFT-based de-noising. A case study focused on a specific CSG well is presented to illustrate the feasibility of the proposed approach, and also to demonstrate that signal processing with autocorrelation analysis can improve the sensitivity of the detection system.

Comments on the locality in density-functional theory

International Nuclear Information System (INIS)

Lindgren, Ingvar; Salomonson, Sten

2003-01-01

The 'locality hypothesis' in density-functional theory (DFT), implying that the functional derivative is equivalent to a multiplicative local function, forms the basis of models of Kohn-Sham type. This has been generally accepted by the community since the advent of the model, and has later been formally proved for a large class of functionals. The hypothesis has recently been questioned by Nesbet [Phys. Rev. A 58, R12 (1998) and Phys. Rev. A 65, 010502 (2001)], who claims that it fails for the kinetic-energy functional for a system with more than two noninteracting electrons with a nondegenerate ground state. This conclusion has been questioned by Gal [Phys. Rev. A 62, 044501 (2000)] and by Holas and March [Phys. Rev. A 64, 016501 (2001)]. We claim that the arguments of Nesbet are incorrect, since the orbital functional used for the kinetic energy is not a unique functional of the total density in the domain of unnormalized orbitals. We have demonstrated that with a proper definition of the kinetic energy, which is a unique density functional also in the unnormalized region, the derivative can be represented by a single local multiplicative function for all v-representable densities. Therefore, we consider the controversy connected with the issue raised by Nesbet as resolved. We believe that the proof of the differentiability given here can be extended to larger groups of DFT functionals, and works along these lines are in progress

Trivial constraints on orbital-free kinetic energy density functionals

Science.gov (United States)

Luo, Kai; Trickey, S. B.

2018-03-01

Approximate kinetic energy density functionals (KEDFs) are central to orbital-free density functional theory. Limitations on the spatial derivative dependencies of KEDFs have been claimed from differential virial theorems. We identify a central defect in the argument: the relationships are not true for an arbitrary density but hold only for the minimizing density and corresponding chemical potential. Contrary to the claims therefore, the relationships are not constraints and provide no independent information about the spatial derivative dependencies of approximate KEDFs. A simple argument also shows that validity for arbitrary v-representable densities is not restored by appeal to the density-potential bijection.

Self-consistent embedding of density-matrix renormalization group wavefunctions in a density functional environment.

Science.gov (United States)

Dresselhaus, Thomas; Neugebauer, Johannes; Knecht, Stefan; Keller, Sebastian; Ma, Yingjin; Reiher, Markus

2015-01-28

We present the first implementation of a density matrix renormalization group algorithm embedded in an environment described by density functional theory. The frozen density embedding scheme is used with a freeze-and-thaw strategy for a self-consistent polarization of the orbital-optimized wavefunction and the environmental densities with respect to each other.

Multivariate Process Control with Autocorrelated Data

DEFF Research Database (Denmark)

Kulahci, Murat

2011-01-01

As sensor and computer technology continues to improve, it becomes a normal occurrence that we confront with high dimensional data sets. As in many areas of industrial statistics, this brings forth various challenges in statistical process control and monitoring. This new high dimensional data...... often exhibit not only cross-­‐correlation among the quality characteristics of interest but also serial dependence as a consequence of high sampling frequency and system dynamics. In practice, the most common method of monitoring multivariate data is through what is called the Hotelling’s T2 statistic....... In this paper, we discuss the effect of autocorrelation (when it is ignored) on multivariate control charts based on these methods and provide some practical suggestions and remedies to overcome this problem....

Rydberg energies using excited state density functional theory

International Nuclear Information System (INIS)

Cheng, C.-L.; Wu Qin; Van Voorhis, Troy

2008-01-01

We utilize excited state density functional theory (eDFT) to study Rydberg states in atoms. We show both analytically and numerically that semilocal functionals can give quite reasonable Rydberg energies from eDFT, even in cases where time dependent density functional theory (TDDFT) fails catastrophically. We trace these findings to the fact that in eDFT the Kohn-Sham potential for each state is computed using the appropriate excited state density. Unlike the ground state potential, which typically falls off exponentially, the sequence of excited state potentials has a component that falls off polynomially with distance, leading to a Rydberg-type series. We also address the rigorous basis of eDFT for these systems. Perdew and Levy have shown using the constrained search formalism that every stationary density corresponds, in principle, to an exact stationary state of the full many-body Hamiltonian. In the present context, this means that the excited state DFT solutions are rigorous as long as they deliver the minimum noninteracting kinetic energy for the given density. We use optimized effective potential techniques to show that, in some cases, the eDFT Rydberg solutions appear to deliver the minimum kinetic energy because the associated density is not pure state v-representable. We thus find that eDFT plays a complementary role to constrained DFT: The former works only if the excited state density is not the ground state of some potential while the latter applies only when the density is a ground state density.

Simultaneous maximization of spatial and temporal autocorrelation in spatio-temporal data

DEFF Research Database (Denmark)

Nielsen, Allan Aasbjerg

2002-01-01

. This is done by solving the generalized eigenproblem represented by the Rayleigh coefficient where is the dispersion of and is the dispersion of the difference between and spatially shifted. Hence, the new variates are obtained from the conjugate eigenvectors and the autocorrelations obtained are , i.e., high...

ON THE EFFECTS OF THE PRESENCE AND METHODS OF THE ELIMINATION HETEROSCEDASTICITY AND AUTOCORRELATION IN THE REGRESSION MODEL

Directory of Open Access Journals (Sweden)

Nina L. Timofeeva

2014-01-01

Full Text Available The article presents the methodological and technical bases for the creation of regression models that adequately reflect reality. The focus is on methods of removing residual autocorrelation in models. Algorithms eliminating heteroscedasticity and autocorrelation of the regression model residuals: reweighted least squares method, the method of Cochran-Orkutta are given. A model of "pure" regression is build, as well as to compare the effect on the dependent variable of the different explanatory variables when the latter are expressed in different units, a standardized form of the regression equation. The scheme of abatement techniques of heteroskedasticity and autocorrelation for the creation of regression models specific to the social and cultural sphere is developed.

Covariant Density Functionals: time-odd channel investigated

International Nuclear Information System (INIS)

Afanasjev, A. V.; Abusara, H.

2009-01-01

The description of exotic nuclear systems and phenomena requires a detailed understanding of all channels of density functional theories. The role of time-odd mean fields, their evidence in experiment, and an accurate description of these fields are subject of current interest. Recent studies advanced the understanding of these fields in energy density functional theories based on the Skyrme force [1,2]. Time-odd mean fields are related to nuclear magnetism in covariant density functional (CDF) theories [3]. They arise from space-like components of vector mesons and Lorentz invariance requires that their coupling strengths are identical to that of time-like components. There were only few limited efforts to understand the role of time-odd mean fields in covariant density functional theory [4,5]. For example, the microscopic role of nuclear magnetism and its impact on rotational properties of nuclei has been studied in Ref. [5]. It is known that time-odd mean fields modify the angular momentum content of the single-particle orbitals and thus the moments of inertia, effective alignments, alignment gains at the band crossings and other physical observables. We aim on more detailed and systematic understanding of the role of time-odd mean fields in covariant density functional theory. This investigation covers both rotating and non-rotating systems. It is shown that contrary to the Skyrme energy density functionals time-odd mean fields of CDF theory always provide additional binding in the systems with broken time-reversal symmetry (rotating nuclei, odd mass nuclei). This additional binding increases with spin and has its maximum exactly at the terminating state [6], where it can reach several MeV. The impact of time-odd mean fields on the properties of rotating systems has been studied in a systematic way (as a function of particle number and deformation) across the nuclear chart [7]. In addition, this contribution extends these studies to non-rotating systems such as

Density functional theory of the electrical double layer: the RFD functional

International Nuclear Information System (INIS)

Gillespie, Dirk; Valisko, Monika; Boda, Dezso

2005-01-01

Density functional theory (DFT) of electrolytes is applied to the electrical double layer under a wide range of conditions. The ions are charged, hard spheres of different size and valence, and the wall creating the double layer is uncharged, weakly charged, and strongly charged. Under all conditions, the density and electrostatic potential profiles calculated using the recently proposed RFD electrostatic functional (Gillespie et al 2002 J. Phys.: Condens. Matter 14 12129; 2003 Phys. Rev. E 68 031503) compare well to Monte Carlo simulations. When the wall is strongly charged, the RFD functional results agree with the results of a simpler perturbative electrostatic DFT, but the two functionals' results qualitatively disagree when the wall is uncharged or weakly charged. The RFD functional reproduces these phenomena of weakly charged double layers. It also reproduces bulk thermodynamic quantities calculated from pair correlation functions

Robustness of variance and autocorrelation as indicators of critical slowing down

NARCIS (Netherlands)

Dakos, V.; Nes, van E.H.; Odorico, D' P.; Scheffer, M.

2012-01-01

Ecosystems close to a critical threshold lose resilience, in the sense that perturbations can more easily push them into an alternative state. Recently, it has been proposed that such loss of resilience may be detected from elevated autocorrelation and variance in the fluctuations of the state of an

Orthogonal bases of radial functions for charge density refinements

International Nuclear Information System (INIS)

Restori, R.

1990-01-01

Charge density determination from X-ray measurements necessitates the evaluation of the Fourier-Bessel transforms of the radial functions used to expand the charge density. Analytical expressions are given here for four sets of orthogonal functions which can substitute for the 'traditional exponential functions' set in least-squares refinements. (orig.)

Time-dependent density-functional tight-binding method with the third-order expansion of electron density.

Science.gov (United States)

Nishimoto, Yoshio

2015-09-07

We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of the third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well.

Energy vs. density on paths toward exact density functionals

DEFF Research Database (Denmark)

Kepp, Kasper Planeta

2018-01-01

Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a “path”. Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness...

A spatio-temporal autocorrelation change detection approach using hyper-temporal satellite data

CSIR Research Space (South Africa)

Kleynhans, W

2013-07-01

Full Text Available -1 IEEE International Geoscience and Remote Sensing Symposium, Melbourne, Australia 21-26 July 2013 A SPATIO-TEMPORAL AUTOCORRELATION CHANGE DETECTION APPROACH USING HYPER-TEMPORAL SATELLITE DATA yzW. Kleynhans, yz,B.P Salmon,zK. J. Wessels...

Spatial Autocorrelation Patterns of Understory Plant Species in a Subtropical Rainforest at Lanjenchi, Southern Taiwan

Directory of Open Access Journals (Sweden)

Su-Wei Fan

2010-06-01

Full Text Available Many studies described relationships between plant species and intrinsic or exogenous factors, but few quantified spatial scales of species patterns. In this study, quantitative methods were used to explore the spatial scale of understory species (including resident and transient species, in order to identify the influential factors of species distribution. Resident species (including herbaceous species, climbers and tree ferns < 1 m high were investigated on seven transects, each 5-meter wide and 300-meter long, at Lanjenchi plot in Nanjenshan Reserve, southern Taiwan. Transient species (seedling of canopy, subcanopy and shrub species < 1 cm diameter at breast height were censused in three of the seven transects. The herb coverage and seedling abundance were calculated for each 5 × 5 m quadrat along the transects, and Moran’s I and Galiano’s new local variance (NLV indices were then used to identify the spatial scale of autocorrelation for each species. Patterns of species abundance of understory layer varied among species at fine scale within 50 meters. Resident species showed a higher proportion of significant autocorrelation than the transient species. Species with large size or prolonged fronds or stems tended to show larger scales in autocorrelation. However, dispersal syndromes and fruit types did not relate to any species’ spatial patterns. Several species showed a significant autocorrelation at a 180-meter class which happened to correspond to the local replicates of topographical features in hilltops. The spatial patterns of understory species at Lanjenchi plot are mainly influenced by species’ intrinsic traits and topographical characteristics.

Multicomponent density-functional theory for time-dependent systems

NARCIS (Netherlands)

Butriy, O.; Ebadi, H.; de Boeij, P. L.; van Leeuwen, R.; Gross, E. K. U.

2007-01-01

We derive the basic formalism of density functional theory for time-dependent electron-nuclear systems. The basic variables of this theory are the electron density in body-fixed frame coordinates and the diagonal of the nuclear N-body density matrix. The body-fixed frame transformation is carried

Improved Density Functional Tight Binding Potentials for Metalloid Aluminum Clusters

Science.gov (United States)

2016-06-01

unlimited IMPROVED DENSITY-FUNCTIONAL TIGHT BINDING POTENTIALS FOR METALLOID ALUMINUM CLUSTERS by Joon H. Kim June 2016 Thesis Advisor...DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE IMPROVED DENSITY-FUNCTIONAL TIGHT BINDING POTENTIALS FOR METALLOID ALUMINUM CLUSTERS 5. FUNDING...repulsive potentials for use in density-functional tight binding (DFTB) simulations of low-valence aluminum metalloid clusters . These systems are under

A density functional approach to ferrogels

Science.gov (United States)

Cremer, P.; Heinen, M.; Menzel, A. M.; Löwen, H.

2017-07-01

Ferrogels consist of magnetic colloidal particles embedded in an elastic polymer matrix. As a consequence, their structural and rheological properties are governed by a competition between magnetic particle-particle interactions and mechanical matrix elasticity. Typically, the particles are permanently fixed within the matrix, which makes them distinguishable by their positions. Over time, particle neighbors do not change due to the fixation by the matrix. Here we present a classical density functional approach for such ferrogels. We map the elastic matrix-induced interactions between neighboring colloidal particles distinguishable by their positions onto effective pairwise interactions between indistinguishable particles similar to a ‘pairwise pseudopotential’. Using Monte-Carlo computer simulations, we demonstrate for one-dimensional dipole-spring models of ferrogels that this mapping is justified. We then use the pseudopotential as an input into classical density functional theory of inhomogeneous fluids and predict the bulk elastic modulus of the ferrogel under various conditions. In addition, we propose the use of an ‘external pseudopotential’ when one switches from the viewpoint of a one-dimensional dipole-spring object to a one-dimensional chain embedded in an infinitely extended bulk matrix. Our mapping approach paves the way to describe various inhomogeneous situations of ferrogels using classical density functional concepts of inhomogeneous fluids.

Recent developments in LIBXC - A comprehensive library of functionals for density functional theory

Science.gov (United States)

Lehtola, Susi; Steigemann, Conrad; Oliveira, Micael J. T.; Marques, Miguel A. L.

2018-01-01

LIBXC is a library of exchange-correlation functionals for density-functional theory. We are concerned with semi-local functionals (or the semi-local part of hybrid functionals), namely local-density approximations, generalized-gradient approximations, and meta-generalized-gradient approximations. Currently we include around 400 functionals for the exchange, correlation, and the kinetic energy, spanning more than 50 years of research. Moreover, LIBXC is by now used by more than 20 codes, not only from the atomic, molecular, and solid-state physics, but also from the quantum chemistry communities.

On the evolution of the density probability density function in strongly self-gravitating systems

International Nuclear Information System (INIS)

Girichidis, Philipp; Konstandin, Lukas; Klessen, Ralf S.; Whitworth, Anthony P.

2014-01-01

The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple approximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form P V (ρ)∝ρ –1.54 for the (volume-weighted) PDF and P M (ρ)∝ρ –0.54 for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates (SFRs). Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured SFRs are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall.

Functional development in density functional theory for superconductors

Energy Technology Data Exchange (ETDEWEB)

Sanna, Antonio; Gross, E.K.U.; Essenberger, Frank [Max Planck Institute of Microstructure Physics, Halle (Saale) (Germany)

2015-07-01

Density functional theory for superconductors (SCDFT) is a fully parameter-free approach to superconductivity that allows for accurate predictions of critical temperature and properties of superconductors. We report on the most recent extensions of the method, in particular the development of new functionals to: (1) incorporate in a correct fashion Migdal's theorem; (2) compute the excitation spectrum; (3) include spin-fluctuation mediated pairing Applications and predictions are shown for a set of materials, including conventional and unconventional superconductors.

Autocorrelation and cross-correlation in time series of homicide and attempted homicide

Science.gov (United States)

Machado Filho, A.; da Silva, M. F.; Zebende, G. F.

2014-04-01

We propose in this paper to establish the relationship between homicides and attempted homicides by a non-stationary time-series analysis. This analysis will be carried out by Detrended Fluctuation Analysis (DFA), Detrended Cross-Correlation Analysis (DCCA), and DCCA cross-correlation coefficient, ρ(n). Through this analysis we can identify a positive cross-correlation between homicides and attempted homicides. At the same time, looked at from the point of view of autocorrelation (DFA), this analysis can be more informative depending on time scale. For short scale (days), we cannot identify auto-correlations, on the scale of weeks DFA presents anti-persistent behavior, and for long time scales (n>90 days) DFA presents a persistent behavior. Finally, the application of this new type of statistical analysis proved to be efficient and, in this sense, this paper can contribute to a more accurate descriptive statistics of crime.

Equation satisfied by electron-electron mutual Coulomb repulsion energy density functional

OpenAIRE

Joubert, Daniel P.

2011-01-01

The electron-electron mutual Coulomb repulsion energy density functional satisfies an equation that links functionals and functional derivatives at N-electron and (N-1)-electron densities for densities determined from the same adiabatic scaled external potential for the N-electron system.

Density-functional theory in one dimension for contact-interacting fermions

International Nuclear Information System (INIS)

Magyar, R.J.; Burke, K.

2004-01-01

A density-functional theory is developed for fermions in one dimension, interacting via a δ function. Such systems provide a natural testing ground for questions of principle, as the local-density approximation should be highly accurate since for this interaction type the exchange contribution to the local-density approximation is intrinsically self-interaction-free. The exact-exchange contribution to the total energy is a local functional of the density. A local-density approximation for correlation is obtained using perturbation theory and Bethe ansatz results for the one-dimensional contact-interacting uniform Fermi gas. The ground-state energies are calculated for two finite systems, the analogs of helium and of Hooke's atom. The local-density approximation is shown to be excellent as expected

Self-contained filtered density function

Science.gov (United States)

Nouri, A. G.; Nik, M. B.; Givi, P.; Livescu, D.; Pope, S. B.

2017-09-01

The filtered density function (FDF) closure is extended to a "self-contained" format to include the subgrid-scale (SGS) statistics of all of the hydro-thermo-chemical variables in turbulent flows. These are the thermodynamic pressure, the specific internal energy, the velocity vector, and the composition field. In this format, the model is comprehensive and facilitates large-eddy simulation (LES) of flows at both low and high compressibility levels. A transport equation is developed for the joint pressure-energy-velocity-composition filtered mass density function (PEVC-FMDF). In this equation, the effect of convection appears in closed form. The coupling of the hydrodynamics and thermochemistry is modeled via a set of stochastic differential equation for each of the transport variables. This yields a self-contained SGS closure. For demonstration, LES is conducted of a turbulent shear flow with transport of a passive scalar. The consistency of the PEVC-FMDF formulation is established, and its overall predictive capability is appraised via comparison with direct numerical simulation (DNS) data.

Signals and memory in tree-ring width and density data

Czech Academy of Sciences Publication Activity Database

Esper, J.; Schneider, L.; Smerdon, J. E.; Schoene, B.; Büntgen, Ulf

2015-01-01

Roč. 35, OCT (2015), s. 62-70 ISSN 1125-7865 Institutional support: RVO:67179843 Keywords : summer temperature-variations * major volcanic - eruptions * european summer * chronologies * climate * variability * reconstruction * precipitation * millennium * centuries * Maximum latewood density * Temperature * Autocorrelation * Superposed epoch analysis * Volcanic eruption * Northern hemisphere Subject RIV: EH - Ecology, Behaviour Impact factor: 2.107, year: 2015

Autocorrelation studies of the arrival directions of UHECRs measured by the surface detector of the Pierre Auger Observatory

Energy Technology Data Exchange (ETDEWEB)

Schulte, Stephan

2011-07-11

The history of cosmic rays started in the beginning of the 20th century. Since then one of the main questions is their origin. Due to the very low flux at the highest energies huge areas have to be instrumented to answer this question. For this purpose the distribution of the arrival directions of cosmic rays is studied. The largest experiment so far is the Pierre Auger Observatory, located in the Pampa in western Argentina with an area of about 3000 km{sup 2}. In recent years it provided many major contributions to the field of cosmic ray physics and its data is the basis of this work. Among other things a correlation analysis of Ultra High Energy Cosmic Rays (UHECRs) with Active Galactic Nuclei (AGN) was performed leading to the first evidence that UHECRs are not isotropically distributed. Here the distribution of arrival directions of cosmic rays at the highest energies (>50 EeV) is examined by using autocorrelation methods to check whether it is compatible with the isotropic expectation or not.This thesis is organised as follows: in the first two chapters a short introduction to the topic is given, followed by a more general discussion on cosmic rays including models of acceleration, possible sources and the propagation of UHECRs in the third chapter. The fourth chapter focuses on the detector design of the Pierre Auger Observatory and event reconstruction at highest energies. Special attention is paid to the monitoring of the High Elevation Auger Telescopes (HEAT). It is a low energy enhancement of the observatory consisting of three tiltable fluorescence telescopes. The calibration of the new sensor setups is described as well as the installation in each HEAT shelter. The next chapter starts with a detailed description of the underlying ideas and motivations of autocorrelation methods: a representation of the 2pt-Correlation Function and its extension, a Minimum Spanning Tree and a Cluster Algorithm with different weighting procedures. The principle of each

Autocorrelation studies of the arrival directions of UHECRs measured by the surface detector of the Pierre Auger Observatory

International Nuclear Information System (INIS)

Schulte, Stephan

2011-01-01

The history of cosmic rays started in the beginning of the 20th century. Since then one of the main questions is their origin. Due to the very low flux at the highest energies huge areas have to be instrumented to answer this question. For this purpose the distribution of the arrival directions of cosmic rays is studied. The largest experiment so far is the Pierre Auger Observatory, located in the Pampa in western Argentina with an area of about 3000 km 2 . In recent years it provided many major contributions to the field of cosmic ray physics and its data is the basis of this work. Among other things a correlation analysis of Ultra High Energy Cosmic Rays (UHECRs) with Active Galactic Nuclei (AGN) was performed leading to the first evidence that UHECRs are not isotropically distributed. Here the distribution of arrival directions of cosmic rays at the highest energies (>50 EeV) is examined by using autocorrelation methods to check whether it is compatible with the isotropic expectation or not.This thesis is organised as follows: in the first two chapters a short introduction to the topic is given, followed by a more general discussion on cosmic rays including models of acceleration, possible sources and the propagation of UHECRs in the third chapter. The fourth chapter focuses on the detector design of the Pierre Auger Observatory and event reconstruction at highest energies. Special attention is paid to the monitoring of the High Elevation Auger Telescopes (HEAT). It is a low energy enhancement of the observatory consisting of three tiltable fluorescence telescopes. The calibration of the new sensor setups is described as well as the installation in each HEAT shelter. The next chapter starts with a detailed description of the underlying ideas and motivations of autocorrelation methods: a representation of the 2pt-Correlation Function and its extension, a Minimum Spanning Tree and a Cluster Algorithm with different weighting procedures. The principle of each

Field test comparison of an autocorrelation technique for determining grain size using a digital 'beachball' camera versus traditional methods

Science.gov (United States)

Barnard, P.L.; Rubin, D.M.; Harney, J.; Mustain, N.

2007-01-01

This extensive field test of an autocorrelation technique for determining grain size from digital images was conducted using a digital bed-sediment camera, or 'beachball' camera. Using 205 sediment samples and >1200 images from a variety of beaches on the west coast of the US, grain size ranging from sand to granules was measured from field samples using both the autocorrelation technique developed by Rubin [Rubin, D.M., 2004. A simple autocorrelation algorithm for determining grain size from digital images of sediment. Journal of Sedimentary Research, 74(1): 160-165.] and traditional methods (i.e. settling tube analysis, sieving, and point counts). To test the accuracy of the digital-image grain size algorithm, we compared results with manual point counts of an extensive image data set in the Santa Barbara littoral cell. Grain sizes calculated using the autocorrelation algorithm were highly correlated with the point counts of the same images (r2 = 0.93; n = 79) and had an error of only 1%. Comparisons of calculated grain sizes and grain sizes measured from grab samples demonstrated that the autocorrelation technique works well on high-energy dissipative beaches with well-sorted sediment such as in the Pacific Northwest (r2 ??? 0.92; n = 115). On less dissipative, more poorly sorted beaches such as Ocean Beach in San Francisco, results were not as good (r2 ??? 0.70; n = 67; within 3% accuracy). Because the algorithm works well compared with point counts of the same image, the poorer correlation with grab samples must be a result of actual spatial and vertical variability of sediment in the field; closer agreement between grain size in the images and grain size of grab samples can be achieved by increasing the sampling volume of the images (taking more images, distributed over a volume comparable to that of a grab sample). In all field tests the autocorrelation method was able to predict the mean and median grain size with ???96% accuracy, which is more than

Auto-correlation analysis of wave heights in the Bay of Bengal

Indian Academy of Sciences (India)

Time series observations of significant wave heights in the Bay of Bengal were subjected to auto- correlation analysis to determine temporal variability scale. The analysis indicates an exponen- tial fall of auto-correlation in the first few hours with a decorrelation time scale of about six hours. A similar figure was found earlier ...

Neutron density fluctuations in point reactor systems with dichotomic reactivity noise

International Nuclear Information System (INIS)

Sako, Okitsugu

1984-01-01

The exactly solvable stochastic point reactor model systems are analyzed through the stochastic Liouville equation. Three kinds of model systems are treated: (1) linear system without delayed neutrons, (2) linear system with one-group of delayed neutrons, and (3) nonlinear system with direct power feedback. The exact expressions for the fluctuations of neutron density, such as the moments, autocorrelation function and power spectral density, are derived in the case where the colored reactivity noise is described by the dichotomic, or two state, Markov process with arbitrary correlation time and intensity, and the effects of the finite correlation time and intensity of the noise on the neutron density fluctuations are investigated. The influence of presence of delayed neutrons and the effect of nonlinearity of system on the neutron density fluctuations are also elucidated. When the reactivity correlation time is very short, the correlation time has almost no effect on the power spectral density, and the relative fluctuation of neutron density in the stationary state is not affected very much by the presence of delayed neutrons and also by the nonlinearity of system. On the other hand, if the reactivity correlation time is very long, the effect of the reactivity noise on the power spectral density appears at very low frequency, and the presence of delayed neutrons has an effect of reducing the neutron density fluctuations. (author)

Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation

Science.gov (United States)

Navarro Pérez, R.; Schunck, N.; Dyhdalo, A.; Furnstahl, R. J.; Bogner, S. K.

2018-05-01

Background: Energy density functional methods provide a generic framework to compute properties of atomic nuclei starting from models of nuclear potentials and the rules of quantum mechanics. Until now, the overwhelming majority of functionals have been constructed either from empirical nuclear potentials such as the Skyrme or Gogny forces, or from systematic gradient-like expansions in the spirit of the density functional theory for atoms. Purpose: We seek to obtain a usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties. Methods: Our energy functional comprises two main components. The first component is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. Contributions to the mean field and the energy of this term are computed by expanding the spatial, finite-range components of the chiral potential onto Gaussian functions. The second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the UNEDF2 optimization protocol to determine the coupling constants of this energy functional. Results: We obtain a set of microscopically constrained functionals for local chiral potentials from leading order up to next-to-next-to-leading order with and without three-body forces and contributions from Δ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, single-particle shell structure

Poincaré plot analysis of autocorrelation function of RR intervals in patients with acute myocardial infarction.

Science.gov (United States)

Chuang, Shin-Shin; Wu, Kung-Tai; Lin, Chen-Yang; Lee, Steven; Chen, Gau-Yang; Kuo, Cheng-Deng

2014-08-01

The Poincaré plot of RR intervals (RRI) is obtained by plotting RRIn+1 against RRIn. The Pearson correlation coefficient (ρRRI), slope (SRRI), Y-intercept (YRRI), standard deviation of instantaneous beat-to-beat RRI variability (SD1RR), and standard deviation of continuous long-term RRI variability (SD2RR) can be defined to characterize the plot. Similarly, the Poincaré plot of autocorrelation function (ACF) of RRI can be obtained by plotting ACFk+1 against ACFk. The corresponding Pearson correlation coefficient (ρACF), slope (SACF), Y-intercept (YACF), SD1ACF, and SD2ACF can be defined similarly to characterize the plot. By comparing the indices of Poincaré plots of RRI and ACF between patients with acute myocardial infarction (AMI) and patients with patent coronary artery (PCA), we found that the ρACF and SACF were significantly larger, whereas the RMSSDACF/SDACF and SD1ACF/SD2ACF were significantly smaller in AMI patients. The ρACF and SACF correlated significantly and negatively with normalized high-frequency power (nHFP), and significantly and positively with normalized very low-frequency power (nVLFP) of heart rate variability in both groups of patients. On the contrary, the RMSSDACF/SDACF and SD1ACF/SD2ACF correlated significantly and positively with nHFP, and significantly and negatively with nVLFP and low-/high-frequency power ratio (LHR) in both groups of patients. We concluded that the ρACF, SACF, RMSSDACF/SDACF, and SD1ACF/SD2ACF, among many other indices of ACF Poincaré plot, can be used to differentiate between patients with AMI and patients with PCA, and that the increase in ρACF and SACF and the decrease in RMSSDACF/SDACF and SD1ACF/SD2ACF suggest an increased sympathetic and decreased vagal modulations in both groups of patients.

Graphene on metals: A van der Waals density functional study

DEFF Research Database (Denmark)

Vanin, Marco; Mortensen, Jens Jørgen; Kelkkanen, Kari André

2010-01-01

We use density functional theory (DFT) with a recently developed van der Waals density functional (vdW-DF) to study the adsorption of graphene on Co, Ni, Pd, Ag, Au, Cu, Pt, and Al(111) surfaces. In contrast to the local-density approximation (LDA) which predicts relatively strong binding for Ni...

A model-free approach to eliminate autocorrelation when testing for process capability

DEFF Research Database (Denmark)

Vanmann, Kerstin; Kulahci, Murat

2008-01-01

There is an increasing use of on-line data acquisition systems in industry. This usually leads to autocorrelated data and implies that the assumption of independent observations has to be re-examined. Most decision procedures for capability analysis assume independent data. In this article we pre...

Bayesian error estimation in density-functional theory

DEFF Research Database (Denmark)

Mortensen, Jens Jørgen; Kaasbjerg, Kristen; Frederiksen, Søren Lund

2005-01-01

We present a practical scheme for performing error estimates for density-functional theory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies...

Nuclear energy density functional from chiral pion-nucleon dynamics revisited

Science.gov (United States)

Kaiser, N.; Weise, W.

2010-05-01

We use a recently improved density-matrix expansion to calculate the nuclear energy density functional in the framework of in-medium chiral perturbation theory. Our calculation treats systematically the effects from 1 π-exchange, iterated 1 π-exchange, and irreducible 2 π-exchange with intermediate Δ-isobar excitations, including Pauli-blocking corrections up to three-loop order. We find that the effective nucleon mass M(ρ) entering the energy density functional is identical to the one of Fermi-liquid theory when employing the improved density-matrix expansion. The strength F(ρ) of the ( surface-term as provided by the pion-exchange dynamics is in good agreement with that of phenomenological Skyrme forces in the density region ρ/2short-range spin-orbit interaction. The strength function F(ρ) multiplying the square of the spin-orbit density comes out much larger than in phenomenological Skyrme forces and it has a pronounced density dependence.

The heat current density correlation function: sum rules and thermal conductivity

International Nuclear Information System (INIS)

Singh, Shaminder; Tankeshwar, K; Pathak, K N; Ranganathan, S

2006-01-01

Expressions for the second and fourth sum rules of the heat current density correlation function have been derived in an appropriate ensemble. The thermal conductivity of Lennard-Jones fluids has been calculated using these sum rules for the heat current density correlation function and the Gaussian form of the memory function. It is found that the results obtained for the thermal conductivity are in good agreement with the molecular dynamics simulation results over a wide range of densities and temperatures. Earlier results obtained using the energy current density correlation function are also discussed

The heat current density correlation function: sum rules and thermal conductivity

Energy Technology Data Exchange (ETDEWEB)

Singh, Shaminder [Department of Physics, Panjab University, Chandigarh-160 014 (India); Tankeshwar, K [Department of Physics, Panjab University, Chandigarh-160 014 (India); Pathak, K N [Department of Physics, Panjab University, Chandigarh-160 014 (India); Ranganathan, S [Department of Physics, Royal Military College, Kingston, ON, K7K 7B4 (Canada)

2006-02-01

Expressions for the second and fourth sum rules of the heat current density correlation function have been derived in an appropriate ensemble. The thermal conductivity of Lennard-Jones fluids has been calculated using these sum rules for the heat current density correlation function and the Gaussian form of the memory function. It is found that the results obtained for the thermal conductivity are in good agreement with the molecular dynamics simulation results over a wide range of densities and temperatures. Earlier results obtained using the energy current density correlation function are also discussed.

A classical density functional theory of ionic liquids.

Science.gov (United States)

Forsman, Jan; Woodward, Clifford E; Trulsson, Martin

2011-04-28

We present a simple, classical density functional approach to the study of simple models of room temperature ionic liquids. Dispersion attractions as well as ion correlation effects and excluded volume packing are taken into account. The oligomeric structure, common to many ionic liquid molecules, is handled by a polymer density functional treatment. The theory is evaluated by comparisons with simulations, with an emphasis on the differential capacitance, an experimentally measurable quantity of significant practical interest.

Role of density modulation in the spatially resolved dynamics of strongly confined liquids.

Science.gov (United States)

Saw, Shibu; Dasgupta, Chandan

2016-08-07

Confinement by walls usually produces a strong modulation in the density of dense liquids near the walls. Using molecular dynamics simulations, we examine the effects of the density modulation on the spatially resolved dynamics of a liquid confined between two parallel walls, using a resolution of a fraction of the interparticle distance in the liquid. The local dynamics is quantified by the relaxation time associated with the temporal autocorrelation function of the local density. We find that this local relaxation time varies in phase with the density modulation. The amplitude of the spatial modulation of the relaxation time can be quite large, depending on the characteristics of the wall and thermodynamic parameters of the liquid. To disentangle the effects of confinement and density modulation on the spatially resolved dynamics, we compare the dynamics of a confined liquid with that of an unconfined one in which a similar density modulation is induced by an external potential. We find several differences indicating that density modulation alone cannot account for all the features seen in the spatially resolved dynamics of confined liquids. We also examine how the dynamics near a wall depends on the separation between the two walls and show that the features seen in our simulations persist in the limit of large wall separation.

Size determinations of plutonium colloids using autocorrelation photon spectroscopy

International Nuclear Information System (INIS)

Triay, I.R.; Rundberg, R.S.; Mitchell, A.J.; Ott, M.A.; Hobart, D.E.; Palmer, P.D.; Newton, T.W.; Thompson, J.L.

1989-01-01

Autocorrelation Photon Spectroscopy (APS) is a light-scattering technique utilized to determine the size distribution of colloidal suspensions. The capabilities of the APS methodology have been assessed by analyzing colloids of known sizes. Plutonium(IV) colloid samples were prepared by a variety of methods including: dilution; peptization; and alpha-induced auto-oxidation of Pu(III). The size of theses Pu colloids was analyzed using APS. The sizes determined for the Pu colloids studied varied from 1 to 370 nanometers. 7 refs., 5 figs., 3 tabs

Self-contained filtered density function

International Nuclear Information System (INIS)

Nouri, Arash G.; Pope, Stephen B.

2017-01-01

The filtered density function (FDF) closure is extended to a “self-contained” format to include the subgrid-scale (SGS) statistics of all of the hydro-thermo-chemical variables in turbulent flows. These are the thermodynamic pressure, the specific internal energy, the velocity vector, and the composition field. In this format, the model is comprehensive and facilitates large-eddy simulation (LES) of flows at both low and high compressibility levels. A transport equation is developed for the joint pressure-energy-velocity-composition filtered mass density function (PEVC-FMDF). In this equation, the effect of convection appears in closed form. The coupling of the hydrodynamics and thermochemistry is modeled via a set of stochastic differential equation for each of the transport variables. This yields a self-contained SGS closure. We demonstrated how LES is conducted of a turbulent shear flow with transport of a passive scalar. Finally, the consistency of the PEVC-FMDF formulation is established, and its overall predictive capability is appraised via comparison with direct numerical simulation (DNS) data.

Temporal separation of the density fluctuation signal measured by light scattering

International Nuclear Information System (INIS)

Antar, G.; Devynk, P.; Laviron, C.; Garbet, X.; Sabot, R.; Fenzi, C.; Hennequin, P.; Truc, A.; Quemeneur, A.; Honore, C.; Gervais, F.

1999-02-01

On Tore Supra, the frequency spectra of the turbulent fluctuations often have two peaks centered on some positive and negative values. These two peaks correspond to a poloidal motion of electron turbulence in opposite directions. In this paper, a criterion is elaborated allowing us to distinguish, in time, density fluctuations convected in the parallel from those in the anti-parallel direction with respect to the analysing wavevector. Two signals are thus extracted out of one. The validity of our model is experimentally checked up by comparing the auto-correlation coefficients and the frequency spectra computed for the whole and the separated signals. Consequently, the frequency spectrum is studied in detail as a function of the analysing wavenumber leading to an accurate determination of some plasma properties. (authors)

Multiconfiguration Pair-Density Functional Theory Is Free From Delocalization Error.

Science.gov (United States)

Bao, Junwei Lucas; Wang, Ying; He, Xiao; Gagliardi, Laura; Truhlar, Donald G

2017-11-16

Delocalization error has been singled out by Yang and co-workers as the dominant error in Kohn-Sham density functional theory (KS-DFT) with conventional approximate functionals. In this Letter, by computing the vertical first ionization energy for well separated He clusters, we show that multiconfiguration pair-density functional theory (MC-PDFT) is free from delocalization error. To put MC-PDFT in perspective, we also compare it with some Kohn-Sham density functionals, including both traditional and modern functionals. Whereas large delocalization errors are almost universal in KS-DFT (the only exception being the very recent corrected functionals of Yang and co-workers), delocalization error is removed by MC-PDFT, which bodes well for its future as a step forward from KS-DFT.

Longitudinal and bulk viscosities of Lennard-Jones fluids

Science.gov (United States)

Tankeshwar, K.; Pathak, K. N.; Ranganathan, S.

1996-12-01

Expressions for the longitudinal and bulk viscosities have been derived using Green Kubo formulae involving the time integral of the longitudinal and bulk stress autocorrelation functions. The time evolution of stress autocorrelation functions are determined using the Mori formalism and a memory function which is obtained from the Mori equation of motion. The memory function is of hyperbolic secant form and involves two parameters which are related to the microscopic sum rules of the respective autocorrelation function. We have derived expressions for the zeroth-, second-and fourth- order sum rules of the longitudinal and bulk stress autocorrelation functions. These involve static correlation functions up to four particles. The final expressions for these have been put in a form suitable for numerical calculations using low- order decoupling approximations. The numerical results have been obtained for the sum rules of longitudinal and bulk stress autocorrelation functions. These have been used to calculate the longitudinal and bulk viscosities and time evolution of the longitudinal stress autocorrelation function of the Lennard-Jones fluids over wide ranges of densities and temperatures. We have compared our results with the available computer simulation data and found reasonable agreement.

Benchmark density functional theory calculations for nanoscale conductance

DEFF Research Database (Denmark)

Strange, Mikkel; Bækgaard, Iben Sig Buur; Thygesen, Kristian Sommer

2008-01-01

We present a set of benchmark calculations for the Kohn-Sham elastic transmission function of five representative single-molecule junctions. The transmission functions are calculated using two different density functional theory methods, namely an ultrasoft pseudopotential plane-wave code...

SURFACE SYMMETRY ENERGY OF NUCLEAR ENERGY DENSITY FUNCTIONALS

Energy Technology Data Exchange (ETDEWEB)

Nikolov, N; Schunck, N; Nazarewicz, W; Bender, M; Pei, J

2010-12-20

We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy density functionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutron-rich matter and description of fission rates for r-process nucleosynthesis.

Logistic regression for southern pine beetle outbreaks with spatial and temporal autocorrelation

Science.gov (United States)

M. L. Gumpertz; C.-T. Wu; John M. Pye

2000-01-01

Regional outbreaks of southern pine beetle (Dendroctonus frontalis Zimm.) show marked spatial and temporal patterns. While these patterns are of interest in themselves, we focus on statistical methods for estimating the effects of underlying environmental factors in the presence of spatial and temporal autocorrelation. The most comprehensive available information on...

Kinetic-energy density functional: Atoms and shell structure

International Nuclear Information System (INIS)

Garcia-Gonzalez, P.; Alvarellos, J.E.; Chacon, E.

1996-01-01

We present a nonlocal kinetic-energy functional which includes an anisotropic average of the density through a symmetrization procedure. This functional allows a better description of the nonlocal effects of the electron system. The main consequence of the symmetrization is the appearance of a clear shell structure in the atomic density profiles, obtained after the minimization of the total energy. Although previous results with some of the nonlocal kinetic functionals have given incipient structures for heavy atoms, only our functional shows a clear shell structure for most of the atoms. The atomic total energies have a good agreement with the exact calculations. Discussion of the chemical potential and the first ionization potential in atoms is included. The functional is also extended to spin-polarized systems. copyright 1996 The American Physical Society

Self-diffusion coefficients of the metastable Lennard-Jones vapor

International Nuclear Information System (INIS)

Nie Chu; Zhou Youhua; Marlow, W H; Hassan, Y A

2008-01-01

Self-diffusion coefficients of a metastable Lennard-Jones vapor were obtained using the memory function formalism and the frequency moments of the velocity autocorrelation function at reduced temperatures from 0.75 to 1.0. The radial density distribution functions used to evaluate the second, fourth and sixth frequency moments of the velocity autocorrelation function were obtained from the restricted canonical ensemble Monte Carlo simulation (Corti and Debenedetti 1994 Chem. Eng. Sci. 49 2717). The self-diffusion coefficients at reduced temperature 0.75 do not vary monotonically as the density increases, and for the other three temperatures the self-diffusion coefficients vary normally

Self-diffusion coefficients of the metastable Lennard-Jones vapor

Energy Technology Data Exchange (ETDEWEB)

Nie Chu; Zhou Youhua [School of Physics and Information Engineering, Jianghan University, Wuhan 430056 (China); Marlow, W H; Hassan, Y A [Department of Nuclear Engineering, Texas A and M University, College Station, TX 77843 (United States)], E-mail: yhzhou@jhun.edu.cn

2008-10-15

Self-diffusion coefficients of a metastable Lennard-Jones vapor were obtained using the memory function formalism and the frequency moments of the velocity autocorrelation function at reduced temperatures from 0.75 to 1.0. The radial density distribution functions used to evaluate the second, fourth and sixth frequency moments of the velocity autocorrelation function were obtained from the restricted canonical ensemble Monte Carlo simulation (Corti and Debenedetti 1994 Chem. Eng. Sci. 49 2717). The self-diffusion coefficients at reduced temperature 0.75 do not vary monotonically as the density increases, and for the other three temperatures the self-diffusion coefficients vary normally.

A classical density functional investigation of nucleation

International Nuclear Information System (INIS)

Ghosh, Satinath; Ghosh, Swapan K.

2009-01-01

Study of nucleation and growth phenomena in condensation is of prime importance in various applications such as crystal growth, nanoparticle synthesis, pattern formation etc. The knowledge of nucleation barrier in condensation is necessary to control the nucleation kinetics, size of the nanoparticles etc. Classical nucleation theory (CNT) assumes the density of the drop as bulk density irrespective of the size of the drop and overestimates the nucleation barrier. Here we are interested in solving the problem analytically using density functional theory (DFT) with square gradient approximation along the lines of Cahn and Hilliard. Nucleation barrier and density profile obtained in this work are consistent with other works based on nonclassical theory. (author)

Nonlocal exchange and kinetic-energy density functionals for electronic systems

International Nuclear Information System (INIS)

Glossman, M.D.; Rubio, A.; Balbas, L.C.; Alonso, J.A.

1992-01-01

The nonlocal weighted density approximation (WDA) to the exchange and kinetic-energy functionals of many electron systems proposed several years ago by Alonso and Girifalco is used to compute, within the framework of density functional theory, the ground-state electronic density and total energy of noble gas atoms and of neutral jellium-like sodium clusters containing up to 500 atoms. These results are compared with analogous calculations using the well known Thomas-Fermi-Weizsacker-Dirac (TFWD) approximations for the kinetic (TFW) and exchange (D) energy density functionals. An outstanding improvement of the total and exchange energies, of the density at the nucleus and of the expectation values is obtained for atoms within the WDA scheme. For sodium clusters the authors notice a sizeable contribution of the nonlocal effects to the total energy and to the density profiles. In the limit of very large clusters these effects should affect the surface energy of the bulk metal

First measurements of subpicosecond electron beam structure by autocorrelation of coherent diffraction radiation

CERN Document Server

Lumpkin, Alex H; Rule, D W

2001-01-01

We report the initial measurements of subpicosecond electron beam structure using a nonintercepting technique based on the autocorrelation of coherent diffraction radiation (CDR). A far infrared (FIR) Michelson interferometer with a Golay detector was used to obtain the autocorrelation. The radiation was generated by a thermionic rf gun beam at 40 MeV as it passed through a 5-mm-tall slit/aperture in a metal screen whose surface was at 45 deg. to the beam direction. For the observed bunch lengths of about 450 fs (FWHM) with a shorter time spike on the leading edge, peak currents of about 100 A are indicated. Also a model was developed and used to calculate the CDR from the back of two metal strips separated by a 5-mm vertical gap. The demonstrated nonintercepting aspect of this method could allow on-line bunch length characterizations to be done during free-electron laser experiments.

Constraints on parton density functions from D0

Energy Technology Data Exchange (ETDEWEB)

Hays, Jonathan M.; /Imperial Coll., London

2008-04-01

Five recent results from D0 which either impact or have the potential to impact on uncertainties in parton density functions are presented. Many analyses at D0 are sensitive to the modeling of the partonic structure of the proton. When theoretical and experimental uncertainties are well controlled there exists the possibility for additional constraints on parton density functions (PDF). Five measurements are presented which either have already been included in global parton fits or have the potential to contribute in the future.

Higher-accuracy van der Waals density functional

DEFF Research Database (Denmark)

Lee, Kyuho; Murray, Éamonn D.; Kong, Lingzhu

2010-01-01

We propose a second version of the van der Waals density functional of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], employing a more accurate semilocal exchange functional and the use of a large-N asymptote gradient correction in determining the vdW kernel. The predicted binding energy...

A comparative study of density functional and density functional tight binding calculations of defects in graphene

Energy Technology Data Exchange (ETDEWEB)

Zobelli, Alberto [Laboratoire de Physique des Solides, Univ. Paris Sud, CNRS UMR, Orsay (France); Ivanovskaya, Viktoria; Wagner, Philipp; Yaya, Abu; Ewels, Chris P. [Institut des Materiaux Jean Rouxel (IMN), CNRS UMR, University of Nantes (France); Suarez-Martinez, Irene [Nanochemistry Research Institute, Curtin University of Technology, Perth, Western Australia (Australia)

2012-02-15

The density functional tight binding approach (DFTB) is well adapted for the study of point and line defects in graphene based systems. After briefly reviewing the use of DFTB in this area, we present a comparative study of defect structures, energies, and dynamics between DFTB results obtained using the dftb+ code, and density functional results using the localized Gaussian orbital code, AIMPRO. DFTB accurately reproduces structures and energies for a range of point defect structures such as vacancies and Stone-Wales defects in graphene, as well as various unfunctionalized and hydroxylated graphene sheet edges. Migration barriers for the vacancy and Stone-Wales defect formation barriers are accurately reproduced using a nudged elastic band approach. Finally we explore the potential for dynamic defect simulations using DFTB, taking as an example electron irradiation damage in graphene. DFTB-MD derived sputtering energy threshold map for a carbon atom in a graphene plane. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Existence of time-dependent density-functional theory for open electronic systems: time-dependent holographic electron density theorem.

Science.gov (United States)

Zheng, Xiao; Yam, ChiYung; Wang, Fan; Chen, GuanHua

2011-08-28

We present the time-dependent holographic electron density theorem (TD-HEDT), which lays the foundation of time-dependent density-functional theory (TDDFT) for open electronic systems. For any finite electronic system, the TD-HEDT formally establishes a one-to-one correspondence between the electron density inside any finite subsystem and the time-dependent external potential. As a result, any electronic property of an open system in principle can be determined uniquely by the electron density function inside the open region. Implications of the TD-HEDT on the practicality of TDDFT are also discussed.

Postfragmentation density function for bacterial aggregates in laminar flow.

Science.gov (United States)

Byrne, Erin; Dzul, Steve; Solomon, Michael; Younger, John; Bortz, David M

2011-04-01

The postfragmentation probability density of daughter flocs is one of the least well-understood aspects of modeling flocculation. We use three-dimensional positional data of Klebsiella pneumoniae bacterial flocs in suspension and the knowledge of hydrodynamic properties of a laminar flow field to construct a probability density function of floc volumes after a fragmentation event. We provide computational results which predict that the primary fragmentation mechanism for large flocs is erosion. The postfragmentation probability density function has a strong dependence on the size of the original floc and indicates that most fragmentation events result in clumps of one to three bacteria eroding from the original floc. We also provide numerical evidence that exhaustive fragmentation yields a limiting density inconsistent with the log-normal density predicted in the literature, most likely due to the heterogeneous nature of K. pneumoniae flocs. To support our conclusions, artificial flocs were generated and display similar postfragmentation density and exhaustive fragmentation. ©2011 American Physical Society

Linking density functional and mode coupling models for supercooled liquids.

Science.gov (United States)

Premkumar, Leishangthem; Bidhoodi, Neeta; Das, Shankar P

2016-03-28

We compare predictions from two familiar models of the metastable supercooled liquid, respectively, constructed with thermodynamic and dynamic approaches. In the so called density functional theory the free energy F[ρ] of the liquid is a functional of the inhomogeneous density ρ(r). The metastable state is identified as a local minimum of F[ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum density function. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-non-ergodicity transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained, respectively, in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.

Linking density functional and mode coupling models for supercooled liquids

Energy Technology Data Exchange (ETDEWEB)

Premkumar, Leishangthem; Bidhoodi, Neeta; Das, Shankar P. [School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067 (India)

2016-03-28

We compare predictions from two familiar models of the metastable supercooled liquid, respectively, constructed with thermodynamic and dynamic approaches. In the so called density functional theory the free energy F[ρ] of the liquid is a functional of the inhomogeneous density ρ(r). The metastable state is identified as a local minimum of F[ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum density function. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-non-ergodicity transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained, respectively, in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.

Density functional theory a practical introduction

CERN Document Server

Sholl, David

2009-01-01

Demonstrates how anyone in math, science, and engineering can master DFT calculations Density functional theory (DFT) is one of the most frequently used computational tools for studying and predicting the properties of isolated molecules, bulk solids, and material interfaces, including surfaces. Although the theoretical underpinnings of DFT are quite complicated, this book demonstrates that the basic concepts underlying the calculations are simple enough to be understood by anyone with a background in chemistry, physics, engineering, or mathematics. The authors show how the widespread availability of powerful DFT codes makes it possible for students and researchers to apply this important computational technique to a broad range of fundamental and applied problems. Density Functional Theory: A Practical Introduction offers a concise, easy-to-follow introduction to the key concepts and practical applications of DFT, focusing on plane-wave DFT. The authors have many years of experience introducing DFT to studen...

Teaching Density Functional Theory Through Experiential Learning

International Nuclear Information System (INIS)

Narasimhan, Shobhana

2015-01-01

Today, quantum mechanical density functional theory is often the method of choice for performing accurate calculations on atomic, molecular and condensed matter systems. Here, I share some of my experiences in teaching the necessary basics of solid state physics, as well as the theory and practice of density functional theory, in a number of workshops held in developing countries over the past two decades. I discuss the advantages of supplementing the usual mathematically formal teaching methods, characteristic of graduate courses, with the use of visual imagery and analogies. I also describe a successful experiment we carried out, which resulted in a joint publication co-authored by 67 lecturers and students participating in a summer school. (paper)

Relationship of Quantum Entanglement to Density Functional Theory

OpenAIRE

Rajagopal, A. K.; Rendell, R. W.

2005-01-01

The maximum von Neumann entropy principle subject to given constraints of mean values of some physical observables determines the density matrix. Similarly the stationary action principle in the case of time-dependent (dissipative) situations under similar constraints yields the density matrix. The free energy and measures of entanglement are expressed in terms of such a density matrix and thus define respective functionals of the mean values. In the light of several model calculations, it is...

Source-Free Exchange-Correlation Magnetic Fields in Density Functional Theory.

Science.gov (United States)

Sharma, S; Gross, E K U; Sanna, A; Dewhurst, J K

2018-03-13

Spin-dependent exchange-correlation energy functionals in use today depend on the charge density and the magnetization density: E xc [ρ, m]. However, it is also correct to define the functional in terms of the curl of m for physical external fields: E xc [ρ,∇ × m]. The exchange-correlation magnetic field, B xc , then becomes source-free. We study this variation of the theory by uniquely removing the source term from local and generalized gradient approximations to the functional. By doing so, the total Kohn-Sham moments are improved for a wide range of materials for both functionals. Significantly, the moments for the pnictides are now in good agreement with experiment. This source-free method is simple to implement in all existing density functional theory codes.

Chemical hardness and density functional theory

Indian Academy of Sciences (India)

Unknown

RALPH G PEARSON. Chemistry Department, University of California, Santa Barbara, CA 93106, USA. Abstract. The concept of chemical hardness is reviewed from a personal point of view. Keywords. Hardness; softness; hard & soft acids bases (HSAB); principle of maximum hardness. (PMH) density functional theory (DFT) ...

Density functional and neural network analysis

DEFF Research Database (Denmark)

Jalkanen, K. J.; Suhai, S.; Bohr, Henrik

1997-01-01

Density functional theory (DFT) calculations have been carried out for hydrated L-alanine, L-alanyl-L-alanine and N-acetyl L-alanine N'-methylamide and examined with respect to the effect of water on the structure, the vibrational frequencies, vibrational absorption (VA) and vibrational circular...

Nuclear energy density functional from chiral pion-nucleon dynamics revisited

OpenAIRE

Kaiser, N.; Weise, W.

2009-01-01

We use a recently improved density-matrix expansion to calculate the nuclear energy density functional in the framework of in-medium chiral perturbation theory. Our calculation treats systematically the effects from $1\\pi$-exchange, iterated $1\\pi$-exchange, and irreducible $2\\pi$-exchange with intermediate $\\Delta$-isobar excitations, including Pauli-blocking corrections up to three-loop order. We find that the effective nucleon mass $M^*(\\rho)$ entering the energy density functional is iden...

Noise-tolerant instantaneous heart rate and R-peak detection using short-term autocorrelation for wearable healthcare systems.

Science.gov (United States)

Fujii, Takahide; Nakano, Masanao; Yamashita, Ken; Konishi, Toshihiro; Izumi, Shintaro; Kawaguchi, Hiroshi; Yoshimoto, Masahiko

2013-01-01

This paper describes a robust method of Instantaneous Heart Rate (IHR) and R-peak detection from noisy electrocardiogram (ECG) signals. Generally, the IHR is calculated from the R-wave interval. Then, the R-waves are extracted from the ECG using a threshold. However, in wearable bio-signal monitoring systems, noise increases the incidence of misdetection and false detection of R-peaks. To prevent incorrect detection, we introduce a short-term autocorrelation (STAC) technique and a small-window autocorrelation (SWAC) technique, which leverages the similarity of QRS complex waveforms. Simulation results show that the proposed method improves the noise tolerance of R-peak detection.

Reduced density matrix functional theory at finite temperature

Energy Technology Data Exchange (ETDEWEB)

Baldsiefen, Tim

2012-10-15

Density functional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to

Reduced density matrix functional theory at finite temperature

International Nuclear Information System (INIS)

Baldsiefen, Tim

2012-10-01

Density functional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to iteratively construct

Analysis of reactor noise; Analiza reaktorskih sumova

Energy Technology Data Exchange (ETDEWEB)

Velickovic, Lj [Institute of Nuclear Sciences Boris Kidric, Vinca, Beograd (Yugoslavia)

1967-11-15

This paper describes the theoretical model for interpretation of experimental results, experimental method for study of reactor noise at the RB reactor, numerical treatment of experimental results by correlation technique for analysis of reactor noise. A computer code was written to obtain autocorrelation function and spectral density function. Experimental results obtained by oscillator technique, pulse technique, and autocorrelation method are presented and discussed.

Improved density functional calculations for atoms, molecules and surfaces

International Nuclear Information System (INIS)

Fricke, B.; Anton, J.; Fritzsche, S.; Sarpe-Tudoran, C.

2005-01-01

The non-collinear and collinear descriptions within relativistic density functional theory is described. We present results of both non-collinear and collinear calculations for atoms, diatomic molecules, and some surface simulations. We find that the accuracy of our density functional calculations for the smaller systems is comparable to good quantum chemical calculations, and thus this method provides a sound basis for larger systems where no such comparison is possible. (author)

Relativistic density functional theory with picture-change corrected electron density based on infinite-order Douglas-Kroll-Hess method

Science.gov (United States)

Oyama, Takuro; Ikabata, Yasuhiro; Seino, Junji; Nakai, Hiromi

2017-07-01

This Letter proposes a density functional treatment based on the two-component relativistic scheme at the infinite-order Douglas-Kroll-Hess (IODKH) level. The exchange-correlation energy and potential are calculated using the electron density based on the picture-change corrected density operator transformed by the IODKH method. Numerical assessments indicated that the picture-change uncorrected density functional terms generate significant errors, on the order of hartree for heavy atoms. The present scheme was found to reproduce the energetics in the four-component treatment with high accuracy.

Stable Blind Deconvolution over the Reals from Additional Autocorrelations

KAUST Repository

Walk, Philipp

2017-10-22

Recently the one-dimensional time-discrete blind deconvolution problem was shown to be solvable uniquely, up to a global phase, by a semi-definite program for almost any signal, provided its autocorrelation is known. We will show in this work that under a sufficient zero separation of the corresponding signal in the $z-$domain, a stable reconstruction against additive noise is possible. Moreover, the stability constant depends on the signal dimension and on the signals magnitude of the first and last coefficients. We give an analytical expression for this constant by using spectral bounds of Vandermonde matrices.

Time-dependent quantum fluid density functional theory of hydrogen ...

Indian Academy of Sciences (India)

WINTEC

density functional theory; quantum fluid dynamics. 1. Introduction ... dynamics of strongly non-linear interaction of atoms with intense ... theory and quantum fluid dynamics in real space. .... clear evidence of bond softening since density in the.

Density functional theory for polymeric systems in 2D

International Nuclear Information System (INIS)

Słyk, Edyta; Bryk, Paweł; Roth, Roland

2016-01-01

We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim’s first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys . 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT. (paper)

Central depression in nucleonic densities: Trend analysis in the nuclear density functional theory approach

Science.gov (United States)

Schuetrumpf, B.; Nazarewicz, W.; Reinhard, P.-G.

2017-08-01

Background: The central depression of nucleonic density, i.e., a reduction of density in the nuclear interior, has been attributed to many factors. For instance, bubble structures in superheavy nuclei are believed to be due to the electrostatic repulsion. In light nuclei, the mechanism behind the density reduction in the interior has been discussed in terms of shell effects associated with occupations of s orbits. Purpose: The main objective of this work is to reveal mechanisms behind the formation of central depression in nucleonic densities in light and heavy nuclei. To this end, we introduce several measures of the internal nucleonic density. Through the statistical analysis, we study the information content of these measures with respect to nuclear matter properties. Method: We apply nuclear density functional theory with Skyrme functionals. Using the statistical tools of linear least square regression, we inspect correlations between various measures of central depression and model parameters, including nuclear matter properties. We study bivariate correlations with selected quantities as well as multiple correlations with groups of parameters. Detailed correlation analysis is carried out for 34Si for which a bubble structure has been reported recently, 48Ca, and N =82 , 126, and 184 isotonic chains. Results: We show that the central depression in medium-mass nuclei is very sensitive to shell effects, whereas for superheavy systems it is firmly driven by the electrostatic repulsion. An appreciable semibubble structure in proton density is predicted for 294Og, which is currently the heaviest nucleus known experimentally. Conclusion: Our correlation analysis reveals that the central density indicators in nuclei below 208Pb carry little information on parameters of nuclear matter; they are predominantly driven by shell structure. On the other hand, in the superheavy nuclei there exists a clear relationship between the central nucleonic density and symmetry energy.

Density Functional Methods for Shock Physics and High Energy Density Science

Science.gov (United States)

Desjarlais, Michael

2017-06-01

Molecular dynamics with density functional theory has emerged over the last two decades as a powerful and accurate framework for calculating thermodynamic and transport properties with broad application to dynamic compression, high energy density science, and warm dense matter. These calculations have been extensively validated against shock and ramp wave experiments, are a principal component of high-fidelity equation of state generation, and are having wide-ranging impacts on inertial confinement fusion, planetary science, and shock physics research. In addition to thermodynamic properties, phase boundaries, and the equation of state, one also has access to electrical conductivity, thermal conductivity, and lower energy optical properties. Importantly, all these properties are obtained within the same theoretical framework and are manifestly consistent. In this talk I will give a brief history and overview of molecular dynamics with density functional theory and its use in calculating a wide variety of thermodynamic and transport properties for materials ranging from ambient to extreme conditions and with comparisons to experimental data. I will also discuss some of the limitations and difficulties, as well as active research areas. Sandia is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

The maximal-density mass function for primordial black hole dark matter

Science.gov (United States)

Lehmann, Benjamin V.; Profumo, Stefano; Yant, Jackson

2018-04-01

The advent of gravitational wave astronomy has rekindled interest in primordial black holes (PBH) as a dark matter candidate. As there are many different observational probes of the PBH density across different masses, constraints on PBH models are dependent on the functional form of the PBH mass function. This complicates general statements about the mass functions allowed by current data, and, in particular, about the maximum total density of PBH. Numerical studies suggest that some forms of extended mass functions face tighter constraints than monochromatic mass functions, but they do not preclude the existence of a functional form for which constraints are relaxed. We use analytical arguments to show that the mass function which maximizes the fraction of the matter density in PBH subject to all constraints is a finite linear combination of monochromatic mass functions. We explicitly compute the maximum fraction of dark matter in PBH for different combinations of current constraints, allowing for total freedom of the mass function. Our framework elucidates the dependence of the maximum PBH density on the form of observational constraints, and we discuss the implications of current and future constraints for the viability of the PBH dark matter paradigm.

Benchmarks for electronically excited states: Time-dependent density functional theory and density functional theory based multireference configuration interaction

DEFF Research Database (Denmark)

Silva-Junior, Mario R.; Schreiber, Marko; Sauer, Stephan P. A.

2008-01-01

Time-dependent density functional theory (TD-DFT) and DFT-based multireference configuration interaction (DFT/MRCI) calculations are reported for a recently proposed benchmark set of 28 medium-sized organic molecules. Vertical excitation energies, oscillator strengths, and excited-state dipole...

Diffuse Waves and Energy Densities Near Boundaries

Science.gov (United States)

Sanchez-Sesma, F. J.; Rodriguez-Castellanos, A.; Campillo, M.; Perton, M.; Luzon, F.; Perez-Ruiz, J. A.

2007-12-01

Green function can be retrieved from averaging cross correlations of motions within a diffuse field. In fact, it has been shown that for an elastic inhomogeneous, anisotropic medium under equipartitioned, isotropic illumination, the average cross correlations are proportional to the imaginary part of Green function. For instance coda waves are due to multiple scattering and their intensities follow diffusive regimes. Coda waves and the noise sample the medium and effectively carry information along their paths. In this work we explore the consequences of assuming both source and receiver at the same point. From the observable side, the autocorrelation is proportional to the energy density at a given point. On the other hand, the imaginary part of the Green function at the source itself is finite because the singularity of Green function is restricted to the real part. The energy density at a point is proportional with the trace of the imaginary part of Green function tensor at the source itself. The Green function availability may allow establishing the theoretical energy density of a seismic diffuse field generated by a background equipartitioned excitation. We study an elastic layer with free surface and overlaying a half space and compute the imaginary part of the Green function for various depths. We show that the resulting spectrum is indeed closely related to the layer dynamic response and the corresponding resonant frequencies are revealed. One implication of present findings lies in the fact that spatial variations may be useful in detecting the presence of a target by its signature in the distribution of diffuse energy. These results may be useful in assessing the seismic response of a given site if strong ground motions are scarce. It suffices having a reasonable illumination from micro earthquakes and noise. We consider that the imaginary part of Green function at the source is a spectral signature of the site. The relative importance of the peaks of

Balancing Exchange Mixing in Density-Functional Approximations for Iron Porphyrin.

Science.gov (United States)

Berryman, Victoria E J; Boyd, Russell J; Johnson, Erin R

2015-07-14

Predicting the correct ground-state multiplicity for iron(II) porphyrin, a high-spin quintet, remains a significant challenge for electronic-structure methods, including commonly employed density functionals. An even greater challenge for these methods is correctly predicting favorable binding of O2 to iron(II) porphyrin, due to the open-shell singlet character of the adduct. In this work, the performance of a modest set of contemporary density-functional approximations is assessed and the results interpreted using Bader delocalization indices. It is found that inclusion of greater proportions of Hartree-Fock exchange, in hybrid or range-separated hybrid functionals, has opposing effects; it improves the ability of the functional to identify the ground state but is detrimental to predicting favorable dioxygen binding. Because of the uncomplementary nature of these properties, accurate prediction of both the relative spin-state energies and the O2 binding enthalpy eludes conventional density-functional approximations.

Geostatistical prediction of microbial water quality throughout a stream network using meteorology, land cover, and spatiotemporal autocorrelation.

Science.gov (United States)

Holcomb, David Andrew; Messier, Kyle P; Serre, Marc L; Rowny, Jakob G; Stewart, Jill R

2018-06-11

Predictive modeling is promising as an inexpensive tool to assess water quality. We developed geostatistical predictive models of microbial water quality that empirically modelled spatiotemporal autocorrelation in measured fecal coliform (FC) bacteria concentrations to improve prediction. We compared five geostatistical models featuring different autocorrelation structures, fit to 676 observations from 19 locations in North Carolina's Jordan Lake watershed using meteorological and land cover predictor variables. Though stream distance metrics (with and without flow-weighting) failed to improve prediction over the Euclidean distance metric, incorporating temporal autocorrelation substantially improved prediction over the space-only models. We predicted FC throughout the stream network daily for one year, designating locations "impaired", "unimpaired", or "unassessed" if the probability of exceeding the state standard was >90%, 10% but <90%, respectively. We could assign impairment status to more of the stream network on days any FC were measured, suggesting frequent sample-based monitoring remains necessary, though implementing spatiotemporal predictive models may reduce the number of concurrent sampling locations required to adequately assess water quality. Together, these results suggest that prioritizing sampling at different times and conditions using geographically sparse monitoring networks is adequate to build robust and informative geostatistical models of water quality impairment.

Joint density-functional theory and its application to systems in solution

Science.gov (United States)

Petrosyan, Sahak A.

The physics of solvation, the interaction of water with solutes, plays a central role in chemistry and biochemistry, and it is essential for the very existence of life. Despite the central importance of water and the advent of the quantum theory early in the twentieth century, the link between the fundamental laws of physics and the observable properties of water remain poorly understood to this day. The central goal of this thesis is to develop a new formalism and framework to make the study of systems (solutes or surfaces) in contact with liquid water as practical and accurate as standard electronic structure calculations without the need for explicit averaging over large ensembles of configurations of water molecules. The thesis introduces a new form of density functional theory for the ab initio description of electronic systems in contact with a molecular liquid environment. This theory rigorously joins an electron density-functional for the electrons of a solute with a classical density-functional theory for the liquid into a single variational principle for the free energy of the combined system. Using the new form of density-functional theory for the ab initio description of electronic systems in contact with a molecular liquid environment, the thesis then presents the first detailed study of the impact of a solvent on the surface chemistry of Cr2O3, the passivating layer of stainless steel alloys. In comparison to a vacuum, we predict that the presence of water has little impact on the adsorption of chloride ions to the oxygen-terminated surface but has a dramatic effect on the binding of hydrogen to that surface. A key ingredient of a successful joint density functional theory is a good approximate functional for describing the solvent. We explore how the simplest examples of the best known class of approximate forms for the classical density functional fail when applied directly to water. The thesis then presents a computationally efficient density-functional

Approach to kinetic energy density functionals: Nonlocal terms with the structure of the von Weizsaecker functional

International Nuclear Information System (INIS)

Garcia-Aldea, David; Alvarellos, J. E.

2008-01-01

We propose a kinetic energy density functional scheme with nonlocal terms based on the von Weizsaecker functional, instead of the more traditional approach where the nonlocal terms have the structure of the Thomas-Fermi functional. The proposed functionals recover the exact kinetic energy and reproduce the linear response function of homogeneous electron systems. In order to assess their quality, we have tested the total kinetic energies as well as the kinetic energy density for atoms. The results show that these nonlocal functionals give as good results as the most sophisticated functionals in the literature. The proposed scheme for constructing the functionals means a step ahead in the field of fully nonlocal kinetic energy functionals, because they are capable of giving better local behavior than the semilocal functionals, yielding at the same time accurate results for total kinetic energies. Moreover, the functionals enjoy the possibility of being evaluated as a single integral in momentum space if an adequate reference density is defined, and then quasilinear scaling for the computational cost can be achieved

A simulation-based approach to capturing auto-correlated demand parameter uncertainty in inventory management

NARCIS (Netherlands)

Akçay, A.E.; Biller, B.; Tayur, S.

2012-01-01

We consider a repeated newsvendor setting where the parameters of the demand distribution are unknown, and we study the problem of setting inventory targets using only a limited amount of historical demand data. We assume that the demand process is autocorrelated and represented by an

Panel data models extended to spatial error autocorrelation or a spatially lagged dependent variable

NARCIS (Netherlands)

Elhorst, J. Paul

2001-01-01

This paper surveys panel data models extended to spatial error autocorrelation or a spatially lagged dependent variable. In particular, it focuses on the specification and estimation of four panel data models commonly used in applied research: the fixed effects model, the random effects model, the

Intermittent electron density and temperature fluctuations and associated fluxes in the Alcator C-Mod scrape-off layer

Science.gov (United States)

Kube, R.; Garcia, O. E.; Theodorsen, A.; Brunner, D.; Kuang, A. Q.; LaBombard, B.; Terry, J. L.

2018-06-01

The Alcator C-Mod mirror Langmuir probe system has been used to sample data time series of fluctuating plasma parameters in the outboard mid-plane far scrape-off layer. We present a statistical analysis of one second long time series of electron density, temperature, radial electric drift velocity and the corresponding particle and electron heat fluxes. These are sampled during stationary plasma conditions in an ohmically heated, lower single null diverted discharge. The electron density and temperature are strongly correlated and feature fluctuation statistics similar to the ion saturation current. Both electron density and temperature time series are dominated by intermittent, large-amplitude burst with an exponential distribution of both burst amplitudes and waiting times between them. The characteristic time scale of the large-amplitude bursts is approximately 15 μ {{s}}. Large-amplitude velocity fluctuations feature a slightly faster characteristic time scale and appear at a faster rate than electron density and temperature fluctuations. Describing these time series as a superposition of uncorrelated exponential pulses, we find that probability distribution functions, power spectral densities as well as auto-correlation functions of the data time series agree well with predictions from the stochastic model. The electron particle and heat fluxes present large-amplitude fluctuations. For this low-density plasma, the radial electron heat flux is dominated by convection, that is, correlations of fluctuations in the electron density and radial velocity. Hot and dense blobs contribute only a minute fraction of the total fluctuation driven heat flux.

Blue functions: probability and current density propagators in non-relativistic quantum mechanics

International Nuclear Information System (INIS)

Withers, L P Jr

2011-01-01

Like a Green function to propagate a particle's wavefunction in time, a Blue function is introduced to propagate the particle's probability and current density. Accordingly, the complete Blue function has four components. They are constructed from path integrals involving a quantity like the action that we call the motion. The Blue function acts on the displaced probability density as the kernel of an integral operator. As a result, we find that the Wigner density occurs as an expression for physical propagation. We also show that, in quantum mechanics, the displaced current density is conserved bilocally (in two places at one time), as expressed by a generalized continuity equation. (paper)

Synthesis, Crystal Structure, Density Function Theory, Molecular ...

African Journals Online (AJOL)

Tropical Journal of Pharmaceutical Research February 2016; 15 (2): 385-392 ... tested for its antimicrobial activities and computational studies including density function test (DFT) and docking ... agonists [4], selective dopamine D3 and D4 ...

Applications of Density Functional Theory in Soft Condensed Matter

Science.gov (United States)

Löwen, Hartmut

Applications of classical density functional theory (DFT) to soft matter systems like colloids, liquid crystals and polymer solutions are discussed with a focus on the freezing transition and on nonequilibrium Brownian dynamics. First, after a brief reminder of equilibrium density functional theory, DFT is applied to the freezing transition of liquids into crystalline lattices. In particular, spherical particles with radially symmetric pair potentials will be treated (like hard spheres, the classical one-component plasma or Gaussian-core particles). Second, the DFT will be generalized towards Brownian dynamics in order to tackle nonequilibrium problems. After a general introduction to Brownian dynamics using the complementary Smoluchowski and Langevin pictures appropriate for the dynamics of colloidal suspensions, the dynamical density functional theory (DDFT) will be derived from the Smoluchowski equation. This will be done first for spherical particles (e.g. hard spheres or Gaussian-cores) without hydrodynamic interactions. Then we show how to incorporate hydrodynamic interactions between the colloidal particles into the DDFT framework and compare to Brownian dynamics computer simulations. Third orientational degrees of freedom (rod-like particles) will be considered as well. In the latter case, the stability of intermediate liquid crystalline phases (isotropic, nematic, smectic-A, plastic crystals etc) can be predicted. Finally, the corresponding dynamical extension of density functional theory towards orientational degrees of freedom is proposed and the collective behaviour of "active" (self-propelled) Brownian particles is briefly discussed.

Plato: A localised orbital based density functional theory code

Science.gov (United States)

Kenny, S. D.; Horsfield, A. P.

2009-12-01

The Plato package allows both orthogonal and non-orthogonal tight-binding as well as density functional theory (DFT) calculations to be performed within a single framework. The package also provides extensive tools for analysing the results of simulations as well as a number of tools for creating input files. The code is based upon the ideas first discussed in Sankey and Niklewski (1989) [1] with extensions to allow high-quality DFT calculations to be performed. DFT calculations can utilise either the local density approximation or the generalised gradient approximation. Basis sets from minimal basis through to ones containing multiple radial functions per angular momenta and polarisation functions can be used. Illustrations of how the package has been employed are given along with instructions for its utilisation. Program summaryProgram title: Plato Catalogue identifier: AEFC_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFC_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 219 974 No. of bytes in distributed program, including test data, etc.: 1 821 493 Distribution format: tar.gz Programming language: C/MPI and PERL Computer: Apple Macintosh, PC, Unix machines Operating system: Unix, Linux and Mac OS X Has the code been vectorised or parallelised?: Yes, up to 256 processors tested RAM: Up to 2 Gbytes per processor Classification: 7.3 External routines: LAPACK, BLAS and optionally ScaLAPACK, BLACS, PBLAS, FFTW Nature of problem: Density functional theory study of electronic structure and total energies of molecules, crystals and surfaces. Solution method: Localised orbital based density functional theory. Restrictions: Tight-binding and density functional theory only, no exact exchange. Unusual features: Both atom centred and uniform meshes available

General framework for fluctuating dynamic density functional theory

Science.gov (United States)

Durán-Olivencia, Miguel A.; Yatsyshin, Peter; Goddard, Benjamin D.; Kalliadasis, Serafim

2017-12-01

We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig’s projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory. The resultant equation has the structure of a dynamical density-functional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier-Stokes equations, originally derived by Landau and Lifshitz

What Density Functional Theory could do for Quantum Information

Science.gov (United States)

Mattsson, Ann

2015-03-01

The Hohenberg-Kohn theorem of Density Functional Theory (DFT), and extensions thereof, tells us that all properties of a system of electrons can be determined through their density, which uniquely determines the many-body wave-function. Given access to the appropriate, universal, functionals of the density we would, in theory, be able to determine all observables of any electronic system, without explicit reference to the wave-function. On the other hand, the wave-function is at the core of Quantum Information (QI), with the wave-function of a set of qubits being the central computational resource in a quantum computer. While there is seemingly little overlap between DFT and QI, reliance upon observables form a key connection. Though the time-evolution of the wave-function and associated phase information is fundamental to quantum computation, the initial and final states of a quantum computer are characterized by observables of the system. While observables can be extracted directly from a system's wave-function, DFT tells us that we may be able to intuit a method for extracting them from its density. In this talk, I will review the fundamentals of DFT and how these principles connect to the world of QI. This will range from DFT's utility in the engineering of physical qubits, to the possibility of using it to efficiently (but approximately) simulate Hamiltonians at the logical level. The apparent paradox of describing algorithms based on the quantum mechanical many-body wave-function with a DFT-like theory based on observables will remain a focus throughout. The ultimate goal of this talk is to initiate a dialog about what DFT could do for QI, in theory and in practice. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

The QTP family of consistent functionals and potentials in Kohn-Sham density functional theory

Energy Technology Data Exchange (ETDEWEB)

Jin, Yifan; Bartlett, Rodney J., E-mail: bartlett@qtp.ufl.edu [Quantum Theory Project and Departments of Chemistry and Physics, University of Florida, Gainesville, Florida 32611 (United States)

2016-07-21

This manuscript presents the second, consistent density functional in the QTP (Quantum Theory Project) family, that is, the CAM-QTP(01). It is a new range-separated exchange-correlation functional in which the non-local exchange contribution is 100% at large separation. It follows the same basic principles of this family that the Kohn-Sham eigenvalues of the occupied orbitals approximately equal the vertical ionization energies, which is not fulfilled by most of the traditional density functional methods. This new CAM-QTP(01) functional significantly improves the accuracy of the vertical excitation energies especially for the Rydberg states in the test set. It also reproduces many other properties such as geometries, reaction barrier heights, and atomization energies.

Distribution function approach to redshift space distortions. Part II: N-body simulations

International Nuclear Information System (INIS)

Okumura, Teppei; Seljak, Uroš; McDonald, Patrick; Desjacques, Vincent

2012-01-01

Measurement of redshift-space distortions (RSD) offers an attractive method to directly probe the cosmic growth history of density perturbations. A distribution function approach where RSD can be written as a sum over density weighted velocity moment correlators has recently been developed. In this paper we use results of N-body simulations to investigate the individual contributions and convergence of this expansion for dark matter. If the series is expanded as a function of powers of μ, cosine of the angle between the Fourier mode and line of sight, then there are a finite number of terms contributing at each order. We present these terms and investigate their contribution to the total as a function of wavevector k. For μ 2 the correlation between density and momentum dominates on large scales. Higher order corrections, which act as a Finger-of-God (FoG) term, contribute 1% at k ∼ 0.015hMpc −1 , 10% at k ∼ 0.05hMpc −1 at z = 0, while for k > 0.15hMpc −1 they dominate and make the total negative. These higher order terms are dominated by density-energy density correlations which contributes negatively to the power, while the contribution from vorticity part of momentum density auto-correlation adds to the total power, but is an order of magnitude lower. For μ 4 term the dominant term on large scales is the scalar part of momentum density auto-correlation, while higher order terms dominate for k > 0.15hMpc −1 . For μ 6 and μ 8 we find it has very little power for k −1 , shooting up by 2–3 orders of magnitude between k −1 and k −1 . We also compare the expansion to the full 2-d P ss (k,μ), as well as to the monopole, quadrupole, and hexadecapole integrals of P ss (k,μ). For these statistics an infinite number of terms contribute and we find that the expansion achieves percent level accuracy for kμ −1 at 6-th order, but breaks down on smaller scales because the series is no longer perturbative. We explore resummation of the terms into Fo

An improved triple collocation algorithm for decomposing autocorrelated and white soil moisture retrieval errors

Science.gov (United States)

If not properly account for, auto-correlated errors in observations can lead to inaccurate results in soil moisture data analysis and reanalysis. Here, we propose a more generalized form of the triple collocation algorithm (GTC) capable of decomposing the total error variance of remotely-sensed surf...

Density functional study of gamma-aminopropyltriethoxysilane

International Nuclear Information System (INIS)

Bistricic, L; Volovsek, V; Daani, V; Leskovac, M

2006-01-01

Density functional theory calculations using Becke's three-parameter exchange functional in combination with the Lee-Young-Parr correlation functional (B3-LYP) and standard 6-311 + G(d,p) basis set were carried out to study the conformational stability and vibrational spectra of gamma-aminopropyltriethoxysilane. Calculations reveal the existence of two stable conformers trans and gauche. The calculated energy for the gauche conformation was found to be 608 cm -1 above the minimum energy of the trans conformation. Temperature dependence of Raman spectra of liquid APTES and DFT calculation enabled us to identify the vibrational bands characteristic for both conformers. It has been shown that there is an increase in the population of gauche conformer with increasing temperature

Open-system Kohn-Sham density functional theory.

Science.gov (United States)

Zhou, Yongxi; Ernzerhof, Matthias

2012-03-07

A simple model for electron transport through molecules is provided by the source-sink potential (SSP) method [F. Goyer, M. Ernzerhof, and M. Zhuang, J. Chem. Phys. 126, 144104 (2007)]. In SSP, the boundary conditions of having an incoming and outgoing electron current are enforced through complex potentials that are added to the Hamiltonian. Depending on the sign of the imaginary part of the potentials, current density is generated or absorbed. In this way, a finite system can be used to model infinite molecular electronic devices. The SSP has originally been developed for the Hückel method and subsequently it has been extended [F. Goyer and M. Ernzerhof, J. Chem. Phys. 134, 174101 (2011)] to the Hubbard model. Here we present a step towards its generalization for first-principles electronic structure theory methods. In particular, drawing on our earlier work, we discuss a new generalized density functional theory for complex non-Hermitian Hamiltonians. This theory enables us to combine SSP and Kohn-Sham theory to obtain a method for the description of open systems that exchange current density with their environment. Similarly, the Hartree-Fock method is extended to the realm of non-Hermitian, SSP containing Hamiltonians. As a proof of principle, we present the first applications of complex-density functional theory (CODFT) as well as non-Hermitian Hartree-Fock theory to electron transport through molecules. © 2012 American Institute of Physics

Density Functional Theory and Materials Modeling at Atomistic Length Scales

Directory of Open Access Journals (Sweden)

Swapan K. Ghosh

2002-04-01

Full Text Available Abstract: We discuss the basic concepts of density functional theory (DFT as applied to materials modeling in the microscopic, mesoscopic and macroscopic length scales. The picture that emerges is that of a single unified framework for the study of both quantum and classical systems. While for quantum DFT, the central equation is a one-particle Schrodinger-like Kohn-Sham equation, the classical DFT consists of Boltzmann type distributions, both corresponding to a system of noninteracting particles in the field of a density-dependent effective potential, the exact functional form of which is unknown. One therefore approximates the exchange-correlation potential for quantum systems and the excess free energy density functional or the direct correlation functions for classical systems. Illustrative applications of quantum DFT to microscopic modeling of molecular interaction and that of classical DFT to a mesoscopic modeling of soft condensed matter systems are highlighted.

Bone mineral density and menstrual function in adolescent female ...

African Journals Online (AJOL)

Bone mineral density and menstrual function in adolescent female long-distance runners - A prospective comparative study of bone structure and menstrual function in adolescent female endurance athletes from five secondary schools in Pretoria.

Semi-local machine-learned kinetic energy density functional with third-order gradients of electron density

Science.gov (United States)

Seino, Junji; Kageyama, Ryo; Fujinami, Mikito; Ikabata, Yasuhiro; Nakai, Hiromi

2018-06-01

A semi-local kinetic energy density functional (KEDF) was constructed based on machine learning (ML). The present scheme adopts electron densities and their gradients up to third-order as the explanatory variables for ML and the Kohn-Sham (KS) kinetic energy density as the response variable in atoms and molecules. Numerical assessments of the present scheme were performed in atomic and molecular systems, including first- and second-period elements. The results of 37 conventional KEDFs with explicit formulae were also compared with those of the ML KEDF with an implicit formula. The inclusion of the higher order gradients reduces the deviation of the total kinetic energies from the KS calculations in a stepwise manner. Furthermore, our scheme with the third-order gradient resulted in the closest kinetic energies to the KS calculations out of the presented functionals.

Response functions of cold neutron matter: density, spin and current fluctuations

Energy Technology Data Exchange (ETDEWEB)

Keller, Jochen; Sedrakian, Armen [Institut fuer Theoretische Physik, Goethe-Universitaet, Frankfurt am Main (Germany)

2014-07-01

We study the response of a single-component pair-correlated baryonic Fermi-liquid to density, spin, and their current perturbations. A complete set of response functions is calculated in the low-temperature regime. We derive the spectral functions of collective excitations associated with the density, density-current, spin, and spin-current perturbations. The dispersion relations of density and spin fluctuations are determined and it is shown that the density fluctuations lead to exciton-like undamped bound states, whereas the spin excitations correspond to diffusive modes above the pair-breaking threshold. The contribution of the collective pair-breaking modes to the specific heat of neutron matter at subnuclear densities is computed and is shown to be comparable to that of the degenerate electron gas at not too low temperatures.

On extending Kohn-Sham density functionals to systems with fractional number of electrons.

Science.gov (United States)

Li, Chen; Lu, Jianfeng; Yang, Weitao

2017-06-07

We analyze four ways of formulating the Kohn-Sham (KS) density functionals with a fractional number of electrons, through extending the constrained search space from the Kohn-Sham and the generalized Kohn-Sham (GKS) non-interacting v-representable density domain for integer systems to four different sets of densities for fractional systems. In particular, these density sets are (I) ensemble interacting N-representable densities, (II) ensemble non-interacting N-representable densities, (III) non-interacting densities by the Janak construction, and (IV) non-interacting densities whose composing orbitals satisfy the Aufbau occupation principle. By proving the equivalence of the underlying first order reduced density matrices associated with these densities, we show that sets (I), (II), and (III) are equivalent, and all reduce to the Janak construction. Moreover, for functionals with the ensemble v-representable assumption at the minimizer, (III) reduces to (IV) and thus justifies the previous use of the Aufbau protocol within the (G)KS framework in the study of the ground state of fractional electron systems, as defined in the grand canonical ensemble at zero temperature. By further analyzing the Aufbau solution for different density functional approximations (DFAs) in the (G)KS scheme, we rigorously prove that there can be one and only one fractional occupation for the Hartree Fock functional, while there can be multiple fractional occupations for general DFAs in the presence of degeneracy. This has been confirmed by numerical calculations using the local density approximation as a representative of general DFAs. This work thus clarifies important issues on density functional theory calculations for fractional electron systems.

Nonlocal and Nonadiabatic Effects in the Charge-Density Response of Solids: A Time-Dependent Density-Functional Approach

Science.gov (United States)

Panholzer, Martin; Gatti, Matteo; Reining, Lucia

2018-04-01

The charge-density response of extended materials is usually dominated by the collective oscillation of electrons, the plasmons. Beyond this feature, however, intriguing many-body effects are observed. They cannot be described by one of the most widely used approaches for the calculation of dielectric functions, which is time-dependent density functional theory (TDDFT) in the adiabatic local density approximation (ALDA). Here, we propose an approximation to the TDDFT exchange-correlation kernel which is nonadiabatic and nonlocal. It is extracted from correlated calculations in the homogeneous electron gas, where we have tabulated it for a wide range of wave vectors and frequencies. A simple mean density approximation allows one to use it in inhomogeneous materials where the density varies on a scale of 1.6 rs or faster. This kernel contains effects that are completely absent in the ALDA; in particular, it correctly describes the double plasmon in the dynamic structure factor of sodium, and it shows the characteristic low-energy peak that appears in systems with low electronic density. It also leads to an overall quantitative improvement of spectra.

A Comparative Density Functional Theory and Density Functional Tight Binding Study of Phases of Nitrogen Including a High Energy Density Material N8

Directory of Open Access Journals (Sweden)

Nicholas Capel

2015-11-01

Full Text Available We present a comparative dispersion-corrected Density Functional Theory (DFT and Density Functional Tight Binding (DFTB-D study of several phases of nitrogen, including the well-known alpha, beta, and gamma phases as well as recently discovered highly energetic phases: covalently bound cubic gauche (cg nitrogen and molecular (vdW-bound N8 crystals. Among several tested parametrizations of N–N interactions for DFTB, we identify only one that is suitable for modeling of all these phases. This work therefore establishes the applicability of DFTB-D to studies of phases, including highly metastable phases, of nitrogen, which will be of great use for modelling of dynamics of reactions involving these phases, which may not be practical with DFT due to large required space and time scales. We also derive a dispersion-corrected DFT (DFT-D setup (atom-centered basis parameters and Grimme dispersion parameters tuned for accurate description simultaneously of several nitrogen allotropes including covalently and vdW-bound crystals and including high-energy phases.

The use of perturbation theory in density-functional theory

International Nuclear Information System (INIS)

Goerling, A.

1996-01-01

Perturbation theory with respect to the electron-electron interaction leads to expressions for the exchange and correlation energies and potentials in terms of Kohn-Sham orbitals and Kohn-Sham eigenvalues. An exact open-quote exchange-only close-quote procedure for solids is introduced. Results for several semiconductors are presented. Perturbation theory expansions for the hardness of molecules and the bad gap of solids are given. Density-functional exchange and correlation energies for excited states are defined and a perturbation theory based Kohn-Sham formalism to treat excited states within density-functional theory is introduced

Comment on "Nonuniqueness of algebraic first-order density-matrix functionals"

Science.gov (United States)

Gritsenko, O. V.

2018-02-01

Wang and Knowles (WK) [Phys. Rev. A 92, 012520 (2015), 10.1103/PhysRevA.92.012520] have given a counterexample to the conventional in reduced density-matrix functional theory representation of the second-order reduced density matrix (2RDM) Γi j ,k l in the basis of the natural orbitals as a function Γi j ,k l(n ) of the orbital occupation numbers (ONs) ni. The observed nonuniqueness of Γi j ,k l for prototype systems of different symmetry has been interpreted as the inherent inability of ON functions to reproduce the 2RDM, due to the insufficient information contained in the 1RDM spectrum. In this Comment, it is argued that, rather than totally invalidating Γi j ,k l(n ) , the WK example exposes its symmetry dependence which, as well as the previously established analogous dependence in density functional theory, is demonstrated with a general formulation based on the Levy constrained search.

Contribution of ultrasound forward scattering to tissue structure study

International Nuclear Information System (INIS)

Edee, M.K.

1987-12-01

In this paper, we show how to get useful information of tissue structure by merely interpreting some experimental graphs such as energy spectral density and autocorrelation function of an ultrasonic beam travelling through tissues. To support these interpretations, we needed just some well-known theorems rather than heavy and complicated mathematical equations, so we measured the dimensions of scatterers within specimens by using the graphical representation of autocorrelation function. We related these measurements to the scattered peaks which appear in energy density spectrum. The values we found were equal to those obtained from biologists within ∼ 15%. (author) 26 refs, 6 figs, tabs

Density functional theory calculations of charge transport properties ...

Indian Academy of Sciences (India)

ZIRAN CHEN

2017-08-04

Aug 4, 2017 ... properties of 'plate-like' coronene topological structures ... Keywords. Organic semiconductors; density functional theory; charge carrier mobility; ambipolar transport; ..... nology Department of Sichuan Province (Grant Number.

Towards improved local hybrid functionals by calibration of exchange-energy densities

International Nuclear Information System (INIS)

Arbuznikov, Alexei V.; Kaupp, Martin

2014-01-01

A new approach for the calibration of (semi-)local and exact exchange-energy densities in the context of local hybrid functionals is reported. The calibration functions are derived from only the electron density and its spatial derivatives, avoiding spatial derivatives of the exact-exchange energy density or other computationally unfavorable contributions. The calibration functions fulfill the seven more important out of nine known exact constraints. It is shown that calibration improves substantially the definition of a non-dynamical correlation energy term for generalized gradient approximation (GGA)-based local hybrids. Moreover, gauge artifacts in the potential-energy curves of noble-gas dimers may be corrected by calibration. The developed calibration functions are then evaluated for a large range of energy-related properties (atomization energies, reaction barriers, ionization potentials, electron affinities, and total atomic energies) of three sets of local hybrids, using a simple one-parameter local-mixing. The functionals are based on (a) local spin-density approximation (LSDA) or (b) Perdew-Burke-Ernzerhof (PBE) exchange and correlation, and on (c) Becke-88 (B88) exchange and Lee-Yang-Parr (LYP) correlation. While the uncalibrated GGA-based functionals usually provide very poor thermochemical data, calibration allows a dramatic improvement, accompanied by only a small deterioration of reaction barriers. In particular, an optimized BLYP-based local-hybrid functional has been found that is a substantial improvement over the underlying global hybrids, as well as over previously reported LSDA-based local hybrids. It is expected that the present calibration approach will pave the way towards new generations of more accurate hyper-GGA functionals based on a local mixing of exchange-energy densities

A density functional study of backbone structures of polydiacetylene: destabilization of butatriene structure

International Nuclear Information System (INIS)

Katagiri, Hideki; Shimoi, Yukihiro; Abe, Shuji

2004-01-01

Backbone structures of polydiacetylene are studied with first-principles electronic structure method using plane-waves within generalized gradient approximation (GGA) of density functional theory. In spin-restricted calculations a coarse k-point sampling gives a potential energy curve with two local minima corresponding to acetylene and butatriene structures. However, the potential barrier between the two structures rapidly decreases with increasing number of k-points, which results in destabilization of the butatriene structure. Spin polarization effects also destabilize the butatriene structure, inducing atom-centered spin-density-wave state. These potential energies were compared with those obtained by Hartree-Fock, density functional within local density approximation (LDA) and GGA, and hybrid density functional methods using a gaussian basis set. The comparison shows that the density functional methods within LDA and GGA favor the destabilization of the butatriene structure in contrast to the Hartree-Fock method

Applications of Skyrme energy-density functional to fusion reactions spanning the fusion barriers

International Nuclear Information System (INIS)

Liu Min; Wang, Ning; Li Zhuxia; Wu Xizhen; Zhao Enguang

2006-01-01

The Skyrme energy density functional has been applied to the study of heavy-ion fusion reactions. The barriers for fusion reactions are calculated by the Skyrme energy density functional with proton and neutron density distributions determined by using restricted density variational (RDV) method within the same energy density functional together with semi-classical approach known as the extended semi-classical Thomas-Fermi method. Based on the fusion barrier obtained, we propose a parametrization of the empirical barrier distribution to take into account the multi-dimensional character of real barrier and then apply it to calculate the fusion excitation functions in terms of barrier penetration concept. A large number of measured fusion excitation functions spanning the fusion barriers can be reproduced well. The competition between suppression and enhancement effects on sub-barrier fusion caused by neutron-shell-closure and excess neutron effects is studied

Isobaric-Isothermal Molecular Dynamics Utilizing Density Functional Theory: An Assessment of the Structure and Density of Water at Near-Ambient Conditions

International Nuclear Information System (INIS)

Schmidt, J.; VandeVondele, J.; Kuo, I.W.; Sebastiani, D.; Siepmann, J.I.; Hutter, J.; Mundy, C.J.

2009-01-01

We present herein a comprehensive density functional theory study toward assessing the accuracy of two popular gradient-corrected exchange correlation functionals on the structure and density of liquid water at near ambient conditions in the isobaric-isothermal ensemble. Our results indicate that both PBE and BLYP functionals under predict the density and over structure the liquid. Adding the dispersion correction due to Grimme(1, 2) improves the predicted densities for both BLYP and PBE in a significant manner. Moreover, the addition of the dispersion correction for BLYP yields an oxygen-oxygen radial distribution function in excellent agreement with experiment. Thus, we conclude that one can obtain a very satisfactory model for water using BLYP and a correction for dispersion.

Non-local energy density functionals: models plus some exact general results

International Nuclear Information System (INIS)

March, N.H.

2001-02-01

Holas and March (Phys. Rev. A51, 2040, 1995) gave a formally exact expression for the force - δV xc (r-tilde)/δr-tilde associated with the exchange-correlation potential V xc (r-tilde) of density functional theory. This forged a precise link between first- and second-order density matrices and V xc (r-tilde). Here models are presented in which these low-order matrices can be related to the ground-state electron density. This allows non-local energy density functionals to be constructed within the framework of such models. Finally, results emerging from these models have led to the derivation of some exact 'nuclear cusp' relations for exchange and correlation energy densities in molecules, clusters and condensed phases. (author)

Statistical study of density fluctuations in the tore supra tokamak

International Nuclear Information System (INIS)

Devynck, P.; Fenzi, C.; Garbet, X.; Laviron, C.

1998-03-01

It is believed that the radial anomalous transport in tokamaks is caused by plasma turbulence. Using infra-red laser scattering technique on the Tore Supra tokamak, statistical properties of the density fluctuations are studied as a function of the scales in ohmic as well as additional heating regimes using the lower hybrid or the ion cyclotron frequencies. The probability distributions are compared to a Gaussian in order to estimate the role of intermittency which is found to be negligible. The temporal behaviour of the three-dimensional spectrum is thoroughly discussed; its multifractal character is reflected in the singularity spectrum. The autocorrelation coefficient as well as their long-time incoherence and statistical independence. We also put forward the existence of fluctuations transfer between two distinct but close wavenumbers. A rather clearer image is thus obtained about the way energy is transferred through the turbulent scales. (author)

Multilevel models for multiple-baseline data: modeling across-participant variation in autocorrelation and residual variance.

Science.gov (United States)

Baek, Eun Kyeng; Ferron, John M

2013-03-01

Multilevel models (MLM) have been used as a method for analyzing multiple-baseline single-case data. However, some concerns can be raised because the models that have been used assume that the Level-1 error covariance matrix is the same for all participants. The purpose of this study was to extend the application of MLM of single-case data in order to accommodate across-participant variation in the Level-1 residual variance and autocorrelation. This more general model was then used in the analysis of single-case data sets to illustrate the method, to estimate the degree to which the autocorrelation and residual variances differed across participants, and to examine whether inferences about treatment effects were sensitive to whether or not the Level-1 error covariance matrix was allowed to vary across participants. The results from the analyses of five published studies showed that when the Level-1 error covariance matrix was allowed to vary across participants, some relatively large differences in autocorrelation estimates and error variance estimates emerged. The changes in modeling the variance structure did not change the conclusions about which fixed effects were statistically significant in most of the studies, but there was one exception. The fit indices did not consistently support selecting either the more complex covariance structure, which allowed the covariance parameters to vary across participants, or the simpler covariance structure. Given the uncertainty in model specification that may arise when modeling single-case data, researchers should consider conducting sensitivity analyses to examine the degree to which their conclusions are sensitive to modeling choices.

Limit theory for the sample autocorrelations and extremes of a GARCH (1,1) process

NARCIS (Netherlands)

Mikosch, T; Starica, C

2000-01-01

The asymptotic theory for the sample autocorrelations and extremes of a GARCH(I, 1) process is provided. Special attention is given to the case when the sum of the ARCH and GARCH parameters is close to 1, that is, when one is close to an infinite Variance marginal distribution. This situation has

Density functional application to strongly correlated electron systems

International Nuclear Information System (INIS)

Eschrig, H.; Koepernik, K.; Chaplygin, I.

2003-01-01

The local spin density approximation plus onsite Coulomb repulsion approach (LSDA+U) to density functional theory is carefully reanalyzed. Its possible link to single-particle Green's function theory is occasionally discussed. A simple and elegant derivation of the important sum rules for the on-site interaction matrix elements linking them to the values of U and J is presented. All necessary expressions for an implementation of LSDA+U into a non-orthogonal basis solver for the Kohn-Sham equations are given, and implementation into the full-potential local-orbital solver (Phys. Rev. B 59 (1999) 1743) is made. Results of application to several planar cuprate structures are reported in detail and conclusions on the interpretation of the physics of the electronic structure of the cuprates are drawn

Density-correlation functions in Calogero-Sutherland models

International Nuclear Information System (INIS)

Minahan, J.A.; Polychronakos, A.P.

1994-01-01

Using arguments from two-dimensional Yang-Mills theory and the collective coordinate formulation of the Calogero-Sutherland model, we conjecture the dynamical density-correlation function for coupling l and 1/l, where l is an integer. We present overwhelming evidence that the conjecture is indeed correct

Density correlation functions in Calogero-Sutherland models

CERN Document Server

Minahan, Joseph A.; Joseph A Minahan; Alexios P Polychronakos

1994-01-01

Using arguments from two dimensional Yang-Mills theory and the collective coordinate formulation of the Calogero-Sutherland model, we conjecture the dynamical density correlation function for coupling l and 1/l, where l is an integer. We present overwhelming evidence that the conjecture is indeed correct.

Multiconfiguration pair-density functional theory: barrier heights and main group and transition metal energetics.

Science.gov (United States)

Carlson, Rebecca K; Li Manni, Giovanni; Sonnenberger, Andrew L; Truhlar, Donald G; Gagliardi, Laura

2015-01-13

Kohn-Sham density functional theory, resting on the representation of the electronic density and kinetic energy by a single Slater determinant, has revolutionized chemistry, but for open-shell systems, the Kohn-Sham Slater determinant has the wrong symmetry properties as compared to an accurate wave function. We have recently proposed a theory, called multiconfiguration pair-density functional theory (MC-PDFT), in which the electronic kinetic energy and classical Coulomb energy are calculated from a multiconfiguration wave function with the correct symmetry properties, and the rest of the energy is calculated from a density functional, called the on-top density functional, that depends on the density and the on-top pair density calculated from this wave function. We also proposed a simple way to approximate the on-top density functional by translation of Kohn-Sham exchange-correlation functionals. The method is much less expensive than other post-SCF methods for calculating the dynamical correlation energy starting with a multiconfiguration self-consistent-field wave function as the reference wave function, and initial tests of the theory were quite encouraging. Here, we provide a broader test of the theory by applying it to bond energies of main-group molecules and transition metal complexes, barrier heights and reaction energies for diverse chemical reactions, proton affinities, and the water dimerization energy. Averaged over 56 data points, the mean unsigned error is 3.2 kcal/mol for MC-PDFT, as compared to 6.9 kcal/mol for Kohn-Sham theory with a comparable density functional. MC-PDFT is more accurate on average than complete active space second-order perturbation theory (CASPT2) for main-group small-molecule bond energies, alkyl bond dissociation energies, transition-metal-ligand bond energies, proton affinities, and the water dimerization energy.

Broadband short pulse measurement by autocorrelation with a sum-frequency generation set-up

International Nuclear Information System (INIS)

Glotin, F.; Jaroszynski, D.; Marcouille, O.

1995-01-01

Previous spectral and laser pulse length measurements carried out on the CLIO FEL at wavelength λ=8.5 μm suggested that very short light pulses could be generated, about 500 fs wide (FWHM). For these measurements a Michelson interferometer with a Te crystal, as a non-linear detector, was used as a second order autocorrelation device. More recent measurements in similar conditions have confirmed that the laser pulses observed are indeed single: they are not followed by other pulses distant by the slippage length Nλ. As the single micropulse length is likely to depend on the slippage, more measurements at different wavelengths would be useful. This is not directly possible with our actual interferometer set-up, based on a phase-matched non-linear crystal. However, we can use the broadband non-linear medium provided by one of our users' experiments: Sum-Frequency Generation over surfaces. With such autocorrelation set-up, interference fringes are no more visible, but this is largely compensated by the frequency range provided. First tests at 8 μm have already been performed to validate the technic, leading to results similar to those obtained with our previous Michelson set-up

Hotspot detection using image pattern recognition based on higher-order local auto-correlation

Science.gov (United States)

Maeda, Shimon; Matsunawa, Tetsuaki; Ogawa, Ryuji; Ichikawa, Hirotaka; Takahata, Kazuhiro; Miyairi, Masahiro; Kotani, Toshiya; Nojima, Shigeki; Tanaka, Satoshi; Nakagawa, Kei; Saito, Tamaki; Mimotogi, Shoji; Inoue, Soichi; Nosato, Hirokazu; Sakanashi, Hidenori; Kobayashi, Takumi; Murakawa, Masahiro; Higuchi, Tetsuya; Takahashi, Eiichi; Otsu, Nobuyuki

2011-04-01

Below 40nm design node, systematic variation due to lithography must be taken into consideration during the early stage of design. So far, litho-aware design using lithography simulation models has been widely applied to assure that designs are printed on silicon without any error. However, the lithography simulation approach is very time consuming, and under time-to-market pressure, repetitive redesign by this approach may result in the missing of the market window. This paper proposes a fast hotspot detection support method by flexible and intelligent vision system image pattern recognition based on Higher-Order Local Autocorrelation. Our method learns the geometrical properties of the given design data without any defects as normal patterns, and automatically detects the design patterns with hotspots from the test data as abnormal patterns. The Higher-Order Local Autocorrelation method can extract features from the graphic image of design pattern, and computational cost of the extraction is constant regardless of the number of design pattern polygons. This approach can reduce turnaround time (TAT) dramatically only on 1CPU, compared with the conventional simulation-based approach, and by distributed processing, this has proven to deliver linear scalability with each additional CPU.

Level Densities and Radiative Strength Functions in 170,171Yb

International Nuclear Information System (INIS)

Agvaanluvsan, U.; Schiller, A.; Becker, J.A.; Berstein, L.A.; Guttormsen, M.; Mitchell, G.E.; Rekstad, J.; Siem, S.; Voinov, A.

2003-01-01

Level densities and radiative strength functions in 171 Yb and 170 Yb nuclei have been measured with the 171 Yb( 3 He, 3 He(prime) γ) 171 Yb and 171 Yb( 3 He, αγ) 170 Yb reactions. A simultaneous determination of the nuclear level density and the radiative strength function was made. The present data adds to and is consistent with previous results for several other rare earth nuclei. The method will be briefly reviewed and the result from the analysis will be presented. The radiative strength function for 171 Yb is compared to previously published work.

Treatment of Layered Structures Using a Semilocal meta-GGA Density Functional

DEFF Research Database (Denmark)

Madsen, Georg; Ferrighi, Lara; Hammer, Bjørk

2010-01-01

Density functional theory calculations on solids consisting of covalently bonded layers held together by dispersive interactions are presented. Utilizing the kinetic energy density in addition to the density and its gradients gives the meta-generalized gradient approximation (MGGA) M06-L enough...

Density-functional theory of atoms and molecules

CERN Document Server

Parr, Robert G

1995-01-01

Provides an account of the fundamental principles of the density-functional theory of the electronic structure of matter and its applications to atoms and molecules. This book contains a discussion of the chemical potential and its derivatives. It is intended for physicists, chemists, and advanced students in chemistry.

Probability density function method for variable-density pressure-gradient-driven turbulence and mixing

International Nuclear Information System (INIS)

Bakosi, Jozsef; Ristorcelli, Raymond J.

2010-01-01

Probability density function (PDF) methods are extended to variable-density pressure-gradient-driven turbulence. We apply the new method to compute the joint PDF of density and velocity in a non-premixed binary mixture of different-density molecularly mixing fluids under gravity. The full time-evolution of the joint PDF is captured in the highly non-equilibrium flow: starting from a quiescent state, transitioning to fully developed turbulence and finally dissipated by molecular diffusion. High-Atwood-number effects (as distinguished from the Boussinesq case) are accounted for: both hydrodynamic turbulence and material mixing are treated at arbitrary density ratios, with the specific volume, mass flux and all their correlations in closed form. An extension of the generalized Langevin model, originally developed for the Lagrangian fluid particle velocity in constant-density shear-driven turbulence, is constructed for variable-density pressure-gradient-driven flows. The persistent small-scale anisotropy, a fundamentally 'non-Kolmogorovian' feature of flows under external acceleration forces, is captured by a tensorial diffusion term based on the external body force. The material mixing model for the fluid density, an active scalar, is developed based on the beta distribution. The beta-PDF is shown to be capable of capturing the mixing asymmetry and that it can accurately represent the density through transition, in fully developed turbulence and in the decay process. The joint model for hydrodynamics and active material mixing yields a time-accurate evolution of the turbulent kinetic energy and Reynolds stress anisotropy without resorting to gradient diffusion hypotheses, and represents the mixing state by the density PDF itself, eliminating the need for dubious mixing measures. Direct numerical simulations of the homogeneous Rayleigh-Taylor instability are used for model validation.

A pair density functional theory utilizing the correlated wave function

International Nuclear Information System (INIS)

Higuchi, M; Higuchi, K

2009-01-01

We propose a practical scheme for calculating the ground-state pair density (PD) by utilizing the correlated wave function. As the correlated wave function, we adopt a linear combination of the single Slater determinants that are constructed from the solutions of the initial scheme [Higuchi M and Higuchi K 2007 Physica B 387, 117]. The single-particle equation is derived by performing the variational principle within the set of PDs that are constructed from such correlated wave functions. Since the search region of the PD is substantially extended as compared with the initial scheme, it is expected that the present scheme can cover more correlation effects. The single-particle equation is practical, and may be easily applied to actual calculations.

Efficient molecular density functional theory using generalized spherical harmonics expansions.

Science.gov (United States)

Ding, Lu; Levesque, Maximilien; Borgis, Daniel; Belloni, Luc

2017-09-07

We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ(r,Ω) around the solute is a function of the position r≡(x,y,z) and of the three Euler angles Ω≡(θ,ϕ,ψ) describing the solvent orientation. The standard density functional, equivalent to the hypernetted-chain closure for the solute-solvent correlations in the liquid theory, is minimized with respect to ρ(r,Ω). The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes. We finally illustrate the formalism by tackling the solvation of molecules of various complexities in water.

Probability-density-function characterization of multipartite entanglement

International Nuclear Information System (INIS)

Facchi, P.; Florio, G.; Pascazio, S.

2006-01-01

We propose a method to characterize and quantify multipartite entanglement for pure states. The method hinges upon the study of the probability density function of bipartite entanglement and is tested on an ensemble of qubits in a variety of situations. This characterization is also compared to several measures of multipartite entanglement

Higher-order terms in the nuclear-energy-density functional

International Nuclear Information System (INIS)

Carlsson, B. G.; Borucki, M.; Dobaczewski, J.

2009-01-01

One of the current projects at the Department of Physics in the University of Jyvaeskylae is to explore more general forms of the Skyrme energy-density functional (EDF). The aim is to find new phenomenological terms which are sensitive to experimental data. In this context we have extended the Skyrme functional by including terms which contain higher orders of derivatives allowing for a better description of finite range effects. This was done by employing an expansion in derivatives in a spherical-tensor formalism [1] motivated by ideas of the density-matrix expansion. The resulting functionals have different number of free parameters depending on the order in derivatives and assumed symmetries, see Fig. 1. The usual Skyrme EDF is obtained as a second order expansion while we keep terms up to sixth order.(author)

Quantal density functional theory II. Approximation methods and applications

International Nuclear Information System (INIS)

Sahni, Viraht

2010-01-01

This book is on approximation methods and applications of Quantal Density Functional Theory (QDFT), a new local effective-potential-energy theory of electronic structure. What distinguishes the theory from traditional density functional theory is that the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and the correlation contribution to the kinetic energy -- the Correlation-Kinetic effects -- are separately and explicitly defined. As such it is possible to study each property of interest as a function of the different electron correlations. Approximations methods based on the incorporation of different electron correlations, as well as a many-body perturbation theory within the context of QDFT, are developed. The applications are to the few-electron inhomogeneous electron gas systems in atoms and molecules, as well as to the many-electron inhomogeneity at metallic surfaces. (orig.)

Pressure and surface tension of soild-liquid interface using Tarazona density functional theory

Directory of Open Access Journals (Sweden)

M. M.

2000-12-01

Full Text Available   The weighted density functional theory proposed by Tarazona is applied to study the solid-liquid interface. In the last two decades the weighted density functional became a useful tool to consider the properties of inhomogeneous liquids. In this theory, the role of the size of molecules or the particles of which the matter is composed, was found to be important. In this resarch we study a hard sphere fluid beside a hard wall. For this study the liquid is an inhomogeneous system. We use the definition of the direct correlation function as a second derivative of free energy with respect to the density. We use this definition and the definition of the weighting function, then we minimize the grand potential with respect to the density to get the Euler Lagrange equation and we obtain an integral equation to find the inhomogeneous density profile. The obtained density profile as a function of the distance from the wall, for different bulk density is plotted in three dimensions. We also calculate the pressure and compare it with the Carnahan-starling results, and finally we obtained the surface tension at liquid-solid interface and compared it with the results of Monte Carlo simulation.

An energy landscape model for glass-forming liquids in three dimensions

DEFF Research Database (Denmark)

Pedersen, Ulf Rørbæk; Hecksher, Tina; Dyre, Jeppe

2006-01-01

different densities at several temperatures. At high densities and low temperatures the model captures the important characteristics of viscous liquid dynamics. We thus observe non-exponential relaxation in the self part of the density auto-correlation function, and fragility plots of the self...

Restoring the consistency with the contact density theorem of a classical density functional theory of ions at a planar electrical double layer.

Science.gov (United States)

Gillespie, Dirk

2014-11-01

Classical density functional theory (DFT) of fluids is a fast and efficient theory to compute the structure of the electrical double layer in the primitive model of ions where ions are modeled as charged, hard spheres in a background dielectric. While the hard-core repulsive component of this ion-ion interaction can be accurately computed using well-established DFTs, the electrostatic component is less accurate. Moreover, many electrostatic functionals fail to satisfy a basic theorem, the contact density theorem, that relates the bulk pressure, surface charge, and ion densities at their distances of closest approach for ions in equilibrium at a smooth, hard, planar wall. One popular electrostatic functional that fails to satisfy the contact density theorem is a perturbation approach developed by Kierlik and Rosinberg [Phys. Rev. A 44, 5025 (1991)PLRAAN1050-294710.1103/PhysRevA.44.5025] and Rosenfeld [J. Chem. Phys. 98, 8126 (1993)JCPSA60021-960610.1063/1.464569], where the full free-energy functional is Taylor-expanded around a bulk (homogeneous) reference fluid. Here, it is shown that this functional fails to satisfy the contact density theorem because it also fails to satisfy the known low-density limit. When the functional is corrected to satisfy this limit, a corrected bulk pressure is derived and it is shown that with this pressure both the contact density theorem and the Gibbs adsorption theorem are satisfied.

Correlation functional in screened-exchange density functional theory procedures.

Science.gov (United States)

Chan, Bun; Kawashima, Yukio; Hirao, Kimihiko

2017-10-15

In the present study, we have explored several prospects for the further development of screened-exchange density functional theory (SX-DFT) procedures. Using the performance of HSE06 as our measure, we find that the use of alternative correlation functionals (as oppose to PBEc in HSE06) also yields adequate results for a diverse set of thermochemical properties. We have further examined the performance of new SX-DFT procedures (termed HSEB-type methods) that comprise the HSEx exchange and a (near-optimal) reparametrized B97c (c OS,0  = c SS,0  = 1, c OS,1  = -1.5, c OS,2  = -0.644, c SS,1  = -0.5, and c SS,2  = 1.10) correlation functionals. The different variants of HSEB all perform comparably to or slightly better than the original HSE-type procedures. These results, together with our fundamental analysis of correlation functionals, point toward various directions for advancing SX-DFT methods. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Building a universal nuclear energy density functional

International Nuclear Information System (INIS)

Bertsch, G F

2007-01-01

This talk describes a new project in SciDAC II in the area of low-energy nuclear physics. The motivation and goals of the SciDAC are presented as well as an outline of the theoretical and computational methodology that will be employed. An important motivation is to have more accurate and reliable predictions of nuclear properties including their binding energies and low-energy reaction rates. The theoretical basis is provided by density functional theory, which the only available theory that can be systematically applied to all nuclei. However, other methodologies based on wave function methods are needed to refine the functionals and to make applications to dynamic processes

Disease Mapping and Regression with Count Data in the Presence of Overdispersion and Spatial Autocorrelation: A Bayesian Model Averaging Approach

Science.gov (United States)

Mohebbi, Mohammadreza; Wolfe, Rory; Forbes, Andrew

2014-01-01

This paper applies the generalised linear model for modelling geographical variation to esophageal cancer incidence data in the Caspian region of Iran. The data have a complex and hierarchical structure that makes them suitable for hierarchical analysis using Bayesian techniques, but with care required to deal with problems arising from counts of events observed in small geographical areas when overdispersion and residual spatial autocorrelation are present. These considerations lead to nine regression models derived from using three probability distributions for count data: Poisson, generalised Poisson and negative binomial, and three different autocorrelation structures. We employ the framework of Bayesian variable selection and a Gibbs sampling based technique to identify significant cancer risk factors. The framework deals with situations where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. The evidence from applying the modelling methodology suggests that modelling strategies based on the use of generalised Poisson and negative binomial with spatial autocorrelation work well and provide a robust basis for inference. PMID:24413702

Coarsening in 3D nonconserved Ising model at zero temperature: Anomaly in structure and slow relaxation of order-parameter autocorrelation

Science.gov (United States)

Chakraborty, Saikat; Das, Subir K.

2017-09-01

Via Monte Carlo simulations we study pattern and aging during coarsening in a nonconserved nearest-neighbor Ising model, following quenches from infinite to zero temperature, in space dimension d = 3. The decay of the order-parameter autocorrelation function appears to obey a power-law behavior, as a function of the ratio between the observation and waiting times, in the large ratio limit. However, the exponent of the power law, estimated accurately via a state-of-the-art method, violates a well-known lower bound. This surprising fact has been discussed in connection with a quantitative picture of the structural anomaly that the 3D Ising model exhibits during coarsening at zero temperature. These results are compared with those for quenches to a temperature above that of the roughening transition.

A-centers in silicon studied with hybrid density functional theory

KAUST Repository

Wang, Hao; Chroneos, Alexander; Londos, C. A.; Schwingenschlö gl, Udo; Sgourou, E. N.

2013-01-01

Density functional theory employing hybrid functional is used to gain fundamental insight into the interaction of vacancies with oxygen interstitials to form defects known as A-centers in silicon. We calculate the formation energy of the defect with respect to the Fermi energy for all possible charge states. It is found that the neutral and doubly negatively charged A-centers dominate. The findings are analyzed in terms of the density of states and discussed in view of previous experimental and theoretical studies.

A-centers in silicon studied with hybrid density functional theory

KAUST Repository

Wang, Hao

2013-07-29

Density functional theory employing hybrid functional is used to gain fundamental insight into the interaction of vacancies with oxygen interstitials to form defects known as A-centers in silicon. We calculate the formation energy of the defect with respect to the Fermi energy for all possible charge states. It is found that the neutral and doubly negatively charged A-centers dominate. The findings are analyzed in terms of the density of states and discussed in view of previous experimental and theoretical studies.

Density-functional errors in ionization potential with increasing system size

Energy Technology Data Exchange (ETDEWEB)

Whittleton, Sarah R.; Sosa Vazquez, Xochitl A.; Isborn, Christine M., E-mail: cisborn@ucmerced.edu [Chemistry and Chemical Biology, School of Natural Sciences, University of California, Merced, 5200 North Lake Road, Merced, California 95343 (United States); Johnson, Erin R., E-mail: erin.johnson@dal.ca [Chemistry and Chemical Biology, School of Natural Sciences, University of California, Merced, 5200 North Lake Road, Merced, California 95343 (United States); Department of Chemistry, Dalhousie University, 6274 Coburg Road, Halifax, Nova Scotia B3H 4R2 (Canada)

2015-05-14

This work investigates the effects of molecular size on the accuracy of density-functional ionization potentials for a set of 28 hydrocarbons, including series of alkanes, alkenes, and oligoacenes. As the system size increases, delocalization error introduces a systematic underestimation of the ionization potential, which is rationalized by considering the fractional-charge behavior of the electronic energies. The computation of the ionization potential with many density-functional approximations is not size-extensive due to excessive delocalization of the incipient positive charge. While inclusion of exact exchange reduces the observed errors, system-specific tuning of long-range corrected functionals does not generally improve accuracy. These results emphasize that good performance of a functional for small molecules is not necessarily transferable to larger systems.

A Density Functional for Liquid 3He Based on the Aziz Potential

Science.gov (United States)

Barranco, M.; Hernández, E. S.; Mayol, R.; Navarro, J.; Pi, M.; Szybisz, L.

2006-09-01

We propose a new class of density functionals for liquid 3He based on the Aziz helium-helium interaction screened at short distances by the microscopically calculated two-body distribution function g(r). Our aim is to reduce to a minumum the unavoidable phenomenological ingredients inherent to any density functional approach. Results for the homogeneous liquid and droplets are presented and discussed.

On Farmer's line, probability density functions, and overall risk

International Nuclear Information System (INIS)

Munera, H.A.; Yadigaroglu, G.

1986-01-01

Limit lines used to define quantitative probabilistic safety goals can be categorized according to whether they are based on discrete pairs of event sequences and associated probabilities, on probability density functions (pdf's), or on complementary cumulative density functions (CCDFs). In particular, the concept of the well-known Farmer's line and its subsequent reinterpretations is clarified. It is shown that Farmer's lines are pdf's and, therefore, the overall risk (defined as the expected value of the pdf) that they represent can be easily calculated. It is also shown that the area under Farmer's line is proportional to probability, while the areas under CCDFs are generally proportional to expected value

Density functional and many-body theories of Hydrogen plasmas

International Nuclear Information System (INIS)

Perrot, F.; Dharma-Wardana, M.W.C.

1983-11-01

This work is an attempt to go beyond the standard description of hot condensed matter using the well-known ''average atom model''. The first part describes a static model using ''Density functional theory'' to calculate self-consistent coupled electron and ion density profiles of the plasma not restricted to a single average atomic sphere. In a second part, the results are used as ingredients for a many-body approach to electronic properties: the one-particle Green-function self-energy is calculated, from which shifted levels, populations and level-widths are deduced. Results for the Hydrogen plasma are reported, with emphasis on the 1s bound state

Ground-state properties of third-row elements with nonlocal density functionals

International Nuclear Information System (INIS)

Bagno, P.; Jepsen, O.; Gunnarsson, O.

1989-01-01

The cohesive energy, the lattice parameter, and the bulk modulus of third-row elements are calculated using the Langreth-Mehl-Hu (LMH), the Perdew-Wang (PW), and the gradient expansion functionals. The PW functional is found to give somewhat better results than the LMH functional and both are found to typically remove half the errors in the local-spin-density (LSD) approximation, while the gradient expansion gives worse results than the local-density approximation. For Fe both the LMH and PW functionals correctly predict a ferromagnetic bcc ground state, while the LSD approximation and the gradient expansion predict a nonmagnetic fcc ground state

Solvent density inhomogeneities and solvation free energies in supercritical diatomic fluids: a density functional approach.

Science.gov (United States)

Husowitz, B; Talanquer, V

2007-02-07

Density functional theory is used to explore the solvation properties of a spherical solute immersed in a supercritical diatomic fluid. The solute is modeled as a hard core Yukawa particle surrounded by a diatomic Lennard-Jones fluid represented by two fused tangent spheres using an interaction site approximation. The authors' approach is particularly suitable for thoroughly exploring the effect of different interaction parameters, such as solute-solvent interaction strength and range, solvent-solvent long-range interactions, and particle size, on the local solvent structure and the solvation free energy under supercritical conditions. Their results indicate that the behavior of the local coordination number in homonuclear diatomic fluids follows trends similar to those reported in previous studies for monatomic fluids. The local density augmentation is particularly sensitive to changes in solute size and is affected to a lesser degree by variations in the solute-solvent interaction strength and range. The associated solvation free energies exhibit a nonmonotonous behavior as a function of density for systems with weak solute-solvent interactions. The authors' results suggest that solute-solvent interaction anisotropies have a major influence on the nature and extent of local solvent density inhomogeneities and on the value of the solvation free energies in supercritical solutions of heteronuclear molecules.

Density functional theory

International Nuclear Information System (INIS)

Freyss, M.

2015-01-01

This chapter gives an introduction to first-principles electronic structure calculations based on the density functional theory (DFT). Electronic structure calculations have a crucial importance in the multi-scale modelling scheme of materials: not only do they enable one to accurately determine physical and chemical properties of materials, they also provide data for the adjustment of parameters (or potentials) in higher-scale methods such as classical molecular dynamics, kinetic Monte Carlo, cluster dynamics, etc. Most of the properties of a solid depend on the behaviour of its electrons, and in order to model or predict them it is necessary to have an accurate method to compute the electronic structure. DFT is based on quantum theory and does not make use of any adjustable or empirical parameter: the only input data are the atomic number of the constituent atoms and some initial structural information. The complicated many-body problem of interacting electrons is replaced by an equivalent single electron problem, in which each electron is moving in an effective potential. DFT has been successfully applied to the determination of structural or dynamical properties (lattice structure, charge density, magnetisation, phonon spectra, etc.) of a wide variety of solids. Its efficiency was acknowledged by the attribution of the Nobel Prize in Chemistry in 1998 to one of its authors, Walter Kohn. A particular attention is given in this chapter to the ability of DFT to model the physical properties of nuclear materials such as actinide compounds. The specificities of the 5f electrons of actinides will be presented, i.e., their more or less high degree of localisation around the nuclei and correlations. The limitations of the DFT to treat the strong 5f correlations are one of the main issues for the DFT modelling of nuclear fuels. Various methods that exist to better treat strongly correlated materials will finally be presented. (author)

Extending density functional embedding theory for covalently bonded systems.

Science.gov (United States)

Yu, Kuang; Carter, Emily A

2017-12-19

Quantum embedding theory aims to provide an efficient solution to obtain accurate electronic energies for systems too large for full-scale, high-level quantum calculations. It adopts a hierarchical approach that divides the total system into a small embedded region and a larger environment, using different levels of theory to describe each part. Previously, we developed a density-based quantum embedding theory called density functional embedding theory (DFET), which achieved considerable success in metals and semiconductors. In this work, we extend DFET into a density-matrix-based nonlocal form, enabling DFET to study the stronger quantum couplings between covalently bonded subsystems. We name this theory density-matrix functional embedding theory (DMFET), and we demonstrate its performance in several test examples that resemble various real applications in both chemistry and biochemistry. DMFET gives excellent results in all cases tested thus far, including predicting isomerization energies, proton transfer energies, and highest occupied molecular orbital-lowest unoccupied molecular orbital gaps for local chromophores. Here, we show that DMFET systematically improves the quality of the results compared with the widely used state-of-the-art methods, such as the simple capped cluster model or the widely used ONIOM method.

Bridge density functional approximation for non-uniform hard core repulsive Yukawa fluid

International Nuclear Information System (INIS)

Zhou Shiqi

2008-01-01

In this work, a bridge density functional approximation (BDFA) (J. Chem. Phys. 112, 8079 (2000)) for a non-uniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa (HCRY) fluid. It is found that the choice of a bulk bridge functional approximation is crucial for both a uniform HCRY fluid and a non-uniform HCRY fluid. A new bridge functional approximation is proposed, which can accurately predict the radial distribution function of the bulk HCRY fluid. With the new bridge functional approximation and its associated bulk second order direct correlation function as input, the BDFA can be used to well calculate the density profile of the HCRY fluid subjected to the influence of varying external fields, and the theoretical predictions are in good agreement with the corresponding simulation data. The calculated results indicate that the present BDFA captures quantitatively the phenomena such as the coexistence of solid-like high density phase and low density gas phase, and the adsorption properties of the HCRY fluid, which qualitatively differ from those of the fluids combining both hard-core repulsion and an attractive tail. (condensed matter: structure, thermal and mechanical properties)

2nd derivatives of the electronic energy in density functional theory

Energy Technology Data Exchange (ETDEWEB)

Dam, H. van

2001-08-01

This document details the equations needed to implement the calculation of vibrational frequencies within the density functional formalism of electronic structure theory. This functionality has been incorporated into the CCP1 DFT module and the required changes to the application programmers interface are outlined. Throughout it is assumed that an implementation of Hartree-Fock vibrational frequencies is available that can be modified to incorporate the density functional formalism. Employing GAMESS-UK as an example the required changes to the Hartree-Fock code are outlined. (author)

JDFTx: Software for joint density-functional theory

Directory of Open Access Journals (Sweden)

Ravishankar Sundararaman

2017-01-01

Full Text Available Density-functional theory (DFT has revolutionized computational prediction of atomic-scale properties from first principles in physics, chemistry and materials science. Continuing development of new methods is necessary for accurate predictions of new classes of materials and properties, and for connecting to nano- and mesoscale properties using coarse-grained theories. JDFTx is a fully-featured open-source electronic DFT software designed specifically to facilitate rapid development of new theories, models and algorithms. Using an algebraic formulation as an abstraction layer, compact C++11 code automatically performs well on diverse hardware including GPUs (Graphics Processing Units. This code hosts the development of joint density-functional theory (JDFT that combines electronic DFT with classical DFT and continuum models of liquids for first-principles calculations of solvated and electrochemical systems. In addition, the modular nature of the code makes it easy to extend and interface with, facilitating the development of multi-scale toolkits that connect to ab initio calculations, e.g. photo-excited carrier dynamics combining electron and phonon calculations with electromagnetic simulations.

Many-body theory and Energy Density Functionals

Energy Technology Data Exchange (ETDEWEB)

Baldo, M. [INFN, Catania (Italy)

2016-07-15

In this paper a method is first presented to construct an Energy Density Functional on a microscopic basis. The approach is based on the Kohn-Sham method, where one introduces explicitly the Nuclear Matter Equation of State, which can be obtained by an accurate many-body calculation. In this way it connects the functional to the bare nucleon-nucleon interaction. It is shown that the resulting functional can be performing as the best Gogny force functional. In the second part of the paper it is shown how one can go beyond the mean-field level and the difficulty that can appear. The method is based on the particle-vibration coupling scheme and a formalism is presented that can handle the correct use of the vibrational degrees of freedom within a microscopic approach. (orig.)

Characterizing the Spatial Density Functions of Neural Arbors

Science.gov (United States)

Teeter, Corinne Michelle

Recently, it has been proposed that a universal function describes the way in which all arbors (axons and dendrites) spread their branches over space. Data from fish retinal ganglion cells as well as cortical and hippocampal arbors from mouse, rat, cat, monkey and human provide evidence that all arbor density functions (adf) can be described by a Gaussian function truncated at approximately two standard deviations. A Gaussian density function implies that there is a minimal set of parameters needed to describe an adf: two or three standard deviations (depending on the dimensionality of the arbor) and an amplitude. However, the parameters needed to completely describe an adf could be further constrained by a scaling law found between the product of the standard deviations and the amplitude of the function. In the following document, I examine the scaling law relationship in order to determine the minimal set of parameters needed to describe an adf. First, I find that the at, two-dimensional arbors of fish retinal ganglion cells require only two out of the three fundamental parameters to completely describe their density functions. Second, the three-dimensional, volume filling, cortical arbors require four fundamental parameters: three standard deviations and the total length of an arbor (which corresponds to the amplitude of the function). Next, I characterize the shape of arbors in the context of the fundamental parameters. I show that the parameter distributions of the fish retinal ganglion cells are largely homogenous. In general, axons are bigger and less dense than dendrites; however, they are similarly shaped. The parameter distributions of these two arbor types overlap and, therefore, can only be differentiated from one another probabilistically based on their adfs. Despite artifacts in the cortical arbor data, different types of arbors (apical dendrites, non-apical dendrites, and axons) can generally be differentiated based on their adfs. In addition, within

Multireference Density Functional Theory with Generalized Auxiliary Systems for Ground and Excited States.

Science.gov (United States)

Chen, Zehua; Zhang, Du; Jin, Ye; Yang, Yang; Su, Neil Qiang; Yang, Weitao

2017-09-21

To describe static correlation, we develop a new approach to density functional theory (DFT), which uses a generalized auxiliary system that is of a different symmetry, such as particle number or spin, from that of the physical system. The total energy of the physical system consists of two parts: the energy of the auxiliary system, which is determined with a chosen density functional approximation (DFA), and the excitation energy from an approximate linear response theory that restores the symmetry to that of the physical system, thus rigorously leading to a multideterminant description of the physical system. The electron density of the physical system is different from that of the auxiliary system and is uniquely determined from the functional derivative of the total energy with respect to the external potential. Our energy functional is thus an implicit functional of the physical system density, but an explicit functional of the auxiliary system density. We show that the total energy minimum and stationary states, describing the ground and excited states of the physical system, can be obtained by a self-consistent optimization with respect to the explicit variable, the generalized Kohn-Sham noninteracting density matrix. We have developed the generalized optimized effective potential method for the self-consistent optimization. Among options of the auxiliary system and the associated linear response theory, reformulated versions of the particle-particle random phase approximation (pp-RPA) and the spin-flip time-dependent density functional theory (SF-TDDFT) are selected for illustration of principle. Numerical results show that our multireference DFT successfully describes static correlation in bond dissociation and double bond rotation.

Density Functional Theory An Advanced Course

CERN Document Server

Dreizler, Reiner M

2011-01-01

Density Functional Theory (DFT) has firmly established itself as the workhorse for the atomic-level simulation of condensed matter phases, pure or composite materials and quantum chemical systems. The present book is a rigorous and detailed introduction to the foundations up to and including such advanced topics as orbital-dependent functionals and both time-dependent and relativistic DFT. Given the many ramifications of contemporary DFT, this text concentrates on the self-contained presentation of the basics of the most widely used DFT variants. This implies a thorough discussion of the corresponding existence theorems and effective single particle equations, as well as of key approximations utilized in implementations. The formal results are complemented by selected quantitative results, which primarily aim at illustrating strengths and weaknesses of a particular approach or functional. DFT for superconducting or nuclear and hadronic systems are not addressed in this work. The structure and material contain...

Density functional theory of polydisperse fluid interfaces

International Nuclear Information System (INIS)

Baus, M.; Bellier-Castella, L.; Xu, H.

2002-01-01

Most colloids usually exhibit one or several polydispersities. A natural framework for the theoretical description of polydisperse systems is provided by the extension of density functional theory to 'continuous' mixtures. This will be illustrated here by the study of both the bulk and interfacial properties of a simple van der Waals model for a polydisperse colloidal fluid. (author)

Derivative discontinuity and exchange-correlation potential of meta-GGAs in density-functional theory.

Science.gov (United States)

Eich, F G; Hellgren, Maria

2014-12-14

We investigate fundamental properties of meta-generalized-gradient approximations (meta-GGAs) to the exchange-correlation energy functional, which have an implicit density dependence via the Kohn-Sham kinetic-energy density. To this purpose, we construct the most simple meta-GGA by expressing the local exchange-correlation energy per particle as a function of a fictitious density, which is obtained by inverting the Thomas-Fermi kinetic-energy functional. This simple functional considerably improves the total energy of atoms as compared to the standard local density approximation. The corresponding exchange-correlation potentials are then determined exactly through a solution of the optimized effective potential equation. These potentials support an additional bound state and exhibit a derivative discontinuity at integer particle numbers. We further demonstrate that through the kinetic-energy density any meta-GGA incorporates a derivative discontinuity. However, we also find that for commonly used meta-GGAs the discontinuity is largely underestimated and in some cases even negative.

Derivative discontinuity and exchange-correlation potential of meta-GGAs in density-functional theory

International Nuclear Information System (INIS)

Eich, F. G.; Hellgren, Maria

2014-01-01

We investigate fundamental properties of meta-generalized-gradient approximations (meta-GGAs) to the exchange-correlation energy functional, which have an implicit density dependence via the Kohn-Sham kinetic-energy density. To this purpose, we construct the most simple meta-GGA by expressing the local exchange-correlation energy per particle as a function of a fictitious density, which is obtained by inverting the Thomas-Fermi kinetic-energy functional. This simple functional considerably improves the total energy of atoms as compared to the standard local density approximation. The corresponding exchange-correlation potentials are then determined exactly through a solution of the optimized effective potential equation. These potentials support an additional bound state and exhibit a derivative discontinuity at integer particle numbers. We further demonstrate that through the kinetic-energy density any meta-GGA incorporates a derivative discontinuity. However, we also find that for commonly used meta-GGAs the discontinuity is largely underestimated and in some cases even negative

Bulk stress auto-correlation function in simple liquids-sum rules

International Nuclear Information System (INIS)

Tankeshwar, K.; Bhandari, R.; Pathak, K.N.

1990-10-01

Expressions for the zeroth, second and fourth frequency sum rules of the bulk stress auto correlation function have been derived. The exact expressions involve static correlation function up to four particles. Because of the non availability of any information about static quadruplet correlation function we use a low order decoupling approximation for this. In this work, we have obtained, separately, the sum rules for the different mechanism of momentum transfer in the fluids. The results are expected to be useful in the study of bulk viscosity of the fluids. (author). 9 refs

Ab initio derivation of model energy density functionals

International Nuclear Information System (INIS)

Dobaczewski, Jacek

2016-01-01

I propose a simple and manageable method that allows for deriving coupling constants of model energy density functionals (EDFs) directly from ab initio calculations performed for finite fermion systems. A proof-of-principle application allows for linking properties of finite nuclei, determined by using the nuclear nonlocal Gogny functional, to the coupling constants of the quasilocal Skyrme functional. The method does not rely on properties of infinite fermion systems but on the ab initio calculations in finite systems. It also allows for quantifying merits of different model EDFs in describing the ab initio results. (letter)

Geometry optimization of molecules within an LCGTO local-density functional approach

International Nuclear Information System (INIS)

Mintmire, J.W.

1990-01-01

We describe our implementation of geometry optimization techniques within the linear combination of Gaussian-type orbitals (LCGTO) approach to local-density functional theory. The algorithm for geometry optimization is based on the evaluation of the gradient of the total energy with respect to internal coordinates within the local-density functional scheme. We present optimization results for a range of small molecules which serve as test cases for our approach

KIDS Nuclear Energy Density Functional: 1st Application in Nuclei

Science.gov (United States)

Gil, Hana; Papakonstantinou, Panagiota; Hyun, Chang Ho; Oh, Yongseok

We apply the KIDS (Korea: IBS-Daegu-Sungkyunkwan) nuclear energy density functional model, which is based on the Fermi momentum expansion, to the study of properties of lj-closed nuclei. The parameters of the model are determined by the nuclear properties at the saturation density and theoretical calculations on pure neutron matter. For applying the model to the study of nuclei, we rely on the Skyrme force model, where the Skyrme force parameters are determined through the KIDS energy density functional. Solving Hartree-Fock equations, we obtain the energies per particle and charge radii of closed magic nuclei, namely, 16O, 28O, 40Ca, 48Ca, 60Ca, 90Zr, 132Sn, and 208Pb. The results are compared with the observed data and further improvement of the model is shortly mentioned.

Density-dependence of functional spiking networks in vitro

Energy Technology Data Exchange (ETDEWEB)

Ham, Michael I [Los Alamos National Laboratory; Gintautuas, Vadas [Los Alamos National Laboratory; Rodriguez, Marko A [Los Alamos National Laboratory; Bettencourt, Luis M A [Los Alamos National Laboratory; Bennett, Ryan [UNIV OF NORTH TEXAS; Santa Maria, Cara L [UNIV OF NORTH TEXAS

2008-01-01

During development, the mammalian brain differentiates into specialized regions with unique functional abilities. While many factors contribute to this functional specialization, we explore the effect neuronal density can have on neuronal interactions. Two types of networks, dense (50,000 neurons and glia support cells) and sparse (12,000 neurons and glia support cells), are studied. A competitive first response model is applied to construct activation graphs that represent pairwise neuronal interactions. By observing the evolution of these graphs during development in vitro we observe that dense networks form activation connections earlier than sparse networks, and that link-!llltropy analysis of the resulting dense activation graphs reveals that balanced directional connections dominate. Information theoretic measures reveal in addition that early functional information interactions (of order 3) are synergetic in both dense and sparse networks. However, during development in vitro, such interactions become redundant in dense, but not sparse networks. Large values of activation graph link-entropy correlate strongly with redundant ensembles observed in the dense networks. Results demonstrate differences between dense and sparse networks in terms of informational groups, pairwise relationships, and activation graphs. These differences suggest that variations in cell density may result in different functional specialization of nervous system tissue also in vivo.

Explaining local-scale species distributions: relative contributions of spatial autocorrelation and landscape heterogeneity for an avian assemblage.

Directory of Open Access Journals (Sweden)

Brady J Mattsson

Full Text Available Understanding interactions between mobile species distributions and landcover characteristics remains an outstanding challenge in ecology. Multiple factors could explain species distributions including endogenous evolutionary traits leading to conspecific clustering and endogenous habitat features that support life history requirements. Birds are a useful taxon for examining hypotheses about the relative importance of these factors among species in a community. We developed a hierarchical Bayes approach to model the relationships between bird species occupancy and local landcover variables accounting for spatial autocorrelation, species similarities, and partial observability. We fit alternative occupancy models to detections of 90 bird species observed during repeat visits to 316 point-counts forming a 400-m grid throughout the Patuxent Wildlife Research Refuge in Maryland, USA. Models with landcover variables performed significantly better than our autologistic and null models, supporting the hypothesis that local landcover heterogeneity is important as an exogenous driver for species distributions. Conspecific clustering alone was a comparatively poor descriptor of local community composition, but there was evidence for spatial autocorrelation in all species. Considerable uncertainty remains whether landcover combined with spatial autocorrelation is most parsimonious for describing bird species distributions at a local scale. Spatial structuring may be weaker at intermediate scales within which dispersal is less frequent, information flows are localized, and landcover types become spatially diversified and therefore exhibit little aggregation. Examining such hypotheses across species assemblages contributes to our understanding of community-level associations with conspecifics and landscape composition.

An autocorrelation method to detect low frequency earthquakes within tremor

Science.gov (United States)

Brown, J.R.; Beroza, G.C.; Shelly, D.R.

2008-01-01

Recent studies have shown that deep tremor in the Nankai Trough under western Shikoku consists of a swarm of low frequency earthquakes (LFEs) that occur as slow shear slip on the down-dip extension of the primary seismogenic zone of the plate interface. The similarity of tremor in other locations suggests a similar mechanism, but the absence of cataloged low frequency earthquakes prevents a similar analysis. In this study, we develop a method for identifying LFEs within tremor. The method employs a matched-filter algorithm, similar to the technique used to infer that tremor in parts of Shikoku is comprised of LFEs; however, in this case we do not assume the origin times or locations of any LFEs a priori. We search for LFEs using the running autocorrelation of tremor waveforms for 6 Hi-Net stations in the vicinity of the tremor source. Time lags showing strong similarity in the autocorrelation represent either repeats, or near repeats, of LFEs within the tremor. We test the method on an hour of Hi-Net recordings of tremor and demonstrates that it extracts both known and previously unidentified LFEs. Once identified, we cross correlate waveforms to measure relative arrival times and locate the LFEs. The results are able to explain most of the tremor as a swarm of LFEs and the locations of newly identified events appear to fill a gap in the spatial distribution of known LFEs. This method should allow us to extend the analysis of Shelly et al. (2007a) to parts of the Nankai Trough in Shikoku that have sparse LFE coverage, and may also allow us to extend our analysis to other regions that experience deep tremor, but where LFEs have not yet been identified. Copyright 2008 by the American Geophysical Union.

Density-functional theory based on the electron distribution on the energy coordinate

Science.gov (United States)

Takahashi, Hideaki

2018-03-01

We developed an electronic density functional theory utilizing a novel electron distribution n(ɛ) as a basic variable to compute ground state energy of a system. n(ɛ) is obtained by projecting the electron density n({\\boldsymbol{r}}) defined on the space coordinate {\\boldsymbol{r}} onto the energy coordinate ɛ specified with the external potential {\\upsilon }ext}({\\boldsymbol{r}}) of interest. It was demonstrated that the Kohn-Sham equation can also be formulated with the exchange-correlation functional E xc[n(ɛ)] that employs the density n(ɛ) as an argument. It turned out an exchange functional proposed in our preliminary development suffices to describe properly the potential energies of several types of chemical bonds with comparable accuracies to the corresponding functional based on local density approximation. As a remarkable feature of the distribution n(ɛ) it inherently involves the spatially non-local information of the exchange hole at the bond dissociation limit in contrast to conventional approximate functionals. By taking advantage of this property we also developed a prototype of the static correlation functional E sc including no empirical parameters, which showed marked improvements in describing the dissociations of covalent bonds in {{{H}}}2,{{{C}}}2{{{H}}}4 and {CH}}4 molecules.

Quantal density functional theory. 2. ed.

International Nuclear Information System (INIS)

Sahni, Viraht

2016-01-01

This book is on quantal density functional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The time-independent QDFT constitutes a special case. The 2 nd edition describes the further development of the theory, and extends it to include the presence of an external magnetostatic field. The theory is based on the 'quantal Newtonian' second and first laws for the individual electron. These laws are in terms of 'classical' fields that pervade all space, and their quantal sources. The fields are separately representative of the electron correlations that must be accounted for in local potential theory. Recent developments show that irrespective of the type of external field the electrons are subject to, the only correlations beyond those due to the Pauli exclusion principle and Coulomb repulsion that need be considered are solely of the correlation-kinetic effects. Foundational to QDFT, the book describes Schroedinger theory from the new perspective of the single electron in terms of the 'quantal Newtonian' laws. Hohenberg-Kohn density functional theory (DFT), new understandings of the theory and its extension to the presence of an external uniform magnetostatic field are described. The physical interpretation via QDFT, in terms of electron correlations, of Kohn-Sham DFT, approximations to it and Slater theory are provided.

Quantal density functional theory. 2. ed.

Energy Technology Data Exchange (ETDEWEB)

Sahni, Viraht

2016-07-01

This book is on quantal density functional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The time-independent QDFT constitutes a special case. The 2{sup nd} edition describes the further development of the theory, and extends it to include the presence of an external magnetostatic field. The theory is based on the 'quantal Newtonian' second and first laws for the individual electron. These laws are in terms of 'classical' fields that pervade all space, and their quantal sources. The fields are separately representative of the electron correlations that must be accounted for in local potential theory. Recent developments show that irrespective of the type of external field the electrons are subject to, the only correlations beyond those due to the Pauli exclusion principle and Coulomb repulsion that need be considered are solely of the correlation-kinetic effects. Foundational to QDFT, the book describes Schroedinger theory from the new perspective of the single electron in terms of the 'quantal Newtonian' laws. Hohenberg-Kohn density functional theory (DFT), new understandings of the theory and its extension to the presence of an external uniform magnetostatic field are described. The physical interpretation via QDFT, in terms of electron correlations, of Kohn-Sham DFT, approximations to it and Slater theory are provided.

Hartree and Exchange in Ensemble Density Functional Theory: Avoiding the Nonuniqueness Disaster.

Science.gov (United States)

Gould, Tim; Pittalis, Stefano

2017-12-15

Ensemble density functional theory is a promising method for the efficient and accurate calculation of excitations of quantum systems, at least if useful functionals can be developed to broaden its domain of practical applicability. Here, we introduce a guaranteed single-valued "Hartree-exchange" ensemble density functional, E_{Hx}[n], in terms of the right derivative of the universal ensemble density functional with respect to the coupling constant at vanishing interaction. We show that E_{Hx}[n] is straightforwardly expressible using block eigenvalues of a simple matrix [Eq. (14)]. Specialized expressions for E_{Hx}[n] from the literature, including those involving superpositions of Slater determinants, can now be regarded as originating from the unifying picture presented here. We thus establish a clear and practical description for Hartree and exchange in ensemble systems.

Artificial cognitive memory—changing from density driven to functionality driven

Science.gov (United States)

Shi, L. P.; Yi, K. J.; Ramanathan, K.; Zhao, R.; Ning, N.; Ding, D.; Chong, T. C.

2011-03-01

Increasing density based on bit size reduction is currently a main driving force for the development of data storage technologies. However, it is expected that all of the current available storage technologies might approach their physical limits in around 15 to 20 years due to miniaturization. To further advance the storage technologies, it is required to explore a new development trend that is different from density driven. One possible direction is to derive insights from biological counterparts. Unlike physical memories that have a single function of data storage, human memory is versatile. It contributes to functions of data storage, information processing, and most importantly, cognitive functions such as adaptation, learning, perception, knowledge generation, etc. In this paper, a brief review of current data storage technologies are presented, followed by discussions of future storage technology development trend. We expect that the driving force will evolve from density to functionality, and new memory modules associated with additional functions other than only data storage will appear. As an initial step toward building a future generation memory technology, we propose Artificial Cognitive Memory (ACM), a memory based intelligent system. We also present the characteristics of ACM, new technologies that can be used to develop ACM components such as bioinspired element cells (silicon, memristor, phase change, etc.), and possible methodologies to construct a biologically inspired hierarchical system.

Orbital-dependent exchange-correlation functionals in density-functional theory realized by the FLAPW method

Energy Technology Data Exchange (ETDEWEB)

Betzinger, Markus

2011-12-14

In this thesis, we extended the applicability of the full-potential linearized augmented-plane-wave (FLAPW) method, one of the most precise, versatile and generally applicable electronic structure methods for solids working within the framework of density-functional theory (DFT), to orbital-dependent functionals for the exchange-correlation (xc) energy. Two different schemes that deal with orbital-dependent functionals, the Kohn-Sham (KS) and the generalized Kohn-Sham (gKS) formalism, have been realized. Hybrid functionals, combining some amount of the orbital-dependent exact exchange energy with local or semi-local functionals of the density, are implemented within the gKS scheme. We work in particular with the PBE0 hybrid of Perdew, Burke, and Ernzerhof. Our implementation relies on a representation of the non-local exact exchange potential - its calculation constitutes the most time consuming step in a practical calculation - by an auxiliary mixed product basis (MPB). In this way, the matrix elements of the Hamiltonian corresponding to the non-local potential become a Brillouin-zone (BZ) sum over vector-matrix-vector products. Several techniques are developed and explored to further accelerate our numerical scheme. We show PBE0 results for a variety of semiconductors and insulators. In comparison with experiment, the PBE0 functional leads to improved band gaps and an improved description of localized states. Even for the ferromagnetic semiconductor EuO with localized 4f electrons, the electronic and magnetic properties are correctly described by the PBE0 functional. Subsequently, we discuss the construction of the local, multiplicative exact exchange (EXX) potential from the non-local, orbital-dependent exact exchange energy. For this purpose we employ the optimized effective potential (OEP) method. Central ingredients of the OEP equation are the KS wave-function response and the single-particle density response function. We show that a balance between the LAPW

Orbital-dependent exchange-correlation functionals in density-functional theory realized by the FLAPW method

International Nuclear Information System (INIS)

Betzinger, Markus

2011-01-01

In this thesis, we extended the applicability of the full-potential linearized augmented-plane-wave (FLAPW) method, one of the most precise, versatile and generally applicable electronic structure methods for solids working within the framework of density-functional theory (DFT), to orbital-dependent functionals for the exchange-correlation (xc) energy. Two different schemes that deal with orbital-dependent functionals, the Kohn-Sham (KS) and the generalized Kohn-Sham (gKS) formalism, have been realized. Hybrid functionals, combining some amount of the orbital-dependent exact exchange energy with local or semi-local functionals of the density, are implemented within the gKS scheme. We work in particular with the PBE0 hybrid of Perdew, Burke, and Ernzerhof. Our implementation relies on a representation of the non-local exact exchange potential - its calculation constitutes the most time consuming step in a practical calculation - by an auxiliary mixed product basis (MPB). In this way, the matrix elements of the Hamiltonian corresponding to the non-local potential become a Brillouin-zone (BZ) sum over vector-matrix-vector products. Several techniques are developed and explored to further accelerate our numerical scheme. We show PBE0 results for a variety of semiconductors and insulators. In comparison with experiment, the PBE0 functional leads to improved band gaps and an improved description of localized states. Even for the ferromagnetic semiconductor EuO with localized 4f electrons, the electronic and magnetic properties are correctly described by the PBE0 functional. Subsequently, we discuss the construction of the local, multiplicative exact exchange (EXX) potential from the non-local, orbital-dependent exact exchange energy. For this purpose we employ the optimized effective potential (OEP) method. Central ingredients of the OEP equation are the KS wave-function response and the single-particle density response function. We show that a balance between the LAPW

Optical Absorption in Molecular Crystals from Time-Dependent Density Functional Theory

Science.gov (United States)

2017-04-23

Our approach represents a full solid-state calculation, allowing for polarization ef- fects while still capable of capturing inter-molecular dis...AFRL-AFOSR-UK-TR-2017-0030 Optical absorption in molecular crystals from time-dependent density functional theory Leeor Kronik WEIZMANN INSTITUTE OF...from time-dependent density functional theory 5a.  CONTRACT NUMBER 5b.  GRANT NUMBER FA9550-15-1-0290 5c.  PROGRAM ELEMENT NUMBER 61102F 6. AUTHOR(S

Evaluating the coefficients of autocorrelation in a series of annual run-off of the Far East rivers

Energy Technology Data Exchange (ETDEWEB)

Sakharyuk, A V

1981-01-01

An evaluation is made of the coefficients of autocorrelation in series of annual river run-off based on group analysis using data on the distribution law of sampling correlation coefficients of temporal series subordinate to the III type Pearson's distribution.

Exact density functional and wave function embedding schemes based on orbital localization

International Nuclear Information System (INIS)

Hégely, Bence; Nagy, Péter R.; Kállay, Mihály; Ferenczy, György G.

2016-01-01

Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.

Exact density functional and wave function embedding schemes based on orbital localization

Science.gov (United States)

Hégely, Bence; Nagy, Péter R.; Ferenczy, György G.; Kállay, Mihály

2016-08-01

Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.

Exact density functional and wave function embedding schemes based on orbital localization

Energy Technology Data Exchange (ETDEWEB)

Hégely, Bence; Nagy, Péter R.; Kállay, Mihály, E-mail: kallay@mail.bme.hu [MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest (Hungary); Ferenczy, György G. [Medicinal Chemistry Research Group, Research Centre for Natural Sciences, Hungarian Academy of Sciences, Magyar tudósok körútja 2, H-1117 Budapest (Hungary); Department of Biophysics and Radiation Biology, Semmelweis University, Tűzoltó u. 37-47, H-1094 Budapest (Hungary)

2016-08-14

Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.

Synergy between pair coupled cluster doubles and pair density functional theory

Energy Technology Data Exchange (ETDEWEB)

Garza, Alejandro J.; Bulik, Ireneusz W. [Department of Chemistry, Rice University, Houston, Texas 77251-1892 (United States); Henderson, Thomas M. [Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892 (United States); Scuseria, Gustavo E. [Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892 (United States); Chemistry Department, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)

2015-01-28

Pair coupled cluster doubles (pCCD) has been recently studied as a method capable of accounting for static correlation with low polynomial cost. We present three combinations of pCCD with Kohn–Sham functionals of the density and on-top pair density (the probability of finding two electrons on top of each other) to add dynamic correlation to pCCD without double counting. With a negligible increase in computational cost, these pCCD+DFT blends greatly improve upon pCCD in the description of typical problems where static and dynamic correlations are both important. We argue that—as a black-box method with low scaling, size-extensivity, size-consistency, and a simple quasidiagonal two-particle density matrix—pCCD is an excellent match for pair density functionals in this type of fusion of multireference wavefunctions with DFT.

Benchmarking Density Functionals for Chemical Bonds of Gold

DEFF Research Database (Denmark)

Kepp, Kasper Planeta

2017-01-01

Gold plays a major role in nanochemistry, catalysis, and electrochemistry. Accordingly, hundreds of studies apply density functionals to study chemical bonding with gold, yet there is no systematic attempt to assess the accuracy of these methods applied to gold. This paper reports a benchmark aga...

Wigner Function of Density Operator for Negative Binomial Distribution

International Nuclear Information System (INIS)

Xu Xinglei; Li Hongqi

2008-01-01

By using the technique of integration within an ordered product (IWOP) of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator

Approximate self-consistent potentials for density-functional-theory exchange-correlation functionals

International Nuclear Information System (INIS)

Cafiero, Mauricio; Gonzalez, Carlos

2005-01-01

We show that potentials for exchange-correlation functionals within the Kohn-Sham density-functional-theory framework may be written as potentials for simpler functionals multiplied by a factor close to unity, and in a self-consistent field calculation, these effective potentials find the correct self-consistent solutions. This simple theory is demonstrated with self-consistent exchange-only calculations of the atomization energies of some small molecules using the Perdew-Kurth-Zupan-Blaha (PKZB) meta-generalized-gradient-approximation (meta-GGA) exchange functional. The atomization energies obtained with our method agree with or surpass previous meta-GGA calculations performed in a non-self-consistent manner. The results of this work suggest the utility of this simple theory to approximate exchange-correlation potentials corresponding to energy functionals too complicated to generate closed forms for their potentials. We hope that this method will encourage the development of complex functionals which have correct boundary conditions and are free of self-interaction errors without the worry that the functionals are too complex to differentiate to obtain potentials

Magnetic behavior study of samarium nitride using density functional theory

Science.gov (United States)

Som, Narayan N.; Mankad, Venu H.; Dabhi, Shweta D.; Patel, Anjali; Jha, Prafulla K.

2018-02-01

In this work, the state-of-art density functional theory is employed to study the structural, electronic and magnetic properties of samarium nitride (SmN). We have performed calculation for both ferromagnetic and antiferromagnetic states in rock-salt phase. The calculated results of optimized lattice parameter and magnetic moment agree well with the available experimental and theoretical values. From energy band diagram and electronic density of states, we observe a half-metallic behaviour in FM phase of rock salt SmN in while metallicity in AFM I and AFM III phases. We present and discuss our current understanding of the possible half-metallicity together with the magnetic ordering in SmN. The calculated phonon dispersion curves shows dynamical stability of the considered structures. The phonon density of states and Eliashberg functional have also been analysed to understand the superconductivity in SmN.

INTERACTIVE VISUALIZATION OF PROBABILITY AND CUMULATIVE DENSITY FUNCTIONS

KAUST Repository

Potter, Kristin; Kirby, Robert Michael; Xiu, Dongbin; Johnson, Chris R.

2012-01-01

The probability density function (PDF), and its corresponding cumulative density function (CDF), provide direct statistical insight into the characterization of a random process or field. Typically displayed as a histogram, one can infer probabilities of the occurrence of particular events. When examining a field over some two-dimensional domain in which at each point a PDF of the function values is available, it is challenging to assess the global (stochastic) features present within the field. In this paper, we present a visualization system that allows the user to examine two-dimensional data sets in which PDF (or CDF) information is available at any position within the domain. The tool provides a contour display showing the normed difference between the PDFs and an ansatz PDF selected by the user and, furthermore, allows the user to interactively examine the PDF at any particular position. Canonical examples of the tool are provided to help guide the reader into the mapping of stochastic information to visual cues along with a description of the use of the tool for examining data generated from an uncertainty quantification exercise accomplished within the field of electrophysiology.

Path integrals for electronic densities, reactivity indices, and localization functions in quantum systems.

Science.gov (United States)

Putz, Mihai V

2009-11-10

The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.

Path Integrals for Electronic Densities, Reactivity Indices, and Localization Functions in Quantum Systems

Directory of Open Access Journals (Sweden)

Mihai V. Putz

2009-11-01

Full Text Available The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving many-electronic systems.

Pressure and surface tension of solid-liquid interface using Tara zona density functional theory

International Nuclear Information System (INIS)

Moradi, M.; Kavosh Tehrani, M.

2001-01-01

The weighted density functional theory proposed by Tara zona is applied to study the solid-liquid interface. In the last two decades the weighted density functional became a useful tool to consider the properties of inhomogeneous liquids. In this theory, the role of the size of molecules or the particles of which the matter is composed, was found to be important. In this research we study a hard sphere fluid beside a hard wall. For this study the liquid is an inhomogeneous system. We use the definition of the direct correlation function as a second derivative of free energy with respect to the density. We use this definition and the definition of the weighting function, then we minimize the grand potential with respect to the density to get the Euler Lagrange equation and we obtain an integral equation to find the inhomogeneous density profile. The obtained density profile as a function of the distance from the wall, for different bulk density is pitted in three dimensions. We also calculate the pressure and compare it with the Carnahan-Starling results, and finally we obtained the surface tension at liquid-solid interface and compared it with the results of Monte Carlo simulation

Time-dependent density functional theory for multi-component systems

International Nuclear Information System (INIS)

Tiecheng Li; Peiqing Tong

1985-10-01

The Runge-Gross version of Hohenberg-Kohn-Sham's density functional theory is generalized to multi-component systems, both for arbitrary time-dependent pure states and for arbitrary time-dependent ensembles. (author)

Function of Maximal Microvessel Density in Breast Tumor Metastasis

National Research Council Canada - National Science Library

McLeskey, Sandra

2000-01-01

.... These data are gained by quantitating the number of microvessels in "hot spots" of high-density tumor vasculature, implying that such hot spots have functional significance in the process of metastasis...

Obtaining Hartree-Fock and density functional theory doubly excited states with Car-Parrinello density matrix search

Science.gov (United States)

Liang, Wenkel; Isborn, Christine M.; Li, Xiaosong

2009-11-01

The calculation of doubly excited states is one of the major problems plaguing the modern day excited state workhorse methodology of linear response time dependent Hartree-Fock (TDHF) and density function theory (TDDFT). We have previously shown that the use of a resonantly tuned field within real-time TDHF and TDDFT is able to simultaneously excite both the α and β electrons to achieve the two-electron excited states of minimal basis H2 and HeH+ [C. M. Isborn and X. Li, J. Chem. Phys. 129, 204107 (2008)]. We now extend this method to many electron systems with the use of our Car-Parrinello density matrix search (CP-DMS) with a first-principles fictitious mass method for wave function optimization [X. Li, C. L. Moss, W. Liang, and Y. Feng, J. Chem. Phys. 130, 234115 (2009)]. Real-time TDHF/TDDFT is used during the application of the laser field perturbation, driving the electron density toward the doubly excited state. The CP-DMS method then converges the density to the nearest stationary state. We present these stationary state doubly excited state energies and properties at the HF and DFT levels for H2, HeH+, lithium hydride, ethylene, and butadiene.

The importance of spatial models for estimating the strength of density dependence

DEFF Research Database (Denmark)

Thorson, James T.; Skaug, Hans J.; Kristensen, Kasper

2014-01-01

the California Coast. In this case, the nonspatial model estimates implausible oscillatory dynamics on an annual time scale, while the spatial model estimates strong autocorrelation and is supported by model selection tools. We conclude by discussing the importance of improved data archiving techniques, so...... that spatial models can be used to re-examine classic questions regarding the presence and strength of density dependence in wild populations Read More: http://www.esajournals.org/doi/abs/10.1890/14-0739.1...

Computational complexity of time-dependent density functional theory

International Nuclear Information System (INIS)

Whitfield, J D; Yung, M-H; Tempel, D G; Aspuru-Guzik, A; Boixo, S

2014-01-01

Time-dependent density functional theory (TDDFT) is rapidly emerging as a premier method for solving dynamical many-body problems in physics and chemistry. The mathematical foundations of TDDFT are established through the formal existence of a fictitious non-interacting system (known as the Kohn–Sham system), which can reproduce the one-electron reduced probability density of the actual system. We build upon these works and show that on the interior of the domain of existence, the Kohn–Sham system can be efficiently obtained given the time-dependent density. We introduce a V-representability parameter which diverges at the boundary of the existence domain and serves to quantify the numerical difficulty of constructing the Kohn-Sham potential. For bounded values of V-representability, we present a polynomial time quantum algorithm to generate the time-dependent Kohn–Sham potential with controllable error bounds. (paper)

Density Functional Calculations of Solid State Heats of Formation

National Research Council Canada - National Science Library

Politzer, Peter

1999-01-01

It is now feasible to compute quite accurate gas phase heats of formation for relatively small molecules by means of ab initio or density functional techniques and one of several possible approaches...

Time-dependent density functional theory for many-electron systems interacting with cavity photons.

Science.gov (United States)

Tokatly, I V

2013-06-07

Time-dependent (current) density functional theory for many-electron systems strongly coupled to quantized electromagnetic modes of a microcavity is proposed. It is shown that the electron-photon wave function is a unique functional of the electronic (current) density and the expectation values of photonic coordinates. The Kohn-Sham system is constructed, which allows us to calculate the above basic variables by solving self-consistent equations for noninteracting particles. We suggest possible approximations for the exchange-correlation potentials and discuss implications of this approach for the theory of open quantum systems. In particular we show that it naturally leads to time-dependent density functional theory for systems coupled to the Caldeira-Leggett bath.

Temporal and spatial distribution characteristics in the natural plague foci of Chinese Mongolian gerbils based on spatial autocorrelation.

Science.gov (United States)

Du, Hai-Wen; Wang, Yong; Zhuang, Da-Fang; Jiang, Xiao-San

2017-08-07

The nest flea index of Meriones unguiculatus is a critical indicator for the prevention and control of plague, which can be used not only to detect the spatial and temporal distributions of Meriones unguiculatus, but also to reveal its cluster rule. This research detected the temporal and spatial distribution characteristics of the plague natural foci of Mongolian gerbils by body flea index from 2005 to 2014, in order to predict plague outbreaks. Global spatial autocorrelation was used to describe the entire spatial distribution pattern of the body flea index in the natural plague foci of typical Chinese Mongolian gerbils. Cluster and outlier analysis and hot spot analysis were also used to detect the intensity of clusters based on geographic information system methods. The quantity of M. unguiculatus nest fleas in the sentinel surveillance sites from 2005 to 2014 and host density data of the study area from 2005 to 2010 used in this study were provided by Chinese Center for Disease Control and Prevention. The epidemic focus regions of the Mongolian gerbils remain the same as the hot spot regions relating to the body flea index. High clustering areas possess a similar pattern as the distribution pattern of the body flea index indicating that the transmission risk of plague is relatively high. In terms of time series, the area of the epidemic focus gradually increased from 2005 to 2007, declined rapidly in 2008 and 2009, and then decreased slowly and began trending towards stability from 2009 to 2014. For the spatial change, the epidemic focus regions began moving northward from the southwest epidemic focus of the Mongolian gerbils from 2005 to 2007, and then moved from north to south in 2007 and 2008. The body flea index of Chinese gerbil foci reveals significant spatial and temporal aggregation characteristics through the employing of spatial autocorrelation. The diversity of temporary and spatial distribution is mainly affected by seasonal variation, the human

Covariant density functional theory for nuclear matter

Energy Technology Data Exchange (ETDEWEB)

Badarch, U.

2007-07-01

The present thesis is organized as follows. In Chapter 2 we study the Nucleon-Nucleon (NN) interaction in Dirac-Brueckner (DB) approach. We start by considering the NN interaction in free-space in terms of the Bethe-Salpeter (BS) equation to the meson exchange potential model. Then we present the DB approach for nuclear matter by extending the BS equation for the in-medium NN interaction. From the solution of the three-dimensional in-medium BS equation, we derive the DB self-energies and total binding energy which are the main results of the DB approach, which we later incorporate in the field theoretical calculation of the nuclear equation of state. In Chapter 3, we introduce the basic concepts of density functional theory in the context of Quantum Hadrodynamics (QHD-I). We reach the main point of this work in Chapter 4 where we introduce the DDRH approach. In the DDRH theory, the medium dependence of the meson-nucleon vertices is expressed as functionals of the baryon field operators. Because of the complexities of the operator-valued functionals we decide to use the mean-field approximation. In Chapter 5, we contrast microscopic and phenomenological approaches to extracting density dependent meson-baryon vertices. Chapter 6 gives the results of our studies of the EOS of infinite nuclear matter in detail. Using formulas derived in Chapters 4 and 5 we calculate the properties of symmetric and asymmetric nuclear matter and pure neutron matter. (orig.)

Covariant density functional theory for nuclear matter

International Nuclear Information System (INIS)

Badarch, U.

2007-01-01

The present thesis is organized as follows. In Chapter 2 we study the Nucleon-Nucleon (NN) interaction in Dirac-Brueckner (DB) approach. We start by considering the NN interaction in free-space in terms of the Bethe-Salpeter (BS) equation to the meson exchange potential model. Then we present the DB approach for nuclear matter by extending the BS equation for the in-medium NN interaction. From the solution of the three-dimensional in-medium BS equation, we derive the DB self-energies and total binding energy which are the main results of the DB approach, which we later incorporate in the field theoretical calculation of the nuclear equation of state. In Chapter 3, we introduce the basic concepts of density functional theory in the context of Quantum Hadrodynamics (QHD-I). We reach the main point of this work in Chapter 4 where we introduce the DDRH approach. In the DDRH theory, the medium dependence of the meson-nucleon vertices is expressed as functionals of the baryon field operators. Because of the complexities of the operator-valued functionals we decide to use the mean-field approximation. In Chapter 5, we contrast microscopic and phenomenological approaches to extracting density dependent meson-baryon vertices. Chapter 6 gives the results of our studies of the EOS of infinite nuclear matter in detail. Using formulas derived in Chapters 4 and 5 we calculate the properties of symmetric and asymmetric nuclear matter and pure neutron matter. (orig.)

Spin-density functional for exchange anisotropic Heisenberg model

International Nuclear Information System (INIS)

Prata, G.N.; Penteado, P.H.; Souza, F.C.; Libero, Valter L.

2009-01-01

Ground-state energies for antiferromagnetic Heisenberg models with exchange anisotropy are estimated by means of a local-spin approximation made in the context of the density functional theory. Correlation energy is obtained using the non-linear spin-wave theory for homogeneous systems from which the spin functional is built. Although applicable to chains of any size, the results are shown for small number of sites, to exhibit finite-size effects and allow comparison with exact-numerical data from direct diagonalization of small chains.

A density functional theory-based chemical potential equalisation

Indian Academy of Sciences (India)

A chemical potential equalisation scheme is proposed for the calculation of these quantities and hence the dipole polarizability within the framework of density functional theory based linear response theory. The resulting polarizability is expressed in terms of the contributions from individual atoms in the molecule. A few ...

High-Responsivity Graphene-Boron Nitride Photodetector and Autocorrelator in a Silicon Photonic Integrated Circuit.

Science.gov (United States)

Shiue, Ren-Jye; Gao, Yuanda; Wang, Yifei; Peng, Cheng; Robertson, Alexander D; Efetov, Dmitri K; Assefa, Solomon; Koppens, Frank H L; Hone, James; Englund, Dirk

2015-11-11

Graphene and other two-dimensional (2D) materials have emerged as promising materials for broadband and ultrafast photodetection and optical modulation. These optoelectronic capabilities can augment complementary metal-oxide-semiconductor (CMOS) devices for high-speed and low-power optical interconnects. Here, we demonstrate an on-chip ultrafast photodetector based on a two-dimensional heterostructure consisting of high-quality graphene encapsulated in hexagonal boron nitride. Coupled to the optical mode of a silicon waveguide, this 2D heterostructure-based photodetector exhibits a maximum responsivity of 0.36 A/W and high-speed operation with a 3 dB cutoff at 42 GHz. From photocurrent measurements as a function of the top-gate and source-drain voltages, we conclude that the photoresponse is consistent with hot electron mediated effects. At moderate peak powers above 50 mW, we observe a saturating photocurrent consistent with the mechanisms of electron-phonon supercollision cooling. This nonlinear photoresponse enables optical on-chip autocorrelation measurements with picosecond-scale timing resolution and exceptionally low peak powers.

Semiclassical neutral atom as a reference system in density functional theory.

Science.gov (United States)

Constantin, Lucian A; Fabiano, E; Laricchia, S; Della Sala, F

2011-05-06

We use the asymptotic expansions of the semiclassical neutral atom as a reference system in density functional theory to construct accurate generalized gradient approximations (GGAs) for the exchange-correlation and kinetic energies without any empiricism. These asymptotic functionals are among the most accurate GGAs for molecular systems, perform well for solid state, and overcome current GGA state of the art in frozen density embedding calculations. Our results also provide evidence for the conjointness conjecture between exchange and kinetic energies of atomic systems.

FDE-vdW: A van der Waals inclusive subsystem density-functional theory

Energy Technology Data Exchange (ETDEWEB)

Kevorkyants, Ruslan; Pavanello, Michele, E-mail: m.pavanello@rutgers.edu [Department of Chemistry, Rutgers University, Newark, New Jersey 07102 (United States); Eshuis, Henk [Department of Chemistry and Biochemistry, Montclair State University, Montclair, New Jersey 07043 (United States)

2014-07-28

We present a formally exact van der Waals inclusive electronic structure theory, called FDE-vdW, based on the Frozen Density Embedding formulation of subsystem Density-Functional Theory. In subsystem DFT, the energy functional is composed of subsystem additive and non-additive terms. We show that an appropriate definition of the long-range correlation energy is given by the value of the non-additive correlation functional. This functional is evaluated using the fluctuation–dissipation theorem aided by a formally exact decomposition of the response functions into subsystem contributions. FDE-vdW is derived in detail and several approximate schemes are proposed, which lead to practical implementations of the method. We show that FDE-vdW is Casimir-Polder consistent, i.e., it reduces to the generalized Casimir-Polder formula for asymptotic inter-subsystems separations. Pilot calculations of binding energies of 13 weakly bound complexes singled out from the S22 set show a dramatic improvement upon semilocal subsystem DFT, provided that an appropriate exchange functional is employed. The convergence of FDE-vdW with basis set size is discussed, as well as its dependence on the choice of associated density functional approximant.

Autocorrelation analysis of plasma plume light emissions in deep penetration laser welding of steel

Czech Academy of Sciences Publication Activity Database

Mrňa, Libor; Šarbort, Martin; Řeřucha, Šimon; Jedlička, Petr

2017-01-01

Roč. 29, č. 1 (2017), s. 1-10, č. článku 012009. ISSN 1042-346X R&D Projects: GA MŠk(CZ) LO1212; GA MŠk ED0017/01/01 Institutional support: RVO:68081731 Keywords : laser welding * plasma plume * light emissions * autocorrelation analysis * weld depth Subject RIV: BH - Optics, Masers, Lasers OBOR OECD: Optics (including laser optics and quantum optics) Impact factor: 1.492, year: 2016

Range-separated density-functional theory for molecular excitation energies

International Nuclear Information System (INIS)

Rebolini, E.

2014-01-01

Linear-response time-dependent density-functional theory (TDDFT) is nowadays a method of choice to compute molecular excitation energies. However, within the usual adiabatic semi-local approximations, it is not able to describe properly Rydberg, charge-transfer or multiple excitations. Range separation of the electronic interaction allows one to mix rigorously density-functional methods at short range and wave function or Green's function methods at long range. When applied to the exchange functional, it already corrects most of these deficiencies but multiple excitations remain absent as they need a frequency-dependent kernel. In this thesis, the effects of range separation are first assessed on the excitation energies of a partially-interacting system in an analytic and numerical study in order to provide guidelines for future developments of range-separated methods for excitation energy calculations. It is then applied on the exchange and correlation TDDFT kernels in a single-determinant approximation in which the long-range part of the correlation kernel vanishes. A long-range frequency-dependent second-order correlation kernel is then derived from the Bethe-Salpeter equation and added perturbatively to the range-separated TDDFT kernel in order to take into account the effects of double excitations. (author)

A J matrix engine for density functional theory calculations

International Nuclear Information System (INIS)

White, C.A.; Head-Gordon, M.

1996-01-01

We introduce a new method for the formation of the J matrix (Coulomb interaction matrix) within a basis of Cartesian Gaussian functions, as needed in density functional theory and Hartree endash Fock calculations. By summing the density matrix into the underlying Gaussian integral formulas, we have developed a J matrix open-quote open-quote engine close-quote close-quote which forms the exact J matrix without explicitly forming the full set of two electron integral intermediates. Several precomputable quantities have been identified, substantially reducing the number of floating point operations and memory accesses needed in a J matrix calculation. Initial timings indicate a speedup of greater than four times for the (pp parallel pp) class of integrals with speedups increasing to over ten times for (ff parallel ff) integrals. copyright 1996 American Institute of Physics

Covariant density functional theory: The role of the pion

International Nuclear Information System (INIS)

Lalazissis, G. A.; Karatzikos, S.; Serra, M.; Otsuka, T.; Ring, P.

2009-01-01

We investigate the role of the pion in covariant density functional theory. Starting from conventional relativistic mean field (RMF) theory with a nonlinear coupling of the σ meson and without exchange terms we add pions with a pseudovector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of density functionals does not destroy the overall description of the bulk properties by RMF. On the other hand, the noncentral contribution of the pion (tensor coupling) does have effects on single particle energies and on binding energies of certain nuclei.

Tunable non-interacting free-energy functionals: development and applications to low-density aluminum

Science.gov (United States)

Trickey, Samuel; Karasiev, Valentin

We introduce the concept of tunable orbital-free non-interacting free-energy density functionals and present a generalized gradient approximation (GGA) with a subset of parameters defined from constraints and a few free parameters. Those free parameters are tuned to reproduce reference Kohn-Sham (KS) static-lattice pressures for Al at T=8 kK for bulk densities between 0.6 and 2 g/cm3. The tuned functional then is used in OF molecular dynamics (MD) simulations for Al with densities between 0.1 and 2 g/cm3 and T between 6 and 50 kK to calculate the equation of state and generate configurations for electrical conductivity calculations. The tunable functional produces accurate results. Computationally it is very effective especially at elevated temperature. Kohn-Shiam calculations for such low densities are affordable only up to T=10 kK, while other OF approximations, including two-point functionals, fail badly in that regime. Work supported by US DoE Grant DE-SC0002139.

New autocorrelation technique for the IR FEL optical pulse width measurements

Energy Technology Data Exchange (ETDEWEB)

Amirmadhi, F.; Brau, K.A.; Becker, C. [Vanderbilt Univ., Nashville, TN (United States)] [and others

1995-12-31

We have developed a new technique for the autocorrelation measurement of optical pulse width at the Vanderbilt University FEL center. This method is based on nonlinear absorption and transmission characteristics of semiconductors such as Ge, Te and InAs suitable for the wavelength range from 2 to over 6 microns. This approach, aside being simple and low cost, removes the phase matching condition that is generally required for the standard frequency doubling technique and covers a greater wavelength range per nonlinear material. In this paper we will describe the apparatus, explain the principal mechanism involved and compare data which have been acquired with both frequency doubling and two-photon absorption.

Modulation Based on Probability Density Functions

Science.gov (United States)

Williams, Glenn L.

2009-01-01

A proposed method of modulating a sinusoidal carrier signal to convey digital information involves the use of histograms representing probability density functions (PDFs) that characterize samples of the signal waveform. The method is based partly on the observation that when a waveform is sampled (whether by analog or digital means) over a time interval at least as long as one half cycle of the waveform, the samples can be sorted by frequency of occurrence, thereby constructing a histogram representing a PDF of the waveform during that time interval.

Functional methods for arbitrary densities in curved spacetime

International Nuclear Information System (INIS)

Basler, M.

1993-01-01

This paper gives an introduction to the technique of functional differentiation and integration in curved spacetime, applied to examples from quantum field theory. Special attention is drawn on the choice of functional integral measure. Referring to a suggestion by Toms, fields are choosen as arbitrary scalar, spinorial or vectorial densities. The technique developed by Toms for a pure quadratic Lagrangian are extended to the calculation of the generating functional with external sources. Included are two examples of interacting theories, a self-interacting scalar field and a Yang-Mills theory. For these theories the complete set of Feynman graphs depending on the weight of variables is derived. (orig.)

Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections

Energy Technology Data Exchange (ETDEWEB)

Chai, Jeng-Da; Head-Gordon, Martin

2008-06-14

We report re-optimization of a recently proposed long-range corrected (LC) hybrid density functionals [J.-D. Chai and M. Head-Gordon, J. Chem. Phys. 128, 084106 (2008)] to include empirical atom-atom dispersion corrections. The resulting functional, {omega}B97X-D yields satisfactory accuracy for thermochemistry, kinetics, and non-covalent interactions. Tests show that for non-covalent systems, {omega}B97X-D shows slight improvement over other empirical dispersion-corrected density functionals, while for covalent systems and kinetics, it performs noticeably better. Relative to our previous functionals, such as {omega}B97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.

Minimal nuclear energy density functional

Science.gov (United States)

Bulgac, Aurel; Forbes, Michael McNeil; Jin, Shi; Perez, Rodrigo Navarro; Schunck, Nicolas

2018-04-01

We present a minimal nuclear energy density functional (NEDF) called "SeaLL1" that has the smallest number of possible phenomenological parameters to date. SeaLL1 is defined by seven significant phenomenological parameters, each related to a specific nuclear property. It describes the nuclear masses of even-even nuclei with a mean energy error of 0.97 MeV and a standard deviation of 1.46 MeV , two-neutron and two-proton separation energies with rms errors of 0.69 MeV and 0.59 MeV respectively, and the charge radii of 345 even-even nuclei with a mean error ɛr=0.022 fm and a standard deviation σr=0.025 fm . SeaLL1 incorporates constraints on the equation of state (EoS) of pure neutron matter from quantum Monte Carlo calculations with chiral effective field theory two-body (NN ) interactions at the next-to-next-to-next-to leading order (N3LO) level and three-body (NNN ) interactions at the next-to-next-to leading order (N2LO) level. Two of the seven parameters are related to the saturation density and the energy per particle of the homogeneous symmetric nuclear matter, one is related to the nuclear surface tension, two are related to the symmetry energy and its density dependence, one is related to the strength of the spin-orbit interaction, and one is the coupling constant of the pairing interaction. We identify additional phenomenological parameters that have little effect on ground-state properties but can be used to fine-tune features such as the Thomas-Reiche-Kuhn sum rule, the excitation energy of the giant dipole and Gamow-Teller resonances, the static dipole electric polarizability, and the neutron skin thickness.

Density functional study of the bonding in small silicon clusters

International Nuclear Information System (INIS)

Fournier, R.; Sinnott, S.B.; DePristo, A.E.

1992-01-01

We report the ground electronic state, equilibrium geometry, vibrational frequencies, and binding energy for various isomers of Si n (n = 2--8) obtained with the linear combination of atomic orbitals-density functional method. We used both a local density approximation approach and one with gradient corrections. Our local density approximation results concerning the relative stability of electronic states and isomers are in agreement with Hartree--Fock and Moller--Plesset (MP2) calculations [K. Raghavachari and C. M. Rohlfing, J. Chem. Phys. 89, 2219 (1988)]. The binding energies calculated with the gradient corrected functional are in good agreement with experiment (Si 2 and Si 3 ) and with the best theoretical estimates. Our analysis of the bonding reveals two limiting modes of bonding and classes of silicon clusters. One class of clusters is characterized by relatively large s atomic populations and a large number of weak bonds, while the other class of clusters is characterized by relatively small s atomic populations and a small number of strong bonds

Robust functional statistics applied to Probability Density Function shape screening of sEMG data.

Science.gov (United States)

Boudaoud, S; Rix, H; Al Harrach, M; Marin, F

2014-01-01

Recent studies pointed out possible shape modifications of the Probability Density Function (PDF) of surface electromyographical (sEMG) data according to several contexts like fatigue and muscle force increase. Following this idea, criteria have been proposed to monitor these shape modifications mainly using High Order Statistics (HOS) parameters like skewness and kurtosis. In experimental conditions, these parameters are confronted with small sample size in the estimation process. This small sample size induces errors in the estimated HOS parameters restraining real-time and precise sEMG PDF shape monitoring. Recently, a functional formalism, the Core Shape Model (CSM), has been used to analyse shape modifications of PDF curves. In this work, taking inspiration from CSM method, robust functional statistics are proposed to emulate both skewness and kurtosis behaviors. These functional statistics combine both kernel density estimation and PDF shape distances to evaluate shape modifications even in presence of small sample size. Then, the proposed statistics are tested, using Monte Carlo simulations, on both normal and Log-normal PDFs that mimic observed sEMG PDF shape behavior during muscle contraction. According to the obtained results, the functional statistics seem to be more robust than HOS parameters to small sample size effect and more accurate in sEMG PDF shape screening applications.

Stochastic density functional theory at finite temperatures

Science.gov (United States)

Cytter, Yael; Rabani, Eran; Neuhauser, Daniel; Baer, Roi

2018-03-01

Simulations in the warm dense matter regime using finite temperature Kohn-Sham density functional theory (FT-KS-DFT), while frequently used, are computationally expensive due to the partial occupation of a very large number of high-energy KS eigenstates which are obtained from subspace diagonalization. We have developed a stochastic method for applying FT-KS-DFT, that overcomes the bottleneck of calculating the occupied KS orbitals by directly obtaining the density from the KS Hamiltonian. The proposed algorithm scales as O (" close=")N3T3)">N T-1 and is compared with the high-temperature limit scaling O density approximation (LDA); we demonstrate its efficiency, statistical errors, and bias in the estimation of the free energy per electron for a diamond structure silicon. The bias is small compared to the fluctuations and is independent of system size. In addition to calculating the free energy itself, one can also use the method to calculate its derivatives and obtain the equations of state.

Assessment of density-functional approximations: Long-range correlations and self-interaction effects

International Nuclear Information System (INIS)

Jung, J.; Alvarellos, J.E.; Garcia-Gonzalez, P.; Godby, R.W.

2004-01-01

The complex nature of electron-electron correlations is made manifest in the very simple but nontrivial problem of two electrons confined within a sphere. The description of highly nonlocal correlation and self-interaction effects by widely used local and semilocal exchange-correlation energy density functionals is shown to be unsatisfactory in most cases. Even the best such functionals exhibit significant errors in the Kohn-Sham potentials and density profiles

Relationship between the Wigner function and the probability density function in quantum phase space representation

International Nuclear Information System (INIS)

Li Qianshu; Lue Liqiang; Wei Gongmin

2004-01-01

This paper discusses the relationship between the Wigner function, along with other related quasiprobability distribution functions, and the probability density distribution function constructed from the wave function of the Schroedinger equation in quantum phase space, as formulated by Torres-Vega and Frederick (TF). At the same time, a general approach in solving the wave function of the Schroedinger equation of TF quantum phase space theory is proposed. The relationship of the wave functions between the TF quantum phase space representation and the coordinate or momentum representation is thus revealed

Multi-configuration time-dependent density-functional theory based on range separation

DEFF Research Database (Denmark)

Fromager, E.; Knecht, S.; Jensen, Hans Jørgen Aagaard

2013-01-01

Multi-configuration range-separated density-functional theory is extended to the time-dependent regime. An exact variational formulation is derived. The approximation, which consists in combining a long-range Multi-Configuration- Self-Consistent Field (MCSCF) treatment with an adiabatic short...... (srGGA) approximations. As expected, when modeling long-range interactions with the MCSCF model instead of the adiabatic Buijse-Baerends density-matrix functional as recently proposed by Pernal [J. Chem. Phys. 136, 184105 (2012)10.1063/1.4712019], the description of both the 1D doubly-excited state...

Reduced density matrix embedding. General formalism and inter-domain correlation functional.

Science.gov (United States)

Pernal, Katarzyna

2016-08-03

An embedding method for a one-electron reduced density matrix (1-RDM) is proposed. It is based on partitioning of 1-RDM into domains and describing each domain in the effective potential of the other ones. To assure N-representability of the total 1-RDM N-representability and strong-orthogonality conditions are imposed on the domains. The total energy is given as a sum of single-domain energies and domain-domain electron interaction contributions. Higher than two-body inter-domain interaction terms are neglected. The two-body correlation terms are approximated by deriving inter-domain correlation from couplings of density fluctuations of two domains at a time. Unlike in most density embedding methods kinetic energy is treated exactly and it is not required that densities pertaining to the domains are only weakly overlapping. We propose to treat each domain by a corrected perfect-pairing functional. On a few examples it is shown that the embedding reduced density matrix functional method (ERDMF) yields excellent results for molecules that are well described by a single Lewis structure even if strong static intra-domain or dynamic inter-domain correlation effects must be accounted for.

Geometry-based density functional theory an overview

CERN Document Server

Schmidt, M

2003-01-01

An overview of recent developments and applications of a specific density functional approach that originates from Rosenfeld's fundamental measure theory for hard spheres is given. Model systems that were treated include penetrable spheres that interact with a step function pair potential, the Widom-Rowlinson model, the Asakura-Oosawa colloid-polymer mixture, ternary mixtures of spheres, needles, and globular polymers, hard-body amphiphilic mixtures, fluids in porous media, and random sequential adsorption that describes non-equilibrium processes such as colloidal deposition and random car parking. In these systems various physical phenomena were studied, such as correlations in liquids, freezing and demixing phase behaviour, the properties of fluid interfaces with and without orientational order, and wetting and layering phenomena at walls.

Geometry-based density functional theory: an overview

Science.gov (United States)

Schmidt, Matthias

2003-01-01

An overview of recent developments and applications of a specific density functional approach that originates from Rosenfeld's fundamental measure theory for hard spheres is given. Model systems that were treated include penetrable spheres that interact with a step function pair potential, the Widom-Rowlinson model, the Asakura-Oosawa colloid-polymer mixture, ternary mixtures of spheres, needles, and globular polymers, hard-body amphiphilic mixtures, fluids in porous media, and random sequential adsorption that describes non-equilibrium processes such as colloidal deposition and random car parking. In these systems various physical phenomena were studied, such as correlations in liquids, freezing and demixing phase behaviour, the properties of fluid interfaces with and without orientational order, and wetting and layering phenomena at walls.

Geometry-based density functional theory: an overview

International Nuclear Information System (INIS)

Schmidt, Matthias

2003-01-01

An overview of recent developments and applications of a specific density functional approach that originates from Rosenfeld's fundamental measure theory for hard spheres is given. Model systems that were treated include penetrable spheres that interact with a step function pair potential, the Widom-Rowlinson model, the Asakura-Oosawa colloid-polymer mixture, ternary mixtures of spheres, needles, and globular polymers, hard-body amphiphilic mixtures, fluids in porous media, and random sequential adsorption that describes non-equilibrium processes such as colloidal deposition and random car parking. In these systems various physical phenomena were studied, such as correlations in liquids, freezing and demixing phase behaviour, the properties of fluid interfaces with and without orientational order, and wetting and layering phenomena at walls

Time-dependent density-functional theory concepts and applications

CERN Document Server

Ullrich, Carsten A

2011-01-01

Time-dependent density-functional theory (TDDFT) describes the quantum dynamics of interacting electronic many-body systems formally exactly and in a practical and efficient manner. TDDFT has become the leading method for calculating excitation energies and optical properties of large molecules, with accuracies that rival traditional wave-function based methods, but at a fraction of the computational cost.This book is the first graduate-level text on the concepts and applications of TDDFT, including many examples and exercises, and extensive coverage of the literature. The book begins with a s

Extended Lagrangian Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids

International Nuclear Information System (INIS)

Aradi, Balint; Frauenheim, Thomas

2015-01-01

A computationally fast quantum mechanical molecular dynamics scheme using an extended Lagrangian density functional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended Lagrangian Born-Oppenheimer molecular dynamics. Furthermore, for systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can also be applied to a broad range of problems in materials science, chemistry, and biology

Extended Lagrangian Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids.

Science.gov (United States)

Aradi, Bálint; Niklasson, Anders M N; Frauenheim, Thomas

2015-07-14

A computationally fast quantum mechanical molecular dynamics scheme using an extended Lagrangian density functional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended Lagrangian Born-Oppenheimer molecular dynamics. For systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can be applied to a broad range of problems in materials science, chemistry, and biology.

Density-functional theory simulation of large quantum dots

Science.gov (United States)

Jiang, Hong; Baranger, Harold U.; Yang, Weitao

2003-10-01

Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. Here an efficient method for the simulation of quantum dots using density-function theory is developed; it includes the particle-in-the-box representation of the Kohn-Sham orbitals, an efficient conjugate-gradient method to directly minimize the total energy, a Fourier convolution approach for the calculation of the Hartree potential, and a simplified multigrid technique to accelerate the convergence. We test the methodology in a two-dimensional model system and show that numerical studies of large quantum dots with several hundred electrons become computationally affordable. In the noninteracting limit, the classical dynamics of the system we study can be continuously varied from integrable to fully chaotic. The qualitative difference in the noninteracting classical dynamics has an effect on the quantum properties of the interacting system: integrable classical dynamics leads to higher-spin states and a broader distribution of spacing between Coulomb blockade peaks.

Long-range-corrected Rung 3.5 density functional approximations

Science.gov (United States)

Janesko, Benjamin G.; Proynov, Emil; Scalmani, Giovanni; Frisch, Michael J.

2018-03-01

Rung 3.5 functionals are a new class of approximations for density functional theory. They provide a flexible intermediate between exact (Hartree-Fock, HF) exchange and semilocal approximations for exchange. Existing Rung 3.5 functionals inherit semilocal functionals' limitations in atomic cores and density tails. Here we address those limitations using range-separated admixture of HF exchange. We present three new functionals. LRC-ωΠLDA combines long-range HF exchange with short-range Rung 3.5 ΠLDA exchange. SLC-ΠLDA combines short- and long-range HF exchange with middle-range ΠLDA exchange. LRC-ωΠLDA-AC incorporates a combination of HF, semilocal, and Rung 3.5 exchange in the short range, based on an adiabatic connection. We test these in a new Rung 3.5 implementation including up to analytic fourth derivatives. LRC-ωΠLDA and SLC-ΠLDA improve atomization energies and reaction barriers by a factor of 8 compared to the full-range ΠLDA. LRC-ωΠLDA-AC brings further improvement approaching the accuracy of standard long-range corrected schemes LC-ωPBE and SLC-PBE. The new functionals yield highest occupied orbital energies closer to experimental ionization potentials and describe correctly the weak charge-transfer complex of ethylene and dichlorine and the hole-spin distribution created by an Al defect in quartz. This study provides a framework for more flexible range-separated Rung 3.5 approximations.

Density functional approach for pairing in finite size systems

International Nuclear Information System (INIS)

Hupin, G.

2011-09-01

The combination of functional theory where the energy is written as a functional of the density, and the configuration mixing method, provides an efficient description of nuclear ground and excited state properties. The specific pathologies that have been recently observed, show the lack of a clear underlying justification associated to the breaking and the restoration of symmetries within density functional theory. This thesis focuses on alternative treatments of pairing correlations in finite many body systems that consider the breaking and the restoration of the particle number conservation. The energy is written as a functional of a projected quasi-particle vacuum and can be linked to the one obtained within the configuration mixing framework. This approach has been applied to make the projection either before or after the application of the variational principle. It is more flexible than the usual configuration mixing method since it can handle more general effective interactions than the latter. The application to the Krypton isotopes shows the feasibility and the efficiency of the method to describe pairing near closed shell nuclei. Following a parallel path, a theory where the energy is written as a functional of the occupation number and natural orbitals is proposed. The new functional is benchmarked in an exactly solvable model, the pairing Hamiltonian. The efficiency and the applicability of the new theory have been tested for various pairing strengths, single particle energy spectra and numbers of particles. (author)

Density functional theory for field emission from carbon nano-structures.

Science.gov (United States)

Li, Zhibing

2015-12-01

Electron field emission is understood as a quantum mechanical many-body problem in which an electronic quasi-particle of the emitter is converted into an electron in vacuum. Fundamental concepts of field emission, such as the field enhancement factor, work-function, edge barrier and emission current density, will be investigated, using carbon nanotubes and graphene as examples. A multi-scale algorithm basing on density functional theory is introduced. We will argue that such a first principle approach is necessary and appropriate for field emission of nano-structures, not only for a more accurate quantitative description, but, more importantly, for deeper insight into field emission. Copyright © 2015 The Author. Published by Elsevier B.V. All rights reserved.

Recent advances in density functional methods, pt. 1-2

CERN Document Server

Chong, Delano P

1995-01-01

Of all the different areas in computational chemistry, density functional theory (DFT) enjoys the most rapid development. Even at the level of the local density approximation (LDA), which is computationally less demanding, DFT can usually provide better answers than Hartree-Fock formalism for large systems such as clusters and solids. For atoms and molecules, the results from DFT often rival those obtained by ab initio quantum chemistry, partly because larger basis sets can be used. Such encouraging results have in turn stimulated workers to further investigate the formal theory as well as the

Graph approach to the gradient expansion of density functionals

International Nuclear Information System (INIS)

Kozlowski, P.M.; Nalewajski, R.F.

1986-01-01

A graph representation of terms in the gradient expansion of the kinetic energy density functional is presented. They briefly discuss the implications of the virial theorem for the graph structure and relations between possible graphs at a given order of expansion

Density functional theory in surface science and heterogeneous catalysis

DEFF Research Database (Denmark)

Nørskov, Jens Kehlet; Scheffler, M.; Toulhoat, H.

2006-01-01

Solid surfaces are used extensively as catalysts throughout the chemical industry, in the energy sector, and in environmental protection. Recently, density functional theory has started providing new insight into the atomic-scale mechanisms of heterogeneous catalysis, helping to interpret the large...

A density functional for sparse matter

DEFF Research Database (Denmark)

Langreth, D.C.; Lundqvist, Bengt; Chakarova-Kack, S.D.

2009-01-01

forces in molecules, to adsorbed molecules, like benzene, naphthalene, phenol and adenine on graphite, alumina and metals, to polymer and carbon nanotube (CNT) crystals, and hydrogen storage in graphite and metal-organic frameworks (MOFs), and to the structure of DNA and of DNA with intercalators......Sparse matter is abundant and has both strong local bonds and weak nonbonding forces, in particular nonlocal van der Waals (vdW) forces between atoms separated by empty space. It encompasses a broad spectrum of systems, like soft matter, adsorption systems and biostructures. Density-functional...... theory (DFT), long since proven successful for dense matter, seems now to have come to a point, where useful extensions to sparse matter are available. In particular, a functional form, vdW-DF (Dion et al 2004 Phys. Rev. Lett. 92 246401; Thonhauser et al 2007 Phys. Rev. B 76 125112), has been proposed...

Perspective: Fundamental aspects of time-dependent density functional theory

Energy Technology Data Exchange (ETDEWEB)

Maitra, Neepa T. [Department of Physics and Astronomy, Hunter College and the Physics Program at the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065 (United States)

2016-06-14

In the thirty-two years since the birth of the foundational theorems, time-dependent density functional theory has had a tremendous impact on calculations of electronic spectra and dynamics in chemistry, biology, solid-state physics, and materials science. Alongside the wide-ranging applications, there has been much progress in understanding fundamental aspects of the functionals and the theory itself. This Perspective looks back to some of these developments, reports on some recent progress and current challenges for functionals, and speculates on future directions to improve the accuracy of approximations used in this relatively young theory.

Density functional calculations for atoms, molecules and clusters

International Nuclear Information System (INIS)

Gunnarsson, O.; Jones, R.O.

1980-01-01

The density functional formalism provides a framework for including exchange and correlation effects in the calculation of ground state properties of many-electron systems. The reduction of the problem to the solution of single-particle equations leads to important numerical advantages over other ab initio methods of incorporating correlation effects. The essential features of the scheme are outlined and results obtained for atomic and molecular systems are surveyed. The local spin density (LSD) approximation gives generally good results for systems where the bonding involves s and p electrons, but results are less satisfactory for d-bonded systems. Non-local modifications to the LSD approximation have been tested on atomic systems yielding much improved total energies. (Auth.)

The correlation function for density perturbations in an expanding universe. IV - The evolution of the correlation function. [galaxy distribution

Science.gov (United States)

Mcclelland, J.; Silk, J.

1979-01-01

The evolution of the two-point correlation function for the large-scale distribution of galaxies in an expanding universe is studied on the assumption that the perturbation densities lie in a Gaussian distribution centered on any given mass scale. The perturbations are evolved according to the Friedmann equation, and the correlation function for the resulting distribution of perturbations at the present epoch is calculated. It is found that: (1) the computed correlation function gives a satisfactory fit to the observed function in cosmological models with a density parameter (Omega) of approximately unity, provided that a certain free parameter is suitably adjusted; (2) the power-law slope in the nonlinear regime reflects the initial fluctuation spectrum, provided that the density profile of individual perturbations declines more rapidly than the -2.4 power of distance; and (3) both positive and negative contributions to the correlation function are predicted for cosmological models with Omega less than unity.

LETTER TO THE EDITOR: Exhaustive search for low-autocorrelation binary sequences

Science.gov (United States)

Mertens, S.

1996-09-01

Binary sequences with low autocorrelations are important in communication engineering and in statistical mechanics as ground states of the Bernasconi model. Computer searches are the main tool in the construction of such sequences. Owing to the exponential size 0305-4470/29/18/005/img1 of the configuration space, exhaustive searches are limited to short sequences. We discuss an exhaustive search algorithm with run-time characteristic 0305-4470/29/18/005/img2 and apply it to compile a table of exact ground states of the Bernasconi model up to N = 48. The data suggest F > 9 for the optimal merit factor in the limit 0305-4470/29/18/005/img3.

Coherence resonance in low-density jets

Science.gov (United States)

Zhu, Yuanhang; Gupta, Vikrant; Li, Larry K. B.

2017-11-01

Coherence resonance is a phenomenon in which the response of a stable nonlinear system to noise exhibits a peak in coherence at an intermediate noise amplitude. We report the first experimental evidence of coherence resonance in a purely hydrodynamic system, a low-density jet whose variants can be found in many natural and engineering systems. This evidence comprises four parts: (i) the jet's response amplitude increases as the Reynolds number approaches the instability boundary under a constant noise amplitude; (ii) as the noise amplitude increases, the amplitude distribution of the jet response first becomes unimodal, then bimodal, and finally unimodal again; (iii) a distinct peak emerges in the coherence factor at an intermediate noise amplitude; and (iv) for a subcritical Hopf bifurcation, the decay rate of the autocorrelation function exhibits a maximum at an intermediate noise amplitude, but for a supercritical Hopf bifurcation, the decay rate decreases monotonically with increasing noise amplitude. It is clear that coherence resonance can provide valuable information about a system's nonlinearity even in the unconditionally stable regime, opening up new possibilities for its use in system identification and flow control. This work was supported by the Research Grants Council of Hong Kong (Project No. 16235716 and 26202815).

The Superstatistical Nature and Interoccurrence Time of Atmospheric Mercury Concentration Fluctuations

Science.gov (United States)

The probability density function (PDF) of the time intervals between subsequent extreme events in atmospheric Hg0 concentration data series from different latitudes has been investigated. The Hg0 dynamic possesses a long-term memory autocorrelation function. Above a fixed thresh...

Differentiability in density-functional theory: Further study of the locality theorem

International Nuclear Information System (INIS)

Lindgren, Ingvar; Salomonson, Sten

2004-01-01

The locality theorem in density-functional theory (DFT) states that the functional derivative of the Hohenberg-Kohn universal functional can be expressed as a local multiplicative potential function, and this is the basis of DFT and of the successful Kohn-Sham model. Nesbet has in several papers [Phys. Rev. A 58, R12 (1998); ibid.65, 010502 (2001); Adv. Quant. Chem, 43, 1 (2003)] claimed that this theorem is in conflict with fundamental quantum physics, and as a consequence that the Hohenberg-Kohn theory cannot be generally valid. We have commented upon these works [Comment, Phys. Rev. A 67, 056501 (2003)] and recently extended the arguments [Adv. Quantum Chem. 43, 95 (2003)]. We have shown that there is no such conflict and that the locality theorem is inherently exact. In the present work we have furthermore verified this numerically by constructing a local Kohn-Sham potential for the 1s2s 3 S state of helium that generates the many-body electron density and shown that the corresponding 2s Kohn-Sham orbital eigenvalue agrees with the ionization energy to nine digits. Similar result is obtained with the Hartree-Fock density. Therefore, in addition to verifying the locality theorem, this result also confirms the so-called ionization-potential theorem

Functional approach for pairing in finite systems: How to define restoration of broken symmetries in Energy Density Functional theory?

International Nuclear Information System (INIS)

Hupin, G; Lacroix, D; Bender, M

2011-01-01

The Multi-Reference Energy Density Functional (MR-EDF) approach (also called configuration mixing or Generator Coordinate Method), that is commonly used to treat pairing in finite nuclei and project onto particle number, is re-analyzed. It is shown that, under certain conditions, the MR-EDF energy can be interpreted as a functional of the one-body density matrix of the projected state with good particle number. Based on this observation, we propose a new approach, called Symmetry-Conserving EDF (SC-EDF), where the breaking and restoration of symmetry are accounted for simultaneously. We show, that such an approach is free from pathologies recently observed in MR-EDF and can be used with a large flexibility on the density dependence of the functional.

Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions

International Nuclear Information System (INIS)

Gebremariam, B.; Bogner, S.K.; Duguet, T.

2011-01-01

The density matrix expansion (DME) of Negele and Vautherin is a convenient tool to map finite-range physics associated with vacuum two- and three-nucleon interactions into the form of a Skyrme-like energy density functional (EDF) with density-dependent couplings. In this work, we apply the improved formulation of the DME proposed recently in (arXiv:0910.4979) by Gebremariam et al. to the non-local Fock energy obtained from chiral effective field theory (EFT) two-nucleon (NN) interactions at next-to-next-to-leading-order (N 2 LO). The structure of the chiral interactions is such that each coupling in the DME Fock functional can be decomposed into a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the universal long-range pion exchanges. This motivates a new microscopically-guided Skyrme phenomenology where the density-dependent couplings associated with the underlying pion-exchange interactions are added to standard empirical Skyrme functionals, and the density-independent Skyrme parameters subsequently refit to data. A link to a downloadable Mathematica notebook containing the novel density-dependent couplings is provided.

A density functional theory study of the influence of exchange-correlation functionals on the properties of FeAs.

Science.gov (United States)

Griffin, Sinéad M; Spaldin, Nicola A

2017-06-01

We use density functional theory within the local density approximation (LDA), LDA  +  U, generalised gradient approximation (GGA), GGA  +  U, and hybrid-functional methods to calculate the properties of iron monoarsenide. FeAs, which forms in the MnP structure, is of current interest for potential spintronic applications as well as being the parent compound for the pnictide superconductors. We compare the calculated structural, magnetic and electronic properties obtained using the different functionals to each other and to experiment, and investigate the origin of a recently reported magnetic spiral. Our results indicate the appropriateness or otherwise of the various functionals for describing FeAs and the related Fe-pnictide superconductors.

Heat capacity of liquids: A hydrodynamic approach

Directory of Open Access Journals (Sweden)

T. Bryk

2015-03-01

Full Text Available We study autocorrelation functions of energy, heat and entropy densities obtained by molecular dynamics simulations of supercritical Ar and compare them with the predictions of the hydrodynamic theory. It is shown that the predicted by the hydrodynamic theory single-exponential shape of the entropy density autocorrelation functions is perfectly reproduced for small wave numbers by the molecular dynamics simulations and permits the calculation of the wavenumber-dependent specific heat at constant pressure. The estimated wavenumber-dependent specific heats at constant volume and pressure, Cv(k and Cp(k, are shown to be in the long-wavelength limit in good agreement with the macroscopic experimental values of Cv and Cp for the studied thermodynamic points of supercritical Ar.

Reducing Systematic Errors in Oxide Species with Density Functional Theory Calculations

DEFF Research Database (Denmark)

Christensen, Rune; Hummelshøj, Jens S.; Hansen, Heine Anton

2015-01-01

Density functional theory calculations can be used to gain valuable insight into the fundamental reaction processes in metal−oxygen systems, e.g., metal−oxygen batteries. Here, the ability of a range of different exchange-correlation functionals to reproduce experimental enthalpies of formation...

Describing a Strongly Correlated Model System with Density Functional Theory.

Science.gov (United States)

Kong, Jing; Proynov, Emil; Yu, Jianguo; Pachter, Ruth

2017-07-06

The linear chain of hydrogen atoms, a basic prototype for the transition from a metal to Mott insulator, is studied with a recent density functional theory model functional for nondynamic and strong correlation. The computed cohesive energy curve for the transition agrees well with accurate literature results. The variation of the electronic structure in this transition is characterized with a density functional descriptor that yields the atomic population of effectively localized electrons. These new methods are also applied to the study of the Peierls dimerization of the stretched even-spaced Mott insulator to a chain of H 2 molecules, a different insulator. The transitions among the two insulating states and the metallic state of the hydrogen chain system are depicted in a semiquantitative phase diagram. Overall, we demonstrate the capability of studying strongly correlated materials with a mean-field model at the fundamental level, in contrast to the general pessimistic view on such a feasibility.

On the locus and spread of pseudo-density functions in the time-frequency plane

NARCIS (Netherlands)

Janssen, A.J.E.M.

1982-01-01

Various time-frequency pseudo-density functions used in signal analysis are compared with respect to spread. Among the members of Cohen's class of pseudo-density functions satisfying the finite support property as well as Moyal's formula, the Wigner distribution is the most well-behaved one in the

Analyzing the financial crisis using the entropy density function

Science.gov (United States)

Oh, Gabjin; Kim, Ho-yong; Ahn, Seok-Won; Kwak, Wooseop

2015-02-01

The risk that is created by nonlinear interactions among subjects in economic systems is assumed to increase during an abnormal state of a financial market. Nevertheless, investigating the systemic risk in financial markets following the global financial crisis is not sufficient. In this paper, we analyze the entropy density function in the return time series for several financial markets, such as the S&P500, KOSPI, and DAX indices, from October 2002 to December 2011 and analyze the variability in the entropy value over time. We find that the entropy density function of the S&P500 index during the subprime crisis exhibits a significant decrease compared to that in other periods, whereas the other markets, such as those in Germany and Korea, exhibit no significant decrease during the market crisis. These findings demonstrate that the S&P500 index generated a regular pattern in the return time series during the financial crisis.

A general range-separated double-hybrid density-functional theory.

Science.gov (United States)

Kalai, Cairedine; Toulouse, Julien

2018-04-28

A range-separated double-hybrid (RSDH) scheme which generalizes the usual range-separated hybrids and double hybrids is developed. This scheme consistently uses a two-parameter Coulomb-attenuating-method (CAM)-like decomposition of the electron-electron interaction for both exchange and correlation in order to combine Hartree-Fock exchange and second-order Møller-Plesset (MP2) correlation with a density functional. The RSDH scheme relies on an exact theory which is presented in some detail. Several semi-local approximations are developed for the short-range exchange-correlation density functional involved in this scheme. After finding optimal values for the two parameters of the CAM-like decomposition, the RSDH scheme is shown to have a relatively small basis dependence and to provide atomization energies, reaction barrier heights, and weak intermolecular interactions globally more accurate or comparable to range-separated MP2 or standard MP2. The RSDH scheme represents a new family of double hybrids with minimal empiricism which could be useful for general chemical applications.

Level densities of iron isotopes and lower-energy enhancement of y-strength function

International Nuclear Information System (INIS)

Voinov, A V; Grimes, S M; Agvaanluvsan, U; Algin, E; Belgya, T; Brune, C R; Guttormsen, M; Hornish, M J; Massey, T N; Mitchell, G; Rekstad, J; Schiller, A; Siem, S

2005-01-01

The neutron spectrum from the 55 Mn(d,n) 56 Fe reaction has been measured at E d = 7 MeV. The level density of 56 Fe obtained from neutron evaporation spectrum has been compared to the level density from Oslo-type 57 Fe( 3 He, aγ) 56 Fe experiment [1]. The good agreement supports the recent results [1, 8] including an availability of a low-energy enhancement in the γ-strength function for iron isotopes. The new level density function allowed us to investigate an excitation energy dependence of this enhancement, which is shown to increase with increasing excitation energy

International Workshop on Electronic Density Functional Theory : Recent Progress and New Directions

CERN Document Server

Vignale, Giovanni; Das, Mukunda

1998-01-01

This book is an outcome of the International Workshop on Electronic Density Functional Theory, held at Griffith University in Brisbane, Australia, in July 1996. Density functional theory, standing as it does at the boundary between the disciplines of physics, chemistry, and materials science, is a great mixer. Invited experts from North America, Europe, and Australia mingled with students from several disciplines, rapidly taking up the informal style for which Australia is famous. A list of participants is given at the end of the book. Density functional theory (DFT) is a subtle approach to the very difficult problem of predicting the behavior of many interacting particles. A major application is the study of many-electron systems. This was the workshop theme, embracing inter alia computational chemistry and condensed matter physics. DFT circumvents the more conceptually straightforward (but more computationally intensive) approach in which one solves the many-body Schrodinger equation. It relies instead on r...

Linear density response function in the projector augmented wave method