Imaginary Domain Research Articles

Cubic scalingGW: Towards fast quasiparticle calculations

Within the framework of the full potential projector-augmented wave methodology, we present a promising low-scaling $GW$ implementation. It allows for quasiparticle calculations with a scaling that is cubic in the system size and linear in the number of $k$ points used to sample the Brillouin zone. This is achieved by calculating the polarizability and self-energy in the real space and imaginary time domain. The transformation from the imaginary time to the frequency domain is done by an efficient discrete Fourier transformation with only a few nonuniform grid points. Fast Fourier transformations are used to go from real space to reciprocal space and vice versa. The analytic continuation from the imaginary to the real frequency axis is performed by exploiting Thiele's reciprocal difference approach. Finally, the method is applied successfully to predict the quasiparticle energies and spectral functions of typical semiconductors (Si, GaAs, SiC, and ZnO), insulators (C, BN, MgO, and LiF), and metals (Cu and SrVO$_3$). The results are compared with conventional $GW$ calculations. Good agreement is achieved, highlighting the strength of the present method.

Efficient Temperature-Dependent Green's Functions Methods for Realistic Systems: Compact Grids for Orthogonal Polynomial Transforms.

The Matsubara Green's function that is used to describe temperature-dependent behavior is expressed on a numerical grid. While such a grid usually has a couple of hundred points for low-energy model systems, for realistic systems with large basis sets the size of an accurate grid can be tens of thousands of points, constituting a severe computational and memory bottleneck. In this paper, we determine efficient imaginary time grids for the temperature-dependent Matsubara Green's function formalism that can be used for calculations on realistic systems. We show that, because of the use of an orthogonal polynomial transform, we can restrict the imaginary time grid to a few hundred points and reach micro-Hartree accuracy in the electronic energy evaluation. Moreover, we show that only a limited number of orthogonal polynomial expansion coefficients are necessary to preserve accuracy when working with a dual representation of the Green's function or self-energy and transforming between the imaginary time and frequency domain.

How the fast Padé transform handles noise for MRS data from the ovary: importance for ovarian cancer diagnostics

Advanced signal processing through the fast Pade transform (FPT) can enhance resolution and generates quantitative metabolic information for magnetic resonance spectroscopy (MRS). Herein, we apply both \(\hbox {FPT}^{(\pm )}\) variants to in vitro MRS data as encoded from benign and malignant ovarian cyst fluid and perform detailed analysis with several noise levels. In the presence of higher background noise, all genuine metabolites were unambiguously identified and their concentrations precisely computed, using small fractions of the total signal length by both FPT variants. In the \(\hbox {FPT}^{(-)}\), signal–noise separation was accomplished with the help of the “Stability test”, whereby the non-physical information is binned and denoised spectra are generated. In the \(\hbox {FPT}^{(+)}\) even more stringent signal–noise separation was achieved: the spurious resonances reside exclusively in the negative imaginary frequency domain, whereas the genuine content is all in the positive imaginary frequency region. Pole-zero coincidence of spurious resonance remained complete in the \(\hbox {FPT}^{(+)}\) even at higher noise levels. Via the \(\hbox {FPT}^{(+)}\), a denoised spectrum is generated automatically, without the need for the “Stability test”. The two variants \(\hbox {FPT}^{(\pm )}\) provide self-contained cross-validation of the reconstructed spectral parameters, from which the metabolite concentrations of benign and malignant ovarian cyst fluid are reliably computed. These results are particularly promising for more effective ovarian cancer diagnostics, overcoming the major obstacles that have hindered MRS from becoming the method of choice for non-invasive assessment of ovarian lesions.

Changes in Estimated Dislocation Density during Creep in Martensitic Heat-Resistant Steel

An equation for dislocation density during creep was introduced for martensitic heat-resistant steel using Orowan’s equation and a thermal activation equation of Kauzmann type based on several assumptions. The dislocation density discussed here corresponds to the number of dislocations swept out of an imaginary deformable domain in an activated state and is not the so-called mobile dislocation density. The one adjustable parameter, the actual deformable domain size, was adopted in the equation as a size intermediate of the lath martensite and packet. The activation energy and volume, and , were calculated using creep curves for 9Cr-1W tempered martensitic steel as a function of creep strain. The changes in the dislocation density during creep were estimated nondestructively to be roughly to using the values of and . The obtained densities were approximately comparable to the values of total dislocation density reported for directly observed ferritic/martensitic steels. It was found that the dislocation density of 9Cr-1W steel initially increased and then decreased in a transition creep range, which relate to hardening and recovery, respectively. This point of inversion from hardening to recovery can be confirmed easily and nondestructively far before the time to minimum creep rate and as a matter of course the time to rupture. It is suggested that monitoring of the dislocation density can predict the unexpected decrease in long-term rupture strength in advance.

Communication: The description of strong correlation within self-consistent Green's function second-order perturbation theory

We report an implementation of self-consistent Green's function many-body theory within a second-order approximation (GF2) for application with molecular systems. This is done by iterative solution of the Dyson equation expressed in matrix form in an atomic orbital basis, where the Green's function and self-energy are built on the imaginary frequency and imaginary time domain, respectively, and fast Fourier transform is used to efficiently transform these quantities as needed. We apply this method to several archetypical examples of strong correlation, such as a H32 finite lattice that displays a highly multireference electronic ground state even at equilibrium lattice spacing. In all cases, GF2 gives a physically meaningful description of the metal to insulator transition in these systems, without resorting to spin-symmetry breaking. Our results show that self-consistent Green's function many-body theory offers a viable route to describing strong correlations while remaining within a computationally tractable single-particle formalism.

Low Scaling Algorithms for the Random Phase Approximation: Imaginary Time and Laplace Transformations.

In this paper, we determine efficient imaginary frequency and imaginary time grids for second-order Møller-Plesset (MP) perturbation theory. The least-squares and Minimax quadratures are compared for periodic systems, finding that the Minimax quadrature performs slightly better for the considered materials. We show that the imaginary frequency grids developed for second order also perform well for the correlation energy in the direct random phase approximation. Furthermore, we show that the polarizabilities on the imaginary time axis can be Fourier-transformed to the imaginary frequency domain, since the time and frequency Minimax grids are dual to each other. The same duality is observed for the least-squares grids. The transformation from imaginary time to imaginary frequency allows one to reduce the time complexity to cubic (in system size), so that random phase approximation (RPA) correlation energies become accessible for large systems.

Rawlsian and Deleuzian Versions of the Imaginary Domain: A Comparison

ABSTRACTAre Drucilla Cornell's goals of protecting “minimum conditions for individuation” by orienting feminist theory around a notion of personhood equipped with an “imaginary domain” best served by her theoretical reliance on Kant and Rawls? This essay takes up threads from recent debates over “recognition” as a liberal political ideal and contrasts Cornell's Rawlsian version of the imaginary domain with the way this concept might work to women's benefit if it were reconceived along Deleuzian lines.

Rawlsian and Deleuzian Versions of the Imaginary Domain: A Comparison

ABSTRACT Are Drucilla Cornell's goals of protecting “minimum conditions for individuation” by orienting feminist theory around a notion of personhood equipped with an “imaginary domain” best served by her theoretical reliance on Kant and Rawls? This essay takes up threads from recent debates over “recognition” as a liberal political ideal and contrasts Cornell's Rawlsian version of the imaginary domain with the way this concept might work to women's benefit if it were reconceived along Deleuzian lines.

Reading the Planetary Archipelago of the Torres Strait

This essay makes use of the Western concept of the archipelago as a starting point for an examination of island to island relations in the Torres Strait, Australia, as they are rehearsed in the imaginary domain of story, in both its written and oral modes. The essay deploys Spivak’s notions of planetarity and Bloch’s concept of utopianism as ways of charting the relationship between two Torres Strait stories, one old, one new. In so doing, the essay seeks to identify the capacity of Torres Strait literature and storytelling to re-conceive relations of space and time and to acknowledge a spatial and temporal mobility running parallel to the circumscribed trajectories of late modernity.

Compound Fault Feature Separation of Rolling Bearing Based on Complex Wavelet and Energy Operator Demodulation

Compound fault feature separation is a difficult problem in diagnosis field of mechanical system. For the rolling bearing with compound fault on outer and inner race, feature separation technology based on complex wavelet transform and energy operator demodulation is introduced. Through continuous wavelet transform, coefficients of mixed fault signal can be achieved in different wavelet transform domain (i.e. real, imaginary, modulus and phase domain). Furthermore, wavelet power spectrum contours and time average wavelet energy spectrum are applied to extract the scales which hold rich fault information, and the wavelet coefficient slice of specific scale is also drawn. For wavelet coefficients in different domain, spectrum analysis and energy operator demodulation can be used successfully to separate mixed fault. The comparison of feature extraction effect between complex wavelet and real wavelet transform shows that complex wavelet transform is obviously better than the latter.

Dynamic polarizabilities of Zn and Cd and dispersion coefficients involving group 12 atoms

The refractive index data for Zn and Cd measured by Goebel and Hohm are analyzed with a three-term Maxwell-Sellmeier expression which incorporates the experimental oscillator strengths of the first two dipole transitions. These expressions are extended to imaginary frequencies for the determination of the upper and lower bounds of the dynamic polarizabilities α(iω), from which the van der Waals coefficients of two-body interactions and the non-additive three-body interactions are generated. The determined C(6) values for Zn(2) (359±8 a.u.) and Cd(2) (686±10 a.u.) are much larger than those originally estimated by Goebel and Hohm. This is because their one-term approximation of α(ω), which fits the measurements very well in the normal frequency range, greatly underestimates α(iω) when the frequency is extended into the imaginary domain. On the other hand, the present results of heteronuclear interactions verify once again that Tang's one-term approximation of α(iω) leads to accurate combining rules. The two- and three-body interaction coefficients between group 12 atoms (Zn, Cd, Hg) and the alkali, alkaline-earth, rare-gas atoms, and some molecules are estimated with these combining rules.

Recycling History and Assembling Counter-Histories of the Shamsi Community in M.G. Vassanji'sThe Gunny SackandThe Book of Secrets

History pursued and interpreted through anecdotes is counter-history. Fictional narratives juxtaposed with historical facts succeed in delivering embedded and hitherto concealed records. This is indeed one of the recent postmodern and new historical techniques assimilated for creating the archives of counter-historical narratives from individual and collective memories. The fictional instances limned in Vassanji's works synchronise well enough with the factual events to describe the backdrop and contextual information for imaginary domains.

Research on the Physical Mechanism of Motor Imagery

The motor imagery to be widely used in BCI systems, the traditional focus on EEG analysis in feature extraction and classification, this paper of EEG from the left and right imaginary frequency domain, time domain and brain mapping analysis on the EEG, to analyze the characteristics of EEG signals about imagination.

Measured and Modeled Dielectric Properties of Soils at 50 Megahertz

Commercial soil water sensors of the capacitance and impedance type generally operate at low (<200 MHz) frequencies where the soil dielectric properties are frequency dependent, especially for soils high in clay. In this work, we examined the dielectric properties of four soil materials (fine sand, sandy loam, loam, and clay) at 50 MHz using Hydra impedance sensor real and imaginary permittivity measurements and time domain reflectometry (TDR) apparent permittivity and bulk soil electrical conductivity (EC) measurements. The results showed that the Hydra sensor real and imaginary permittivity increased with increasing soil clay content and that relaxation loss was a significant part of the total energy loss, except for the fine sand, where the relaxation loss was zero. Model calculations showed that the relative contribution of surface conductivity to bulk soil EC increased over the contribution of pore water conductivity as clay content increased. Application of a soil permittivity model showed that the observed real permittivity ε′ and relaxation loss εrel″ for all soils except the fine sand could not be explained using simple mixing rules. The underestimation of the modeled ε′ and εrel″ for soils with non‐negligible clay content was attributed to interfacial polarizations that were not included in the model. The modeled contribution of bound water to relaxation loss was found to be small.

Real time dynamics from quantum Monte Carlo data: A genetic algorithm approach

The intriguing task of evaluating, in a Quantum Monte Carlo simulation, the dynamic structure factor of a condensed matter sample, hence gaining informations about the elementry excitations which may be observed in a thermal neutrons scattering experiment, is yet a very delicate one. The difficulties arise because, in a simulation, dynamics takes place in the imaginary time domain, and analytic continuation is required to translate the results into real time dynamical correlations functions. This is far from trivial since one has to care for the role of the statistical noise, which, if not properly taken into account, may lead to uncontrolled incertainties and only qualitatively interesting results. We suggest a new analytic continuation technique, relying on genetic optimization algorithms, and assuming the first few momenta as the only prior knoledge about the spectral function. As an example, we show the results of the method when applied to the study of a sample of 4He atoms at zero-temperature in te liquid phase.

A new adaptation of mapping method to study mixing of multiphase flows in mixers with complex geometries

The main objective of the present work is to modify the traditional mapping method for the simulation of distributive mixing of multiphase flows in geometries involving moving parts such as, internal mixers or twin-screw extruders without a limitation on their geometrical periodicity. The periodicity condition, limits the results of traditional mapping method to tracking mapping mesh between specific discrete time intervals or distances for that geometry is repeated, hence, result is only for fixed orientation of rotors. Imaginary domain method is introduced to track mapping mesh from one state to the next free of geometrical periodicity limitations. In this work the method is introduced and its applicability and accuracy is discussed in details. A two-dimensional (2D) simulation of mixing of two Newtonian fluids with different viscosities in an intermeshing internal mixer is used as a test case study. In this example the key issues of ability to predict mixing state in details for all orientations of rotors is presented. To reduce diffusion errors of mapping method in the boundaries of the rotors, mapping mesh refinement technique that relies upon one single reference mesh is also presented.

Superstition or Modernity?

Superstition or Modernity?

The Shadow of Heterosexuality

In this essay, Cornell first invokes the concept of ‘imaginary domain’ to challenge the legal legitimacy of heterosexism in any form. She then claims that the imposition of heterosexism on the imaginary is a trauma whose severity can be grasped only with the help of psychoanalysis. Second, she argues that we cannot understand or undermine the power of heterosexist ideas without an alternative ethic of love. In beginning to think about a love that would necessarily pit itself against heterosexism, Cornell draws on Jacques Derrida's metaphor of the lovance.

The Shadow of Heterosexuality

In this essay, Cornell first invokes the concept of ‘imaginary domain’ to challenge the legal legitimacy of heterosexism in any form. She then claims that the imposition of heterosexism on the imaginary is a trauma whose severity can be grasped only with the help of psychoanalysis. Second, she argues that we cannot understand or undermine the power of heterosexist ideas without an alternative ethic of love. In beginning to think about a love that would necessarily pit itself against heterosexism, Cornell draws on Jacques Derrida's metaphor of the lovance.

Nonlinear fractional dynamics on a lattice with long range interactions

A unified approach has been developed to study nonlinear dynamics of a 1D lattice of particles with long-range power-law interaction. A classical case is treated in the framework of the generalization of the well-known Frenkel–Kontorova chain model for the non-nearest interactions. Quantum dynamics is considered following Davydov's approach for molecular excitons. In the continuum limit the problem is reduced to dynamical equations with fractional derivatives resulting from the fractional power of the long-range interaction. Fractional generalizations of the sine-Gordon, nonlinear Schrödinger, and Hilbert–Schrödinger equations have been found. There exists a critical value of the power s of the long-range potential. Below the critical value ( s < 3 , s ≠ 1 , 2) we obtain equations with fractional derivatives while for s ⩾ 3 we have the well-known nonlinear dynamical equations with space derivatives of integer order. Long-range interaction impact on the quantum lattice propagator has been studied. We have shown that the quantum exciton propagator exhibits transition from the well-known Gaussian-like behavior to a power-law decay due to the long-range interaction. A link between 1D quantum lattice dynamics in the imaginary time domain and a random walk model has been discussed.