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At least 127 records · Page 7

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DOE OSTI2014

First-order nonadiabatic coupling matrix elements between excited states: A Lagrangian formulation at the CIS, RPA, TD-HF, and TD-DFT levels

Analytic expressions for the first-order nonadiabatic coupling matrix elements between electronically excited states are first formulated exactly via both time-independent equation of motion and time-dependent response theory, and are then approximated at the configuration interaction singles, particle-hole/particle-particle random phase approximation, and time-dependent density functional theory/Hartree-Fock levels of theory. Note that, to get the Pulay terms arising from the derivatives of basis functions, the standard response theory designed for electronic perturbations has to be extended to nuclear derivatives. The results are further recast into a Lagrangian form that is similar to that for excited-state energy gradients and allows to use atomic orbital based direct algorithms for large molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1994

Comparison of the compressive strengths for stitched and toughened composite systems

The compression strength of a stitched and a toughened matrix graphite/epoxy composite was determined and compared to a baseline unstitched untoughened composite. Two different layups with a variety of test lengths were tested under both ambient and hot/wet conditions. No significant difference in strength was seen for the different materials when the gage lengths of the specimens were long enough to lead to a buckling failure. For shorter specimens, a 30 percent reduction in strength from the baseline was seen due to stitching for both a 48-ply quasi-isotropic and a (0/45/0/-45/90/-45/0/45/0)s laminate. Analysis of the results suggested that the decrease in strength was due to increased fiber misalignment due to the stitches. An observed increasing strength with decreasing gage length, which was seen for all materials, was explained with a size effect model. The model assumed a random distribution of flaws (misaligned fibers). The toughened materials showed a small increase in strength over the baseline material for both laminates presumably due to the compensating effects of a more compliant matrix and straighter fibers in the toughened material. The hot/wet strength of the stitched and baseline material fell 30 percent below their ambient strengths for shorter, nonbuckling specimen, while the strength of the toughened matrix material only fell 20 percent. Video images of the failing specimen were recorded and showed local failures prior to global collapse of the specimen. These images support the theory of a random distribution of flaws controlling composite failure. Failed specimen appearance, however, seems to be a misleading indication of the cause of failure.

Reeder, James R.↗

NASA NTRS1990

Remote sensing of Earth terrain

The layered random medium model is used to investigate the fully polarimetric scattering of electromagnetic waves from vegetation. The vegetation canopy is modeled as an anisotropic random medium containing nonspherical scatterers with preferred alignment. The underlying medium is considered as a homogeneous half space. The scattering effect of the vegetation canopy are characterized by 3-D correlation functions with variances and correlation lengths respectively corresponding to the fluctuation strengths and the physical geometries of the scatterers. The strong fluctuation theory is used to calculate the anisotropic effective permittivity tensor of the random medium and the distorted Born approximation is then applied to obtain the covariance matrix which describes the fully polarimetric scattering properties of the vegetation field. This model accounts for all the interaction processes between the boundaries and the scatterers and includes all the coherent effects due to wave propagation in different directions such as the constructive and destructive interferences. For a vegetation canopy with low attenuation, the boundary between the vegetation and the underlying medium can give rise to significant coherent effects.

Kong, Jin AU↗

DOE OSTI2018

Extended Lagrangian Excited State Molecular Dynamics

In this work, an extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born–Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both for the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. In conclusion, the XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree–Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation

Despite their unmatched success for many applications, commonly used local, semi-local, and hybrid density functionals still face challenges when it comes to describing long-range interactions, static correlation, and electron delocalization. Density functionals of both the occupied and virtual orbitals are able to address these problems. The particle-hole (ph-) Random Phase Approximation (RPA), a functional of occupied and virtual orbitals, has recently known a revival within the density functional theory community. Following up on an idea introduced in our recent communication [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)], we formulate more general adiabatic connections for the correlation energy in terms of pairing matrix fluctuations described by the particle-particle (pp-) propagator. With numerical examples of the pp-RPA, the lowest-order approximation to the pp-propagator, we illustrate the potential of density functional approximations based on pairing matrix fluctuations. The pp-RPA is size-extensive, self-interaction free, fully anti-symmetric, describes the strong static correlation limit in H{sub 2}, and eliminates delocalization errors in H{sub 2}{sup +} and other single-bond systems. It gives surprisingly good non-bonded interaction energies – competitive with the ph-RPA – with the correct R{sup −6} asymptotic decay as a function of the separation R, which we argue is mainly attributable to its correct second-order energy term. While the pp-RPA tends to underestimate absolute correlation energies, it gives good relative energies: much better atomization energies than the ph-RPA, as it has no tendency to underbind, and reaction energies of similar quality. The adiabatic connection in terms of pairing matrix fluctuation paves the way for promising new density functional approximations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Doorway states in the random-phase approximation

By coupling a doorway state to a sea of random background states, we develop the theory of doorway states in the framework of the random-phase approximation (RPA). Because of the symmetry of the RPA equations, that theory is radically different from the standard description of doorway states in the shell model. We derive the Pastur equation in the limit of large matrix dimension and show that the results agree with those of matrix diagonalization in large spaces. The complexity of the Pastur equation does not allow for an analytical approach that would approximately describe the doorway state. Our numerical results display unexpected features: The coupling of the doorway state with states of opposite energy leads to strong mutual attraction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1983

Ultrasonic wave propagation in two-phase media: Spherical inclusions

The scattering theory, recently developed via the extended method of equivalent inclusion, is used to study the propagation of time-harmonic waves in two-phase media of elastic matrix with randomly distributed elastic spherical inclusion materials. The elastic moduli and mass density of the composite medium are determined as functions of frequencies when given properties and concentration of the spheres and the matrix. Velocity and attenuation of ultrasonic waves in two-phase media are determined for cases of distributed spheres and localized damage. An averaging theorem that requires the equivalence of the strain energy and the kinetic energy between the effective medium and the original matrix with spherical inhomogeneities is employed to derive the effective moduli and mass density. The functional dependency of these quantities upon frequencies and concentration provides a method of data analysis in ultrasonic evaluation of material properties. Numerical results or moduli, velocity and/or attenuation as functions of concentration of inclusion material, or porosity, are graphically displayed.

Fu, L. S.↗

NASA NTRS1984

Ultrasonic wave propagation in two-phase media - Spherical inclusions

Fu, L. S.↗

DOE OSTI2017

New theory of diffusive and coherent nature of optical wave via a quantum walk

We propose a new theory on a relation between diffusive and coherent nature in one dimensional wave mechanics based on a quantum walk. It is known that the quantum walk in homogeneous matrices provides the coherent property of wave mechanics. Using the recent result of a localization phenomenon in a one-dimensional quantum walk (Konno, 2010), we numerically show that the randomized localized matrices suppress the coherence and give diffusive nature. - Highlights: • A relation between diffusive and coherent nature of wave is obtained. • A rigorous decoherent process is observed in quantum walk. • Quantum walk for a point-process is numerically considered. • Transfer matrix theory with S-matrix in optics is connected with quantum walk.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions

Electronic transport through chaotic quantum dots exhibits universal behaviour which can be understood through the semiclassical approximation. Within the approximation, calculation of transport moments reduces to codifying classical correlations between scattering trajectories. These can be represented as ribbon graphs and we develop an algorithmic combinatorial method to generate all such graphs with a given genus. This provides an expansion of the linear transport moments for systems both with and without time reversal symmetry. The computational implementation is then able to progress several orders further than previous semiclassical formulae as well as those derived from an asymptotic expansion of random matrix results. The patterns observed also suggest a general form for the higher orders.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1984

Radiative transfer theory for active remote sensing of a layer of nonspherical particles

The radiative transfer theory is applied to calculate the scattering by a layer of randomly positioned and oriented nonspherical particles. The scattering amplitude functions of each individual particle are calculated with Waterman's T matrix method, which utilizes vector spherical wave functions for expansion of incident, scattered, and surface fields. The orientation of the particles is described by a probability density function of the Eulerian angles of rotation. A rotation matrix is used to relate the T matrix of the principal frame to that of the natural frame of the particle. The extinction matrix and phase matrix of the radiative transfer equations are expressed in terms of the T matrix elements. The extinction matrix for nonspherical particles is generally nondiagonal. There are only two attenuation rates in a specified direction of propagation. The radiative transfer equations are solved by an iterative method to first order in albedo. Numerical results are illustrated as functions of incidence angle and frequency with applications to active remote sensing.

Tsang, L.↗

DOE OSTI2018

Large N expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs

In this paper we explain the relation between the free energy of the SYK model for N Majorana fermions with a random q-body interaction and the moments of its spectral density. The high temperature expansion of the free energy gives the cumulants of the spectral density. Using that the cumulants are extensive we find the p dependence of the 1/N 2 correction of the 2p-th moments obtained in [1]. Conversely, the 1/N 2 corrections to the moments give the correction (even q) to the β 6 coefficient of the high temperature expansion of the free energy for arbitrary q. Our result agrees with the 1/q 3 correction obtained by Tarnopolsky using a mean field expansion. These considerations also lead to a more powerful method for solving the moment problem and intersection-graph enumeration problems. We take advantage of this and push the moment calculation to 1/N 3 order and find surprisingly simple enumeration identities for intersection graphs. The 1/N 3 corrections to the moments, give corrections to the β 8 coefficient (for even q) of the high temperature expansion of the free energy which have not been calculated before. Results for odd q, where the SYK “Hamiltonian” is the supercharge of a supersymmetric theory are discussed as well.

1/N Expansion↗

DOE OSTI2025

Structured interactions drive abrupt transitions in the spatial organization of microbial communities

Bacteria possess diverse mechanisms to regulate their motility in response to environmental and physiological signals, enabling them to navigate complex habitats and adapt their behavior. Some of these mechanisms are species specific and enable cells to modulate their movement based on the ecological identity of neighboring species. Here, we introduce a model in which bacteria interact via local signals that either enhance or suppress the motility of neighboring cells depending on species type. Through large-scale simulations and a coarse-grained stochastic model, we demonstrate the emergence of a sharp transition driven by nucleation processes: increasing the density of motility-suppressing interactions drives the system from a fully mixed, motile phase to a state characterized by large, stationary bacterial clusters. Remarkably, in systems with a large number of interacting species, this transition can be triggered solely by altering the structure of the motility-regulation interaction matrix while maintaining species and interaction densities constant. In particular, we find that heterogeneous and modular interactions promote the transition more readily than homogeneous random ones. These findings add a dimension to the theory of motility-induced phase separation and contribute to the ongoing effort to understand microbial interactions, suggesting that structured, nonrandom ones may be key to reproducing commonly observed spatial patterns in microbial communities.

bacterial communities↗

DOE OSTI2017

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

To describe static correlation, we create 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 demonstrate 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 findings show that our multireference DFT successfully describes static correlation in bond dissociation and double bond rotation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1988

Multiple input/output random vibration control system

A multi-input/output random vibration control algorithm was developed based on system identification concepts derived from random vibration spectral analysis theory. The unique features of the algorithm are: (1) the number of input excitors and the number of output control responses need not be identical; (2) the system inverse response matrix is obtained directly from the input/output spectral matrix; and (3) the system inverse response matrix is updated every control loop cycle to accommodate system amplitude nonlinearities. A laboratory demonstration case of two imputs with three outputs is presented to demonstrate the system capabilities.

Unruh, James F.↗

NASA NTRS1990

Scattering from randomly oriented scatterers with strong permittivity fluctuations

Strong permittivity fluctuation theory is used to solve the problem of scattering from a medium composed of completely randomly oriented scatterers under a low frequency limit. Gaussian statistics are not assumed for the renormalized scattering sources. Numerical results on effective permittivity are illustrated for oblate and prolate spheroidal scatterers and compared with the results for spherical scatterers. The results are consistent with discrete scatterer theory. The effective permittivity of a random medium embedded with nonspherical scatterers shows a higher imaginary part than the spherical scatterer case with equal correlation volume. Under the distorted Born approximation, the polarimetric covariance matrix for the backscattered electric field is calculated for half-space randomly oriented scatterers. The nonspherical geometry of the scatterers shows significant effects on the cross-polarized backscattering returns, and the correlation coefficient between HH and VV returns. The polarimetric backscattering coefficients can provide useful information in distinguishing the geometry of scatterers.

Yueh, S. H.↗

DOE OSTI2017

Impact of carrier localization on recombination in InGaN quantum wells and the efficiency of nitride light-emitting diodes: Insights from theory and numerical simulations

We investigate the effect of carrier localization due to random alloy fluctuations on the radiative and Auger recombination rates in InGaN quantum wells as a function of alloy composition, crystal orientation, carrier density, and temperature. Our results show that alloy fluctuations reduce individual transition matrix elements by the separate localization of electrons and holes, but this effect is overcompensated by the additional transitions enabled by translational symmetry breaking and the resulting lack of momentum conservation. Thus, we find that localization increases both radiative and Auger recombination rates, but that Auger recombination rates increase by one order of magnitude more than radiative rates. Moreover, we demonstrate that localization has an overall detrimental effect on the efficiency-droop and green-gap problems of InGaN light-emitting diodes.

36 MATERIALS SCIENCE↗

DOE OSTI2012

A statistical approach to multifield inflation: many-field perturbations beyond slow roll

We study multifield contributions to the scalar power spectrum in an ensemble of six-field inflationary models obtained in string theory. We identify examples in which inflation occurs by chance, near an approximate inflection point, and we compute the primordial perturbations numerically, both exactly and using an array of truncated models. The scalar mass spectrum and the number of fluctuating fields are accurately described by a simple random matrix model. During the approach to the inflection point, bending trajectories and violations of slow roll are commonplace, and 'many-field' effects, in which three or more fields influence the perturbations, are often important. However, in a large fraction of models consistent with constraints on the tilt the signatures of multifield evolution occur on unobservably large scales. Our scenario is a concrete microphysical realization of quasi-single-field inflation, with scalar masses of order H, but the cubic and quartic couplings are typically too small to produce detectable non-Gaussianity. We argue that our results are characteristic of a broader class of models arising from multifield potentials that are natural in the Wilsonian sense.

79 ASTRONOMY AND ASTROPHYSICS↗